TSTP Solution File: NUM923+8 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : NUM923+8 : TPTP v8.1.0. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Mon Jul 18 13:33:12 EDT 2022
% Result : Timeout 286.53s 286.27s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM923+8 : TPTP v8.1.0. Released v5.3.0.
% 0.13/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n004.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Wed Jul 6 14:14:07 EDT 2022
% 0.13/0.34 % CPUTime :
% 7.58/7.60 ============================== Prover9 ===============================
% 7.58/7.60 Prover9 (32) version 2009-11A, November 2009.
% 7.58/7.60 Process 17036 was started by sandbox2 on n004.cluster.edu,
% 7.58/7.60 Wed Jul 6 14:14:14 2022
% 7.58/7.60 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_16883_n004.cluster.edu".
% 7.58/7.60 ============================== end of head ===========================
% 7.58/7.60
% 7.58/7.60 ============================== INPUT =================================
% 7.58/7.60
% 7.58/7.60 % Reading from file /tmp/Prover9_16883_n004.cluster.edu
% 7.58/7.60
% 7.58/7.60 set(prolog_style_variables).
% 7.58/7.60 set(auto2).
% 7.58/7.60 % set(auto2) -> set(auto).
% 7.58/7.60 % set(auto) -> set(auto_inference).
% 7.58/7.60 % set(auto) -> set(auto_setup).
% 7.58/7.60 % set(auto_setup) -> set(predicate_elim).
% 7.58/7.60 % set(auto_setup) -> assign(eq_defs, unfold).
% 7.58/7.60 % set(auto) -> set(auto_limits).
% 7.58/7.60 % set(auto_limits) -> assign(max_weight, "100.000").
% 7.58/7.60 % set(auto_limits) -> assign(sos_limit, 20000).
% 7.58/7.60 % set(auto) -> set(auto_denials).
% 7.58/7.60 % set(auto) -> set(auto_process).
% 7.58/7.60 % set(auto2) -> assign(new_constants, 1).
% 7.58/7.60 % set(auto2) -> assign(fold_denial_max, 3).
% 7.58/7.60 % set(auto2) -> assign(max_weight, "200.000").
% 7.58/7.60 % set(auto2) -> assign(max_hours, 1).
% 7.58/7.60 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 7.58/7.60 % set(auto2) -> assign(max_seconds, 0).
% 7.58/7.60 % set(auto2) -> assign(max_minutes, 5).
% 7.58/7.60 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 7.58/7.60 % set(auto2) -> set(sort_initial_sos).
% 7.58/7.60 % set(auto2) -> assign(sos_limit, -1).
% 7.58/7.60 % set(auto2) -> assign(lrs_ticks, 3000).
% 7.58/7.60 % set(auto2) -> assign(max_megs, 400).
% 7.58/7.60 % set(auto2) -> assign(stats, some).
% 7.58/7.60 % set(auto2) -> clear(echo_input).
% 7.58/7.60 % set(auto2) -> set(quiet).
% 7.58/7.60 % set(auto2) -> clear(print_initial_clauses).
% 7.58/7.60 % set(auto2) -> clear(print_given).
% 7.58/7.60 assign(lrs_ticks,-1).
% 7.58/7.60 assign(sos_limit,10000).
% 7.58/7.60 assign(order,kbo).
% 7.58/7.60 set(lex_order_vars).
% 7.58/7.60 clear(print_given).
% 7.58/7.60
% 7.58/7.60 % formulas(sos). % not echoed (5741 formulas)
% 7.58/7.60
% 7.58/7.60 ============================== end of input ==========================
% 7.58/7.60
% 7.58/7.60 % From the command line: assign(max_seconds, 300).
% 7.58/7.60
% 7.58/7.60 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 7.58/7.60
% 7.58/7.60 % Formulas that are not ordinary clauses:
% 7.58/7.60 1 (all X_a (archim1727834104eiling(X_a) -> ti(fun(X_a,int),archimedean_ceiling(X_a)) = archimedean_ceiling(X_a))) # label(tsy_c_Archimedean__Field_Oceiling_res) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.60 2 (all X_a (archim1727834104eiling(X_a) -> ti(fun(X_a,int),archim2085082626_floor(X_a)) = archim2085082626_floor(X_a))) # label(tsy_c_Archimedean__Field_Ofloor__ceiling__class_Ofloor_res) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.60 3 (all X_a all X_b (comm_monoid_add(X_b) -> ti(fun(fun(X_a,X_b),fun(fun(X_a,bool),X_b)),big_co1399186613setsum(X_a,X_b)) = big_co1399186613setsum(X_a,X_b))) # label(tsy_c_Big__Operators_Ocomm__monoid__add__class_Osetsum_res) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.60 4 (all X_a all X_b (comm_monoid_mult(X_b) -> ti(fun(fun(X_a,X_b),fun(fun(X_a,bool),X_b)),big_co302546470etprod(X_a,X_b)) = big_co302546470etprod(X_a,X_b))) # label(tsy_c_Big__Operators_Ocomm__monoid__mult__class_Osetprod_res) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.60 5 (all X_a all X_b ti(fun(fun(X_a,fun(X_b,bool)),fun(product_prod(fun(X_a,bool),fun(X_b,bool)),bool)),bijR(X_a,X_b)) = bijR(X_a,X_b)) # label(tsy_c_BijectionRel_ObijR_res) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.60 6 (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].
% 7.58/7.60 7 (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].
% 7.58/7.60 8 (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].
% 7.58/7.60 9 (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].
% 7.58/7.60 10 (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].
% 7.58/7.60 11 (all X_a ti(fun(X_a,fun(fun(code_code_numeral,X_a),fun(code_code_numeral,X_a))),code_c600343653l_case(X_a)) = code_c600343653l_case(X_a)) # label(tsy_c_Code__Numeral_Ocode__numeral_Ocode__numeral__case_res) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.60 12 (all X_a (comple44059174attice(X_a) -> ti(fun(fun(X_a,bool),X_a),complete_Sup_Sup(X_a)) = complete_Sup_Sup(X_a))) # label(tsy_c_Complete__Lattice_OSup__class_OSup_1_res) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.60 13 (all X_a ti(fun(fun(real,fun(real,X_a)),fun(complex,X_a)),complex_case(X_a)) = complex_case(X_a)) # label(tsy_c_Complex_Ocomplex_Ocomplex__case_res) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.60 14 (all X_a ti(fun(fun(real,fun(real,X_a)),fun(complex,X_a)),complex_rec(X_a)) = complex_rec(X_a)) # label(tsy_c_Complex_Ocomplex_Ocomplex__rec_res) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.60 15 (all X_a (real_normed_field(X_a) -> ti(fun(fun(X_a,X_a),fun(X_a,fun(X_a,bool))),deriv(X_a)) = deriv(X_a))) # label(tsy_c_Deriv_Oderiv_res) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.60 16 (all X_a (semiring_div(X_a) -> ti(fun(X_a,fun(X_a,X_a)),div_div(X_a)) = div_div(X_a))) # label(tsy_c_Divides_Odiv__class_Odiv_res) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.60 17 (all X_a (semiring_div(X_a) -> ti(fun(X_a,fun(X_a,X_a)),div_mod(X_a)) = div_mod(X_a))) # label(tsy_c_Divides_Odiv__class_Omod_res) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.60 18 (all X_a (inverse(X_a) & real_normed_vector(X_a) -> ti(fun(X_a,fun(X_a,X_a)),inverse_divide(X_a)) = inverse_divide(X_a))) # label(tsy_c_Fields_Oinverse__class_Odivide_0_res) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.60 19 (all X_a (division_ring(X_a) -> ti(fun(X_a,fun(X_a,X_a)),inverse_divide(X_a)) = inverse_divide(X_a))) # label(tsy_c_Fields_Oinverse__class_Odivide_1_res) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.60 20 (all X_a (division_ring(X_a) -> ti(fun(X_a,X_a),inverse_inverse(X_a)) = inverse_inverse(X_a))) # label(tsy_c_Fields_Oinverse__class_Oinverse_res) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.60 21 (all X_a ti(fun(fun(X_a,bool),nat),finite_card(X_a)) = finite_card(X_a)) # label(tsy_c_Finite__Set_Ocard_res) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.60 22 (all X_a ti(fun(fun(X_a,bool),bool),finite_finite_1(X_a)) = finite_finite_1(X_a)) # label(tsy_c_Finite__Set_Ofinite_res) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.60 23 (all X_a all X_b ti(fun(fun(product_prod(X_a,X_b),bool),fun(X_a,fun(X_b,bool))),in_rel(X_a,X_b)) = in_rel(X_a,X_b)) # label(tsy_c_FunDef_Oin__rel_res) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.60 24 (all X_a (abs_if(X_a) -> ti(fun(X_a,X_a),abs_abs(X_a)) = abs_abs(X_a))) # label(tsy_c_Groups_Oabs__class_Oabs_0_res) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.60 25 (all X_a (ordere142940540dd_abs(X_a) -> ti(fun(X_a,X_a),abs_abs(X_a)) = abs_abs(X_a))) # label(tsy_c_Groups_Oabs__class_Oabs_1_res) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.60 26 (all X_a (minus(X_a) -> ti(fun(X_a,fun(X_a,X_a)),minus_minus(X_a)) = minus_minus(X_a))) # label(tsy_c_Groups_Ominus__class_Ominus_res) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.60 27 (all X_a (one(X_a) -> ti(X_a,one_one(X_a)) = one_one(X_a))) # label(tsy_c_Groups_Oone__class_Oone_res) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.60 28 (all X_a (plus(X_a) & linorder(X_a) & dvd(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].
% 7.58/7.60 29 (all X_a (monoid_add(X_a) -> ti(fun(X_a,fun(X_a,X_a)),plus_plus(X_a)) = plus_plus(X_a))) # label(tsy_c_Groups_Oplus__class_Oplus_1_res) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.60 30 (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_2_res) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.60 31 (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_3_res) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.60 32 (all X_a (sgn_div_norm(X_a) -> ti(fun(X_a,X_a),sgn_sgn(X_a)) = sgn_sgn(X_a))) # label(tsy_c_Groups_Osgn__class_Osgn_0_res) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.60 33 (all X_a (sgn_if(X_a) -> ti(fun(X_a,X_a),sgn_sgn(X_a)) = sgn_sgn(X_a))) # label(tsy_c_Groups_Osgn__class_Osgn_1_res) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.60 34 (all X_a (dvd(X_a) -> ti(fun(X_a,fun(X_a,X_a)),times_times(X_a)) = times_times(X_a))) # label(tsy_c_Groups_Otimes__class_Otimes_0_res) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.60 35 (all X_a (power(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].
% 7.58/7.60 36 (all X_a (mult_zero(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_2_res) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.60 37 (all X_a (no_zero_divisors(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_3_res) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.60 38 (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_4_res) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.60 39 (all X_a (ab_semigroup_mult(X_a) -> ti(fun(X_a,fun(X_a,X_a)),times_times(X_a)) = times_times(X_a))) # label(tsy_c_Groups_Otimes__class_Otimes_5_res) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.60 40 (all X_a (uminus(X_a) -> ti(fun(X_a,X_a),uminus_uminus(X_a)) = uminus_uminus(X_a))) # label(tsy_c_Groups_Ouminus__class_Ouminus_res) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.60 41 (all X_a (zero(X_a) -> ti(X_a,zero_zero(X_a)) = zero_zero(X_a))) # label(tsy_c_Groups_Ozero__class_Ozero_res) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.60 42 (all X_a (metric_space(X_a) -> ti(fun(fun(X_a,bool),X_a),the(X_a)) = the(X_a))) # label(tsy_c_HOL_OThe_0_res) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.60 43 (all X_a all X_b ti(fun(fun(product_prod(X_a,X_b),bool),product_prod(X_a,X_b)),the(product_prod(X_a,X_b))) = the(product_prod(X_a,X_b))) # label(tsy_c_HOL_OThe_2_res) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.60 44 (all X_a (comm_monoid_add(X_a) & topological_space(X_a) -> ti(fun(fun(X_a,bool),X_a),the(X_a)) = the(X_a))) # label(tsy_c_HOL_OThe_3_res) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.60 45 (all X_a ti(X_a,undefined(X_a)) = undefined(X_a)) # label(tsy_c_HOL_Oundefined_res) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.60 46 (all X_a ti(fun(fun(X_a,bool),X_a),hilbert_Eps(X_a)) = hilbert_Eps(X_a)) # label(tsy_c_Hilbert__Choice_OEps_res) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.60 47 (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].
% 7.58/7.60 48 (all X_a (semiring_1(X_a) -> ti(fun(X_a,bool),iszero(X_a)) = iszero(X_a))) # label(tsy_c_Int_Oiszero_res) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.60 49 (all X_a (number(X_a) -> ti(fun(int,X_a),number_number_of(X_a)) = number_number_of(X_a))) # label(tsy_c_Int_Onumber__class_Onumber__of_res) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.60 50 (all X_a (ring_1(X_a) -> ti(fun(X_a,bool),ring_1_Ints(X_a)) = ring_1_Ints(X_a))) # label(tsy_c_Int_Oring__1__class_OInts_res) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.60 51 (all X_a (ring_1(X_a) -> ti(fun(int,X_a),ring_1_of_int(X_a)) = ring_1_of_int(X_a))) # label(tsy_c_Int_Oring__1__class_Oof__int_res) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.60 52 (all X_b all X_a (topological_space(X_a) & topological_space(X_b) -> ti(fun(fun(X_a,X_b),fun(X_a,bool)),isCont(X_a,X_b)) = isCont(X_a,X_b))) # label(tsy_c_Lim_OisCont_res) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.60 53 (all X_a (topological_space(X_a) -> ti(fun(X_a,filter(X_a)),at(X_a)) = at(X_a))) # label(tsy_c_Limits_Oat_res) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.60 54 (all X_a all X_b (topological_space(X_b) -> ti(fun(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool))),tendsto(X_a,X_b)) = tendsto(X_a,X_b))) # label(tsy_c_Limits_Otendsto_res) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.60 55 (all X_a ti(fun(filter(X_a),bool),trivial_limit(X_a)) = trivial_limit(X_a)) # label(tsy_c_Limits_Otrivial__limit_res) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.60 56 (all X_a ti(fun(X_a,fun(fun(nat,X_a),fun(nat,X_a))),nat_case(X_a)) = nat_case(X_a)) # label(tsy_c_Nat_Onat_Onat__case_res) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.60 57 (all X_a ti(fun(X_a,fun(fun(nat,fun(X_a,X_a)),fun(nat,X_a))),nat_rec(X_a)) = nat_rec(X_a)) # label(tsy_c_Nat_Onat_Onat__rec_res) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.60 58 (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].
% 7.58/7.60 59 (all X_a (semiring_1(X_a) -> ti(fun(fun(X_a,X_a),fun(nat,fun(X_a,X_a))),semiri532925092at_aux(X_a)) = semiri532925092at_aux(X_a))) # label(tsy_c_Nat_Osemiring__1__class_Oof__nat__aux_res) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.60 60 (all X_a ti(fun(list(X_a),nat),size_size(list(X_a))) = size_size(list(X_a))) # label(tsy_c_Nat_Osize__class_Osize_0_res) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.60 61 (all X_a all X_b ti(fun(fun(X_a,X_b),fun(fun(X_a,bool),bool)),nat_tr1645093318rphism(X_a,X_b)) = nat_tr1645093318rphism(X_a,X_b)) # label(tsy_c_Nat__Transfer_Otransfer__morphism_res) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.60 62 (all X_a ti(fun(product_prod(int,int),X_a),abs_Frac(X_a)) = abs_Frac(X_a)) # label(tsy_c_Nitpick_OAbs__Frac_res) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.60 63 (all X_a ti(fun(int,fun(int,X_a)),frac(X_a)) = frac(X_a)) # label(tsy_c_Nitpick_Ofrac_res) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.60 64 (all X_a ti(fun(int,X_a),number_of_frac(X_a)) = number_of_frac(X_a)) # label(tsy_c_Nitpick_Onumber__of__frac_res) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.60 65 (all X_a ti(X_a,one_frac(X_a)) = one_frac(X_a)) # label(tsy_c_Nitpick_Oone__frac_res) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.60 66 (all X_a all X_b ti(fun(fun(X_a,bool),fun(fun(X_b,bool),fun(product_prod(X_a,X_b),bool))),prod(X_a,X_b)) = prod(X_a,X_b)) # label(tsy_c_Nitpick_Oprod_res) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.60 67 (all X_a ti(fun(fun(product_prod(X_a,X_a),bool),bool),refl(X_a)) = refl(X_a)) # label(tsy_c_Nitpick_Orefl_H_res) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.60 68 (all X_a ti(X_a,zero_frac(X_a)) = zero_frac(X_a)) # label(tsy_c_Nitpick_Ozero__frac_res) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.60 69 (all X_a (ord(X_a) -> ti(fun(fun(X_a,fun(X_a,bool)),fun(X_a,fun(X_a,X_a))),max(X_a)) = max(X_a))) # label(tsy_c_Orderings_Oord_Omax_res) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.60 70 (all X_a (ord(X_a) -> ti(fun(fun(X_a,fun(X_a,bool)),fun(X_a,fun(X_a,X_a))),min_1(X_a)) = min_1(X_a))) # label(tsy_c_Orderings_Oord_Omin_res) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.60 71 (all X_a (ord(X_a) -> ti(fun(X_a,fun(X_a,bool)),ord_less(X_a)) = ord_less(X_a))) # label(tsy_c_Orderings_Oord__class_Oless_res) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.60 72 (all X_b (ord(X_b) -> ti(fun(X_b,fun(X_b,bool)),ord_less_eq(X_b)) = ord_less_eq(X_b))) # label(tsy_c_Orderings_Oord__class_Oless__eq_res) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.60 73 (all X_a (ord(X_a) -> ti(fun(X_a,fun(X_a,X_a)),ord_max(X_a)) = ord_max(X_a))) # label(tsy_c_Orderings_Oord__class_Omax_res) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.60 74 (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].
% 7.58/7.60 75 (all X_a (order(X_a) -> ti(fun(fun(nat,fun(nat,bool)),fun(fun(nat,X_a),bool)),mono(nat,X_a)) = mono(nat,X_a))) # label(tsy_c_Orderings_Oorder_Omono_res) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.60 76 (all X_a (order(X_a) -> ti(fun(fun(nat,fun(nat,bool)),fun(fun(nat,X_a),bool)),strict_mono(nat,X_a)) = strict_mono(nat,X_a))) # label(tsy_c_Orderings_Oorder_Ostrict__mono_res) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.60 77 (all X_a ti(fun(X_a,fun(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(nat,X_a)))),power_1(X_a)) = power_1(X_a)) # label(tsy_c_Power_Opower_Opower_res) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.60 78 (all X_a (power(X_a) -> ti(fun(X_a,fun(nat,X_a)),power_power(X_a)) = power_power(X_a))) # label(tsy_c_Power_Opower__class_Opower_res) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.60 79 (all X_a ti(fun(fun(X_a,bool),fun(fun(X_a,bool),bool)),powp(X_a)) = powp(X_a)) # label(tsy_c_Predicate_OPowp_res) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.60 80 (all X_a all X_b ti(fun(X_a,fun(X_b,product_prod(X_a,X_b))),product_Pair(X_a,X_b)) = product_Pair(X_a,X_b)) # label(tsy_c_Product__Type_OPair_res) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.60 81 (all X_c all X_b all X_a ti(fun(fun(X_c,X_b),fun(product_prod(X_a,X_c),product_prod(X_a,X_b))),product_apsnd(X_c,X_b,X_a)) = product_apsnd(X_c,X_b,X_a)) # label(tsy_c_Product__Type_Oapsnd_res) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.60 82 (all X_b all X_c all X_a ti(fun(fun(product_prod(X_b,X_c),X_a),fun(X_b,fun(X_c,X_a))),product_curry(X_b,X_c,X_a)) = product_curry(X_b,X_c,X_a)) # label(tsy_c_Product__Type_Ocurry_res) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.60 83 (all X_a all X_b ti(fun(product_prod(X_a,X_b),X_a),product_fst(X_a,X_b)) = product_fst(X_a,X_b)) # label(tsy_c_Product__Type_Ofst_res) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.60 84 (all X_b all X_c all X_a ti(fun(fun(X_b,fun(X_c,X_a)),fun(product_prod(X_b,X_c),X_a)),produc1605651328_split(X_b,X_c,X_a)) = produc1605651328_split(X_b,X_c,X_a)) # label(tsy_c_Product__Type_Ointernal__split_res) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.60 85 (all X_a all X_b all X_c ti(fun(fun(X_a,fun(X_b,X_c)),fun(product_prod(X_a,X_b),X_c)),product_prod_case(X_a,X_b,X_c)) = product_prod_case(X_a,X_b,X_c)) # label(tsy_c_Product__Type_Oprod_Oprod__case_res) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.60 86 (all X_b all X_c all X_a ti(fun(fun(X_b,fun(X_c,X_a)),fun(product_prod(X_b,X_c),X_a)),product_prod_rec(X_b,X_c,X_a)) = product_prod_rec(X_b,X_c,X_a)) # label(tsy_c_Product__Type_Oprod_Oprod__rec_res) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.60 87 (all X_a all X_b ti(fun(fun(X_a,nat),fun(fun(X_b,nat),fun(product_prod(X_a,X_b),nat))),product_prod_size(X_a,X_b)) = product_prod_size(X_a,X_b)) # label(tsy_c_Product__Type_Oprod_Oprod__size_res) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.60 88 (all X_a all X_b ti(fun(product_prod(X_a,X_b),X_b),product_snd(X_a,X_b)) = product_snd(X_a,X_b)) # label(tsy_c_Product__Type_Osnd_res) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.60 89 (all X_a (field_char_0(X_a) -> ti(fun(X_a,bool),field_char_0_Rats(X_a)) = field_char_0_Rats(X_a))) # label(tsy_c_Rat_Ofield__char__0__class_ORats_res) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.60 90 (all X_c all X_b all X_a (real_normed_vector(X_a) & real_normed_vector(X_b) & real_normed_vector(X_c) -> ti(fun(fun(X_a,fun(X_b,X_c)),bool),bounded_bilinear(X_a,X_b,X_c)) = bounded_bilinear(X_a,X_b,X_c))) # label(tsy_c_RealVector_Obounded__bilinear_res) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.60 91 (all X_a (dist_norm(X_a) -> ti(fun(X_a,fun(X_a,real)),dist_dist(X_a)) = dist_dist(X_a))) # label(tsy_c_RealVector_Odist__class_Odist_0_res) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.60 92 (all X_a (metric_space(X_a) -> ti(fun(X_a,fun(X_a,real)),dist_dist(X_a)) = dist_dist(X_a))) # label(tsy_c_RealVector_Odist__class_Odist_1_res) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.60 93 (all X_a (sgn_div_norm(X_a) -> ti(fun(X_a,real),norm_norm(X_a)) = norm_norm(X_a))) # label(tsy_c_RealVector_Onorm__class_Onorm_0_res) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.60 94 (all X_a (dist_norm(X_a) -> ti(fun(X_a,real),norm_norm(X_a)) = norm_norm(X_a))) # label(tsy_c_RealVector_Onorm__class_Onorm_1_res) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.60 95 (all X_a (real_algebra_1(X_a) -> ti(fun(real,X_a),of_real(X_a)) = of_real(X_a))) # label(tsy_c_RealVector_Oof__real_res) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.60 96 (all X_a (sgn_div_norm(X_a) -> ti(fun(real,fun(X_a,X_a)),scaleR_scaleR(X_a)) = scaleR_scaleR(X_a))) # label(tsy_c_RealVector_OscaleR__class_OscaleR_0_res) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.60 97 (all X_a (real_vector(X_a) -> ti(fun(real,fun(X_a,X_a)),scaleR_scaleR(X_a)) = scaleR_scaleR(X_a))) # label(tsy_c_RealVector_OscaleR__class_OscaleR_1_res) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.60 98 (all X_a (dvd(X_a) -> ti(fun(X_a,fun(X_a,bool)),dvd_dvd(X_a)) = dvd_dvd(X_a))) # label(tsy_c_Rings_Odvd__class_Odvd_res) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.60 99 (all X_a (real_normed_vector(X_a) -> ti(fun(fun(nat,X_a),bool),bseq(X_a)) = bseq(X_a))) # label(tsy_c_SEQ_OBseq_res) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.60 100 (all X_a (metric_space(X_a) -> ti(fun(fun(nat,X_a),bool),cauchy(X_a)) = cauchy(X_a))) # label(tsy_c_SEQ_OCauchy_res) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.60 101 (all X_a (metric_space(X_a) -> ti(fun(fun(nat,X_a),X_a),lim(X_a)) = lim(X_a))) # label(tsy_c_SEQ_Olim_res) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.60 102 (all X_a (order(X_a) -> ti(fun(fun(nat,X_a),bool),monoseq(X_a)) = monoseq(X_a))) # label(tsy_c_SEQ_Omonoseq_res) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.60 103 (all X_a (comm_monoid_add(X_a) & topological_space(X_a) -> ti(fun(fun(nat,X_a),X_a),suminf(X_a)) = suminf(X_a))) # label(tsy_c_Series_Osuminf_res) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.60 104 (all X_a (comm_monoid_add(X_a) & topological_space(X_a) -> ti(fun(fun(nat,X_a),bool),summable(X_a)) = summable(X_a))) # label(tsy_c_Series_Osummable_res) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.60 105 (all X_a (comm_monoid_add(X_a) & topological_space(X_a) -> ti(fun(fun(nat,X_a),fun(X_a,bool)),sums(X_a)) = sums(X_a))) # label(tsy_c_Series_Osums_res) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.60 106 (all X_a (order(X_a) -> ti(fun(X_a,fun(X_a,fun(X_a,bool))),ord_atLeastAtMost(X_a)) = ord_atLeastAtMost(X_a))) # label(tsy_c_SetInterval_Oord__class_OatLeastAtMost_res) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.60 107 (all X_a (ord(X_a) -> ti(fun(X_a,fun(X_a,fun(X_a,bool))),ord_atLeastLessThan(X_a)) = ord_atLeastLessThan(X_a))) # label(tsy_c_SetInterval_Oord__class_OatLeastLessThan_res) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.60 108 (all X_a (ord(X_a) -> ti(fun(X_a,fun(X_a,bool)),ord_atMost(X_a)) = ord_atMost(X_a))) # label(tsy_c_SetInterval_Oord__class_OatMost_res) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.60 109 (all X_a (dense_linorder(X_a) -> ti(fun(X_a,fun(X_a,fun(X_a,bool))),ord_gr676655987ssThan(X_a)) = ord_gr676655987ssThan(X_a))) # label(tsy_c_SetInterval_Oord__class_OgreaterThanLessThan_0_res) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.60 110 (all X_a (ordered_ab_group_add(X_a) -> ti(fun(X_a,fun(X_a,fun(X_a,bool))),ord_gr676655987ssThan(X_a)) = ord_gr676655987ssThan(X_a))) # label(tsy_c_SetInterval_Oord__class_OgreaterThanLessThan_2_res) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.60 111 (all X_a (ord(X_a) -> ti(fun(X_a,fun(X_a,bool)),ord_lessThan(X_a)) = ord_lessThan(X_a))) # label(tsy_c_SetInterval_Oord__class_OlessThan_res) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.60 112 (all X_a ti(fun(fun(X_a,bool),fun(X_a,bool)),collect(X_a)) = collect(X_a)) # label(tsy_c_Set_OCollect_res) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.60 113 (all X_a ti(fun(fun(X_a,bool),fun(fun(X_a,bool),bool)),pow(X_a)) = pow(X_a)) # label(tsy_c_Set_OPow_res) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.60 114 (all X_b all X_a ti(fun(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool))),image(X_b,X_a)) = image(X_b,X_a)) # label(tsy_c_Set_Oimage_res) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.60 115 (all X_a all X_b ti(fun(fun(X_a,bool),fun(fun(X_b,bool),fun(sum_sum(X_a,X_b),bool))),sum_Plus(X_a,X_b)) = sum_Plus(X_a,X_b)) # label(tsy_c_Sum__Type_OPlus_res) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.60 116 (all X_a (ring_1(X_a) -> ti(fun(fun(nat,X_a),fun(nat,X_a)),diffs(X_a)) = diffs(X_a))) # label(tsy_c_Transcendental_Odiffs_res) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.60 117 (all X_a (real_normed_field(X_a) & banach(X_a) -> ti(fun(X_a,X_a),exp(X_a)) = exp(X_a))) # label(tsy_c_Transcendental_Oexp_res) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.60 118 (all X_a ti(fun(fun(X_a,fun(X_a,bool)),fun(X_a,bool)),accp(X_a)) = accp(X_a)) # label(tsy_c_Wellfounded_Oaccp_res) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.60 119 (all X_a ti(fun(product_prod(fun(X_a,bool),fun(X_a,bool)),bool),finite_psubset(X_a)) = finite_psubset(X_a)) # label(tsy_c_Wellfounded_Ofinite__psubset_res) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.60 120 (all X_a all X_b ti(fun(fun(product_prod(X_a,X_a),bool),fun(fun(product_prod(X_b,X_b),bool),fun(product_prod(product_prod(X_a,X_b),product_prod(X_a,X_b)),bool))),lex_prod(X_a,X_b)) = lex_prod(X_a,X_b)) # label(tsy_c_Wellfounded_Olex__prod_res) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.60 121 (all X_a ti(fun(fun(X_a,nat),fun(product_prod(X_a,X_a),bool)),measure(X_a)) = measure(X_a)) # label(tsy_c_Wellfounded_Omeasure_res) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.60 122 (all X_a ti(fun(fun(X_a,nat),fun(fun(product_prod(X_a,X_a),bool),fun(product_prod(X_a,X_a),bool))),mlex_prod(X_a)) = mlex_prod(X_a)) # label(tsy_c_Wellfounded_Omlex__prod_res) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.60 123 (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].
% 7.58/7.60 124 (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].
% 7.58/7.60 125 (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].
% 7.58/7.60 126 (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].
% 7.58/7.60 127 (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].
% 7.58/7.60 128 (all B_1_1 (hBOOL(ti(bool,B_1_1)) <-> hBOOL(B_1_1))) # label(tsy_c_hBOOL_arg1) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.60 129 (all X_a ti(fun(X_a,fun(fun(X_a,bool),bool)),member(X_a)) = member(X_a)) # label(tsy_c_member_res) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.60 130 (all A_1 all R_4 all B all M_1 all C all D all N_1 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_1),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),R_4),B))),M_1)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),C),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),R_4),D))),N_1)) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),M_1)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),N_1))),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),R_4),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),M_1)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),D),N_1))))) # label(fact_0_xzgcda__linear__aux1) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.60 131 (all X_a (ring(X_a) -> (all X all Y 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),times_times(X_a),X),Y)),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),plus_plus(X_a),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),minus_minus(X_a),Y),B))),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),X),A_1)),B))))) # label(fact_1_mult__diff__mult) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.60 132 (all X_a (real_normed_algebra(X_a) -> (all X all Y 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),times_times(X_a),X),Y)),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),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),X),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),Y),B))),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),X),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,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),Y),B)))))) # label(fact_2_mult_Oprod__diff__prod) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.60 133 (all X_a (ring(X_a) -> (all Aa all E_2 all C_1 all Ba 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),times_times(X_a),Aa),E_2)),C_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Ba),E_2)),D_1) <-> ti(X_a,C_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),Ba),Aa)),E_2)),D_1))))) # label(fact_3_eq__add__iff2) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.60 134 (all X_a (ring(X_a) -> (all Aa all E_2 all C_1 all Ba 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),times_times(X_a),Aa),E_2)),C_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Ba),E_2)),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),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),Aa),Ba)),E_2)),C_1) = ti(X_a,D_1))))) # label(fact_4_eq__add__iff1) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.60 135 (all X_1 (hBOOL(hAPP(int,bool,twoSqu1091635170sum2sq,X_1)) <-> (exists A_3 exists B_3 hAPP(product_prod(int,int),int,twoSqu1094008024sum2sq,hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),A_3),B_3)) = X_1))) # label(fact_5_is__sum2sq__def) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.60 136 (all A_1 all B all C (hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A_1),B) = C -> A_1 = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),C),B))) # label(fact_6_Int2_Oaux1) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.60 137 (all W all Z1 all Z2 hAPP(int,int,hAPP(int,fun(int,int),times_times(int),W),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),Z1)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),W),Z2))) # label(fact_7_zdiff__zmult__distrib2) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.60 138 (all Z1 all Z2 all W 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) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Z1),W)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Z2),W))) # label(fact_8_zdiff__zmult__distrib) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.60 139 (all W all Z1 all Z2 hAPP(int,int,hAPP(int,fun(int,int),times_times(int),W),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),Z1)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),W),Z2))) # label(fact_9_zadd__zmult__distrib2) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.60 140 (all Z1 all Z2 all W 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) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Z1),W)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Z2),W))) # label(fact_10_zadd__zmult__distrib) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.60 141 (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_11_diff__add__cancel) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.60 142 (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_12_ab__semigroup__mult__class_Omult__ac_I1_J) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.60 143 (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_13_add__right__imp__eq) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.60 144 (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_14_add__imp__eq) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.60 145 (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_15_add__left__imp__eq) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.60 146 (all X_a (cancel_semigroup_add(X_a) -> (all Ba all Aa all C_1 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Ba),Aa) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C_1),Aa) <-> ti(X_a,Ba) = ti(X_a,C_1))))) # label(fact_16_add__right__cancel) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.60 147 (all X_a (cancel_semigroup_add(X_a) -> (all Aa all Ba all C_1 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Aa),Ba) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Aa),C_1) <-> ti(X_a,Ba) = ti(X_a,C_1))))) # label(fact_17_add__left__cancel) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.60 148 (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_18_ab__semigroup__add__class_Oadd__ac_I1_J) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.60 149 (all X_a (ab_group_add(X_a) -> (all Aa all Ba all C_1 all D_1 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),Aa),Ba) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),C_1),D_1) -> (ti(X_a,Aa) = ti(X_a,Ba) <-> ti(X_a,C_1) = ti(X_a,D_1)))))) # label(fact_19_diff__eq__diff__eq) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.60 150 (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_20_zmult__assoc) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.60 151 (all Z all W hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Z),W) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),W),Z)) # label(fact_21_zmult__commute) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.60 152 (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_22_zadd__assoc) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.60 153 (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_23_zadd__left__commute) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.60 154 (all Z all W hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Z),W) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),W),Z)) # label(fact_24_zadd__commute) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.60 155 (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_25_combine__common__factor) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.60 156 (all X_a (real_normed_algebra(X_a) -> (all X all Y all Ya 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),X),Y)),Ya) = 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),Ya)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Y),Ya))))) # label(fact_26_mult__left_Oadd) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.60 157 (all X_a (real_normed_algebra(X_a) -> (all A_1 all A_5 all B 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),A_5)),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),B)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_5),B))))) # label(fact_27_mult_Oadd__left) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.60 158 (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_28_comm__semiring__class_Odistrib) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.60 159 (all X_a (real_normed_algebra(X_a) -> (all Xa_1 all X all Y hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Xa_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X),Y)) = 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),Xa_1),X)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Xa_1),Y))))) # label(fact_29_mult__right_Oadd) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.60 160 (all X_a (real_normed_algebra(X_a) -> (all A_1 all B all B_4 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),plus_plus(X_a),B),B_4)) = 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),B)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B_4))))) # label(fact_30_mult_Oadd__right) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.60 161 (all X_a (real_normed_algebra(X_a) -> (all X all Y all Ya hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),X),Y)),Ya) = 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),times_times(X_a),X),Ya)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Y),Ya))))) # label(fact_31_mult__left_Odiff) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.60 162 (all X_a (real_normed_algebra(X_a) -> (all A_1 all A_5 all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_1),A_5)),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),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_5),B))))) # label(fact_32_mult_Odiff__left) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.60 163 (all X_a (real_normed_algebra(X_a) -> (all Xa_1 all X all Y hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Xa_1),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),minus_minus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Xa_1),X)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Xa_1),Y))))) # label(fact_33_mult__right_Odiff) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.60 164 (all X_a (real_normed_algebra(X_a) -> (all A_1 all B all B_4 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),minus_minus(X_a),B),B_4)) = 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),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_4))))) # label(fact_34_mult_Odiff__right) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.60 165 (all X_a (ab_group_add(X_a) -> (all A_1 all C all B all D 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),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B),D)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_1),B)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),C),D))))) # label(fact_35_add__diff__add) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.60 166 (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_36_add__diff__cancel) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.60 167 (all X_a (semiri456707255roduct(X_a) -> (all W_1 all Y_1 all X_1 all Z_1 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),W_1),Y_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X_1),Z_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),W_1),Z_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X_1),Y_1)) <-> ti(X_a,W_1) = ti(X_a,X_1) | ti(X_a,Y_1) = ti(X_a,Z_1))))) # label(fact_37_crossproduct__eq) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.60 168 (all X_a (comm_semiring_1(X_a) -> (all A_1 all M_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),times_times(X_a),A_1),M_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),M_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)),M_1)))) # label(fact_38_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.60 169 (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_39_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.60 170 (all X_a (semiri456707255roduct(X_a) -> (all C_1 all D_1 all Aa all Ba (ti(X_a,Aa) != ti(X_a,Ba) & ti(X_a,C_1) != ti(X_a,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),times_times(X_a),Aa),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Ba),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),times_times(X_a),Aa),D_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Ba),C_1)))))) # label(fact_40_crossproduct__noteq) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.60 171 (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_41_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.60 172 (all X_b all X_a (minus(X_a) -> (all A_2 all B_1 all X_1 hAPP(X_b,X_a,hAPP(fun(X_b,X_a),fun(X_b,X_a),hAPP(fun(X_b,X_a),fun(fun(X_b,X_a),fun(X_b,X_a)),minus_minus(fun(X_b,X_a)),A_2),B_1),X_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_b,X_a,A_2,X_1)),hAPP(X_b,X_a,B_1,X_1))))) # label(fact_42_minus__apply) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.60 173 (all X_a all X_b (minus(X_b) -> (all A_2 all B_1 all X_2 hAPP(X_a,X_b,hAPP(fun(X_a,X_b),fun(X_a,X_b),hAPP(fun(X_a,X_b),fun(fun(X_a,X_b),fun(X_a,X_b)),minus_minus(fun(X_a,X_b)),A_2),B_1),X_2) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),hAPP(X_a,X_b,A_2,X_2)),hAPP(X_a,X_b,B_1,X_2))))) # label(fact_43_fun__diff__def) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.60 174 (all X_b all X_a all A_1 all B all A_5 all B_4 (hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),A_1),B) = hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),A_5),B_4) -> -(ti(X_a,A_1) = ti(X_a,A_5) -> ti(X_b,B) != ti(X_b,B_4)))) # label(fact_44_Pair__inject) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.60 175 (all X_b all X_a all Aa all Ba all A_7 all B_6 (hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),Aa),Ba) = hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),A_7),B_6) <-> ti(X_a,Aa) = ti(X_a,A_7) & ti(X_b,Ba) = ti(X_b,B_6))) # label(fact_45_Pair__eq) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.60 176 (all X_a all X_b all P_1 ((all X1 hBOOL(hAPP(product_prod(X_a,X_b),bool,P_1,X1))) <-> (all A_3 all B_3 hBOOL(hAPP(product_prod(X_a,X_b),bool,P_1,hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),A_3),B_3)))))) # label(fact_46_split__paired__All) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.60 177 (all X_a (comm_semiring_1(X_a) -> (all A_1 all B all C all D hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),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)) = 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))))) # label(fact_47_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.60 178 (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_48_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.60 179 (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_49_times_Oidem) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.60 180 (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_50_mult__idem) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.60 181 (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_51_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.60 182 (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_52_mult__left__idem) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.60 183 (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_53_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.60 184 (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_54_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.60 185 (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_55_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.60 186 (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_56_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.60 187 (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_57_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.60 188 (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_58_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.60 189 (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_59_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.60 190 (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_60_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.60 191 (all X_a (comm_semiring_1(X_a) -> (all A_1 all C all D 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)) = 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))))) # label(fact_61_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.60 192 (all X_a (comm_semiring_1(X_a) -> (all A_1 all C all D 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)) = 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)))) # label(fact_62_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.60 193 (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_63_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.60 194 (all X_b all X_c all X_a all F1 all Aa all Ba hAPP(product_prod(X_b,X_c),X_a,hAPP(fun(X_b,fun(X_c,X_a)),fun(product_prod(X_b,X_c),X_a),product_prod_rec(X_b,X_c,X_a),F1),hAPP(X_c,product_prod(X_b,X_c),hAPP(X_b,fun(X_c,product_prod(X_b,X_c)),product_Pair(X_b,X_c),Aa),Ba)) = hAPP(X_c,X_a,hAPP(X_b,fun(X_c,X_a),F1,Aa),Ba)) # label(fact_64_prod_Orecs) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.60 195 (all X_a all X_b all P_1 ((exists X1 hBOOL(hAPP(product_prod(X_a,X_b),bool,P_1,X1))) <-> (exists A_3 exists B_3 hBOOL(hAPP(product_prod(X_a,X_b),bool,P_1,hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),A_3),B_3)))))) # label(fact_65_split__paired__Ex) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.60 196 (all X_a all X_b all X_c all X_d all X_e all X_f all X_1 all P_1 ((all A_3 all B_3 all C_4 all D_3 all E all F_3 hBOOL(hAPP(product_prod(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f))))),bool,P_1,hAPP(product_prod(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f)))),product_prod(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f))))),hAPP(X_a,fun(product_prod(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f)))),product_prod(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f)))))),product_Pair(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f))))),A_3),hAPP(product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f))),product_prod(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f)))),hAPP(X_b,fun(product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f))),product_prod(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f))))),product_Pair(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f)))),B_3),hAPP(product_prod(X_d,product_prod(X_e,X_f)),product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f))),hAPP(X_c,fun(product_prod(X_d,product_prod(X_e,X_f)),product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f)))),product_Pair(X_c,product_prod(X_d,product_prod(X_e,X_f))),C_4),hAPP(product_prod(X_e,X_f),product_prod(X_d,product_prod(X_e,X_f)),hAPP(X_d,fun(product_prod(X_e,X_f),product_prod(X_d,product_prod(X_e,X_f))),product_Pair(X_d,product_prod(X_e,X_f)),D_3),hAPP(X_f,product_prod(X_e,X_f),hAPP(X_e,fun(X_f,product_prod(X_e,X_f)),product_Pair(X_e,X_f),E),F_3)))))))) -> hBOOL(hAPP(product_prod(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f))))),bool,P_1,X_1)))) # label(fact_66_prod__induct6) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.60 197 (all X_a all X_b all X_c all X_d all X_e all X_f all Y -(all A_3 all B_3 all C_4 all D_3 all E all F_3 ti(product_prod(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f))))),Y) != hAPP(product_prod(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f)))),product_prod(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f))))),hAPP(X_a,fun(product_prod(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f)))),product_prod(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f)))))),product_Pair(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f))))),A_3),hAPP(product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f))),product_prod(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f)))),hAPP(X_b,fun(product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f))),product_prod(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f))))),product_Pair(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f)))),B_3),hAPP(product_prod(X_d,product_prod(X_e,X_f)),product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f))),hAPP(X_c,fun(product_prod(X_d,product_prod(X_e,X_f)),product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f)))),product_Pair(X_c,product_prod(X_d,product_prod(X_e,X_f))),C_4),hAPP(product_prod(X_e,X_f),product_prod(X_d,product_prod(X_e,X_f)),hAPP(X_d,fun(product_prod(X_e,X_f),product_prod(X_d,product_prod(X_e,X_f))),product_Pair(X_d,product_prod(X_e,X_f)),D_3),hAPP(X_f,product_prod(X_e,X_f),hAPP(X_e,fun(X_f,product_prod(X_e,X_f)),product_Pair(X_e,X_f),E),F_3))))))) # label(fact_67_prod__cases6) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.61 198 (all X_a all X_b all X_c all X_d all X_e all X_1 all P_1 ((all A_3 all B_3 all C_4 all D_3 all E hBOOL(hAPP(product_prod(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,X_e)))),bool,P_1,hAPP(product_prod(X_b,product_prod(X_c,product_prod(X_d,X_e))),product_prod(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,X_e)))),hAPP(X_a,fun(product_prod(X_b,product_prod(X_c,product_prod(X_d,X_e))),product_prod(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,X_e))))),product_Pair(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,X_e)))),A_3),hAPP(product_prod(X_c,product_prod(X_d,X_e)),product_prod(X_b,product_prod(X_c,product_prod(X_d,X_e))),hAPP(X_b,fun(product_prod(X_c,product_prod(X_d,X_e)),product_prod(X_b,product_prod(X_c,product_prod(X_d,X_e)))),product_Pair(X_b,product_prod(X_c,product_prod(X_d,X_e))),B_3),hAPP(product_prod(X_d,X_e),product_prod(X_c,product_prod(X_d,X_e)),hAPP(X_c,fun(product_prod(X_d,X_e),product_prod(X_c,product_prod(X_d,X_e))),product_Pair(X_c,product_prod(X_d,X_e)),C_4),hAPP(X_e,product_prod(X_d,X_e),hAPP(X_d,fun(X_e,product_prod(X_d,X_e)),product_Pair(X_d,X_e),D_3),E))))))) -> hBOOL(hAPP(product_prod(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,X_e)))),bool,P_1,X_1)))) # label(fact_68_prod__induct5) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.61 199 (all X_a all X_b all X_c all X_d all X_e all Y -(all A_3 all B_3 all C_4 all D_3 all E ti(product_prod(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,X_e)))),Y) != hAPP(product_prod(X_b,product_prod(X_c,product_prod(X_d,X_e))),product_prod(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,X_e)))),hAPP(X_a,fun(product_prod(X_b,product_prod(X_c,product_prod(X_d,X_e))),product_prod(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,X_e))))),product_Pair(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,X_e)))),A_3),hAPP(product_prod(X_c,product_prod(X_d,X_e)),product_prod(X_b,product_prod(X_c,product_prod(X_d,X_e))),hAPP(X_b,fun(product_prod(X_c,product_prod(X_d,X_e)),product_prod(X_b,product_prod(X_c,product_prod(X_d,X_e)))),product_Pair(X_b,product_prod(X_c,product_prod(X_d,X_e))),B_3),hAPP(product_prod(X_d,X_e),product_prod(X_c,product_prod(X_d,X_e)),hAPP(X_c,fun(product_prod(X_d,X_e),product_prod(X_c,product_prod(X_d,X_e))),product_Pair(X_c,product_prod(X_d,X_e)),C_4),hAPP(X_e,product_prod(X_d,X_e),hAPP(X_d,fun(X_e,product_prod(X_d,X_e)),product_Pair(X_d,X_e),D_3),E)))))) # label(fact_69_prod__cases5) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.61 200 (all X_a all X_b all X_c all X_d all X_1 all P_1 ((all A_3 all B_3 all C_4 all D_3 hBOOL(hAPP(product_prod(X_a,product_prod(X_b,product_prod(X_c,X_d))),bool,P_1,hAPP(product_prod(X_b,product_prod(X_c,X_d)),product_prod(X_a,product_prod(X_b,product_prod(X_c,X_d))),hAPP(X_a,fun(product_prod(X_b,product_prod(X_c,X_d)),product_prod(X_a,product_prod(X_b,product_prod(X_c,X_d)))),product_Pair(X_a,product_prod(X_b,product_prod(X_c,X_d))),A_3),hAPP(product_prod(X_c,X_d),product_prod(X_b,product_prod(X_c,X_d)),hAPP(X_b,fun(product_prod(X_c,X_d),product_prod(X_b,product_prod(X_c,X_d))),product_Pair(X_b,product_prod(X_c,X_d)),B_3),hAPP(X_d,product_prod(X_c,X_d),hAPP(X_c,fun(X_d,product_prod(X_c,X_d)),product_Pair(X_c,X_d),C_4),D_3)))))) -> hBOOL(hAPP(product_prod(X_a,product_prod(X_b,product_prod(X_c,X_d))),bool,P_1,X_1)))) # label(fact_70_prod__induct4) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.61 201 (all X_a all X_b all X_c all X_d all Y -(all A_3 all B_3 all C_4 all D_3 ti(product_prod(X_a,product_prod(X_b,product_prod(X_c,X_d))),Y) != hAPP(product_prod(X_b,product_prod(X_c,X_d)),product_prod(X_a,product_prod(X_b,product_prod(X_c,X_d))),hAPP(X_a,fun(product_prod(X_b,product_prod(X_c,X_d)),product_prod(X_a,product_prod(X_b,product_prod(X_c,X_d)))),product_Pair(X_a,product_prod(X_b,product_prod(X_c,X_d))),A_3),hAPP(product_prod(X_c,X_d),product_prod(X_b,product_prod(X_c,X_d)),hAPP(X_b,fun(product_prod(X_c,X_d),product_prod(X_b,product_prod(X_c,X_d))),product_Pair(X_b,product_prod(X_c,X_d)),B_3),hAPP(X_d,product_prod(X_c,X_d),hAPP(X_c,fun(X_d,product_prod(X_c,X_d)),product_Pair(X_c,X_d),C_4),D_3))))) # label(fact_71_prod__cases4) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.61 202 (all X_a all X_b all X_c all X_1 all P_1 ((all A_3 all B_3 all C_4 hBOOL(hAPP(product_prod(X_a,product_prod(X_b,X_c)),bool,P_1,hAPP(product_prod(X_b,X_c),product_prod(X_a,product_prod(X_b,X_c)),hAPP(X_a,fun(product_prod(X_b,X_c),product_prod(X_a,product_prod(X_b,X_c))),product_Pair(X_a,product_prod(X_b,X_c)),A_3),hAPP(X_c,product_prod(X_b,X_c),hAPP(X_b,fun(X_c,product_prod(X_b,X_c)),product_Pair(X_b,X_c),B_3),C_4))))) -> hBOOL(hAPP(product_prod(X_a,product_prod(X_b,X_c)),bool,P_1,X_1)))) # label(fact_72_prod__induct3) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.61 203 (all X_a all X_b all X_c all Y -(all A_3 all B_3 all C_4 ti(product_prod(X_a,product_prod(X_b,X_c)),Y) != hAPP(product_prod(X_b,X_c),product_prod(X_a,product_prod(X_b,X_c)),hAPP(X_a,fun(product_prod(X_b,X_c),product_prod(X_a,product_prod(X_b,X_c))),product_Pair(X_a,product_prod(X_b,X_c)),A_3),hAPP(X_c,product_prod(X_b,X_c),hAPP(X_b,fun(X_c,product_prod(X_b,X_c)),product_Pair(X_b,X_c),B_3),C_4)))) # label(fact_73_prod__cases3) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.61 204 (all X_a all X_b all P_4 -(all X_2 all Y_2 ti(product_prod(X_a,X_b),P_4) != hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),X_2),Y_2))) # label(fact_74_PairE) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.61 205 (all X_a all X_b all F all G ((all X_2 hAPP(X_a,X_b,F,X_2) = hAPP(X_a,X_b,G,X_2)) -> ti(fun(X_a,X_b),F) = ti(fun(X_a,X_b),G))) # label(fact_75_ext) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.61 206 (all X_a all X_1 all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_2)) <-> hBOOL(hAPP(X_a,bool,A_2,X_1)))) # label(fact_76_mem__def) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.61 207 (all X_a all P_1 hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),P_1) = ti(fun(X_a,bool),P_1)) # label(fact_77_Collect__def) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.61 208 (all X_a all X_b all Y -(all A_3 all B_3 ti(product_prod(X_a,X_b),Y) != hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),A_3),B_3))) # label(fact_78_prod_Oexhaust) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.61 209 (all X_b all X_c all X_a all C_1 all Aa all Ba hAPP(product_prod(X_b,X_c),X_a,hAPP(fun(X_b,fun(X_c,X_a)),fun(product_prod(X_b,X_c),X_a),produc1605651328_split(X_b,X_c,X_a),C_1),hAPP(X_c,product_prod(X_b,X_c),hAPP(X_b,fun(X_c,product_prod(X_b,X_c)),product_Pair(X_b,X_c),Aa),Ba)) = hAPP(X_c,X_a,hAPP(X_b,fun(X_c,X_a),C_1,Aa),Ba)) # label(fact_79_internal__split__conv) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.61 210 (all X_a all X_b all F all Aa all Ba (hBOOL(hAPP(product_prod(X_a,X_b),bool,F,hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),Aa),Ba))) -> hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),hAPP(fun(product_prod(X_a,X_b),bool),fun(X_a,fun(X_b,bool)),product_curry(X_a,X_b,bool),F),Aa),Ba)))) # label(fact_80_curryI) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.61 211 (all X_a (ordered_ring(X_a) -> (all Aa all E_2 all C_1 all Ba all 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),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Aa),E_2)),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Ba),E_2)),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),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),Aa),Ba)),E_2)),C_1)),D_1)))))) # label(fact_81_le__add__iff1) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.61 212 (all X_a (ordered_ring(X_a) -> (all Aa all E_2 all C_1 all Ba all 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),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Aa),E_2)),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Ba),E_2)),D_1))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),Ba),Aa)),E_2)),D_1))))))) # label(fact_82_le__add__iff2) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.61 213 (all X_a (ring_1(X_a) -> (all X 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),times_times(X_a),X),X)),one_one(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),X),one_one(X_a))),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),X),one_one(X_a)))))) # label(fact_83_real__squared__diff__one__factored) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.61 214 (all X_a (ordered_ring(X_a) -> (all Aa all E_2 all C_1 all Ba all 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),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Aa),E_2)),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Ba),E_2)),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),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),Aa),Ba)),E_2)),C_1)),D_1)))))) # label(fact_84_less__add__iff1) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.61 215 (all X_a (ordered_ring(X_a) -> (all Aa all E_2 all C_1 all Ba all 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),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Aa),E_2)),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Ba),E_2)),D_1))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),Ba),Aa)),E_2)),D_1))))))) # label(fact_85_less__add__iff2) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.61 216 (all X_a (number_ring(X_a) -> (all V all W all C hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(int,X_a,number_number_of(X_a),V)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(int,X_a,number_number_of(X_a),W)),C)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),V),W))),C)))) # label(fact_86_add__number__of__diff1) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.61 217 (all X_c all X_a all X_b all F all Aa all Ba hAPP(X_c,X_a,hAPP(X_b,fun(X_c,X_a),hAPP(fun(product_prod(X_b,X_c),X_a),fun(X_b,fun(X_c,X_a)),product_curry(X_b,X_c,X_a),F),Aa),Ba) = hAPP(product_prod(X_b,X_c),X_a,F,hAPP(X_c,product_prod(X_b,X_c),hAPP(X_b,fun(X_c,product_prod(X_b,X_c)),product_Pair(X_b,X_c),Aa),Ba))) # label(fact_87_curry__conv) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.61 218 (all X_a all X_c all X_b (real_normed_vector(X_b) & real_normed_vector(X_c) & real_normed_vector(X_a) -> (all X_1 all Y_1 all Aa all Ba all Prod (hBOOL(hAPP(fun(X_a,fun(X_b,X_c)),bool,bounded_bilinear(X_a,X_b,X_c),Prod)) -> hAPP(X_c,X_c,hAPP(X_c,fun(X_c,X_c),minus_minus(X_c),hAPP(X_b,X_c,hAPP(X_a,fun(X_b,X_c),Prod,X_1),Y_1)),hAPP(X_b,X_c,hAPP(X_a,fun(X_b,X_c),Prod,Aa),Ba)) = hAPP(X_c,X_c,hAPP(X_c,fun(X_c,X_c),plus_plus(X_c),hAPP(X_c,X_c,hAPP(X_c,fun(X_c,X_c),plus_plus(X_c),hAPP(X_b,X_c,hAPP(X_a,fun(X_b,X_c),Prod,hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),X_1),Aa)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),Y_1),Ba))),hAPP(X_b,X_c,hAPP(X_a,fun(X_b,X_c),Prod,hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),X_1),Aa)),Ba))),hAPP(X_b,X_c,hAPP(X_a,fun(X_b,X_c),Prod,Aa),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),Y_1),Ba))))))) # label(fact_88_bounded__bilinear_Oprod__diff__prod) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.61 219 (all X_b all X_a all R_3 all X_1 all Y_1 (hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),hAPP(fun(product_prod(X_a,X_b),bool),fun(X_a,fun(X_b,bool)),in_rel(X_a,X_b),R_3),X_1),Y_1)) <-> hBOOL(hAPP(fun(product_prod(X_a,X_b),bool),bool,hAPP(product_prod(X_a,X_b),fun(fun(product_prod(X_a,X_b),bool),bool),member(product_prod(X_a,X_b)),hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),X_1),Y_1)),R_3)))) # label(fact_89_in__rel__def) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.61 220 (all X_b all X_a all F all Aa all Ba (hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),hAPP(fun(product_prod(X_a,X_b),bool),fun(X_a,fun(X_b,bool)),product_curry(X_a,X_b,bool),F),Aa),Ba)) -> hBOOL(hAPP(product_prod(X_a,X_b),bool,F,hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),Aa),Ba))))) # label(fact_90_curryE) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.61 221 (all X_a (one(X_a) -> (all X_1 (one_one(X_a) = ti(X_a,X_1) <-> ti(X_a,X_1) = one_one(X_a))))) # label(fact_91_one__reorient) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.61 222 (all W_1 all Z_1 (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_1),one_one(int)))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),W_1),Z_1)))) # label(fact_92_zle__add1__eq__le) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.61 223 (all X_a (number(X_a) -> (all W_1 all X_1 (hAPP(int,X_a,number_number_of(X_a),W_1) = ti(X_a,X_1) <-> ti(X_a,X_1) = hAPP(int,X_a,number_number_of(X_a),W_1))))) # label(fact_93_number__of__reorient) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.61 224 (all X_a (number(X_a) & linorder(X_a) -> (all V_1 all W_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(int,X_a,number_number_of(X_a),V_1)),hAPP(int,X_a,number_number_of(X_a),W_1))) <-> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(int,X_a,number_number_of(X_a),W_1)),hAPP(int,X_a,number_number_of(X_a),V_1))))))) # label(fact_94_le__number__of__eq__not__less) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.61 225 (all X_a (number_ring(X_a) & ring_char_0(X_a) -> (all X_1 all Y_1 (hAPP(int,X_a,number_number_of(X_a),X_1) = hAPP(int,X_a,number_number_of(X_a),Y_1) <-> X_1 = Y_1)))) # label(fact_95_eq__number__of) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.61 226 (all X_a (number_ring(X_a) & linordered_idom(X_a) -> (all X_1 all Y_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(int,X_a,number_number_of(X_a),X_1)),hAPP(int,X_a,number_number_of(X_a),Y_1))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X_1),Y_1)))))) # label(fact_96_less__number__of) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.61 227 (all X_a (number_ring(X_a) & linordered_idom(X_a) -> (all X_1 all Y_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(int,X_a,number_number_of(X_a),X_1)),hAPP(int,X_a,number_number_of(X_a),Y_1))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X_1),Y_1)))))) # label(fact_97_le__number__of) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.61 228 (all W_1 all Z_1 (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_1)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_1),Z_1)))) # label(fact_98_add1__zle__eq) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.61 229 (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_99_linorder__neqE__linordered__idom) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.61 230 (all W all Z (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W),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),one_one(int))),Z)))) # label(fact_100_zless__imp__add1__zle) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.61 231 (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)) -> (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))))))) # label(fact_101_order__le__neq__implies__less) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.61 232 (all W_1 all Z_1 (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_1),one_one(int)))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_1),Z_1)))) # label(fact_102_zle__diff1__eq) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.61 233 (all X_a (linordered_semidom(X_a) -> (all N_1 all M_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),M_1)) -> (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_1),N_1)))))))) # label(fact_103_less__1__mult) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.61 234 (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_104_less__add__one) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.61 235 (all X_a (ordere223160158up_add(X_a) -> (all C all D 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)) -> 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)))))))) # label(fact_105_add__le__less__mono) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.61 236 (all X_a (ordere223160158up_add(X_a) -> (all C all D 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)) -> 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)))))))) # label(fact_106_add__less__le__mono) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.61 237 (all Z_4 all Z all W_3 all W (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_3),W)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Z_4),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_4)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),W),Z)))))) # label(fact_107_zadd__zless__mono) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.61 238 (all W_1 all Z_1 (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_1),one_one(int)))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_1),Z_1)) | W_1 = Z_1)) # label(fact_108_zless__add1__eq) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.61 239 (all X_a (ordere236663937imp_le(X_a) -> (all Aa all C_1 all Ba (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Aa),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Ba),C_1))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),Ba)))))) # label(fact_109_add__less__cancel__right) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.61 240 (all X_a (ordere236663937imp_le(X_a) -> (all C_1 all Aa all Ba (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C_1),Aa)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C_1),Ba))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),Ba)))))) # label(fact_110_add__less__cancel__left) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.61 241 (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_111_add__strict__right__mono) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.61 242 (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_112_add__strict__left__mono) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.61 243 (all X_a (ordere223160158up_add(X_a) -> (all C all D 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)) -> 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)))))))) # label(fact_113_add__strict__mono) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.61 244 (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_114_add__less__imp__less__right) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.61 245 (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_115_add__less__imp__less__left) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.61 246 (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_116_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.61 247 (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_117_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.61 248 (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_118_mult__1__left) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.61 249 (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_119_mult__1) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.61 250 (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_120_mult__1__right) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.61 251 (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_121_mult_Ocomm__neutral) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.61 252 (all X_a (ordered_ab_group_add(X_a) -> (all Aa all Ba all C_1 all D_1 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),Aa),Ba) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),C_1),D_1) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),Ba)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),D_1))))))) # label(fact_122_diff__eq__diff__less) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.61 253 (all X_a (ordere236663937imp_le(X_a) -> (all Aa all C_1 all Ba (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Aa),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Ba),C_1))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Aa),Ba)))))) # label(fact_123_add__le__cancel__right) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.61 254 (all X_a (ordere236663937imp_le(X_a) -> (all C_1 all Aa all Ba (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C_1),Aa)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C_1),Ba))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Aa),Ba)))))) # label(fact_124_add__le__cancel__left) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.61 255 (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_125_add__right__mono) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.61 256 (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_126_add__left__mono) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.61 257 (all X_a (ordere779506340up_add(X_a) -> (all C all D 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)) -> 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)))))))) # label(fact_127_add__mono) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.61 258 (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_128_add__le__imp__le__right) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.61 259 (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_129_add__le__imp__le__left) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.61 260 (all X_a (ordered_ab_group_add(X_a) -> (all Aa all Ba all C_1 all D_1 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),Aa),Ba) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),C_1),D_1) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Aa),Ba)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C_1),D_1))))))) # label(fact_130_diff__eq__diff__less__eq) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.61 261 (all V all W hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),V)),hAPP(int,int,number_number_of(int),W)) = hAPP(int,int,number_number_of(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),V),W))) # label(fact_131_times__numeral__code_I5_J) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.61 262 (all V all W hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,number_number_of(int),V)),hAPP(int,int,number_number_of(int),W)) = hAPP(int,int,number_number_of(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),V),W))) # label(fact_132_plus__numeral__code_I9_J) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.61 263 (all K_4 all I_1 all J_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),I_1),J_2)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),I_1),K_4)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),J_2),K_4))))) # label(fact_133_zadd__strict__right__mono) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.61 264 (all K_4 all I_1 all J_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),I_1),J_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),K_4),I_1)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),K_4),J_2))))) # label(fact_134_zadd__left__mono) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.61 265 (all Z hAPP(int,int,hAPP(int,fun(int,int),times_times(int),one_one(int)),Z) = Z) # label(fact_135_zmult__1) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.61 266 (all Z hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Z),one_one(int)) = Z) # label(fact_136_zmult__1__right) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.61 267 (all X_a all X_c all X_b (real_normed_vector(X_b) & real_normed_vector(X_c) & real_normed_vector(X_a) -> (all Aa all Ba all B_6 all Prod (hBOOL(hAPP(fun(X_a,fun(X_b,X_c)),bool,bounded_bilinear(X_a,X_b,X_c),Prod)) -> hAPP(X_b,X_c,hAPP(X_a,fun(X_b,X_c),Prod,Aa),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),Ba),B_6)) = hAPP(X_c,X_c,hAPP(X_c,fun(X_c,X_c),plus_plus(X_c),hAPP(X_b,X_c,hAPP(X_a,fun(X_b,X_c),Prod,Aa),Ba)),hAPP(X_b,X_c,hAPP(X_a,fun(X_b,X_c),Prod,Aa),B_6)))))) # label(fact_137_bounded__bilinear_Oadd__right) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.61 268 (all X_a all X_c all X_b (real_normed_vector(X_b) & real_normed_vector(X_c) & real_normed_vector(X_a) -> (all Aa all A_7 all Ba all Prod (hBOOL(hAPP(fun(X_a,fun(X_b,X_c)),bool,bounded_bilinear(X_a,X_b,X_c),Prod)) -> hAPP(X_b,X_c,hAPP(X_a,fun(X_b,X_c),Prod,hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Aa),A_7)),Ba) = hAPP(X_c,X_c,hAPP(X_c,fun(X_c,X_c),plus_plus(X_c),hAPP(X_b,X_c,hAPP(X_a,fun(X_b,X_c),Prod,Aa),Ba)),hAPP(X_b,X_c,hAPP(X_a,fun(X_b,X_c),Prod,A_7),Ba)))))) # label(fact_138_bounded__bilinear_Oadd__left) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.61 269 (all X_a all X_c all X_b (real_normed_vector(X_b) & real_normed_vector(X_c) & real_normed_vector(X_a) -> (all Aa all Ba all B_6 all Prod (hBOOL(hAPP(fun(X_a,fun(X_b,X_c)),bool,bounded_bilinear(X_a,X_b,X_c),Prod)) -> hAPP(X_b,X_c,hAPP(X_a,fun(X_b,X_c),Prod,Aa),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),Ba),B_6)) = hAPP(X_c,X_c,hAPP(X_c,fun(X_c,X_c),minus_minus(X_c),hAPP(X_b,X_c,hAPP(X_a,fun(X_b,X_c),Prod,Aa),Ba)),hAPP(X_b,X_c,hAPP(X_a,fun(X_b,X_c),Prod,Aa),B_6)))))) # label(fact_139_bounded__bilinear_Odiff__right) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.61 270 (all X_a all X_c all X_b (real_normed_vector(X_b) & real_normed_vector(X_c) & real_normed_vector(X_a) -> (all Aa all A_7 all Ba all Prod (hBOOL(hAPP(fun(X_a,fun(X_b,X_c)),bool,bounded_bilinear(X_a,X_b,X_c),Prod)) -> hAPP(X_b,X_c,hAPP(X_a,fun(X_b,X_c),Prod,hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),Aa),A_7)),Ba) = hAPP(X_c,X_c,hAPP(X_c,fun(X_c,X_c),minus_minus(X_c),hAPP(X_b,X_c,hAPP(X_a,fun(X_b,X_c),Prod,Aa),Ba)),hAPP(X_b,X_c,hAPP(X_a,fun(X_b,X_c),Prod,A_7),Ba)))))) # label(fact_140_bounded__bilinear_Odiff__left) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.61 271 (all X_b (number(X_b) & semiring(X_b) -> (all V all B all C hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(int,X_b,number_number_of(X_b),V)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),B),C)) = 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(int,X_b,number_number_of(X_b),V)),B)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(int,X_b,number_number_of(X_b),V)),C))))) # label(fact_141_right__distrib__number__of) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.61 272 (all X_b (number(X_b) & semiring(X_b) -> (all A_1 all B all V 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),A_1),B)),hAPP(int,X_b,number_number_of(X_b),V)) = 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_1),hAPP(int,X_b,number_number_of(X_b),V))),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),B),hAPP(int,X_b,number_number_of(X_b),V)))))) # label(fact_142_left__distrib__number__of) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.61 273 (all X_b (number(X_b) & ring(X_b) -> (all V all B all C hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(int,X_b,number_number_of(X_b),V)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),B),C)) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(int,X_b,number_number_of(X_b),V)),B)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(int,X_b,number_number_of(X_b),V)),C))))) # label(fact_143_right__diff__distrib__number__of) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.61 274 (all X_b (number(X_b) & ring(X_b) -> (all A_1 all B all V 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_1),B)),hAPP(int,X_b,number_number_of(X_b),V)) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),A_1),hAPP(int,X_b,number_number_of(X_b),V))),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),B),hAPP(int,X_b,number_number_of(X_b),V)))))) # label(fact_144_left__diff__distrib__number__of) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.61 275 (all X_a (number_ring(X_a) -> (all V all W hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),V),W)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(int,X_a,number_number_of(X_a),V)),hAPP(int,X_a,number_number_of(X_a),W))))) # label(fact_145_number__of__mult) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.61 276 (all X_a (number_ring(X_a) -> (all V all W hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(int,X_a,number_number_of(X_a),V)),hAPP(int,X_a,number_number_of(X_a),W)) = hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),V),W))))) # label(fact_146_arith__simps_I32_J) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.61 277 (all X_a (number_ring(X_a) -> (all V all W all Z hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(int,X_a,number_number_of(X_a),V)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(int,X_a,number_number_of(X_a),W)),Z)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),V),W))),Z)))) # label(fact_147_mult__number__of__left) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.61 278 (all X_a (number_ring(X_a) -> (all V all W hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),V),W)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(int,X_a,number_number_of(X_a),V)),hAPP(int,X_a,number_number_of(X_a),W))))) # label(fact_148_number__of__add) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.61 279 (all X_a (number_ring(X_a) -> (all V all W hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(int,X_a,number_number_of(X_a),V)),hAPP(int,X_a,number_number_of(X_a),W)) = hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),V),W))))) # label(fact_149_add__number__of__eq) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.61 280 (all X_a (number_ring(X_a) -> (all V all W all Z hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(int,X_a,number_number_of(X_a),V)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(int,X_a,number_number_of(X_a),W)),Z)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),V),W))),Z)))) # label(fact_150_add__number__of__left) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.61 281 (all X_a (number_ring(X_a) -> (all V all W hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),V),W)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(int,X_a,number_number_of(X_a),V)),hAPP(int,X_a,number_number_of(X_a),W))))) # label(fact_151_number__of__diff) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.61 282 (all X_a (comm_semiring_1(X_a) -> (all M_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),M_1),M_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),one_one(X_a)),one_one(X_a))),M_1)))) # label(fact_152_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.61 283 (all X_a (comm_semiring_1(X_a) -> (all M_1 all A_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),M_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),M_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),one_one(X_a))),M_1)))) # label(fact_153_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.61 284 (all X_a (comm_semiring_1(X_a) -> (all A_1 all M_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),M_1)),M_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),one_one(X_a))),M_1)))) # label(fact_154_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.61 285 (all X_b all X_a all F all Aa all Ba (hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),hAPP(fun(product_prod(X_a,X_b),bool),fun(X_a,fun(X_b,bool)),product_curry(X_a,X_b,bool),F),Aa),Ba)) -> hBOOL(hAPP(product_prod(X_a,X_b),bool,F,hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),Aa),Ba))))) # label(fact_155_curryD) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.61 286 (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_156_order__refl) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.61 287 (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_157_xt1_I8_J) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.61 288 (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_158_order__le__less__trans) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.61 289 (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_159_xt1_I7_J) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.61 290 (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_160_order__less__le__trans) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.61 291 (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_161_xt1_I11_J) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.61 292 (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_162_order__le__neq__trans) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.61 293 (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_163_order__le__imp__less__or__eq) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.61 294 (all X_a (linorder(X_a) -> (all X_1 all Y_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),Y_1)) -> (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y_1)) <-> ti(X_a,X_1) = ti(X_a,Y_1)))))) # label(fact_164_linorder__antisym__conv2) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.61 295 (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_165_order__less__imp__le) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.61 296 (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_166_leD) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.61 297 (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_167_xt1_I12_J) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.61 298 (all W hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),W),W))) # label(fact_168_zle__refl) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.61 299 (all K_4 hAPP(int,int,number_number_of(int),K_4) = K_4) # label(fact_169_number__of__is__id) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.61 300 (all Z all W (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Z),W)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),W),Z)))) # label(fact_170_zle__linear) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.61 301 (all Z_1 all W_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Z_1),W_1)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Z_1),W_1)) & Z_1 != W_1)) # label(fact_171_zless__le) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.61 302 (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_172_zless__linear) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.61 303 (all K all L (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),K)),hAPP(int,int,number_number_of(int),L))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),L)))) # label(fact_173_less__number__of__int__code) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.61 304 (all K all L (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),K)),hAPP(int,int,number_number_of(int),L))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),K),L)))) # label(fact_174_less__eq__number__of__int__code) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.61 305 (all K_4 all I_1 all J_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),I_1),J_2)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),J_2),K_4)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),I_1),K_4))))) # label(fact_175_zle__trans) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.61 306 (all Z all W (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Z),W)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),W),Z)) -> Z = W))) # label(fact_176_zle__antisym) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.61 307 (all X_a all X_b (ord(X_b) -> (all F all G (hBOOL(hAPP(fun(X_a,X_b),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,X_b),bool),ord_less_eq(fun(X_a,X_b)),F),G)) <-> (all X_2 hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_a,X_b,F,X_2)),hAPP(X_a,X_b,G,X_2)))))))) # label(fact_177_le__fun__def) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.61 308 (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_178_linorder__linear) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.61 309 (all X_a (order(X_a) -> (all X_1 all Y_1 (ti(X_a,X_1) = ti(X_a,Y_1) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),Y_1)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y_1),X_1)))))) # label(fact_179_order__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.61 310 (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_180_order__eq__refl) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.61 311 (all X_a all X_b (ord(X_b) -> (all X_1 all F all G (hBOOL(hAPP(fun(X_a,X_b),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,X_b),bool),ord_less_eq(fun(X_a,X_b)),F),G)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_a,X_b,F,X_1)),hAPP(X_a,X_b,G,X_1))))))) # label(fact_181_le__funD) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.61 312 (all X_a (order(X_a) -> (all Y_1 all X_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y_1),X_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),Y_1)) <-> ti(X_a,X_1) = ti(X_a,Y_1)))))) # label(fact_182_order__antisym__conv) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.61 313 (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_183_ord__eq__le__trans) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.61 314 (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_184_xt1_I3_J) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.61 315 (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_185_ord__le__eq__trans) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.61 316 (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_186_xt1_I4_J) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.61 317 (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_187_order__antisym) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.61 318 (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_188_order__trans) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.61 319 (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_189_xt1_I5_J) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.61 320 (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_190_xt1_I6_J) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.61 321 (all X_a all X_b (ord(X_b) -> (all X_1 all F all G (hBOOL(hAPP(fun(X_a,X_b),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,X_b),bool),ord_less_eq(fun(X_a,X_b)),F),G)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_a,X_b,F,X_1)),hAPP(X_a,X_b,G,X_1))))))) # label(fact_191_le__funE) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.61 322 (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_192_linorder__le__cases) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.61 323 (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_193_order__less__irrefl) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.61 324 (all X_a (linorder(X_a) -> (all X_1 all Y_1 (ti(X_a,X_1) != ti(X_a,Y_1) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y_1)) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y_1),X_1)))))) # label(fact_194_linorder__neq__iff) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.61 325 (all X_a (linorder(X_a) -> (all X_1 all Y_1 (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y_1)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y_1),X_1)) | ti(X_a,X_1) = ti(X_a,Y_1))))) # label(fact_195_not__less__iff__gr__or__eq) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.61 326 (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_196_linorder__less__linear) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.61 327 (all X_a (linorder(X_a) -> (all Y_1 all X_1 (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y_1),X_1)) -> (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y_1)) <-> ti(X_a,X_1) = ti(X_a,Y_1)))))) # label(fact_197_linorder__antisym__conv3) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.61 328 (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_198_linorder__neqE) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.61 329 (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_199_less__imp__neq) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.61 330 (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_200_order__less__not__sym) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.61 331 (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_201_order__less__imp__not__less) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.61 332 (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_202_order__less__imp__not__eq) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.61 333 (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_203_order__less__imp__not__eq2) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.61 334 (all X_a (preorder(X_a) -> (all P_1 all X_1 all Y_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y_1),X_1)) -> hBOOL(P_1)))))) # label(fact_204_order__less__imp__triv) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.61 335 (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_205_order__less__asym_H) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.61 336 (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_206_xt1_I9_J) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.61 337 (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_207_ord__eq__less__trans) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.61 338 (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_208_xt1_I1_J) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.61 339 (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_209_ord__less__eq__trans) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.61 340 (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_210_xt1_I2_J) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.61 341 (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_211_order__less__trans) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.61 342 (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_212_xt1_I10_J) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.61 343 (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_213_order__less__asym) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.61 344 (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_214_linorder__cases) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.61 345 (all X_a (linorder(X_a) -> (all X_1 all Y_1 (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y_1)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y_1),X_1)))))) # label(fact_215_linorder__not__less) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.61 346 (all X_a (linorder(X_a) -> (all X_1 all Y_1 (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),Y_1)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y_1),X_1)))))) # label(fact_216_linorder__not__le) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.61 347 (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(X_a),Y),X)))))) # label(fact_217_linorder__le__less__linear) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.61 348 (all X_a (order(X_a) -> (all X_1 all Y_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y_1)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),Y_1)) & ti(X_a,X_1) != ti(X_a,Y_1))))) # label(fact_218_order__less__le) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.61 349 (all X_a (preorder(X_a) -> (all X_1 all Y_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y_1)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),Y_1)) & -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y_1),X_1)))))) # label(fact_219_less__le__not__le) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.61 350 (all X_a (order(X_a) -> (all X_1 all Y_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),Y_1)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y_1)) | ti(X_a,X_1) = ti(X_a,Y_1))))) # label(fact_220_order__le__less) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.61 351 (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_221_leI) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.61 352 (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_222_not__leE) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.61 353 (all X_a (linorder(X_a) -> (all X_1 all Y_1 (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),Y_1)) <-> ti(X_a,X_1) = ti(X_a,Y_1)))))) # label(fact_223_linorder__antisym__conv1) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.61 354 (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_224_order__neq__le__trans) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.61 355 (all A_1 all B (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A_1),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),B),one_one(int)))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_1),B)))) # label(fact_225_norR__mem__unique__aux) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.61 356 (all P_1 all I all K (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),I),K)) -> (hBOOL(hAPP(int,bool,P_1,K)) -> ((all I_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),I_2),K)) -> (hBOOL(hAPP(int,bool,P_1,I_2)) -> hBOOL(hAPP(int,bool,P_1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),I_2),one_one(int))))))) -> hBOOL(hAPP(int,bool,P_1,I)))))) # label(fact_226_int__le__induct) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.61 357 (all P_1 all I all K (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),I),K)) -> (hBOOL(hAPP(int,bool,P_1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),K),one_one(int)))) -> ((all I_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),I_2),K)) -> (hBOOL(hAPP(int,bool,P_1,I_2)) -> hBOOL(hAPP(int,bool,P_1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),I_2),one_one(int))))))) -> hBOOL(hAPP(int,bool,P_1,I)))))) # label(fact_227_int__less__induct) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.61 358 (all P_1 all K all I (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),K),I)) -> (hBOOL(hAPP(int,bool,P_1,K)) -> ((all I_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),K),I_2)) -> (hBOOL(hAPP(int,bool,P_1,I_2)) -> hBOOL(hAPP(int,bool,P_1,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),I_2),one_one(int))))))) -> hBOOL(hAPP(int,bool,P_1,I)))))) # label(fact_228_int__ge__induct) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.61 359 (all P_1 all K all I (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),I)) -> (hBOOL(hAPP(int,bool,P_1,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),K),one_one(int)))) -> ((all I_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),I_2)) -> (hBOOL(hAPP(int,bool,P_1,I_2)) -> hBOOL(hAPP(int,bool,P_1,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),I_2),one_one(int))))))) -> hBOOL(hAPP(int,bool,P_1,I)))))) # label(fact_229_int__gr__induct) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.61 360 (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_230_dense__le) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.61 361 (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_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),W_2)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),W_2),Y)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),W_2),Z))))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),Z))))))) # label(fact_231_dense__le__bounded) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.61 362 (all X_b all X_a (order(X_a) & order(X_b) -> (all C_1 all F all Ba all Aa (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Ba),Aa)) -> (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),C_1),hAPP(X_a,X_b,F,Ba))) -> ((all X_2 all Y_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y_2),X_2)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_a,X_b,F,Y_2)),hAPP(X_a,X_b,F,X_2))))) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),C_1),hAPP(X_a,X_b,F,Aa))))))))) # label(fact_232_xt5) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.61 363 (all X_b all X_a (order(X_a) & order(X_b) -> (all C_1 all F all Ba all Aa (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Ba),Aa)) -> (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),C_1),hAPP(X_a,X_b,F,Ba))) -> ((all X_2 all Y_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y_2),X_2)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_a,X_b,F,Y_2)),hAPP(X_a,X_b,F,X_2))))) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),C_1),hAPP(X_a,X_b,F,Aa))))))))) # label(fact_233_xt7) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.61 364 (all X_a all X_b (order(X_b) & order(X_a) -> (all F all C_1 all Aa all Ba (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),Ba)) -> (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_a,X_b,F,Ba)),C_1)) -> ((all X_2 all Y_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_2),Y_2)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_a,X_b,F,X_2)),hAPP(X_a,X_b,F,Y_2))))) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_a,X_b,F,Aa)),C_1)))))))) # label(fact_234_order__less__le__subst2) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.61 365 (all X_a all X_b (order(X_b) & order(X_a) -> (all F all C_1 all Aa all Ba (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Aa),Ba)) -> (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_a,X_b,F,Ba)),C_1)) -> ((all X_2 all Y_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_2),Y_2)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_a,X_b,F,X_2)),hAPP(X_a,X_b,F,Y_2))))) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_a,X_b,F,Aa)),C_1)))))))) # label(fact_235_order__le__less__subst2) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.61 366 (all X_a all X_b (ord(X_b) -> (all F all G (hBOOL(hAPP(fun(X_a,X_b),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,X_b),bool),ord_less(fun(X_a,X_b)),F),G)) <-> hBOOL(hAPP(fun(X_a,X_b),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,X_b),bool),ord_less_eq(fun(X_a,X_b)),F),G)) & -hBOOL(hAPP(fun(X_a,X_b),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,X_b),bool),ord_less_eq(fun(X_a,X_b)),G),F)))))) # label(fact_236_less__fun__def) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.61 367 (all X_a all X_b (ord(X_b) -> (all F all G ((all X_2 hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_a,X_b,F,X_2)),hAPP(X_a,X_b,G,X_2)))) -> hBOOL(hAPP(fun(X_a,X_b),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,X_b),bool),ord_less_eq(fun(X_a,X_b)),F),G)))))) # label(fact_237_le__funI) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.61 368 (all X_b all X_a (order(X_a) & ord(X_b) -> (all C_1 all F all Ba all Aa (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_b,X_a,F,Ba)),Aa)) -> (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),C_1),Ba)) -> ((all X_2 all Y_2 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Y_2),X_2)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_b,X_a,F,Y_2)),hAPP(X_b,X_a,F,X_2))))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_b,X_a,F,C_1)),Aa)))))))) # label(fact_238_xt6) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.61 369 (all X_b all X_a (order(X_a) & order(X_b) -> (all C_1 all F all Ba all Aa (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_b,X_a,F,Ba)),Aa)) -> (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),C_1),Ba)) -> ((all X_2 all Y_2 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),Y_2),X_2)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_b,X_a,F,Y_2)),hAPP(X_b,X_a,F,X_2))))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_b,X_a,F,C_1)),Aa)))))))) # label(fact_239_xt4) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.61 370 (all X_a all X_b (order(X_b) & order(X_a) -> (all C_1 all Aa all F all Ba (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Aa),hAPP(X_b,X_a,F,Ba))) -> (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Ba),C_1)) -> ((all X_2 all Y_2 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_2),Y_2)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_b,X_a,F,X_2)),hAPP(X_b,X_a,F,Y_2))))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),hAPP(X_b,X_a,F,C_1))))))))) # label(fact_240_order__le__less__subst1) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.61 371 (all X_a all X_b (order(X_b) & order(X_a) -> (all C_1 all Aa all F all Ba (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),hAPP(X_b,X_a,F,Ba))) -> (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),Ba),C_1)) -> ((all X_2 all Y_2 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),X_2),Y_2)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_b,X_a,F,X_2)),hAPP(X_b,X_a,F,Y_2))))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),hAPP(X_b,X_a,F,C_1))))))))) # label(fact_241_order__less__le__subst1) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.61 372 (all I all P_1 all K (hBOOL(hAPP(int,bool,P_1,K)) -> ((all I_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),K),I_2)) -> (hBOOL(hAPP(int,bool,P_1,I_2)) -> hBOOL(hAPP(int,bool,P_1,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)) -> (hBOOL(hAPP(int,bool,P_1,I_2)) -> hBOOL(hAPP(int,bool,P_1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),I_2),one_one(int))))))) -> hBOOL(hAPP(int,bool,P_1,I)))))) # label(fact_242_int__induct) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.61 373 (all B all A_1 all C (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_1),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_eq(int),A_1),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),A_1))))) # label(fact_243_Euler_Oaux2) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.61 374 (all X_1 all P_1 ((all A_3 ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),A_3)) -> hBOOL(hAPP(int,bool,P_1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A_3),one_one(int))))) -> hBOOL(hAPP(int,bool,P_1,A_3)))) -> hBOOL(hAPP(int,bool,P_1,X_1)))) # label(fact_244_d22set__induct__old) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.62 375 (all X_a (linord626643107strict(X_a) -> (all V all U all Y 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),Y),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),U)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),V)) -> (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),U),V) = one_one(X_a) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),U),X)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),V),Y))),A_1)))))))))) # label(fact_245_convex__bound__lt) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.62 376 (all X_a (archim1727834104eiling(X_a) -> (all V_1 all X_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),V_1)),hAPP(X_a,int,archimedean_ceiling(X_a),X_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),minus_minus(X_a),hAPP(int,X_a,number_number_of(X_a),V_1)),one_one(X_a))),X_1)))))) # label(fact_246_number__of__le__ceiling) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.62 377 (all X_a (archim1727834104eiling(X_a) -> (all X_1 all V_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(X_a,int,archimedean_ceiling(X_a),X_1)),hAPP(int,int,number_number_of(int),V_1))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(int,X_a,number_number_of(X_a),V_1)),one_one(X_a)))))))) # label(fact_247_ceiling__less__number__of) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.62 378 (all X_a (archim1727834104eiling(X_a) -> (all X_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(X_a,int,archimedean_ceiling(X_a),X_1))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),X_1)))))) # label(fact_248_zero__less__ceiling) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.62 379 (all X_a (archim1727834104eiling(X_a) -> (all X_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(X_a,int,archimedean_ceiling(X_a),X_1)),zero_zero(int))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),zero_zero(X_a))))))) # label(fact_249_ceiling__le__zero) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.62 380 (all X_a (archim1727834104eiling(X_a) -> hAPP(X_a,int,archimedean_ceiling(X_a),zero_zero(X_a)) = zero_zero(int))) # label(fact_250_ceiling__zero) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.62 381 (all X_a (zero(X_a) -> (all X_1 (zero_zero(X_a) = ti(X_a,X_1) <-> ti(X_a,X_1) = zero_zero(X_a))))) # label(fact_251_zero__reorient) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.62 382 (all X_a (archim1727834104eiling(X_a) -> (all X_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(X_a,int,archimedean_ceiling(X_a),X_1)),one_one(int))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),zero_zero(X_a))))))) # label(fact_252_ceiling__less__one) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.62 383 (all X_a (archim1727834104eiling(X_a) -> (all X_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),hAPP(X_a,int,archimedean_ceiling(X_a),X_1))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),X_1)))))) # label(fact_253_one__le__ceiling) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.62 384 (all X_a (no_zero_divisors(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) = zero_zero(X_a) -> ti(X_a,A_1) = zero_zero(X_a) | ti(X_a,B) = zero_zero(X_a))))) # label(fact_254_divisors__zero) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.62 385 (all X_a (no_zero_divisors(X_a) -> (all B all A_1 (ti(X_a,A_1) != zero_zero(X_a) -> (ti(X_a,B) != zero_zero(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_255_no__zero__divisors) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.62 386 (all X_a (ring_n68954251visors(X_a) -> (all Aa all Ba (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Aa),Ba) = zero_zero(X_a) <-> ti(X_a,Aa) = zero_zero(X_a) | ti(X_a,Ba) = zero_zero(X_a))))) # label(fact_256_mult__eq__0__iff) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.62 387 (all X_a (real_normed_algebra(X_a) -> (all X hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),zero_zero(X_a)) = zero_zero(X_a)))) # label(fact_257_mult__right_Ozero) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.62 388 (all X_a (real_normed_algebra(X_a) -> (all A_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),zero_zero(X_a)) = zero_zero(X_a)))) # label(fact_258_mult_Ozero__right) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.62 389 (all X_a (mult_zero(X_a) -> (all A_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),zero_zero(X_a)) = zero_zero(X_a)))) # label(fact_259_mult__zero__right) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.62 390 (all X_a (real_normed_algebra(X_a) -> (all Y hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),zero_zero(X_a)),Y) = zero_zero(X_a)))) # label(fact_260_mult__left_Ozero) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.62 391 (all X_a (real_normed_algebra(X_a) -> (all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),zero_zero(X_a)),B) = zero_zero(X_a)))) # label(fact_261_mult_Ozero__left) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.62 392 (all X_a (mult_zero(X_a) -> (all A_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),zero_zero(X_a)),A_1) = zero_zero(X_a)))) # label(fact_262_mult__zero__left) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.62 393 (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),zero_zero(X_a)) = zero_zero(X_a)))) # label(fact_263_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.62 394 (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),zero_zero(X_a)),A_1) = zero_zero(X_a)))) # label(fact_264_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.62 395 (all X_a (linord219039673up_add(X_a) -> (all Aa (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Aa),Aa) = zero_zero(X_a) <-> ti(X_a,Aa) = zero_zero(X_a))))) # label(fact_265_double__eq__0__iff) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.62 396 (all X_a (comm_monoid_add(X_a) -> (all A_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),zero_zero(X_a)) = ti(X_a,A_1)))) # label(fact_266_add_Ocomm__neutral) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.62 397 (all X_a (monoid_add(X_a) -> (all A_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),zero_zero(X_a)) = ti(X_a,A_1)))) # label(fact_267_add__0__right) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.62 398 (all X_a (linord219039673up_add(X_a) -> (all Aa (zero_zero(X_a) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Aa),Aa) <-> ti(X_a,Aa) = zero_zero(X_a))))) # label(fact_268_double__zero__sym) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.62 399 (all X_a (comm_monoid_add(X_a) -> (all A_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),zero_zero(X_a)),A_1) = ti(X_a,A_1)))) # label(fact_269_add__0) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.62 400 (all X_a (monoid_add(X_a) -> (all A_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),zero_zero(X_a)),A_1) = ti(X_a,A_1)))) # label(fact_270_add__0__left) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.62 401 (all X_a (semiri456707255roduct(X_a) -> (all Ba all Aa (ti(X_a,Ba) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Ba),Aa) <-> ti(X_a,Aa) = zero_zero(X_a))))) # label(fact_271_add__0__iff) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.62 402 (all X_a (comm_semiring_1(X_a) -> (all A_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),zero_zero(X_a)) = ti(X_a,A_1)))) # label(fact_272_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.62 403 (all X_a (comm_semiring_1(X_a) -> (all A_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),zero_zero(X_a)),A_1) = ti(X_a,A_1)))) # label(fact_273_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.62 404 (all X_a (zero_neq_one(X_a) -> zero_zero(X_a) != one_one(X_a))) # label(fact_274_zero__neq__one) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.62 405 (all X_a (zero_neq_one(X_a) -> one_one(X_a) != zero_zero(X_a))) # label(fact_275_one__neq__zero) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.62 406 (all X_a (group_add(X_a) -> (all Aa all Ba (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),Aa),Ba) = zero_zero(X_a) <-> ti(X_a,Aa) = ti(X_a,Ba))))) # label(fact_276_right__minus__eq) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.62 407 (all X_a (ab_group_add(X_a) -> (all Aa all Ba (ti(X_a,Aa) = ti(X_a,Ba) <-> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),Aa),Ba) = zero_zero(X_a))))) # label(fact_277_eq__iff__diff__eq__0) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.62 408 (all X_a (group_add(X_a) -> (all A_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_1),A_1) = zero_zero(X_a)))) # label(fact_278_diff__self) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.62 409 (all X_a (group_add(X_a) -> (all A_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_1),zero_zero(X_a)) = ti(X_a,A_1)))) # label(fact_279_diff__0__right) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.62 410 (all Z hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Z),zero_zero(int)) = Z) # label(fact_281_zadd__0__right) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.62 411 (all Z hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),zero_zero(int)),Z) = Z) # label(fact_282_zadd__0) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.62 412 (all X_a (archim1727834104eiling(X_a) -> (all X all Y (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(X_a,int,archimedean_ceiling(X_a),X)),hAPP(X_a,int,archimedean_ceiling(X_a),Y))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)))))) # label(fact_283_ceiling__less__cancel) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.62 413 (all X_a (archim1727834104eiling(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(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(X_a,int,archimedean_ceiling(X_a),Y)),hAPP(X_a,int,archimedean_ceiling(X_a),X))))))) # label(fact_284_ceiling__mono) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.62 414 (all X_a (archim1727834104eiling(X_a) -> hAPP(X_a,int,archimedean_ceiling(X_a),one_one(X_a)) = one_one(int))) # label(fact_285_ceiling__one) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.62 415 (all X_b all X_a all X_c (real_normed_vector(X_c) & real_normed_vector(X_a) & real_normed_vector(X_b) -> (all Aa all Prod (hBOOL(hAPP(fun(X_a,fun(X_b,X_c)),bool,bounded_bilinear(X_a,X_b,X_c),Prod)) -> hAPP(X_b,X_c,hAPP(X_a,fun(X_b,X_c),Prod,Aa),zero_zero(X_b)) = zero_zero(X_c))))) # label(fact_286_bounded__bilinear_Ozero__right) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.62 416 (all X_b all X_a all X_c (real_normed_vector(X_c) & real_normed_vector(X_a) & real_normed_vector(X_b) -> (all Ba all Prod (hBOOL(hAPP(fun(X_a,fun(X_b,X_c)),bool,bounded_bilinear(X_a,X_b,X_c),Prod)) -> hAPP(X_b,X_c,hAPP(X_a,fun(X_b,X_c),Prod,zero_zero(X_a)),Ba) = zero_zero(X_c))))) # label(fact_287_bounded__bilinear_Ozero__left) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.62 417 (all X_a (archim1727834104eiling(X_a) -> (all V hAPP(X_a,int,archimedean_ceiling(X_a),hAPP(int,X_a,number_number_of(X_a),V)) = hAPP(int,int,number_number_of(int),V)))) # label(fact_288_ceiling__number__of) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.62 418 (all X_a (linordered_ring(X_a) -> (all A_1 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),A_1)))))) # label(fact_289_zero__le__square) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.62 419 (all X_a (linord581940658strict(X_a) -> (all Aa all Ba (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Aa),Ba))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),Aa)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),Ba)) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Aa),zero_zero(X_a))) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Ba),zero_zero(X_a))))))) # label(fact_290_zero__le__mult__iff) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.62 420 (all X_a (linord581940658strict(X_a) -> (all Aa all Ba (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Aa),Ba)),zero_zero(X_a))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),Aa)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Ba),zero_zero(X_a))) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Aa),zero_zero(X_a))) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),Ba)))))) # label(fact_291_mult__le__0__iff) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.62 421 (all X_a (ordere453448008miring(X_a) -> (all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),B)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)))))))) # label(fact_292_mult__nonneg__nonneg) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.62 422 (all X_a (ordere453448008miring(X_a) -> (all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)),zero_zero(X_a)))))))) # label(fact_293_mult__nonneg__nonpos) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.62 423 (all X_a (ordere453448008miring(X_a) -> (all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),A_1)),zero_zero(X_a)))))))) # label(fact_294_mult__nonneg__nonpos2) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.62 424 (all X_a (ordere453448008miring(X_a) -> (all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),zero_zero(X_a))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),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),times_times(X_a),A_1),B)),zero_zero(X_a)))))))) # label(fact_295_mult__nonpos__nonneg) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.62 425 (all X_a (ordered_ring(X_a) -> (all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),zero_zero(X_a))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),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_296_mult__nonpos__nonpos) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.62 426 (all X_a (ordered_semiring(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),zero_zero(X_a)),C)) -> 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),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),C)))))))) # label(fact_297_mult__right__mono) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.62 427 (all X_a (ordered_semiring(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),zero_zero(X_a)),C)) -> 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),C),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),B)))))))) # label(fact_298_mult__left__mono) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.62 428 (all X_a (ordere1490568538miring(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),zero_zero(X_a)),C)) -> 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),C),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),B)))))))) # label(fact_299_comm__mult__left__mono) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.62 429 (all X_a (ordered_ring(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)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),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_300_mult__right__mono__neg) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.62 430 (all X_a (ordered_ring(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)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),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_301_mult__left__mono__neg) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.62 431 (all X_a (ordered_semiring(X_a) -> (all C all D 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)) -> (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)),C)) -> 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),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),D)))))))))) # label(fact_302_mult__mono_H) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.62 432 (all X_a (ordered_semiring(X_a) -> (all C all D 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)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),B)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),C)) -> 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),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),D)))))))))) # label(fact_303_mult__mono) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.62 433 (all X_a (ordered_ring(X_a) -> (all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),A_1)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),B)) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),zero_zero(X_a))) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),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_304_split__mult__pos__le) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.62 434 (all X_a (ordere453448008miring(X_a) -> (all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),A_1)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),zero_zero(X_a))) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),zero_zero(X_a))) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),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),times_times(X_a),A_1),B)),zero_zero(X_a))))))) # label(fact_305_split__mult__neg__le) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.62 435 (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_306_not__square__less__zero) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.62 436 (all X_a (linord581940658strict(X_a) -> (all Aa all C_1 all Ba (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Aa),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Ba),C_1))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C_1)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),Ba)) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),zero_zero(X_a))) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Ba),Aa)))))) # label(fact_307_mult__less__cancel__right__disj) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.62 437 (all X_a (linord581940658strict(X_a) -> (all C_1 all Aa all Ba (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1),Aa)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1),Ba))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C_1)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),Ba)) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),zero_zero(X_a))) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Ba),Aa)))))) # label(fact_308_mult__less__cancel__left__disj) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.62 438 (all X_a (linord581940658strict(X_a) -> (all Aa all Ba all C_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C_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),C_1),Aa)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1),Ba))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),Ba))))))) # label(fact_309_mult__less__cancel__left__pos) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.62 439 (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_310_mult__pos__pos) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.62 440 (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_311_mult__pos__neg) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.62 441 (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_312_mult__pos__neg2) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.62 442 (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_313_zero__less__mult__pos) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.62 443 (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_314_zero__less__mult__pos2) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.62 444 (all X_a (linord581940658strict(X_a) -> (all Aa all Ba all C_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),zero_zero(X_a))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1),Aa)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1),Ba))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Ba),Aa))))))) # label(fact_315_mult__less__cancel__left__neg) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.62 445 (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_316_mult__neg__pos) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.62 446 (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_317_mult__neg__neg) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.62 447 (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_318_mult__strict__right__mono) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.62 448 (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_319_mult__strict__left__mono) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.62 449 (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_320_comm__mult__strict__left__mono) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.62 450 (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_321_mult__strict__right__mono__neg) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.62 451 (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_322_mult__strict__left__mono__neg) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.62 452 (all X_a (linord219039673up_add(X_a) -> (all Aa (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Aa),Aa))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),Aa)))))) # label(fact_323_zero__le__double__add__iff__zero__le__single__add) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.62 453 (all X_a (linord219039673up_add(X_a) -> (all Aa (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Aa),Aa)),zero_zero(X_a))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Aa),zero_zero(X_a))))))) # label(fact_324_double__add__le__zero__iff__single__add__le__zero) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.62 454 (all X_a (ordere216010020id_add(X_a) -> (all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),B)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)))))))) # label(fact_325_add__nonneg__nonneg) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.62 455 (all X_a (ordere216010020id_add(X_a) -> (all Y_1 all X_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),X_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),Y_1)) -> (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X_1),Y_1) = zero_zero(X_a) <-> ti(X_a,X_1) = zero_zero(X_a) & ti(X_a,Y_1) = zero_zero(X_a))))))) # label(fact_326_add__nonneg__eq__0__iff) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.62 456 (all X_a (ordere216010020id_add(X_a) -> (all B all C all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),C)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)))))))) # label(fact_327_add__increasing) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.62 457 (all X_a (ordere216010020id_add(X_a) -> (all B all A_1 all C (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),C)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),A_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)))))))) # label(fact_328_add__increasing2) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.62 458 (all X_a (ordere216010020id_add(X_a) -> (all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),zero_zero(X_a))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)),zero_zero(X_a)))))))) # label(fact_329_add__nonpos__nonpos) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.62 459 (all X_a (linord219039673up_add(X_a) -> (all Aa (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Aa),Aa))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),Aa)))))) # label(fact_330_zero__less__double__add__iff__zero__less__single__add) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.62 460 (all X_a (linordered_idom(X_a) -> (all Aa (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Aa),Aa)),zero_zero(X_a))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),zero_zero(X_a))))))) # label(fact_331_even__less__0__iff) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.62 461 (all X_a (linord219039673up_add(X_a) -> (all Aa (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Aa),Aa)),zero_zero(X_a))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),zero_zero(X_a))))))) # label(fact_332_double__add__less__zero__iff__single__add__less__zero) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.62 462 (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_333_add__pos__pos) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.62 463 (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_334_pos__add__strict) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.62 464 (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_335_add__neg__neg) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.62 465 (all X_a (linordered_semidom(X_a) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),one_one(X_a))))) # label(fact_336_zero__le__one) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.62 466 (all X_a (linordered_semidom(X_a) -> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),one_one(X_a)),zero_zero(X_a))))) # label(fact_337_not__one__le__zero) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.62 467 (all X_a (linordered_semidom(X_a) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),one_one(X_a))))) # label(fact_338_zero__less__one) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.62 468 (all X_a (linordered_semidom(X_a) -> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),zero_zero(X_a))))) # label(fact_339_not__one__less__zero) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.62 469 (all X_a (ordered_ab_group_add(X_a) -> (all Aa all Ba (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Aa),Ba)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),Aa),Ba)),zero_zero(X_a))))))) # label(fact_340_le__iff__diff__le__0) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.62 470 (all X_a (semiri456707255roduct(X_a) -> (all C all D all A_1 all B all R_4 (ti(X_a,R_4) != zero_zero(X_a) -> (ti(X_a,A_1) = ti(X_a,B) & ti(X_a,C) != ti(X_a,D) -> 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),times_times(X_a),R_4),C)) != hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),R_4),D))))))) # label(fact_341_add__scale__eq__noteq) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.62 471 (all X_a (ordered_ab_group_add(X_a) -> (all Aa all Ba (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),Ba)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),Aa),Ba)),zero_zero(X_a))))))) # label(fact_342_less__iff__diff__less__0) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.62 472 (all A_1 all X (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),X)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X),A_1)) -> (X != hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A_1),one_one(int)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A_1),one_one(int)))))))) # label(fact_343_Euler_Oaux1) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.62 473 (all K_4 all I_1 all J_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),I_1),J_2)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),K_4)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K_4),I_1)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K_4),J_2)))))) # label(fact_345_zmult__zless__mono2) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.62 474 (all Z hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),Z)),Z) != zero_zero(int)) # label(fact_346_odd__nonzero) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.62 475 (all K all L (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),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),L)),zero_zero(int))))) # label(fact_347_less__bin__lemma) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.62 476 (all X_a (archim1727834104eiling(X_a) -> (all X_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),hAPP(X_a,int,archimedean_ceiling(X_a),X_1))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),X_1)))))) # label(fact_348_one__less__ceiling) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.62 477 (all X_a (archim1727834104eiling(X_a) -> (all X_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(X_a,int,archimedean_ceiling(X_a),X_1)),one_one(int))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),one_one(X_a))))))) # label(fact_349_ceiling__le__one) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.62 478 (all X_a (archim1727834104eiling(X_a) -> (all V_1 all X_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),V_1)),hAPP(X_a,int,archimedean_ceiling(X_a),X_1))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(int,X_a,number_number_of(X_a),V_1)),X_1)))))) # label(fact_350_number__of__less__ceiling) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.62 479 (all X_a (archim1727834104eiling(X_a) -> (all X_1 all V_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(X_a,int,archimedean_ceiling(X_a),X_1)),hAPP(int,int,number_number_of(int),V_1))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),hAPP(int,X_a,number_number_of(X_a),V_1))))))) # label(fact_351_ceiling__le__number__of) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.62 480 (all X_a (archim1727834104eiling(X_a) -> (all X hAPP(X_a,int,archimedean_ceiling(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X),one_one(X_a))) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(X_a,int,archimedean_ceiling(X_a),X)),one_one(int))))) # label(fact_352_ceiling__add__one) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.62 481 (all X_a (archim1727834104eiling(X_a) -> (all X all V hAPP(X_a,int,archimedean_ceiling(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X),hAPP(int,X_a,number_number_of(X_a),V))) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(X_a,int,archimedean_ceiling(X_a),X)),hAPP(int,int,number_number_of(int),V))))) # label(fact_353_ceiling__add__number__of) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.62 482 (all X_a (archim1727834104eiling(X_a) -> (all X hAPP(X_a,int,archimedean_ceiling(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),X),one_one(X_a))) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(X_a,int,archimedean_ceiling(X_a),X)),one_one(int))))) # label(fact_354_ceiling__diff__one) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.62 483 (all X_a (archim1727834104eiling(X_a) -> (all X all V hAPP(X_a,int,archimedean_ceiling(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),X),hAPP(int,X_a,number_number_of(X_a),V))) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(X_a,int,archimedean_ceiling(X_a),X)),hAPP(int,int,number_number_of(int),V))))) # label(fact_355_ceiling__diff__number__of) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.62 484 (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_eq(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))) -> (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_eq(X_a),A_1),B))))))) # label(fact_356_mult__left__le__imp__le) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.62 485 (all X_a (linord20386208strict(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),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))) -> (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_eq(X_a),A_1),B))))))) # label(fact_357_mult__right__le__imp__le) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.62 486 (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),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))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),C)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B))))))) # label(fact_358_mult__less__imp__less__left) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.62 487 (all X_a (linordered_semiring(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),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))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),C)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B))))))) # label(fact_359_mult__left__less__imp__less) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.62 488 (all X_a (linord20386208strict(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),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))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),C)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B))))))) # label(fact_360_mult__less__imp__less__right) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.62 489 (all X_a (linordered_semiring(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),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))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),C)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B))))))) # label(fact_361_mult__right__less__imp__less) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.62 490 (all X_a (linord20386208strict(X_a) -> (all C all D 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)) -> (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)),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),D)))))))))) # label(fact_362_mult__le__less__imp__less) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.62 491 (all X_a (linord20386208strict(X_a) -> (all C all D 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)) -> (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)),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),D)))))))))) # label(fact_363_mult__less__le__imp__less) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.62 492 (all X_a (linord20386208strict(X_a) -> (all C all D 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)) -> (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)),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),D)))))))))) # label(fact_364_mult__strict__mono_H) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.62 493 (all X_a (linord20386208strict(X_a) -> (all C all D 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)) -> (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_eq(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),D)))))))))) # label(fact_365_mult__strict__mono) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.62 494 (all X_a (linord581940658strict(X_a) -> (all Aa all Ba all C_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),zero_zero(X_a))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1),Aa)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1),Ba))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Ba),Aa))))))) # label(fact_366_mult__le__cancel__left__neg) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.62 495 (all X_a (linord581940658strict(X_a) -> (all Aa all Ba all C_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C_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),times_times(X_a),C_1),Aa)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1),Ba))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Aa),Ba))))))) # label(fact_367_mult__le__cancel__left__pos) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.62 496 (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_368_add__nonpos__neg) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.62 497 (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_369_add__neg__nonpos) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.62 498 (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_370_add__strict__increasing2) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.62 499 (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_371_add__strict__increasing) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.62 500 (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_372_add__nonneg__pos) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.62 501 (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_373_add__pos__nonneg) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.62 502 (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_374_mult__left__le__one__le) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.62 503 (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_375_mult__right__le__one__le) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.62 504 (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_376_zero__less__two) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.62 505 (all Z_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),Z_1)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),Z_1)))) # label(fact_377_int__one__le__iff__zero__less) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.62 506 (all N all M (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),M)) -> (hAPP(int,int,hAPP(int,fun(int,int),times_times(int),M),N) = one_one(int) <-> M = one_one(int) & N = one_one(int)))) # label(fact_378_pos__zmult__eq__1__iff) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.62 507 (all Z_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),Z_1)),Z_1)),zero_zero(int))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Z_1),zero_zero(int))))) # label(fact_379_odd__less__0) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.62 508 (all X_a (linord1278240602ring_1(X_a) -> (all V all U all Y 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),Y),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),U)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),V)) -> (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),U),V) = 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),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),U),X)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),V),Y))),A_1)))))))))) # label(fact_380_convex__bound__le) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.62 509 (all Z (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Z)) -> 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)),Z))))) # label(fact_381_le__imp__0__less) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.62 510 (all R_4 all Q_2 all A_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A_1)) -> (A_1 = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),R_4),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),Q_2)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),R_4),A_1)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),Q_2)))))) # label(fact_382_self__quotient__aux1) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.62 511 (all R_4 all Q_2 all A_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A_1)) -> (A_1 = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),R_4),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),Q_2)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),R_4)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Q_2),one_one(int))))))) # label(fact_383_self__quotient__aux2) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.62 512 (all B all Q_2 all R_4 all B_4 all Q_5 all R_5 (hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),Q_2)),R_4) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B_4),Q_5)),R_5) -> (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),B_4),Q_5)),R_5)),zero_zero(int))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),R_4),B)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),R_5)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B_4)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B_4),B)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Q_5),Q_2))))))))) # label(fact_384_zdiv__mono2__neg__lemma) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.62 513 (all B all Q_5 all R_5 all Q_2 all R_4 (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),B),Q_5)),R_5)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),Q_2)),R_4))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),R_4),zero_zero(int))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),R_4)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),R_5)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Q_2),Q_5))))))) # label(fact_385_unique__quotient__lemma__neg) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.62 514 (all B all Q_2 all R_4 all B_4 all Q_5 all R_5 (hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),Q_2)),R_4) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B_4),Q_5)),R_5) -> (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),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B_4),Q_5)),R_5))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),R_5),B_4)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),R_4)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B_4)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B_4),B)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Q_2),Q_5))))))))) # label(fact_386_zdiv__mono2__lemma) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.62 515 (all B all Q_5 all R_5 all Q_2 all R_4 (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),B),Q_5)),R_5)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),Q_2)),R_4))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),R_5)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),R_5),B)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),R_4),B)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Q_5),Q_2))))))) # label(fact_387_unique__quotient__lemma) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.62 516 (all B_4 all Q_5 all R_5 (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),B_4),Q_5)),R_5)),zero_zero(int))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),R_5)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B_4)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Q_5),zero_zero(int))))))) # label(fact_388_q__neg__lemma) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.62 517 (all B_4 all Q_5 all R_5 (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),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B_4),Q_5)),R_5))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),R_5),B_4)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B_4)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Q_5)))))) # label(fact_389_q__pos__lemma) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.62 518 (all X_a (linord581940658strict(X_a) -> (all X_1 all Y_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X_1),X_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Y_1),Y_1)))) <-> ti(X_a,X_1) != zero_zero(X_a) | ti(X_a,Y_1) != zero_zero(X_a))))) # label(fact_390_sum__squares__gt__zero__iff) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.62 519 (all X_a (linordered_ring(X_a) -> (all X all Y -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),X)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Y),Y))),zero_zero(X_a)))))) # label(fact_391_not__sum__squares__lt__zero) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.62 520 (all X_a (linord581940658strict(X_a) -> (all X_1 all Y_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),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_1),X_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Y_1),Y_1))),zero_zero(X_a))) <-> ti(X_a,X_1) = zero_zero(X_a) & ti(X_a,Y_1) = zero_zero(X_a))))) # label(fact_392_sum__squares__le__zero__iff) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.62 521 (all X_a (linord581940658strict(X_a) -> (all X_1 all Y_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),X_1),X_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Y_1),Y_1)) = zero_zero(X_a) <-> ti(X_a,X_1) = zero_zero(X_a) & ti(X_a,Y_1) = zero_zero(X_a))))) # label(fact_393_sum__squares__eq__zero__iff) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.62 522 (all X_a (linordered_ring(X_a) -> (all X all Y hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),X)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Y),Y))))))) # label(fact_394_sum__squares__ge__zero) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.62 523 (all M_1 all R_4 all S_4 all T_6 all N_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),N_1)) -> (hAPP(int,product_prod(int,product_prod(int,int)),hAPP(int,fun(int,product_prod(int,product_prod(int,int))),xzgcd,M_1),N_1) = hAPP(product_prod(int,int),product_prod(int,product_prod(int,int)),hAPP(int,fun(product_prod(int,int),product_prod(int,product_prod(int,int))),product_Pair(int,product_prod(int,int)),R_4),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),S_4),T_6)) -> R_4 = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),S_4),M_1)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),T_6),N_1))))) # label(fact_395_xzgcd__linear) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.62 524 (all M_1 all N_1 all R_5 all S_5 all S_4 all T_7 all T_6 all Rn all Sn_1 all Tn_1 all R_4 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),R_4)) -> (hAPP(int,product_prod(int,product_prod(int,int)),hAPP(int,fun(int,product_prod(int,product_prod(int,int))),hAPP(int,fun(int,fun(int,product_prod(int,product_prod(int,int)))),hAPP(int,fun(int,fun(int,fun(int,product_prod(int,product_prod(int,int))))),hAPP(int,fun(int,fun(int,fun(int,fun(int,product_prod(int,product_prod(int,int)))))),hAPP(int,fun(int,fun(int,fun(int,fun(int,fun(int,product_prod(int,product_prod(int,int))))))),hAPP(int,fun(int,fun(int,fun(int,fun(int,fun(int,fun(int,product_prod(int,product_prod(int,int)))))))),hAPP(int,fun(int,fun(int,fun(int,fun(int,fun(int,fun(int,fun(int,product_prod(int,product_prod(int,int))))))))),xzgcda,M_1),N_1),R_5),R_4),S_5),S_4),T_7),T_6) = hAPP(product_prod(int,int),product_prod(int,product_prod(int,int)),hAPP(int,fun(product_prod(int,int),product_prod(int,product_prod(int,int))),product_Pair(int,product_prod(int,int)),Rn),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),Sn_1),Tn_1)) -> (R_5 = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),S_5),M_1)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),T_7),N_1)) -> (R_4 = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),S_4),M_1)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),T_6),N_1)) -> Rn = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Sn_1),M_1)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Tn_1),N_1))))))) # label(fact_396_xzgcda__linear) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.62 525 (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_397_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.62 526 (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_398_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.62 527 (all B all A_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A_1)) -> (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_1),B))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B))))) # label(fact_399_pos__zmult__pos) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.62 528 (all K all P_1 all D_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D_1)) -> ((all X_2 (hBOOL(hAPP(int,bool,P_1,X_2)) -> hBOOL(hAPP(int,bool,P_1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X_2),D_1))))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),K)) -> (all X_2 (hBOOL(hAPP(int,bool,P_1,X_2)) -> hBOOL(hAPP(int,bool,P_1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X_2),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K),D_1)))))))))) # label(fact_401_decr__mult__lemma) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.62 529 (all K all P_1 all D_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D_1)) -> ((all X_2 (hBOOL(hAPP(int,bool,P_1,X_2)) -> hBOOL(hAPP(int,bool,P_1,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X_2),D_1))))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),K)) -> (all X_2 (hBOOL(hAPP(int,bool,P_1,X_2)) -> hBOOL(hAPP(int,bool,P_1,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X_2),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K),D_1)))))))))) # label(fact_402_incr__mult__lemma) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.62 530 (all X_a (linord1117847801e_zero(X_a) -> (all X all Y ((all Z_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),Z_2)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z_2),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),Z_2),X)),Y))))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y)))))) # label(fact_403_field__le__mult__one__interval) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.62 531 (all A_1 all B all Q_2 all R_4 (A_1 = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),Q_2)),R_4) -> ((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_eq(int),zero_zero(int)),R_4)) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),R_4),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),R_4)) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),R_4),zero_zero(int)))) -> hBOOL(hAPP(product_prod(int,int),bool,hAPP(int,fun(product_prod(int,int),bool),hAPP(int,fun(int,fun(product_prod(int,int),bool)),divmod_int_rel,A_1),B),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),Q_2),R_4)))))) # label(fact_404_divmod__int__relI) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.62 532 (all M_1 all N_1 hAPP(int,product_prod(int,product_prod(int,int)),hAPP(int,fun(int,product_prod(int,product_prod(int,int))),xzgcd,M_1),N_1) = hAPP(int,product_prod(int,product_prod(int,int)),hAPP(int,fun(int,product_prod(int,product_prod(int,int))),hAPP(int,fun(int,fun(int,product_prod(int,product_prod(int,int)))),hAPP(int,fun(int,fun(int,fun(int,product_prod(int,product_prod(int,int))))),hAPP(int,fun(int,fun(int,fun(int,fun(int,product_prod(int,product_prod(int,int)))))),hAPP(int,fun(int,fun(int,fun(int,fun(int,fun(int,product_prod(int,product_prod(int,int))))))),hAPP(int,fun(int,fun(int,fun(int,fun(int,fun(int,fun(int,product_prod(int,product_prod(int,int)))))))),hAPP(int,fun(int,fun(int,fun(int,fun(int,fun(int,fun(int,fun(int,product_prod(int,product_prod(int,int))))))))),xzgcda,M_1),N_1),M_1),N_1),one_one(int)),zero_zero(int)),zero_zero(int)),one_one(int))) # label(fact_405_xzgcd__def) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.62 533 (all B (B != zero_zero(int) -> hBOOL(hAPP(product_prod(int,int),bool,hAPP(int,fun(product_prod(int,int),bool),hAPP(int,fun(int,fun(product_prod(int,int),bool)),divmod_int_rel,zero_zero(int)),B),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),zero_zero(int)),zero_zero(int)))))) # label(fact_406_divmod__int__rel__0) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.62 534 (all A_1 all Q_2 all R_4 (hBOOL(hAPP(product_prod(int,int),bool,hAPP(int,fun(product_prod(int,int),bool),hAPP(int,fun(int,fun(product_prod(int,int),bool)),divmod_int_rel,A_1),A_1),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),Q_2),R_4))) -> (A_1 != zero_zero(int) -> R_4 = zero_zero(int)))) # label(fact_407_self__remainder) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.62 535 (all Q_5 all R_5 all A_1 all B all Q_2 all R_4 (hBOOL(hAPP(product_prod(int,int),bool,hAPP(int,fun(product_prod(int,int),bool),hAPP(int,fun(int,fun(product_prod(int,int),bool)),divmod_int_rel,A_1),B),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),Q_2),R_4))) -> (hBOOL(hAPP(product_prod(int,int),bool,hAPP(int,fun(product_prod(int,int),bool),hAPP(int,fun(int,fun(product_prod(int,int),bool)),divmod_int_rel,A_1),B),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),Q_5),R_5))) -> (B != zero_zero(int) -> Q_2 = Q_5)))) # label(fact_408_unique__quotient) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.62 536 (all Q_5 all R_5 all A_1 all B all Q_2 all R_4 (hBOOL(hAPP(product_prod(int,int),bool,hAPP(int,fun(product_prod(int,int),bool),hAPP(int,fun(int,fun(product_prod(int,int),bool)),divmod_int_rel,A_1),B),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),Q_2),R_4))) -> (hBOOL(hAPP(product_prod(int,int),bool,hAPP(int,fun(product_prod(int,int),bool),hAPP(int,fun(int,fun(product_prod(int,int),bool)),divmod_int_rel,A_1),B),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),Q_5),R_5))) -> (B != zero_zero(int) -> R_4 = R_5)))) # label(fact_409_unique__remainder) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.62 537 (all A_1 all Q_2 all R_4 (hBOOL(hAPP(product_prod(int,int),bool,hAPP(int,fun(product_prod(int,int),bool),hAPP(int,fun(int,fun(product_prod(int,int),bool)),divmod_int_rel,A_1),A_1),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),Q_2),R_4))) -> (A_1 != zero_zero(int) -> Q_2 = one_one(int)))) # label(fact_410_self__quotient) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.62 538 (all P_2 all P_1 all X_1 ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X_1)) -> (hBOOL(P_1) <-> hBOOL(P_2))) -> ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X_1)) -> hBOOL(P_1)) <-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X_1)) -> hBOOL(P_2))))) # label(fact_411_imp__le__cong) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.62 539 (all P_2 all P_1 all X_1 ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X_1)) -> (hBOOL(P_1) <-> hBOOL(P_2))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X_1)) & hBOOL(P_1) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X_1)) & hBOOL(P_2)))) # label(fact_412_conj__le__cong) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.62 540 (all X_a (linordered_field(X_a) -> (all X all Y ((all E (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),E)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Y),E))))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y)))))) # label(fact_414_field__le__epsilon) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.62 541 (all X_a (linorder(X_a) -> (all T_6 exists Z_2 all X_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_2),Z_2)) -> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),T_6),X_2)))))) # label(fact_415_minf_I8_J) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.62 542 (all X_a (linorder(X_a) -> (all T_6 exists Z_2 all X_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z_2),X_2)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),T_6),X_2)))))) # label(fact_416_pinf_I8_J) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.63 543 (all X_a (linorder(X_a) -> (all T_6 exists Z_2 all X_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_2),Z_2)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_2),T_6)))))) # label(fact_417_minf_I6_J) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.63 544 (all X_a (linorder(X_a) -> (all T_6 exists Z_2 all X_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z_2),X_2)) -> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_2),T_6)))))) # label(fact_418_pinf_I6_J) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.63 545 (all P_1 all P1 all D_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D_1)) -> ((all X_2 all K_1 (hBOOL(hAPP(int,bool,P1,X_2)) <-> hBOOL(hAPP(int,bool,P1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X_2),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K_1),D_1)))))) -> ((exists Z_2 all X_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X_2),Z_2)) -> (hBOOL(hAPP(int,bool,P_1,X_2)) <-> hBOOL(hAPP(int,bool,P1,X_2))))) -> ((exists X1 hBOOL(hAPP(int,bool,P1,X1))) -> (exists X1 hBOOL(hAPP(int,bool,P_1,X1)))))))) # label(fact_419_minusinfinity) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.63 546 (all P_1 all P_2 all D_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D_1)) -> ((all X_2 all K_1 (hBOOL(hAPP(int,bool,P_2,X_2)) <-> hBOOL(hAPP(int,bool,P_2,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X_2),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K_1),D_1)))))) -> ((exists Z_2 all X_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Z_2),X_2)) -> (hBOOL(hAPP(int,bool,P_1,X_2)) <-> hBOOL(hAPP(int,bool,P_2,X_2))))) -> ((exists X1 hBOOL(hAPP(int,bool,P_2,X1))) -> (exists X1 hBOOL(hAPP(int,bool,P_1,X1)))))))) # label(fact_420_plusinfinity) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.63 547 (all Y all X ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Y),X)) -> hAPP(int,int,hAPP(int,fun(int,int),nat_tsub,X),Y) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X),Y)) & (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Y),X)) -> hAPP(int,int,hAPP(int,fun(int,int),nat_tsub,X),Y) = zero_zero(int)))) # label(fact_421_tsub__def) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.63 548 (all N_1 ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),N_1),zero_zero(int))) -> hAPP(int,int,zfact,N_1) = one_one(int)) & (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),N_1),zero_zero(int))) -> hAPP(int,int,zfact,N_1) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),N_1),hAPP(int,int,zfact,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),N_1),one_one(int))))))) # label(fact_422_zfact_Osimps) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.63 549 (all X_a (archim1727834104eiling(X_a) -> (all X_1 all V_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(X_a,int,archim2085082626_floor(X_a),X_1)),hAPP(int,int,number_number_of(int),V_1))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(int,X_a,number_number_of(X_a),V_1)),one_one(X_a)))))))) # label(fact_423_floor__le__number__of) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.63 550 (all X_a (archim1727834104eiling(X_a) -> hAPP(X_a,int,archim2085082626_floor(X_a),zero_zero(X_a)) = zero_zero(int))) # label(fact_424_floor__zero) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.63 551 (all X_a (archim1727834104eiling(X_a) -> (all X all Y (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(X_a,int,archim2085082626_floor(X_a),X)),hAPP(X_a,int,archim2085082626_floor(X_a),Y))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)))))) # label(fact_425_floor__less__cancel) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.63 552 (all X_a (archim1727834104eiling(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(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(X_a,int,archim2085082626_floor(X_a),X)),hAPP(X_a,int,archim2085082626_floor(X_a),Y))))))) # label(fact_426_floor__mono) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.63 553 (all X_a (archim1727834104eiling(X_a) -> hAPP(X_a,int,archim2085082626_floor(X_a),one_one(X_a)) = one_one(int))) # label(fact_427_floor__one) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.63 554 (all X_a (archim1727834104eiling(X_a) -> (all V hAPP(X_a,int,archim2085082626_floor(X_a),hAPP(int,X_a,number_number_of(X_a),V)) = hAPP(int,int,number_number_of(int),V)))) # label(fact_428_floor__number__of) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.63 555 (all X_a (archim1727834104eiling(X_a) -> (all X_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(X_a,int,archim2085082626_floor(X_a),X_1)),zero_zero(int))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),zero_zero(X_a))))))) # label(fact_429_floor__less__zero) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.63 556 (all X_a (archim1727834104eiling(X_a) -> (all X_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(X_a,int,archim2085082626_floor(X_a),X_1))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),X_1)))))) # label(fact_430_zero__le__floor) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.63 557 (all X_a (archim1727834104eiling(X_a) -> (all X_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(X_a,int,archim2085082626_floor(X_a),X_1))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),one_one(X_a)),X_1)))))) # label(fact_431_zero__less__floor) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.63 558 (all X_a (archim1727834104eiling(X_a) -> (all X_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(X_a,int,archim2085082626_floor(X_a),X_1)),zero_zero(int))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),one_one(X_a))))))) # label(fact_432_floor__le__zero) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.63 559 (all X_a (archim1727834104eiling(X_a) -> (all X_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(X_a,int,archim2085082626_floor(X_a),X_1)),one_one(int))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),one_one(X_a))))))) # label(fact_433_floor__less__one) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.63 560 (all X_a (archim1727834104eiling(X_a) -> (all X_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),hAPP(X_a,int,archim2085082626_floor(X_a),X_1))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),one_one(X_a)),X_1)))))) # label(fact_434_one__le__floor) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.63 561 (all X_a (archim1727834104eiling(X_a) -> (all X_1 all V_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(X_a,int,archim2085082626_floor(X_a),X_1)),hAPP(int,int,number_number_of(int),V_1))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),hAPP(int,X_a,number_number_of(X_a),V_1))))))) # label(fact_435_floor__less__number__of) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.63 562 (all X_a (archim1727834104eiling(X_a) -> (all V_1 all X_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),V_1)),hAPP(X_a,int,archim2085082626_floor(X_a),X_1))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(int,X_a,number_number_of(X_a),V_1)),X_1)))))) # label(fact_436_number__of__le__floor) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.63 563 (all X_a (archim1727834104eiling(X_a) -> (all X hAPP(X_a,int,archim2085082626_floor(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X),one_one(X_a))) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(X_a,int,archim2085082626_floor(X_a),X)),one_one(int))))) # label(fact_437_floor__add__one) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.63 564 (all X_a (archim1727834104eiling(X_a) -> (all X all V hAPP(X_a,int,archim2085082626_floor(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X),hAPP(int,X_a,number_number_of(X_a),V))) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(X_a,int,archim2085082626_floor(X_a),X)),hAPP(int,int,number_number_of(int),V))))) # label(fact_438_floor__add__number__of) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.63 565 (all X_a (archim1727834104eiling(X_a) -> (all X hAPP(X_a,int,archim2085082626_floor(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),X),one_one(X_a))) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(X_a,int,archim2085082626_floor(X_a),X)),one_one(int))))) # label(fact_439_floor__diff__one) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.63 566 (all X_a (archim1727834104eiling(X_a) -> (all X all V hAPP(X_a,int,archim2085082626_floor(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),X),hAPP(int,X_a,number_number_of(X_a),V))) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(X_a,int,archim2085082626_floor(X_a),X)),hAPP(int,int,number_number_of(int),V))))) # label(fact_440_floor__diff__number__of) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.63 567 (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),nat_tsub,X),Y)))))) # label(fact_441_Nat__Transfer_Otransfer__nat__int__function__closures_I3_J) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.63 568 (all Y all X (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Y),X)) -> hAPP(int,int,hAPP(int,fun(int,int),nat_tsub,X),Y) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X),Y))) # label(fact_442_tsub__eq) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.63 569 (all X_a (archim1727834104eiling(X_a) -> (all V_1 all X_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),V_1)),hAPP(X_a,int,archim2085082626_floor(X_a),X_1))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(int,X_a,number_number_of(X_a),V_1)),one_one(X_a))),X_1)))))) # label(fact_443_number__of__less__floor) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.63 570 (all B all A_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),B)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(real,int,archim2085082626_floor(real),A_1)),hAPP(real,int,archim2085082626_floor(real),B))),hAPP(real,int,archim2085082626_floor(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A_1),B))))))) # label(fact_444_le__mult__floor) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.63 571 (all B all A_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B)) -> hBOOL(hAPP(product_prod(int,int),bool,hAPP(int,fun(product_prod(int,int),bool),hAPP(int,fun(int,fun(product_prod(int,int),bool)),divmod_int_rel,A_1),B),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),posDivAlg,A_1),B)))))) # label(fact_445_posDivAlg__correct) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.63 572 (all Z all X all D (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Z),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X),Z))),one_one(int))),D)))))) # label(fact_446_incr__lemma) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.63 573 (all X all Z all D (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X),Z))),one_one(int))),D))),Z)))) # label(fact_447_decr__lemma) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.63 574 (all X_a (linordered_idom(X_a) -> (all Aa (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Aa),ring_1_Ints(X_a))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),one_one(X_a)),Aa)),Aa)),zero_zero(X_a))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),zero_zero(X_a)))))))) # label(fact_448_Ints__odd__less__0) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.63 575 (all Aa all Ba all Qa all R_1 (hBOOL(hAPP(product_prod(int,int),bool,hAPP(int,fun(product_prod(int,int),bool),hAPP(int,fun(int,fun(product_prod(int,int),bool)),divmod_int_rel,Aa),Ba),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),Qa),R_1))) -> hBOOL(hAPP(product_prod(int,int),bool,hAPP(int,fun(product_prod(int,int),bool),hAPP(int,fun(int,fun(product_prod(int,int),bool)),divmod_int_rel,hAPP(int,int,uminus_uminus(int),Aa)),Ba),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),hAPP(int,int,hAPP(int,fun(int,int),hAPP(bool,fun(int,fun(int,int)),if(int),hAPP(int,bool,hAPP(int,fun(int,bool),fequal(int),R_1),zero_zero(int))),hAPP(int,int,uminus_uminus(int),Qa)),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,uminus_uminus(int),Qa)),one_one(int)))),hAPP(int,int,hAPP(int,fun(int,int),hAPP(bool,fun(int,fun(int,int)),if(int),hAPP(int,bool,hAPP(int,fun(int,bool),fequal(int),R_1),zero_zero(int))),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),Ba),R_1))))))) # label(fact_449_zminus1__lemma) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.63 576 (all Aa all Ba (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),Ba)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Ba),Aa)) -> hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Ba),hAPP(int,fun(int,bool),d22set,Aa)))))) # label(fact_450_d22set__mem) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.63 577 (all X_a (archim1727834104eiling(X_a) -> (all X_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(X_a,int,archimedean_ceiling(X_a),X_1))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(int,X_a,number_number_of(X_a),min)),X_1)))))) # label(fact_451_zero__le__ceiling) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.63 578 (all X_a (archim1727834104eiling(X_a) -> (all X_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(X_a,int,archimedean_ceiling(X_a),X_1)),zero_zero(int))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),hAPP(int,X_a,number_number_of(X_a),min))))))) # label(fact_452_ceiling__less__zero) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.63 579 (all P_1 all N all K (hBOOL(hAPP(int,bool,P_1,hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),N),K))) <-> (K = zero_zero(int) -> hBOOL(hAPP(int,bool,P_1,N))) & (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),K)) -> (all I_2 all J_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),J_1)) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),J_1),K)) & N = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K),I_2)),J_1) -> hBOOL(hAPP(int,bool,P_1,J_1))))) & (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),zero_zero(int))) -> (all I_2 all J_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),J_1)) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),J_1),zero_zero(int))) & N = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K),I_2)),J_1) -> hBOOL(hAPP(int,bool,P_1,J_1))))))) # label(fact_453_split__zmod) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.63 580 (all X_1 all Y_1 all Z_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Z_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),X_1),Z_1)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),Y_1),Z_1))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_1),Y_1))))) # label(fact_454_real__mult__le__cancel__iff1) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.63 581 (all X_1 all Y_1 all Z_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Z_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),Z_1),X_1)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),Z_1),Y_1))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_1),Y_1))))) # label(fact_455_real__mult__le__cancel__iff2) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.63 582 (all X_1 all Y_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_1),Y_1)) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),X_1),Y_1)),zero_zero(real))))) # label(fact_456_real__le__eq__diff) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.63 583 (all K_4 all L_4 (hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),K_4),hAPP(int,int,uminus_uminus(int),L_4)) != zero_zero(int) -> hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),K_4),L_4) != zero_zero(int))) # label(fact_457_zmod__zminus2__not__zero) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.63 584 (all K_4 all L_4 (hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,uminus_uminus(int),K_4)),L_4) != zero_zero(int) -> hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),K_4),L_4) != zero_zero(int))) # label(fact_458_zmod__zminus1__not__zero) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.63 585 (all Aa all Ba all C_1 (C_1 != zero_zero(real) -> (hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C_1),Aa) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C_1),Ba) <-> Aa = Ba))) # label(fact_459_real__mult__left__cancel) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.63 586 (all Aa all Ba all C_1 (C_1 != zero_zero(real) -> (hAPP(real,real,hAPP(real,fun(real,real),times_times(real),Aa),C_1) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),Ba),C_1) <-> Aa = Ba))) # label(fact_460_real__mult__right__cancel) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.63 587 (all X_1 all Y_1 (hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),X_1),X_1)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),Y_1),Y_1)) = zero_zero(real) <-> X_1 = zero_zero(real) & Y_1 = zero_zero(real))) # label(fact_461_real__two__squares__add__zero__iff) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.63 588 (all X all Y all Z (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Z)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),Y)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),Z),X)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),Z),Y)))))) # label(fact_462_real__mult__less__mono2) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.63 589 (all Y all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Y)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),X),Y)))))) # label(fact_463_real__mult__order) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.63 590 (all X_1 all Y_1 all Z_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Z_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),X_1),Z_1)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),Y_1),Z_1))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_1),Y_1))))) # label(fact_464_real__mult__less__iff1) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.63 591 (all X_a (ring_div(X_a) -> (all A_1 all B all A_5 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),A_1),B) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),A_5),B) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(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),div_mod(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),A_5)),B))))) # label(fact_466_mod__minus__cong) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.63 592 (all X_a (semiring_div(X_a) -> (all A_1 all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),A_1),B)),B) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),A_1),B)))) # label(fact_467_mod__mod__trivial) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.63 593 (all X all M_1 hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,uminus_uminus(int),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),X),M_1))),M_1) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,uminus_uminus(int),X)),M_1)) # label(fact_468_zminus__zmod) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.63 594 (all A_1 all B hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,uminus_uminus(int),A_1)),hAPP(int,int,uminus_uminus(int),B)) = hAPP(int,int,uminus_uminus(int),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_1),B))) # label(fact_469_zmod__zminus__zminus) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.63 595 (all X_a (ring_div(X_a) -> (all A_1 all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(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),div_mod(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),A_1),B))),B)))) # label(fact_470_mod__minus__eq) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.63 596 (all A_1 all B hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_1),hAPP(int,int,uminus_uminus(int),B)) = hAPP(int,int,uminus_uminus(int),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,uminus_uminus(int),A_1)),B))) # label(fact_471_zmod__zminus2) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.63 597 (all X_a (number_ring(X_a) -> (all W hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(int,X_a,number_number_of(X_a),W)) = hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,uminus_uminus(int),W))))) # label(fact_472_arith__simps_I30_J) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.63 598 (all X_a (number_ring(X_a) -> (all W hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,uminus_uminus(int),W)) = hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(int,X_a,number_number_of(X_a),W))))) # label(fact_473_number__of__minus) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.63 599 (all K_4 hAPP(int,int,hAPP(int,fun(int,int),times_times(int),min),K_4) = hAPP(int,int,uminus_uminus(int),K_4)) # label(fact_475_mult__Min) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.63 600 (all W hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),W),W))) # label(fact_476_real__le__refl) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.63 601 (all Z all W (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),Z),W)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),W),Z)))) # label(fact_477_real__le__linear) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.63 602 (all Z all X all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X),Y)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),Z),X)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),Z),Y))))) # label(fact_478_real__add__left__mono) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.63 603 (all K_4 all I_1 all J_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),I_1),J_2)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),J_2),K_4)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),I_1),K_4))))) # label(fact_479_real__le__trans) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.63 604 (all Z all W (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),Z),W)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),W),Z)) -> Z = W))) # label(fact_480_real__le__antisym) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.63 605 (all X_a (ordere142940540dd_abs(X_a) -> (all A_1 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),A_1)),hAPP(X_a,X_a,abs_abs(X_a),A_1)))))) # label(fact_481_abs__ge__minus__self) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.63 606 (all X_a (ordere142940540dd_abs(X_a) -> (all Aa all Ba (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,abs_abs(X_a),Aa)),Ba)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Aa),Ba)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),Aa)),Ba)))))) # label(fact_482_abs__le__iff) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.63 607 (all X_a (ordere142940540dd_abs(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),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,abs_abs(X_a),A_1)),B))))))) # label(fact_483_abs__leI) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.63 608 (all X_a (ordere142940540dd_abs(X_a) -> (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,abs_abs(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),A_1)),B)))))) # label(fact_484_abs__le__D2) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.63 609 (all X_a (boolean_algebra(X_a) -> (all X_1 all Y_1 (hAPP(X_a,X_a,uminus_uminus(X_a),X_1) = hAPP(X_a,X_a,uminus_uminus(X_a),Y_1) <-> ti(X_a,X_1) = ti(X_a,Y_1))))) # label(fact_485_compl__eq__compl__iff) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.63 610 (all X_b all X_a (uminus(X_a) -> (all A_2 all X_1 hAPP(X_b,X_a,hAPP(fun(X_b,X_a),fun(X_b,X_a),uminus_uminus(fun(X_b,X_a)),A_2),X_1) = hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(X_b,X_a,A_2,X_1))))) # label(fact_486_uminus__apply) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.63 611 (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_487_double__compl) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.63 612 (all X_a all X_b (uminus(X_b) -> (all A_2 all X_2 hAPP(X_a,X_b,hAPP(fun(X_a,X_b),fun(X_a,X_b),uminus_uminus(fun(X_a,X_b)),A_2),X_2) = hAPP(X_b,X_b,uminus_uminus(X_b),hAPP(X_a,X_b,A_2,X_2))))) # label(fact_488_fun__Compl__def) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.63 613 (all X_a (ring_1(X_a) -> (all Aa (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Aa),ring_1_Ints(X_a))) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),Aa)),ring_1_Ints(X_a))))))) # label(fact_489_Ints__minus) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.63 614 (all Z1 all Z2 all W hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),Z1),Z2)),W) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),Z1),W)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),Z2),W))) # label(fact_490_real__add__mult__distrib) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.63 615 (all Z1 all Z2 all Z3 hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),Z1),Z2)),Z3) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),Z1),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),Z2),Z3))) # label(fact_491_real__mult__assoc) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.63 616 (all X_a (group_add(X_a) -> (all Aa all Ba (hAPP(X_a,X_a,uminus_uminus(X_a),Aa) = hAPP(X_a,X_a,uminus_uminus(X_a),Ba) <-> ti(X_a,Aa) = ti(X_a,Ba))))) # label(fact_492_neg__equal__iff__equal) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.63 617 (all X_a (group_add(X_a) -> (all Aa all Ba (hAPP(X_a,X_a,uminus_uminus(X_a),Aa) = ti(X_a,Ba) <-> hAPP(X_a,X_a,uminus_uminus(X_a),Ba) = ti(X_a,Aa))))) # label(fact_493_minus__equation__iff) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.63 618 (all X_a (group_add(X_a) -> (all Aa all Ba (ti(X_a,Aa) = hAPP(X_a,X_a,uminus_uminus(X_a),Ba) <-> ti(X_a,Ba) = hAPP(X_a,X_a,uminus_uminus(X_a),Aa))))) # label(fact_494_equation__minus__iff) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.63 619 (all Z all W hAPP(real,real,hAPP(real,fun(real,real),times_times(real),Z),W) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),W),Z)) # label(fact_495_real__mult__commute) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.63 620 (all X_a (ordere142940540dd_abs(X_a) -> (all A_1 hAPP(X_a,X_a,abs_abs(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),A_1)) = hAPP(X_a,X_a,abs_abs(X_a),A_1)))) # label(fact_496_abs__minus__cancel) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.63 621 (all X_a (ordere142940540dd_abs(X_a) -> (all A_1 hAPP(X_a,X_a,abs_abs(X_a),hAPP(X_a,X_a,abs_abs(X_a),A_1)) = hAPP(X_a,X_a,abs_abs(X_a),A_1)))) # label(fact_497_abs__idempotent) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.63 622 (all Z hAPP(int,int,uminus_uminus(int),hAPP(int,int,uminus_uminus(int),Z)) = Z) # label(fact_498_zminus__zminus) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.63 623 (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_499_minus__minus) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.63 624 (all Z hAPP(real,real,hAPP(real,fun(real,real),times_times(real),one_one(real)),Z) = Z) # label(fact_500_real__mult__1) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.63 625 (all X_a (linordered_idom(X_a) -> (all Aa all Ba (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,abs_abs(X_a),Aa)),Ba)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),Ba)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),Aa)),Ba)))))) # label(fact_501_abs__less__iff) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.63 626 (all X_1 all Y_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_1),Y_1)) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_1),Y_1)) | X_1 = Y_1)) # label(fact_502_less__eq__real__def) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.63 627 (all X_1 all Y_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_1),Y_1)) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_1),Y_1)) & X_1 != Y_1)) # label(fact_503_real__less__def) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.63 628 (all X_a (ordere142940540dd_abs(X_a) -> (all A_1 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),hAPP(X_a,X_a,abs_abs(X_a),A_1))),zero_zero(X_a)))))) # label(fact_504_abs__minus__le__zero) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.63 629 (all X_a (ordere142940540dd_abs(X_a) -> (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))) -> hAPP(X_a,X_a,abs_abs(X_a),A_1) = hAPP(X_a,X_a,uminus_uminus(X_a),A_1))))) # label(fact_505_abs__of__nonpos) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.63 630 (all X_a (ordere142940540dd_abs(X_a) -> (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))) -> hAPP(X_a,X_a,abs_abs(X_a),A_1) = hAPP(X_a,X_a,uminus_uminus(X_a),A_1))))) # label(fact_506_abs__of__neg) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.63 631 (all X_a (abs_if(X_a) -> (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))) -> hAPP(X_a,X_a,abs_abs(X_a),A_1) = hAPP(X_a,X_a,uminus_uminus(X_a),A_1)) & (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),zero_zero(X_a))) -> hAPP(X_a,X_a,abs_abs(X_a),A_1) = ti(X_a,A_1)))))) # label(fact_507_abs__if) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.63 632 (all X_a (number_ring(X_a) & linordered_idom(X_a) -> hAPP(X_a,X_a,abs_abs(X_a),hAPP(int,X_a,number_number_of(X_a),min)) = one_one(X_a))) # label(fact_508_abs__minus__one) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.63 633 (all X_a (number_ring(X_a) -> (all W all Z 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),hAPP(int,X_a,number_number_of(X_a),W))),Z) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,uminus_uminus(int),W))),Z)))) # label(fact_509_minus__number__of__mult) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.63 634 (all X_a (number_ring(X_a) -> (all Z hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(int,X_a,number_number_of(X_a),min)),Z) = hAPP(X_a,X_a,uminus_uminus(X_a),Z)))) # label(fact_510_mult__minus1) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.63 635 (all X_a (number_ring(X_a) -> (all Z hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Z),hAPP(int,X_a,number_number_of(X_a),min)) = hAPP(X_a,X_a,uminus_uminus(X_a),Z)))) # label(fact_511_mult__minus1__right) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.63 636 (all X_a (number_ring(X_a) -> hAPP(int,X_a,number_number_of(X_a),min) = hAPP(X_a,X_a,uminus_uminus(X_a),one_one(X_a)))) # label(fact_512_number__of__Min) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.63 637 (all X_a (number_ring(X_a) -> hAPP(X_a,X_a,uminus_uminus(X_a),one_one(X_a)) = hAPP(int,X_a,number_number_of(X_a),min))) # label(fact_513_arith__simps_I31_J) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.63 638 (all I_1 ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),I_1),zero_zero(int))) -> hAPP(int,int,abs_abs(int),I_1) = hAPP(int,int,uminus_uminus(int),I_1)) & (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),I_1),zero_zero(int))) -> hAPP(int,int,abs_abs(int),I_1) = I_1))) # label(fact_514_zabs__def) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.63 639 (all A_1 hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_1),hAPP(int,int,number_number_of(int),min)) = zero_zero(int)) # label(fact_515_zmod__minus1__right) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.63 640 (all A_1 all B ((hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_1),B) = zero_zero(int) -> hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,uminus_uminus(int),A_1)),B) = zero_zero(int)) & (hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_1),B) != zero_zero(int) -> hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,uminus_uminus(int),A_1)),B) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),B),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_1),B))))) # label(fact_516_zmod__zminus1__eq__if) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.63 641 (all A_1 all B ((hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_1),B) = zero_zero(int) -> hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_1),hAPP(int,int,uminus_uminus(int),B)) = zero_zero(int)) & (hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_1),B) != zero_zero(int) -> hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_1),hAPP(int,int,uminus_uminus(int),B)) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_1),B)),B)))) # label(fact_517_zmod__zminus2__eq__if) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.63 642 (all Z_1 (hAPP(int,int,abs_abs(int),Z_1) = one_one(int) <-> Z_1 = one_one(int) | Z_1 = hAPP(int,int,number_number_of(int),min))) # label(fact_518_abs__eq__1__iff) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.63 643 (all X_a (semiring_div(X_a) -> (all A_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),zero_zero(X_a)),A_1) = zero_zero(X_a)))) # label(fact_519_mod__0) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.63 644 (all X_a (semiring_div(X_a) -> (all A_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),A_1),zero_zero(X_a)) = ti(X_a,A_1)))) # label(fact_520_mod__by__0) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.63 645 (all X_a (semiring_div(X_a) -> (all A_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),A_1),A_1) = zero_zero(X_a)))) # label(fact_521_mod__self) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.63 646 (all X_a (ordere142940540dd_abs(X_a) -> (all Aa (hAPP(X_a,X_a,abs_abs(X_a),Aa) = zero_zero(X_a) <-> ti(X_a,Aa) = zero_zero(X_a))))) # label(fact_522_abs__eq__0) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.63 647 (all X_a (ordere142940540dd_abs(X_a) -> hAPP(X_a,X_a,abs_abs(X_a),zero_zero(X_a)) = zero_zero(X_a))) # label(fact_523_abs__zero) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.63 648 (all X_a (ordere142940540dd_abs(X_a) -> (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,abs_abs(X_a),A_1)),B)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B)))))) # label(fact_524_abs__le__D1) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.63 649 (all X_a (ordere142940540dd_abs(X_a) -> (all A_1 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),hAPP(X_a,X_a,abs_abs(X_a),A_1)))))) # label(fact_525_abs__ge__self) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.63 650 (all X_a (semiring_div(X_a) -> (all B all B_4 all A_1 all C all A_5 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),A_1),C) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),A_5),C) -> (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),B),C) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),B_4),C) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(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),div_mod(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_5),B_4)),C)))))) # label(fact_526_mod__mult__cong) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.63 651 (all X_a (semiring_div(X_a) -> (all A_1 all C all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(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),div_mod(X_a),A_1),C)),B)),C) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)),C)))) # label(fact_527_zmod__simps_I4_J) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.63 652 (all X_a (semiring_div(X_a) -> (all A_1 all C all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(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)) = 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),div_mod(X_a),A_1),B)),C)))) # label(fact_528_mod__mult__mult2) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.63 653 (all X_a (semiring_div(X_a) -> (all C all A_1 all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(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)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),A_1),B))))) # label(fact_529_mod__mult__mult1) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.63 654 (all X_a (semiring_div(X_a) -> (all A_1 all B all C hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(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),div_mod(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),div_mod(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),B),C))),C)))) # label(fact_530_mod__mult__eq) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.63 655 (all X_a (semiring_div(X_a) -> (all A_1 all B all C hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(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),div_mod(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),div_mod(X_a),A_1),C)),B)),C)))) # label(fact_531_mod__mult__left__eq) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.63 656 (all X_a (semiring_div(X_a) -> (all A_1 all B all C hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(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),div_mod(X_a),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),div_mod(X_a),B),C))),C)))) # label(fact_532_mod__mult__right__eq) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.63 657 (all X_a (semiring_div(X_a) -> (all B all B_4 all A_1 all C all A_5 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),A_1),C) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),A_5),C) -> (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),B),C) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),B_4),C) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(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),div_mod(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_5),B_4)),C)))))) # label(fact_533_mod__add__cong) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.63 658 (all X_a (semiring_div(X_a) -> (all A_1 all C all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),A_1),C)),B)),C) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)),C)))) # label(fact_534_zmod__simps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.63 659 (all X_a (semiring_div(X_a) -> (all A_1 all B all C hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),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),div_mod(X_a),B),C))),C) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)),C)))) # label(fact_535_zmod__simps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.63 660 (all X_a (semiring_div(X_a) -> (all A_1 all B all C hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(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),div_mod(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),B),C))),C)))) # label(fact_536_mod__add__eq) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.63 661 (all X_a (semiring_div(X_a) -> (all A_1 all B all C hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(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),div_mod(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),A_1),C)),B)),C)))) # label(fact_537_mod__add__left__eq) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.63 662 (all X_a (semiring_div(X_a) -> (all A_1 all B all C hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(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),div_mod(X_a),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),div_mod(X_a),B),C))),C)))) # label(fact_538_mod__add__right__eq) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.63 663 (all X_a (semiring_div(X_a) -> (all B all A_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B),A_1)),B) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),A_1),B)))) # label(fact_539_mod__add__self1) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.63 664 (all X_a (semiring_div(X_a) -> (all A_1 all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)),B) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),A_1),B)))) # label(fact_540_mod__add__self2) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.63 665 (all X_a (linordered_idom(X_a) -> (all A_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,abs_abs(X_a),A_1)),hAPP(X_a,X_a,abs_abs(X_a),A_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),A_1)))) # label(fact_541_abs__mult__self) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.63 666 (all X_a (linordered_idom(X_a) -> (all A_1 all B hAPP(X_a,X_a,abs_abs(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,abs_abs(X_a),A_1)),hAPP(X_a,X_a,abs_abs(X_a),B))))) # label(fact_542_abs__mult) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.63 667 (all X_a (ordere142940540dd_abs(X_a) -> (all A_1 all B hAPP(X_a,X_a,abs_abs(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,abs_abs(X_a),A_1)),hAPP(X_a,X_a,abs_abs(X_a),B))) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,abs_abs(X_a),A_1)),hAPP(X_a,X_a,abs_abs(X_a),B))))) # label(fact_543_abs__add__abs) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.63 668 (all X_a (ring_div(X_a) -> (all B all B_4 all A_1 all C all A_5 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),A_1),C) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),A_5),C) -> (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),B),C) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),B_4),C) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_1),B)),C) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_5),B_4)),C)))))) # label(fact_544_mod__diff__cong) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.63 669 (all X_a (ring_div(X_a) -> (all A_1 all B all C hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_1),B)),C) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),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),div_mod(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),B),C))),C)))) # label(fact_545_mod__diff__eq) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.63 670 (all X_a (ring_div(X_a) -> (all A_1 all B all C hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_1),B)),C) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),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),div_mod(X_a),A_1),C)),B)),C)))) # label(fact_546_mod__diff__left__eq) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.63 671 (all X_a (ring_div(X_a) -> (all A_1 all B all C hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_1),B)),C) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),B),C))),C)))) # label(fact_547_mod__diff__right__eq) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.63 672 (all X_a (linordered_idom(X_a) -> hAPP(X_a,X_a,abs_abs(X_a),one_one(X_a)) = one_one(X_a))) # label(fact_548_abs__one) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.63 673 (all X_a (ordere142940540dd_abs(X_a) -> (all A_1 all B hAPP(X_a,X_a,abs_abs(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,abs_abs(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),B),A_1))))) # label(fact_549_abs__minus__commute) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.63 674 (all X_a (archim1727834104eiling(X_a) -> (all X hAPP(X_a,int,archim2085082626_floor(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),X)) = hAPP(int,int,uminus_uminus(int),hAPP(X_a,int,archimedean_ceiling(X_a),X))))) # label(fact_550_floor__minus) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.63 675 (all X_a (archim1727834104eiling(X_a) -> (all X hAPP(X_a,int,archimedean_ceiling(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),X)) = hAPP(int,int,uminus_uminus(int),hAPP(X_a,int,archim2085082626_floor(X_a),X))))) # label(fact_551_ceiling__minus) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.63 676 (all X_a (archim1727834104eiling(X_a) -> (all X hAPP(X_a,int,archimedean_ceiling(X_a),X) = hAPP(int,int,uminus_uminus(int),hAPP(X_a,int,archim2085082626_floor(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),X)))))) # label(fact_552_ceiling__def) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.63 677 (all X_a (linord219039673up_add(X_a) -> (all Aa (hAPP(X_a,X_a,uminus_uminus(X_a),Aa) = ti(X_a,Aa) <-> ti(X_a,Aa) = zero_zero(X_a))))) # label(fact_553_neg__equal__zero) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.63 678 (all X_a (group_add(X_a) -> (all Aa (hAPP(X_a,X_a,uminus_uminus(X_a),Aa) = zero_zero(X_a) <-> ti(X_a,Aa) = zero_zero(X_a))))) # label(fact_554_neg__equal__0__iff__equal) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.63 679 (all X_a (linord219039673up_add(X_a) -> (all Aa (ti(X_a,Aa) = hAPP(X_a,X_a,uminus_uminus(X_a),Aa) <-> ti(X_a,Aa) = zero_zero(X_a))))) # label(fact_555_equal__neg__zero) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.63 680 (all X_a (group_add(X_a) -> (all Aa (zero_zero(X_a) = hAPP(X_a,X_a,uminus_uminus(X_a),Aa) <-> zero_zero(X_a) = ti(X_a,Aa))))) # label(fact_556_neg__0__equal__iff__equal) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.63 681 (all X_a (group_add(X_a) -> hAPP(X_a,X_a,uminus_uminus(X_a),zero_zero(X_a)) = zero_zero(X_a))) # label(fact_557_minus__zero) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.63 682 (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_558_compl__le__swap2) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.63 683 (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_559_compl__le__swap1) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.63 684 (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_560_compl__mono) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.63 685 (all X_a (boolean_algebra(X_a) -> (all X_1 all Y_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),X_1)),hAPP(X_a,X_a,uminus_uminus(X_a),Y_1))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y_1),X_1)))))) # label(fact_561_compl__le__compl__iff) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.63 686 (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_562_le__imp__neg__le) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.63 687 (all X_a (ordered_ab_group_add(X_a) -> (all Ba all Aa (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),Ba)),hAPP(X_a,X_a,uminus_uminus(X_a),Aa))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Aa),Ba)))))) # label(fact_563_neg__le__iff__le) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.63 688 (all X_a (ordered_ab_group_add(X_a) -> (all Aa all Ba (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),Aa)),Ba)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),Ba)),Aa)))))) # label(fact_564_minus__le__iff) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.63 689 (all X_a (ordered_ab_group_add(X_a) -> (all Aa all Ba (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Aa),hAPP(X_a,X_a,uminus_uminus(X_a),Ba))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Ba),hAPP(X_a,X_a,uminus_uminus(X_a),Aa))))))) # label(fact_565_le__minus__iff) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.63 690 (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_566_compl__less__swap2) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.63 691 (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_567_compl__less__swap1) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.63 692 (all X_a (boolean_algebra(X_a) -> (all X_1 all Y_1 (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_1)),hAPP(X_a,X_a,uminus_uminus(X_a),Y_1))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y_1),X_1)))))) # label(fact_568_compl__less__compl__iff) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.63 693 (all X_a (ordered_ab_group_add(X_a) -> (all Ba all Aa (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),Ba)),hAPP(X_a,X_a,uminus_uminus(X_a),Aa))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),Ba)))))) # label(fact_569_neg__less__iff__less) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.63 694 (all X_a (ordered_ab_group_add(X_a) -> (all Aa all Ba (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),Aa)),Ba)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),Ba)),Aa)))))) # label(fact_570_minus__less__iff) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.63 695 (all X_a (ordered_ab_group_add(X_a) -> (all Aa all Ba (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),hAPP(X_a,X_a,uminus_uminus(X_a),Ba))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Ba),hAPP(X_a,X_a,uminus_uminus(X_a),Aa))))))) # label(fact_571_less__minus__iff) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.63 696 (all X_a (idom(X_a) -> (all Aa all Ba (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Aa),Aa) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Ba),Ba) <-> ti(X_a,Aa) = ti(X_a,Ba) | ti(X_a,Aa) = hAPP(X_a,X_a,uminus_uminus(X_a),Ba))))) # label(fact_572_square__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.63 697 (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_573_minus__mult__minus) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.63 698 (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_574_minus__mult__commute) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.63 699 (all X_a (real_normed_algebra(X_a) -> (all X all Y 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),X)),Y) = 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),X),Y))))) # label(fact_575_mult__left_Ominus) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.63 700 (all X_a (real_normed_algebra(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,uminus_uminus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B))))) # label(fact_576_mult_Ominus__left) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.63 701 (all X_a (real_normed_algebra(X_a) -> (all Xa_1 all X hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Xa_1),hAPP(X_a,X_a,uminus_uminus(X_a),X)) = 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),Xa_1),X))))) # label(fact_577_mult__right_Ominus) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.63 702 (all X_a (real_normed_algebra(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,uminus_uminus(X_a),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))))) # label(fact_578_mult_Ominus__right) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.63 703 (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_579_minus__mult__left) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.63 704 (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_580_minus__mult__right) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.63 705 (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_581_minus__add__cancel) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.63 706 (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_582_add__minus__cancel) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.63 707 (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_583_minus__add) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.63 708 (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_584_minus__add__distrib) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.63 709 (all A_1 hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_1),A_1) = zero_zero(int)) # label(fact_585_zmod__self) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.63 710 (all B hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),zero_zero(int)),B) = zero_zero(int)) # label(fact_586_zmod__zero) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.63 711 (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),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,uminus_uminus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_1),B))))) # label(fact_587_minus__diff__minus) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.63 712 (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_588_minus__diff__eq) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.63 713 (all A_1 all B all C hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),B),C))),C) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),B)),C)) # label(fact_589_zmod__simps_I3_J) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.63 714 (all A_1 all B all C hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),B)),C) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),B),C))),C)) # label(fact_590_zmod__zmult1__eq) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.63 715 (all X all M_1 all Y hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),X),M_1)),Y)),M_1) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X),Y)),M_1)) # label(fact_592_zdiff__zmod__left) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.63 716 (all X all Y all M_1 hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),Y),M_1))),M_1) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X),Y)),M_1)) # label(fact_593_zdiff__zmod__right) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.63 717 (all Z all W hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,uminus_uminus(int),Z)),W) = hAPP(int,int,uminus_uminus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Z),W))) # label(fact_594_zmult__zminus) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.63 718 (all W hAPP(int,int,uminus_uminus(int),hAPP(int,int,number_number_of(int),W)) = hAPP(int,int,number_number_of(int),hAPP(int,int,uminus_uminus(int),W))) # label(fact_596_minus__numeral__code_I5_J) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.63 719 (all Z all W hAPP(int,int,uminus_uminus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Z),W)) = 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))) # label(fact_598_zminus__zadd__distrib) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.63 720 (all X_a all X_c all X_b (real_normed_vector(X_b) & real_normed_vector(X_c) & real_normed_vector(X_a) -> (all Aa all Ba all Prod (hBOOL(hAPP(fun(X_a,fun(X_b,X_c)),bool,bounded_bilinear(X_a,X_b,X_c),Prod)) -> hAPP(X_b,X_c,hAPP(X_a,fun(X_b,X_c),Prod,hAPP(X_a,X_a,uminus_uminus(X_a),Aa)),Ba) = hAPP(X_c,X_c,uminus_uminus(X_c),hAPP(X_b,X_c,hAPP(X_a,fun(X_b,X_c),Prod,Aa),Ba)))))) # label(fact_599_bounded__bilinear_Ominus__left) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.63 721 (all X_a all X_c all X_b (real_normed_vector(X_b) & real_normed_vector(X_c) & real_normed_vector(X_a) -> (all Aa all Ba all Prod (hBOOL(hAPP(fun(X_a,fun(X_b,X_c)),bool,bounded_bilinear(X_a,X_b,X_c),Prod)) -> hAPP(X_b,X_c,hAPP(X_a,fun(X_b,X_c),Prod,Aa),hAPP(X_b,X_b,uminus_uminus(X_b),Ba)) = hAPP(X_c,X_c,uminus_uminus(X_c),hAPP(X_b,X_c,hAPP(X_a,fun(X_b,X_c),Prod,Aa),Ba)))))) # label(fact_600_bounded__bilinear_Ominus__right) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.63 722 (all X_a (number_ring(X_a) & linordered_idom(X_a) -> (all X ((hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(int,X_a,number_number_of(X_a),X)),zero_zero(X_a))) -> hAPP(X_a,X_a,abs_abs(X_a),hAPP(int,X_a,number_number_of(X_a),X)) = hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(int,X_a,number_number_of(X_a),X))) & (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(int,X_a,number_number_of(X_a),X)),zero_zero(X_a))) -> hAPP(X_a,X_a,abs_abs(X_a),hAPP(int,X_a,number_number_of(X_a),X)) = hAPP(int,X_a,number_number_of(X_a),X)))))) # label(fact_601_abs__number__of) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.63 723 (all X_a (ring_1(X_a) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),zero_zero(X_a)),ring_1_Ints(X_a))))) # label(fact_602_Ints__0) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.63 724 (all X_a (ring_1(X_a) -> (all Ba all Aa (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Aa),ring_1_Ints(X_a))) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Ba),ring_1_Ints(X_a))) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Aa),Ba)),ring_1_Ints(X_a)))))))) # label(fact_603_Ints__mult) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.63 725 (all X_a (ring_1(X_a) -> (all Ba all Aa (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Aa),ring_1_Ints(X_a))) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Ba),ring_1_Ints(X_a))) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Aa),Ba)),ring_1_Ints(X_a)))))))) # label(fact_604_Ints__add) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.63 726 (all X_a (number_ring(X_a) -> (all W_1 hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),hAPP(int,X_a,number_number_of(X_a),W_1)),ring_1_Ints(X_a)))))) # label(fact_605_Ints__number__of) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.64 727 (all X_a (ring_1(X_a) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),one_one(X_a)),ring_1_Ints(X_a))))) # label(fact_606_Ints__1) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.64 728 (all X_a (ring_1(X_a) -> (all Ba all Aa (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Aa),ring_1_Ints(X_a))) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Ba),ring_1_Ints(X_a))) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),Aa),Ba)),ring_1_Ints(X_a)))))))) # label(fact_607_Ints__diff) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.64 729 (all X_a (semiring_div(X_a) -> (all B all A_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),A_1)),B) = zero_zero(X_a)))) # label(fact_608_mod__mult__self1__is__0) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.64 730 (all X_a (semiring_div(X_a) -> (all A_1 all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)),B) = zero_zero(X_a)))) # label(fact_609_mod__mult__self2__is__0) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.64 731 (all X_a (ordere142940540dd_abs(X_a) -> (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)) -> hAPP(X_a,X_a,abs_abs(X_a),A_1) = ti(X_a,A_1))))) # label(fact_610_abs__of__nonneg) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.64 732 (all X_a (ordere142940540dd_abs(X_a) -> (all Aa (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,abs_abs(X_a),Aa)),zero_zero(X_a))) <-> ti(X_a,Aa) = zero_zero(X_a))))) # label(fact_611_abs__le__zero__iff) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.64 733 (all X_a (ordere142940540dd_abs(X_a) -> (all A_1 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),hAPP(X_a,X_a,abs_abs(X_a),A_1)))))) # label(fact_612_abs__ge__zero) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.64 734 (all X_a (ordere142940540dd_abs(X_a) -> (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)) -> hAPP(X_a,X_a,abs_abs(X_a),A_1) = ti(X_a,A_1))))) # label(fact_613_abs__of__pos) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.64 735 (all X_a (ordere142940540dd_abs(X_a) -> (all Aa (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,abs_abs(X_a),Aa))) <-> ti(X_a,Aa) != zero_zero(X_a))))) # label(fact_614_zero__less__abs__iff) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.64 736 (all X_a (ordere142940540dd_abs(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,abs_abs(X_a),A_1)),zero_zero(X_a)))))) # label(fact_615_abs__not__less__zero) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.64 737 (all X_a (semiring_div(X_a) -> (all A_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),A_1),one_one(X_a)) = zero_zero(X_a)))) # label(fact_616_mod__by__1) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.64 738 (all X_a (linordered_idom(X_a) -> (all B all D all A_1 all C (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,abs_abs(X_a),A_1)),C)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,abs_abs(X_a),B)),D)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,abs_abs(X_a),A_1)),hAPP(X_a,X_a,abs_abs(X_a),B))),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),D)))))))) # label(fact_617_abs__mult__less) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.64 739 (all X_a (semiring_div(X_a) -> (all A_1 all C all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),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),times_times(X_a),C),B))),B) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),A_1),B)))) # label(fact_618_mod__mult__self1) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.64 740 (all X_a (semiring_div(X_a) -> (all A_1 all B all C hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),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),times_times(X_a),B),C))),B) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),A_1),B)))) # label(fact_619_mod__mult__self2) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.64 741 (all X_a (ordere142940540dd_abs(X_a) -> (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,abs_abs(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,abs_abs(X_a),A_1)),hAPP(X_a,X_a,abs_abs(X_a),B))))))) # label(fact_620_abs__triangle__ineq) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.64 742 (all X_a (ordere142940540dd_abs(X_a) -> (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,abs_abs(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_a,X_a,abs_abs(X_a),A_1)),hAPP(X_a,X_a,abs_abs(X_a),B)))),hAPP(X_a,X_a,abs_abs(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_1),B))))))) # label(fact_621_abs__triangle__ineq3) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.64 743 (all X_a (ordere142940540dd_abs(X_a) -> (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),minus_minus(X_a),hAPP(X_a,X_a,abs_abs(X_a),A_1)),hAPP(X_a,X_a,abs_abs(X_a),B))),hAPP(X_a,X_a,abs_abs(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_1),B))))))) # label(fact_622_abs__triangle__ineq2) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.64 744 (all X_a (ordere142940540dd_abs(X_a) -> (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),minus_minus(X_a),hAPP(X_a,X_a,abs_abs(X_a),A_1)),hAPP(X_a,X_a,abs_abs(X_a),B))),hAPP(X_a,X_a,abs_abs(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),B),A_1))))))) # label(fact_623_abs__triangle__ineq2__sym) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.64 745 (all X_a (linordered_idom(X_a) -> (all X_1 all Aa all R_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,abs_abs(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),X_1),Aa))),R_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),minus_minus(X_a),Aa),R_1)),X_1)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Aa),R_1))))))) # label(fact_624_abs__diff__less__iff) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.64 746 (all Aa all Ba (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Aa),Ba)) -> -hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Ba),hAPP(int,fun(int,bool),d22set,Aa))))) # label(fact_625_d22set__le__swap) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.64 747 (all X_a (linord219039673up_add(X_a) -> (all Aa (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),Aa)),Aa)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),Aa)))))) # label(fact_626_minus__le__self__iff) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.64 748 (all X_a (ordered_ab_group_add(X_a) -> (all Aa (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),Aa)),zero_zero(X_a))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),Aa)))))) # label(fact_627_neg__le__0__iff__le) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.64 749 (all X_a (linord219039673up_add(X_a) -> (all Aa (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Aa),hAPP(X_a,X_a,uminus_uminus(X_a),Aa))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Aa),zero_zero(X_a))))))) # label(fact_628_le__minus__self__iff) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.64 750 (all X_a (ordered_ab_group_add(X_a) -> (all Aa (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),hAPP(X_a,X_a,uminus_uminus(X_a),Aa))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Aa),zero_zero(X_a))))))) # label(fact_629_neg__0__le__iff__le) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.64 751 (all Ba all Aa (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Ba),hAPP(int,fun(int,bool),d22set,Aa))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Ba),Aa)))) # label(fact_630_d22set__le) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.64 752 (all X_a (linord219039673up_add(X_a) -> (all Aa (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),Aa)),Aa)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),Aa)))))) # label(fact_631_neg__less__nonneg) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.64 753 (all X_a (ordered_ab_group_add(X_a) -> (all Aa (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),Aa)),zero_zero(X_a))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),Aa)))))) # label(fact_632_neg__less__0__iff__less) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.64 754 (all X_a (linordered_idom(X_a) -> (all Aa (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),hAPP(X_a,X_a,uminus_uminus(X_a),Aa))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),zero_zero(X_a))))))) # label(fact_633_less__minus__self__iff) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.64 755 (all X_a (ordered_ab_group_add(X_a) -> (all Aa (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,uminus_uminus(X_a),Aa))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),zero_zero(X_a))))))) # label(fact_634_neg__0__less__iff__less) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.64 756 (all X_a (group_add(X_a) -> (all A_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),hAPP(X_a,X_a,uminus_uminus(X_a),A_1)) = zero_zero(X_a)))) # label(fact_635_right__minus) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.64 757 (all X_a (group_add(X_a) -> (all Aa all Ba (ti(X_a,Aa) = hAPP(X_a,X_a,uminus_uminus(X_a),Ba) <-> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Aa),Ba) = zero_zero(X_a))))) # label(fact_636_eq__neg__iff__add__eq__0) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.64 758 (all X_a (group_add(X_a) -> (all 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)),A_1) = zero_zero(X_a)))) # label(fact_637_left__minus) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.64 759 (all X_a (ab_group_add(X_a) -> (all 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)),A_1) = zero_zero(X_a)))) # label(fact_638_ab__left__minus) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.64 760 (all X_a (group_add(X_a) -> (all X_1 all Y_1 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X_1),Y_1) = zero_zero(X_a) <-> ti(X_a,Y_1) = hAPP(X_a,X_a,uminus_uminus(X_a),X_1))))) # label(fact_639_add__eq__0__iff) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.64 761 (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),B) = zero_zero(X_a) -> hAPP(X_a,X_a,uminus_uminus(X_a),A_1) = ti(X_a,B))))) # label(fact_640_minus__unique) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.64 762 (all X_a (group_add(X_a) -> (all A_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),zero_zero(X_a)),A_1) = hAPP(X_a,X_a,uminus_uminus(X_a),A_1)))) # label(fact_641_diff__0) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.64 763 (all X_a (ring_11004092258visors(X_a) -> (all X_1 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X_1),X_1) = one_one(X_a) <-> ti(X_a,X_1) = one_one(X_a) | ti(X_a,X_1) = hAPP(X_a,X_a,uminus_uminus(X_a),one_one(X_a)))))) # label(fact_642_square__eq__1__iff) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.64 764 (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_643_comm__ring__1__class_Onormalizing__ring__rules_I1_J) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.64 765 (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_644_diff__minus__eq__add) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.64 766 (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_645_ab__diff__minus) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.64 767 (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_646_Groups_Odiff__def) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.64 768 (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_647_comm__ring__1__class_Onormalizing__ring__rules_I2_J) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.64 769 (all A_1 all 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),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_1),B)),B)))) # label(fact_648_pos__mod__bound) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.64 770 (all A_1 all 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),B),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_1),B))))) # label(fact_649_neg__mod__bound) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.64 771 (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),div_mod(int),X),Y)))))) # label(fact_650_Divides_Otransfer__nat__int__function__closures_I2_J) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.64 772 (all K_4 all M_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),M_1)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),M_1),K_4)),M_1)))) # label(fact_651_zmod__le__nonneg__dividend) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.64 773 (all M all D_1 (hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),M),D_1) = zero_zero(int) <-> (exists Q_3 M = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),D_1),Q_3)))) # label(fact_652_zmod__eq__0__iff) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.64 774 (all M_1 all N_1 (hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),M_1),N_1)) = one_one(int) -> hAPP(int,int,abs_abs(int),M_1) = one_one(int))) # label(fact_653_abs__zmult__eq__1) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.64 775 (all Z hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,uminus_uminus(int),Z)),Z) = zero_zero(int)) # label(fact_654_zadd__zminus__inverse2) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.64 776 (all Z all W hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Z),hAPP(int,int,uminus_uminus(int),W)) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),Z),W)) # label(fact_656_diff__int__def__symmetric) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.64 777 (all Z all W hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),Z),W) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Z),hAPP(int,int,uminus_uminus(int),W))) # label(fact_657_diff__int__def) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.64 778 (all B (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B)) -> hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,number_number_of(int),min)),B) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),B),one_one(int)))) # label(fact_658_zmod__minus1) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.64 779 (all X_a (ordered_ring_abs(X_a) -> (all B all A_1 ((hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),A_1)) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),zero_zero(X_a)))) & (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),B)) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),zero_zero(X_a)))) -> hAPP(X_a,X_a,abs_abs(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,abs_abs(X_a),A_1)),hAPP(X_a,X_a,abs_abs(X_a),B)))))) # label(fact_659_abs__eq__mult) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.64 780 (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)) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,abs_abs(X_a),Y)),X) = hAPP(X_a,X_a,abs_abs(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Y),X)))))) # label(fact_660_abs__mult__pos) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.64 781 (all X_a (ordere142940540dd_abs(X_a) -> (all A_1 all B all C all D hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,abs_abs(X_a),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)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),D)))),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,abs_abs(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_1),C))),hAPP(X_a,X_a,abs_abs(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),B),D)))))))) # label(fact_661_abs__diff__triangle__ineq) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.64 782 (all X_a (ordere142940540dd_abs(X_a) -> (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,abs_abs(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),plus_plus(X_a),hAPP(X_a,X_a,abs_abs(X_a),A_1)),hAPP(X_a,X_a,abs_abs(X_a),B))))))) # label(fact_662_abs__triangle__ineq4) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.64 783 (all X_a (ring_char_0(X_a) -> (all Aa (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Aa),ring_1_Ints(X_a))) -> (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Aa),Aa) = zero_zero(X_a) <-> ti(X_a,Aa) = zero_zero(X_a)))))) # label(fact_663_Ints__double__eq__0__iff) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.64 784 (all Z_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,abs_abs(int),Z_1)),one_one(int))) <-> Z_1 = zero_zero(int))) # label(fact_664_zabs__less__one__iff) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.64 785 (all B all A_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A_1),zero_zero(int))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),A_1)) -> hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_1),B) = A_1))) # label(fact_665_mod__neg__neg__trivial) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.64 786 (all A_1 all 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_eq(int),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_1),B)),zero_zero(int))) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_1),B))))) # label(fact_666_neg__mod__conj) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.64 787 (all A_1 all 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_eq(int),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_1),B)),zero_zero(int))))) # label(fact_667_neg__mod__sign) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.64 788 (all B all A_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_1),B)) -> hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_1),B) = A_1))) # label(fact_668_mod__pos__pos__trivial) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.64 789 (all A_1 all 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_eq(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_1),B))) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_1),B)),B)))) # label(fact_669_pos__mod__conj) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.64 790 (all A_1 all 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_eq(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_1),B))))) # label(fact_670_pos__mod__sign) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.64 791 (all B hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),posDivAlg,zero_zero(int)),B) = hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),zero_zero(int)),zero_zero(int))) # label(fact_671_posDivAlg__0) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.64 792 (all X_a (number_ring(X_a) -> (all V all W hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(int,X_a,number_number_of(X_a),V)),hAPP(int,X_a,number_number_of(X_a),W)) = hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),V),hAPP(int,int,uminus_uminus(int),W)))))) # label(fact_672_diff__number__of__eq) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.64 793 (all M_1 all N_1 (hAPP(int,int,hAPP(int,fun(int,int),times_times(int),M_1),N_1) = one_one(int) -> M_1 = one_one(int) | M_1 = hAPP(int,int,number_number_of(int),min))) # label(fact_673_pos__zmult__eq__1__iff__lemma) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.64 794 (all M all N (hAPP(int,int,hAPP(int,fun(int,int),times_times(int),M),N) = one_one(int) <-> M = one_one(int) & N = one_one(int) | M = hAPP(int,int,number_number_of(int),min) & N = hAPP(int,int,number_number_of(int),min))) # label(fact_674_zmult__eq__1__iff) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.64 795 (all V all W hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,number_number_of(int),V)),hAPP(int,int,number_number_of(int),W)) = hAPP(int,int,number_number_of(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),V),hAPP(int,int,uminus_uminus(int),W)))) # label(fact_675_minus__numeral__code_I6_J) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.64 796 (all A_1 all B all Q_2 all R_4 (hBOOL(hAPP(product_prod(int,int),bool,hAPP(int,fun(product_prod(int,int),bool),hAPP(int,fun(int,fun(product_prod(int,int),bool)),divmod_int_rel,A_1),B),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),Q_2),R_4))) -> (B != zero_zero(int) -> hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_1),B) = R_4))) # label(fact_676_divmod__int__rel__mod) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.64 797 (all Ba all Aa (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Ba),hAPP(int,fun(int,bool),d22set,Aa))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),Ba)))) # label(fact_677_d22set__g__1) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.64 798 (all B all A_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A_1)) -> (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_1),B)),zero_zero(int))) -> hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_1),B) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A_1),B)))) # label(fact_678_mod__pos__neg__trivial) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.64 799 (all X_a (number_ring(X_a) -> (all V all C all W hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(int,X_a,number_number_of(X_a),V)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),C),hAPP(int,X_a,number_number_of(X_a),W))) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),V),hAPP(int,int,uminus_uminus(int),W)))),C)))) # label(fact_679_add__number__of__diff2) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.64 800 (all X_a (ring_char_0(X_a) -> (all Aa (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Aa),ring_1_Ints(X_a))) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),one_one(X_a)),Aa)),Aa) != zero_zero(X_a))))) # label(fact_680_Ints__odd__nonzero) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.64 801 (all A_8 all B_7 all Q_4 all Y (A_8 = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B_7),Q_4)),Y) -> ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B_7)) -> 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(int),Y),B_7))) & (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B_7)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B_7),Y)) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Y),zero_zero(int)))) -> (B_7 != zero_zero(int) -> hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_8),B_7) = Y)))) # label(fact_681_divmod__int__rel__mod__eq) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.64 802 (all Q_2 all B all R_4 all C (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),C)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),R_4)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),R_4),zero_zero(int))) -> 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),B),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),Q_2),C))),R_4)),zero_zero(int))))))) # label(fact_682_zmult2__lemma__aux2) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.64 803 (all Q_2 all B all R_4 all C (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),C)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),R_4)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),R_4),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),C)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),Q_2),C))),R_4))))))) # label(fact_683_zmult2__lemma__aux1) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.64 804 (all Q_2 all B all R_4 all C (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),C)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),R_4)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),R_4),B)) -> 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),B),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),Q_2),C))),R_4)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),C))))))) # label(fact_684_zmult2__lemma__aux4) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.64 805 (all Q_2 all B all R_4 all C (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),C)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),R_4)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),R_4),B)) -> 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),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),Q_2),C))),R_4))))))) # label(fact_685_zmult2__lemma__aux3) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.64 806 (all M_6 all D_4 (hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),M_6),D_4) = zero_zero(int) -> (exists Q_3 M_6 = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),D_4),Q_3)))) # label(fact_686_zmod__eq__0D) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.64 807 (all K_4 all L_4 ((L_4 = zero_zero(int) -> hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),pdivmod,K_4),L_4) = hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),zero_zero(int)),hAPP(int,int,abs_abs(int),K_4))) & (L_4 != zero_zero(int) -> hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),pdivmod,K_4),L_4) = hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),posDivAlg,hAPP(int,int,abs_abs(int),K_4)),hAPP(int,int,abs_abs(int),L_4))))) # label(fact_687_pdivmod__posDivAlg) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.64 808 (all K_4 all L_4 ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),L_4)) -> hAPP(int,int,hAPP(int,fun(int,int),z3mod,K_4),L_4) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),K_4),L_4)) & (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),L_4)) -> hAPP(int,int,hAPP(int,fun(int,int),z3mod,K_4),L_4) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),K_4),hAPP(int,int,uminus_uminus(int),L_4))))) # label(fact_688_z3mod__def) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.64 809 (all M_1 all N_1 all R_5 all S_5 all S_4 all T_7 all T_6 all R_4 ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),R_4),zero_zero(int))) -> hAPP(int,product_prod(int,product_prod(int,int)),hAPP(int,fun(int,product_prod(int,product_prod(int,int))),hAPP(int,fun(int,fun(int,product_prod(int,product_prod(int,int)))),hAPP(int,fun(int,fun(int,fun(int,product_prod(int,product_prod(int,int))))),hAPP(int,fun(int,fun(int,fun(int,fun(int,product_prod(int,product_prod(int,int)))))),hAPP(int,fun(int,fun(int,fun(int,fun(int,fun(int,product_prod(int,product_prod(int,int))))))),hAPP(int,fun(int,fun(int,fun(int,fun(int,fun(int,fun(int,product_prod(int,product_prod(int,int)))))))),hAPP(int,fun(int,fun(int,fun(int,fun(int,fun(int,fun(int,fun(int,product_prod(int,product_prod(int,int))))))))),xzgcda,M_1),N_1),R_5),R_4),S_5),S_4),T_7),T_6) = hAPP(product_prod(int,int),product_prod(int,product_prod(int,int)),hAPP(int,fun(product_prod(int,int),product_prod(int,product_prod(int,int))),product_Pair(int,product_prod(int,int)),R_5),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),S_5),T_7))) & (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),R_4),zero_zero(int))) -> hAPP(int,product_prod(int,product_prod(int,int)),hAPP(int,fun(int,product_prod(int,product_prod(int,int))),hAPP(int,fun(int,fun(int,product_prod(int,product_prod(int,int)))),hAPP(int,fun(int,fun(int,fun(int,product_prod(int,product_prod(int,int))))),hAPP(int,fun(int,fun(int,fun(int,fun(int,product_prod(int,product_prod(int,int)))))),hAPP(int,fun(int,fun(int,fun(int,fun(int,fun(int,product_prod(int,product_prod(int,int))))))),hAPP(int,fun(int,fun(int,fun(int,fun(int,fun(int,fun(int,product_prod(int,product_prod(int,int)))))))),hAPP(int,fun(int,fun(int,fun(int,fun(int,fun(int,fun(int,fun(int,product_prod(int,product_prod(int,int))))))))),xzgcda,M_1),N_1),R_5),R_4),S_5),S_4),T_7),T_6) = hAPP(int,product_prod(int,product_prod(int,int)),hAPP(int,fun(int,product_prod(int,product_prod(int,int))),hAPP(int,fun(int,fun(int,product_prod(int,product_prod(int,int)))),hAPP(int,fun(int,fun(int,fun(int,product_prod(int,product_prod(int,int))))),hAPP(int,fun(int,fun(int,fun(int,fun(int,product_prod(int,product_prod(int,int)))))),hAPP(int,fun(int,fun(int,fun(int,fun(int,fun(int,product_prod(int,product_prod(int,int))))))),hAPP(int,fun(int,fun(int,fun(int,fun(int,fun(int,fun(int,product_prod(int,product_prod(int,int)))))))),hAPP(int,fun(int,fun(int,fun(int,fun(int,fun(int,fun(int,fun(int,product_prod(int,product_prod(int,int))))))))),xzgcda,M_1),N_1),R_4),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),R_5),R_4)),S_4),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),S_5),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),R_5),R_4)),S_4))),T_6),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),T_7),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),R_5),R_4)),T_6)))))) # label(fact_689_xzgcda_Osimps) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.64 810 (all K all F all N ((all I_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),N)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(nat,int,F,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_2),one_one(nat)))),hAPP(nat,int,F,I_2)))),one_one(int))))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,F,zero_zero(nat))),K)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),K),hAPP(nat,int,F,N))) -> (exists I_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_2),N)) & hAPP(nat,int,F,I_2) = K)))))) # label(fact_690_nat0__intermed__int__val) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.64 811 (all K all F all N ((all I_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),N)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(nat,int,F,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_2),one_one(nat)))),hAPP(nat,int,F,I_2)))),one_one(int))))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,F,zero_zero(nat))),K)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),K),hAPP(nat,int,F,N))) -> (exists I_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_2),N)) & hAPP(nat,int,F,I_2) = K)))))) # label(fact_691_int__val__lemma) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.64 812 (all K all F all N all M ((all I_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),I_2)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),N)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(nat,int,F,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_2),one_one(nat)))),hAPP(nat,int,F,I_2)))),one_one(int))))) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,F,M)),K)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),K),hAPP(nat,int,F,N))) -> (exists I_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),I_2)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_2),N)) & hAPP(nat,int,F,I_2) = K))))))) # label(fact_692_nat__intermed__int__val) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.64 813 (all B hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),negDivAlg,hAPP(int,int,number_number_of(int),min)),B) = hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),hAPP(int,int,number_number_of(int),min)),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),B),one_one(int)))) # label(fact_693_negDivAlg__minus1) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.64 814 (all C all A_1 all B all Q_2 all R_4 (hBOOL(hAPP(product_prod(int,int),bool,hAPP(int,fun(product_prod(int,int),bool),hAPP(int,fun(int,fun(product_prod(int,int),bool)),divmod_int_rel,A_1),B),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),Q_2),R_4))) -> (B != zero_zero(int) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),C)) -> hBOOL(hAPP(product_prod(int,int),bool,hAPP(int,fun(product_prod(int,int),bool),hAPP(int,fun(int,fun(product_prod(int,int),bool)),divmod_int_rel,A_1),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),C)),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),Q_2),C)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),Q_2),C))),R_4)))))))) # label(fact_694_zmult2__lemma) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.64 815 (all X_1 (-hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),X_1),X_1))) <-> X_1 = zero_zero(real))) # label(fact_695_not__real__square__gt__zero) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.64 816 (all M_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),M_1),N_1)),N_1)))) # label(fact_696_mod__le__divisor) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.64 817 (all M all D_1 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),M),D_1) = zero_zero(nat) <-> (exists Q_3 M = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),D_1),Q_3)))) # label(fact_697_mod__eq__0__iff) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.64 818 (all N_1 all M_1 ((M_1 = zero_zero(nat) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),N_1) = zero_zero(nat)) & (M_1 != zero_zero(nat) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),N_1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),one_one(nat))),N_1))))) # label(fact_698_mult__eq__if) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.64 819 (all M_1 all N_1 ((hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_1)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),M_1),N_1) = M_1) & (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_1)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),M_1),N_1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),N_1)),N_1)))) # label(fact_699_mod__if) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.64 820 (all M_1 all N_1 (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_1)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),M_1),N_1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),N_1)),N_1))) # label(fact_700_mod__geq) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.64 821 (all M_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),M_1),N_1)),N_1)))) # label(fact_701_mod__less__divisor) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.64 822 (all M_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_1)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),M_1),N_1) = M_1)) # label(fact_702_mod__less) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.64 823 (all Q_2 all R_4 all B all C (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),R_4),B)) -> 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),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),Q_2),C))),R_4)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),C)))))) # label(fact_703_mod__lemma) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.64 824 (all P_1 all N all K (hBOOL(hAPP(nat,bool,P_1,hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),N),K))) <-> (K = zero_zero(nat) -> hBOOL(hAPP(nat,bool,P_1,N))) & (K != zero_zero(nat) -> (all I_2 all J_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),J_1),K)) -> (N = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),I_2)),J_1) -> hBOOL(hAPP(nat,bool,P_1,J_1)))))))) # label(fact_704_split__mod) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.64 825 (all R_4 ((hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),R_4),zero_zero(real))) -> hAPP(real,real,abs_abs(real),R_4) = hAPP(real,real,uminus_uminus(real),R_4)) & (-hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),R_4),zero_zero(real))) -> hAPP(real,real,abs_abs(real),R_4) = R_4))) # label(fact_705_real__abs__def) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.64 826 (all A_1 ((hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A_1),zero_zero(real))) -> hAPP(real,real,abs_abs(real),A_1) = hAPP(real,real,uminus_uminus(real),A_1)) & (-hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A_1),zero_zero(real))) -> hAPP(real,real,abs_abs(real),A_1) = A_1))) # label(fact_706_abs__real__def) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.64 827 (all K_4 all N_1 all M_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_4),N_1)),M_1)),N_1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),M_1),N_1)) # label(fact_707_mod__mult__self3) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.64 828 (all N_1 all M_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_1),M_1)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),M_1),N_1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),N_1)),N_1))) # label(fact_708_le__mod__geq) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.64 829 (all M_1 all N_1 hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),M_1),N_1)),M_1))) # label(fact_709_mod__less__eq__dividend) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.64 830 (all X all Y all L_4 all M_1 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),Y)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,uminus_uminus(real),L_4)),hAPP(real,real,uminus_uminus(real),M_1))))),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),hAPP(real,real,uminus_uminus(real),L_4)))),hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),Y),hAPP(real,real,uminus_uminus(real),M_1))))))) # label(fact_710_abs__sum__triangle__ineq) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.64 831 (all X_1 all R_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),X_1)),R_1)) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,uminus_uminus(real),R_1)),X_1)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_1),R_1)))) # label(fact_711_abs__le__interval__iff) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.64 832 (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_712_termination__basic__simps_I3_J) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.64 833 (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_713_termination__basic__simps_I4_J) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.64 834 (all R_4 all S_4 hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),R_4),S_4) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),R_4),hAPP(real,real,uminus_uminus(real),S_4))) # label(fact_714_real__diff__def) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.64 835 (all X all Y hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),X),Y) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),hAPP(real,real,uminus_uminus(real),Y))) # label(fact_715_minus__real__def) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.64 836 (all X all Y hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),hAPP(real,real,uminus_uminus(real),Y))) = hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),Y),hAPP(real,real,uminus_uminus(real),X)))) # label(fact_716_abs__minus__add__cancel) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.64 837 (all X -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,abs_abs(real),X)),one_one(real))),X))) # label(fact_717_abs__add__one__not__less__self) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.64 838 (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_718_termination__basic__simps_I5_J) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.64 839 (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_719_termination__basic__simps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.64 840 (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_720_termination__basic__simps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.64 841 (all B hAPP(int,int,hAPP(int,fun(int,int),div_div(int),zero_zero(int)),B) = zero_zero(int)) # label(fact_721_zdiv__zero) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.64 842 (all X hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),one_one(real)),hAPP(real,real,abs_abs(real),X))))) # label(fact_722_abs__add__one__gt__zero) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.64 843 (all X_1 all Y_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X_1),Y_1))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,uminus_uminus(real),X_1)),Y_1)))) # label(fact_723_real__0__less__add__iff) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.64 844 (all X_1 all Y_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X_1),Y_1)),zero_zero(real))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),Y_1),hAPP(real,real,uminus_uminus(real),X_1))))) # label(fact_724_real__add__less__0__iff) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.64 845 (all X_1 all Y_1 (hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X_1),Y_1) = zero_zero(real) <-> Y_1 = hAPP(real,real,uminus_uminus(real),X_1))) # label(fact_725_real__add__eq__0__iff) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.64 846 (all X_1 all Aa (hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X_1),hAPP(real,real,uminus_uminus(real),Aa)) = zero_zero(real) <-> X_1 = Aa)) # label(fact_726_real__add__minus__iff) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.64 847 (all A_1 all B hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_1),hAPP(int,int,uminus_uminus(int),B)) = hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,uminus_uminus(int),A_1)),B)) # label(fact_727_zdiv__zminus2) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.64 848 (all A_1 all B hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,uminus_uminus(int),A_1)),hAPP(int,int,uminus_uminus(int),B)) = hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_1),B)) # label(fact_728_zdiv__zminus__zminus) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.64 849 (all X_a (semiring_div(X_a) -> (all A_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),A_1),zero_zero(X_a)) = zero_zero(X_a)))) # label(fact_729_div__by__0) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.64 850 (all X_a (semiring_div(X_a) -> (all A_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),zero_zero(X_a)),A_1) = zero_zero(X_a)))) # label(fact_730_div__0) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.64 851 (all X_a (semiring_div(X_a) -> (all A_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),A_1),one_one(X_a)) = ti(X_a,A_1)))) # label(fact_731_div__by__1) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.64 852 (all B all A_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_1),zero_zero(int))) -> (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),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_1),B)),zero_zero(int)))))) # label(fact_732_div__neg__pos__less0) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.64 853 (all Aa all Ba (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Ba),zero_zero(int))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),Aa),Ba)),zero_zero(int))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),Aa))))) # label(fact_733_neg__imp__zdiv__neg__iff) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.64 854 (all Aa all Ba (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),Ba)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),Aa),Ba)),zero_zero(int))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Aa),zero_zero(int)))))) # label(fact_734_pos__imp__zdiv__neg__iff) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.64 855 (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),div_div(int),X),Y)))))) # label(fact_735_Divides_Otransfer__nat__int__function__closures_I1_J) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.64 856 (all A_1 (A_1 != zero_zero(int) -> hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_1),A_1) = one_one(int))) # label(fact_736_zdiv__self) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.64 857 (all A_1 all B hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_1),B)),B) = zero_zero(int)) # label(fact_737_zmod__zdiv__trivial) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.64 858 (all A_1 (hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_1),zero_zero(int)) = zero_zero(int) & hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_1),zero_zero(int)) = A_1)) # label(fact_738_DIVISION__BY__ZERO) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.64 859 (all X_1 all Y_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X_1),Y_1)),zero_zero(real))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),Y_1),hAPP(real,real,uminus_uminus(real),X_1))))) # label(fact_739_real__add__le__0__iff) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.64 860 (all X_1 all Y_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X_1),Y_1))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,uminus_uminus(real),X_1)),Y_1)))) # label(fact_740_real__0__le__add__iff) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.64 861 (all U all X hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),U),U))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),X),X)))) # label(fact_741_real__minus__mult__self__le) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.64 862 (all A_1 all B all C hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A_1),B)),C) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_1),C)),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),B),C))),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_1),C)),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),B),C))),C))) # label(fact_742_zdiv__zadd1__eq) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.64 863 (all K_4 all L_4 hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),pdivmod,K_4),L_4) = hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,abs_abs(int),K_4)),hAPP(int,int,abs_abs(int),L_4))),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,abs_abs(int),K_4)),hAPP(int,int,abs_abs(int),L_4)))) # label(fact_743_pdivmod__def) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.64 864 (all X_a (semiring_div(X_a) -> (all A_1 all B all C ((ti(X_a,C) = zero_zero(X_a) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(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)) = zero_zero(X_a)) & (ti(X_a,C) != zero_zero(X_a) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(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)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),A_1),B)))))) # label(fact_744_div__mult__mult1__if) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.64 865 (all X_a (semiring_div(X_a) -> (all A_1 all B (ti(X_a,B) != zero_zero(X_a) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)),B) = ti(X_a,A_1))))) # label(fact_745_div__mult__self2__is__id) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.64 866 (all X_a (semiring_div(X_a) -> (all A_1 all B (ti(X_a,B) != zero_zero(X_a) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),A_1)),B) = ti(X_a,A_1))))) # label(fact_746_div__mult__self1__is__id) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.64 867 (all X_a (semiring_div(X_a) -> (all A_1 all B all C (ti(X_a,C) != zero_zero(X_a) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(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)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),A_1),B))))) # label(fact_747_div__mult__mult2) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.64 868 (all X_a (semiring_div(X_a) -> (all A_1 all B all C (ti(X_a,C) != zero_zero(X_a) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(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)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),A_1),B))))) # label(fact_748_div__mult__mult1) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.64 869 (all X_a (semiring_div(X_a) -> (all A_1 (ti(X_a,A_1) != zero_zero(X_a) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),A_1),A_1) = one_one(X_a))))) # label(fact_749_div__self) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.64 870 (all X_a (semiring_div(X_a) -> (all A_1 all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),A_1),B)),B) = zero_zero(X_a)))) # label(fact_750_mod__div__trivial) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.64 871 (all L_4 all K_4 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K_4),zero_zero(int))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),L_4)) -> hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),negDivAlg,K_4),L_4) = hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),K_4),L_4)),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),K_4),L_4))))) # label(fact_751_negDivAlg__div__mod) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.64 872 (all I all K (hAPP(int,int,hAPP(int,fun(int,int),div_div(int),I),K) = zero_zero(int) <-> K = zero_zero(int) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),I)) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),I),K)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),I),zero_zero(int))) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),I)))) # label(fact_752_zdiv__eq__0__iff) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.64 873 (all Aa all Ba (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),Ba)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),Aa),Ba))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Aa))))) # label(fact_753_pos__imp__zdiv__nonneg__iff) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.64 874 (all I all K (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),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),I),K))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),K),I))))) # label(fact_754_pos__imp__zdiv__pos__iff) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.64 875 (all Ba all Aa (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Aa)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),Aa),Ba))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Ba),Aa)) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),Ba))))) # label(fact_755_nonneg1__imp__zdiv__pos__iff) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.64 876 (all B all B_4 all A_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B_4)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B_4),B)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_1),B)),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_1),B_4))))))) # label(fact_756_zdiv__mono2) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.64 877 (all B all A_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A_1)) -> (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_eq(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_1),B)),zero_zero(int)))))) # label(fact_757_div__nonneg__neg__le0) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.64 878 (all B all A_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_1),B)) -> hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_1),B) = zero_zero(int)))) # label(fact_758_div__pos__pos__trivial) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.64 879 (all Aa all Ba (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Ba),zero_zero(int))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),Aa),Ba))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Aa),zero_zero(int)))))) # label(fact_759_neg__imp__zdiv__nonneg__iff) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.64 880 (all B all A_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A_1),zero_zero(int))) -> (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_eq(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_1),B)),zero_zero(int)))))) # label(fact_760_div__nonpos__pos__le0) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.64 881 (all B all B_4 all A_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_1),zero_zero(int))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B_4)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B_4),B)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_1),B_4)),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_1),B))))))) # label(fact_761_zdiv__mono2__neg) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.64 882 (all B all A_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A_1),zero_zero(int))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),A_1)) -> hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_1),B) = zero_zero(int)))) # label(fact_762_div__neg__neg__trivial) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.64 883 (all B all A_1 all A_5 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A_1),A_5)) -> (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_eq(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_1),B)),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_5),B)))))) # label(fact_763_zdiv__mono1) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.64 884 (all B all A_1 all A_5 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A_1),A_5)) -> (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_eq(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_5),B)),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_1),B)))))) # label(fact_764_zdiv__mono1__neg) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.64 885 (all K_4 all X (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),X)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),K_4)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),X),K_4)),X))))) # label(fact_765_int__div__less__self) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.64 886 (all A_1 all B all C (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),C)) -> hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_1),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),C)) = hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_1),B)),C))) # label(fact_766_zdiv__zmult2__eq) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.64 887 (all X all Y all Z (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),Z)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Y),Z))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),X),Z)),Y))))) # label(fact_767_div__prop1) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.64 888 (all A_1 all B A_1 = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_1),B))),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_1),B))) # label(fact_768_zmod__zdiv__equality) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.64 889 (all A_1 all B all C hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),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_1),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),B),C))),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),B),C))),C))) # label(fact_769_zdiv__zmult1__eq) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.64 890 (all B all A_1 all K_4 hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_1),B))),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_1),B))),K_4) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A_1),K_4)) # label(fact_770_zdiv__zmod__equality) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.64 891 (all A_1 all B all K_4 hAPP(int,int,hAPP(int,fun(int,int),plus_plus(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),div_div(int),A_1),B)),B)),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_1),B))),K_4) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A_1),K_4)) # label(fact_771_zdiv__zmod__equality2) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.64 892 (all M_1 all N_1 hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),M_1),N_1) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),M_1),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),M_1),N_1)),N_1))) # label(fact_772_zmod__zdiv__equality_H) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.64 893 (all N_1 all M_1 hAPP(int,int,hAPP(int,fun(int,int),times_times(int),N_1),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),M_1),N_1)) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),M_1),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),M_1),N_1))) # label(fact_773_zmult__div__cancel) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.64 894 (all A_1 hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_1),hAPP(int,int,number_number_of(int),min)) = hAPP(int,int,uminus_uminus(int),A_1)) # label(fact_774_zdiv__minus1__right) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.64 895 (all X_a (semiring_div(X_a) -> (all A_1 all C all B (ti(X_a,B) != zero_zero(X_a) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),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),times_times(X_a),B),C))),B) = 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),div_div(X_a),A_1),B)))))) # label(fact_775_div__mult__self2) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.64 896 (all X_a (semiring_div(X_a) -> (all A_1 all C all B (ti(X_a,B) != zero_zero(X_a) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),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),times_times(X_a),C),B))),B) = 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),div_div(X_a),A_1),B)))))) # label(fact_776_div__mult__self1) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.64 897 (all A_1 all B all Q_2 all R_4 (hBOOL(hAPP(product_prod(int,int),bool,hAPP(int,fun(product_prod(int,int),bool),hAPP(int,fun(int,fun(product_prod(int,int),bool)),divmod_int_rel,A_1),B),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),Q_2),R_4))) -> (B != zero_zero(int) -> hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_1),B) = Q_2))) # label(fact_777_divmod__int__rel__div) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.64 898 (all X_a (semiring_div(X_a) -> (all A_1 all B (ti(X_a,B) != zero_zero(X_a) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)),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),div_div(X_a),A_1),B)),one_one(X_a)))))) # label(fact_778_div__add__self2) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.64 899 (all X_a (semiring_div(X_a) -> (all A_1 all B (ti(X_a,B) != zero_zero(X_a) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B),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,hAPP(X_a,fun(X_a,X_a),div_div(X_a),A_1),B)),one_one(X_a)))))) # label(fact_779_div__add__self1) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.64 900 (all X_a (semiring_div(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),div_mod(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,hAPP(X_a,fun(X_a,X_a),div_div(X_a),A_1),B)),B)) = ti(X_a,A_1)))) # label(fact_780_semiring__div__class_Omod__div__equality_H) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.64 901 (all X_a (semiring_div(X_a) -> (all B all A_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),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),A_1),B))),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),A_1),B)) = ti(X_a,A_1)))) # label(fact_781_mod__div__equality2) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.65 902 (all X_a (semiring_div(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),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),A_1),B)),B)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),A_1),B)) = ti(X_a,A_1)))) # label(fact_782_mod__div__equality) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.65 903 (all X_a (semiring_div(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),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),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),A_1),B))),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(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),C)))) # label(fact_783_div__mod__equality2) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.65 904 (all X_a (semiring_div(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),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),div_div(X_a),A_1),B)),B)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(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),C)))) # label(fact_784_div__mod__equality) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.65 905 (all X all Y (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),Y)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Y),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),X),Y))),X)))) # label(fact_785_zdiv__leq__prop) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.65 906 (all B (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B)) -> hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,number_number_of(int),min)),B) = hAPP(int,int,number_number_of(int),min))) # label(fact_786_div__eq__minus1) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.65 907 (all A_1 all B all M_1 hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A_1),B) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),M_1),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_1),M_1)),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),B),M_1)))),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_1),M_1)),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),B),M_1)))) # label(fact_787_zcong__zmod__aux) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.65 908 (all R_4 all S_4 all T_6 all R_5 all S_5 all M_1 all T_7 all N_1 (R_5 = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),S_5),M_1)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),T_7),N_1)) -> (R_4 = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),S_4),M_1)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),T_6),N_1)) -> hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),R_5),R_4) = 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),S_5),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),R_5),R_4)),S_4))),M_1)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),T_7),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),R_5),R_4)),T_6))),N_1))))) # label(fact_788_xzgcda__linear__aux2) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.65 909 (all A_1 all B (B != zero_zero(int) -> hBOOL(hAPP(product_prod(int,int),bool,hAPP(int,fun(product_prod(int,int),bool),hAPP(int,fun(int,fun(product_prod(int,int),bool)),divmod_int_rel,A_1),B),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_1),B)),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_1),B)))))) # label(fact_789_divmod__int__rel__div__mod) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.65 910 (all B all A_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_1),zero_zero(int))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B)) -> hBOOL(hAPP(product_prod(int,int),bool,hAPP(int,fun(product_prod(int,int),bool),hAPP(int,fun(int,fun(product_prod(int,int),bool)),divmod_int_rel,A_1),B),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),negDivAlg,A_1),B)))))) # label(fact_790_negDivAlg__correct) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.65 911 (all P_1 all N all K (hBOOL(hAPP(int,bool,P_1,hAPP(int,int,hAPP(int,fun(int,int),div_div(int),N),K))) <-> (K = zero_zero(int) -> hBOOL(hAPP(int,bool,P_1,zero_zero(int)))) & (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),K)) -> (all I_2 all J_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),J_1)) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),J_1),K)) & N = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K),I_2)),J_1) -> hBOOL(hAPP(int,bool,P_1,I_2))))) & (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),zero_zero(int))) -> (all I_2 all J_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),J_1)) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),J_1),zero_zero(int))) & N = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K),I_2)),J_1) -> hBOOL(hAPP(int,bool,P_1,I_2))))))) # label(fact_791_split__zdiv) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.65 912 (all A_8 all B_7 all Y all R_6 (A_8 = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B_7),Y)),R_6) -> ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B_7)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),R_6)) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),R_6),B_7))) & (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B_7)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B_7),R_6)) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),R_6),zero_zero(int)))) -> (B_7 != zero_zero(int) -> hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_8),B_7) = Y)))) # label(fact_792_divmod__int__rel__div__eq) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.65 913 (all X all Y all Z (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),Z)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Y),Z)),Z))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),X),Z)),Y))))) # label(fact_793_div__prop2) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.65 914 (all A_1 all B all C (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),C)) -> hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_1),hAPP(int,int,hAPP(int,fun(int,int),times_times(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),B),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_1),B)),C))),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_1),B)))) # label(fact_794_zmod__zmult2__eq) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.65 915 (all A_1 all B (B != zero_zero(int) -> (hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_1),B) = zero_zero(int) -> hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_1),hAPP(int,int,uminus_uminus(int),B)) = hAPP(int,int,uminus_uminus(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_1),B))) & (hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_1),B) != zero_zero(int) -> hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_1),hAPP(int,int,uminus_uminus(int),B)) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,uminus_uminus(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_1),B))),one_one(int))))) # label(fact_795_zdiv__zminus2__eq__if) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.65 916 (all A_1 all B (B != zero_zero(int) -> (hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_1),B) = zero_zero(int) -> hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,uminus_uminus(int),A_1)),B) = hAPP(int,int,uminus_uminus(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_1),B))) & (hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_1),B) != zero_zero(int) -> hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,uminus_uminus(int),A_1)),B) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,uminus_uminus(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_1),B))),one_one(int))))) # label(fact_796_zdiv__zminus1__eq__if) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.65 917 (all B all Bq all Br all A_1 all C all Aq all Ar (hBOOL(hAPP(product_prod(int,int),bool,hAPP(int,fun(product_prod(int,int),bool),hAPP(int,fun(int,fun(product_prod(int,int),bool)),divmod_int_rel,A_1),C),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),Aq),Ar))) -> (hBOOL(hAPP(product_prod(int,int),bool,hAPP(int,fun(product_prod(int,int),bool),hAPP(int,fun(int,fun(product_prod(int,int),bool)),divmod_int_rel,B),C),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),Bq),Br))) -> (C != zero_zero(int) -> hBOOL(hAPP(product_prod(int,int),bool,hAPP(int,fun(product_prod(int,int),bool),hAPP(int,fun(int,fun(product_prod(int,int),bool)),divmod_int_rel,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A_1),B)),C),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Aq),Bq)),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Ar),Br)),C))),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Ar),Br)),C)))))))) # label(fact_797_zadd1__lemma) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.65 918 (all L_4 all K_4 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),K_4)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),L_4)) -> hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),posDivAlg,K_4),L_4) = hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),K_4),L_4)),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),K_4),L_4))))) # label(fact_798_posDivAlg__div__mod) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.65 919 (all B all A_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A_1)) -> (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_1),B)),zero_zero(int))) -> hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_1),B) = hAPP(int,int,number_number_of(int),min)))) # label(fact_799_div__pos__neg__trivial) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.65 920 (all P_1 all N all K (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),P_1,hAPP(int,int,hAPP(int,fun(int,int),div_div(int),N),K)),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),N),K))) <-> (all I_2 all J_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),J_1)) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),J_1),K)) & N = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K),I_2)),J_1) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),P_1,I_2),J_1))))))) # label(fact_800_split__pos__lemma) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.65 921 (all P_1 all N all K (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),zero_zero(int))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),P_1,hAPP(int,int,hAPP(int,fun(int,int),div_div(int),N),K)),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),N),K))) <-> (all I_2 all J_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),J_1)) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),J_1),zero_zero(int))) & N = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K),I_2)),J_1) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),P_1,I_2),J_1))))))) # label(fact_801_split__neg__lemma) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.65 922 (all A_1 all B all C all Q_2 all R_4 (hBOOL(hAPP(product_prod(int,int),bool,hAPP(int,fun(product_prod(int,int),bool),hAPP(int,fun(int,fun(product_prod(int,int),bool)),divmod_int_rel,B),C),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),Q_2),R_4))) -> (C != zero_zero(int) -> hBOOL(hAPP(product_prod(int,int),bool,hAPP(int,fun(product_prod(int,int),bool),hAPP(int,fun(int,fun(product_prod(int,int),bool)),divmod_int_rel,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),B)),C),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),Q_2)),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),R_4)),C))),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),R_4)),C))))))) # label(fact_802_zmult1__lemma) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.65 923 (all K_4 all L_4 ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),L_4)) -> hAPP(int,int,hAPP(int,fun(int,int),z3div,K_4),L_4) = hAPP(int,int,hAPP(int,fun(int,int),div_div(int),K_4),L_4)) & (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),L_4)) -> hAPP(int,int,hAPP(int,fun(int,int),z3div,K_4),L_4) = hAPP(int,int,uminus_uminus(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),K_4),hAPP(int,int,uminus_uminus(int),L_4)))))) # label(fact_803_z3div__def) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.65 924 (all N_1 hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),N_1))) # label(fact_804_le0) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.65 925 (all N_1 -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),zero_zero(nat)))) # label(fact_805_less__zeroE) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.65 926 (all X_a (semiring_div(X_a) -> (all A_1 all B ti(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,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),div_div(X_a),A_1),B)),B)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),A_1),B))))) # label(fact_806_mod__div__decomp) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.65 927 (all U all V all X all Y (X = Y -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),U)),V)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),U)),Y))),V))))) # label(fact_807_sin__bound__lemma) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.65 928 (all U_1 all M all N 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(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))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(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)))))) # label(fact_808_nat__less__add__iff2) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.65 929 (all U_1 all M all N all J all I (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),J),I)) -> (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),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))) <-> 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),J)),U_1)),M)),N))))) # label(fact_809_nat__less__add__iff1) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.65 930 (all X all Y all C (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),C),zero_zero(real))) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),X)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),hAPP(real,real,abs_abs(real),Y)))) -> X = zero_zero(real)))) # label(fact_810_rabs__ratiotest__lemma) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.65 931 (all K all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),N))) <-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N))))) # label(fact_811_mult__le__cancel1) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.65 932 (all M_1 all N_1 all K_4 ((K_4 = zero_zero(nat) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_4),M_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_4),N_1)) = zero_zero(nat)) & (K_4 != zero_zero(nat) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_4),M_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_4),N_1)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),M_1),N_1)))) # label(fact_812_nat__mult__div__cancel__disj) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.65 933 (all A_1 all B all C hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),A_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),C)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),A_1),B)),C)) # label(fact_813_div__mult2__eq) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.65 934 (all K_4 all M_1 all N_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_4),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),M_1),N_1)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_4),M_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_4),N_1))) # label(fact_814_mod__mult__distrib2) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.65 935 (all M_1 all N_1 all K_4 hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),M_1),N_1)),K_4) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),K_4)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N_1),K_4))) # label(fact_815_mod__mult__distrib) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.65 936 (all M_1 all N_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),M_1),N_1)),N_1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),M_1),N_1))) # label(fact_816_div__mod__equality_H) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.65 937 (all N_1 all M_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),M_1),N_1)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),M_1),N_1))) # label(fact_817_mult__div__cancel) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.65 938 (all M_1 all N_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),M_1),N_1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),M_1),N_1)),N_1))) # label(fact_818_Divides_Omod__div__equality_H) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.65 939 (all K_4 all M_1 all N_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_4),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),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_4),M_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_4),N_1))) # label(fact_819_diff__mult__distrib2) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.65 940 (all M_1 all N_1 all K_4 hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),N_1)),K_4) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),K_4)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N_1),K_4))) # label(fact_820_diff__mult__distrib) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.65 941 (all I_1 all J_2 all K_4 hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I_1),J_2)),K_4) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I_1),K_4)),J_2)) # label(fact_821_diff__commute) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.65 942 (all M_1 all N_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),N_1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N_1),M_1)) # label(fact_822_nat__mult__commute) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.65 943 (all M_1 all N_1 all K_4 hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),N_1)),K_4) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N_1),K_4))) # label(fact_823_nat__mult__assoc) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.65 944 (all A_1 all B all C hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A_1),B)),C) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),A_1),C)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),B),C))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),A_1),C)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),B),C))),C))) # label(fact_824_div__add1__eq) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.65 945 (all A_1 all B all C hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A_1),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_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),B),C))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),B),C))),C))) # label(fact_825_div__mult1__eq) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.65 946 (all A_1 all B all C hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),A_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(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),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),A_1),B)),C))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),A_1),B))) # label(fact_826_mod__mult2__eq) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.65 947 (all K_4 all M_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),N_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),M_1),K_4)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),N_1),K_4))))) # label(fact_827_div__le__mono) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.65 948 (all M_1 all N_1 hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),M_1),N_1)),M_1))) # label(fact_828_div__le__dividend) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.65 949 (all M_1 all N_1 all K_4 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K_4)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_4),M_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_4),N_1)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),M_1),N_1))) # label(fact_829_nat__mult__div__cancel1) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.65 950 (all M_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),N_1)),N_1) = M_1)) # label(fact_830_div__mult__self__is__m) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.65 951 (all M_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N_1),M_1)),N_1) = M_1)) # label(fact_831_div__mult__self1__is__m) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.65 952 (all M_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_1)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),M_1),N_1) = zero_zero(nat))) # label(fact_832_div__less) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.65 953 (all P_1 all N all K (hBOOL(hAPP(nat,bool,P_1,hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),N),K))) <-> (K = zero_zero(nat) -> hBOOL(hAPP(nat,bool,P_1,zero_zero(nat)))) & (K != zero_zero(nat) -> (all I_2 all J_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),J_1),K)) -> (N = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),I_2)),J_1) -> hBOOL(hAPP(nat,bool,P_1,I_2)))))))) # label(fact_833_split__div) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.65 954 (all K_4 all N_1 all M_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),M_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),N_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),K_4),N_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),K_4),M_1)))))) # label(fact_834_div__le__mono2) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.65 955 (all M_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),one_one(nat)),N_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),M_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),M_1),N_1)),M_1))))) # label(fact_835_div__less__dividend) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.65 956 (all N_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),zero_zero(nat)),N_1) = zero_zero(nat)) # label(fact_836_mult__0) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.65 957 (all M_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),zero_zero(nat)) = zero_zero(nat)) # label(fact_837_mult__0__right) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.65 958 (all M all N (hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),N) = zero_zero(nat) <-> M = zero_zero(nat) | N = zero_zero(nat))) # label(fact_838_mult__is__0) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.65 959 (all K all M all N (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) <-> K = zero_zero(nat) | M = N)) # label(fact_839_nat__mult__eq__cancel__disj) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.65 960 (all K all M all N (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) <-> M = N | K = zero_zero(nat))) # label(fact_840_mult__cancel1) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.65 961 (all M all K all N (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),K) <-> M = N | K = zero_zero(nat))) # label(fact_841_mult__cancel2) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.65 962 (all M_1 all N_1 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),N_1) = zero_zero(nat) -> (hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),M_1) = zero_zero(nat) -> M_1 = N_1))) # label(fact_842_diffs0__imp__equal) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.65 963 (all M_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),M_1) = zero_zero(nat)) # label(fact_843_diff__self__eq__0) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.65 964 (all M_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),zero_zero(nat)) = M_1) # label(fact_844_minus__nat_Odiff__0) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.65 965 (all N_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),zero_zero(nat)),N_1) = zero_zero(nat)) # label(fact_845_diff__0__eq__0) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.65 966 (all P_1 all M all N ((hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),P_1,N),M))) -> ((M = N -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),P_1,N),M))) -> ((hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),M)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),P_1,N),M))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),P_1,N),M)))))) # label(fact_846_nat__less__cases) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.65 967 (all S_4 all T_6 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),S_4),T_6)) -> S_4 != T_6)) # label(fact_847_less__not__refl3) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.65 968 (all N_1 all M_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),M_1)) -> M_1 != N_1)) # label(fact_848_less__not__refl2) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.65 969 (all N_1 -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),N_1))) # label(fact_849_less__irrefl__nat) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.65 970 (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_850_linorder__neqE__nat) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.65 971 (all M all N (M != N <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),M)))) # label(fact_851_nat__neq__iff) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.65 972 (all N_1 -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),N_1))) # label(fact_852_less__not__refl) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.65 973 (all L_4 all M_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),L_4)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),L_4),N_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),L_4),M_1)))))) # label(fact_853_diff__less__mono2) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.65 974 (all N_1 all J_2 all K_4 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),J_2),K_4)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_2),N_1)),K_4)))) # label(fact_854_less__imp__diff__less) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.65 975 (all M_1 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_1),N_1)),N_1) = M_1) # label(fact_855_diff__add__inverse2) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.65 976 (all N_1 all M_1 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_1)),N_1) = M_1) # label(fact_856_diff__add__inverse) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.65 977 (all I_1 all J_2 all K_4 hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I_1),J_2)),K_4) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J_2),K_4))) # label(fact_857_diff__diff__left) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.65 978 (all K_4 all M_1 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_4),M_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_4),N_1)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),N_1)) # label(fact_858_Nat_Odiff__cancel) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.65 979 (all M_1 all K_4 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_1),K_4)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_1),K_4)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),N_1)) # label(fact_859_diff__cancel2) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.65 980 (all M all K all N (hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),K) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),K) <-> M = N)) # label(fact_860_nat__add__right__cancel) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.65 981 (all K all M all N (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) <-> M = N)) # label(fact_861_nat__add__left__cancel) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.65 982 (all M_1 all N_1 all K_4 hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),N_1)),K_4) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_1),K_4))) # label(fact_862_nat__add__assoc) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.65 983 (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_863_nat__add__left__commute) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.65 984 (all M_1 all N_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),N_1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_1),M_1)) # label(fact_864_nat__add__commute) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.65 985 (all K_4 all M_1 all N_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_4),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),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_4),M_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_4),N_1))) # label(fact_865_add__mult__distrib2) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.65 986 (all M_1 all N_1 all K_4 hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),N_1)),K_4) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),K_4)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N_1),K_4))) # label(fact_866_add__mult__distrib) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.65 987 (all I_1 all U all J_2 all K_4 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)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J_2),U)),K_4)) = 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_1),J_2)),U)),K_4)) # label(fact_867_left__add__mult__distrib) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.65 988 (all M_1 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_1),N_1)),M_1))) # label(fact_868_Nat_Odiff__le__self) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.65 989 (all L_4 all M_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),N_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),L_4),N_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),L_4),M_1))))) # label(fact_869_diff__le__mono2) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.65 990 (all L_4 all M_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),N_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),L_4)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),L_4))))) # label(fact_870_diff__le__mono) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.65 991 (all I_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_1),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_1)) = I_1)) # label(fact_871_diff__diff__cancel) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.65 992 (all N all K all M (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K),M)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K),N)) -> (hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),K) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),K) <-> M = N)))) # label(fact_872_eq__diff__iff) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.65 993 (all N_1 all K_4 all M_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_4),M_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_4),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_1),K_4)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),K_4)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),N_1)))) # label(fact_873_Nat_Odiff__diff__eq) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.65 994 (all N all K all M (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K),M)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K),N)) -> (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),K)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),K))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N)))))) # label(fact_874_le__diff__iff) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.65 995 (all N_1 hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_1),N_1))) # label(fact_875_le__refl) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.65 996 (all M_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),N_1)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_1),M_1)))) # label(fact_876_nat__le__linear) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.65 997 (all M_1 all N_1 (M_1 = N_1 -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),N_1)))) # label(fact_877_eq__imp__le) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.65 998 (all K_4 all I_1 all J_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_1),J_2)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),J_2),K_4)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_1),K_4))))) # label(fact_878_le__trans) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.65 999 (all M_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),N_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_1),M_1)) -> M_1 = N_1))) # label(fact_879_le__antisym) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.65 1000 (all K_4 all L_4 all I_1 all J_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_1),J_2)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_4),L_4)) -> 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_1),K_4)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J_2),L_4)))))) # label(fact_880_mult__le__mono) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.65 1001 (all K_4 all I_1 all J_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_1),J_2)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_4),I_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_4),J_2))))) # label(fact_881_mult__le__mono2) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.65 1002 (all K_4 all I_1 all J_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_1),J_2)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I_1),K_4)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J_2),K_4))))) # label(fact_882_mult__le__mono1) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.65 1003 (all M_1 hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),M_1))))) # label(fact_883_le__cube) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.65 1004 (all M_1 hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),M_1)))) # label(fact_884_le__square) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.65 1005 (all N_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),one_one(nat)),N_1) = N_1) # label(fact_885_nat__mult__1) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.65 1006 (all M all N (one_one(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),N) <-> M = one_one(nat) & N = one_one(nat))) # label(fact_886_nat__1__eq__mult__iff) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.65 1007 (all N_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N_1),one_one(nat)) = N_1) # label(fact_887_nat__mult__1__right) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.65 1008 (all M all N (hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),N) = one_one(nat) <-> M = one_one(nat) & N = one_one(nat))) # label(fact_888_nat__mult__eq__1__iff) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.65 1009 (all M 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),times_times(nat),M),N))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),M)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)))) # label(fact_889_nat__0__less__mult__iff) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.65 1010 (all K all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(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))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N)))) # label(fact_890_mult__less__cancel1) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.65 1011 (all M all K all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(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),K))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N)))) # label(fact_891_mult__less__cancel2) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.65 1012 (all M all N all K (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K)) -> (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) <-> M = N))) # label(fact_892_nat__mult__eq__cancel1) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.65 1013 (all M all N all K (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(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))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N))))) # label(fact_893_nat__mult__less__cancel1) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.65 1014 (all K_4 all I_1 all J_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),J_2)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K_4)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I_1),K_4)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J_2),K_4)))))) # label(fact_894_mult__less__mono1) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.65 1015 (all K_4 all I_1 all J_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),J_2)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K_4)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_4),I_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_4),J_2)))))) # label(fact_895_mult__less__mono2) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.65 1016 (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_896_gr0I) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.65 1017 (all M_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_1)) -> N_1 != zero_zero(nat))) # label(fact_897_gr__implies__not0) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.65 1018 (all N_1 -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),zero_zero(nat)))) # label(fact_898_less__nat__zero__code) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.65 1019 (all N (N != zero_zero(nat) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)))) # label(fact_899_neq0__conv) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.65 1020 (all N_1 -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),zero_zero(nat)))) # label(fact_900_not__less0) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.65 1021 (all M_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),M_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),N_1)),M_1))))) # label(fact_901_diff__less) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.65 1022 (all N all M (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),M))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N)))) # label(fact_902_zero__less__diff) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.65 1023 (all N_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),zero_zero(nat)),N_1) = N_1) # label(fact_903_plus__nat_Oadd__0) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.65 1024 (all M_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),zero_zero(nat)) = M_1) # label(fact_904_Nat_Oadd__0__right) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.65 1025 (all M all N (hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N) = zero_zero(nat) <-> M = zero_zero(nat) & N = zero_zero(nat))) # label(fact_905_add__is__0) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.65 1026 (all M_1 all N_1 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),N_1) = M_1 -> N_1 = zero_zero(nat))) # label(fact_906_add__eq__self__zero) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.65 1027 (all N_1 all M_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_1),M_1)) = zero_zero(nat)) # label(fact_907_diff__add__0) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.65 1028 (all M all N (hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N) = zero_zero(nat) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N)))) # label(fact_908_diff__is__0__eq) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.65 1029 (all M_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),N_1)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),N_1) = zero_zero(nat))) # label(fact_909_diff__is__0__eq_H) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.65 1030 (all N_1 hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),N_1))) # label(fact_910_less__eq__nat_Osimps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.65 1031 (all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N),zero_zero(nat))) <-> N = zero_zero(nat))) # label(fact_911_le__0__eq) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.65 1032 (all I_1 all J_2 -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_1),J_2)),I_1))) # label(fact_912_not__add__less1) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.65 1033 (all J_2 all I_1 -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J_2),I_1)),I_1))) # label(fact_913_not__add__less2) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.65 1034 (all K all M 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),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K),N))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N)))) # label(fact_914_nat__add__left__cancel__less) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.65 1035 (all M_1 all I_1 all J_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),J_2)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J_2),M_1))))) # label(fact_915_trans__less__add1) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.65 1036 (all M_1 all I_1 all J_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),J_2)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),J_2))))) # label(fact_916_trans__less__add2) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.65 1037 (all K_4 all I_1 all J_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),J_2)) -> 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_4)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J_2),K_4))))) # label(fact_917_add__less__mono1) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.65 1038 (all K_4 all L_4 all I_1 all J_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),J_2)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),K_4),L_4)) -> 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_4)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J_2),L_4)))))) # label(fact_918_add__less__mono) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.65 1039 (all M_1 all N_1 all K_4 all L_4 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),K_4),L_4)) -> (hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),L_4) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_4),N_1) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_1))))) # label(fact_919_less__add__eq__less) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.65 1040 (all I_1 all J_2 all K_4 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_1),J_2)),K_4)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),K_4)))) # label(fact_920_add__lessD1) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.65 1041 (all M_1 all N_1 (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_1)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),N_1)) = M_1)) # label(fact_921_add__diff__inverse) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.65 1042 (all I all J all K (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J),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),K)),J)))) # label(fact_922_less__diff__conv) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.65 1043 (all M_1 all N_1 (M_1 = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),N_1) -> N_1 = one_one(nat) | M_1 = zero_zero(nat))) # label(fact_923_mult__eq__self__implies__10) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.65 1044 (all M_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_1)) | M_1 = N_1 -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),N_1)))) # label(fact_924_less__or__eq__imp__le) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.65 1045 (all M_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),N_1)) -> (M_1 != N_1 -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_1))))) # label(fact_925_le__neq__implies__less) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.65 1046 (all M_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),N_1)))) # label(fact_926_less__imp__le__nat) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.65 1047 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N)) | M = N)) # label(fact_927_le__eq__less__or__eq) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.65 1048 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N)) & M != N)) # label(fact_928_nat__less__le) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.65 1049 (all N all K all M (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K),M)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K),N)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),K)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),K))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N)))))) # label(fact_929_less__diff__iff) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.65 1050 (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_930_diff__less__mono) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.65 1051 (all I_1 all K_4 all J_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_4),J_2)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_2),K_4)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_1),K_4)),J_2))) # label(fact_931_diff__diff__right) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.65 1052 (all J all K all I (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),K)),I)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),J),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I),K))))) # label(fact_932_le__diff__conv) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.65 1053 (all M_1 all K_4 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_4),N_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),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_1)),K_4))))) # label(fact_933_le__add__diff) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.65 1054 (all N_1 all M_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_1),M_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_1),N_1)) = M_1)) # label(fact_934_le__add__diff__inverse) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.65 1055 (all I_1 all K_4 all J_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_4),J_2)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_2),K_4)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_1),J_2)),K_4))) # label(fact_935_add__diff__assoc) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.65 1056 (all I all K all J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K),J)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J),K))) <-> 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)),J))))) # label(fact_936_le__diff__conv2) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.65 1057 (all N_1 all M_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_1),M_1)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),N_1)),N_1) = M_1)) # label(fact_937_le__add__diff__inverse2) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.65 1058 (all K 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),J),I) = K <-> J = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K),I)))) # label(fact_938_le__imp__diff__is__add) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.65 1059 (all I_1 all K_4 all J_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_4),J_2)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_1),J_2)),K_4) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_2),K_4)))) # label(fact_939_diff__add__assoc) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.65 1060 (all I_1 all K_4 all J_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_4),J_2)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_2),K_4)),I_1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J_2),I_1)),K_4))) # label(fact_940_add__diff__assoc2) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.65 1061 (all I_1 all K_4 all J_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_4),J_2)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J_2),I_1)),K_4) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_2),K_4)),I_1))) # label(fact_941_diff__add__assoc2) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.65 1062 (all U_1 all M all N 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),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) <-> 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)))) # label(fact_942_nat__eq__add__iff2) # label(axiom) # label(non_clause). [assumption].
% 7.58/7.65 1063 (all U all M_1 all N_1 all I_1 all J_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_1),J_2)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),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_2),U)),N_1)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(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_2),I_1)),U)),N_1)))) # label(fact_943_nat__diff__add__eq2) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.65 1064 (all U_1 all M all N 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),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))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(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)))))) # label(fact_944_nat__le__add__iff2) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.65 1065 (all U_1 all M all N 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),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) <-> 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))) # label(fact_945_nat__eq__add__iff1) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.65 1066 (all U all M_1 all N_1 all J_2 all I_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),J_2),I_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),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_2),U)),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_1),J_2)),U)),M_1)),N_1))) # label(fact_946_nat__diff__add__eq1) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.65 1067 (all U_1 all M all N all J all I (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),J),I)) -> (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),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))) <-> 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),J)),U_1)),M)),N))))) # label(fact_947_nat__le__add__iff1) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.65 1068 (all M_1 all K_4 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_1),K_4)),N_1)) -> -(hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),N_1)) -> -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_4),N_1))))) # label(fact_948_add__leE) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.65 1069 (all M_1 all K_4 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_1),K_4)),N_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),N_1)))) # label(fact_949_add__leD1) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.65 1070 (all M_1 all K_4 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_1),K_4)),N_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_4),N_1)))) # label(fact_950_add__leD2) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.65 1071 (all K_4 all L_4 all I_1 all J_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_1),J_2)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_4),L_4)) -> 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_4)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J_2),L_4)))))) # label(fact_951_add__le__mono) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.66 1072 (all K_4 all I_1 all J_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_1),J_2)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_1),K_4)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J_2),K_4))))) # label(fact_952_add__le__mono1) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.66 1073 (all M_1 all I_1 all J_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_1),J_2)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),J_2))))) # label(fact_953_trans__le__add2) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.66 1074 (all M_1 all I_1 all J_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_1),J_2)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J_2),M_1))))) # label(fact_954_trans__le__add1) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.66 1075 (all K all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K),N))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N)))) # label(fact_955_nat__add__left__cancel__le) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.66 1076 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N)) <-> (exists K_1 N = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),K_1)))) # label(fact_956_le__iff__add) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.66 1077 (all K all L (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K),L)) <-> (exists N_2 L = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K),N_2)))) # label(fact_957_le__Suc__ex__iff) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.66 1078 (all N_1 all M_1 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_1)))) # label(fact_958_le__add1) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.66 1079 (all N_1 all M_1 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_1),N_1)))) # label(fact_959_le__add2) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.66 1080 (all X_1 all Y_1 all Z_1 (X_1 = hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),Y_1),Z_1) <-> Y_1 = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X_1),Z_1))) # label(fact_960_eq__diff__eq_H) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.66 1081 (all M 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),plus_plus(nat),M),N))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),M)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)))) # label(fact_961_add__gr__0) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.66 1082 (all P_1 all Aa all Ba (hBOOL(hAPP(nat,bool,P_1,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),Aa),Ba))) <-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Aa),Ba)) -> hBOOL(hAPP(nat,bool,P_1,zero_zero(nat)))) & (all D_3 (Aa = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Ba),D_3) -> hBOOL(hAPP(nat,bool,P_1,D_3)))))) # label(fact_962_nat__diff__split) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.66 1083 (all P_1 all Aa all Ba (hBOOL(hAPP(nat,bool,P_1,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),Aa),Ba))) <-> -(hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Aa),Ba)) & -hBOOL(hAPP(nat,bool,P_1,zero_zero(nat))) | (exists D_3 (Aa = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Ba),D_3) & -hBOOL(hAPP(nat,bool,P_1,D_3))))))) # label(fact_963_nat__diff__split__asm) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.66 1084 (all M all N all K (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K)) -> (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),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),N))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N))))) # label(fact_964_nat__mult__le__cancel1) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.66 1085 (all M all K all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),K)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N),K))) <-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N))))) # label(fact_965_mult__le__cancel2) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.66 1086 (all N all P_1 (-hBOOL(hAPP(nat,bool,P_1,zero_zero(nat))) -> (hBOOL(hAPP(nat,bool,P_1,N)) -> (exists K_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),K_1),N)) & (all I_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_2),K_1)) -> -hBOOL(hAPP(nat,bool,P_1,I_2)))) & hBOOL(hAPP(nat,bool,P_1,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_1),one_one(nat))))))))) # label(fact_966_ex__least__nat__less) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.66 1087 (all X all N_1 all Y (hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),X),N_1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),Y),N_1) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Y),X)) -> (exists Q_3 X = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Y),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N_1),Q_3)))))) # label(fact_967_nat__mod__eq__lemma) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.66 1088 (all M_1 all D all R_4 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),M_1),D) = R_4 -> (exists Q_3 M_1 = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),R_4),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),Q_3),D))))) # label(fact_968_mod__eqD) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.66 1089 (all X_1 all N all Y_1 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),X_1),N) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),Y_1),N) <-> (exists Q1 exists Q2 hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N),Q1)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Y_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N),Q2))))) # label(fact_969_nat__mod__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.66 1090 (all M_6 all D_4 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),M_6),D_4) = zero_zero(nat) -> (exists Q_3 M_6 = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),D_4),Q_3)))) # label(fact_970_mod__eq__0D) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.66 1091 (all M all K all F ((all M_3 all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_3),N_2)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,F,M_3)),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)),K)),hAPP(nat,nat,F,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),K)))))) # label(fact_971_mono__nat__linear__lb) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.66 1092 (all N all P_1 (-hBOOL(hAPP(nat,bool,P_1,zero_zero(nat))) -> (hBOOL(hAPP(nat,bool,P_1,N)) -> (exists K_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_1),N)) & (all I_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),K_1)) -> -hBOOL(hAPP(nat,bool,P_1,I_2)))) & hBOOL(hAPP(nat,bool,P_1,K_1))))))) # label(fact_972_ex__least__nat__le) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.66 1093 (all I_1 all J_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),J_2)) -> (exists K_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K_1)) & hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_1),K_1) = J_2)))) # label(fact_973_less__imp__add__positive) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.66 1094 (all N_1 all M_1 all K_4 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K_4)) -> (hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_4),N_1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_4),M_1) -> N_1 = M_1))) # label(fact_974_mult__left__cancel) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.66 1095 (all A_1 all B all C all Q_2 all R_4 (hBOOL(hAPP(product_prod(nat,nat),bool,hAPP(nat,fun(product_prod(nat,nat),bool),hAPP(nat,fun(nat,fun(product_prod(nat,nat),bool)),divmod_nat_rel,B),C),hAPP(nat,product_prod(nat,nat),hAPP(nat,fun(nat,product_prod(nat,nat)),product_Pair(nat,nat),Q_2),R_4))) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),C)) -> hBOOL(hAPP(product_prod(nat,nat),bool,hAPP(nat,fun(product_prod(nat,nat),bool),hAPP(nat,fun(nat,fun(product_prod(nat,nat),bool)),divmod_nat_rel,hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A_1),B)),C),hAPP(nat,product_prod(nat,nat),hAPP(nat,fun(nat,product_prod(nat,nat)),product_Pair(nat,nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A_1),Q_2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A_1),R_4)),C))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A_1),R_4)),C))))))) # label(fact_975_divmod__nat__rel__mult1__eq) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.66 1096 (all C all A_1 all B all Q_2 all R_4 (hBOOL(hAPP(product_prod(nat,nat),bool,hAPP(nat,fun(product_prod(nat,nat),bool),hAPP(nat,fun(nat,fun(product_prod(nat,nat),bool)),divmod_nat_rel,A_1),B),hAPP(nat,product_prod(nat,nat),hAPP(nat,fun(nat,product_prod(nat,nat)),product_Pair(nat,nat),Q_2),R_4))) -> (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)),C)) -> hBOOL(hAPP(product_prod(nat,nat),bool,hAPP(nat,fun(product_prod(nat,nat),bool),hAPP(nat,fun(nat,fun(product_prod(nat,nat),bool)),divmod_nat_rel,A_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),C)),hAPP(nat,product_prod(nat,nat),hAPP(nat,fun(nat,product_prod(nat,nat)),product_Pair(nat,nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),Q_2),C)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),Q_2),C))),R_4)))))))) # label(fact_976_divmod__nat__rel__mult2__eq) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.66 1097 (all B all A_1 all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A_1),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),B)) -> (exists D_3 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),D_3)) & (all Y_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),X),Y_2))),D_3)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A_1),Y_2)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),Y_2),B))))))))) # label(fact_977_lemma__interval) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.66 1098 (all K_4 all L_4 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_4),L_4)) -> (exists N_2 L_4 = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_4),N_2)))) # label(fact_978_le__Suc__ex) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.66 1099 (all I all J all F ((all I_2 all J_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),J_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,F,I_2)),hAPP(nat,nat,F,J_1))))) -> (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,F,I)),hAPP(nat,nat,F,J)))))) # label(fact_979_less__mono__imp__le__mono) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.66 1100 (all D2 all D1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),D1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),D2)) -> (exists E (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),E)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),E),D1)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),E),D2))))))) # label(fact_980_real__lbound__gt__zero) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.66 1101 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X)) -> hAPP(real,nat,natceiling,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),one_one(real))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(real,nat,natceiling,X)),one_one(nat)))) # label(fact_981_natceiling__add__one) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.66 1102 (all Qr_2 all M_1 all N_1 all Qr_1 (hBOOL(hAPP(product_prod(nat,nat),bool,hAPP(nat,fun(product_prod(nat,nat),bool),hAPP(nat,fun(nat,fun(product_prod(nat,nat),bool)),divmod_nat_rel,M_1),N_1),Qr_1)) -> (hBOOL(hAPP(product_prod(nat,nat),bool,hAPP(nat,fun(product_prod(nat,nat),bool),hAPP(nat,fun(nat,fun(product_prod(nat,nat),bool)),divmod_nat_rel,M_1),N_1),Qr_2)) -> Qr_1 = Qr_2))) # label(fact_982_divmod__nat__rel__unique) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.66 1103 (all N_1 hAPP(real,nat,natceiling,hAPP(int,real,number_number_of(real),N_1)) = hAPP(int,nat,number_number_of(nat),N_1)) # label(fact_983_natceiling__number__of__eq) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.66 1104 (all M_1 all N_1 all Q_2 all R_4 (hBOOL(hAPP(product_prod(nat,nat),bool,hAPP(nat,fun(product_prod(nat,nat),bool),hAPP(nat,fun(nat,fun(product_prod(nat,nat),bool)),divmod_nat_rel,M_1),N_1),hAPP(nat,product_prod(nat,nat),hAPP(nat,fun(nat,product_prod(nat,nat)),product_Pair(nat,nat),Q_2),R_4))) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),M_1),N_1) = Q_2)) # label(fact_984_div__eq) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.66 1105 (all M_1 all N_1 all Q_2 all R_4 (hBOOL(hAPP(product_prod(nat,nat),bool,hAPP(nat,fun(product_prod(nat,nat),bool),hAPP(nat,fun(nat,fun(product_prod(nat,nat),bool)),divmod_nat_rel,M_1),N_1),hAPP(nat,product_prod(nat,nat),hAPP(nat,fun(nat,product_prod(nat,nat)),product_Pair(nat,nat),Q_2),R_4))) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),M_1),N_1) = R_4)) # label(fact_985_mod__eq) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.66 1106 (all X hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),hAPP(real,nat,natceiling,X)))) # label(fact_987_zero__le__natceiling) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.66 1107 (all X all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X),Y)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(real,nat,natceiling,X)),hAPP(real,nat,natceiling,Y))))) # label(fact_988_natceiling__mono) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.66 1108 (all M_1 all N_1 hBOOL(hAPP(product_prod(nat,nat),bool,hAPP(nat,fun(product_prod(nat,nat),bool),hAPP(nat,fun(nat,fun(product_prod(nat,nat),bool)),divmod_nat_rel,M_1),N_1),hAPP(nat,product_prod(nat,nat),hAPP(nat,fun(nat,product_prod(nat,nat)),product_Pair(nat,nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),M_1),N_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),M_1),N_1))))) # label(fact_990_divmod__nat__rel) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.66 1109 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X),zero_zero(real))) -> hAPP(real,nat,natceiling,X) = zero_zero(nat))) # label(fact_991_natceiling__neg) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.66 1110 (all X_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(real,nat,natceiling,X_1)),one_one(nat))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_1),one_one(real))))) # label(fact_992_natceiling__le__eq__one) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.66 1111 (all B all Bq all Br all A_1 all C all Aq all Ar (hBOOL(hAPP(product_prod(nat,nat),bool,hAPP(nat,fun(product_prod(nat,nat),bool),hAPP(nat,fun(nat,fun(product_prod(nat,nat),bool)),divmod_nat_rel,A_1),C),hAPP(nat,product_prod(nat,nat),hAPP(nat,fun(nat,product_prod(nat,nat)),product_Pair(nat,nat),Aq),Ar))) -> (hBOOL(hAPP(product_prod(nat,nat),bool,hAPP(nat,fun(product_prod(nat,nat),bool),hAPP(nat,fun(nat,fun(product_prod(nat,nat),bool)),divmod_nat_rel,B),C),hAPP(nat,product_prod(nat,nat),hAPP(nat,fun(nat,product_prod(nat,nat)),product_Pair(nat,nat),Bq),Br))) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),C)) -> hBOOL(hAPP(product_prod(nat,nat),bool,hAPP(nat,fun(product_prod(nat,nat),bool),hAPP(nat,fun(nat,fun(product_prod(nat,nat),bool)),divmod_nat_rel,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A_1),B)),C),hAPP(nat,product_prod(nat,nat),hAPP(nat,fun(nat,product_prod(nat,nat)),product_Pair(nat,nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Aq),Bq)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Ar),Br)),C))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Ar),Br)),C)))))))) # label(fact_993_divmod__nat__rel__add1__eq) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.66 1112 (all B all A_1 all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A_1),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),B)) -> (exists D_3 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),D_3)) & (all Y_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),X),Y_2))),D_3)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A_1),Y_2)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),Y_2),B))))))))) # label(fact_994_lemma__interval__lt) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.66 1113 (all M_1 all N_1 -(all Q_3 all R_2 -hBOOL(hAPP(product_prod(nat,nat),bool,hAPP(nat,fun(product_prod(nat,nat),bool),hAPP(nat,fun(nat,fun(product_prod(nat,nat),bool)),divmod_nat_rel,M_1),N_1),hAPP(nat,product_prod(nat,nat),hAPP(nat,fun(nat,product_prod(nat,nat)),product_Pair(nat,nat),Q_3),R_2))))) # label(fact_995_divmod__nat__rel__ex) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.66 1114 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X)) -> hAPP(real,nat,natfloor,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),one_one(real))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(real,nat,natfloor,X)),one_one(nat)))) # label(fact_996_natfloor__add__one) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.66 1115 (all N all M (hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N),M) = one_one(nat) <-> N = one_one(nat) & M = one_one(nat))) # label(fact_997_nat__mult__eq__one) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.66 1116 (all N_1 all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(nat,real,real_1(nat),N_1)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,real_1(nat),N_1)),one_one(real)))) -> hAPP(real,nat,natceiling,X) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_1),one_one(nat))))) # label(fact_998_natceiling__eq) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.66 1117 (all X all N_1 (-hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),N_1))) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X)) -> hAPP(real,nat,natceiling,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),hAPP(int,real,number_number_of(real),N_1))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(real,nat,natceiling,X)),hAPP(int,nat,number_number_of(nat),N_1))))) # label(fact_999_natceiling__add__number__of) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.66 1118 (all B all A_1 ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),B)) -> hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),divmod_int,A_1),B) = hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),posDivAlg,A_1),B)) & (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),B)) -> (A_1 = zero_zero(int) -> hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),divmod_int,A_1),B) = hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),zero_zero(int)),zero_zero(int))) & (A_1 != zero_zero(int) -> hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),divmod_int,A_1),B) = hAPP(product_prod(int,int),product_prod(int,int),negateSnd,hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),negDivAlg,hAPP(int,int,uminus_uminus(int),A_1)),hAPP(int,int,uminus_uminus(int),B)))))) & (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B)) -> hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),divmod_int,A_1),B) = hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),negDivAlg,A_1),B)) & (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B)) -> hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),divmod_int,A_1),B) = hAPP(product_prod(int,int),product_prod(int,int),negateSnd,hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),posDivAlg,hAPP(int,int,uminus_uminus(int),A_1)),hAPP(int,int,uminus_uminus(int),B))))))) # label(fact_1000_divmod__int__def) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.66 1119 (all P_4 all Q_2 hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),divmod_int,P_4),Q_2) = hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),P_4),Q_2)),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),P_4),Q_2))) # label(fact_1001_divmod__int__mod__div) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.66 1120 (all N_1 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(nat,real,real_1(nat),N_1)))) # label(fact_1002_real__of__nat__ge__zero) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.66 1121 (all N_1 hAPP(real,nat,natfloor,hAPP(nat,real,real_1(nat),N_1)) = N_1) # label(fact_1003_natfloor__real__of__nat) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.66 1122 (all N hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),hAPP(nat,real,real_1(nat),N)),ring_1_Ints(real)))) # label(fact_1004_Ints__real__of__nat) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.66 1123 (all N_1 hAPP(real,nat,natfloor,hAPP(int,real,number_number_of(real),N_1)) = hAPP(int,nat,number_number_of(nat),N_1)) # label(fact_1005_natfloor__number__of__eq) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.66 1124 (all N all M (hAPP(nat,real,real_1(nat),N) = hAPP(nat,real,real_1(nat),M) <-> N = M)) # label(fact_1006_real__of__nat__inject) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.66 1125 (all V ((hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V))) -> hAPP(nat,real,real_1(nat),hAPP(int,nat,number_number_of(nat),V)) = zero_zero(real)) & (-hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V))) -> hAPP(nat,real,real_1(nat),hAPP(int,nat,number_number_of(nat),V)) = hAPP(int,real,number_number_of(real),V)))) # label(fact_1007_real__of__nat__number__of) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.66 1126 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,real_1(nat),hAPP(real,nat,natfloor,X))),X)))) # label(fact_1008_real__natfloor__le) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.66 1127 (all X all A_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,real_1(nat),X)),A_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X),hAPP(real,nat,natfloor,A_1))))) # label(fact_1009_le__natfloor) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.66 1128 (all X hAPP(real,real,abs_abs(real),hAPP(nat,real,real_1(nat),X)) = hAPP(nat,real,real_1(nat),X)) # label(fact_1010_abs__real__of__nat__cancel) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.66 1129 (all N_1 hAPP(real,nat,natceiling,hAPP(nat,real,real_1(nat),N_1)) = N_1) # label(fact_1013_natceiling__real__of__nat) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.66 1130 (all Aa all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Aa),hAPP(real,nat,natfloor,X_1))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,real_1(nat),Aa)),X_1))))) # label(fact_1014_le__natfloor__eq) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.66 1131 (all X hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,real_1(nat),hAPP(real,nat,natfloor,X))),one_one(real))))) # label(fact_1015_real__natfloor__add__one__gt) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.66 1132 (all A_1 all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,real_1(nat),A_1)),X)) -> hAPP(real,nat,natfloor,hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),X),hAPP(nat,real,real_1(nat),A_1))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(real,nat,natfloor,X)),A_1))) # label(fact_1016_natfloor__subtract) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.66 1133 (all X hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),X),one_one(real))),hAPP(nat,real,real_1(nat),hAPP(real,nat,natfloor,X))))) # label(fact_1017_real__natfloor__gt__diff__one) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.66 1134 (all N (hAPP(nat,real,real_1(nat),N) = zero_zero(real) <-> N = zero_zero(nat))) # label(fact_1019_real__of__nat__zero__iff) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.66 1135 (all N_1 -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(nat,real,real_1(nat),N_1)),zero_zero(real)))) # label(fact_1020_not__real__of__nat__less__zero) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.66 1136 (all N all M (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(nat,real,real_1(nat),N)),hAPP(nat,real,real_1(nat),M))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),M)))) # label(fact_1021_real__of__nat__less__iff) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.66 1137 (all N all M (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,real_1(nat),N)),hAPP(nat,real,real_1(nat),M))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N),M)))) # label(fact_1022_real__of__nat__le__iff) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.66 1138 (all N_1 all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),hAPP(nat,real,real_1(nat),N_1))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(real,nat,natfloor,X)),N_1))))) # label(fact_1023_less__natfloor) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.66 1139 (all M_1 all N_1 hAPP(nat,real,real_1(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),N_1)) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,real_1(nat),M_1)),hAPP(nat,real,real_1(nat),N_1))) # label(fact_1024_real__of__nat__mult) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.66 1140 (all A_1 all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X)) -> hAPP(real,nat,natfloor,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),hAPP(nat,real,real_1(nat),A_1))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(real,nat,natfloor,X)),A_1))) # label(fact_1025_natfloor__add) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.66 1141 (all M_1 all N_1 hAPP(nat,real,real_1(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),N_1)) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,real_1(nat),M_1)),hAPP(nat,real,real_1(nat),N_1))) # label(fact_1026_real__of__nat__add) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.66 1142 (all Z 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),hAPP(real,nat,natfloor,Z)),one_one(nat))),N_1)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),Z),hAPP(nat,real,real_1(nat),N_1))))) # label(fact_1027_ge__natfloor__plus__one__imp__gt) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.66 1143 (all N_1 all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,real_1(nat),N_1)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,real_1(nat),N_1)),one_one(real)))) -> hAPP(real,nat,natfloor,X) = N_1))) # label(fact_1028_natfloor__eq) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.66 1144 (all X_1 all N (-hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),N))) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(int,nat,number_number_of(nat),N)),hAPP(real,nat,natfloor,X_1))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,number_number_of(real),N)),X_1)))))) # label(fact_1030_le__natfloor__eq__number__of) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.66 1145 (all X hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X),hAPP(nat,real,real_1(nat),hAPP(real,nat,natceiling,X))))) # label(fact_1031_real__natceiling__ge) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.66 1146 (all Z_5 (hBOOL(hAPP(int,bool,nat_neg,Z_5)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Z_5),zero_zero(int))))) # label(fact_1032_neg__def) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.66 1147 (all X_1 (-hBOOL(hAPP(int,bool,nat_neg,X_1)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X_1)))) # label(fact_1033_not__neg__eq__ge__0) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.66 1148 (all V (hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V))) -> hAPP(int,nat,number_number_of(nat),V) = zero_zero(nat))) # label(fact_1034_neg__imp__number__of__eq__0) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.66 1149 (all X hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),hAPP(real,nat,natfloor,X)))) # label(fact_1037_zero__le__natfloor) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.66 1150 (all X all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X),Y)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(real,nat,natfloor,X)),hAPP(real,nat,natfloor,Y))))) # label(fact_1038_natfloor__mono) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.66 1151 (all X all N_1 (-hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),N_1))) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X)) -> hAPP(real,nat,natfloor,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),hAPP(int,real,number_number_of(real),N_1))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(real,nat,natfloor,X)),hAPP(int,nat,number_number_of(nat),N_1))))) # label(fact_1040_natfloor__add__number__of) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.66 1152 (all N (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,real_1(nat),N)),zero_zero(real))) <-> N = zero_zero(nat))) # label(fact_1041_real__of__nat__le__zero__cancel__iff) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.66 1153 (all N_1 all M_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_1),M_1)) -> hAPP(nat,real,real_1(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),N_1)) = hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(nat,real,real_1(nat),M_1)),hAPP(nat,real,real_1(nat),N_1)))) # label(fact_1042_real__of__nat__diff) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.66 1154 (all X all A_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X),hAPP(nat,real,real_1(nat),A_1))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(real,nat,natceiling,X)),A_1)))) # label(fact_1043_natceiling__le) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.66 1155 (all V_1 all V_2 (hAPP(int,nat,number_number_of(nat),V_1) = hAPP(int,nat,number_number_of(nat),V_2) <-> (hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V_1))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),V_2)),zero_zero(int)))) & (-hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V_1))) -> (hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V_2))) -> hAPP(int,int,number_number_of(int),V_1) = zero_zero(int)) & (-hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V_2))) -> V_1 = V_2)))) # label(fact_1044_eq__nat__number__of) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.66 1156 (all V_3 all K_4 all V ((hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V))) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),V)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),V_3)),K_4)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),V_3)),K_4)) & (-hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V))) -> (hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V_3))) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),V)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),V_3)),K_4)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),V)),K_4)) & (-hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V_3))) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),V)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),V_3)),K_4)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),V),V_3))),K_4))))) # label(fact_1045_nat__number__of__add__left) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.66 1157 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X),zero_zero(real))) -> hAPP(real,nat,natfloor,X) = zero_zero(nat))) # label(fact_1046_natfloor__neg) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.66 1158 (all N (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(nat,real,real_1(nat),N))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)))) # label(fact_1047_real__of__nat__gt__zero__cancel__iff) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.66 1159 (all N all M (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),M)) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,real_1(nat),N)),one_one(real))),hAPP(nat,real,real_1(nat),M))))) # label(fact_1048_nat__less__real__le) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.66 1160 (all Q_2 all R_4 hAPP(product_prod(int,int),product_prod(int,int),negateSnd,hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),Q_2),R_4)) = hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),Q_2),hAPP(int,int,uminus_uminus(int),R_4))) # label(fact_1049_negateSnd__eq) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.66 1161 (all N all M (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N),M)) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(nat,real,real_1(nat),N)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,real_1(nat),M)),one_one(real)))))) # label(fact_1050_nat__le__real__less) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.66 1162 (all Aa all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(real,nat,natceiling,X_1)),Aa)) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_1),hAPP(nat,real,real_1(nat),Aa)))))) # label(fact_1051_natceiling__le__eq) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.66 1163 (all A_1 all B all Qr_1 (hBOOL(hAPP(product_prod(int,int),bool,hAPP(int,fun(product_prod(int,int),bool),hAPP(int,fun(int,fun(product_prod(int,int),bool)),divmod_int_rel,hAPP(int,int,uminus_uminus(int),A_1)),hAPP(int,int,uminus_uminus(int),B)),Qr_1)) -> hBOOL(hAPP(product_prod(int,int),bool,hAPP(int,fun(product_prod(int,int),bool),hAPP(int,fun(int,fun(product_prod(int,int),bool)),divmod_int_rel,A_1),B),hAPP(product_prod(int,int),product_prod(int,int),negateSnd,Qr_1))))) # label(fact_1052_divmod__int__rel__neg) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.66 1164 (all A_1 all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,real_1(nat),A_1)),X)) -> hAPP(real,nat,natceiling,hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),X),hAPP(nat,real,real_1(nat),A_1))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(real,nat,natceiling,X)),A_1))) # label(fact_1053_natceiling__subtract) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.66 1165 (all A_1 all B (B != zero_zero(int) -> hBOOL(hAPP(product_prod(int,int),bool,hAPP(int,fun(product_prod(int,int),bool),hAPP(int,fun(int,fun(product_prod(int,int),bool)),divmod_int_rel,A_1),B),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),divmod_int,A_1),B))))) # label(fact_1054_divmod__int__correct) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.66 1166 (all X_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),one_one(nat)),hAPP(real,nat,natfloor,X_1))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),one_one(real)),X_1)))) # label(fact_1055_le__natfloor__eq__one) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.66 1167 (all A_1 all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X)) -> hAPP(real,nat,natceiling,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),hAPP(nat,real,real_1(nat),A_1))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(real,nat,natceiling,X)),A_1))) # label(fact_1056_natceiling__add) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.66 1168 (all X_1 all N (-hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),N))) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(real,nat,natceiling,X_1)),hAPP(int,nat,number_number_of(nat),N))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_1),hAPP(int,real,number_number_of(real),N))))))) # label(fact_1057_natceiling__le__eq__number__of) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.66 1169 (all B all A_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),B)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(real,nat,natfloor,A_1)),hAPP(real,nat,natfloor,B))),hAPP(real,nat,natfloor,hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A_1),B))))))) # label(fact_1058_le__mult__natfloor) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.66 1170 (all R_4 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),R_4)) -> (exists N_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,real_1(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_2),one_one(nat)))),R_4)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),R_4),hAPP(nat,real,real_1(nat),N_2))))))) # label(fact_1059_reals__Archimedean6) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.66 1171 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> (all Y_2 exists N_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),Y_2),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,real_1(nat),N_2)),X)))))) # label(fact_1060_reals__Archimedean3) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.66 1172 (all X exists N_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),hAPP(nat,real,real_1(nat),N_2)))) # label(fact_1061_reals__Archimedean2) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.66 1173 (all W (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),W)),zero_zero(int))) -> hAPP(int,int,hAPP(int,fun(int,int),div_div(int),one_one(int)),hAPP(int,int,number_number_of(int),W)) = hAPP(product_prod(int,int),int,product_fst(int,int),hAPP(product_prod(int,int),product_prod(int,int),negateSnd,hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),negDivAlg,hAPP(int,int,uminus_uminus(int),one_one(int))),hAPP(int,int,uminus_uminus(int),hAPP(int,int,number_number_of(int),W))))))) # label(fact_1062_div__pos__neg__1__number__of) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.66 1174 (all W (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),W)),zero_zero(int))) -> hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),one_one(int)),hAPP(int,int,number_number_of(int),W)) = hAPP(product_prod(int,int),int,product_snd(int,int),hAPP(product_prod(int,int),product_prod(int,int),negateSnd,hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),negDivAlg,hAPP(int,int,uminus_uminus(int),one_one(int))),hAPP(int,int,uminus_uminus(int),hAPP(int,int,number_number_of(int),W))))))) # label(fact_1063_mod__pos__neg__1__number__of) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.66 1175 (all Y all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),one_one(real)),X)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Y)) -> hAPP(real,nat,natfloor,hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),X),hAPP(nat,real,real_1(nat),Y))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(real,nat,natfloor,X)),Y)))) # label(fact_1064_natfloor__div__nat) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.66 1176 (all B all A_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_1),zero_zero(int))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),zero_zero(int))) -> hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_1),B) = hAPP(product_prod(int,int),int,product_fst(int,int),hAPP(product_prod(int,int),product_prod(int,int),negateSnd,hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),posDivAlg,hAPP(int,int,uminus_uminus(int),A_1)),hAPP(int,int,uminus_uminus(int),B))))))) # label(fact_1065_div__neg__neg) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.66 1177 (all B all A_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_1),zero_zero(int))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),zero_zero(int))) -> hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_1),B) = hAPP(product_prod(int,int),int,product_snd(int,int),hAPP(product_prod(int,int),product_prod(int,int),negateSnd,hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),posDivAlg,hAPP(int,int,uminus_uminus(int),A_1)),hAPP(int,int,uminus_uminus(int),B))))))) # label(fact_1066_mod__neg__neg) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.66 1178 (all X_a all X_b all P_4 all Q_2 (hAPP(product_prod(X_a,X_b),X_a,product_fst(X_a,X_b),P_4) = hAPP(product_prod(X_a,X_b),X_a,product_fst(X_a,X_b),Q_2) -> (hAPP(product_prod(X_a,X_b),X_b,product_snd(X_a,X_b),P_4) = hAPP(product_prod(X_a,X_b),X_b,product_snd(X_a,X_b),Q_2) -> ti(product_prod(X_a,X_b),P_4) = ti(product_prod(X_a,X_b),Q_2)))) # label(fact_1067_prod__eqI) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.66 1179 (all X_a all X_b all S_3 all T_3 (ti(product_prod(X_a,X_b),S_3) = ti(product_prod(X_a,X_b),T_3) <-> hAPP(product_prod(X_a,X_b),X_a,product_fst(X_a,X_b),S_3) = hAPP(product_prod(X_a,X_b),X_a,product_fst(X_a,X_b),T_3) & hAPP(product_prod(X_a,X_b),X_b,product_snd(X_a,X_b),S_3) = hAPP(product_prod(X_a,X_b),X_b,product_snd(X_a,X_b),T_3))) # label(fact_1068_prod__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.66 1180 (all X_a all X_b all T_6 ti(product_prod(X_a,X_b),T_6) = hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),hAPP(product_prod(X_a,X_b),X_a,product_fst(X_a,X_b),T_6)),hAPP(product_prod(X_a,X_b),X_b,product_snd(X_a,X_b),T_6))) # label(fact_1069_surjective__pairing) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.66 1181 (all X_b all X_a all P_4 hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),hAPP(product_prod(X_a,X_b),X_a,product_fst(X_a,X_b),P_4)),hAPP(product_prod(X_a,X_b),X_b,product_snd(X_a,X_b),P_4)) = ti(product_prod(X_a,X_b),P_4)) # label(fact_1070_pair__collapse) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.66 1182 (all X_a (division_ring(X_a) -> (all A_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),zero_zero(X_a)),A_1) = zero_zero(X_a)))) # label(fact_1071_divide__zero__left) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.66 1183 (all X_a (divisi14063676e_zero(X_a) -> (all A_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),A_1),zero_zero(X_a)) = zero_zero(X_a)))) # label(fact_1072_divide__zero) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.66 1184 (all X_a (real_normed_field(X_a) -> (all Y hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),zero_zero(X_a)),Y) = zero_zero(X_a)))) # label(fact_1073_divide_Ozero) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.66 1185 (all X_a (field_inverse_zero(X_a) -> (all X all Y all Z all W 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),inverse_divide(X_a),X),Y)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),Z),W)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),Z)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Y),W))))) # label(fact_1074_times__divide__times__eq) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.66 1186 (all X_a (division_ring(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),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),B),C)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)),C)))) # label(fact_1075_times__divide__eq__right) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.66 1187 (all X_a (division_ring(X_a) -> (all A_1 all B all C hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(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),inverse_divide(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),B),C))))) # label(fact_1076_add__divide__distrib) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.66 1188 (all X_a (real_normed_field(X_a) -> (all X all Y all Ya hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X),Y)),Ya) = 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),inverse_divide(X_a),X),Ya)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),Y),Ya))))) # label(fact_1077_divide_Oadd) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.66 1189 (all X_a (division_ring(X_a) -> (all A_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),A_1),one_one(X_a)) = ti(X_a,A_1)))) # label(fact_1078_divide__1) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.66 1190 (all X_a (division_ring(X_a) -> (all A_1 all B all C hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_1),B)),C) = 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),inverse_divide(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),B),C))))) # label(fact_1079_diff__divide__distrib) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.66 1191 (all X_a (real_normed_field(X_a) -> (all X all Y all Ya hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),X),Y)),Ya) = 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),inverse_divide(X_a),X),Ya)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),Y),Ya))))) # label(fact_1080_divide_Odiff) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.66 1192 (all X_a (real_normed_field(X_a) -> (all X all Y hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),X)),Y) = hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),X),Y))))) # label(fact_1081_divide_Ominus) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.66 1193 (all X_a (field_inverse_zero(X_a) -> (all A_1 all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(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),inverse_divide(X_a),A_1),B)))) # label(fact_1082_minus__divide__divide) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.66 1194 (all X_a (division_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),inverse_divide(X_a),A_1),B)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),A_1)),B)))) # label(fact_1083_minus__divide__left) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.66 1195 (all X_a (field_inverse_zero(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),inverse_divide(X_a),A_1),B)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),A_1),hAPP(X_a,X_a,uminus_uminus(X_a),B))))) # label(fact_1084_minus__divide__right) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.66 1196 (all X_a (linord1117847801e_zero(X_a) -> (all A_1 all B hAPP(X_a,X_a,abs_abs(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),A_1),B)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),hAPP(X_a,X_a,abs_abs(X_a),A_1)),hAPP(X_a,X_a,abs_abs(X_a),B))))) # label(fact_1085_abs__divide) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.66 1197 (all R_4 all A_1 hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),R_4),A_1)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),R_4),R_4)) = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A_1),R_4)) # label(fact_1086_real__divide__square__eq) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.66 1198 (all X_a all X_b all X all Y all A_1 (hAPP(product_prod(X_a,X_b),X_a,product_fst(X_a,X_b),hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),X),Y)) = ti(X_a,A_1) -> ti(X_a,X) = ti(X_a,A_1))) # label(fact_1087_fst__eqD) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.66 1199 (all X_a all X_b all A_1 all B hAPP(product_prod(X_a,X_b),X_a,product_fst(X_a,X_b),hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),A_1),B)) = ti(X_a,A_1)) # label(fact_1088_fst__conv) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.66 1200 (all X_b all X_a all X all Y all A_1 (hAPP(product_prod(X_b,X_a),X_a,product_snd(X_b,X_a),hAPP(X_a,product_prod(X_b,X_a),hAPP(X_b,fun(X_a,product_prod(X_b,X_a)),product_Pair(X_b,X_a),X),Y)) = ti(X_a,A_1) -> ti(X_a,Y) = ti(X_a,A_1))) # label(fact_1089_snd__eqD) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.66 1201 (all X_b all X_a all A_1 all B hAPP(product_prod(X_b,X_a),X_a,product_snd(X_b,X_a),hAPP(X_a,product_prod(X_b,X_a),hAPP(X_b,fun(X_a,product_prod(X_b,X_a)),product_Pair(X_b,X_a),A_1),B)) = ti(X_a,B)) # label(fact_1090_snd__conv) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.66 1202 (all X_a (linord1117847801e_zero(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),C),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),B),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),A_1),C)))))))) # label(fact_1091_divide__right__mono__neg) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.66 1203 (all X_a (linord1117847801e_zero(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),zero_zero(X_a)),C)) -> 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),inverse_divide(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),B),C)))))))) # label(fact_1092_divide__right__mono) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.66 1204 (all X_a (linord1117847801e_zero(X_a) -> (all Aa all Ba (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),Aa),Ba)),zero_zero(X_a))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),Aa)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Ba),zero_zero(X_a))) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Aa),zero_zero(X_a))) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),Ba)))))) # label(fact_1093_divide__le__0__iff) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.66 1205 (all X_a (linord1117847801e_zero(X_a) -> (all Aa all Ba (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),Aa),Ba))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),Aa)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),Ba)) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Aa),zero_zero(X_a))) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Ba),zero_zero(X_a))))))) # label(fact_1094_zero__le__divide__iff) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.66 1206 (all X_a (linord1117847801e_zero(X_a) -> (all Aa all Ba (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),inverse_divide(X_a),Aa),Ba))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),Aa)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),Ba)) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),zero_zero(X_a))) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Ba),zero_zero(X_a))))))) # label(fact_1095_zero__less__divide__iff) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.66 1207 (all X_a (linord1117847801e_zero(X_a) -> (all Aa all Ba (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),Aa),Ba)),zero_zero(X_a))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),Aa)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Ba),zero_zero(X_a))) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),zero_zero(X_a))) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),Ba)))))) # label(fact_1096_divide__less__0__iff) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.66 1208 (all X_a (linord1117847801e_zero(X_a) -> (all Aa all C_1 all Ba (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),Aa),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),Ba),C_1))) <-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),Ba))) & (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Ba),Aa))) & ti(X_a,C_1) != zero_zero(X_a))))) # label(fact_1097_divide__less__cancel) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.66 1209 (all X_a (linordered_field(X_a) -> (all Y all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),X)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),Y)) -> 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),inverse_divide(X_a),X),Y)))))))) # label(fact_1098_divide__pos__pos) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.66 1210 (all X_a (linordered_field(X_a) -> (all Y all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),X)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),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),inverse_divide(X_a),X),Y)),zero_zero(X_a)))))))) # label(fact_1099_divide__pos__neg) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.66 1211 (all X_a (linordered_field(X_a) -> (all Y all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),zero_zero(X_a))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),Y)) -> 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),inverse_divide(X_a),X),Y)),zero_zero(X_a)))))))) # label(fact_1100_divide__neg__pos) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.66 1212 (all X_a (linordered_field(X_a) -> (all Y all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),zero_zero(X_a))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),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),inverse_divide(X_a),X),Y)))))))) # label(fact_1101_divide__neg__neg) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.66 1213 (all X_a (linordered_field(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),inverse_divide(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),B),C)))))))) # label(fact_1102_divide__strict__right__mono) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.66 1214 (all X_a (linordered_field(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),inverse_divide(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),B),C)))))))) # label(fact_1103_divide__strict__right__mono__neg) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.66 1215 (all X_a (division_ring(X_a) -> (all A_1 all B all C (ti(X_a,C) != zero_zero(X_a) -> (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),C) = ti(X_a,B) -> ti(X_a,A_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),B),C)))))) # label(fact_1104_eq__divide__imp) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.66 1216 (all X_a (division_ring(X_a) -> (all B all A_1 all C (ti(X_a,C) != zero_zero(X_a) -> (ti(X_a,B) = 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),inverse_divide(X_a),B),C) = ti(X_a,A_1)))))) # label(fact_1105_divide__eq__imp) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.66 1217 (all X_a (field(X_a) -> (all X_1 all W_1 all Z_1 all Y_1 (ti(X_a,Y_1) != zero_zero(X_a) -> (ti(X_a,Z_1) != zero_zero(X_a) -> (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),X_1),Y_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),W_1),Z_1) <-> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X_1),Z_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),W_1),Y_1))))))) # label(fact_1106_frac__eq__eq) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.66 1218 (all X_a (field_inverse_zero(X_a) -> (all A_1 all B all C (ti(X_a,C) != zero_zero(X_a) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(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)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),A_1),B))))) # label(fact_1107_mult__divide__mult__cancel__left) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.66 1219 (all X_a (field_inverse_zero(X_a) -> (all A_1 all B all C (ti(X_a,C) != zero_zero(X_a) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(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)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),A_1),B))))) # label(fact_1108_mult__divide__mult__cancel__right) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.66 1220 (all X_a (division_ring(X_a) -> (all Ba all Aa all C_1 (ti(X_a,C_1) != zero_zero(X_a) -> (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),Ba),C_1) = ti(X_a,Aa) <-> ti(X_a,Ba) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Aa),C_1)))))) # label(fact_1109_nonzero__divide__eq__eq) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.66 1221 (all X_a (division_ring(X_a) -> (all Aa all Ba all C_1 (ti(X_a,C_1) != zero_zero(X_a) -> (ti(X_a,Aa) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),Ba),C_1) <-> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Aa),C_1) = ti(X_a,Ba)))))) # label(fact_1110_nonzero__eq__divide__eq) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.66 1222 (all X_a (field_inverse_zero(X_a) -> (all Ba all C_1 all Aa (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),Ba),C_1) = ti(X_a,Aa) <-> (ti(X_a,C_1) != zero_zero(X_a) -> ti(X_a,Ba) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Aa),C_1)) & (ti(X_a,C_1) = zero_zero(X_a) -> ti(X_a,Aa) = zero_zero(X_a)))))) # label(fact_1111_divide__eq__eq) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.66 1223 (all X_a (field_inverse_zero(X_a) -> (all Aa all Ba all C_1 (ti(X_a,Aa) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),Ba),C_1) <-> (ti(X_a,C_1) != zero_zero(X_a) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Aa),C_1) = ti(X_a,Ba)) & (ti(X_a,C_1) = zero_zero(X_a) -> ti(X_a,Aa) = zero_zero(X_a)))))) # label(fact_1112_eq__divide__eq) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.66 1224 (all X_a (divisi14063676e_zero(X_a) -> (all A_1 ((ti(X_a,A_1) = zero_zero(X_a) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),A_1),A_1) = zero_zero(X_a)) & (ti(X_a,A_1) != zero_zero(X_a) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),A_1),A_1) = one_one(X_a)))))) # label(fact_1113_divide__self__if) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.66 1225 (all X_a (division_ring(X_a) -> (all A_1 (ti(X_a,A_1) != zero_zero(X_a) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),A_1),A_1) = one_one(X_a))))) # label(fact_1114_divide__self) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.66 1226 (all X_a (division_ring(X_a) -> (all Aa all Ba (ti(X_a,Ba) != zero_zero(X_a) -> (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),Aa),Ba) = one_one(X_a) <-> ti(X_a,Aa) = ti(X_a,Ba)))))) # label(fact_1115_right__inverse__eq) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.66 1227 (all X_a (division_ring(X_a) -> (all A_1 all B (ti(X_a,B) != zero_zero(X_a) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(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),inverse_divide(X_a),A_1),B))))) # label(fact_1116_nonzero__minus__divide__divide) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.66 1228 (all X_a (division_ring(X_a) -> (all A_1 all B (ti(X_a,B) != zero_zero(X_a) -> hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),A_1),B)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),A_1),hAPP(X_a,X_a,uminus_uminus(X_a),B)))))) # label(fact_1117_nonzero__minus__divide__right) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.66 1229 (all X_a (linordered_field(X_a) -> (all A_1 all B (ti(X_a,B) != zero_zero(X_a) -> hAPP(X_a,X_a,abs_abs(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),A_1),B)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),hAPP(X_a,X_a,abs_abs(X_a),A_1)),hAPP(X_a,X_a,abs_abs(X_a),B)))))) # label(fact_1118_nonzero__abs__divide) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.66 1230 (all X_1 all Y_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),X_1),Y_1))) <-> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_1),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),Y_1))) & (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X_1)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),Y_1),zero_zero(real)))))) # label(fact_1119_real__0__le__divide__iff) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.66 1231 (all F all Aa all Ba hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,F,Aa)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,F,Ba)),hAPP(real,real,F,Aa))),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),Ba),Aa))),Aa)) = hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,F,Ba)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,F,Ba)),hAPP(real,real,F,Aa))),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),Ba),Aa))),Ba))) # label(fact_1120_lemma__MVT) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.66 1232 (all A_1 all B hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_1),B) = hAPP(product_prod(int,int),int,product_snd(int,int),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),divmod_int,A_1),B))) # label(fact_1121_mod__int__def) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.66 1233 (all A_1 all B hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_1),B) = hAPP(product_prod(int,int),int,product_fst(int,int),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),divmod_int,A_1),B))) # label(fact_1122_div__int__def) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.66 1234 (all X_a (linord1117847801e_zero(X_a) -> (all Aa all C_1 all Ba (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),Aa),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),Ba),C_1))) <-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Aa),Ba))) & (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Ba),Aa))))))) # label(fact_1123_divide__le__cancel) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.66 1235 (all X_a (linordered_field(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(X_a),zero_zero(X_a)),Y)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),X),Y)))))))) # label(fact_1124_divide__nonneg__pos) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.66 1236 (all X_a (linordered_field(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(X_a),Y),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),X),Y)),zero_zero(X_a)))))))) # label(fact_1125_divide__nonneg__neg) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.66 1237 (all X_a (linordered_field(X_a) -> (all Z all W all Y all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),X)) -> (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),zero_zero(X_a)),W)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),W),Z)) -> 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),inverse_divide(X_a),X),Z)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),Y),W)))))))))) # label(fact_1126_frac__less2) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.66 1238 (all X_a (linordered_field(X_a) -> (all Z all W 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(X_a),X),Y)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),W)) -> (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(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),X),Z)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),Y),W)))))))))) # label(fact_1127_frac__less) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.66 1239 (all X_a (linordered_field(X_a) -> (all Z all W 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),X),Y)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),W)) -> (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),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),X),Z)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),Y),W)))))))))) # label(fact_1128_frac__le) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.66 1240 (all X_a (linordered_field(X_a) -> (all Y all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),zero_zero(X_a))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),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),inverse_divide(X_a),X),Y)),zero_zero(X_a)))))))) # label(fact_1129_divide__nonpos__pos) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.66 1241 (all X_a (linordered_field(X_a) -> (all Y all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),zero_zero(X_a))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),X),Y)))))))) # label(fact_1130_divide__nonpos__neg) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.66 1242 (all X_a (linordered_field(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),C),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))) -> 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),inverse_divide(X_a),C),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),C),B))))))))) # label(fact_1131_divide__strict__left__mono__neg) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.66 1243 (all X_a (linordered_field(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),zero_zero(X_a)),C)) -> (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),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),C),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),C),B))))))))) # label(fact_1132_divide__strict__left__mono) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.66 1244 (all X_a (linordered_field(X_a) -> (all Ba all Aa all C_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),zero_zero(X_a))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),Ba),C_1)),Aa)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Aa),C_1)),Ba))))))) # label(fact_1133_neg__divide__less__eq) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.67 1245 (all X_a (linordered_field(X_a) -> (all Aa all Ba all C_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),zero_zero(X_a))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),Ba),C_1))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Ba),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Aa),C_1)))))))) # label(fact_1134_neg__less__divide__eq) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.67 1246 (all X_a (linordered_field(X_a) -> (all Z all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),Y)) -> (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),Z),Y)),X)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),X),Y)))))))) # label(fact_1135_mult__imp__less__div__pos) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.67 1247 (all X_a (linordered_field(X_a) -> (all X all Z all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),Y)) -> (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),times_times(X_a),Z),Y))) -> 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),inverse_divide(X_a),X),Y)),Z))))))) # label(fact_1136_mult__imp__div__pos__less) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.67 1248 (all X_a (linordered_field(X_a) -> (all Ba all Aa all C_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C_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),inverse_divide(X_a),Ba),C_1)),Aa)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Ba),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Aa),C_1)))))))) # label(fact_1137_pos__divide__less__eq) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.67 1249 (all X_a (linordered_field(X_a) -> (all Aa all Ba all C_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),Ba),C_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),Aa),C_1)),Ba))))))) # label(fact_1138_pos__less__divide__eq) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.67 1250 (all X_a (linord1117847801e_zero(X_a) -> (all Ba all C_1 all Aa (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),Ba),C_1)),Aa)) <-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Ba),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Aa),C_1)))) & (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Aa),C_1)),Ba))) & (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_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)),Aa)))))))) # label(fact_1139_divide__less__eq) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.67 1251 (all X_a (linord1117847801e_zero(X_a) -> (all Aa all Ba all C_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),Ba),C_1))) <-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C_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),Aa),C_1)),Ba))) & (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Ba),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Aa),C_1)))) & (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),zero_zero(X_a))))))))) # label(fact_1140_less__divide__eq) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.67 1252 (all X_a (field(X_a) -> (all X all W all Z all Y (ti(X_a,Y) != zero_zero(X_a) -> (ti(X_a,Z) != zero_zero(X_a) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),X),Y)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),W),Z)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),Z)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),W),Y))),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Y),Z))))))) # label(fact_1141_add__frac__eq) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.67 1253 (all X_a (field(X_a) -> (all X all Y all Z (ti(X_a,Z) != zero_zero(X_a) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),X),Z)),Y) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Z),Y))),Z))))) # label(fact_1142_divide__add__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.67 1254 (all X_a (field_inverse_zero(X_a) -> (all X all Z all Y (ti(X_a,Y) != zero_zero(X_a) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),X),Y)),Z) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Z),Y))),Y))))) # label(fact_1143_add__frac__num) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.67 1255 (all X_a (field(X_a) -> (all X all Y all Z (ti(X_a,Z) != zero_zero(X_a) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),Y),Z)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Z),X)),Y)),Z))))) # label(fact_1144_add__divide__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.67 1256 (all X_a (field_inverse_zero(X_a) -> (all Z all X all Y (ti(X_a,Y) != zero_zero(X_a) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Z),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),X),Y)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Z),Y))),Y))))) # label(fact_1145_add__num__frac) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.67 1257 (all X_a (field_inverse_zero(X_a) & number(X_a) -> (all Ba all W_1 all Aa (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),Ba),hAPP(int,X_a,number_number_of(X_a),W_1)) = ti(X_a,Aa) <-> (hAPP(int,X_a,number_number_of(X_a),W_1) != zero_zero(X_a) -> ti(X_a,Ba) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Aa),hAPP(int,X_a,number_number_of(X_a),W_1))) & (hAPP(int,X_a,number_number_of(X_a),W_1) = zero_zero(X_a) -> ti(X_a,Aa) = zero_zero(X_a)))))) # label(fact_1146_divide__eq__eq__number__of1) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.67 1258 (all X_a (field_inverse_zero(X_a) & number(X_a) -> (all Ba all C_1 all W_1 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),Ba),C_1) = hAPP(int,X_a,number_number_of(X_a),W_1) <-> (ti(X_a,C_1) != zero_zero(X_a) -> ti(X_a,Ba) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(int,X_a,number_number_of(X_a),W_1)),C_1)) & (ti(X_a,C_1) = zero_zero(X_a) -> hAPP(int,X_a,number_number_of(X_a),W_1) = zero_zero(X_a)))))) # label(fact_1147_divide__eq__eq__number__of) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.67 1259 (all X_a (field_inverse_zero(X_a) & number(X_a) -> (all W_1 all Ba all C_1 (hAPP(int,X_a,number_number_of(X_a),W_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),Ba),C_1) <-> (ti(X_a,C_1) != zero_zero(X_a) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(int,X_a,number_number_of(X_a),W_1)),C_1) = ti(X_a,Ba)) & (ti(X_a,C_1) = zero_zero(X_a) -> hAPP(int,X_a,number_number_of(X_a),W_1) = zero_zero(X_a)))))) # label(fact_1148_eq__divide__eq__number__of) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.67 1260 (all X_a (field_inverse_zero(X_a) & number(X_a) -> (all Aa all Ba all W_1 (ti(X_a,Aa) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),Ba),hAPP(int,X_a,number_number_of(X_a),W_1)) <-> (hAPP(int,X_a,number_number_of(X_a),W_1) != zero_zero(X_a) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Aa),hAPP(int,X_a,number_number_of(X_a),W_1)) = ti(X_a,Ba)) & (hAPP(int,X_a,number_number_of(X_a),W_1) = zero_zero(X_a) -> ti(X_a,Aa) = zero_zero(X_a)))))) # label(fact_1149_eq__divide__eq__number__of1) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.67 1261 (all X_a (field(X_a) -> (all X all W all Z all Y (ti(X_a,Y) != zero_zero(X_a) -> (ti(X_a,Z) != zero_zero(X_a) -> 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),inverse_divide(X_a),X),Y)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),W),Z)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),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),times_times(X_a),X),Z)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),W),Y))),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Y),Z))))))) # label(fact_1150_diff__frac__eq) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.67 1262 (all X_a (field(X_a) -> (all X all Y all Z (ti(X_a,Z) != zero_zero(X_a) -> 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),inverse_divide(X_a),X),Z)),Y) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Z),Y))),Z))))) # label(fact_1151_divide__diff__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.67 1263 (all X_a (field(X_a) -> (all X all Y all Z (ti(X_a,Z) != zero_zero(X_a) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),Y),Z)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),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),times_times(X_a),Z),X)),Y)),Z))))) # label(fact_1152_diff__divide__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.67 1264 (all X_a (linordered_field(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),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(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),one_one(X_a)),one_one(X_a)))),B)))))) # label(fact_1153_gt__half__sum) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.67 1265 (all X_a (linordered_field(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),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(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),one_one(X_a)),one_one(X_a))))))))) # label(fact_1154_less__half__sum) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.67 1266 (all X_a (real_field(X_a) -> (all A_1 all B all C all D all H_2 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),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),times_times(X_a),A_1),B)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),D))),H_2) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),B),D)),H_2))),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),inverse_divide(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_1),C)),H_2)),D))))) # label(fact_1155_DERIV__mult__lemma) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.67 1267 (all X_a (linord1117847801e_zero(X_a) -> (all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),Y)) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),hAPP(X_a,X_a,abs_abs(X_a),X)),Y) = hAPP(X_a,X_a,abs_abs(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),X),Y)))))) # label(fact_1156_abs__div__pos) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.67 1268 (all X_a (field_inverse_zero(X_a) & number_ring(X_a) -> (all X hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),X),hAPP(int,X_a,number_number_of(X_a),min)) = hAPP(X_a,X_a,uminus_uminus(X_a),X)))) # label(fact_1157_divide__minus1) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.67 1269 (all N_1 all X hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,real_1(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),N_1),X))),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(nat,real,real_1(nat),N_1)),hAPP(nat,real,real_1(nat),X))))) # label(fact_1158_real__of__nat__div4) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.67 1270 (all X_a (linord1117847801e_zero(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),C),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))) -> 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),inverse_divide(X_a),C),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),C),B))))))))) # label(fact_1159_divide__left__mono__neg) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.67 1271 (all X_a (linordered_field(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)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),C)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(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_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),C),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),C),B))))))))) # label(fact_1160_divide__left__mono) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.67 1272 (all X_a (linordered_field(X_a) -> (all Ba all Aa all C_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),zero_zero(X_a))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),Ba),C_1)),Aa)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Aa),C_1)),Ba))))))) # label(fact_1161_neg__divide__le__eq) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.67 1273 (all X_a (linordered_field(X_a) -> (all Aa all Ba all C_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),zero_zero(X_a))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Aa),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),Ba),C_1))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Ba),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Aa),C_1)))))))) # label(fact_1162_neg__le__divide__eq) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.67 1274 (all X_a (linordered_field(X_a) -> (all Z all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),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),times_times(X_a),Z),Y)),X)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Z),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),X),Y)))))))) # label(fact_1163_mult__imp__le__div__pos) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.67 1275 (all X_a (linordered_field(X_a) -> (all X all Z all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),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),times_times(X_a),Z),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),inverse_divide(X_a),X),Y)),Z))))))) # label(fact_1164_mult__imp__div__pos__le) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.67 1276 (all X_a (linordered_field(X_a) -> (all Ba all Aa all C_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C_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),inverse_divide(X_a),Ba),C_1)),Aa)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Ba),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Aa),C_1)))))))) # label(fact_1165_pos__divide__le__eq) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.67 1277 (all X_a (linordered_field(X_a) -> (all Aa all Ba all C_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Aa),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),Ba),C_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),times_times(X_a),Aa),C_1)),Ba))))))) # label(fact_1166_pos__le__divide__eq) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.67 1278 (all X_a (linord1117847801e_zero(X_a) -> (all Ba all C_1 all Aa (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),Ba),C_1)),Aa)) <-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Ba),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Aa),C_1)))) & (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Aa),C_1)),Ba))) & (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),Aa)))))))) # label(fact_1167_divide__le__eq) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.67 1279 (all X_a (linord1117847801e_zero(X_a) -> (all Aa all Ba all C_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Aa),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),Ba),C_1))) <-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C_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),times_times(X_a),Aa),C_1)),Ba))) & (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Ba),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Aa),C_1)))) & (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Aa),zero_zero(X_a))))))))) # label(fact_1168_le__divide__eq) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.67 1280 (all X_a (linord1117847801e_zero(X_a) & number(X_a) -> (all Ba all W_1 all Aa (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),Ba),hAPP(int,X_a,number_number_of(X_a),W_1))),Aa)) <-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(int,X_a,number_number_of(X_a),W_1))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Ba),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Aa),hAPP(int,X_a,number_number_of(X_a),W_1))))) & (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(int,X_a,number_number_of(X_a),W_1))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(int,X_a,number_number_of(X_a),W_1)),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Aa),hAPP(int,X_a,number_number_of(X_a),W_1))),Ba))) & (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(int,X_a,number_number_of(X_a),W_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)),Aa)))))))) # label(fact_1169_divide__less__eq__number__of1) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.67 1281 (all X_a (linord1117847801e_zero(X_a) & number(X_a) -> (all Ba all C_1 all W_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),inverse_divide(X_a),Ba),C_1)),hAPP(int,X_a,number_number_of(X_a),W_1))) <-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Ba),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(int,X_a,number_number_of(X_a),W_1)),C_1)))) & (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(int,X_a,number_number_of(X_a),W_1)),C_1)),Ba))) & (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_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)),hAPP(int,X_a,number_number_of(X_a),W_1))))))))) # label(fact_1170_divide__less__eq__number__of) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.67 1282 (all X_a (linord1117847801e_zero(X_a) & number(X_a) -> (all W_1 all Ba all C_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(int,X_a,number_number_of(X_a),W_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),Ba),C_1))) <-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C_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),hAPP(int,X_a,number_number_of(X_a),W_1)),C_1)),Ba))) & (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Ba),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(int,X_a,number_number_of(X_a),W_1)),C_1)))) & (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(int,X_a,number_number_of(X_a),W_1)),zero_zero(X_a))))))))) # label(fact_1171_less__divide__eq__number__of) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.67 1283 (all X_a (linord1117847801e_zero(X_a) & number(X_a) -> (all Aa all Ba all W_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),Ba),hAPP(int,X_a,number_number_of(X_a),W_1)))) <-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(int,X_a,number_number_of(X_a),W_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),Aa),hAPP(int,X_a,number_number_of(X_a),W_1))),Ba))) & (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(int,X_a,number_number_of(X_a),W_1))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(int,X_a,number_number_of(X_a),W_1)),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Ba),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Aa),hAPP(int,X_a,number_number_of(X_a),W_1))))) & (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(int,X_a,number_number_of(X_a),W_1)),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),zero_zero(X_a))))))))) # label(fact_1172_less__divide__eq__number__of1) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.67 1284 (all X_a (field_inverse_zero(X_a) & number_ring(X_a) -> (all X hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),hAPP(int,X_a,number_number_of(X_a),min)),X) = hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),one_one(X_a)),X))))) # label(fact_1173_minus1__divide) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.67 1285 (all B all A_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_1),zero_zero(int))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B)) -> hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_1),B) = hAPP(product_prod(int,int),int,product_snd(int,int),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),negDivAlg,A_1),B))))) # label(fact_1174_mod__neg__pos) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.67 1286 (all B all A_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_1),zero_zero(int))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B)) -> hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_1),B) = hAPP(product_prod(int,int),int,product_fst(int,int),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),negDivAlg,A_1),B))))) # label(fact_1175_div__neg__pos) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.67 1287 (all X_a (linord1117847801e_zero(X_a) & number(X_a) -> (all Ba all W_1 all Aa (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),Ba),hAPP(int,X_a,number_number_of(X_a),W_1))),Aa)) <-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(int,X_a,number_number_of(X_a),W_1))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Ba),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Aa),hAPP(int,X_a,number_number_of(X_a),W_1))))) & (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(int,X_a,number_number_of(X_a),W_1))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(int,X_a,number_number_of(X_a),W_1)),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Aa),hAPP(int,X_a,number_number_of(X_a),W_1))),Ba))) & (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(int,X_a,number_number_of(X_a),W_1)),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),Aa)))))))) # label(fact_1176_divide__le__eq__number__of1) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.67 1288 (all X_a (linord1117847801e_zero(X_a) & number(X_a) -> (all Ba all C_1 all W_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),inverse_divide(X_a),Ba),C_1)),hAPP(int,X_a,number_number_of(X_a),W_1))) <-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Ba),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(int,X_a,number_number_of(X_a),W_1)),C_1)))) & (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(int,X_a,number_number_of(X_a),W_1)),C_1)),Ba))) & (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),hAPP(int,X_a,number_number_of(X_a),W_1))))))))) # label(fact_1177_divide__le__eq__number__of) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.67 1289 (all X_a (linord1117847801e_zero(X_a) & number(X_a) -> (all W_1 all Ba all C_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(int,X_a,number_number_of(X_a),W_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),Ba),C_1))) <-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C_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),times_times(X_a),hAPP(int,X_a,number_number_of(X_a),W_1)),C_1)),Ba))) & (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Ba),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(int,X_a,number_number_of(X_a),W_1)),C_1)))) & (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(int,X_a,number_number_of(X_a),W_1)),zero_zero(X_a))))))))) # label(fact_1178_le__divide__eq__number__of) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.67 1290 (all X_a (linord1117847801e_zero(X_a) & number(X_a) -> (all Aa all Ba all W_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Aa),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),Ba),hAPP(int,X_a,number_number_of(X_a),W_1)))) <-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(int,X_a,number_number_of(X_a),W_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),times_times(X_a),Aa),hAPP(int,X_a,number_number_of(X_a),W_1))),Ba))) & (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(int,X_a,number_number_of(X_a),W_1))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(int,X_a,number_number_of(X_a),W_1)),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Ba),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Aa),hAPP(int,X_a,number_number_of(X_a),W_1))))) & (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(int,X_a,number_number_of(X_a),W_1)),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Aa),zero_zero(X_a))))))))) # label(fact_1179_le__divide__eq__number__of1) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.67 1291 (all B all A_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),B)) -> hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_1),B) = hAPP(product_prod(int,int),int,product_snd(int,int),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),posDivAlg,A_1),B))))) # label(fact_1180_mod__pos__pos) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.67 1292 (all B all A_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),B)) -> hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_1),B) = hAPP(product_prod(int,int),int,product_fst(int,int),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),posDivAlg,A_1),B))))) # label(fact_1181_div__pos__pos) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.67 1293 (all N_1 all X hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(nat,real,real_1(nat),N_1)),hAPP(nat,real,real_1(nat),X))),hAPP(nat,real,real_1(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),N_1),X)))))) # label(fact_1182_real__of__nat__div2) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.67 1294 (all N_1 all X hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(nat,real,real_1(nat),N_1)),hAPP(nat,real,real_1(nat),X))),hAPP(nat,real,real_1(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),N_1),X)))),one_one(real)))) # label(fact_1183_real__of__nat__div3) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.67 1295 (all W (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),W))) -> hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),one_one(int)),hAPP(int,int,number_number_of(int),W)) = hAPP(product_prod(int,int),int,product_snd(int,int),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),posDivAlg,one_one(int)),hAPP(int,int,number_number_of(int),W))))) # label(fact_1184_mod__pos__pos__1__number__of) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.67 1296 (all W (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),W))) -> hAPP(int,int,hAPP(int,fun(int,int),div_div(int),one_one(int)),hAPP(int,int,number_number_of(int),W)) = hAPP(product_prod(int,int),int,product_fst(int,int),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),posDivAlg,one_one(int)),hAPP(int,int,number_number_of(int),W))))) # label(fact_1185_div__pos__pos__1__number__of) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.67 1297 (all B all A_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),zero_zero(int))) -> hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_1),B) = hAPP(product_prod(int,int),int,product_snd(int,int),hAPP(product_prod(int,int),product_prod(int,int),negateSnd,hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),negDivAlg,hAPP(int,int,uminus_uminus(int),A_1)),hAPP(int,int,uminus_uminus(int),B))))))) # label(fact_1186_mod__pos__neg) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.67 1298 (all X all D (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),D)) -> hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(nat,real,real_1(nat),X)),hAPP(nat,real,real_1(nat),D)) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,real_1(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),X),D))),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(nat,real,real_1(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),X),D))),hAPP(nat,real,real_1(nat),D))))) # label(fact_1187_real__of__nat__div__aux) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.67 1299 (all B all A_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),zero_zero(int))) -> hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_1),B) = hAPP(product_prod(int,int),int,product_fst(int,int),hAPP(product_prod(int,int),product_prod(int,int),negateSnd,hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),negDivAlg,hAPP(int,int,uminus_uminus(int),A_1)),hAPP(int,int,uminus_uminus(int),B))))))) # label(fact_1188_div__pos__neg) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.67 1300 (all X_b all X_a all Q_1 all Qa all P_1 all Pa (hBOOL(hAPP(X_a,bool,P_1,Pa)) -> (hBOOL(hAPP(X_b,bool,Q_1,Qa)) -> hBOOL(hAPP(X_a,bool,P_1,hAPP(product_prod(X_a,X_b),X_a,product_fst(X_a,X_b),hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),Pa),Qa)))) & hBOOL(hAPP(X_b,bool,Q_1,hAPP(product_prod(X_a,X_b),X_b,product_snd(X_a,X_b),hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),Pa),Qa))))))) # label(fact_1189_conjI__realizer) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.67 1301 (all X_b all X_a all P_1 all Y_1 all X_1 (hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),P_1,Y_1),X_1)) -> hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),P_1,hAPP(product_prod(X_b,X_a),X_a,product_snd(X_b,X_a),hAPP(X_a,product_prod(X_b,X_a),hAPP(X_b,fun(X_a,product_prod(X_b,X_a)),product_Pair(X_b,X_a),X_1),Y_1))),hAPP(product_prod(X_b,X_a),X_b,product_fst(X_b,X_a),hAPP(X_a,product_prod(X_b,X_a),hAPP(X_b,fun(X_a,product_prod(X_b,X_a)),product_Pair(X_b,X_a),X_1),Y_1)))))) # label(fact_1190_exI__realizer) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.67 1302 (all Y all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),X)),one_one(real))) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,abs_abs(real),Y)),one_one(real))) -> hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,arctan,X)),hAPP(real,real,arctan,Y)) = hAPP(real,real,arctan,hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),Y)),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),one_one(real)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),X),Y))))))) # label(fact_1191_arctan__add) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.67 1303 (all S_3 all T_3 all Aa all Ba (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Aa),Ba)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),S_3),T_3)) -> hBOOL(hAPP(fun(product_prod(product_prod(nat,nat),product_prod(nat,nat)),bool),bool,hAPP(product_prod(product_prod(nat,nat),product_prod(nat,nat)),fun(fun(product_prod(product_prod(nat,nat),product_prod(nat,nat)),bool),bool),member(product_prod(product_prod(nat,nat),product_prod(nat,nat))),hAPP(product_prod(nat,nat),product_prod(product_prod(nat,nat),product_prod(nat,nat)),hAPP(product_prod(nat,nat),fun(product_prod(nat,nat),product_prod(product_prod(nat,nat),product_prod(nat,nat))),product_Pair(product_prod(nat,nat),product_prod(nat,nat)),hAPP(nat,product_prod(nat,nat),hAPP(nat,fun(nat,product_prod(nat,nat)),product_Pair(nat,nat),Aa),S_3)),hAPP(nat,product_prod(nat,nat),hAPP(nat,fun(nat,product_prod(nat,nat)),product_Pair(nat,nat),Ba),T_3))),pair_less))))) # label(fact_1192_pair__lessI2) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.67 1304 (all V_3 all V ((hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V))) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(int,nat,number_number_of(nat),V)),hAPP(int,nat,number_number_of(nat),V_3)) = zero_zero(nat)) & (-hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V))) -> (hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V_3))) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(int,nat,number_number_of(nat),V)),hAPP(int,nat,number_number_of(nat),V_3)) = hAPP(int,nat,number_number_of(nat),V)) & (-hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V_3))) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(int,nat,number_number_of(nat),V)),hAPP(int,nat,number_number_of(nat),V_3)) = hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,number_number_of(int),V)),hAPP(int,int,number_number_of(int),V_3))))))) # label(fact_1193_mod__nat__number__of) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.67 1305 (all V_3 all V ((hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V))) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(int,nat,number_number_of(nat),V)),hAPP(int,nat,number_number_of(nat),V_3)) = zero_zero(nat)) & (-hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V))) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(int,nat,number_number_of(nat),V)),hAPP(int,nat,number_number_of(nat),V_3)) = hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,number_number_of(int),V)),hAPP(int,int,number_number_of(int),V_3)))))) # label(fact_1194_div__nat__number__of) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.67 1306 (all M_1 all N_1 hAPP(nat,product_prod(nat,nat),hAPP(nat,fun(nat,product_prod(nat,nat)),divmod_nat,M_1),N_1) = hAPP(nat,product_prod(nat,nat),hAPP(nat,fun(nat,product_prod(nat,nat)),product_Pair(nat,nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),M_1),N_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),M_1),N_1))) # label(fact_1195_divmod__nat__div__mod) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.67 1307 (all M_1 all N_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),M_1),N_1) = hAPP(product_prod(nat,nat),nat,product_snd(nat,nat),hAPP(nat,product_prod(nat,nat),hAPP(nat,fun(nat,product_prod(nat,nat)),divmod_nat,M_1),N_1))) # label(fact_1196_mod__nat__def) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.67 1308 (all M_1 all N_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),M_1),N_1) = hAPP(product_prod(nat,nat),nat,product_fst(nat,nat),hAPP(nat,product_prod(nat,nat),hAPP(nat,fun(nat,product_prod(nat,nat)),divmod_nat,M_1),N_1))) # label(fact_1197_div__nat__def) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.67 1309 (all X hAPP(real,real,arctan,hAPP(real,real,uminus_uminus(real),X)) = hAPP(real,real,uminus_uminus(real),hAPP(real,real,arctan,X))) # label(fact_1198_arctan__minus) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.67 1310 (all X_1 all Y_1 all P_1 ((hBOOL(P_1) -> hAPP(int,nat,nat_1,X_1) = hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),hAPP(bool,fun(int,fun(int,int)),if(int),P_1),X_1),Y_1))) & (-hBOOL(P_1) -> hAPP(int,nat,nat_1,Y_1) = hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),hAPP(bool,fun(int,fun(int,int)),if(int),P_1),X_1),Y_1))))) # label(fact_1199_nat__if__cong) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.67 1311 (all X all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),Y)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,arctan,X)),hAPP(real,real,arctan,Y))))) # label(fact_1200_arctan__monotone) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.67 1312 (all X all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X),Y)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,arctan,X)),hAPP(real,real,arctan,Y))))) # label(fact_1202_arctan__monotone_H) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.67 1313 (all X hAPP(real,nat,natceiling,X) = hAPP(int,nat,nat_1,hAPP(real,int,archimedean_ceiling(real),X))) # label(fact_1203_natceiling__def) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.67 1314 (all Z_3 all Z_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Z_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Z_3)) -> (hAPP(int,nat,nat_1,Z_1) = hAPP(int,nat,nat_1,Z_3) <-> Z_1 = Z_3)))) # label(fact_1206_eq__nat__nat__iff) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.67 1315 (all P_1 ((exists X1 hBOOL(hAPP(nat,bool,P_1,X1))) <-> (exists X_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X_2)) & hBOOL(hAPP(nat,bool,P_1,hAPP(int,nat,nat_1,X_2))))))) # label(fact_1207_ex__nat) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.67 1316 (all P_1 ((all X1 hBOOL(hAPP(nat,bool,P_1,X1))) <-> (all X_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X_2)) -> hBOOL(hAPP(nat,bool,P_1,hAPP(int,nat,nat_1,X_2))))))) # label(fact_1208_all__nat) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.67 1317 (all Y_1 all X_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Y_1)) -> (hAPP(int,nat,nat_1,X_1) = hAPP(int,nat,nat_1,Y_1) <-> X_1 = Y_1)))) # label(fact_1209_transfer__nat__int__relations_I1_J) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.67 1318 (all V hAPP(int,nat,number_number_of(nat),V) = hAPP(int,nat,nat_1,hAPP(int,int,number_number_of(int),V))) # label(fact_1210_nat__number__of__def) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.67 1319 (all W hAPP(int,nat,nat_1,hAPP(int,int,number_number_of(int),W)) = hAPP(int,nat,number_number_of(nat),W)) # label(fact_1211_nat__number__of) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.67 1320 (all Z (hBOOL(hAPP(int,bool,nat_neg,Z)) -> hAPP(int,nat,nat_1,Z) = zero_zero(nat))) # label(fact_1213_neg__nat) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.67 1321 (all X hAPP(real,nat,natfloor,X) = hAPP(int,nat,nat_1,hAPP(real,int,archim2085082626_floor(real),X))) # label(fact_1214_natfloor__def) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.67 1322 (all M_1 all N_1 hBOOL(hAPP(product_prod(nat,nat),bool,hAPP(nat,fun(product_prod(nat,nat),bool),hAPP(nat,fun(nat,fun(product_prod(nat,nat),bool)),divmod_nat_rel,M_1),N_1),hAPP(nat,product_prod(nat,nat),hAPP(nat,fun(nat,product_prod(nat,nat)),divmod_nat,M_1),N_1)))) # label(fact_1215_divmod__nat__rel__divmod__nat) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.67 1323 (all M_1 all N_1 all Qr_1 (hBOOL(hAPP(product_prod(nat,nat),bool,hAPP(nat,fun(product_prod(nat,nat),bool),hAPP(nat,fun(nat,fun(product_prod(nat,nat),bool)),divmod_nat_rel,M_1),N_1),Qr_1)) -> hAPP(nat,product_prod(nat,nat),hAPP(nat,fun(nat,product_prod(nat,nat)),divmod_nat,M_1),N_1) = Qr_1)) # label(fact_1216_divmod__nat__eq) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.67 1324 (all Z (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Z),zero_zero(int))) -> hAPP(int,nat,nat_1,Z) = zero_zero(nat))) # label(fact_1217_nat__le__0) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.67 1325 (all I (hAPP(int,nat,nat_1,I) = zero_zero(nat) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),I),zero_zero(int))))) # label(fact_1218_nat__0__iff) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.67 1326 (all W_1 all Z_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),Z_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(int,nat,nat_1,W_1)),hAPP(int,nat,nat_1,Z_1))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_1),Z_1))))) # label(fact_1219_nat__mono__iff) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.67 1327 (all W_1 all Z_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(int,nat,nat_1,W_1)),hAPP(int,nat,nat_1,Z_1))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),Z_1)) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_1),Z_1)))) # label(fact_1220_zless__nat__conj) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.67 1328 (all Y_1 all X_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Y_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(int,nat,nat_1,X_1)),hAPP(int,nat,nat_1,Y_1))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X_1),Y_1)))))) # label(fact_1221_transfer__nat__int__relations_I3_J) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.67 1329 (all W all Z hAPP(int,nat,nat_1,hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),W),Z))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,nat_1,hAPP(int,int,abs_abs(int),W))),hAPP(int,nat,nat_1,hAPP(int,int,abs_abs(int),Z)))) # label(fact_1222_nat__abs__mult__distrib) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.67 1330 (all M all N all Qr (hBOOL(hAPP(product_prod(nat,nat),bool,hAPP(nat,fun(product_prod(nat,nat),bool),hAPP(nat,fun(nat,fun(product_prod(nat,nat),bool)),divmod_nat_rel,M),N),Qr)) <-> M = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(product_prod(nat,nat),nat,product_fst(nat,nat),Qr)),N)),hAPP(product_prod(nat,nat),nat,product_snd(nat,nat),Qr)) & (N = zero_zero(nat) -> hAPP(product_prod(nat,nat),nat,product_fst(nat,nat),Qr) = zero_zero(nat)) & (N != zero_zero(nat) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),hAPP(product_prod(nat,nat),nat,product_snd(nat,nat),Qr))) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(product_prod(nat,nat),nat,product_snd(nat,nat),Qr)),N))) & (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),hAPP(product_prod(nat,nat),nat,product_snd(nat,nat),Qr))) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(product_prod(nat,nat),nat,product_snd(nat,nat),Qr)),zero_zero(nat))))))) # label(fact_1223_divmod__nat__rel__def) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.67 1331 (all Z_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(int,nat,nat_1,Z_1))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),Z_1)))) # label(fact_1224_zero__less__nat__eq) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.67 1332 (all Z_1 all W_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),W_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(int,nat,nat_1,W_1)),hAPP(int,nat,nat_1,Z_1))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_1),Z_1))))) # label(fact_1225_nat__less__eq__zless) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.67 1333 (all Y_1 all X_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Y_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(int,nat,nat_1,X_1)),hAPP(int,nat,nat_1,Y_1))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X_1),Y_1)))))) # label(fact_1226_transfer__nat__int__relations_I2_J) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.67 1334 (all Z_1 all W_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),W_1)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Z_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(int,nat,nat_1,W_1)),hAPP(int,nat,nat_1,Z_1))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),W_1),Z_1))))) # label(fact_1227_nat__le__eq__zle) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.67 1335 (all Z_4 all Z (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Z)) -> hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Z),Z_4)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,nat_1,Z)),hAPP(int,nat,nat_1,Z_4)))) # label(fact_1228_nat__mult__distrib) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.67 1336 (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)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,nat_1,X)),hAPP(int,nat,nat_1,Y)) = hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X),Y))))) # label(fact_1229_Nat__Transfer_Otransfer__nat__int__functions_I2_J) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.67 1337 (all Z_4 all Z (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Z)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Z_4)) -> hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Z),Z_4)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,nat_1,Z)),hAPP(int,nat,nat_1,Z_4))))) # label(fact_1230_nat__add__distrib) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.67 1338 (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)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,nat_1,X)),hAPP(int,nat,nat_1,Y)) = hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X),Y))))) # label(fact_1231_Nat__Transfer_Otransfer__nat__int__functions_I1_J) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.67 1339 (all M_1 hAPP(nat,product_prod(nat,nat),hAPP(nat,fun(nat,product_prod(nat,nat)),divmod_nat,M_1),zero_zero(nat)) = hAPP(nat,product_prod(nat,nat),hAPP(nat,fun(nat,product_prod(nat,nat)),product_Pair(nat,nat),zero_zero(nat)),M_1)) # label(fact_1232_divmod__nat__zero) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.67 1340 (all Z all Z_4 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Z_4)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Z_4),Z)) -> hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),Z),Z_4)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(int,nat,nat_1,Z)),hAPP(int,nat,nat_1,Z_4))))) # label(fact_1233_nat__diff__distrib) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.67 1341 (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)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(int,nat,nat_1,X)),hAPP(int,nat,nat_1,Y)) = hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),div_div(int),X),Y))))) # label(fact_1234_Divides_Otransfer__nat__int__functions_I1_J) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.67 1342 (all Y all X (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X)) -> hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),div_div(int),X),Y)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(int,nat,nat_1,X)),hAPP(int,nat,nat_1,Y)))) # label(fact_1235_nat__div__distrib) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.67 1343 (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)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(int,nat,nat_1,X)),hAPP(int,nat,nat_1,Y)) = hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),X),Y))))) # label(fact_1236_Divides_Otransfer__nat__int__functions_I2_J) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.67 1344 (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)) -> hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),X),Y)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(int,nat,nat_1,X)),hAPP(int,nat,nat_1,Y))))) # label(fact_1237_nat__mod__distrib) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.67 1345 (all S_3 all T_3 all Aa all Ba (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Aa),Ba)) -> hBOOL(hAPP(fun(product_prod(product_prod(nat,nat),product_prod(nat,nat)),bool),bool,hAPP(product_prod(product_prod(nat,nat),product_prod(nat,nat)),fun(fun(product_prod(product_prod(nat,nat),product_prod(nat,nat)),bool),bool),member(product_prod(product_prod(nat,nat),product_prod(nat,nat))),hAPP(product_prod(nat,nat),product_prod(product_prod(nat,nat),product_prod(nat,nat)),hAPP(product_prod(nat,nat),fun(product_prod(nat,nat),product_prod(product_prod(nat,nat),product_prod(nat,nat))),product_Pair(product_prod(nat,nat),product_prod(nat,nat)),hAPP(nat,product_prod(nat,nat),hAPP(nat,fun(nat,product_prod(nat,nat)),product_Pair(nat,nat),Aa),S_3)),hAPP(nat,product_prod(nat,nat),hAPP(nat,fun(nat,product_prod(nat,nat)),product_Pair(nat,nat),Ba),T_3))),pair_less)))) # label(fact_1238_pair__lessI1) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.67 1346 (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)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(int,nat,nat_1,X)),hAPP(int,nat,nat_1,Y)) = hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),nat_tsub,X),Y))))) # label(fact_1239_Nat__Transfer_Otransfer__nat__int__functions_I3_J) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.67 1347 (all Z_4 all Z (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Z),zero_zero(int))) -> hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Z),Z_4)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,nat_1,hAPP(int,int,uminus_uminus(int),Z))),hAPP(int,nat,nat_1,hAPP(int,int,uminus_uminus(int),Z_4))))) # label(fact_1240_nat__mult__distrib__neg) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.67 1348 (all M_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_1)) -> hAPP(nat,product_prod(nat,nat),hAPP(nat,fun(nat,product_prod(nat,nat)),divmod_nat,M_1),N_1) = hAPP(nat,product_prod(nat,nat),hAPP(nat,fun(nat,product_prod(nat,nat)),product_Pair(nat,nat),zero_zero(nat)),M_1))) # label(fact_1241_divmod__nat__base) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.67 1349 (all I_1 all N_1 hAPP(nat,nat,hAPP(int,fun(nat,nat),nat_aux,I_1),N_1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,nat_1,I_1)),N_1)) # label(fact_1242_nat__aux__def) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.67 1350 (all X_b all X_a all P_1 all Pa (hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),P_1,hAPP(product_prod(X_b,X_a),X_a,product_snd(X_b,X_a),Pa)),hAPP(product_prod(X_b,X_a),X_b,product_fst(X_b,X_a),Pa))) -> -(all X_2 all Y_2 -hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),P_1,Y_2),X_2))))) # label(fact_1244_exE__realizer_H) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.67 1351 (all M_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_1),M_1)) -> hAPP(nat,product_prod(nat,nat),hAPP(nat,fun(nat,product_prod(nat,nat)),divmod_nat,M_1),N_1) = hAPP(nat,product_prod(nat,nat),hAPP(nat,fun(nat,product_prod(nat,nat)),product_Pair(nat,nat),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),N_1)),N_1))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),N_1)),N_1))))) # label(fact_1245_divmod__nat__step) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.67 1352 (all V_3 ((hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V_3))) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,suc,zero_zero(nat))),hAPP(int,nat,number_number_of(nat),V_3)) = hAPP(nat,nat,suc,zero_zero(nat))) & (-hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V_3))) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,suc,zero_zero(nat))),hAPP(int,nat,number_number_of(nat),V_3)) = hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),one_one(int)),hAPP(int,int,number_number_of(int),V_3)))))) # label(fact_1246_one__mod__nat__number__of) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.67 1353 (all V_3 hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,suc,zero_zero(nat))),hAPP(int,nat,number_number_of(nat),V_3)) = hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),div_div(int),one_one(int)),hAPP(int,int,number_number_of(int),V_3)))) # label(fact_1247_one__div__nat__number__of) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.67 1354 (all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,number_number_of(real),min)),Y)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),Y),one_one(real))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(real,real,arccos,Y)))))) # label(fact_1248_arccos__lbound) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.67 1355 (all X_a all X_b all F all A_2 hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),nat_tr1645093318rphism(X_a,X_b),F),A_2))) # label(fact_1249_transfer__morphismI) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.67 1356 (all M_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,M_1)),hAPP(nat,nat,suc,N_1))))) # label(fact_1250_Suc__mono) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.67 1357 (all N_1 hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),hAPP(nat,nat,suc,N_1)))) # label(fact_1251_lessI) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.67 1358 (all N_1 hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,suc,N_1)))) # label(fact_1252_zero__less__Suc) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.67 1359 (all X all Y (hAPP(nat,nat,suc,X) = hAPP(nat,nat,suc,Y) -> X = Y)) # label(fact_1253_Suc__inject) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.67 1360 (all Nat all Nat_5 (hAPP(nat,nat,suc,Nat) = hAPP(nat,nat,suc,Nat_5) <-> Nat = Nat_5)) # label(fact_1254_nat_Oinject) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.67 1361 (all N_1 hAPP(nat,nat,suc,N_1) != N_1) # label(fact_1255_Suc__n__not__n) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.67 1362 (all N_1 N_1 != hAPP(nat,nat,suc,N_1)) # label(fact_1256_n__not__Suc__n) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.67 1363 (all M_1 zero_zero(nat) != hAPP(nat,nat,suc,M_1)) # label(fact_1257_Zero__not__Suc) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.67 1364 (all Nat_4 zero_zero(nat) != hAPP(nat,nat,suc,Nat_4)) # label(fact_1258_nat_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.67 1365 (all M_1 hAPP(nat,nat,suc,M_1) != zero_zero(nat)) # label(fact_1259_Suc__not__Zero) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.67 1366 (all Nat_3 hAPP(nat,nat,suc,Nat_3) != zero_zero(nat)) # label(fact_1260_nat_Osimps_I3_J) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.67 1367 (all M_1 zero_zero(nat) != hAPP(nat,nat,suc,M_1)) # label(fact_1261_Zero__neq__Suc) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.67 1368 (all M_1 hAPP(nat,nat,suc,M_1) != zero_zero(nat)) # label(fact_1262_Suc__neq__Zero) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.67 1369 (all M all N (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),hAPP(nat,nat,suc,M))))) # label(fact_1263_not__less__eq) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.67 1370 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),hAPP(nat,nat,suc,N))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N)) | M = N)) # label(fact_1264_less__Suc__eq) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.67 1371 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,M)),hAPP(nat,nat,suc,N))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N)))) # label(fact_1265_Suc__less__eq) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.67 1372 (all N all M (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),M)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),hAPP(nat,nat,suc,M))) <-> N = M))) # label(fact_1266_not__less__less__Suc__eq) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.67 1373 (all N_1 all M_1 (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),M_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),hAPP(nat,nat,suc,M_1))) -> M_1 = N_1))) # label(fact_1267_less__antisym) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.67 1374 (all M_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),hAPP(nat,nat,suc,N_1))))) # label(fact_1268_less__SucI) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.67 1375 (all M_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_1)) -> (hAPP(nat,nat,suc,M_1) != N_1 -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,M_1)),N_1))))) # label(fact_1269_Suc__lessI) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.67 1376 (all K_4 all I_1 all J_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),J_2)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),J_2),K_4)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,I_1)),K_4))))) # label(fact_1270_less__trans__Suc) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.67 1377 (all M_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),hAPP(nat,nat,suc,N_1))) -> (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_1)) -> M_1 = N_1))) # label(fact_1271_less__SucE) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.67 1378 (all M_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,M_1)),N_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_1)))) # label(fact_1272_Suc__lessD) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.67 1379 (all M_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,M_1)),hAPP(nat,nat,suc,N_1))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_1)))) # label(fact_1273_Suc__less__SucD) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.67 1380 (all X_a all X_b all F all A_2 hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),nat_tr1645093318rphism(X_a,X_b),F),A_2))) # label(fact_1274_transfer__morphism__def) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.67 1381 (all M_1 all N_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),hAPP(nat,nat,suc,N_1)) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),N_1))) # label(fact_1275_add__Suc__right) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.67 1382 (all M_1 all N_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,suc,M_1)),N_1) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),N_1))) # label(fact_1276_add__Suc) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.67 1383 (all M_1 all N_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,suc,M_1)),N_1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),hAPP(nat,nat,suc,N_1))) # label(fact_1277_add__Suc__shift) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.67 1384 (all M_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,M_1)),N_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),N_1)))) # label(fact_1278_Suc__leD) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.67 1385 (all M_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),hAPP(nat,nat,suc,N_1))) -> (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),N_1)) -> M_1 = hAPP(nat,nat,suc,N_1)))) # label(fact_1279_le__SucE) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.67 1386 (all M_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),N_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),hAPP(nat,nat,suc,N_1))))) # label(fact_1280_le__SucI) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.67 1387 (all N all M (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,N)),hAPP(nat,nat,suc,M))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N),M)))) # label(fact_1281_Suc__le__mono) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.67 1388 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),hAPP(nat,nat,suc,N))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N)) | M = hAPP(nat,nat,suc,N))) # label(fact_1282_le__Suc__eq) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.67 1389 (all M all N (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,N)),M)))) # label(fact_1283_not__less__eq__eq) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.67 1390 (all N_1 -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,N_1)),N_1))) # label(fact_1284_Suc__n__not__le__n) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.67 1391 (all K all M all N (hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,K)),M) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,K)),N) <-> M = N)) # label(fact_1285_Suc__mult__cancel1) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.67 1392 (all M_1 all N_1 all K_4 hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,M_1)),N_1)),hAPP(nat,nat,suc,K_4)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),N_1)),K_4)) # label(fact_1286_Suc__diff__diff) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.67 1393 (all M_1 all N_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,M_1)),hAPP(nat,nat,suc,N_1)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),N_1)) # label(fact_1287_diff__Suc__Suc) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.67 1394 (all M_1 all N_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,suc,M_1)),N_1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),M_1),N_1))),N_1)) # label(fact_1288_mod__Suc__eq__Suc__mod) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.67 1395 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),hAPP(nat,nat,suc,N))) <-> M = zero_zero(nat) | (exists J_1 (M = hAPP(nat,nat,suc,J_1) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),J_1),N)))))) # label(fact_1289_less__Suc__eq__0__disj) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.68 1396 (all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),hAPP(nat,nat,suc,zero_zero(nat)))) <-> N = zero_zero(nat))) # label(fact_1290_less__Suc0) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.68 1397 (all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) <-> (exists M_3 N = hAPP(nat,nat,suc,M_3)))) # label(fact_1291_gr0__conv__Suc) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.68 1398 (all M all N (hAPP(nat,nat,suc,zero_zero(nat)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N) <-> M = hAPP(nat,nat,suc,zero_zero(nat)) & N = zero_zero(nat) | M = zero_zero(nat) & N = hAPP(nat,nat,suc,zero_zero(nat)))) # label(fact_1292_one__is__add) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.68 1399 (all M all N (hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N) = hAPP(nat,nat,suc,zero_zero(nat)) <-> M = hAPP(nat,nat,suc,zero_zero(nat)) & N = zero_zero(nat) | M = zero_zero(nat) & N = hAPP(nat,nat,suc,zero_zero(nat)))) # label(fact_1293_add__is__1) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.68 1400 (all M all N (hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),N) = hAPP(nat,nat,suc,zero_zero(nat)) <-> M = hAPP(nat,nat,suc,zero_zero(nat)) & N = hAPP(nat,nat,suc,zero_zero(nat)))) # label(fact_1294_mult__eq__1__iff) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.68 1401 (all I_1 all M_1 hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_1),M_1))))) # label(fact_1295_less__add__Suc1) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.68 1402 (all I_1 all M_1 hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),I_1))))) # label(fact_1296_less__add__Suc2) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.68 1403 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N)) <-> (exists K_1 N = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),K_1))))) # label(fact_1297_less__iff__Suc__add) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.68 1404 (all M_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,M_1)),N_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_1)))) # label(fact_1299_Suc__le__lessD) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.68 1405 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),hAPP(nat,nat,suc,M))) <-> N = M))) # label(fact_1300_le__less__Suc__eq) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.68 1406 (all M_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,M_1)),N_1)))) # label(fact_1301_Suc__leI) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.68 1407 (all M_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),N_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),hAPP(nat,nat,suc,N_1))))) # label(fact_1302_le__imp__less__Suc) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.68 1408 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,M)),N)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N)))) # label(fact_1303_Suc__le__eq) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.68 1409 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),hAPP(nat,nat,suc,N))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N)))) # label(fact_1304_less__Suc__eq__le) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.68 1410 (all N all M (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),M)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,N)),M)))) # label(fact_1305_less__eq__Suc__le) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.68 1411 (all K all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,K)),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,K)),N))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N)))) # label(fact_1306_Suc__mult__less__cancel1) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.68 1412 (all M_1 all N_1 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),N_1)),hAPP(nat,nat,suc,M_1)))) # label(fact_1307_diff__less__Suc) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.68 1413 (all M_1 all N_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,M_1)),N_1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),N_1))) # label(fact_1308_mult__Suc) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.68 1414 (all M_1 all N_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),hAPP(nat,nat,suc,N_1)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),N_1))) # label(fact_1309_mult__Suc__right) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.68 1415 (all K all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,K)),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,K)),N))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N)))) # label(fact_1310_Suc__mult__le__cancel1) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.68 1416 (all N_1 hAPP(nat,nat,suc,N_1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),N_1)) # label(fact_1311_Suc__eq__plus1__left) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.68 1417 (all N_1 hAPP(nat,nat,suc,N_1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_1),one_one(nat))) # label(fact_1312_Suc__eq__plus1) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.68 1418 (all N_1 all M_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_1),M_1)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,M_1)),N_1) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),N_1)))) # label(fact_1313_Suc__diff__le) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.68 1419 (all N_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,N_1)),one_one(nat)) = N_1) # label(fact_1314_diff__Suc__1) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.68 1420 (all M_1 all N_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),hAPP(nat,nat,suc,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_1),one_one(nat))),N_1)) # label(fact_1315_diff__Suc__eq__diff__pred) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.68 1421 (all M_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),M_1),hAPP(nat,nat,suc,zero_zero(nat))) = M_1) # label(fact_1316_div__1) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.68 1422 (all M_1 all N_1 ((hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),M_1),N_1)) = N_1 -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,suc,M_1)),N_1) = zero_zero(nat)) & (hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),M_1),N_1)) != N_1 -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,suc,M_1)),N_1) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),M_1),N_1))))) # label(fact_1317_mod__Suc) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.68 1423 (all M_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),M_1),hAPP(nat,nat,suc,zero_zero(nat))) = zero_zero(nat)) # label(fact_1318_mod__1) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.68 1424 (all M_1 all K_4 (M_1 != hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),K_4) -> (M_1 != hAPP(nat,nat,suc,zero_zero(nat)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),M_1))))) # label(fact_1319_one__less__m) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.68 1425 (all M_1 all K_4 (M_1 != hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),K_4) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),K_4))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),K_4))))) # label(fact_1320_one__less__k) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.68 1426 (all M_1 all K_4 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K_4)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),M_1)) -> (hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),N_1) = K_4 -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),K_4))))))) # label(fact_1321_prod__mn__less__k) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.68 1427 (all N_1 all M_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),M_1)) -> (hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),N_1) = M_1 -> N_1 = hAPP(nat,nat,suc,zero_zero(nat))))) # label(fact_1322_mn__eq__m__one) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.68 1428 (all M_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),N_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),M_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),N_1)))))) # label(fact_1323_n__less__m__mult__n) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.68 1429 (all M_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),N_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),M_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N_1),M_1)))))) # label(fact_1324_n__less__n__mult__m) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.68 1430 (all M_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),N_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),M_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),N_1)))))) # label(fact_1325_one__less__mult) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.68 1431 (all I_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),hAPP(nat,nat,suc,I_1))),N_1)))) # label(fact_1326_diff__Suc__less) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.68 1432 (all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)) -> hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),hAPP(nat,nat,suc,zero_zero(nat)))) = N_1)) # label(fact_1327_Suc__pred) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.68 1433 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,zero_zero(nat))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),N))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,zero_zero(nat))),M)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,zero_zero(nat))),N)))) # label(fact_1328_one__le__mult__iff) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.68 1434 (all N_1 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(nat,real,real_1(nat),hAPP(nat,nat,suc,N_1))))) # label(fact_1329_real__of__nat__Suc__gt__zero) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.68 1435 (all M_1 all K_4 all J_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_4),J_2)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_2),K_4))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),K_4)),hAPP(nat,nat,suc,J_2)))) # label(fact_1332_diff__Suc__diff__eq1) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.68 1436 (all M_1 all K_4 all J_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_4),J_2)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_2),K_4))),M_1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,J_2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_4),M_1)))) # label(fact_1333_diff__Suc__diff__eq2) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.68 1437 (all N_1 hAPP(nat,real,real_1(nat),hAPP(nat,nat,suc,N_1)) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,real_1(nat),N_1)),one_one(real))) # label(fact_1334_real__of__nat__Suc) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.68 1438 (all K_4 all N_1 all M_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_4),N_1)),M_1))),N_1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,suc,M_1)),N_1)) # label(fact_1335_mod__mult__self4) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.68 1439 (all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)) -> hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),one_one(nat))) = N_1)) # label(fact_1336_Suc__diff__1) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.68 1440 (all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)) -> N_1 = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),one_one(nat))))) # label(fact_1337_Suc__pred_H) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.68 1441 (all N_1 all M_1 ((M_1 = zero_zero(nat) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),N_1) = N_1) & (M_1 != zero_zero(nat) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),N_1) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),one_one(nat))),N_1))))) # label(fact_1338_add__eq__if) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.68 1442 (all M_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)) -> (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_1)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),M_1),N_1) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),N_1)),N_1))))) # label(fact_1339_div__geq) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.68 1443 (all M_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_1)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),M_1),N_1) = zero_zero(nat)) & (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_1)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),M_1),N_1) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),N_1)),N_1))))) # label(fact_1340_div__if) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.68 1444 (all M_1 all K_4 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),one_one(nat)),K_4)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_4),M_1))),K_4) = one_one(nat))) # label(fact_1341_Suc__times__mod__eq) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.68 1445 (all N_1 all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(nat,real,real_1(nat),N_1)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),hAPP(nat,real,real_1(nat),hAPP(nat,nat,suc,N_1)))) -> hAPP(int,nat,nat_1,hAPP(real,int,archim2085082626_floor(real),X)) = N_1))) # label(fact_1342_floor__eq3) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.68 1446 (all Z_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),hAPP(int,nat,nat_1,Z_1))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),Z_1)))) # label(fact_1343_one__less__nat__eq) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.68 1447 (all V (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(int,nat,number_number_of(nat),V))) -> hAPP(int,nat,number_number_of(nat),V) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(int,nat,number_number_of(nat),V)),one_one(nat))))) # label(fact_1344_expand__Suc) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.68 1448 (all Z (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Z)) -> hAPP(nat,nat,suc,hAPP(int,nat,nat_1,Z)) = hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),Z)))) # label(fact_1345_Suc__nat__eq__nat__zadd1) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.68 1449 (all Qa all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N),Qa)),M)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N),hAPP(nat,nat,suc,Qa)))) <-> Qa = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),M),N)))) # label(fact_1346_split__div__lemma) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.68 1450 (all P_1 all M all N (hBOOL(hAPP(nat,bool,P_1,hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),M),N))) <-> N = zero_zero(nat) & hBOOL(hAPP(nat,bool,P_1,zero_zero(nat))) | (exists Q_3 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N),Q_3)),M)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N),hAPP(nat,nat,suc,Q_3)))) & hBOOL(hAPP(nat,bool,P_1,Q_3)))))) # label(fact_1347_split__div_H) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.68 1451 (all M_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_1),M_1)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),M_1),N_1) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),N_1)),N_1))))) # label(fact_1348_le__div__geq) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.68 1452 (all N_1 all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,real_1(nat),N_1)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),hAPP(nat,real,real_1(nat),hAPP(nat,nat,suc,N_1)))) -> hAPP(int,nat,nat_1,hAPP(real,int,archim2085082626_floor(real),X)) = N_1))) # label(fact_1349_floor__eq4) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.68 1453 (all X_a all X_b all F all G all Pa hAPP(product_prod(X_a,X_b),nat,hAPP(fun(X_b,nat),fun(product_prod(X_a,X_b),nat),hAPP(fun(X_a,nat),fun(fun(X_b,nat),fun(product_prod(X_a,X_b),nat)),product_prod_size(X_a,X_b),F),G),Pa) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(X_a,nat,F,hAPP(product_prod(X_a,X_b),X_a,product_fst(X_a,X_b),Pa))),hAPP(X_b,nat,G,hAPP(product_prod(X_a,X_b),X_b,product_snd(X_a,X_b),Pa)))),hAPP(nat,nat,suc,zero_zero(nat)))) # label(fact_1350_prod__size__simp) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.68 1454 (all X all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Y)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X)) -> (exists N_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,real_1(nat),N_2)),Y)),X)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,real_1(nat),hAPP(nat,nat,suc,N_2))),Y)))))))) # label(fact_1351_reals__Archimedean4) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.68 1455 (all R_4 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),R_4)) -> (exists N_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,real_1(nat),N_2)),R_4)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),R_4),hAPP(nat,real,real_1(nat),hAPP(nat,nat,suc,N_2)))))))) # label(fact_1352_reals__Archimedean6a) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.68 1456 (all A_1 all C hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,suc,A_1)),C) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),A_1),C)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,suc,zero_zero(nat))),C))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),A_1),C)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,suc,zero_zero(nat))),C))),C))) # label(fact_1353_div__Suc) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.68 1457 (all I all P_1 all Pa ((all I_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),Pa)) -> (hBOOL(hAPP(nat,bool,P_1,I_2)) -> hBOOL(hAPP(nat,bool,P_1,hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,suc,I_2)),Pa)))))) -> (hBOOL(hAPP(nat,bool,P_1,I)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),Pa)) -> hBOOL(hAPP(nat,bool,P_1,zero_zero(nat))))))) # label(fact_1354_mod__induct__0) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.68 1458 (all J all I all P_1 all Pa ((all I_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),Pa)) -> (hBOOL(hAPP(nat,bool,P_1,I_2)) -> hBOOL(hAPP(nat,bool,P_1,hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,suc,I_2)),Pa)))))) -> (hBOOL(hAPP(nat,bool,P_1,I)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),Pa)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),J),Pa)) -> hBOOL(hAPP(nat,bool,P_1,J))))))) # label(fact_1355_mod__induct) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.68 1459 (all P_1 all I all J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I),J)) -> (hBOOL(hAPP(nat,bool,P_1,J)) -> ((all I_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),J)) -> (hBOOL(hAPP(nat,bool,P_1,hAPP(nat,nat,suc,I_2))) -> hBOOL(hAPP(nat,bool,P_1,I_2))))) -> hBOOL(hAPP(nat,bool,P_1,I)))))) # label(fact_1356_inc__induct) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.68 1460 (all X (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat))))) -> X = zero_zero(nat) | X = hAPP(nat,nat,suc,zero_zero(nat)))) # label(fact_1357_nat__lt__two__imp__zero__or__one) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.68 1461 (all M_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_1)) -> (exists K_1 N_1 = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),K_1))))) # label(fact_1358_less__imp__Suc__add) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.68 1462 (all M all No_1 all F ((all N_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,F,N_2)),hAPP(nat,real,F,hAPP(nat,nat,suc,N_2))))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,F,M)),hAPP(nat,real,F,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),No_1)))))) # label(fact_1359_lemma__f__mono__add) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.68 1463 (all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)) -> (exists M_3 N_1 = hAPP(nat,nat,suc,M_3)))) # label(fact_1360_gr0__implies__Suc) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.68 1464 (all X_a (order(X_a) -> (all N all N_5 all F ((all N_2 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(nat,X_a,F,N_2)),hAPP(nat,X_a,F,hAPP(nat,nat,suc,N_2))))) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N),N_5)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(nat,X_a,F,N)),hAPP(nat,X_a,F,N_5)))))))) # label(fact_1361_lift__Suc__mono__le) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.68 1465 (all X_a (order(X_a) -> (all N all N_5 all F ((all N_2 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,F,N_2)),hAPP(nat,X_a,F,hAPP(nat,nat,suc,N_2))))) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),N_5)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,F,N)),hAPP(nat,X_a,F,N_5)))))))) # label(fact_1362_lift__Suc__mono__less) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.68 1466 (all X_a (order(X_a) -> (all N all M all F ((all N_2 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,F,N_2)),hAPP(nat,X_a,F,hAPP(nat,nat,suc,N_2))))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,F,N)),hAPP(nat,X_a,F,M))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),M))))))) # label(fact_1363_lift__Suc__mono__less__iff) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.68 1467 (all N_1 all V ((hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V))) -> hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),V)),N_1)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),N_1)) & (-hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V))) -> hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),V)),N_1)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,succ,V))),N_1)))) # label(fact_1364_Suc__nat__number__of__add) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.68 1468 (all I all P_1 all K (hBOOL(hAPP(nat,bool,P_1,K)) -> ((all N_2 (hBOOL(hAPP(nat,bool,P_1,hAPP(nat,nat,suc,N_2))) -> hBOOL(hAPP(nat,bool,P_1,N_2)))) -> hBOOL(hAPP(nat,bool,P_1,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),K),I)))))) # label(fact_1365_zero__induct__lemma) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.68 1469 (all N_1 all M_5 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,N_1)),M_5)) -> (exists M_3 M_5 = hAPP(nat,nat,suc,M_3)))) # label(fact_1366_Suc__le__D) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.68 1470 (all I_1 all K_4 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),K_4)) -> (K_4 != hAPP(nat,nat,suc,I_1) -> -(all J_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),J_1)) -> K_4 != hAPP(nat,nat,suc,J_1)))))) # label(fact_1367_lessE) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.68 1471 (all I_1 all K_4 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,I_1)),K_4)) -> -(all J_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),J_1)) -> K_4 != hAPP(nat,nat,suc,J_1))))) # label(fact_1368_Suc__lessE) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.68 1472 (all N_1 (N_1 != zero_zero(nat) -> (exists M_3 N_1 = hAPP(nat,nat,suc,M_3)))) # label(fact_1369_not0__implies__Suc) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.68 1473 (all K_4 hAPP(int,int,succ,K_4) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),K_4),one_one(int))) # label(fact_1370_succ__def) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.68 1474 (all K_4 hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),K_4),min) = hAPP(int,int,succ,K_4)) # label(fact_1371_diff__bin__simps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.68 1475 (all X_a (number_ring(X_a) -> (all K_4 hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,succ,K_4)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),one_one(X_a)),hAPP(int,X_a,number_number_of(X_a),K_4))))) # label(fact_1372_number__of__succ) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.68 1476 (all V ((hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V))) -> hAPP(nat,nat,suc,hAPP(int,nat,number_number_of(nat),V)) = one_one(nat)) & (-hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V))) -> hAPP(nat,nat,suc,hAPP(int,nat,number_number_of(nat),V)) = hAPP(int,nat,number_number_of(nat),hAPP(int,int,succ,V))))) # label(fact_1373_Suc__nat__number__of) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.68 1477 (all P_1 (-hBOOL(hAPP(nat,bool,P_1,zero_zero(nat))) -> ((exists X1 hBOOL(hAPP(nat,bool,P_1,X1))) -> (exists N_2 (-hBOOL(hAPP(nat,bool,P_1,N_2)) & hBOOL(hAPP(nat,bool,P_1,hAPP(nat,nat,suc,N_2)))))))) # label(fact_1374_exists__least__lemma) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.68 1478 (all Y (Y != zero_zero(nat) -> -(all Nat_2 Y != hAPP(nat,nat,suc,Nat_2)))) # label(fact_1375_nat_Oexhaust) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.68 1479 (all P_1 all K (hBOOL(hAPP(nat,bool,P_1,K)) -> ((all N_2 (hBOOL(hAPP(nat,bool,P_1,hAPP(nat,nat,suc,N_2))) -> hBOOL(hAPP(nat,bool,P_1,N_2)))) -> hBOOL(hAPP(nat,bool,P_1,zero_zero(nat)))))) # label(fact_1376_zero__induct) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.68 1480 (all N all P_1 (hBOOL(hAPP(nat,bool,P_1,zero_zero(nat))) -> ((all N_2 (hBOOL(hAPP(nat,bool,P_1,N_2)) -> hBOOL(hAPP(nat,bool,P_1,hAPP(nat,nat,suc,N_2))))) -> hBOOL(hAPP(nat,bool,P_1,N))))) # label(fact_1377_nat__induct) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.68 1481 (all K_4 all M_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),M_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),K_4)) -> hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),K_4),M_1)),K_4) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),K_4),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),hAPP(nat,nat,suc,zero_zero(nat))))))) # label(fact_1378_int__power__div__base) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.68 1482 (all S_3 all T_3 all Aa all Ba (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Aa),Ba)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),S_3),T_3)) -> hBOOL(hAPP(fun(product_prod(product_prod(nat,nat),product_prod(nat,nat)),bool),bool,hAPP(product_prod(product_prod(nat,nat),product_prod(nat,nat)),fun(fun(product_prod(product_prod(nat,nat),product_prod(nat,nat)),bool),bool),member(product_prod(product_prod(nat,nat),product_prod(nat,nat))),hAPP(product_prod(nat,nat),product_prod(product_prod(nat,nat),product_prod(nat,nat)),hAPP(product_prod(nat,nat),fun(product_prod(nat,nat),product_prod(product_prod(nat,nat),product_prod(nat,nat))),product_Pair(product_prod(nat,nat),product_prod(nat,nat)),hAPP(nat,product_prod(nat,nat),hAPP(nat,fun(nat,product_prod(nat,nat)),product_Pair(nat,nat),Aa),S_3)),hAPP(nat,product_prod(nat,nat),hAPP(nat,fun(nat,product_prod(nat,nat)),product_Pair(nat,nat),Ba),T_3))),pair_leq))))) # label(fact_1379_pair__leqI2) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.68 1483 (all X_a (comm_semiring_1(X_a) -> (all X all Y all Q_2 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_2) = 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_2)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),Y),Q_2))))) # label(fact_1380_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.68 1484 (all X_a (comm_semiring_1(X_a) -> (all X all P_4 all Q_2 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_4)),Q_2) = 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_4),Q_2))))) # label(fact_1381_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.68 1485 (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_1382_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.68 1486 (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_1383_zpower__zpower) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.68 1487 (all X all M_1 all Y hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),X),M_1)),Y)),M_1) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),X),Y)),M_1)) # label(fact_1384_zpower__zmod) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.68 1488 (all X_a (ring_1(X_a) -> (all N all Aa (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Aa),ring_1_Ints(X_a))) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),Aa),N)),ring_1_Ints(X_a))))))) # label(fact_1385_Ints__power) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.68 1489 (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),zero_zero(nat)) = one_one(X_a)))) # label(fact_1386_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.68 1490 (all X_a (comm_semiring_1(X_a) -> (all X all Q_2 hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),hAPP(nat,nat,suc,Q_2)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),Q_2))))) # label(fact_1387_comm__semiring__1__class_Onormalizing__semiring__rules_I35_J) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.68 1491 (all X_a (comm_semiring_1(X_a) -> (all X all Q_2 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),Q_2)) = hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),hAPP(nat,nat,suc,Q_2))))) # label(fact_1388_comm__semiring__1__class_Onormalizing__semiring__rules_I27_J) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.68 1492 (all X_a (comm_semiring_1(X_a) -> (all X all Q_2 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_2)),X) = hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),hAPP(nat,nat,suc,Q_2))))) # label(fact_1389_comm__semiring__1__class_Onormalizing__semiring__rules_I28_J) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.68 1493 (all X_a (comm_semiring_1(X_a) -> (all X all P_4 all Q_2 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_4)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),Q_2)) = 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_4),Q_2))))) # label(fact_1390_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.68 1494 (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_1391_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.68 1495 (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_1392_zpower__zadd__distrib) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.68 1496 (all X_a (power(X_a) & mult_zero(X_a) & no_zero_divisors(X_a) & zero_neq_one(X_a) -> (all Aa all W_1 (hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),Aa),hAPP(int,nat,number_number_of(nat),W_1)) = zero_zero(X_a) <-> ti(X_a,Aa) = zero_zero(X_a) & hAPP(int,nat,number_number_of(nat),W_1) != zero_zero(nat))))) # label(fact_1393_power__eq__0__iff__number__of) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.68 1497 (all X_a (idom(X_a) -> (all X_1 all Y_1 (hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X_1),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat)))) = hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),Y_1),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat)))) <-> ti(X_a,X_1) = ti(X_a,Y_1) | ti(X_a,X_1) = hAPP(X_a,X_a,uminus_uminus(X_a),Y_1))))) # label(fact_1394_realpow__two__disj) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.68 1498 (all X all N_1 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),hAPP(int,int,abs_abs(int),X)),N_1)))) # label(fact_1395_zero__le__zpower__abs) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.68 1499 (all X_a (linordered_semidom(X_a) -> (all N_1 all R_4 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),R_4)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),R_4),one_one(X_a))) -> 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),R_4),hAPP(nat,nat,suc,N_1))),R_4))))))) # label(fact_1396_realpow__Suc__le__self) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.68 1500 (all X_a (power(X_a) & semiring_0(X_a) -> (all W ((hAPP(int,nat,number_number_of(nat),W) = zero_zero(nat) -> hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),zero_zero(X_a)),hAPP(int,nat,number_number_of(nat),W)) = one_one(X_a)) & (hAPP(int,nat,number_number_of(nat),W) != zero_zero(nat) -> hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),zero_zero(X_a)),hAPP(int,nat,number_number_of(nat),W)) = zero_zero(X_a)))))) # label(fact_1397_power__0__left__number__of) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.68 1501 (all X_a (monoid_mult(X_a) -> (all Y all P_4 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),P_4),N_1)) -> hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),Y),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,N_1)),P_4)) = 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),Y),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),P_4))),Y))))) # label(fact_1398_lemma__realpow__diff) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.68 1502 (all X_a (number_ring(X_a) & linordered_idom(X_a) -> (all N_1 hAPP(X_a,X_a,abs_abs(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(int,X_a,number_number_of(X_a),min)),N_1)) = one_one(X_a)))) # label(fact_1399_abs__power__minus__one) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.68 1503 (all X_1 all N (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),hAPP(int,int,abs_abs(int),X_1)),N))) <-> X_1 != zero_zero(int) | N = zero_zero(nat))) # label(fact_1400_zero__less__zpower__abs__iff) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.68 1504 (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),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat))))),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),Y),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat))))) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),X),Y)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X),Y))))) # label(fact_1401_realpow__two__diff) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.68 1505 (all X_a (power(X_a) -> (all M_1 all N_1 ((N_1 = zero_zero(nat) -> hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),M_1),N_1) = one_one(X_a)) & (N_1 != zero_zero(nat) -> hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),M_1),N_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),M_1),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),M_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),one_one(nat))))))))) # label(fact_1402_realpow__num__eq__if) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.68 1506 (all X_a (monoid_mult(X_a) -> (all X all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),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),X),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),one_one(nat)))),X) = hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),N_1))))) # label(fact_1403_realpow__minus__mult) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.68 1507 (all A_1 all P_4 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),P_4)) -> hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A_1),hAPP(int,nat,nat_1,P_4)) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(int,nat,nat_1,P_4)),one_one(nat)))))) # label(fact_1404_Euler_Oaux__1) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.68 1508 (all S_3 all T_3 all Aa all Ba (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Aa),Ba)) -> hBOOL(hAPP(fun(product_prod(product_prod(nat,nat),product_prod(nat,nat)),bool),bool,hAPP(product_prod(product_prod(nat,nat),product_prod(nat,nat)),fun(fun(product_prod(product_prod(nat,nat),product_prod(nat,nat)),bool),bool),member(product_prod(product_prod(nat,nat),product_prod(nat,nat))),hAPP(product_prod(nat,nat),product_prod(product_prod(nat,nat),product_prod(nat,nat)),hAPP(product_prod(nat,nat),fun(product_prod(nat,nat),product_prod(product_prod(nat,nat),product_prod(nat,nat))),product_Pair(product_prod(nat,nat),product_prod(nat,nat)),hAPP(nat,product_prod(nat,nat),hAPP(nat,fun(nat,product_prod(nat,nat)),product_Pair(nat,nat),Aa),S_3)),hAPP(nat,product_prod(nat,nat),hAPP(nat,fun(nat,product_prod(nat,nat)),product_Pair(nat,nat),Ba),T_3))),pair_leq)))) # label(fact_1405_pair__leqI1) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.68 1509 (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_1406_power__strict__mono) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.68 1510 (all X_a (field(X_a) -> (all N_1 all M_1 all A_1 (ti(X_a,A_1) != zero_zero(X_a) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_1),M_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),minus_minus(nat),M_1),N_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),M_1)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N_1))))))) # label(fact_1407_power__diff) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.68 1511 (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(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),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_1408_one__less__power) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.68 1512 (all X_a (linordered_semidom(X_a) -> (all X_1 all Y_1 all Ba (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),Ba)) -> (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),Ba),X_1)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),Ba),Y_1))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X_1),Y_1))))))) # label(fact_1409_power__increasing__iff) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.68 1513 (all X_a (linordered_semidom(X_a) -> (all M_1 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_1)),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_1),N_1))))))) # label(fact_1410_power__le__imp__le__exp) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.68 1514 (all X_a (linordered_semidom(X_a) -> (all A_1 all N_1 all N_6 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_1),N_6)) -> (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),A_1),one_one(X_a))) -> 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_6)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N_1))))))))) # label(fact_1411_power__decreasing) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.68 1515 (all M_1 all N_1 hAPP(nat,real,real_1(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),M_1),N_1)) = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(nat,real,real_1(nat),M_1)),N_1)) # label(fact_1412_real__of__nat__power) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.68 1516 (all M_1 all N_1 hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(nat,real,real_1(nat),M_1)),N_1) = hAPP(nat,real,real_1(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),M_1),N_1))) # label(fact_1413_power__real__of__nat) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.68 1517 (all N_1 all X (X = hAPP(nat,real,real_1(nat),hAPP(real,nat,natfloor,X)) -> hAPP(real,nat,natfloor,hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),N_1)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),hAPP(real,nat,natfloor,X)),N_1))) # label(fact_1414_natfloor__power) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.68 1518 (all M all N (hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),M),N) = zero_zero(nat) <-> N != zero_zero(nat) & M = zero_zero(nat))) # label(fact_1415_nat__power__eq__0__iff) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.68 1519 (all X_1 all N all Y_1 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),X_1),hAPP(nat,nat,suc,N)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),Y_1),hAPP(nat,nat,suc,N)) <-> X_1 = Y_1)) # label(fact_1416_exp__mono__eq) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.68 1520 (all X_1 all M (hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),X_1),M) = hAPP(nat,nat,suc,zero_zero(nat)) <-> M = zero_zero(nat) | X_1 = hAPP(nat,nat,suc,zero_zero(nat)))) # label(fact_1417_nat__power__eq__Suc__0__iff) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.68 1521 (all N_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),hAPP(nat,nat,suc,zero_zero(nat))),N_1) = hAPP(nat,nat,suc,zero_zero(nat))) # label(fact_1418_power__Suc__0) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.68 1522 (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_1419_nat__zero__less__power__iff) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.68 1523 (all M_1 all N_1 all I_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),I_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),I_1),M_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),I_1),N_1))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_1))))) # label(fact_1420_nat__power__less__imp__less) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.68 1524 (all N_1 all I_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,zero_zero(nat))),I_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,zero_zero(nat))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),I_1),N_1))))) # label(fact_1421_nat__one__le__power) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.68 1525 (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))) <-> N = zero_zero(nat) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X_1)))) # label(fact_1422_zero__less__power__nat__eq) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.68 1526 (all X_1 all N all Y_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),X_1),hAPP(nat,nat,suc,N))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),Y_1),hAPP(nat,nat,suc,N)))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X_1),Y_1)))) # label(fact_1423_exp__mono__lt) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.68 1527 (all X_1 all N (hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),X_1),N) = one_one(nat) <-> X_1 = one_one(nat) | N = zero_zero(nat))) # label(fact_1424_exp__eq__1) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.68 1528 (all X_1 all N all Y_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),X_1),hAPP(nat,nat,suc,N))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),Y_1),hAPP(nat,nat,suc,N)))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X_1),Y_1)))) # label(fact_1425_exp__mono__le) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.68 1529 (all X_1 all W_1 (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),hAPP(int,nat,number_number_of(nat),W_1)))) <-> hAPP(int,nat,number_number_of(nat),W_1) = zero_zero(nat) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X_1)))) # label(fact_1426_zero__less__power__nat__eq__number__of) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.68 1530 (all P_4 all M_1 ((M_1 = zero_zero(nat) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),P_4),M_1) = one_one(nat)) & (M_1 != zero_zero(nat) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),P_4),M_1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),P_4),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),P_4),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),one_one(nat))))))) # label(fact_1427_power__eq__if) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.68 1531 (all N_1 all X (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),hAPP(int,nat,nat_1,X)),N_1) = hAPP(int,nat,nat_1,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),X),N_1)))) # label(fact_1428_Nat__Transfer_Otransfer__nat__int__functions_I4_J) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.68 1532 (all N_1 all Z (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Z)) -> hAPP(int,nat,nat_1,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),Z),N_1)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),hAPP(int,nat,nat_1,Z)),N_1))) # label(fact_1429_nat__power__eq) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.68 1533 (all W all V ((hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V))) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),hAPP(int,nat,number_number_of(nat),V)),hAPP(int,nat,number_number_of(nat),W)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),zero_zero(nat)),hAPP(int,nat,number_number_of(nat),W))) & (-hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V))) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),hAPP(int,nat,number_number_of(nat),V)),hAPP(int,nat,number_number_of(nat),W)) = hAPP(int,nat,nat_1,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,number_number_of(int),V)),hAPP(int,nat,number_number_of(nat),W)))))) # label(fact_1430_power__nat__number__of__number__of) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.68 1534 (all N_1 all V ((hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V))) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),hAPP(int,nat,number_number_of(nat),V)),N_1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),zero_zero(nat)),N_1)) & (-hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V))) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),hAPP(int,nat,number_number_of(nat),V)),N_1) = hAPP(int,nat,nat_1,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,number_number_of(int),V)),N_1))))) # label(fact_1431_power__nat__number__of) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.68 1535 (all X_a (ring_11004092258visors(X_a) -> (all N_1 all A_1 (ti(X_a,A_1) != zero_zero(X_a) -> hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N_1) != zero_zero(X_a))))) # label(fact_1432_field__power__not__zero) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.68 1536 (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_1433_power__commutes) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.68 1537 (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_1434_power__mult__distrib) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.68 1538 (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_1435_power__one) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.68 1539 (all X_a (field_inverse_zero(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),inverse_divide(X_a),A_1),B)),N_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(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_1436_power__divide) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.68 1540 (all X_a (monoid_mult(X_a) -> (all A_1 all M_1 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_1),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_1)),N_1)))) # label(fact_1437_power__mult) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.68 1541 (all X_a (linordered_idom(X_a) -> (all A_1 all N_1 hAPP(X_a,X_a,abs_abs(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),hAPP(X_a,X_a,abs_abs(X_a),A_1)),N_1)))) # label(fact_1438_power__abs) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.68 1542 (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_1439_power__one__right) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.68 1543 (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),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)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N_1))))))) # label(fact_1440_zero__le__power) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.68 1544 (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_eq(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(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),B),N_1)))))))) # label(fact_1441_power__mono) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.68 1545 (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_1442_zero__less__power) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.68 1546 (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_1443_one__le__power) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.68 1547 (all X_a (linordered_semidom(X_a) -> (all M all N all Aa (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),Aa)) -> (hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),Aa),M) = hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),Aa),N) <-> M = N))))) # label(fact_1444_power__inject__exp) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.68 1548 (all X_a (power(X_a) & mult_zero(X_a) & no_zero_divisors(X_a) & zero_neq_one(X_a) -> (all Aa all N (hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),Aa),N) = zero_zero(X_a) <-> ti(X_a,Aa) = zero_zero(X_a) & N != zero_zero(nat))))) # label(fact_1445_power__eq__0__iff) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.68 1549 (all X_a (power(X_a) & semiring_0(X_a) -> (all N_1 hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),zero_zero(X_a)),hAPP(nat,nat,suc,N_1)) = zero_zero(X_a)))) # label(fact_1446_power__0__Suc) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.68 1550 (all X_a (field(X_a) -> (all A_1 all N_1 all B (ti(X_a,B) != zero_zero(X_a) -> 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),inverse_divide(X_a),A_1),B)),N_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(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_1447_nonzero__power__divide) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.68 1551 (all X_a (power(X_a) -> (all A_1 hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),zero_zero(nat)) = one_one(X_a)))) # label(fact_1448_power__0) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.68 1552 (all X_a (power(X_a) -> (all A_1 all N_1 hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),hAPP(nat,nat,suc,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_1449_power__Suc) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.68 1553 (all X_a (monoid_mult(X_a) -> (all A_1 all N_1 hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),hAPP(nat,nat,suc,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)))) # label(fact_1450_power__Suc2) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.68 1554 (all X_a (monoid_mult(X_a) -> (all A_1 all M_1 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_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),A_1),M_1)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N_1))))) # label(fact_1451_power__add) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.68 1555 (all X_a (field_inverse_zero(X_a) -> (all A_1 all N_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(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)) = 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),inverse_divide(X_a),one_one(X_a)),A_1)),N_1)))) # label(fact_1452_power__one__over) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.68 1556 (all X_a (linordered_idom(X_a) -> (all A_1 all N_1 hAPP(X_a,X_a,abs_abs(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),A_1)),N_1)) = hAPP(X_a,X_a,abs_abs(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N_1))))) # label(fact_1453_abs__power__minus) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.68 1557 (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_1454_power__less__imp__less__base) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.68 1558 (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_1455_power__gt1__lemma) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.68 1559 (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_1456_power__less__power__Suc) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.68 1560 (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),hAPP(nat,nat,suc,N_1)) = hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),B),hAPP(nat,nat,suc,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)) -> ti(X_a,A_1) = ti(X_a,B))))))) # label(fact_1457_power__inject__base) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.68 1561 (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_eq(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),hAPP(nat,nat,suc,N_1))),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),B),hAPP(nat,nat,suc,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_eq(X_a),A_1),B))))))) # label(fact_1458_power__le__imp__le__base) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.68 1562 (all X_a (power(X_a) & semiring_0(X_a) -> (all N_1 ((N_1 = zero_zero(nat) -> hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),zero_zero(X_a)),N_1) = one_one(X_a)) & (N_1 != zero_zero(nat) -> hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),zero_zero(X_a)),N_1) = zero_zero(X_a)))))) # label(fact_1459_power__0__left) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.68 1563 (all X_a (linordered_idom(X_a) -> (all A_1 all N_1 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(X_a,X_a,abs_abs(X_a),A_1)),N_1)))))) # label(fact_1460_zero__le__power__abs) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.68 1564 (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(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),hAPP(nat,nat,suc,N_1)))))))) # label(fact_1461_power__gt1) # label(axiom) # label(non_clause). [assumption].
% 7.67/7.68 1565 (all X_a (linordered_semidom(X_a) -> (all A_1 all N_1 all N_6 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),N_6)) -> (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_6)))))))) # label(fact_1462_power__strict__increasing) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.68 1566 (all X_a (linordered_semidom(X_a) -> (all M_1 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_1)),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_1),N_1))))))) # label(fact_1463_power__less__imp__less__exp) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.68 1567 (all X_a (linordered_semidom(X_a) -> (all X_1 all Y_1 all Ba (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),Ba)) -> (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),Ba),X_1)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),Ba),Y_1))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X_1),Y_1))))))) # label(fact_1464_power__strict__increasing__iff) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.68 1568 (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_1465_power__minus) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.68 1569 (all X_a (linordered_semidom(X_a) -> (all A_1 all N_1 all N_6 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_1),N_6)) -> (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_6)))))))) # label(fact_1466_power__increasing) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.68 1570 (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),A_1),one_one(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),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_1)))))))) # label(fact_1467_power__Suc__less) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.68 1571 (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),A_1),one_one(X_a))) -> 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),hAPP(nat,nat,suc,N_1))),one_one(X_a)))))))) # label(fact_1468_power__Suc__less__one) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.68 1572 (all X_a (linordered_semidom(X_a) -> (all A_1 all N_1 all N_6 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),N_6)) -> (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),A_1),one_one(X_a))) -> 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_6)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N_1))))))))) # label(fact_1469_power__strict__decreasing) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.68 1573 (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_1470_power__eq__imp__eq__base) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.68 1574 (all N_1 all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,real_1(nat),N_1)),X)),one_one(real))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),one_one(real))),N_1))))) # label(fact_1471_LIMSEQ__inverse__realpow__zero__lemma) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.68 1575 (all A_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A_1)) -> (exists R_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),R_2)) & hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),R_2),N_1) = A_1))))) # label(fact_1472_realpow__pos__nth) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.68 1576 (all A_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A_1)) -> (exists X_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X_2)) & hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X_2),N_1) = A_1 & (all Y_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Y_2)) & hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),Y_2),N_1) = A_1 -> Y_2 = X_2))))))) # label(fact_1473_realpow__pos__nth__unique) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1577 (all N_1 (hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,number_number_of(int),min)),N_1) = one_one(int) | hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,number_number_of(int),min)),N_1) = hAPP(int,int,number_number_of(int),min))) # label(fact_1474_neg__one__power) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1578 (all N_1 all A_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A_1)) -> (exists R_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),R_2)) & hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),R_2),hAPP(nat,nat,suc,N_1)) = A_1)))) # label(fact_1475_realpow__pos__nth2) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1579 (all X_a (power(X_a) -> power_power(X_a) = hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(nat,X_a)),hAPP(X_a,fun(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(nat,X_a))),power_1(X_a),one_one(X_a)),times_times(X_a)))) # label(fact_1476_power__power__power) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1580 (all X_a all One all Times all Aa hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(nat,X_a)),hAPP(X_a,fun(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(nat,X_a))),power_1(X_a),One),Times),Aa),zero_zero(nat)) = ti(X_a,One)) # label(fact_1477_power_Opower_Opower__0) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1581 (all X_a all One all Times all Aa all N hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(nat,X_a)),hAPP(X_a,fun(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(nat,X_a))),power_1(X_a),One),Times),Aa),hAPP(nat,nat,suc,N)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),Times,Aa),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(nat,X_a)),hAPP(X_a,fun(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(nat,X_a))),power_1(X_a),One),Times),Aa),N))) # label(fact_1478_power_Opower_Opower__Suc) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1582 (all X_1 (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),zEven)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X_1)) -> hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,number_number_of(int),min)),hAPP(int,nat,nat_1,X_1)) = one_one(int)))) # label(fact_1479_EvenOdd_Oneg__one__even__power) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1583 (all X_1 (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),zOdd)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X_1)) -> hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,number_number_of(int),min)),hAPP(int,nat,nat_1,X_1)) = hAPP(int,int,number_number_of(int),min)))) # label(fact_1480_EvenOdd_Oneg__one__odd__power) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1584 (all Y_1 all X_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Y_1)) -> ((hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),zEven)) <-> hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Y_1),zEven))) -> hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,number_number_of(int),min)),hAPP(int,nat,nat_1,X_1)) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,number_number_of(int),min)),hAPP(int,nat,nat_1,Y_1)))))) # label(fact_1481_neg__one__power__parity) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1585 (all N_1 all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,real_1(int),N_1)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(int,real,real_1(int),N_1)),one_one(real)))) -> hAPP(real,int,archimedean_ceiling(real),X) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),N_1),one_one(int))))) # label(fact_1482_ceiling__eq2) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1586 (all Aa all X_1 (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),zOdd)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X_1)) -> hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,uminus_uminus(int),Aa)),hAPP(int,nat,nat_1,X_1)) = hAPP(int,int,uminus_uminus(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),Aa),hAPP(int,nat,nat_1,X_1)))))) # label(fact_1483_neg__odd__power) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1587 (all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,number_number_of(real),min)),Y)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),Y),one_one(real))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,arccos,Y))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,arccos,Y)),pi))))) # label(fact_1484_arccos__lt__bounded) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1588 (all X_1 -(hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),zOdd)) & hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),zEven)))) # label(fact_1485_even__odd__conj) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1589 (all X_1 (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),zOdd)) <-> -hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),zEven)))) # label(fact_1486_odd__iff__not__even) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1590 (all X_1 (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),zOdd)) | hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),zEven)))) # label(fact_1487_even__odd__disj) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1591 (all X_1 (-hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),zOdd)) -> hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),zEven)))) # label(fact_1488_not__odd__impl__even) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1592 (all Y_1 all X_1 (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),zOdd)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Y_1),zOdd)) -> hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X_1),Y_1)),zEven))))) # label(fact_1489_odd__minus__odd) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1593 (all Y_1 all X_1 (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),zOdd)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Y_1),zEven)) -> hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X_1),Y_1)),zOdd))))) # label(fact_1490_odd__minus__even) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1594 (all Y_1 all X_1 (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),zEven)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Y_1),zOdd)) -> hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X_1),Y_1)),zOdd))))) # label(fact_1491_even__minus__odd) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1595 (all Aa all Ba (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Aa),Ba)),zOdd)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Aa),zEven)) -> hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Ba),zOdd))))) # label(fact_1492_even__plus__odd__prop2) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1596 (all Aa all Ba (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Aa),Ba)),zOdd)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Aa),zOdd)) -> hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Ba),zEven))))) # label(fact_1493_even__plus__odd__prop1) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1597 (all Ba all Aa (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Aa),zEven)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Ba),zOdd)) -> hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Aa),Ba)),zOdd))))) # label(fact_1494_IntNatAux_Oeven__plus__odd) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1598 (all Ba all Aa (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Aa),zOdd)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Ba),zOdd)) -> hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Aa),Ba)),zEven))))) # label(fact_1495_IntNatAux_Oodd__plus__odd) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1599 (all X_1 all Y_1 (hAPP(int,real,real_1(int),X_1) = hAPP(int,real,real_1(int),Y_1) <-> X_1 = Y_1)) # label(fact_1496_real__of__int__inject) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1600 (all N_1 hAPP(real,int,archim2085082626_floor(real),hAPP(int,real,real_1(int),N_1)) = N_1) # label(fact_1498_floor__real__of__int) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1601 (all X_1 (hAPP(int,real,real_1(int),hAPP(real,int,archim2085082626_floor(real),X_1)) = X_1 <-> (exists N_2 X_1 = hAPP(int,real,real_1(int),N_2)))) # label(fact_1499_real__of__int__floor__cancel) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1602 (all X_1 (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),zOdd)) -> hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X_1),one_one(int))),zEven)))) # label(fact_1500_odd__minus__one__even) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1603 (all N_1 hAPP(real,int,archimedean_ceiling(real),hAPP(int,real,real_1(int),N_1)) = N_1) # label(fact_1501_ceiling__real__of__int) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1604 (all X_1 (hAPP(int,real,real_1(int),hAPP(real,int,archimedean_ceiling(real),X_1)) = X_1 <-> (exists N_2 X_1 = hAPP(int,real,real_1(int),N_2)))) # label(fact_1502_real__of__int__ceiling__cancel) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1605 (all X_1 all Y_1 (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),X_1),Y_1)),zEven)) -> hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),zEven)) | hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Y_1),zEven)))) # label(fact_1504_EvenOdd_Oeven__product) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1606 (all Y_1 all X_1 (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),zEven)) -> 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),X_1),Y_1)),zEven)))) # label(fact_1505_even__times__either) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1607 (all Y_1 all X_1 (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),zEven)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Y_1),zEven)) -> hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X_1),Y_1)),zEven))))) # label(fact_1506_EvenOdd_Oeven__plus__even) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1608 (all Y_1 all X_1 (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),zEven)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Y_1),zEven)) -> hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X_1),Y_1)),zEven))))) # label(fact_1507_even__minus__even) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1609 (all X_1 all Y_1 (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X_1),Y_1)),zEven)) <-> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),zEven)) <-> hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Y_1),zEven))))) # label(fact_1508_even__diff) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1610 (all X_1 all Y_1 (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),X_1),Y_1)),zOdd)) -> hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),zOdd)))) # label(fact_1509_odd__mult__odd__prop) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1611 (all Y_1 all X_1 (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),zOdd)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Y_1),zOdd)) -> 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),X_1),Y_1)),zOdd))))) # label(fact_1510_EvenOdd_Oodd__times__odd) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1612 (all X_1 (hAPP(int,real,real_1(int),X_1) = zero_zero(real) <-> X_1 = zero_zero(int))) # label(fact_1511_real__of__int__zero__cancel) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1613 (all X_1 all Y_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,real_1(int),X_1)),hAPP(int,real,real_1(int),Y_1))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X_1),Y_1)))) # label(fact_1513_real__of__int__less__iff) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1614 (all X_1 all Y_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,real_1(int),X_1)),hAPP(int,real,real_1(int),Y_1))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X_1),Y_1)))) # label(fact_1514_real__of__int__le__iff) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1615 (all X all Y hAPP(int,real,real_1(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X),Y)) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,real_1(int),X)),hAPP(int,real,real_1(int),Y))) # label(fact_1515_real__of__int__mult) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1616 (all V hAPP(int,real,real_1(int),hAPP(int,int,number_number_of(int),V)) = hAPP(int,real,number_number_of(real),V)) # label(fact_1517_real__number__of) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1617 (all X all Y hAPP(int,real,real_1(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X),Y)) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(int,real,real_1(int),X)),hAPP(int,real,real_1(int),Y))) # label(fact_1518_real__of__int__add) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1618 (all X all N_1 hAPP(int,real,real_1(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),X),N_1)) = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,real_1(int),X)),N_1)) # label(fact_1519_real__of__int__power) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1619 (all X all N_1 hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,real_1(int),X)),N_1) = hAPP(int,real,real_1(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),X),N_1))) # label(fact_1520_power__real__of__int) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1620 (all X all Y hAPP(int,real,real_1(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X),Y)) = hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(int,real,real_1(int),X)),hAPP(int,real,real_1(int),Y))) # label(fact_1521_real__of__int__diff) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1621 (all X hAPP(int,real,real_1(int),hAPP(int,int,uminus_uminus(int),X)) = hAPP(real,real,uminus_uminus(real),hAPP(int,real,real_1(int),X))) # label(fact_1525_real__of__int__minus) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1622 (all X_1 hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),hAPP(int,real,real_1(int),X_1)),ring_1_Ints(real)))) # label(fact_1526_Ints__real__of__int) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1623 (all X hAPP(int,real,real_1(int),hAPP(int,int,abs_abs(int),X)) = hAPP(real,real,abs_abs(real),hAPP(int,real,real_1(int),X))) # label(fact_1527_real__of__int__abs) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1624 (all R_4 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,real_1(int),hAPP(real,int,archim2085082626_floor(real),R_4))),R_4))) # label(fact_1528_real__of__int__floor__le) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1625 (all R_4 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),R_4),hAPP(int,real,real_1(int),hAPP(real,int,archimedean_ceiling(real),R_4))))) # label(fact_1529_real__of__int__ceiling__ge) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1626 (all X_a (archim1727834104eiling(X_a) -> (all R_4 hAPP(real,int,archim2085082626_floor(real),hAPP(int,real,real_1(int),hAPP(X_a,int,archimedean_ceiling(X_a),R_4))) = hAPP(X_a,int,archimedean_ceiling(X_a),R_4)))) # label(fact_1530_floor__ceiling) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1627 (all X_a (archim1727834104eiling(X_a) -> (all R_4 hAPP(real,int,archimedean_ceiling(real),hAPP(int,real,real_1(int),hAPP(X_a,int,archim2085082626_floor(X_a),R_4))) = hAPP(X_a,int,archim2085082626_floor(X_a),R_4)))) # label(fact_1531_ceiling__floor) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1628 (all N_1 all X hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,real_1(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),N_1),X))),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(int,real,real_1(int),N_1)),hAPP(int,real,real_1(int),X))))) # label(fact_1532_real__of__int__div4) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1629 (all X_1 all Aa (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(real,int,archim2085082626_floor(real),X_1)),Aa)) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_1),hAPP(int,real,real_1(int),Aa))))) # label(fact_1533_floor__less__eq) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1630 (all A_1 all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,real_1(int),A_1)),X)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A_1),hAPP(real,int,archim2085082626_floor(real),X))))) # label(fact_1534_le__floor) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1631 (all Aa all X_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Aa),hAPP(real,int,archim2085082626_floor(real),X_1))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,real_1(int),Aa)),X_1)))) # label(fact_1535_le__floor__eq) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1632 (all A_1 all X (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A_1),hAPP(real,int,archim2085082626_floor(real),X))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,real_1(int),A_1)),X)))) # label(fact_1536_real__le__floor) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1633 (all Aa all X_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Aa),hAPP(real,int,archimedean_ceiling(real),X_1))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,real_1(int),Aa)),X_1)))) # label(fact_1537_less__ceiling__eq) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1634 (all X all A_1 hAPP(real,int,archim2085082626_floor(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),hAPP(int,real,real_1(int),A_1))) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(real,int,archim2085082626_floor(real),X)),A_1)) # label(fact_1538_floor__add) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1635 (all X_1 all Aa (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(real,int,archimedean_ceiling(real),X_1)),Aa)) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_1),hAPP(int,real,real_1(int),Aa))))) # label(fact_1539_ceiling__le__eq) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1636 (all X all A_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X),hAPP(int,real,real_1(int),A_1))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(real,int,archimedean_ceiling(real),X)),A_1)))) # label(fact_1540_ceiling__le) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1637 (all X all A_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(real,int,archimedean_ceiling(real),X)),A_1)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X),hAPP(int,real,real_1(int),A_1))))) # label(fact_1541_ceiling__le__real) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1638 (all N_1 all X (X = hAPP(int,real,real_1(int),hAPP(real,int,archim2085082626_floor(real),X)) -> hAPP(real,int,archim2085082626_floor(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),N_1)) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(real,int,archim2085082626_floor(real),X)),N_1))) # label(fact_1542_floor__power) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1639 (all X all A_1 hAPP(real,int,archim2085082626_floor(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),X),hAPP(int,real,real_1(int),A_1))) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(real,int,archim2085082626_floor(real),X)),A_1)) # label(fact_1543_floor__subtract) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1640 (all X all A_1 hAPP(real,int,archimedean_ceiling(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),hAPP(int,real,real_1(int),A_1))) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(real,int,archimedean_ceiling(real),X)),A_1)) # label(fact_1544_ceiling__add) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1641 (all N_1 hAPP(real,int,archim2085082626_floor(real),hAPP(real,real,uminus_uminus(real),hAPP(int,real,real_1(int),N_1))) = hAPP(int,int,uminus_uminus(int),N_1)) # label(fact_1545_floor__minus__real__of__int) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1642 (all X all A_1 hAPP(real,int,archimedean_ceiling(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),X),hAPP(int,real,real_1(int),A_1))) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(real,int,archimedean_ceiling(real),X)),A_1)) # label(fact_1546_ceiling__subtract) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1643 (all X_1 all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),X_1),N)),zEven)) <-> hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),zEven))))) # label(fact_1547_power__preserves__even) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1644 (all N (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(int,real,real_1(int),N))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),N)))) # label(fact_1548_real__of__int__gt__zero__cancel__iff) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1645 (all N (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,real_1(int),N)),zero_zero(real))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),N),zero_zero(int))))) # label(fact_1549_real__of__int__lt__zero__cancel__iff) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1646 (all N (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,real_1(int),N)),zero_zero(real))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),N),zero_zero(int))))) # label(fact_1550_real__of__int__le__zero__cancel__iff) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1647 (all N (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(int,real,real_1(int),N))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),N)))) # label(fact_1551_real__of__int__ge__zero__cancel__iff) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1648 (all M all N (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,real_1(int),M)),hAPP(int,real,number_number_of(real),N))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),M),hAPP(int,int,number_number_of(int),N))))) # label(fact_1552_number__of__less__real__of__int__iff2) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1649 (all N all M (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,number_number_of(real),N)),hAPP(int,real,real_1(int),M))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),N)),M)))) # label(fact_1553_number__of__less__real__of__int__iff) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1650 (all M all N (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,real_1(int),M)),hAPP(int,real,number_number_of(real),N))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),M),hAPP(int,int,number_number_of(int),N))))) # label(fact_1554_number__of__le__real__of__int__iff2) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1651 (all N all M (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,number_number_of(real),N)),hAPP(int,real,real_1(int),M))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),N)),M)))) # label(fact_1555_number__of__le__real__of__int__iff) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1652 (all N all M (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),N),M)) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(int,real,real_1(int),N)),one_one(real))),hAPP(int,real,real_1(int),M))))) # label(fact_1556_int__less__real__le) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1653 (all N all M (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),N),M)) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,real_1(int),N)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(int,real,real_1(int),M)),one_one(real)))))) # label(fact_1557_int__le__real__less) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1654 (all N_1 all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,real_1(int),N_1)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(int,real,real_1(int),X)),one_one(real)))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),N_1),X)))) # label(fact_1558_lemma__floor2) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1655 (all X (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X)) -> hAPP(nat,real,real_1(nat),hAPP(int,nat,nat_1,X)) = hAPP(int,real,real_1(int),X))) # label(fact_1559_real__nat__eq__real) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1656 (all X_1 all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),X_1),N)),zOdd)) <-> hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),zOdd))))) # label(fact_1560_power__preserves__odd) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1657 (all R_4 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),R_4),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(int,real,real_1(int),hAPP(real,int,archim2085082626_floor(real),R_4))),one_one(real))))) # label(fact_1561_real__of__int__floor__add__one__ge) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1658 (all R_4 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),R_4),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(int,real,real_1(int),hAPP(real,int,archim2085082626_floor(real),R_4))),one_one(real))))) # label(fact_1562_real__of__int__floor__add__one__gt) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1659 (all N_1 all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,real_1(int),N_1)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(int,real,real_1(int),N_1)),one_one(real)))) -> hAPP(real,int,archim2085082626_floor(real),X) = N_1))) # label(fact_1563_floor__eq) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1660 (all R_4 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),R_4),one_one(real))),hAPP(int,real,real_1(int),hAPP(real,int,archim2085082626_floor(real),R_4))))) # label(fact_1564_real__of__int__floor__ge__diff__one) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1661 (all R_4 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),R_4),one_one(real))),hAPP(int,real,real_1(int),hAPP(real,int,archim2085082626_floor(real),R_4))))) # label(fact_1565_real__of__int__floor__gt__diff__one) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1662 (all R_4 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,real_1(int),hAPP(real,int,archimedean_ceiling(real),R_4))),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),R_4),one_one(real))))) # label(fact_1566_real__of__int__ceiling__le__add__one) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1663 (all R_4 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(int,real,real_1(int),hAPP(real,int,archimedean_ceiling(real),R_4))),one_one(real))),R_4))) # label(fact_1567_real__of__int__ceiling__diff__one__le) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1664 (all N_1 all M_1 all R_4 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,real_1(int),M_1)),R_4)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),R_4),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(int,real,real_1(int),N_1)),one_one(real)))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),M_1),N_1))))) # label(fact_1568_lemma__floor) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1665 (all N_1 all X hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(int,real,real_1(int),N_1)),hAPP(int,real,real_1(int),X))),hAPP(int,real,real_1(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),N_1),X)))))) # label(fact_1569_real__of__int__div2) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1666 (all N_1 all X hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(int,real,real_1(int),N_1)),hAPP(int,real,real_1(int),X))),hAPP(int,real,real_1(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),N_1),X)))),one_one(real)))) # label(fact_1570_real__of__int__div3) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1667 (all X all D (D != zero_zero(int) -> hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(int,real,real_1(int),X)),hAPP(int,real,real_1(int),D)) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(int,real,real_1(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),X),D))),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(int,real,real_1(int),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),X),D))),hAPP(int,real,real_1(int),D))))) # label(fact_1571_real__of__int__div__aux) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1668 (all N_1 all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,real_1(int),N_1)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(int,real,real_1(int),N_1)),one_one(real)))) -> hAPP(real,int,archim2085082626_floor(real),X) = N_1))) # label(fact_1572_floor__eq2) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1669 (all Aa all X_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Aa),hAPP(real,int,archim2085082626_floor(real),X_1))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(int,real,real_1(int),Aa)),one_one(real))),X_1)))) # label(fact_1573_less__floor__eq) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1670 (all X_1 all Aa (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(real,int,archim2085082626_floor(real),X_1)),Aa)) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_1),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(int,real,real_1(int),Aa)),one_one(real)))))) # label(fact_1574_floor__le__eq) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1671 (all N_1 all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(int,real,real_1(int),N_1)),one_one(real))),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X),hAPP(int,real,real_1(int),N_1))) -> hAPP(real,int,archimedean_ceiling(real),X) = N_1))) # label(fact_1575_ceiling__eq3) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1672 (all X_1 all Aa (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(real,int,archimedean_ceiling(real),X_1)),Aa)) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_1),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(int,real,real_1(int),Aa)),one_one(real)))))) # label(fact_1576_ceiling__less__eq) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1673 (all Aa all X_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Aa),hAPP(real,int,archimedean_ceiling(real),X_1))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(int,real,real_1(int),Aa)),one_one(real))),X_1)))) # label(fact_1577_le__ceiling__eq) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1674 (all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,number_number_of(real),min)),Y)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),Y),one_one(real))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,arccos,Y)),pi))))) # label(fact_1578_arccos__ubound) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1675 (all N_1 all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,real_1(int),N_1)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(int,real,real_1(int),N_1)),one_one(real)))) -> hAPP(real,int,archimedean_ceiling(real),X) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),N_1),one_one(int))))) # label(fact_1579_ceiling__eq) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1676 (all Aa all X_1 (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),zEven)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X_1)) -> hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,uminus_uminus(int),Aa)),hAPP(int,nat,nat_1,X_1)) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),Aa),hAPP(int,nat,nat_1,X_1))))) # label(fact_1580_neg__even__power) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1677 (all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,number_number_of(real),min)),Y)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),Y),one_one(real))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(real,real,arccos,Y))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,arccos,Y)),pi))))) # label(fact_1581_arccos__bounded) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1678 (all R_4 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),R_4),zero_zero(real))) -> (exists N_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,real_1(int),N_2)),R_4)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),R_4),hAPP(int,real,real_1(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),N_2),one_one(int))))))))) # label(fact_1582_reals__Archimedean__6c__int) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1679 (all R_4 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),R_4)) -> (exists N_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,real_1(int),N_2)),R_4)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),R_4),hAPP(int,real,real_1(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),N_2),one_one(int))))))))) # label(fact_1583_reals__Archimedean__6b__int) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1680 (all R_4 exists N_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,real_1(int),N_2)),R_4)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),R_4),hAPP(int,real,real_1(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),N_2),one_one(int))))))) # label(fact_1584_real__lb__ub__int) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1681 (all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,number_number_of(real),min)),Y)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),Y),one_one(real))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(real,real,arccos,Y))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,arccos,Y)),pi)) & hAPP(real,real,cos,hAPP(real,real,arccos,Y)) = Y))) # label(fact_1585_arccos) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1682 (all N_1 hAPP(real,real,cos,hAPP(real,real,hAPP(real,fun(real,real),times_times(real),pi),hAPP(nat,real,real_1(nat),N_1))) = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),min)),N_1)) # label(fact_1586_cos__npi2) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1683 (all N_1 hAPP(real,real,cos,hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,real_1(nat),N_1)),pi)) = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),min)),N_1)) # label(fact_1587_cos__npi) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1684 (all X hAPP(real,real,cos,hAPP(real,real,uminus_uminus(real),X)) = hAPP(real,real,cos,X)) # label(fact_1588_cos__minus) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1685 (all X hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,cos,X)),one_one(real)))) # label(fact_1589_cos__le__one) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1686 (all X hAPP(real,real,cos,hAPP(real,real,arctan,X)) != zero_zero(real)) # label(fact_1591_cos__arctan__not__zero) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1687 (all X all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),Y)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),Y),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X),pi)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,cos,X)),hAPP(real,real,cos,Y))))))) # label(fact_1592_cos__monotone__0__pi_H) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1688 (all X hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,number_number_of(real),min)),hAPP(real,real,cos,X)))) # label(fact_1593_cos__ge__minus__one) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1689 (all X hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),hAPP(real,real,cos,X))),one_one(real)))) # label(fact_1594_abs__cos__le__one) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1690 (all X hAPP(real,real,cos,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),pi)) = hAPP(real,real,uminus_uminus(real),hAPP(real,real,cos,X))) # label(fact_1596_cos__periodic__pi) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1691 (all X all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),Y)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),Y),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X),pi)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,cos,X)),hAPP(real,real,cos,Y))))))) # label(fact_1597_cos__monotone__0__pi) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1692 (all X all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,uminus_uminus(real),pi)),Y)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),Y),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X),zero_zero(real))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,cos,Y)),hAPP(real,real,cos,X))))))) # label(fact_1598_cos__monotone__minus__pi__0_H) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1693 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X),pi)) -> hAPP(real,real,arccos,hAPP(real,real,cos,X)) = X))) # label(fact_1599_arccos__cos) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1694 (all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),Y)),one_one(real))) -> hAPP(real,real,cos,hAPP(real,real,arccos,Y)) = Y)) # label(fact_1600_cos__arccos__abs) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1695 (all X all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,uminus_uminus(real),pi)),Y)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),Y),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X),zero_zero(real))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,cos,Y)),hAPP(real,real,cos,X))))))) # label(fact_1601_cos__monotone__minus__pi__0) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1696 (all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,number_number_of(real),min)),Y)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),Y),one_one(real))) -> hAPP(real,real,cos,hAPP(real,real,arccos,Y)) = Y))) # label(fact_1602_cos__arccos) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1697 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X),zero_zero(real))) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,uminus_uminus(real),pi)),X)) -> hAPP(real,real,arccos,hAPP(real,real,cos,X)) = hAPP(real,real,uminus_uminus(real),X)))) # label(fact_1603_arccos__cos2) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1698 (all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,number_number_of(real),min)),Y)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),Y),one_one(real))) -> (exists X_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X_2)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_2),pi)) & hAPP(real,real,cos,X_2) = Y & (all Y_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),Y_2)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),Y_2),pi)) & hAPP(real,real,cos,Y_2) = Y -> Y_2 = X_2))))))) # label(fact_1604_cos__total) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1699 (all Y all X (hAPP(real,real,cos,X) != zero_zero(real) -> (hAPP(real,real,cos,Y) != zero_zero(real) -> (hAPP(real,real,cos,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),Y)) != zero_zero(real) -> hAPP(real,real,tan,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),Y)) = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,tan,X)),hAPP(real,real,tan,Y))),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),one_one(real)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,tan,X)),hAPP(real,real,tan,Y)))))))) # label(fact_1605_tan__add) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1700 (all Y all X (hAPP(real,real,cos,X) != zero_zero(real) -> (hAPP(real,real,cos,Y) != zero_zero(real) -> hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),one_one(real)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,tan,X)),hAPP(real,real,tan,Y))) = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,cos,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),Y))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,cos,X)),hAPP(real,real,cos,Y)))))) # label(fact_1606_lemma__tan__add1) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1701 (all V ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V),pls)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),hAPP(int,nat,number_number_of(nat),V)) = one_one(nat)) & (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V),pls)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),hAPP(int,nat,number_number_of(nat),V)) = hAPP(int,nat,number_number_of(nat),hAPP(int,int,succ,V))))) # label(fact_1607_nat__1__add__number__of) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1702 (all V ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V),pls)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),V)),one_one(nat)) = one_one(nat)) & (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V),pls)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),V)),one_one(nat)) = hAPP(int,nat,number_number_of(nat),hAPP(int,int,succ,V))))) # label(fact_1608_nat__number__of__add__1) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1703 (all X_a (number_semiring(X_a) -> (all V (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),V)) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(int,X_a,number_number_of(X_a),V)),one_one(X_a)) = hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,succ,V)))))) # label(fact_1609_semiring__number__of__add__1) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1704 (all W hAPP(int,int,hAPP(int,fun(int,int),times_times(int),pls),W) = pls) # label(fact_1614_mult__Pls) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1705 (all K_4 hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),pls),K_4) = K_4) # label(fact_1615_add__Pls) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1706 (all K_4 hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),K_4),pls) = K_4) # label(fact_1616_add__Pls__right) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1707 (all K_4 hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),K_4),pls) = K_4) # label(fact_1617_diff__bin__simps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1708 (all X hAPP(real,real,tan,hAPP(real,real,uminus_uminus(real),X)) = hAPP(real,real,uminus_uminus(real),hAPP(real,real,tan,X))) # label(fact_1621_tan__minus) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1709 (all Y hAPP(real,real,tan,hAPP(real,real,arctan,Y)) = Y) # label(fact_1622_tan__arctan) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1710 (all X_a (number_ring(X_a) -> zero_zero(X_a) = hAPP(int,X_a,number_number_of(X_a),pls))) # label(fact_1623_semiring__norm_I112_J) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1711 (all X_a (number_ring(X_a) -> hAPP(int,X_a,number_number_of(X_a),pls) = zero_zero(X_a))) # label(fact_1624_number__of__Pls) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1712 (all X_a (number_semiring(X_a) -> hAPP(int,X_a,number_number_of(X_a),pls) = zero_zero(X_a))) # label(fact_1625_semiring__numeral__0__eq__0) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1713 (all X_a (number_ring(X_a) -> (all A_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(int,X_a,number_number_of(X_a),pls)),A_1) = ti(X_a,A_1)))) # label(fact_1626_add__numeral__0) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1714 (all X_a (number_ring(X_a) -> (all A_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),hAPP(int,X_a,number_number_of(X_a),pls)) = ti(X_a,A_1)))) # label(fact_1627_add__numeral__0__right) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1715 (all X hAPP(real,real,tan,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),pi)) = hAPP(real,real,tan,X)) # label(fact_1638_tan__periodic__pi) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1716 (all X_a (field_inverse_zero(X_a) & number_ring(X_a) -> (all X hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),X),hAPP(int,X_a,number_number_of(X_a),pls)) = zero_zero(X_a)))) # label(fact_1641_divide__Numeral0) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1717 (all V_1 (zero_zero(nat) = hAPP(int,nat,number_number_of(nat),V_1) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),V_1),pls)))) # label(fact_1642_eq__0__number__of) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1718 (all V_1 (hAPP(int,nat,number_number_of(nat),V_1) = zero_zero(nat) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),V_1),pls)))) # label(fact_1643_eq__number__of__0) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1719 (all V_1 all V_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(int,nat,number_number_of(nat),V_1)),hAPP(int,nat,number_number_of(nat),V_2))) <-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V_1),V_2)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),V_2))) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V_1),V_2)))) # label(fact_1644_less__nat__number__of) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1720 (all V_1 all V_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(int,nat,number_number_of(nat),V_1)),hAPP(int,nat,number_number_of(nat),V_2))) <-> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),V_1),V_2)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),V_1),pls))))) # label(fact_1646_le__nat__number__of) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1721 (all X_a (number_ring(X_a) & linordered_idom(X_a) -> (all Y_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(int,X_a,number_number_of(X_a),Y_1))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),Y_1)))))) # label(fact_1647_less__special_I1_J) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1722 (all X_a (number_ring(X_a) & linordered_idom(X_a) -> (all X_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(int,X_a,number_number_of(X_a),X_1)),zero_zero(X_a))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X_1),pls)))))) # label(fact_1648_less__special_I3_J) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1723 (all X_a (number_ring(X_a) & linordered_idom(X_a) -> (all Y_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),hAPP(int,X_a,number_number_of(X_a),Y_1))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),Y_1)))))) # label(fact_1649_le__special_I1_J) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1724 (all X_a (number_ring(X_a) & linordered_idom(X_a) -> (all X_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(int,X_a,number_number_of(X_a),X_1)),zero_zero(X_a))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X_1),pls)))))) # label(fact_1650_le__special_I3_J) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1725 (all X_a (number_semiring(X_a) -> (all V_3 all V (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),V)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),V_3)) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(int,X_a,number_number_of(X_a),V)),hAPP(int,X_a,number_number_of(X_a),V_3)) = hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),V),V_3))))))) # label(fact_1651_semiring__mult__number__of) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1726 (all X_a (number_semiring(X_a) -> (all V_3 all V (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),V)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),V_3)) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(int,X_a,number_number_of(X_a),V)),hAPP(int,X_a,number_number_of(X_a),V_3)) = hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),V),V_3))))))) # label(fact_1652_semiring__add__number__of) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1727 (all V_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(int,nat,number_number_of(nat),V_1))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),V_1)))) # label(fact_1653_less__0__number__of) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1728 (all V_3 all V ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V),pls)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),V)),hAPP(int,nat,number_number_of(nat),V_3)) = hAPP(int,nat,number_number_of(nat),V_3)) & (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V),pls)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V_3),pls)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),V)),hAPP(int,nat,number_number_of(nat),V_3)) = hAPP(int,nat,number_number_of(nat),V)) & (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V_3),pls)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),V)),hAPP(int,nat,number_number_of(nat),V_3)) = hAPP(int,nat,number_number_of(nat),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),V),V_3)))))) # label(fact_1654_add__nat__number__of) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1729 (all N_1 hAPP(real,real,tan,hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,real_1(nat),N_1)),pi)) = zero_zero(real)) # label(fact_1655_tan__npi) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1730 (all X all N_1 hAPP(real,real,tan,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),N_1)),pi))) = hAPP(real,real,tan,X)) # label(fact_1656_tan__periodic__n) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1731 (all X all N_1 hAPP(real,real,tan,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,real_1(nat),N_1)),pi))) = hAPP(real,real,tan,X)) # label(fact_1657_tan__periodic__nat) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1732 (all X all I_1 hAPP(real,real,tan,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,real_1(int),I_1)),pi))) = hAPP(real,real,tan,X)) # label(fact_1658_tan__periodic__int) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1733 (all V_3 all K_4 all V ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V),pls)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),V)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),V_3)),K_4)) = zero_zero(nat)) & (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V),pls)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),V)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),V_3)),K_4)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),V),V_3))),K_4)))) # label(fact_1659_nat__number__of__mult__left) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1734 (all V_3 all V ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V),pls)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),V)),hAPP(int,nat,number_number_of(nat),V_3)) = zero_zero(nat)) & (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V),pls)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),V)),hAPP(int,nat,number_number_of(nat),V_3)) = hAPP(int,nat,number_number_of(nat),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),V),V_3))))) # label(fact_1660_mult__nat__number__of) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1735 (all X_a (number_semiring(X_a) -> (all V (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),V)) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),one_one(X_a)),hAPP(int,X_a,number_number_of(X_a),V)) = hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,succ,V)))))) # label(fact_1661_semiring__1__add__number__of) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1736 (all X_a (number_ring(X_a) -> (all Y_1 (zero_zero(X_a) = hAPP(int,X_a,number_number_of(X_a),Y_1) <-> hBOOL(hAPP(X_a,bool,iszero(X_a),hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),pls),hAPP(int,int,uminus_uminus(int),Y_1))))))))) # label(fact_1662_eq__special_I1_J) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1737 (all X_a (number_ring(X_a) -> (all X_1 (hAPP(int,X_a,number_number_of(X_a),X_1) = zero_zero(X_a) <-> hBOOL(hAPP(X_a,bool,iszero(X_a),hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X_1),hAPP(int,int,uminus_uminus(int),pls))))))))) # label(fact_1663_eq__special_I3_J) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1738 (all V ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),V),pls)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(int,nat,number_number_of(nat),V)),one_one(nat)) = zero_zero(nat)) & (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),V),pls)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(int,nat,number_number_of(nat),V)),one_one(nat)) = hAPP(int,nat,number_number_of(nat),hAPP(int,int,pred,V))))) # label(fact_1664_nat__number__of__diff__1) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1739 (all M_1 all V (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),V)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,M_1)),hAPP(int,nat,number_number_of(nat),V)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,pred,V))))) # label(fact_1665_Suc__diff__number__of) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1740 (all X_a (number_ring(X_a) -> (all V hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(int,X_a,number_number_of(X_a),V)),one_one(X_a)) = hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),V),hAPP(int,int,uminus_uminus(int),hAPP(int,int,bit1,pls))))))) # label(fact_1666_diff__special_I2_J) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1741 (all X_a (number_ring(X_a) -> (all W hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),one_one(X_a)),hAPP(int,X_a,number_number_of(X_a),W)) = hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,bit1,pls)),hAPP(int,int,uminus_uminus(int),W)))))) # label(fact_1667_diff__special_I1_J) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1742 (all X_a (number_ring(X_a) & ring_char_0(X_a) -> (all W -hBOOL(hAPP(X_a,bool,iszero(X_a),hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,bit1,W))))))) # label(fact_1668_iszero__number__of__Bit1) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1743 (all K all L (hAPP(int,int,bit1,K) = hAPP(int,int,bit1,L) <-> K = L)) # label(fact_1669_rel__simps_I51_J) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1744 (all K_4 hAPP(int,int,uminus_uminus(int),hAPP(int,int,bit1,K_4)) = hAPP(int,int,bit1,hAPP(int,int,pred,hAPP(int,int,uminus_uminus(int),K_4)))) # label(fact_1670_minus__Bit1) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1745 (all K_4 hAPP(int,int,bit1,K_4) != pls) # label(fact_1671_rel__simps_I46_J) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1746 (all L_4 pls != hAPP(int,int,bit1,L_4)) # label(fact_1672_rel__simps_I39_J) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1747 (all K all L (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,K)),hAPP(int,int,bit1,L))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),L)))) # label(fact_1673_rel__simps_I17_J) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1748 (all K1 all K2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,K1)),hAPP(int,int,bit1,K2))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K1),K2)))) # label(fact_1674_less__int__code_I16_J) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1749 (all K all L (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,K)),hAPP(int,int,bit1,L))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),K),L)))) # label(fact_1675_rel__simps_I34_J) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1750 (all K1 all K2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,K1)),hAPP(int,int,bit1,K2))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),K1),K2)))) # label(fact_1676_less__eq__int__code_I16_J) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1751 (all K (hAPP(int,int,bit1,K) = min <-> K = min)) # label(fact_1677_rel__simps_I47_J) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1752 (all L (min = hAPP(int,int,bit1,L) <-> min = L)) # label(fact_1678_rel__simps_I43_J) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1753 (all X_a (number_ring(X_a) -> -hBOOL(hAPP(X_a,bool,iszero(X_a),hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,bit1,pls)))))) # label(fact_1680_not__iszero__Numeral1) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1754 (all X hAPP(int,int,succ,hAPP(int,int,pred,X)) = X) # label(fact_1681_succ__pred) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1755 (all X_a (semiring_1(X_a) -> (all Z_1 (hBOOL(hAPP(X_a,bool,iszero(X_a),Z_1)) <-> ti(X_a,Z_1) = zero_zero(X_a))))) # label(fact_1682_iszero__def) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1756 (all X_a (semiring_1(X_a) -> hBOOL(hAPP(X_a,bool,iszero(X_a),zero_zero(X_a))))) # label(fact_1683_iszero__0) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1757 (all X_a (semiring_1(X_a) -> -hBOOL(hAPP(X_a,bool,iszero(X_a),one_one(X_a))))) # label(fact_1684_not__iszero__1) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1758 (all K (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,K)),pls)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),pls)))) # label(fact_1685_rel__simps_I12_J) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1759 (all W_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,W_1)),zero_zero(int))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_1),zero_zero(int))))) # label(fact_1686_bin__less__0__simps_I4_J) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1760 (all K (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),hAPP(int,int,bit1,K))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),K)))) # label(fact_1687_rel__simps_I22_J) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1761 (all K_4 hAPP(int,int,bit1,K_4) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),K_4)),K_4)) # label(fact_1688_Bit1__def) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1762 (all K (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,K)),min)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),min)))) # label(fact_1689_rel__simps_I13_J) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1763 (all K (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),min),hAPP(int,int,bit1,K))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),min),K)))) # label(fact_1690_rel__simps_I9_J) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1764 (all K (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,K)),min)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),K),min)))) # label(fact_1691_rel__simps_I30_J) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1765 (all K (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),min),hAPP(int,int,bit1,K))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),min),K)))) # label(fact_1692_rel__simps_I26_J) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1766 (all W_1 (hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),hAPP(int,int,bit1,W_1)))) <-> hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),W_1))))) # label(fact_1693_neg__number__of__Bit1) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1767 (all K all L (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),K),L)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,pred,K)),L)))) # label(fact_1695_le__iff__pred__less) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1768 (all K_4 hAPP(int,int,pred,K_4) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),K_4),one_one(int))) # label(fact_1697_pred__def) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1769 (all K_4 hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),min),K_4) = hAPP(int,int,pred,K_4)) # label(fact_1698_add__Min) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1770 (all K_4 hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),K_4),min) = hAPP(int,int,pred,K_4)) # label(fact_1699_add__Min__right) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1771 (all X_a (number_ring(X_a) -> (all W hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,bit1,W)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),one_one(X_a)),hAPP(int,X_a,number_number_of(X_a),W))),hAPP(int,X_a,number_number_of(X_a),W))))) # label(fact_1700_number__of__Bit1) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1772 (all X_a (number_ring(X_a) -> (all A_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,bit1,pls))) = ti(X_a,A_1)))) # label(fact_1701_mult__numeral__1__right) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1773 (all X_a (number_ring(X_a) -> (all A_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,bit1,pls))),A_1) = ti(X_a,A_1)))) # label(fact_1702_mult__numeral__1) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1774 (all X_a (number_ring(X_a) -> one_one(X_a) = hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,bit1,pls)))) # label(fact_1703_semiring__norm_I110_J) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1775 (all X_a (number_ring(X_a) -> hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,bit1,pls)) = one_one(X_a))) # label(fact_1704_numeral__1__eq__1) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1776 (all X_a (number_semiring(X_a) -> hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,bit1,pls)) = one_one(X_a))) # label(fact_1705_semiring__numeral__1__eq__1) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1777 (all X_a (number_ring(X_a) -> (all X_1 (hAPP(int,X_a,number_number_of(X_a),X_1) = one_one(X_a) <-> hBOOL(hAPP(X_a,bool,iszero(X_a),hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X_1),hAPP(int,int,uminus_uminus(int),hAPP(int,int,bit1,pls)))))))))) # label(fact_1706_eq__special_I4_J) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1778 (all X_a (number_ring(X_a) -> (all Y_1 (one_one(X_a) = hAPP(int,X_a,number_number_of(X_a),Y_1) <-> hBOOL(hAPP(X_a,bool,iszero(X_a),hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,bit1,pls)),hAPP(int,int,uminus_uminus(int),Y_1))))))))) # label(fact_1707_eq__special_I2_J) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1779 (all X_a (field(X_a) & number_ring(X_a) -> (all A_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),A_1),hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,bit1,pls))) = ti(X_a,A_1)))) # label(fact_1708_divide__numeral__1) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1780 (all X_a (field(X_a) & number_ring(X_a) -> (all X hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),X),hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,bit1,pls))) = ti(X_a,X)))) # label(fact_1709_divide__Numeral1) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1781 (all K (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),hAPP(int,int,bit1,K))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),K)))) # label(fact_1710_rel__simps_I5_J) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1782 (all K (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,K)),pls)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),pls)))) # label(fact_1711_rel__simps_I29_J) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1783 (all L_4 hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),pls),hAPP(int,int,bit1,L_4)) = hAPP(int,int,bit1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),min),L_4))) # label(fact_1715_diff__bin__simps_I4_J) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1784 (all X_a (number_ring(X_a) -> hBOOL(hAPP(X_a,bool,iszero(X_a),hAPP(int,X_a,number_number_of(X_a),pls))))) # label(fact_1717_iszero__Numeral0) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1785 (all X_a (number_ring(X_a) -> -hBOOL(hAPP(X_a,bool,iszero(X_a),hAPP(int,X_a,number_number_of(X_a),min))))) # label(fact_1718_nonzero__number__of__Min) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1786 (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),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,hAPP(int,int,bit1,pls)))) = 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),A_1)),A_1)))) # label(fact_1719_power3__eq__cube) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1787 (all N_1 hAPP(nat,nat,suc,hAPP(nat,nat,suc,hAPP(nat,nat,suc,N_1))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,hAPP(int,int,bit1,pls)))),N_1)) # label(fact_1722_Suc3__eq__add__3) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1788 (all A_1 hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,uminus_uminus(int),A_1)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,hAPP(int,int,bit1,pls)))) = hAPP(int,int,uminus_uminus(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,hAPP(int,int,bit1,pls)))))) # label(fact_1725_power3__minus) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1789 (all X hAPP(int,int,abs_abs(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,hAPP(int,int,bit1,pls))))) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,abs_abs(int),X)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,hAPP(int,int,bit1,pls))))) # label(fact_1726_abs__power3__distrib) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1790 (all X_a (number_ring(X_a) -> (all W hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,pred,W)) = 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),one_one(X_a))),hAPP(int,X_a,number_number_of(X_a),W))))) # label(fact_1727_number__of__pred) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1791 (all X_a (number_ring(X_a) & linordered_idom(X_a) -> (all X_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(int,X_a,number_number_of(X_a),X_1)),one_one(X_a))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X_1),hAPP(int,int,bit1,pls))))))) # label(fact_1728_less__special_I4_J) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1792 (all X_a (number_ring(X_a) & linordered_idom(X_a) -> (all Y_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),hAPP(int,X_a,number_number_of(X_a),Y_1))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,pls)),Y_1)))))) # label(fact_1729_less__special_I2_J) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1793 (all X_a (number_ring(X_a) & linordered_idom(X_a) -> (all X_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(int,X_a,number_number_of(X_a),X_1)),one_one(X_a))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X_1),hAPP(int,int,bit1,pls))))))) # label(fact_1730_le__special_I4_J) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1794 (all X_a (number_ring(X_a) & linordered_idom(X_a) -> (all Y_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),one_one(X_a)),hAPP(int,X_a,number_number_of(X_a),Y_1))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,pls)),Y_1)))))) # label(fact_1731_le__special_I2_J) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1795 (all X_a (number_ring(X_a) -> (all W hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),one_one(X_a)),hAPP(int,X_a,number_number_of(X_a),W)) = hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,bit1,pls)),W))))) # label(fact_1732_add__special_I2_J) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1796 (all X_a (number_ring(X_a) -> (all V hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(int,X_a,number_number_of(X_a),V)),one_one(X_a)) = hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),V),hAPP(int,int,bit1,pls)))))) # label(fact_1733_add__special_I3_J) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1797 (all M_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(int,nat,number_number_of(nat),pls)),N_1)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,M_1)),N_1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,pls)))))) # label(fact_1734_Suc__diff__eq__diff__pred) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1798 (all M_1 all V hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,suc,hAPP(nat,nat,suc,hAPP(nat,nat,suc,M_1)))),hAPP(int,nat,number_number_of(nat),V)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,hAPP(int,int,bit1,pls)))),M_1)),hAPP(int,nat,number_number_of(nat),V))) # label(fact_1735_Suc__div__eq__add3__div__number__of) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1799 (all M_1 all N_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,suc,hAPP(nat,nat,suc,hAPP(nat,nat,suc,M_1)))),N_1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,hAPP(int,int,bit1,pls)))),M_1)),N_1)) # label(fact_1736_Suc__div__eq__add3__div) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1800 (all M_1 all N_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),M_1),hAPP(nat,nat,suc,hAPP(nat,nat,suc,hAPP(nat,nat,suc,N_1)))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),M_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,hAPP(int,int,bit1,pls)))),N_1))) # label(fact_1737_div__Suc__eq__div__add3) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.69 1801 (all M_1 all V hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,suc,hAPP(nat,nat,suc,hAPP(nat,nat,suc,M_1)))),hAPP(int,nat,number_number_of(nat),V)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,hAPP(int,int,bit1,pls)))),M_1)),hAPP(int,nat,number_number_of(nat),V))) # label(fact_1738_Suc__mod__eq__add3__mod__number__of) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.70 1802 (all M_1 all N_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,suc,hAPP(nat,nat,suc,hAPP(nat,nat,suc,M_1)))),N_1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,hAPP(int,int,bit1,pls)))),M_1)),N_1)) # label(fact_1739_Suc__mod__eq__add3__mod) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.70 1803 (all M_1 all N_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),M_1),hAPP(nat,nat,suc,hAPP(nat,nat,suc,hAPP(nat,nat,suc,N_1)))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),M_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,hAPP(int,int,bit1,pls)))),N_1))) # label(fact_1740_mod__Suc__eq__mod__add3) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.70 1804 (all V_1 (hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),hAPP(int,int,pred,V_1)))) <-> hAPP(int,nat,number_number_of(nat),V_1) = zero_zero(nat))) # label(fact_1741_neg__number__of__pred__iff__0) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.70 1805 (all X_a (number_ring(X_a) -> (all X_1 all Y_1 (hAPP(int,X_a,number_number_of(X_a),X_1) = hAPP(int,X_a,number_number_of(X_a),Y_1) <-> hBOOL(hAPP(X_a,bool,iszero(X_a),hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X_1),hAPP(int,int,uminus_uminus(int),Y_1))))))))) # label(fact_1742_eq__number__of__eq) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.70 1806 (all X (hAPP(real,real,cos,X) != zero_zero(real) -> (hAPP(real,real,cos,hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),X)) != zero_zero(real) -> hAPP(real,real,tan,hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),X)) = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),hAPP(real,real,tan,X))),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),one_one(real)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,tan,X)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))))) # label(fact_1743_tan__double) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.70 1807 (all M_1 hAPP(real,real,cos,hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),pi),hAPP(nat,real,real_1(nat),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),M_1))))),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) = zero_zero(real)) # label(fact_1744_cos__pi__eq__zero) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.70 1808 (all P_4 hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),P_4),one_one(int))),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) = hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),P_4),one_one(int))),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))) # label(fact_1745_Euler_Oaux____2) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.70 1809 (all B all A_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A_1),zero_zero(int))) -> hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),B))),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),A_1)) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),B),one_one(int))),A_1))),one_one(int)))) # label(fact_1746_neg__zmod__mult__2) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.70 1810 (all V all W ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),W))) -> hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit1,V))),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,W))) = 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,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,number_number_of(int),V)),hAPP(int,int,number_number_of(int),W)))),one_one(int))) & (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),W))) -> hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit1,V))),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,W))) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,number_number_of(int),V)),one_one(int))),hAPP(int,int,number_number_of(int),W)))),one_one(int))))) # label(fact_1747_zmod__number__of__Bit1) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.70 1811 (all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),hAPP(real,real,arctan,Y))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,arctan,Y)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) & hAPP(real,real,tan,hAPP(real,real,arctan,Y)) = Y)) # label(fact_1748_arctan) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.70 1812 (all K all L (hAPP(int,int,bit0,K) = hAPP(int,int,bit0,L) <-> K = L)) # label(fact_1749_rel__simps_I48_J) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.70 1813 (all K_4 all L_4 hAPP(int,int,bit0,K_4) != hAPP(int,int,bit1,L_4)) # label(fact_1750_rel__simps_I49_J) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.70 1814 (all K_4 all L_4 hAPP(int,int,bit1,K_4) != hAPP(int,int,bit0,L_4)) # label(fact_1751_rel__simps_I50_J) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.70 1815 (all L (pls = hAPP(int,int,bit0,L) <-> pls = L)) # label(fact_1753_rel__simps_I38_J) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.70 1816 (all K (hAPP(int,int,bit0,K) = pls <-> K = pls)) # label(fact_1754_rel__simps_I44_J) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.70 1817 (all K1 all K2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit0,K1)),hAPP(int,int,bit0,K2))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K1),K2)))) # label(fact_1755_less__int__code_I13_J) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.70 1818 (all K all L (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit0,K)),hAPP(int,int,bit0,L))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),L)))) # label(fact_1756_rel__simps_I14_J) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.70 1819 (all K1 all K2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit0,K1)),hAPP(int,int,bit0,K2))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),K1),K2)))) # label(fact_1757_less__eq__int__code_I13_J) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.70 1820 (all K all L (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit0,K)),hAPP(int,int,bit0,L))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),K),L)))) # label(fact_1758_rel__simps_I31_J) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.70 1821 (all K_4 all L_4 hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,bit0,K_4)),L_4) = hAPP(int,int,bit0,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K_4),L_4))) # label(fact_1759_mult__Bit0) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.70 1822 (all K_4 hAPP(int,int,bit0,K_4) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),K_4),K_4)) # label(fact_1760_Bit0__def) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.70 1823 (all K_4 all L_4 hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,bit0,K_4)),hAPP(int,int,bit0,L_4)) = hAPP(int,int,bit0,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),K_4),L_4))) # label(fact_1761_add__Bit0__Bit0) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.70 1824 (all K_4 all L_4 hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,bit0,K_4)),hAPP(int,int,bit0,L_4)) = hAPP(int,int,bit0,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),K_4),L_4))) # label(fact_1762_diff__bin__simps_I7_J) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.70 1825 (all L_4 min != hAPP(int,int,bit0,L_4)) # label(fact_1763_rel__simps_I42_J) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.70 1826 (all K_4 hAPP(int,int,bit0,K_4) != min) # label(fact_1764_rel__simps_I45_J) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.70 1827 (all K_4 hAPP(int,int,uminus_uminus(int),hAPP(int,int,bit0,K_4)) = hAPP(int,int,bit0,hAPP(int,int,uminus_uminus(int),K_4))) # label(fact_1765_minus__Bit0) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.70 1828 (all K1 all K2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,K1)),hAPP(int,int,bit0,K2))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K1),K2)))) # label(fact_1766_less__int__code_I15_J) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.70 1829 (all K all L (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,K)),hAPP(int,int,bit0,L))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),L)))) # label(fact_1767_rel__simps_I16_J) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.70 1830 (all K (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit0,K)),pls)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),pls)))) # label(fact_1768_rel__simps_I10_J) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.70 1831 (all K (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),hAPP(int,int,bit0,K))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),K)))) # label(fact_1769_rel__simps_I4_J) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.70 1832 (all W_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit0,W_1)),zero_zero(int))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_1),zero_zero(int))))) # label(fact_1770_bin__less__0__simps_I3_J) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.70 1833 (all K all L (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit0,K)),hAPP(int,int,bit1,L))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),K),L)))) # label(fact_1771_rel__simps_I32_J) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.70 1834 (all K1 all K2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit0,K1)),hAPP(int,int,bit1,K2))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),K1),K2)))) # label(fact_1772_less__eq__int__code_I14_J) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.70 1835 (all K (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit0,K)),pls)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),K),pls)))) # label(fact_1773_rel__simps_I27_J) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.70 1836 (all K (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),hAPP(int,int,bit0,K))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),K)))) # label(fact_1774_rel__simps_I21_J) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.70 1837 (all K_4 all L_4 hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,bit1,K_4)),hAPP(int,int,bit0,L_4)) = hAPP(int,int,bit1,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),K_4),L_4))) # label(fact_1775_add__Bit1__Bit0) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.70 1838 (all K_4 all L_4 hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,bit0,K_4)),hAPP(int,int,bit1,L_4)) = hAPP(int,int,bit1,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),K_4),L_4))) # label(fact_1776_add__Bit0__Bit1) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.70 1839 (all K_4 all L_4 hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,bit1,K_4)),hAPP(int,int,bit0,L_4)) = hAPP(int,int,bit1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),K_4),L_4))) # label(fact_1777_diff__bin__simps_I9_J) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.70 1840 (all K_4 all L_4 hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,bit1,K_4)),hAPP(int,int,bit1,L_4)) = hAPP(int,int,bit0,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),K_4),L_4))) # label(fact_1778_diff__bin__simps_I10_J) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.70 1841 (all L_4 hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),pls),hAPP(int,int,bit0,L_4)) = hAPP(int,int,bit0,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),pls),L_4))) # label(fact_1779_diff__bin__simps_I3_J) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.70 1842 (all K (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),min),hAPP(int,int,bit0,K))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),min),K)))) # label(fact_1780_rel__simps_I8_J) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.70 1843 (all K (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit0,K)),min)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),K),min)))) # label(fact_1781_rel__simps_I28_J) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.70 1844 (all V all W hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,V))),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,W))) = hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,number_number_of(int),V)),hAPP(int,int,number_number_of(int),W))) # label(fact_1782_zdiv__number__of__Bit0) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.70 1845 (all W_1 (hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,W_1)))) <-> hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),W_1))))) # label(fact_1783_neg__number__of__Bit0) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.70 1846 (all K_4 hAPP(int,int,pred,hAPP(int,int,bit1,K_4)) = hAPP(int,int,bit0,K_4)) # label(fact_1784_pred__Bit1) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.70 1847 (all K_4 hAPP(int,int,pred,hAPP(int,int,bit0,K_4)) = hAPP(int,int,bit1,hAPP(int,int,pred,K_4))) # label(fact_1785_pred__Bit0) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.70 1848 (all X_a (number_ring(X_a) & ring_char_0(X_a) -> (all W_1 (hBOOL(hAPP(X_a,bool,iszero(X_a),hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,bit0,W_1)))) <-> hBOOL(hAPP(X_a,bool,iszero(X_a),hAPP(int,X_a,number_number_of(X_a),W_1))))))) # label(fact_1787_iszero__number__of__Bit0) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.70 1849 (all K_4 hAPP(int,int,succ,hAPP(int,int,bit1,K_4)) = hAPP(int,int,bit0,hAPP(int,int,succ,K_4))) # label(fact_1788_succ__Bit1) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.70 1850 (all K_4 hAPP(int,int,succ,hAPP(int,int,bit0,K_4)) = hAPP(int,int,bit1,K_4)) # label(fact_1789_succ__Bit0) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.70 1851 (all X_a (number_ring(X_a) -> (all W hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,bit0,W)) = 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),zero_zero(X_a)),hAPP(int,X_a,number_number_of(X_a),W))),hAPP(int,X_a,number_number_of(X_a),W))))) # label(fact_1790_number__of__Bit0) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.70 1852 (all K all L (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit0,K)),hAPP(int,int,bit1,L))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),K),L)))) # label(fact_1791_rel__simps_I15_J) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.70 1853 (all K1 all K2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit0,K1)),hAPP(int,int,bit1,K2))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),K1),K2)))) # label(fact_1792_less__int__code_I14_J) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.70 1854 (all K all L (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,K)),hAPP(int,int,bit0,L))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),L)))) # label(fact_1793_rel__simps_I33_J) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.70 1855 (all K1 all K2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,K1)),hAPP(int,int,bit0,K2))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K1),K2)))) # label(fact_1794_less__eq__int__code_I15_J) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.70 1856 (all K_4 all L_4 hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,bit1,K_4)),L_4) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,bit0,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K_4),L_4))),L_4)) # label(fact_1795_mult__Bit1) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.70 1857 (all K (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit0,K)),min)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),K),min)))) # label(fact_1796_rel__simps_I11_J) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.70 1858 (all K (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),min),hAPP(int,int,bit0,K))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),min),K)))) # label(fact_1797_rel__simps_I25_J) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.70 1859 (all L_4 hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),min),hAPP(int,int,bit1,L_4)) = hAPP(int,int,bit0,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),min),L_4))) # label(fact_1798_diff__bin__simps_I6_J) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.70 1860 (all L_4 hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),min),hAPP(int,int,bit0,L_4)) = hAPP(int,int,bit1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),min),L_4))) # label(fact_1799_diff__bin__simps_I5_J) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.70 1861 (all K_4 all L_4 hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,bit0,K_4)),hAPP(int,int,bit1,L_4)) = hAPP(int,int,bit1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,pred,K_4)),L_4))) # label(fact_1800_diff__bin__simps_I8_J) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.70 1862 (all K_4 all L_4 hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,bit1,K_4)),hAPP(int,int,bit1,L_4)) = hAPP(int,int,bit0,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),K_4),hAPP(int,int,succ,L_4)))) # label(fact_1801_add__Bit1__Bit1) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.70 1863 (all X_a (number_ring(X_a) -> (all W 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))),hAPP(int,X_a,number_number_of(X_a),W)) = hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,bit0,W))))) # label(fact_1802_double__number__of__Bit0) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.70 1864 (all N_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),N_1))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,N_1)))) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),hAPP(int,int,bit1,N_1)))))) # label(fact_1803_number__of1) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.70 1865 (all X hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) # label(fact_1804_quartic__square__square) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.70 1866 (all X_a (number_semiring(X_a) -> (all Z hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),Z) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Z),Z)))) # label(fact_1805_semiring__mult__2) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.70 1867 (all X_a (number_ring(X_a) -> (all Z hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),Z) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Z),Z)))) # label(fact_1806_mult__2) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.70 1868 (all X_a (number_semiring(X_a) -> (all Z hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Z),hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Z),Z)))) # label(fact_1807_semiring__mult__2__right) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.70 1869 (all X_a (number_ring(X_a) -> (all Z hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Z),hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Z),Z)))) # label(fact_1808_mult__2__right) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.70 1870 (all X_a (number_semiring(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)) = hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) # label(fact_1809_semiring__one__add__one__is__two) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.70 1871 (all X_a (number_ring(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)) = hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) # label(fact_1810_one__add__one__is__two) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.70 1872 (all X_a (ring_11004092258visors(X_a) -> (all Aa (hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),Aa),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = zero_zero(X_a) <-> ti(X_a,Aa) = zero_zero(X_a))))) # label(fact_1811_zero__eq__power2) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.70 1873 (all X_a (semiring_1(X_a) -> hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),zero_zero(X_a)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = zero_zero(X_a))) # label(fact_1812_zero__power2) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.70 1874 (all X_a (comm_semiring_1(X_a) -> (all X hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),X) = hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))) # label(fact_1813_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.70 1875 (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),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),A_1)))) # label(fact_1814_power2__eq__square) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.70 1876 (all X_a (semiring_1(X_a) -> hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),one_one(X_a)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = one_one(X_a))) # label(fact_1815_one__power2) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.70 1877 (all X_a (ring_1(X_a) -> (all A_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)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))) # label(fact_1819_power2__minus) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.70 1878 (all X_a (monoid_mult(X_a) -> (all A_1 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),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),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),N_1)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))) # label(fact_1820_power__even__eq) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.70 1879 (all N_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(nat,nat,suc,hAPP(nat,nat,suc,N_1))) # label(fact_1821_add__2__eq__Suc_H) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.70 1880 (all N_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),N_1) = hAPP(nat,nat,suc,hAPP(nat,nat,suc,N_1))) # label(fact_1822_add__2__eq__Suc) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.70 1881 (all X_a (linordered_idom(X_a) -> (all A_1 hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(X_a,X_a,abs_abs(X_a),A_1)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))) # label(fact_1824_power2__abs) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.70 1882 (all X_a (linordered_idom(X_a) -> (all A_1 hAPP(X_a,X_a,abs_abs(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) = hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))) # label(fact_1825_abs__power2) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.70 1883 (all Z hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),Z) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Z),Z)) # label(fact_1826_nat__mult__2) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.70 1884 (all Z hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),Z),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Z),Z)) # label(fact_1827_nat__mult__2__right) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.70 1885 (all X_1 all Y_1 all Z_1 (X_1 = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),Y_1),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),Z_1)) <-> hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),X_1) = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),Y_1),Z_1))) # label(fact_1830_eq__divide__2__times__iff) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.70 1886 (all M_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,suc,hAPP(nat,nat,suc,M_1))),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),M_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) # label(fact_1832_div2__Suc__Suc) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.70 1887 (all X hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))) # label(fact_1833_power2__ge__self) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.70 1888 (all M_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,suc,hAPP(nat,nat,suc,M_1))),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),M_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) # label(fact_1834_mod2__Suc__Suc) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.70 1889 (all A_1 hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,hAPP(int,int,bit1,pls))))) # label(fact_1837_cube__square) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.70 1890 (all X hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),X),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),X),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) = X) # label(fact_1838_real__sum__of__halves) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.70 1891 (all M_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),M_1)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = M_1) # label(fact_1839_add__self__div__2) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.70 1892 (all V all W hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,V))),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,W))) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,number_number_of(int),V)),hAPP(int,int,number_number_of(int),W)))) # label(fact_1840_zmod__number__of__Bit0) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.70 1893 (all Aa all Ba (hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),Aa),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),Ba),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) <-> hAPP(int,int,abs_abs(int),Aa) = hAPP(int,int,abs_abs(int),Ba))) # label(fact_1842_power2__eq__iff__abs__eq) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.70 1894 (all A_1 hAPP(int,int,abs_abs(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,abs_abs(int),A_1)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) # label(fact_1843_abs__power2__distrib) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.70 1895 (all X_1 all K (X_1 = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),K) -> hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),zEven)))) # label(fact_1844_zEvenI) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.70 1896 (all X_a (linord1117847801e_zero(X_a) & number_ring(X_a) -> (all R_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),inverse_divide(X_a),R_1),hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),R_1)))))) # label(fact_1845_half__gt__zero__iff) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.70 1897 (all X_a (linord1117847801e_zero(X_a) & number_ring(X_a) -> (all R_4 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),R_4)) -> 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),inverse_divide(X_a),R_4),hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))))) # label(fact_1846_half__gt__zero) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.70 1898 (all X_a (linordered_semidom(X_a) -> (all X all Y (hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),Y),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) -> (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)) -> ti(X_a,X) = ti(X_a,Y))))))) # label(fact_1847_power2__eq__imp__eq) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.70 1899 (all X_a (linordered_semidom(X_a) -> (all X all Y (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),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),Y),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) -> (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),X),Y))))))) # label(fact_1848_power2__le__imp__le) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.70 1900 (all X_a (linordered_idom(X_a) -> (all A_1 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))))) # label(fact_1849_zero__le__power2) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.70 1901 (all X_a (linordered_idom(X_a) -> (all 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),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),zero_zero(X_a)))))) # label(fact_1850_power2__less__0) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.70 1902 (all X_a (linordered_idom(X_a) -> (all Aa (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),Aa),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) <-> ti(X_a,Aa) != zero_zero(X_a))))) # label(fact_1851_zero__less__power2) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.70 1903 (all X_a (linordered_idom(X_a) -> (all X_1 all Y_1 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),Y_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) = zero_zero(X_a) <-> ti(X_a,X_1) = zero_zero(X_a) & ti(X_a,Y_1) = zero_zero(X_a))))) # label(fact_1852_sum__power2__eq__zero__iff) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.70 1904 (all X_b (monoid_mult(X_b) & number(X_b) -> (all W hAPP(nat,X_b,hAPP(X_b,fun(nat,X_b),power_power(X_b),hAPP(int,X_b,number_number_of(X_b),W)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(int,X_b,number_number_of(X_b),W)),hAPP(int,X_b,number_number_of(X_b),W))))) # label(fact_1853_power2__eq__square__number__of) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.70 1905 (all X_a (ring_11004092258visors(X_a) -> (all Aa (hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),Aa),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = one_one(X_a) <-> ti(X_a,Aa) = one_one(X_a) | ti(X_a,Aa) = hAPP(X_a,X_a,uminus_uminus(X_a),one_one(X_a)))))) # label(fact_1854_power2__eq__1__iff) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.70 1906 (all X_a (comm_semiring_1(X_a) -> (all X all N_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),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),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),X),N_1)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),N_1))))) # label(fact_1855_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.70 1907 (all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) -> N_1 = zero_zero(nat) | N_1 = hAPP(nat,nat,suc,zero_zero(nat)))) # label(fact_1856_less__2__cases) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.70 1908 (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)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),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),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),N_1))))) # label(fact_1857_ring__1__class_Opower__minus__even) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.70 1909 (all X_1 all Y_1 (hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),Y_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) = zero_zero(real) <-> X_1 = zero_zero(real) & Y_1 = zero_zero(real))) # label(fact_1859_realpow__two__sum__zero__iff) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.70 1910 (all X hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),X)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) # label(fact_1862_four__x__squared) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.70 1911 (all N_1 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),one_one(real)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),N_1)))) # label(fact_1863_two__realpow__ge__one) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.70 1912 (all X_1 (hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),X_1),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) != zero_zero(int) <-> hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),X_1),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = one_one(int))) # label(fact_1864_neq__one__mod__two) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.70 1913 (all N_1 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(nat,real,real_1(nat),N_1)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),N_1)))) # label(fact_1865_two__realpow__gt) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.70 1914 (all X all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),Y)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),Y)),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),Y)))) # label(fact_1866_real__gt__half__sum) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.70 1915 (all X all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),Y)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),Y)),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))) # label(fact_1867_real__less__half__sum) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.70 1916 (all U all X hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,uminus_uminus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),U),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))) # label(fact_1868_realpow__square__minus__le) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.70 1917 (all M_1 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),M_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) = zero_zero(nat) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),M_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) = one_one(nat) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),M_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) = hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),M_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) = hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,hAPP(int,int,bit1,pls))))) # label(fact_1869_mod__exhaust__less__4) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.70 1918 (all B all A_1 hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),B),A_1)),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),A_1) = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),B),A_1)),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) # label(fact_1873_real__average__minus__second) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.70 1919 (all A_1 all B hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A_1),B)),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),A_1) = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),B),A_1)),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) # label(fact_1874_real__average__minus__first) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.70 1920 (all A_1 (hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = one_one(int) -> hAPP(int,int,abs_abs(int),A_1) = one_one(int))) # label(fact_1875_power2__eq1__iff) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.70 1921 (all X_1 (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),zEven)) -> hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),X_1),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = zero_zero(int))) # label(fact_1876_even__div__2__prop1) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.70 1922 (all X_1 all Y_1 (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Y_1),zEven)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X_1),Y_1)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),X_1),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),Y_1),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))))) # label(fact_1877_even__div__2__l) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.70 1923 (all X_1 (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),zEven)) -> hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),X_1),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) = X_1)) # label(fact_1878_even__div__2__prop2) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.70 1924 (all Y_1 all X_1 (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),zEven)) -> hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X_1),Y_1)),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),X_1),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),Y_1))) # label(fact_1879_even__prod__div__2) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.70 1925 (all Y_1 all X_1 (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),zEven)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Y_1),zEven)) -> hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X_1),Y_1)),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),X_1),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),Y_1),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))) # label(fact_1880_even__sum__div__2) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.70 1926 (all X_a (linordered_semidom(X_a) -> (all X all Y (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),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),Y),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) -> (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(X_a),X),Y))))))) # label(fact_1881_power2__less__imp__less) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.70 1927 (all X_a (linord1117847801e_zero(X_a) & number_ring(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),inverse_divide(X_a),one_one(X_a)),hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))) # label(fact_1882_half) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.70 1928 (all X_a (linordered_idom(X_a) -> (all X_1 all Y_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),Y_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),zero_zero(X_a))) <-> ti(X_a,X_1) = zero_zero(X_a) & ti(X_a,Y_1) = zero_zero(X_a))))) # label(fact_1883_sum__power2__le__zero__iff) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.70 1929 (all X_a (linordered_idom(X_a) -> (all X all Y hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),Y),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))))) # label(fact_1884_sum__power2__ge__zero) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.70 1930 (all X_a (linordered_idom(X_a) -> (all X all Y -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),Y),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),zero_zero(X_a)))))) # label(fact_1885_not__sum__power2__lt__zero) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.70 1931 (all X_a (linordered_idom(X_a) -> (all X_1 all Y_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),Y_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))) <-> ti(X_a,X_1) != zero_zero(X_a) | ti(X_a,Y_1) != zero_zero(X_a))))) # label(fact_1886_sum__power2__gt__zero__iff) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.70 1932 (all X_a (number_semiring(X_a) -> (all X all Y 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),plus_plus(X_a),X),Y)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = 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),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),Y),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),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),hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),X)),Y))))) # label(fact_1887_power2__sum) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.70 1933 (all X_a (linordered_idom(X_a) -> (all A_1 all N_1 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),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),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),N_1))))))) # label(fact_1888_zero__le__even__power_H) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.70 1934 (all X_a (linordered_idom(X_a) -> (all A_1 all K_4 (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),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),K_4))),zero_zero(X_a))) -> ti(X_a,A_1) = zero_zero(X_a))))) # label(fact_1889_even__power__le__0__imp__0) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.70 1935 (all X_a (comm_semiring_1(X_a) -> (all X all N_1 hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),N_1))) = 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),times_times(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),N_1)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),N_1)))))) # label(fact_1890_comm__semiring__1__class_Onormalizing__semiring__rules_I37_J) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.70 1936 (all X_a (monoid_mult(X_a) -> (all A_1 all N_1 hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),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),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N_1)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))) # label(fact_1891_power__odd__eq) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.70 1937 (all X_a (ring_1(X_a) -> (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),one_one(X_a))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),N_1)) = one_one(X_a)))) # label(fact_1892_power__minus1__even) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.70 1938 (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(int),X),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) -> X = zero_zero(int) | X = one_one(int)))) # label(fact_1893_int__pos__lt__two__imp__zero__or__one) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.70 1939 (all N_1 (N_1 != zero_zero(nat) -> hAPP(nat,nat,suc,hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),N_1)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),N_1))) # label(fact_1894_Suc__Suc__mult__two__diff__two) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.70 1940 (all N_1 (N_1 != zero_zero(nat) -> hAPP(nat,nat,suc,hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),N_1)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),N_1))) # label(fact_1895_lemma__Suc__Suc__4n__diff__2) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.70 1941 (all X_a (archim1727834104eiling(X_a) -> (all X_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),hAPP(X_a,int,archim2085082626_floor(X_a),X_1))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),X_1)))))) # label(fact_1896_one__less__floor) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.70 1942 (all X_a (archim1727834104eiling(X_a) -> (all X_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(X_a,int,archim2085082626_floor(X_a),X_1)),one_one(int))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))))) # label(fact_1897_floor__le__one) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.70 1943 (all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),one_one(nat)),N_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),N_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))) # label(fact_1898_div__2__gt__zero) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.70 1944 (all M (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),M),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) <-> hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),M),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = one_one(nat))) # label(fact_1899_mod2__gr__0) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.70 1945 (all N_1 hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,real_1(nat),N_1)),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) = hAPP(nat,real,real_1(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),N_1))) # label(fact_1900_fact__lemma) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.70 1946 (all V all W ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),W))) -> hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit1,V))),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,W))) = hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,number_number_of(int),V)),hAPP(int,int,number_number_of(int),W))) & (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),W))) -> hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit1,V))),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,W))) = hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,number_number_of(int),V)),one_one(int))),hAPP(int,int,number_number_of(int),W))))) # label(fact_1903_zdiv__number__of__Bit1) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.70 1947 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,abs_abs(real),X)),one_one(real))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),one_one(real))))) # label(fact_1904_less__one__imp__sqr__less__one) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.70 1948 (all A_1 all B hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A_1),B)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),A_1)),B))),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) # label(fact_1905_zadd__power2) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.70 1949 (all A_1 all B hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A_1),B)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,hAPP(int,int,bit1,pls)))) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,hAPP(int,int,bit1,pls))))),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit1,hAPP(int,int,bit1,pls)))),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),B))),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit1,hAPP(int,int,bit1,pls)))),A_1)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,hAPP(int,int,bit1,pls)))))) # label(fact_1906_zadd__power3) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.70 1950 (all X all Y hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),Y),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X),Y)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X),Y))) # label(fact_1907_diff__square) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.70 1951 (all A_1 all B hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A_1),B)),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A_1),B)) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) # label(fact_1908_zspecial__product) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.70 1952 (all X hAPP(real,real,cos,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),pi))) = hAPP(real,real,cos,X)) # label(fact_1912_cos__periodic) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.70 1953 (all X_1 all K (X_1 = 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,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),K)),one_one(int)) -> hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),zOdd)))) # label(fact_1914_zOddI) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.70 1954 (all X hAPP(real,real,tan,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),pi))) = hAPP(real,real,tan,X)) # label(fact_1915_tan__periodic) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.70 1955 (all Y hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,arctan,Y)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))) # label(fact_1917_arctan__ubound) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.70 1956 (all X_a (number_ring(X_a) -> (all X all Y 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),minus_minus(X_a),X),Y)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = 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),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),Y),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),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),hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),X)),Y))))) # label(fact_1919_power2__diff) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.70 1957 (all X_a (linordered_idom(X_a) -> (all A_1 all N_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),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)))))) # label(fact_1920_odd__0__le__power__imp__0__le) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.70 1958 (all X_a (linordered_idom(X_a) -> (all N_1 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),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),N_1)))),zero_zero(X_a))))))) # label(fact_1921_odd__power__less__zero) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.70 1959 (all X_a (ring_1(X_a) -> (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),one_one(X_a))),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),N_1))) = hAPP(X_a,X_a,uminus_uminus(X_a),one_one(X_a))))) # label(fact_1922_power__minus1__odd) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.70 1960 (all X_a (number_ring(X_a) -> (all N_1 hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(int,X_a,number_number_of(X_a),min)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),N_1)) = one_one(X_a)))) # label(fact_1923_power__m1__even) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.70 1961 (all X_a (number_ring(X_a) -> (all N_1 hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(int,X_a,number_number_of(X_a),min)),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),N_1))) = hAPP(int,X_a,number_number_of(X_a),min)))) # label(fact_1924_power__m1__odd) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.70 1962 (all N_1 (N_1 != zero_zero(nat) -> hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),N_1)),one_one(nat))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),N_1))) # label(fact_1925_Suc__mult__two__diff__one) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.70 1963 (all P_4 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),P_4)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),P_4),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))))) # label(fact_1926_Int2_Oaux__2) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.70 1964 (all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_1),one_one(nat))),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))) # label(fact_1927_Suc__n__div__2__gt__zero) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.70 1965 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,cos,hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),X))),one_one(real)))))) # label(fact_1928_cos__double__less__one) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.70 1966 (all P_4 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),P_4)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(int,nat,nat_1,P_4)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),P_4),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))) # label(fact_1929_Int2_Oaux__1) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.70 1967 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,cos,X)))))) # label(fact_1930_cos__gt__zero) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.70 1968 (all A_1 all B hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A_1),B)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,hAPP(int,int,bit1,pls)))) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,hAPP(int,int,bit1,pls))))),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit1,hAPP(int,int,bit1,pls)))),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),B))),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit1,hAPP(int,int,bit1,pls)))),A_1)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,hAPP(int,int,bit1,pls)))))) # label(fact_1931_zdiff__power3) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.70 1969 (all A_1 all B hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A_1),B)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),A_1)),B))),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) # label(fact_1932_zdiff__power2) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.70 1970 (all N_1 hAPP(real,real,cos,hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),hAPP(nat,real,real_1(nat),N_1))),pi)) = one_one(real)) # label(fact_1935_cos__2npi) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.70 1971 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,tan,X)))))) # label(fact_1936_tan__gt__zero) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.70 1972 (all X all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),Y)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),Y),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,tan,Y)),hAPP(real,real,tan,X))))))) # label(fact_1937_tan__monotone) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.70 1973 (all X_1 all Y_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),Y_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),Y_1),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),X_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_1),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),Y_1),X_1)) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,tan,Y_1)),hAPP(real,real,tan,X_1))))))))) # label(fact_1938_tan__monotone_H) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.70 1974 (all Y hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),one_one(real)),hAPP(real,real,tan,Y)) = hAPP(real,real,tan,hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),Y))) # label(fact_1939_tan__inverse) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.70 1975 (all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),hAPP(real,real,arctan,Y))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,arctan,Y)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))) # label(fact_1940_arctan__bounded) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.70 1976 (all Y hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),hAPP(real,real,arctan,Y)))) # label(fact_1941_arctan__lbound) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.70 1977 (all B all A_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A_1),zero_zero(int))) -> hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),B))),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),A_1)) = hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),B),one_one(int))),A_1))) # label(fact_1942_neg__zdiv__mult__2) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.70 1978 (all B all A_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A_1)) -> hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),B))),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),A_1)) = hAPP(int,int,hAPP(int,fun(int,int),div_div(int),B),A_1))) # label(fact_1943_pos__zdiv__mult__2) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.70 1979 (all B all A_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A_1)) -> hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),B))),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),A_1)) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),B),A_1))))) # label(fact_1944_pos__zmod__mult__2) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.70 1980 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(real,real,cos,X)))))) # label(fact_1945_cos__ge__zero) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.70 1981 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,cos,X)))))) # label(fact_1946_cos__gt__zero__pi) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.70 1982 (all Pa (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),Pa)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Pa),zOdd)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),Pa),one_one(int))),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))))) # label(fact_1947_Euler_Oaux__2) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.70 1983 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,uminus_uminus(real),pi)),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),zero_zero(real))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,tan,X)),zero_zero(real)))))) # label(fact_1948_tan__less__zero) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.70 1984 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) -> hAPP(real,real,arctan,hAPP(real,real,tan,X)) = X))) # label(fact_1950_arctan__tan) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.70 1985 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,abs_abs(real),X)),one_one(real))) -> (exists Z_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))),Z_2)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),Z_2),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))) & hAPP(real,real,tan,Z_2) = X)))) # label(fact_1951_tan__total__pi4) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.70 1986 (all Y_1 all X_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),X_1)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),zOdd)) -> (exists N_2 hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),Y_1),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),N_2),X_1))))),X_1)))))) # label(fact_1952_best__odd__division__abs) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.70 1987 (all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),Y)) -> (exists X_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X_2)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_2),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) & hAPP(real,real,tan,X_2) = Y)))) # label(fact_1953_tan__total__pos) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.70 1988 (all Y all X (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),X)) -> (exists N_2 hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),Y),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),N_2),X))))),X))))) # label(fact_1954_best__division__abs) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.71 1989 (all P_4 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit1,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),P_4)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),P_4),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),P_4),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),P_4),one_one(int)))),hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),P_4),hAPP(int,int,number_number_of(int),hAPP(int,int,bit1,hAPP(int,int,bit1,pls))))))))) # label(fact_1955_inv__inv__aux) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.71 1990 (all M_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),M_1)) -> hAPP(nat,nat,suc,hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),M_1),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) = hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),M_1),one_one(int))))) # label(fact_1956_inv__is__inv__aux) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.71 1991 (all Y exists X_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),X_2)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_2),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) & hAPP(real,real,tan,X_2) = Y & (all Y_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),Y_2)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),Y_2),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) & hAPP(real,real,tan,Y_2) = Y -> Y_2 = X_2)))) # label(fact_1957_tan__total) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.71 1992 (all Y exists X_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),X_2)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_2),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) & hAPP(real,real,tan,X_2) = Y)) # label(fact_1958_lemma__tan__total1) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.71 1993 (all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Y)) -> (exists X_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X_2)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_2),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),Y),hAPP(real,real,tan,X_2))))))) # label(fact_1959_lemma__tan__total) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.71 1994 (all X_1 (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),zOdd)) -> -(all K_1 X_1 != 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,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),K_1)),one_one(int))))) # label(fact_1960_zOddE) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.71 1995 (all X all Y hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),Y)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),Y),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),X)),Y))) # label(fact_1961_real__sum__squared__expand) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.71 1996 (exists X_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X_2)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_2),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) & hAPP(real,real,cos,X_2) = zero_zero(real) & (all Y_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),Y_2)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),Y_2),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) & hAPP(real,real,cos,Y_2) = zero_zero(real) -> Y_2 = X_2)))) # label(fact_1962_cos__is__zero) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.71 1997 (all X_1 (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),zEven)) -> -(all K_1 X_1 != hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),K_1)))) # label(fact_1963_zEvenE) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.71 1998 (all W (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,number_number_of(int),W))) -> (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),one_one(int)),hAPP(int,int,number_number_of(int),W)))) -> hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),negDivAlg,one_one(int)),hAPP(int,int,number_number_of(int),W)) = hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),hAPP(int,int,number_number_of(int),min)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),hAPP(int,int,number_number_of(int),W)))) & (-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),one_one(int)),hAPP(int,int,number_number_of(int),W)))) -> hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),negDivAlg,one_one(int)),hAPP(int,int,number_number_of(int),W)) = hAPP(product_prod(int,int),product_prod(int,int),hAPP(int,fun(product_prod(int,int),product_prod(int,int)),adjust,hAPP(int,int,number_number_of(int),W)),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),negDivAlg,one_one(int)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),hAPP(int,int,number_number_of(int),W))))))) # label(fact_1964_negDivAlg__eqn__1__number__of) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.71 1999 (all W all V (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,number_number_of(int),V))) -> (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),hAPP(int,int,number_number_of(int),W)),hAPP(int,int,number_number_of(int),V)))) -> hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),negDivAlg,hAPP(int,int,number_number_of(int),W)),hAPP(int,int,number_number_of(int),V)) = hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),hAPP(int,int,number_number_of(int),min)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,number_number_of(int),W)),hAPP(int,int,number_number_of(int),V)))) & (-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),hAPP(int,int,number_number_of(int),W)),hAPP(int,int,number_number_of(int),V)))) -> hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),negDivAlg,hAPP(int,int,number_number_of(int),W)),hAPP(int,int,number_number_of(int),V)) = hAPP(product_prod(int,int),product_prod(int,int),hAPP(int,fun(product_prod(int,int),product_prod(int,int)),adjust,hAPP(int,int,number_number_of(int),V)),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),negDivAlg,hAPP(int,int,number_number_of(int),W)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),hAPP(int,int,number_number_of(int),V))))))) # label(fact_1965_negDivAlg__eqn__number__of) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.71 2000 (all A_1 all 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_eq(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A_1),B))) -> hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),negDivAlg,A_1),B) = hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),hAPP(int,int,number_number_of(int),min)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A_1),B))) & (-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),A_1),B))) -> hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),negDivAlg,A_1),B) = hAPP(product_prod(int,int),product_prod(int,int),hAPP(int,fun(product_prod(int,int),product_prod(int,int)),adjust,B),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),negDivAlg,A_1),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),B)))))) # label(fact_1966_negDivAlg__eqn) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.71 2001 (all A_1 all 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_1),B)) -> hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),posDivAlg,A_1),B) = hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),zero_zero(int)),A_1)) & (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_1),B)) -> hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),posDivAlg,A_1),B) = hAPP(product_prod(int,int),product_prod(int,int),hAPP(int,fun(product_prod(int,int),product_prod(int,int)),adjust,B),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),posDivAlg,A_1),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),B)))))) # label(fact_1967_posDivAlg__eqn) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.71 2002 (all W all V (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,number_number_of(int),V))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),W)),hAPP(int,int,number_number_of(int),V))) -> hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),posDivAlg,hAPP(int,int,number_number_of(int),W)),hAPP(int,int,number_number_of(int),V)) = hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),zero_zero(int)),hAPP(int,int,number_number_of(int),W))) & (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),W)),hAPP(int,int,number_number_of(int),V))) -> hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),posDivAlg,hAPP(int,int,number_number_of(int),W)),hAPP(int,int,number_number_of(int),V)) = hAPP(product_prod(int,int),product_prod(int,int),hAPP(int,fun(product_prod(int,int),product_prod(int,int)),adjust,hAPP(int,int,number_number_of(int),V)),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),posDivAlg,hAPP(int,int,number_number_of(int),W)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),hAPP(int,int,number_number_of(int),V))))))) # label(fact_1968_posDivAlg__eqn__number__of) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.71 2003 (all A_1 all B ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_1),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),zero_zero(int))) -> hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),posDivAlg,A_1),B) = hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),zero_zero(int)),A_1)) & (-(hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_1),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),zero_zero(int)))) -> hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),posDivAlg,A_1),B) = hAPP(product_prod(int,int),product_prod(int,int),hAPP(int,fun(product_prod(int,int),product_prod(int,int)),adjust,B),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),posDivAlg,A_1),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),B)))))) # label(fact_1969_posDivAlg_Osimps) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.71 2004 (all W (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,number_number_of(int),W))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),hAPP(int,int,number_number_of(int),W))) -> hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),posDivAlg,one_one(int)),hAPP(int,int,number_number_of(int),W)) = hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),zero_zero(int)),one_one(int))) & (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),hAPP(int,int,number_number_of(int),W))) -> hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),posDivAlg,one_one(int)),hAPP(int,int,number_number_of(int),W)) = hAPP(product_prod(int,int),product_prod(int,int),hAPP(int,fun(product_prod(int,int),product_prod(int,int)),adjust,hAPP(int,int,number_number_of(int),W)),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),posDivAlg,one_one(int)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),hAPP(int,int,number_number_of(int),W))))))) # label(fact_1970_posDivAlg__eqn__1__number__of) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.71 2005 (all A_1 all B ((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),A_1),B))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),zero_zero(int))) -> hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),negDivAlg,A_1),B) = hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),hAPP(int,int,number_number_of(int),min)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A_1),B))) & (-(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),A_1),B))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),zero_zero(int)))) -> hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),negDivAlg,A_1),B) = hAPP(product_prod(int,int),product_prod(int,int),hAPP(int,fun(product_prod(int,int),product_prod(int,int)),adjust,B),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),negDivAlg,A_1),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),B)))))) # label(fact_1971_negDivAlg_Osimps) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.71 2006 (all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,number_number_of(real),min)),Y)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),Y),one_one(real))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),hAPP(real,real,arcsin,Y))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,arcsin,Y)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))))) # label(fact_1972_arcsin__lt__bounded) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.71 2007 (all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,number_number_of(real),min)),Y)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),Y),one_one(real))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),hAPP(real,real,arcsin,Y))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,arcsin,Y)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))))) # label(fact_1973_arcsin__bounded) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.71 2008 (all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,number_number_of(real),min)),Y)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),Y),one_one(real))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),hAPP(real,real,arcsin,Y)))))) # label(fact_1974_arcsin__lbound) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.71 2009 (all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,number_number_of(real),min)),Y)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),Y),one_one(real))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,arcsin,Y)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))))) # label(fact_1975_arcsin__ubound) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.71 2010 (all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)) -> hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),min)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),N_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),hAPP(nat,real,real_1(nat),hAPP(nat,nat,fact_fact(nat),N_1)))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),zero_zero(real)),N_1)) = zero_zero(real))) # label(fact_1976_lemma__STAR__cos) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.71 2011 (all N_1 hAPP(nat,real,real_1(nat),hAPP(nat,nat,fact_fact(nat),N_1)) != zero_zero(real)) # label(fact_1977_real__of__nat__fact__not__zero) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.71 2012 (all N_1 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(nat,real,real_1(nat),hAPP(nat,nat,fact_fact(nat),N_1))))) # label(fact_1978_real__of__nat__fact__ge__zero) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.71 2013 (all N_1 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(nat,real,real_1(nat),hAPP(nat,nat,fact_fact(nat),N_1))))) # label(fact_1979_real__of__nat__fact__gt__zero) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.71 2014 (all N_1 all M_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),hAPP(nat,nat,suc,M_1))) -> hAPP(nat,nat,fact_fact(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,M_1)),N_1)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,M_1)),N_1)),hAPP(nat,nat,fact_fact(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),N_1))))) # label(fact_1980_fact__diff__Suc) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.71 2015 (all N_1 all M_1 ((M_1 = zero_zero(nat) -> hAPP(nat,nat,fact_fact(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),N_1)) = hAPP(nat,nat,fact_fact(nat),N_1)) & (M_1 != zero_zero(nat) -> hAPP(nat,nat,fact_fact(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),N_1)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),N_1)),hAPP(nat,nat,fact_fact(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),one_one(nat))),N_1)))))) # label(fact_1981_fact__add__num__eq__if2__nat) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.71 2016 (all M_1 all N_1 ((hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),N_1) = zero_zero(nat) -> hAPP(nat,nat,fact_fact(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),N_1)) = one_one(nat)) & (hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),N_1) != zero_zero(nat) -> hAPP(nat,nat,fact_fact(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),N_1)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),N_1)),hAPP(nat,nat,fact_fact(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),N_1)),one_one(nat))))))) # label(fact_1982_fact__add__num__eq__if__nat) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.71 2017 (all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)) -> hAPP(nat,nat,fact_fact(nat),N_1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N_1),hAPP(nat,nat,fact_fact(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),one_one(nat)))))) # label(fact_1983_fact__reduce__nat) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.71 2018 (all M_1 ((M_1 = zero_zero(nat) -> hAPP(nat,nat,fact_fact(nat),M_1) = one_one(nat)) & (M_1 != zero_zero(nat) -> hAPP(nat,nat,fact_fact(nat),M_1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),hAPP(nat,nat,fact_fact(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),one_one(nat))))))) # label(fact_1984_fact__num__eq__if__nat) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.71 2019 (all N hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),hAPP(bool,fun(real,fun(real,real)),if(real),hAPP(nat,bool,even_odd_even(nat),N)),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),min)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),hAPP(nat,nat,suc,zero_zero(nat)))),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),hAPP(nat,real,real_1(nat),hAPP(nat,nat,fact_fact(nat),N))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),zero_zero(real)),N)) = zero_zero(real)) # label(fact_1985_lemma__STAR__sin) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.71 2020 (all X_1 all Y_1 (hBOOL(hAPP(nat,bool,even_odd_even(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X_1),Y_1))) <-> hBOOL(hAPP(nat,bool,even_odd_even(nat),X_1)) | hBOOL(hAPP(nat,bool,even_odd_even(nat),Y_1)))) # label(fact_1987_even__product__nat) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.71 2021 (all X_1 all Y_1 (hBOOL(hAPP(nat,bool,even_odd_even(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X_1),Y_1))) <-> hBOOL(hAPP(nat,bool,even_odd_even(nat),X_1)) & hBOOL(hAPP(nat,bool,even_odd_even(nat),Y_1)) | -hBOOL(hAPP(nat,bool,even_odd_even(nat),X_1)) & -hBOOL(hAPP(nat,bool,even_odd_even(nat),Y_1)))) # label(fact_1988_even__sum__nat) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.71 2022 (all M all N (hBOOL(hAPP(nat,bool,even_odd_even(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N))) <-> (hBOOL(hAPP(nat,bool,even_odd_even(nat),M)) <-> hBOOL(hAPP(nat,bool,even_odd_even(nat),N))))) # label(fact_1989_even__add) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.71 2023 (all M all N (-hBOOL(hAPP(nat,bool,even_odd_even(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N))) <-> -(-hBOOL(hAPP(nat,bool,even_odd_even(nat),M)) <-> -hBOOL(hAPP(nat,bool,even_odd_even(nat),N))))) # label(fact_1990_odd__add) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.71 2024 (all X_1 (hBOOL(hAPP(nat,bool,even_odd_even(nat),hAPP(nat,nat,suc,X_1))) <-> -hBOOL(hAPP(nat,bool,even_odd_even(nat),X_1)))) # label(fact_1991_even__Suc) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.71 2025 (all X_a (linordered_idom(X_a) -> (all X all Y all N_1 (-hBOOL(hAPP(nat,bool,even_odd_even(nat),N_1)) -> (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(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),N_1)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),Y),N_1)))))))) # label(fact_1993_power__mono__odd) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.71 2026 (all N_1 (-hBOOL(hAPP(nat,bool,even_odd_even(nat),N_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)))) # label(fact_1994_odd__pos) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.71 2027 (all X_a (comm_ring_1(X_a) -> (all X all N_1 ((hBOOL(hAPP(nat,bool,even_odd_even(nat),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),X)),N_1) = hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),N_1)) & (-hBOOL(hAPP(nat,bool,even_odd_even(nat),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),X)),N_1) = hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),N_1))))))) # label(fact_1995_neg__power__if) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.71 2028 (all X_a (comm_ring_1(X_a) -> (all X all N_1 (hBOOL(hAPP(nat,bool,even_odd_even(nat),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),X)),N_1) = hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),N_1))))) # label(fact_1996_Parity_Opower__minus__even) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.71 2029 (all X_a (comm_ring_1(X_a) -> (all X all N_1 (-hBOOL(hAPP(nat,bool,even_odd_even(nat),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),X)),N_1) = hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),N_1)))))) # label(fact_1997_power__minus__odd) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.71 2030 (all X_a (linordered_idom(X_a) -> (all X all N_1 (hBOOL(hAPP(nat,bool,even_odd_even(nat),N_1)) -> hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(X_a,X_a,abs_abs(X_a),X)),N_1) = hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),N_1))))) # label(fact_1998_power__even__abs) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.71 2031 (all X_1 all Y_1 (hBOOL(hAPP(nat,bool,even_odd_even(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X_1),Y_1))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X_1),Y_1)) | hBOOL(hAPP(nat,bool,even_odd_even(nat),X_1)) & hBOOL(hAPP(nat,bool,even_odd_even(nat),Y_1)) | -hBOOL(hAPP(nat,bool,even_odd_even(nat),X_1)) & -hBOOL(hAPP(nat,bool,even_odd_even(nat),Y_1)))) # label(fact_1999_even__difference__nat) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.71 2032 (all X_a (linordered_idom(X_a) -> (all X_1 all N (-hBOOL(hAPP(nat,bool,even_odd_even(nat),N)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X_1),N))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),X_1))))))) # label(fact_2000_zero__le__odd__power) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.71 2033 (all X_a (monoid_mult(X_a) & linordered_ring(X_a) -> (all X all N_1 (hBOOL(hAPP(nat,bool,even_odd_even(nat),N_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),N_1))))))) # label(fact_2001_zero__le__even__power) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.71 2034 (all X_a (linordered_idom(X_a) -> (all Aa all N (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),Aa),N))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),Aa)) | hBOOL(hAPP(nat,bool,even_odd_even(nat),N)))))) # label(fact_2002_zero__le__power__iff) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.71 2035 (all X_a (linordered_idom(X_a) -> (all X_1 all N (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X_1),N))) <-> hBOOL(hAPP(nat,bool,even_odd_even(nat),N)) | -hBOOL(hAPP(nat,bool,even_odd_even(nat),N)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),X_1)))))) # label(fact_2003_zero__le__power__eq) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.71 2036 (all X_a (linordered_idom(X_a) -> (all X_1 all N (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),X_1),N)),zero_zero(X_a))) <-> -hBOOL(hAPP(nat,bool,even_odd_even(nat),N)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),zero_zero(X_a))))))) # label(fact_2004_power__less__zero__eq) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.71 2037 (all X_a (comm_ring_1(X_a) -> (all X (-hBOOL(hAPP(nat,bool,even_odd_even(nat),X)) -> 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))),X) = hAPP(X_a,X_a,uminus_uminus(X_a),one_one(X_a)))))) # label(fact_2005_minus__one__odd__power) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.71 2038 (all X_a (comm_ring_1(X_a) -> (all X (hBOOL(hAPP(nat,bool,even_odd_even(nat),X)) -> 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))),X) = one_one(X_a))))) # label(fact_2006_minus__one__even__power) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.71 2039 (all X_a (comm_ring_1(X_a) -> (all X ((hBOOL(hAPP(nat,bool,even_odd_even(nat),X)) -> 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))),X) = one_one(X_a)) & (-hBOOL(hAPP(nat,bool,even_odd_even(nat),X)) -> 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))),X) = hAPP(X_a,X_a,uminus_uminus(X_a),one_one(X_a))))))) # label(fact_2007_minus__one__even__odd__power) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.71 2040 (all X_a (linordered_idom(X_a) -> (all X all Y all N_1 (hBOOL(hAPP(nat,bool,even_odd_even(nat),N_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,abs_abs(X_a),X)),hAPP(X_a,X_a,abs_abs(X_a),Y))) -> 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),X),N_1)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),Y),N_1)))))))) # label(fact_2008_power__mono__even) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.71 2041 (all X_1 (hBOOL(hAPP(nat,bool,even_odd_even(nat),X_1)) <-> (exists Y_2 X_1 = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat)))),Y_2)))) # label(fact_2009_even__nat__equiv__def2) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.71 2042 (all X_1 (-hBOOL(hAPP(nat,bool,even_odd_even(nat),X_1)) <-> (exists Y_2 X_1 = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat)))),Y_2))))) # label(fact_2010_odd__nat__equiv__def2) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.71 2043 (all X_a (number_ring(X_a) -> (all X (-hBOOL(hAPP(nat,bool,even_odd_even(nat),X)) -> hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(int,X_a,number_number_of(X_a),min)),X) = hAPP(int,X_a,number_number_of(X_a),min))))) # label(fact_2011_Parity_Oneg__one__odd__power) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.71 2044 (all X_a (linordered_idom(X_a) -> (all X all W (hBOOL(hAPP(nat,bool,even_odd_even(nat),hAPP(int,nat,number_number_of(nat),W))) -> hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(X_a,X_a,abs_abs(X_a),X)),hAPP(int,nat,number_number_of(nat),W)) = hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),hAPP(int,nat,number_number_of(nat),W)))))) # label(fact_2012_power__even__abs__number__of) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.71 2045 (all X (hBOOL(hAPP(nat,bool,even_odd_even(nat),X)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,suc,X)),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat)))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),X),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat)))))) # label(fact_2013_even__nat__plus__one__div__two) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.71 2046 (all X (-hBOOL(hAPP(nat,bool,even_odd_even(nat),X)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,suc,X)),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat)))) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),X),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat))))))) # label(fact_2014_odd__nat__plus__one__div__two) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.71 2047 (all X (-hBOOL(hAPP(nat,bool,even_odd_even(nat),X)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),X),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat)))) = hAPP(nat,nat,suc,zero_zero(nat)))) # label(fact_2015_odd__nat__mod__two__eq__one) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.71 2048 (all X (hBOOL(hAPP(nat,bool,even_odd_even(nat),X)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),X),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat)))) = zero_zero(nat))) # label(fact_2016_even__nat__mod__two__eq__zero) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.71 2049 (all X_1 (-hBOOL(hAPP(nat,bool,even_odd_even(nat),X_1)) <-> hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),X_1),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat)))) = hAPP(nat,nat,suc,zero_zero(nat)))) # label(fact_2017_odd__nat__equiv__def) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.71 2050 (all X_1 (hBOOL(hAPP(nat,bool,even_odd_even(nat),X_1)) <-> hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),X_1),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat)))) = zero_zero(nat))) # label(fact_2018_even__nat__equiv__def) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.71 2051 (all X_1 all Y_1 (hBOOL(hAPP(nat,bool,even_odd_even(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),X_1),Y_1))) <-> hBOOL(hAPP(nat,bool,even_odd_even(nat),X_1)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Y_1)))) # label(fact_2019_even__power__nat) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.71 2052 (all X_a (linordered_idom(X_a) -> (all X_1 all N (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),X_1),N)),zero_zero(X_a))) <-> N != zero_zero(nat) & (-hBOOL(hAPP(nat,bool,even_odd_even(nat),N)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),zero_zero(X_a))) | hBOOL(hAPP(nat,bool,even_odd_even(nat),N)) & ti(X_a,X_1) = zero_zero(X_a)))))) # label(fact_2020_power__le__zero__eq) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.71 2053 (all X_a (linordered_idom(X_a) -> (all X_1 all N (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),X_1),N))) <-> N = zero_zero(nat) | hBOOL(hAPP(nat,bool,even_odd_even(nat),N)) & ti(X_a,X_1) != zero_zero(X_a) | -hBOOL(hAPP(nat,bool,even_odd_even(nat),N)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),X_1)))))) # label(fact_2021_zero__less__power__eq) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.71 2054 (all X_a (linordered_idom(X_a) -> (all X_1 all W_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X_1),hAPP(int,nat,number_number_of(nat),W_1)))) <-> hBOOL(hAPP(nat,bool,even_odd_even(nat),hAPP(int,nat,number_number_of(nat),W_1))) | -hBOOL(hAPP(nat,bool,even_odd_even(nat),hAPP(int,nat,number_number_of(nat),W_1))) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),X_1)))))) # label(fact_2022_zero__le__power__eq__number__of) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.71 2055 (all X_a (linordered_idom(X_a) -> (all X_1 all W_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),X_1),hAPP(int,nat,number_number_of(nat),W_1))),zero_zero(X_a))) <-> -hBOOL(hAPP(nat,bool,even_odd_even(nat),hAPP(int,nat,number_number_of(nat),W_1))) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),zero_zero(X_a))))))) # label(fact_2023_power__less__zero__eq__number__of) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.71 2056 (all X_a (number_ring(X_a) -> (all X ((hBOOL(hAPP(nat,bool,even_odd_even(nat),X)) -> hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(int,X_a,number_number_of(X_a),min)),X) = one_one(X_a)) & (-hBOOL(hAPP(nat,bool,even_odd_even(nat),X)) -> hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(int,X_a,number_number_of(X_a),min)),X) = hAPP(int,X_a,number_number_of(X_a),min)))))) # label(fact_2024_neg__one__even__odd__power) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.71 2057 (all X_a (number_ring(X_a) -> (all X (hBOOL(hAPP(nat,bool,even_odd_even(nat),X)) -> hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(int,X_a,number_number_of(X_a),min)),X) = one_one(X_a))))) # label(fact_2025_Parity_Oneg__one__even__power) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.71 2058 (all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> (hBOOL(hAPP(nat,bool,even_odd_even(nat),N)) <-> -hBOOL(hAPP(nat,bool,even_odd_even(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),one_one(nat))))))) # label(fact_2026_even__num__iff) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.71 2059 (all X (hBOOL(hAPP(nat,bool,even_odd_even(nat),X)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat)))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),X),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat))))) = X)) # label(fact_2027_even__nat__div__two__times__two) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.71 2060 (all X (-hBOOL(hAPP(nat,bool,even_odd_even(nat),X)) -> hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat)))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),X),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat)))))) = X)) # label(fact_2028_odd__nat__div__two__times__two__plus__one) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.71 2061 (all X_a (linordered_idom(X_a) -> (all X_1 all W_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),X_1),hAPP(int,nat,number_number_of(nat),W_1))),zero_zero(X_a))) <-> hAPP(int,nat,number_number_of(nat),W_1) != zero_zero(nat) & (-hBOOL(hAPP(nat,bool,even_odd_even(nat),hAPP(int,nat,number_number_of(nat),W_1))) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),zero_zero(X_a))) | hBOOL(hAPP(nat,bool,even_odd_even(nat),hAPP(int,nat,number_number_of(nat),W_1))) & ti(X_a,X_1) = zero_zero(X_a)))))) # label(fact_2029_power__le__zero__eq__number__of) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.71 2062 (all X_a (linordered_idom(X_a) -> (all X_1 all W_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),X_1),hAPP(int,nat,number_number_of(nat),W_1)))) <-> hAPP(int,nat,number_number_of(nat),W_1) = zero_zero(nat) | hBOOL(hAPP(nat,bool,even_odd_even(nat),hAPP(int,nat,number_number_of(nat),W_1))) & ti(X_a,X_1) != zero_zero(X_a) | -hBOOL(hAPP(nat,bool,even_odd_even(nat),hAPP(int,nat,number_number_of(nat),W_1))) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),X_1)))))) # label(fact_2030_zero__less__power__eq__number__of) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.71 2063 (all N (hBOOL(hAPP(nat,bool,even_odd_even(nat),N)) <-> (exists M_3 N = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),M_3)))) # label(fact_2031_even__mult__two__ex) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.71 2064 (all N (hBOOL(hAPP(nat,bool,even_odd_even(nat),N)) <-> hBOOL(hAPP(nat,bool,even_odd_even(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),N),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))))) # label(fact_2032_even__even__mod__4__iff) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.71 2065 (all N (-hBOOL(hAPP(nat,bool,even_odd_even(nat),N)) <-> (exists M_3 N = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),M_3))))) # label(fact_2033_odd__Suc__mult__two__ex) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.71 2066 (all N_1 (hBOOL(hAPP(nat,bool,even_odd_even(nat),N_1)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_1),one_one(nat))),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),N_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) # label(fact_2034_lemma__even__div2) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.71 2067 (all N_1 hAPP(nat,nat,fact_fact(nat),N_1) != zero_zero(nat)) # label(fact_2035_fact__nonzero__nat) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.71 2068 (all M_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),N_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,fact_fact(nat),M_1)),hAPP(nat,nat,fact_fact(nat),N_1))))) # label(fact_2036_fact__mono__nat) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.71 2069 (all N_1 (-hBOOL(hAPP(nat,bool,even_odd_even(nat),N_1)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_1),one_one(nat))),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),N_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))) # label(fact_2038_lemma__not__even__div2) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.71 2070 (all N_1 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),N_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) = hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,hAPP(int,int,bit1,pls))) -> -hBOOL(hAPP(nat,bool,even_odd_even(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),one_one(nat))),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))) # label(fact_2039_lemma__odd__mod__4__div__2) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.71 2071 (all N_1 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),N_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) = one_one(nat) -> hBOOL(hAPP(nat,bool,even_odd_even(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),one_one(nat))),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))) # label(fact_2040_lemma__even__mod__4__div__2) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.71 2072 (all N_1 all M_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),M_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,fact_fact(nat),M_1)),hAPP(nat,nat,fact_fact(nat),N_1)))))) # label(fact_2043_fact__less__mono__nat) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.71 2073 (all N_1 hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,fact_fact(nat),N_1)))) # label(fact_2044_fact__gt__zero__nat) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.71 2074 (all X_1 (hAPP(real,real,cos,X_1) = zero_zero(real) <-> (exists N_2 (-hBOOL(hAPP(nat,bool,even_odd_even(nat),N_2)) & X_1 = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,real_1(nat),N_2)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))) | (exists N_2 (-hBOOL(hAPP(nat,bool,even_odd_even(nat),N_2)) & X_1 = hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,real_1(nat),N_2)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))))) # label(fact_2045_cos__zero__iff) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.71 2075 (all X hAPP(nat,nat,fact_fact(nat),hAPP(nat,nat,suc,X)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,X)),hAPP(nat,nat,fact_fact(nat),X))) # label(fact_2046_Fact_Ofact__Suc) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.71 2076 (all N_1 hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),one_one(nat)),hAPP(nat,nat,fact_fact(nat),N_1)))) # label(fact_2047_fact__ge__one__nat) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.71 2077 (all N_1 hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,zero_zero(nat))),hAPP(nat,nat,fact_fact(nat),N_1)))) # label(fact_2048_fact__ge__Suc__0__nat) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.71 2078 (all N_1 hAPP(nat,nat,fact_fact(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_1),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),N_1),one_one(nat))),hAPP(nat,nat,fact_fact(nat),N_1))) # label(fact_2049_fact__plus__one__nat) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.71 2079 (all M_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),N_1)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,fact_fact(nat),N_1)),hAPP(nat,nat,fact_fact(nat),M_1)) = zero_zero(nat))) # label(fact_2050_fact__mod) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.71 2080 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X)) -> (hAPP(real,real,cos,X) = zero_zero(real) -> (exists N_2 (-hBOOL(hAPP(nat,bool,even_odd_even(nat),N_2)) & X = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,real_1(nat),N_2)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))))) # label(fact_2051_cos__zero__lemma) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.71 2081 (all N_1 (-hBOOL(hAPP(nat,bool,even_odd_even(nat),N_1)) -> (exists X_2 hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),N_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),X_2)),one_one(nat))))) # label(fact_2052_odd__square) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.71 2082 (all X_2 ((hBOOL(hAPP(nat,bool,even_odd_even(nat),X_2)) -> hAPP(nat,real,sin_coeff,X_2) = zero_zero(real)) & (-hBOOL(hAPP(nat,bool,even_odd_even(nat),X_2)) -> hAPP(nat,real,sin_coeff,X_2) = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),min)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X_2),hAPP(nat,nat,suc,zero_zero(nat)))),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),hAPP(nat,real,real_1(nat),hAPP(nat,nat,fact_fact(nat),X_2)))))) # label(fact_2053_sin__coeff__def) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.71 2083 (all N_1 (hBOOL(hAPP(nat,bool,even_odd_even(nat),N_1)) -> (exists X_2 hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),N_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),X_2)))) # label(fact_2054_even__square) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.71 2084 (all X_2 ((hBOOL(hAPP(nat,bool,even_odd_even(nat),X_2)) -> hAPP(nat,real,cos_coeff,X_2) = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),min)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),X_2),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),hAPP(nat,real,real_1(nat),hAPP(nat,nat,fact_fact(nat),X_2)))) & (-hBOOL(hAPP(nat,bool,even_odd_even(nat),X_2)) -> hAPP(nat,real,cos_coeff,X_2) = zero_zero(real)))) # label(fact_2055_cos__coeff__def) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.71 2085 (all P_4 all A_1 hAPP(int,int,hAPP(int,fun(int,int),inv,P_4),A_1) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A_1),hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),P_4),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))),P_4)) # label(fact_2056_WilsonRuss_Oinv__def) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.71 2086 (all X (X != zero_zero(real) -> hAPP(real,real,arctan,hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),one_one(real)),X)) = hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,sgn_sgn(real),X)),pi)),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(real,real,arctan,X)))) # label(fact_2057_arctan__inverse) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.71 2087 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) -> hAPP(real,real,tan,X) = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,sin,hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),X))),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,cos,hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),X))),one_one(real)))))) # label(fact_2058_tan__half) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.71 2088 (all N_1 hAPP(real,real,sin,hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,real_1(nat),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),N_1)))),pi)),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),min)),N_1)) # label(fact_2059_sin__cos__npi) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.71 2089 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),one_one(real)),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X),zero_zero(real))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,ln,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),one_one(real)),X))),X))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))))) # label(fact_2060_abs__ln__one__plus__x__minus__x__bound__nonpos) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.71 2090 (all X_a (linordered_idom(X_a) -> (all A_1 hAPP(X_a,X_a,sgn_sgn(X_a),hAPP(X_a,X_a,sgn_sgn(X_a),A_1)) = hAPP(X_a,X_a,sgn_sgn(X_a),A_1)))) # label(fact_2062_sgn__sgn) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.71 2091 (all X hAPP(real,real,sin,hAPP(real,real,uminus_uminus(real),X)) = hAPP(real,real,uminus_uminus(real),hAPP(real,real,sin,X))) # label(fact_2063_sin__minus) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.71 2092 (all X_a (real_normed_vector(X_a) -> (all X_1 (hAPP(X_a,X_a,sgn_sgn(X_a),X_1) = zero_zero(X_a) <-> ti(X_a,X_1) = zero_zero(X_a))))) # label(fact_2064_sgn__zero__iff) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.71 2093 (all X_a (linordered_idom(X_a) -> (all Aa (hAPP(X_a,X_a,sgn_sgn(X_a),Aa) = zero_zero(X_a) <-> ti(X_a,Aa) = zero_zero(X_a))))) # label(fact_2065_sgn__0__0) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.71 2094 (all X_a (real_normed_vector(X_a) -> hAPP(X_a,X_a,sgn_sgn(X_a),zero_zero(X_a)) = zero_zero(X_a))) # label(fact_2066_sgn__zero) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.71 2095 (all X_a (sgn_if(X_a) -> hAPP(X_a,X_a,sgn_sgn(X_a),zero_zero(X_a)) = zero_zero(X_a))) # label(fact_2067_sgn0) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.71 2096 (all X_a (real_n1866405975lgebra(X_a) -> (all X all Y hAPP(X_a,X_a,sgn_sgn(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),hAPP(X_a,X_a,sgn_sgn(X_a),X)),hAPP(X_a,X_a,sgn_sgn(X_a),Y))))) # label(fact_2068_sgn__mult) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.71 2097 (all X_a (linordered_idom(X_a) -> (all A_1 all B hAPP(X_a,X_a,sgn_sgn(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,sgn_sgn(X_a),A_1)),hAPP(X_a,X_a,sgn_sgn(X_a),B))))) # label(fact_2069_sgn__times) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.71 2098 (all X_a (real_n2089651433ebra_1(X_a) -> hAPP(X_a,X_a,sgn_sgn(X_a),one_one(X_a)) = one_one(X_a))) # label(fact_2070_sgn__one) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.71 2099 (all X_a (real_normed_vector(X_a) -> (all X hAPP(X_a,X_a,sgn_sgn(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),X)) = hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(X_a,X_a,sgn_sgn(X_a),X))))) # label(fact_2071_sgn__minus) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.71 2100 (all X hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,sin,X)),one_one(real)))) # label(fact_2072_sin__le__one) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.71 2101 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,ln,X)),X)))) # label(fact_2074_ln__less__self) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.71 2102 (all Y_1 all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Y_1)) -> (hAPP(real,real,ln,X_1) = hAPP(real,real,ln,Y_1) <-> X_1 = Y_1)))) # label(fact_2075_ln__inj__iff) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.71 2103 (all Y_1 all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Y_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,ln,X_1)),hAPP(real,real,ln,Y_1))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_1),Y_1)))))) # label(fact_2076_ln__less__cancel__iff) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.71 2104 (all X_a (linordered_idom(X_a) -> (all Aa (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,sgn_sgn(X_a),Aa)),zero_zero(X_a))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),zero_zero(X_a))))))) # label(fact_2078_sgn__less) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.71 2105 (all X_a (linordered_idom(X_a) -> (all Aa (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,sgn_sgn(X_a),Aa))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),Aa)))))) # label(fact_2079_sgn__greater) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.71 2106 (all X hAPP(real,real,sgn_sgn(real),X) = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),X),hAPP(real,real,abs_abs(real),X))) # label(fact_2080_real__sgn__eq) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.71 2107 (all X_a (linordered_idom(X_a) -> (all X hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,sgn_sgn(X_a),X)),hAPP(X_a,X_a,abs_abs(X_a),X)) = ti(X_a,X)))) # label(fact_2081_mult__sgn__abs) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.71 2108 (all X_a (linordered_idom(X_a) -> (all K_4 hAPP(X_a,X_a,abs_abs(X_a),K_4) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),K_4),hAPP(X_a,X_a,sgn_sgn(X_a),K_4))))) # label(fact_2082_abs__sgn) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.71 2109 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> (hAPP(real,real,ln,X) = hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),X),one_one(real)) -> X = one_one(real)))) # label(fact_2083_ln__eq__minus__one) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.71 2110 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X),pi)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(real,real,sin,X)))))) # label(fact_2084_sin__ge__zero) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.71 2111 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),pi)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,sin,X)))))) # label(fact_2085_sin__gt__zero__pi) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.71 2112 (all X hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,number_number_of(real),min)),hAPP(real,real,sin,X)))) # label(fact_2086_sin__ge__minus__one) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.71 2113 (all X (hAPP(real,real,cos,X) = one_one(real) -> hAPP(real,real,sin,X) = zero_zero(real))) # label(fact_2087_cos__one__sin__zero) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.71 2114 (all X hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),hAPP(real,real,sin,X))),one_one(real)))) # label(fact_2088_abs__sin__le__one) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.71 2115 (all X all Y hAPP(real,real,sin,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),Y)) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,sin,X)),hAPP(real,real,cos,Y))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,cos,X)),hAPP(real,real,sin,Y)))) # label(fact_2089_sin__add) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.71 2116 (all X all Y hAPP(real,real,sin,hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),X),Y)) = hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,sin,X)),hAPP(real,real,cos,Y))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,cos,X)),hAPP(real,real,sin,Y)))) # label(fact_2090_sin__diff) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.71 2117 (all X all Y hAPP(real,real,sin,hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),X),Y)) = hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,cos,Y)),hAPP(real,real,sin,X))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,sin,Y)),hAPP(real,real,cos,X)))) # label(fact_2091_sin__diff2) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.71 2118 (all X hAPP(real,real,sin,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),pi),X)) = hAPP(real,real,uminus_uminus(real),hAPP(real,real,sin,X))) # label(fact_2092_sin__periodic__pi2) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.71 2119 (all X hAPP(real,real,sin,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),pi)) = hAPP(real,real,uminus_uminus(real),hAPP(real,real,sin,X))) # label(fact_2093_sin__periodic__pi) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.71 2120 (all Y_1 all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Y_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,ln,X_1)),hAPP(real,real,ln,Y_1))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_1),Y_1)))))) # label(fact_2094_ln__le__cancel__iff) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.71 2121 (all X hAPP(real,real,tan,X) = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,sin,X)),hAPP(real,real,cos,X))) # label(fact_2095_tan__def) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.71 2122 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),one_one(real)),X)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(real,real,ln,X))))) # label(fact_2096_ln__ge__zero) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.71 2123 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),X)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,ln,X))))) # label(fact_2097_ln__gt__zero) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.71 2124 (all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,ln,X_1))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),X_1))))) # label(fact_2098_ln__gt__zero__iff) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.71 2125 (all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X_1)) -> (hAPP(real,real,ln,X_1) = zero_zero(real) <-> X_1 = one_one(real)))) # label(fact_2099_ln__eq__zero__iff) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.71 2126 (all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,ln,X_1)),zero_zero(real))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_1),one_one(real)))))) # label(fact_2100_ln__less__zero__iff) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.71 2127 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),one_one(real))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,ln,X)),zero_zero(real)))))) # label(fact_2101_ln__less__zero) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.71 2128 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,ln,X))) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),X))))) # label(fact_2102_ln__gt__zero__imp__gt__one) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.71 2129 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> hAPP(real,real,sgn_sgn(real),X) = one_one(real))) # label(fact_2103_real__sgn__pos) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.71 2130 (all X_a (linordered_idom(X_a) -> (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)) -> hAPP(X_a,X_a,sgn_sgn(X_a),A_1) = one_one(X_a))))) # label(fact_2104_sgn__pos) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.71 2131 (all X_a (linordered_idom(X_a) -> (all Aa (hAPP(X_a,X_a,sgn_sgn(X_a),Aa) = one_one(X_a) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),Aa)))))) # label(fact_2105_sgn__1__pos) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.71 2132 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,ln,X)),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),X),one_one(real)))))) # label(fact_2106_ln__le__minus__one) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.71 2133 (all N_1 hAPP(real,real,sin,hAPP(real,real,hAPP(real,fun(real,real),times_times(real),pi),hAPP(nat,real,real_1(nat),N_1))) = zero_zero(real)) # label(fact_2107_sin__npi2) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.71 2134 (all N_1 hAPP(real,real,sin,hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,real_1(nat),N_1)),pi)) = zero_zero(real)) # label(fact_2108_sin__npi) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.71 2135 (all X hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,cos,X)),hAPP(real,real,cos,X))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,sin,X)),hAPP(real,real,sin,X))) = one_one(real)) # label(fact_2109_sin__cos__squared__add3) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.71 2136 (all X (hAPP(real,real,sin,X) = zero_zero(real) -> hAPP(real,real,abs_abs(real),hAPP(real,real,cos,X)) = one_one(real))) # label(fact_2110_sin__zero__abs__cos__one) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.71 2137 (all X all Y hAPP(real,real,cos,hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),X),Y)) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,cos,Y)),hAPP(real,real,cos,X))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,sin,Y)),hAPP(real,real,sin,X)))) # label(fact_2111_cos__diff2) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.71 2138 (all X all Y hAPP(real,real,cos,hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),X),Y)) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,cos,X)),hAPP(real,real,cos,Y))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,sin,X)),hAPP(real,real,sin,Y)))) # label(fact_2112_cos__diff) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.71 2139 (all X all Y hAPP(real,real,cos,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),Y)) = hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,cos,X)),hAPP(real,real,cos,Y))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,sin,X)),hAPP(real,real,sin,Y)))) # label(fact_2113_cos__add) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.71 2140 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(real,real,ln,X))) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),one_one(real)),X))))) # label(fact_2114_ln__ge__zero__imp__ge__one) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.71 2141 (all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(real,real,ln,X_1))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),one_one(real)),X_1))))) # label(fact_2115_ln__ge__zero__iff) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.71 2142 (all Y all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Y)) -> hAPP(real,real,ln,hAPP(real,real,hAPP(real,fun(real,real),times_times(real),X),Y)) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,ln,X)),hAPP(real,real,ln,Y))))) # label(fact_2116_ln__mult) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.71 2143 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,ln,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),one_one(real)),X))),X)))) # label(fact_2117_ln__add__one__self__le__self) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.71 2144 (all Y all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Y)) -> hAPP(real,real,ln,hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),X),Y)) = hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,ln,X)),hAPP(real,real,ln,Y))))) # label(fact_2118_ln__div) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.71 2145 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,number_number_of(real),min)),X)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,ln,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),one_one(real)),X))),X)))) # label(fact_2119_ln__add__one__self__le__self2) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.71 2146 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),one_one(real))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,ln,hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),one_one(real)),X))),hAPP(real,real,uminus_uminus(real),X)))))) # label(fact_2120_ln__one__minus__pos__upper__bound) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.71 2147 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),one_one(real))) -> hAPP(real,real,ln,hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),one_one(real)),X)) = hAPP(real,real,uminus_uminus(real),hAPP(real,real,ln,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),one_one(real)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),X),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),one_one(real)),X))))))) # label(fact_2121_aux5) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.71 2148 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),zero_zero(real))) -> hAPP(real,real,sgn_sgn(real),X) = hAPP(int,real,number_number_of(real),min))) # label(fact_2122_real__sgn__neg) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.71 2149 (all A_1 ((A_1 = zero_zero(real) -> hAPP(real,real,sgn_sgn(real),A_1) = zero_zero(real)) & (A_1 != zero_zero(real) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A_1)) -> hAPP(real,real,sgn_sgn(real),A_1) = one_one(real)) & (-hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A_1)) -> hAPP(real,real,sgn_sgn(real),A_1) = hAPP(real,real,uminus_uminus(real),one_one(real)))))) # label(fact_2123_sgn__real__def) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.71 2150 (all X ((X = zero_zero(real) -> hAPP(real,real,sgn_sgn(real),X) = zero_zero(real)) & (X != zero_zero(real) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> hAPP(real,real,sgn_sgn(real),X) = one_one(real)) & (-hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> hAPP(real,real,sgn_sgn(real),X) = hAPP(real,real,uminus_uminus(real),one_one(real)))))) # label(fact_2124_real__sgn__def) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.71 2151 (all X_a (linordered_idom(X_a) -> (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))) -> hAPP(X_a,X_a,sgn_sgn(X_a),A_1) = hAPP(X_a,X_a,uminus_uminus(X_a),one_one(X_a)))))) # label(fact_2125_sgn__neg) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.71 2152 (all X_a (linordered_idom(X_a) -> (all Aa (hAPP(X_a,X_a,sgn_sgn(X_a),Aa) = hAPP(X_a,X_a,uminus_uminus(X_a),one_one(X_a)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),zero_zero(X_a))))))) # label(fact_2126_sgn__1__neg) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.71 2153 (all X_a (sgn_if(X_a) -> (all X ((ti(X_a,X) = zero_zero(X_a) -> hAPP(X_a,X_a,sgn_sgn(X_a),X) = zero_zero(X_a)) & (ti(X_a,X) != zero_zero(X_a) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),X)) -> hAPP(X_a,X_a,sgn_sgn(X_a),X) = one_one(X_a)) & (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),X)) -> hAPP(X_a,X_a,sgn_sgn(X_a),X) = hAPP(X_a,X_a,uminus_uminus(X_a),one_one(X_a)))))))) # label(fact_2127_sgn__if) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.71 2154 (all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,number_number_of(real),min)),Y)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),Y),one_one(real))) -> hAPP(real,real,sin,hAPP(real,real,arcsin,Y)) = Y))) # label(fact_2128_sin__arcsin) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.71 2155 (all N_1 all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> hAPP(real,real,ln,hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),N_1)) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,real_1(nat),N_1)),hAPP(real,real,ln,X)))) # label(fact_2129_ln__realpow) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.71 2156 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,sin,X)))))) # label(fact_2130_sin__gt__zero) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.71 2157 (all X hAPP(real,real,sin,hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),X)) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),hAPP(real,real,sin,X))),hAPP(real,real,cos,X))) # label(fact_2131_sin__double) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.71 2158 (all Y all X (hAPP(real,real,cos,X) != zero_zero(real) -> (hAPP(real,real,cos,Y) != zero_zero(real) -> hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,tan,X)),hAPP(real,real,tan,Y)) = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,sin,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),Y))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,cos,X)),hAPP(real,real,cos,Y)))))) # label(fact_2132_add__tan__eq) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.71 2159 (all X hAPP(real,real,sin,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),pi))) = hAPP(real,real,sin,X)) # label(fact_2134_sin__periodic) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.72 2160 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,sin,X)))))) # label(fact_2137_sin__gt__zero2) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.72 2161 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X),one_one(real))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),X),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),hAPP(real,real,ln,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),one_one(real)),X))))))) # label(fact_2138_ln__one__plus__pos__lower__bound) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.72 2162 (all R_4 all A_1 hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),R_4),hAPP(real,real,cos,A_1))),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),R_4),hAPP(real,real,sin,A_1))),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),R_4),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) # label(fact_2139_sin__cos__squared__add2__mult) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.72 2163 (all N_1 hAPP(real,real,sin,hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),hAPP(nat,real,real_1(nat),N_1))),pi)) = zero_zero(real)) # label(fact_2140_sin__2npi) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.72 2164 (all X hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,sin,X)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,cos,X)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) = one_one(real)) # label(fact_2141_sin__cos__squared__add) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.72 2165 (all X hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,cos,X)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,sin,X)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) = one_one(real)) # label(fact_2142_sin__cos__squared__add2) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.72 2166 (all X hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,sin,X)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),one_one(real)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,cos,X)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) # label(fact_2143_sin__squared__eq) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.72 2167 (all X hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,cos,X)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),one_one(real)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,sin,X)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) # label(fact_2144_cos__squared__eq) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.72 2168 (all X all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),Y)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),Y),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,sin,Y)),hAPP(real,real,sin,X))))))) # label(fact_2145_sin__monotone__2pi_H) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.72 2169 (all X hAPP(real,real,cos,X) = hAPP(real,real,sin,hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),X))) # label(fact_2146_cos__sin__eq) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.72 2170 (all X hAPP(real,real,sin,X) = hAPP(real,real,cos,hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),X))) # label(fact_2147_sin__cos__eq) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.72 2171 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X),one_one(real))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,ln,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),one_one(real)),X))),X))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))))) # label(fact_2148_abs__ln__one__plus__x__minus__x__bound__nonneg) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.72 2172 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,uminus_uminus(real),pi)),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),zero_zero(real))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,sin,X)),zero_zero(real)))))) # label(fact_2149_sin__less__zero) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.72 2173 (all X hAPP(real,real,cos,hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),X)) = hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,cos,X)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,sin,X)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) # label(fact_2150_cos__double) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.72 2174 (all X hAPP(real,real,uminus_uminus(real),hAPP(real,real,sin,X)) = hAPP(real,real,cos,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))) # label(fact_2152_minus__sin__cos__eq) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.72 2175 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) -> hAPP(real,real,arcsin,hAPP(real,real,sin,X)) = X))) # label(fact_2153_arcsin__sin) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.72 2176 (all X all Y hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,sin,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),Y))),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,sin,X)),hAPP(real,real,cos,Y))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,cos,X)),hAPP(real,real,sin,Y))))),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,cos,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),Y))),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,cos,X)),hAPP(real,real,cos,Y))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,sin,X)),hAPP(real,real,sin,Y))))),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) = zero_zero(real)) # label(fact_2154_sin__cos__add) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.72 2177 (all X hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,sin,hAPP(real,real,uminus_uminus(real),X))),hAPP(real,real,sin,X))),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,cos,hAPP(real,real,uminus_uminus(real),X))),hAPP(real,real,cos,X))),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) = zero_zero(real)) # label(fact_2155_sin__cos__minus) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.72 2178 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),one_one(real)),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,uminus_uminus(real),X)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))),hAPP(real,real,ln,hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),one_one(real)),X))))))) # label(fact_2156_ln__one__minus__pos__lower__bound) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.72 2179 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),X)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),one_one(real)),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,ln,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),one_one(real)),X))),X))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))))) # label(fact_2157_abs__ln__one__plus__x__minus__x__bound) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.72 2180 (all X all M_1 hAPP(real,real,sin,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,real_1(nat),hAPP(nat,nat,suc,M_1))),pi)),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) = hAPP(real,real,cos,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,real_1(nat),M_1)),pi)),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))) # label(fact_2158_sin__expansion__lemma) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.72 2181 (all X_1 (hAPP(real,real,sin,X_1) = zero_zero(real) <-> (exists N_2 (hBOOL(hAPP(nat,bool,even_odd_even(nat),N_2)) & X_1 = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,real_1(nat),N_2)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))) | (exists N_2 (hBOOL(hAPP(nat,bool,even_odd_even(nat),N_2)) & X_1 = hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,real_1(nat),N_2)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))))) # label(fact_2159_sin__zero__iff) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.72 2182 (all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,number_number_of(real),min)),Y)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),Y),one_one(real))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),hAPP(real,real,arcsin,Y))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,arcsin,Y)),pi)) & hAPP(real,real,sin,hAPP(real,real,arcsin,Y)) = Y))) # label(fact_2160_arcsin__pi) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.72 2183 (all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,number_number_of(real),min)),Y)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),Y),one_one(real))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),hAPP(real,real,arcsin,Y))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,arcsin,Y)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) & hAPP(real,real,sin,hAPP(real,real,arcsin,Y)) = Y))) # label(fact_2161_arcsin) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.72 2184 (all X all M_1 hAPP(real,real,cos,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,real_1(nat),hAPP(nat,nat,suc,M_1))),pi)),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) = hAPP(real,real,uminus_uminus(real),hAPP(real,real,sin,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,real_1(nat),M_1)),pi)),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))) # label(fact_2162_cos__expansion__lemma) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.72 2185 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X)) -> (hAPP(real,real,sin,X) = zero_zero(real) -> (exists N_2 (hBOOL(hAPP(nat,bool,even_odd_even(nat),N_2)) & X = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,real_1(nat),N_2)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))))) # label(fact_2163_sin__zero__lemma) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.72 2186 (all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,number_number_of(real),min)),Y)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),Y),one_one(real))) -> (exists X_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),X_2)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_2),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) & hAPP(real,real,sin,X_2) = Y & (all Y_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),Y_2)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),Y_2),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) & hAPP(real,real,sin,Y_2) = Y -> Y_2 = X_2))))))) # label(fact_2164_sin__total) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.72 2187 (all N_1 all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X),one_one(real))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,inverse_inverse(real),hAPP(nat,real,real_1(nat),hAPP(nat,nat,fact_fact(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),one_one(real)),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),N_1))))))) # label(fact_2165_Ln_Oaux1) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.72 2188 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,number_number_of(real),min)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X),one_one(real))) -> hAPP(real,real,cos,hAPP(real,real,arcsin,X)) = hAPP(real,real,sqrt,hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),one_one(real)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))))) # label(fact_2166_cos__arcsin) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.72 2189 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,number_number_of(real),min)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X),one_one(real))) -> hAPP(real,real,sin,hAPP(real,real,arccos,X)) = hAPP(real,real,sqrt,hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),one_one(real)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))))) # label(fact_2167_sin__arccos) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.72 2190 (all X_a (linord1117847801e_zero(X_a) -> (all A_1 hAPP(X_a,X_a,abs_abs(X_a),hAPP(X_a,X_a,inverse_inverse(X_a),A_1)) = hAPP(X_a,X_a,inverse_inverse(X_a),hAPP(X_a,X_a,abs_abs(X_a),A_1))))) # label(fact_2168_abs__inverse) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.72 2191 (all X hAPP(real,real,sqrt,hAPP(real,real,uminus_uminus(real),X)) = hAPP(real,real,uminus_uminus(real),hAPP(real,real,sqrt,X))) # label(fact_2170_real__sqrt__minus) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.72 2192 (all X_a (division_ring(X_a) -> (all A_1 all B (hAPP(X_a,X_a,inverse_inverse(X_a),A_1) = hAPP(X_a,X_a,inverse_inverse(X_a),B) -> (ti(X_a,A_1) != zero_zero(X_a) -> (ti(X_a,B) != zero_zero(X_a) -> ti(X_a,A_1) = ti(X_a,B))))))) # label(fact_2171_nonzero__inverse__eq__imp__eq) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.72 2193 (all X_a (division_ring(X_a) -> (all A_1 (hAPP(X_a,X_a,inverse_inverse(X_a),A_1) = zero_zero(X_a) -> ti(X_a,A_1) = zero_zero(X_a))))) # label(fact_2172_inverse__zero__imp__zero) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.72 2194 (all X_a (division_ring(X_a) -> (all A_1 (ti(X_a,A_1) != zero_zero(X_a) -> hAPP(X_a,X_a,inverse_inverse(X_a),hAPP(X_a,X_a,inverse_inverse(X_a),A_1)) = ti(X_a,A_1))))) # label(fact_2173_nonzero__inverse__inverse__eq) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.72 2195 (all X_a (division_ring(X_a) -> (all A_1 (ti(X_a,A_1) != zero_zero(X_a) -> hAPP(X_a,X_a,inverse_inverse(X_a),A_1) != zero_zero(X_a))))) # label(fact_2174_nonzero__imp__inverse__nonzero) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.72 2196 (all X_a (divisi14063676e_zero(X_a) -> (all Aa (hAPP(X_a,X_a,inverse_inverse(X_a),Aa) = zero_zero(X_a) <-> ti(X_a,Aa) = zero_zero(X_a))))) # label(fact_2175_inverse__nonzero__iff__nonzero) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.72 2197 (all X_a (divisi14063676e_zero(X_a) -> hAPP(X_a,X_a,inverse_inverse(X_a),zero_zero(X_a)) = zero_zero(X_a))) # label(fact_2176_inverse__zero) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.72 2198 (all X_a (field_inverse_zero(X_a) -> hAPP(X_a,X_a,inverse_inverse(X_a),zero_zero(X_a)) = zero_zero(X_a))) # label(fact_2177_field__inverse__zero) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.72 2199 (all X_a (field_inverse_zero(X_a) -> (all A_1 all B hAPP(X_a,X_a,inverse_inverse(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,inverse_inverse(X_a),A_1)),hAPP(X_a,X_a,inverse_inverse(X_a),B))))) # label(fact_2178_inverse__mult__distrib) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.72 2200 (all X_1 all Y_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,sqrt,X_1)),hAPP(real,real,sqrt,Y_1))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_1),Y_1)))) # label(fact_2179_real__sqrt__le__iff) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.72 2201 (all X all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X),Y)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,sqrt,X)),hAPP(real,real,sqrt,Y))))) # label(fact_2180_real__sqrt__le__mono) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.72 2202 (all X_1 (hAPP(real,real,sqrt,X_1) = zero_zero(real) <-> X_1 = zero_zero(real))) # label(fact_2181_real__sqrt__eq__0__iff) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.72 2203 (all X_a (divisi14063676e_zero(X_a) -> (all A_1 hAPP(X_a,X_a,inverse_inverse(X_a),hAPP(X_a,X_a,inverse_inverse(X_a),A_1)) = ti(X_a,A_1)))) # label(fact_2183_inverse__inverse__eq) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.72 2204 (all X_a (divisi14063676e_zero(X_a) -> (all Aa all Ba (hAPP(X_a,X_a,inverse_inverse(X_a),Aa) = hAPP(X_a,X_a,inverse_inverse(X_a),Ba) <-> ti(X_a,Aa) = ti(X_a,Ba))))) # label(fact_2184_inverse__eq__iff__eq) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.72 2205 (all X_a (divisi14063676e_zero(X_a) -> (all A_1 all B (hAPP(X_a,X_a,inverse_inverse(X_a),A_1) = hAPP(X_a,X_a,inverse_inverse(X_a),B) -> ti(X_a,A_1) = ti(X_a,B))))) # label(fact_2185_inverse__eq__imp__eq) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.72 2206 (all X hAPP(real,real,sqrt,hAPP(real,real,inverse_inverse(real),X)) = hAPP(real,real,inverse_inverse(real),hAPP(real,real,sqrt,X))) # label(fact_2186_real__sqrt__inverse) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.72 2207 (all X_1 all Y_1 (hAPP(real,real,sqrt,X_1) = hAPP(real,real,sqrt,Y_1) <-> X_1 = Y_1)) # label(fact_2187_real__sqrt__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.72 2208 (all X_a (field_inverse_zero(X_a) -> (all A_1 all B hAPP(X_a,X_a,inverse_inverse(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),A_1),B)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),B),A_1)))) # label(fact_2188_inverse__divide) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.72 2209 (all X all Y hAPP(real,real,sqrt,hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),X),Y)) = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,sqrt,X)),hAPP(real,real,sqrt,Y))) # label(fact_2189_real__sqrt__divide) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.72 2210 (all X_1 (hAPP(real,real,sqrt,X_1) = one_one(real) <-> X_1 = one_one(real))) # label(fact_2191_real__sqrt__eq__1__iff) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.72 2211 (all X all K_4 hAPP(real,real,sqrt,hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),K_4)) = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,sqrt,X)),K_4)) # label(fact_2192_real__sqrt__power) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.72 2212 (all X_a (divisi14063676e_zero(X_a) -> (all A_1 hAPP(X_a,X_a,inverse_inverse(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),A_1)) = hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(X_a,X_a,inverse_inverse(X_a),A_1))))) # label(fact_2193_inverse__minus__eq) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.72 2213 (all X_a (divisi14063676e_zero(X_a) -> (all A_1 all N_1 hAPP(X_a,X_a,inverse_inverse(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),hAPP(X_a,X_a,inverse_inverse(X_a),A_1)),N_1)))) # label(fact_2194_power__inverse) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.72 2214 (all X all Y hAPP(real,real,sqrt,hAPP(real,real,hAPP(real,fun(real,real),times_times(real),X),Y)) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,sqrt,X)),hAPP(real,real,sqrt,Y))) # label(fact_2195_real__sqrt__mult) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.72 2215 (all X_a (division_ring(X_a) -> hAPP(X_a,X_a,inverse_inverse(X_a),one_one(X_a)) = one_one(X_a))) # label(fact_2196_inverse__1) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.72 2216 (all X_a (field_inverse_zero(X_a) -> (all X_1 (hAPP(X_a,X_a,inverse_inverse(X_a),X_1) = one_one(X_a) <-> ti(X_a,X_1) = one_one(X_a))))) # label(fact_2197_inverse__eq__1__iff) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.72 2217 (all X all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),Y)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,sqrt,X)),hAPP(real,real,sqrt,Y))))) # label(fact_2198_real__sqrt__less__mono) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.72 2218 (all X_1 all Y_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,sqrt,X_1)),hAPP(real,real,sqrt,Y_1))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_1),Y_1)))) # label(fact_2199_real__sqrt__less__iff) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.72 2219 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X)) -> hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,sqrt,X)),X) = hAPP(real,real,inverse_inverse(real),hAPP(real,real,sqrt,X)))) # label(fact_2200_sqrt__divide__self__eq) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.72 2220 (all X_a (linord1117847801e_zero(X_a) -> (all Aa (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),hAPP(X_a,X_a,inverse_inverse(X_a),Aa))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),Aa)))))) # label(fact_2201_inverse__nonnegative__iff__nonnegative) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.72 2221 (all X_a (linord1117847801e_zero(X_a) -> (all Aa (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,inverse_inverse(X_a),Aa)),zero_zero(X_a))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Aa),zero_zero(X_a))))))) # label(fact_2202_inverse__nonpositive__iff__nonpositive) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.72 2222 (all X_a (linordered_field(X_a) -> (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,inverse_inverse(X_a),A_1)),hAPP(X_a,X_a,inverse_inverse(X_a),B))) -> (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),B),A_1))))))) # label(fact_2203_inverse__less__imp__less__neg) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.72 2223 (all X_a (linordered_field(X_a) -> (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,inverse_inverse(X_a),A_1)),hAPP(X_a,X_a,inverse_inverse(X_a),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),B),A_1))))))) # label(fact_2204_inverse__less__imp__less) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.72 2224 (all X_a (linordered_field(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,inverse_inverse(X_a),A_1)),zero_zero(X_a))) -> (ti(X_a,A_1) != zero_zero(X_a) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),zero_zero(X_a)))))))) # label(fact_2205_inverse__negative__imp__negative) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.72 2225 (all X_a (linordered_field(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),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,inverse_inverse(X_a),B)),hAPP(X_a,X_a,inverse_inverse(X_a),A_1)))))))) # label(fact_2206_less__imp__inverse__less__neg) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.72 2226 (all X_a (linordered_field(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),zero_zero(X_a)),A_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,inverse_inverse(X_a),B)),hAPP(X_a,X_a,inverse_inverse(X_a),A_1)))))))) # label(fact_2207_less__imp__inverse__less) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.72 2227 (all X_a (linordered_field(X_a) -> (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),hAPP(X_a,X_a,inverse_inverse(X_a),A_1)),zero_zero(X_a))))))) # label(fact_2208_negative__imp__inverse__negative) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.72 2228 (all X_a (linordered_field(X_a) -> (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,inverse_inverse(X_a),A_1))) -> (ti(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)),A_1))))))) # label(fact_2209_inverse__positive__imp__positive) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.72 2229 (all X_a (linordered_field(X_a) -> (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(X_a,X_a,inverse_inverse(X_a),A_1))))))) # label(fact_2210_positive__imp__inverse__positive) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.72 2230 (all X_a (linord1117847801e_zero(X_a) -> (all Aa (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,inverse_inverse(X_a),Aa)),zero_zero(X_a))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),zero_zero(X_a))))))) # label(fact_2211_inverse__negative__iff__negative) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.72 2231 (all X_a (linord1117847801e_zero(X_a) -> (all Aa (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,inverse_inverse(X_a),Aa))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),Aa)))))) # label(fact_2212_inverse__positive__iff__positive) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.72 2232 (all X_a (division_ring(X_a) -> (all B all A_1 (ti(X_a,A_1) != zero_zero(X_a) -> (ti(X_a,B) != zero_zero(X_a) -> hAPP(X_a,X_a,inverse_inverse(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,inverse_inverse(X_a),B)),hAPP(X_a,X_a,inverse_inverse(X_a),A_1))))))) # label(fact_2213_nonzero__inverse__mult__distrib) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.72 2233 (all X_a (division_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),A_1),B) = one_one(X_a) -> hAPP(X_a,X_a,inverse_inverse(X_a),A_1) = ti(X_a,B))))) # label(fact_2214_inverse__unique) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.72 2234 (all X_a (division_ring(X_a) -> (all N_1 all A_1 (ti(X_a,A_1) != zero_zero(X_a) -> hAPP(X_a,X_a,inverse_inverse(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),hAPP(X_a,X_a,inverse_inverse(X_a),A_1)),N_1))))) # label(fact_2215_nonzero__power__inverse) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.72 2235 (all Y_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(real,real,sqrt,Y_1))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),Y_1)))) # label(fact_2216_real__sqrt__ge__0__iff) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.72 2236 (all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,sqrt,X_1)),zero_zero(real))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_1),zero_zero(real))))) # label(fact_2217_real__sqrt__le__0__iff) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.72 2237 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(real,real,sqrt,X))))) # label(fact_2218_real__sqrt__ge__zero) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.72 2238 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X)) -> (hAPP(real,real,sqrt,X) = zero_zero(real) -> X = zero_zero(real)))) # label(fact_2219_real__sqrt__eq__zero__cancel) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.72 2239 (all Y_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,sqrt,Y_1))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Y_1)))) # label(fact_2220_real__sqrt__gt__0__iff) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.72 2240 (all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,sqrt,X_1)),zero_zero(real))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_1),zero_zero(real))))) # label(fact_2221_real__sqrt__lt__0__iff) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.72 2241 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> hAPP(real,real,sqrt,X) != zero_zero(real))) # label(fact_2222_real__sqrt__not__eq__zero) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.72 2242 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,sqrt,X))))) # label(fact_2223_real__sqrt__gt__zero) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.72 2243 (all X_a (division_ring(X_a) -> (all A_1 (ti(X_a,A_1) != zero_zero(X_a) -> hAPP(X_a,X_a,inverse_inverse(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),A_1)) = hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(X_a,X_a,inverse_inverse(X_a),A_1)))))) # label(fact_2224_nonzero__inverse__minus__eq) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.72 2244 (all X_a (division_ring(X_a) -> (all A_1 all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(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,inverse_inverse(X_a),B))))) # label(fact_2225_divide__inverse) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.72 2245 (all X_a (field(X_a) -> (all A_1 all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(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,inverse_inverse(X_a),B))))) # label(fact_2226_field__divide__inverse) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.72 2246 (all X_a (linordered_field(X_a) -> (all A_1 (ti(X_a,A_1) != zero_zero(X_a) -> hAPP(X_a,X_a,abs_abs(X_a),hAPP(X_a,X_a,inverse_inverse(X_a),A_1)) = hAPP(X_a,X_a,inverse_inverse(X_a),hAPP(X_a,X_a,abs_abs(X_a),A_1)))))) # label(fact_2227_nonzero__abs__inverse) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.72 2247 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),one_one(real)),X)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),one_one(real)),hAPP(real,real,sqrt,X))))) # label(fact_2228_real__sqrt__ge__one) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.72 2248 (all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,sqrt,X_1)),one_one(real))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_1),one_one(real))))) # label(fact_2229_real__sqrt__le__1__iff) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.72 2249 (all Y_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),one_one(real)),hAPP(real,real,sqrt,Y_1))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),one_one(real)),Y_1)))) # label(fact_2230_real__sqrt__ge__1__iff) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.72 2250 (all Y_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),hAPP(real,real,sqrt,Y_1))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),Y_1)))) # label(fact_2231_real__sqrt__gt__1__iff) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.72 2251 (all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,sqrt,X_1)),one_one(real))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_1),one_one(real))))) # label(fact_2232_real__sqrt__lt__1__iff) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.72 2252 (all X_a (field(X_a) -> (all A_1 hAPP(X_a,X_a,inverse_inverse(X_a),A_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),one_one(X_a)),A_1)))) # label(fact_2233_field__class_Onormalizing__field__rules_I2_J) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.72 2253 (all X_a (division_ring(X_a) -> (all A_1 hAPP(X_a,X_a,inverse_inverse(X_a),A_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),one_one(X_a)),A_1)))) # label(fact_2234_inverse__eq__divide) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.72 2254 (all X hAPP(real,real,sqrt,hAPP(real,real,hAPP(real,fun(real,real),times_times(real),X),X)) = hAPP(real,real,abs_abs(real),X)) # label(fact_2235_real__sqrt__abs2) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.72 2255 (all R all S_6 hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),R),S_6) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),R),hAPP(real,real,inverse_inverse(real),S_6))) # label(fact_2236_real__divide__def) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.72 2256 (all X all Y hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),X),Y) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),X),hAPP(real,real,inverse_inverse(real),Y))) # label(fact_2237_divide__real__def) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.72 2257 (all X_a (linordered_field(X_a) -> (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,inverse_inverse(X_a),A_1)),hAPP(X_a,X_a,inverse_inverse(X_a),B))) -> (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_eq(X_a),B),A_1))))))) # label(fact_2238_inverse__le__imp__le__neg) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.72 2258 (all X_a (linordered_field(X_a) -> (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,inverse_inverse(X_a),A_1)),hAPP(X_a,X_a,inverse_inverse(X_a),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_eq(X_a),B),A_1))))))) # label(fact_2239_inverse__le__imp__le) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.72 2259 (all X_a (linordered_field(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(X_a),B),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,inverse_inverse(X_a),B)),hAPP(X_a,X_a,inverse_inverse(X_a),A_1)))))))) # label(fact_2240_le__imp__inverse__le__neg) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.72 2260 (all X_a (linordered_field(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(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),hAPP(X_a,X_a,inverse_inverse(X_a),B)),hAPP(X_a,X_a,inverse_inverse(X_a),A_1)))))))) # label(fact_2241_le__imp__inverse__le) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.72 2261 (all X_a (linord1117847801e_zero(X_a) -> (all X_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,inverse_inverse(X_a),X_1)),one_one(X_a))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),zero_zero(X_a))) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),one_one(X_a)),X_1)))))) # label(fact_2242_inverse__le__1__iff) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.72 2262 (all X_a (linordered_field(X_a) -> (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),A_1),one_one(X_a))) -> 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,inverse_inverse(X_a),A_1)))))))) # label(fact_2243_one__less__inverse) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.72 2263 (all X_a (linord1117847801e_zero(X_a) -> (all X_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,inverse_inverse(X_a),X_1))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),X_1)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),one_one(X_a))))))) # label(fact_2244_one__less__inverse__iff) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.72 2264 (all X_a (division_ring(X_a) -> (all B all A_1 (ti(X_a,A_1) != zero_zero(X_a) -> (ti(X_a,B) != zero_zero(X_a) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,inverse_inverse(X_a),A_1)),hAPP(X_a,X_a,inverse_inverse(X_a),B)) = 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),hAPP(X_a,X_a,inverse_inverse(X_a),A_1)),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,inverse_inverse(X_a),B))))))) # label(fact_2245_division__ring__inverse__add) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.72 2265 (all X_a (field(X_a) -> (all B all A_1 (ti(X_a,A_1) != zero_zero(X_a) -> (ti(X_a,B) != zero_zero(X_a) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,inverse_inverse(X_a),A_1)),hAPP(X_a,X_a,inverse_inverse(X_a),B)) = 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),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,inverse_inverse(X_a),A_1))),hAPP(X_a,X_a,inverse_inverse(X_a),B))))))) # label(fact_2246_inverse__add) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.72 2266 (all X_a (division_ring(X_a) -> (all A_1 (ti(X_a,A_1) != zero_zero(X_a) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),hAPP(X_a,X_a,inverse_inverse(X_a),A_1)) = one_one(X_a))))) # label(fact_2247_right__inverse) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.72 2267 (all X_a (field(X_a) -> (all A_1 (ti(X_a,A_1) != zero_zero(X_a) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,inverse_inverse(X_a),A_1)),A_1) = one_one(X_a))))) # label(fact_2248_field__inverse) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.72 2268 (all X_a (division_ring(X_a) -> (all A_1 (ti(X_a,A_1) != zero_zero(X_a) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,inverse_inverse(X_a),A_1)),A_1) = one_one(X_a))))) # label(fact_2249_left__inverse) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.72 2269 (all X_a (division_ring(X_a) -> (all B all A_1 (ti(X_a,A_1) != zero_zero(X_a) -> (ti(X_a,B) != zero_zero(X_a) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_a,X_a,inverse_inverse(X_a),A_1)),hAPP(X_a,X_a,inverse_inverse(X_a),B)) = 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),hAPP(X_a,X_a,inverse_inverse(X_a),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),B),A_1))),hAPP(X_a,X_a,inverse_inverse(X_a),B))))))) # label(fact_2250_division__ring__inverse__diff) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.72 2270 (all X_a (division_ring(X_a) -> (all A_1 (ti(X_a,A_1) != zero_zero(X_a) -> hAPP(X_a,X_a,inverse_inverse(X_a),A_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),one_one(X_a)),A_1))))) # label(fact_2251_nonzero__inverse__eq__divide) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.72 2271 (all X_a (field(X_a) & number_ring(X_a) -> hAPP(X_a,X_a,inverse_inverse(X_a),hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,bit1,pls))) = hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,bit1,pls)))) # label(fact_2252_inverse__numeral__1) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.72 2272 (all X_b (division_ring(X_b) & number(X_b) -> (all W hAPP(X_b,X_b,inverse_inverse(X_b),hAPP(int,X_b,number_number_of(X_b),W)) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),inverse_divide(X_b),one_one(X_b)),hAPP(int,X_b,number_number_of(X_b),W))))) # label(fact_2253_inverse__eq__divide__number__of) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.72 2273 (all X all Y hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X),hAPP(real,real,sqrt,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),X),X)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),Y),Y)))))) # label(fact_2254_le__real__sqrt__sumsq) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.72 2274 (all Y all U all X1_1 all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X1_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),X1_1),Y)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),X),U))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),Y),hAPP(real,real,inverse_inverse(real),X))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),U),hAPP(real,real,inverse_inverse(real),X1_1)))))))) # label(fact_2255_real__mult__inverse__cancel2) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.72 2275 (all Y all U all X1_1 all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X1_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),X1_1),Y)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),X),U))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,inverse_inverse(real),X)),Y)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,inverse_inverse(real),X1_1)),U))))))) # label(fact_2256_real__mult__inverse__cancel) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.72 2276 (all X (X != zero_zero(real) -> hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,inverse_inverse(real),X)),X) = one_one(real))) # label(fact_2257_real__mult__inverse__left) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.72 2277 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,inverse_inverse(real),hAPP(real,real,sqrt,X))),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(real,real,inverse_inverse(real),X))) # label(fact_2258_real__inv__sqrt__pow2) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.72 2278 (all X_a (linord1117847801e_zero(X_a) -> (all Aa all Ba (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,inverse_inverse(X_a),Aa)),hAPP(X_a,X_a,inverse_inverse(X_a),Ba))) <-> (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),Aa),Ba))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Ba),Aa))) & (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Aa),Ba)),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),Ba))))))) # label(fact_2259_inverse__less__iff) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.72 2279 (all X_a (linord1117847801e_zero(X_a) -> (all Aa all Ba (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,inverse_inverse(X_a),Aa)),hAPP(X_a,X_a,inverse_inverse(X_a),Ba))) <-> (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),Aa),Ba))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Ba),Aa))) & (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Aa),Ba)),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Aa),Ba))))))) # label(fact_2260_inverse__le__iff) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.72 2280 (all X_a (linordered_field(X_a) -> (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),A_1),one_one(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),one_one(X_a)),hAPP(X_a,X_a,inverse_inverse(X_a),A_1)))))))) # label(fact_2261_one__le__inverse) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.72 2281 (all X_a (linord1117847801e_zero(X_a) -> (all X_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,inverse_inverse(X_a),X_1)),one_one(X_a))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),zero_zero(X_a))) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),X_1)))))) # label(fact_2262_inverse__less__1__iff) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.72 2282 (all X_a (linord1117847801e_zero(X_a) -> (all X_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),one_one(X_a)),hAPP(X_a,X_a,inverse_inverse(X_a),X_1))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),X_1)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),one_one(X_a))))))) # label(fact_2263_one__le__inverse__iff) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.72 2283 (all X_a (division_ring(X_a) -> (all B all A_1 (ti(X_a,A_1) != zero_zero(X_a) -> (ti(X_a,B) != zero_zero(X_a) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_a,X_a,inverse_inverse(X_a),A_1)),hAPP(X_a,X_a,inverse_inverse(X_a),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),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,inverse_inverse(X_a),A_1)),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,inverse_inverse(X_a),B)))))))) # label(fact_2264_inverse__diff__inverse) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.72 2284 (all X all Y hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(real,real,sqrt,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),X),X)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),Y),Y)))))) # label(fact_2265_real__sqrt__mult__self__sum__ge__zero) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.72 2285 (all N_1 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(real,real,inverse_inverse(real),hAPP(nat,real,real_1(nat),hAPP(nat,nat,fact_fact(nat),N_1)))))) # label(fact_2266_inv__real__of__nat__fact__ge__zero) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.72 2286 (all N_1 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,inverse_inverse(real),hAPP(nat,real,real_1(nat),hAPP(nat,nat,fact_fact(nat),N_1)))))) # label(fact_2267_inv__real__of__nat__fact__gt__zero) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.72 2287 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> hAPP(real,real,ln,hAPP(real,real,inverse_inverse(real),X)) = hAPP(real,real,uminus_uminus(real),hAPP(real,real,ln,X)))) # label(fact_2268_ln__inverse) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.72 2288 (all X_a (real_normed_field(X_a) -> (all H_2 all B all A_1 (ti(X_a,A_1) != zero_zero(X_a) -> (ti(X_a,B) != zero_zero(X_a) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_a,X_a,inverse_inverse(X_a),A_1)),hAPP(X_a,X_a,inverse_inverse(X_a),B))),H_2) = 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),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,inverse_inverse(X_a),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_1),B)),H_2))),hAPP(X_a,X_a,inverse_inverse(X_a),B)))))))) # label(fact_2269_DERIV__inverse__lemma) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.72 2289 (all I_1 ((I_1 = zero_zero(int) -> hAPP(int,int,sgn_sgn(int),I_1) = zero_zero(int)) & (I_1 != zero_zero(int) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),I_1)) -> hAPP(int,int,sgn_sgn(int),I_1) = one_one(int)) & (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),I_1)) -> hAPP(int,int,sgn_sgn(int),I_1) = hAPP(int,int,uminus_uminus(int),one_one(int)))))) # label(fact_2270_zsgn__def) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.72 2290 (all X hAPP(real,real,sqrt,hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) = hAPP(real,real,abs_abs(real),X)) # label(fact_2274_real__sqrt__abs) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.72 2291 (all X_1 (hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,sqrt,X_1)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = X_1 <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X_1)))) # label(fact_2276_real__sqrt__pow2__iff) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.72 2292 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X)) -> hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,sqrt,X)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = X)) # label(fact_2277_real__sqrt__pow2) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.72 2293 (all Y all X (hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),Y),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = X -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),Y)) -> hAPP(real,real,sqrt,X) = Y))) # label(fact_2278_real__sqrt__unique) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.72 2294 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,sqrt,X)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))) # label(fact_2279_real__sqrt__pow2__gt__zero) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.72 2295 (all U (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),U)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),U),hAPP(real,real,sqrt,hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),U)))) # label(fact_2280_lemma__real__divide__sqrt__less) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.72 2296 (all A_1 all C all B all D hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,sqrt,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A_1),C)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),B),D)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,sqrt,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))),hAPP(real,real,sqrt,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),C),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),D),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))))) # label(fact_2281_real__sqrt__sum__squares__triangle__ineq) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.72 2297 (all Y all X hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),Y),hAPP(real,real,sqrt,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),Y),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))))) # label(fact_2282_real__sqrt__sum__squares__ge2) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.72 2298 (all X all Y hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X),hAPP(real,real,sqrt,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),Y),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))))) # label(fact_2283_real__sqrt__sum__squares__ge1) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.72 2299 (all X all Y (hAPP(real,real,sqrt,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),Y),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) = X -> Y = zero_zero(real))) # label(fact_2284_real__sqrt__sum__squares__eq__cancel) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.72 2300 (all X all Y (hAPP(real,real,sqrt,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),Y),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) = Y -> X = zero_zero(real))) # label(fact_2285_real__sqrt__sum__squares__eq__cancel2) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.72 2301 (all X all Y all Xa_1 all Ya hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,sqrt,hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),Y),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),Xa_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),Ya),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),Y),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),Xa_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),Ya),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))) # label(fact_2286_real__sqrt__sum__squares__mult__squared__eq) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.72 2302 (all X all Y hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(real,real,sqrt,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),Y),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))))) # label(fact_2291_real__sqrt__sum__squares__ge__zero) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.72 2303 (all Y all X hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),Y)),hAPP(real,real,sqrt,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),Y),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))))) # label(fact_2292_real__sqrt__ge__abs2) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.72 2304 (all X all Y hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),X)),hAPP(real,real,sqrt,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),Y),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))))) # label(fact_2293_real__sqrt__ge__abs1) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.72 2305 (all X all Y all Xa_1 all Ya hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(real,real,sqrt,hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),Y),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),Xa_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),Ya),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))))) # label(fact_2295_real__sqrt__sum__squares__mult__ge__zero) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.72 2306 (all X_5 all Y_4 hAPP(real,real,cos,hAPP(real,real,arccos,hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),X_5),hAPP(real,real,sqrt,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X_5),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),Y_4),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))))) = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),X_5),hAPP(real,real,sqrt,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X_5),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),Y_4),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))) # label(fact_2296_cos__arccos__lemma1) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.72 2307 (all X all Y hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),X),hAPP(real,real,sqrt,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),Y),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))))),one_one(real)))) # label(fact_2297_cos__x__y__le__one) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.72 2308 (all Y all X all U (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,abs_abs(real),X)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),U),hAPP(real,real,sqrt,hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,abs_abs(real),Y)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),U),hAPP(real,real,sqrt,hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,sqrt,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),Y),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))),U))))) # label(fact_2298_real__sqrt__sum__squares__less) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.72 2309 (all X (hAPP(real,real,cos,X) != zero_zero(real) -> hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),one_one(real)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,tan,X)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,inverse_inverse(real),hAPP(real,real,cos,X))),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) # label(fact_2299_tan__sec) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.72 2310 (all Y all X all U (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),U)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),U),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),Y),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),U),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),Y)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,sqrt,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),Y),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))),U)))))))) # label(fact_2300_lemma__sqrt__hcomplex__capprox) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.72 2311 (all X hAPP(real,real,arctan,X) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),hAPP(real,real,arctan,hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),X),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),one_one(real)),hAPP(real,real,sqrt,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),one_one(real)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))))))) # label(fact_2301_arctan__half) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.72 2312 (all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),Y)),one_one(real))) -> hAPP(real,real,sin,hAPP(real,real,arccos,Y)) = hAPP(real,real,sqrt,hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),one_one(real)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),Y),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))) # label(fact_2302_sin__arccos__abs) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.72 2313 (all X_5 all Y_4 hAPP(real,real,sin,hAPP(real,real,arccos,hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),X_5),hAPP(real,real,sqrt,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X_5),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),Y_4),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))))) = hAPP(real,real,sqrt,hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),one_one(real)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),X_5),hAPP(real,real,sqrt,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X_5),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),Y_4),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))) # label(fact_2303_sin__arccos__lemma1) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.72 2314 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> (exists N_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,inverse_inverse(real),hAPP(nat,real,real_1(nat),hAPP(nat,nat,suc,N_2)))),X))))) # label(fact_2304_reals__Archimedean) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.72 2315 (all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,number_number_of(real),min)),X_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_1),one_one(real))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),arccos),X_1),hAPP(real,real,inverse_inverse(real),hAPP(real,real,uminus_uminus(real),hAPP(real,real,sqrt,hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),one_one(real)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))))))))) # label(fact_2305_DERIV__arccos) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.72 2316 (all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,number_number_of(real),min)),X_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_1),one_one(real))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),arcsin),X_1),hAPP(real,real,inverse_inverse(real),hAPP(real,real,sqrt,hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),one_one(real)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))))))) # label(fact_2306_DERIV__arcsin) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.72 2317 (all P_1 all N all Aa all Ba (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),Aa),Ba)) -> hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(product_prod(real,real),real,product_snd(real,real),hAPP(nat,product_prod(real,real),hAPP(real,fun(nat,product_prod(real,real)),hAPP(real,fun(real,fun(nat,product_prod(real,real))),hAPP(fun(product_prod(real,real),bool),fun(real,fun(real,fun(nat,product_prod(real,real)))),bolzano_bisect,P_1),Aa),Ba),N))),hAPP(product_prod(real,real),real,product_fst(real,real),hAPP(nat,product_prod(real,real),hAPP(real,fun(nat,product_prod(real,real)),hAPP(real,fun(real,fun(nat,product_prod(real,real))),hAPP(fun(product_prod(real,real),bool),fun(real,fun(real,fun(nat,product_prod(real,real)))),bolzano_bisect,P_1),Aa),Ba),N))) = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),Ba),Aa)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),N)))) # label(fact_2307_Bolzano__bisect__diff) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.72 2318 (all X_a (real_normed_field(X_a) -> (all C_1 all X_1 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1)),X_1),C_1))))) # label(fact_2308_DERIV__cmult__Id) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.72 2319 (all X_a (real_normed_field(X_a) -> (all E_3 all F all X_1 all D_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),F),X_1),D_2)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),F),X_1),E_3)) -> ti(X_a,D_2) = ti(X_a,E_3)))))) # label(fact_2309_DERIV__unique) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.72 2320 (all X_a (real_normed_field(X_a) -> (all Y_3 all F all X_1 all X_3 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),F),X_1),X_3)) -> (ti(X_a,X_3) = ti(X_a,Y_3) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),F),X_1),Y_3))))))) # label(fact_2310_DERIV__cong) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.72 2321 (all X_a (real_normed_field(X_a) -> (all E_3 all F all X_1 all D_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),F),X_1),D_2)) -> (ti(X_a,D_2) = ti(X_a,E_3) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),F),X_1),E_3))))))) # label(fact_2311_Deriv_Olemma__DERIV__subst) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.72 2322 (all P_1 all Aa all Ba hAPP(nat,product_prod(real,real),hAPP(real,fun(nat,product_prod(real,real)),hAPP(real,fun(real,fun(nat,product_prod(real,real))),hAPP(fun(product_prod(real,real),bool),fun(real,fun(real,fun(nat,product_prod(real,real)))),bolzano_bisect,P_1),Aa),Ba),zero_zero(nat)) = hAPP(real,product_prod(real,real),hAPP(real,fun(real,product_prod(real,real)),product_Pair(real,real),Aa),Ba)) # label(fact_2312_Bolzano__bisect_Osimps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.72 2323 (all P_1 all Aa all Ba (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),Aa),Ba)) -> (all N_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(product_prod(real,real),real,product_fst(real,real),hAPP(nat,product_prod(real,real),hAPP(real,fun(nat,product_prod(real,real)),hAPP(real,fun(real,fun(nat,product_prod(real,real))),hAPP(fun(product_prod(real,real),bool),fun(real,fun(real,fun(nat,product_prod(real,real)))),bolzano_bisect,P_1),Aa),Ba),N_2))),hAPP(product_prod(real,real),real,product_snd(real,real),hAPP(nat,product_prod(real,real),hAPP(real,fun(nat,product_prod(real,real)),hAPP(real,fun(real,fun(nat,product_prod(real,real))),hAPP(fun(product_prod(real,real),bool),fun(real,fun(real,fun(nat,product_prod(real,real)))),bolzano_bisect,P_1),Aa),Ba),N_2))))))) # label(fact_2313_Bolzano__bisect__le) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.73 2324 (all X_1 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),sin),X_1),hAPP(real,real,cos,X_1)))) # label(fact_2314_DERIV__sin) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.73 2325 (all X_1 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),cos),X_1),hAPP(real,real,uminus_uminus(real),hAPP(real,real,sin,X_1))))) # label(fact_2315_DERIV__cos) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.73 2326 (all P_1 all Aa all Ba (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),Aa),Ba)) -> (all N_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(product_prod(real,real),real,product_fst(real,real),hAPP(nat,product_prod(real,real),hAPP(real,fun(nat,product_prod(real,real)),hAPP(real,fun(real,fun(nat,product_prod(real,real))),hAPP(fun(product_prod(real,real),bool),fun(real,fun(real,fun(nat,product_prod(real,real)))),bolzano_bisect,P_1),Aa),Ba),N_2))),hAPP(product_prod(real,real),real,product_fst(real,real),hAPP(nat,product_prod(real,real),hAPP(real,fun(nat,product_prod(real,real)),hAPP(real,fun(real,fun(nat,product_prod(real,real))),hAPP(fun(product_prod(real,real),bool),fun(real,fun(real,fun(nat,product_prod(real,real)))),bolzano_bisect,P_1),Aa),Ba),hAPP(nat,nat,suc,N_2)))))))) # label(fact_2316_Bolzano__bisect__fst__le__Suc) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.73 2327 (all P_1 all Aa all Ba (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),Aa),Ba)) -> (all N_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(product_prod(real,real),real,product_snd(real,real),hAPP(nat,product_prod(real,real),hAPP(real,fun(nat,product_prod(real,real)),hAPP(real,fun(real,fun(nat,product_prod(real,real))),hAPP(fun(product_prod(real,real),bool),fun(real,fun(real,fun(nat,product_prod(real,real)))),bolzano_bisect,P_1),Aa),Ba),hAPP(nat,nat,suc,N_2)))),hAPP(product_prod(real,real),real,product_snd(real,real),hAPP(nat,product_prod(real,real),hAPP(real,fun(nat,product_prod(real,real)),hAPP(real,fun(real,fun(nat,product_prod(real,real))),hAPP(fun(product_prod(real,real),bool),fun(real,fun(real,fun(nat,product_prod(real,real)))),bolzano_bisect,P_1),Aa),Ba),N_2))))))) # label(fact_2317_Bolzano__bisect__Suc__le__snd) # label(axiom) # label(non_clause). [assumption].
% 7.70/7.73 2328 (all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X_1)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),ln),X_1),hAPP(real,real,inverse_inverse(real),X_1))))) # label(fact_2318_DERIV__ln) # label(axiom) # label(non_clause). [assumption].
% 7.76/7.73 2329 (all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X_1)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),ln),X_1),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),one_one(real)),X_1))))) # label(fact_2319_DERIV__ln__divide) # label(axiom) # label(non_clause). [assumption].
% 7.76/7.73 2330 (all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X_1)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),sqrt),X_1),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,inverse_inverse(real),hAPP(real,real,sqrt,X_1))),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))) # label(fact_2320_DERIV__real__sqrt) # label(axiom) # label(non_clause). [assumption].
% 7.76/7.73 2331 (all X_1 (hAPP(real,real,cos,X_1) != zero_zero(real) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),tan),X_1),hAPP(real,real,inverse_inverse(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,cos,X_1)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))))) # label(fact_2321_DERIV__tan) # label(axiom) # label(non_clause). [assumption].
% 7.76/7.73 2332 (all X_1 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),arctan),X_1),hAPP(real,real,inverse_inverse(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),one_one(real)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))))) # label(fact_2322_DERIV__arctan) # label(axiom) # label(non_clause). [assumption].
% 7.76/7.73 2333 (all D_2 all X_1 (X_1 != zero_zero(real) -> ((hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X_1)) -> D_2 = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,inverse_inverse(real),hAPP(real,real,sqrt,X_1))),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) -> ((hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_1),zero_zero(real))) -> D_2 = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,uminus_uminus(real),hAPP(real,real,inverse_inverse(real),hAPP(real,real,sqrt,X_1)))),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),sqrt),X_1),D_2)))))) # label(fact_2323_DERIV__real__sqrt__generic) # label(axiom) # label(non_clause). [assumption].
% 7.76/7.73 2334 (all V_1 all K all Aa all Ba (Aa != Ba -> ((all X_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),V_1),X_2),K))) -> hAPP(real,real,V_1,hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),Aa),Ba)),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,V_1,Aa)),hAPP(real,real,V_1,Ba))),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))) # label(fact_2324_DERIV__const__average) # label(axiom) # label(non_clause). [assumption].
% 7.76/7.73 2335 (all D_1 all F all X_1 all L (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),F),X_1),L)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),D_1)) -> ((all Y_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),X_1),Y_2))),D_1)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,F,Y_2)),hAPP(real,real,F,X_1))))) -> L = zero_zero(real))))) # label(fact_2325_DERIV__local__max) # label(axiom) # label(non_clause). [assumption].
% 7.76/7.73 2336 (all D_1 all F all X_1 all L (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),F),X_1),L)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),D_1)) -> ((all Y_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),X_1),Y_2))),D_1)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,F,X_1)),hAPP(real,real,F,Y_2))))) -> L = zero_zero(real))))) # label(fact_2326_DERIV__local__min) # label(axiom) # label(non_clause). [assumption].
% 7.76/7.73 2337 (all D_1 all F all X_1 all L (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),F),X_1),L)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),D_1)) -> ((all Y_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),X_1),Y_2))),D_1)) -> hAPP(real,real,F,X_1) = hAPP(real,real,F,Y_2))) -> L = zero_zero(real))))) # label(fact_2327_DERIV__local__const) # label(axiom) # label(non_clause). [assumption].
% 7.76/7.73 2338 (all N all Aa all Ba all P_1 ((all A_3 all B_3 all C_4 (hBOOL(hAPP(product_prod(real,real),bool,P_1,hAPP(real,product_prod(real,real),hAPP(real,fun(real,product_prod(real,real)),product_Pair(real,real),A_3),B_3))) -> (hBOOL(hAPP(product_prod(real,real),bool,P_1,hAPP(real,product_prod(real,real),hAPP(real,fun(real,product_prod(real,real)),product_Pair(real,real),B_3),C_4))) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A_3),B_3)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B_3),C_4)) -> hBOOL(hAPP(product_prod(real,real),bool,P_1,hAPP(real,product_prod(real,real),hAPP(real,fun(real,product_prod(real,real)),product_Pair(real,real),A_3),C_4)))))))) -> (-hBOOL(hAPP(product_prod(real,real),bool,P_1,hAPP(real,product_prod(real,real),hAPP(real,fun(real,product_prod(real,real)),product_Pair(real,real),Aa),Ba))) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),Aa),Ba)) -> -hBOOL(hAPP(product_prod(real,real),bool,P_1,hAPP(real,product_prod(real,real),hAPP(real,fun(real,product_prod(real,real)),product_Pair(real,real),hAPP(product_prod(real,real),real,product_fst(real,real),hAPP(nat,product_prod(real,real),hAPP(real,fun(nat,product_prod(real,real)),hAPP(real,fun(real,fun(nat,product_prod(real,real))),hAPP(fun(product_prod(real,real),bool),fun(real,fun(real,fun(nat,product_prod(real,real)))),bolzano_bisect,P_1),Aa),Ba),N))),hAPP(product_prod(real,real),real,product_snd(real,real),hAPP(nat,product_prod(real,real),hAPP(real,fun(nat,product_prod(real,real)),hAPP(real,fun(real,fun(nat,product_prod(real,real))),hAPP(fun(product_prod(real,real),bool),fun(real,fun(real,fun(nat,product_prod(real,real)))),bolzano_bisect,P_1),Aa),Ba),N))))))))) # label(fact_2328_not__P__Bolzano__bisect) # label(axiom) # label(non_clause). [assumption].
% 7.76/7.73 2339 (all Aa all Ba all P_1 ((all A_3 all B_3 all C_4 (hBOOL(hAPP(product_prod(real,real),bool,P_1,hAPP(real,product_prod(real,real),hAPP(real,fun(real,product_prod(real,real)),product_Pair(real,real),A_3),B_3))) & hBOOL(hAPP(product_prod(real,real),bool,P_1,hAPP(real,product_prod(real,real),hAPP(real,fun(real,product_prod(real,real)),product_Pair(real,real),B_3),C_4))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A_3),B_3)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B_3),C_4)) -> hBOOL(hAPP(product_prod(real,real),bool,P_1,hAPP(real,product_prod(real,real),hAPP(real,fun(real,product_prod(real,real)),product_Pair(real,real),A_3),C_4))))) -> (-hBOOL(hAPP(product_prod(real,real),bool,P_1,hAPP(real,product_prod(real,real),hAPP(real,fun(real,product_prod(real,real)),product_Pair(real,real),Aa),Ba))) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),Aa),Ba)) -> (all N_2 -hBOOL(hAPP(product_prod(real,real),bool,P_1,hAPP(real,product_prod(real,real),hAPP(real,fun(real,product_prod(real,real)),product_Pair(real,real),hAPP(product_prod(real,real),real,product_fst(real,real),hAPP(nat,product_prod(real,real),hAPP(real,fun(nat,product_prod(real,real)),hAPP(real,fun(real,fun(nat,product_prod(real,real))),hAPP(fun(product_prod(real,real),bool),fun(real,fun(real,fun(nat,product_prod(real,real)))),bolzano_bisect,P_1),Aa),Ba),N_2))),hAPP(product_prod(real,real),real,product_snd(real,real),hAPP(nat,product_prod(real,real),hAPP(real,fun(nat,product_prod(real,real)),hAPP(real,fun(real,fun(nat,product_prod(real,real))),hAPP(fun(product_prod(real,real),bool),fun(real,fun(real,fun(nat,product_prod(real,real)))),bolzano_bisect,P_1),Aa),Ba),N_2)))))))))) # label(fact_2329_not__P__Bolzano__bisect_H) # label(axiom) # label(non_clause). [assumption].
% 7.76/7.73 2340 (all F all X_1 all L (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),F),X_1),L)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),L)) -> (exists D_3 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),D_3)) & (all H_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),H_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),H_1),D_3)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,F,hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),X_1),H_1))),hAPP(real,real,F,X_1))))))))))) # label(fact_2330_DERIV__pos__inc__left) # label(axiom) # label(non_clause). [assumption].
% 7.76/7.73 2341 (all F all X_1 all L (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),F),X_1),L)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),L),zero_zero(real))) -> (exists D_3 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),D_3)) & (all H_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),H_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),H_1),D_3)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,F,X_1)),hAPP(real,real,F,hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),X_1),H_1)))))))))))) # label(fact_2331_DERIV__neg__dec__left) # label(axiom) # label(non_clause). [assumption].
% 7.76/7.73 2342 (all F all X_1 all L (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),F),X_1),L)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),L)) -> (exists D_3 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),D_3)) & (all H_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),H_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),H_1),D_3)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,F,X_1)),hAPP(real,real,F,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X_1),H_1)))))))))))) # label(fact_2332_DERIV__pos__inc__right) # label(axiom) # label(non_clause). [assumption].
% 7.76/7.73 2343 (all F all X_1 all L (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),F),X_1),L)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),L),zero_zero(real))) -> (exists D_3 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),D_3)) & (all H_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),H_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),H_1),D_3)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,F,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X_1),H_1))),hAPP(real,real,F,X_1))))))))))) # label(fact_2333_DERIV__neg__dec__right) # label(axiom) # label(non_clause). [assumption].
% 7.76/7.73 2344 (all F all K all Aa all Ba (Aa != Ba -> ((all X_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),F),X_2),K))) -> hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,F,Ba)),hAPP(real,real,F,Aa))),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),Ba),Aa)) = K))) # label(fact_2334_DERIV__const__ratio__const2) # label(axiom) # label(non_clause). [assumption].
% 7.76/7.73 2345 (all F all K all Aa all Ba (Aa != Ba -> ((all X_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),F),X_2),K))) -> hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,F,Ba)),hAPP(real,real,F,Aa)) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),Ba),Aa)),K)))) # label(fact_2335_DERIV__const__ratio__const) # label(axiom) # label(non_clause). [assumption].
% 7.76/7.73 2346 (all D_2 all X_1 all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> (X_1 != zero_zero(real) -> ((hBOOL(hAPP(nat,bool,even_odd_even(nat),N)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X_1)) -> D_2 = hAPP(real,real,inverse_inverse(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,real_1(nat),N)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,hAPP(nat,fun(real,real),root,N),X_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),hAPP(nat,nat,suc,zero_zero(nat)))))))) -> ((hBOOL(hAPP(nat,bool,even_odd_even(nat),N)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_1),zero_zero(real))) -> D_2 = hAPP(real,real,uminus_uminus(real),hAPP(real,real,inverse_inverse(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,real_1(nat),N)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,hAPP(nat,fun(real,real),root,N),X_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),hAPP(nat,nat,suc,zero_zero(nat))))))))) -> ((-hBOOL(hAPP(nat,bool,even_odd_even(nat),N)) -> D_2 = hAPP(real,real,inverse_inverse(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,real_1(nat),N)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,hAPP(nat,fun(real,real),root,N),X_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),hAPP(nat,nat,suc,zero_zero(nat))))))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(nat,fun(real,real),root,N)),X_1),D_2)))))))) # label(fact_2336_DERIV__real__root__generic) # label(axiom) # label(non_clause). [assumption].
% 7.76/7.73 2347 (all X_1 all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> (hBOOL(hAPP(nat,bool,even_odd_even(nat),N)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_1),zero_zero(real))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(nat,fun(real,real),root,N)),X_1),hAPP(real,real,inverse_inverse(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,uminus_uminus(real),hAPP(nat,real,real_1(nat),N))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,hAPP(nat,fun(real,real),root,N),X_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),hAPP(nat,nat,suc,zero_zero(nat)))))))))))) # label(fact_2337_DERIV__even__real__root) # label(axiom) # label(non_clause). [assumption].
% 7.76/7.73 2348 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),one_one(real)),X)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,ln,X)),X)))) # label(fact_2338_ln__bound) # label(axiom) # label(non_clause). [assumption].
% 7.76/7.73 2349 (all X_1 all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X_1)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(nat,fun(real,real),root,N)),X_1),hAPP(real,real,inverse_inverse(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,real_1(nat),N)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,hAPP(nat,fun(real,real),root,N),X_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),hAPP(nat,nat,suc,zero_zero(nat))))))))))) # label(fact_2339_DERIV__real__root) # label(axiom) # label(non_clause). [assumption].
% 7.76/7.73 2350 (all N_1 hAPP(real,real,hAPP(nat,fun(real,real),root,N_1),zero_zero(real)) = zero_zero(real)) # label(fact_2340_real__root__zero) # label(axiom) # label(non_clause). [assumption].
% 7.76/7.73 2351 (all X hAPP(real,real,hAPP(nat,fun(real,real),root,hAPP(nat,nat,suc,zero_zero(nat))),X) = X) # label(fact_2341_real__root__Suc__0) # label(axiom) # label(non_clause). [assumption].
% 7.76/7.73 2352 (all X all N_1 all M_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),M_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)) -> hAPP(real,real,hAPP(nat,fun(real,real),root,M_1),hAPP(real,real,hAPP(nat,fun(real,real),root,N_1),X)) = hAPP(real,real,hAPP(nat,fun(real,real),root,N_1),hAPP(real,real,hAPP(nat,fun(real,real),root,M_1),X))))) # label(fact_2342_real__root__commute) # label(axiom) # label(non_clause). [assumption].
% 7.76/7.73 2353 (all X_1 all Y_1 all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> (hAPP(real,real,hAPP(nat,fun(real,real),root,N),X_1) = hAPP(real,real,hAPP(nat,fun(real,real),root,N),Y_1) <-> X_1 = Y_1))) # label(fact_2343_real__root__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 7.76/7.73 2354 (all X all N_1 (-hBOOL(hAPP(nat,bool,even_odd_even(nat),N_1)) -> hAPP(real,real,hAPP(nat,fun(real,real),root,N_1),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),N_1)) = X)) # label(fact_2344_odd__real__root__power__cancel) # label(axiom) # label(non_clause). [assumption].
% 7.76/7.73 2355 (all X all N_1 (-hBOOL(hAPP(nat,bool,even_odd_even(nat),N_1)) -> hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,hAPP(nat,fun(real,real),root,N_1),X)),N_1) = X)) # label(fact_2345_odd__real__root__pow) # label(axiom) # label(non_clause). [assumption].
% 7.76/7.73 2356 (all Y all X all N_1 (-hBOOL(hAPP(nat,bool,even_odd_even(nat),N_1)) -> (hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),Y),N_1) = X -> hAPP(real,real,hAPP(nat,fun(real,real),root,N_1),X) = Y))) # label(fact_2346_odd__real__root__unique) # label(axiom) # label(non_clause). [assumption].
% 7.76/7.73 2357 (all X all Y all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X),Y)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(nat,fun(real,real),root,N_1),X)),hAPP(real,real,hAPP(nat,fun(real,real),root,N_1),Y)))))) # label(fact_2347_real__root__le__mono) # label(axiom) # label(non_clause). [assumption].
% 7.76/7.73 2358 (all X_1 all Y_1 all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(nat,fun(real,real),root,N),X_1)),hAPP(real,real,hAPP(nat,fun(real,real),root,N),Y_1))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_1),Y_1))))) # label(fact_2348_real__root__le__iff) # label(axiom) # label(non_clause). [assumption].
% 7.76/7.73 2359 (all X_1 all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> (hAPP(real,real,hAPP(nat,fun(real,real),root,N),X_1) = zero_zero(real) <-> X_1 = zero_zero(real)))) # label(fact_2349_real__root__eq__0__iff) # label(axiom) # label(non_clause). [assumption].
% 7.76/7.73 2360 (all X all Y all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),Y)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(nat,fun(real,real),root,N_1),X)),hAPP(real,real,hAPP(nat,fun(real,real),root,N_1),Y)))))) # label(fact_2350_real__root__less__mono) # label(axiom) # label(non_clause). [assumption].
% 7.76/7.73 2361 (all X_1 all Y_1 all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(nat,fun(real,real),root,N),X_1)),hAPP(real,real,hAPP(nat,fun(real,real),root,N),Y_1))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_1),Y_1))))) # label(fact_2351_real__root__less__iff) # label(axiom) # label(non_clause). [assumption].
% 7.76/7.73 2362 (all X all Y all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)) -> hAPP(real,real,hAPP(nat,fun(real,real),root,N_1),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),X),Y)) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(nat,fun(real,real),root,N_1),X)),hAPP(real,real,hAPP(nat,fun(real,real),root,N_1),Y)))) # label(fact_2352_real__root__mult) # label(axiom) # label(non_clause). [assumption].
% 7.76/7.73 2363 (all X all N_1 all M_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),M_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)) -> hAPP(real,real,hAPP(nat,fun(real,real),root,hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),N_1)),X) = hAPP(real,real,hAPP(nat,fun(real,real),root,M_1),hAPP(real,real,hAPP(nat,fun(real,real),root,N_1),X))))) # label(fact_2353_real__root__mult__exp) # label(axiom) # label(non_clause). [assumption].
% 7.76/7.73 2364 (all X all K_4 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)) -> hAPP(real,real,hAPP(nat,fun(real,real),root,N_1),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),K_4)) = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,hAPP(nat,fun(real,real),root,N_1),X)),K_4))) # label(fact_2354_real__root__power) # label(axiom) # label(non_clause). [assumption].
% 7.76/7.73 2365 (all X_1 all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> (hAPP(real,real,hAPP(nat,fun(real,real),root,N),X_1) = one_one(real) <-> X_1 = one_one(real)))) # label(fact_2355_real__root__eq__1__iff) # label(axiom) # label(non_clause). [assumption].
% 7.76/7.73 2366 (all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)) -> hAPP(real,real,hAPP(nat,fun(real,real),root,N_1),one_one(real)) = one_one(real))) # label(fact_2356_real__root__one) # label(axiom) # label(non_clause). [assumption].
% 7.76/7.73 2367 (all X all Y all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)) -> hAPP(real,real,hAPP(nat,fun(real,real),root,N_1),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),X),Y)) = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(nat,fun(real,real),root,N_1),X)),hAPP(real,real,hAPP(nat,fun(real,real),root,N_1),Y)))) # label(fact_2357_real__root__divide) # label(axiom) # label(non_clause). [assumption].
% 7.76/7.73 2368 (all X all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)) -> hAPP(real,real,hAPP(nat,fun(real,real),root,N_1),hAPP(real,real,uminus_uminus(real),X)) = hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(nat,fun(real,real),root,N_1),X)))) # label(fact_2358_real__root__minus) # label(axiom) # label(non_clause). [assumption].
% 7.76/7.73 2369 (all X all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)) -> hAPP(real,real,hAPP(nat,fun(real,real),root,N_1),hAPP(real,real,abs_abs(real),X)) = hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(nat,fun(real,real),root,N_1),X)))) # label(fact_2359_real__root__abs) # label(axiom) # label(non_clause). [assumption].
% 7.76/7.73 2370 (all X all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)) -> hAPP(real,real,hAPP(nat,fun(real,real),root,N_1),hAPP(real,real,inverse_inverse(real),X)) = hAPP(real,real,inverse_inverse(real),hAPP(real,real,hAPP(nat,fun(real,real),root,N_1),X)))) # label(fact_2360_real__root__inverse) # label(axiom) # label(non_clause). [assumption].
% 7.76/7.73 2371 (all X all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(real,real,hAPP(nat,fun(real,real),root,N_1),X)))))) # label(fact_2361_real__root__ge__zero) # label(axiom) # label(non_clause). [assumption].
% 7.76/7.73 2372 (all X_1 all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(nat,fun(real,real),root,N),X_1)),zero_zero(real))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_1),zero_zero(real)))))) # label(fact_2362_real__root__le__0__iff) # label(axiom) # label(non_clause). [assumption].
% 7.76/7.73 2373 (all Y_1 all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(real,real,hAPP(nat,fun(real,real),root,N),Y_1))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),Y_1))))) # label(fact_2363_real__root__ge__0__iff) # label(axiom) # label(non_clause). [assumption].
% 7.76/7.73 2374 (all Y_1 all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,hAPP(nat,fun(real,real),root,N),Y_1))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Y_1))))) # label(fact_2364_real__root__gt__0__iff) # label(axiom) # label(non_clause). [assumption].
% 7.76/7.73 2375 (all X_1 all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(nat,fun(real,real),root,N),X_1)),zero_zero(real))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_1),zero_zero(real)))))) # label(fact_2365_real__root__lt__0__iff) # label(axiom) # label(non_clause). [assumption].
% 7.76/7.73 2376 (all X all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,hAPP(nat,fun(real,real),root,N_1),X)))))) # label(fact_2366_real__root__gt__zero) # label(axiom) # label(non_clause). [assumption].
% 7.76/7.73 2377 (all X all N_6 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),N_6)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),one_one(real)),X)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(nat,fun(real,real),root,N_6),X)),hAPP(real,real,hAPP(nat,fun(real,real),root,N_1),X))))))) # label(fact_2367_real__root__decreasing) # label(axiom) # label(non_clause). [assumption].
% 7.76/7.73 2378 (all X_1 all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(nat,fun(real,real),root,N),X_1)),one_one(real))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_1),one_one(real)))))) # label(fact_2368_real__root__le__1__iff) # label(axiom) # label(non_clause). [assumption].
% 7.76/7.73 2379 (all Y_1 all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),one_one(real)),hAPP(real,real,hAPP(nat,fun(real,real),root,N),Y_1))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),one_one(real)),Y_1))))) # label(fact_2369_real__root__ge__1__iff) # label(axiom) # label(non_clause). [assumption].
% 7.76/7.73 2380 (all X all N_6 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),N_6)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),X)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(nat,fun(real,real),root,N_6),X)),hAPP(real,real,hAPP(nat,fun(real,real),root,N_1),X))))))) # label(fact_2370_real__root__strict__decreasing) # label(axiom) # label(non_clause). [assumption].
% 7.76/7.73 2381 (all X_1 all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(nat,fun(real,real),root,N),X_1)),one_one(real))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_1),one_one(real)))))) # label(fact_2371_real__root__lt__1__iff) # label(axiom) # label(non_clause). [assumption].
% 7.76/7.73 2382 (all Y_1 all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),hAPP(real,real,hAPP(nat,fun(real,real),root,N),Y_1))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),Y_1))))) # label(fact_2372_real__root__gt__1__iff) # label(axiom) # label(non_clause). [assumption].
% 7.76/7.73 2383 (all N_1 all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> hAPP(real,real,hAPP(nat,fun(real,real),root,hAPP(nat,nat,suc,N_1)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),hAPP(nat,nat,suc,N_1))) = X)) # label(fact_2373_real__root__pos) # label(axiom) # label(non_clause). [assumption].
% 7.76/7.73 2384 (all Y all X all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),Y)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(nat,fun(real,real),root,N_1),X)),hAPP(real,real,hAPP(nat,fun(real,real),root,N_1),Y))))))) # label(fact_2374_real__root__less__mono__lemma) # label(axiom) # label(non_clause). [assumption].
% 7.76/7.73 2385 (all X_5 all N_7 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_7)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X_5)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(real,real,hAPP(nat,fun(real,real),root,N_7),X_5)))))) # label(fact_2375_real__root__pos__pos) # label(axiom) # label(non_clause). [assumption].
% 7.76/7.73 2386 (all Y all X all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),Y)) -> hAPP(real,real,hAPP(nat,fun(real,real),root,N_1),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),X),Y)) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(nat,fun(real,real),root,N_1),X)),hAPP(real,real,hAPP(nat,fun(real,real),root,N_1),Y)))))) # label(fact_2376_real__root__mult__lemma) # label(axiom) # label(non_clause). [assumption].
% 7.76/7.73 2387 (all X all N_1 all M_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),M_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> hAPP(real,real,hAPP(nat,fun(real,real),root,hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),N_1)),X) = hAPP(real,real,hAPP(nat,fun(real,real),root,M_1),hAPP(real,real,hAPP(nat,fun(real,real),root,N_1),X)))))) # label(fact_2377_real__root__pos__mult__exp) # label(axiom) # label(non_clause). [assumption].
% 7.76/7.73 2388 (all X all Y all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),Y)) -> (hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),Y),N_1) = X -> hAPP(real,real,hAPP(nat,fun(real,real),root,N_1),X) = Y)))) # label(fact_2378_real__root__pos__unique) # label(axiom) # label(non_clause). [assumption].
% 7.76/7.73 2389 (all X all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X)) -> hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,hAPP(nat,fun(real,real),root,N_1),X)),N_1) = X))) # label(fact_2379_real__root__pow__pos2) # label(axiom) # label(non_clause). [assumption].
% 7.76/7.73 2390 (all X all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X)) -> hAPP(real,real,hAPP(nat,fun(real,real),root,N_1),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),N_1)) = X))) # label(fact_2380_real__root__pos2) # label(axiom) # label(non_clause). [assumption].
% 7.76/7.73 2391 (all X all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,hAPP(nat,fun(real,real),root,N_1),X)),N_1) = X))) # label(fact_2381_real__root__pow__pos) # label(axiom) # label(non_clause). [assumption].
% 7.76/7.73 2392 (all X all N_6 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),N_6)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X),one_one(real))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(nat,fun(real,real),root,N_1),X)),hAPP(real,real,hAPP(nat,fun(real,real),root,N_6),X)))))))) # label(fact_2382_real__root__increasing) # label(axiom) # label(non_clause). [assumption].
% 7.76/7.73 2393 (all X all N_6 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),N_6)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),one_one(real))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(nat,fun(real,real),root,N_1),X)),hAPP(real,real,hAPP(nat,fun(real,real),root,N_6),X)))))))) # label(fact_2383_real__root__strict__increasing) # label(axiom) # label(non_clause). [assumption].
% 7.76/7.73 2394 (all X all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X)) -> hAPP(real,real,hAPP(nat,fun(real,real),root,N_1),hAPP(real,real,inverse_inverse(real),X)) = hAPP(real,real,inverse_inverse(real),hAPP(real,real,hAPP(nat,fun(real,real),root,N_1),X))))) # label(fact_2385_real__root__inverse__lemma) # label(axiom) # label(non_clause). [assumption].
% 7.76/7.73 2395 (all X_1 all N (-hBOOL(hAPP(nat,bool,even_odd_even(nat),N)) -> (X_1 != zero_zero(real) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(nat,fun(real,real),root,N)),X_1),hAPP(real,real,inverse_inverse(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,real_1(nat),N)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,hAPP(nat,fun(real,real),root,N),X_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),hAPP(nat,nat,suc,zero_zero(nat))))))))))) # label(fact_2386_DERIV__odd__real__root) # label(axiom) # label(non_clause). [assumption].
% 7.76/7.73 2396 (all Aa all Ba (hBOOL(hAPP(product_prod(int,int),bool,hAPP(fun(product_prod(int,int),fun(product_prod(int,int),bool)),fun(product_prod(int,int),bool),accp(product_prod(int,int)),negDivAlg_rel),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),Aa),Ba))) -> (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),Aa),Ba))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Ba),zero_zero(int))) -> hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),negDivAlg,Aa),Ba) = hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),hAPP(int,int,number_number_of(int),min)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Aa),Ba))) & (-(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),Aa),Ba))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Ba),zero_zero(int)))) -> hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),negDivAlg,Aa),Ba) = hAPP(product_prod(int,int),product_prod(int,int),hAPP(int,fun(product_prod(int,int),product_prod(int,int)),adjust,Ba),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),negDivAlg,Aa),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),Ba)))))) # label(fact_2387_negDivAlg_Opsimps) # label(axiom) # label(non_clause). [assumption].
% 7.76/7.73 2397 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X),one_one(real))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,exp(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),X),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),one_one(real)),X)))))) # label(fact_2388_aux4) # label(axiom) # label(non_clause). [assumption].
% 7.76/7.73 2398 (all F all F_2 all Aa all Ba (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),Aa),Ba)) -> ((all X_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),Aa),X_2)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_2),Ba)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),F),X_2),hAPP(real,real,F_2,X_2))))) -> (exists Z_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),Aa),Z_2)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),Z_2),Ba)) & hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,F,Ba)),hAPP(real,real,F,Aa)) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),Ba),Aa)),hAPP(real,real,F_2,Z_2))))))) # label(fact_2389_MVT2) # label(axiom) # label(non_clause). [assumption].
% 7.76/7.73 2399 (all X all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Y)) -> (exists R_2 exists A_3 (X = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),R_2),hAPP(real,real,cos,A_3)) & Y = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),R_2),hAPP(real,real,sin,A_3)))))) # label(fact_2390_polar__ex1) # label(axiom) # label(non_clause). [assumption].
% 7.76/7.73 2400 (all X all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),Y)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,exp(real),X)),hAPP(real,real,exp(real),Y))))) # label(fact_2391_exp__less__mono) # label(axiom) # label(non_clause). [assumption].
% 7.76/7.73 2401 (all X_1 all Y_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,exp(real),X_1)),hAPP(real,real,exp(real),Y_1))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_1),Y_1)))) # label(fact_2392_exp__le__cancel__iff) # label(axiom) # label(non_clause). [assumption].
% 7.76/7.73 2402 (all X_1 all Y_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,exp(real),X_1)),hAPP(real,real,exp(real),Y_1))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_1),Y_1)))) # label(fact_2393_exp__less__cancel__iff) # label(axiom) # label(non_clause). [assumption].
% 7.76/7.73 2403 (all X all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,exp(real),X)),hAPP(real,real,exp(real),Y))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),Y)))) # label(fact_2394_exp__less__cancel) # label(axiom) # label(non_clause). [assumption].
% 7.76/7.73 2404 (all X_1 all Y_1 (hAPP(real,real,exp(real),X_1) = hAPP(real,real,exp(real),Y_1) <-> X_1 = Y_1)) # label(fact_2395_exp__inj__iff) # label(axiom) # label(non_clause). [assumption].
% 7.76/7.73 2405 (all X hAPP(real,real,abs_abs(real),hAPP(real,real,exp(real),X)) = hAPP(real,real,exp(real),X)) # label(fact_2396_abs__exp__cancel) # label(axiom) # label(non_clause). [assumption].
% 7.76/7.73 2406 (all Y all X (hAPP(real,real,exp(real),Y) = X -> hAPP(real,real,ln,X) = Y)) # label(fact_2397_ln__unique) # label(axiom) # label(non_clause). [assumption].
% 7.76/7.73 2407 (all U all X (hAPP(real,real,exp(real),U) = X -> hAPP(real,real,ln,X) = U)) # label(fact_2398_exp__ln__eq) # label(axiom) # label(non_clause). [assumption].
% 7.76/7.73 2408 (all X hAPP(real,real,ln,hAPP(real,real,exp(real),X)) = X) # label(fact_2399_ln__exp) # label(axiom) # label(non_clause). [assumption].
% 7.76/7.73 2409 (all X_a (real_normed_field(X_a) & banach(X_a) -> (all X hAPP(X_a,X_a,exp(X_a),X) != zero_zero(X_a)))) # label(fact_2400_exp__not__eq__zero) # label(axiom) # label(non_clause). [assumption].
% 7.76/7.73 2410 (all X_a (real_normed_field(X_a) & banach(X_a) -> (all X_1 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),exp(X_a)),X_1),hAPP(X_a,X_a,exp(X_a),X_1)))))) # label(fact_2401_DERIV__exp) # label(axiom) # label(non_clause). [assumption].
% 7.76/7.73 2411 (all X -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,exp(real),X)),zero_zero(real)))) # label(fact_2402_not__exp__le__zero) # label(axiom) # label(non_clause). [assumption].
% 7.76/7.73 2412 (all X hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(real,real,exp(real),X)))) # label(fact_2403_exp__ge__zero) # label(axiom) # label(non_clause). [assumption].
% 7.76/7.73 2413 (all X hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,exp(real),X)))) # label(fact_2404_exp__gt__zero) # label(axiom) # label(non_clause). [assumption].
% 7.76/7.73 2414 (all X -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,exp(real),X)),zero_zero(real)))) # label(fact_2405_not__exp__less__zero) # label(axiom) # label(non_clause). [assumption].
% 7.76/7.73 2415 (all X_1 (hAPP(real,real,exp(real),X_1) = one_one(real) <-> X_1 = zero_zero(real))) # label(fact_2406_exp__eq__one__iff) # label(axiom) # label(non_clause). [assumption].
% 7.76/7.73 2416 (all X_a (real_normed_field(X_a) & banach(X_a) -> hAPP(X_a,X_a,exp(X_a),zero_zero(X_a)) = one_one(X_a))) # label(fact_2407_exp__zero) # label(axiom) # label(non_clause). [assumption].
% 7.76/7.73 2417 (all X_a (real_normed_field(X_a) & banach(X_a) -> (all X all Y hAPP(X_a,X_a,exp(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X),Y)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,exp(X_a),X)),hAPP(X_a,X_a,exp(X_a),Y))))) # label(fact_2408_exp__add) # label(axiom) # label(non_clause). [assumption].
% 7.76/7.73 2418 (all X_a (real_normed_field(X_a) & banach(X_a) -> (all X all Y hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,exp(X_a),X)),hAPP(X_a,X_a,exp(X_a),Y)) = hAPP(X_a,X_a,exp(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X),Y))))) # label(fact_2409_mult__exp__exp) # label(axiom) # label(non_clause). [assumption].
% 7.76/7.73 2419 (all X_a (real_normed_field(X_a) & banach(X_a) -> (all X all Y hAPP(X_a,X_a,exp(X_a),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),inverse_divide(X_a),hAPP(X_a,X_a,exp(X_a),X)),hAPP(X_a,X_a,exp(X_a),Y))))) # label(fact_2410_exp__diff) # label(axiom) # label(non_clause). [assumption].
% 7.76/7.73 2420 (all X_a (real_normed_field(X_a) & banach(X_a) -> (all X hAPP(X_a,X_a,exp(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),X)) = hAPP(X_a,X_a,inverse_inverse(X_a),hAPP(X_a,X_a,exp(X_a),X))))) # label(fact_2411_exp__minus) # label(axiom) # label(non_clause). [assumption].
% 7.76/7.73 2421 (all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),one_one(real)),hAPP(real,real,exp(real),X_1))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X_1)))) # label(fact_2412_one__le__exp__iff) # label(axiom) # label(non_clause). [assumption].
% 7.76/7.73 2422 (all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,exp(real),X_1)),one_one(real))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_1),zero_zero(real))))) # label(fact_2413_exp__le__one__iff) # label(axiom) # label(non_clause). [assumption].
% 7.76/7.73 2423 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),hAPP(real,real,exp(real),X))))) # label(fact_2414_exp__gt__one) # label(axiom) # label(non_clause). [assumption].
% 7.76/7.73 2424 (all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,exp(real),X_1)),one_one(real))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_1),zero_zero(real))))) # label(fact_2415_exp__less__one__iff) # label(axiom) # label(non_clause). [assumption].
% 7.76/7.73 2425 (all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),hAPP(real,real,exp(real),X_1))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X_1)))) # label(fact_2416_one__less__exp__iff) # label(axiom) # label(non_clause). [assumption].
% 7.76/7.73 2426 (all X hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),one_one(real)),X)),hAPP(real,real,exp(real),X)))) # label(fact_2417_exp__ge__add__one__self) # label(axiom) # label(non_clause). [assumption].
% 7.76/7.73 2427 (all N_1 all X hAPP(real,real,exp(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,real_1(nat),N_1)),X)) = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,exp(real),X)),N_1)) # label(fact_2418_exp__real__of__nat__mult) # label(axiom) # label(non_clause). [assumption].
% 7.76/7.73 2428 (all X_1 (hAPP(real,real,exp(real),hAPP(real,real,ln,X_1)) = X_1 <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X_1)))) # label(fact_2419_exp__ln__iff) # label(axiom) # label(non_clause). [assumption].
% 7.76/7.73 2429 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> hAPP(real,real,exp(real),hAPP(real,real,ln,X)) = X)) # label(fact_2420_exp__ln) # label(axiom) # label(non_clause). [assumption].
% 7.76/7.73 2430 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),one_one(real)),X)),hAPP(real,real,exp(real),X))))) # label(fact_2421_exp__ge__add__one__self__aux) # label(axiom) # label(non_clause). [assumption].
% 7.76/7.73 2431 (all Y all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,exp(real),one_one(real))),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X),Y)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,ln,Y)),Y)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,ln,X)),X)))))) # label(fact_2422_ln__x__over__x__mono) # label(axiom) # label(non_clause). [assumption].
% 7.76/7.73 2432 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X),one_one(real))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,exp(real),X)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),one_one(real)),X)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))))) # label(fact_2423_exp__bound) # label(axiom) # label(non_clause). [assumption].
% 7.76/7.73 2433 (all P_1 all A0 all A1 (hBOOL(hAPP(product_prod(int,int),bool,hAPP(fun(product_prod(int,int),fun(product_prod(int,int),bool)),fun(product_prod(int,int),bool),accp(product_prod(int,int)),negDivAlg_rel),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),A0),A1))) -> ((all A_3 all B_3 (hBOOL(hAPP(product_prod(int,int),bool,hAPP(fun(product_prod(int,int),fun(product_prod(int,int),bool)),fun(product_prod(int,int),bool),accp(product_prod(int,int)),negDivAlg_rel),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),A_3),B_3))) -> ((-(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),A_3),B_3))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B_3),zero_zero(int)))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),P_1,A_3),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),B_3)))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),P_1,A_3),B_3))))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),P_1,A0),A1))))) # label(fact_2424_negDivAlg_Opinduct) # label(axiom) # label(non_clause). [assumption].
% 7.76/7.73 2434 (all Aa all Ba (hBOOL(hAPP(product_prod(int,int),bool,hAPP(fun(product_prod(int,int),fun(product_prod(int,int),bool)),fun(product_prod(int,int),bool),accp(product_prod(int,int)),posDivAlg_rel),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),Aa),Ba))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Aa),Ba)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Ba),zero_zero(int))) -> hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),posDivAlg,Aa),Ba) = hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),zero_zero(int)),Aa)) & (-(hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Aa),Ba)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Ba),zero_zero(int)))) -> hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),posDivAlg,Aa),Ba) = hAPP(product_prod(int,int),product_prod(int,int),hAPP(int,fun(product_prod(int,int),product_prod(int,int)),adjust,Ba),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),posDivAlg,Aa),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),Ba)))))) # label(fact_2425_posDivAlg_Opsimps) # label(axiom) # label(non_clause). [assumption].
% 7.76/7.73 2435 (all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),one_one(real)),Y)) -> (exists X_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X_2)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_2),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),Y),one_one(real)))) & hAPP(real,real,exp(real),X_2) = Y)))) # label(fact_2426_lemma__exp__total) # label(axiom) # label(non_clause). [assumption].
% 7.76/7.73 2436 (all P_1 all A0 all A1 (hBOOL(hAPP(product_prod(int,int),bool,hAPP(fun(product_prod(int,int),fun(product_prod(int,int),bool)),fun(product_prod(int,int),bool),accp(product_prod(int,int)),posDivAlg_rel),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),A0),A1))) -> ((all A_3 all B_3 (hBOOL(hAPP(product_prod(int,int),bool,hAPP(fun(product_prod(int,int),fun(product_prod(int,int),bool)),fun(product_prod(int,int),bool),accp(product_prod(int,int)),posDivAlg_rel),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),A_3),B_3))) -> ((-(hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_3),B_3)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B_3),zero_zero(int)))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),P_1,A_3),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),B_3)))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),P_1,A_3),B_3))))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),P_1,A0),A1))))) # label(fact_2427_posDivAlg_Opinduct) # label(axiom) # label(non_clause). [assumption].
% 7.76/7.73 2437 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> hAPP(real,real,hAPP(real,fun(real,real),log,hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),X) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,ln,hAPP(real,real,exp(real),one_one(real)))),hAPP(real,real,ln,hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))),hAPP(real,real,ln,X)))) # label(fact_2428_log__base__10__eq1) # label(axiom) # label(non_clause). [assumption].
% 7.76/7.73 2438 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> hAPP(real,real,hAPP(real,fun(real,real),log,hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),X) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),log,hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),hAPP(real,real,exp(real),one_one(real)))),hAPP(real,real,ln,X)))) # label(fact_2429_log__base__10__eq2) # label(axiom) # label(non_clause). [assumption].
% 7.76/7.73 2439 (all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Y)) -> (exists X_2 hAPP(real,real,exp(real),X_2) = Y))) # label(fact_2430_exp__total) # label(axiom) # label(non_clause). [assumption].
% 7.76/7.73 2440 (all X all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),Y),zero_zero(real))) -> (exists R_2 exists A_3 (X = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),R_2),hAPP(real,real,cos,A_3)) & Y = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),R_2),hAPP(real,real,sin,A_3)))))) # label(fact_2431_polar__ex2) # label(axiom) # label(non_clause). [assumption].
% 7.76/7.73 2441 (all A_1 hAPP(real,real,hAPP(real,fun(real,real),log,A_1),one_one(real)) = zero_zero(real)) # label(fact_2432_log__one) # label(axiom) # label(non_clause). [assumption].
% 7.76/7.73 2442 (all A_1 all X hAPP(real,real,hAPP(real,fun(real,real),log,A_1),X) = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,ln,X)),hAPP(real,real,ln,A_1))) # label(fact_2433_Log_Olog__def) # label(axiom) # label(non_clause). [assumption].
% 7.76/7.73 2443 (all Y_1 all X_1 all Aa (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),Aa)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Y_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),log,Aa),X_1)),hAPP(real,real,hAPP(real,fun(real,real),log,Aa),Y_1))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_1),Y_1))))))) # label(fact_2434_log__less__cancel__iff) # label(axiom) # label(non_clause). [assumption].
% 7.76/7.73 2444 (all A_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A_1)) -> (A_1 != one_one(real) -> hAPP(real,real,hAPP(real,fun(real,real),log,A_1),A_1) = one_one(real)))) # label(fact_2435_log__eq__one) # label(axiom) # label(non_clause). [assumption].
% 7.76/7.73 2445 (all X hAPP(real,real,ln,X) = hAPP(real,real,hAPP(real,fun(real,real),log,hAPP(real,real,exp(real),one_one(real))),X)) # label(fact_2436_log__ln) # label(axiom) # label(non_clause). [assumption].
% 7.76/7.73 2446 (all Y_1 all X_1 all Aa (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),Aa)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Y_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),log,Aa),X_1)),hAPP(real,real,hAPP(real,fun(real,real),log,Aa),Y_1))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_1),Y_1))))))) # label(fact_2437_log__le__cancel__iff) # label(axiom) # label(non_clause). [assumption].
% 7.76/7.73 2447 (all B all N_1 all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> hAPP(real,real,hAPP(real,fun(real,real),log,B),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),N_1)) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,real_1(nat),N_1)),hAPP(real,real,hAPP(real,fun(real,real),log,B),X)))) # label(fact_2438_log__nat__power) # label(axiom) # label(non_clause). [assumption].
% 7.76/7.73 2448 (all Y all X all A_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A_1)) -> (A_1 != one_one(real) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Y)) -> hAPP(real,real,hAPP(real,fun(real,real),log,A_1),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),X),Y)) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),log,A_1),X)),hAPP(real,real,hAPP(real,fun(real,real),log,A_1),Y))))))) # label(fact_2439_log__mult) # label(axiom) # label(non_clause). [assumption].
% 7.76/7.73 2449 (all Y all X all A_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A_1)) -> (A_1 != one_one(real) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Y)) -> hAPP(real,real,hAPP(real,fun(real,real),log,A_1),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),X),Y)) = hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,hAPP(real,fun(real,real),log,A_1),X)),hAPP(real,real,hAPP(real,fun(real,real),log,A_1),Y))))))) # label(fact_2440_log__divide) # label(axiom) # label(non_clause). [assumption].
% 7.76/7.73 2450 (all X all A_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A_1)) -> (A_1 != one_one(real) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> hAPP(real,real,hAPP(real,fun(real,real),log,A_1),hAPP(real,real,inverse_inverse(real),X)) = hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),log,A_1),X)))))) # label(fact_2441_log__inverse) # label(axiom) # label(non_clause). [assumption].
% 7.76/7.73 2451 (all X all B all A_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A_1)) -> (A_1 != one_one(real) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B)) -> (B != one_one(real) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> hAPP(real,real,hAPP(real,fun(real,real),log,A_1),X) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,ln,B)),hAPP(real,real,ln,A_1))),hAPP(real,real,hAPP(real,fun(real,real),log,B),X)))))))) # label(fact_2442_log__eq__div__ln__mult__log) # label(axiom) # label(non_clause). [assumption].
% 7.76/7.73 2452 (all X (-hBOOL(hAPP(int,bool,even_odd_even(int),X)) -> 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,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),X),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),one_one(int)) = X)) # label(fact_2443_two__times__odd__div__two__plus__one) # label(axiom) # label(non_clause). [assumption].
% 7.76/7.73 2453 (all X_1 all Y_1 all F ((all X_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),F),X_2),zero_zero(real)))) -> hAPP(real,real,F,X_1) = hAPP(real,real,F,Y_1))) # label(fact_2444_DERIV__isconst__all) # label(axiom) # label(non_clause). [assumption].
% 7.76/7.73 2454 (all K_4 ((K_4 = zero_zero(code_code_numeral) -> hAPP(code_code_numeral,int,code_int_of,K_4) = zero_zero(int)) & (K_4 != zero_zero(code_code_numeral) -> (hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),K_4),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = zero_zero(code_code_numeral) -> hAPP(code_code_numeral,int,code_int_of,K_4) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),hAPP(code_code_numeral,int,code_int_of,hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),K_4),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))) & (hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),K_4),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) != zero_zero(code_code_numeral) -> hAPP(code_code_numeral,int,code_int_of,K_4) = 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,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),hAPP(code_code_numeral,int,code_int_of,hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),K_4),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))),one_one(int)))))) # label(fact_2445_Code__Numeral_Oint__of__code) # label(axiom) # label(non_clause). [assumption].
% 7.76/7.73 2455 (all A_1 all P_4 (hBOOL(hAPP(int,bool,zprime,P_4)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit1,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),P_4)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_1),P_4)) -> hAPP(int,int,hAPP(int,fun(int,int),inv,P_4),hAPP(int,int,hAPP(int,fun(int,int),inv,P_4),A_1)) = A_1))))) # label(fact_2446_inv__inv) # label(axiom) # label(non_clause). [assumption].
% 7.76/7.73 2456 (all X_1 (hBOOL(hAPP(int,bool,even_odd_even(int),hAPP(int,int,uminus_uminus(int),X_1))) <-> hBOOL(hAPP(int,bool,even_odd_even(int),X_1)))) # label(fact_2447_even__neg) # label(axiom) # label(non_clause). [assumption].
% 7.76/7.73 2457 (all X_1 all Y_1 (hBOOL(hAPP(int,bool,even_odd_even(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X_1),Y_1))) <-> hBOOL(hAPP(int,bool,even_odd_even(int),X_1)) & hBOOL(hAPP(int,bool,even_odd_even(int),Y_1)) | -hBOOL(hAPP(int,bool,even_odd_even(int),X_1)) & -hBOOL(hAPP(int,bool,even_odd_even(int),Y_1)))) # label(fact_2449_even__difference) # label(axiom) # label(non_clause). [assumption].
% 7.76/7.73 2458 (all Y all X (-hBOOL(hAPP(int,bool,even_odd_even(int),X)) -> (-hBOOL(hAPP(int,bool,even_odd_even(int),Y)) -> hBOOL(hAPP(int,bool,even_odd_even(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X),Y)))))) # label(fact_2450_Parity_Oodd__plus__odd) # label(axiom) # label(non_clause). [assumption].
% 7.76/7.73 2459 (all Y all X (-hBOOL(hAPP(int,bool,even_odd_even(int),X)) -> (hBOOL(hAPP(int,bool,even_odd_even(int),Y)) -> -hBOOL(hAPP(int,bool,even_odd_even(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X),Y)))))) # label(fact_2451_odd__plus__even) # label(axiom) # label(non_clause). [assumption].
% 7.76/7.73 2460 (all Y all X (hBOOL(hAPP(int,bool,even_odd_even(int),X)) -> (-hBOOL(hAPP(int,bool,even_odd_even(int),Y)) -> -hBOOL(hAPP(int,bool,even_odd_even(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X),Y)))))) # label(fact_2452_Parity_Oeven__plus__odd) # label(axiom) # label(non_clause). [assumption].
% 7.76/7.73 2461 (all Y all X (hBOOL(hAPP(int,bool,even_odd_even(int),X)) -> (hBOOL(hAPP(int,bool,even_odd_even(int),Y)) -> hBOOL(hAPP(int,bool,even_odd_even(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X),Y)))))) # label(fact_2453_Parity_Oeven__plus__even) # label(axiom) # label(non_clause). [assumption].
% 7.76/7.73 2462 (all X_1 all Y_1 (hBOOL(hAPP(int,bool,even_odd_even(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X_1),Y_1))) <-> hBOOL(hAPP(int,bool,even_odd_even(int),X_1)) & hBOOL(hAPP(int,bool,even_odd_even(int),Y_1)) | -hBOOL(hAPP(int,bool,even_odd_even(int),X_1)) & -hBOOL(hAPP(int,bool,even_odd_even(int),Y_1)))) # label(fact_2454_even__sum) # label(axiom) # label(non_clause). [assumption].
% 7.76/7.73 2463 (all Y all X (-hBOOL(hAPP(int,bool,even_odd_even(int),X)) -> (-hBOOL(hAPP(int,bool,even_odd_even(int),Y)) -> -hBOOL(hAPP(int,bool,even_odd_even(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X),Y)))))) # label(fact_2455_Parity_Oodd__times__odd) # label(axiom) # label(non_clause). [assumption].
% 7.76/7.73 2464 (all X all Y (hBOOL(hAPP(int,bool,even_odd_even(int),Y)) -> hBOOL(hAPP(int,bool,even_odd_even(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X),Y))))) # label(fact_2456_anything__times__even) # label(axiom) # label(non_clause). [assumption].
% 7.76/7.73 2465 (all Y all X (hBOOL(hAPP(int,bool,even_odd_even(int),X)) -> hBOOL(hAPP(int,bool,even_odd_even(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X),Y))))) # label(fact_2457_even__times__anything) # label(axiom) # label(non_clause). [assumption].
% 7.76/7.73 2466 (all X_1 all Y_1 (hBOOL(hAPP(int,bool,even_odd_even(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X_1),Y_1))) <-> hBOOL(hAPP(int,bool,even_odd_even(int),X_1)) | hBOOL(hAPP(int,bool,even_odd_even(int),Y_1)))) # label(fact_2458_Parity_Oeven__product) # label(axiom) # label(non_clause). [assumption].
% 7.76/7.73 2467 (all N_1 all X (-hBOOL(hAPP(int,bool,even_odd_even(int),X)) -> -hBOOL(hAPP(int,bool,even_odd_even(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),X),N_1))))) # label(fact_2461_odd__pow) # label(axiom) # label(non_clause). [assumption].
% 7.76/7.73 2468 (all X_1 all N (hBOOL(hAPP(int,bool,even_odd_even(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),X_1),N))) <-> hBOOL(hAPP(int,bool,even_odd_even(int),X_1)) & N != zero_zero(nat))) # label(fact_2462_even__power) # label(axiom) # label(non_clause). [assumption].
% 7.76/7.73 2469 (all A_1 all P_4 (hBOOL(hAPP(int,bool,zprime,P_4)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),A_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_1),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),P_4),one_one(int)))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),inv,P_4),A_1)),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),P_4),one_one(int)))))))) # label(fact_2465_inv__less__p__minus__1) # label(axiom) # label(non_clause). [assumption].
% 7.76/7.73 2470 (all A_1 all P_4 (hBOOL(hAPP(int,bool,zprime,P_4)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),A_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_1),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),P_4),one_one(int)))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),hAPP(int,int,hAPP(int,fun(int,int),inv,P_4),A_1))))))) # label(fact_2466_inv__g__1) # label(axiom) # label(non_clause). [assumption].
% 7.76/7.73 2471 (all A_1 all P_4 (hBOOL(hAPP(int,bool,zprime,P_4)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),A_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_1),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),P_4),one_one(int)))) -> hAPP(int,int,hAPP(int,fun(int,int),inv,P_4),A_1) != hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),P_4),one_one(int)))))) # label(fact_2467_inv__not__p__minus__1) # label(axiom) # label(non_clause). [assumption].
% 7.76/7.73 2472 (all A_1 all P_4 (hBOOL(hAPP(int,bool,zprime,P_4)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),A_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_1),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),P_4),one_one(int)))) -> hAPP(int,int,hAPP(int,fun(int,int),inv,P_4),A_1) != one_one(int))))) # label(fact_2468_inv__not__1) # label(axiom) # label(non_clause). [assumption].
% 7.76/7.73 2473 (all A_1 all P_4 (hBOOL(hAPP(int,bool,zprime,P_4)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),A_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_1),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),P_4),one_one(int)))) -> A_1 != hAPP(int,int,hAPP(int,fun(int,int),inv,P_4),A_1))))) # label(fact_2469_inv__distinct) # label(axiom) # label(non_clause). [assumption].
% 7.76/7.73 2474 (all X_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X_1)) -> (hBOOL(hAPP(int,bool,even_odd_even(int),X_1)) <-> hBOOL(hAPP(nat,bool,even_odd_even(nat),hAPP(int,nat,nat_1,X_1)))))) # label(fact_2470_pos__int__even__equiv__nat__even) # label(axiom) # label(non_clause). [assumption].
% 7.76/7.73 2475 (all P_4 (hBOOL(hAPP(int,bool,zprime,P_4)) -> (P_4 != hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))) -> (P_4 != hAPP(int,int,number_number_of(int),hAPP(int,int,bit1,hAPP(int,int,bit1,pls))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit1,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),P_4)))))) # label(fact_2471_prime__g__5) # label(axiom) # label(non_clause). [assumption].
% 7.76/7.73 2476 (all A_1 all P_4 (hBOOL(hAPP(int,bool,zprime,P_4)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),A_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_1),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),P_4),one_one(int)))) -> hAPP(int,int,hAPP(int,fun(int,int),inv,P_4),A_1) != zero_zero(int))))) # label(fact_2472_inv__not__0) # label(axiom) # label(non_clause). [assumption].
% 7.76/7.73 2477 (all X_1 (hBOOL(hAPP(int,bool,even_odd_even(int),X_1)) <-> (exists Y_2 X_1 = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),Y_2)))) # label(fact_2473_even__equiv__def) # label(axiom) # label(non_clause). [assumption].
% 7.76/7.73 2478 (all Pa (hBOOL(hAPP(int,bool,zprime,Pa)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Pa),zOdd)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),Pa))))) # label(fact_2474_zprime__zOdd__eq__grt__2) # label(axiom) # label(non_clause). [assumption].
% 7.76/7.73 2479 (all X_1 (hBOOL(hAPP(int,bool,even_odd_even(int),X_1)) <-> hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),X_1),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = zero_zero(int))) # label(fact_2475_even__def) # label(axiom) # label(non_clause). [assumption].
% 7.76/7.73 2480 (all X (hBOOL(hAPP(int,bool,even_odd_even(int),X)) -> hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),X),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) = X)) # label(fact_2476_two__times__even__div__two) # label(axiom) # label(non_clause). [assumption].
% 7.76/7.73 2481 (all X_1 (-hBOOL(hAPP(int,bool,even_odd_even(int),X_1)) <-> (exists Y_2 X_1 = 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,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),Y_2)),one_one(int))))) # label(fact_2478_odd__equiv__def) # label(axiom) # label(non_clause). [assumption].
% 7.76/7.73 2482 (all X (-hBOOL(hAPP(int,bool,even_odd_even(int),X)) -> hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X),one_one(int))),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),X),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),one_one(int)))) # label(fact_2479_odd__plus__one__div__two) # label(axiom) # label(non_clause). [assumption].
% 7.76/7.73 2483 (all X (hBOOL(hAPP(int,bool,even_odd_even(int),X)) -> hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X),one_one(int))),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(int,int,hAPP(int,fun(int,int),div_div(int),X),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) # label(fact_2480_even__plus__one__div__two) # label(axiom) # label(non_clause). [assumption].
% 7.76/7.74 2484 (all N_1 all M_1 hAPP(code_code_numeral,product_prod(code_code_numeral,code_code_numeral),hAPP(code_code_numeral,fun(code_code_numeral,product_prod(code_code_numeral,code_code_numeral)),code_d418564891umeral,N_1),M_1) = hAPP(code_code_numeral,product_prod(code_code_numeral,code_code_numeral),hAPP(code_code_numeral,fun(code_code_numeral,product_prod(code_code_numeral,code_code_numeral)),product_Pair(code_code_numeral,code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),N_1),M_1)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),N_1),M_1))) # label(fact_2481_div__mod__code__numeral__def) # label(axiom) # label(non_clause). [assumption].
% 7.76/7.74 2485 (all Ba all Aa all Pa (hBOOL(hAPP(int,bool,zprime,Pa)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit1,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),Pa)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Aa),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),Pa),one_one(int)))) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Ba),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),wset,Aa),Pa))) -> hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),hAPP(int,int,hAPP(int,fun(int,int),inv,Pa),Ba)),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),wset,Aa),Pa)))))))) # label(fact_2482_wset__mem__inv__mem) # label(axiom) # label(non_clause). [assumption].
% 7.76/7.74 2486 (all Ba all Aa all Pa (hBOOL(hAPP(int,bool,zprime,Pa)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit1,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),Pa)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Aa),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),Pa),one_one(int)))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),Ba)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Ba),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),Pa),one_one(int)))) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),hAPP(int,int,hAPP(int,fun(int,int),inv,Pa),Ba)),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),wset,Aa),Pa))) -> hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Ba),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),wset,Aa),Pa)))))))))) # label(fact_2483_wset__inv__mem__mem) # label(axiom) # label(non_clause). [assumption].
% 7.76/7.74 2487 (all A_1 all P_4 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),P_4)) -> (hBOOL(hAPP(int,bool,zprime,P_4)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_1),zero_zero(int)),P_4)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,zero_zero(int)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A_1),hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),P_4),one_one(int))),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))),P_4)))))) # label(fact_2484_Euler__part2) # label(axiom) # label(non_clause). [assumption].
% 7.76/7.74 2488 (all M_1 hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,M_1),zero_zero(int)),M_1))) # label(fact_2485_zcong__id) # label(axiom) # label(non_clause). [assumption].
% 7.76/7.74 2489 (all Aa all Ba (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,Aa),Ba),zero_zero(int))) <-> Aa = Ba)) # label(fact_2486_IntPrimes_Ozcong__zero) # label(axiom) # label(non_clause). [assumption].
% 7.76/7.74 2490 (all Aa all Ba all M (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,Aa),Ba),M)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),Aa),M)),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),Ba),M)),M)))) # label(fact_2487_zcong__zmod) # label(axiom) # label(non_clause). [assumption].
% 7.76/7.74 2491 (all A_1 all B hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_1),B),one_one(int)))) # label(fact_2488_zcong__1) # label(axiom) # label(non_clause). [assumption].
% 7.76/7.74 2492 (all C all D all A_1 all B all M_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_1),B),M_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,C),D),M_1)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),C)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),D)),M_1))))) # label(fact_2489_zcong__zmult) # label(axiom) # label(non_clause). [assumption].
% 7.76/7.74 2493 (all K_4 all A_1 all B all M_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_1),B),M_1)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K_4),A_1)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K_4),B)),M_1)))) # label(fact_2490_zcong__scalar2) # label(axiom) # label(non_clause). [assumption].
% 7.76/7.74 2494 (all K_4 all A_1 all B all M_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_1),B),M_1)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),K_4)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),K_4)),M_1)))) # label(fact_2491_zcong__scalar) # label(axiom) # label(non_clause). [assumption].
% 7.76/7.74 2495 (all C_1 all D_1 all Aa all Ba all M (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,Aa),Ba),M)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,C_1),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),D_1),Aa)),M)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,C_1),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),D_1),Ba)),M))))) # label(fact_2492_zcong__zmult__prop2) # label(axiom) # label(non_clause). [assumption].
% 7.76/7.74 2496 (all C_1 all D_1 all Aa all Ba all M (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,Aa),Ba),M)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,C_1),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Aa),D_1)),M)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,C_1),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Ba),D_1)),M))))) # label(fact_2493_zcong__zmult__prop1) # label(axiom) # label(non_clause). [assumption].
% 7.76/7.74 2497 (all A_1 all M_1 all B hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),M_1)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),M_1)),M_1))) # label(fact_2494_zcong__zmult__self) # label(axiom) # label(non_clause). [assumption].
% 7.76/7.74 2498 (all C all D all A_1 all B all M_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_1),B),M_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,C),D),M_1)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A_1),C)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),B),D)),M_1))))) # label(fact_2495_zcong__zadd) # label(axiom) # label(non_clause). [assumption].
% 7.76/7.74 2499 (all C all A_1 all B all M_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_1),B),M_1)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A_1),C)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),B),C)),M_1)))) # label(fact_2496_zcong__shift) # label(axiom) # label(non_clause). [assumption].
% 7.76/7.74 2500 (all C all D all A_1 all B all M_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_1),B),M_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,C),D),M_1)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A_1),C)),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),B),D)),M_1))))) # label(fact_2497_zcong__zdiff) # label(axiom) # label(non_clause). [assumption].
% 7.76/7.74 2501 (all Aa all Ba all M (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,Aa),Ba),hAPP(int,int,uminus_uminus(int),M))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,Aa),Ba),M)))) # label(fact_2498_zcong__zminus) # label(axiom) # label(non_clause). [assumption].
% 7.76/7.74 2502 (all Z all X all Y all M_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,X),Y),M_1)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),X),Z)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),Y),Z)),M_1)))) # label(fact_2499_zcong__zpower) # label(axiom) # label(non_clause). [assumption].
% 7.76/7.74 2503 (all Aa all Ba all M (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,Aa),Ba),M)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,Ba),Aa),M)))) # label(fact_2500_zcong__sym) # label(axiom) # label(non_clause). [assumption].
% 7.76/7.74 2504 (all K_4 all M_1 hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,K_4),K_4),M_1))) # label(fact_2501_zcong__refl) # label(axiom) # label(non_clause). [assumption].
% 7.76/7.74 2505 (all D all C all A_1 all B all M_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_1),B),M_1)) -> (B = C -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,C),D),M_1)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_1),D),M_1)))))) # label(fact_2502_zcong__eq__trans) # label(axiom) # label(non_clause). [assumption].
% 7.76/7.74 2506 (all C all A_1 all B all M_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_1),B),M_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,B),C),M_1)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_1),C),M_1))))) # label(fact_2503_zcong__trans) # label(axiom) # label(non_clause). [assumption].
% 7.76/7.74 2507 (all B all M_1 all A_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_1),M_1)) -> (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),A_1)) -> -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_1),B),M_1))))))) # label(fact_2504_zcong__not) # label(axiom) # label(non_clause). [assumption].
% 7.76/7.74 2508 (all M_1 all X (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),X)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X),M_1)) -> -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,X),zero_zero(int)),M_1))))) # label(fact_2505_zcong__not__zero) # label(axiom) # label(non_clause). [assumption].
% 7.76/7.74 2509 (all M_1 all Y all X (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),X)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),Y)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),M_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,X),Y),M_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X),M_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Y),M_1)) -> X = Y))))))) # label(fact_2506_zcong__less__eq) # label(axiom) # label(non_clause). [assumption].
% 7.76/7.74 2510 (all Aa all Ba all M (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,Aa),Ba),M)) <-> (exists K_1 Ba = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Aa),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),M),K_1))))) # label(fact_2507_zcong__iff__lin) # label(axiom) # label(non_clause). [assumption].
% 7.76/7.74 2511 (all M_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(int),X),M_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,X),zero_zero(int)),M_1)) -> X = zero_zero(int))))) # label(fact_2508_Int2_Ozcong__zero) # label(axiom) # label(non_clause). [assumption].
% 7.76/7.74 2512 (all M_1 all A_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_1),M_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_1),zero_zero(int)),M_1)) -> A_1 = zero_zero(int))))) # label(fact_2509_zcong__zless__0) # label(axiom) # label(non_clause). [assumption].
% 7.76/7.74 2513 (all B all M_1 all A_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_1),M_1)) -> (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),B),M_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_1),B),M_1)) -> A_1 = B)))))) # label(fact_2510_zcong__zless__imp__eq) # label(axiom) # label(non_clause). [assumption].
% 7.76/7.74 2514 (all Aa all Ba all M (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),M)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,Aa),Ba),M)) <-> hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),Aa),M) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),Ba),M)))) # label(fact_2511_zcong__zmod__eq) # label(axiom) # label(non_clause). [assumption].
% 7.76/7.74 2515 (all Aa all Pa (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Aa),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),Pa),one_one(int)))),one_one(int)),Pa)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,Aa),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),Pa),one_one(int))),Pa)))) # label(fact_2512_inv__not__p__minus__1__aux) # label(axiom) # label(non_clause). [assumption].
% 7.76/7.74 2516 (all Z all X all Y all P_4 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),X),Y)),one_one(int)),P_4)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,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))),one_one(int)),P_4)))) # label(fact_2513_zcong__zpower__zmult) # label(axiom) # label(non_clause). [assumption].
% 7.76/7.74 2517 (all Pa all Aa (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),Aa)) -> hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Aa),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),wset,Aa),Pa))))) # label(fact_2514_wset__mem__mem) # label(axiom) # label(non_clause). [assumption].
% 7.76/7.74 2518 (all Y all X all P_4 (hBOOL(hAPP(int,bool,zprime,P_4)) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,X),zero_zero(int)),P_4)) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,Y),zero_zero(int)),P_4)) -> -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X),Y)),zero_zero(int)),P_4)))))) # label(fact_2515_zcong__zmult__prop3) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.74 2519 (all B all A_1 all P_4 (hBOOL(hAPP(int,bool,zprime,P_4)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A_1)) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_1),zero_zero(int)),P_4)) & -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,B),zero_zero(int)),P_4)) -> -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),B)),zero_zero(int)),P_4)))))) # label(fact_2516_zcong__zprime__prod__zero__contra) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.74 2520 (all B all A_1 all P_4 (hBOOL(hAPP(int,bool,zprime,P_4)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),B)),zero_zero(int)),P_4)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_1),zero_zero(int)),P_4)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,B),zero_zero(int)),P_4)))))) # label(fact_2517_zcong__zprime__prod__zero) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.74 2521 (all Ba all Pa all Aa (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),Aa)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Ba),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),wset,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),Aa),one_one(int))),Pa))) -> hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Ba),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),wset,Aa),Pa)))))) # label(fact_2518_wset__subset) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.74 2522 (all A_1 all P_4 (hBOOL(hAPP(int,bool,zprime,P_4)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),A_1)),one_one(int)),P_4)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_1),one_one(int)),P_4)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_1),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),P_4),one_one(int))),P_4)))))) # label(fact_2519_zcong__square) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.74 2523 (all A_1 all P_4 (hBOOL(hAPP(int,bool,zprime,P_4)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_1),P_4)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),A_1)),one_one(int)),P_4)) -> A_1 = one_one(int) | A_1 = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),P_4),one_one(int))))))) # label(fact_2520_zcong__square__zless) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.74 2524 (all Ba all Aa all Pa (hBOOL(hAPP(int,bool,zprime,Pa)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Aa),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),Pa),one_one(int)))) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Ba),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),wset,Aa),Pa))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),Ba)))))) # label(fact_2521_wset__g__1) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.74 2525 (all Ba all Aa all Pa (hBOOL(hAPP(int,bool,zprime,Pa)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Aa),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),Pa),one_one(int)))) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Ba),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),wset,Aa),Pa))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Ba),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),Pa),one_one(int)))))))) # label(fact_2522_wset__less) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.74 2526 (all A_1 all P_4 (hBOOL(hAPP(int,bool,zprime,P_4)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_1),P_4)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),hAPP(int,int,hAPP(int,fun(int,int),inv,P_4),A_1))),one_one(int)),P_4)))))) # label(fact_2523_inv__is__inv) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.74 2527 (all Ba all Pa all Aa (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),Aa)) -> (-hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Ba),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),wset,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),Aa),one_one(int))),Pa))) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Ba),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),wset,Aa),Pa))) -> Ba = Aa | Ba = hAPP(int,int,hAPP(int,fun(int,int),inv,Pa),Aa))))) # label(fact_2524_wset__mem__imp__or) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.74 2528 (all P_4 (hBOOL(hAPP(int,bool,zprime,P_4)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(int,int,zfact,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),P_4),one_one(int)))),hAPP(int,int,number_number_of(int),min)),P_4)))) # label(fact_2525_Wilson__Russ) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.74 2529 (all M_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),M_1)) -> -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,one_one(int)),hAPP(int,int,number_number_of(int),min)),M_1)))) # label(fact_2526_one__not__neg__one__mod__m) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.74 2530 (all X all P_4 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),P_4)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,X),hAPP(int,int,number_number_of(int),min)),P_4)) -> -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,X),one_one(int)),P_4))))) # label(fact_2527_zcong__neg__1__impl__ne__1) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.74 2531 (all J_2 all K_4 all M_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),M_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,number_number_of(int),min)),J_2)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,number_number_of(int),min)),K_4)),M_1)) -> hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,number_number_of(int),min)),J_2) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,number_number_of(int),min)),K_4)))) # label(fact_2528_neg__one__power__eq__mod__m) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.74 2532 (all Ba all Aa all Pa (hBOOL(hAPP(int,bool,zprime,Pa)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Aa),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),Pa),one_one(int)))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),Ba)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Ba),Aa)) -> hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Ba),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),wset,Aa),Pa)))))))) # label(fact_2529_wset__mem) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.74 2533 (all Pa (hBOOL(hAPP(int,bool,zprime,Pa)) -> hAPP(int,fun(int,bool),d22set,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),Pa),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) = hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),wset,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),Pa),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),Pa))) # label(fact_2530_d22set__eq__wset) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.74 2534 (all A_1 all P_4 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),P_4)) -> (hBOOL(hAPP(int,bool,zprime,P_4)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(int,int,hAPP(int,fun(int,int),legendre,A_1),P_4)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A_1),hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),P_4),one_one(int))),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))),P_4))))) # label(fact_2531_Euler__Criterion) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.74 2535 (all A_1 all P_4 (hBOOL(hAPP(int,bool,zprime,P_4)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),P_4)) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_1),zero_zero(int)),P_4)) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),quadRes,P_4),A_1)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(int,int,zfact,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),P_4),one_one(int)))),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A_1),hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),P_4),one_one(int))),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))),P_4))))))) # label(fact_2532_zfact__prop) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.74 2536 (all X all P_4 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),P_4)) -> (hBOOL(hAPP(int,bool,zprime,P_4)) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,X),zero_zero(int)),P_4)) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),quadRes,P_4),X)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),X),hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),P_4),one_one(int))),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))),hAPP(int,int,number_number_of(int),min)),P_4))))))) # label(fact_2533_Euler__part1) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.74 2537 (all X all P_4 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),P_4)) -> (hBOOL(hAPP(int,bool,zprime,P_4)) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,X),zero_zero(int)),P_4)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),quadRes,P_4),X)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),X),hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),P_4),one_one(int))),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))),one_one(int)),P_4))))))) # label(fact_2534_Euler__part3) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.74 2538 (all A_1 all P_4 ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_1),zero_zero(int)),P_4)) -> hAPP(int,int,hAPP(int,fun(int,int),legendre,A_1),P_4) = zero_zero(int)) & (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_1),zero_zero(int)),P_4)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),quadRes,P_4),A_1)) -> hAPP(int,int,hAPP(int,fun(int,int),legendre,A_1),P_4) = one_one(int)) & (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),quadRes,P_4),A_1)) -> hAPP(int,int,hAPP(int,fun(int,int),legendre,A_1),P_4) = hAPP(int,int,number_number_of(int),min))))) # label(fact_2535_Legendre__def) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.74 2539 (all M all X_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),quadRes,M),X_1)) <-> (exists Y_2 hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),Y_2),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),X_1),M))))) # label(fact_2536_QuadRes__def) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.74 2540 (all A_1 all M_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),M_1)) -> (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,hAPP(int,fun(int,bool),ord_less(int),X_2),M_1)) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_1),X_2),M_1)) & (all Y_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Y_2)) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Y_2),M_1)) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_1),Y_2),M_1)) -> Y_2 = X_2)))))) # label(fact_2537_zcong__zless__unique) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.74 2541 (all N_1 all I_1 ((I_1 = zero_zero(code_code_numeral) -> hAPP(nat,nat,hAPP(code_code_numeral,fun(nat,nat),code_nat_of_aux,I_1),N_1) = N_1) & (I_1 != zero_zero(code_code_numeral) -> hAPP(nat,nat,hAPP(code_code_numeral,fun(nat,nat),code_nat_of_aux,I_1),N_1) = hAPP(nat,nat,hAPP(code_code_numeral,fun(nat,nat),code_nat_of_aux,hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),minus_minus(code_code_numeral),I_1),one_one(code_code_numeral))),hAPP(nat,nat,suc,N_1))))) # label(fact_2538_nat__of__aux__code) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.74 2542 (all X all M_1 hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,X),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),X),M_1)),M_1))) # label(fact_2539_mod__mod__is__mod) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.74 2543 (all X all M_1 all Y (hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),X),M_1) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),Y),M_1) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,X),Y),M_1)))) # label(fact_2540_Residues_Oaux) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.74 2544 (all J_2 all A_1 all P_4 (hBOOL(hAPP(int,bool,zprime,P_4)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),P_4)) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_1),zero_zero(int)),P_4)) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,J_2),zero_zero(int)),P_4)) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),quadRes,P_4),A_1)) -> -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,J_2),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),hAPP(int,int,hAPP(int,fun(int,int),multInv,P_4),J_2))),P_4)))))))) # label(fact_2541_MultInvPair__distinct) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.74 2545 (all X all P_4 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),P_4)) -> (hBOOL(hAPP(int,bool,zprime,P_4)) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,X),zero_zero(int)),P_4)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),multInv,P_4),X)),X)),one_one(int)),P_4)))))) # label(fact_2542_MultInv__prop2a) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.74 2546 (all X all P_4 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),P_4)) -> (hBOOL(hAPP(int,bool,zprime,P_4)) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,X),zero_zero(int)),P_4)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X),hAPP(int,int,hAPP(int,fun(int,int),multInv,P_4),X))),one_one(int)),P_4)))))) # label(fact_2543_MultInv__prop2) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.74 2547 (all P_4 (hBOOL(hAPP(int,bool,zprime,P_4)) -> hAPP(int,nat,phi,P_4) = hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),P_4),one_one(int))))) # label(fact_2544_phi__prime) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.74 2548 (all J_2 all A_1 all P_4 all K_4 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,J_2),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),hAPP(int,int,hAPP(int,fun(int,int),multInv,P_4),K_4))),P_4)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),J_2),K_4)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),hAPP(int,int,hAPP(int,fun(int,int),multInv,P_4),K_4))),K_4)),P_4)))) # label(fact_2545_aux______1) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.74 2549 (all J_2 all K_4 all A_1 all P_4 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),J_2),K_4)),A_1),P_4)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),multInv,P_4),J_2)),J_2)),K_4)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),multInv,P_4),J_2)),A_1)),P_4)))) # label(fact_2546_aux______3) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.74 2550 (all X all Y all P_4 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),P_4)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,X),Y),P_4)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(int,int,hAPP(int,fun(int,int),multInv,P_4),X)),hAPP(int,int,hAPP(int,fun(int,int),multInv,P_4),Y)),P_4))))) # label(fact_2547_MultInv__prop1) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.74 2551 (all A_1 all J_2 all K_4 all P_4 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),P_4)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,J_2),K_4),P_4)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),hAPP(int,int,hAPP(int,fun(int,int),multInv,P_4),J_2))),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),hAPP(int,int,hAPP(int,fun(int,int),multInv,P_4),K_4))),P_4))))) # label(fact_2548_MultInv__zcong__prop1) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.74 2552 (all P_4 all X hAPP(int,int,hAPP(int,fun(int,int),multInv,P_4),X) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),X),hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),P_4),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))) # label(fact_2549_MultInv__def) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.74 2553 (all Y all X all P_4 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),P_4)) -> (hBOOL(hAPP(int,bool,zprime,P_4)) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,X),zero_zero(int)),P_4)) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,Y),zero_zero(int)),P_4)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(int,int,hAPP(int,fun(int,int),multInv,P_4),X)),hAPP(int,int,hAPP(int,fun(int,int),multInv,P_4),Y)),P_4)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,X),Y),P_4)))))))) # label(fact_2550_MultInv__prop5) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.74 2554 (all X all P_4 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),P_4)) -> (hBOOL(hAPP(int,bool,zprime,P_4)) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,X),zero_zero(int)),P_4)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(int,int,hAPP(int,fun(int,int),multInv,P_4),hAPP(int,int,hAPP(int,fun(int,int),multInv,P_4),X))),X),P_4)))))) # label(fact_2551_MultInv__prop4) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.74 2555 (all X all P_4 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),P_4)) -> (hBOOL(hAPP(int,bool,zprime,P_4)) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,X),zero_zero(int)),P_4)) -> -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(int,int,hAPP(int,fun(int,int),multInv,P_4),X)),zero_zero(int)),P_4)))))) # label(fact_2552_MultInv__prop3) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.74 2556 (all X all P_4 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),P_4)) -> (hBOOL(hAPP(int,bool,zprime,P_4)) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,X),zero_zero(int)),P_4)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(int,int,hAPP(int,fun(int,int),multInv,P_4),hAPP(int,int,hAPP(int,fun(int,int),multInv,P_4),X))),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X),hAPP(int,int,hAPP(int,fun(int,int),multInv,P_4),X))),hAPP(int,int,hAPP(int,fun(int,int),multInv,P_4),hAPP(int,int,hAPP(int,fun(int,int),multInv,P_4),X)))),P_4)))))) # label(fact_2553_Int2_Oaux____1) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.74 2557 (all X all P_4 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),P_4)) -> (hBOOL(hAPP(int,bool,zprime,P_4)) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,X),zero_zero(int)),P_4)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X),hAPP(int,int,hAPP(int,fun(int,int),multInv,P_4),X))),hAPP(int,int,hAPP(int,fun(int,int),multInv,P_4),hAPP(int,int,hAPP(int,fun(int,int),multInv,P_4),X)))),X),P_4)))))) # label(fact_2554_Int2_Oaux____2) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.74 2558 (all J_2 all K_4 all A_1 all P_4 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),P_4)) -> (hBOOL(hAPP(int,bool,zprime,P_4)) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_1),zero_zero(int)),P_4)) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,K_4),zero_zero(int)),P_4)) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,J_2),zero_zero(int)),P_4)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),hAPP(int,int,hAPP(int,fun(int,int),multInv,P_4),J_2))),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),hAPP(int,int,hAPP(int,fun(int,int),multInv,P_4),K_4))),P_4)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,J_2),K_4),P_4))))))))) # label(fact_2555_MultInv__zcong__prop3) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.74 2559 (all A_1 all J_2 all K_4 all P_4 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),P_4)) -> (hBOOL(hAPP(int,bool,zprime,P_4)) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,K_4),zero_zero(int)),P_4)) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,J_2),zero_zero(int)),P_4)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,J_2),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),hAPP(int,int,hAPP(int,fun(int,int),multInv,P_4),K_4))),P_4)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,K_4),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),hAPP(int,int,hAPP(int,fun(int,int),multInv,P_4),J_2))),P_4)))))))) # label(fact_2556_MultInv__zcong__prop2) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.74 2560 (all J_2 all A_1 all K_4 all P_4 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),P_4)) -> (hBOOL(hAPP(int,bool,zprime,P_4)) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,K_4),zero_zero(int)),P_4)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),J_2),K_4)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),hAPP(int,int,hAPP(int,fun(int,int),multInv,P_4),K_4))),K_4)),P_4)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),J_2),K_4)),A_1),P_4))))))) # label(fact_2557_aux______2) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.74 2561 (all K_4 all A_1 all J_2 all P_4 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),P_4)) -> (hBOOL(hAPP(int,bool,zprime,P_4)) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,J_2),zero_zero(int)),P_4)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),multInv,P_4),J_2)),J_2)),K_4)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),multInv,P_4),J_2)),A_1)),P_4)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,K_4),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),hAPP(int,int,hAPP(int,fun(int,int),multInv,P_4),J_2))),P_4))))))) # label(fact_2558_aux______4) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.74 2562 (all Pa hAPP(int,fun(int,bool),sr,Pa) = hAPP(fun(int,bool),fun(int,bool),collect(int),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),combs(int,bool,bool),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(int,fun(int,bool),ord_less_eq(int),zero_zero(int)))),hAPP(int,fun(int,bool),hAPP(fun(int,fun(int,bool)),fun(int,fun(int,bool)),combc(int,int,bool),ord_less(int)),Pa)))) # label(fact_2559_SR__def) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.74 2563 (all X all Y all M_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),M_1)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),standardRes,M_1),X)),hAPP(int,int,hAPP(int,fun(int,int),standardRes,M_1),Y))),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X),Y)),M_1)))) # label(fact_2560_StandardRes__prop4) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.74 2564 (all X_a (semiring_1(X_a) -> (all X (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X)) -> hAPP(nat,X_a,semiring_1_of_nat(X_a),hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),X))) = 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),hAPP(int,nat,nat_1,X))),hAPP(nat,X_a,semiring_1_of_nat(X_a),hAPP(int,nat,nat_1,X))))))) # label(fact_2561_of__nat__double) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.74 2565 (all A_1 all B hAPP(complex,complex,inverse_inverse(complex),hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,A_1),B)) = hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A_1),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,uminus_uminus(real),B)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))) # label(fact_2562_complex__inverse) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.74 2566 (all N_1 all M_1 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_1)))) # label(fact_2563_negative__zle) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.74 2567 (all N_1 all M_1 hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,uminus_uminus(int),hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,N_1)))),hAPP(nat,int,semiring_1_of_nat(int),M_1)))) # label(fact_2564_negative__zless) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.74 2568 (all Aa all Ba (hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,Aa),Ba) = zero_zero(complex) <-> Aa = zero_zero(real) & Ba = zero_zero(real))) # label(fact_2566_Complex__eq__0) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.74 2569 (all X_a (number_semiring(X_a) -> (all N_1 hAPP(int,X_a,number_number_of(X_a),hAPP(nat,int,semiring_1_of_nat(int),N_1)) = hAPP(nat,X_a,semiring_1_of_nat(X_a),N_1)))) # label(fact_2567_number__of__int) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.74 2570 (all X all Y hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),X),Y) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),X),hAPP(complex,complex,inverse_inverse(complex),Y))) # label(fact_2568_complex__divide__def) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.74 2571 (all M_1 hAPP(int,int,abs_abs(int),hAPP(nat,int,semiring_1_of_nat(int),M_1)) = hAPP(nat,int,semiring_1_of_nat(int),M_1)) # label(fact_2569_abs__int__eq) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.74 2572 (all X_a (linordered_idom(X_a) -> (all N_1 hAPP(X_a,X_a,abs_abs(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),N_1)) = hAPP(nat,X_a,semiring_1_of_nat(X_a),N_1)))) # label(fact_2572_abs__of__nat) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.74 2573 (all N_1 hAPP(int,nat,nat_1,hAPP(nat,int,semiring_1_of_nat(int),N_1)) = N_1) # label(fact_2573_nat__int) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.74 2574 (all X_a (archim1727834104eiling(X_a) -> (all N_1 hAPP(X_a,int,archimedean_ceiling(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),N_1)) = hAPP(nat,int,semiring_1_of_nat(int),N_1)))) # label(fact_2574_ceiling__of__nat) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.74 2575 (all X_a (semiring_char_0(X_a) -> (all M all N (hAPP(nat,X_a,semiring_1_of_nat(X_a),M) = hAPP(nat,X_a,semiring_1_of_nat(X_a),N) <-> M = N)))) # label(fact_2575_of__nat__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.74 2576 (all X_a (archim1727834104eiling(X_a) -> (all N_1 hAPP(X_a,int,archim2085082626_floor(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),N_1)) = hAPP(nat,int,semiring_1_of_nat(int),N_1)))) # label(fact_2576_floor__of__nat) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.74 2577 (all A_1 all B all C all D hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,A_1),B)),hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,C),D)) = hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A_1),C)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),B),D))) # label(fact_2577_complex__add) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.74 2578 (all Real1 all Real2 all Real1_2 all Real2_2 (hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,Real1),Real2) = hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,Real1_2),Real2_2) <-> Real1 = Real1_2 & Real2 = Real2_2)) # label(fact_2578_complex_Oinject) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.74 2579 (all A_1 all B hAPP(complex,complex,uminus_uminus(complex),hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,A_1),B)) = hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,hAPP(real,real,uminus_uminus(real),A_1)),hAPP(real,real,uminus_uminus(real),B))) # label(fact_2579_complex__minus) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.74 2580 (all X_a (ring_1(X_a) -> (all N hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),N)),ring_1_Ints(X_a)))))) # label(fact_2580_Ints__of__nat) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.74 2581 (all N_1 -hBOOL(hAPP(int,bool,nat_neg,hAPP(nat,int,semiring_1_of_nat(int),N_1)))) # label(fact_2581_not__neg__int) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.74 2582 (all A_1 all B all C all D hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,A_1),B)),hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,C),D)) = hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A_1),C)),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),B),D))) # label(fact_2582_complex__diff) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.74 2583 (all X_1 all Pa (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),hAPP(int,fun(int,bool),sr,Pa))) -> hAPP(int,int,hAPP(int,fun(int,int),standardRes,Pa),X_1) = X_1)) # label(fact_2583_StandardRes__SR__prop) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.74 2584 (all X all M_1 hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,X),hAPP(int,int,hAPP(int,fun(int,int),standardRes,M_1),X)),M_1))) # label(fact_2584_StandardRes__prop1) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.74 2585 (all M_1 all X hAPP(int,int,hAPP(int,fun(int,int),standardRes,M_1),X) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),X),M_1)) # label(fact_2585_StandardRes__def) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.74 2586 (all X_a (linordered_semidom(X_a) -> (all M_1 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),hAPP(nat,X_a,semiring_1_of_nat(X_a),M_1)))))) # label(fact_2586_zero__le__imp__of__nat) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.74 2587 (all X_a (linordered_semidom(X_a) -> (all N_1 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),hAPP(nat,X_a,semiring_1_of_nat(X_a),N_1)))))) # label(fact_2587_of__nat__0__le__iff) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.74 2588 (all X_a (linordered_semidom(X_a) -> (all M_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_1)),zero_zero(X_a)))))) # label(fact_2588_of__nat__less__0__iff) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.74 2589 (all X_a (semiring_1(X_a) -> hAPP(nat,X_a,semiring_1_of_nat(X_a),zero_zero(nat)) = zero_zero(X_a))) # label(fact_2589_of__nat__0) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.74 2590 (all X_a (linordered_semidom(X_a) -> (all M all N (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))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N)))))) # label(fact_2590_of__nat__less__iff) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.74 2591 (all X_a (linordered_semidom(X_a) -> (all M_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),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_1)),hAPP(nat,X_a,semiring_1_of_nat(X_a),N_1))))))) # label(fact_2591_less__imp__of__nat__less) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.74 2592 (all X_a (linordered_semidom(X_a) -> (all M_1 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_1)),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_1),N_1)))))) # label(fact_2592_of__nat__less__imp__less) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.74 2593 (all X_a (linordered_semidom(X_a) -> (all M all N (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),M)),hAPP(nat,X_a,semiring_1_of_nat(X_a),N))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N)))))) # label(fact_2593_of__nat__le__iff) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.74 2594 (all X_a (semiring_1(X_a) -> (all M_1 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_1),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_1)),hAPP(nat,X_a,semiring_1_of_nat(X_a),N_1))))) # label(fact_2594_of__nat__add) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.74 2595 (all X_a (semiring_1(X_a) -> (all M_1 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_1),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_1)),hAPP(nat,X_a,semiring_1_of_nat(X_a),N_1))))) # label(fact_2595_of__nat__mult) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.74 2596 (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_2596_of__nat__1) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.74 2597 (all X_a (semiring_char_0(X_a) -> (all N_1 hAPP(nat,X_a,semiring_1_of_nat(X_a),hAPP(nat,nat,fact_fact(nat),N_1)) != zero_zero(X_a)))) # label(fact_2597_of__nat__fact__not__zero) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.74 2598 (all N (hAPP(nat,int,semiring_1_of_nat(int),N) = zero_zero(int) <-> N = zero_zero(nat))) # label(fact_2598_int__eq__0__conv) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.74 2599 (all X_a (semiring_1(X_a) -> (all M_1 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_1),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_1)),N_1)))) # label(fact_2601_of__nat__power) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.74 2600 (all K_4 -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,semiring_1_of_nat(int),K_4)),zero_zero(int)))) # label(fact_2602_int__less__0__conv) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.74 2601 (all N_1 hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(nat,int,semiring_1_of_nat(int),N_1)))) # label(fact_2603_zero__zle__int) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.74 2602 (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_2604_Nat__Transfer_Otransfer__nat__int__function__closures_I9_J) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.74 2603 (all P_1 ((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,P_1,X_2)))) <-> (exists X_2 hBOOL(hAPP(int,bool,P_1,hAPP(nat,int,semiring_1_of_nat(int),X_2)))))) # label(fact_2605_transfer__int__nat__quantifiers_I2_J) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.74 2604 (all P_1 ((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,P_1,X_2)))) <-> (all X_2 hBOOL(hAPP(int,bool,P_1,hAPP(nat,int,semiring_1_of_nat(int),X_2)))))) # label(fact_2606_transfer__int__nat__quantifiers_I1_J) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.74 2605 (all M all N (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,semiring_1_of_nat(int),M)),hAPP(nat,int,semiring_1_of_nat(int),N))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N)))) # label(fact_2607_zless__int) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.74 2606 (all X_1 all Y_1 (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_1))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X_1),Y_1)))) # label(fact_2608_Nat__Transfer_Otransfer__int__nat__relations_I2_J) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.74 2607 (all M all N (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,semiring_1_of_nat(int),M)),hAPP(nat,int,semiring_1_of_nat(int),N))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N)))) # label(fact_2609_zle__int) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.74 2608 (all X_1 all Y_1 (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_1))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X_1),Y_1)))) # label(fact_2610_Nat__Transfer_Otransfer__int__nat__relations_I3_J) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.74 2609 (all M_1 all N_1 hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(nat,int,semiring_1_of_nat(int),M_1)),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_1),N_1))) # label(fact_2611_zmult__int) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.74 2610 (all M_1 all N_1 hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),N_1)) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(nat,int,semiring_1_of_nat(int),M_1)),hAPP(nat,int,semiring_1_of_nat(int),N_1))) # label(fact_2612_int__mult) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.74 2611 (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_2613_Nat__Transfer_Otransfer__int__nat__functions_I2_J) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.74 2612 (all W_1 all Z_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),W_1),Z_1)) <-> (exists N_2 Z_1 = 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_2614_zle__iff__zadd) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.74 2613 (all M_1 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_1)),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_1),N_1))),Z)) # label(fact_2615_zadd__int__left) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.74 2614 (all M_1 all N_1 hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,semiring_1_of_nat(int),M_1)),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_1),N_1))) # label(fact_2616_zadd__int) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.74 2615 (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_2617_Nat__Transfer_Otransfer__int__nat__functions_I1_J) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.74 2616 (all N all M (hAPP(int,int,uminus_uminus(int),hAPP(nat,int,semiring_1_of_nat(int),N)) = hAPP(nat,int,semiring_1_of_nat(int),M) <-> N = zero_zero(nat) & M = zero_zero(nat))) # label(fact_2620_negative__eq__positive) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.74 2617 (all N_1 all M_1 -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_1))))) # label(fact_2621_not__int__zless__negative) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.74 2618 (all Aa all Ba all W_1 (hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,Aa),Ba) = hAPP(int,complex,number_number_of(complex),W_1) <-> Aa = hAPP(int,real,number_number_of(real),W_1) & Ba = zero_zero(real))) # label(fact_2622_Complex__eq__number__of) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.74 2619 (all Aa all Ba (hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,Aa),Ba) = one_one(complex) <-> Aa = one_one(real) & Ba = zero_zero(real))) # label(fact_2623_Complex__eq__1) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.74 2620 (all N_1 hAPP(int,real,real_1(int),hAPP(nat,int,semiring_1_of_nat(int),N_1)) = hAPP(nat,real,real_1(nat),N_1)) # label(fact_2625_real__of__int__of__nat__eq) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.74 2621 (all X all Y hAPP(int,int,hAPP(int,fun(int,int),div_div(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),div_div(nat),X),Y))) # label(fact_2626_Divides_Otransfer__int__nat__functions_I1_J) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.74 2622 (all A_1 all B hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),A_1),B)) = hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(nat,int,semiring_1_of_nat(int),A_1)),hAPP(nat,int,semiring_1_of_nat(int),B))) # label(fact_2627_zdiv__int) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.74 2623 (all X all Y hAPP(int,int,hAPP(int,fun(int,int),div_mod(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),div_mod(nat),X),Y))) # label(fact_2628_Divides_Otransfer__int__nat__functions_I2_J) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.74 2624 (all A_1 all B hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),A_1),B)) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(nat,int,semiring_1_of_nat(int),A_1)),hAPP(nat,int,semiring_1_of_nat(int),B))) # label(fact_2629_zmod__int) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.74 2625 (all M_1 all N_1 hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(nat,int,semiring_1_of_nat(int),M_1)),N_1) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),M_1),N_1))) # label(fact_2630_zpower__int) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.74 2626 (all M_1 all N_1 hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),M_1),N_1)) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(nat,int,semiring_1_of_nat(int),M_1)),N_1)) # label(fact_2631_int__power) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.74 2627 (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_2632_Nat__Transfer_Otransfer__int__nat__functions_I4_J) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.74 2628 (all Z (-hBOOL(hAPP(int,bool,nat_neg,Z)) -> hAPP(nat,int,semiring_1_of_nat(int),hAPP(int,nat,nat_1,Z)) = Z)) # label(fact_2633_not__neg__nat) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.74 2629 (all N_1 hAPP(real,int,archim2085082626_floor(real),hAPP(nat,real,real_1(nat),N_1)) = hAPP(nat,int,semiring_1_of_nat(int),N_1)) # label(fact_2634_floor__real__of__nat) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.74 2630 (all X_1 (hBOOL(hAPP(int,bool,even_odd_even(int),hAPP(nat,int,semiring_1_of_nat(int),X_1))) <-> hBOOL(hAPP(nat,bool,even_odd_even(nat),X_1)))) # label(fact_2635_Parity_Otransfer__int__nat__relations) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.74 2631 (all X_1 (hBOOL(hAPP(nat,bool,even_odd_even(nat),X_1)) <-> hBOOL(hAPP(int,bool,even_odd_even(int),hAPP(nat,int,semiring_1_of_nat(int),X_1))))) # label(fact_2636_even__nat__def) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.74 2632 (all N_1 hAPP(real,int,archimedean_ceiling(real),hAPP(nat,real,real_1(nat),N_1)) = hAPP(nat,int,semiring_1_of_nat(int),N_1)) # label(fact_2637_ceiling__real__of__nat) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.74 2633 (all X all Y hAPP(int,int,hAPP(int,fun(int,int),nat_tsub,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),minus_minus(nat),X),Y))) # label(fact_2638_Nat__Transfer_Otransfer__int__nat__functions_I3_J) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.74 2634 (all X_a (semiring_1(X_a) -> (all M_1 hAPP(nat,X_a,semiring_1_of_nat(X_a),hAPP(nat,nat,suc,M_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),one_one(X_a)),hAPP(nat,X_a,semiring_1_of_nat(X_a),M_1))))) # label(fact_2639_of__nat__Suc) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.74 2635 (all X all P_4 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),P_4)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),standardRes,P_4),X)),P_4)))) # label(fact_2640_StandardRes__ubound) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.74 2636 (all X_a (linordered_semidom(X_a) -> (all N_1 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),hAPP(nat,X_a,semiring_1_of_nat(X_a),hAPP(nat,nat,fact_fact(nat),N_1))))))) # label(fact_2641_of__nat__fact__ge__zero) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.74 2637 (all X_a (linordered_semidom(X_a) -> (all N_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,semiring_1_of_nat(X_a),hAPP(nat,nat,fact_fact(nat),N_1))))))) # label(fact_2642_of__nat__fact__gt__zero) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.74 2638 (all X_a (ring_1(X_a) -> (all N_1 all M_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_1),M_1)) -> hAPP(nat,X_a,semiring_1_of_nat(X_a),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),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_1)),hAPP(nat,X_a,semiring_1_of_nat(X_a),N_1)))))) # label(fact_2643_of__nat__diff) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.74 2639 (all X_1 all Pa (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,X_1),zero_zero(int)),Pa)) <-> hAPP(int,int,hAPP(int,fun(int,int),standardRes,Pa),X_1) != zero_zero(int))) # label(fact_2644_StandardRes__prop3) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.74 2640 (all M all X_1 (hAPP(int,int,hAPP(int,fun(int,int),standardRes,M),X_1) = zero_zero(int) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,X_1),zero_zero(int)),M)))) # label(fact_2645_StandardRes__eq__zcong) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.74 2641 (all N (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,semiring_1_of_nat(int),N)),zero_zero(int))) <-> N = zero_zero(nat))) # label(fact_2646_int__le__0__conv) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.74 2642 (all W_1 all Z_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_1),Z_1)) <-> (exists N_2 Z_1 = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),W_1),hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,N_2)))))) # label(fact_2648_zless__iff__Suc__zadd) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.74 2643 (all M_1 hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,M_1)) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),M_1))) # label(fact_2649_int__Suc) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.74 2644 (all Z (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Z)) -> hAPP(nat,int,semiring_1_of_nat(int),hAPP(int,nat,nat_1,Z)) = Z)) # label(fact_2650_nat__0__le) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.74 2645 (all M all Z_1 (hAPP(nat,int,semiring_1_of_nat(int),M) = Z_1 <-> M = hAPP(int,nat,nat_1,Z_1) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Z_1)))) # label(fact_2651_int__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.74 2646 (all Z ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Z)) -> hAPP(nat,int,semiring_1_of_nat(int),hAPP(int,nat,nat_1,Z)) = Z) & (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Z)) -> hAPP(nat,int,semiring_1_of_nat(int),hAPP(int,nat,nat_1,Z)) = zero_zero(int)))) # label(fact_2652_int__nat__eq) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.74 2647 (all M all Z_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),hAPP(int,nat,nat_1,Z_1))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,semiring_1_of_nat(int),M)),Z_1)))) # label(fact_2653_zless__nat__eq__int__zless) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.74 2648 (all N all M (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,semiring_1_of_nat(int),N)),hAPP(int,int,uminus_uminus(int),hAPP(nat,int,semiring_1_of_nat(int),M)))) <-> N = zero_zero(nat) & M = zero_zero(nat))) # label(fact_2654_int__zle__neg) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.74 2649 (all N_1 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))),zero_zero(int)))) # label(fact_2655_negative__zle__0) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.74 2650 (all N_1 hAPP(int,nat,nat_1,hAPP(int,int,uminus_uminus(int),hAPP(nat,int,semiring_1_of_nat(int),N_1))) = zero_zero(nat)) # label(fact_2656_nat__zminus__int) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.74 2651 (all N_1 all M_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_1),M_1)) -> hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(nat,int,semiring_1_of_nat(int),M_1)),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_1),N_1)))) # label(fact_2657_zdiff__int) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.74 2652 (all A_1 all B all C all D hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,A_1),B)),hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,C),D)) = hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A_1),C)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),D))),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A_1),D)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),C)))) # label(fact_2658_complex__mult) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.74 2653 (all N_1 hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,uminus_uminus(int),hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,N_1)))))) # label(fact_2659_neg__zminus__int) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.74 2654 (all X_a (linordered_semidom(X_a) -> (all N (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(nat,X_a,semiring_1_of_nat(X_a),N))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)))))) # label(fact_2660_of__nat__0__less__iff) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.74 2655 (all X_a (linordered_field(X_a) -> (all N_1 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),hAPP(X_a,X_a,inverse_inverse(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),hAPP(nat,nat,fact_fact(nat),N_1)))))))) # label(fact_2661_inv__of__nat__fact__ge__zero) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.74 2656 (all X_a (linordered_field(X_a) -> (all N_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,inverse_inverse(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),hAPP(nat,nat,fact_fact(nat),N_1)))))))) # label(fact_2662_inv__of__nat__fact__gt__zero) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.74 2657 (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_2663_zero__less__int__conv) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.74 2658 (all K_4 all I_1 all J_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),I_1),J_2)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K_4)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(nat,int,semiring_1_of_nat(int),K_4)),I_1)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(nat,int,semiring_1_of_nat(int),K_4)),J_2)))))) # label(fact_2664_zmult__zless__mono2__lemma) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.74 2659 (all P_1 all I (hBOOL(hAPP(nat,bool,P_1,hAPP(int,nat,nat_1,I))) <-> (all N_2 (I = hAPP(nat,int,semiring_1_of_nat(int),N_2) -> hBOOL(hAPP(nat,bool,P_1,N_2)))) & (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),I),zero_zero(int))) -> hBOOL(hAPP(nat,bool,P_1,zero_zero(nat)))))) # label(fact_2666_split__nat) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.75 2660 (all W_1 all M (hAPP(int,nat,nat_1,W_1) = M <-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),W_1)) -> W_1 = hAPP(nat,int,semiring_1_of_nat(int),M)) & (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),W_1)) -> M = zero_zero(nat)))) # label(fact_2667_nat__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.75 2661 (all M all W_1 (M = hAPP(int,nat,nat_1,W_1) <-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),W_1)) -> W_1 = hAPP(nat,int,semiring_1_of_nat(int),M)) & (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),W_1)) -> M = zero_zero(nat)))) # label(fact_2668_nat__eq__iff2) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.75 2662 (all N_1 hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,uminus_uminus(int),hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,N_1)))),zero_zero(int)))) # label(fact_2669_negative__zless__0) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.75 2663 (all N_1 -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,uminus_uminus(int),hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,N_1)))))) # label(fact_2670_not__zle__0__negative) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.75 2664 (all M all V_1 (hAPP(nat,int,semiring_1_of_nat(int),M) = hAPP(int,int,number_number_of(int),V_1) <-> M = hAPP(int,nat,nat_1,hAPP(int,int,number_number_of(int),V_1)) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),V_1))))) # label(fact_2671_int__eq__iff__number__of) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.75 2665 (all V ((hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V))) -> hAPP(nat,int,semiring_1_of_nat(int),hAPP(int,nat,number_number_of(nat),V)) = zero_zero(int)) & (-hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V))) -> hAPP(nat,int,semiring_1_of_nat(int),hAPP(int,nat,number_number_of(nat),V)) = hAPP(int,int,number_number_of(int),V)))) # label(fact_2672_int__nat__number__of) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.75 2666 (all X all P_4 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),P_4)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),standardRes,P_4),X))))) # label(fact_2673_StandardRes__lbound) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.75 2667 (all X1_2 all X2_2 all M (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),M)) -> (hAPP(int,int,hAPP(int,fun(int,int),standardRes,M),X1_2) = hAPP(int,int,hAPP(int,fun(int,int),standardRes,M),X2_2) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,X1_2),X2_2),M))))) # label(fact_2674_StandardRes__prop2) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.75 2668 (all N_1 hAPP(real,int,archim2085082626_floor(real),hAPP(real,real,uminus_uminus(real),hAPP(nat,real,real_1(nat),N_1))) = hAPP(int,int,uminus_uminus(int),hAPP(nat,int,semiring_1_of_nat(int),N_1))) # label(fact_2675_floor__minus__real__of__nat) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.75 2669 (all X_a (number_ring(X_a) -> (all V ((hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V))) -> hAPP(nat,X_a,semiring_1_of_nat(X_a),hAPP(int,nat,number_number_of(nat),V)) = zero_zero(X_a)) & (-hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V))) -> hAPP(nat,X_a,semiring_1_of_nat(X_a),hAPP(int,nat,number_number_of(nat),V)) = hAPP(int,X_a,number_number_of(X_a),V)))))) # label(fact_2676_of__nat__number__of__eq) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.75 2670 (all M all W_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),W_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(int,nat,nat_1,W_1)),M)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_1),hAPP(nat,int,semiring_1_of_nat(int),M)))))) # label(fact_2678_nat__less__iff) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.75 2671 (all P_1 all X_1 all Y_1 (hBOOL(hAPP(int,bool,P_1,hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X_1),Y_1)))) <-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Y_1),X_1)) -> hBOOL(hAPP(int,bool,P_1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(nat,int,semiring_1_of_nat(int),X_1)),hAPP(nat,int,semiring_1_of_nat(int),Y_1))))) & (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X_1),Y_1)) -> hBOOL(hAPP(int,bool,P_1,zero_zero(int)))))) # label(fact_2679_zdiff__int__split) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.75 2672 (all X_a (number_ring(X_a) & linordered_idom(X_a) -> (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),N_1)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),N_1)))))) # label(fact_2680_of__nat__less__two__power) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.75 2673 (all X_a (number_ring(X_a) -> (all V ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),V))) -> hAPP(nat,X_a,semiring_1_of_nat(X_a),hAPP(int,nat,number_number_of(nat),V)) = hAPP(int,X_a,number_number_of(X_a),V)) & (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),V))) -> hAPP(nat,X_a,semiring_1_of_nat(X_a),hAPP(int,nat,number_number_of(nat),V)) = zero_zero(X_a)))))) # label(fact_2681_of__nat__number__of__lemma) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.75 2674 (all X_a (archim1804426504_field(X_a) -> (all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),X)) -> (exists N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_2)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,inverse_inverse(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),N_2))),X)))))))) # label(fact_2682_ex__inverse__of__nat__less) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.75 2675 (all X_a (archim1804426504_field(X_a) -> (all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),X)) -> (exists N_2 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,inverse_inverse(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),hAPP(nat,nat,suc,N_2)))),X))))))) # label(fact_2683_ex__inverse__of__nat__Suc__less) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.75 2676 (all X_1 all Aa all Pa (hBOOL(hAPP(int,bool,zprime,Pa)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),Pa)) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,Aa),zero_zero(int)),Pa)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),hAPP(int,fun(int,bool),sRStar,Pa))) -> hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),hAPP(int,int,hAPP(int,fun(int,int),standardRes,Pa),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Aa),hAPP(int,int,hAPP(int,fun(int,int),multInv,Pa),X_1)))),hAPP(int,fun(int,bool),sRStar,Pa)))))))) # label(fact_2684_SRStar__mult__prop2) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.75 2677 (all X_a (real_normed_field(X_a) -> (all N_1 all Z all K_5 all H_2 (ti(X_a,H_2) != zero_zero(X_a) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),Z)),K_5)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Z),H_2))),K_5)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),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),inverse_divide(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),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),plus_plus(X_a),Z),H_2)),N_1)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),Z),N_1))),H_2)),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),N_1)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),Z),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),hAPP(nat,nat,suc,zero_zero(nat)))))))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,semiring_1_of_nat(real),N_1)),hAPP(nat,real,semiring_1_of_nat(real),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),hAPP(nat,nat,suc,zero_zero(nat)))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),K_5),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))),hAPP(X_a,real,norm_norm(X_a),H_2)))))))))) # label(fact_2685_lemma__termdiff3) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.75 2678 (all X_1 all Y_1 (hAPP(nat,int,semiring_1_of_nat(int),X_1) = hAPP(nat,int,semiring_1_of_nat(int),Y_1) <-> X_1 = Y_1)) # label(fact_2686_Nat__Transfer_Otransfer__int__nat__relations_I1_J) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.75 2679 (all X_1 all Y_1 all P_1 ((hBOOL(P_1) -> 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),P_1),X_1),Y_1))) & (-hBOOL(P_1) -> hAPP(nat,int,semiring_1_of_nat(int),Y_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),P_1),X_1),Y_1))))) # label(fact_2687_int__if__cong) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.75 2680 (all X_a (real_n2089651433ebra_1(X_a) -> (all N_1 hAPP(X_a,real,norm_norm(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),N_1)) = hAPP(nat,real,semiring_1_of_nat(real),N_1)))) # label(fact_2688_norm__of__nat) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.75 2681 (all M all N (hAPP(nat,int,semiring_1_of_nat(int),M) = hAPP(nat,int,semiring_1_of_nat(int),N) <-> M = N)) # label(fact_2689_int__int__eq) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.75 2682 (all X_a (real_normed_vector(X_a) -> (all A_1 all B hAPP(X_a,real,norm_norm(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,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),B),A_1))))) # label(fact_2690_norm__minus__commute) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.75 2683 (all X all Y hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),X),Y) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),X),hAPP(complex,complex,uminus_uminus(complex),Y))) # label(fact_2691_complex__diff__def) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.75 2684 (all R_4 hAPP(real,real,norm_norm(real),R_4) = hAPP(real,real,abs_abs(real),R_4)) # label(fact_2692_real__norm__def) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.75 2685 (all X_a (real_normed_vector(X_a) -> (all A_1 hAPP(real,real,abs_abs(real),hAPP(X_a,real,norm_norm(X_a),A_1)) = hAPP(X_a,real,norm_norm(X_a),A_1)))) # label(fact_2693_abs__norm__cancel) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.75 2686 (all X_a (real_normed_vector(X_a) -> (all X hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),X)) = hAPP(X_a,real,norm_norm(X_a),X)))) # label(fact_2694_norm__minus__cancel) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.75 2687 (all X_a (real_normed_vector(X_a) -> (all X_1 (hAPP(X_a,real,norm_norm(X_a),X_1) = zero_zero(real) <-> ti(X_a,X_1) = zero_zero(X_a))))) # label(fact_2695_norm__eq__zero) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.75 2688 (all X_a (real_normed_vector(X_a) -> hAPP(X_a,real,norm_norm(X_a),zero_zero(X_a)) = zero_zero(real))) # label(fact_2696_norm__zero) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.75 2689 (all X_1 all Pa (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),hAPP(int,fun(int,bool),sRStar,Pa))) -> hAPP(int,int,hAPP(int,fun(int,int),standardRes,Pa),X_1) = X_1)) # label(fact_2697_StandardRes__SRStar__prop3) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.75 2690 (all X_a (real_n1866405975lgebra(X_a) -> (all X all Y hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),Y)) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(X_a,real,norm_norm(X_a),X)),hAPP(X_a,real,norm_norm(X_a),Y))))) # label(fact_2698_norm__mult) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.75 2691 (all X_a (real_normed_vector(X_a) -> (all X hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(X_a,real,norm_norm(X_a),X)))))) # label(fact_2699_norm__ge__zero) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.75 2692 (all X_a (real_normed_vector(X_a) -> (all X -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,norm_norm(X_a),X)),zero_zero(real)))))) # label(fact_2700_norm__not__less__zero) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.75 2693 (all X_a (real_n2089651433ebra_1(X_a) -> hAPP(X_a,real,norm_norm(X_a),one_one(X_a)) = one_one(real))) # label(fact_2701_norm__one) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.75 2694 (all X_a (real_n1866405975lgebra(X_a) -> (all X all N_1 hAPP(X_a,real,norm_norm(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),N_1)) = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(X_a,real,norm_norm(X_a),X)),N_1)))) # label(fact_2702_norm__power) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.75 2695 (all X_a (field_inverse_zero(X_a) & real_normed_field(X_a) -> (all A_1 all B hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),A_1),B)) = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(X_a,real,norm_norm(X_a),A_1)),hAPP(X_a,real,norm_norm(X_a),B))))) # label(fact_2703_norm__divide) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.75 2696 (all B all A_1 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),B),A_1))),hAPP(complex,real,norm_norm(complex),B))),hAPP(complex,real,norm_norm(complex),A_1)))) # label(fact_2704_complex__mod__triangle__ineq2) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.75 2697 (all X hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,uminus_uminus(real),hAPP(complex,real,norm_norm(complex),X))),hAPP(complex,real,norm_norm(complex),X)))) # label(fact_2705_complex__mod__minus__le__complex__mod) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.75 2698 (all X_a (divisi14063676e_zero(X_a) & real_n1866405975lgebra(X_a) -> (all A_1 hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,inverse_inverse(X_a),A_1)) = hAPP(real,real,inverse_inverse(real),hAPP(X_a,real,norm_norm(X_a),A_1))))) # label(fact_2706_norm__inverse) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.75 2699 (all X_1 all Pa (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),hAPP(int,fun(int,bool),sRStar,Pa))) -> hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),hAPP(int,fun(int,bool),sr,Pa))))) # label(fact_2707_SRStar__SR__prop) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.75 2700 (all X_a (real_normed_vector(X_a) -> (all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),X_1)),zero_zero(real))) <-> ti(X_a,X_1) = zero_zero(X_a))))) # label(fact_2708_norm__le__zero__iff) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.75 2701 (all X_a (real_normed_vector(X_a) -> (all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(X_a,real,norm_norm(X_a),X_1))) <-> ti(X_a,X_1) != zero_zero(X_a))))) # label(fact_2709_zero__less__norm__iff) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.75 2702 (all X_a (real_normed_algebra(X_a) -> (all X all Y hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),Y))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(X_a,real,norm_norm(X_a),X)),hAPP(X_a,real,norm_norm(X_a),Y))))))) # label(fact_2710_norm__mult__ineq) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.75 2703 (all X_a (real_normed_algebra(X_a) -> (all Y all S_4 all X all R_4 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,norm_norm(X_a),X)),R_4)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,norm_norm(X_a),Y)),S_4)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),Y))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),R_4),S_4)))))))) # label(fact_2711_norm__mult__less) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.75 2704 (all X_a (real_normed_field(X_a) -> (all A_1 all B (ti(X_a,B) != zero_zero(X_a) -> hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),A_1),B)) = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(X_a,real,norm_norm(X_a),A_1)),hAPP(X_a,real,norm_norm(X_a),B)))))) # label(fact_2712_nonzero__norm__divide) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.75 2705 (all X_a (real_normed_vector(X_a) -> (all X all Y hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X),Y))),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(X_a,real,norm_norm(X_a),X)),hAPP(X_a,real,norm_norm(X_a),Y))))))) # label(fact_2713_norm__triangle__ineq) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.75 2706 (all X_a (real_normed_vector(X_a) -> (all Y all S_4 all X all R_4 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,norm_norm(X_a),X)),R_4)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,norm_norm(X_a),Y)),S_4)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X),Y))),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),R_4),S_4)))))))) # label(fact_2714_norm__add__less) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.75 2707 (all X_a (real_normed_vector(X_a) -> (all A_1 all B hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_1),B))),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(X_a,real,norm_norm(X_a),A_1)),hAPP(X_a,real,norm_norm(X_a),B))))))) # label(fact_2715_norm__triangle__ineq4) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.75 2708 (all X_a (real_n2089651433ebra_1(X_a) -> (all X all N_1 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),N_1))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(X_a,real,norm_norm(X_a),X)),N_1)))))) # label(fact_2716_norm__power__ineq) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.75 2709 (all X_a (real_normed_vector(X_a) -> (all A_1 all B hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(X_a,real,norm_norm(X_a),A_1)),hAPP(X_a,real,norm_norm(X_a),B))),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B))))))) # label(fact_2717_norm__diff__ineq) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.75 2710 (all X_a (real_normed_vector(X_a) -> (all A_1 all B hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(X_a,real,norm_norm(X_a),A_1)),hAPP(X_a,real,norm_norm(X_a),B))),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_1),B))))))) # label(fact_2718_norm__triangle__ineq2) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.75 2711 (all Pa hAPP(int,fun(int,bool),sRStar,Pa) = hAPP(fun(int,bool),fun(int,bool),collect(int),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),combs(int,bool,bool),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(int,fun(int,bool),ord_less(int),zero_zero(int)))),hAPP(int,fun(int,bool),hAPP(fun(int,fun(int,bool)),fun(int,fun(int,bool)),combc(int,int,bool),ord_less(int)),Pa)))) # label(fact_2719_SRStar__def) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.75 2712 (all X_a (number_ring(X_a) & real_n2089651433ebra_1(X_a) -> (all W hAPP(X_a,real,norm_norm(X_a),hAPP(int,X_a,number_number_of(X_a),W)) = hAPP(real,real,abs_abs(real),hAPP(int,real,number_number_of(real),W))))) # label(fact_2720_norm__number__of) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.75 2713 (all X_a (real_n1866405975lgebra(X_a) -> (all A_1 (ti(X_a,A_1) != zero_zero(X_a) -> hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,inverse_inverse(X_a),A_1)) = hAPP(real,real,inverse_inverse(real),hAPP(X_a,real,norm_norm(X_a),A_1)))))) # label(fact_2721_nonzero__norm__inverse) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.75 2714 (all X_1 all Pa (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),hAPP(int,fun(int,bool),sRStar,Pa))) -> -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,X_1),zero_zero(int)),Pa)))) # label(fact_2722_StandardRes__SRStar__prop1a) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.75 2715 (all X_a (real_normed_vector(X_a) -> (all X all Y all C (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),C),zero_zero(real))) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),X)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),hAPP(X_a,real,norm_norm(X_a),Y)))) -> ti(X_a,X) = zero_zero(X_a)))))) # label(fact_2723_norm__ratiotest__lemma) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.75 2716 (all X_a (real_normed_vector(X_a) -> (all A_1 all B all C all D hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),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)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),D)))),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_1),C))),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),B),D)))))))) # label(fact_2724_norm__diff__triangle__ineq) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.75 2717 (all X_a (real_normed_vector(X_a) -> (all A_1 all B hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(X_a,real,norm_norm(X_a),A_1)),hAPP(X_a,real,norm_norm(X_a),B)))),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_1),B))))))) # label(fact_2725_norm__triangle__ineq3) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.75 2718 (all X_a (real_normed_vector(X_a) -> (all X ((ti(X_a,X) = zero_zero(X_a) -> hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,sgn_sgn(X_a),X)) = zero_zero(real)) & (ti(X_a,X) != zero_zero(X_a) -> hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,sgn_sgn(X_a),X)) = one_one(real)))))) # label(fact_2726_norm__sgn) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.75 2719 (all A_1 hAPP(complex,real,norm_norm(complex),hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,hAPP(real,real,cos,A_1)),hAPP(real,real,sin,A_1))) = one_one(real)) # label(fact_2727_cmod__unit__one) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.75 2720 (all X_a all X_b (real_normed_vector(X_b) -> (all X_3 ((exists K_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),K_2)) & (all N_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_b,real,norm_norm(X_b),hAPP(X_a,X_b,X_3,N_2))),K_2))))) <-> (exists N_3 all N_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_b,real,norm_norm(X_b),hAPP(X_a,X_b,X_3,N_2))),hAPP(nat,real,real_1(nat),hAPP(nat,nat,suc,N_3))))))))) # label(fact_2728_lemma__NBseq__def) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.75 2721 (all X_a all X_b (real_normed_vector(X_b) -> (all X_3 ((exists K_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),K_2)) & (all N_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_b,real,norm_norm(X_b),hAPP(X_a,X_b,X_3,N_2))),K_2))))) <-> (exists N_3 all N_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_b,real,norm_norm(X_b),hAPP(X_a,X_b,X_3,N_2))),hAPP(nat,real,real_1(nat),hAPP(nat,nat,suc,N_3))))))))) # label(fact_2729_lemma__NBseq__def2) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.75 2722 (all X_a (real_n1866405975lgebra(X_a) -> (all R_4 all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),R_4),hAPP(X_a,real,norm_norm(X_a),X))) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),R_4)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,inverse_inverse(X_a),X))),hAPP(real,real,inverse_inverse(real),R_4)))))))) # label(fact_2730_Bseq__inverse__lemma) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.75 2723 (all X all Y hAPP(complex,real,norm_norm(complex),hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,X),Y)) = hAPP(real,real,sqrt,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),Y),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))) # label(fact_2731_complex__norm) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.75 2724 (all X_1 all Pa (hBOOL(hAPP(int,bool,zprime,Pa)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),Pa)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),hAPP(int,fun(int,bool),sRStar,Pa))) -> hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),hAPP(int,int,hAPP(int,fun(int,int),standardRes,Pa),X_1)),hAPP(int,fun(int,bool),sRStar,Pa))))))) # label(fact_2732_StandardRes__SRStar__prop4) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.75 2725 (all X_1 all Pa (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),Pa)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),hAPP(int,int,hAPP(int,fun(int,int),standardRes,Pa),X_1)),hAPP(int,fun(int,bool),sRStar,Pa))) <-> -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,X_1),zero_zero(int)),Pa))))) # label(fact_2733_StandardRes__SRStar__prop1) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.75 2726 (all Y_1 all X_1 all Pa (hBOOL(hAPP(int,bool,zprime,Pa)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),Pa)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),hAPP(int,fun(int,bool),sRStar,Pa))) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Y_1),hAPP(int,fun(int,bool),sRStar,Pa))) -> hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),hAPP(int,int,hAPP(int,fun(int,int),standardRes,Pa),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X_1),Y_1))),hAPP(int,fun(int,bool),sRStar,Pa)))))))) # label(fact_2734_SRStar__mult__prop1) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.75 2727 (all X_1 all Pa (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),Pa)) -> (hBOOL(hAPP(int,bool,zprime,Pa)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),hAPP(int,fun(int,bool),sRStar,Pa))) -> hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),hAPP(int,int,hAPP(int,fun(int,int),standardRes,Pa),hAPP(int,int,hAPP(int,fun(int,int),multInv,Pa),X_1))),hAPP(int,fun(int,bool),sRStar,Pa))))))) # label(fact_2735_StandardRes__SRStar__prop2) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.75 2728 (all X_c all X_b all X_a (real_normed_vector(X_a) & real_normed_vector(X_b) & real_normed_vector(X_c) -> (all Prod (hBOOL(hAPP(fun(X_a,fun(X_b,X_c)),bool,bounded_bilinear(X_a,X_b,X_c),Prod)) -> (exists K_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),K_2)) & (all A_3 all B_3 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_c,real,norm_norm(X_c),hAPP(X_b,X_c,hAPP(X_a,fun(X_b,X_c),Prod,A_3),B_3))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(X_a,real,norm_norm(X_a),A_3)),hAPP(X_b,real,norm_norm(X_b),B_3))),K_2)))))))))) # label(fact_2736_bounded__bilinear_Opos__bounded) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.75 2729 (all X_a (real_normed_field(X_a) -> (all Y exists K_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),K_2)) & (all X_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),X_2),Y))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(X_a,real,norm_norm(X_a),X_2)),K_2)))))))) # label(fact_2737_divide_Opos__bounded) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.75 2730 (all X_b all X_a (ord(X_a) & real_normed_vector(X_b) -> (all X_3 all M_2 ((all N_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),M_2),N_2)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_b,real,norm_norm(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),hAPP(X_a,X_b,X_3,M_2)),hAPP(X_a,X_b,X_3,N_2)))),one_one(real))))) -> (all N_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),M_2),N_2)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_b,real,norm_norm(X_b),hAPP(X_a,X_b,X_3,N_2))),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),one_one(real)),hAPP(X_b,real,norm_norm(X_b),hAPP(X_a,X_b,X_3,M_2))))))))))) # label(fact_2738_lemmaCauchy) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.75 2731 (all X_a (real_normed_algebra(X_a) -> (exists K_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),K_2)) & (all A_3 all B_3 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_3),B_3))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(X_a,real,norm_norm(X_a),A_3)),hAPP(X_a,real,norm_norm(X_a),B_3))),K_2)))))))) # label(fact_2739_mult_Opos__bounded) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.75 2732 (all X_a (real_normed_algebra(X_a) -> (all Y exists K_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),K_2)) & (all X_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X_2),Y))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(X_a,real,norm_norm(X_a),X_2)),K_2)))))))) # label(fact_2740_mult__left_Opos__bounded) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.75 2733 (all X_a (real_normed_algebra(X_a) -> (all X exists K_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),K_2)) & (all X_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),X_2))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(X_a,real,norm_norm(X_a),X_2)),K_2)))))))) # label(fact_2741_mult__right_Opos__bounded) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.75 2734 (all X_c all X_b all X_a (real_normed_vector(X_a) & real_normed_vector(X_b) & real_normed_vector(X_c) -> (all Prod (hBOOL(hAPP(fun(X_a,fun(X_b,X_c)),bool,bounded_bilinear(X_a,X_b,X_c),Prod)) -> (exists K_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),K_2)) & (all A_3 all B_3 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_c,real,norm_norm(X_c),hAPP(X_b,X_c,hAPP(X_a,fun(X_b,X_c),Prod,A_3),B_3))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(X_a,real,norm_norm(X_a),A_3)),hAPP(X_b,real,norm_norm(X_b),B_3))),K_2)))))))))) # label(fact_2742_bounded__bilinear_Ononneg__bounded) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.75 2735 (all X (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X),zero_zero(int))) -> (exists N_2 X = hAPP(int,int,uminus_uminus(int),hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,N_2)))))) # label(fact_2743_negD) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.75 2736 (all X_a (real_normed_field(X_a) -> (all Y exists K_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),K_2)) & (all X_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),X_2),Y))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(X_a,real,norm_norm(X_a),X_2)),K_2)))))))) # label(fact_2744_divide_Ononneg__bounded) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.75 2737 (all K_4 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),K_4)) -> (exists N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_2)) & K_4 = hAPP(nat,int,semiring_1_of_nat(int),N_2))))) # label(fact_2745_zero__less__imp__eq__int) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.75 2738 (all X_a (real_normed_algebra(X_a) -> (exists K_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),K_2)) & (all A_3 all B_3 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_3),B_3))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(X_a,real,norm_norm(X_a),A_3)),hAPP(X_a,real,norm_norm(X_a),B_3))),K_2)))))))) # label(fact_2746_mult_Ononneg__bounded) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.75 2739 (all X_a (real_normed_algebra(X_a) -> (all X exists K_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),K_2)) & (all X_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),X_2))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(X_a,real,norm_norm(X_a),X_2)),K_2)))))))) # label(fact_2747_mult__right_Ononneg__bounded) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.75 2740 (all X_a (real_normed_algebra(X_a) -> (all Y exists K_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),K_2)) & (all X_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X_2),Y))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(X_a,real,norm_norm(X_a),X_2)),K_2)))))))) # label(fact_2748_mult__left_Ononneg__bounded) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.75 2741 (all X_c all X_b all X_a (real_normed_vector(X_a) & real_normed_vector(X_b) & real_normed_vector(X_c) -> (all Prod (hBOOL(hAPP(fun(X_a,fun(X_b,X_c)),bool,bounded_bilinear(X_a,X_b,X_c),Prod)) -> (exists K_2 all A_3 all B_3 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_c,real,norm_norm(X_c),hAPP(X_b,X_c,hAPP(X_a,fun(X_b,X_c),Prod,A_3),B_3))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(X_a,real,norm_norm(X_a),A_3)),hAPP(X_b,real,norm_norm(X_b),B_3))),K_2)))))))) # label(fact_2749_bounded__bilinear_Obounded) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.75 2742 (all X_a (real_normed_field(X_a) -> (all Y exists K_2 all X_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),X_2),Y))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(X_a,real,norm_norm(X_a),X_2)),K_2)))))) # label(fact_2750_divide_Obounded) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.75 2743 (all X_a (real_normed_algebra(X_a) -> (all Y exists K_2 all X_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X_2),Y))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(X_a,real,norm_norm(X_a),X_2)),K_2)))))) # label(fact_2751_mult__left_Obounded) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.75 2744 (all X_a (real_normed_algebra(X_a) -> (all X exists K_2 all X_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),X_2))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(X_a,real,norm_norm(X_a),X_2)),K_2)))))) # label(fact_2752_mult__right_Obounded) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.75 2745 (all X_a (real_normed_algebra(X_a) -> (exists K_2 all A_3 all B_3 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_3),B_3))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(X_a,real,norm_norm(X_a),A_3)),hAPP(X_a,real,norm_norm(X_a),B_3))),K_2)))))) # label(fact_2753_mult_Obounded) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.75 2746 (all X_a (archim1804426504_field(X_a) -> (all Y all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),X)) -> (exists N_2 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),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),N_2)),X)))))))) # label(fact_2754_ex__less__of__nat__mult) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.75 2747 (all Real1_1 all Real2_1 hAPP(complex,nat,complex_size,hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,Real1_1),Real2_1)) = zero_zero(nat)) # label(fact_2755_complex_Osize_I1_J) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.75 2748 (all X all Y ((Y = zero_zero(nat) -> hAPP(nat,product_prod(int,int),hAPP(nat,fun(nat,product_prod(int,int)),bezw,X),Y) = hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),one_one(int)),zero_zero(int))) & (Y != zero_zero(nat) -> hAPP(nat,product_prod(int,int),hAPP(nat,fun(nat,product_prod(int,int)),bezw,X),Y) = hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),hAPP(product_prod(int,int),int,product_snd(int,int),hAPP(nat,product_prod(int,int),hAPP(nat,fun(nat,product_prod(int,int)),bezw,Y),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),X),Y)))),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(product_prod(int,int),int,product_fst(int,int),hAPP(nat,product_prod(int,int),hAPP(nat,fun(nat,product_prod(int,int)),bezw,Y),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),X),Y)))),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(product_prod(int,int),int,product_snd(int,int),hAPP(nat,product_prod(int,int),hAPP(nat,fun(nat,product_prod(int,int)),bezw,Y),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),X),Y)))),hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),X),Y)))))))) # label(fact_2756_bezw_Osimps) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.75 2749 (all X hAPP(nat,product_prod(int,int),hAPP(nat,fun(nat,product_prod(int,int)),bezw,X),zero_zero(nat)) = hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),one_one(int)),zero_zero(int))) # label(fact_2757_bezw__0) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.75 2750 (all X all Y (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Y)) -> hAPP(nat,product_prod(int,int),hAPP(nat,fun(nat,product_prod(int,int)),bezw,X),Y) = hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),hAPP(product_prod(int,int),int,product_snd(int,int),hAPP(nat,product_prod(int,int),hAPP(nat,fun(nat,product_prod(int,int)),bezw,Y),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),X),Y)))),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(product_prod(int,int),int,product_fst(int,int),hAPP(nat,product_prod(int,int),hAPP(nat,fun(nat,product_prod(int,int)),bezw,Y),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),X),Y)))),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(product_prod(int,int),int,product_snd(int,int),hAPP(nat,product_prod(int,int),hAPP(nat,fun(nat,product_prod(int,int)),bezw,Y),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),X),Y)))),hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),X),Y))))))) # label(fact_2758_bezw__non__0) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.75 2751 (all K_4 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),K_4)) -> (exists N_2 K_4 = hAPP(nat,int,semiring_1_of_nat(int),N_2)))) # label(fact_2759_zero__le__imp__eq__int) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.75 2752 (all Z (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Z)) -> -(all M_3 Z != hAPP(nat,int,semiring_1_of_nat(int),M_3)))) # label(fact_2760_nonneg__eq__int) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.75 2753 (all K_4 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),K_4)) -> -(all N_2 K_4 != hAPP(nat,int,semiring_1_of_nat(int),N_2)))) # label(fact_2761_nonneg__int__cases) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.75 2754 (all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),Y),zero_zero(real))) -> hAPP(real,real,cos,hAPP(complex,real,arg,hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,zero_zero(real)),Y))) = zero_zero(real))) # label(fact_2762_cos__arg__i__mult__zero__neg) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.75 2755 (all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Y)) -> hAPP(real,real,cos,hAPP(complex,real,arg,hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,zero_zero(real)),Y))) = zero_zero(real))) # label(fact_2763_cos__arg__i__mult__zero__pos) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.75 2756 (all X hAPP(nat,int,semiring_1_of_nat(int),hAPP(int,nat,nat_1,hAPP(int,int,abs_abs(int),X))) = hAPP(int,int,abs_abs(int),X)) # label(fact_2764_int__nat__abs) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.75 2757 (all Y (Y != zero_zero(real) -> hAPP(real,real,cos,hAPP(complex,real,arg,hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,zero_zero(real)),Y))) = zero_zero(real))) # label(fact_2765_cos__arg__i__mult__zero) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.75 2758 (all Real1_1 all Real2_1 hAPP(complex,nat,size_size(complex),hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,Real1_1),Real2_1)) = zero_zero(nat)) # label(fact_2766_complex_Osize_I2_J) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.75 2759 (all Pa (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),Pa)) -> hAPP(nat,int,semiring_1_of_nat(int),hAPP(fun(int,bool),nat,finite_card(int),hAPP(int,fun(int,bool),sRStar,Pa))) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),Pa),one_one(int)))) # label(fact_2767_SRStar__card) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.75 2760 (all Z -(all M_3 all N_2 Z != hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(nat,int,semiring_1_of_nat(int),M_3)),hAPP(nat,int,semiring_1_of_nat(int),N_2)))) # label(fact_2768_int__diff__cases) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.75 2761 (all J all Aa all Pa (hBOOL(hAPP(int,bool,zprime,Pa)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),Pa)) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,Aa),zero_zero(int)),Pa)) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),quadRes,Pa),Aa)) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,J),zero_zero(int)),Pa)) -> hAPP(fun(int,bool),nat,finite_card(int),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),hAPP(int,fun(int,fun(int,fun(int,bool))),multInvPair,Aa),Pa),J)) = hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))))) # label(fact_2769_MultInvPair__card__two) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.75 2762 (all Aa all Pa (hBOOL(hAPP(int,bool,zprime,Pa)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),Pa)) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,Aa),zero_zero(int)),Pa)) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),quadRes,Pa),Aa)) -> (all X_2 (hBOOL(hAPP(fun(fun(int,bool),bool),bool,hAPP(fun(int,bool),fun(fun(fun(int,bool),bool),bool),member(fun(int,bool)),X_2),hAPP(int,fun(fun(int,bool),bool),hAPP(int,fun(int,fun(fun(int,bool),bool)),setS,Aa),Pa))) -> hAPP(fun(int,bool),nat,finite_card(int),X_2) = hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))))) # label(fact_2770_SetS__elems__card) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.75 2763 (all W ii != hAPP(int,complex,number_number_of(complex),W)) # label(fact_2774_complex__i__not__number__of) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.75 2764 (all X hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),ii),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),ii),X)) = hAPP(complex,complex,uminus_uminus(complex),X)) # label(fact_2775_complex__i__mult__minus) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.75 2765 (all X_1 all Y_1 (hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,X_1),Y_1) = ii <-> X_1 = zero_zero(real) & Y_1 = one_one(real))) # label(fact_2778_Complex__eq__i) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.75 2766 (all A_1 all B hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,A_1),B)),ii) = hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,hAPP(real,real,uminus_uminus(real),B)),A_1)) # label(fact_2779_Complex__mult__i) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.75 2767 (all A_1 all B hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),ii),hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,A_1),B)) = hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,hAPP(real,real,uminus_uminus(real),B)),A_1)) # label(fact_2780_i__mult__Complex) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.75 2768 (all Aa all Pa (hBOOL(hAPP(int,bool,zprime,Pa)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),Pa)) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,Aa),zero_zero(int)),Pa)) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),quadRes,Pa),Aa)) -> hAPP(nat,int,semiring_1_of_nat(int),hAPP(fun(fun(int,bool),bool),nat,finite_card(fun(int,bool)),hAPP(int,fun(fun(int,bool),bool),hAPP(int,fun(int,fun(fun(int,bool),bool)),setS,Aa),Pa))) = hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),Pa),one_one(int))),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))))) # label(fact_2783_SetS__card) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.75 2769 (all X all Y hAPP(complex,complex,inverse_inverse(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(real,complex,of_real(complex),X)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),ii),hAPP(real,complex,of_real(complex),Y)))) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),hAPP(real,complex,of_real(complex),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),X),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),Y),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),ii),hAPP(real,complex,of_real(complex),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),Y),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),Y),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))))) # label(fact_2784_complex__inverse__complex__split) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.75 2770 (all Aa all Pa (hBOOL(hAPP(int,bool,zprime,Pa)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),Pa)) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,Aa),zero_zero(int)),Pa)) -> hAPP(fun(fun(int,bool),bool),fun(int,bool),complete_Sup_Sup(fun(int,bool)),hAPP(int,fun(fun(int,bool),bool),hAPP(int,fun(int,fun(fun(int,bool),bool)),setS,Aa),Pa)) = hAPP(int,fun(int,bool),sRStar,Pa))))) # label(fact_2785_MultInvPair__prop2) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.75 2771 (all X_a (real_algebra_1(X_a) -> (all X_1 all Y_1 (hAPP(real,X_a,of_real(X_a),X_1) = hAPP(real,X_a,of_real(X_a),Y_1) <-> X_1 = Y_1)))) # label(fact_2786_of__real__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.75 2772 (all X_a (real_algebra_1(X_a) -> hAPP(real,X_a,of_real(X_a),zero_zero(real)) = zero_zero(X_a))) # label(fact_2787_of__real__0) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.75 2773 (all X_a (real_algebra_1(X_a) & real_normed_vector(X_a) -> hAPP(real,X_a,of_real(X_a),zero_zero(real)) = zero_zero(X_a))) # label(fact_2788_of__real_Ozero) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.75 2774 (all X_a (real_algebra_1(X_a) -> (all X_1 (hAPP(real,X_a,of_real(X_a),X_1) = zero_zero(X_a) <-> X_1 = zero_zero(real))))) # label(fact_2789_of__real__eq__0__iff) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.75 2775 (all X_a (real_algebra_1(X_a) -> (all X all Y hAPP(real,X_a,of_real(X_a),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),X),Y)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(real,X_a,of_real(X_a),X)),hAPP(real,X_a,of_real(X_a),Y))))) # label(fact_2790_of__real__mult) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.75 2776 (all X_a (number_ring(X_a) & real_algebra_1(X_a) -> (all W hAPP(real,X_a,of_real(X_a),hAPP(int,real,number_number_of(real),W)) = hAPP(int,X_a,number_number_of(X_a),W)))) # label(fact_2791_of__real__number__of__eq) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.75 2777 (all X_a (real_algebra_1(X_a) -> (all X all Y hAPP(real,X_a,of_real(X_a),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),Y)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(real,X_a,of_real(X_a),X)),hAPP(real,X_a,of_real(X_a),Y))))) # label(fact_2792_of__real__add) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.75 2778 (all X_a (real_algebra_1(X_a) & real_normed_vector(X_a) -> (all X all Y hAPP(real,X_a,of_real(X_a),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),Y)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(real,X_a,of_real(X_a),X)),hAPP(real,X_a,of_real(X_a),Y))))) # label(fact_2793_of__real_Oadd) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.75 2779 (all X_a (real_algebra_1(X_a) -> hAPP(real,X_a,of_real(X_a),one_one(real)) = one_one(X_a))) # label(fact_2794_of__real__1) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.75 2780 (all X_a (real_algebra_1(X_a) -> (all X all N_1 hAPP(real,X_a,of_real(X_a),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),N_1)) = hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(real,X_a,of_real(X_a),X)),N_1)))) # label(fact_2795_of__real__power) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.75 2781 (all X_1 all Y_1 all Xa_2 (hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,X_1),Y_1) = hAPP(real,complex,of_real(complex),Xa_2) <-> X_1 = Xa_2 & Y_1 = zero_zero(real))) # label(fact_2796_complex__eq__cancel__iff2) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.75 2782 (all R_4 hAPP(real,complex,of_real(complex),R_4) = hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,R_4),zero_zero(real))) # label(fact_2797_complex__of__real__def) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.75 2783 (all X_a (field_inverse_zero(X_a) & real_field(X_a) -> (all X all Y hAPP(real,X_a,of_real(X_a),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),X),Y)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),hAPP(real,X_a,of_real(X_a),X)),hAPP(real,X_a,of_real(X_a),Y))))) # label(fact_2798_of__real__divide) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.75 2784 (all X_a (real_algebra_1(X_a) -> (all X all Y hAPP(real,X_a,of_real(X_a),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),X),Y)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(real,X_a,of_real(X_a),X)),hAPP(real,X_a,of_real(X_a),Y))))) # label(fact_2799_of__real__diff) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.75 2785 (all X_a (real_algebra_1(X_a) & real_normed_vector(X_a) -> (all X all Y hAPP(real,X_a,of_real(X_a),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),X),Y)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(real,X_a,of_real(X_a),X)),hAPP(real,X_a,of_real(X_a),Y))))) # label(fact_2800_of__real_Odiff) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.75 2786 (all X_a (real_algebra_1(X_a) -> (all X hAPP(real,X_a,of_real(X_a),hAPP(real,real,uminus_uminus(real),X)) = hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(real,X_a,of_real(X_a),X))))) # label(fact_2801_of__real__minus) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.75 2787 (all X_a (real_algebra_1(X_a) & real_normed_vector(X_a) -> (all X hAPP(real,X_a,of_real(X_a),hAPP(real,real,uminus_uminus(real),X)) = hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(real,X_a,of_real(X_a),X))))) # label(fact_2802_of__real_Ominus) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.75 2788 (all X_a (real_n2089651433ebra_1(X_a) -> (all R_4 hAPP(X_a,real,norm_norm(X_a),hAPP(real,X_a,of_real(X_a),R_4)) = hAPP(real,real,abs_abs(real),R_4)))) # label(fact_2803_norm__of__real) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.75 2789 (all X_a (divisi14063676e_zero(X_a) & real_div_algebra(X_a) -> (all X hAPP(real,X_a,of_real(X_a),hAPP(real,real,inverse_inverse(real),X)) = hAPP(X_a,X_a,inverse_inverse(X_a),hAPP(real,X_a,of_real(X_a),X))))) # label(fact_2804_of__real__inverse) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.75 2790 (all X_a (real_normed_field(X_a) & banach(X_a) -> (all X hAPP(X_a,X_a,exp(X_a),hAPP(real,X_a,of_real(X_a),X)) = hAPP(real,X_a,of_real(X_a),hAPP(real,real,exp(real),X))))) # label(fact_2805_exp__of__real) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.75 2791 (all X_a (real_algebra_1(X_a) -> (all N_1 hAPP(real,X_a,of_real(X_a),hAPP(nat,real,semiring_1_of_nat(real),N_1)) = hAPP(nat,X_a,semiring_1_of_nat(X_a),N_1)))) # label(fact_2806_of__real__of__nat__eq) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.75 2792 (all X_a (real_n2089651433ebra_1(X_a) -> (all R_4 hAPP(X_a,X_a,sgn_sgn(X_a),hAPP(real,X_a,of_real(X_a),R_4)) = hAPP(real,X_a,of_real(X_a),hAPP(real,real,sgn_sgn(real),R_4))))) # label(fact_2807_sgn__of__real) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.75 2793 (all Z hAPP(complex,complex,sgn_sgn(complex),Z) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),Z),hAPP(real,complex,of_real(complex),hAPP(complex,real,norm_norm(complex),Z)))) # label(fact_2808_sgn__eq) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.75 2794 (all X_a (real_field(X_a) -> (all X all Y (Y != zero_zero(real) -> hAPP(real,X_a,of_real(X_a),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),X),Y)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),hAPP(real,X_a,of_real(X_a),X)),hAPP(real,X_a,of_real(X_a),Y)))))) # label(fact_2809_nonzero__of__real__divide) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.75 2795 (all X_a (real_div_algebra(X_a) -> (all X (X != zero_zero(real) -> hAPP(real,X_a,of_real(X_a),hAPP(real,real,inverse_inverse(real),X)) = hAPP(X_a,X_a,inverse_inverse(X_a),hAPP(real,X_a,of_real(X_a),X)))))) # label(fact_2810_nonzero__of__real__inverse) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.75 2796 (all X all Y all R_4 hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,X),Y)),hAPP(real,complex,of_real(complex),R_4)) = hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,hAPP(real,real,hAPP(real,fun(real,real),times_times(real),X),R_4)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),Y),R_4))) # label(fact_2811_Complex__mult__complex__of__real) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.75 2797 (all R_4 all X all Y hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(real,complex,of_real(complex),R_4)),hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,X),Y)) = hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,hAPP(real,real,hAPP(real,fun(real,real),times_times(real),R_4),X)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),R_4),Y))) # label(fact_2812_complex__of__real__mult__Complex) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.75 2798 (all R_4 all X all Y hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(real,complex,of_real(complex),R_4)),hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,X),Y)) = hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),R_4),X)),Y)) # label(fact_2813_complex__of__real__add__Complex) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.75 2799 (all X all Y all R_4 hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,X),Y)),hAPP(real,complex,of_real(complex),R_4)) = hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),R_4)),Y)) # label(fact_2814_Complex__add__complex__of__real) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.75 2800 (all R_4 hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),ii),hAPP(real,complex,of_real(complex),R_4)) = hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,zero_zero(real)),R_4)) # label(fact_2816_i__complex__of__real) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.75 2801 (all R_4 hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(real,complex,of_real(complex),R_4)),ii) = hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,zero_zero(real)),R_4)) # label(fact_2817_complex__of__real__i) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.75 2802 (all R_4 all A_1 hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(real,complex,of_real(complex),R_4)),hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,hAPP(real,real,cos,A_1)),hAPP(real,real,sin,A_1)))) = hAPP(real,real,abs_abs(real),R_4)) # label(fact_2819_cmod__complex__polar) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.75 2803 (all X_a (real_algebra_1(X_a) & real_normed_vector(X_a) -> (exists K_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),K_2)) & (all X_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),hAPP(real,X_a,of_real(X_a),X_2))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,norm_norm(real),X_2)),K_2)))))))) # label(fact_2820_of__real_Opos__bounded) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.75 2804 (all X_a (real_algebra_1(X_a) & real_normed_vector(X_a) -> (exists K_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),K_2)) & (all X_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),hAPP(real,X_a,of_real(X_a),X_2))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,norm_norm(real),X_2)),K_2)))))))) # label(fact_2821_of__real_Ononneg__bounded) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.75 2805 (all A_1 all B hAPP(complex,complex,expi,hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),A_1),B)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,expi,A_1)),hAPP(complex,complex,expi,B))) # label(fact_2823_expi__add) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.75 2806 (all X_a (real_algebra_1(X_a) & real_normed_vector(X_a) -> (exists K_2 all X_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),hAPP(real,X_a,of_real(X_a),X_2))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,norm_norm(real),X_2)),K_2)))))) # label(fact_2825_of__real_Obounded) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.75 2807 (all Z exists R_2 exists A_3 Z = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(real,complex,of_real(complex),R_2)),hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,hAPP(real,real,cos,A_3)),hAPP(real,real,sin,A_3)))) # label(fact_2826_complex__split__polar) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.75 2808 (all X_a all A_2 all X_3 all C_2 (hBOOL(hAPP(fun(fun(X_a,bool),bool),bool,hAPP(fun(X_a,bool),fun(fun(fun(X_a,bool),bool),bool),member(fun(X_a,bool)),X_3),C_2)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_2),X_3)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_2),hAPP(fun(fun(X_a,bool),bool),fun(X_a,bool),complete_Sup_Sup(fun(X_a,bool)),C_2)))))) # label(fact_2827_UnionI) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.75 2809 (all X_a all B_1 all A_2 (hBOOL(hAPP(fun(fun(X_a,bool),bool),bool,hAPP(fun(X_a,bool),fun(fun(fun(X_a,bool),bool),bool),member(fun(X_a,bool)),B_1),A_2)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),B_1),hAPP(fun(fun(X_a,bool),bool),fun(X_a,bool),complete_Sup_Sup(fun(X_a,bool)),A_2))))) # label(fact_2828_Union__upper) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.75 2810 (all X_a all A_2 all B_1 (hBOOL(hAPP(fun(fun(X_a,bool),bool),bool,hAPP(fun(fun(X_a,bool),bool),fun(fun(fun(X_a,bool),bool),bool),ord_less_eq(fun(fun(X_a,bool),bool)),A_2),B_1)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(fun(fun(X_a,bool),bool),fun(X_a,bool),complete_Sup_Sup(fun(X_a,bool)),A_2)),hAPP(fun(fun(X_a,bool),bool),fun(X_a,bool),complete_Sup_Sup(fun(X_a,bool)),B_1))))) # label(fact_2829_Union__mono) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.75 2811 (all X_a (comple44059174attice(X_a) -> (all A_2 all Ba (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(fun(X_a,bool),X_a,complete_Sup_Sup(X_a),A_2)),Ba)) <-> (all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_2)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_2),Ba)))))))) # label(fact_2830_Sup__le__iff) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.75 2812 (all X_a (comple44059174attice(X_a) -> (all X_1 all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_2)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),hAPP(fun(X_a,bool),X_a,complete_Sup_Sup(X_a),A_2))))))) # label(fact_2831_complete__lattice__class_OSup__upper) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.75 2813 (all X_a (comple44059174attice(X_a) -> (all A_2 all B_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_2),B_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(fun(X_a,bool),X_a,complete_Sup_Sup(X_a),A_2)),hAPP(fun(X_a,bool),X_a,complete_Sup_Sup(X_a),B_1))))))) # label(fact_2832_Sup__subset__mono) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.75 2814 (all X_a (comple44059174attice(X_a) -> (all V_1 all U_1 all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),U_1),A_2)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),V_1),U_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),V_1),hAPP(fun(X_a,bool),X_a,complete_Sup_Sup(X_a),A_2)))))))) # label(fact_2833_complete__lattice__class_OSup__upper2) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.75 2815 (all X_a (comple1803745165norder(X_a) -> (all Aa all S (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),hAPP(fun(X_a,bool),X_a,complete_Sup_Sup(X_a),S))) <-> (exists X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),S)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),X_2)))))))) # label(fact_2834_less__Sup__iff) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.75 2816 (all X_a all A_2 all C_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_2),hAPP(fun(fun(X_a,bool),bool),fun(X_a,bool),complete_Sup_Sup(fun(X_a,bool)),C_2))) -> -(all X_4 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_2),X_4)) -> -hBOOL(hAPP(fun(fun(X_a,bool),bool),bool,hAPP(fun(X_a,bool),fun(fun(fun(X_a,bool),bool),bool),member(fun(X_a,bool)),X_4),C_2)))))) # label(fact_2835_UnionE) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.75 2817 (all Aa all Pa (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),Pa)) -> hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),hAPP(fun(fun(int,bool),bool),fun(int,bool),complete_Sup_Sup(fun(int,bool)),hAPP(int,fun(fun(int,bool),bool),hAPP(int,fun(int,fun(fun(int,bool),bool)),setS,Aa),Pa)))))) # label(fact_2836_Union__SetS__finite) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.75 2818 (all X_a (comple44059174attice(X_a) -> (all Z_1 all A_2 ((all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_2)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_2),Z_1)))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(fun(X_a,bool),X_a,complete_Sup_Sup(X_a),A_2)),Z_1)))))) # label(fact_2837_complete__lattice__class_OSup__least) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.75 2819 (all Aa all Pa hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),wset,Aa),Pa)))) # label(fact_2838_wset__fin) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.75 2820 (all Aa hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),hAPP(int,fun(int,bool),d22set,Aa)))) # label(fact_2839_d22set__fin) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.75 2821 (all Aa all Pa all X_2 (hBOOL(hAPP(fun(fun(int,bool),bool),bool,hAPP(fun(int,bool),fun(fun(fun(int,bool),bool),bool),member(fun(int,bool)),X_2),hAPP(int,fun(fun(int,bool),bool),hAPP(int,fun(int,fun(fun(int,bool),bool)),setS,Aa),Pa))) -> hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),X_2)))) # label(fact_2840_SetS__elems__finite) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.75 2822 (all X_a all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2)) -> 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,number_number_of(int),min)),hAPP(fun(X_a,bool),nat,finite_card(X_a),A_2))),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,number_number_of(int),min)),hAPP(fun(X_a,bool),nat,finite_card(X_a),A_2))) = one_one(int))) # label(fact_2841_neg__one__special) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.75 2823 (all Pa (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),Pa)) -> hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),hAPP(int,fun(int,bool),sRStar,Pa))))) # label(fact_2842_SRStar__finite) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.75 2824 (all X_a all A_2 all B_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),B_1)) -> hBOOL(hAPP(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_a,bool),nat,finite_card(X_a),A_2)),hAPP(fun(X_a,bool),nat,finite_card(X_a),B_1))),hAPP(fun(X_a,bool),nat,finite_card(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_2),B_1)))))) # label(fact_2843_diff__card__le__card__Diff) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.75 2825 (all X_a all A_2 all B_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),B_1)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),B_1),A_2)) -> hAPP(fun(X_a,bool),nat,finite_card(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_2),B_1)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(fun(X_a,bool),nat,finite_card(X_a),A_2)),hAPP(fun(X_a,bool),nat,finite_card(X_a),B_1))))) # label(fact_2844_card__Diff__subset) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.75 2826 (all X_a all A_2 all B_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),B_1)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_2),B_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X_a,bool),nat,finite_card(X_a),B_1)),hAPP(fun(X_a,bool),nat,finite_card(X_a),A_2))) -> ti(fun(X_a,bool),A_2) = ti(fun(X_a,bool),B_1))))) # label(fact_2845_card__seteq) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.75 2827 (all X_a all B_1 all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2)) -> hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_2),B_1))))) # label(fact_2846_finite__Diff) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.75 2828 (all X_a all A_2 all B_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),B_1)) -> (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_2),B_1))) <-> hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2))))) # label(fact_2847_finite__Diff2) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.75 2829 (all X_a (finite_finite(X_a) -> (all A_2 hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2))))) # label(fact_2848_finite__code) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.75 2830 (all X_a (finite_finite(X_a) -> (all A_2 hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2))))) # label(fact_2849_finite) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.75 2831 (all Aa all Pa (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),Pa)) -> hBOOL(hAPP(fun(fun(int,bool),bool),bool,finite_finite_1(fun(int,bool)),hAPP(int,fun(fun(int,bool),bool),hAPP(int,fun(int,fun(fun(int,bool),bool)),setS,Aa),Pa))))) # label(fact_2850_SetS__finite) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.75 2832 (all X_a all A_2 all B_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),B_1)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_2),B_1)) -> hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2))))) # label(fact_2851_rev__finite__subset) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.75 2833 (all X_a all A_2 all B_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_2),B_1)) -> (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),B_1)) -> hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2))))) # label(fact_2852_finite__subset) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.75 2834 (all X_a all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),hAPP(fun(fun(X_a,bool),bool),fun(X_a,bool),complete_Sup_Sup(fun(X_a,bool)),A_2))) -> hBOOL(hAPP(fun(fun(X_a,bool),bool),bool,finite_finite_1(fun(X_a,bool)),A_2)))) # label(fact_2853_finite__UnionD) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.75 2835 (all X_a all A_2 (-hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2)) -> hAPP(fun(X_a,bool),nat,finite_card(X_a),A_2) = zero_zero(nat))) # label(fact_2854_card__infinite) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.75 2836 (all X_a all A_2 all B_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),B_1)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less(fun(X_a,bool)),A_2),B_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(X_a,bool),nat,finite_card(X_a),A_2)),hAPP(fun(X_a,bool),nat,finite_card(X_a),B_1)))))) # label(fact_2855_psubset__card__mono) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.75 2837 (all X_a all A_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(fun(X_a,bool),nat,finite_card(X_a),A_2))) -> hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2)))) # label(fact_2856_card__ge__0__finite) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.75 2838 (all X_a all A_2 all B_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),B_1)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_2),B_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(X_a,bool),nat,finite_card(X_a),A_2)),hAPP(fun(X_a,bool),nat,finite_card(X_a),B_1))) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less(fun(X_a,bool)),A_2),B_1)))))) # label(fact_2857_card__psubset) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.75 2839 (all X_a all A_2 all B_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),B_1)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_2),B_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X_a,bool),nat,finite_card(X_a),A_2)),hAPP(fun(X_a,bool),nat,finite_card(X_a),B_1)))))) # label(fact_2858_card__mono) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.75 2840 (all X_a all A_2 (hBOOL(hAPP(fun(fun(X_a,bool),bool),bool,finite_finite_1(fun(X_a,bool)),A_2)) -> ((all M_4 (hBOOL(hAPP(fun(fun(X_a,bool),bool),bool,hAPP(fun(X_a,bool),fun(fun(fun(X_a,bool),bool),bool),member(fun(X_a,bool)),M_4),A_2)) -> hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),M_4)))) -> hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),hAPP(fun(fun(X_a,bool),bool),fun(X_a,bool),complete_Sup_Sup(fun(X_a,bool)),A_2)))))) # label(fact_2859_finite__Union) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.75 2841 (all X_a all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2)) -> (((exists X_2 hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_2))) -> one_one(nat) = zero_zero(nat)) -> hAPP(fun(X_a,bool),nat,finite_card(X_a),A_2) = zero_zero(nat)))) # label(fact_2860_card_Oneutral) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.75 2842 (all X_a all C_1 all A_2 all B_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_2),B_1))) -> -(hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),A_2)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),B_1))))) # label(fact_2861_DiffE) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.75 2843 (all X_a all A_2 all B_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_2),B_1)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),B_1),A_2)) -> ti(fun(X_a,bool),A_2) = ti(fun(X_a,bool),B_1)))) # label(fact_2862_equalityI) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.75 2844 (all X_a all C_1 all A_2 all B_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_2),B_1)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),A_2)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),B_1))))) # label(fact_2863_subsetD) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.75 2845 (all X_a all B_1 all C_1 all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),A_2)) -> (-hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),B_1)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_2),B_1)))))) # label(fact_2864_DiffI) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.75 2846 (all X_a all C_1 all A_2 all B_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less(fun(X_a,bool)),A_2),B_1)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),A_2)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),B_1))))) # label(fact_2865_psubsetD) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.75 2847 (all X_a all C_2 all A_2 all B_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less(fun(X_a,bool)),A_2),B_1)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less(fun(X_a,bool)),B_1),C_2)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less(fun(X_a,bool)),A_2),C_2))))) # label(fact_2866_psubset__trans) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.75 2848 (all X_a all A_2 all B_1 (ti(fun(X_a,bool),A_2) = ti(fun(X_a,bool),B_1) -> -(hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_2),B_1)) -> -hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),B_1),A_2))))) # label(fact_2867_equalityE) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 2849 (all X_a all C_2 all A_2 all B_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_2),B_1)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),B_1),C_2)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_2),C_2))))) # label(fact_2868_subset__trans) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 2850 (all X_a all X_1 all A_2 all B_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_2),B_1)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_2)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),B_1))))) # label(fact_2869_set__mp) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 2851 (all X_a all B_1 all X_1 all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_2)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_2),B_1)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),B_1))))) # label(fact_2870_set__rev__mp) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 2852 (all X_a all X_1 all A_2 all B_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_2),B_1)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_2)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),B_1))))) # label(fact_2871_in__mono) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 2853 (all X_a all A_2 all B_1 (ti(fun(X_a,bool),A_2) = ti(fun(X_a,bool),B_1) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),B_1),A_2)))) # label(fact_2872_equalityD2) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 2854 (all X_a all A_2 all B_1 (ti(fun(X_a,bool),A_2) = ti(fun(X_a,bool),B_1) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_2),B_1)))) # label(fact_2873_equalityD1) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 2855 (all X_a all A_2 all B_1 (ti(fun(X_a,bool),A_2) = ti(fun(X_a,bool),B_1) <-> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_2),B_1)) & hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),B_1),A_2)))) # label(fact_2874_set__eq__subset) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 2856 (all X_a all A_2 hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_2),A_2))) # label(fact_2875_subset__refl) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 2857 (all X_a all A_2 all B_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less(fun(X_a,bool)),A_2),B_1)) <-> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_2),B_1)) & ti(fun(X_a,bool),A_2) != ti(fun(X_a,bool),B_1))) # label(fact_2876_psubset__eq) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 2858 (all X_a all A_2 all B_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_2),B_1)) <-> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less(fun(X_a,bool)),A_2),B_1)) | ti(fun(X_a,bool),A_2) = ti(fun(X_a,bool),B_1))) # label(fact_2877_subset__iff__psubset__eq) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 2859 (all X_a all A_2 all B_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less(fun(X_a,bool)),A_2),B_1)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_2),B_1)))) # label(fact_2878_psubset__imp__subset) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 2860 (all X_a all C_2 all A_2 all B_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less(fun(X_a,bool)),A_2),B_1)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),B_1),C_2)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less(fun(X_a,bool)),A_2),C_2))))) # label(fact_2879_psubset__subset__trans) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 2861 (all X_a all C_2 all A_2 all B_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_2),B_1)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less(fun(X_a,bool)),B_1),C_2)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less(fun(X_a,bool)),A_2),C_2))))) # label(fact_2880_subset__psubset__trans) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 2862 (all X_a all A_2 all B_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_2),B_1)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),uminus_uminus(fun(X_a,bool)),B_1)),hAPP(fun(X_a,bool),fun(X_a,bool),uminus_uminus(fun(X_a,bool)),A_2))))) # label(fact_2881_Compl__anti__mono) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 2863 (all X_a all A_2 all B_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),uminus_uminus(fun(X_a,bool)),A_2)),hAPP(fun(X_a,bool),fun(X_a,bool),uminus_uminus(fun(X_a,bool)),B_1))) <-> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),B_1),A_2)))) # label(fact_2882_Compl__subset__Compl__iff) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 2864 (all X_a all A_2 all B_1 hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_2),B_1) = hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,bool)),combs(X_a,bool,bool),hAPP(fun(X_a,bool),fun(X_a,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,fun(bool,bool))),combb(bool,fun(bool,bool),X_a),fconj),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(X_a,bool)),combc(X_a,fun(X_a,bool),bool),member(X_a)),A_2))),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(bool,bool),fun(fun(X_a,bool),fun(X_a,bool)),combb(bool,bool,X_a),fNot),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(X_a,bool)),combc(X_a,fun(X_a,bool),bool),member(X_a)),B_1))))) # label(fact_2883_set__diff__eq) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 2865 (all X_a all C_1 all A_2 all B_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_2),B_1))) <-> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),A_2)) & -hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),B_1)))) # label(fact_2884_Diff__iff) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 2866 (all X_a all A_2 all B_1 hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_2),B_1)),B_1) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_2),B_1)) # label(fact_2885_Diff__idemp) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 2867 (all X_a all C_1 all A_2 all B_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_2),B_1))) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),A_2)))) # label(fact_2886_DiffD1) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 2868 (all X_a all C_1 all A_2 all B_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_2),B_1))) -> -hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),B_1)))) # label(fact_2887_DiffD2) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 2869 (all X_a all A_2 all B_1 hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_2),B_1)),A_2))) # label(fact_2888_Diff__subset) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 2870 (all X_a all D_2 all B_1 all A_2 all C_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_2),C_2)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),D_2),B_1)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_2),B_1)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),C_2),D_2)))))) # label(fact_2889_Diff__mono) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 2871 (all X_a all C_2 all A_2 all B_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_2),B_1)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),B_1),C_2)) -> hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),B_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),C_2),A_2)) = ti(fun(X_a,bool),A_2)))) # label(fact_2890_double__diff) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 2872 (all X_a all B_1 all A_2 ((all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_2)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),B_1)))) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_2),B_1)))) # label(fact_2891_subsetI) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 2873 (all X_a all A_2 all B_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less(fun(X_a,bool)),A_2),B_1)) -> (exists B_3 hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),B_3),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),B_1),A_2)))))) # label(fact_2892_psubset__imp__ex__mem) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 2874 (all X_a all C_2 all A_2 ((all X_4 (hBOOL(hAPP(fun(fun(X_a,bool),bool),bool,hAPP(fun(X_a,bool),fun(fun(fun(X_a,bool),bool),bool),member(fun(X_a,bool)),X_4),A_2)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),X_4),C_2)))) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(fun(fun(X_a,bool),bool),fun(X_a,bool),complete_Sup_Sup(fun(X_a,bool)),A_2)),C_2)))) # label(fact_2893_Union__least) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 2875 (all X_a all C_1 all A_2 (-hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),A_2)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),hAPP(fun(X_a,bool),fun(X_a,bool),uminus_uminus(fun(X_a,bool)),A_2))))) # label(fact_2894_ComplI) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 2876 (all X_a all A_2 hAPP(fun(X_a,bool),fun(X_a,bool),uminus_uminus(fun(X_a,bool)),A_2) = hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(bool,bool),fun(fun(X_a,bool),fun(X_a,bool)),combb(bool,bool,X_a),fNot),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(X_a,bool)),combc(X_a,fun(X_a,bool),bool),member(X_a)),A_2)))) # label(fact_2895_Compl__eq) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 2877 (all X_a all A_2 hAPP(fun(X_a,bool),fun(X_a,bool),uminus_uminus(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),uminus_uminus(fun(X_a,bool)),A_2)) = ti(fun(X_a,bool),A_2)) # label(fact_2896_double__complement) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 2878 (all X_a all C_1 all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),hAPP(fun(X_a,bool),fun(X_a,bool),uminus_uminus(fun(X_a,bool)),A_2))) <-> -hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),A_2)))) # label(fact_2897_Compl__iff) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 2879 (all X_a all A_2 all B_1 (hAPP(fun(X_a,bool),fun(X_a,bool),uminus_uminus(fun(X_a,bool)),A_2) = hAPP(fun(X_a,bool),fun(X_a,bool),uminus_uminus(fun(X_a,bool)),B_1) <-> ti(fun(X_a,bool),A_2) = ti(fun(X_a,bool),B_1))) # label(fact_2898_Compl__eq__Compl__iff) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 2880 (all X_a all C_1 all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),hAPP(fun(X_a,bool),fun(X_a,bool),uminus_uminus(fun(X_a,bool)),A_2))) -> -hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),A_2)))) # label(fact_2899_ComplD) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 2881 (all X_a all C_1 all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),hAPP(fun(X_a,bool),fun(X_a,bool),uminus_uminus(fun(X_a,bool)),A_2))) -> -hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),A_2)))) # label(fact_2900_ComplE) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 2882 (all X_a all F1 all Real1 all Real2 hAPP(complex,X_a,hAPP(fun(real,fun(real,X_a)),fun(complex,X_a),complex_rec(X_a),F1),hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,Real1),Real2)) = hAPP(real,X_a,hAPP(real,fun(real,X_a),F1,Real1),Real2)) # label(fact_2901_complex_Orecs) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 2883 (all X_a all F1 all Real1 all Real2 hAPP(complex,X_a,hAPP(fun(real,fun(real,X_a)),fun(complex,X_a),complex_case(X_a),F1),hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,Real1),Real2)) = hAPP(real,X_a,hAPP(real,fun(real,X_a),F1,Real1),Real2)) # label(fact_2902_complex_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 2884 (all X_a (archim1804426504_field(X_a) -> (all X exists N_2 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),hAPP(nat,X_a,semiring_1_of_nat(X_a),N_2)))))) # label(fact_2903_ex__less__of__nat) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 2885 (all X_a (archim1804426504_field(X_a) -> (all X exists N_2 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),hAPP(nat,X_a,semiring_1_of_nat(X_a),N_2)))))) # label(fact_2904_ex__le__of__nat) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 2886 (all X_a all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2)) -> hAPP(fun(fun(X_a,bool),bool),nat,finite_card(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),pow(X_a),A_2)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat)))),hAPP(fun(X_a,bool),nat,finite_card(X_a),A_2)))) # label(fact_2905_card__Pow) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 2887 (all F all Aa all Ba (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),Aa),Ba)) -> ((all X_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),Aa),X_2)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_2),Ba)) -> (exists Y_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),F),X_2),Y_2)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),Y_2),zero_zero(real))))))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,F,Ba)),hAPP(real,real,F,Aa)))))) # label(fact_2906_DERIV__neg__imp__decreasing) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 2888 (all X_a all A_2 all B_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_2),B_1)) -> hBOOL(hAPP(fun(fun(X_a,bool),bool),bool,hAPP(fun(X_a,bool),fun(fun(fun(X_a,bool),bool),bool),member(fun(X_a,bool)),A_2),hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),pow(X_a),B_1))))) # label(fact_2907_PowI) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 2889 (all X_a all A_2 hBOOL(hAPP(fun(fun(X_a,bool),bool),bool,hAPP(fun(X_a,bool),fun(fun(fun(X_a,bool),bool),bool),member(fun(X_a,bool)),A_2),hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),pow(X_a),A_2)))) # label(fact_2908_Pow__top) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 2890 (all X_a all A_2 hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),pow(X_a),A_2) = hAPP(fun(fun(X_a,bool),bool),fun(fun(X_a,bool),bool),collect(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),hAPP(fun(fun(X_a,bool),fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(fun(X_a,bool),bool)),combc(fun(X_a,bool),fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool))),A_2))) # label(fact_2909_Pow__def) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 2891 (all X_a all A_2 all B_1 (hBOOL(hAPP(fun(fun(X_a,bool),bool),bool,hAPP(fun(X_a,bool),fun(fun(fun(X_a,bool),bool),bool),member(fun(X_a,bool)),A_2),hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),pow(X_a),B_1))) <-> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_2),B_1)))) # label(fact_2910_Pow__iff) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 2892 (all X_a all A_2 all B_1 (hBOOL(hAPP(fun(fun(X_a,bool),bool),bool,hAPP(fun(X_a,bool),fun(fun(fun(X_a,bool),bool),bool),member(fun(X_a,bool)),A_2),hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),pow(X_a),B_1))) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_2),B_1)))) # label(fact_2911_PowD) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 2893 (all X_a all A_2 hAPP(fun(fun(X_a,bool),bool),fun(X_a,bool),complete_Sup_Sup(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),pow(X_a),A_2)) = ti(fun(X_a,bool),A_2)) # label(fact_2912_Union__Pow__eq) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 2894 (all X_a all A_2 all B_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_2),B_1)) -> hBOOL(hAPP(fun(fun(X_a,bool),bool),bool,hAPP(fun(fun(X_a,bool),bool),fun(fun(fun(X_a,bool),bool),bool),ord_less_eq(fun(fun(X_a,bool),bool)),hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),pow(X_a),A_2)),hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),pow(X_a),B_1))))) # label(fact_2913_Pow__mono) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 2895 (all X_a all A_2 (hBOOL(hAPP(fun(fun(X_a,bool),bool),bool,finite_finite_1(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),pow(X_a),A_2))) <-> hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2)))) # label(fact_2914_finite__Pow__iff) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 2896 (all X_a all A_2 hBOOL(hAPP(fun(fun(X_a,bool),bool),bool,hAPP(fun(fun(X_a,bool),bool),fun(fun(fun(X_a,bool),bool),bool),ord_less_eq(fun(fun(X_a,bool),bool)),A_2),hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),pow(X_a),hAPP(fun(fun(X_a,bool),bool),fun(X_a,bool),complete_Sup_Sup(fun(X_a,bool)),A_2))))) # label(fact_2915_subset__Pow__Union) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 2897 (all F all Aa all Ba (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),Aa),Ba)) -> ((all X_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),Aa),X_2)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_2),Ba)) -> (exists Y_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),F),X_2),Y_2)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Y_2)))))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,F,Aa)),hAPP(real,real,F,Ba)))))) # label(fact_2916_DERIV__pos__imp__increasing) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 2898 (all X all Y (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,X),Y)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X),Y)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),Y),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))))) # label(fact_2917_coprime__sos) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 2899 (all X_a all R1_1 all R2_1 (hBOOL(hAPP(fun(X_a,fun(X_a,bool)),bool,hAPP(fun(X_a,fun(X_a,bool)),fun(fun(X_a,fun(X_a,bool)),bool),ord_less_eq(fun(X_a,fun(X_a,bool))),R1_1),R2_1)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(fun(X_a,fun(X_a,bool)),fun(X_a,bool),accp(X_a),R2_1)),hAPP(fun(X_a,fun(X_a,bool)),fun(X_a,bool),accp(X_a),R1_1))))) # label(fact_2918_accp__subset) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 2900 (all Aa all Ba (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,Aa),Ba)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,Ba),Aa)))) # label(fact_2919_coprime__commute) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 2901 (all D all A_1 all B (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,D),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A_1),B))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,D),B)))) # label(fact_2920_coprime__lmul2) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 2902 (all D all A_1 all B (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,D),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A_1),B))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,D),A_1)))) # label(fact_2921_coprime__rmul2) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 2903 (all B all D all A_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,D),A_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,D),B)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,D),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A_1),B)))))) # label(fact_2922_coprime__mul) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 2904 (all D_1 all Aa all Ba (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,D_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),Aa),Ba))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,D_1),Aa)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,D_1),Ba)))) # label(fact_2923_coprime__mul__eq) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 2905 (all A_1 hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,one_one(nat)),A_1))) # label(fact_2924_coprime__1_H) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 2906 (all A_1 hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,A_1),one_one(nat)))) # label(fact_2925_coprime__1) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 2907 (all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,N),N)) <-> N = one_one(nat))) # label(fact_2926_coprime__refl) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 2908 (all N_1 all A_1 all B (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,A_1),B)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A_1),N_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),B),N_1))))) # label(fact_2927_coprime__exp__imp) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 2909 (all N_1 all D all A_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,D),A_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,D),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A_1),N_1))))) # label(fact_2928_coprime__exp) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 2910 (all A_1 hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,hAPP(nat,nat,suc,zero_zero(nat))),A_1))) # label(fact_2929_coprime__Suc0_H) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 2911 (all A_1 hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,A_1),hAPP(nat,nat,suc,zero_zero(nat))))) # label(fact_2930_coprime__Suc0) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 2912 (all D_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,D_1),zero_zero(nat))) <-> D_1 = one_one(nat))) # label(fact_2931_coprime__0) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 2913 (all D_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,zero_zero(nat)),D_1)) <-> D_1 = one_one(nat))) # label(fact_2932_coprime__0_H) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 2914 (all N_1 hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_1),one_one(nat))),N_1))) # label(fact_2933_coprime__plus1) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 2915 (all Aa all N all Ba (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),Aa),hAPP(nat,nat,suc,N))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),Ba),hAPP(nat,nat,suc,N)))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,Aa),Ba)))) # label(fact_2934_coprime__exp2) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 2916 (all N_1 (N_1 != zero_zero(nat) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),one_one(nat))),N_1)))) # label(fact_2935_coprime__minus1) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 2917 (all X_a all R_1 all Aa (hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,fun(X_a,bool)),fun(X_a,bool),accp(X_a),R_1),Aa)) <-> (exists X_2 (ti(X_a,Aa) = ti(X_a,X_2) & (all Xa (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),R_1,Xa),X_2)) -> hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,fun(X_a,bool)),fun(X_a,bool),accp(X_a),R_1),Xa)))))))) # label(fact_2936_accp_Osimps) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 2918 (all X_a all Aa all R_1 all Ba (hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,fun(X_a,bool)),fun(X_a,bool),accp(X_a),R_1),Ba)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),R_1,Aa),Ba)) -> hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,fun(X_a,bool)),fun(X_a,bool),accp(X_a),R_1),Aa))))) # label(fact_2937_accp__downward) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 2919 (all Aa all Ba (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,Aa),Ba)) <-> (exists X_2 exists Y_2 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),Aa),X_2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),Ba),Y_2)) = one_one(nat) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),Ba),X_2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),Aa),Y_2)) = one_one(nat))))) # label(fact_2938_coprime__bezout) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 2920 (all Nat_1 hAPP(nat,nat,nat_size,hAPP(nat,nat,suc,Nat_1)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,nat_size,Nat_1)),hAPP(nat,nat,suc,zero_zero(nat)))) # label(fact_2939_nat_Osize_I2_J) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 2921 (all A_1 all B (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,A_1),B)) -> (B != one_one(nat) -> (exists X_2 exists Y_2 hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A_1),X_2) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),Y_2)),one_one(nat)))))) # label(fact_2940_coprime__bezout__strong) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 2922 (all Nat_1 hAPP(nat,nat,size_size(nat),hAPP(nat,nat,suc,Nat_1)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,size_size(nat),Nat_1)),hAPP(nat,nat,suc,zero_zero(nat)))) # label(fact_2942_nat_Osize_I4_J) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 2923 (all Z exists A_3 exists R_2 Z = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(real,complex,of_real(complex),R_2)),hAPP(complex,complex,expi,A_3))) # label(fact_2943_complex__expi__Ex) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 2924 (all X_3 all M (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),M)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),resSet,M),X_3)) -> hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),X_3))))) # label(fact_2944_ResSet__finite) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 2925 (all N_1 hAPP(nat,nat,size_size(nat),N_1) = N_1) # label(fact_2945_nat__size) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 2926 (all M all X_3 (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),resSet,M),X_3)) <-> (all Y1 all Y2 (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Y1),X_3)) & hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Y2),X_3)) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,Y1),Y2),M)) -> Y1 = Y2)))) # label(fact_2946_ResSet__def) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 2927 (all Pa hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),resSet,Pa),hAPP(int,fun(int,bool),sRStar,Pa)))) # label(fact_2948_ResSet__SRStar__prop) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 2928 (all Z hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),Z),hAPP(complex,complex,cnj,Z))) = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(complex,real,norm_norm(complex),Z)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) # label(fact_2950_complex__mod__mult__cnj) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 2929 (all X_a all X_b all Aa all Ba all A_7 all B_6 all R_1 all S_3 (hBOOL(hAPP(fun(product_prod(product_prod(X_a,X_b),product_prod(X_a,X_b)),bool),bool,hAPP(product_prod(product_prod(X_a,X_b),product_prod(X_a,X_b)),fun(fun(product_prod(product_prod(X_a,X_b),product_prod(X_a,X_b)),bool),bool),member(product_prod(product_prod(X_a,X_b),product_prod(X_a,X_b))),hAPP(product_prod(X_a,X_b),product_prod(product_prod(X_a,X_b),product_prod(X_a,X_b)),hAPP(product_prod(X_a,X_b),fun(product_prod(X_a,X_b),product_prod(product_prod(X_a,X_b),product_prod(X_a,X_b))),product_Pair(product_prod(X_a,X_b),product_prod(X_a,X_b)),hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),Aa),Ba)),hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),A_7),B_6))),hAPP(fun(product_prod(X_b,X_b),bool),fun(product_prod(product_prod(X_a,X_b),product_prod(X_a,X_b)),bool),hAPP(fun(product_prod(X_a,X_a),bool),fun(fun(product_prod(X_b,X_b),bool),fun(product_prod(product_prod(X_a,X_b),product_prod(X_a,X_b)),bool)),lex_prod(X_a,X_b),R_1),S_3))) <-> hBOOL(hAPP(fun(product_prod(X_a,X_a),bool),bool,hAPP(product_prod(X_a,X_a),fun(fun(product_prod(X_a,X_a),bool),bool),member(product_prod(X_a,X_a)),hAPP(X_a,product_prod(X_a,X_a),hAPP(X_a,fun(X_a,product_prod(X_a,X_a)),product_Pair(X_a,X_a),Aa),A_7)),R_1)) | ti(X_a,Aa) = ti(X_a,A_7) & hBOOL(hAPP(fun(product_prod(X_b,X_b),bool),bool,hAPP(product_prod(X_b,X_b),fun(fun(product_prod(X_b,X_b),bool),bool),member(product_prod(X_b,X_b)),hAPP(X_b,product_prod(X_b,X_b),hAPP(X_b,fun(X_b,product_prod(X_b,X_b)),product_Pair(X_b,X_b),Ba),B_6)),S_3)))) # label(fact_2951_in__lex__prod) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 2930 (all X hAPP(complex,complex,cnj,hAPP(real,complex,of_real(complex),X)) = hAPP(real,complex,of_real(complex),X)) # label(fact_2952_complex__cnj__complex__of__real) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 2931 (all X all Y hAPP(complex,complex,cnj,hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),X),Y)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),hAPP(complex,complex,cnj,X)),hAPP(complex,complex,cnj,Y))) # label(fact_2953_complex__cnj__divide) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 2932 (all X all N_1 hAPP(complex,complex,cnj,hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),X),N_1)) = hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),hAPP(complex,complex,cnj,X)),N_1)) # label(fact_2954_complex__cnj__power) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 2933 (all N_1 hAPP(complex,complex,cnj,hAPP(nat,complex,semiring_1_of_nat(complex),N_1)) = hAPP(nat,complex,semiring_1_of_nat(complex),N_1)) # label(fact_2955_complex__cnj__of__nat) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 2934 (all X all Y hAPP(complex,complex,cnj,hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),X),Y)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,cnj,X)),hAPP(complex,complex,cnj,Y))) # label(fact_2957_complex__cnj__mult) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 2935 (all X all Y hAPP(complex,complex,cnj,hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),X),Y)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(complex,complex,cnj,X)),hAPP(complex,complex,cnj,Y))) # label(fact_2958_cnj_Oadd) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 2936 (all W hAPP(complex,complex,cnj,hAPP(int,complex,number_number_of(complex),W)) = hAPP(int,complex,number_number_of(complex),W)) # label(fact_2959_complex__cnj__number__of) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 2937 (all Z_1 (hAPP(complex,complex,cnj,Z_1) = zero_zero(complex) <-> Z_1 = zero_zero(complex))) # label(fact_2961_complex__cnj__zero__iff) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 2938 (all Z hAPP(complex,complex,cnj,hAPP(complex,complex,cnj,Z)) = Z) # label(fact_2962_complex__cnj__cnj) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 2939 (all X_1 all Y_1 (hAPP(complex,complex,cnj,X_1) = hAPP(complex,complex,cnj,Y_1) <-> X_1 = Y_1)) # label(fact_2963_complex__cnj__cancel__iff) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 2940 (all X hAPP(complex,complex,cnj,hAPP(complex,complex,inverse_inverse(complex),X)) = hAPP(complex,complex,inverse_inverse(complex),hAPP(complex,complex,cnj,X))) # label(fact_2964_complex__cnj__inverse) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 2941 (all Z hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,cnj,Z)) = hAPP(complex,real,norm_norm(complex),Z)) # label(fact_2965_complex__mod__cnj) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 2942 (all X all Y hAPP(complex,complex,cnj,hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),X),Y)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),hAPP(complex,complex,cnj,X)),hAPP(complex,complex,cnj,Y))) # label(fact_2966_cnj_Odiff) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 2943 (all X hAPP(complex,complex,cnj,hAPP(complex,complex,uminus_uminus(complex),X)) = hAPP(complex,complex,uminus_uminus(complex),hAPP(complex,complex,cnj,X))) # label(fact_2967_cnj_Ominus) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 2944 (all A_1 all B hAPP(complex,complex,cnj,hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,A_1),B)) = hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,A_1),hAPP(real,real,uminus_uminus(real),B))) # label(fact_2968_complex__cnj) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 2945 (exists K_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),K_2)) & (all X_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,cnj,X_2))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(complex,real,norm_norm(complex),X_2)),K_2)))))) # label(fact_2970_cnj_Opos__bounded) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 2946 (exists K_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),K_2)) & (all X_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,cnj,X_2))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(complex,real,norm_norm(complex),X_2)),K_2)))))) # label(fact_2971_cnj_Ononneg__bounded) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 2947 (exists K_2 all X_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,cnj,X_2))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(complex,real,norm_norm(complex),X_2)),K_2)))) # label(fact_2972_cnj_Obounded) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 2948 (all Z hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),Z),hAPP(complex,complex,cnj,Z)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(real,complex,of_real(complex),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),hAPP(complex,real,im,Z)))),ii)) # label(fact_2973_complex__diff__cnj) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 2949 (all Z hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),Z),hAPP(complex,complex,cnj,Z)) = hAPP(real,complex,of_real(complex),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),hAPP(complex,real,re,Z)))) # label(fact_2974_complex__add__cnj) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 2950 (all Code_numeral_2 hAPP(code_code_numeral,nat,code_c271388182l_size,hAPP(code_code_numeral,code_code_numeral,code_S1047413653umeral,Code_numeral_2)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(code_code_numeral,nat,code_c271388182l_size,Code_numeral_2)),hAPP(nat,nat,suc,zero_zero(nat)))) # label(fact_2975_code__numeral_Osize_I2_J) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 2951 (all Z hAPP(complex,real,re,hAPP(real,complex,of_real(complex),Z)) = Z) # label(fact_2976_Re__complex__of__real) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 2952 (all X all Y hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),X),Y) = hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(complex,real,re,X)),hAPP(complex,real,re,Y))),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(complex,real,im,X)),hAPP(complex,real,im,Y)))) # label(fact_2977_complex__add__def) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 2953 (all X all Y hAPP(complex,real,im,hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),X),Y)) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(complex,real,re,X)),hAPP(complex,real,im,Y))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(complex,real,im,X)),hAPP(complex,real,re,Y)))) # label(fact_2978_complex__Im__mult) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 2954 (all Code_numeral all Code_numeral_5 (hAPP(code_code_numeral,code_code_numeral,code_S1047413653umeral,Code_numeral) = hAPP(code_code_numeral,code_code_numeral,code_S1047413653umeral,Code_numeral_5) <-> Code_numeral = Code_numeral_5)) # label(fact_2979_code__numeral_Oinject) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 2955 (all X_1 all Y_1 (X_1 = Y_1 <-> hAPP(complex,real,re,X_1) = hAPP(complex,real,re,Y_1) & hAPP(complex,real,im,X_1) = hAPP(complex,real,im,Y_1))) # label(fact_2980_complex__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 2956 (all X all Y (hAPP(complex,real,re,X) = hAPP(complex,real,re,Y) -> (hAPP(complex,real,im,X) = hAPP(complex,real,im,Y) -> X = Y))) # label(fact_2981_complex__eqI) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 2957 (all Z hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,hAPP(complex,real,re,Z)),hAPP(complex,real,im,Z)) = Z) # label(fact_2982_complex__surj) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 2958 (all X all Y hAPP(complex,real,re,hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,X),Y)) = X) # label(fact_2983_Re) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 2959 (all X all Y hAPP(complex,real,im,hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,X),Y)) = Y) # label(fact_2984_Im) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 2960 (all X all Y hAPP(complex,real,re,hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),X),Y)) = hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(complex,real,re,X)),hAPP(complex,real,re,Y))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(complex,real,im,X)),hAPP(complex,real,im,Y)))) # label(fact_2985_complex__Re__mult) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 2961 (all X hAPP(complex,complex,uminus_uminus(complex),X) = hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,hAPP(real,real,uminus_uminus(real),hAPP(complex,real,re,X))),hAPP(real,real,uminus_uminus(real),hAPP(complex,real,im,X)))) # label(fact_2986_complex__minus__def) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 2962 (all Z hAPP(complex,complex,cnj,Z) = hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,hAPP(complex,real,re,Z)),hAPP(real,real,uminus_uminus(real),hAPP(complex,real,im,Z)))) # label(fact_2987_cnj__def) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 2963 (all X hAPP(complex,real,re,hAPP(complex,complex,cnj,X)) = hAPP(complex,real,re,X)) # label(fact_2988_complex__Re__cnj) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 2964 (all X hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(complex,real,re,X)),hAPP(complex,real,norm_norm(complex),X)))) # label(fact_2989_complex__Re__le__cmod) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 2965 (all X hAPP(complex,real,im,hAPP(complex,complex,cnj,X)) = hAPP(real,real,uminus_uminus(real),hAPP(complex,real,im,X))) # label(fact_2990_complex__Im__cnj) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 2966 (all Z hAPP(complex,real,im,hAPP(real,complex,of_real(complex),Z)) = zero_zero(real)) # label(fact_2992_Im__complex__of__real) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 2967 (all Code_numeral_4 hAPP(code_code_numeral,code_code_numeral,code_S1047413653umeral,Code_numeral_4) != zero_zero(code_code_numeral)) # label(fact_2994_code__numeral_Osimps_I3_J) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 2968 (all Code_numeral_3 zero_zero(code_code_numeral) != hAPP(code_code_numeral,code_code_numeral,code_S1047413653umeral,Code_numeral_3)) # label(fact_2995_code__numeral_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 2969 (all X all Y hAPP(complex,real,re,hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),X),Y)) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(complex,real,re,X)),hAPP(complex,real,re,Y))) # label(fact_2999_Re_Oadd) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 2970 (all X all Y hAPP(complex,real,im,hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),X),Y)) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(complex,real,im,X)),hAPP(complex,real,im,Y))) # label(fact_3000_Im_Oadd) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 2971 (all V hAPP(complex,real,im,hAPP(int,complex,number_number_of(complex),V)) = zero_zero(real)) # label(fact_3002_complex__Im__number__of) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 2972 (all X hAPP(complex,real,re,hAPP(complex,complex,uminus_uminus(complex),X)) = hAPP(real,real,uminus_uminus(real),hAPP(complex,real,re,X))) # label(fact_3003_Re_Ominus) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 2973 (all V hAPP(complex,real,re,hAPP(int,complex,number_number_of(complex),V)) = hAPP(int,real,number_number_of(real),V)) # label(fact_3004_complex__Re__number__of) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 2974 (all X hAPP(complex,real,im,hAPP(complex,complex,uminus_uminus(complex),X)) = hAPP(real,real,uminus_uminus(real),hAPP(complex,real,im,X))) # label(fact_3005_Im_Ominus) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 2975 (all X all Y hAPP(complex,real,re,hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),X),Y)) = hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(complex,real,re,X)),hAPP(complex,real,re,Y))) # label(fact_3006_Re_Odiff) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 2976 (all X all Y hAPP(complex,real,im,hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),X),Y)) = hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(complex,real,im,X)),hAPP(complex,real,im,Y))) # label(fact_3007_Im_Odiff) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 2977 (all X all Y hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),X),Y) = hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(complex,real,re,X)),hAPP(complex,real,re,Y))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(complex,real,im,X)),hAPP(complex,real,im,Y)))),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(complex,real,re,X)),hAPP(complex,real,im,Y))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(complex,real,im,X)),hAPP(complex,real,re,Y))))) # label(fact_3008_complex__mult__def) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 2978 (all N_1 hAPP(complex,real,im,hAPP(nat,complex,semiring_1_of_nat(complex),N_1)) = zero_zero(real)) # label(fact_3009_complex__Im__of__nat) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 2979 (all N_1 hAPP(complex,real,re,hAPP(nat,complex,semiring_1_of_nat(complex),N_1)) = hAPP(nat,real,semiring_1_of_nat(real),N_1)) # label(fact_3010_complex__Re__of__nat) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 2980 (all X hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),hAPP(complex,real,re,X))),hAPP(complex,real,norm_norm(complex),X)))) # label(fact_3011_abs__Re__le__cmod) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 2981 (all X hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),hAPP(complex,real,im,X))),hAPP(complex,real,norm_norm(complex),X)))) # label(fact_3012_abs__Im__le__cmod) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 2982 (all Z hAPP(complex,real,im,hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),Z),hAPP(complex,complex,cnj,Z))) = zero_zero(real)) # label(fact_3013_complex__In__mult__cnj__zero) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 2983 (all Z hAPP(complex,real,re,hAPP(complex,complex,sgn_sgn(complex),Z)) = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(complex,real,re,Z)),hAPP(complex,real,norm_norm(complex),Z))) # label(fact_3014_Re__sgn) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 2984 (all Z hAPP(complex,real,im,hAPP(complex,complex,sgn_sgn(complex),Z)) = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(complex,real,im,Z)),hAPP(complex,real,norm_norm(complex),Z))) # label(fact_3015_Im__sgn) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 2985 (all Z hAPP(complex,real,norm_norm(complex),Z) = hAPP(real,real,sqrt,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(complex,real,re,Z)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(complex,real,im,Z)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))) # label(fact_3016_cmod__def) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 2986 (all X hAPP(complex,real,re,hAPP(complex,complex,inverse_inverse(complex),X)) = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(complex,real,re,X)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(complex,real,re,X)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(complex,real,im,X)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))) # label(fact_3017_complex__Re__inverse) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 2987 (all N_1 hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),minus_minus(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,code_S1047413653umeral,N_1)),one_one(code_code_numeral)) = N_1) # label(fact_3018_Suc__code__numeral__minus__one) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 2988 (all X hAPP(complex,real,im,hAPP(complex,complex,inverse_inverse(complex),X)) = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,uminus_uminus(real),hAPP(complex,real,im,X))),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(complex,real,re,X)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(complex,real,im,X)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))) # label(fact_3019_complex__Im__inverse) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 2989 (all Z hAPP(complex,real,norm_norm(complex),Z) = hAPP(real,real,sqrt,hAPP(complex,real,re,hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),Z),hAPP(complex,complex,cnj,Z))))) # label(fact_3020_complex__mod__sqrt__Re__mult__cnj) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 2990 (all Z hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),Z),hAPP(complex,complex,cnj,Z)) = hAPP(real,complex,of_real(complex),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(complex,real,re,Z)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(complex,real,im,Z)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))) # label(fact_3021_complex__mult__cnj) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 2991 (all X hAPP(complex,complex,inverse_inverse(complex),X) = hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(complex,real,re,X)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(complex,real,re,X)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(complex,real,im,X)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,uminus_uminus(real),hAPP(complex,real,im,X))),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(complex,real,re,X)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(complex,real,im,X)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))) # label(fact_3022_complex__inverse__def) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 2992 (exists K_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),K_2)) & (all X_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,norm_norm(real),hAPP(complex,real,im,X_2))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(complex,real,norm_norm(complex),X_2)),K_2)))))) # label(fact_3023_Im_Opos__bounded) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 2993 (exists K_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),K_2)) & (all X_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,norm_norm(real),hAPP(complex,real,re,X_2))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(complex,real,norm_norm(complex),X_2)),K_2)))))) # label(fact_3024_Re_Opos__bounded) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 2994 (exists K_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),K_2)) & (all X_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,norm_norm(real),hAPP(complex,real,im,X_2))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(complex,real,norm_norm(complex),X_2)),K_2)))))) # label(fact_3025_Im_Ononneg__bounded) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 2995 (exists K_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),K_2)) & (all X_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,norm_norm(real),hAPP(complex,real,re,X_2))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(complex,real,norm_norm(complex),X_2)),K_2)))))) # label(fact_3026_Re_Ononneg__bounded) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 2996 (exists K_2 all X_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,norm_norm(real),hAPP(complex,real,im,X_2))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(complex,real,norm_norm(complex),X_2)),K_2)))) # label(fact_3027_Im_Obounded) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 2997 (exists K_2 all X_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,norm_norm(real),hAPP(complex,real,re,X_2))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(complex,real,norm_norm(complex),X_2)),K_2)))) # label(fact_3028_Re_Obounded) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 2998 (all Code_numeral_2 hAPP(code_code_numeral,nat,size_size(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,code_S1047413653umeral,Code_numeral_2)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(code_code_numeral,nat,size_size(code_code_numeral),Code_numeral_2)),hAPP(nat,nat,suc,zero_zero(nat)))) # label(fact_3029_code__numeral_Osize_I4_J) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 2999 (all Y (Y != zero_zero(code_code_numeral) -> -(all Code_numeral_1 Y != hAPP(code_code_numeral,code_code_numeral,code_S1047413653umeral,Code_numeral_1)))) # label(fact_3030_code__numeral_Oexhaust) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 3000 (all Z hAPP(complex,complex,expi,Z) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(real,complex,of_real(complex),hAPP(real,real,exp(real),hAPP(complex,real,re,Z)))),hAPP(real,complex,cis,hAPP(complex,real,im,Z)))) # label(fact_3031_expi__def) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 3001 (all A_1 hAPP(complex,real,re,hAPP(real,complex,cis,A_1)) = hAPP(real,real,cos,A_1)) # label(fact_3032_Re__cis) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 3002 (all A_1 hAPP(complex,real,im,hAPP(real,complex,cis,A_1)) = hAPP(real,real,sin,A_1)) # label(fact_3033_Im__cis) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 3003 (all A_1 all B hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(real,complex,cis,A_1)),hAPP(real,complex,cis,B)) = hAPP(real,complex,cis,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A_1),B))) # label(fact_3034_cis__mult) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 3004 (all A_1 hAPP(complex,complex,inverse_inverse(complex),hAPP(real,complex,cis,A_1)) = hAPP(real,complex,cis,hAPP(real,real,uminus_uminus(real),A_1))) # label(fact_3036_cis__inverse) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 3005 (all A_1 all B hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),hAPP(real,complex,cis,A_1)),hAPP(real,complex,cis,B)) = hAPP(real,complex,cis,hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A_1),B))) # label(fact_3037_cis__divide) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 3006 (all A_1 hAPP(real,complex,cis,A_1) = hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,hAPP(real,real,cos,A_1)),hAPP(real,real,sin,A_1))) # label(fact_3038_cis__def) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 3007 (all A_1 all N_1 hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),hAPP(real,complex,cis,A_1)),N_1) = hAPP(real,complex,cis,hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,real_1(nat),N_1)),A_1))) # label(fact_3039_DeMoivre) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 3008 (all N_1 all A_1 hAPP(real,complex,cis,hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,real_1(nat),hAPP(nat,nat,suc,N_1))),A_1)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(real,complex,cis,A_1)),hAPP(real,complex,cis,hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,real_1(nat),N_1)),A_1)))) # label(fact_3040_cis__real__of__nat__Suc__mult) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 3009 (all N_1 all A_1 hAPP(real,real,cos,hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,real_1(nat),N_1)),A_1)) = hAPP(complex,real,re,hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),hAPP(real,complex,cis,A_1)),N_1))) # label(fact_3042_cos__n__Re__cis__pow__n) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 3010 (all N_1 all A_1 hAPP(real,real,sin,hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,real_1(nat),N_1)),A_1)) = hAPP(complex,real,im,hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),hAPP(real,complex,cis,A_1)),N_1))) # label(fact_3043_sin__n__Im__cis__pow__n) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 3011 (all X_a all S all T_4 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),T_4)) -> (-hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),S)) -> -hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),S),T_4)))))) # label(fact_3044_Diff__infinite__finite) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 3012 (all N_1 all M_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),N_1),M_1)) -> M_1 = zero_zero(nat) | M_1 = N_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),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),N_1)),M_1)))) # label(fact_3045_divides__cases) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 3013 (all X_a all S all T_4 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),S),T_4)) -> (-hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),S)) -> -hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),T_4))))) # label(fact_3046_infinite__super) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 3014 (all X hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),X))) # label(fact_3047_dvd_Oorder__refl) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 3015 (all X_a (comm_semiring_1(X_a) -> (all A_1 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_1),zero_zero(X_a)))))) # label(fact_3048_dvd__0__right) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 3016 (all K_4 hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,suc,zero_zero(nat))),K_4))) # label(fact_3049_dvd__1__left) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 3017 (all E_1 all B all D all A_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),D),A_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),E_1),B)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,A_1),B)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,D),E_1)))))) # label(fact_3050_coprime__divisors) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 3018 (all N_1 all X all Y (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),Y)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),X),N_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),Y),N_1))))) # label(fact_3051_divides__exp) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 3019 (all X_a (comm_semiring_1(X_a) -> (all N_1 all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),X),Y)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),N_1)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),Y),N_1))))))) # label(fact_3052_dvd__power__same) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 3020 (all A_1 -(hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),zero_zero(nat)),A_1)) & -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),zero_zero(nat))))) # label(fact_3053_gcd__lcm__complete__lattice__nat_Onot__top__less) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 3021 (all A_1 hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),zero_zero(nat)))) # label(fact_3054_gcd__lcm__complete__lattice__nat_Otop__greatest) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 3022 (all Aa (Aa != zero_zero(nat) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Aa),zero_zero(nat))) & -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),zero_zero(nat)),Aa)))) # label(fact_3055_gcd__lcm__complete__lattice__nat_Oless__top) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 3023 (all Aa (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),zero_zero(nat)),Aa)) <-> Aa = zero_zero(nat))) # label(fact_3056_gcd__lcm__complete__lattice__nat_Otop__unique) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 3024 (all A_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),zero_zero(nat)),A_1)) -> A_1 = zero_zero(nat))) # label(fact_3057_gcd__lcm__complete__lattice__nat_Otop__le) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 3025 (all A_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),one_one(nat))) -> A_1 = one_one(nat))) # label(fact_3058_gcd__lcm__complete__lattice__nat_Ole__bot) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 3026 (all Aa (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Aa),one_one(nat))) <-> Aa = one_one(nat))) # label(fact_3059_gcd__lcm__complete__lattice__nat_Obot__unique) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 3027 (all Aa (Aa != one_one(nat) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),one_one(nat)),Aa)) & -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Aa),one_one(nat))))) # label(fact_3060_gcd__lcm__complete__lattice__nat_Obot__less) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 3028 (all A_1 hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),one_one(nat)),A_1))) # label(fact_3061_gcd__lcm__complete__lattice__nat_Obot__least) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 3029 (all A_1 -(hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),one_one(nat))) & -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),one_one(nat)),A_1)))) # label(fact_3062_gcd__lcm__complete__lattice__nat_Onot__less__bot) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 3030 (all X_a (comm_semiring_1(X_a) -> (all A_1 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),one_one(X_a)),A_1))))) # label(fact_3063_one__dvd) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 3031 (all M (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),M),one_one(nat))) <-> M = one_one(nat))) # label(fact_3064_nat__dvd__1__iff__1) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 3032 (all X_a (comm_semiring_1(X_a) -> (all C all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_1),B)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_1),C)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(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_3065_dvd__add) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 3033 (all X_a (comm_semiring_1(X_a) -> (all A_1 all B hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)))))) # label(fact_3066_dvd__triv__left) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 3034 (all X_a (comm_semiring_1(X_a) -> (all A_1 all B hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),A_1)))))) # label(fact_3067_dvd__triv__right) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 3035 (all X_a (comm_semiring_1(X_a) -> (all C all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_1),B)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(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_3068_dvd__mult2) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 3036 (all X_a (comm_semiring_1(X_a) -> (all B all A_1 all C (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_1),C)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(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_3069_dvd__mult) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 3037 (all X_a (comm_semiring_1(X_a) -> (all C all D all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_1),B)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),C),D)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(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),D)))))))) # label(fact_3070_mult__dvd__mono) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 3038 (all X_a (dvd(X_a) -> (all A_1 all B all K_4 (ti(X_a,A_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),K_4) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),B),A_1)))))) # label(fact_3071_dvdI) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 3039 (all X_a (comm_semiring_1(X_a) -> (all A_1 all B all C (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)),C)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_1),C)))))) # label(fact_3072_dvd__mult__left) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 3040 (all X_a (comm_semiring_1(X_a) -> (all A_1 all B all C (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)),C)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),B),C)))))) # label(fact_3073_dvd__mult__right) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 3041 (all C all A_1 all B (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),B)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A_1),C)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),C))))) # label(fact_3074_divides__mul__r) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 3042 (all C all A_1 all B (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),B)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),C),A_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),C),B))))) # label(fact_3075_divides__mul__l) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 3043 (all B all D all A_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),D),A_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),D),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A_1),B))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),D),B))))) # label(fact_3076_divides__add__revr) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 3044 (all K all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),K),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),K))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),K),N)))) # label(fact_3077_dvd__reduce) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 3045 (all X_a (comm_semiring_1(X_a) -> (all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),zero_zero(X_a)),A_1)) -> ti(X_a,A_1) = zero_zero(X_a))))) # label(fact_3078_dvd__0__left) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 3046 (all X_a (semiring_div(X_a) -> (all M all K all N (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),K),N)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),K),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),M),N))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),K),M))))))) # label(fact_3079_dvd__mod__iff) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 3047 (all X_a (semiring_div(X_a) -> (all A_1 all C all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),C),B)) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),A_1),B)),C) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),A_1),C))))) # label(fact_3080_mod__mod__cancel) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 3048 (all X_a (semiring_div(X_a) -> (all N_1 all K_4 all M_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),K_4),M_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),K_4),N_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),K_4),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),M_1),N_1)))))))) # label(fact_3081_dvd__mod) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 3049 (all X_a (semiring_div(X_a) -> (all K_4 all M_1 all N_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),K_4),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),M_1),N_1))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),K_4),N_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),K_4),M_1))))))) # label(fact_3082_dvd__mod__imp__dvd) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 3050 (all X_a (semiring_div(X_a) -> (all C_1 all Aa all Ba (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),Aa),Ba)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),Aa),C_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),Ba),Aa)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),C_1),Aa))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),Ba),C_1)))))))) # label(fact_3083_div__dvd__div) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 3051 (all X -(hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),X)) & -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),X)))) # label(fact_3084_dvd_Oless__irrefl) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 3052 (all X_1 all Y_1 (X_1 = Y_1 <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_1),Y_1)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y_1),X_1)))) # label(fact_3085_dvd_Oeq__iff) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 3053 (all X_1 all Y_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_1),Y_1)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_1),Y_1)) & -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y_1),X_1)) | X_1 = Y_1)) # label(fact_3086_dvd_Ole__less) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 3054 (all X_1 all Y_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_1),Y_1)) & -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y_1),X_1)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_1),Y_1)) & X_1 != Y_1)) # label(fact_3087_dvd_Oless__le) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 3055 (all X_1 all Y_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_1),Y_1)) & -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y_1),X_1)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_1),Y_1)) & -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y_1),X_1)))) # label(fact_3088_dvd_Oless__le__not__le) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 3056 (all A_1 all B (A_1 != B -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),B)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),B)) & -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),B),A_1))))) # label(fact_3089_dvd_Oneq__le__trans) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 3057 (all X all Y (X = Y -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),Y)))) # label(fact_3090_dvd_Oeq__refl) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.76 3058 (all Y_1 all X_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y_1),X_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_1),Y_1)) <-> X_1 = Y_1))) # label(fact_3091_dvd_Oantisym__conv) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.77 3059 (all X all Y (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),Y)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),Y)) & -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y),X)) | X = Y)) # label(fact_3092_dvd_Ole__imp__less__or__eq) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.77 3060 (all A_1 all B (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),B)) -> (A_1 != B -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),B)) & -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),B),A_1))))) # label(fact_3093_dvd_Ole__neq__trans) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.77 3061 (all C all A_1 all B (A_1 = B -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),B),C)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),C))))) # label(fact_3094_dvd_Oord__eq__le__trans) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.77 3062 (all C all A_1 all B (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),B)) -> (B = C -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),C))))) # label(fact_3095_dvd_Oord__le__eq__trans) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.77 3063 (all M_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),M_1),N_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),N_1),M_1)) -> M_1 = N_1))) # label(fact_3096_dvd__antisym) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.77 3064 (all X all Y (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),Y)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y),X)) -> X = Y))) # label(fact_3097_dvd_Oantisym) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.77 3065 (all Z all X all Y (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),Y)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y),Z)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),Z))))) # label(fact_3098_dvd_Oorder__trans) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.77 3066 (all C all A_1 all B (A_1 = B -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),B),C)) & -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),C),B)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),C)) & -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),C),A_1))))) # label(fact_3099_dvd_Oord__eq__less__trans) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.77 3067 (all Z all X all Y (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),Y)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y),Z)) & -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Z),Y)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),Z)) & -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Z),X))))) # label(fact_3100_dvd_Ole__less__trans) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.77 3068 (all X all Y (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),Y)) & -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y),X)) -> X != Y)) # label(fact_3101_dvd_Oless__imp__neq) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.77 3069 (all X all Y (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),Y)) & -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y),X)) -> -(hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y),X)) & -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),Y))))) # label(fact_3102_dvd_Oless__not__sym) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.77 3070 (all X all Y (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),Y)) & -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y),X)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),Y)))) # label(fact_3103_dvd_Oless__imp__le) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.77 3071 (all X all Y (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),Y)) & -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y),X)) -> -(hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y),X)) & -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),Y))))) # label(fact_3104_dvd_Oless__imp__not__less) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.77 3072 (all X all Y (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),Y)) & -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y),X)) -> X != Y)) # label(fact_3105_dvd_Oless__imp__not__eq) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.77 3073 (all X all Y (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),Y)) & -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y),X)) -> Y != X)) # label(fact_3106_dvd_Oless__imp__not__eq2) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.77 3074 (all P_1 all X_1 all Y_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_1),Y_1)) & -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y_1),X_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y_1),X_1)) & -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_1),Y_1)) -> hBOOL(P_1)))) # label(fact_3107_dvd_Oless__imp__triv) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.77 3075 (all C all A_1 all B (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),B)) & -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),B),A_1)) -> (B = C -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),C)) & -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),C),A_1))))) # label(fact_3108_dvd_Oord__less__eq__trans) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.77 3076 (all Z all X all Y (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),Y)) & -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y),X)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y),Z)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),Z)) & -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Z),X))))) # label(fact_3109_dvd_Oless__le__trans) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.77 3077 (all A_1 all B (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),B)) & -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),B),A_1)) -> -(hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),B),A_1)) & -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),B))))) # label(fact_3110_dvd_Oless__asym_H) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.77 3078 (all Z all X all Y (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),Y)) & -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y),X)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y),Z)) & -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Z),Y)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),Z)) & -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Z),X))))) # label(fact_3111_dvd_Oless__trans) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.77 3079 (all X all Y (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),Y)) & -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y),X)) -> -(hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y),X)) & -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),Y))))) # label(fact_3112_dvd_Oless__asym) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.77 3080 (all X_a (comm_semiring_1(X_a) -> (all A_1 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_1),A_1))))) # label(fact_3113_dvd__refl) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.77 3081 (all X_a (comm_semiring_1(X_a) -> (all C all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_1),B)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),B),C)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_1),C))))))) # label(fact_3114_dvd__trans) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.77 3082 (all X_1 all Y_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_1),Y_1)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y_1),X_1)) <-> X_1 = Y_1)) # label(fact_3115_divides__antisym) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.77 3083 (all X_a (linordered_idom(X_a) -> (all L_4 all K_4 (hAPP(X_a,X_a,abs_abs(X_a),L_4) = hAPP(X_a,X_a,abs_abs(X_a),K_4) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),L_4),K_4)))))) # label(fact_3116_dvd__if__abs__eq) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.77 3084 (all X_a (linordered_idom(X_a) -> (all M all K (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),hAPP(X_a,X_a,abs_abs(X_a),M)),K)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),M),K)))))) # label(fact_3117_abs__dvd__iff) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.77 3085 (all X_a (linordered_idom(X_a) -> (all M all K (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),M),hAPP(X_a,X_a,abs_abs(X_a),K))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),M),K)))))) # label(fact_3118_dvd__abs__iff) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.77 3086 (all X_a (comm_ring_1(X_a) -> (all Z all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),X),Y)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),X),Z)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),Y),Z)))))))) # label(fact_3119_dvd__diff) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.77 3087 (all N_1 all K_4 all M_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),K_4),M_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),K_4),N_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),K_4),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),N_1)))))) # label(fact_3120_dvd__diff__nat) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.77 3088 (all X_a (comm_ring_1(X_a) -> (all X_1 all Y_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),X_1)),Y_1)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),X_1),Y_1)))))) # label(fact_3121_minus__dvd__iff) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.77 3089 (all X_a (comm_ring_1(X_a) -> (all X_1 all Y_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),X_1),hAPP(X_a,X_a,uminus_uminus(X_a),Y_1))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),X_1),Y_1)))))) # label(fact_3122_dvd__minus__iff) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.77 3090 (all X_a (idom(X_a) -> (all C_1 all Aa all Ba (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1),Aa)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1),Ba))) <-> ti(X_a,C_1) = zero_zero(X_a) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),Aa),Ba)))))) # label(fact_3123_dvd__mult__cancel__left) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.77 3091 (all X_a (idom(X_a) -> (all Aa all C_1 all Ba (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Aa),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Ba),C_1))) <-> ti(X_a,C_1) = zero_zero(X_a) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),Aa),Ba)))))) # label(fact_3124_dvd__mult__cancel__right) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.77 3092 (all X_a (semiring_div(X_a) -> (all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_1),B)) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),B),A_1) = zero_zero(X_a))))) # label(fact_3125_dvd__imp__mod__0) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.77 3093 (all X_a (semiring_div(X_a) -> (all Aa all Ba (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),Aa),Ba)) <-> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),Ba),Aa) = zero_zero(X_a))))) # label(fact_3126_dvd__eq__mod__eq__0) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.77 3094 (all X_a (semiring_div(X_a) -> (all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(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,hAPP(X_a,fun(X_a,X_a),div_div(X_a),B),A_1)) = ti(X_a,B))))) # label(fact_3127_dvd__mult__div__cancel) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.77 3095 (all X_a (semiring_div(X_a) -> (all A_1 all C all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),C),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),div_div(X_a),B),C)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)),C))))) # label(fact_3128_div__mult__swap) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.77 3096 (all X_a (semiring_div(X_a) -> (all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(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,hAPP(X_a,fun(X_a,X_a),div_div(X_a),B),A_1)),A_1) = ti(X_a,B))))) # label(fact_3129_dvd__div__mult__self) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.77 3097 (all X_a (semiring_div(X_a) -> (all C all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(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,hAPP(X_a,fun(X_a,X_a),div_div(X_a),B),A_1)),C) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),C)),A_1))))) # label(fact_3130_dvd__div__mult) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.77 3098 (all X_a (semiring_div(X_a) -> (all Z all W all Y all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),Y),X)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),Z),W)) -> 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),div_div(X_a),X),Y)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),W),Z)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),W)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Y),Z))))))) # label(fact_3131_div__mult__div__if__dvd) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.77 3099 (all X_a (semiring_div(X_a) -> (all Y all Z all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),Z),X)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),Z),Y)) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X),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),div_div(X_a),X),Z)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),Y),Z))))))) # label(fact_3132_div__add) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.77 3100 (all X_a (comm_semiring_1(X_a) -> (all A_1 all M_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),N_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),M_1)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N_1))))))) # label(fact_3133_le__imp__power__dvd) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.77 3101 (all X_a (comm_semiring_1(X_a) -> (all N_1 all M_1 all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),X),Y)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_1),M_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),N_1)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),Y),M_1)))))))) # label(fact_3134_dvd__power__le) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.77 3102 (all X_a (comm_semiring_1(X_a) -> (all M_1 all A_1 all N_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N_1)),B)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),N_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),M_1)),B))))))) # label(fact_3135_power__le__dvd) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.77 3103 (all X_a (semiring_div(X_a) -> (all N_1 all Y all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),Y),X)) -> 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),div_div(X_a),X),Y)),N_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),N_1)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),Y),N_1)))))) # label(fact_3136_div__power) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.77 3104 (all X_a (ring_div(X_a) -> (all Y all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),Y),X)) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),X)),Y) = hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),X),Y)))))) # label(fact_3137_dvd__neg__div) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.77 3105 (all X_a (ring_div(X_a) -> (all Y all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),Y),X)) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),X),hAPP(X_a,X_a,uminus_uminus(X_a),Y)) = hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),X),Y)))))) # label(fact_3138_dvd__div__neg) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.77 3106 (all M (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),M),hAPP(nat,nat,suc,zero_zero(nat)))) <-> M = hAPP(nat,nat,suc,zero_zero(nat)))) # label(fact_3139_dvd__1__iff__1) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.77 3107 (all N_1 all M_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),M_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_1)) -> -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),N_1),M_1))))) # label(fact_3140_nat__dvd__not__less) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.77 3108 (all M_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),M_1),N_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),M_1))))) # label(fact_3141_dvd__pos__nat) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.77 3109 (all A_1 all B (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),B)) -> B = zero_zero(nat) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A_1),B)))) # label(fact_3142_divides__ge) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.77 3110 (all M_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),M_1),N_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),N_1)) | N_1 = zero_zero(nat))) # label(fact_3143_divides__le) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.77 3111 (all M all K all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(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),K))) <-> K = zero_zero(nat) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),M),N)))) # label(fact_3144_nat__mult__dvd__cancel__disj_H) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.77 3112 (all K all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(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))) <-> K = zero_zero(nat) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),M),N)))) # label(fact_3145_nat__mult__dvd__cancel__disj) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.77 3113 (all K_4 all M_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),K_4),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),N_1))) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),K_4),M_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_1),M_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),K_4),N_1)))))) # label(fact_3146_dvd__diffD1) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.77 3114 (all K_4 all M_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),K_4),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),N_1))) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),K_4),N_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_1),M_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),K_4),M_1)))))) # label(fact_3147_dvd__diffD) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.77 3115 (all A_1 all N_1 all B (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A_1),N_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),B),N_1))) -> (N_1 != zero_zero(nat) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),B))))) # label(fact_3148_divides__rev) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.77 3116 (all X all Y all N_1 (N_1 != zero_zero(nat) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),X),N_1)),Y)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),Y))))) # label(fact_3149_divides__exp2) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.77 3117 (all Aa all Ba all N (N != zero_zero(nat) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),Aa),N)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),Ba),N))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Aa),Ba))))) # label(fact_3150_pow__divides__eq__nat) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.77 3118 (all N_1 all X all Y (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),Y)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),Y),hAPP(nat,nat,suc,N_1)))))) # label(fact_3151_divides__rexp) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.77 3119 (all N_1 all M_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_1),M_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,fact_fact(nat),N_1)),hAPP(nat,nat,fact_fact(nat),M_1))))) # label(fact_3152_fact__dvd) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.77 3120 (all N_1 all M_1 all R_4 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),M_1),R_4)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),N_1),R_4)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,M_1),N_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),N_1)),R_4)))))) # label(fact_3153_divides__mul) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.77 3121 (all D all A_1 all B (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),D),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A_1),B))) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,D),A_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),D),B))))) # label(fact_3154_coprime__divprod) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.77 3122 (all Aa all Ba (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,Aa),Ba)) <-> (all D_3 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),D_3),Aa)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),D_3),Ba)) <-> D_3 = one_one(nat))))) # label(fact_3155_coprime) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.77 3123 (all X_a (dvd(X_a) & semiring_0(X_a) -> (all P_1 all L ((exists X_2 hBOOL(hAPP(X_a,bool,P_1,hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),L),X_2)))) <-> (exists X_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),L),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X_2),zero_zero(X_a)))) & hBOOL(hAPP(X_a,bool,P_1,X_2)))))))) # label(fact_3156_unity__coeff__ex) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.77 3124 (all X_a (comm_ring(X_a) & dvd(X_a) -> (all T_3 all D_1 all D_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),D_1),D_2)) -> (all X_2 all K_1 (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),D_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X_2),T_3))) <-> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),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),minus_minus(X_a),X_2),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),K_1),D_2))),T_3))))))))) # label(fact_3157_inf__period_I4_J) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.77 3125 (all X_a (comm_ring(X_a) & dvd(X_a) -> (all T_3 all D_1 all D_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),D_1),D_2)) -> (all X_2 all K_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),D_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X_2),T_3))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),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),minus_minus(X_a),X_2),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),K_1),D_2))),T_3))))))))) # label(fact_3158_inf__period_I3_J) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.77 3126 (all X_a (semiring_div(X_a) -> (all D_1 all Ba all C_1 all Aa (ti(X_a,Aa) != zero_zero(X_a) -> (ti(X_a,C_1) != zero_zero(X_a) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),Aa),Ba)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),C_1),D_1)) -> (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),Ba),Aa) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),D_1),C_1) <-> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Ba),C_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Aa),D_1))))))))) # label(fact_3159_dvd__div__div__eq__mult) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.77 3127 (all X_a (semiring_div(X_a) -> (all C_1 all Ba all Aa (ti(X_a,Aa) != zero_zero(X_a) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),Aa),Ba)) -> (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),Ba),Aa) = ti(X_a,C_1) <-> ti(X_a,Ba) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1),Aa))))))) # label(fact_3160_dvd__div__eq__mult) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.77 3128 (all X_a (semiring_div(X_a) & number(X_a) -> (all X_1 all Y_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),hAPP(int,X_a,number_number_of(X_a),X_1)),hAPP(int,X_a,number_number_of(X_a),Y_1))) <-> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),hAPP(int,X_a,number_number_of(X_a),Y_1)),hAPP(int,X_a,number_number_of(X_a),X_1)) = zero_zero(X_a))))) # label(fact_3161_dvd__eq__mod__eq__0__number__of) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.77 3129 (all K_4 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),K_4),N_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_4),N_1))))) # label(fact_3162_dvd__imp__le) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.77 3130 (all K_4 all M_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_4),M_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_4),N_1))) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K_4)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),M_1),N_1))))) # label(fact_3163_dvd__mult__cancel) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.77 3131 (all M all N all K (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(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))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),M),N))))) # label(fact_3164_nat__mult__dvd__cancel1) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.77 3132 (all N_1 all M_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),one_one(nat)),M_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),N_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),M_1),hAPP(nat,nat,fact_fact(nat),N_1)))))) # label(fact_3165_dvd__fact__nat) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.77 3133 (all X_a (comm_semiring_1(X_a) -> (all X all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)) | ti(X_a,X) = one_one(X_a) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),X),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),N_1))))))) # label(fact_3166_dvd__power) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.77 3134 (all X all Q_2 all N_1 all R_4 (X = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),Q_2),N_1)),R_4) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),R_4)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),R_4),N_1)) -> -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),N_1),X)))))) # label(fact_3167_divides__div__not) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.77 3135 (all N all M (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),M)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N),M)),M)) <-> N = one_one(nat)))) # label(fact_3168_dvd__mult__cancel2) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.77 3136 (all N all M (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),M)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),N)),M)) <-> N = one_one(nat)))) # label(fact_3169_dvd__mult__cancel1) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.77 3137 (all I_1 all M_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),I_1),M_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),I_1),N_1))) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),one_one(nat)),I_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),N_1))))) # label(fact_3170_power__dvd__imp__le) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.77 3138 (all N (hBOOL(hAPP(nat,bool,even_odd_even(nat),N)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),N)))) # label(fact_3171_even__dvd) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.77 3139 (all X_1 (hBOOL(hAPP(nat,bool,even_odd_even(nat),X_1)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),X_1)))) # label(fact_3172_nat__even__iff__2__dvd) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.77 3140 (all N_1 all D (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),D)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),D),N_1)) -> hAPP(nat,real,real_1(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),N_1),D)) = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(nat,real,real_1(nat),N_1)),hAPP(nat,real,real_1(nat),D))))) # label(fact_3173_real__of__nat__div) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.77 3141 (all N all N_5 all F ((all N_2 hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,F,N_2)),hAPP(nat,nat,F,hAPP(nat,nat,suc,N_2))))) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N),N_5)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,F,N)),hAPP(nat,nat,F,N_5)))))) # label(fact_3174_dvd_Olift__Suc__mono__le) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.77 3142 (all N all M all F ((all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,F,N_2)),hAPP(nat,nat,F,hAPP(nat,nat,suc,N_2)))) & -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,F,hAPP(nat,nat,suc,N_2))),hAPP(nat,nat,F,N_2))))) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,F,N)),hAPP(nat,nat,F,M))) & -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,F,M)),hAPP(nat,nat,F,N))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),M))))) # label(fact_3175_dvd_Olift__Suc__mono__less__iff) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.77 3143 (all N all N_5 all F ((all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,F,N_2)),hAPP(nat,nat,F,hAPP(nat,nat,suc,N_2)))) & -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,F,hAPP(nat,nat,suc,N_2))),hAPP(nat,nat,F,N_2))))) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),N_5)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,F,N)),hAPP(nat,nat,F,N_5))) & -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,F,N_5)),hAPP(nat,nat,F,N)))))) # label(fact_3176_dvd_Olift__Suc__mono__less) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.77 3144 (all D hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(int,int,abs_abs(int),D)),D))) # label(fact_3177_zdvd__self__abs2) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.77 3145 (all D hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),D),hAPP(int,int,abs_abs(int),D)))) # label(fact_3178_zdvd__self__abs1) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.77 3146 (all N_1 all F_4 all M_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),F_4),M_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),F_4),N_1)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),F_4),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),M_1),N_1)))))) # label(fact_3179_zdvd__zmod) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.77 3147 (all K_4 all M_1 all N_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),K_4),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),M_1),N_1))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),K_4),N_1)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),K_4),M_1))))) # label(fact_3180_zdvd__zmod__imp__zdvd) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.77 3148 (all A_1 all B (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A_1),B)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),B),A_1)) -> hAPP(int,int,abs_abs(int),A_1) = hAPP(int,int,abs_abs(int),B)))) # label(fact_3181_zdvd__antisym__abs) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.77 3149 (all K_4 all M_1 all N_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),K_4),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),M_1),N_1))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),K_4),N_1)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),K_4),M_1))))) # label(fact_3182_zdvd__zdiffD) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.77 3150 (all D_1 all T_3 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),D_1),T_3)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(int,int,uminus_uminus(int),D_1)),T_3)))) # label(fact_3183_uminus__dvd__conv_I1_J) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.77 3151 (all D_1 all T_3 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),D_1),T_3)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),D_1),hAPP(int,int,uminus_uminus(int),T_3))))) # label(fact_3184_uminus__dvd__conv_I2_J) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.77 3152 (all N_1 all M_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),M_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),M_1),N_1)) -> -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),N_1),M_1))))) # label(fact_3185_zdvd__not__zless) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.77 3153 (all N_1 all M_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),M_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),N_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),M_1),N_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),N_1),M_1)) -> M_1 = N_1))))) # label(fact_3186_zdvd__antisym__nonneg) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.77 3154 (all N_1 all M_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),N_1),M_1)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),M_1),zero_zero(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),N_1),M_1)))) # label(fact_3187_zdvd__bounds) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.77 3155 (all M all T_3 all K (K != zero_zero(int) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),M),T_3)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K),M)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K),T_3)))))) # label(fact_3188_zdvd__mono) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.77 3156 (all K_4 all M_1 all N_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K_4),M_1)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K_4),N_1))) -> (K_4 != zero_zero(int) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),M_1),N_1))))) # label(fact_3189_zdvd__mult__cancel) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.77 3157 (all C_1 all X_1 all T_3 all Aa all D_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),Aa),D_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),Aa),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X_1),T_3))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),Aa),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X_1),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C_1),D_1))),T_3)))))) # label(fact_3190_zdvd__period) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.77 3158 (all K all N all M (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),K),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),N),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K),M)))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),K),N)))) # label(fact_3191_zdvd__reduce) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.77 3159 (all Aa all M (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,Aa),zero_zero(int)),M)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),M),Aa)))) # label(fact_3192_zcong__zero__equiv__div) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.77 3160 (all X_1 all Pa (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,X_1),zero_zero(int)),Pa)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),Pa),X_1)))) # label(fact_3193_zcong__eq__zdvd__prop) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.77 3161 (all X_1 all Y_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(nat,int,semiring_1_of_nat(int),X_1)),hAPP(nat,int,semiring_1_of_nat(int),Y_1))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_1),Y_1)))) # label(fact_3194_Nat__Transfer_Otransfer__int__nat__relations_I4_J) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.77 3162 (all X_1 all Y_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_1),Y_1)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(nat,int,semiring_1_of_nat(int),X_1)),hAPP(nat,int,semiring_1_of_nat(int),Y_1))))) # label(fact_3195_zdvd__int) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.77 3163 (all A_1 all N_1 all B (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A_1),N_1)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),B),N_1))) -> (N_1 != zero_zero(nat) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A_1),B))))) # label(fact_3196_pow__divides__pow__int) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.77 3164 (all Aa all Ba all N (N != zero_zero(nat) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),Aa),N)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),Ba),N))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),Aa),Ba))))) # label(fact_3197_pow__divides__eq__int) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.77 3165 (all N_1 all M_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),N_1),M_1)) -> hAPP(int,int,hAPP(int,fun(int,int),times_times(int),N_1),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),M_1),N_1)) = M_1)) # label(fact_3198_zdvd__mult__div__cancel) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.77 3166 (all X_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),X_1),one_one(int))) <-> hAPP(int,int,abs_abs(int),X_1) = one_one(int))) # label(fact_3199_zdvd1__eq) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.77 3167 (all Aa all Ba all M (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,Aa),Ba),M)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),M),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),Aa),Ba))))) # label(fact_3200_zcong__def) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.77 3168 (all X_1 all N all Y_1 (hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),X_1),N) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),Y_1),N) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),N),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X_1),Y_1))))) # label(fact_3201_zmod__eq__dvd__iff) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.77 3169 (all M_1 all N_1 all P_4 (hBOOL(hAPP(int,bool,zprime,P_4)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),P_4),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),M_1),N_1))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),P_4),M_1)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),P_4),N_1))))) # label(fact_3202_zprime__zdvd__zmult__better) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.77 3170 (all Y all X (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),Y),X)) -> hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),X),Y)) = hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,abs_abs(int),X)),hAPP(int,int,abs_abs(int),Y)))) # label(fact_3203_abs__div) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.77 3171 (all A_1 all N_1 all P_4 (hBOOL(hAPP(int,bool,zprime,P_4)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),P_4),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A_1),N_1))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),P_4),A_1))))) # label(fact_3204_zprime__zdvd__power) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.77 3172 (all Z all N_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),Z),N_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),N_1)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Z),N_1))))) # label(fact_3205_zdvd__imp__le) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.77 3173 (all P_4 all Y all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),P_4),Y)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),P_4),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),Y),N_1)))))) # label(fact_3206_zpower__zdvd__prop1) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.77 3174 (all A_1 all B all M_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),M_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),M_1),B)) -> hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_1),B)),M_1) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_1),M_1)))) # label(fact_3207_zmod__zdvd__zmod) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.77 3175 (all X_1 all Y_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(int,int,number_number_of(int),X_1)),hAPP(int,int,number_number_of(int),Y_1))) <-> hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,number_number_of(int),Y_1)),hAPP(int,int,number_number_of(int),X_1)) = zero_zero(int))) # label(fact_3208_zdvd__iff__zmod__eq__0__number__of) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.77 3176 (all D all I_1 (I_1 != zero_zero(int) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),D),I_1)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,abs_abs(int),D)),hAPP(int,int,abs_abs(int),I_1)))))) # label(fact_3209_dvd__imp__le__int) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.77 3177 (all N_1 all A_1 all B all P_4 (hBOOL(hAPP(int,bool,zprime,P_4)) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),P_4),B)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),P_4),N_1)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),B))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),P_4),N_1)),A_1)))))) # label(fact_3210_zprime__power__zdvd__cancel__right) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.77 3178 (all N_1 all B all A_1 all P_4 (hBOOL(hAPP(int,bool,zprime,P_4)) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),P_4),A_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),P_4),N_1)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),B))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),P_4),N_1)),B)))))) # label(fact_3211_zprime__power__zdvd__cancel__left) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.77 3179 (all Y_1 all X_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Y_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(int,nat,nat_1,X_1)),hAPP(int,nat,nat_1,Y_1))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),X_1),Y_1)))))) # label(fact_3212_transfer__nat__int__relations_I4_J) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.77 3180 (all N all M (M != zero_zero(int) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),M),N)),M)) <-> hAPP(int,int,abs_abs(int),N) = one_one(int)))) # label(fact_3213_zdvd__mult__cancel1) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.77 3181 (all N_1 all P_4 all M_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),M_1)) -> (hBOOL(hAPP(int,bool,zprime,P_4)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),P_4),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),M_1),N_1))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),P_4),M_1)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),P_4),N_1)))))) # label(fact_3214_zprime__zdvd__zmult) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.77 3182 (all N_1 all D (D != zero_zero(int) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),D),N_1)) -> hAPP(int,real,real_1(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),N_1),D)) = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(int,real,real_1(int),N_1)),hAPP(int,real,real_1(int),D))))) # label(fact_3215_real__of__int__div) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.77 3183 (all Z_1 all M (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),Z_1),hAPP(nat,int,semiring_1_of_nat(int),M))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(int,nat,nat_1,hAPP(int,int,abs_abs(int),Z_1))),M)))) # label(fact_3216_dvd__int__iff) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.77 3184 (all M all Z_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(nat,int,semiring_1_of_nat(int),M)),Z_1)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),M),hAPP(int,nat,nat_1,hAPP(int,int,abs_abs(int),Z_1)))))) # label(fact_3217_int__dvd__iff) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.77 3185 (all Y all N_1 all P_4 (hBOOL(hAPP(int,bool,zprime,P_4)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),P_4),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),Y),N_1))) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),P_4),Y)))))) # label(fact_3218_zpower__zdvd__prop2) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.77 3186 (all Pa (hBOOL(hAPP(int,bool,zprime,Pa)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),Pa)) & (all M_3 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),M_3)) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),M_3),Pa)) -> M_3 = one_one(int) | M_3 = Pa)))) # label(fact_3219_zprime__def) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.77 3187 (all X_1 (hBOOL(hAPP(int,bool,even_odd_even(int),X_1)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),X_1)))) # label(fact_3220_int__even__iff__2__dvd) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.77 3188 (all Z_1 all M (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(int,nat,nat_1,Z_1)),M)) <-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Z_1)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),Z_1),hAPP(nat,int,semiring_1_of_nat(int),M)))) & (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Z_1)) -> M = zero_zero(nat)))) # label(fact_3221_nat__dvd__iff) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.77 3189 (all X all P_4 (hBOOL(hAPP(int,bool,zprime,P_4)) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),P_4),X)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),X),hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),P_4),one_one(int))))),one_one(int)),P_4))))) # label(fact_3222_Little__Fermat) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.77 3190 (all Y all X all P_4 (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,X),zero_zero(int)),P_4)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),Y),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),X),P_4)) -> -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),P_4),Y))))) # label(fact_3223_Euler_Oaux____1) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.77 3191 (all A_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),A_1)) -> (exists P_5 (hBOOL(hAPP(int,bool,zprime,P_5)) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),P_5),A_1)))))) # label(fact_3224_zprime__factor__exists) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.77 3192 (all X_a (plus(X_a) & linorder(X_a) & dvd(X_a) -> (all D_1 all S_3 exists Z_2 all X_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_2),Z_2)) -> (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),D_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X_2),S_3))) <-> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),D_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X_2),S_3)))))))) # label(fact_3225_minf_I10_J) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.77 3193 (all X_a (plus(X_a) & linorder(X_a) & dvd(X_a) -> (all D_1 all S_3 exists Z_2 all X_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z_2),X_2)) -> (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),D_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X_2),S_3))) <-> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),D_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X_2),S_3)))))))) # label(fact_3226_pinf_I10_J) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.77 3194 (all X_a (plus(X_a) & linorder(X_a) & dvd(X_a) -> (all D_1 all S_3 exists Z_2 all X_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z_2),X_2)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),D_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X_2),S_3))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),D_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X_2),S_3)))))))) # label(fact_3227_pinf_I9_J) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.77 3195 (all X_a (plus(X_a) & linorder(X_a) & dvd(X_a) -> (all D_1 all S_3 exists Z_2 all X_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_2),Z_2)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),D_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X_2),S_3))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),D_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X_2),S_3)))))))) # label(fact_3228_minf_I9_J) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.77 3196 (all X_a (dvd(X_a) -> (all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),B),A_1)) -> -(all K_1 ti(X_a,A_1) != hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),K_1)))))) # label(fact_3229_dvdE) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.77 3197 (all M_1 all P_4 (hBOOL(hAPP(nat,bool,prime,P_4)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),P_4),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),M_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),P_4),M_1))))) # label(fact_3230_prime__dvd__power__two) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.77 3198 (all K_4 ((K_4 = zero_zero(quickcheck_code_int) -> hAPP(quickcheck_code_int,int,quickcheck_int_of,K_4) = zero_zero(int)) & (K_4 != zero_zero(quickcheck_code_int) -> (hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),K_4),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = zero_zero(quickcheck_code_int) -> hAPP(quickcheck_code_int,int,quickcheck_int_of,K_4) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),hAPP(quickcheck_code_int,int,quickcheck_int_of,hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),K_4),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))) & (hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),K_4),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) != zero_zero(quickcheck_code_int) -> hAPP(quickcheck_code_int,int,quickcheck_int_of,K_4) = 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,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),hAPP(quickcheck_code_int,int,quickcheck_int_of,hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),K_4),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))),one_one(int)))))) # label(fact_3232_Quickcheck__Narrowing_Oint__of__code) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.77 3199 (all Q_2 all P_4 (hBOOL(hAPP(nat,bool,prime,P_4)) -> (hBOOL(hAPP(nat,bool,prime,Q_2)) -> (P_4 != Q_2 -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,P_4),Q_2)))))) # label(fact_3233_distinct__prime__coprime) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.77 3200 (all N all M (hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),N),M)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(quickcheck_code_int,int,quickcheck_int_of,N)),hAPP(quickcheck_code_int,int,quickcheck_int_of,M))))) # label(fact_3234_less__eq__code__int__def) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.77 3201 (all N all M (hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),N),M)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(quickcheck_code_int,int,quickcheck_int_of,N)),hAPP(quickcheck_code_int,int,quickcheck_int_of,M))))) # label(fact_3235_less__code__int__def) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.77 3202 (all K_4 hAPP(quickcheck_code_int,int,quickcheck_int_of,hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),K_4)) = hAPP(int,int,number_number_of(int),K_4)) # label(fact_3238_int__of__number) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.77 3203 (all X_1 all Y_1 (hAPP(quickcheck_code_int,int,quickcheck_int_of,X_1) = hAPP(quickcheck_code_int,int,quickcheck_int_of,Y_1) <-> X_1 = Y_1)) # label(fact_3239_code__int_Oint__of__inject) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.77 3204 (all K all L (hAPP(quickcheck_code_int,int,quickcheck_int_of,K) = hAPP(quickcheck_code_int,int,quickcheck_int_of,L) <-> K = L)) # label(fact_3240_Quickcheck__Narrowing_Oint__of__inject) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.77 3205 (all Q_2 all P_4 (hBOOL(hAPP(nat,bool,prime,P_4)) -> (hBOOL(hAPP(nat,bool,prime,Q_2)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),P_4),Q_2)) -> P_4 = Q_2)))) # label(fact_3241_primes__eq) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.77 3206 (all P_4 (hBOOL(hAPP(nat,bool,prime,P_4)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),P_4)))) # label(fact_3243_prime__g__zero) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.77 3207 (all Aa all Ba all Pa (hBOOL(hAPP(nat,bool,prime,Pa)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Pa),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),Aa),Ba))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Pa),Aa)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Pa),Ba))))) # label(fact_3244_prime__divprod__eq) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.77 3208 (all A_1 all B all P_4 (hBOOL(hAPP(nat,bool,prime,P_4)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),P_4),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A_1),B))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),P_4),A_1)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),P_4),B))))) # label(fact_3245_prime__divprod) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.77 3209 (all M_1 all N_1 all P_4 (hBOOL(hAPP(nat,bool,prime,P_4)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),P_4),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),N_1))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),P_4),M_1)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),P_4),N_1))))) # label(fact_3246_prime__dvd__mult) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.77 3210 (all P_4 all Q_2 (hBOOL(hAPP(nat,bool,prime,hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),P_4),Q_2))) -> P_4 = one_one(nat) | Q_2 = one_one(nat))) # label(fact_3247_prime__product) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.77 3211 (all A_1 all N_1 all P_4 (hBOOL(hAPP(nat,bool,prime,P_4)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),P_4),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A_1),N_1))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),P_4),A_1))))) # label(fact_3248_prime__dvd__power) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.77 3212 (all X all N_1 all P_4 (hBOOL(hAPP(nat,bool,prime,P_4)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),P_4),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),X),N_1))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),P_4),X))))) # label(fact_3249_prime__divexp) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.77 3213 (all X all N_1 all P_4 (hBOOL(hAPP(nat,bool,prime,P_4)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),P_4),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),X),N_1))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),P_4),N_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),X),N_1)))))) # label(fact_3250_prime__divexp__n) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.77 3214 (all Pa all N (hBOOL(hAPP(nat,bool,prime,hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),Pa),N))) <-> hBOOL(hAPP(nat,bool,prime,Pa)) & N = one_one(nat))) # label(fact_3251_prime__exp) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.77 3215 (all P_4 all A_1 all B (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,A_1),B)) -> -(hBOOL(hAPP(nat,bool,prime,P_4)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),P_4),A_1)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),P_4),B))))) # label(fact_3252_coprime__prime) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.77 3216 (all N_1 all P_4 (hBOOL(hAPP(nat,bool,prime,P_4)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),P_4),N_1)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,P_4),N_1)))) # label(fact_3253_prime__coprime__strong) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.77 3217 (all Aa all Ba (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,Aa),Ba)) <-> (all P_5 -(hBOOL(hAPP(nat,bool,prime,P_5)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),P_5),Aa)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),P_5),Ba)))))) # label(fact_3254_coprime__prime__eq) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.77 3218 (all A_1 (hBOOL(hAPP(nat,bool,prime,A_1)) -> hBOOL(hAPP(int,bool,zprime,hAPP(nat,int,semiring_1_of_nat(int),A_1))))) # label(fact_3255_prime__impl__zprime__int) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.77 3219 (all P_4 (hBOOL(hAPP(nat,bool,prime,P_4)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),P_4)))) # label(fact_3257_prime__g__one) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.77 3220 (all P_4 (hBOOL(hAPP(nat,bool,prime,P_4)) -> -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),P_4),hAPP(nat,nat,suc,zero_zero(nat)))))) # label(fact_3258_prime__nd__one) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.77 3221 (all M_1 all N_1 all P_4 (hBOOL(hAPP(nat,bool,prime,P_4)) -> (N_1 != zero_zero(nat) -> (N_1 = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),P_4),M_1) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_1)))))) # label(fact_3259_prime__factor__lt) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.77 3222 (all Pa (hBOOL(hAPP(nat,bool,prime,Pa)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),one_one(nat)),Pa)) & (all M_3 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),M_3),Pa)) -> M_3 = one_one(nat) | M_3 = Pa)))) # label(fact_3260_prime__def) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.77 3223 (all D_1 all K all Pa (hBOOL(hAPP(nat,bool,prime,Pa)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),D_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),Pa),K))) <-> (exists I_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_2),K)) & D_1 = hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),Pa),I_2)))))) # label(fact_3261_divides__primepow) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.77 3224 (all N_1 all A_1 all B all P_4 (hBOOL(hAPP(nat,bool,prime,P_4)) -> (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),P_4),B)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),P_4),N_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A_1),B))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),P_4),N_1)),A_1)))))) # label(fact_3262_prime__power__dvd__cancel__right) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.77 3225 (all X all P_4 (hBOOL(hAPP(nat,bool,prime,P_4)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X),P_4)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,X),P_4)))))) # label(fact_3263_prime__coprime__lt) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.77 3226 (all N_1 all P_4 (hBOOL(hAPP(nat,bool,prime,P_4)) -> N_1 = one_one(nat) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),P_4),N_1)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,P_4),N_1)))) # label(fact_3264_prime__coprime) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.77 3227 (all M_1 all P_4 (hBOOL(hAPP(nat,bool,prime,P_4)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),P_4),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),M_1),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat)))))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),P_4),M_1))))) # label(fact_3266_prime__dvd__square) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.77 3228 (all N_1 all A_1 all B all P_4 (hBOOL(hAPP(nat,bool,prime,P_4)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,A_1),B)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),P_4),N_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A_1),B))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),P_4),N_1)),A_1)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),P_4),N_1)),B)))))) # label(fact_3267_prime__divprod__pow) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.77 3229 (all P_4 (hBOOL(hAPP(nat,bool,prime,P_4)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),P_4)))) # label(fact_3268_prime__ge__2) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.77 3230 (all P_4 (hBOOL(hAPP(nat,bool,prime,P_4)) -> P_4 = hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))) | -hBOOL(hAPP(nat,bool,even_odd_even(nat),P_4)))) # label(fact_3269_prime__odd) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.77 3231 (all N_1 all M_1 hAPP(quickcheck_code_int,product_prod(quickcheck_code_int,quickcheck_code_int),hAPP(quickcheck_code_int,fun(quickcheck_code_int,product_prod(quickcheck_code_int,quickcheck_code_int)),quickc495462417de_int,N_1),M_1) = hAPP(quickcheck_code_int,product_prod(quickcheck_code_int,quickcheck_code_int),hAPP(quickcheck_code_int,fun(quickcheck_code_int,product_prod(quickcheck_code_int,quickcheck_code_int)),product_Pair(quickcheck_code_int,quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),N_1),M_1)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),N_1),M_1))) # label(fact_3270_div__mod__code__int__def) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.77 3232 (all I_1 hAPP(quickcheck_code_int,nat,quickcheck_nat_of,I_1) = hAPP(int,nat,nat_1,hAPP(quickcheck_code_int,int,quickcheck_int_of,I_1))) # label(fact_3271_nat__of__def) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.77 3233 (all X all Y (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,X),Y)) -> (exists P_5 (hBOOL(hAPP(nat,bool,prime,P_5)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),P_5),X)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),P_5),Y)))))) # label(fact_3272_coprime__prime__dvd__ex) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.77 3234 (all X all K_4 all N_1 all P_4 (hBOOL(hAPP(nat,bool,prime,P_4)) -> (N_1 != zero_zero(nat) -> (hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),X),N_1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),P_4),K_4) -> (exists I_2 X = hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),P_4),I_2)))))) # label(fact_3273_prime__power__exp) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.77 3235 (all N_1 (N_1 != one_one(nat) -> (exists P_5 (hBOOL(hAPP(nat,bool,prime,P_5)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),P_5),N_1)))))) # label(fact_3274_prime__factor) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.77 3236 (all A_1 all P_4 (hBOOL(hAPP(nat,bool,prime,P_4)) -> (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),P_4),A_1)) -> (exists X_2 exists Y_2 hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A_1),X_2) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),P_4),Y_2)),one_one(nat)))))) # label(fact_3275_bezout__prime) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.77 3237 (all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),N_1)) & -hBOOL(hAPP(nat,bool,prime,N_1)) -> (exists M_3 exists K_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),M_3)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),K_1)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_3),N_1)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),K_1),N_1)) & N_1 = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_3),K_1))))) # label(fact_3276_not__prime__ex__mk) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.77 3238 (all N_1 exists P_5 (hBOOL(hAPP(nat,bool,prime,P_5)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),P_5)))) # label(fact_3277_euclid) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.77 3239 (all P_1 all A0 (hBOOL(hAPP(int,bool,hAPP(fun(int,fun(int,bool)),fun(int,bool),accp(int),quickc1265749348ro_rel),A0)) -> ((all I_2 (hBOOL(hAPP(int,bool,hAPP(fun(int,fun(int,bool)),fun(int,bool),accp(int),quickc1265749348ro_rel),I_2)) -> ((-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),I_2),zero_zero(int))) -> (I_2 != zero_zero(int) -> hBOOL(hAPP(int,bool,P_1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),I_2),one_one(int)))))) -> hBOOL(hAPP(int,bool,P_1,I_2))))) -> hBOOL(hAPP(int,bool,P_1,A0))))) # label(fact_3278_around__zero_Opinduct) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.78 3240 (all R_4 all A_1 all N_1 hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),hAPP(real,complex,hAPP(real,fun(real,complex),rcis,R_4),A_1)),N_1) = hAPP(real,complex,hAPP(real,fun(real,complex),rcis,hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),R_4),N_1)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,real_1(nat),N_1)),A_1))) # label(fact_3279_DeMoivre2) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.78 3241 (all X ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X)) -> hAPP(int,int,fact_fact(int),X) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,fact_fact(nat),hAPP(int,nat,nat_1,X)))) & (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X)) -> hAPP(int,int,fact_fact(int),X) = zero_zero(int)))) # label(fact_3280_fact__int__def) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.78 3242 (all X_a all A_2 all B_1 (hBOOL(hAPP(fun(product_prod(fun(X_a,bool),fun(X_a,bool)),bool),bool,hAPP(product_prod(fun(X_a,bool),fun(X_a,bool)),fun(fun(product_prod(fun(X_a,bool),fun(X_a,bool)),bool),bool),member(product_prod(fun(X_a,bool),fun(X_a,bool))),hAPP(fun(X_a,bool),product_prod(fun(X_a,bool),fun(X_a,bool)),hAPP(fun(X_a,bool),fun(fun(X_a,bool),product_prod(fun(X_a,bool),fun(X_a,bool))),product_Pair(fun(X_a,bool),fun(X_a,bool)),A_2),B_1)),finite_psubset(X_a))) <-> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less(fun(X_a,bool)),A_2),B_1)) & hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),B_1)))) # label(fact_3281_in__finite__psubset) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.78 3243 (all M_1 all N_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),M_1),N_1)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,fact_fact(int),M_1)),hAPP(int,int,fact_fact(int),N_1))))) # label(fact_3282_fact__mono__int) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.78 3244 (all M_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),M_1),zero_zero(int))) -> hAPP(int,int,fact_fact(int),M_1) = zero_zero(int))) # label(fact_3284_fact__neg__int) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.78 3245 (all N_1 all M_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),M_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),M_1),N_1)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,fact_fact(int),M_1)),hAPP(int,int,fact_fact(int),N_1)))))) # label(fact_3285_fact__less__mono__int) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.78 3246 (all M_1 hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,fact_fact(int),M_1)))) # label(fact_3286_fact__ge__zero__int) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.78 3247 (all N_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),N_1)) -> hAPP(int,int,fact_fact(int),N_1) != zero_zero(int))) # label(fact_3287_fact__nonzero__int) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.78 3248 (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(int,int,fact_fact(int),X))))) # label(fact_3288_transfer__nat__int__factorial__closure) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.78 3249 (all X hAPP(int,int,fact_fact(int),hAPP(nat,int,semiring_1_of_nat(int),X)) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,fact_fact(nat),X))) # label(fact_3290_transfer__int__nat__factorial) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.78 3250 (all R_4 hAPP(real,complex,hAPP(real,fun(real,complex),rcis,R_4),zero_zero(real)) = hAPP(real,complex,of_real(complex),R_4)) # label(fact_3291_rcis__zero__arg) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.78 3251 (all R_4 all A_1 hAPP(complex,real,norm_norm(complex),hAPP(real,complex,hAPP(real,fun(real,complex),rcis,R_4),A_1)) = hAPP(real,real,abs_abs(real),R_4)) # label(fact_3292_complex__mod__rcis) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.78 3252 (all A_1 hAPP(real,complex,cis,A_1) = hAPP(real,complex,hAPP(real,fun(real,complex),rcis,one_one(real)),A_1)) # label(fact_3293_cis__rcis__eq) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.78 3253 (all A_1 hAPP(real,complex,hAPP(real,fun(real,complex),rcis,zero_zero(real)),A_1) = zero_zero(complex)) # label(fact_3294_rcis__zero__mod) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.78 3254 (all N_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),N_1)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,fact_fact(int),N_1))))) # label(fact_3295_fact__gt__zero__int) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.78 3255 (all N_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),N_1)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),hAPP(int,int,fact_fact(int),N_1))))) # label(fact_3296_fact__ge__one__int) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.78 3256 (all M_1 all K_4 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),K_4)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,fact_fact(int),M_1)),hAPP(int,int,fact_fact(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),M_1),K_4)))))) # label(fact_3297_fact__mono__int__aux) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.78 3257 (all N_1 all M_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),M_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),M_1),N_1)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),M_1),hAPP(int,int,fact_fact(int),N_1)))))) # label(fact_3298_dvd__fact__int) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.78 3258 (all R_4 all A_1 hAPP(complex,real,re,hAPP(real,complex,hAPP(real,fun(real,complex),rcis,R_4),A_1)) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),R_4),hAPP(real,real,cos,A_1))) # label(fact_3299_Re__rcis) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.78 3259 (all R_4 all A_1 hAPP(complex,real,im,hAPP(real,complex,hAPP(real,fun(real,complex),rcis,R_4),A_1)) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),R_4),hAPP(real,real,sin,A_1))) # label(fact_3300_Im__rcis) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.78 3260 (all R1 all A_1 all R2 all B hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(real,complex,hAPP(real,fun(real,complex),rcis,R1),A_1)),hAPP(real,complex,hAPP(real,fun(real,complex),rcis,R2),B)) = hAPP(real,complex,hAPP(real,fun(real,complex),rcis,hAPP(real,real,hAPP(real,fun(real,real),times_times(real),R1),R2)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A_1),B))) # label(fact_3301_rcis__mult) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.78 3261 (all X (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X)) -> hAPP(nat,nat,fact_fact(nat),hAPP(int,nat,nat_1,X)) = hAPP(int,nat,nat_1,hAPP(int,int,fact_fact(int),X)))) # label(fact_3302_transfer__nat__int__factorial) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.78 3262 (all R1 all A_1 all R2 all B hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),hAPP(real,complex,hAPP(real,fun(real,complex),rcis,R1),A_1)),hAPP(real,complex,hAPP(real,fun(real,complex),rcis,R2),B)) = hAPP(real,complex,hAPP(real,fun(real,complex),rcis,hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),R1),R2)),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A_1),B))) # label(fact_3303_rcis__divide) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.78 3263 (all R_4 all A_1 hAPP(real,complex,hAPP(real,fun(real,complex),rcis,R_4),A_1) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(real,complex,of_real(complex),R_4)),hAPP(real,complex,cis,A_1))) # label(fact_3304_rcis__def) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.78 3264 (all M_1 all K_4 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),K_4)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),M_1)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,fact_fact(int),M_1)),hAPP(int,int,fact_fact(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),M_1),one_one(int))),K_4))))))) # label(fact_3305_fact__less__mono__int__aux) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.78 3265 (all N_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),N_1)) -> hAPP(int,int,fact_fact(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),N_1),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),N_1),one_one(int))),hAPP(int,int,fact_fact(int),N_1)))) # label(fact_3306_fact__plus__one__int) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.78 3266 (all N_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),N_1)) -> hAPP(int,int,fact_fact(int),N_1) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),N_1),hAPP(int,int,fact_fact(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),N_1),one_one(int)))))) # label(fact_3307_fact__reduce__int) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.78 3267 (all R_4 all A_1 hAPP(complex,complex,inverse_inverse(complex),hAPP(real,complex,hAPP(real,fun(real,complex),rcis,R_4),A_1)) = hAPP(real,complex,hAPP(real,fun(real,complex),rcis,hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),one_one(real)),R_4)),hAPP(real,real,uminus_uminus(real),A_1))) # label(fact_3308_rcis__inverse) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.78 3268 (all X_b all X_a all B_1 all A_2 ((hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2)) & hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),B_1)) -> hAPP(fun(sum_sum(X_a,X_b),bool),nat,finite_card(sum_sum(X_a,X_b)),hAPP(fun(X_b,bool),fun(sum_sum(X_a,X_b),bool),hAPP(fun(X_a,bool),fun(fun(X_b,bool),fun(sum_sum(X_a,X_b),bool)),sum_Plus(X_a,X_b),A_2),B_1)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(fun(X_a,bool),nat,finite_card(X_a),A_2)),hAPP(fun(X_b,bool),nat,finite_card(X_b),B_1))) & (-(hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2)) & hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),B_1))) -> hAPP(fun(sum_sum(X_a,X_b),bool),nat,finite_card(sum_sum(X_a,X_b)),hAPP(fun(X_b,bool),fun(sum_sum(X_a,X_b),bool),hAPP(fun(X_a,bool),fun(fun(X_b,bool),fun(sum_sum(X_a,X_b),bool)),sum_Plus(X_a,X_b),A_2),B_1)) = zero_zero(nat)))) # label(fact_3309_card__Plus__conv__if) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.78 3269 (all I_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),I_1)) -> hAPP(list(int),nat,size_size(list(int)),hAPP(int,list(int),quickc666637781d_zero,I_1)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),hAPP(int,nat,nat_1,I_1))),one_one(nat)))) # label(fact_3310_length__around__zero) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.78 3270 (all Aa all Pa (hBOOL(hAPP(int,bool,zprime,Pa)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Aa),Pa)) -> hAPP(fun(int,bool),nat,finite_card(int),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),bnorRset,Aa),Pa)) = hAPP(int,nat,nat_1,Aa)))) # label(fact_3311_Bnor__prime) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.78 3271 (all X_a all X_b all A_2 all B_1 (hBOOL(hAPP(fun(sum_sum(X_a,X_b),bool),bool,finite_finite_1(sum_sum(X_a,X_b)),hAPP(fun(X_b,bool),fun(sum_sum(X_a,X_b),bool),hAPP(fun(X_a,bool),fun(fun(X_b,bool),fun(sum_sum(X_a,X_b),bool)),sum_Plus(X_a,X_b),A_2),B_1))) <-> hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2)) & hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),B_1)))) # label(fact_3312_finite__Plus__iff) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.78 3272 (all X_b all X_a all B_1 all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),B_1)) -> hBOOL(hAPP(fun(sum_sum(X_a,X_b),bool),bool,finite_finite_1(sum_sum(X_a,X_b)),hAPP(fun(X_b,bool),fun(sum_sum(X_a,X_b),bool),hAPP(fun(X_a,bool),fun(fun(X_b,bool),fun(sum_sum(X_a,X_b),bool)),sum_Plus(X_a,X_b),A_2),B_1)))))) # label(fact_3313_finite__Plus) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.78 3273 (all X_a all X_b all A_2 all B_1 (hBOOL(hAPP(fun(sum_sum(X_a,X_b),bool),bool,finite_finite_1(sum_sum(X_a,X_b)),hAPP(fun(X_b,bool),fun(sum_sum(X_a,X_b),bool),hAPP(fun(X_a,bool),fun(fun(X_b,bool),fun(sum_sum(X_a,X_b),bool)),sum_Plus(X_a,X_b),A_2),B_1))) -> hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2)))) # label(fact_3314_finite__PlusD_I1_J) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.78 3274 (all X_a all X_b all A_2 all B_1 (hBOOL(hAPP(fun(sum_sum(X_a,X_b),bool),bool,finite_finite_1(sum_sum(X_a,X_b)),hAPP(fun(X_b,bool),fun(sum_sum(X_a,X_b),bool),hAPP(fun(X_a,bool),fun(fun(X_b,bool),fun(sum_sum(X_a,X_b),bool)),sum_Plus(X_a,X_b),A_2),B_1))) -> hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),B_1)))) # label(fact_3315_finite__PlusD_I2_J) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.78 3275 (all Ba all Aa all M (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Ba),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),bnorRset,Aa),M))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Ba),Aa)))) # label(fact_3316_Bnor__mem__zle) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.78 3276 (all M all Aa all Ba (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Aa),Ba)) -> -hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Ba),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),bnorRset,Aa),M))))) # label(fact_3317_Bnor__mem__zle__swap) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.78 3277 (all Aa all M hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),bnorRset,Aa),M)))) # label(fact_3318_Bnor__fin) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.78 3278 (all Ba all Aa all M (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Ba),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),bnorRset,Aa),M))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),Ba)))) # label(fact_3319_Bnor__mem__zg) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.78 3279 (all X_b all X_a all B_1 all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),B_1)) -> hAPP(fun(sum_sum(X_a,X_b),bool),nat,finite_card(sum_sum(X_a,X_b)),hAPP(fun(X_b,bool),fun(sum_sum(X_a,X_b),bool),hAPP(fun(X_a,bool),fun(fun(X_b,bool),fun(sum_sum(X_a,X_b),bool)),sum_Plus(X_a,X_b),A_2),B_1)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(fun(X_a,bool),nat,finite_card(X_a),A_2)),hAPP(fun(X_b,bool),nat,finite_card(X_b),B_1))))) # label(fact_3320_card__Plus) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.78 3280 (all Aa all Ba all P_1 ((all A_3 all B_3 all C_4 (hBOOL(hAPP(product_prod(real,real),bool,P_1,hAPP(real,product_prod(real,real),hAPP(real,fun(real,product_prod(real,real)),product_Pair(real,real),A_3),B_3))) & hBOOL(hAPP(product_prod(real,real),bool,P_1,hAPP(real,product_prod(real,real),hAPP(real,fun(real,product_prod(real,real)),product_Pair(real,real),B_3),C_4))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A_3),B_3)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B_3),C_4)) -> hBOOL(hAPP(product_prod(real,real),bool,P_1,hAPP(real,product_prod(real,real),hAPP(real,fun(real,product_prod(real,real)),product_Pair(real,real),A_3),C_4))))) -> ((all X_2 exists D_3 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),D_3)) & (all A_3 all B_3 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A_3),X_2)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_2),B_3)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),B_3),A_3)),D_3)) -> hBOOL(hAPP(product_prod(real,real),bool,P_1,hAPP(real,product_prod(real,real),hAPP(real,fun(real,product_prod(real,real)),product_Pair(real,real),A_3),B_3))))))) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),Aa),Ba)) -> hBOOL(hAPP(product_prod(real,real),bool,P_1,hAPP(real,product_prod(real,real),hAPP(real,fun(real,product_prod(real,real)),product_Pair(real,real),Aa),Ba))))))) # label(fact_3321_lemma__BOLZANO) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.78 3281 (all P_1 ((all A_3 all B_3 all C_4 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A_3),B_3)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B_3),C_4)) & hBOOL(hAPP(product_prod(real,real),bool,P_1,hAPP(real,product_prod(real,real),hAPP(real,fun(real,product_prod(real,real)),product_Pair(real,real),A_3),B_3))) & hBOOL(hAPP(product_prod(real,real),bool,P_1,hAPP(real,product_prod(real,real),hAPP(real,fun(real,product_prod(real,real)),product_Pair(real,real),B_3),C_4))) -> hBOOL(hAPP(product_prod(real,real),bool,P_1,hAPP(real,product_prod(real,real),hAPP(real,fun(real,product_prod(real,real)),product_Pair(real,real),A_3),C_4))))) & (all X_2 exists D_3 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),D_3)) & (all A_3 all B_3 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A_3),X_2)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_2),B_3)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),B_3),A_3)),D_3)) -> hBOOL(hAPP(product_prod(real,real),bool,P_1,hAPP(real,product_prod(real,real),hAPP(real,fun(real,product_prod(real,real)),product_Pair(real,real),A_3),B_3))))))) -> (all A_3 all B_3 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A_3),B_3)) -> hBOOL(hAPP(product_prod(real,real),bool,P_1,hAPP(real,product_prod(real,real),hAPP(real,fun(real,product_prod(real,real)),product_Pair(real,real),A_3),B_3))))))) # label(fact_3322_lemma__BOLZANO2) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.78 3282 (all X all Y hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(product_prod(int,int),int,product_fst(int,int),hAPP(nat,product_prod(int,int),hAPP(nat,fun(nat,product_prod(int,int)),bezw,X),Y))),hAPP(nat,int,semiring_1_of_nat(int),X))),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(product_prod(int,int),int,product_snd(int,int),hAPP(nat,product_prod(int,int),hAPP(nat,fun(nat,product_prod(int,int)),bezw,X),Y))),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),gcd_gcd(nat),X),Y))) # label(fact_3323_bezw__aux) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.78 3283 (all M_1 all N_1 hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),M_1),N_1)),N_1))) # label(fact_3324_gcd__dvd2__nat) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.78 3284 (all M_1 all N_1 hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),M_1),N_1)),M_1))) # label(fact_3325_gcd__dvd1__nat) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.78 3285 (all M_1 all N_1 all K_4 hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),M_1),N_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_4),N_1)))) # label(fact_3326_gcd__dvd__prod__nat) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.78 3286 (all N_1 all M_1 all A_1 all B (hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),A_1),B) = one_one(nat) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A_1),N_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),B),M_1)) = one_one(nat))) # label(fact_3327_coprime__exp2__nat) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.78 3287 (all A_1 all B (B != zero_zero(nat) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),A_1),B)),B)))) # label(fact_3328_gcd__le2__nat) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.78 3288 (all B all A_1 (A_1 != zero_zero(nat) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),A_1),B)),A_1)))) # label(fact_3329_gcd__le1__nat) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.78 3289 (all M_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),M_1),hAPP(nat,nat,suc,zero_zero(nat))) = hAPP(nat,nat,suc,zero_zero(nat))) # label(fact_3330_gcd__Suc__0) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.78 3290 (all M 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),gcd_gcd(nat),M),N))) <-> M != zero_zero(nat) | N != zero_zero(nat))) # label(fact_3331_gcd__pos__nat) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.78 3291 (all A_1 all N_1 all B hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A_1),N_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),B),N_1)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),A_1),B)),N_1)) # label(fact_3332_gcd__exp__nat) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.78 3292 (all A_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),A_1),A_1) = A_1) # label(fact_3333_gcd__semilattice__nat_Oinf_Oidem) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.78 3293 (all X hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),X),X) = X) # label(fact_3334_gcd__idem__nat) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.78 3294 (all A_1 all B hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),A_1),B) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),B),A_1)) # label(fact_3335_gcd__commute__nat) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.78 3295 (all X all Y hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),X),Y) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),Y),X)) # label(fact_3336_gcd__semilattice__nat_Oinf__commute) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.78 3296 (all A_1 all B hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),A_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),A_1),B)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),A_1),B)) # label(fact_3337_gcd__semilattice__nat_Oinf_Oleft__idem) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.78 3297 (all X all Y hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),X),hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),X),Y)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),X),Y)) # label(fact_3338_gcd__semilattice__nat_Oinf__left__idem) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.78 3298 (all B all A_1 all C hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),A_1),C)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),A_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),B),C))) # label(fact_3339_gcd__left__commute__nat) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.78 3299 (all X all Y all Z hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),X),hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),Y),Z)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),Y),hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),X),Z))) # label(fact_3340_gcd__semilattice__nat_Oinf__left__commute) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.78 3300 (all A_1 all B all C hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),A_1),B)),C) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),A_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),B),C))) # label(fact_3341_gcd__assoc__nat) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.78 3301 (all X all Y all Z hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),X),Y)),Z) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),X),hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),Y),Z))) # label(fact_3342_gcd__semilattice__nat_Oinf__assoc) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.78 3302 (all K_4 all M_1 all N_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_4),hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),M_1),N_1)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_4),M_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_4),N_1))) # label(fact_3343_gcd__mult__distrib__nat) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.78 3303 (all M_1 all N_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),N_1)),N_1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),M_1),N_1)) # label(fact_3344_gcd__add1__nat) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.78 3304 (all M_1 all N_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),M_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),N_1)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),M_1),N_1)) # label(fact_3345_gcd__add2__nat) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.78 3305 (all A_1 all B all X (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),B),X)) & -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),B)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),A_1),B)),X)) & -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),A_1),B))))) # label(fact_3346_gcd__semilattice__nat_Oless__infI2) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.78 3306 (all B all A_1 all X (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),X)) & -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),A_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),A_1),B)),X)) & -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),A_1),B))))) # label(fact_3347_gcd__semilattice__nat_Oless__infI1) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.78 3307 (all X all A_1 all B (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),A_1),B))) -> -(hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),A_1)) -> -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),B))))) # label(fact_3348_gcd__semilattice__nat_Ole__infE) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.78 3308 (all K_4 all M_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),K_4),hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),M_1),N_1))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),K_4),N_1)))) # label(fact_3349_dvd__gcd__D2__nat) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.78 3309 (all K_4 all M_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),K_4),hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),M_1),N_1))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),K_4),M_1)))) # label(fact_3350_dvd__gcd__D1__nat) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.78 3310 (all B all D all A_1 all C (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),C)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),B),D)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),A_1),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),C),D)))))) # label(fact_3351_gcd__semilattice__nat_Oinf__mono) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.78 3311 (all Z all X all Y (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),Y)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),Z)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),Y),Z)))))) # label(fact_3352_gcd__semilattice__nat_Oinf__greatest) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.78 3312 (all B all X all A_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),A_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),B)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),A_1),B)))))) # label(fact_3353_gcd__semilattice__nat_Ole__infI) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.78 3313 (all N_1 all K_4 all M_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),K_4),M_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),K_4),N_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),K_4),hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),M_1),N_1)))))) # label(fact_3354_gcd__greatest__nat) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.78 3314 (all Y all X (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y),X)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),X),Y) = Y)) # label(fact_3355_gcd__proj2__if__dvd__nat) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.78 3315 (all X all Y (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),Y)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),X),Y) = X)) # label(fact_3356_gcd__proj1__if__dvd__nat) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.78 3316 (all A_1 all B all X (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),B),X)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),A_1),B)),X)))) # label(fact_3357_gcd__semilattice__nat_Ole__infI2) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.78 3317 (all B all A_1 all X (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),X)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),A_1),B)),X)))) # label(fact_3358_gcd__semilattice__nat_Ole__infI1) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.78 3318 (all Ba all D_1 all Aa (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),D_1),Aa)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),D_1),Ba)) & (all E (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),E),Aa)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),E),Ba)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),E),D_1)))) <-> D_1 = hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),Aa),Ba))) # label(fact_3359_gcd__unique__nat) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.78 3319 (all X_1 all Y_1 all Z_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),Y_1),Z_1))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_1),Y_1)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_1),Z_1)))) # label(fact_3360_gcd__semilattice__nat_Ole__inf__iff) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.78 3320 (all K all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),K),hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),M),N))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),K),M)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),K),N)))) # label(fact_3361_gcd__greatest__iff__nat) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.78 3321 (all X_1 all Y_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_1),Y_1)) <-> hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),X_1),Y_1) = X_1)) # label(fact_3362_gcd__semilattice__nat_Ole__iff__inf) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.78 3322 (all X all Y hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),X),Y)),Y))) # label(fact_3363_gcd__semilattice__nat_Oinf__le2) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.78 3323 (all X all Y hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),X),Y)),X))) # label(fact_3364_gcd__semilattice__nat_Oinf__le1) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.78 3324 (all X hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),one_one(nat)),X) = one_one(nat)) # label(fact_3365_gcd__lcm__complete__lattice__nat_Oinf__bot__left) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.78 3325 (all M_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),M_1),one_one(nat)) = one_one(nat)) # label(fact_3366_gcd__1__nat) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.78 3326 (all X hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),X),one_one(nat)) = one_one(nat)) # label(fact_3367_gcd__lcm__complete__lattice__nat_Oinf__bot__right) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.78 3327 (all X_1 all Y_1 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),X_1),Y_1) = zero_zero(nat) <-> X_1 = zero_zero(nat) & Y_1 = zero_zero(nat))) # label(fact_3368_gcd__lcm__complete__lattice__nat_Oinf__eq__top__iff) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.78 3328 (all M all N (hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),M),N) = zero_zero(nat) <-> M = zero_zero(nat) & N = zero_zero(nat))) # label(fact_3369_gcd__zero__nat) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.78 3329 (all X hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),X),zero_zero(nat)) = X) # label(fact_3370_gcd__0__nat) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.78 3330 (all X hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),zero_zero(nat)),X) = X) # label(fact_3371_gcd__0__left__nat) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.78 3331 (all X all Y hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),X),Y) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),Y),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),X),Y))) # label(fact_3372_gcd__red__nat) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.78 3332 (all N_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),hAPP(nat,nat,suc,N_1)),N_1) = one_one(nat)) # label(fact_3373_coprime__Suc__nat) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.78 3333 (all M_1 all K_4 all N_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(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),K_4),M_1)),N_1)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),M_1),N_1)) # label(fact_3374_gcd__add__mult__nat) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.78 3334 (all X all A_1 all B (hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),A_1),B) = one_one(nat) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),A_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),B)) -> X = one_one(nat))))) # label(fact_3375_coprime__common__divisor__nat) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.78 3335 (all Aa all Ba (hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),Aa),Ba) = one_one(nat) <-> (all D_3 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),D_3),Aa)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),D_3),Ba)) <-> D_3 = one_one(nat))))) # label(fact_3376_coprime__nat) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.78 3336 (all N_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_1),one_one(nat))),N_1) = one_one(nat)) # label(fact_3377_coprime__plus__one__nat) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.78 3337 (all D all A_1 all B (hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),D),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A_1),B)) = one_one(nat) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),D),B) = one_one(nat))) # label(fact_3378_coprime__rmult__nat) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.78 3338 (all D all A_1 all B (hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),D),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A_1),B)) = one_one(nat) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),D),A_1) = one_one(nat))) # label(fact_3379_coprime__lmult__nat) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.78 3339 (all Ba all C_1 all Aa all D_1 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),Aa),D_1) = one_one(nat) -> (hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),Ba),C_1) = one_one(nat) -> (hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),Aa),C_1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),Ba),D_1) <-> Aa = Ba & C_1 = D_1)))) # label(fact_3380_coprime__crossproduct__nat) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.78 3340 (all B all D all A_1 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),D),A_1) = one_one(nat) -> (hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),D),B) = one_one(nat) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),D),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A_1),B)) = one_one(nat)))) # label(fact_3381_coprime__mult__nat) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.78 3341 (all M_1 all K_4 all N_1 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),K_4),N_1) = one_one(nat) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_4),M_1)),N_1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),M_1),N_1))) # label(fact_3382_gcd__mult__cancel__nat) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.78 3342 (all D_1 all Aa all Ba (hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),D_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),Aa),Ba)) = one_one(nat) <-> hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),D_1),Aa) = one_one(nat) & hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),D_1),Ba) = one_one(nat))) # label(fact_3383_coprime__mul__eq__nat) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.78 3343 (all N_1 all M_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_1),M_1)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),N_1)),N_1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),M_1),N_1))) # label(fact_3384_gcd__diff1__nat) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.78 3344 (all M_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),N_1)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),M_1)),N_1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),M_1),N_1))) # label(fact_3385_gcd__diff2__nat) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.78 3345 (all X all Y ((Y = zero_zero(nat) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),X),Y) = X) & (Y != zero_zero(nat) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),X),Y) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),Y),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),X),Y))))) # label(fact_3386_gcd__nat_Osimps) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.78 3346 (all X all Y (Y != zero_zero(nat) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),X),Y) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),Y),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),X),Y)))) # label(fact_3387_gcd__non__0__nat) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.78 3347 (all N_1 all D all A_1 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),D),A_1) = one_one(nat) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),D),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A_1),N_1)) = one_one(nat))) # label(fact_3388_coprime__exp__nat) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.78 3348 (all B_4 all A_5 all A_1 all B (hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),A_1),B) != zero_zero(nat) -> (A_1 = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A_5),hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),A_1),B)) -> (B = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B_4),hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),A_1),B)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),A_5),B_4) = one_one(nat))))) # label(fact_3389_gcd__coprime__nat) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.78 3349 (all N_1 (N_1 != zero_zero(nat) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),one_one(nat))),N_1) = one_one(nat))) # label(fact_3390_coprime__minus__one__nat) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.78 3350 (all N_1 all M_1 all R_4 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),M_1),R_4)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),N_1),R_4)) -> (hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),M_1),N_1) = one_one(nat) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),N_1)),R_4)))))) # label(fact_3391_divides__mult__nat) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.78 3351 (all M all K all N (hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),K),N) = one_one(nat) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),K),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),N))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),K),M))))) # label(fact_3392_coprime__dvd__mult__iff__nat) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.78 3352 (all M_1 all K_4 all N_1 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),K_4),N_1) = one_one(nat) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),K_4),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),N_1))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),K_4),M_1))))) # label(fact_3393_coprime__dvd__mult__nat) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.78 3353 (all B all A_1 (A_1 != zero_zero(nat) | B != zero_zero(nat) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),A_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),A_1),B))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),A_1),B))) = one_one(nat))) # label(fact_3394_div__gcd__coprime__nat) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.78 3354 (all X all Y all M_1 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X),Y)),M_1) = one_one(nat) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),X),M_1) = one_one(nat))) # label(fact_3395_invertible__coprime__nat) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.78 3355 (all Aa all Ba (hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),Aa),Ba) = one_one(nat) <-> (all D_3 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),D_3),Aa)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),D_3),Ba)) <-> D_3 = hAPP(nat,nat,suc,zero_zero(nat)))))) # label(fact_3396_coprime__Suc__0__nat) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.78 3356 (all A_1 all B (hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),A_1),B) != zero_zero(nat) -> (exists A_4 exists B_2 (A_1 = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A_4),hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),A_1),B)) & B = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B_2),hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),A_1),B)) & hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),A_4),B_2) = one_one(nat))))) # label(fact_3397_gcd__coprime__exists__nat) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.78 3357 (all B all A_1 (A_1 != zero_zero(nat) -> (exists X_2 exists Y_2 hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A_1),X_2) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),Y_2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),A_1),B))))) # label(fact_3398_bezout__nat) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.78 3358 (all X_3 (hBOOL(hAPP(fun(nat,real),bool,cauchy(real),X_3)) <-> (all J_1 exists M_4 all M_3 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_4),M_3)) -> (all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_4),N_2)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(nat,real,X_3,M_3)),hAPP(nat,real,X_3,N_2)))),hAPP(real,real,inverse_inverse(real),hAPP(nat,real,real_1(nat),hAPP(nat,nat,suc,J_1))))))))))) # label(fact_3399_Cauchy__iff2) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.78 3359 (all X_a (real_normed_vector(X_a) -> (all E_2 all X_3 (hBOOL(hAPP(fun(nat,X_a),bool,cauchy(X_a),X_3)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),E_2)) -> (exists M_4 all M_3 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_4),M_3)) -> (all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_4),N_2)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(nat,X_a,X_3,M_3)),hAPP(nat,X_a,X_3,N_2)))),E_2))))))))))) # label(fact_3400_CauchyD) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.78 3360 (all X_a (real_normed_vector(X_a) -> (all X_3 (hBOOL(hAPP(fun(nat,X_a),bool,cauchy(X_a),X_3)) <-> (all E (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),E)) -> (exists M_4 all M_3 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_4),M_3)) -> (all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_4),N_2)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(nat,X_a,X_3,M_3)),hAPP(nat,X_a,X_3,N_2)))),E)))))))))))) # label(fact_3401_Cauchy__iff) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.78 3361 (all X_a (real_normed_vector(X_a) -> (all X_3 ((all E (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),E)) -> (exists M_4 all M_3 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_4),M_3)) -> (all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_4),N_2)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(nat,X_a,X_3,M_3)),hAPP(nat,X_a,X_3,N_2)))),E)))))))) -> hBOOL(hAPP(fun(nat,X_a),bool,cauchy(X_a),X_3)))))) # label(fact_3402_CauchyI) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.78 3362 (all X_a all X_1 all Y_1 all F (hBOOL(hAPP(fun(product_prod(X_a,X_a),bool),bool,hAPP(product_prod(X_a,X_a),fun(fun(product_prod(X_a,X_a),bool),bool),member(product_prod(X_a,X_a)),hAPP(X_a,product_prod(X_a,X_a),hAPP(X_a,fun(X_a,product_prod(X_a,X_a)),product_Pair(X_a,X_a),X_1),Y_1)),hAPP(fun(X_a,nat),fun(product_prod(X_a,X_a),bool),measure(X_a),F))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(X_a,nat,F,X_1)),hAPP(X_a,nat,F,Y_1))))) # label(fact_3403_in__measure) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.78 3363 (all A_1 all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),one_one(real)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A_1)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,ln,X)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(real,fun(real,real),powr,X),A_1)),A_1)))))) # label(fact_3404_ln__powr__bound) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.78 3364 (all A_1 all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A_1)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),powr,hAPP(real,real,ln,X)),A_1)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),powr,A_1),A_1)),X)))))) # label(fact_3405_ln__powr__bound2) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.78 3365 (all A_1 hAPP(real,real,hAPP(real,fun(real,real),powr,one_one(real)),A_1) = one_one(real)) # label(fact_3406_powr__one__eq__one) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.78 3366 (all X all A_1 hAPP(real,real,hAPP(real,fun(real,real),powr,X),A_1) != zero_zero(real)) # label(fact_3407_powr__not__zero) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.78 3367 (all X all A_1 all B hAPP(real,real,hAPP(real,fun(real,real),powr,hAPP(real,real,hAPP(real,fun(real,real),powr,X),A_1)),B) = hAPP(real,real,hAPP(real,fun(real,real),powr,hAPP(real,real,hAPP(real,fun(real,real),powr,X),B)),A_1)) # label(fact_3408_powr__powr__swap) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.78 3368 (all X all A_1 all B hAPP(real,real,hAPP(real,fun(real,real),powr,hAPP(real,real,hAPP(real,fun(real,real),powr,X),A_1)),B) = hAPP(real,real,hAPP(real,fun(real,real),powr,X),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A_1),B))) # label(fact_3409_powr__powr) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.78 3369 (all X all Y hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),powr,X),Y)))) # label(fact_3410_powr__ge__pzero) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.78 3370 (all Y all X all A_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A_1),zero_zero(real))) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),Y)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),powr,Y),A_1)),hAPP(real,real,hAPP(real,fun(real,real),powr,X),A_1))))))) # label(fact_3411_powr__less__mono2__neg) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.78 3371 (all Y all X all A_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),Y)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),powr,X),A_1)),hAPP(real,real,hAPP(real,fun(real,real),powr,Y),A_1))))))) # label(fact_3412_powr__less__mono2) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.78 3372 (all X all A_1 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),powr,X),A_1)))) # label(fact_3413_powr__gt__zero) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.78 3373 (all X all A_1 all B (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A_1),B)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),one_one(real)),X)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),powr,X),A_1)),hAPP(real,real,hAPP(real,fun(real,real),powr,X),B)))))) # label(fact_3414_powr__mono) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.78 3374 (all X hAPP(real,real,hAPP(real,fun(real,real),powr,X),zero_zero(real)) = one_one(real)) # label(fact_3415_powr__zero__eq__one) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.78 3375 (all X all A_1 all B (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),powr,X),A_1)),hAPP(real,real,hAPP(real,fun(real,real),powr,X),B))) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),X)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A_1),B))))) # label(fact_3416_powr__less__cancel) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.78 3376 (all X all A_1 all B (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A_1),B)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),X)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),powr,X),A_1)),hAPP(real,real,hAPP(real,fun(real,real),powr,X),B)))))) # label(fact_3417_powr__less__mono) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.78 3377 (all Aa all Ba all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),X_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),powr,X_1),Aa)),hAPP(real,real,hAPP(real,fun(real,real),powr,X_1),Ba))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),Aa),Ba))))) # label(fact_3418_powr__less__cancel__iff) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.78 3378 (all X all A_1 all B hAPP(real,real,hAPP(real,fun(real,real),powr,X),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A_1),B)) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),powr,X),A_1)),hAPP(real,real,hAPP(real,fun(real,real),powr,X),B))) # label(fact_3419_powr__add) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.78 3379 (all X all A_1 all B hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(real,fun(real,real),powr,X),A_1)),hAPP(real,real,hAPP(real,fun(real,real),powr,X),B)) = hAPP(real,real,hAPP(real,fun(real,real),powr,X),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A_1),B))) # label(fact_3420_powr__divide2) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.78 3380 (all X all A_1 hAPP(real,real,hAPP(real,fun(real,real),powr,X),hAPP(real,real,uminus_uminus(real),A_1)) = hAPP(real,real,inverse_inverse(real),hAPP(real,real,hAPP(real,fun(real,real),powr,X),A_1))) # label(fact_3421_powr__minus) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.78 3381 (all Y all X all A_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X),Y)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),powr,X),A_1)),hAPP(real,real,hAPP(real,fun(real,real),powr,Y),A_1))))))) # label(fact_3422_powr__mono2) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.78 3382 (all A_1 all Y all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Y)) -> hAPP(real,real,hAPP(real,fun(real,real),powr,hAPP(real,real,hAPP(real,fun(real,real),times_times(real),X),Y)),A_1) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),powr,X),A_1)),hAPP(real,real,hAPP(real,fun(real,real),powr,Y),A_1))))) # label(fact_3423_powr__mult) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.78 3383 (all A_1 all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),one_one(real)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A_1)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),one_one(real)),hAPP(real,real,hAPP(real,fun(real,real),powr,X),A_1)))))) # label(fact_3424_ge__one__powr__ge__zero) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.78 3384 (all Aa all Ba all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),X_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),powr,X_1),Aa)),hAPP(real,real,hAPP(real,fun(real,real),powr,X_1),Ba))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),Aa),Ba))))) # label(fact_3425_powr__le__cancel__iff) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.78 3385 (all X_1 (hAPP(real,real,hAPP(real,fun(real,real),powr,X_1),one_one(real)) = X_1 <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X_1)))) # label(fact_3426_powr__one__gt__zero__iff) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.78 3386 (all A_1 all Y all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Y)) -> hAPP(real,real,hAPP(real,fun(real,real),powr,hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),X),Y)),A_1) = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(real,fun(real,real),powr,X),A_1)),hAPP(real,real,hAPP(real,fun(real,real),powr,Y),A_1))))) # label(fact_3427_powr__divide) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.78 3387 (all X all A_1 hAPP(real,real,hAPP(real,fun(real,real),powr,X),hAPP(real,real,uminus_uminus(real),A_1)) = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),one_one(real)),hAPP(real,real,hAPP(real,fun(real,real),powr,X),A_1))) # label(fact_3428_powr__minus__divide) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.78 3388 (all X all A_1 hAPP(real,real,hAPP(real,fun(real,real),powr,X),A_1) = hAPP(real,real,exp(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A_1),hAPP(real,real,ln,X)))) # label(fact_3429_powr__def) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.78 3389 (all N_1 all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> hAPP(real,real,hAPP(real,fun(real,real),powr,X),hAPP(nat,real,real_1(nat),N_1)) = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),N_1))) # label(fact_3430_powr__realpow) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.78 3390 (all Y all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Y)) -> hAPP(real,real,ln,hAPP(real,real,hAPP(real,fun(real,real),powr,X),Y)) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),Y),hAPP(real,real,ln,X))))) # label(fact_3431_ln__powr) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.78 3391 (all Y all A_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A_1)) -> (A_1 != one_one(real) -> hAPP(real,real,hAPP(real,fun(real,real),log,A_1),hAPP(real,real,hAPP(real,fun(real,real),powr,A_1),Y)) = Y))) # label(fact_3432_log__powr__cancel) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.78 3392 (all X all A_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A_1)) -> (A_1 != one_one(real) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> hAPP(real,real,hAPP(real,fun(real,real),powr,A_1),hAPP(real,real,hAPP(real,fun(real,real),log,A_1),X)) = X)))) # label(fact_3433_powr__log__cancel) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.78 3393 (all B all Y all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),Y)) -> hAPP(real,real,hAPP(real,fun(real,real),log,B),hAPP(real,real,hAPP(real,fun(real,real),powr,X),Y)) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),Y),hAPP(real,real,hAPP(real,fun(real,real),log,B),X))))) # label(fact_3434_log__powr) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.78 3394 (all N_1 all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)) -> (X = zero_zero(real) -> hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),N_1) = zero_zero(real)) & (X != zero_zero(real) -> hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),N_1) = hAPP(real,real,hAPP(real,fun(real,real),powr,X),hAPP(nat,real,real_1(nat),N_1)))))) # label(fact_3435_powr__realpow2) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.78 3395 (all C all N_1 all A_1 all B (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,A_1),B)) -> (hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A_1),B) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),C),N_1) -> (exists R_2 exists S_1 (A_1 = hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),R_2),N_1) & B = hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),S_1),N_1)))))) # label(fact_3436_coprime__pow) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.78 3396 (all X all Y all K_4 all P_4 (hBOOL(hAPP(nat,bool,prime,P_4)) -> (hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X),Y) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),P_4),K_4) -> (exists I_2 exists J_1 (X = hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),P_4),I_2) & Y = hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),P_4),J_1)))))) # label(fact_3437_prime__power__mult) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.78 3397 (all X all M_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),M_1)) -> (hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,X),M_1) = one_one(int) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),X),hAPP(int,nat,phi,M_1))),one_one(int)),M_1))))) # label(fact_3438_Euler__Fermat) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.78 3398 (all I_1 all J_2 hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,I_1),J_2)),J_2))) # label(fact_3439_zgcd__zdvd2) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.78 3399 (all I_1 all J_2 hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,I_1),J_2)),I_1))) # label(fact_3440_zgcd__zdvd1) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.78 3400 (all K_4 all M_1 all N_1 hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K_4),M_1)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K_4),N_1)) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,abs_abs(int),K_4)),hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,M_1),N_1))) # label(fact_3441_zgcd__zmult__distrib2__abs) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.78 3401 (all I_1 all J_2 hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,I_1),J_2)))) # label(fact_3442_zgcd__pos) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.78 3402 (all M_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),M_1)) -> hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,M_1),M_1) = M_1)) # label(fact_3443_zgcd__self) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.78 3403 (all X all 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),legacy_zgcd,X),Y)))) # label(fact_3444_zgcd__geq__zero) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.78 3404 (all M_1 hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,M_1),zero_zero(int)) = hAPP(int,int,abs_abs(int),M_1)) # label(fact_3445_zgcd__0) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.78 3405 (all M_1 hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,zero_zero(int)),M_1) = hAPP(int,int,abs_abs(int),M_1)) # label(fact_3446_zgcd__0__left) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.78 3406 (all M_1 all N_1 all K_4 hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,M_1),N_1)),hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K_4),M_1)),N_1)))) # label(fact_3447_zgcd__zdvd__zgcd__zmult) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.78 3407 (all N_1 all A_1 all B (hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,A_1),B) = one_one(int) -> hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A_1),N_1)),B) = one_one(int))) # label(fact_3448_zgcd__1__power__left__distrib) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.78 3408 (all N_1 all A_1 all B (hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,A_1),B) = one_one(int) -> hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A_1),N_1)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),B),N_1)) = one_one(int))) # label(fact_3449_zgcd__1__power__distrib) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.78 3409 (all A_1 all B all N_1 hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,A_1),B)),N_1) = hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A_1),N_1)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),B),N_1))) # label(fact_3450_zgcd__power__distrib) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.78 3410 (all I_1 all J_2 hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,I_1),J_2) = hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,J_2),I_1)) # label(fact_3451_zgcd__commute) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.78 3411 (all K_4 all M_1 all N_1 hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,K_4),hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,M_1),N_1)) = hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,M_1),hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,K_4),N_1))) # label(fact_3452_zgcd__left__commute) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.78 3412 (all K_4 all M_1 all N_1 hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,K_4),M_1)),N_1) = hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,K_4),hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,M_1),N_1))) # label(fact_3453_zgcd__assoc) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.78 3413 (all I_1 all J_2 hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,I_1),hAPP(int,int,uminus_uminus(int),J_2)) = hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,I_1),J_2)) # label(fact_3454_zgcd__zminus2) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.78 3414 (all I_1 all J_2 hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,hAPP(int,int,uminus_uminus(int),I_1)),J_2) = hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,I_1),J_2)) # label(fact_3455_zgcd__zminus) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.78 3415 (all M_1 all N_1 all K_4 hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),M_1),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),N_1),K_4))),N_1) = hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,M_1),N_1)) # label(fact_3456_zgcd__zadd__zmult) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.78 3416 (all N_1 all K_4 all M_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),K_4),M_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),K_4),N_1)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),K_4),hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,M_1),N_1)))))) # label(fact_3457_zgcd__greatest) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.78 3417 (all K all M all N (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),K),hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,M),N))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),K),M)) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),K),N)))) # label(fact_3458_zgcd__greatest__iff) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.78 3418 (all N_1 all K_4 all M_1 (hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,K_4),M_1) = one_one(int) -> (hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,N_1),M_1) = one_one(int) -> hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K_4),N_1)),M_1) = one_one(int)))) # label(fact_3459_zgcd__zgcd__zmult) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.78 3419 (all M_1 all K_4 all N_1 (hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,K_4),N_1) = one_one(int) -> hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K_4),M_1)),N_1) = hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,M_1),N_1))) # label(fact_3460_zgcd__zmult__cancel) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.78 3420 (all M_1 hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,M_1),one_one(int)) = one_one(int)) # label(fact_3461_zgcd__1) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.78 3421 (all M_1 hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,one_one(int)),M_1) = one_one(int)) # label(fact_3462_zgcd__1__left) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.78 3422 (all I all J (hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,I),J) = zero_zero(int) <-> I = zero_zero(int) & J = zero_zero(int))) # label(fact_3463_zgcd0) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.78 3423 (all M_1 all N_1 hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,M_1),N_1) = hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,N_1),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),M_1),N_1))) # label(fact_3464_zgcd__eq) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.78 3424 (all N_1 all K_4 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),K_4)) -> hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K_4),N_1)),K_4) = K_4)) # label(fact_3465_zgcd__zmult__eq__self2) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.78 3425 (all M_1 all N_1 all K_4 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),K_4)) -> hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K_4),hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,M_1),N_1)) = hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K_4),M_1)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K_4),N_1)))) # label(fact_3466_zgcd__zmult__distrib2) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.78 3426 (all N_1 all K_4 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),K_4)) -> hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,K_4),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K_4),N_1)) = K_4)) # label(fact_3467_zgcd__zmult__eq__self) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.79 3427 (all N all M (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),M)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),M),N)) <-> hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,N),M) = M))) # label(fact_3468_zdvd__iff__zgcd) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.79 3428 (all M_1 all N_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),N_1)) -> hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,M_1),N_1) = hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,N_1),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),M_1),N_1)))) # label(fact_3469_zgcd__non__0) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.79 3429 (all B all A_1 (A_1 != zero_zero(int) | B != zero_zero(int) -> hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_1),hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,A_1),B))),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),B),hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,A_1),B))) = one_one(int))) # label(fact_3470_div__zgcd__relprime) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.79 3430 (all N_1 all A_1 all B all M_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_1),B),M_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_1),B),N_1)) -> (hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,M_1),N_1) = one_one(int) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_1),B),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),M_1),N_1))))))) # label(fact_3471_zcong__zgcd__zmult__zmod) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.79 3431 (all M (hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,zero_zero(int)),M) = one_one(int) <-> hAPP(int,int,abs_abs(int),M) = one_one(int))) # label(fact_3472_zgcd__0__1__iff) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.79 3432 (all M_1 all K_4 all N_1 (hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,K_4),N_1) = one_one(int) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K_4),M_1)),N_1)),hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,M_1),N_1))))) # label(fact_3473_zgcd__zmult__zdvd__zgcd) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.79 3433 (all M_1 all N_1 all K_4 (hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,N_1),K_4) = one_one(int) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),K_4),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),M_1),N_1))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),K_4),M_1))))) # label(fact_3474_zrelprime__zdvd__zmult) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.79 3434 (all K_4 all I_1 all J_2 (hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,I_1),J_2) = one_one(int) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),I_1),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K_4),J_2))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),I_1),K_4))))) # label(fact_3475_zrelprime__dvd__mult) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.79 3435 (all K all L hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,K),L) = hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),hAPP(bool,fun(int,fun(int,int)),if(int),hAPP(int,bool,hAPP(int,fun(int,bool),fequal(int),L),zero_zero(int))),K),hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,L),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,abs_abs(int),K)),hAPP(int,int,abs_abs(int),L)))))) # label(fact_3476_zgcd__code) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.79 3436 (all N_1 all P_4 (hBOOL(hAPP(int,bool,zprime,P_4)) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),P_4),N_1)) -> hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,N_1),P_4) = one_one(int)))) # label(fact_3477_zprime__imp__zrelprime) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.79 3437 (all Aa all Ba (hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,Aa),Ba) = one_one(int) <-> -(exists P_5 (hBOOL(hAPP(int,bool,zprime,P_5)) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),P_5),Aa)) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),P_5),Ba)))))) # label(fact_3478_zgcd1__iff__no__common__primedivisor) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.79 3438 (all B all A_1 all M_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),M_1)) -> (hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,A_1),M_1) = one_one(int) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_1),B),M_1)) -> hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,B),M_1) = one_one(int))))) # label(fact_3479_zgcd__zcong__zgcd) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.79 3439 (all N_1 all P_4 (hBOOL(hAPP(int,bool,zprime,P_4)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),N_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),N_1),P_4)) -> hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,N_1),P_4) = one_one(int))))) # label(fact_3480_zless__zprime__imp__zrelprime) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.79 3440 (all Aa all Ba all K all M (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),M)) -> (hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,K),M) = one_one(int) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K),Aa)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K),Ba)),M)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,Aa),Ba),M)))))) # label(fact_3481_zcong__cancel2) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.79 3441 (all Aa all Ba all K all M (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),M)) -> (hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,K),M) = one_one(int) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Aa),K)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Ba),K)),M)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,Aa),Ba),M)))))) # label(fact_3482_zcong__cancel) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.79 3442 (all M_1 all N_1 all K_4 (hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,N_1),K_4) = one_one(int) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),K_4),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),M_1),N_1))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),M_1)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),K_4),M_1)))))) # label(fact_3483_zrelprime__zdvd__zmult__aux) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.79 3443 (all Aa all Ba all M (hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,Ba),M) = one_one(int) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),Ba)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Ba),Aa)) -> hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Ba),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),bnorRset,Aa),M))))))) # label(fact_3484_Bnor__mem__if) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.79 3444 (all Aa all Ba all C_1 all X_1 (hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Aa),Ba) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),C_1),hAPP(int,nat,nat_1,X_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),one_one(nat)),hAPP(int,nat,nat_1,X_1))) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),zOdd)) -> (hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,Aa),Ba) = one_one(int) -> (exists K_1 Aa = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),K_1),hAPP(int,nat,nat_1,X_1)))))))) # label(fact_3485_int__relprime__odd__power__divisors) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.79 3445 (all M all K all N (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),N)) -> (hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,M),N) = K <-> (exists S_1 exists T_5 hAPP(int,product_prod(int,product_prod(int,int)),hAPP(int,fun(int,product_prod(int,product_prod(int,int))),xzgcd,M),N) = hAPP(product_prod(int,int),product_prod(int,product_prod(int,int)),hAPP(int,fun(product_prod(int,int),product_prod(int,product_prod(int,int))),product_Pair(int,product_prod(int,int)),K),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),S_1),T_5)))))) # label(fact_3486_xzgcd__correct) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.79 3446 (all A_1 all B all C all N_1 (hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),B) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),C),N_1) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),one_one(nat)),N_1)) -> (hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,A_1),B) = one_one(int) -> (exists K_1 hAPP(int,int,abs_abs(int),A_1) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),K_1),N_1)))))) # label(fact_3487_int__relprime__power__divisors) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.79 3447 (all M_1 all N_1 all R_5 all R_4 all S_5 all S_4 all T_7 all T_6 all K_4 ((exists Sn exists Tn hAPP(int,product_prod(int,product_prod(int,int)),hAPP(int,fun(int,product_prod(int,product_prod(int,int))),hAPP(int,fun(int,fun(int,product_prod(int,product_prod(int,int)))),hAPP(int,fun(int,fun(int,fun(int,product_prod(int,product_prod(int,int))))),hAPP(int,fun(int,fun(int,fun(int,fun(int,product_prod(int,product_prod(int,int)))))),hAPP(int,fun(int,fun(int,fun(int,fun(int,fun(int,product_prod(int,product_prod(int,int))))))),hAPP(int,fun(int,fun(int,fun(int,fun(int,fun(int,fun(int,product_prod(int,product_prod(int,int)))))))),hAPP(int,fun(int,fun(int,fun(int,fun(int,fun(int,fun(int,fun(int,product_prod(int,product_prod(int,int))))))))),xzgcda,M_1),N_1),R_5),R_4),S_5),S_4),T_7),T_6) = hAPP(product_prod(int,int),product_prod(int,product_prod(int,int)),hAPP(int,fun(product_prod(int,int),product_prod(int,product_prod(int,int))),product_Pair(int,product_prod(int,int)),K_4),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),Sn),Tn))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),R_4)) -> hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,R_5),R_4) = K_4))) # label(fact_3488_xzgcd__correct__aux2) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.79 3448 (all B all A_1 all N_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),N_1)) -> (hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,A_1),N_1) = one_one(int) -> (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,hAPP(int,fun(int,bool),ord_less(int),X_2),N_1)) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),X_2)),B),N_1)) & (all Y_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Y_2)) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Y_2),N_1)) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),Y_2)),B),N_1)) -> Y_2 = X_2))))))) # label(fact_3489_zcong__lineq__unique) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.79 3449 (all A_1 all N_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),N_1)) -> (hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,A_1),N_1) = one_one(int) -> (exists X_2 hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),X_2)),one_one(int)),N_1)))))) # label(fact_3490_zcong__lineq__ex) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.79 3450 (all M_1 all N_1 all S_5 all S_4 all T_7 all T_6 all R_5 all R_4 all K_4 (hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,R_5),R_4) = K_4 -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),R_4)) -> (exists Sn exists Tn hAPP(int,product_prod(int,product_prod(int,int)),hAPP(int,fun(int,product_prod(int,product_prod(int,int))),hAPP(int,fun(int,fun(int,product_prod(int,product_prod(int,int)))),hAPP(int,fun(int,fun(int,fun(int,product_prod(int,product_prod(int,int))))),hAPP(int,fun(int,fun(int,fun(int,fun(int,product_prod(int,product_prod(int,int)))))),hAPP(int,fun(int,fun(int,fun(int,fun(int,fun(int,product_prod(int,product_prod(int,int))))))),hAPP(int,fun(int,fun(int,fun(int,fun(int,fun(int,fun(int,product_prod(int,product_prod(int,int)))))))),hAPP(int,fun(int,fun(int,fun(int,fun(int,fun(int,fun(int,fun(int,product_prod(int,product_prod(int,int))))))))),xzgcda,M_1),N_1),R_5),R_4),S_5),S_4),T_7),T_6) = hAPP(product_prod(int,int),product_prod(int,product_prod(int,int)),hAPP(int,fun(product_prod(int,int),product_prod(int,product_prod(int,int))),product_Pair(int,product_prod(int,int)),K_4),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),Sn),Tn)))))) # label(fact_3491_xzgcd__correct__aux1) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.79 3451 (all Aa all Ba all C_1 all D_1 all X_1 (hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Aa),Ba)),C_1) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),D_1),hAPP(int,nat,nat_1,X_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),one_one(nat)),hAPP(int,nat,nat_1,X_1))) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),zOdd)) -> (hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,Aa),Ba) = one_one(int) -> (hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,Ba),C_1) = one_one(int) -> (hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,C_1),Aa) = one_one(int) -> (exists K_1 exists L_3 exists M_3 (Aa = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),K_1),hAPP(int,nat,nat_1,X_1)) & Ba = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),L_3),hAPP(int,nat,nat_1,X_1)) & C_1 = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),M_3),hAPP(int,nat,nat_1,X_1))))))))))) # label(fact_3492_int__triple__relprime__odd__power__divisors) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.79 3452 (all M_1 all K_4 all N_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),N_1)) -> (hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,M_1),N_1) = K_4 -> (exists S_1 exists T_5 K_4 = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),S_1),M_1)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),T_5),N_1)))))) # label(fact_3493_zgcd__ex__linear) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.79 3453 (all A_1 all B all C all D all N_1 (hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),B)),C) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),D),N_1) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),one_one(nat)),N_1)) -> (hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,A_1),B) = one_one(int) -> (hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,B),C) = one_one(int) -> (hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,C),A_1) = one_one(int) -> (exists K_1 exists L_3 exists M_3 (hAPP(int,int,abs_abs(int),A_1) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),K_1),N_1) & hAPP(int,int,abs_abs(int),B) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),L_3),N_1) & hAPP(int,int,abs_abs(int),C) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),M_3),N_1))))))))) # label(fact_3494_int__triple__relprime__power__divisors) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.79 3454 (all B all A_1 (A_1 != zero_zero(int) | B != zero_zero(int) -> (exists C_4 exists D_3 (A_1 = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,A_1),B)),C_4) & B = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,A_1),B)),D_3) & hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,C_4),D_3) = one_one(int))))) # label(fact_3495_make__zrelprime) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.79 3455 (all X_a (real_normed_vector(X_a) -> (all X_3 (hBOOL(hAPP(fun(nat,X_a),bool,bseq(X_a),X_3)) <-> (exists K_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),K_1)) & (exists X_2 all N_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(nat,X_a,X_3,N_2)),hAPP(X_a,X_a,uminus_uminus(X_a),X_2)))),K_1))))))))) # label(fact_3496_Bseq__iff2) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.79 3456 (all X_a (real_normed_vector(X_a) -> (all X_3 (hBOOL(hAPP(fun(nat,X_a),bool,cauchy(X_a),X_3)) -> hBOOL(hAPP(fun(nat,X_a),bool,bseq(X_a),X_3)))))) # label(fact_3497_Cauchy__Bseq) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.79 3457 (all X_a (real_normed_vector(X_a) -> (all X_3 (hBOOL(hAPP(fun(nat,X_a),bool,bseq(X_a),X_3)) <-> (exists K_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),K_2)) & (all N_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),hAPP(nat,X_a,X_3,N_2))),K_2))))))))) # label(fact_3498_Bseq__def) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.79 3458 (all X_a (real_normed_vector(X_a) -> (all X_3 (hBOOL(hAPP(fun(nat,X_a),bool,bseq(X_a),X_3)) <-> (exists N_3 all N_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),hAPP(nat,X_a,X_3,N_2))),hAPP(nat,real,real_1(nat),hAPP(nat,nat,suc,N_3))))))))) # label(fact_3499_Bseq__iff) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.79 3459 (all X_a (real_normed_vector(X_a) -> (all X_3 (hBOOL(hAPP(fun(nat,X_a),bool,bseq(X_a),X_3)) <-> (exists N_3 all N_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,norm_norm(X_a),hAPP(nat,X_a,X_3,N_2))),hAPP(nat,real,real_1(nat),hAPP(nat,nat,suc,N_3))))))))) # label(fact_3500_Bseq__iff1a) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.79 3460 (all X_a (real_normed_vector(X_a) -> (all X_3 (hBOOL(hAPP(fun(nat,X_a),bool,bseq(X_a),X_3)) <-> (exists K_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),K_1)) & (exists N_3 all N_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(nat,X_a,X_3,N_2)),hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(nat,X_a,X_3,N_3))))),K_1))))))))) # label(fact_3501_Bseq__iff3) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.79 3461 (all X_a (real_normed_vector(X_a) -> (all X_3 (hBOOL(hAPP(fun(nat,X_a),bool,bseq(X_a),X_3)) -> (exists K_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),K_2)) & (all N_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),hAPP(nat,X_a,X_3,N_2))),K_2))))))))) # label(fact_3502_BseqD) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.79 3462 (all X_a (real_normed_vector(X_a) -> (all X_3 all K_3 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),K_3)) -> ((all N_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),hAPP(nat,X_a,X_3,N_2))),K_3))) -> hBOOL(hAPP(fun(nat,X_a),bool,bseq(X_a),X_3))))))) # label(fact_3503_BseqI) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.79 3463 (all X_a (real_normed_vector(X_a) -> (all X_3 all K_3 all N_4 ((all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_4),N_2)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),hAPP(nat,X_a,X_3,N_2))),K_3)))) -> hBOOL(hAPP(fun(nat,X_a),bool,bseq(X_a),X_3)))))) # label(fact_3504_BseqI2_H) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.79 3464 (all X_a (real_normed_vector(X_a) -> (all X_3 all K_3 ((all N_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),hAPP(nat,X_a,X_3,N_2))),K_3))) -> hBOOL(hAPP(fun(nat,X_a),bool,bseq(X_a),X_3)))))) # label(fact_3505_BseqI_H) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.79 3465 (all X_a (real_normed_vector(X_a) -> (all X_3 (hBOOL(hAPP(fun(nat,X_a),bool,bseq(X_a),X_3)) -> -(all K_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),K_2)) -> -(all N_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),hAPP(nat,X_a,X_3,N_2))),K_2))))))))) # label(fact_3506_BseqE) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.79 3466 (all Y all X exists R_2 exists A_3 (X = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),R_2),hAPP(real,real,cos,A_3)) & Y = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),R_2),hAPP(real,real,sin,A_3)))) # label(fact_3507_polar__Ex) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.79 3467 (all X_a (metric_space(X_a) -> (all X2_1 all X1_1 all Y all E_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),X1_1),Y)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),E_1),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),X2_1),Y)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),E_1),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),X1_1),X2_1)),E_1))))))) # label(fact_3508_dist__triangle__half__l) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.79 3468 (all X_a (metric_space(X_a) -> (all X2_1 all Y all X1_1 all E_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),Y),X1_1)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),E_1),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),Y),X2_1)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),E_1),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),X1_1),X2_1)),E_1))))))) # label(fact_3509_dist__triangle__half__r) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.79 3469 (all X_a (metric_space(X_a) -> (all X all Y -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),X),Y)),zero_zero(real)))))) # label(fact_3510_dist__not__less__zero) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.79 3470 (all X_a (metric_space(X_a) -> (all X_1 all Y_1 (ti(X_a,X_1) != ti(X_a,Y_1) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),X_1),Y_1))))))) # label(fact_3511_dist__nz) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.79 3471 (all X_a (metric_space(X_a) -> (all X_1 all Y_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),X_1),Y_1))) <-> ti(X_a,X_1) != ti(X_a,Y_1))))) # label(fact_3512_zero__less__dist__iff) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.79 3472 (all X_a (metric_space(X_a) -> (all X all Y (ti(X_a,X) != ti(X_a,Y) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),X),Y))))))) # label(fact_3513_dist__pos__lt) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.79 3473 (all X_a (dist_norm(X_a) -> (all X all Y hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),X),Y) = hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),X),Y))))) # label(fact_3514_dist__norm) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.79 3474 (all X_a (metric_space(X_a) -> (all X_1 all Y_1 (hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),X_1),Y_1) = zero_zero(real) <-> ti(X_a,X_1) = ti(X_a,Y_1))))) # label(fact_3515_dist__eq__0__iff) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.79 3475 (all X_a (metric_space(X_a) -> (all X hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),X),X) = zero_zero(real)))) # label(fact_3516_dist__self) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.79 3476 (all X_a (metric_space(X_a) -> (all X all Y hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),X),Y) = hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),Y),X)))) # label(fact_3517_dist__commute) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.79 3477 (all X_a (metric_space(X_a) -> (all X_1 all Y_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),X_1),Y_1)),zero_zero(real))) <-> ti(X_a,X_1) = ti(X_a,Y_1))))) # label(fact_3518_dist__le__zero__iff) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.79 3478 (all X_a (metric_space(X_a) -> (all X all Y hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),X),Y)))))) # label(fact_3519_zero__le__dist) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.79 3479 (all X_a (metric_space(X_a) -> (all X all Z all Y all E_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),X),Z)),hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),Y),Z))),E_1)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),X),Y)),E_1)))))) # label(fact_3520_dist__triangle__lt) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.79 3480 (all X_a (metric_space(X_a) -> (all X all Z all Y all E_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),X),Z)),hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),Y),Z))),E_1)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),X),Y)),E_1)))))) # label(fact_3521_dist__triangle__le) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.79 3481 (all X_a (metric_space(X_a) -> (all Y all Z all X hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),Y),Z)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),X),Y)),hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),X),Z))))))) # label(fact_3522_dist__triangle__alt) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.79 3482 (all X_a (metric_space(X_a) -> (all X all Z all Y hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),X),Z)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),X),Y)),hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),Y),Z))))))) # label(fact_3523_dist__triangle) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.79 3483 (all X_a (metric_space(X_a) -> (all X all Y all Z hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),X),Y)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),X),Z)),hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),Y),Z))))))) # label(fact_3524_dist__triangle2) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.79 3484 (all X_a (metric_space(X_a) -> (all X all Y all A_1 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),X),Y)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),A_1),X)),hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),A_1),Y))))))) # label(fact_3525_dist__triangle3) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.79 3485 (all X all Y hAPP(real,real,hAPP(real,fun(real,real),dist_dist(real),X),Y) = hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),X),Y))) # label(fact_3526_dist__real__def) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.79 3486 (all X all Y hAPP(complex,real,hAPP(complex,fun(complex,real),dist_dist(complex),X),Y) = hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),X),Y))) # label(fact_3527_dist__complex__def) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.79 3487 (all X_a (metric_space(X_a) -> (all X_3 (hBOOL(hAPP(fun(nat,X_a),bool,cauchy(X_a),X_3)) <-> (all E (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),E)) -> (exists M_4 all M_3 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_4),M_3)) -> (all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_4),N_2)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),hAPP(nat,X_a,X_3,M_3)),hAPP(nat,X_a,X_3,N_2))),E)))))))))))) # label(fact_3528_Cauchy__def) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.79 3488 (all X_a (metric_space(X_a) -> (all E_2 all X_3 (hBOOL(hAPP(fun(nat,X_a),bool,cauchy(X_a),X_3)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),E_2)) -> (exists M_4 all M_3 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_4),M_3)) -> (all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_4),N_2)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),hAPP(nat,X_a,X_3,M_3)),hAPP(nat,X_a,X_3,N_2))),E_2))))))))))) # label(fact_3529_metric__CauchyD) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.79 3489 (all X_a (real_normed_vector(X_a) -> (all X hAPP(X_a,real,norm_norm(X_a),X) = hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),X),zero_zero(X_a))))) # label(fact_3530_norm__conv__dist) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.79 3490 (all X_a (metric_space(X_a) -> (all X_3 ((all E (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),E)) -> (exists M_4 all M_3 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_4),M_3)) -> (all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_4),N_2)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),hAPP(nat,X_a,X_3,M_3)),hAPP(nat,X_a,X_3,N_2))),E)))))))) -> hBOOL(hAPP(fun(nat,X_a),bool,cauchy(X_a),X_3)))))) # label(fact_3531_metric__CauchyI) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.79 3491 (all Z_1 all P_1 ((all N_2 hBOOL(hAPP(int,bool,P_1,hAPP(nat,int,semiring_1_of_nat(int),N_2)))) -> ((all N_2 hBOOL(hAPP(int,bool,P_1,hAPP(int,int,uminus_uminus(int),hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,N_2)))))) -> hBOOL(hAPP(int,bool,P_1,Z_1))))) # label(fact_3532_int__of__nat__induct) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.79 3492 (all Z ((all N_2 Z != hAPP(nat,int,semiring_1_of_nat(int),N_2)) -> -(all N_2 Z != hAPP(int,int,uminus_uminus(int),hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,N_2)))))) # label(fact_3533_int__cases) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.79 3493 (all F all Aa all Ba (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),Aa),Ba)) -> ((all X_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),Aa),X_2)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_2),Ba)) -> (exists Y_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),F),X_2),Y_2)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),Y_2)))))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,F,Aa)),hAPP(real,real,F,Ba)))))) # label(fact_3534_DERIV__nonneg__imp__nonincreasing) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.79 3494 (all F all Aa all Ba (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),Aa),Ba)) -> ((all X_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),Aa),X_2)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_2),Ba)) -> (exists Y_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),F),X_2),Y_2)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),Y_2),zero_zero(real))))))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,F,Ba)),hAPP(real,real,F,Aa)))))) # label(fact_3535_DERIV__nonpos__imp__nonincreasing) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.79 3495 (all M all N all P_1 ((all M_3 hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),P_1,M_3),zero_zero(nat)))) -> ((all M_3 all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_2)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),P_1,N_2),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),M_3),N_2))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),P_1,M_3),N_2))))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),P_1,M),N))))) # label(fact_3536_gcd__nat__induct) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.79 3496 (all X_a all F1 all F2 all Code_numeral hAPP(code_code_numeral,X_a,hAPP(fun(code_code_numeral,X_a),fun(code_code_numeral,X_a),hAPP(X_a,fun(fun(code_code_numeral,X_a),fun(code_code_numeral,X_a)),code_c600343653l_case(X_a),F1),F2),hAPP(code_code_numeral,code_code_numeral,code_S1047413653umeral,Code_numeral)) = hAPP(code_code_numeral,X_a,F2,Code_numeral)) # label(fact_3537_code__numeral_Osimps_I5_J) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.79 3497 (all N_1 all P_4 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),one_one(nat)),P_4)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),P_4),N_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),P_4),hAPP(nat,nat,fact,N_1)))))) # label(fact_3538_divides__fact) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.79 3498 (all N_1 all M_1 hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),N_1),M_1) = hAPP(int,quickcheck_code_int,quickcheck_of_int,hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(quickcheck_code_int,int,quickcheck_int_of,N_1)),hAPP(quickcheck_code_int,int,quickcheck_int_of,M_1)))) # label(fact_3539_mod__code__int__def) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.79 3499 (all N all M (hAPP(int,quickcheck_code_int,quickcheck_of_int,N) = hAPP(int,quickcheck_code_int,quickcheck_of_int,M) <-> N = M)) # label(fact_3540_Quickcheck__Narrowing_Oof__int__inject) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.79 3500 (all X hAPP(int,quickcheck_code_int,quickcheck_of_int,hAPP(quickcheck_code_int,int,quickcheck_int_of,X)) = X) # label(fact_3541_int__of__inverse) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.79 3501 (all K_4 hAPP(int,quickcheck_code_int,quickcheck_of_int,hAPP(quickcheck_code_int,int,quickcheck_int_of,K_4)) = K_4) # label(fact_3542_of__int__int__of) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.79 3502 (all N_1 hAPP(quickcheck_code_int,int,quickcheck_int_of,hAPP(int,quickcheck_code_int,quickcheck_of_int,N_1)) = N_1) # label(fact_3543_int__of__of__int) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.79 3503 (all M_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),N_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,fact,M_1)),hAPP(nat,nat,fact,N_1))))) # label(fact_3545_fact__mono) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.79 3504 (all N_1 all M_1 hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),N_1),M_1) = hAPP(int,quickcheck_code_int,quickcheck_of_int,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(quickcheck_code_int,int,quickcheck_int_of,N_1)),hAPP(quickcheck_code_int,int,quickcheck_int_of,M_1)))) # label(fact_3546_times__code__int__def) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.79 3505 (all N_1 all M_1 hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),N_1),M_1) = hAPP(int,quickcheck_code_int,quickcheck_of_int,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(quickcheck_code_int,int,quickcheck_int_of,N_1)),hAPP(quickcheck_code_int,int,quickcheck_int_of,M_1)))) # label(fact_3547_plus__code__int__def) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.79 3506 (all N_1 all M_1 hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),minus_minus(quickcheck_code_int),N_1),M_1) = hAPP(int,quickcheck_code_int,quickcheck_of_int,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(quickcheck_code_int,int,quickcheck_int_of,N_1)),hAPP(quickcheck_code_int,int,quickcheck_int_of,M_1)))) # label(fact_3548_minus__code__int__def) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.79 3507 (all N_1 hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,fact,N_1)))) # label(fact_3550_fact__lt) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.79 3508 (all N_1 hAPP(nat,nat,fact,hAPP(nat,nat,suc,N_1)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,N_1)),hAPP(nat,nat,fact,N_1))) # label(fact_3552_fact_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.79 3509 (all N_1 hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),one_one(nat)),hAPP(nat,nat,fact,N_1)))) # label(fact_3553_fact__le) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.79 3510 (all X_a all F1 all F2 hAPP(code_code_numeral,X_a,hAPP(fun(code_code_numeral,X_a),fun(code_code_numeral,X_a),hAPP(X_a,fun(fun(code_code_numeral,X_a),fun(code_code_numeral,X_a)),code_c600343653l_case(X_a),F1),F2),zero_zero(code_code_numeral)) = ti(X_a,F1)) # label(fact_3555_code__numeral_Osimps_I4_J) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.79 3511 (all N_1 all M_1 hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),N_1),M_1) = hAPP(int,quickcheck_code_int,quickcheck_of_int,hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(quickcheck_code_int,int,quickcheck_int_of,N_1)),hAPP(quickcheck_code_int,int,quickcheck_int_of,M_1)))) # label(fact_3556_div__code__int__def) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.79 3512 (all N_1 exists P_5 (hBOOL(hAPP(nat,bool,prime,P_5)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),P_5)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),P_5),hAPP(nat,nat,suc,hAPP(nat,nat,fact,N_1)))))) # label(fact_3557_euclid__bound) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.79 3513 (all F ((all I_2 hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,F,hAPP(nat,nat,suc,I_2))),hAPP(nat,nat,F,I_2)))) -> (exists I_2 all K_1 hAPP(nat,nat,F,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_2),K_1)) = hAPP(nat,nat,F,I_2)))) # label(fact_3558_weak__decr__stable) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.79 3514 (all P_1 all A0 all A1 (hBOOL(hAPP(product_prod(int,int),bool,hAPP(fun(product_prod(int,int),fun(product_prod(int,int),bool)),fun(product_prod(int,int),bool),accp(product_prod(int,int)),norm_frac_rel),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),A0),A1))) -> ((all A_3 all B_3 (hBOOL(hAPP(product_prod(int,int),bool,hAPP(fun(product_prod(int,int),fun(product_prod(int,int),bool)),fun(product_prod(int,int),bool),accp(product_prod(int,int)),norm_frac_rel),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),A_3),B_3))) -> ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B_3),zero_zero(int))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),P_1,hAPP(int,int,uminus_uminus(int),A_3)),hAPP(int,int,uminus_uminus(int),B_3)))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),P_1,A_3),B_3))))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),P_1,A0),A1))))) # label(fact_3559_norm__frac_Opinduct) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.79 3515 (all X_a all R_1 (hBOOL(hAPP(fun(product_prod(X_a,X_a),bool),bool,refl(X_a),R_1)) <-> (all X_2 hBOOL(hAPP(fun(product_prod(X_a,X_a),bool),bool,hAPP(product_prod(X_a,X_a),fun(fun(product_prod(X_a,X_a),bool),bool),member(product_prod(X_a,X_a)),hAPP(X_a,product_prod(X_a,X_a),hAPP(X_a,fun(X_a,product_prod(X_a,X_a)),product_Pair(X_a,X_a),X_2),X_2)),R_1))))) # label(fact_3560_Nitpick_Orefl_H__def) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.79 3516 (all P_1 all A0 all A1 (hBOOL(hAPP(product_prod(int,int),bool,hAPP(fun(product_prod(int,int),fun(product_prod(int,int),bool)),fun(product_prod(int,int),bool),accp(product_prod(int,int)),upto_rel),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),A0),A1))) -> ((all I_2 all J_1 (hBOOL(hAPP(product_prod(int,int),bool,hAPP(fun(product_prod(int,int),fun(product_prod(int,int),bool)),fun(product_prod(int,int),bool),accp(product_prod(int,int)),upto_rel),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),I_2),J_1))) -> ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),I_2),J_1)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),P_1,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),I_2),one_one(int))),J_1))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),P_1,I_2),J_1))))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),P_1,A0),A1))))) # label(fact_3561_upto_Opinduct) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.79 3517 (all P_1 all A0 all A1 (hBOOL(hAPP(product_prod(int,int),bool,hAPP(fun(product_prod(int,int),fun(product_prod(int,int),bool)),fun(product_prod(int,int),bool),accp(product_prod(int,int)),lazy_small_lazy_rel),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),A0),A1))) -> ((all D_3 all I_2 (hBOOL(hAPP(product_prod(int,int),bool,hAPP(fun(product_prod(int,int),fun(product_prod(int,int),bool)),fun(product_prod(int,int),bool),accp(product_prod(int,int)),lazy_small_lazy_rel),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),D_3),I_2))) -> ((-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),D_3),I_2)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),P_1,D_3),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),I_2),one_one(int))))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),P_1,D_3),I_2))))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),P_1,A0),A1))))) # label(fact_3562_small__lazy_H_Opinduct) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.79 3518 (all X_a all Xs all Ys (hAPP(list(X_a),nat,size_size(list(X_a)),Xs) != hAPP(list(X_a),nat,size_size(list(X_a)),Ys) -> Xs != Ys)) # label(fact_3563_neq__if__length__neq) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.79 3519 (all X_a all M_2 (hBOOL(hAPP(fun(list(X_a),bool),bool,finite_finite_1(list(X_a)),M_2)) -> (exists N_2 all X_2 (hBOOL(hAPP(fun(list(X_a),bool),bool,hAPP(list(X_a),fun(fun(list(X_a),bool),bool),member(list(X_a)),X_2),M_2)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(list(X_a),nat,size_size(list(X_a)),X_2)),N_2)))))) # label(fact_3564_finite__maxlen) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.79 3520 (all X_a (ring_1(X_a) -> (all K_4 ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K_4),zero_zero(int))) -> hAPP(int,X_a,ring_1_of_int(X_a),K_4) = hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),hAPP(int,nat,nat_1,hAPP(int,int,uminus_uminus(int),K_4))))) & (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K_4),zero_zero(int))) -> hAPP(int,X_a,ring_1_of_int(X_a),K_4) = hAPP(nat,X_a,semiring_1_of_nat(X_a),hAPP(int,nat,nat_1,K_4))))))) # label(fact_3565_of__int__of__nat) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.79 3521 (all M hAPP(int,fun(int,bool),norRRset,M) = hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),bnorRset,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),M),one_one(int))),M)) # label(fact_3566_norRRset__def) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.79 3522 (all X_a (archim1727834104eiling(X_a) -> (all X hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),hAPP(int,X_a,ring_1_of_int(X_a),hAPP(X_a,int,archimedean_ceiling(X_a),X))))))) # label(fact_3567_le__of__int__ceiling) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.79 3523 (all X_a (archim1727834104eiling(X_a) -> (all X hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(int,X_a,ring_1_of_int(X_a),hAPP(X_a,int,archim2085082626_floor(X_a),X))),X))))) # label(fact_3568_of__int__floor__le) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.79 3524 (all X_a (ring_1(X_a) -> (all Z hAPP(int,X_a,ring_1_of_int(X_a),hAPP(int,int,uminus_uminus(int),Z)) = hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(int,X_a,ring_1_of_int(X_a),Z))))) # label(fact_3569_of__int__minus) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.79 3525 (all X_a (ring_1(X_a) -> (all Z all N_1 hAPP(int,X_a,ring_1_of_int(X_a),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),Z),N_1)) = hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(int,X_a,ring_1_of_int(X_a),Z)),N_1)))) # label(fact_3570_of__int__power) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.79 3526 (all X_a (linordered_idom(X_a) -> (all W_1 all Z_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(int,X_a,ring_1_of_int(X_a),W_1)),hAPP(int,X_a,ring_1_of_int(X_a),Z_1))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_1),Z_1)))))) # label(fact_3571_of__int__less__iff) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.79 3527 (all X_a (linordered_idom(X_a) -> (all W_1 all Z_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(int,X_a,ring_1_of_int(X_a),W_1)),hAPP(int,X_a,ring_1_of_int(X_a),Z_1))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),W_1),Z_1)))))) # label(fact_3572_of__int__le__iff) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.79 3528 (all N_1 hAPP(int,int,ring_1_of_int(int),hAPP(nat,int,semiring_1_of_nat(int),N_1)) = hAPP(nat,int,semiring_1_of_nat(int),N_1)) # label(fact_3573_of__int__int__eq) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.79 3529 (all X_a (real_algebra_1(X_a) -> (all Z hAPP(real,X_a,of_real(X_a),hAPP(int,real,ring_1_of_int(real),Z)) = hAPP(int,X_a,ring_1_of_int(X_a),Z)))) # label(fact_3574_of__real__of__int__eq) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.79 3530 (all X_a (archim1727834104eiling(X_a) -> (all Z hAPP(X_a,int,archim2085082626_floor(X_a),hAPP(int,X_a,ring_1_of_int(X_a),Z)) = Z))) # label(fact_3577_floor__of__int) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.79 3531 (all X_a (ring_char_0(X_a) -> (all W_1 all Z_1 (hAPP(int,X_a,ring_1_of_int(X_a),W_1) = hAPP(int,X_a,ring_1_of_int(X_a),Z_1) <-> W_1 = Z_1)))) # label(fact_3578_of__int__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.79 3532 (all X_a (archim1727834104eiling(X_a) -> (all Z hAPP(X_a,int,archimedean_ceiling(X_a),hAPP(int,X_a,ring_1_of_int(X_a),Z)) = Z))) # label(fact_3579_ceiling__of__int) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.79 3533 (all X_a (ring_1(X_a) -> (all Z_1 hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),hAPP(int,X_a,ring_1_of_int(X_a),Z_1)),ring_1_Ints(X_a)))))) # label(fact_3580_Ints__of__int) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.79 3534 (all X_a (real_n2089651433ebra_1(X_a) -> (all Z hAPP(X_a,real,norm_norm(X_a),hAPP(int,X_a,ring_1_of_int(X_a),Z)) = hAPP(real,real,abs_abs(real),hAPP(int,real,ring_1_of_int(real),Z))))) # label(fact_3581_norm__of__int) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.79 3535 (all Z hAPP(complex,complex,cnj,hAPP(int,complex,ring_1_of_int(complex),Z)) = hAPP(int,complex,ring_1_of_int(complex),Z)) # label(fact_3582_complex__cnj__of__int) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.79 3536 (all Z hAPP(complex,real,re,hAPP(int,complex,ring_1_of_int(complex),Z)) = hAPP(int,real,ring_1_of_int(real),Z)) # label(fact_3583_complex__Re__of__int) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.79 3537 (all X_a (ring_1(X_a) -> hAPP(int,X_a,ring_1_of_int(X_a),one_one(int)) = one_one(X_a))) # label(fact_3584_of__int__1) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.79 3538 (all X_a (number_ring(X_a) -> (all V hAPP(int,X_a,ring_1_of_int(X_a),hAPP(int,int,number_number_of(int),V)) = hAPP(int,X_a,number_number_of(X_a),V)))) # label(fact_3585_of__int__number__of__eq) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.79 3539 (all W hAPP(int,complex,number_number_of(complex),W) = hAPP(int,complex,ring_1_of_int(complex),W)) # label(fact_3586_complex__number__of__def) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.79 3540 (all X_a (number_ring(X_a) -> (all K_4 hAPP(int,X_a,number_number_of(X_a),K_4) = hAPP(int,X_a,ring_1_of_int(X_a),K_4)))) # label(fact_3587_number__of__eq) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.79 3541 (all W hAPP(int,int,number_number_of(int),W) = hAPP(int,int,ring_1_of_int(int),W)) # label(fact_3588_int__number__of__def) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.79 3542 (all X hAPP(int,real,number_number_of(real),X) = hAPP(int,real,ring_1_of_int(real),X)) # label(fact_3589_number__of__real__def) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.79 3543 (all X_a (ring_1(X_a) -> hAPP(int,X_a,ring_1_of_int(X_a),zero_zero(int)) = zero_zero(X_a))) # label(fact_3590_of__int__0) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.79 3544 (all X_a (ring_char_0(X_a) -> (all Z_1 (zero_zero(X_a) = hAPP(int,X_a,ring_1_of_int(X_a),Z_1) <-> Z_1 = zero_zero(int))))) # label(fact_3591_of__int__0__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.79 3545 (all X_a (ring_char_0(X_a) -> (all Z_1 (hAPP(int,X_a,ring_1_of_int(X_a),Z_1) = zero_zero(X_a) <-> Z_1 = zero_zero(int))))) # label(fact_3592_of__int__eq__0__iff) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.79 3546 (all X_a (ring_1(X_a) -> (all N_1 hAPP(int,X_a,ring_1_of_int(X_a),hAPP(nat,int,semiring_1_of_nat(int),N_1)) = hAPP(nat,X_a,semiring_1_of_nat(X_a),N_1)))) # label(fact_3593_of__int__of__nat__eq) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.79 3547 (all Z hAPP(complex,real,im,hAPP(int,complex,ring_1_of_int(complex),Z)) = zero_zero(real)) # label(fact_3594_complex__Im__of__int) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.79 3548 (all X_a (ring_1(X_a) -> (all W all Z hAPP(int,X_a,ring_1_of_int(X_a),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),W),Z)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(int,X_a,ring_1_of_int(X_a),W)),hAPP(int,X_a,ring_1_of_int(X_a),Z))))) # label(fact_3595_of__int__mult) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.79 3549 (all X_a (ring_1(X_a) -> (all W all Z hAPP(int,X_a,ring_1_of_int(X_a),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),W),Z)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(int,X_a,ring_1_of_int(X_a),W)),hAPP(int,X_a,ring_1_of_int(X_a),Z))))) # label(fact_3596_of__int__add) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.79 3550 (all X_a (ring_1(X_a) -> (all W all Z hAPP(int,X_a,ring_1_of_int(X_a),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),W),Z)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(int,X_a,ring_1_of_int(X_a),W)),hAPP(int,X_a,ring_1_of_int(X_a),Z))))) # label(fact_3597_of__int__diff) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.79 3551 (all X_a (number_ring(X_a) -> hAPP(int,X_a,ring_1_of_int(X_a),hAPP(int,int,number_number_of(int),min)) = hAPP(int,X_a,number_number_of(X_a),min))) # label(fact_3598_of__int__m1) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.79 3552 (all X_a (archim1727834104eiling(X_a) -> (all X_1 all Z_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(X_a,int,archim2085082626_floor(X_a),X_1)),Z_1)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),hAPP(int,X_a,ring_1_of_int(X_a),Z_1))))))) # label(fact_3599_floor__less__iff) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.79 3553 (all X_a (archim1727834104eiling(X_a) -> (all Z_1 all X_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Z_1),hAPP(X_a,int,archim2085082626_floor(X_a),X_1))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(int,X_a,ring_1_of_int(X_a),Z_1)),X_1)))))) # label(fact_3600_le__floor__iff) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.79 3554 (all X_a (archim1727834104eiling(X_a) -> (all Z_1 all X_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Z_1),hAPP(X_a,int,archimedean_ceiling(X_a),X_1))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(int,X_a,ring_1_of_int(X_a),Z_1)),X_1)))))) # label(fact_3601_less__ceiling__iff) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.79 3555 (all X_a (archim1727834104eiling(X_a) -> (all X_1 all Z_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(X_a,int,archimedean_ceiling(X_a),X_1)),Z_1)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),hAPP(int,X_a,ring_1_of_int(X_a),Z_1))))))) # label(fact_3602_ceiling__le__iff) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.79 3556 (all X_a (archim1727834104eiling(X_a) -> (all X all Z hAPP(X_a,int,archim2085082626_floor(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X),hAPP(int,X_a,ring_1_of_int(X_a),Z))) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(X_a,int,archim2085082626_floor(X_a),X)),Z)))) # label(fact_3603_floor__add__of__int) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.79 3557 (all X_a (archim1727834104eiling(X_a) -> (all X all Z hAPP(X_a,int,archimedean_ceiling(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X),hAPP(int,X_a,ring_1_of_int(X_a),Z))) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(X_a,int,archimedean_ceiling(X_a),X)),Z)))) # label(fact_3604_ceiling__add__of__int) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.79 3558 (all X_a (archim1727834104eiling(X_a) -> (all X all Z hAPP(X_a,int,archim2085082626_floor(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),X),hAPP(int,X_a,ring_1_of_int(X_a),Z))) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(X_a,int,archim2085082626_floor(X_a),X)),Z)))) # label(fact_3605_floor__diff__of__int) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.79 3559 (all X_a (archim1727834104eiling(X_a) -> (all X all Z hAPP(X_a,int,archimedean_ceiling(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),X),hAPP(int,X_a,ring_1_of_int(X_a),Z))) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(X_a,int,archimedean_ceiling(X_a),X)),Z)))) # label(fact_3606_ceiling__diff__of__int) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.79 3560 (all X_a (linordered_idom(X_a) -> (all Z_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(int,X_a,ring_1_of_int(X_a),Z_1)),zero_zero(X_a))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Z_1),zero_zero(int))))))) # label(fact_3607_of__int__less__0__iff) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.79 3561 (all X_a (linordered_idom(X_a) -> (all Z_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(int,X_a,ring_1_of_int(X_a),Z_1))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),Z_1)))))) # label(fact_3608_of__int__0__less__iff) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.79 3562 (all X_a (linordered_idom(X_a) -> (all Z_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(int,X_a,ring_1_of_int(X_a),Z_1)),zero_zero(X_a))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Z_1),zero_zero(int))))))) # label(fact_3609_of__int__le__0__iff) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.79 3563 (all X_a (linordered_idom(X_a) -> (all Z_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),hAPP(int,X_a,ring_1_of_int(X_a),Z_1))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Z_1)))))) # label(fact_3610_of__int__0__le__iff) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.79 3564 (all X_a (ring_1(X_a) -> (all Z (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Z)) -> hAPP(nat,X_a,semiring_1_of_nat(X_a),hAPP(int,nat,nat_1,Z)) = hAPP(int,X_a,ring_1_of_int(X_a),Z))))) # label(fact_3611_of__nat__nat) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.79 3565 (all X_a (archim1727834104eiling(X_a) -> (all Z all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(int,X_a,ring_1_of_int(X_a),Z)),X)) -> (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),plus_plus(X_a),hAPP(int,X_a,ring_1_of_int(X_a),Z)),one_one(X_a)))) -> hAPP(X_a,int,archim2085082626_floor(X_a),X) = Z))))) # label(fact_3612_floor__unique) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.79 3566 (all X_a (archim1727834104eiling(X_a) -> (all Z all 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),minus_minus(X_a),hAPP(int,X_a,ring_1_of_int(X_a),Z)),one_one(X_a))),X)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),hAPP(int,X_a,ring_1_of_int(X_a),Z))) -> hAPP(X_a,int,archimedean_ceiling(X_a),X) = Z))))) # label(fact_3613_ceiling__unique) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.79 3567 (all X_a (archim1727834104eiling(X_a) -> (all 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),minus_minus(X_a),hAPP(int,X_a,ring_1_of_int(X_a),hAPP(X_a,int,archimedean_ceiling(X_a),X))),one_one(X_a))),X)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),hAPP(int,X_a,ring_1_of_int(X_a),hAPP(X_a,int,archimedean_ceiling(X_a),X)))))))) # label(fact_3614_ceiling__correct) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.79 3568 (all X_a (archim1727834104eiling(X_a) -> (all Z_1 all X_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Z_1),hAPP(X_a,int,archim2085082626_floor(X_a),X_1))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(int,X_a,ring_1_of_int(X_a),Z_1)),one_one(X_a))),X_1)))))) # label(fact_3615_less__floor__iff) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.79 3569 (all X_a (archim1727834104eiling(X_a) -> (all X_1 all Z_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(X_a,int,archim2085082626_floor(X_a),X_1)),Z_1)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(int,X_a,ring_1_of_int(X_a),Z_1)),one_one(X_a)))))))) # label(fact_3616_floor__le__iff) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.79 3570 (all X_a (archim1727834104eiling(X_a) -> (all X_1 all Z_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(X_a,int,archimedean_ceiling(X_a),X_1)),Z_1)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(int,X_a,ring_1_of_int(X_a),Z_1)),one_one(X_a)))))))) # label(fact_3617_ceiling__less__iff) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.79 3571 (all X_a (archim1727834104eiling(X_a) -> (all Z_1 all X_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Z_1),hAPP(X_a,int,archimedean_ceiling(X_a),X_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),minus_minus(X_a),hAPP(int,X_a,ring_1_of_int(X_a),Z_1)),one_one(X_a))),X_1)))))) # label(fact_3618_le__ceiling__iff) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.79 3572 (all X_a (archim1727834104eiling(X_a) -> (all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(int,X_a,ring_1_of_int(X_a),hAPP(X_a,int,archim2085082626_floor(X_a),X))),X)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),hAPP(int,X_a,ring_1_of_int(X_a),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(X_a,int,archim2085082626_floor(X_a),X)),one_one(int))))))))) # label(fact_3619_floor__correct) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.79 3573 (all M hAPP(int,nat,phi,M) = hAPP(fun(int,bool),nat,finite_card(int),hAPP(int,fun(int,bool),norRRset,M))) # label(fact_3620_phi__def) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.79 3574 (all Aa all M (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),M)) -> (hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,Aa),M) = one_one(int) -> (exists X_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,Aa),X_2),M)) & hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_2),hAPP(int,fun(int,bool),norRRset,M))) & (all Y_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,Aa),Y_2),M)) & hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Y_2),hAPP(int,fun(int,bool),norRRset,M))) -> Y_2 = X_2))))))) # label(fact_3621_norR__mem__unique) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.79 3575 (all X_1 all M (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),M)) -> (hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,X_1),M) = one_one(int) -> hAPP(fun(int,bool),nat,finite_card(int),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),noXRRset,M),X_1)) = hAPP(fun(int,bool),nat,finite_card(int),hAPP(int,fun(int,bool),norRRset,M))))) # label(fact_3622_card__nor__eq__noX) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.79 3576 (all X_a (archim1804426504_field(X_a) -> (all X exists Z_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(int,X_a,ring_1_of_int(X_a),Z_2)),X)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),hAPP(int,X_a,ring_1_of_int(X_a),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Z_2),one_one(int))))))))) # label(fact_3623_floor__exists) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.79 3577 (all X_a (archim1804426504_field(X_a) -> (all X exists X_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(int,X_a,ring_1_of_int(X_a),X_2)),X)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),hAPP(int,X_a,ring_1_of_int(X_a),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X_2),one_one(int))))) & (all Y_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(int,X_a,ring_1_of_int(X_a),Y_2)),X)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),hAPP(int,X_a,ring_1_of_int(X_a),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Y_2),one_one(int))))) -> Y_2 = X_2)))))) # label(fact_3624_floor__exists1) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.79 3578 (all X_1 all M (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),M)) -> (hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,X_1),M) = one_one(int) -> hBOOL(hAPP(int,bool,hAPP(fun(int,bool),fun(int,bool),is_RRset,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),noXRRset,M),X_1)),M))))) # label(fact_3625_noX__is__RRset) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.79 3579 (all Aa all A_2 all M (hBOOL(hAPP(int,bool,hAPP(fun(int,bool),fun(int,bool),is_RRset,A_2),M)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Aa),A_2)) -> hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,Aa),M) = one_one(int)))) # label(fact_3626_RRset__gcd) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.79 3580 (all Aa all Ba all A_2 all M (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),M)) -> (hBOOL(hAPP(int,bool,hAPP(fun(int,bool),fun(int,bool),is_RRset,A_2),M)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,Aa),Ba),M)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Aa),A_2)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Ba),A_2)) -> Aa = Ba)))))) # label(fact_3627_RRset__zcong__eq) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.79 3581 (all Aa all A_2 all M (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),M)) -> (hBOOL(hAPP(int,bool,hAPP(fun(int,bool),fun(int,bool),is_RRset,A_2),M)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Aa),A_2)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,Aa),hAPP(int,int,hAPP(int,fun(int,int),hAPP(fun(int,bool),fun(int,fun(int,int)),rRset2norRR,A_2),M),Aa)),M)) & hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),hAPP(int,int,hAPP(int,fun(int,int),hAPP(fun(int,bool),fun(int,fun(int,int)),rRset2norRR,A_2),M),Aa)),hAPP(int,fun(int,bool),norRRset,M))))))) # label(fact_3628_RRset2norRR__correct) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.79 3582 (all Aa all A_2 all M (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),M)) -> (hBOOL(hAPP(int,bool,hAPP(fun(int,bool),fun(int,bool),is_RRset,A_2),M)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Aa),A_2)) -> hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),hAPP(int,int,hAPP(int,fun(int,int),hAPP(fun(int,bool),fun(int,fun(int,int)),rRset2norRR,A_2),M),Aa)),hAPP(int,fun(int,bool),norRRset,M))))))) # label(fact_3629_RRset2norRR__correct2) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.79 3583 (all Aa all A_2 all M (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),M)) -> (hBOOL(hAPP(int,bool,hAPP(fun(int,bool),fun(int,bool),is_RRset,A_2),M)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Aa),A_2)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,Aa),hAPP(int,int,hAPP(int,fun(int,int),hAPP(fun(int,bool),fun(int,fun(int,int)),rRset2norRR,A_2),M),Aa)),M)))))) # label(fact_3630_RRset2norRR__correct1) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.79 3584 (all X_a (ring_1(X_a) -> (all P_1 all Qa (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Qa),ring_1_Ints(X_a))) -> ((all Z_2 hBOOL(hAPP(X_a,bool,P_1,hAPP(int,X_a,ring_1_of_int(X_a),Z_2)))) -> hBOOL(hAPP(X_a,bool,P_1,Qa))))))) # label(fact_3631_Ints__induct) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.79 3585 (all X_a (ring_1(X_a) -> (all Qa (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Qa),ring_1_Ints(X_a))) -> -(all Z_2 ti(X_a,Qa) != hAPP(int,X_a,ring_1_of_int(X_a),Z_2)))))) # label(fact_3632_Ints__cases) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.79 3586 (all X_a (archim1804426504_field(X_a) -> (all X exists Z_2 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),hAPP(int,X_a,ring_1_of_int(X_a),Z_2)))))) # label(fact_3633_ex__less__of__int) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.79 3587 (all X_a (archim1804426504_field(X_a) -> (all X exists Z_2 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(int,X_a,ring_1_of_int(X_a),Z_2)),X))))) # label(fact_3634_ex__of__int__less) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.79 3588 (all X_a (archim1804426504_field(X_a) -> (all X exists Z_2 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),hAPP(int,X_a,ring_1_of_int(X_a),Z_2)))))) # label(fact_3635_ex__le__of__int) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.79 3589 (all A_2 all M (hBOOL(hAPP(int,bool,hAPP(fun(int,bool),fun(int,bool),is_RRset,A_2),M)) <-> hBOOL(hAPP(fun(fun(int,bool),bool),bool,hAPP(fun(int,bool),fun(fun(fun(int,bool),bool),bool),member(fun(int,bool)),A_2),hAPP(int,fun(fun(int,bool),bool),rsetR,M))) & hAPP(fun(int,bool),nat,finite_card(int),A_2) = hAPP(int,nat,phi,M))) # label(fact_3636_is__RRset__def) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.79 3590 (all A_2 all M (hBOOL(hAPP(fun(fun(int,bool),bool),bool,hAPP(fun(int,bool),fun(fun(fun(int,bool),bool),bool),member(fun(int,bool)),A_2),hAPP(int,fun(fun(int,bool),bool),rsetR,M))) -> hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A_2)))) # label(fact_3637_RsetR__fin) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.79 3591 (all Aa all M (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Aa),M)) -> hBOOL(hAPP(fun(fun(int,bool),bool),bool,hAPP(fun(int,bool),fun(fun(fun(int,bool),bool),bool),member(fun(int,bool)),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),bnorRset,Aa),M)),hAPP(int,fun(fun(int,bool),bool),rsetR,M))))) # label(fact_3638_Bnor__in__RsetR) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.79 3592 (all A_2 all M (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),M)) -> (hBOOL(hAPP(int,bool,hAPP(fun(int,bool),fun(int,bool),is_RRset,A_2),M)) -> hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,int),fun(fun(int,bool),fun(int,bool)),image(int,int),hAPP(int,fun(int,int),hAPP(fun(int,bool),fun(int,fun(int,int)),rRset2norRR,A_2),M)),A_2) = hAPP(int,fun(int,bool),norRRset,M)))) # label(fact_3639_RRset2norRR__eq__norR) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.79 3593 (all X all Y hAPP(int,int,hAPP(int,fun(int,int),int_lcm,X),Y) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),nat_lcm,hAPP(int,nat,nat_1,hAPP(int,int,abs_abs(int),X))),hAPP(int,nat,nat_1,hAPP(int,int,abs_abs(int),Y))))) # label(fact_3640_Nitpick_Oint__lcm__def) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.80 3594 (all X_a all X_b all A_2 all Ba all F all X_1 (ti(X_a,Ba) = hAPP(X_b,X_a,F,X_1) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_2)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Ba),hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),A_2)))))) # label(fact_3641_image__eqI) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.80 3595 (all X_b all X_a all H all F_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),F_1)) -> hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),H),F_1))))) # label(fact_3642_finite__imageI) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.80 3596 (all X_b all X_a all B_1 all F all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),B_1),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),A_2))) -> hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),B_1))))) # label(fact_3643_finite__surj) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.80 3597 (all X_a all X_b all F all A_2 all B_1 hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),A_2)),hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),B_1))),hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),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_2),B_1))))) # label(fact_3644_image__diff__subset) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.80 3598 (all X_b all X_a all F all A_2 all B_1 (hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),A_2) = ti(fun(X_a,bool),B_1) -> hAPP(fun(fun(X_b,bool),bool),fun(fun(X_a,bool),bool),hAPP(fun(fun(X_b,bool),fun(X_a,bool)),fun(fun(fun(X_b,bool),bool),fun(fun(X_a,bool),bool)),image(fun(X_b,bool),fun(X_a,bool)),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F)),hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),pow(X_b),A_2)) = hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),pow(X_a),B_1))) # label(fact_3645_image__Pow__surj) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.80 3599 (all X_b all X_a all Ba all F all X_1 all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_2)) -> (ti(X_b,Ba) = hAPP(X_a,X_b,F,X_1) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Ba),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),A_2)))))) # label(fact_3646_rev__image__eqI) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.80 3600 (all X_b all X_a all F all X_1 all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_2)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),hAPP(X_a,X_b,F,X_1)),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),A_2))))) # label(fact_3647_imageI) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.80 3601 (all X_a all X_b all Z_1 all F all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Z_1),hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),A_2))) <-> (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_2)) & ti(X_a,Z_1) = hAPP(X_b,X_a,F,X_2))))) # label(fact_3648_image__iff) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.80 3602 (all X_a all X_b all F all A_2 all B_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),A_2)),B_1)) -> hBOOL(hAPP(fun(fun(X_a,bool),bool),bool,hAPP(fun(fun(X_a,bool),bool),fun(fun(fun(X_a,bool),bool),bool),ord_less_eq(fun(fun(X_a,bool),bool)),hAPP(fun(fun(X_b,bool),bool),fun(fun(X_a,bool),bool),hAPP(fun(fun(X_b,bool),fun(X_a,bool)),fun(fun(fun(X_b,bool),bool),fun(fun(X_a,bool),bool)),image(fun(X_b,bool),fun(X_a,bool)),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F)),hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),pow(X_b),A_2))),hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),pow(X_a),B_1))))) # label(fact_3649_image__Pow__mono) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.80 3603 (all X_b all X_a all F all A_2 all B_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_2),B_1)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),A_2)),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),B_1))))) # label(fact_3650_image__mono) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.80 3604 (all X_a all X_b all B_1 all F all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),B_1),hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),A_2))) <-> (exists AA (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)),AA),A_2)) & ti(fun(X_a,bool),B_1) = hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),AA))))) # label(fact_3651_subset__image__iff) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.80 3605 (all X_b all X_a all F all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2)) -> 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_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),A_2))),hAPP(fun(X_a,bool),nat,finite_card(X_a),A_2))))) # label(fact_3652_card__image__le) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.80 3606 (all F all A_2 all M (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),M)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),resSet,M),A_2)) -> ((all X_2 (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_2),A_2)) -> (all Xa (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xa),A_2)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(int,int,F,X_2)),hAPP(int,int,F,Xa)),M)) -> X_2 = Xa))))) -> hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),resSet,M),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,int),fun(fun(int,bool),fun(int,bool)),image(int,int),F),A_2))))))) # label(fact_3653_ResSet__image) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.80 3607 (all X_b all X_a all F all A_2 all B_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),B_1)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),B_1),hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),A_2))) -> (exists C_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)),C_3),A_2)) & hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),C_3)) & ti(fun(X_a,bool),B_1) = hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),C_3)))))) # label(fact_3654_finite__subset__image) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.80 3608 (all A_2 (hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A_2)) <-> 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_2))))) # label(fact_3655_transfer__nat__int__set__relations_I1_J) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.80 3609 (all A_2 hAPP(fun(nat,bool),nat,finite_card(nat),A_2) = 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_2))) # label(fact_3656_Nat__Transfer_Otransfer__nat__int__set__functions_I1_J) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.80 3610 (all X_1 all A_2 (hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X_1),A_2)) <-> 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_2))))) # label(fact_3657_transfer__nat__int__set__relations_I2_J) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.80 3611 (all A_2 all B_1 (A_2 = B_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_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)),B_1))) # label(fact_3658_transfer__nat__int__set__relations_I3_J) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.80 3612 (all A_2 hAPP(fun(int,bool),fun(nat,bool),hAPP(fun(int,nat),fun(fun(int,bool),fun(nat,bool)),image(int,nat),nat_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_2)) = A_2) # label(fact_3659_transfer__int__nat__set__return__embed) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.80 3613 (all A_2 all B_1 (hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,bool),fun(fun(nat,bool),bool),ord_less(fun(nat,bool)),A_2),B_1)) <-> 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_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)),B_1))))) # label(fact_3660_transfer__nat__int__set__relations_I4_J) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.80 3614 (all A_2 all B_1 (hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,bool),fun(fun(nat,bool),bool),ord_less_eq(fun(nat,bool)),A_2),B_1)) <-> 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_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)),B_1))))) # label(fact_3661_transfer__nat__int__set__relations_I5_J) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.80 3615 (all Aa all Pa hAPP(int,fun(fun(int,bool),bool),hAPP(int,fun(int,fun(fun(int,bool),bool)),setS,Aa),Pa) = hAPP(fun(int,bool),fun(fun(int,bool),bool),hAPP(fun(int,fun(int,bool)),fun(fun(int,bool),fun(fun(int,bool),bool)),image(int,fun(int,bool)),hAPP(int,fun(int,fun(int,bool)),hAPP(int,fun(int,fun(int,fun(int,bool))),multInvPair,Aa),Pa)),hAPP(int,fun(int,bool),sRStar,Pa))) # label(fact_3662_SetS__def) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.80 3616 (all X_a all X_b all B_1 all F all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),B_1),hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),A_2))) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_2)) -> hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),B_1))))) # label(fact_3663_finite__surjI) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.80 3617 (all X_b all X_a all F all B_1 all A_2 ((all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_2)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),hAPP(X_a,X_b,F,X_2)),B_1)))) -> hBOOL(hAPP(fun(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_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),A_2)),B_1)))) # label(fact_3664_image__subsetI) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.80 3618 (all S (-hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),S)) <-> (all M_3 exists N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_3),N_2)) & hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),N_2),S)))))) # label(fact_3665_infinite__nat__iff__unbounded__le) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.80 3619 (all S (-hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),S)) <-> (all M_3 exists N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_3),N_2)) & hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),N_2),S)))))) # label(fact_3666_infinite__nat__iff__unbounded) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.80 3620 (all X all Y hAPP(nat,nat,hAPP(nat,fun(nat,nat),nat_lcm,X),Y) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X),Y)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),nat_gcd,X),Y))) # label(fact_3667_Nitpick_Onat__lcm__def) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.80 3621 (all B_1 all A_2 (hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A_2)) -> (hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,B_1)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(fun(int,bool),fun(fun(int,bool),bool),ord_less(fun(int,bool)),A_2),B_1)) <-> hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,bool),fun(fun(nat,bool),bool),ord_less(fun(nat,bool)),hAPP(fun(int,bool),fun(nat,bool),hAPP(fun(int,nat),fun(fun(int,bool),fun(nat,bool)),image(int,nat),nat_1),A_2)),hAPP(fun(int,bool),fun(nat,bool),hAPP(fun(int,nat),fun(fun(int,bool),fun(nat,bool)),image(int,nat),nat_1),B_1))))))) # label(fact_3668_transfer__int__nat__set__relations_I4_J) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.80 3622 (all X all Y hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),X),Y) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),nat_gcd,X),Y)) # label(fact_3669_gcd__eq__nitpick__gcd) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.80 3623 (all X_1 all A_2 (hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A_2)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),A_2)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X_1))))) # label(fact_3670_Nat__Transfer_Otransfer__nat__int__set__function__closures_I6_J) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.80 3624 (all S (hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,S)) <-> (all X_2 (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_2),S)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X_2)))))) # label(fact_3671_nat__set__def) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.80 3625 (all C_2 hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,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)),C_2)))) # label(fact_3672_Nat__Transfer_Otransfer__int__nat__set__function__closures_I5_J) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.80 3626 (all B_1 all A_2 (hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A_2)) -> (hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,B_1)) -> (A_2 = B_1 <-> hAPP(fun(int,bool),fun(nat,bool),hAPP(fun(int,nat),fun(fun(int,bool),fun(nat,bool)),image(int,nat),nat_1),A_2) = hAPP(fun(int,bool),fun(nat,bool),hAPP(fun(int,nat),fun(fun(int,bool),fun(nat,bool)),image(int,nat),nat_1),B_1))))) # label(fact_3673_transfer__int__nat__set__relations_I3_J) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.80 3627 (all X all Y ((Y = zero_zero(nat) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),nat_gcd,X),Y) = X) & (Y != zero_zero(nat) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),nat_gcd,X),Y) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),nat_gcd,Y),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),X),Y))))) # label(fact_3674_nat__gcd_Osimps) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.80 3628 (all A_2 (hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A_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)),hAPP(fun(int,bool),fun(nat,bool),hAPP(fun(int,nat),fun(fun(int,bool),fun(nat,bool)),image(int,nat),nat_1),A_2)) = A_2)) # label(fact_3675_transfer__nat__int__set__return__embed) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.80 3629 (all A_2 (hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A_2)) -> (hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A_2)) <-> hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),hAPP(fun(int,bool),fun(nat,bool),hAPP(fun(int,nat),fun(fun(int,bool),fun(nat,bool)),image(int,nat),nat_1),A_2)))))) # label(fact_3676_transfer__int__nat__set__relations_I1_J) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.80 3630 (all A_2 (hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A_2)) -> hAPP(fun(int,bool),nat,finite_card(int),A_2) = hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(fun(int,bool),fun(nat,bool),hAPP(fun(int,nat),fun(fun(int,bool),fun(nat,bool)),image(int,nat),nat_1),A_2)))) # label(fact_3677_Nat__Transfer_Otransfer__int__nat__set__functions_I1_J) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.80 3631 (all B_1 all A_2 (hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A_2)) -> (hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,B_1)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(fun(int,bool),fun(fun(int,bool),bool),ord_less_eq(fun(int,bool)),A_2),B_1)) <-> hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,bool),fun(fun(nat,bool),bool),ord_less_eq(fun(nat,bool)),hAPP(fun(int,bool),fun(nat,bool),hAPP(fun(int,nat),fun(fun(int,bool),fun(nat,bool)),image(int,nat),nat_1),A_2)),hAPP(fun(int,bool),fun(nat,bool),hAPP(fun(int,nat),fun(fun(int,bool),fun(nat,bool)),image(int,nat),nat_1),B_1))))))) # label(fact_3678_transfer__int__nat__set__relations_I5_J) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.80 3632 (all X_1 all Y_1 (hBOOL(hAPP(product_prod(nat,nat),bool,hAPP(fun(product_prod(nat,nat),fun(product_prod(nat,nat),bool)),fun(product_prod(nat,nat),bool),accp(product_prod(nat,nat)),nat_gcd_rel),hAPP(nat,product_prod(nat,nat),hAPP(nat,fun(nat,product_prod(nat,nat)),product_Pair(nat,nat),X_1),Y_1))) -> (Y_1 = zero_zero(nat) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),nat_gcd,X_1),Y_1) = X_1) & (Y_1 != zero_zero(nat) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),nat_gcd,X_1),Y_1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),nat_gcd,Y_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),X_1),Y_1))))) # label(fact_3679_nat__gcd_Opsimps) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.80 3633 (all X all Y hAPP(int,int,hAPP(int,fun(int,int),int_gcd,X),Y) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),nat_gcd,hAPP(int,nat,nat_1,hAPP(int,int,abs_abs(int),X))),hAPP(int,nat,nat_1,hAPP(int,int,abs_abs(int),Y))))) # label(fact_3680_Nitpick_Oint__gcd__def) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.80 3634 (all P_1 all A0 all A1 (hBOOL(hAPP(product_prod(nat,nat),bool,hAPP(fun(product_prod(nat,nat),fun(product_prod(nat,nat),bool)),fun(product_prod(nat,nat),bool),accp(product_prod(nat,nat)),nat_gcd_rel),hAPP(nat,product_prod(nat,nat),hAPP(nat,fun(nat,product_prod(nat,nat)),product_Pair(nat,nat),A0),A1))) -> ((all X_2 all Y_2 (hBOOL(hAPP(product_prod(nat,nat),bool,hAPP(fun(product_prod(nat,nat),fun(product_prod(nat,nat),bool)),fun(product_prod(nat,nat),bool),accp(product_prod(nat,nat)),nat_gcd_rel),hAPP(nat,product_prod(nat,nat),hAPP(nat,fun(nat,product_prod(nat,nat)),product_Pair(nat,nat),X_2),Y_2))) -> ((Y_2 != zero_zero(nat) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),P_1,Y_2),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),X_2),Y_2)))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),P_1,X_2),Y_2))))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),P_1,A0),A1))))) # label(fact_3681_nat__gcd_Opinduct) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.80 3635 (all N_4 (hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),N_4)) <-> (exists M_3 all X_2 (hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X_2),N_4)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X_2),M_3)))))) # label(fact_3682_finite__nat__set__iff__bounded__le) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.80 3636 (all N_4 (hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),N_4)) <-> (exists M_3 all X_2 (hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X_2),N_4)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X_2),M_3)))))) # label(fact_3683_finite__nat__set__iff__bounded) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.80 3637 (all N all N_4 ((all X_2 (hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X_2),N_4)) -> 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_4)))) # label(fact_3684_bounded__nat__set__is__finite) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.80 3638 (all L all U_1 hAPP(fun(int,bool),nat,finite_card(int),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_gr676655987ssThan(int),L),U_1)) = hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),U_1),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),L),one_one(int))))) # label(fact_3685_card__greaterThanLessThan__int) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.80 3639 (all L all U_1 hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_gr676655987ssThan(int),L),U_1)))) # label(fact_3686_finite__greaterThanLessThan__int) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.80 3640 (all X_a (ordered_ab_group_add(X_a) -> (all X_1 all Y_1 hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,X_a),fun(fun(X_a,bool),fun(X_a,bool)),image(X_a,X_a),uminus_uminus(X_a)),hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_gr676655987ssThan(X_a),X_1),Y_1)) = hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_gr676655987ssThan(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),Y_1)),hAPP(X_a,X_a,uminus_uminus(X_a),X_1))))) # label(fact_3687_image__uminus__greaterThanLessThan) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.80 3641 (all X_1 (hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),X_1),field_char_0_Rats(real))) -> -(all M_3 all N_2 (N_2 != zero_zero(nat) -> (hAPP(real,real,abs_abs(real),X_1) = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(nat,real,real_1(nat),M_3)),hAPP(nat,real,real_1(nat),N_2)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),M_3),N_2) != one_one(nat)))))) # label(fact_3688_Rats__abs__nat__div__natE) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.80 3642 (all X_a zero_frac(X_a) = hAPP(product_prod(int,int),X_a,abs_Frac(X_a),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),zero_zero(int)),one_one(int)))) # label(fact_3689_Nitpick_Ozero__frac__def) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.80 3643 (all L all U_1 hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_gr676655987ssThan(nat),L),U_1)))) # label(fact_3690_finite__greaterThanLessThan) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.80 3644 (all N hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),hAPP(nat,real,real_1(nat),N)),field_char_0_Rats(real)))) # label(fact_3691_Rats__real__nat) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.80 3645 (all L all U_1 hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_gr676655987ssThan(nat),L),U_1)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1),hAPP(nat,nat,suc,L))) # label(fact_3692_card__greaterThanLessThan) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.80 3646 (all X_a one_frac(X_a) = hAPP(product_prod(int,int),X_a,abs_Frac(X_a),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),one_one(int)),one_one(int)))) # label(fact_3693_Nitpick_Oone__frac__def) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.80 3647 (all X_a all N_1 hAPP(int,X_a,number_of_frac(X_a),N_1) = hAPP(product_prod(int,int),X_a,abs_Frac(X_a),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),N_1),one_one(int)))) # label(fact_3694_Nitpick_Onumber__of__frac__def) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.80 3648 (all Y_1 all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_1),Y_1)) -> (exists X_2 (hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),X_2),field_char_0_Rats(real))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_1),X_2)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_2),Y_1))))))) # label(fact_3695_Rats__dense__in__nn__real) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.80 3649 (all F all Y_1 all X_1 all Aa all Ba (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),Aa),Ba)) -> (hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),X_1),hAPP(real,fun(real,bool),hAPP(real,fun(real,fun(real,bool)),ord_gr676655987ssThan(real),Aa),Ba))) -> (hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),Y_1),hAPP(real,fun(real,bool),hAPP(real,fun(real,fun(real,bool)),ord_gr676655987ssThan(real),Aa),Ba))) -> ((all X_2 (hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),X_2),hAPP(real,fun(real,bool),hAPP(real,fun(real,fun(real,bool)),ord_gr676655987ssThan(real),Aa),Ba))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),F),X_2),zero_zero(real))))) -> hAPP(real,real,F,X_1) = hAPP(real,real,F,Y_1)))))) # label(fact_3696_DERIV__isconst3) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.80 3650 (all X_a (field_char_0(X_a) -> (all Aa (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Aa),field_char_0_Rats(X_a))) -> (ti(X_a,Aa) != zero_zero(X_a) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),hAPP(X_a,X_a,inverse_inverse(X_a),Aa)),field_char_0_Rats(X_a)))))))) # label(fact_3697_nonzero__Rats__inverse) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.80 3651 (all X_a (field_char_0(X_a) -> (all Ba all Aa (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Aa),field_char_0_Rats(X_a))) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Ba),field_char_0_Rats(X_a))) -> (ti(X_a,Ba) != zero_zero(X_a) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),Aa),Ba)),field_char_0_Rats(X_a))))))))) # label(fact_3698_nonzero__Rats__divide) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.80 3652 (all K (hBOOL(hAPP(rat,bool,iszero(rat),hAPP(int,rat,number_number_of(rat),K))) <-> hBOOL(hAPP(int,bool,iszero(int),hAPP(int,int,number_number_of(int),K))))) # label(fact_3699_iszero__rat) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.80 3653 (all X_a (field_char_0(X_a) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),zero_zero(X_a)),field_char_0_Rats(X_a))))) # label(fact_3700_Rats__0) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.80 3654 (all X_a (field_char_0(X_a) -> (all Ba all Aa (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Aa),field_char_0_Rats(X_a))) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Ba),field_char_0_Rats(X_a))) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Aa),Ba)),field_char_0_Rats(X_a)))))))) # label(fact_3701_Rats__mult) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.80 3655 (all X_a (field_char_0(X_a) -> (all Ba all Aa (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Aa),field_char_0_Rats(X_a))) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Ba),field_char_0_Rats(X_a))) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Aa),Ba)),field_char_0_Rats(X_a)))))))) # label(fact_3702_Rats__add) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.80 3656 (all X_a (number_ring(X_a) & field_char_0(X_a) -> (all W_1 hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),hAPP(int,X_a,number_number_of(X_a),W_1)),field_char_0_Rats(X_a)))))) # label(fact_3703_Rats__number__of) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.80 3657 (all X_a (field_char_0(X_a) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),one_one(X_a)),field_char_0_Rats(X_a))))) # label(fact_3704_Rats__1) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.80 3658 (all X_a (field_char_0(X_a) -> (all Ba all Aa (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Aa),field_char_0_Rats(X_a))) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Ba),field_char_0_Rats(X_a))) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),Aa),Ba)),field_char_0_Rats(X_a)))))))) # label(fact_3705_Rats__diff) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.80 3659 (all X_a (field_char_0(X_a) -> (all N all Aa (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Aa),field_char_0_Rats(X_a))) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),Aa),N)),field_char_0_Rats(X_a))))))) # label(fact_3706_Rats__power) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.80 3660 (all X_a (field_char_0(X_a) -> (all Aa (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Aa),field_char_0_Rats(X_a))) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),Aa)),field_char_0_Rats(X_a))))))) # label(fact_3707_Rats__minus) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.80 3661 (all X_a (field_inverse_zero(X_a) & field_char_0(X_a) -> (all Ba all Aa (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Aa),field_char_0_Rats(X_a))) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Ba),field_char_0_Rats(X_a))) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),Aa),Ba)),field_char_0_Rats(X_a)))))))) # label(fact_3708_Rats__divide) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.80 3662 (all X_a (field_char_0(X_a) -> (all N hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),N)),field_char_0_Rats(X_a)))))) # label(fact_3709_Rats__of__nat) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.80 3663 (all X_a (field_inverse_zero(X_a) & field_char_0(X_a) -> (all Aa (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Aa),field_char_0_Rats(X_a))) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),hAPP(X_a,X_a,inverse_inverse(X_a),Aa)),field_char_0_Rats(X_a))))))) # label(fact_3710_Rats__inverse) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.80 3664 (all X_a (field_char_0(X_a) -> (all Z_1 hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),hAPP(int,X_a,ring_1_of_int(X_a),Z_1)),field_char_0_Rats(X_a)))))) # label(fact_3711_Rats__of__int) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.80 3665 (all X_1 all Y_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_1),Y_1)) -> (exists X_2 (hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),X_2),field_char_0_Rats(real))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_1),X_2)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_2),Y_1)))))) # label(fact_3712_Rats__dense__in__real) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.80 3666 (all Y_1 all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),Y_1),X_1)) -> hAPP(fun(real,bool),real,complete_Sup_Sup(real),hAPP(real,fun(real,bool),hAPP(real,fun(real,fun(real,bool)),ord_gr676655987ssThan(real),Y_1),X_1)) = X_1)) # label(fact_3713_Sup__greaterThanLessThan) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.80 3667 (all X_1 all X_3 (hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),X_1),X_3)) -> ((exists Z_2 all X_2 (hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),X_2),X_3)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_2),Z_2)))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_1),hAPP(fun(real,bool),real,complete_Sup_Sup(real),X_3)))))) # label(fact_3714_Sup__upper__EX) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.80 3668 (all Z_1 all X_1 all X_3 (hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),X_1),X_3)) -> ((all X_2 (hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),X_2),X_3)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_2),Z_1)))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_1),hAPP(fun(real,bool),real,complete_Sup_Sup(real),X_3)))))) # label(fact_3715_SupInf_OSup__upper) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.80 3669 (all K_4 hAPP(product_prod(int,int),rat,frct,hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),hAPP(int,int,number_number_of(int),K_4)),one_one(int))) = hAPP(int,rat,number_number_of(rat),K_4)) # label(fact_3716_Frct__code__post_I4_J) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.80 3670 (all K_4 hAPP(product_prod(int,int),rat,frct,hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),K_4),zero_zero(int))) = zero_zero(rat)) # label(fact_3717_Frct__code__post_I2_J) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.80 3671 (all K_4 hAPP(product_prod(int,int),rat,frct,hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),zero_zero(int)),K_4)) = zero_zero(rat)) # label(fact_3718_Frct__code__post_I1_J) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.80 3672 (all K_4 all L_4 hAPP(product_prod(int,int),rat,frct,hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),hAPP(int,int,number_number_of(int),K_4)),hAPP(int,int,number_number_of(int),L_4))) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),hAPP(int,rat,number_number_of(rat),K_4)),hAPP(int,rat,number_number_of(rat),L_4))) # label(fact_3720_Frct__code__post_I6_J) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.80 3673 (all K_4 hAPP(product_prod(int,int),rat,frct,hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),one_one(int)),hAPP(int,int,number_number_of(int),K_4))) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),one_one(rat)),hAPP(int,rat,number_number_of(rat),K_4))) # label(fact_3721_Frct__code__post_I5_J) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.80 3674 (all Z_1 all X_3 (hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),Z_1),X_3)) -> ((all X_2 (hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),X_2),X_3)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_2),Z_1)))) -> hAPP(fun(real,bool),real,complete_Sup_Sup(real),X_3) = Z_1))) # label(fact_3722_Sup__eq__maximum) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.80 3675 (all Z_1 all Y_1 all X_1 all X_3 (hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),X_1),X_3)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),Y_1),X_1)) -> ((all X_2 (hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),X_2),X_3)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_2),Z_1)))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),Y_1),hAPP(fun(real,bool),real,complete_Sup_Sup(real),X_3))))))) # label(fact_3723_SupInf_OSup__upper2) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.80 3676 (all Q_2 ((hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),Q_2),zero_zero(rat))) -> hAPP(rat,rat,abs_abs(rat),Q_2) = hAPP(rat,rat,uminus_uminus(rat),Q_2)) & (-hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),Q_2),zero_zero(rat))) -> hAPP(rat,rat,abs_abs(rat),Q_2) = Q_2))) # label(fact_3724_abs__rat__def) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.80 3677 (all Q_2 ((Q_2 = zero_zero(rat) -> hAPP(rat,rat,sgn_sgn(rat),Q_2) = zero_zero(rat)) & (Q_2 != zero_zero(rat) -> (hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),Q_2)) -> hAPP(rat,rat,sgn_sgn(rat),Q_2) = one_one(rat)) & (-hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),Q_2)) -> hAPP(rat,rat,sgn_sgn(rat),Q_2) = hAPP(rat,rat,uminus_uminus(rat),one_one(rat)))))) # label(fact_3725_sgn__rat__def) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.80 3678 (all Q_2 all R_4 hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),Q_2),R_4) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),Q_2),hAPP(rat,rat,inverse_inverse(rat),R_4))) # label(fact_3726_divide__rat__def) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.80 3679 (all P_4 all Q_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Q_2),zero_zero(int))) -> hAPP(product_prod(int,int),product_prod(int,int),normalize,hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),P_4),Q_2)) = hAPP(product_prod(int,int),product_prod(int,int),normalize,hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),hAPP(int,int,uminus_uminus(int),P_4)),hAPP(int,int,uminus_uminus(int),Q_2))))) # label(fact_3727_normalize__negative) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.80 3680 (all P_4 hAPP(rat,product_prod(int,int),quotient_of,hAPP(rat,rat,sgn_sgn(rat),P_4)) = hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),hAPP(int,int,sgn_sgn(int),hAPP(product_prod(int,int),int,product_fst(int,int),hAPP(rat,product_prod(int,int),quotient_of,P_4)))),one_one(int))) # label(fact_3728_rat__sgn__code) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.80 3681 (all Q_2 all R_4 hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),Q_2),R_4) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),Q_2),hAPP(rat,rat,uminus_uminus(rat),R_4))) # label(fact_3729_diff__rat__def) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.80 3682 (all Aa all Ba (hAPP(rat,product_prod(int,int),quotient_of,Aa) = hAPP(rat,product_prod(int,int),quotient_of,Ba) <-> Aa = Ba)) # label(fact_3730_quotient__of__inject__eq) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.80 3683 (all A_1 all B (hAPP(rat,product_prod(int,int),quotient_of,A_1) = hAPP(rat,product_prod(int,int),quotient_of,B) -> A_1 = B)) # label(fact_3731_quotient__of__inject) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.80 3684 (all Z_1 all W_1 (hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),Z_1),W_1)) <-> hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),Z_1),W_1)) & Z_1 != W_1)) # label(fact_3732_less__rat__def) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.80 3685 (all R_4 all P_4 all Q_2 (hAPP(rat,product_prod(int,int),quotient_of,R_4) = hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),P_4),Q_2) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),Q_2)))) # label(fact_3733_quotient__of__denom__pos) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.80 3686 (all R_4 all P_4 all Q_2 (hAPP(product_prod(int,int),product_prod(int,int),normalize,R_4) = hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),P_4),Q_2) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),Q_2)))) # label(fact_3735_normalize__denom__pos) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.80 3687 (all P_4 hAPP(product_prod(int,int),product_prod(int,int),normalize,hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),P_4),zero_zero(int))) = hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),zero_zero(int)),one_one(int))) # label(fact_3736_normalize__denom__zero) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.80 3688 (all P_4 all R_4 all S_4 all Q_2 (Q_2 != zero_zero(int) -> (S_4 != zero_zero(int) -> (hAPP(product_prod(int,int),product_prod(int,int),normalize,hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),P_4),Q_2)) = hAPP(product_prod(int,int),product_prod(int,int),normalize,hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),R_4),S_4)) -> hAPP(int,int,hAPP(int,fun(int,int),times_times(int),P_4),S_4) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),R_4),Q_2))))) # label(fact_3737_normalize__crossproduct) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.80 3689 (all K_4 hAPP(rat,product_prod(int,int),quotient_of,hAPP(int,rat,number_number_of(rat),K_4)) = hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),hAPP(int,int,number_number_of(int),K_4)),one_one(int))) # label(fact_3739_quotient__of__number_I3_J) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.80 3690 (all R_4 (hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),R_4)) -> -(all S_1 (hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),S_1)) -> (all T_5 (hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),T_5)) -> R_4 != hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),S_1),T_5))))))) # label(fact_3740_obtain__pos__sum) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.80 3691 (all X_1 all Y_1 (hBOOL(hAPP(fun(product_prod(product_prod(int,int),product_prod(int,int)),bool),bool,hAPP(product_prod(product_prod(int,int),product_prod(int,int)),fun(fun(product_prod(product_prod(int,int),product_prod(int,int)),bool),bool),member(product_prod(product_prod(int,int),product_prod(int,int))),hAPP(product_prod(int,int),product_prod(product_prod(int,int),product_prod(int,int)),hAPP(product_prod(int,int),fun(product_prod(int,int),product_prod(product_prod(int,int),product_prod(int,int))),product_Pair(product_prod(int,int),product_prod(int,int)),X_1),Y_1)),ratrel)) <-> hAPP(product_prod(int,int),int,product_snd(int,int),X_1) != zero_zero(int) & hAPP(product_prod(int,int),int,product_snd(int,int),Y_1) != zero_zero(int) & hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(product_prod(int,int),int,product_fst(int,int),X_1)),hAPP(product_prod(int,int),int,product_snd(int,int),Y_1)) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(product_prod(int,int),int,product_fst(int,int),Y_1)),hAPP(product_prod(int,int),int,product_snd(int,int),X_1)))) # label(fact_3741_ratrel__iff) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.80 3692 (all K_4 hAPP(int,rat,hAPP(int,fun(int,rat),fract,one_one(int)),hAPP(int,int,number_number_of(int),K_4)) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),one_one(rat)),hAPP(int,rat,number_number_of(rat),K_4))) # label(fact_3742_Fract__1__number__of) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.80 3693 (all R_4 all S_4 hAPP(rat,real,ratreal,hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),hAPP(int,rat,number_number_of(rat),R_4)),hAPP(int,rat,number_number_of(rat),S_4))) = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(int,real,number_number_of(real),R_4)),hAPP(int,real,number_number_of(real),S_4))) # label(fact_3743_Ratreal__number__of__quotient2) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.80 3694 (all A_1 all B all P_4 all Q_2 (hAPP(rat,product_prod(int,int),quotient_of,hAPP(int,rat,hAPP(int,fun(int,rat),fract,A_1),B)) = hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),P_4),Q_2) -> hAPP(int,rat,hAPP(int,fun(int,rat),fract,P_4),Q_2) = hAPP(int,rat,hAPP(int,fun(int,rat),fract,A_1),B))) # label(fact_3744_quotient__of__eq) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.80 3695 (all A_1 all B hAPP(rat,rat,uminus_uminus(rat),hAPP(int,rat,hAPP(int,fun(int,rat),fract,A_1),B)) = hAPP(int,rat,hAPP(int,fun(int,rat),fract,hAPP(int,int,uminus_uminus(int),A_1)),B)) # label(fact_3745_minus__rat) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.80 3696 (all A_1 all B all C all D hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),hAPP(int,rat,hAPP(int,fun(int,rat),fract,A_1),B)),hAPP(int,rat,hAPP(int,fun(int,rat),fract,C),D)) = hAPP(int,rat,hAPP(int,fun(int,rat),fract,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),D)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),C))) # label(fact_3746_divide__rat) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.80 3697 (all K_4 all L_4 hAPP(int,rat,hAPP(int,fun(int,rat),fract,K_4),L_4) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),hAPP(int,rat,ring_1_of_int(rat),K_4)),hAPP(int,rat,ring_1_of_int(rat),L_4))) # label(fact_3747_Fract__of__int__quotient) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.80 3698 (all K_4 hAPP(int,rat,hAPP(int,fun(int,rat),fract,K_4),one_one(int)) = hAPP(int,rat,ring_1_of_int(rat),K_4)) # label(fact_3748_Fract__of__int__eq) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.80 3699 (all K_4 hAPP(int,rat,ring_1_of_int(rat),K_4) = hAPP(int,rat,hAPP(int,fun(int,rat),fract,K_4),one_one(int))) # label(fact_3749_of__int__rat) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.80 3700 (all K_4 hAPP(int,rat,hAPP(int,fun(int,rat),fract,zero_zero(int)),K_4) = zero_zero(rat)) # label(fact_3750_rat__number__collapse_I1_J) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.80 3701 (all A_1 all C hAPP(int,rat,hAPP(int,fun(int,rat),fract,zero_zero(int)),A_1) = hAPP(int,rat,hAPP(int,fun(int,rat),fract,zero_zero(int)),C)) # label(fact_3751_eq__rat_I3_J) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.80 3702 (all K_4 hAPP(int,rat,hAPP(int,fun(int,rat),fract,K_4),zero_zero(int)) = zero_zero(rat)) # label(fact_3752_rat__number__collapse_I4_J) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.80 3703 (all A_1 hAPP(int,rat,hAPP(int,fun(int,rat),fract,A_1),zero_zero(int)) = hAPP(int,rat,hAPP(int,fun(int,rat),fract,zero_zero(int)),one_one(int))) # label(fact_3755_eq__rat_I2_J) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.80 3704 (all K_4 hAPP(int,rat,hAPP(int,fun(int,rat),fract,hAPP(nat,int,semiring_1_of_nat(int),K_4)),one_one(int)) = hAPP(nat,rat,semiring_1_of_nat(rat),K_4)) # label(fact_3756_Fract__of__nat__eq) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.80 3705 (all K_4 hAPP(nat,rat,semiring_1_of_nat(rat),K_4) = hAPP(int,rat,hAPP(int,fun(int,rat),fract,hAPP(nat,int,semiring_1_of_nat(int),K_4)),one_one(int))) # label(fact_3757_of__nat__rat) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.80 3706 (all W hAPP(int,rat,number_number_of(rat),W) = hAPP(int,rat,hAPP(int,fun(int,rat),fract,W),one_one(int))) # label(fact_3758_rat__number__of__def) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.80 3707 (all X hAPP(real,int,archim2085082626_floor(real),hAPP(rat,real,ratreal,X)) = hAPP(rat,int,archim2085082626_floor(rat),X)) # label(fact_3759_real__floor__code) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.80 3708 (all A_1 all B hAPP(rat,int,archim2085082626_floor(rat),hAPP(int,rat,hAPP(int,fun(int,rat),fract,A_1),B)) = hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_1),B)) # label(fact_3760_floor__Fract) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.80 3709 (all A_1 all B hAPP(rat,rat,inverse_inverse(rat),hAPP(int,rat,hAPP(int,fun(int,rat),fract,A_1),B)) = hAPP(int,rat,hAPP(int,fun(int,rat),fract,B),A_1)) # label(fact_3761_inverse__rat) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.80 3710 (all A_1 all B hAPP(int,rat,hAPP(int,fun(int,rat),fract,hAPP(int,int,uminus_uminus(int),A_1)),hAPP(int,int,uminus_uminus(int),B)) = hAPP(int,rat,hAPP(int,fun(int,rat),fract,A_1),B)) # label(fact_3762_minus__rat__cancel) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.80 3711 (all A_1 all B all C (C != zero_zero(int) -> hAPP(int,rat,hAPP(int,fun(int,rat),fract,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),A_1)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),B)) = hAPP(int,rat,hAPP(int,fun(int,rat),fract,A_1),B))) # label(fact_3763_mult__rat__cancel) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.80 3712 (all Aa all C_1 all D_1 all Ba (Ba != zero_zero(int) -> (D_1 != zero_zero(int) -> (hAPP(int,rat,hAPP(int,fun(int,rat),fract,Aa),Ba) = hAPP(int,rat,hAPP(int,fun(int,rat),fract,C_1),D_1) <-> hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Aa),D_1) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C_1),Ba))))) # label(fact_3764_eq__rat_I1_J) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.80 3713 (all A_1 all B all C all D hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(int,rat,hAPP(int,fun(int,rat),fract,A_1),B)),hAPP(int,rat,hAPP(int,fun(int,rat),fract,C),D)) = hAPP(int,rat,hAPP(int,fun(int,rat),fract,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),C)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),D))) # label(fact_3765_mult__rat) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.80 3714 (all A_1 all B hAPP(rat,rat,abs_abs(rat),hAPP(int,rat,hAPP(int,fun(int,rat),fract,A_1),B)) = hAPP(int,rat,hAPP(int,fun(int,rat),fract,hAPP(int,int,abs_abs(int),A_1)),hAPP(int,int,abs_abs(int),B))) # label(fact_3766_abs__rat) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.80 3715 (all A_1 all B all P_4 all Q_2 (hAPP(product_prod(int,int),product_prod(int,int),normalize,hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),A_1),B)) = hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),P_4),Q_2) -> hAPP(int,rat,hAPP(int,fun(int,rat),fract,P_4),Q_2) = hAPP(int,rat,hAPP(int,fun(int,rat),fract,A_1),B))) # label(fact_3767_normalize__eq) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.80 3716 (all X_1 all Y_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(rat,real,ratreal,X_1)),hAPP(rat,real,ratreal,Y_1))) <-> hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),X_1),Y_1)))) # label(fact_3768_real__less__code) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.80 3717 (all K_4 hAPP(int,real,number_number_of(real),K_4) = hAPP(rat,real,ratreal,hAPP(int,rat,number_number_of(rat),K_4))) # label(fact_3771_number__of__real__code) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.80 3718 (all K_4 hAPP(rat,real,ratreal,hAPP(int,rat,number_number_of(rat),K_4)) = hAPP(int,real,number_number_of(real),K_4)) # label(fact_3772_Ratreal__number__collapse_I3_J) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.80 3719 (all X_1 all Y_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(rat,real,ratreal,X_1)),hAPP(rat,real,ratreal,Y_1))) <-> hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),X_1),Y_1)))) # label(fact_3775_real__less__eq__code) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.80 3720 (all X all Y hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(rat,real,ratreal,X)),hAPP(rat,real,ratreal,Y)) = hAPP(rat,real,ratreal,hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),X),Y))) # label(fact_3776_real__plus__code) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.80 3721 (all X all Y hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(rat,real,ratreal,X)),hAPP(rat,real,ratreal,Y)) = hAPP(rat,real,ratreal,hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),X),Y))) # label(fact_3777_real__minus__code) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.80 3722 (all X hAPP(real,real,uminus_uminus(real),hAPP(rat,real,ratreal,X)) = hAPP(rat,real,ratreal,hAPP(rat,rat,uminus_uminus(rat),X))) # label(fact_3778_real__uminus__code) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.80 3723 (all X all Y hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(rat,real,ratreal,X)),hAPP(rat,real,ratreal,Y)) = hAPP(rat,real,ratreal,hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),X),Y))) # label(fact_3779_real__divide__code) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.80 3724 (all X all Y hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(rat,real,ratreal,X)),hAPP(rat,real,ratreal,Y)) = hAPP(rat,real,ratreal,hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),X),Y))) # label(fact_3780_real__times__code) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.80 3725 (all X hAPP(real,real,inverse_inverse(real),hAPP(rat,real,ratreal,X)) = hAPP(rat,real,ratreal,hAPP(rat,rat,inverse_inverse(rat),X))) # label(fact_3781_real__inverse__code) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.80 3726 (all K_4 hAPP(int,rat,number_number_of(rat),K_4) = hAPP(int,rat,hAPP(int,fun(int,rat),fract,hAPP(int,int,number_number_of(int),K_4)),one_one(int))) # label(fact_3783_rat__number__expand_I3_J) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.80 3727 (all K_4 hAPP(int,rat,hAPP(int,fun(int,rat),fract,hAPP(int,int,number_number_of(int),K_4)),one_one(int)) = hAPP(int,rat,number_number_of(rat),K_4)) # label(fact_3784_rat__number__collapse_I3_J) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.80 3728 (all K_4 all L_4 hAPP(int,rat,hAPP(int,fun(int,rat),fract,hAPP(int,int,number_number_of(int),K_4)),hAPP(int,int,number_number_of(int),L_4)) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),hAPP(int,rat,number_number_of(rat),K_4)),hAPP(int,rat,number_number_of(rat),L_4))) # label(fact_3785_Fract__number__of__quotient) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.80 3729 (all A_1 all B hAPP(rat,product_prod(int,int),quotient_of,hAPP(int,rat,hAPP(int,fun(int,rat),fract,A_1),B)) = hAPP(product_prod(int,int),product_prod(int,int),normalize,hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),A_1),B))) # label(fact_3786_quotient__of__Fract) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.80 3730 (all P_4 hAPP(product_prod(int,int),rat,frct,P_4) = hAPP(int,rat,hAPP(int,fun(int,rat),fract,hAPP(product_prod(int,int),int,product_fst(int,int),P_4)),hAPP(product_prod(int,int),int,product_snd(int,int),P_4))) # label(fact_3787_Frct__def) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.80 3731 (all Aa all C_1 all D_1 all Ba (Ba != zero_zero(int) -> (D_1 != zero_zero(int) -> (hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(int,rat,hAPP(int,fun(int,rat),fract,Aa),Ba)),hAPP(int,rat,hAPP(int,fun(int,rat),fract,C_1),D_1))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Aa),D_1)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Ba),D_1))),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C_1),Ba)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Ba),D_1)))))))) # label(fact_3788_less__rat) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.80 3732 (all R_4 all S_4 hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(rat,real,ratreal,hAPP(int,rat,number_number_of(rat),R_4))),hAPP(rat,real,ratreal,hAPP(int,rat,number_number_of(rat),S_4))) = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(int,real,number_number_of(real),R_4)),hAPP(int,real,number_number_of(real),S_4))) # label(fact_3789_Ratreal__number__of__quotient) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.80 3733 (all A_1 all B hAPP(rat,rat,sgn_sgn(rat),hAPP(int,rat,hAPP(int,fun(int,rat),fract,A_1),B)) = hAPP(int,rat,ring_1_of_int(rat),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,sgn_sgn(int),A_1)),hAPP(int,int,sgn_sgn(int),B)))) # label(fact_3790_sgn__rat) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.80 3734 (all Aa all Ba (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),Ba)) -> (hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(int,rat,hAPP(int,fun(int,rat),fract,Aa),Ba)),zero_zero(rat))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Aa),zero_zero(int)))))) # label(fact_3791_Fract__less__zero__iff) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.80 3735 (all Aa all Ba (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),Ba)) -> (hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(int,rat,hAPP(int,fun(int,rat),fract,Aa),Ba))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),Aa))))) # label(fact_3792_zero__less__Fract__iff) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.80 3736 (all Aa all C_1 all D_1 all Ba (Ba != zero_zero(int) -> (D_1 != zero_zero(int) -> (hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(int,rat,hAPP(int,fun(int,rat),fract,Aa),Ba)),hAPP(int,rat,hAPP(int,fun(int,rat),fract,C_1),D_1))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Aa),D_1)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Ba),D_1))),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C_1),Ba)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Ba),D_1)))))))) # label(fact_3793_le__rat) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.80 3737 (all A_1 all C all D all B (B != zero_zero(int) -> (D != zero_zero(int) -> hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(int,rat,hAPP(int,fun(int,rat),fract,A_1),B)),hAPP(int,rat,hAPP(int,fun(int,rat),fract,C),D)) = hAPP(int,rat,hAPP(int,fun(int,rat),fract,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),D)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),B))),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),D))))) # label(fact_3794_add__rat) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.80 3738 (all A_1 all C all D all B (B != zero_zero(int) -> (D != zero_zero(int) -> hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),hAPP(int,rat,hAPP(int,fun(int,rat),fract,A_1),B)),hAPP(int,rat,hAPP(int,fun(int,rat),fract,C),D)) = hAPP(int,rat,hAPP(int,fun(int,rat),fract,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),D)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),B))),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),D))))) # label(fact_3795_diff__rat) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.80 3739 (all Aa all Ba (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),Ba)) -> (hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),one_one(rat)),hAPP(int,rat,hAPP(int,fun(int,rat),fract,Aa),Ba))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Ba),Aa))))) # label(fact_3796_one__less__Fract__iff) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.80 3740 (all Aa all Ba (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),Ba)) -> (hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(int,rat,hAPP(int,fun(int,rat),fract,Aa),Ba)),one_one(rat))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Aa),Ba))))) # label(fact_3797_Fract__less__one__iff) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.80 3741 (all M_1 all N_1 (N_1 != zero_zero(int) -> hAPP(int,rat,hAPP(int,fun(int,rat),fract,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),M_1),N_1)),N_1) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(int,rat,hAPP(int,fun(int,rat),fract,M_1),N_1)),one_one(rat)))) # label(fact_3798_Fract__add__one) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.80 3742 (all Aa all Ba (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),Ba)) -> (hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(int,rat,hAPP(int,fun(int,rat),fract,Aa),Ba)),zero_zero(rat))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Aa),zero_zero(int)))))) # label(fact_3799_Fract__le__zero__iff) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.80 3743 (all Aa all Ba (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),Ba)) -> (hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),hAPP(int,rat,hAPP(int,fun(int,rat),fract,Aa),Ba))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Aa))))) # label(fact_3800_zero__le__Fract__iff) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.80 3744 (all A_1 all B (hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(int,rat,ring_1_of_int(rat),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_1),B))),hAPP(int,rat,hAPP(int,fun(int,rat),fract,A_1),B))) & hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(int,rat,hAPP(int,fun(int,rat),fract,A_1),B)),hAPP(int,rat,ring_1_of_int(rat),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_1),B)),one_one(int))))))) # label(fact_3801_rat__floor__lemma) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.80 3745 (all Aa all Ba (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),Ba)) -> (hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),one_one(rat)),hAPP(int,rat,hAPP(int,fun(int,rat),fract,Aa),Ba))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Ba),Aa))))) # label(fact_3802_one__le__Fract__iff) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.80 3746 (all Aa all Ba (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),Ba)) -> (hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(int,rat,hAPP(int,fun(int,rat),fract,Aa),Ba)),one_one(rat))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Aa),Ba))))) # label(fact_3803_Fract__le__one__iff) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.80 3747 (all Qa all P_1 ((all A_3 all B_3 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B_3)) -> hBOOL(hAPP(rat,bool,P_1,hAPP(int,rat,hAPP(int,fun(int,rat),fract,A_3),B_3))))) -> hBOOL(hAPP(rat,bool,P_1,Qa)))) # label(fact_3804_Rat__induct__pos) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.80 3748 (all X_a all R_3 all F all X_1 all Y_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(X_a,nat,F,X_1)),hAPP(X_a,nat,F,Y_1))) -> (hBOOL(hAPP(fun(product_prod(X_a,X_a),bool),bool,hAPP(product_prod(X_a,X_a),fun(fun(product_prod(X_a,X_a),bool),bool),member(product_prod(X_a,X_a)),hAPP(X_a,product_prod(X_a,X_a),hAPP(X_a,fun(X_a,product_prod(X_a,X_a)),product_Pair(X_a,X_a),X_1),Y_1)),R_3)) -> hBOOL(hAPP(fun(product_prod(X_a,X_a),bool),bool,hAPP(product_prod(X_a,X_a),fun(fun(product_prod(X_a,X_a),bool),bool),member(product_prod(X_a,X_a)),hAPP(X_a,product_prod(X_a,X_a),hAPP(X_a,fun(X_a,product_prod(X_a,X_a)),product_Pair(X_a,X_a),X_1),Y_1)),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(X_a,X_a),bool),hAPP(fun(X_a,nat),fun(fun(product_prod(X_a,X_a),bool),fun(product_prod(X_a,X_a),bool)),mlex_prod(X_a),F),R_3)))))) # label(fact_3805_mlex__leq) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.80 3749 (all X_a all R_3 all F all X_1 all Y_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(X_a,nat,F,X_1)),hAPP(X_a,nat,F,Y_1))) -> hBOOL(hAPP(fun(product_prod(X_a,X_a),bool),bool,hAPP(product_prod(X_a,X_a),fun(fun(product_prod(X_a,X_a),bool),bool),member(product_prod(X_a,X_a)),hAPP(X_a,product_prod(X_a,X_a),hAPP(X_a,fun(X_a,product_prod(X_a,X_a)),product_Pair(X_a,X_a),X_1),Y_1)),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(X_a,X_a),bool),hAPP(fun(X_a,nat),fun(fun(product_prod(X_a,X_a),bool),fun(product_prod(X_a,X_a),bool)),mlex_prod(X_a),F),R_3))))) # label(fact_3806_mlex__less) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.80 3750 (all Ba all Qa all R_1 hAPP(product_prod(int,int),product_prod(int,int),hAPP(int,fun(product_prod(int,int),product_prod(int,int)),adjust,Ba),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),Qa),R_1)) = hAPP(product_prod(int,int),product_prod(int,int),hAPP(product_prod(int,int),fun(product_prod(int,int),product_prod(int,int)),hAPP(bool,fun(product_prod(int,int),fun(product_prod(int,int),product_prod(int,int))),if(product_prod(int,int)),hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),R_1),Ba))),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,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,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),Qa)),one_one(int))),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),R_1),Ba))),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),Qa)),R_1))) # label(fact_3807_adjust__eq) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.80 3751 (all X_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,real)),combs(real,real,real),hAPP(fun(real,real),fun(real,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,fun(real,real))),combb(real,fun(real,real),real),plus_plus(real)),hAPP(nat,fun(real,real),hAPP(fun(real,fun(nat,real)),fun(nat,fun(real,real)),combc(real,nat,real),hAPP(fun(real,real),fun(real,fun(nat,real)),hAPP(fun(real,fun(nat,real)),fun(fun(real,real),fun(real,fun(nat,real))),combb(real,fun(nat,real),real),power_power(real)),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,real)),combs(real,real,real),hAPP(fun(real,real),fun(real,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,fun(real,real))),combb(real,fun(real,real),real),plus_plus(real)),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,real),fun(fun(real,real),fun(real,real)),combb(real,real,real),sin),uminus_uminus(real)))),sin))),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),hAPP(nat,fun(real,real),hAPP(fun(real,fun(nat,real)),fun(nat,fun(real,real)),combc(real,nat,real),hAPP(fun(real,real),fun(real,fun(nat,real)),hAPP(fun(real,fun(nat,real)),fun(fun(real,real),fun(real,fun(nat,real))),combb(real,fun(nat,real),real),power_power(real)),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,real)),combs(real,real,real),hAPP(fun(real,real),fun(real,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,fun(real,real))),combb(real,fun(real,real),real),minus_minus(real)),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,real),fun(fun(real,real),fun(real,real)),combb(real,real,real),cos),uminus_uminus(real)))),cos))),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),X_2),zero_zero(real)))) # label(fact_3808_lemma__DERIV__sin__cos__minus) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.80 3752 (all X_a all Q_1 all P_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),P_1))) | hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),Q_1))) -> hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,bool)),combs(X_a,bool,bool),hAPP(fun(X_a,bool),fun(X_a,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,fun(bool,bool))),combb(bool,fun(bool,bool),X_a),fconj),P_1)),Q_1)))))) # label(fact_3809_finite__Collect__conjI) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.80 3753 (all K 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))))) # label(fact_3810_finite__Collect__less__nat) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.80 3754 (all K 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))))) # label(fact_3811_finite__Collect__le__nat) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.80 3755 (all X_a all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2)) -> hBOOL(hAPP(fun(fun(X_a,bool),bool),bool,finite_finite_1(fun(X_a,bool)),hAPP(fun(fun(X_a,bool),bool),fun(fun(X_a,bool),bool),collect(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),hAPP(fun(fun(X_a,bool),fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(fun(X_a,bool),bool)),combc(fun(X_a,bool),fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool))),A_2)))))) # label(fact_3812_finite__Collect__subsets) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.80 3756 (all P_1 hAPP(fun(int,bool),fun(int,bool),collect(int),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),combs(int,bool,bool),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(int,fun(int,bool),ord_less_eq(int),zero_zero(int)))),P_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)),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(fun(nat,int),fun(nat,bool),hAPP(fun(int,bool),fun(fun(nat,int),fun(nat,bool)),combb(int,bool,nat),P_1),semiring_1_of_nat(int))))) # label(fact_3814_Nat__Transfer_Otransfer__int__nat__set__functions_I5_J) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.80 3757 (all N (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),N)) -> hAPP(nat,int,semiring_1_of_nat(int),hAPP(fun(int,bool),nat,finite_card(int),hAPP(fun(int,bool),fun(int,bool),collect(int),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),combs(int,bool,bool),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(int,fun(int,bool),ord_less(int),zero_zero(int)))),hAPP(int,fun(int,bool),hAPP(fun(int,fun(int,bool)),fun(int,fun(int,bool)),combc(int,int,bool),ord_less_eq(int)),N))))) = N)) # label(fact_3815_int__card__bdd__int__set__l__le) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.80 3758 (all X_a (real_normed_field(X_a) -> (all G all E_3 all F all X_1 all D_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),F),X_1),D_2)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),G),X_1),E_3)) -> (hAPP(X_a,X_a,G,X_1) != zero_zero(X_a) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),hAPP(fun(X_a,X_a),fun(X_a,X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,X_a),fun(X_a,X_a)),combs(X_a,X_a,X_a),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,X_a),fun(X_a,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),X_a),inverse_divide(X_a)),F)),G)),X_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),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),times_times(X_a),D_2),hAPP(X_a,X_a,G,X_1))),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,F,X_1)),E_3))),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,G,X_1)),hAPP(X_a,X_a,G,X_1))))))))))) # label(fact_3816_DERIV__divide) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.80 3759 (all N (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),N)) -> hAPP(fun(int,bool),nat,finite_card(int),hAPP(fun(int,bool),fun(int,bool),collect(int),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),combs(int,bool,bool),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(int,fun(int,bool),ord_less_eq(int),zero_zero(int)))),hAPP(int,fun(int,bool),hAPP(fun(int,fun(int,bool)),fun(int,fun(int,bool)),combc(int,int,bool),ord_less(int)),N)))) = hAPP(int,nat,nat_1,N))) # label(fact_3817_card__bdd__int__set__l) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.80 3760 (all N (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),N)) -> hAPP(fun(int,bool),nat,finite_card(int),hAPP(fun(int,bool),fun(int,bool),collect(int),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),combs(int,bool,bool),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(int,fun(int,bool),ord_less(int),zero_zero(int)))),hAPP(int,fun(int,bool),hAPP(fun(int,fun(int,bool)),fun(int,fun(int,bool)),combc(int,int,bool),ord_less_eq(int)),N)))) = hAPP(int,nat,nat_1,N))) # label(fact_3818_card__bdd__int__set__l__le) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.80 3761 (all N hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),hAPP(fun(int,bool),fun(int,bool),collect(int),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),combs(int,bool,bool),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(int,fun(int,bool),ord_less(int),zero_zero(int)))),hAPP(int,fun(int,bool),hAPP(fun(int,fun(int,bool)),fun(int,fun(int,bool)),combc(int,int,bool),ord_less_eq(int)),N)))))) # label(fact_3819_bdd__int__set__l__le__finite) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.80 3762 (all N hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),hAPP(fun(int,bool),fun(int,bool),collect(int),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),combs(int,bool,bool),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(int,fun(int,bool),ord_less_eq(int),zero_zero(int)))),hAPP(int,fun(int,bool),hAPP(fun(int,fun(int,bool)),fun(int,fun(int,bool)),combc(int,int,bool),ord_less(int)),N)))))) # label(fact_3820_bdd__int__set__l__finite) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.80 3763 (all K all Xa_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,real),fun(fun(real,real),fun(real,real)),combb(real,real,real),cos),hAPP(real,fun(real,real),hAPP(fun(real,fun(real,real)),fun(real,fun(real,real)),combc(real,real,real),plus_plus(real)),K))),Xa_2),hAPP(real,real,uminus_uminus(real),hAPP(real,real,sin,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),Xa_2),K)))))) # label(fact_3821_DERIV__cos__add) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.80 3764 (all X_2 hAPP(nat,fun(nat,bool),ord_less(nat),X_2) = hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X_2))) # label(fact_3822_less__eq__Suc__le__raw) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.80 3765 (all X_a (real_normed_field(X_a) -> (all G all E_3 all F all X_1 all D_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),F),X_1),D_2)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),G),X_1),E_3)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),hAPP(fun(X_a,X_a),fun(X_a,X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,X_a),fun(X_a,X_a)),combs(X_a,X_a,X_a),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,X_a),fun(X_a,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),X_a),plus_plus(X_a)),F)),hAPP(fun(X_a,X_a),fun(X_a,X_a),hAPP(fun(X_a,X_a),fun(fun(X_a,X_a),fun(X_a,X_a)),combb(X_a,X_a,X_a),uminus_uminus(X_a)),G))),X_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),D_2),hAPP(X_a,X_a,uminus_uminus(X_a),E_3))))))))) # label(fact_3823_DERIV__add__minus) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.80 3766 (all X_a (real_normed_field(X_a) -> (all G all Db all F all X_1 all Da (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),F),X_1),Da)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),G),X_1),Db)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),hAPP(fun(X_a,X_a),fun(X_a,X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,X_a),fun(X_a,X_a)),combs(X_a,X_a,X_a),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,X_a),fun(X_a,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),X_a),times_times(X_a)),F)),G)),X_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),Da),hAPP(X_a,X_a,G,X_1))),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Db),hAPP(X_a,X_a,F,X_1)))))))))) # label(fact_3824_DERIV__mult) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.80 3767 (all X_a (real_normed_field(X_a) -> (all G all E_3 all F all X_1 all D_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),F),X_1),D_2)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),G),X_1),E_3)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),hAPP(fun(X_a,X_a),fun(X_a,X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,X_a),fun(X_a,X_a)),combs(X_a,X_a,X_a),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,X_a),fun(X_a,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),X_a),times_times(X_a)),F)),G)),X_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,F,X_1)),E_3)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),D_2),hAPP(X_a,X_a,G,X_1)))))))))) # label(fact_3825_DERIV__mult_H) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.81 3768 (all X_1 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,real)),combs(real,real,real),hAPP(fun(real,real),fun(real,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,fun(real,real))),combb(real,fun(real,real),real),times_times(real)),sin)),sin)),X_1),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,cos,X_1)),hAPP(real,real,sin,X_1))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,cos,X_1)),hAPP(real,real,sin,X_1)))))) # label(fact_3826_DERIV__sin__sin__mult) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.81 3769 (all K all Xa_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,real),fun(fun(real,real),fun(real,real)),combb(real,real,real),sin),hAPP(real,fun(real,real),hAPP(fun(real,fun(real,real)),fun(real,fun(real,real)),combc(real,real,real),plus_plus(real)),K))),Xa_2),hAPP(real,real,cos,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),Xa_2),K))))) # label(fact_3827_DERIV__sin__add) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.81 3770 (all X_a (real_normed_field(X_a) -> (all G all E_3 all F all X_1 all D_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),F),X_1),D_2)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),G),X_1),E_3)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),hAPP(fun(X_a,X_a),fun(X_a,X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,X_a),fun(X_a,X_a)),combs(X_a,X_a,X_a),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,X_a),fun(X_a,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),X_a),plus_plus(X_a)),F)),G)),X_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),D_2),E_3)))))))) # label(fact_3828_DERIV__add) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.81 3771 (all X_a (real_normed_field(X_a) -> (all G all E_3 all F all X_1 all D_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),F),X_1),D_2)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),G),X_1),E_3)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),hAPP(fun(X_a,X_a),fun(X_a,X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,X_a),fun(X_a,X_a)),combs(X_a,X_a,X_a),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,X_a),fun(X_a,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),X_a),minus_minus(X_a)),F)),G)),X_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),D_2),E_3)))))))) # label(fact_3829_DERIV__diff) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.81 3772 (all X_a (real_normed_vector(X_a) -> (all K all X_3 (hBOOL(hAPP(fun(nat,X_a),bool,bseq(X_a),X_3)) -> hBOOL(hAPP(fun(nat,X_a),bool,bseq(X_a),hAPP(fun(nat,nat),fun(nat,X_a),hAPP(fun(nat,X_a),fun(fun(nat,nat),fun(nat,X_a)),combb(nat,X_a,nat),X_3),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),K)))))))) # label(fact_3830_Bseq__ignore__initial__segment) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.81 3773 (all X_a (real_normed_vector(X_a) -> (all X_3 all K (hBOOL(hAPP(fun(nat,X_a),bool,bseq(X_a),hAPP(fun(nat,nat),fun(nat,X_a),hAPP(fun(nat,X_a),fun(fun(nat,nat),fun(nat,X_a)),combb(nat,X_a,nat),X_3),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),K)))) -> hBOOL(hAPP(fun(nat,X_a),bool,bseq(X_a),X_3)))))) # label(fact_3831_Bseq__offset) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.81 3774 (all X_b all X_c all X_a all X_2 all Xa all Xb hAPP(X_b,X_c,hAPP(X_a,fun(X_b,X_c),hAPP(fun(product_prod(X_a,X_b),X_c),fun(X_a,fun(X_b,X_c)),product_curry(X_a,X_b,X_c),X_2),Xa),Xb) = hAPP(product_prod(X_a,X_b),X_c,X_2,hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),Xa),Xb))) # label(fact_3832_curry__def) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.81 3775 (all X_1 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_eq(nat)),X_1))) = hAPP(nat,nat,suc,X_1)) # label(fact_3833_card__bdd__nat__set__le) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.81 3776 (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_eq(nat)),N))) = hAPP(nat,nat,suc,N)) # label(fact_3834_card__Collect__le__nat) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.81 3777 (all X_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)),X_1))))) # label(fact_3835_bdd__nat__set__le__finite) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.81 3778 (all W hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,W)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),W)),hAPP(int,nat,number_number_of(nat),W))) # label(fact_3836_nat__number__of__Bit0) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.81 3779 (all P_1 hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,hAPP(fun(int,bool),fun(int,bool),collect(int),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),combs(int,bool,bool),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(int,fun(int,bool),ord_less_eq(int),zero_zero(int)))),P_1))))) # label(fact_3837_Nat__Transfer_Otransfer__int__nat__set__function__closures_I4_J) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.81 3780 (all P_1 hAPP(fun(nat,bool),fun(nat,bool),collect(nat),P_1) = hAPP(fun(int,bool),fun(nat,bool),hAPP(fun(int,nat),fun(fun(int,bool),fun(nat,bool)),image(int,nat),nat_1),hAPP(fun(int,bool),fun(int,bool),collect(int),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),combs(int,bool,bool),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(int,fun(int,bool),ord_less_eq(int),zero_zero(int)))),hAPP(fun(int,nat),fun(int,bool),hAPP(fun(nat,bool),fun(fun(int,nat),fun(int,bool)),combb(nat,bool,int),P_1),nat_1))))) # label(fact_3838_Nat__Transfer_Otransfer__nat__int__set__functions_I5_J) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.81 3781 (all N hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),hAPP(fun(int,bool),fun(int,bool),collect(int),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),combs(int,bool,bool),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(int,fun(int,bool),ord_less_eq(int),zero_zero(int)))),hAPP(int,fun(int,bool),hAPP(fun(int,fun(int,bool)),fun(int,fun(int,bool)),combc(int,int,bool),ord_less_eq(int)),N)))))) # label(fact_3839_bdd__int__set__le__finite) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.81 3782 (all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_1),one_one(real))) -> hBOOL(hAPP(fun(nat,real),bool,bseq(real),hAPP(real,fun(nat,real),power_power(real),X_1)))))) # label(fact_3840_Bseq__realpow) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.81 3783 (all Z_1 all Z_3 ((hBOOL(hAPP(int,bool,nat_neg,Z_3)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(int,nat,nat_1,Z_1)),hAPP(int,nat,nat_1,Z_3)) = hAPP(int,nat,nat_1,Z_1)) & (-hBOOL(hAPP(int,bool,nat_neg,Z_3)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(int,nat,nat_1,Z_1)),hAPP(int,nat,nat_1,Z_3)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),hAPP(bool,fun(nat,fun(nat,nat)),if(nat),hAPP(int,bool,nat_neg,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),Z_1),Z_3))),zero_zero(nat)),hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),Z_1),Z_3)))))) # label(fact_3841_diff__nat__eq__if) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.81 3784 (all X_a (real_normed_field(X_a) -> (all X_1 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),combi(X_a)),X_1),one_one(X_a)))))) # label(fact_3842_DERIV__ident) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.81 3785 (all X_a (real_normed_field(X_a) -> (all K all X_1 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),hAPP(X_a,fun(X_a,X_a),combk(X_a,X_a),K)),X_1),zero_zero(X_a)))))) # label(fact_3843_DERIV__const) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.81 3786 (all X_a (real_normed_field(X_a) -> (all C_1 all F all X_1 all D_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),F),X_1),D_2)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),hAPP(X_a,fun(X_a,X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(X_a,X_a)),combc(X_a,X_a,X_a),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,X_a),fun(X_a,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),X_a),inverse_divide(X_a)),F)),C_1)),X_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),D_2),C_1))))))) # label(fact_3844_DERIV__cdivide) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.81 3787 (all M (M != zero_zero(nat) -> 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),dvd_dvd(nat)),M)))))) # label(fact_3845_finite__divisors__nat) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.81 3788 (all I (I != zero_zero(int) -> hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),hAPP(fun(int,bool),fun(int,bool),collect(int),hAPP(int,fun(int,bool),hAPP(fun(int,fun(int,bool)),fun(int,fun(int,bool)),combc(int,int,bool),dvd_dvd(int)),I)))))) # label(fact_3846_finite__divisors__int) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.81 3789 (all X_a all Y_3 hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,X_a),fun(fun(X_a,bool),fun(X_a,bool)),image(X_a,X_a),combi(X_a)),Y_3) = ti(fun(X_a,bool),Y_3)) # label(fact_3847_image__ident) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.81 3790 (all X_b all X_a all X_c all F all G all A_2 hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),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),G),A_2)) = hAPP(fun(X_c,bool),fun(X_a,bool),hAPP(fun(X_c,X_a),fun(fun(X_c,bool),fun(X_a,bool)),image(X_c,X_a),hAPP(fun(X_c,X_b),fun(X_c,X_a),hAPP(fun(X_b,X_a),fun(fun(X_c,X_b),fun(X_c,X_a)),combb(X_b,X_a,X_c),F),G)),A_2)) # label(fact_3848_image__image) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.81 3791 (all X_a all P_1 all Q_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,bool)),combs(X_a,bool,bool),hAPP(fun(X_a,bool),fun(X_a,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,fun(bool,bool))),combb(bool,fun(bool,bool),X_a),fdisj),P_1)),Q_1)))) <-> hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),P_1))) & hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),Q_1))))) # label(fact_3850_finite__Collect__disjI) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.81 3792 (all X_3 (hBOOL(hAPP(fun(nat,complex),bool,cauchy(complex),X_3)) -> hBOOL(hAPP(fun(nat,complex),bool,cauchy(complex),hAPP(fun(nat,complex),fun(nat,complex),hAPP(fun(complex,complex),fun(fun(nat,complex),fun(nat,complex)),combb(complex,complex,nat),cnj),X_3))))) # label(fact_3851_cnj_OCauchy) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.81 3793 (all X_3 (hBOOL(hAPP(fun(nat,complex),bool,cauchy(complex),X_3)) -> hBOOL(hAPP(fun(nat,real),bool,cauchy(real),hAPP(fun(nat,complex),fun(nat,real),hAPP(fun(complex,real),fun(fun(nat,complex),fun(nat,real)),combb(complex,real,nat),re),X_3))))) # label(fact_3852_Re_OCauchy) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.81 3794 (all X_3 (hBOOL(hAPP(fun(nat,complex),bool,cauchy(complex),X_3)) -> hBOOL(hAPP(fun(nat,real),bool,cauchy(real),hAPP(fun(nat,complex),fun(nat,real),hAPP(fun(complex,real),fun(fun(nat,complex),fun(nat,real)),combb(complex,real,nat),im),X_3))))) # label(fact_3853_Im_OCauchy) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.81 3795 (all X_c all X_b all X_a (real_normed_vector(X_a) & real_normed_vector(X_b) & real_normed_vector(X_c) -> (all Prod (hBOOL(hAPP(fun(X_a,fun(X_b,X_c)),bool,bounded_bilinear(X_a,X_b,X_c),Prod)) -> hBOOL(hAPP(fun(X_b,fun(X_a,X_c)),bool,bounded_bilinear(X_b,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),Prod))))))) # label(fact_3854_bounded__bilinear_Oflip) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.81 3796 (all G all X_1 all M (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),G),X_1),M)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,real),fun(fun(real,real),fun(real,real)),combb(real,real,real),cos),G)),X_1),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,uminus_uminus(real),hAPP(real,real,sin,hAPP(real,real,G,X_1)))),M))))) # label(fact_3855_DERIV__fun__cos) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.81 3797 (all G all X_1 all M (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),G),X_1),M)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,real),fun(fun(real,real),fun(real,real)),combb(real,real,real),sin),G)),X_1),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,cos,hAPP(real,real,G,X_1))),M))))) # label(fact_3856_DERIV__fun__sin) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.81 3798 (all X_a (real_normed_field(X_a) -> (all C_1 all F all X_1 all D_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),F),X_1),D_2)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),hAPP(fun(X_a,X_a),fun(X_a,X_a),hAPP(fun(X_a,X_a),fun(fun(X_a,X_a),fun(X_a,X_a)),combb(X_a,X_a,X_a),hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1)),F)),X_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1),D_2))))))) # label(fact_3857_DERIV__cmult) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.81 3799 (all X_a (real_normed_field(X_a) -> (all G all E_3 all F all X_1 all D_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),F),X_1),D_2)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),G),hAPP(X_a,X_a,F,X_1)),E_3)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),hAPP(fun(X_a,X_a),fun(X_a,X_a),hAPP(fun(X_a,X_a),fun(fun(X_a,X_a),fun(X_a,X_a)),combb(X_a,X_a,X_a),G),F)),X_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),E_3),D_2)))))))) # label(fact_3858_DERIV__chain_H) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.81 3800 (all X_a (real_normed_field(X_a) -> (all Db all F all G all X_1 all Da (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),F),hAPP(X_a,X_a,G,X_1)),Da)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),G),X_1),Db)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),hAPP(fun(X_a,X_a),fun(X_a,X_a),hAPP(fun(X_a,X_a),fun(fun(X_a,X_a),fun(X_a,X_a)),combb(X_a,X_a,X_a),F),G)),X_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Da),Db)))))))) # label(fact_3859_DERIV__chain2) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.81 3801 (all X_a (real_normed_field(X_a) & banach(X_a) -> (all G all X_1 all M (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),G),X_1),M)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),hAPP(fun(X_a,X_a),fun(X_a,X_a),hAPP(fun(X_a,X_a),fun(fun(X_a,X_a),fun(X_a,X_a)),combb(X_a,X_a,X_a),exp(X_a)),G)),X_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,exp(X_a),hAPP(X_a,X_a,G,X_1))),M))))))) # label(fact_3860_DERIV__fun__exp) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.81 3802 (all X_a (real_normed_algebra(X_a) -> hBOOL(hAPP(fun(X_a,fun(X_a,X_a)),bool,bounded_bilinear(X_a,X_a,X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(X_a,X_a)),combc(X_a,X_a,X_a),times_times(X_a)))))) # label(fact_3861_mult_Oflip) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.81 3803 (all X_a (real_normed_vector(X_a) -> (all X_3 (hBOOL(hAPP(fun(nat,X_a),bool,bseq(X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(X_a,X_a),fun(fun(nat,X_a),fun(nat,X_a)),combb(X_a,X_a,nat),uminus_uminus(X_a)),X_3))) <-> hBOOL(hAPP(fun(nat,X_a),bool,bseq(X_a),X_3)))))) # label(fact_3862_Bseq__minus__iff) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.81 3804 (all X_a all P_1 hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(bool,bool),fun(fun(X_a,bool),fun(X_a,bool)),combb(bool,bool,X_a),fNot),P_1)) = hAPP(fun(X_a,bool),fun(X_a,bool),uminus_uminus(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),P_1))) # label(fact_3863_Collect__neg__eq) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.81 3805 (all X_a (real_normed_field(X_a) -> (all F all X_1 all D_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),F),X_1),D_2)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),hAPP(fun(X_a,X_a),fun(X_a,X_a),hAPP(fun(X_a,X_a),fun(fun(X_a,X_a),fun(X_a,X_a)),combb(X_a,X_a,X_a),uminus_uminus(X_a)),F)),X_1),hAPP(X_a,X_a,uminus_uminus(X_a),D_2))))))) # label(fact_3864_DERIV__minus) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.81 3806 (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_3865_card__Collect__less__nat) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.81 3807 (all X_1 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)),X_1))) = X_1) # label(fact_3866_card__bdd__nat__set__l) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.81 3808 (all X_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)),X_1))))) # label(fact_3867_bdd__nat__set__l__finite) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.81 3809 (all X_a all A_2 all F all N (ti(fun(X_a,bool),A_2) = hAPP(fun(nat,bool),fun(X_a,bool),hAPP(fun(nat,X_a),fun(fun(nat,bool),fun(X_a,bool)),image(nat,X_a),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_a,bool),bool,finite_finite_1(X_a),A_2)))) # label(fact_3868_nat__seg__image__imp__finite) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.81 3810 (all P_1 all I 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),P_1)),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),I)))))) # label(fact_3869_finite__M__bounded__by__nat) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.81 3811 (all Z all W hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),Z),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,W))) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),Z),hAPP(int,nat,number_number_of(nat),W))),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),Z),hAPP(int,nat,number_number_of(nat),W)))) # label(fact_3870_zpower__number__of__even) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.81 3812 (all X_a (monoid_mult(X_a) -> (all Z all W hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),Z),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,W))) = 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),Z),hAPP(int,nat,number_number_of(nat),W))),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),Z),hAPP(int,nat,number_number_of(nat),W)))))) # label(fact_3871_power__number__of__even) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.81 3813 (all X_b (monoid_mult(X_b) & number(X_b) -> (all V all W hAPP(nat,X_b,hAPP(X_b,fun(nat,X_b),power_power(X_b),hAPP(int,X_b,number_number_of(X_b),V)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,W))) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(nat,X_b,hAPP(X_b,fun(nat,X_b),power_power(X_b),hAPP(int,X_b,number_number_of(X_b),V)),hAPP(int,nat,number_number_of(nat),W))),hAPP(nat,X_b,hAPP(X_b,fun(nat,X_b),power_power(X_b),hAPP(int,X_b,number_number_of(X_b),V)),hAPP(int,nat,number_number_of(nat),W)))))) # label(fact_3872_power__number__of__even__number__of) # label(axiom) # label(non_clause). [assumption].
% 7.78/7.81 3814 (all I all M_2 (-hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),zero_zero(nat)),M_2)) -> hAPP(fun(nat,bool),nat,finite_card(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),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,bool),fun(nat,bool)),combc(nat,fun(nat,bool),bool),hAPP(fun(nat,nat),fun(nat,fun(fun(nat,bool),bool)),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,nat),fun(nat,fun(fun(nat,bool),bool))),combb(nat,fun(fun(nat,bool),bool),nat),member(nat)),suc)),M_2))),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),I)))) = hAPP(fun(nat,bool),nat,finite_card(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),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)),M_2))),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),hAPP(nat,nat,suc,I))))))) # label(fact_3873_card__less__Suc2) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.81 3815 (all I all M_2 (hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),zero_zero(nat)),M_2)) -> hAPP(fun(nat,bool),nat,finite_card(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),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)),M_2))),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),hAPP(nat,nat,suc,I))))) != zero_zero(nat))) # label(fact_3874_card__less) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.81 3816 (all I all M_2 (hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),zero_zero(nat)),M_2)) -> hAPP(nat,nat,suc,hAPP(fun(nat,bool),nat,finite_card(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),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,bool),fun(nat,bool)),combc(nat,fun(nat,bool),bool),hAPP(fun(nat,nat),fun(nat,fun(fun(nat,bool),bool)),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,nat),fun(nat,fun(fun(nat,bool),bool))),combb(nat,fun(fun(nat,bool),bool),nat),member(nat)),suc)),M_2))),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),I))))) = hAPP(fun(nat,bool),nat,finite_card(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),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)),M_2))),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),hAPP(nat,nat,suc,I))))))) # label(fact_3875_card__less__Suc) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.81 3817 (all N hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),hAPP(fun(int,bool),fun(int,bool),collect(int),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),combs(int,bool,bool),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(int,fun(int,bool),ord_less(int),zero_zero(int)))),hAPP(int,fun(int,bool),hAPP(fun(int,fun(int,bool)),fun(int,fun(int,bool)),combc(int,int,bool),ord_less(int)),N)))))) # label(fact_3876_bdd__int__set__l__l__finite) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.81 3818 (all X_a (real_normed_field(X_a) -> (all F all X_1 all D_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),F),X_1),D_2)) -> (hAPP(X_a,X_a,F,X_1) != zero_zero(X_a) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),hAPP(fun(X_a,X_a),fun(X_a,X_a),hAPP(fun(X_a,X_a),fun(fun(X_a,X_a),fun(X_a,X_a)),combb(X_a,X_a,X_a),inverse_inverse(X_a)),F)),X_1),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),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,inverse_inverse(X_a),hAPP(X_a,X_a,F,X_1))),D_2)),hAPP(X_a,X_a,inverse_inverse(X_a),hAPP(X_a,X_a,F,X_1))))))))))) # label(fact_3877_DERIV__inverse_H) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.81 3819 (all M all X_1 hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),noXRRset,M),X_1) = hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,int),fun(fun(int,bool),fun(int,bool)),image(int,int),hAPP(int,fun(int,int),hAPP(fun(int,fun(int,int)),fun(int,fun(int,int)),combc(int,int,int),times_times(int)),X_1)),hAPP(int,fun(int,bool),norRRset,M))) # label(fact_3878_noXRRset__def) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.81 3820 (all N all G all X_1 all M (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),G),X_1),M)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(nat,fun(real,real),hAPP(fun(real,fun(nat,real)),fun(nat,fun(real,real)),combc(real,nat,real),hAPP(fun(real,real),fun(real,fun(nat,real)),hAPP(fun(real,fun(nat,real)),fun(fun(real,real),fun(real,fun(nat,real))),combb(real,fun(nat,real),real),power_power(real)),G)),N)),X_1),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,real_1(nat),N)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,G,X_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),one_one(nat))))),M))))) # label(fact_3879_DERIV__fun__pow) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.81 3821 (all N (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),N)) -> hAPP(fun(int,bool),nat,finite_card(int),hAPP(fun(int,bool),fun(int,bool),collect(int),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),combs(int,bool,bool),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(int,fun(int,bool),ord_less_eq(int),zero_zero(int)))),hAPP(int,fun(int,bool),hAPP(fun(int,fun(int,bool)),fun(int,fun(int,bool)),combc(int,int,bool),ord_less_eq(int)),N)))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,nat_1,N)),one_one(nat)))) # label(fact_3880_card__bdd__int__set__le) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.81 3822 (all N (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),N)) -> hAPP(nat,int,semiring_1_of_nat(int),hAPP(fun(int,bool),nat,finite_card(int),hAPP(fun(int,bool),fun(int,bool),collect(int),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),combs(int,bool,bool),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(int,fun(int,bool),ord_less(int),zero_zero(int)))),hAPP(int,fun(int,bool),hAPP(fun(int,fun(int,bool)),fun(int,fun(int,bool)),combc(int,int,bool),ord_less(int)),N))))) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),N),one_one(int)))) # label(fact_3881_int__card__bdd__int__set__l__l) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.81 3823 (all N (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),N)) -> hAPP(fun(int,bool),nat,finite_card(int),hAPP(fun(int,bool),fun(int,bool),collect(int),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),combs(int,bool,bool),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(int,fun(int,bool),ord_less(int),zero_zero(int)))),hAPP(int,fun(int,bool),hAPP(fun(int,fun(int,bool)),fun(int,fun(int,bool)),combc(int,int,bool),ord_less(int)),N)))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(int,nat,nat_1,N)),one_one(nat)))) # label(fact_3882_card__bdd__int__set__l__l) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.81 3824 (all X_1 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,real)),combs(real,real,real),hAPP(fun(real,real),fun(real,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,fun(real,real))),combb(real,fun(real,real),real),times_times(real)),cos)),cos)),X_1),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,uminus_uminus(real),hAPP(real,real,sin,X_1))),hAPP(real,real,cos,X_1))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,uminus_uminus(real),hAPP(real,real,sin,X_1))),hAPP(real,real,cos,X_1)))))) # label(fact_3883_DERIV__cos__cos__mult) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.81 3825 (all V_1 all N (hAPP(int,nat,number_number_of(nat),V_1) = hAPP(nat,nat,suc,N) <-> -hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),hAPP(int,int,pred,V_1)))) & (-hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),hAPP(int,int,pred,V_1)))) -> hAPP(int,nat,nat_1,hAPP(int,int,number_number_of(int),hAPP(int,int,pred,V_1))) = N))) # label(fact_3884_eq__number__of__Suc) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.81 3826 (all N all V_1 (hAPP(nat,nat,suc,N) = hAPP(int,nat,number_number_of(nat),V_1) <-> -hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),hAPP(int,int,pred,V_1)))) & (-hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),hAPP(int,int,pred,V_1)))) -> hAPP(int,nat,nat_1,hAPP(int,int,number_number_of(int),hAPP(int,int,pred,V_1))) = N))) # label(fact_3885_Suc__eq__number__of) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.81 3827 (all X_a (real_normed_field(X_a) -> (all N all F all X_1 all D_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),F),X_1),D_2)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),hAPP(nat,fun(X_a,X_a),hAPP(fun(X_a,fun(nat,X_a)),fun(nat,fun(X_a,X_a)),combc(X_a,nat,X_a),hAPP(fun(X_a,X_a),fun(X_a,fun(nat,X_a)),hAPP(fun(X_a,fun(nat,X_a)),fun(fun(X_a,X_a),fun(X_a,fun(nat,X_a))),combb(X_a,fun(nat,X_a),X_a),power_power(X_a)),F)),hAPP(nat,nat,suc,N))),X_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),one_one(X_a)),hAPP(nat,X_a,semiring_1_of_nat(X_a),N))),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),D_2),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(X_a,X_a,F,X_1)),N))))))))) # label(fact_3886_DERIV__power__Suc) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.81 3828 (all X_a (real_normed_field(X_a) -> (all X_1 (ti(X_a,X_1) != zero_zero(X_a) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),inverse_inverse(X_a)),X_1),hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(X_a,X_a,inverse_inverse(X_a),X_1)),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat))))))))))) # label(fact_3887_DERIV__inverse) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.81 3829 (all X_a (real_normed_field(X_a) -> (all N all F all X_1 all D_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),F),X_1),D_2)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),hAPP(nat,fun(X_a,X_a),hAPP(fun(X_a,fun(nat,X_a)),fun(nat,fun(X_a,X_a)),combc(X_a,nat,X_a),hAPP(fun(X_a,X_a),fun(X_a,fun(nat,X_a)),hAPP(fun(X_a,fun(nat,X_a)),fun(fun(X_a,X_a),fun(X_a,fun(nat,X_a))),combb(X_a,fun(nat,X_a),X_a),power_power(X_a)),F)),N)),X_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),N)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),D_2),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(X_a,X_a,F,X_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),hAPP(nat,nat,suc,zero_zero(nat)))))))))))) # label(fact_3888_DERIV__power) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.81 3830 (all W ((hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),W))) -> hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,W)) = zero_zero(nat)) & (-hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),W))) -> hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,W)) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),W)),hAPP(int,nat,number_number_of(nat),W)))))) # label(fact_3889_nat__number__of__Bit1) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.81 3831 (all N all X_1 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(nat,fun(real,real),hAPP(fun(real,fun(nat,real)),fun(nat,fun(real,real)),combc(real,nat,real),power_power(real)),N)),X_1),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,real_1(nat),N)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),hAPP(nat,nat,suc,zero_zero(nat)))))))) # label(fact_3890_DERIV__pow) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.81 3832 (all X_1 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,real)),combs(real,real,real),hAPP(fun(real,real),fun(real,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,fun(real,real))),combb(real,fun(real,real),real),times_times(real)),cos)),cos)),X_1),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,min))),hAPP(real,real,cos,X_1))),hAPP(real,real,sin,X_1))))) # label(fact_3891_DERIV__cos__cos__mult2) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.81 3833 (all V_1 all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(int,nat,number_number_of(nat),V_1)),hAPP(nat,nat,suc,N))) <-> (-hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),hAPP(int,int,pred,V_1)))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(int,nat,nat_1,hAPP(int,int,number_number_of(int),hAPP(int,int,pred,V_1)))),N))))) # label(fact_3892_less__number__of__Suc) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.81 3834 (all N all V_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,N)),hAPP(int,nat,number_number_of(nat),V_1))) <-> -hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),hAPP(int,int,pred,V_1)))) & (-hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),hAPP(int,int,pred,V_1)))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),hAPP(int,nat,nat_1,hAPP(int,int,number_number_of(int),hAPP(int,int,pred,V_1)))))))) # label(fact_3893_less__Suc__number__of) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.81 3835 (all N all V_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,N)),hAPP(int,nat,number_number_of(nat),V_1))) <-> -hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),hAPP(int,int,pred,V_1)))) & (-hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),hAPP(int,int,pred,V_1)))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N),hAPP(int,nat,nat_1,hAPP(int,int,number_number_of(int),hAPP(int,int,pred,V_1)))))))) # label(fact_3894_le__Suc__number__of) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.81 3836 (all V_1 all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(int,nat,number_number_of(nat),V_1)),hAPP(nat,nat,suc,N))) <-> (-hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),hAPP(int,int,pred,V_1)))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(int,nat,nat_1,hAPP(int,int,number_number_of(int),hAPP(int,int,pred,V_1)))),N))))) # label(fact_3895_le__number__of__Suc) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.81 3837 (all X_3 all M (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),M)) -> hBOOL(hAPP(fun(int,bool),bool,hAPP(fun(int,bool),fun(fun(int,bool),bool),ord_less_eq(fun(int,bool)),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,int),fun(fun(int,bool),fun(int,bool)),image(int,int),hAPP(int,fun(int,int),standardRes,M)),X_3)),hAPP(fun(int,bool),fun(int,bool),collect(int),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),combs(int,bool,bool),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(int,fun(int,bool),ord_less_eq(int),zero_zero(int)))),hAPP(int,fun(int,bool),hAPP(fun(int,fun(int,bool)),fun(int,fun(int,bool)),combc(int,int,bool),ord_less(int)),M))))))) # label(fact_3896_SR__pos) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.81 3838 (all X_a (real_normed_field(X_a) -> (all G all E_2 all F all X_1 all D_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),F),X_1),D_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),G),X_1),E_2)) -> (hAPP(X_a,X_a,G,X_1) != zero_zero(X_a) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),hAPP(fun(X_a,X_a),fun(X_a,X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,X_a),fun(X_a,X_a)),combs(X_a,X_a,X_a),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,X_a),fun(X_a,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),X_a),inverse_divide(X_a)),F)),G)),X_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),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),times_times(X_a),D_1),hAPP(X_a,X_a,G,X_1))),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),E_2),hAPP(X_a,X_a,F,X_1)))),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(X_a,X_a,G,X_1)),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat))))))))))))) # label(fact_3897_DERIV__quotient) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.81 3839 (all X_a (monoid_mult(X_a) -> (all Z all W ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),W))) -> hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),Z),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,W))) = 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),Z),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),Z),hAPP(int,nat,number_number_of(nat),W)))),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),Z),hAPP(int,nat,number_number_of(nat),W)))) & (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),W))) -> hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),Z),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,W))) = one_one(X_a)))))) # label(fact_3898_power__number__of__odd) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.81 3840 (all X_a (real_normed_field(X_a) -> (all F all X_1 all D_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),F),X_1),D_1)) -> (hAPP(X_a,X_a,F,X_1) != zero_zero(X_a) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),hAPP(fun(X_a,X_a),fun(X_a,X_a),hAPP(fun(X_a,X_a),fun(fun(X_a,X_a),fun(X_a,X_a)),combb(X_a,X_a,X_a),inverse_inverse(X_a)),F)),X_1),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),D_1),hAPP(X_a,X_a,inverse_inverse(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(X_a,X_a,F,X_1)),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat)))))))))))))) # label(fact_3899_DERIV__inverse__fun) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.81 3841 (all X_1 all A_2 all M (hBOOL(hAPP(fun(fun(int,bool),bool),bool,hAPP(fun(int,bool),fun(fun(fun(int,bool),bool),bool),member(fun(int,bool)),A_2),hAPP(int,fun(fun(int,bool),bool),rsetR,M))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),M)) -> (hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,X_1),M) = one_one(int) -> hBOOL(hAPP(fun(fun(int,bool),bool),bool,hAPP(fun(int,bool),fun(fun(fun(int,bool),bool),bool),member(fun(int,bool)),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,int),fun(fun(int,bool),fun(int,bool)),image(int,int),hAPP(int,fun(int,int),hAPP(fun(int,fun(int,int)),fun(int,fun(int,int)),combc(int,int,int),times_times(int)),X_1)),A_2)),hAPP(int,fun(fun(int,bool),bool),rsetR,M))))))) # label(fact_3900_RsetR__zmult__mono) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.81 3842 (all Z all W ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),W))) -> hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),Z),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,W))) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Z),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),Z),hAPP(int,nat,number_number_of(nat),W)))),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),Z),hAPP(int,nat,number_number_of(nat),W)))) & (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),W))) -> hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),Z),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,W))) = one_one(int)))) # label(fact_3901_zpower__number__of__odd) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.81 3843 (all X_1 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,real)),combs(real,real,real),hAPP(fun(real,real),fun(real,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,fun(real,real))),combb(real,fun(real,real),real),times_times(real)),sin)),sin)),X_1),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),hAPP(real,real,cos,X_1))),hAPP(real,real,sin,X_1))))) # label(fact_3902_DERIV__sin__sin__mult2) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.81 3844 (all Ba all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X_1)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(real,fun(real,real),log,Ba)),X_1),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),one_one(real)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,ln,Ba)),X_1)))))) # label(fact_3903_DERIV__log) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.81 3845 (all X_b (monoid_mult(X_b) & number(X_b) -> (all V all W ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),W))) -> hAPP(nat,X_b,hAPP(X_b,fun(nat,X_b),power_power(X_b),hAPP(int,X_b,number_number_of(X_b),V)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,W))) = 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),times_times(X_b),hAPP(int,X_b,number_number_of(X_b),V)),hAPP(nat,X_b,hAPP(X_b,fun(nat,X_b),power_power(X_b),hAPP(int,X_b,number_number_of(X_b),V)),hAPP(int,nat,number_number_of(nat),W)))),hAPP(nat,X_b,hAPP(X_b,fun(nat,X_b),power_power(X_b),hAPP(int,X_b,number_number_of(X_b),V)),hAPP(int,nat,number_number_of(nat),W)))) & (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),W))) -> hAPP(nat,X_b,hAPP(X_b,fun(nat,X_b),power_power(X_b),hAPP(int,X_b,number_number_of(X_b),V)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,W))) = one_one(X_b)))))) # label(fact_3904_power__number__of__odd__number__of) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.81 3846 (all X_1 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,real)),combs(real,real,real),hAPP(fun(real,real),fun(real,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,fun(real,real))),combb(real,fun(real,real),real),times_times(real)),cos)),cos)),X_1),hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),hAPP(real,real,cos,X_1))),hAPP(real,real,sin,X_1)))))) # label(fact_3905_DERIV__cos__cos__mult3) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.81 3847 (all X_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,real)),combs(real,real,real),hAPP(fun(real,real),fun(real,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,fun(real,real))),combb(real,fun(real,real),real),plus_plus(real)),hAPP(nat,fun(real,real),hAPP(fun(real,fun(nat,real)),fun(nat,fun(real,real)),combc(real,nat,real),hAPP(fun(real,real),fun(real,fun(nat,real)),hAPP(fun(real,fun(nat,real)),fun(fun(real,real),fun(real,fun(nat,real))),combb(real,fun(nat,real),real),power_power(real)),sin)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),hAPP(nat,fun(real,real),hAPP(fun(real,fun(nat,real)),fun(nat,fun(real,real)),combc(real,nat,real),hAPP(fun(real,real),fun(real,fun(nat,real)),hAPP(fun(real,fun(nat,real)),fun(fun(real,real),fun(real,fun(nat,real))),combb(real,fun(nat,real),real),power_power(real)),cos)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),X_2),zero_zero(real)))) # label(fact_3906_DERIV__sin__circle__all__zero) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.81 3848 (all X_1 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(nat,fun(real,real),hAPP(fun(real,fun(nat,real)),fun(nat,fun(real,real)),combc(real,nat,real),hAPP(fun(real,real),fun(real,fun(nat,real)),hAPP(fun(real,fun(nat,real)),fun(fun(real,real),fun(real,fun(nat,real))),combb(real,fun(nat,real),real),power_power(real)),sin)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),X_1),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),hAPP(real,real,cos,X_1))),hAPP(real,real,sin,X_1))))) # label(fact_3907_DERIV__sin__realpow2a) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.81 3849 (all X_1 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(nat,fun(real,real),hAPP(fun(real,fun(nat,real)),fun(nat,fun(real,real)),combc(real,nat,real),hAPP(fun(real,real),fun(real,fun(nat,real)),hAPP(fun(real,fun(nat,real)),fun(fun(real,real),fun(real,fun(nat,real))),combb(real,fun(nat,real),real),power_power(real)),sin)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),X_1),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,cos,X_1)),hAPP(real,real,sin,X_1))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,cos,X_1)),hAPP(real,real,sin,X_1)))))) # label(fact_3908_DERIV__sin__realpow2) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.81 3850 (all V_1 all V_2 ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V_2),pls)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(int,nat,number_number_of(nat),V_1)),hAPP(int,nat,number_number_of(nat),V_2)) = hAPP(int,nat,number_number_of(nat),V_1)) & (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V_2),pls)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(int,nat,number_number_of(nat),V_1)),hAPP(int,nat,number_number_of(nat),V_2)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),hAPP(bool,fun(nat,fun(nat,nat)),if(nat),hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),V_1),hAPP(int,int,uminus_uminus(int),V_2))))),zero_zero(nat)),hAPP(int,nat,nat_1,hAPP(int,int,number_number_of(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),V_1),hAPP(int,int,uminus_uminus(int),V_2)))))))) # label(fact_3909_diff__nat__number__of) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.81 3851 (all X_1 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(nat,fun(real,real),hAPP(fun(real,fun(nat,real)),fun(nat,fun(real,real)),combc(real,nat,real),hAPP(fun(real,real),fun(real,fun(nat,real)),hAPP(fun(real,fun(nat,real)),fun(fun(real,real),fun(real,fun(nat,real))),combb(real,fun(nat,real),real),power_power(real)),cos)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),X_1),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,min))),hAPP(real,real,cos,X_1))),hAPP(real,real,sin,X_1))))) # label(fact_3910_DERIV__cos__realpow2a) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.81 3852 (all X_1 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(nat,fun(real,real),hAPP(fun(real,fun(nat,real)),fun(nat,fun(real,real)),combc(real,nat,real),hAPP(fun(real,real),fun(real,fun(nat,real)),hAPP(fun(real,fun(nat,real)),fun(fun(real,real),fun(real,fun(nat,real))),combb(real,fun(nat,real),real),power_power(real)),cos)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),X_1),hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),hAPP(real,real,cos,X_1))),hAPP(real,real,sin,X_1)))))) # label(fact_3911_DERIV__cos__realpow2b) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.81 3853 (all X_1 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(nat,fun(real,real),hAPP(fun(real,fun(nat,real)),fun(nat,fun(real,real)),combc(real,nat,real),hAPP(fun(real,real),fun(real,fun(nat,real)),hAPP(fun(real,fun(nat,real)),fun(fun(real,real),fun(real,fun(nat,real))),combb(real,fun(nat,real),real),power_power(real)),cos)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),X_1),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,uminus_uminus(real),hAPP(real,real,sin,X_1))),hAPP(real,real,cos,X_1))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,uminus_uminus(real),hAPP(real,real,sin,X_1))),hAPP(real,real,cos,X_1)))))) # label(fact_3912_DERIV__cos__realpow2) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.81 3854 (all X_1 (hAPP(real,real,cos,X_1) != zero_zero(real) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,real)),combs(real,real,real),hAPP(fun(real,real),fun(real,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,fun(real,real))),combb(real,fun(real,real),real),inverse_divide(real)),sin)),cos)),X_1),hAPP(real,real,inverse_inverse(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,cos,X_1)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))))) # label(fact_3913_lemma__DERIV__tan) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.81 3855 (all Y_1 all X_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,real)),combs(real,real,real),hAPP(fun(real,real),fun(real,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,fun(real,real))),combb(real,fun(real,real),real),plus_plus(real)),hAPP(nat,fun(real,real),hAPP(fun(real,fun(nat,real)),fun(nat,fun(real,real)),combc(real,nat,real),hAPP(fun(real,real),fun(real,fun(nat,real)),hAPP(fun(real,fun(nat,real)),fun(fun(real,real),fun(real,fun(nat,real))),combb(real,fun(nat,real),real),power_power(real)),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,real)),combs(real,real,real),hAPP(fun(real,real),fun(real,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,fun(real,real))),combb(real,fun(real,real),real),minus_minus(real)),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,real),fun(fun(real,real),fun(real,real)),combb(real,real,real),sin),hAPP(real,fun(real,real),hAPP(fun(real,fun(real,real)),fun(real,fun(real,real)),combc(real,real,real),plus_plus(real)),Y_1)))),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,real)),combs(real,real,real),hAPP(fun(real,real),fun(real,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,fun(real,real))),combb(real,fun(real,real),real),plus_plus(real)),hAPP(real,fun(real,real),hAPP(fun(real,fun(real,real)),fun(real,fun(real,real)),combc(real,real,real),hAPP(fun(real,real),fun(real,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,fun(real,real))),combb(real,fun(real,real),real),times_times(real)),sin)),hAPP(real,real,cos,Y_1)))),hAPP(real,fun(real,real),hAPP(fun(real,fun(real,real)),fun(real,fun(real,real)),combc(real,real,real),hAPP(fun(real,real),fun(real,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,fun(real,real))),combb(real,fun(real,real),real),times_times(real)),cos)),hAPP(real,real,sin,Y_1)))))),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),hAPP(nat,fun(real,real),hAPP(fun(real,fun(nat,real)),fun(nat,fun(real,real)),combc(real,nat,real),hAPP(fun(real,real),fun(real,fun(nat,real)),hAPP(fun(real,fun(nat,real)),fun(fun(real,real),fun(real,fun(nat,real))),combb(real,fun(nat,real),real),power_power(real)),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,real)),combs(real,real,real),hAPP(fun(real,real),fun(real,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,fun(real,real))),combb(real,fun(real,real),real),minus_minus(real)),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,real),fun(fun(real,real),fun(real,real)),combb(real,real,real),cos),hAPP(real,fun(real,real),hAPP(fun(real,fun(real,real)),fun(real,fun(real,real)),combc(real,real,real),plus_plus(real)),Y_1)))),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,real)),combs(real,real,real),hAPP(fun(real,real),fun(real,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,fun(real,real))),combb(real,fun(real,real),real),minus_minus(real)),hAPP(real,fun(real,real),hAPP(fun(real,fun(real,real)),fun(real,fun(real,real)),combc(real,real,real),hAPP(fun(real,real),fun(real,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,fun(real,real))),combb(real,fun(real,real),real),times_times(real)),cos)),hAPP(real,real,cos,Y_1)))),hAPP(real,fun(real,real),hAPP(fun(real,fun(real,real)),fun(real,fun(real,real)),combc(real,real,real),hAPP(fun(real,real),fun(real,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,fun(real,real))),combb(real,fun(real,real),real),times_times(real)),sin)),hAPP(real,real,sin,Y_1)))))),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),X_2),zero_zero(real)))) # label(fact_3914_lemma__DERIV__sin__cos__add) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.81 3856 (all X_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,real)),combs(real,real,real),hAPP(fun(real,real),fun(real,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,fun(real,real))),combb(real,fun(real,real),real),plus_plus(real)),hAPP(nat,fun(real,real),hAPP(fun(real,fun(nat,real)),fun(nat,fun(real,real)),combc(real,nat,real),hAPP(fun(real,real),fun(real,fun(nat,real)),hAPP(fun(real,fun(nat,real)),fun(fun(real,real),fun(real,fun(nat,real))),combb(real,fun(nat,real),real),power_power(real)),sin)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),hAPP(nat,fun(real,real),hAPP(fun(real,fun(nat,real)),fun(nat,fun(real,real)),combc(real,nat,real),hAPP(fun(real,real),fun(real,fun(nat,real)),hAPP(fun(real,fun(nat,real)),fun(fun(real,real),fun(real,fun(nat,real))),combb(real,fun(nat,real),real),power_power(real)),cos)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),X_2),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),hAPP(real,real,cos,X_2))),hAPP(real,real,sin,X_2))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),hAPP(real,real,cos,X_2))),hAPP(real,real,sin,X_2)))))) # label(fact_3915_DERIV__sin__circle__all) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.81 3857 (all Aa all Ba (hBOOL(hAPP(product_prod(int,int),bool,hAPP(fun(product_prod(int,int),fun(product_prod(int,int),bool)),fun(product_prod(int,int),bool),accp(product_prod(int,int)),norm_frac_rel),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),Aa),Ba))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Ba),zero_zero(int))) -> hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),norm_frac,Aa),Ba) = hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),norm_frac,hAPP(int,int,uminus_uminus(int),Aa)),hAPP(int,int,uminus_uminus(int),Ba))) & (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Ba),zero_zero(int))) -> (Aa = zero_zero(int) | Ba = zero_zero(int) -> hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),norm_frac,Aa),Ba) = hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),zero_zero(int)),one_one(int))) & (-(Aa = zero_zero(int) | Ba = zero_zero(int)) -> hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),norm_frac,Aa),Ba) = hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),Aa),hAPP(int,int,hAPP(int,fun(int,int),int_gcd,Aa),Ba))),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),Ba),hAPP(int,int,hAPP(int,fun(int,int),int_gcd,Aa),Ba))))))) # label(fact_3916_norm__frac_Opsimps) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.81 3858 (all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),X_1)),one_one(real))) -> hBOOL(hAPP(fun(nat,real),bool,monoseq(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),hAPP(real,fun(real,real),inverse_divide(real),one_one(real))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),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),plus_plus(nat)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),times_times(nat)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),one_one(nat)))))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),hAPP(real,fun(nat,real),power_power(real),X_1)),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),plus_plus(nat)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),times_times(nat)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),one_one(nat)))))))) # label(fact_3917_monoseq__arctan__series) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.81 3859 (all X_a (ordered_ab_group_add(X_a) -> (all Aa (hBOOL(hAPP(fun(nat,X_a),bool,monoseq(X_a),Aa)) -> hBOOL(hAPP(fun(nat,X_a),bool,monoseq(X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(X_a,X_a),fun(fun(nat,X_a),fun(nat,X_a)),combb(X_a,X_a,nat),uminus_uminus(X_a)),Aa))))))) # label(fact_3918_monoseq__minus) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.81 3860 (all X_a (order(X_a) -> (all X_3 (hBOOL(hAPP(fun(nat,X_a),bool,monoseq(X_a),X_3)) <-> (all N_2 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(nat,X_a,X_3,N_2)),hAPP(nat,X_a,X_3,hAPP(nat,nat,suc,N_2))))) | (all N_2 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(nat,X_a,X_3,hAPP(nat,nat,suc,N_2))),hAPP(nat,X_a,X_3,N_2)))))))) # label(fact_3919_monoseq__Suc) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.81 3861 (all X_a (order(X_a) -> (all X_3 (hBOOL(hAPP(fun(nat,X_a),bool,monoseq(X_a),X_3)) <-> (all M_3 all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_3),N_2)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(nat,X_a,X_3,M_3)),hAPP(nat,X_a,X_3,N_2))))) | (all M_3 all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_3),N_2)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(nat,X_a,X_3,N_2)),hAPP(nat,X_a,X_3,M_3))))))))) # label(fact_3920_monoseq__def) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.81 3862 (all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_1),one_one(real))) -> hBOOL(hAPP(fun(nat,real),bool,monoseq(real),hAPP(real,fun(nat,real),power_power(real),X_1)))))) # label(fact_3921_monoseq__realpow) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.81 3863 (all A_1 all B ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),zero_zero(int))) -> hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),norm_frac,A_1),B) = hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),norm_frac,hAPP(int,int,uminus_uminus(int),A_1)),hAPP(int,int,uminus_uminus(int),B))) & (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),zero_zero(int))) -> (A_1 = zero_zero(int) | B = zero_zero(int) -> hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),norm_frac,A_1),B) = hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),zero_zero(int)),one_one(int))) & (-(A_1 = zero_zero(int) | B = zero_zero(int)) -> hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),norm_frac,A_1),B) = hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_1),hAPP(int,int,hAPP(int,fun(int,int),int_gcd,A_1),B))),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),B),hAPP(int,int,hAPP(int,fun(int,int),int_gcd,A_1),B))))))) # label(fact_3922_norm__frac_Osimps) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.81 3864 (all Z_1 hAPP(complex,real,arg,Z_1) = hAPP(fun(real,bool),real,hilbert_Eps(real),hAPP(fun(real,bool),fun(real,bool),hAPP(fun(real,fun(bool,bool)),fun(fun(real,bool),fun(real,bool)),combs(real,bool,bool),hAPP(fun(real,bool),fun(real,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(real,bool),fun(real,fun(bool,bool))),combb(bool,fun(bool,bool),real),fconj),hAPP(fun(real,real),fun(real,bool),hAPP(fun(real,bool),fun(fun(real,real),fun(real,bool)),combb(real,bool,real),hAPP(real,fun(real,bool),fequal(real),hAPP(complex,real,re,hAPP(complex,complex,sgn_sgn(complex),Z_1)))),cos))),hAPP(fun(real,bool),fun(real,bool),hAPP(fun(real,fun(bool,bool)),fun(fun(real,bool),fun(real,bool)),combs(real,bool,bool),hAPP(fun(real,bool),fun(real,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(real,bool),fun(real,fun(bool,bool))),combb(bool,fun(bool,bool),real),fconj),hAPP(fun(real,real),fun(real,bool),hAPP(fun(real,bool),fun(fun(real,real),fun(real,bool)),combb(real,bool,real),hAPP(real,fun(real,bool),fequal(real),hAPP(complex,real,im,hAPP(complex,complex,sgn_sgn(complex),Z_1)))),sin))),hAPP(fun(real,bool),fun(real,bool),hAPP(fun(real,fun(bool,bool)),fun(fun(real,bool),fun(real,bool)),combs(real,bool,bool),hAPP(fun(real,bool),fun(real,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(real,bool),fun(real,fun(bool,bool))),combb(bool,fun(bool,bool),real),fconj),hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,uminus_uminus(real),pi)))),hAPP(real,fun(real,bool),hAPP(fun(real,fun(real,bool)),fun(real,fun(real,bool)),combc(real,real,bool),ord_less_eq(real)),pi)))))) # label(fact_3923_arg__def) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.81 3865 (all Aa all Pa (hBOOL(hAPP(int,bool,zprime,Pa)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),Pa)) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,Aa),zero_zero(int)),Pa)) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),quadRes,Pa),Aa)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(fun(int,bool),int,hAPP(fun(int,int),fun(fun(int,bool),int),big_co302546470etprod(int,int),combi(int)),hAPP(fun(fun(int,bool),bool),fun(int,bool),complete_Sup_Sup(fun(int,bool)),hAPP(int,fun(fun(int,bool),bool),hAPP(int,fun(int,fun(fun(int,bool),bool)),setS,Aa),Pa)))),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),Aa),hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),Pa),one_one(int))),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))),Pa))))))) # label(fact_3924_Union__SetS__setprod__prop1) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.81 3866 (all X_b all X_a (comm_monoid_mult(X_a) & ring_1(X_a) -> (all F all A_2 hAPP(int,X_a,ring_1_of_int(X_a),hAPP(fun(X_b,bool),int,hAPP(fun(X_b,int),fun(fun(X_b,bool),int),big_co302546470etprod(X_b,int),F),A_2)) = hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co302546470etprod(X_b,X_a),hAPP(fun(X_b,int),fun(X_b,X_a),hAPP(fun(int,X_a),fun(fun(X_b,int),fun(X_b,X_a)),combb(int,X_a,X_b),ring_1_of_int(X_a)),F)),A_2)))) # label(fact_3925_of__int__setprod) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.81 3867 (all X_b all X_a (comm_monoid_mult(X_a) & semiring_1(X_a) -> (all F all A_2 hAPP(nat,X_a,semiring_1_of_nat(X_a),hAPP(fun(X_b,bool),nat,hAPP(fun(X_b,nat),fun(fun(X_b,bool),nat),big_co302546470etprod(X_b,nat),F),A_2)) = hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co302546470etprod(X_b,X_a),hAPP(fun(X_b,nat),fun(X_b,X_a),hAPP(fun(nat,X_a),fun(fun(X_b,nat),fun(X_b,X_a)),combb(nat,X_a,X_b),semiring_1_of_nat(X_a)),F)),A_2)))) # label(fact_3926_of__nat__setprod) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.81 3868 (all Aa hAPP(fun(int,bool),int,hAPP(fun(int,int),fun(fun(int,bool),int),big_co302546470etprod(int,int),combi(int)),hAPP(int,fun(int,bool),d22set,Aa)) = hAPP(int,int,zfact,Aa)) # label(fact_3927_d22set__prod__zfact) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.81 3869 (all Aa all M (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Aa),M)) -> hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,hAPP(fun(int,bool),int,hAPP(fun(int,int),fun(fun(int,bool),int),big_co302546470etprod(int,int),combi(int)),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),bnorRset,Aa),M))),M) = one_one(int))) # label(fact_3928_Bnor__prod__zgcd) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.81 3870 (all Aa all M all X_1 (X_1 != zero_zero(int) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Aa),M)) -> hAPP(fun(int,bool),int,hAPP(fun(int,int),fun(fun(int,bool),int),big_co302546470etprod(int,int),combi(int)),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,int),fun(fun(int,bool),fun(int,bool)),image(int,int),hAPP(int,fun(int,int),hAPP(fun(int,fun(int,int)),fun(int,fun(int,int)),combc(int,int,int),times_times(int)),X_1)),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),bnorRset,Aa),M))) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(fun(int,bool),int,hAPP(fun(int,int),fun(fun(int,bool),int),big_co302546470etprod(int,int),combi(int)),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),bnorRset,Aa),M))),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),X_1),hAPP(fun(int,bool),nat,finite_card(int),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),bnorRset,Aa),M))))))) # label(fact_3929_Bnor__prod__power) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.81 3871 (all X_1 all Aa all Pa (hBOOL(hAPP(int,bool,zprime,Pa)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),Pa)) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,Aa),zero_zero(int)),Pa)) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),quadRes,Pa),Aa)) -> (hBOOL(hAPP(fun(fun(int,bool),bool),bool,hAPP(fun(int,bool),fun(fun(fun(int,bool),bool),bool),member(fun(int,bool)),X_1),hAPP(int,fun(fun(int,bool),bool),hAPP(int,fun(int,fun(fun(int,bool),bool)),setS,Aa),Pa))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(fun(int,bool),int,hAPP(fun(int,int),fun(fun(int,bool),int),big_co302546470etprod(int,int),combi(int)),X_1)),Aa),Pa)))))))) # label(fact_3930_SetS__setprod__prop) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.81 3872 (all Aa all Pa (hBOOL(hAPP(int,bool,zprime,Pa)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit1,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),Pa)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Aa),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),Pa),one_one(int)))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(fun(int,bool),int,hAPP(fun(int,int),fun(fun(int,bool),int),big_co302546470etprod(int,int),combi(int)),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),wset,Aa),Pa))),one_one(int)),Pa)))))) # label(fact_3931_wset__zcong__prod__1) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.81 3873 (all Aa all Pa (hBOOL(hAPP(int,bool,zprime,Pa)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),Pa)) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,Aa),zero_zero(int)),Pa)) -> hAPP(fun(int,bool),int,hAPP(fun(int,int),fun(fun(int,bool),int),big_co302546470etprod(int,int),combi(int)),hAPP(fun(fun(int,bool),bool),fun(int,bool),complete_Sup_Sup(fun(int,bool)),hAPP(int,fun(fun(int,bool),bool),hAPP(int,fun(int,fun(fun(int,bool),bool)),setS,Aa),Pa))) = hAPP(int,int,zfact,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),Pa),one_one(int))))))) # label(fact_3932_Union__SetS__setprod__prop2) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.81 3874 (all X_a all X_b (comm_monoid_mult(X_b) -> (all Ba all C_1 all Aa all S (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),S)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Aa),S)) -> hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co302546470etprod(X_a,X_b),hAPP(X_b,fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(X_b,fun(X_a,X_b)),combc(X_a,X_b,X_b),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,X_b)),hAPP(fun(X_a,fun(X_b,fun(X_b,X_b))),fun(fun(X_a,X_b),fun(X_a,fun(X_b,X_b))),combs(X_a,X_b,fun(X_b,X_b)),hAPP(fun(X_a,bool),fun(X_a,fun(X_b,fun(X_b,X_b))),hAPP(fun(bool,fun(X_b,fun(X_b,X_b))),fun(fun(X_a,bool),fun(X_a,fun(X_b,fun(X_b,X_b)))),combb(bool,fun(X_b,fun(X_b,X_b)),X_a),if(X_b)),hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,fun(X_a,bool)),fun(X_a,fun(X_a,bool)),combc(X_a,X_a,bool),fequal(X_a)),Aa))),Ba)),C_1)),S) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(X_a,X_b,Ba,Aa)),hAPP(nat,X_b,hAPP(X_b,fun(nat,X_b),power_power(X_b),C_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(fun(X_a,bool),nat,finite_card(X_a),S)),one_one(nat))))) & (-hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Aa),S)) -> hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co302546470etprod(X_a,X_b),hAPP(X_b,fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(X_b,fun(X_a,X_b)),combc(X_a,X_b,X_b),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,X_b)),hAPP(fun(X_a,fun(X_b,fun(X_b,X_b))),fun(fun(X_a,X_b),fun(X_a,fun(X_b,X_b))),combs(X_a,X_b,fun(X_b,X_b)),hAPP(fun(X_a,bool),fun(X_a,fun(X_b,fun(X_b,X_b))),hAPP(fun(bool,fun(X_b,fun(X_b,X_b))),fun(fun(X_a,bool),fun(X_a,fun(X_b,fun(X_b,X_b)))),combb(bool,fun(X_b,fun(X_b,X_b)),X_a),if(X_b)),hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,fun(X_a,bool)),fun(X_a,fun(X_a,bool)),combc(X_a,X_a,bool),fequal(X_a)),Aa))),Ba)),C_1)),S) = hAPP(nat,X_b,hAPP(X_b,fun(nat,X_b),power_power(X_b),C_1),hAPP(fun(X_a,bool),nat,finite_card(X_a),S))))))) # label(fact_3933_setprod__gen__delta) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.82 3875 (all F all A_2 (hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A_2)) -> ((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,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,F,X_2))))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(fun(int,bool),int,hAPP(fun(int,int),fun(fun(int,bool),int),big_co302546470etprod(int,int),F),A_2)))))) # label(fact_3934_transfer__nat__int__sum__prod__closure_I2_J) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.82 3876 (all X_a all F all F_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),F_1)) -> (hAPP(fun(X_a,bool),nat,hAPP(fun(X_a,nat),fun(fun(X_a,bool),nat),big_co302546470etprod(X_a,nat),F),F_1) = one_one(nat) <-> (all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),F_1)) -> hAPP(X_a,nat,F,X_2) = one_one(nat)))))) # label(fact_3935_setprod__eq__1__iff) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.82 3877 (all X_a all F all S (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),S)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(fun(X_a,bool),nat,hAPP(fun(X_a,nat),fun(fun(X_a,bool),nat),big_co302546470etprod(X_a,nat),F),S))) <-> (all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),S)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(X_a,nat,F,X_2)))))))) # label(fact_3936_setprod__pos__nat__iff) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.82 3878 (all X_a all F all A_2 hAPP(nat,real,real_1(nat),hAPP(fun(X_a,bool),nat,hAPP(fun(X_a,nat),fun(fun(X_a,bool),nat),big_co302546470etprod(X_a,nat),F),A_2)) = hAPP(fun(X_a,bool),real,hAPP(fun(X_a,real),fun(fun(X_a,bool),real),big_co302546470etprod(X_a,real),hAPP(fun(X_a,nat),fun(X_a,real),hAPP(fun(nat,real),fun(fun(X_a,nat),fun(X_a,real)),combb(nat,real,X_a),real_1(nat)),F)),A_2)) # label(fact_3937_real__of__nat__setprod) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.82 3879 (all X_a all F all A_2 hAPP(int,real,real_1(int),hAPP(fun(X_a,bool),int,hAPP(fun(X_a,int),fun(fun(X_a,bool),int),big_co302546470etprod(X_a,int),F),A_2)) = hAPP(fun(X_a,bool),real,hAPP(fun(X_a,real),fun(fun(X_a,bool),real),big_co302546470etprod(X_a,real),hAPP(fun(X_a,int),fun(X_a,real),hAPP(fun(int,real),fun(fun(X_a,int),fun(X_a,real)),combb(int,real,X_a),real_1(int)),F)),A_2)) # label(fact_3938_real__of__int__setprod) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.82 3880 (all X_a all F all A_2 hAPP(nat,int,semiring_1_of_nat(int),hAPP(fun(X_a,bool),nat,hAPP(fun(X_a,nat),fun(fun(X_a,bool),nat),big_co302546470etprod(X_a,nat),F),A_2)) = hAPP(fun(X_a,bool),int,hAPP(fun(X_a,int),fun(fun(X_a,bool),int),big_co302546470etprod(X_a,int),hAPP(fun(X_a,nat),fun(X_a,int),hAPP(fun(nat,int),fun(fun(X_a,nat),fun(X_a,int)),combb(nat,int,X_a),semiring_1_of_nat(int)),F)),A_2)) # label(fact_3939_int__setprod) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.82 3881 (all X_a all F all A_2 hAPP(fun(X_a,bool),nat,hAPP(fun(X_a,nat),fun(fun(X_a,bool),nat),big_co302546470etprod(X_a,nat),F),A_2) = hAPP(int,nat,nat_1,hAPP(fun(X_a,bool),int,hAPP(fun(X_a,int),fun(fun(X_a,bool),int),big_co302546470etprod(X_a,int),hAPP(fun(X_a,nat),fun(X_a,int),hAPP(fun(nat,int),fun(fun(X_a,nat),fun(X_a,int)),combb(nat,int,X_a),semiring_1_of_nat(int)),F)),A_2))) # label(fact_3940_transfer__nat__int__sum__prod2_I2_J) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.82 3882 (all X_a (comm_monoid_add(X_a) & comm_monoid_mult(X_a) -> (all F all A_2 hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co302546470etprod(nat,X_a),F),A_2) = hAPP(fun(int,bool),X_a,hAPP(fun(int,X_a),fun(fun(int,bool),X_a),big_co302546470etprod(int,X_a),hAPP(fun(int,nat),fun(int,X_a),hAPP(fun(nat,X_a),fun(fun(int,nat),fun(int,X_a)),combb(nat,X_a,int),F),nat_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_2))))) # label(fact_3941_transfer__nat__int__sum__prod_I2_J) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.82 3883 (all X_a (comm_monoid_add(X_a) & comm_monoid_mult(X_a) -> (all F all A_2 (hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A_2)) -> hAPP(fun(int,bool),X_a,hAPP(fun(int,X_a),fun(fun(int,bool),X_a),big_co302546470etprod(int,X_a),F),A_2) = hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co302546470etprod(nat,X_a),hAPP(fun(nat,int),fun(nat,X_a),hAPP(fun(int,X_a),fun(fun(nat,int),fun(nat,X_a)),combb(int,X_a,nat),F),semiring_1_of_nat(int))),hAPP(fun(int,bool),fun(nat,bool),hAPP(fun(int,nat),fun(fun(int,bool),fun(nat,bool)),image(int,nat),nat_1),A_2)))))) # label(fact_3942_transfer__int__nat__sum__prod_I2_J) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.82 3884 (all X_b all X_a (comm_monoid_mult(X_a) -> (all F all G all A_2 hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co302546470etprod(X_b,X_a),hAPP(fun(X_b,X_a),fun(X_b,X_a),hAPP(fun(X_b,fun(X_a,X_a)),fun(fun(X_b,X_a),fun(X_b,X_a)),combs(X_b,X_a,X_a),hAPP(fun(X_b,X_a),fun(X_b,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_b,X_a),fun(X_b,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),X_b),times_times(X_a)),F)),G)),A_2) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co302546470etprod(X_b,X_a),F),A_2)),hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co302546470etprod(X_b,X_a),G),A_2))))) # label(fact_3943_setprod__timesf) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.82 3885 (all X_b all X_a (comm_monoid_mult(X_a) -> (all A_2 hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co302546470etprod(X_b,X_a),hAPP(X_a,fun(X_b,X_a),combk(X_a,X_b),one_one(X_a))),A_2) = one_one(X_a)))) # label(fact_3944_setprod__1) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.82 3886 (all X_b all X_a (linordered_field(X_a) -> (all F all A_2 hAPP(X_a,X_a,abs_abs(X_a),hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co302546470etprod(X_b,X_a),F),A_2)) = hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co302546470etprod(X_b,X_a),hAPP(fun(X_b,X_a),fun(X_b,X_a),hAPP(fun(X_a,X_a),fun(fun(X_b,X_a),fun(X_b,X_a)),combb(X_a,X_a,X_b),abs_abs(X_a)),F)),A_2)))) # label(fact_3945_abs__setprod) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.82 3887 (all X_a all X_b (comm_semiring_1(X_b) & no_zero_divisors(X_b) -> (all F all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2)) -> (hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co302546470etprod(X_a,X_b),F),A_2) = zero_zero(X_b) <-> (exists X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_2)) & hAPP(X_a,X_b,F,X_2) = zero_zero(X_b)))))))) # label(fact_3946_setprod__zero__iff) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.82 3888 (all X_a all X_b (comm_semiring_1(X_b) -> (all F all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2)) -> ((exists X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_2)) & hAPP(X_a,X_b,F,X_2) = zero_zero(X_b))) -> hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co302546470etprod(X_a,X_b),F),A_2) = zero_zero(X_b)))))) # label(fact_3947_setprod__zero) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.82 3889 (all X_a all X_b (comm_monoid_mult(X_b) -> (all G all A_2 (-hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2)) -> hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co302546470etprod(X_a,X_b),G),A_2) = one_one(X_b))))) # label(fact_3948_setprod_Oinfinite) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.82 3890 (all X_a all X_b (comm_monoid_mult(X_b) -> (all F all A_2 (-hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2)) -> hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co302546470etprod(X_a,X_b),F),A_2) = one_one(X_b))))) # label(fact_3949_setprod__infinite) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.82 3891 (all X_a all X_b (comm_semiring_1(X_b) -> (all F all I all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),I),A_2)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),dvd_dvd(X_b),hAPP(X_a,X_b,F,I)),hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co302546470etprod(X_a,X_b),F),A_2)))))))) # label(fact_3950_dvd__setprod) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.82 3892 (all X_a all X_b (comm_monoid_mult(X_b) -> (all G all H all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2)) -> hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co302546470etprod(X_a,X_b),hAPP(fun(X_a,X_b),fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,X_b)),combs(X_a,X_b,X_b),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,fun(X_b,X_b))),combb(X_b,fun(X_b,X_b),X_a),times_times(X_b)),G)),H)),A_2) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co302546470etprod(X_a,X_b),G),A_2)),hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co302546470etprod(X_a,X_b),H),A_2)))))) # label(fact_3951_setprod_Odistrib) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.82 3893 (all X_a all X_b (comm_monoid_mult(X_b) -> (all Ba all Aa all S (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),S)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Aa),S)) -> hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co302546470etprod(X_a,X_b),hAPP(X_b,fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(X_b,fun(X_a,X_b)),combc(X_a,X_b,X_b),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,X_b)),hAPP(fun(X_a,fun(X_b,fun(X_b,X_b))),fun(fun(X_a,X_b),fun(X_a,fun(X_b,X_b))),combs(X_a,X_b,fun(X_b,X_b)),hAPP(fun(X_a,bool),fun(X_a,fun(X_b,fun(X_b,X_b))),hAPP(fun(bool,fun(X_b,fun(X_b,X_b))),fun(fun(X_a,bool),fun(X_a,fun(X_b,fun(X_b,X_b)))),combb(bool,fun(X_b,fun(X_b,X_b)),X_a),if(X_b)),hAPP(X_a,fun(X_a,bool),fequal(X_a),Aa))),Ba)),one_one(X_b))),S) = hAPP(X_a,X_b,Ba,Aa)) & (-hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Aa),S)) -> hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co302546470etprod(X_a,X_b),hAPP(X_b,fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(X_b,fun(X_a,X_b)),combc(X_a,X_b,X_b),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,X_b)),hAPP(fun(X_a,fun(X_b,fun(X_b,X_b))),fun(fun(X_a,X_b),fun(X_a,fun(X_b,X_b))),combs(X_a,X_b,fun(X_b,X_b)),hAPP(fun(X_a,bool),fun(X_a,fun(X_b,fun(X_b,X_b))),hAPP(fun(bool,fun(X_b,fun(X_b,X_b))),fun(fun(X_a,bool),fun(X_a,fun(X_b,fun(X_b,X_b)))),combb(bool,fun(X_b,fun(X_b,X_b)),X_a),if(X_b)),hAPP(X_a,fun(X_a,bool),fequal(X_a),Aa))),Ba)),one_one(X_b))),S) = one_one(X_b)))))) # label(fact_3952_setprod__delta_H) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.82 3894 (all X_a all X_b (comm_monoid_mult(X_b) -> (all Ba all Aa all S (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),S)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Aa),S)) -> hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co302546470etprod(X_a,X_b),hAPP(X_b,fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(X_b,fun(X_a,X_b)),combc(X_a,X_b,X_b),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,X_b)),hAPP(fun(X_a,fun(X_b,fun(X_b,X_b))),fun(fun(X_a,X_b),fun(X_a,fun(X_b,X_b))),combs(X_a,X_b,fun(X_b,X_b)),hAPP(fun(X_a,bool),fun(X_a,fun(X_b,fun(X_b,X_b))),hAPP(fun(bool,fun(X_b,fun(X_b,X_b))),fun(fun(X_a,bool),fun(X_a,fun(X_b,fun(X_b,X_b)))),combb(bool,fun(X_b,fun(X_b,X_b)),X_a),if(X_b)),hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,fun(X_a,bool)),fun(X_a,fun(X_a,bool)),combc(X_a,X_a,bool),fequal(X_a)),Aa))),Ba)),one_one(X_b))),S) = hAPP(X_a,X_b,Ba,Aa)) & (-hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Aa),S)) -> hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co302546470etprod(X_a,X_b),hAPP(X_b,fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(X_b,fun(X_a,X_b)),combc(X_a,X_b,X_b),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,X_b)),hAPP(fun(X_a,fun(X_b,fun(X_b,X_b))),fun(fun(X_a,X_b),fun(X_a,fun(X_b,X_b))),combs(X_a,X_b,fun(X_b,X_b)),hAPP(fun(X_a,bool),fun(X_a,fun(X_b,fun(X_b,X_b))),hAPP(fun(bool,fun(X_b,fun(X_b,X_b))),fun(fun(X_a,bool),fun(X_a,fun(X_b,fun(X_b,X_b)))),combb(bool,fun(X_b,fun(X_b,X_b)),X_a),if(X_b)),hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,fun(X_a,bool)),fun(X_a,fun(X_a,bool)),combc(X_a,X_a,bool),fequal(X_a)),Aa))),Ba)),one_one(X_b))),S) = one_one(X_b)))))) # label(fact_3953_setprod__delta) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.82 3895 (all X_a all X_b (field_inverse_zero(X_b) -> (all F all G all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2)) -> hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co302546470etprod(X_a,X_b),hAPP(fun(X_a,X_b),fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,X_b)),combs(X_a,X_b,X_b),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,fun(X_b,X_b))),combb(X_b,fun(X_b,X_b),X_a),inverse_divide(X_b)),F)),G)),A_2) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),inverse_divide(X_b),hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co302546470etprod(X_a,X_b),F),A_2)),hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co302546470etprod(X_a,X_b),G),A_2)))))) # label(fact_3954_setprod__dividef) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.82 3896 (all X_a all X_b (comm_monoid_mult(X_b) & dvd(X_b) -> (all F all A_2 all B_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),B_1)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_2),B_1)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),dvd_dvd(X_b),hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co302546470etprod(X_a,X_b),F),A_2)),hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co302546470etprod(X_a,X_b),F),B_1)))))))) # label(fact_3955_setprod__dvd__setprod__subset) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.82 3897 (all X_a all X_b (comm_monoid_mult(X_b) -> (all Y_1 all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2)) -> hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co302546470etprod(X_a,X_b),hAPP(X_b,fun(X_a,X_b),combk(X_b,X_a),Y_1)),A_2) = hAPP(nat,X_b,hAPP(X_b,fun(nat,X_b),power_power(X_b),Y_1),hAPP(fun(X_a,bool),nat,finite_card(X_a),A_2)))))) # label(fact_3956_setprod__constant) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.82 3898 (all X_a all X_b (comm_monoid_mult(X_b) -> (all F all S all T_4 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),T_4)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),S),T_4)) -> ((all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),T_4),S))) -> hAPP(X_a,X_b,F,X_2) = one_one(X_b))) -> hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co302546470etprod(X_a,X_b),F),T_4) = hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co302546470etprod(X_a,X_b),F),S))))))) # label(fact_3957_setprod__mono__one__right) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.82 3899 (all X_a all X_b (comm_monoid_mult(X_b) -> (all F all S all T_4 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),T_4)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),S),T_4)) -> ((all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),T_4),S))) -> hAPP(X_a,X_b,F,X_2) = one_one(X_b))) -> hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co302546470etprod(X_a,X_b),F),S) = hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co302546470etprod(X_a,X_b),F),T_4))))))) # label(fact_3958_setprod__mono__one__left) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.82 3900 (all X_a (comm_monoid_add(X_a) & comm_monoid_mult(X_a) -> (all F all G all A_2 all B_1 (A_2 = B_1 -> (hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,B_1)) -> ((all X_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X_2)) -> hAPP(int,X_a,F,X_2) = hAPP(int,X_a,G,X_2))) -> hAPP(fun(int,bool),X_a,hAPP(fun(int,X_a),fun(fun(int,bool),X_a),big_co302546470etprod(int,X_a),F),A_2) = hAPP(fun(int,bool),X_a,hAPP(fun(int,X_a),fun(fun(int,bool),X_a),big_co302546470etprod(int,X_a),G),B_1))))))) # label(fact_3959_transfer__nat__int__sum__prod__cong_I2_J) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.82 3901 (all X_a all F all S (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),S)) -> ((all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),S)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(X_a,nat,F,X_2))))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(fun(X_a,bool),nat,hAPP(fun(X_a,nat),fun(fun(X_a,bool),nat),big_co302546470etprod(X_a,nat),F),S)))))) # label(fact_3960_setprod__pos__nat) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.82 3902 (all X_a all X_b all Ba all F all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Ba),hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),A_2))) -> -(all X_2 (ti(X_a,Ba) = hAPP(X_b,X_a,F,X_2) -> -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_2)))))) # label(fact_3961_imageE) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.82 3903 (all X_a all X_b (comm_semiring_1(X_b) -> (all F all G all A_2 all B_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),B_1)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_2),B_1)) -> ((all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_2)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),dvd_dvd(X_b),hAPP(X_a,X_b,F,X_2)),hAPP(X_a,X_b,G,X_2))))) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),dvd_dvd(X_b),hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co302546470etprod(X_a,X_b),F),A_2)),hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co302546470etprod(X_a,X_b),G),B_1))))))))) # label(fact_3962_setprod__dvd__setprod__subset2) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.82 3904 (all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),X_1)),one_one(real))) -> hAPP(real,real,arctan,X_1) = hAPP(fun(nat,real),real,suminf(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),min)))),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),hAPP(real,fun(real,real),inverse_divide(real),one_one(real))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),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),plus_plus(nat)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),times_times(nat)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),one_one(nat)))))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),hAPP(real,fun(nat,real),power_power(real),X_1)),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),plus_plus(nat)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),times_times(nat)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),one_one(nat)))))))) # label(fact_3963_arctan__series) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.82 3905 (all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,abs_abs(real),X_1)),one_one(real))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(fun(real,fun(nat,real)),fun(real,real),hAPP(fun(fun(nat,real),real),fun(fun(real,fun(nat,real)),fun(real,real)),combb(fun(nat,real),real,real),suminf(real)),hAPP(fun(real,fun(nat,real)),fun(real,fun(nat,real)),hAPP(fun(fun(nat,real),fun(nat,real)),fun(fun(real,fun(nat,real)),fun(real,fun(nat,real))),combb(fun(nat,real),fun(nat,real),real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),min))))),hAPP(fun(real,fun(nat,real)),fun(real,fun(nat,real)),hAPP(fun(fun(nat,real),fun(nat,real)),fun(fun(real,fun(nat,real)),fun(real,fun(nat,real))),combb(fun(nat,real),fun(nat,real),real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),hAPP(real,fun(real,real),inverse_divide(real),one_one(real))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),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),plus_plus(nat)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),times_times(nat)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),one_one(nat))))))),hAPP(fun(nat,nat),fun(real,fun(nat,real)),hAPP(fun(real,fun(fun(nat,nat),fun(nat,real))),fun(fun(nat,nat),fun(real,fun(nat,real))),combc(real,fun(nat,nat),fun(nat,real)),hAPP(fun(real,fun(nat,real)),fun(real,fun(fun(nat,nat),fun(nat,real))),hAPP(fun(fun(nat,real),fun(fun(nat,nat),fun(nat,real))),fun(fun(real,fun(nat,real)),fun(real,fun(fun(nat,nat),fun(nat,real)))),combb(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),real),combb(nat,real,nat)),power_power(real))),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),plus_plus(nat)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),times_times(nat)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),one_one(nat))))))),X_1),hAPP(fun(nat,real),real,suminf(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),min)))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),hAPP(real,fun(nat,real),power_power(real),X_1)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),times_times(nat)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))))))) # label(fact_3964_DERIV__arctan__series) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.82 3906 (all X_a (comm_monoid_add(X_a) & t2_space(X_a) -> hAPP(fun(nat,X_a),X_a,suminf(X_a),hAPP(X_a,fun(nat,X_a),combk(X_a,nat),zero_zero(X_a))) = zero_zero(X_a))) # label(fact_3965_suminf__zero) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.82 3907 (all X_1 hAPP(real,real,sin,X_1) = hAPP(fun(nat,real),real,suminf(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),sin_coeff)),hAPP(real,fun(nat,real),power_power(real),X_1)))) # label(fact_3966_sin__def) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.82 3908 (all X_2 hAPP(real,real,sin,X_2) = hAPP(fun(nat,real),real,suminf(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),sin_coeff)),hAPP(real,fun(nat,real),power_power(real),X_2)))) # label(fact_3967_lemma__sin__ext) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.82 3909 (all X_1 hAPP(real,real,cos,X_1) = hAPP(fun(nat,real),real,suminf(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),cos_coeff)),hAPP(real,fun(nat,real),power_power(real),X_1)))) # label(fact_3968_cos__def) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.82 3910 (all X_2 hAPP(real,real,cos,X_2) = hAPP(fun(nat,real),real,suminf(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),cos_coeff)),hAPP(real,fun(nat,real),power_power(real),X_2)))) # label(fact_3969_lemma__cos__ext) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.82 3911 (all X_a (real_n2089651433ebra_1(X_a) -> (all F hAPP(fun(nat,X_a),X_a,suminf(X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),times_times(X_a)),F)),hAPP(X_a,fun(nat,X_a),power_power(X_a),zero_zero(X_a)))) = hAPP(nat,X_a,F,zero_zero(nat))))) # label(fact_3970_powser__zero) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.82 3912 (all X_1 hAPP(real,real,uminus_uminus(real),hAPP(real,real,sin,X_1)) = hAPP(fun(nat,real),real,suminf(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),uminus_uminus(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),sin_coeff)),hAPP(real,fun(nat,real),power_power(real),X_1))))) # label(fact_3971_lemma__sin__minus) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.82 3913 (all X_1 hAPP(real,real,exp(real),X_1) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),one_one(real)),X_1)),hAPP(fun(nat,real),real,suminf(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),inverse_inverse(real)),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),hAPP(fun(nat,nat),fun(nat,nat),hAPP(fun(nat,nat),fun(fun(nat,nat),fun(nat,nat)),combb(nat,nat,nat),fact_fact(nat)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),hAPP(real,fun(nat,real),power_power(real),X_1)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))))) # label(fact_3972_exp__first__two__terms) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.82 3914 (all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_1),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) -> hAPP(real,real,ln,X_1) = hAPP(fun(nat,real),real,suminf(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),min)))),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),hAPP(real,fun(real,real),inverse_divide(real),one_one(real))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),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(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),X_1),one_one(real)))),suc)))))) # label(fact_3974_ln__series) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.82 3915 (all X_a (ring_1(X_a) -> (all K ((K = zero_zero(int) -> hAPP(int,X_a,ring_1_of_int(X_a),K) = zero_zero(X_a)) & (K != zero_zero(int) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),zero_zero(int))) -> hAPP(int,X_a,ring_1_of_int(X_a),K) = hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(int,X_a,ring_1_of_int(X_a),hAPP(int,int,uminus_uminus(int),K)))) & (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),zero_zero(int))) -> hAPP(int,X_a,ring_1_of_int(X_a),K) = hAPP(product_prod(int,int),X_a,hAPP(fun(int,fun(int,X_a)),fun(product_prod(int,int),X_a),product_prod_case(int,int,X_a),hAPP(fun(int,X_a),fun(int,fun(int,X_a)),hAPP(fun(int,fun(X_a,fun(int,X_a))),fun(fun(int,X_a),fun(int,fun(int,X_a))),combs(int,X_a,fun(int,X_a)),hAPP(fun(int,fun(int,fun(X_a,X_a))),fun(int,fun(X_a,fun(int,X_a))),hAPP(fun(fun(int,fun(X_a,X_a)),fun(X_a,fun(int,X_a))),fun(fun(int,fun(int,fun(X_a,X_a))),fun(int,fun(X_a,fun(int,X_a)))),combb(fun(int,fun(X_a,X_a)),fun(X_a,fun(int,X_a)),int),combc(int,X_a,X_a)),hAPP(fun(int,X_a),fun(int,fun(int,fun(X_a,X_a))),hAPP(fun(X_a,fun(int,fun(X_a,X_a))),fun(fun(int,X_a),fun(int,fun(int,fun(X_a,X_a)))),combb(X_a,fun(int,fun(X_a,X_a)),int),hAPP(fun(int,fun(X_a,fun(X_a,X_a))),fun(X_a,fun(int,fun(X_a,X_a))),combc(int,X_a,fun(X_a,X_a)),hAPP(fun(int,bool),fun(int,fun(X_a,fun(X_a,X_a))),hAPP(fun(bool,fun(X_a,fun(X_a,X_a))),fun(fun(int,bool),fun(int,fun(X_a,fun(X_a,X_a)))),combb(bool,fun(X_a,fun(X_a,X_a)),int),if(X_a)),hAPP(int,fun(int,bool),hAPP(fun(int,fun(int,bool)),fun(int,fun(int,bool)),combc(int,int,bool),fequal(int)),zero_zero(int))))),hAPP(fun(int,X_a),fun(int,X_a),hAPP(fun(int,fun(X_a,X_a)),fun(fun(int,X_a),fun(int,X_a)),combs(int,X_a,X_a),hAPP(fun(int,X_a),fun(int,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(int,X_a),fun(int,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),int),plus_plus(X_a)),ring_1_of_int(X_a))),ring_1_of_int(X_a))))),hAPP(X_a,fun(int,X_a),hAPP(fun(int,fun(X_a,X_a)),fun(X_a,fun(int,X_a)),combc(int,X_a,X_a),hAPP(fun(int,X_a),fun(int,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(int,X_a),fun(int,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),int),plus_plus(X_a)),hAPP(fun(int,X_a),fun(int,X_a),hAPP(fun(int,fun(X_a,X_a)),fun(fun(int,X_a),fun(int,X_a)),combs(int,X_a,X_a),hAPP(fun(int,X_a),fun(int,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(int,X_a),fun(int,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),int),plus_plus(X_a)),ring_1_of_int(X_a))),ring_1_of_int(X_a)))),one_one(X_a)))),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),divmod_int,K),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))))))) # label(fact_3975_of__int__num) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.82 3916 (all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),X_1)),one_one(real))) -> hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),min)))),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),hAPP(real,fun(real,real),inverse_divide(real),one_one(real))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),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),plus_plus(nat)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),times_times(nat)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),one_one(nat)))))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),hAPP(real,fun(nat,real),power_power(real),X_1)),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),plus_plus(nat)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),times_times(nat)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),one_one(nat))))))))) # label(fact_3976_summable__arctan__series) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.82 3917 (all X_a (comm_monoid_add(X_a) & topological_space(X_a) -> hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),hAPP(X_a,fun(nat,X_a),combk(X_a,nat),zero_zero(X_a)))))) # label(fact_3977_summable__zero) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.82 3918 (all X_c all X_a all X_b all F all Aa all Ba all A_2 (hBOOL(hAPP(fun(product_prod(X_a,X_b),bool),bool,hAPP(product_prod(X_a,X_b),fun(fun(product_prod(X_a,X_b),bool),bool),member(product_prod(X_a,X_b)),hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),Aa),Ba)),A_2)) -> hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),hAPP(X_b,X_c,hAPP(X_a,fun(X_b,X_c),F,Aa),Ba)),hAPP(fun(product_prod(X_a,X_b),bool),fun(X_c,bool),hAPP(fun(product_prod(X_a,X_b),X_c),fun(fun(product_prod(X_a,X_b),bool),fun(X_c,bool)),image(product_prod(X_a,X_b),X_c),hAPP(fun(X_a,fun(X_b,X_c)),fun(product_prod(X_a,X_b),X_c),product_prod_case(X_a,X_b,X_c),F)),A_2))))) # label(fact_3978_pair__imageI) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.82 3919 (all X_a (real_normed_field(X_a) -> (all Y_3 all X_3 (hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),X_3)) -> (hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),Y_3)) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(fun(nat,X_a),X_a,suminf(X_a),X_3)),hAPP(fun(nat,X_a),X_a,suminf(X_a),Y_3)) = hAPP(fun(nat,X_a),X_a,suminf(X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),plus_plus(X_a)),X_3)),Y_3))))))) # label(fact_3979_suminf__add) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.82 3920 (all X_a (real_normed_field(X_a) -> (all Y_3 all X_3 (hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),X_3)) -> (hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),Y_3)) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(fun(nat,X_a),X_a,suminf(X_a),X_3)),hAPP(fun(nat,X_a),X_a,suminf(X_a),Y_3)) = hAPP(fun(nat,X_a),X_a,suminf(X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),minus_minus(X_a)),X_3)),Y_3))))))) # label(fact_3980_suminf__diff) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.82 3921 (all X_a (real_normed_field(X_a) -> (all C_1 all F (hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),F)) -> hAPP(fun(nat,X_a),X_a,suminf(X_a),hAPP(X_a,fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(X_a,fun(nat,X_a)),combc(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),inverse_divide(X_a)),F)),C_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),hAPP(fun(nat,X_a),X_a,suminf(X_a),F)),C_1))))) # label(fact_3981_suminf__divide) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.82 3922 (all X_a (real_normed_field(X_a) -> (all Y_1 all X_3 (hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),X_3)) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),hAPP(fun(nat,X_a),X_a,suminf(X_a),X_3)),Y_1) = hAPP(fun(nat,X_a),X_a,suminf(X_a),hAPP(X_a,fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(X_a,fun(nat,X_a)),combc(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),inverse_divide(X_a)),X_3)),Y_1)))))) # label(fact_3982_divide_Osuminf) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.82 3923 (all X_a (real_normed_algebra(X_a) -> (all Y_1 all X_3 (hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),X_3)) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(fun(nat,X_a),X_a,suminf(X_a),X_3)),Y_1) = hAPP(fun(nat,X_a),X_a,suminf(X_a),hAPP(X_a,fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(X_a,fun(nat,X_a)),combc(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),times_times(X_a)),X_3)),Y_1)))))) # label(fact_3983_mult__left_Osuminf) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.82 3924 (all X_a (real_normed_algebra(X_a) -> (all X_1 all X_3 (hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),X_3)) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X_1),hAPP(fun(nat,X_a),X_a,suminf(X_a),X_3)) = hAPP(fun(nat,X_a),X_a,suminf(X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(X_a,X_a),fun(fun(nat,X_a),fun(nat,X_a)),combb(X_a,X_a,nat),hAPP(X_a,fun(X_a,X_a),times_times(X_a),X_1)),X_3)))))) # label(fact_3984_mult__right_Osuminf) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.82 3925 (all X_a (real_normed_algebra(X_a) -> (all C_1 all F (hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),F)) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(fun(nat,X_a),X_a,suminf(X_a),F)),C_1) = hAPP(fun(nat,X_a),X_a,suminf(X_a),hAPP(X_a,fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(X_a,fun(nat,X_a)),combc(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),times_times(X_a)),F)),C_1)))))) # label(fact_3985_suminf__mult2) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.82 3926 (all X_a (real_normed_algebra(X_a) -> (all C_1 all F (hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),F)) -> hAPP(fun(nat,X_a),X_a,suminf(X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(X_a,X_a),fun(fun(nat,X_a),fun(nat,X_a)),combb(X_a,X_a,nat),hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1)),F)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1),hAPP(fun(nat,X_a),X_a,suminf(X_a),F)))))) # label(fact_3986_suminf__mult) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.82 3927 (all X_a (real_normed_field(X_a) -> (all X_3 (hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),X_3)) -> hAPP(fun(nat,X_a),X_a,suminf(X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(X_a,X_a),fun(fun(nat,X_a),fun(nat,X_a)),combb(X_a,X_a,nat),uminus_uminus(X_a)),X_3)) = hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(fun(nat,X_a),X_a,suminf(X_a),X_3)))))) # label(fact_3987_suminf__minus) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.82 3928 (all X_b all X_c all X_a all F all Pa hAPP(product_prod(X_b,X_c),X_a,hAPP(fun(X_b,fun(X_c,X_a)),fun(product_prod(X_b,X_c),X_a),product_prod_case(X_b,X_c,X_a),F),Pa) = hAPP(X_c,X_a,hAPP(X_b,fun(X_c,X_a),F,hAPP(product_prod(X_b,X_c),X_b,product_fst(X_b,X_c),Pa)),hAPP(product_prod(X_b,X_c),X_c,product_snd(X_b,X_c),Pa))) # label(fact_3988_prod__case__beta) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.82 3929 (all X_a all X_b all X_c produc1605651328_split(X_a,X_b,X_c) = product_prod_case(X_a,X_b,X_c)) # label(fact_3989_internal__split__def) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.82 3930 (all X_b all X_c all X_a all F1 all Aa all Ba hAPP(product_prod(X_b,X_c),X_a,hAPP(fun(X_b,fun(X_c,X_a)),fun(product_prod(X_b,X_c),X_a),product_prod_case(X_b,X_c,X_a),F1),hAPP(X_c,product_prod(X_b,X_c),hAPP(X_b,fun(X_c,product_prod(X_b,X_c)),product_Pair(X_b,X_c),Aa),Ba)) = hAPP(X_c,X_a,hAPP(X_b,fun(X_c,X_a),F1,Aa),Ba)) # label(fact_3990_Product__Type_Oprod_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.82 3931 (all X_b all X_c all X_a all F all Aa all Ba hAPP(product_prod(X_b,X_c),X_a,hAPP(fun(X_b,fun(X_c,X_a)),fun(product_prod(X_b,X_c),X_a),product_prod_case(X_b,X_c,X_a),F),hAPP(X_c,product_prod(X_b,X_c),hAPP(X_b,fun(X_c,product_prod(X_b,X_c)),product_Pair(X_b,X_c),Aa),Ba)) = hAPP(X_c,X_a,hAPP(X_b,fun(X_c,X_a),F,Aa),Ba)) # label(fact_3991_split__conv) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.82 3932 (all X_a (banach(X_a) -> (all F all G ((exists N_3 all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_3),N_2)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),hAPP(nat,X_a,F,N_2))),hAPP(nat,real,G,N_2))))) -> (hBOOL(hAPP(fun(nat,real),bool,summable(real),G)) -> hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),F))))))) # label(fact_3992_summable__comparison__test) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.82 3933 (all X_a all X_b all X_c all F hAPP(fun(X_a,fun(X_b,X_c)),fun(product_prod(X_a,X_b),X_c),product_prod_case(X_a,X_b,X_c),hAPP(fun(product_prod(X_a,X_b),X_c),fun(X_a,fun(X_b,X_c)),product_curry(X_a,X_b,X_c),F)) = ti(fun(product_prod(X_a,X_b),X_c),F)) # label(fact_3993_split__curry) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.82 3934 (all X_a all X_b all X_c all F hAPP(fun(product_prod(X_a,X_b),X_c),fun(X_a,fun(X_b,X_c)),product_curry(X_a,X_b,X_c),hAPP(fun(X_a,fun(X_b,X_c)),fun(product_prod(X_a,X_b),X_c),product_prod_case(X_a,X_b,X_c),F)) = ti(fun(X_a,fun(X_b,X_c)),F)) # label(fact_3994_curry__split) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.82 3935 (all X_c all X_a all X_b all C_1 all Pa all Qa (ti(product_prod(X_a,X_b),Pa) = ti(product_prod(X_a,X_b),Qa) -> hAPP(product_prod(X_a,X_b),X_c,hAPP(fun(X_a,fun(X_b,X_c)),fun(product_prod(X_a,X_b),X_c),product_prod_case(X_a,X_b,X_c),C_1),Pa) = hAPP(product_prod(X_a,X_b),X_c,hAPP(fun(X_a,fun(X_b,X_c)),fun(product_prod(X_a,X_b),X_c),product_prod_case(X_a,X_b,X_c),C_1),Qa))) # label(fact_3995_split__weak__cong) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.82 3936 (all X_a (real_normed_field(X_a) & banach(X_a) -> (all Z_1 all F all X_1 (hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),times_times(X_a)),F)),hAPP(X_a,fun(nat,X_a),power_power(X_a),X_1)))) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,norm_norm(X_a),Z_1)),hAPP(X_a,real,norm_norm(X_a),X_1))) -> hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,X_a),fun(nat,real),hAPP(fun(X_a,real),fun(fun(nat,X_a),fun(nat,real)),combb(X_a,real,nat),norm_norm(X_a)),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),times_times(X_a)),F)),hAPP(X_a,fun(nat,X_a),power_power(X_a),Z_1)))))))))) # label(fact_3996_powser__insidea) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.82 3937 (all F (hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),abs_abs(real)),F))) -> hBOOL(hAPP(fun(nat,real),bool,summable(real),F)))) # label(fact_3997_summable__rabs__cancel) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.82 3938 (all X_a (real_normed_field(X_a) -> (all X_3 (hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),X_3)) -> hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(X_a,X_a),fun(fun(nat,X_a),fun(nat,X_a)),combb(X_a,X_a,nat),uminus_uminus(X_a)),X_3))))))) # label(fact_3998_summable__minus) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.82 3939 (all X_a (real_normed_algebra(X_a) -> (all C_1 all F (hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),F)) -> hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(X_a,X_a),fun(fun(nat,X_a),fun(nat,X_a)),combb(X_a,X_a,nat),hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1)),F))))))) # label(fact_3999_summable__mult) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.82 3940 (all X_a (real_normed_algebra(X_a) -> (all C_1 all F (hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),F)) -> hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),hAPP(X_a,fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(X_a,fun(nat,X_a)),combc(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),times_times(X_a)),F)),C_1))))))) # label(fact_4000_summable__mult2) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.82 3941 (all X_a (real_normed_algebra(X_a) -> (all X_1 all X_3 (hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),X_3)) -> hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(X_a,X_a),fun(fun(nat,X_a),fun(nat,X_a)),combb(X_a,X_a,nat),hAPP(X_a,fun(X_a,X_a),times_times(X_a),X_1)),X_3))))))) # label(fact_4001_mult__right_Osummable) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.82 3942 (all X_a (real_normed_algebra(X_a) -> (all Y_1 all X_3 (hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),X_3)) -> hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),hAPP(X_a,fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(X_a,fun(nat,X_a)),combc(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),times_times(X_a)),X_3)),Y_1))))))) # label(fact_4002_mult__left_Osummable) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.82 3943 (all X_a (banach(X_a) -> (all F (hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,X_a),fun(nat,real),hAPP(fun(X_a,real),fun(fun(nat,X_a),fun(nat,real)),combb(X_a,real,nat),norm_norm(X_a)),F))) -> hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),F)))))) # label(fact_4003_summable__norm__cancel) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.82 3944 (all X_b all X_c all X_a all X_d all X_e all F all G all Pa hAPP(product_prod(X_b,X_c),X_a,hAPP(fun(X_b,fun(X_c,X_a)),fun(product_prod(X_b,X_c),X_a),product_prod_case(X_b,X_c,X_a),F),hAPP(product_prod(X_d,X_e),product_prod(X_b,X_c),hAPP(fun(X_d,fun(X_e,product_prod(X_b,X_c))),fun(product_prod(X_d,X_e),product_prod(X_b,X_c)),product_prod_case(X_d,X_e,product_prod(X_b,X_c)),G),Pa)) = hAPP(product_prod(X_d,X_e),X_a,hAPP(fun(X_d,fun(X_e,X_a)),fun(product_prod(X_d,X_e),X_a),product_prod_case(X_d,X_e,X_a),hAPP(fun(X_d,fun(X_e,product_prod(X_b,X_c))),fun(X_d,fun(X_e,X_a)),hAPP(fun(fun(X_e,product_prod(X_b,X_c)),fun(X_e,X_a)),fun(fun(X_d,fun(X_e,product_prod(X_b,X_c))),fun(X_d,fun(X_e,X_a))),combb(fun(X_e,product_prod(X_b,X_c)),fun(X_e,X_a),X_d),hAPP(fun(product_prod(X_b,X_c),X_a),fun(fun(X_e,product_prod(X_b,X_c)),fun(X_e,X_a)),combb(product_prod(X_b,X_c),X_a,X_e),hAPP(fun(X_b,fun(X_c,X_a)),fun(product_prod(X_b,X_c),X_a),product_prod_case(X_b,X_c,X_a),F))),G)),Pa)) # label(fact_4004_split__twice) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.82 3945 (all X_b all X_a all Pa hAPP(product_prod(X_b,X_a),X_a,product_snd(X_b,X_a),Pa) = hAPP(product_prod(X_b,X_a),X_a,hAPP(fun(X_b,fun(X_a,X_a)),fun(product_prod(X_b,X_a),X_a),product_prod_case(X_b,X_a,X_a),hAPP(fun(X_a,X_a),fun(X_b,fun(X_a,X_a)),combk(fun(X_a,X_a),X_b),combi(X_a))),Pa)) # label(fact_4005_snd__def) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.82 3946 (all X_a all X_b all Pa hAPP(product_prod(X_a,X_b),X_a,product_fst(X_a,X_b),Pa) = hAPP(product_prod(X_a,X_b),X_a,hAPP(fun(X_a,fun(X_b,X_a)),fun(product_prod(X_a,X_b),X_a),product_prod_case(X_a,X_b,X_a),combk(X_a,X_b)),Pa)) # label(fact_4006_fst__def) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.82 3947 (all X_a (real_algebra_1(X_a) & real_normed_vector(X_a) -> (all X_3 (hBOOL(hAPP(fun(nat,real),bool,summable(real),X_3)) -> hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),hAPP(fun(nat,real),fun(nat,X_a),hAPP(fun(real,X_a),fun(fun(nat,real),fun(nat,X_a)),combb(real,X_a,nat),of_real(X_a)),X_3))))))) # label(fact_4007_of__real_Osummable) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.82 3948 (all X_a (real_normed_field(X_a) -> (all Y_1 all X_3 (hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),X_3)) -> hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),hAPP(X_a,fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(X_a,fun(nat,X_a)),combc(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),inverse_divide(X_a)),X_3)),Y_1))))))) # label(fact_4008_divide_Osummable) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.82 3949 (all X_a (real_normed_field(X_a) -> (all C_1 all F (hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),F)) -> hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),hAPP(X_a,fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(X_a,fun(nat,X_a)),combc(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),inverse_divide(X_a)),F)),C_1))))))) # label(fact_4009_summable__divide) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.82 3950 (all X_a all X_b all X_c all F hAPP(fun(X_a,fun(X_b,X_c)),fun(product_prod(X_a,X_b),X_c),product_prod_case(X_a,X_b,X_c),hAPP(fun(X_a,fun(X_b,product_prod(X_a,X_b))),fun(X_a,fun(X_b,X_c)),hAPP(fun(fun(X_b,product_prod(X_a,X_b)),fun(X_b,X_c)),fun(fun(X_a,fun(X_b,product_prod(X_a,X_b))),fun(X_a,fun(X_b,X_c))),combb(fun(X_b,product_prod(X_a,X_b)),fun(X_b,X_c),X_a),hAPP(fun(product_prod(X_a,X_b),X_c),fun(fun(X_b,product_prod(X_a,X_b)),fun(X_b,X_c)),combb(product_prod(X_a,X_b),X_c,X_b),F)),product_Pair(X_a,X_b))) = ti(fun(product_prod(X_a,X_b),X_c),F)) # label(fact_4010_split__eta) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.82 3951 (all X_a (real_normed_field(X_a) -> (all Y_3 all X_3 (hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),X_3)) -> (hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),Y_3)) -> hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),minus_minus(X_a)),X_3)),Y_3)))))))) # label(fact_4011_summable__diff) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.82 3952 (all X_a (real_normed_vector(X_a) -> (all K all F (hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),F)) -> hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),hAPP(fun(nat,nat),fun(nat,X_a),hAPP(fun(nat,X_a),fun(fun(nat,nat),fun(nat,X_a)),combb(nat,X_a,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)))))))) # label(fact_4012_summable__ignore__initial__segment) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.82 3953 (all X_a (real_normed_field(X_a) -> (all Y_3 all X_3 (hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),X_3)) -> (hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),Y_3)) -> hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),plus_plus(X_a)),X_3)),Y_3)))))))) # label(fact_4013_summable__add) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.82 3954 (all X_a all X_b all X_c all X_2 all Xa hAPP(product_prod(X_a,X_b),X_c,hAPP(fun(X_a,fun(X_b,X_c)),fun(product_prod(X_a,X_b),X_c),product_prod_case(X_a,X_b,X_c),X_2),Xa) = hAPP(X_b,X_c,hAPP(X_a,fun(X_b,X_c),X_2,hAPP(product_prod(X_a,X_b),X_a,product_fst(X_a,X_b),Xa)),hAPP(product_prod(X_a,X_b),X_b,product_snd(X_a,X_b),Xa))) # label(fact_4014_split__def) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.82 3955 (all X_a all X_b all X_c all X_d all F all G hAPP(fun(product_prod(X_a,X_b),X_b),fun(product_prod(X_a,X_b),X_c),hAPP(fun(product_prod(X_a,X_b),fun(X_b,X_c)),fun(fun(product_prod(X_a,X_b),X_b),fun(product_prod(X_a,X_b),X_c)),combs(product_prod(X_a,X_b),X_b,X_c),hAPP(fun(product_prod(X_a,X_b),X_d),fun(product_prod(X_a,X_b),fun(X_b,X_c)),hAPP(fun(X_d,fun(X_b,X_c)),fun(fun(product_prod(X_a,X_b),X_d),fun(product_prod(X_a,X_b),fun(X_b,X_c))),combb(X_d,fun(X_b,X_c),product_prod(X_a,X_b)),F),hAPP(fun(product_prod(X_a,X_b),X_a),fun(product_prod(X_a,X_b),X_d),hAPP(fun(X_a,X_d),fun(fun(product_prod(X_a,X_b),X_a),fun(product_prod(X_a,X_b),X_d)),combb(X_a,X_d,product_prod(X_a,X_b)),G),product_fst(X_a,X_b)))),product_snd(X_a,X_b)) = hAPP(fun(X_a,fun(X_b,X_c)),fun(product_prod(X_a,X_b),X_c),product_prod_case(X_a,X_b,X_c),hAPP(fun(X_a,X_d),fun(X_a,fun(X_b,X_c)),hAPP(fun(X_d,fun(X_b,X_c)),fun(fun(X_a,X_d),fun(X_a,fun(X_b,X_c))),combb(X_d,fun(X_b,X_c),X_a),F),G))) # label(fact_4015_split__comp__eq) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.82 3956 (all X_b all X_c all X_a all P_1 all Z_1 hAPP(product_prod(X_b,X_c),X_a,hAPP(fun(X_b,fun(X_c,X_a)),fun(product_prod(X_b,X_c),X_a),product_prod_case(X_b,X_c,X_a),P_1),Z_1) = hAPP(X_c,X_a,hAPP(X_b,fun(X_c,X_a),P_1,hAPP(product_prod(X_b,X_c),X_b,product_fst(X_b,X_c),Z_1)),hAPP(product_prod(X_b,X_c),X_c,product_snd(X_b,X_c),Z_1))) # label(fact_4016_split__beta) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.82 3957 (all X_a (banach(X_a) -> (all F all G ((exists N_3 all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_3),N_2)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),hAPP(nat,X_a,F,N_2))),hAPP(nat,real,G,N_2))))) -> (hBOOL(hAPP(fun(nat,real),bool,summable(real),G)) -> hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,X_a),fun(nat,real),hAPP(fun(X_a,real),fun(fun(nat,X_a),fun(nat,real)),combb(X_a,real,nat),norm_norm(X_a)),F)))))))) # label(fact_4017_summable__norm__comparison__test) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.82 3958 (all F all G ((exists N_3 all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_3),N_2)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),hAPP(nat,real,F,N_2))),hAPP(nat,real,G,N_2))))) -> (hBOOL(hAPP(fun(nat,real),bool,summable(real),G)) -> hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),abs_abs(real)),F)))))) # label(fact_4018_summable__rabs__comparison__test) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.82 3959 (all F (hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),abs_abs(real)),F))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),hAPP(fun(nat,real),real,suminf(real),F))),hAPP(fun(nat,real),real,suminf(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),abs_abs(real)),F)))))) # label(fact_4019_summable__rabs) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.82 3960 (all X_a (real_algebra_1(X_a) & real_normed_vector(X_a) -> (all X_3 (hBOOL(hAPP(fun(nat,real),bool,summable(real),X_3)) -> hAPP(real,X_a,of_real(X_a),hAPP(fun(nat,real),real,suminf(real),X_3)) = hAPP(fun(nat,X_a),X_a,suminf(X_a),hAPP(fun(nat,real),fun(nat,X_a),hAPP(fun(real,X_a),fun(fun(nat,real),fun(nat,X_a)),combb(real,X_a,nat),of_real(X_a)),X_3)))))) # label(fact_4020_of__real_Osuminf) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.82 3961 (all X_1 hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),sin_coeff)),hAPP(real,fun(nat,real),power_power(real),X_1))))) # label(fact_4021_summable__sin) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.82 3962 (all X_1 hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),cos_coeff)),hAPP(real,fun(nat,real),power_power(real),X_1))))) # label(fact_4022_summable__cos) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.82 3963 (all X_a (banach(X_a) -> (all F (hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,X_a),fun(nat,real),hAPP(fun(X_a,real),fun(fun(nat,X_a),fun(nat,real)),combb(X_a,real,nat),norm_norm(X_a)),F))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),hAPP(fun(nat,X_a),X_a,suminf(X_a),F))),hAPP(fun(nat,real),real,suminf(real),hAPP(fun(nat,X_a),fun(nat,real),hAPP(fun(X_a,real),fun(fun(nat,X_a),fun(nat,real)),combb(X_a,real,nat),norm_norm(X_a)),F)))))))) # label(fact_4023_summable__norm) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.82 3964 (all X_a (real_normed_field(X_a) & banach(X_a) -> (all Z_1 all F all X_1 (hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),times_times(X_a)),F)),hAPP(X_a,fun(nat,X_a),power_power(X_a),X_1)))) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,norm_norm(X_a),Z_1)),hAPP(X_a,real,norm_norm(X_a),X_1))) -> hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),times_times(X_a)),F)),hAPP(X_a,fun(nat,X_a),power_power(X_a),Z_1))))))))) # label(fact_4024_powser__inside) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.82 3965 (all X_a (real_n2089651433ebra_1(X_a) & banach(X_a) -> (all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,norm_norm(X_a),X_1)),one_one(real))) -> hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),hAPP(X_a,fun(nat,X_a),power_power(X_a),X_1))))))) # label(fact_4025_complete__algebra__summable__geometric) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.82 3966 (all X_a (real_normed_field(X_a) -> (all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,norm_norm(X_a),X_1)),one_one(real))) -> hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),hAPP(X_a,fun(nat,X_a),power_power(X_a),X_1))))))) # label(fact_4026_summable__geometric) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.82 3967 (all Pa hAPP(rat,int,archim2085082626_floor(rat),Pa) = hAPP(product_prod(int,int),int,hAPP(fun(int,fun(int,int)),fun(product_prod(int,int),int),product_prod_case(int,int,int),div_div(int)),hAPP(rat,product_prod(int,int),quotient_of,Pa))) # label(fact_4027_rat__floor__code) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.82 3968 (all Pa hAPP(rat,product_prod(int,int),quotient_of,hAPP(rat,rat,uminus_uminus(rat),Pa)) = hAPP(product_prod(int,int),product_prod(int,int),hAPP(fun(int,fun(int,product_prod(int,int))),fun(product_prod(int,int),product_prod(int,int)),product_prod_case(int,int,product_prod(int,int)),hAPP(fun(int,int),fun(int,fun(int,product_prod(int,int))),hAPP(fun(int,fun(int,product_prod(int,int))),fun(fun(int,int),fun(int,fun(int,product_prod(int,int)))),combb(int,fun(int,product_prod(int,int)),int),product_Pair(int,int)),uminus_uminus(int))),hAPP(rat,product_prod(int,int),quotient_of,Pa))) # label(fact_4028_rat__uminus__code) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.82 3969 (all X_1 hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),inverse_inverse(real)),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),fact_fact(nat))))),hAPP(real,fun(nat,real),power_power(real),X_1))))) # label(fact_4029_summable__exp) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.82 3970 (all Pa hAPP(rat,product_prod(int,int),quotient_of,hAPP(rat,rat,abs_abs(rat),Pa)) = hAPP(product_prod(int,int),product_prod(int,int),hAPP(fun(int,fun(int,product_prod(int,int))),fun(product_prod(int,int),product_prod(int,int)),product_prod_case(int,int,product_prod(int,int)),hAPP(fun(int,int),fun(int,fun(int,product_prod(int,int))),hAPP(fun(int,fun(int,product_prod(int,int))),fun(fun(int,int),fun(int,fun(int,product_prod(int,int)))),combb(int,fun(int,product_prod(int,int)),int),product_Pair(int,int)),abs_abs(int))),hAPP(rat,product_prod(int,int),quotient_of,Pa))) # label(fact_4030_rat__abs__code) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.82 3971 (all Aa all Ba hAPP(int,fun(product_prod(int,int),bool),hAPP(int,fun(int,fun(product_prod(int,int),bool)),divmod_int_rel,Aa),Ba) = hAPP(fun(int,fun(int,bool)),fun(product_prod(int,int),bool),product_prod_case(int,int,bool),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,fun(int,int)),fun(int,fun(int,bool)),hAPP(fun(fun(int,int),fun(int,bool)),fun(fun(int,fun(int,int)),fun(int,fun(int,bool))),combb(fun(int,int),fun(int,bool),int),hAPP(fun(int,bool),fun(fun(int,int),fun(int,bool)),combb(int,bool,int),hAPP(int,fun(int,bool),fequal(int),Aa))),hAPP(fun(int,int),fun(int,fun(int,int)),hAPP(fun(int,fun(int,int)),fun(fun(int,int),fun(int,fun(int,int))),combb(int,fun(int,int),int),plus_plus(int)),hAPP(int,fun(int,int),times_times(int),Ba)))))),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),combs(int,bool,bool),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(bool,bool),fun(fun(int,bool),fun(int,bool)),combb(bool,bool,int),hAPP(bool,fun(bool,bool),fimplies,hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),Ba))),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),combs(int,bool,bool),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(int,fun(int,bool),ord_less_eq(int),zero_zero(int)))),hAPP(int,fun(int,bool),hAPP(fun(int,fun(int,bool)),fun(int,fun(int,bool)),combc(int,int,bool),ord_less(int)),Ba))))),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(bool,bool),fun(fun(int,bool),fun(int,bool)),combb(bool,bool,int),hAPP(bool,fun(bool,bool),fimplies,hAPP(bool,bool,fNot,hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),Ba)))),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),combs(int,bool,bool),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(int,fun(int,bool),ord_less(int),Ba))),hAPP(int,fun(int,bool),hAPP(fun(int,fun(int,bool)),fun(int,fun(int,bool)),combc(int,int,bool),ord_less_eq(int)),zero_zero(int)))))))) # label(fact_4031_divmod__int__rel__def) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.82 3972 (all Pa hAPP(rat,product_prod(int,int),quotient_of,hAPP(rat,rat,inverse_inverse(rat),Pa)) = hAPP(product_prod(int,int),product_prod(int,int),hAPP(fun(int,fun(int,product_prod(int,int))),fun(product_prod(int,int),product_prod(int,int)),product_prod_case(int,int,product_prod(int,int)),hAPP(fun(int,fun(int,product_prod(int,int))),fun(int,fun(int,product_prod(int,int))),hAPP(fun(int,fun(fun(int,product_prod(int,int)),fun(int,product_prod(int,int)))),fun(fun(int,fun(int,product_prod(int,int))),fun(int,fun(int,product_prod(int,int)))),combs(int,fun(int,product_prod(int,int)),fun(int,product_prod(int,int))),hAPP(fun(int,fun(product_prod(int,int),product_prod(int,int))),fun(int,fun(fun(int,product_prod(int,int)),fun(int,product_prod(int,int)))),hAPP(fun(fun(product_prod(int,int),product_prod(int,int)),fun(fun(int,product_prod(int,int)),fun(int,product_prod(int,int)))),fun(fun(int,fun(product_prod(int,int),product_prod(int,int))),fun(int,fun(fun(int,product_prod(int,int)),fun(int,product_prod(int,int))))),combb(fun(product_prod(int,int),product_prod(int,int)),fun(fun(int,product_prod(int,int)),fun(int,product_prod(int,int))),int),combb(product_prod(int,int),product_prod(int,int),int)),hAPP(product_prod(int,int),fun(int,fun(product_prod(int,int),product_prod(int,int))),hAPP(fun(int,fun(product_prod(int,int),fun(product_prod(int,int),product_prod(int,int)))),fun(product_prod(int,int),fun(int,fun(product_prod(int,int),product_prod(int,int)))),combc(int,product_prod(int,int),fun(product_prod(int,int),product_prod(int,int))),hAPP(fun(int,bool),fun(int,fun(product_prod(int,int),fun(product_prod(int,int),product_prod(int,int)))),hAPP(fun(bool,fun(product_prod(int,int),fun(product_prod(int,int),product_prod(int,int)))),fun(fun(int,bool),fun(int,fun(product_prod(int,int),fun(product_prod(int,int),product_prod(int,int))))),combb(bool,fun(product_prod(int,int),fun(product_prod(int,int),product_prod(int,int))),int),if(product_prod(int,int))),hAPP(int,fun(int,bool),hAPP(fun(int,fun(int,bool)),fun(int,fun(int,bool)),combc(int,int,bool),fequal(int)),zero_zero(int)))),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),zero_zero(int)),one_one(int))))),hAPP(fun(int,int),fun(int,fun(int,product_prod(int,int))),hAPP(fun(int,fun(int,fun(int,product_prod(int,int)))),fun(fun(int,int),fun(int,fun(int,product_prod(int,int)))),combs(int,int,fun(int,product_prod(int,int))),hAPP(fun(int,fun(int,fun(int,product_prod(int,int)))),fun(int,fun(int,fun(int,product_prod(int,int)))),hAPP(fun(fun(int,fun(int,product_prod(int,int))),fun(int,fun(int,product_prod(int,int)))),fun(fun(int,fun(int,fun(int,product_prod(int,int)))),fun(int,fun(int,fun(int,product_prod(int,int))))),combb(fun(int,fun(int,product_prod(int,int))),fun(int,fun(int,product_prod(int,int))),int),combc(int,int,product_prod(int,int))),hAPP(fun(int,fun(int,int)),fun(int,fun(int,fun(int,product_prod(int,int)))),hAPP(fun(fun(int,int),fun(int,fun(int,product_prod(int,int)))),fun(fun(int,fun(int,int)),fun(int,fun(int,fun(int,product_prod(int,int))))),combb(fun(int,int),fun(int,fun(int,product_prod(int,int))),int),hAPP(fun(int,fun(int,product_prod(int,int))),fun(fun(int,int),fun(int,fun(int,product_prod(int,int)))),combb(int,fun(int,product_prod(int,int)),int),product_Pair(int,int))),hAPP(fun(int,int),fun(int,fun(int,int)),hAPP(fun(int,fun(int,int)),fun(fun(int,int),fun(int,fun(int,int))),combb(int,fun(int,int),int),times_times(int)),sgn_sgn(int))))),abs_abs(int)))),hAPP(rat,product_prod(int,int),quotient_of,Pa))) # label(fact_4033_rat__inverse__code) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.82 3973 (all X_1 hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),inverse_inverse(real)),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),hAPP(fun(nat,nat),fun(nat,nat),hAPP(fun(nat,nat),fun(fun(nat,nat),fun(nat,nat)),combb(nat,nat,nat),fact_fact(nat)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),hAPP(real,fun(nat,real),power_power(real),X_1)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))))) # label(fact_4034_exp__tail__after__first__two__terms__summable) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.83 3974 (all Ba hAPP(int,fun(product_prod(int,int),product_prod(int,int)),adjust,Ba) = hAPP(fun(int,fun(int,product_prod(int,int))),fun(product_prod(int,int),product_prod(int,int)),product_prod_case(int,int,product_prod(int,int)),hAPP(fun(int,fun(int,product_prod(int,int))),fun(int,fun(int,product_prod(int,int))),hAPP(fun(int,fun(fun(int,product_prod(int,int)),fun(int,product_prod(int,int)))),fun(fun(int,fun(int,product_prod(int,int))),fun(int,fun(int,product_prod(int,int)))),combs(int,fun(int,product_prod(int,int)),fun(int,product_prod(int,int))),hAPP(fun(int,fun(int,fun(product_prod(int,int),product_prod(int,int)))),fun(int,fun(fun(int,product_prod(int,int)),fun(int,product_prod(int,int)))),hAPP(fun(fun(int,fun(product_prod(int,int),product_prod(int,int))),fun(fun(int,product_prod(int,int)),fun(int,product_prod(int,int)))),fun(fun(int,fun(int,fun(product_prod(int,int),product_prod(int,int)))),fun(int,fun(fun(int,product_prod(int,int)),fun(int,product_prod(int,int))))),combb(fun(int,fun(product_prod(int,int),product_prod(int,int))),fun(fun(int,product_prod(int,int)),fun(int,product_prod(int,int))),int),combs(int,product_prod(int,int),product_prod(int,int))),hAPP(fun(int,fun(int,product_prod(int,int))),fun(int,fun(int,fun(product_prod(int,int),product_prod(int,int)))),hAPP(fun(fun(int,product_prod(int,int)),fun(int,fun(product_prod(int,int),product_prod(int,int)))),fun(fun(int,fun(int,product_prod(int,int))),fun(int,fun(int,fun(product_prod(int,int),product_prod(int,int))))),combb(fun(int,product_prod(int,int)),fun(int,fun(product_prod(int,int),product_prod(int,int))),int),hAPP(fun(int,fun(product_prod(int,int),fun(product_prod(int,int),product_prod(int,int)))),fun(fun(int,product_prod(int,int)),fun(int,fun(product_prod(int,int),product_prod(int,int)))),combs(int,product_prod(int,int),fun(product_prod(int,int),product_prod(int,int))),hAPP(fun(int,bool),fun(int,fun(product_prod(int,int),fun(product_prod(int,int),product_prod(int,int)))),hAPP(fun(bool,fun(product_prod(int,int),fun(product_prod(int,int),product_prod(int,int)))),fun(fun(int,bool),fun(int,fun(product_prod(int,int),fun(product_prod(int,int),product_prod(int,int))))),combb(bool,fun(product_prod(int,int),fun(product_prod(int,int),product_prod(int,int))),int),if(product_prod(int,int))),hAPP(fun(int,int),fun(int,bool),hAPP(fun(int,bool),fun(fun(int,int),fun(int,bool)),combb(int,bool,int),hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int))),hAPP(int,fun(int,int),hAPP(fun(int,fun(int,int)),fun(int,fun(int,int)),combc(int,int,int),minus_minus(int)),Ba))))),hAPP(fun(int,int),fun(int,fun(int,product_prod(int,int))),hAPP(fun(int,fun(fun(int,int),fun(int,product_prod(int,int)))),fun(fun(int,int),fun(int,fun(int,product_prod(int,int)))),combc(int,fun(int,int),fun(int,product_prod(int,int))),hAPP(fun(int,fun(int,product_prod(int,int))),fun(int,fun(fun(int,int),fun(int,product_prod(int,int)))),hAPP(fun(fun(int,product_prod(int,int)),fun(fun(int,int),fun(int,product_prod(int,int)))),fun(fun(int,fun(int,product_prod(int,int))),fun(int,fun(fun(int,int),fun(int,product_prod(int,int))))),combb(fun(int,product_prod(int,int)),fun(fun(int,int),fun(int,product_prod(int,int))),int),combb(int,product_prod(int,int),int)),hAPP(fun(int,int),fun(int,fun(int,product_prod(int,int))),hAPP(fun(int,fun(int,product_prod(int,int))),fun(fun(int,int),fun(int,fun(int,product_prod(int,int)))),combb(int,fun(int,product_prod(int,int)),int),product_Pair(int,int)),hAPP(int,fun(int,int),hAPP(fun(int,fun(int,int)),fun(int,fun(int,int)),combc(int,int,int),hAPP(fun(int,int),fun(int,fun(int,int)),hAPP(fun(int,fun(int,int)),fun(fun(int,int),fun(int,fun(int,int))),combb(int,fun(int,int),int),plus_plus(int)),hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),one_one(int))))),hAPP(int,fun(int,int),hAPP(fun(int,fun(int,int)),fun(int,fun(int,int)),combc(int,int,int),minus_minus(int)),Ba))))),hAPP(fun(int,int),fun(int,fun(int,product_prod(int,int))),hAPP(fun(int,fun(int,product_prod(int,int))),fun(fun(int,int),fun(int,fun(int,product_prod(int,int)))),combb(int,fun(int,product_prod(int,int)),int),product_Pair(int,int)),hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))) # label(fact_4035_adjust__def) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.83 3975 (all X0 all F all R_3 ((all X_2 (hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),X_2),hAPP(real,fun(real,bool),hAPP(real,fun(real,fun(real,bool)),ord_gr676655987ssThan(real),hAPP(real,real,uminus_uminus(real),R_3)),R_3))) -> hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),F)),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),suc)))),hAPP(real,fun(nat,real),power_power(real),X_2)))))) -> (hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),X0),hAPP(real,fun(real,bool),hAPP(real,fun(real,fun(real,bool)),ord_gr676655987ssThan(real),hAPP(real,real,uminus_uminus(real),R_3)),R_3))) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),R_3)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(fun(real,fun(nat,real)),fun(real,real),hAPP(fun(fun(nat,real),real),fun(fun(real,fun(nat,real)),fun(real,real)),combb(fun(nat,real),real,real),suminf(real)),hAPP(fun(real,fun(nat,real)),fun(real,fun(nat,real)),hAPP(fun(fun(nat,real),fun(nat,real)),fun(fun(real,fun(nat,real)),fun(real,fun(nat,real))),combb(fun(nat,real),fun(nat,real),real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),F))),hAPP(fun(nat,nat),fun(real,fun(nat,real)),hAPP(fun(real,fun(fun(nat,nat),fun(nat,real))),fun(fun(nat,nat),fun(real,fun(nat,real))),combc(real,fun(nat,nat),fun(nat,real)),hAPP(fun(real,fun(nat,real)),fun(real,fun(fun(nat,nat),fun(nat,real))),hAPP(fun(fun(nat,real),fun(fun(nat,nat),fun(nat,real))),fun(fun(real,fun(nat,real)),fun(real,fun(fun(nat,nat),fun(nat,real)))),combb(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),real),combb(nat,real,nat)),power_power(real))),suc)))),X0),hAPP(fun(nat,real),real,suminf(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),F)),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),suc)))),hAPP(real,fun(nat,real),power_power(real),X0))))))))) # label(fact_4036_DERIV__power__series_H) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.83 3976 (all X_a all X_c all X_b all Z_1 all C_1 all Aa all Ba (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Z_1),hAPP(X_c,fun(X_a,bool),hAPP(X_b,fun(X_c,fun(X_a,bool)),C_1,Aa),Ba))) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Z_1),hAPP(product_prod(X_b,X_c),fun(X_a,bool),hAPP(fun(X_b,fun(X_c,fun(X_a,bool))),fun(product_prod(X_b,X_c),fun(X_a,bool)),product_prod_case(X_b,X_c,fun(X_a,bool)),C_1),hAPP(X_c,product_prod(X_b,X_c),hAPP(X_b,fun(X_c,product_prod(X_b,X_c)),product_Pair(X_b,X_c),Aa),Ba)))))) # label(fact_4038_mem__splitI) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.83 3977 (all X_b all X_a all F1 all Aa all Ba (hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),F1,Aa),Ba)) -> hBOOL(hAPP(product_prod(X_a,X_b),bool,hAPP(fun(X_a,fun(X_b,bool)),fun(product_prod(X_a,X_b),bool),product_prod_case(X_a,X_b,bool),F1),hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),Aa),Ba))))) # label(fact_4039_prod__caseI) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.83 3978 (all X_b all X_a all F all Aa all Ba (hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),F,Aa),Ba)) -> hBOOL(hAPP(product_prod(X_a,X_b),bool,hAPP(fun(X_a,fun(X_b,bool)),fun(product_prod(X_a,X_b),bool),product_prod_case(X_a,X_b,bool),F),hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),Aa),Ba))))) # label(fact_4040_splitI) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.83 3979 (all X_3 (hBOOL(hAPP(fun(nat,complex),bool,summable(complex),X_3)) -> hAPP(complex,complex,cnj,hAPP(fun(nat,complex),complex,suminf(complex),X_3)) = hAPP(fun(nat,complex),complex,suminf(complex),hAPP(fun(nat,complex),fun(nat,complex),hAPP(fun(complex,complex),fun(fun(nat,complex),fun(nat,complex)),combb(complex,complex,nat),cnj),X_3)))) # label(fact_4041_cnj_Osuminf) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.83 3980 (all X_a all X_b all F all Aa all Ba (hBOOL(hAPP(product_prod(X_a,X_b),bool,hAPP(fun(X_a,fun(X_b,bool)),fun(product_prod(X_a,X_b),bool),product_prod_case(X_a,X_b,bool),F),hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),Aa),Ba))) -> hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),F,Aa),Ba)))) # label(fact_4042_splitD) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.83 3981 (all X_c all X_a all X_b all R_3 all Aa all Ba all C_1 (hBOOL(hAPP(X_c,bool,hAPP(product_prod(X_a,X_b),fun(X_c,bool),hAPP(fun(X_a,fun(X_b,fun(X_c,bool))),fun(product_prod(X_a,X_b),fun(X_c,bool)),product_prod_case(X_a,X_b,fun(X_c,bool)),R_3),hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),Aa),Ba)),C_1)) -> hBOOL(hAPP(X_c,bool,hAPP(X_b,fun(X_c,bool),hAPP(X_a,fun(X_b,fun(X_c,bool)),R_3,Aa),Ba),C_1)))) # label(fact_4043_splitD_H) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.83 3982 (all X_3 (hBOOL(hAPP(fun(nat,complex),bool,summable(complex),X_3)) -> hBOOL(hAPP(fun(nat,complex),bool,summable(complex),hAPP(fun(nat,complex),fun(nat,complex),hAPP(fun(complex,complex),fun(fun(nat,complex),fun(nat,complex)),combb(complex,complex,nat),cnj),X_3))))) # label(fact_4044_cnj_Osummable) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.83 3983 (all X_a all X_b all P_1 all Q_1 all X_2 (hBOOL(hAPP(product_prod(X_a,X_b),bool,hAPP(fun(X_a,fun(X_b,bool)),fun(product_prod(X_a,X_b),bool),product_prod_case(X_a,X_b,bool),hAPP(fun(X_a,fun(X_b,bool)),fun(X_a,fun(X_b,bool)),hAPP(fun(fun(X_b,bool),fun(X_b,bool)),fun(fun(X_a,fun(X_b,bool)),fun(X_a,fun(X_b,bool))),combb(fun(X_b,bool),fun(X_b,bool),X_a),hAPP(fun(bool,bool),fun(fun(X_b,bool),fun(X_b,bool)),combb(bool,bool,X_b),hAPP(bool,fun(bool,bool),fconj,P_1))),Q_1)),X_2)) <-> hBOOL(P_1) & hBOOL(hAPP(product_prod(X_a,X_b),bool,hAPP(fun(X_a,fun(X_b,bool)),fun(product_prod(X_a,X_b),bool),product_prod_case(X_a,X_b,bool),Q_1),X_2)))) # label(fact_4045_split__part) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.83 3984 (all X_3 (hBOOL(hAPP(fun(nat,complex),bool,summable(complex),X_3)) -> hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,complex),fun(nat,real),hAPP(fun(complex,real),fun(fun(nat,complex),fun(nat,real)),combb(complex,real,nat),re),X_3))))) # label(fact_4046_Re_Osummable) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.83 3985 (all X_3 (hBOOL(hAPP(fun(nat,complex),bool,summable(complex),X_3)) -> hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,complex),fun(nat,real),hAPP(fun(complex,real),fun(fun(nat,complex),fun(nat,real)),combb(complex,real,nat),im),X_3))))) # label(fact_4047_Im_Osummable) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.83 3986 (all X_3 (hBOOL(hAPP(fun(nat,complex),bool,summable(complex),X_3)) -> hAPP(complex,real,re,hAPP(fun(nat,complex),complex,suminf(complex),X_3)) = hAPP(fun(nat,real),real,suminf(real),hAPP(fun(nat,complex),fun(nat,real),hAPP(fun(complex,real),fun(fun(nat,complex),fun(nat,real)),combb(complex,real,nat),re),X_3)))) # label(fact_4048_Re_Osuminf) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.83 3987 (all X_3 (hBOOL(hAPP(fun(nat,complex),bool,summable(complex),X_3)) -> hAPP(complex,real,im,hAPP(fun(nat,complex),complex,suminf(complex),X_3)) = hAPP(fun(nat,real),real,suminf(real),hAPP(fun(nat,complex),fun(nat,real),hAPP(fun(complex,real),fun(fun(nat,complex),fun(nat,real)),combb(complex,real,nat),im),X_3)))) # label(fact_4049_Im_Osuminf) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.83 3988 (all X_a finite_psubset(X_a) = hAPP(fun(product_prod(fun(X_a,bool),fun(X_a,bool)),bool),fun(product_prod(fun(X_a,bool),fun(X_a,bool)),bool),collect(product_prod(fun(X_a,bool),fun(X_a,bool))),hAPP(fun(fun(X_a,bool),fun(fun(X_a,bool),bool)),fun(product_prod(fun(X_a,bool),fun(X_a,bool)),bool),product_prod_case(fun(X_a,bool),fun(X_a,bool),bool),hAPP(fun(fun(X_a,bool),bool),fun(fun(X_a,bool),fun(fun(X_a,bool),bool)),hAPP(fun(fun(X_a,bool),fun(fun(fun(X_a,bool),bool),fun(fun(X_a,bool),bool))),fun(fun(fun(X_a,bool),bool),fun(fun(X_a,bool),fun(fun(X_a,bool),bool))),combc(fun(X_a,bool),fun(fun(X_a,bool),bool),fun(fun(X_a,bool),bool)),hAPP(fun(fun(X_a,bool),fun(fun(X_a,bool),fun(bool,bool))),fun(fun(X_a,bool),fun(fun(fun(X_a,bool),bool),fun(fun(X_a,bool),bool))),hAPP(fun(fun(fun(X_a,bool),fun(bool,bool)),fun(fun(fun(X_a,bool),bool),fun(fun(X_a,bool),bool))),fun(fun(fun(X_a,bool),fun(fun(X_a,bool),fun(bool,bool))),fun(fun(X_a,bool),fun(fun(fun(X_a,bool),bool),fun(fun(X_a,bool),bool)))),combb(fun(fun(X_a,bool),fun(bool,bool)),fun(fun(fun(X_a,bool),bool),fun(fun(X_a,bool),bool)),fun(X_a,bool)),combs(fun(X_a,bool),bool,bool)),hAPP(fun(fun(X_a,bool),fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(fun(X_a,bool),fun(bool,bool))),hAPP(fun(fun(fun(X_a,bool),bool),fun(fun(X_a,bool),fun(bool,bool))),fun(fun(fun(X_a,bool),fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(fun(X_a,bool),fun(bool,bool)))),combb(fun(fun(X_a,bool),bool),fun(fun(X_a,bool),fun(bool,bool)),fun(X_a,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(fun(X_a,bool),bool),fun(fun(X_a,bool),fun(bool,bool))),combb(bool,fun(bool,bool),fun(X_a,bool)),fconj)),ord_less(fun(X_a,bool))))),finite_finite_1(X_a))))) # label(fact_4050_finite__psubset__def) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.83 3989 (all M all N ((N = zero_zero(nat) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N)) -> hAPP(nat,product_prod(nat,nat),hAPP(nat,fun(nat,product_prod(nat,nat)),divmod_nat,M),N) = hAPP(nat,product_prod(nat,nat),hAPP(nat,fun(nat,product_prod(nat,nat)),product_Pair(nat,nat),zero_zero(nat)),M)) & (-(N = zero_zero(nat) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N))) -> hAPP(nat,product_prod(nat,nat),hAPP(nat,fun(nat,product_prod(nat,nat)),divmod_nat,M),N) = hAPP(product_prod(nat,nat),product_prod(nat,nat),hAPP(fun(nat,fun(nat,product_prod(nat,nat))),fun(product_prod(nat,nat),product_prod(nat,nat)),product_prod_case(nat,nat,product_prod(nat,nat)),hAPP(fun(nat,nat),fun(nat,fun(nat,product_prod(nat,nat))),hAPP(fun(nat,fun(nat,product_prod(nat,nat))),fun(fun(nat,nat),fun(nat,fun(nat,product_prod(nat,nat)))),combb(nat,fun(nat,product_prod(nat,nat)),nat),product_Pair(nat,nat)),suc)),hAPP(nat,product_prod(nat,nat),hAPP(nat,fun(nat,product_prod(nat,nat)),divmod_nat,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N)),N))))) # label(fact_4052_divmod__nat__if) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.83 3990 (all P_1 all Aa all Ba all N hAPP(nat,product_prod(real,real),hAPP(real,fun(nat,product_prod(real,real)),hAPP(real,fun(real,fun(nat,product_prod(real,real))),hAPP(fun(product_prod(real,real),bool),fun(real,fun(real,fun(nat,product_prod(real,real)))),bolzano_bisect,P_1),Aa),Ba),hAPP(nat,nat,suc,N)) = hAPP(product_prod(real,real),product_prod(real,real),hAPP(fun(real,fun(real,product_prod(real,real))),fun(product_prod(real,real),product_prod(real,real)),product_prod_case(real,real,product_prod(real,real)),hAPP(fun(real,fun(real,product_prod(real,real))),fun(real,fun(real,product_prod(real,real))),hAPP(fun(real,fun(fun(real,product_prod(real,real)),fun(real,product_prod(real,real)))),fun(fun(real,fun(real,product_prod(real,real))),fun(real,fun(real,product_prod(real,real)))),combs(real,fun(real,product_prod(real,real)),fun(real,product_prod(real,real))),hAPP(fun(real,fun(real,fun(product_prod(real,real),product_prod(real,real)))),fun(real,fun(fun(real,product_prod(real,real)),fun(real,product_prod(real,real)))),hAPP(fun(fun(real,fun(product_prod(real,real),product_prod(real,real))),fun(fun(real,product_prod(real,real)),fun(real,product_prod(real,real)))),fun(fun(real,fun(real,fun(product_prod(real,real),product_prod(real,real)))),fun(real,fun(fun(real,product_prod(real,real)),fun(real,product_prod(real,real))))),combb(fun(real,fun(product_prod(real,real),product_prod(real,real))),fun(fun(real,product_prod(real,real)),fun(real,product_prod(real,real))),real),combs(real,product_prod(real,real),product_prod(real,real))),hAPP(fun(real,fun(real,product_prod(real,real))),fun(real,fun(real,fun(product_prod(real,real),product_prod(real,real)))),hAPP(fun(real,fun(fun(real,product_prod(real,real)),fun(real,fun(product_prod(real,real),product_prod(real,real))))),fun(fun(real,fun(real,product_prod(real,real))),fun(real,fun(real,fun(product_prod(real,real),product_prod(real,real))))),combs(real,fun(real,product_prod(real,real)),fun(real,fun(product_prod(real,real),product_prod(real,real)))),hAPP(fun(real,fun(real,fun(product_prod(real,real),fun(product_prod(real,real),product_prod(real,real))))),fun(real,fun(fun(real,product_prod(real,real)),fun(real,fun(product_prod(real,real),product_prod(real,real))))),hAPP(fun(fun(real,fun(product_prod(real,real),fun(product_prod(real,real),product_prod(real,real)))),fun(fun(real,product_prod(real,real)),fun(real,fun(product_prod(real,real),product_prod(real,real))))),fun(fun(real,fun(real,fun(product_prod(real,real),fun(product_prod(real,real),product_prod(real,real))))),fun(real,fun(fun(real,product_prod(real,real)),fun(real,fun(product_prod(real,real),product_prod(real,real)))))),combb(fun(real,fun(product_prod(real,real),fun(product_prod(real,real),product_prod(real,real)))),fun(fun(real,product_prod(real,real)),fun(real,fun(product_prod(real,real),product_prod(real,real)))),real),combs(real,product_prod(real,real),fun(product_prod(real,real),product_prod(real,real)))),hAPP(fun(real,fun(real,bool)),fun(real,fun(real,fun(product_prod(real,real),fun(product_prod(real,real),product_prod(real,real))))),hAPP(fun(fun(real,bool),fun(real,fun(product_prod(real,real),fun(product_prod(real,real),product_prod(real,real))))),fun(fun(real,fun(real,bool)),fun(real,fun(real,fun(product_prod(real,real),fun(product_prod(real,real),product_prod(real,real)))))),combb(fun(real,bool),fun(real,fun(product_prod(real,real),fun(product_prod(real,real),product_prod(real,real)))),real),hAPP(fun(bool,fun(product_prod(real,real),fun(product_prod(real,real),product_prod(real,real)))),fun(fun(real,bool),fun(real,fun(product_prod(real,real),fun(product_prod(real,real),product_prod(real,real))))),combb(bool,fun(product_prod(real,real),fun(product_prod(real,real),product_prod(real,real))),real),if(product_prod(real,real)))),hAPP(fun(real,fun(real,product_prod(real,real))),fun(real,fun(real,bool)),hAPP(fun(fun(real,product_prod(real,real)),fun(real,bool)),fun(fun(real,fun(real,product_prod(real,real))),fun(real,fun(real,bool))),combb(fun(real,product_prod(real,real)),fun(real,bool),real),hAPP(fun(product_prod(real,real),bool),fun(fun(real,product_prod(real,real)),fun(real,bool)),combb(product_prod(real,real),bool,real),P_1)),hAPP(fun(real,fun(real,real)),fun(real,fun(real,product_prod(real,real))),hAPP(fun(real,fun(fun(real,real),fun(real,product_prod(real,real)))),fun(fun(real,fun(real,real)),fun(real,fun(real,product_prod(real,real)))),combs(real,fun(real,real),fun(real,product_prod(real,real))),hAPP(fun(real,fun(real,product_prod(real,real))),fun(real,fun(fun(real,real),fun(real,product_prod(real,real)))),hAPP(fun(fun(real,product_prod(real,real)),fun(fun(real,real),fun(real,product_prod(real,real)))),fun(fun(real,fun(real,product_prod(real,real))),fun(real,fun(fun(real,real),fun(real,product_prod(real,real))))),combb(fun(real,product_prod(real,real)),fun(fun(real,real),fun(real,product_prod(real,real))),real),combb(real,product_prod(real,real),real)),product_Pair(real,real))),hAPP(real,fun(real,fun(real,real)),hAPP(fun(real,fun(real,fun(real,real))),fun(real,fun(real,fun(real,real))),combc(real,real,fun(real,real)),hAPP(fun(real,fun(real,fun(real,real))),fun(real,fun(real,fun(real,real))),hAPP(fun(fun(real,fun(real,real)),fun(real,fun(real,real))),fun(fun(real,fun(real,fun(real,real))),fun(real,fun(real,fun(real,real)))),combb(fun(real,fun(real,real)),fun(real,fun(real,real)),real),combc(real,real,real)),hAPP(fun(real,fun(real,real)),fun(real,fun(real,fun(real,real))),hAPP(fun(fun(real,real),fun(real,fun(real,real))),fun(fun(real,fun(real,real)),fun(real,fun(real,fun(real,real)))),combb(fun(real,real),fun(real,fun(real,real)),real),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,fun(real,real))),combb(real,fun(real,real),real),inverse_divide(real))),plus_plus(real)))),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))))),hAPP(fun(real,real),fun(real,fun(real,product_prod(real,real))),hAPP(fun(real,fun(fun(real,real),fun(real,product_prod(real,real)))),fun(fun(real,real),fun(real,fun(real,product_prod(real,real)))),combc(real,fun(real,real),fun(real,product_prod(real,real))),hAPP(fun(real,fun(real,fun(real,product_prod(real,real)))),fun(real,fun(fun(real,real),fun(real,product_prod(real,real)))),hAPP(fun(fun(real,fun(real,product_prod(real,real))),fun(fun(real,real),fun(real,product_prod(real,real)))),fun(fun(real,fun(real,fun(real,product_prod(real,real)))),fun(real,fun(fun(real,real),fun(real,product_prod(real,real))))),combb(fun(real,fun(real,product_prod(real,real))),fun(fun(real,real),fun(real,product_prod(real,real))),real),combs(real,real,product_prod(real,real))),hAPP(fun(real,fun(real,real)),fun(real,fun(real,fun(real,product_prod(real,real)))),hAPP(fun(fun(real,real),fun(real,fun(real,product_prod(real,real)))),fun(fun(real,fun(real,real)),fun(real,fun(real,fun(real,product_prod(real,real))))),combb(fun(real,real),fun(real,fun(real,product_prod(real,real))),real),hAPP(fun(real,fun(real,product_prod(real,real))),fun(fun(real,real),fun(real,fun(real,product_prod(real,real)))),combb(real,fun(real,product_prod(real,real)),real),product_Pair(real,real))),hAPP(real,fun(real,fun(real,real)),hAPP(fun(real,fun(real,fun(real,real))),fun(real,fun(real,fun(real,real))),combc(real,real,fun(real,real)),hAPP(fun(real,fun(real,fun(real,real))),fun(real,fun(real,fun(real,real))),hAPP(fun(fun(real,fun(real,real)),fun(real,fun(real,real))),fun(fun(real,fun(real,fun(real,real))),fun(real,fun(real,fun(real,real)))),combb(fun(real,fun(real,real)),fun(real,fun(real,real)),real),combc(real,real,real)),hAPP(fun(real,fun(real,real)),fun(real,fun(real,fun(real,real))),hAPP(fun(fun(real,real),fun(real,fun(real,real))),fun(fun(real,fun(real,real)),fun(real,fun(real,fun(real,real)))),combb(fun(real,real),fun(real,fun(real,real)),real),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,fun(real,real))),combb(real,fun(real,real),real),inverse_divide(real))),plus_plus(real)))),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))),combi(real))))),hAPP(fun(real,fun(real,real)),fun(real,fun(real,product_prod(real,real))),hAPP(fun(real,fun(fun(real,real),fun(real,product_prod(real,real)))),fun(fun(real,fun(real,real)),fun(real,fun(real,product_prod(real,real)))),combs(real,fun(real,real),fun(real,product_prod(real,real))),hAPP(fun(real,fun(real,product_prod(real,real))),fun(real,fun(fun(real,real),fun(real,product_prod(real,real)))),hAPP(fun(fun(real,product_prod(real,real)),fun(fun(real,real),fun(real,product_prod(real,real)))),fun(fun(real,fun(real,product_prod(real,real))),fun(real,fun(fun(real,real),fun(real,product_prod(real,real))))),combb(fun(real,product_prod(real,real)),fun(fun(real,real),fun(real,product_prod(real,real))),real),combb(real,product_prod(real,real),real)),product_Pair(real,real))),hAPP(real,fun(real,fun(real,real)),hAPP(fun(real,fun(real,fun(real,real))),fun(real,fun(real,fun(real,real))),combc(real,real,fun(real,real)),hAPP(fun(real,fun(real,fun(real,real))),fun(real,fun(real,fun(real,real))),hAPP(fun(fun(real,fun(real,real)),fun(real,fun(real,real))),fun(fun(real,fun(real,fun(real,real))),fun(real,fun(real,fun(real,real)))),combb(fun(real,fun(real,real)),fun(real,fun(real,real)),real),combc(real,real,real)),hAPP(fun(real,fun(real,real)),fun(real,fun(real,fun(real,real))),hAPP(fun(fun(real,real),fun(real,fun(real,real))),fun(fun(real,fun(real,real)),fun(real,fun(real,fun(real,real)))),combb(fun(real,real),fun(real,fun(real,real)),real),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,fun(real,real))),combb(real,fun(real,real),real),inverse_divide(real))),plus_plus(real)))),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))),hAPP(nat,product_prod(real,real),hAPP(real,fun(nat,product_prod(real,real)),hAPP(real,fun(real,fun(nat,product_prod(real,real))),hAPP(fun(product_prod(real,real),bool),fun(real,fun(real,fun(nat,product_prod(real,real)))),bolzano_bisect,P_1),Aa),Ba),N))) # label(fact_4053_Bolzano__bisect_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.83 3991 (all X_a (banach(X_a) -> (all F all N_4 all C_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),C_1),one_one(real))) -> ((all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_4),N_2)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),hAPP(nat,X_a,F,hAPP(nat,nat,suc,N_2)))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C_1),hAPP(X_a,real,norm_norm(X_a),hAPP(nat,X_a,F,N_2))))))) -> hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),F))))))) # label(fact_4054_ratio__test) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.83 3992 (all X_a (banach(X_a) -> (all F all C_1 all N_4 ((all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_4),N_2)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),hAPP(nat,X_a,F,hAPP(nat,nat,suc,N_2)))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C_1),hAPP(X_a,real,norm_norm(X_a),hAPP(nat,X_a,F,N_2))))))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),C_1)) | hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),F)))))) # label(fact_4055_ratio__test__lemma2) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.83 3993 (all Aa all R_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),R_1)) -> (hBOOL(hAPP(fun(nat,real),bool,summable(real),Aa)) -> (exists N_3 all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_3),N_2)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,abs_abs(real),hAPP(fun(nat,real),real,suminf(real),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),Aa),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),N_2))))),R_1))))))) # label(fact_4056_suminf__exist__split) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.83 3994 (all X_c all X_a all X_b all Z_1 all C_1 all Pa ((all A_3 all B_3 (ti(product_prod(X_a,X_b),Pa) = hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),A_3),B_3) -> hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),Z_1),hAPP(X_b,fun(X_c,bool),hAPP(X_a,fun(X_b,fun(X_c,bool)),C_1,A_3),B_3))))) -> hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),Z_1),hAPP(product_prod(X_a,X_b),fun(X_c,bool),hAPP(fun(X_a,fun(X_b,fun(X_c,bool))),fun(product_prod(X_a,X_b),fun(X_c,bool)),product_prod_case(X_a,X_b,fun(X_c,bool)),C_1),Pa))))) # label(fact_4057_mem__splitI2) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.83 3995 (all X_c all X_a all X_b all C_1 all Pa all Z_1 (hBOOL(hAPP(X_c,bool,hAPP(product_prod(X_a,X_b),fun(X_c,bool),hAPP(fun(X_a,fun(X_b,fun(X_c,bool))),fun(product_prod(X_a,X_b),fun(X_c,bool)),product_prod_case(X_a,X_b,fun(X_c,bool)),C_1),Pa),Z_1)) -> -(all X_2 all Y_2 (ti(product_prod(X_a,X_b),Pa) = hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),X_2),Y_2) -> -hBOOL(hAPP(X_c,bool,hAPP(X_b,fun(X_c,bool),hAPP(X_a,fun(X_b,fun(X_c,bool)),C_1,X_2),Y_2),Z_1)))))) # label(fact_4058_splitE_H) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.83 3996 (all X_a all X_b all X_c all Z_1 all C_1 all Pa (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Z_1),hAPP(product_prod(X_b,X_c),fun(X_a,bool),hAPP(fun(X_b,fun(X_c,fun(X_a,bool))),fun(product_prod(X_b,X_c),fun(X_a,bool)),product_prod_case(X_b,X_c,fun(X_a,bool)),C_1),Pa))) -> -(all X_2 all Y_2 (ti(product_prod(X_b,X_c),Pa) = hAPP(X_c,product_prod(X_b,X_c),hAPP(X_b,fun(X_c,product_prod(X_b,X_c)),product_Pair(X_b,X_c),X_2),Y_2) -> -hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Z_1),hAPP(X_c,fun(X_a,bool),hAPP(X_b,fun(X_c,fun(X_a,bool)),C_1,X_2),Y_2))))))) # label(fact_4059_mem__splitE) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.83 3997 (all X_c all X_b all X_a all C_1 all X_1 all Pa ((all A_3 all B_3 (hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),A_3),B_3) = ti(product_prod(X_a,X_b),Pa) -> hBOOL(hAPP(X_c,bool,hAPP(X_b,fun(X_c,bool),hAPP(X_a,fun(X_b,fun(X_c,bool)),C_1,A_3),B_3),X_1)))) -> hBOOL(hAPP(X_c,bool,hAPP(product_prod(X_a,X_b),fun(X_c,bool),hAPP(fun(X_a,fun(X_b,fun(X_c,bool))),fun(product_prod(X_a,X_b),fun(X_c,bool)),product_prod_case(X_a,X_b,fun(X_c,bool)),C_1),Pa),X_1)))) # label(fact_4060_splitI2_H) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.83 3998 (all X_a all X_b all C_1 all Pa ((all A_3 all B_3 (ti(product_prod(X_a,X_b),Pa) = hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),A_3),B_3) -> hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),C_1,A_3),B_3)))) -> hBOOL(hAPP(product_prod(X_a,X_b),bool,hAPP(fun(X_a,fun(X_b,bool)),fun(product_prod(X_a,X_b),bool),product_prod_case(X_a,X_b,bool),C_1),Pa)))) # label(fact_4061_splitI2) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.83 3999 (all X_a all X_b all C_1 all Pa (hBOOL(hAPP(product_prod(X_a,X_b),bool,hAPP(fun(X_a,fun(X_b,bool)),fun(product_prod(X_a,X_b),bool),product_prod_case(X_a,X_b,bool),C_1),Pa)) -> -(all X_2 all Y_2 (ti(product_prod(X_a,X_b),Pa) = hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),X_2),Y_2) -> -hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),C_1,X_2),Y_2)))))) # label(fact_4062_splitE) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.83 4000 (all L all K ((K = zero_zero(int) -> hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),divmod_int,K),L) = hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),zero_zero(int)),zero_zero(int))) & (K != zero_zero(int) -> (L = zero_zero(int) -> hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),divmod_int,K),L) = hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),zero_zero(int)),K)) & (L != zero_zero(int) -> hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),divmod_int,K),L) = hAPP(product_prod(int,int),product_prod(int,int),hAPP(fun(int,int),fun(product_prod(int,int),product_prod(int,int)),product_apsnd(int,int,int),hAPP(int,fun(int,int),times_times(int),hAPP(int,int,sgn_sgn(int),L))),hAPP(product_prod(int,int),product_prod(int,int),hAPP(product_prod(int,int),fun(product_prod(int,int),product_prod(int,int)),hAPP(bool,fun(product_prod(int,int),fun(product_prod(int,int),product_prod(int,int))),if(product_prod(int,int)),hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),L)),hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),K))),hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),L),zero_zero(int))),hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),zero_zero(int))))),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),pdivmod,K),L)),hAPP(product_prod(int,int),product_prod(int,int),hAPP(fun(int,fun(int,product_prod(int,int))),fun(product_prod(int,int),product_prod(int,int)),product_prod_case(int,int,product_prod(int,int)),hAPP(fun(int,fun(int,product_prod(int,int))),fun(int,fun(int,product_prod(int,int))),hAPP(fun(int,fun(fun(int,product_prod(int,int)),fun(int,product_prod(int,int)))),fun(fun(int,fun(int,product_prod(int,int))),fun(int,fun(int,product_prod(int,int)))),combs(int,fun(int,product_prod(int,int)),fun(int,product_prod(int,int))),hAPP(fun(int,fun(int,fun(product_prod(int,int),product_prod(int,int)))),fun(int,fun(fun(int,product_prod(int,int)),fun(int,product_prod(int,int)))),hAPP(fun(fun(int,fun(product_prod(int,int),product_prod(int,int))),fun(fun(int,product_prod(int,int)),fun(int,product_prod(int,int)))),fun(fun(int,fun(int,fun(product_prod(int,int),product_prod(int,int)))),fun(int,fun(fun(int,product_prod(int,int)),fun(int,product_prod(int,int))))),combb(fun(int,fun(product_prod(int,int),product_prod(int,int))),fun(fun(int,product_prod(int,int)),fun(int,product_prod(int,int))),int),combs(int,product_prod(int,int),product_prod(int,int))),hAPP(fun(int,product_prod(int,int)),fun(int,fun(int,fun(product_prod(int,int),product_prod(int,int)))),hAPP(fun(product_prod(int,int),fun(int,fun(product_prod(int,int),product_prod(int,int)))),fun(fun(int,product_prod(int,int)),fun(int,fun(int,fun(product_prod(int,int),product_prod(int,int))))),combb(product_prod(int,int),fun(int,fun(product_prod(int,int),product_prod(int,int))),int),hAPP(fun(int,fun(product_prod(int,int),fun(product_prod(int,int),product_prod(int,int)))),fun(product_prod(int,int),fun(int,fun(product_prod(int,int),product_prod(int,int)))),combc(int,product_prod(int,int),fun(product_prod(int,int),product_prod(int,int))),hAPP(fun(int,bool),fun(int,fun(product_prod(int,int),fun(product_prod(int,int),product_prod(int,int)))),hAPP(fun(bool,fun(product_prod(int,int),fun(product_prod(int,int),product_prod(int,int)))),fun(fun(int,bool),fun(int,fun(product_prod(int,int),fun(product_prod(int,int),product_prod(int,int))))),combb(bool,fun(product_prod(int,int),fun(product_prod(int,int),product_prod(int,int))),int),if(product_prod(int,int))),hAPP(int,fun(int,bool),hAPP(fun(int,fun(int,bool)),fun(int,fun(int,bool)),combc(int,int,bool),fequal(int)),zero_zero(int))))),hAPP(int,fun(int,product_prod(int,int)),hAPP(fun(int,fun(int,product_prod(int,int))),fun(int,fun(int,product_prod(int,int))),combc(int,int,product_prod(int,int)),hAPP(fun(int,int),fun(int,fun(int,product_prod(int,int))),hAPP(fun(int,fun(int,product_prod(int,int))),fun(fun(int,int),fun(int,fun(int,product_prod(int,int)))),combb(int,fun(int,product_prod(int,int)),int),product_Pair(int,int)),uminus_uminus(int))),zero_zero(int))))),hAPP(fun(int,int),fun(int,fun(int,product_prod(int,int))),hAPP(fun(int,fun(fun(int,int),fun(int,product_prod(int,int)))),fun(fun(int,int),fun(int,fun(int,product_prod(int,int)))),combc(int,fun(int,int),fun(int,product_prod(int,int))),hAPP(fun(int,fun(int,product_prod(int,int))),fun(int,fun(fun(int,int),fun(int,product_prod(int,int)))),hAPP(fun(fun(int,product_prod(int,int)),fun(fun(int,int),fun(int,product_prod(int,int)))),fun(fun(int,fun(int,product_prod(int,int))),fun(int,fun(fun(int,int),fun(int,product_prod(int,int))))),combb(fun(int,product_prod(int,int)),fun(fun(int,int),fun(int,product_prod(int,int))),int),combb(int,product_prod(int,int),int)),hAPP(fun(int,int),fun(int,fun(int,product_prod(int,int))),hAPP(fun(int,fun(int,product_prod(int,int))),fun(fun(int,int),fun(int,fun(int,product_prod(int,int)))),combb(int,fun(int,product_prod(int,int)),int),product_Pair(int,int)),hAPP(int,fun(int,int),hAPP(fun(int,fun(int,int)),fun(int,fun(int,int)),combc(int,int,int),hAPP(fun(int,int),fun(int,fun(int,int)),hAPP(fun(int,fun(int,int)),fun(fun(int,int),fun(int,fun(int,int))),combb(int,fun(int,int),int),minus_minus(int)),uminus_uminus(int))),one_one(int))))),hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,abs_abs(int),L))))),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),pdivmod,K),L)))))))) # label(fact_4063_divmod__int__pdivmod) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.83 4001 (all X_a all X_c all X_b all F all X_1 all Y_1 hAPP(product_prod(X_a,X_c),product_prod(X_a,X_b),hAPP(fun(X_c,X_b),fun(product_prod(X_a,X_c),product_prod(X_a,X_b)),product_apsnd(X_c,X_b,X_a),F),hAPP(X_c,product_prod(X_a,X_c),hAPP(X_a,fun(X_c,product_prod(X_a,X_c)),product_Pair(X_a,X_c),X_1),Y_1)) = hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),X_1),hAPP(X_c,X_b,F,Y_1))) # label(fact_4064_apsnd__conv) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.83 4002 (all X_a all X_c all X_b all F all X_1 all G (hAPP(product_prod(X_a,X_c),product_prod(X_a,X_b),hAPP(fun(X_c,X_b),fun(product_prod(X_a,X_c),product_prod(X_a,X_b)),product_apsnd(X_c,X_b,X_a),F),X_1) = hAPP(product_prod(X_a,X_c),product_prod(X_a,X_b),hAPP(fun(X_c,X_b),fun(product_prod(X_a,X_c),product_prod(X_a,X_b)),product_apsnd(X_c,X_b,X_a),G),X_1) <-> hAPP(X_c,X_b,F,hAPP(product_prod(X_a,X_c),X_c,product_snd(X_a,X_c),X_1)) = hAPP(X_c,X_b,G,hAPP(product_prod(X_a,X_c),X_c,product_snd(X_a,X_c),X_1)))) # label(fact_4065_apsnd__eq__conv) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.83 4003 (all X_b all X_a all X_c all F all X_1 hAPP(product_prod(X_b,X_a),X_a,product_snd(X_b,X_a),hAPP(product_prod(X_b,X_c),product_prod(X_b,X_a),hAPP(fun(X_c,X_a),fun(product_prod(X_b,X_c),product_prod(X_b,X_a)),product_apsnd(X_c,X_a,X_b),F),X_1)) = hAPP(X_c,X_a,F,hAPP(product_prod(X_b,X_c),X_c,product_snd(X_b,X_c),X_1))) # label(fact_4066_snd__apsnd) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.83 4004 (all X_a all X_b all X_c all F all X_1 hAPP(product_prod(X_a,X_b),X_a,product_fst(X_a,X_b),hAPP(product_prod(X_a,X_c),product_prod(X_a,X_b),hAPP(fun(X_c,X_b),fun(product_prod(X_a,X_c),product_prod(X_a,X_b)),product_apsnd(X_c,X_b,X_a),F),X_1)) = hAPP(product_prod(X_a,X_c),X_a,product_fst(X_a,X_c),X_1)) # label(fact_4067_fst__apsnd) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.83 4005 (all L all K ((K = zero_zero(int) -> hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),divmod_int,K),L) = hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),zero_zero(int)),zero_zero(int))) & (K != zero_zero(int) -> (L = zero_zero(int) -> hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),divmod_int,K),L) = hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),zero_zero(int)),K)) & (L != zero_zero(int) -> hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),divmod_int,K),L) = hAPP(product_prod(int,int),product_prod(int,int),hAPP(fun(int,int),fun(product_prod(int,int),product_prod(int,int)),product_apsnd(int,int,int),hAPP(int,fun(int,int),times_times(int),hAPP(int,int,sgn_sgn(int),L))),hAPP(product_prod(int,int),product_prod(int,int),hAPP(product_prod(int,int),fun(product_prod(int,int),product_prod(int,int)),hAPP(bool,fun(product_prod(int,int),fun(product_prod(int,int),product_prod(int,int))),if(product_prod(int,int)),hAPP(int,bool,hAPP(int,fun(int,bool),fequal(int),hAPP(int,int,sgn_sgn(int),K)),hAPP(int,int,sgn_sgn(int),L))),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),pdivmod,K),L)),hAPP(product_prod(int,int),product_prod(int,int),hAPP(fun(int,fun(int,product_prod(int,int))),fun(product_prod(int,int),product_prod(int,int)),product_prod_case(int,int,product_prod(int,int)),hAPP(fun(int,fun(int,product_prod(int,int))),fun(int,fun(int,product_prod(int,int))),hAPP(fun(int,fun(fun(int,product_prod(int,int)),fun(int,product_prod(int,int)))),fun(fun(int,fun(int,product_prod(int,int))),fun(int,fun(int,product_prod(int,int)))),combs(int,fun(int,product_prod(int,int)),fun(int,product_prod(int,int))),hAPP(fun(int,fun(int,fun(product_prod(int,int),product_prod(int,int)))),fun(int,fun(fun(int,product_prod(int,int)),fun(int,product_prod(int,int)))),hAPP(fun(fun(int,fun(product_prod(int,int),product_prod(int,int))),fun(fun(int,product_prod(int,int)),fun(int,product_prod(int,int)))),fun(fun(int,fun(int,fun(product_prod(int,int),product_prod(int,int)))),fun(int,fun(fun(int,product_prod(int,int)),fun(int,product_prod(int,int))))),combb(fun(int,fun(product_prod(int,int),product_prod(int,int))),fun(fun(int,product_prod(int,int)),fun(int,product_prod(int,int))),int),combs(int,product_prod(int,int),product_prod(int,int))),hAPP(fun(int,product_prod(int,int)),fun(int,fun(int,fun(product_prod(int,int),product_prod(int,int)))),hAPP(fun(product_prod(int,int),fun(int,fun(product_prod(int,int),product_prod(int,int)))),fun(fun(int,product_prod(int,int)),fun(int,fun(int,fun(product_prod(int,int),product_prod(int,int))))),combb(product_prod(int,int),fun(int,fun(product_prod(int,int),product_prod(int,int))),int),hAPP(fun(int,fun(product_prod(int,int),fun(product_prod(int,int),product_prod(int,int)))),fun(product_prod(int,int),fun(int,fun(product_prod(int,int),product_prod(int,int)))),combc(int,product_prod(int,int),fun(product_prod(int,int),product_prod(int,int))),hAPP(fun(int,bool),fun(int,fun(product_prod(int,int),fun(product_prod(int,int),product_prod(int,int)))),hAPP(fun(bool,fun(product_prod(int,int),fun(product_prod(int,int),product_prod(int,int)))),fun(fun(int,bool),fun(int,fun(product_prod(int,int),fun(product_prod(int,int),product_prod(int,int))))),combb(bool,fun(product_prod(int,int),fun(product_prod(int,int),product_prod(int,int))),int),if(product_prod(int,int))),hAPP(int,fun(int,bool),hAPP(fun(int,fun(int,bool)),fun(int,fun(int,bool)),combc(int,int,bool),fequal(int)),zero_zero(int))))),hAPP(int,fun(int,product_prod(int,int)),hAPP(fun(int,fun(int,product_prod(int,int))),fun(int,fun(int,product_prod(int,int))),combc(int,int,product_prod(int,int)),hAPP(fun(int,int),fun(int,fun(int,product_prod(int,int))),hAPP(fun(int,fun(int,product_prod(int,int))),fun(fun(int,int),fun(int,fun(int,product_prod(int,int)))),combb(int,fun(int,product_prod(int,int)),int),product_Pair(int,int)),uminus_uminus(int))),zero_zero(int))))),hAPP(fun(int,int),fun(int,fun(int,product_prod(int,int))),hAPP(fun(int,fun(fun(int,int),fun(int,product_prod(int,int)))),fun(fun(int,int),fun(int,fun(int,product_prod(int,int)))),combc(int,fun(int,int),fun(int,product_prod(int,int))),hAPP(fun(int,fun(int,product_prod(int,int))),fun(int,fun(fun(int,int),fun(int,product_prod(int,int)))),hAPP(fun(fun(int,product_prod(int,int)),fun(fun(int,int),fun(int,product_prod(int,int)))),fun(fun(int,fun(int,product_prod(int,int))),fun(int,fun(fun(int,int),fun(int,product_prod(int,int))))),combb(fun(int,product_prod(int,int)),fun(fun(int,int),fun(int,product_prod(int,int))),int),combb(int,product_prod(int,int),int)),hAPP(fun(int,int),fun(int,fun(int,product_prod(int,int))),hAPP(fun(int,fun(int,product_prod(int,int))),fun(fun(int,int),fun(int,fun(int,product_prod(int,int)))),combb(int,fun(int,product_prod(int,int)),int),product_Pair(int,int)),hAPP(int,fun(int,int),hAPP(fun(int,fun(int,int)),fun(int,fun(int,int)),combc(int,int,int),hAPP(fun(int,int),fun(int,fun(int,int)),hAPP(fun(int,fun(int,int)),fun(fun(int,int),fun(int,fun(int,int))),combb(int,fun(int,int),int),minus_minus(int)),uminus_uminus(int))),one_one(int))))),hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,abs_abs(int),L))))),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),pdivmod,K),L)))))))) # label(fact_4069_divmod__int__code) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.83 4006 (all F all G ((all N_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),hAPP(nat,real,F,N_2))),hAPP(nat,real,G,N_2)))) -> (hBOOL(hAPP(fun(nat,real),bool,summable(real),G)) -> hBOOL(hAPP(fun(nat,real),bool,summable(real),F)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(fun(nat,real),real,suminf(real),F)),hAPP(fun(nat,real),real,suminf(real),G)))))) # label(fact_4070_summable__le2) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.83 4007 (all F (hBOOL(hAPP(fun(nat,real),bool,summable(real),F)) -> ((all N_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(nat,real,F,N_2)))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(fun(nat,real),real,suminf(real),F)))))) # label(fact_4071_suminf__gt__zero) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.83 4008 (all F (hBOOL(hAPP(fun(nat,real),bool,summable(real),F)) -> ((all N_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(nat,real,F,N_2)))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(fun(nat,real),real,suminf(real),F)))))) # label(fact_4072_suminf__ge__zero) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.83 4009 (all F ((all N_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(nat,real,F,N_2)))) -> (hBOOL(hAPP(fun(nat,real),bool,summable(real),F)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(fun(nat,real),real,suminf(real),F)))))) # label(fact_4073_suminf__0__le) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.83 4010 (all D_1 hAPP(int,fun(product_prod(int,int),bool),int_ge_less_than,D_1) = hAPP(fun(product_prod(int,int),bool),fun(product_prod(int,int),bool),collect(product_prod(int,int)),hAPP(fun(int,fun(int,bool)),fun(product_prod(int,int),bool),product_prod_case(int,int,bool),hAPP(fun(int,fun(int,bool)),fun(int,fun(int,bool)),hAPP(fun(int,fun(fun(int,bool),fun(int,bool))),fun(fun(int,fun(int,bool)),fun(int,fun(int,bool))),combs(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(int,fun(int,bool),ord_less_eq(int),D_1)))),ord_less(int))))) # label(fact_4074_int__ge__less__than__def) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.83 4011 (all D_1 hAPP(int,fun(product_prod(int,int),bool),int_ge_less_than2,D_1) = hAPP(fun(product_prod(int,int),bool),fun(product_prod(int,int),bool),collect(product_prod(int,int)),hAPP(fun(int,fun(int,bool)),fun(product_prod(int,int),bool),product_prod_case(int,int,bool),hAPP(fun(int,fun(int,bool)),fun(int,fun(int,bool)),hAPP(fun(fun(int,bool),fun(int,bool)),fun(fun(int,fun(int,bool)),fun(int,fun(int,bool))),combb(fun(int,bool),fun(int,bool),int),hAPP(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),combs(int,bool,bool),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(int,fun(int,bool),ord_less_eq(int),D_1)))),ord_less(int))))) # label(fact_4075_int__ge__less__than2__def) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.83 4012 (all X_1 hBOOL(hAPP(real,bool,hAPP(fun(nat,real),fun(real,bool),sums(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),inverse_divide(real)),hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),min)))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),hAPP(fun(nat,nat),fun(nat,nat),hAPP(fun(nat,nat),fun(fun(nat,nat),fun(nat,nat)),combb(nat,nat,nat),fact_fact(nat)),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),plus_plus(nat)),hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),one_one(nat))))))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),hAPP(real,fun(nat,real),power_power(real),X_1)),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),plus_plus(nat)),hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),one_one(nat))))),hAPP(real,real,sin,X_1)))) # label(fact_4076_sin__paired) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.83 4013 (all X_a (real_algebra_1(X_a) & real_normed_vector(X_a) -> (all X_3 (hBOOL(hAPP(fun(nat,real),bool,cauchy(real),X_3)) -> hBOOL(hAPP(fun(nat,X_a),bool,cauchy(X_a),hAPP(fun(nat,real),fun(nat,X_a),hAPP(fun(real,X_a),fun(fun(nat,real),fun(nat,X_a)),combb(real,X_a,nat),of_real(X_a)),X_3))))))) # label(fact_4077_of__real_OCauchy) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.83 4014 (all X_a (comm_monoid_add(X_a) & topological_space(X_a) -> hBOOL(hAPP(X_a,bool,hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),hAPP(X_a,fun(nat,X_a),combk(X_a,nat),zero_zero(X_a))),zero_zero(X_a))))) # label(fact_4078_sums__zero) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.83 4015 (all X_a (real_normed_field(X_a) -> (all X_3 all Aa (hBOOL(hAPP(X_a,bool,hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),X_3),Aa)) -> hBOOL(hAPP(X_a,bool,hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(X_a,X_a),fun(fun(nat,X_a),fun(nat,X_a)),combb(X_a,X_a,nat),uminus_uminus(X_a)),X_3)),hAPP(X_a,X_a,uminus_uminus(X_a),Aa))))))) # label(fact_4079_sums__minus) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.83 4016 (all X_a (real_normed_algebra(X_a) -> (all C_1 all F all Aa (hBOOL(hAPP(X_a,bool,hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),F),Aa)) -> hBOOL(hAPP(X_a,bool,hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(X_a,X_a),fun(fun(nat,X_a),fun(nat,X_a)),combb(X_a,X_a,nat),hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1)),F)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1),Aa))))))) # label(fact_4080_sums__mult) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.83 4017 (all X_a (real_normed_algebra(X_a) -> (all C_1 all F all Aa (hBOOL(hAPP(X_a,bool,hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),F),Aa)) -> hBOOL(hAPP(X_a,bool,hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),hAPP(X_a,fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(X_a,fun(nat,X_a)),combc(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),times_times(X_a)),F)),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Aa),C_1))))))) # label(fact_4081_sums__mult2) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.83 4018 (all X_a (real_normed_algebra(X_a) -> (all X_1 all X_3 all Aa (hBOOL(hAPP(X_a,bool,hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),X_3),Aa)) -> hBOOL(hAPP(X_a,bool,hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(X_a,X_a),fun(fun(nat,X_a),fun(nat,X_a)),combb(X_a,X_a,nat),hAPP(X_a,fun(X_a,X_a),times_times(X_a),X_1)),X_3)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X_1),Aa))))))) # label(fact_4082_mult__right_Osums) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.83 4019 (all X_a (real_normed_algebra(X_a) -> (all Y_1 all X_3 all Aa (hBOOL(hAPP(X_a,bool,hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),X_3),Aa)) -> hBOOL(hAPP(X_a,bool,hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),hAPP(X_a,fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(X_a,fun(nat,X_a)),combc(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),times_times(X_a)),X_3)),Y_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Aa),Y_1))))))) # label(fact_4083_mult__left_Osums) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.83 4020 (all X_a (real_algebra_1(X_a) & real_normed_vector(X_a) -> (all X_3 all Aa (hBOOL(hAPP(real,bool,hAPP(fun(nat,real),fun(real,bool),sums(real),X_3),Aa)) -> hBOOL(hAPP(X_a,bool,hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),hAPP(fun(nat,real),fun(nat,X_a),hAPP(fun(real,X_a),fun(fun(nat,real),fun(nat,X_a)),combb(real,X_a,nat),of_real(X_a)),X_3)),hAPP(real,X_a,of_real(X_a),Aa))))))) # label(fact_4084_of__real_Osums) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.83 4021 (all X_a (real_normed_field(X_a) -> (all Y_1 all X_3 all Aa (hBOOL(hAPP(X_a,bool,hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),X_3),Aa)) -> hBOOL(hAPP(X_a,bool,hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),hAPP(X_a,fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(X_a,fun(nat,X_a)),combc(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),inverse_divide(X_a)),X_3)),Y_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),Aa),Y_1))))))) # label(fact_4085_divide_Osums) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.83 4022 (all X_a (real_normed_field(X_a) -> (all C_1 all F all Aa (hBOOL(hAPP(X_a,bool,hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),F),Aa)) -> hBOOL(hAPP(X_a,bool,hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),hAPP(X_a,fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(X_a,fun(nat,X_a)),combc(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),inverse_divide(X_a)),F)),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),Aa),C_1))))))) # label(fact_4086_sums__divide) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.83 4023 (all X_a (real_normed_field(X_a) -> (all Y_3 all Ba all X_3 all Aa (hBOOL(hAPP(X_a,bool,hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),X_3),Aa)) -> (hBOOL(hAPP(X_a,bool,hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),Y_3),Ba)) -> hBOOL(hAPP(X_a,bool,hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),minus_minus(X_a)),X_3)),Y_3)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),Aa),Ba)))))))) # label(fact_4087_sums__diff) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.83 4024 (all X_a (real_normed_field(X_a) -> (all Y_3 all Ba all X_3 all Aa (hBOOL(hAPP(X_a,bool,hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),X_3),Aa)) -> (hBOOL(hAPP(X_a,bool,hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),Y_3),Ba)) -> hBOOL(hAPP(X_a,bool,hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),plus_plus(X_a)),X_3)),Y_3)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Aa),Ba)))))))) # label(fact_4088_sums__add) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.83 4025 (all X_a (comm_monoid_add(X_a) & t2_space(X_a) -> (all F all S_3 (hBOOL(hAPP(X_a,bool,hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),F),S_3)) -> ti(X_a,S_3) = hAPP(fun(nat,X_a),X_a,suminf(X_a),F))))) # label(fact_4089_sums__unique) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.83 4026 (all X_a (comm_monoid_add(X_a) & topological_space(X_a) -> (all F all L (hBOOL(hAPP(X_a,bool,hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),F),L)) -> hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),F)))))) # label(fact_4090_sums__summable) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.83 4027 (all X_a (comm_monoid_add(X_a) & topological_space(X_a) -> (all F (hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),F)) <-> (exists X1 hBOOL(hAPP(X_a,bool,hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),F),X1))))))) # label(fact_4091_summable__def) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.83 4028 (all X_a (comm_monoid_add(X_a) & t2_space(X_a) -> (all F all X_1 (hBOOL(hAPP(X_a,bool,hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),F),X_1)) <-> hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),F)) & hAPP(fun(nat,X_a),X_a,suminf(X_a),F) = ti(X_a,X_1))))) # label(fact_4092_sums__iff) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.83 4029 (all X_a (comm_monoid_add(X_a) & t2_space(X_a) -> (all F (hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),F)) -> hBOOL(hAPP(X_a,bool,hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),F),hAPP(fun(nat,X_a),X_a,suminf(X_a),F))))))) # label(fact_4093_summable__sums) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.83 4030 (all X_a (comm_monoid_add(X_a) & topological_space(X_a) -> (all S_3 all F (hAPP(nat,X_a,F,zero_zero(nat)) = zero_zero(X_a) -> (hBOOL(hAPP(X_a,bool,hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),hAPP(fun(nat,nat),fun(nat,X_a),hAPP(fun(nat,X_a),fun(fun(nat,nat),fun(nat,X_a)),combb(nat,X_a,nat),F),suc)),S_3)) -> hBOOL(hAPP(X_a,bool,hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),F),S_3))))))) # label(fact_4094_sums__Suc__imp) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.83 4031 (all X_a (real_normed_vector(X_a) -> (all F all L (hBOOL(hAPP(X_a,bool,hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),hAPP(fun(nat,nat),fun(nat,X_a),hAPP(fun(nat,X_a),fun(fun(nat,nat),fun(nat,X_a)),combb(nat,X_a,nat),F),suc)),L)) -> hBOOL(hAPP(X_a,bool,hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),F),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),L),hAPP(nat,X_a,F,zero_zero(nat))))))))) # label(fact_4095_sums__Suc) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.83 4032 (all X_1 hBOOL(hAPP(real,bool,hAPP(fun(nat,real),fun(real,bool),sums(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),sin_coeff)),hAPP(real,fun(nat,real),power_power(real),X_1))),hAPP(real,real,sin,X_1)))) # label(fact_4096_sin__converges) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.83 4033 (all X_1 hBOOL(hAPP(real,bool,hAPP(fun(nat,real),fun(real,bool),sums(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),cos_coeff)),hAPP(real,fun(nat,real),power_power(real),X_1))),hAPP(real,real,cos,X_1)))) # label(fact_4097_cos__converges) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.83 4034 (all X_a (real_normed_field(X_a) -> (all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,norm_norm(X_a),X_1)),one_one(real))) -> hBOOL(hAPP(X_a,bool,hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),hAPP(X_a,fun(nat,X_a),power_power(X_a),X_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),one_one(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),one_one(X_a)),X_1)))))))) # label(fact_4098_geometric__sums) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.84 4035 (all X_a (real_normed_algebra(X_a) -> (all Y_1 all X_3 (hBOOL(hAPP(fun(nat,X_a),bool,cauchy(X_a),X_3)) -> hBOOL(hAPP(fun(nat,X_a),bool,cauchy(X_a),hAPP(X_a,fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(X_a,fun(nat,X_a)),combc(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),times_times(X_a)),X_3)),Y_1))))))) # label(fact_4100_mult__left_OCauchy) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.84 4036 (all X_a (real_normed_algebra(X_a) -> (all X_1 all X_3 (hBOOL(hAPP(fun(nat,X_a),bool,cauchy(X_a),X_3)) -> hBOOL(hAPP(fun(nat,X_a),bool,cauchy(X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(X_a,X_a),fun(fun(nat,X_a),fun(nat,X_a)),combb(X_a,X_a,nat),hAPP(X_a,fun(X_a,X_a),times_times(X_a),X_1)),X_3))))))) # label(fact_4101_mult__right_OCauchy) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.84 4037 (all X_a (real_normed_field(X_a) -> (all Y_1 all X_3 (hBOOL(hAPP(fun(nat,X_a),bool,cauchy(X_a),X_3)) -> hBOOL(hAPP(fun(nat,X_a),bool,cauchy(X_a),hAPP(X_a,fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(X_a,fun(nat,X_a)),combc(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),inverse_divide(X_a)),X_3)),Y_1))))))) # label(fact_4102_divide_OCauchy) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.84 4038 (all X_1 hBOOL(hAPP(real,bool,hAPP(fun(nat,real),fun(real,bool),sums(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),one_one(real)),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))) # label(fact_4103_Ln_Oaux2) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.84 4039 (all G all X_1 (hBOOL(hAPP(real,bool,hAPP(fun(nat,real),fun(real,bool),sums(real),G),X_1)) -> hBOOL(hAPP(real,bool,hAPP(fun(nat,real),fun(real,bool),sums(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(real,fun(nat,fun(real,real)),hAPP(fun(nat,fun(real,fun(real,real))),fun(real,fun(nat,fun(real,real))),combc(nat,real,fun(real,real)),hAPP(fun(nat,bool),fun(nat,fun(real,fun(real,real))),hAPP(fun(bool,fun(real,fun(real,real))),fun(fun(nat,bool),fun(nat,fun(real,fun(real,real)))),combb(bool,fun(real,fun(real,real)),nat),if(real)),even_odd_even(nat))),zero_zero(real))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),G),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),div_div(nat)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),minus_minus(nat)),one_one(nat)))),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))),X_1)))) # label(fact_4104_sums__if_H) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.84 4040 (all F all Y_1 all G all X_1 (hBOOL(hAPP(real,bool,hAPP(fun(nat,real),fun(real,bool),sums(real),G),X_1)) -> (hBOOL(hAPP(real,bool,hAPP(fun(nat,real),fun(real,bool),sums(real),F),Y_1)) -> hBOOL(hAPP(real,bool,hAPP(fun(nat,real),fun(real,bool),sums(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(nat,fun(real,fun(real,real))),fun(fun(nat,real),fun(nat,fun(real,real))),combs(nat,real,fun(real,real)),hAPP(fun(nat,bool),fun(nat,fun(real,fun(real,real))),hAPP(fun(bool,fun(real,fun(real,real))),fun(fun(nat,bool),fun(nat,fun(real,fun(real,real)))),combb(bool,fun(real,fun(real,real)),nat),if(real)),even_odd_even(nat))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),F),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),div_div(nat)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),G),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),div_div(nat)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),minus_minus(nat)),one_one(nat)))),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X_1),Y_1)))))) # label(fact_4105_sums__if) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.84 4041 (all X_1 hBOOL(hAPP(real,bool,hAPP(fun(nat,real),fun(real,bool),sums(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),inverse_divide(real)),hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),min)))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),hAPP(fun(nat,nat),fun(nat,nat),hAPP(fun(nat,nat),fun(fun(nat,nat),fun(nat,nat)),combb(nat,nat,nat),fact_fact(nat)),hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),hAPP(real,fun(nat,real),power_power(real),X_1)),hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))),hAPP(real,real,cos,X_1)))) # label(fact_4106_cos__paired) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.84 4042 (all X_a (real_normed_vector(X_a) & ring_1(X_a) -> (all C_1 all X_1 (hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),times_times(X_a)),hAPP(fun(nat,X_a),fun(nat,X_a),diffs(X_a),C_1))),hAPP(X_a,fun(nat,X_a),power_power(X_a),X_1)))) -> hBOOL(hAPP(X_a,bool,hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),times_times(X_a)),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),times_times(X_a)),semiring_1_of_nat(X_a))),C_1))),hAPP(fun(nat,nat),fun(nat,X_a),hAPP(fun(nat,X_a),fun(fun(nat,nat),fun(nat,X_a)),combb(nat,X_a,nat),hAPP(X_a,fun(nat,X_a),power_power(X_a),X_1)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),minus_minus(nat)),hAPP(nat,nat,suc,zero_zero(nat)))))),hAPP(fun(nat,X_a),X_a,suminf(X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),times_times(X_a)),hAPP(fun(nat,X_a),fun(nat,X_a),diffs(X_a),C_1))),hAPP(X_a,fun(nat,X_a),power_power(X_a),X_1))))))))) # label(fact_4107_diffs__equiv) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.84 4043 (all X_a all Aa all F all V_1 all N hAPP(nat,X_a,hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(X_a,fun(fun(nat,X_a),fun(nat,X_a)),nat_case(X_a),Aa),F),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),V_1)),N)) = 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),hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),hAPP(int,int,pred,V_1)))),hAPP(nat,X_a,hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(X_a,fun(fun(nat,X_a),fun(nat,X_a)),nat_case(X_a),Aa),F),N)),hAPP(nat,X_a,F,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,nat_1,hAPP(int,int,number_number_of(int),hAPP(int,int,pred,V_1)))),N)))) # label(fact_4108_nat__case__add__eq__if) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.84 4044 (all X_3 all Aa (hBOOL(hAPP(complex,bool,hAPP(fun(nat,complex),fun(complex,bool),sums(complex),X_3),Aa)) -> hBOOL(hAPP(complex,bool,hAPP(fun(nat,complex),fun(complex,bool),sums(complex),hAPP(fun(nat,complex),fun(nat,complex),hAPP(fun(complex,complex),fun(fun(nat,complex),fun(nat,complex)),combb(complex,complex,nat),cnj),X_3)),hAPP(complex,complex,cnj,Aa))))) # label(fact_4109_cnj_Osums) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.84 4045 (all X_a all F1 all F2 all Nat hAPP(nat,X_a,hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(X_a,fun(fun(nat,X_a),fun(nat,X_a)),nat_case(X_a),F1),F2),hAPP(nat,nat,suc,Nat)) = hAPP(nat,X_a,F2,Nat)) # label(fact_4110_nat__case__Suc) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.84 4046 (all X_a (real_algebra_1(X_a) -> (all F all X_2 hAPP(nat,X_a,hAPP(fun(nat,X_a),fun(nat,X_a),diffs(X_a),hAPP(fun(nat,real),fun(nat,X_a),hAPP(fun(real,X_a),fun(fun(nat,real),fun(nat,X_a)),combb(real,X_a,nat),of_real(X_a)),F)),X_2) = hAPP(real,X_a,of_real(X_a),hAPP(nat,real,hAPP(fun(nat,real),fun(nat,real),diffs(real),F),X_2))))) # label(fact_4111_diffs__of__real) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.84 4047 (all X_a all F1 all F2 hAPP(nat,X_a,hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(X_a,fun(fun(nat,X_a),fun(nat,X_a)),nat_case(X_a),F1),F2),zero_zero(nat)) = ti(X_a,F1)) # label(fact_4112_nat__case__0) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.84 4048 (all X_a (ring_1(X_a) -> (all C_1 all X_2 hAPP(nat,X_a,hAPP(fun(nat,X_a),fun(nat,X_a),diffs(X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(X_a,X_a),fun(fun(nat,X_a),fun(nat,X_a)),combb(X_a,X_a,nat),uminus_uminus(X_a)),C_1)),X_2) = hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(nat,X_a,hAPP(fun(nat,X_a),fun(nat,X_a),diffs(X_a),C_1),X_2))))) # label(fact_4113_diffs__minus) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.84 4049 (all X_3 all Aa (hBOOL(hAPP(complex,bool,hAPP(fun(nat,complex),fun(complex,bool),sums(complex),X_3),Aa)) -> hBOOL(hAPP(real,bool,hAPP(fun(nat,real),fun(real,bool),sums(real),hAPP(fun(nat,complex),fun(nat,real),hAPP(fun(complex,real),fun(fun(nat,complex),fun(nat,real)),combb(complex,real,nat),re),X_3)),hAPP(complex,real,re,Aa))))) # label(fact_4114_Re_Osums) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.84 4050 (all X_3 all Aa (hBOOL(hAPP(complex,bool,hAPP(fun(nat,complex),fun(complex,bool),sums(complex),X_3),Aa)) -> hBOOL(hAPP(real,bool,hAPP(fun(nat,real),fun(real,bool),sums(real),hAPP(fun(nat,complex),fun(nat,real),hAPP(fun(complex,real),fun(fun(nat,complex),fun(nat,real)),combb(complex,real,nat),im),X_3)),hAPP(complex,real,im,Aa))))) # label(fact_4115_Im_Osums) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.84 4051 (all N hAPP(nat,real,hAPP(fun(nat,real),fun(nat,real),diffs(real),sin_coeff),N) = hAPP(nat,real,cos_coeff,N)) # label(fact_4116_sin__fdiffs2) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.84 4052 (all X_a (ring_1(X_a) -> (all C_1 all X_2 hAPP(nat,X_a,hAPP(fun(nat,X_a),fun(nat,X_a),diffs(X_a),C_1),X_2) = 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),hAPP(nat,nat,suc,X_2))),hAPP(nat,X_a,C_1,hAPP(nat,nat,suc,X_2)))))) # label(fact_4118_diffs__def) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.84 4053 (all X_2 hAPP(nat,real,hAPP(fun(nat,real),fun(nat,real),diffs(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),inverse_inverse(real)),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),fact_fact(nat)))),X_2) = hAPP(real,real,inverse_inverse(real),hAPP(nat,real,real_1(nat),hAPP(nat,nat,fact_fact(nat),X_2)))) # label(fact_4119_exp__fdiffs) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.84 4054 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,M)),N)) <-> hBOOL(hAPP(nat,bool,hAPP(fun(nat,bool),fun(nat,bool),hAPP(bool,fun(fun(nat,bool),fun(nat,bool)),nat_case(bool),fFalse),hAPP(nat,fun(nat,bool),ord_less_eq(nat),M)),N)))) # label(fact_4120_less__eq__nat_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.84 4055 (all X_2 hAPP(nat,real,hAPP(fun(nat,real),fun(nat,real),diffs(real),cos_coeff),X_2) = hAPP(real,real,uminus_uminus(real),hAPP(nat,real,sin_coeff,X_2))) # label(fact_4121_cos__fdiffs) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.84 4056 (all N hAPP(nat,real,hAPP(fun(nat,real),fun(nat,real),diffs(real),cos_coeff),N) = hAPP(real,real,uminus_uminus(real),hAPP(nat,real,sin_coeff,N))) # label(fact_4122_cos__fdiffs2) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.84 4057 (all M all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),hAPP(nat,nat,suc,N)) = hAPP(nat,nat,hAPP(fun(nat,nat),fun(nat,nat),hAPP(nat,fun(fun(nat,nat),fun(nat,nat)),nat_case(nat),zero_zero(nat)),combi(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N))) # label(fact_4123_diff__Suc) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.84 4058 (all X_a (real_normed_field(X_a) & banach(X_a) -> (all X_1 all C_1 all K_3 (hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),times_times(X_a)),C_1)),hAPP(X_a,fun(nat,X_a),power_power(X_a),K_3)))) -> (hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),times_times(X_a)),hAPP(fun(nat,X_a),fun(nat,X_a),diffs(X_a),C_1))),hAPP(X_a,fun(nat,X_a),power_power(X_a),K_3)))) -> (hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),times_times(X_a)),hAPP(fun(nat,X_a),fun(nat,X_a),diffs(X_a),hAPP(fun(nat,X_a),fun(nat,X_a),diffs(X_a),C_1)))),hAPP(X_a,fun(nat,X_a),power_power(X_a),K_3)))) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,norm_norm(X_a),X_1)),hAPP(X_a,real,norm_norm(X_a),K_3))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),hAPP(fun(X_a,fun(nat,X_a)),fun(X_a,X_a),hAPP(fun(fun(nat,X_a),X_a),fun(fun(X_a,fun(nat,X_a)),fun(X_a,X_a)),combb(fun(nat,X_a),X_a,X_a),suminf(X_a)),hAPP(fun(X_a,fun(nat,X_a)),fun(X_a,fun(nat,X_a)),hAPP(fun(fun(nat,X_a),fun(nat,X_a)),fun(fun(X_a,fun(nat,X_a)),fun(X_a,fun(nat,X_a))),combb(fun(nat,X_a),fun(nat,X_a),X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),times_times(X_a)),C_1))),power_power(X_a)))),X_1),hAPP(fun(nat,X_a),X_a,suminf(X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),times_times(X_a)),hAPP(fun(nat,X_a),fun(nat,X_a),diffs(X_a),C_1))),hAPP(X_a,fun(nat,X_a),power_power(X_a),X_1)))))))))))) # label(fact_4124_termdiffs) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.84 4059 (all X_a all Aa all F all V_1 hAPP(nat,X_a,hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(X_a,fun(fun(nat,X_a),fun(nat,X_a)),nat_case(X_a),Aa),F),hAPP(int,nat,number_number_of(nat),V_1)) = 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),hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),hAPP(int,int,pred,V_1)))),Aa),hAPP(nat,X_a,F,hAPP(int,nat,nat_1,hAPP(int,int,number_number_of(int),hAPP(int,int,pred,V_1)))))) # label(fact_4125_nat__case__number__of) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.84 4060 (all X_c all X_b all X_a all Q_1 all F all P_1 all Pa (hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),P_1,hAPP(product_prod(X_b,X_a),X_a,product_snd(X_b,X_a),Pa)),hAPP(product_prod(X_b,X_a),X_b,product_fst(X_b,X_a),Pa))) -> ((all X_2 all Y_2 (hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),P_1,Y_2),X_2)) -> hBOOL(hAPP(X_c,bool,Q_1,hAPP(X_a,X_c,hAPP(X_b,fun(X_a,X_c),F,X_2),Y_2))))) -> hBOOL(hAPP(X_c,bool,Q_1,hAPP(product_prod(X_b,X_a),X_c,hAPP(fun(X_b,fun(X_a,X_c)),fun(product_prod(X_b,X_a),X_c),product_prod_case(X_b,X_a,X_c),F),Pa)))))) # label(fact_4126_exE__realizer) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.84 4061 (all X_a all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2)) <-> (exists N_2 exists F_3 ti(fun(X_a,bool),A_2) = hAPP(fun(nat,bool),fun(X_a,bool),hAPP(fun(nat,X_a),fun(fun(nat,bool),fun(X_a,bool)),image(nat,X_a),F_3),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_4127_finite__conv__nat__seg__image) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.84 4062 (all X_a all F all X_1 all A_2 ((all I_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),I_2),A_2)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),hAPP(X_a,nat,F,I_2)),X_1) = one_one(nat))) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),hAPP(fun(X_a,bool),nat,hAPP(fun(X_a,nat),fun(fun(X_a,bool),nat),big_co302546470etprod(X_a,nat),F),A_2)),X_1) = one_one(nat))) # label(fact_4128_setprod__coprime__nat) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.84 4063 (all F all G ((all N_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,F,N_2)),hAPP(nat,real,G,N_2)))) -> (hBOOL(hAPP(fun(nat,real),bool,summable(real),F)) -> (hBOOL(hAPP(fun(nat,real),bool,summable(real),G)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(fun(nat,real),real,suminf(real),F)),hAPP(fun(nat,real),real,suminf(real),G))))))) # label(fact_4129_summable__le) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.84 4064 (all X_a (order(X_a) -> (all X_3 ((all M_3 all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_3),N_2)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(nat,X_a,X_3,M_3)),hAPP(nat,X_a,X_3,N_2))))) -> hBOOL(hAPP(fun(nat,X_a),bool,monoseq(X_a),X_3)))))) # label(fact_4130_monoI1) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.84 4065 (all X_a (order(X_a) -> (all X_3 ((all M_3 all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_3),N_2)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(nat,X_a,X_3,N_2)),hAPP(nat,X_a,X_3,M_3))))) -> hBOOL(hAPP(fun(nat,X_a),bool,monoseq(X_a),X_3)))))) # label(fact_4131_monoI2) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.84 4066 (all Y_1 hAPP(real,real,arctan,Y_1) = hAPP(fun(real,bool),real,the(real),hAPP(fun(real,bool),fun(real,bool),hAPP(fun(real,fun(bool,bool)),fun(fun(real,bool),fun(real,bool)),combs(real,bool,bool),hAPP(fun(real,bool),fun(real,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(real,bool),fun(real,fun(bool,bool))),combb(bool,fun(bool,bool),real),fconj),hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))),hAPP(fun(real,bool),fun(real,bool),hAPP(fun(real,fun(bool,bool)),fun(fun(real,bool),fun(real,bool)),combs(real,bool,bool),hAPP(fun(real,bool),fun(real,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(real,bool),fun(real,fun(bool,bool))),combb(bool,fun(bool,bool),real),fconj),hAPP(real,fun(real,bool),hAPP(fun(real,fun(real,bool)),fun(real,fun(real,bool)),combc(real,real,bool),ord_less(real)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))),hAPP(real,fun(real,bool),hAPP(fun(real,fun(real,bool)),fun(real,fun(real,bool)),combc(real,real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),hAPP(fun(real,fun(real,bool)),fun(fun(real,real),fun(real,fun(real,bool))),combb(real,fun(real,bool),real),fequal(real)),tan)),Y_1))))) # label(fact_4132_arctan__def) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.84 4067 (all Y_1 hAPP(real,real,arcsin,Y_1) = hAPP(fun(real,bool),real,the(real),hAPP(fun(real,bool),fun(real,bool),hAPP(fun(real,fun(bool,bool)),fun(fun(real,bool),fun(real,bool)),combs(real,bool,bool),hAPP(fun(real,bool),fun(real,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(real,bool),fun(real,fun(bool,bool))),combb(bool,fun(bool,bool),real),fconj),hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))),hAPP(fun(real,bool),fun(real,bool),hAPP(fun(real,fun(bool,bool)),fun(fun(real,bool),fun(real,bool)),combs(real,bool,bool),hAPP(fun(real,bool),fun(real,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(real,bool),fun(real,fun(bool,bool))),combb(bool,fun(bool,bool),real),fconj),hAPP(real,fun(real,bool),hAPP(fun(real,fun(real,bool)),fun(real,fun(real,bool)),combc(real,real,bool),ord_less_eq(real)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))),hAPP(real,fun(real,bool),hAPP(fun(real,fun(real,bool)),fun(real,fun(real,bool)),combc(real,real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),hAPP(fun(real,fun(real,bool)),fun(fun(real,real),fun(real,fun(real,bool))),combb(real,fun(real,bool),real),fequal(real)),sin)),Y_1))))) # label(fact_4133_arcsin__def) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.84 4068 (all X_1 hAPP(real,real,ln,X_1) = hAPP(fun(real,bool),real,the(real),hAPP(real,fun(real,bool),hAPP(fun(real,fun(real,bool)),fun(real,fun(real,bool)),combc(real,real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),hAPP(fun(real,fun(real,bool)),fun(fun(real,real),fun(real,fun(real,bool))),combb(real,fun(real,bool),real),fequal(real)),exp(real))),X_1))) # label(fact_4134_ln__def) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.84 4069 (all X_a (comm_monoid_add(X_a) & topological_space(X_a) -> (all F hAPP(fun(nat,X_a),X_a,suminf(X_a),F) = hAPP(fun(X_a,bool),X_a,the(X_a),hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),F))))) # label(fact_4135_suminf__def) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.84 4070 (all N all X_1 ((hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X_1)) -> hAPP(real,real,hAPP(nat,fun(real,real),root,N),X_1) = hAPP(fun(real,bool),real,the(real),hAPP(fun(real,bool),fun(real,bool),hAPP(fun(real,fun(bool,bool)),fun(fun(real,bool),fun(real,bool)),combs(real,bool,bool),hAPP(fun(real,bool),fun(real,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(real,bool),fun(real,fun(bool,bool))),combb(bool,fun(bool,bool),real),fconj),hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)))),hAPP(real,fun(real,bool),hAPP(fun(real,fun(real,bool)),fun(real,fun(real,bool)),combc(real,real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),hAPP(fun(real,fun(real,bool)),fun(fun(real,real),fun(real,fun(real,bool))),combb(real,fun(real,bool),real),fequal(real)),hAPP(nat,fun(real,real),hAPP(fun(real,fun(nat,real)),fun(nat,fun(real,real)),combc(real,nat,real),power_power(real)),N))),X_1)))) & (-hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_1),zero_zero(real))) -> hAPP(real,real,hAPP(nat,fun(real,real),root,N),X_1) = hAPP(real,real,uminus_uminus(real),hAPP(fun(real,bool),real,the(real),hAPP(fun(real,bool),fun(real,bool),hAPP(fun(real,fun(bool,bool)),fun(fun(real,bool),fun(real,bool)),combs(real,bool,bool),hAPP(fun(real,bool),fun(real,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(real,bool),fun(real,fun(bool,bool))),combb(bool,fun(bool,bool),real),fconj),hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)))),hAPP(real,fun(real,bool),hAPP(fun(real,fun(real,bool)),fun(real,fun(real,bool)),combc(real,real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),hAPP(fun(real,fun(real,bool)),fun(fun(real,real),fun(real,fun(real,bool))),combb(real,fun(real,bool),real),fequal(real)),hAPP(nat,fun(real,real),hAPP(fun(real,fun(nat,real)),fun(nat,fun(real,real)),combc(real,nat,real),power_power(real)),N))),hAPP(real,real,uminus_uminus(real),X_1)))))) & (-hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_1),zero_zero(real))) -> hAPP(real,real,hAPP(nat,fun(real,real),root,N),X_1) = zero_zero(real))))) # label(fact_4136_root__def) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.84 4071 (all Y_1 hAPP(real,real,arccos,Y_1) = hAPP(fun(real,bool),real,the(real),hAPP(fun(real,bool),fun(real,bool),hAPP(fun(real,fun(bool,bool)),fun(fun(real,bool),fun(real,bool)),combs(real,bool,bool),hAPP(fun(real,bool),fun(real,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(real,bool),fun(real,fun(bool,bool))),combb(bool,fun(bool,bool),real),fconj),hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)))),hAPP(fun(real,bool),fun(real,bool),hAPP(fun(real,fun(bool,bool)),fun(fun(real,bool),fun(real,bool)),combs(real,bool,bool),hAPP(fun(real,bool),fun(real,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(real,bool),fun(real,fun(bool,bool))),combb(bool,fun(bool,bool),real),fconj),hAPP(real,fun(real,bool),hAPP(fun(real,fun(real,bool)),fun(real,fun(real,bool)),combc(real,real,bool),ord_less_eq(real)),pi))),hAPP(real,fun(real,bool),hAPP(fun(real,fun(real,bool)),fun(real,fun(real,bool)),combc(real,real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),hAPP(fun(real,fun(real,bool)),fun(fun(real,real),fun(real,fun(real,bool))),combb(real,fun(real,bool),real),fequal(real)),cos)),Y_1))))) # label(fact_4137_arccos__def) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.84 4072 (all X_a (order(X_a) -> (all X_3 ((all N_2 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(nat,X_a,X_3,hAPP(nat,nat,suc,N_2))),hAPP(nat,X_a,X_3,N_2)))) -> hBOOL(hAPP(fun(nat,X_a),bool,monoseq(X_a),X_3)))))) # label(fact_4140_mono__SucI2) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.84 4073 (all X_a (order(X_a) -> (all X_3 ((all N_2 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(nat,X_a,X_3,N_2)),hAPP(nat,X_a,X_3,hAPP(nat,nat,suc,N_2))))) -> hBOOL(hAPP(fun(nat,X_a),bool,monoseq(X_a),X_3)))))) # label(fact_4141_mono__SucI1) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.84 4074 (all X_a all X_b all P_1 hAPP(fun(product_prod(X_a,X_b),bool),product_prod(X_a,X_b),the(product_prod(X_a,X_b)),P_1) = hAPP(fun(product_prod(X_a,X_b),bool),product_prod(X_a,X_b),the(product_prod(X_a,X_b)),hAPP(fun(X_a,fun(X_b,bool)),fun(product_prod(X_a,X_b),bool),product_prod_case(X_a,X_b,bool),hAPP(fun(X_a,fun(X_b,product_prod(X_a,X_b))),fun(X_a,fun(X_b,bool)),hAPP(fun(fun(X_b,product_prod(X_a,X_b)),fun(X_b,bool)),fun(fun(X_a,fun(X_b,product_prod(X_a,X_b))),fun(X_a,fun(X_b,bool))),combb(fun(X_b,product_prod(X_a,X_b)),fun(X_b,bool),X_a),hAPP(fun(product_prod(X_a,X_b),bool),fun(fun(X_b,product_prod(X_a,X_b)),fun(X_b,bool)),combb(product_prod(X_a,X_b),bool,X_b),P_1)),product_Pair(X_a,X_b))))) # label(fact_4142_split__paired__The) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.84 4075 (all X_a all X_b all X_1 all Y_1 hAPP(fun(product_prod(X_a,X_b),bool),product_prod(X_a,X_b),the(product_prod(X_a,X_b)),hAPP(fun(X_a,fun(X_b,bool)),fun(product_prod(X_a,X_b),bool),product_prod_case(X_a,X_b,bool),hAPP(fun(X_b,bool),fun(X_a,fun(X_b,bool)),hAPP(fun(X_a,fun(fun(X_b,bool),fun(X_b,bool))),fun(fun(X_b,bool),fun(X_a,fun(X_b,bool))),combc(X_a,fun(X_b,bool),fun(X_b,bool)),hAPP(fun(X_a,fun(bool,bool)),fun(X_a,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_a,fun(bool,bool)),fun(X_a,fun(fun(X_b,bool),fun(X_b,bool)))),combb(fun(bool,bool),fun(fun(X_b,bool),fun(X_b,bool)),X_a),combb(bool,bool,X_b)),hAPP(fun(X_a,bool),fun(X_a,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,fun(bool,bool))),combb(bool,fun(bool,bool),X_a),fconj),hAPP(X_a,fun(X_a,bool),fequal(X_a),X_1)))),hAPP(X_b,fun(X_b,bool),fequal(X_b),Y_1)))) = hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),X_1),Y_1)) # label(fact_4143_The__split__eq) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.84 4076 (all M all N hAPP(nat,product_prod(nat,nat),hAPP(nat,fun(nat,product_prod(nat,nat)),divmod_nat,M),N) = hAPP(fun(product_prod(nat,nat),bool),product_prod(nat,nat),the(product_prod(nat,nat)),hAPP(nat,fun(product_prod(nat,nat),bool),hAPP(nat,fun(nat,fun(product_prod(nat,nat),bool)),divmod_nat_rel,M),N))) # label(fact_4144_divmod__nat__def) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.84 4077 (all X_a all X_b all P_1 hAPP(fun(product_prod(X_a,X_b),bool),product_prod(X_a,X_b),the(product_prod(X_a,X_b)),hAPP(fun(X_a,fun(X_b,bool)),fun(product_prod(X_a,X_b),bool),product_prod_case(X_a,X_b,bool),P_1)) = hAPP(fun(product_prod(X_a,X_b),bool),product_prod(X_a,X_b),the(product_prod(X_a,X_b)),hAPP(fun(product_prod(X_a,X_b),X_b),fun(product_prod(X_a,X_b),bool),hAPP(fun(product_prod(X_a,X_b),fun(X_b,bool)),fun(fun(product_prod(X_a,X_b),X_b),fun(product_prod(X_a,X_b),bool)),combs(product_prod(X_a,X_b),X_b,bool),hAPP(fun(product_prod(X_a,X_b),X_a),fun(product_prod(X_a,X_b),fun(X_b,bool)),hAPP(fun(X_a,fun(X_b,bool)),fun(fun(product_prod(X_a,X_b),X_a),fun(product_prod(X_a,X_b),fun(X_b,bool))),combb(X_a,fun(X_b,bool),product_prod(X_a,X_b)),P_1),product_fst(X_a,X_b))),product_snd(X_a,X_b)))) # label(fact_4145_The__split) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.84 4078 (all X_1 hAPP(real,int,archim2085082626_floor(real),X_1) = hAPP(fun(int,bool),int,the(int),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),combs(int,bool,bool),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(real,fun(int,bool),hAPP(fun(int,fun(real,bool)),fun(real,fun(int,bool)),combc(int,real,bool),hAPP(fun(int,real),fun(int,fun(real,bool)),hAPP(fun(real,fun(real,bool)),fun(fun(int,real),fun(int,fun(real,bool))),combb(real,fun(real,bool),int),ord_less_eq(real)),ring_1_of_int(real))),X_1))),hAPP(fun(int,real),fun(int,bool),hAPP(fun(real,bool),fun(fun(int,real),fun(int,bool)),combb(real,bool,int),hAPP(real,fun(real,bool),ord_less(real),X_1)),hAPP(fun(int,int),fun(int,real),hAPP(fun(int,real),fun(fun(int,int),fun(int,real)),combb(int,real,int),ring_1_of_int(real)),hAPP(int,fun(int,int),hAPP(fun(int,fun(int,int)),fun(int,fun(int,int)),combc(int,int,int),plus_plus(int)),one_one(int))))))) # label(fact_4146_floor__real__def) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.84 4079 (all X_1 hAPP(rat,int,archim2085082626_floor(rat),X_1) = hAPP(fun(int,bool),int,the(int),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),combs(int,bool,bool),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(rat,fun(int,bool),hAPP(fun(int,fun(rat,bool)),fun(rat,fun(int,bool)),combc(int,rat,bool),hAPP(fun(int,rat),fun(int,fun(rat,bool)),hAPP(fun(rat,fun(rat,bool)),fun(fun(int,rat),fun(int,fun(rat,bool))),combb(rat,fun(rat,bool),int),ord_less_eq(rat)),ring_1_of_int(rat))),X_1))),hAPP(fun(int,rat),fun(int,bool),hAPP(fun(rat,bool),fun(fun(int,rat),fun(int,bool)),combb(rat,bool,int),hAPP(rat,fun(rat,bool),ord_less(rat),X_1)),hAPP(fun(int,int),fun(int,rat),hAPP(fun(int,rat),fun(fun(int,int),fun(int,rat)),combb(int,rat,int),ring_1_of_int(rat)),hAPP(int,fun(int,int),hAPP(fun(int,fun(int,int)),fun(int,fun(int,int)),combc(int,int,int),plus_plus(int)),one_one(int))))))) # label(fact_4147_floor__rat__def) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.84 4080 (all X_a all X_b (comm_monoid_mult(X_b) -> (all G all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2)) -> ((all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_2)) -> hAPP(X_a,X_b,G,X_2) = one_one(X_b))) -> hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co302546470etprod(X_a,X_b),G),A_2) = one_one(X_b)))))) # label(fact_4148_setprod_Oneutral) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.84 4081 (all X_a all X_b (linordered_semidom(X_b) -> (all F all A_2 ((all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_2)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),zero_zero(X_b)),hAPP(X_a,X_b,F,X_2))))) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),zero_zero(X_b)),hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co302546470etprod(X_a,X_b),F),A_2))))))) # label(fact_4149_setprod__pos) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.84 4082 (all X_a all X_b (linordered_semidom(X_b) -> (all G all F all A_2 ((all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_2)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),zero_zero(X_b)),hAPP(X_a,X_b,F,X_2))) & hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_a,X_b,F,X_2)),hAPP(X_a,X_b,G,X_2))))) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co302546470etprod(X_a,X_b),F),A_2)),hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co302546470etprod(X_a,X_b),G),A_2))))))) # label(fact_4150_setprod__mono) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.84 4083 (all X_a all X_b (linordered_semidom(X_b) -> (all F all A_2 ((all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_2)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),zero_zero(X_b)),hAPP(X_a,X_b,F,X_2))))) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),zero_zero(X_b)),hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co302546470etprod(X_a,X_b),F),A_2))))))) # label(fact_4151_setprod__nonneg) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.84 4084 (all X_a all Aa all F all V_1 all N hAPP(nat,X_a,hAPP(fun(nat,fun(X_a,X_a)),fun(nat,X_a),hAPP(X_a,fun(fun(nat,fun(X_a,X_a)),fun(nat,X_a)),nat_rec(X_a),Aa),F),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),V_1)),N)) = 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),hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),hAPP(int,int,pred,V_1)))),hAPP(nat,X_a,hAPP(fun(nat,fun(X_a,X_a)),fun(nat,X_a),hAPP(X_a,fun(fun(nat,fun(X_a,X_a)),fun(nat,X_a)),nat_rec(X_a),Aa),F),N)),hAPP(X_a,X_a,hAPP(nat,fun(X_a,X_a),F,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,nat_1,hAPP(int,int,number_number_of(int),hAPP(int,int,pred,V_1)))),N)),hAPP(nat,X_a,hAPP(fun(nat,fun(X_a,X_a)),fun(nat,X_a),hAPP(X_a,fun(fun(nat,fun(X_a,X_a)),fun(nat,X_a)),nat_rec(X_a),Aa),F),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,nat_1,hAPP(int,int,number_number_of(int),hAPP(int,int,pred,V_1)))),N))))) # label(fact_4152_nat__rec__add__eq__if) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.84 4085 (all Aa all A_2 all M ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),M)) & hBOOL(hAPP(int,bool,hAPP(fun(int,bool),fun(int,bool),is_RRset,A_2),M)) & hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Aa),A_2)) -> hAPP(int,int,hAPP(int,fun(int,int),hAPP(fun(int,bool),fun(int,fun(int,int)),rRset2norRR,A_2),M),Aa) = hAPP(fun(int,bool),int,hilbert_Eps(int),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),combs(int,bool,bool),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(int,fun(int,bool),hAPP(fun(int,fun(int,bool)),fun(int,fun(int,bool)),combc(int,int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,Aa)),M))),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)),hAPP(int,fun(int,bool),norRRset,M))))) & (-(hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),M)) & hBOOL(hAPP(int,bool,hAPP(fun(int,bool),fun(int,bool),is_RRset,A_2),M)) & hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Aa),A_2))) -> hAPP(int,int,hAPP(int,fun(int,int),hAPP(fun(int,bool),fun(int,fun(int,int)),rRset2norRR,A_2),M),Aa) = zero_zero(int)))) # label(fact_4153_RRset2norRR__def) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.84 4086 (all X_a all F1 all F2 all Nat hAPP(nat,X_a,hAPP(fun(nat,fun(X_a,X_a)),fun(nat,X_a),hAPP(X_a,fun(fun(nat,fun(X_a,X_a)),fun(nat,X_a)),nat_rec(X_a),F1),F2),hAPP(nat,nat,suc,Nat)) = hAPP(X_a,X_a,hAPP(nat,fun(X_a,X_a),F2,Nat),hAPP(nat,X_a,hAPP(fun(nat,fun(X_a,X_a)),fun(nat,X_a),hAPP(X_a,fun(fun(nat,fun(X_a,X_a)),fun(nat,X_a)),nat_rec(X_a),F1),F2),Nat))) # label(fact_4154_nat__rec__Suc) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.84 4087 (all X_a all F1 all F2 hAPP(nat,X_a,hAPP(fun(nat,fun(X_a,X_a)),fun(nat,X_a),hAPP(X_a,fun(fun(nat,fun(X_a,X_a)),fun(nat,X_a)),nat_rec(X_a),F1),F2),zero_zero(nat)) = ti(X_a,F1)) # label(fact_4155_nat__rec__0) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.84 4088 (all Aa all A_2 all M (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),M)) -> (hBOOL(hAPP(int,bool,hAPP(fun(int,bool),fun(int,bool),is_RRset,A_2),M)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Aa),A_2)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,Aa),hAPP(fun(int,bool),int,hilbert_Eps(int),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),combs(int,bool,bool),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(int,fun(int,bool),hAPP(fun(int,fun(int,bool)),fun(int,fun(int,bool)),combc(int,int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,Aa)),M))),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)),hAPP(int,fun(int,bool),norRRset,M))))),M)) & hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),hAPP(fun(int,bool),int,hilbert_Eps(int),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),combs(int,bool,bool),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(int,fun(int,bool),hAPP(fun(int,fun(int,bool)),fun(int,fun(int,bool)),combc(int,int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,Aa)),M))),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)),hAPP(int,fun(int,bool),norRRset,M))))),hAPP(int,fun(int,bool),norRRset,M))))))) # label(fact_4156_aux__some) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.84 4089 (all X_a all Aa all F all V_1 hAPP(nat,X_a,hAPP(fun(nat,fun(X_a,X_a)),fun(nat,X_a),hAPP(X_a,fun(fun(nat,fun(X_a,X_a)),fun(nat,X_a)),nat_rec(X_a),Aa),F),hAPP(int,nat,number_number_of(nat),V_1)) = 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),hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),hAPP(int,int,pred,V_1)))),Aa),hAPP(X_a,X_a,hAPP(nat,fun(X_a,X_a),F,hAPP(int,nat,nat_1,hAPP(int,int,number_number_of(int),hAPP(int,int,pred,V_1)))),hAPP(nat,X_a,hAPP(fun(nat,fun(X_a,X_a)),fun(nat,X_a),hAPP(X_a,fun(fun(nat,fun(X_a,X_a)),fun(nat,X_a)),nat_rec(X_a),Aa),F),hAPP(int,nat,nat_1,hAPP(int,int,number_number_of(int),hAPP(int,int,pred,V_1))))))) # label(fact_4157_nat__rec__number__of) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.84 4090 (all X_a (semiring_1(X_a) -> (all N hAPP(nat,X_a,semiring_1_of_nat(X_a),N) = hAPP(X_a,X_a,hAPP(nat,fun(X_a,X_a),hAPP(fun(X_a,X_a),fun(nat,fun(X_a,X_a)),semiri532925092at_aux(X_a),hAPP(X_a,fun(X_a,X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(X_a,X_a)),combc(X_a,X_a,X_a),plus_plus(X_a)),one_one(X_a))),N),zero_zero(X_a))))) # label(fact_4158_semiring__1__class_Oof__nat__code) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.84 4091 (all X_b all X_a all A_2 all B_1 hAPP(fun(X_b,bool),fun(product_prod(X_a,X_b),bool),hAPP(fun(X_a,bool),fun(fun(X_b,bool),fun(product_prod(X_a,X_b),bool)),prod(X_a,X_b),A_2),B_1) = hAPP(fun(product_prod(X_a,X_b),bool),fun(product_prod(X_a,X_b),bool),collect(product_prod(X_a,X_b)),hAPP(fun(X_a,fun(X_b,bool)),fun(product_prod(X_a,X_b),bool),product_prod_case(X_a,X_b,bool),hAPP(fun(X_b,bool),fun(X_a,fun(X_b,bool)),hAPP(fun(X_a,fun(fun(X_b,bool),fun(X_b,bool))),fun(fun(X_b,bool),fun(X_a,fun(X_b,bool))),combc(X_a,fun(X_b,bool),fun(X_b,bool)),hAPP(fun(X_a,fun(bool,bool)),fun(X_a,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_a,fun(bool,bool)),fun(X_a,fun(fun(X_b,bool),fun(X_b,bool)))),combb(fun(bool,bool),fun(fun(X_b,bool),fun(X_b,bool)),X_a),combb(bool,bool,X_b)),hAPP(fun(X_a,bool),fun(X_a,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,fun(bool,bool))),combb(bool,fun(bool,bool),X_a),fconj),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(X_a,bool)),combc(X_a,fun(X_a,bool),bool),member(X_a)),A_2)))),hAPP(fun(X_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_1))))) # label(fact_4159_Nitpick_Oprod__def) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.84 4092 (all X_a (semiring_1(X_a) -> (all Inc all I hAPP(X_a,X_a,hAPP(nat,fun(X_a,X_a),hAPP(fun(X_a,X_a),fun(nat,fun(X_a,X_a)),semiri532925092at_aux(X_a),Inc),zero_zero(nat)),I) = ti(X_a,I)))) # label(fact_4160_of__nat__aux_Osimps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.84 4093 (all X_a (semiring_1(X_a) -> (all Inc all N all I hAPP(X_a,X_a,hAPP(nat,fun(X_a,X_a),hAPP(fun(X_a,X_a),fun(nat,fun(X_a,X_a)),semiri532925092at_aux(X_a),Inc),hAPP(nat,nat,suc,N)),I) = hAPP(X_a,X_a,hAPP(nat,fun(X_a,X_a),hAPP(fun(X_a,X_a),fun(nat,fun(X_a,X_a)),semiri532925092at_aux(X_a),Inc),N),hAPP(X_a,X_a,Inc,I))))) # label(fact_4161_of__nat__aux_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.84 4094 (all X_1 all N hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,sin,X_1)),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(real,fun(nat,fun(real,real)),hAPP(fun(nat,fun(real,fun(real,real))),fun(real,fun(nat,fun(real,real))),combc(nat,real,fun(real,real)),hAPP(fun(nat,bool),fun(nat,fun(real,fun(real,real))),hAPP(fun(bool,fun(real,fun(real,real))),fun(fun(nat,bool),fun(nat,fun(real,fun(real,real)))),combb(bool,fun(real,fun(real,real)),nat),if(real)),even_odd_even(nat))),zero_zero(real))),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),inverse_divide(real)),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),min))),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),div_div(nat)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),minus_minus(nat)),hAPP(nat,nat,suc,zero_zero(nat))))),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),fact_fact(nat)))))),hAPP(real,fun(nat,real),power_power(real),X_1))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),N))))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,inverse_inverse(real),hAPP(nat,real,real_1(nat),hAPP(nat,nat,fact_fact(nat),N)))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,abs_abs(real),X_1)),N))))) # label(fact_4162_Maclaurin__sin__bound) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.84 4095 (all U_1 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_1)))))) # label(fact_4163_finite__less__ub) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.84 4096 (all L all U_1 hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),L),U_1)))) # label(fact_4164_finite__atLeastLessThan) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.84 4097 (all X_b all X_a (ordere142940540dd_abs(X_a) -> (all F all A_2 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,abs_abs(X_a),hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co1399186613setsum(X_b,X_a),F),A_2))),hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co1399186613setsum(X_b,X_a),hAPP(fun(X_b,X_a),fun(X_b,X_a),hAPP(fun(X_a,X_a),fun(fun(X_b,X_a),fun(X_b,X_a)),combb(X_a,X_a,X_b),abs_abs(X_a)),F)),A_2)))))) # label(fact_4165_setsum__abs) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.84 4098 (all X_b all X_a (ordere142940540dd_abs(X_a) -> (all F all A_2 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co1399186613setsum(X_b,X_a),hAPP(fun(X_b,X_a),fun(X_b,X_a),hAPP(fun(X_a,X_a),fun(fun(X_b,X_a),fun(X_b,X_a)),combb(X_a,X_a,X_b),abs_abs(X_a)),F)),A_2)))))) # label(fact_4166_setsum__abs__ge__zero) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.84 4099 (all X_a (real_normed_vector(X_a) -> (all K all F all S_3 (hBOOL(hAPP(X_a,bool,hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),F),S_3)) -> hBOOL(hAPP(X_a,bool,hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),hAPP(fun(nat,nat),fun(nat,X_a),hAPP(fun(nat,X_a),fun(fun(nat,nat),fun(nat,X_a)),combb(nat,X_a,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))),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),S_3),hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),K))))))))) # label(fact_4167_sums__split__initial__segment) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.84 4100 (all X_a (real_normed_vector(X_a) -> (all K all F (hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),F)) -> hAPP(fun(nat,X_a),X_a,suminf(X_a),F) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),K))),hAPP(fun(nat,X_a),X_a,suminf(X_a),hAPP(fun(nat,nat),fun(nat,X_a),hAPP(fun(nat,X_a),fun(fun(nat,nat),fun(nat,X_a)),combb(nat,X_a,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)))))))) # label(fact_4168_suminf__split__initial__segment) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.84 4101 (all X_a (real_normed_vector(X_a) -> (all K all S_3 all F (hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),F)) -> (hAPP(fun(nat,X_a),X_a,suminf(X_a),F) = ti(X_a,S_3) -> hAPP(fun(nat,X_a),X_a,suminf(X_a),hAPP(fun(nat,nat),fun(nat,X_a),hAPP(fun(nat,X_a),fun(fun(nat,nat),fun(nat,X_a)),combb(nat,X_a,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))) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),S_3),hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),K)))))))) # label(fact_4169_suminf__minus__initial__segment) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.84 4102 (all X_b all X_a (semiring_1(X_a) -> (all F all A_2 hAPP(nat,X_a,semiring_1_of_nat(X_a),hAPP(fun(X_b,bool),nat,hAPP(fun(X_b,nat),fun(fun(X_b,bool),nat),big_co1399186613setsum(X_b,nat),F),A_2)) = hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co1399186613setsum(X_b,X_a),hAPP(fun(X_b,nat),fun(X_b,X_a),hAPP(fun(nat,X_a),fun(fun(X_b,nat),fun(X_b,X_a)),combb(nat,X_a,X_b),semiring_1_of_nat(X_a)),F)),A_2)))) # label(fact_4170_of__nat__setsum) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.84 4103 (all X_b all X_a (ring_1(X_a) -> (all F all A_2 hAPP(int,X_a,ring_1_of_int(X_a),hAPP(fun(X_b,bool),int,hAPP(fun(X_b,int),fun(fun(X_b,bool),int),big_co1399186613setsum(X_b,int),F),A_2)) = hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co1399186613setsum(X_b,X_a),hAPP(fun(X_b,int),fun(X_b,X_a),hAPP(fun(int,X_a),fun(fun(X_b,int),fun(X_b,X_a)),combb(int,X_a,X_b),ring_1_of_int(X_a)),F)),A_2)))) # label(fact_4171_of__int__setsum) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.84 4104 (all X_a (ring_1(X_a) -> (all F all N all R_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),N))),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),N)),R_1)) = hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),hAPP(X_a,fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(X_a,fun(nat,X_a)),combc(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),minus_minus(X_a)),F)),R_1)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),N))))) # label(fact_4172_sumr__diff__mult__const2) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.84 4105 (all X_a (monoid_mult(X_a) & comm_semiring_0(X_a) -> (all X_1 all Y_1 all N hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),times_times(X_a)),hAPP(X_a,fun(nat,X_a),power_power(X_a),X_1))),hAPP(fun(nat,nat),fun(nat,X_a),hAPP(fun(nat,X_a),fun(fun(nat,nat),fun(nat,X_a)),combb(nat,X_a,nat),hAPP(X_a,fun(nat,X_a),power_power(X_a),Y_1)),hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,N))))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,suc,N))) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Y_1),hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),times_times(X_a)),hAPP(X_a,fun(nat,X_a),power_power(X_a),X_1))),hAPP(fun(nat,nat),fun(nat,X_a),hAPP(fun(nat,X_a),fun(fun(nat,nat),fun(nat,X_a)),combb(nat,X_a,nat),hAPP(X_a,fun(nat,X_a),power_power(X_a),Y_1)),hAPP(nat,fun(nat,nat),minus_minus(nat),N)))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,suc,N))))))) # label(fact_4173_lemma__realpow__diff__sumr) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.84 4106 (all X_a (comm_monoid_add(X_a) & power(X_a) -> (all X_1 all Y_1 all N hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),times_times(X_a)),hAPP(X_a,fun(nat,X_a),power_power(X_a),X_1))),hAPP(fun(nat,nat),fun(nat,X_a),hAPP(fun(nat,X_a),fun(fun(nat,nat),fun(nat,X_a)),combb(nat,X_a,nat),hAPP(X_a,fun(nat,X_a),power_power(X_a),Y_1)),hAPP(nat,fun(nat,nat),minus_minus(nat),N)))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,suc,N))) = hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),times_times(X_a)),hAPP(fun(nat,nat),fun(nat,X_a),hAPP(fun(nat,X_a),fun(fun(nat,nat),fun(nat,X_a)),combb(nat,X_a,nat),hAPP(X_a,fun(nat,X_a),power_power(X_a),X_1)),hAPP(nat,fun(nat,nat),minus_minus(nat),N)))),hAPP(X_a,fun(nat,X_a),power_power(X_a),Y_1))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,suc,N)))))) # label(fact_4174_lemma__realpow__rev__sumr) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.84 4107 (all F all N all R_1 hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),N))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,real_1(nat),N)),R_1)) = hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(real,fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(real,fun(nat,real)),combc(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),minus_minus(real)),F)),R_1)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),N))) # label(fact_4175_sumr__diff__mult__const) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.84 4108 (all X_a (comm_monoid_add(X_a) -> (all F all K all N hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),hAPP(fun(nat,fun(nat,bool)),fun(nat,X_a),hAPP(fun(fun(nat,bool),X_a),fun(fun(nat,fun(nat,bool)),fun(nat,X_a)),combb(fun(nat,bool),X_a,nat),hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F)),hAPP(fun(nat,nat),fun(nat,fun(nat,bool)),hAPP(fun(nat,fun(nat,fun(nat,bool))),fun(fun(nat,nat),fun(nat,fun(nat,bool))),combs(nat,nat,fun(nat,bool)),hAPP(fun(nat,nat),fun(nat,fun(nat,fun(nat,bool))),hAPP(fun(nat,fun(nat,fun(nat,bool))),fun(fun(nat,nat),fun(nat,fun(nat,fun(nat,bool)))),combb(nat,fun(nat,fun(nat,bool)),nat),ord_atLeastLessThan(nat)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),times_times(nat)),K))),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),plus_plus(nat)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),times_times(nat)),K))),K)))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),N)) = hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N),K)))))) # label(fact_4176_sumr__group) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.84 4109 (all X_b all X_a (real_normed_vector(X_a) -> (all F all A_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co1399186613setsum(X_b,X_a),F),A_2))),hAPP(fun(X_b,bool),real,hAPP(fun(X_b,real),fun(fun(X_b,bool),real),big_co1399186613setsum(X_b,real),hAPP(fun(X_b,X_a),fun(X_b,real),hAPP(fun(X_a,real),fun(fun(X_b,X_a),fun(X_b,real)),combb(X_a,real,X_b),norm_norm(X_a)),F)),A_2)))))) # label(fact_4177_norm__setsum) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.84 4110 (all X_a (comm_monoid_add(X_a) -> (all F all M all K all N hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),K)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),K))) = hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),hAPP(fun(nat,nat),fun(nat,X_a),hAPP(fun(nat,X_a),fun(fun(nat,nat),fun(nat,X_a)),combb(nat,X_a,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))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),M),N))))) # label(fact_4178_setsum__shift__bounds__nat__ivl) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.84 4111 (all X_a (field(X_a) -> (all N all X_1 (ti(X_a,X_1) != one_one(X_a) -> hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),hAPP(X_a,fun(nat,X_a),power_power(X_a),X_1)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),N)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X_1),N)),one_one(X_a))),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),X_1),one_one(X_a))))))) # label(fact_4179_geometric__sum) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.84 4112 (all X_a (comm_monoid_add(X_a) -> (all F all N all K hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),K))) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),hAPP(fun(nat,nat),fun(nat,X_a),hAPP(fun(nat,X_a),fun(fun(nat,nat),fun(nat,X_a)),combb(nat,X_a,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))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),N))),hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),K)))))) # label(fact_4180_sumr__offset3) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.84 4113 (all K all N_2 all F_3 hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),F_3),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_2),K))) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),F_3),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),K))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),N_2))),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),F_3),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),K)))) # label(fact_4181_sumr__offset4) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.84 4114 (all K all N all F_3 hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),F_3),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),K))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),N)) = hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),F_3),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),K)))),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),F_3),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),K)))) # label(fact_4182_sumr__offset2) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.84 4115 (all X_a (ab_group_add(X_a) -> (all F all K all N hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),hAPP(fun(nat,nat),fun(nat,X_a),hAPP(fun(nat,X_a),fun(fun(nat,nat),fun(nat,X_a)),combb(nat,X_a,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))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),N)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),K)))),hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),K)))))) # label(fact_4183_sumr__offset) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.84 4116 (all X_b all X_a (real_normed_field(X_a) -> (all G all A_2 all Y_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co1399186613setsum(X_b,X_a),G),A_2)),Y_1) = hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co1399186613setsum(X_b,X_a),hAPP(X_a,fun(X_b,X_a),hAPP(fun(X_b,fun(X_a,X_a)),fun(X_a,fun(X_b,X_a)),combc(X_b,X_a,X_a),hAPP(fun(X_b,X_a),fun(X_b,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_b,X_a),fun(X_b,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),X_b),inverse_divide(X_a)),G)),Y_1)),A_2)))) # label(fact_4184_divide_Osetsum) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.84 4117 (all X_a all X_b (comm_monoid_add(X_b) -> (all F all P_1 all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2)) -> hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),F),hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,bool)),combs(X_a,bool,bool),hAPP(fun(X_a,bool),fun(X_a,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,fun(bool,bool))),combb(bool,fun(bool,bool),X_a),fconj),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(X_a,bool)),combc(X_a,fun(X_a,bool),bool),member(X_a)),A_2))),P_1))) = hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),hAPP(X_b,fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(X_b,fun(X_a,X_b)),combc(X_a,X_b,X_b),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,X_b)),hAPP(fun(X_a,fun(X_b,fun(X_b,X_b))),fun(fun(X_a,X_b),fun(X_a,fun(X_b,X_b))),combs(X_a,X_b,fun(X_b,X_b)),hAPP(fun(X_a,bool),fun(X_a,fun(X_b,fun(X_b,X_b))),hAPP(fun(bool,fun(X_b,fun(X_b,X_b))),fun(fun(X_a,bool),fun(X_a,fun(X_b,fun(X_b,X_b)))),combb(bool,fun(X_b,fun(X_b,X_b)),X_a),if(X_b)),P_1)),F)),zero_zero(X_b))),A_2))))) # label(fact_4185_setsum__restrict__set_H_H) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.84 4118 (all X_a all X_b (comm_monoid_add(X_b) -> (all F all B_1 all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2)) -> hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),F),hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,bool)),combs(X_a,bool,bool),hAPP(fun(X_a,bool),fun(X_a,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,fun(bool,bool))),combb(bool,fun(bool,bool),X_a),fconj),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(X_a,bool)),combc(X_a,fun(X_a,bool),bool),member(X_a)),A_2))),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(X_a,bool)),combc(X_a,fun(X_a,bool),bool),member(X_a)),B_1)))) = hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),hAPP(X_b,fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(X_b,fun(X_a,X_b)),combc(X_a,X_b,X_b),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,X_b)),hAPP(fun(X_a,fun(X_b,fun(X_b,X_b))),fun(fun(X_a,X_b),fun(X_a,fun(X_b,X_b))),combs(X_a,X_b,fun(X_b,X_b)),hAPP(fun(X_a,bool),fun(X_a,fun(X_b,fun(X_b,X_b))),hAPP(fun(bool,fun(X_b,fun(X_b,X_b))),fun(fun(X_a,bool),fun(X_a,fun(X_b,fun(X_b,X_b)))),combb(bool,fun(X_b,fun(X_b,X_b)),X_a),if(X_b)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(X_a,bool)),combc(X_a,fun(X_a,bool),bool),member(X_a)),B_1))),F)),zero_zero(X_b))),A_2))))) # label(fact_4186_setsum__restrict__set_H) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.84 4119 (all X_a (comm_monoid_add(X_a) -> (all F all M all N hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),hAPP(nat,nat,suc,M)),hAPP(nat,nat,suc,N))) = hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),hAPP(fun(nat,nat),fun(nat,X_a),hAPP(fun(nat,X_a),fun(fun(nat,nat),fun(nat,X_a)),combb(nat,X_a,nat),F),suc)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),M),N))))) # label(fact_4187_setsum__shift__bounds__Suc__ivl) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.84 4120 (all X_b all X_a all X_c (comm_monoid_add(X_c) -> (all F all R_3 all T_4 all S (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),S)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),T_4)) -> hAPP(fun(X_a,bool),X_c,hAPP(fun(X_a,X_c),fun(fun(X_a,bool),X_c),big_co1399186613setsum(X_a,X_c),hAPP(fun(X_a,fun(X_b,bool)),fun(X_a,X_c),hAPP(fun(X_a,fun(fun(X_b,bool),X_c)),fun(fun(X_a,fun(X_b,bool)),fun(X_a,X_c)),combs(X_a,fun(X_b,bool),X_c),hAPP(fun(X_a,fun(X_b,X_c)),fun(X_a,fun(fun(X_b,bool),X_c)),hAPP(fun(fun(X_b,X_c),fun(fun(X_b,bool),X_c)),fun(fun(X_a,fun(X_b,X_c)),fun(X_a,fun(fun(X_b,bool),X_c))),combb(fun(X_b,X_c),fun(fun(X_b,bool),X_c),X_a),big_co1399186613setsum(X_b,X_c)),F)),hAPP(fun(X_a,fun(X_b,bool)),fun(X_a,fun(X_b,bool)),hAPP(fun(fun(X_b,bool),fun(X_b,bool)),fun(fun(X_a,fun(X_b,bool)),fun(X_a,fun(X_b,bool))),combb(fun(X_b,bool),fun(X_b,bool),X_a),collect(X_b)),hAPP(fun(X_a,fun(X_b,bool)),fun(X_a,fun(X_b,bool)),hAPP(fun(fun(X_b,bool),fun(X_b,bool)),fun(fun(X_a,fun(X_b,bool)),fun(X_a,fun(X_b,bool))),combb(fun(X_b,bool),fun(X_b,bool),X_a),hAPP(fun(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)),T_4)))),R_3)))),S) = 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,fun(X_a,bool)),fun(X_b,X_c),hAPP(fun(X_b,fun(fun(X_a,bool),X_c)),fun(fun(X_b,fun(X_a,bool)),fun(X_b,X_c)),combs(X_b,fun(X_a,bool),X_c),hAPP(fun(X_b,fun(X_a,X_c)),fun(X_b,fun(fun(X_a,bool),X_c)),hAPP(fun(fun(X_a,X_c),fun(fun(X_a,bool),X_c)),fun(fun(X_b,fun(X_a,X_c)),fun(X_b,fun(fun(X_a,bool),X_c))),combb(fun(X_a,X_c),fun(fun(X_a,bool),X_c),X_b),big_co1399186613setsum(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),F))),hAPP(fun(X_b,fun(X_a,bool)),fun(X_b,fun(X_a,bool)),hAPP(fun(fun(X_a,bool),fun(X_a,bool)),fun(fun(X_b,fun(X_a,bool)),fun(X_b,fun(X_a,bool))),combb(fun(X_a,bool),fun(X_a,bool),X_b),collect(X_a)),hAPP(fun(X_b,fun(X_a,bool)),fun(X_b,fun(X_a,bool)),hAPP(fun(fun(X_a,bool),fun(X_a,bool)),fun(fun(X_b,fun(X_a,bool)),fun(X_b,fun(X_a,bool))),combb(fun(X_a,bool),fun(X_a,bool),X_b),hAPP(fun(X_a,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,bool)),combs(X_a,bool,bool),hAPP(fun(X_a,bool),fun(X_a,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,fun(bool,bool))),combb(bool,fun(bool,bool),X_a),fconj),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(X_a,bool)),combc(X_a,fun(X_a,bool),bool),member(X_a)),S)))),hAPP(fun(X_a,fun(X_b,bool)),fun(X_b,fun(X_a,bool)),combc(X_a,X_b,bool),R_3))))),T_4)))))) # label(fact_4188_setsum__setsum__restrict) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.84 4121 (all X_b all X_a (real_algebra_1(X_a) & real_normed_vector(X_a) -> (all G all A_2 hAPP(real,X_a,of_real(X_a),hAPP(fun(X_b,bool),real,hAPP(fun(X_b,real),fun(fun(X_b,bool),real),big_co1399186613setsum(X_b,real),G),A_2)) = hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co1399186613setsum(X_b,X_a),hAPP(fun(X_b,real),fun(X_b,X_a),hAPP(fun(real,X_a),fun(fun(X_b,real),fun(X_b,X_a)),combb(real,X_a,X_b),of_real(X_a)),G)),A_2)))) # label(fact_4189_of__real_Osetsum) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.84 4122 (all X_b all X_a (real_normed_algebra(X_a) -> (all G all A_2 all Y_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co1399186613setsum(X_b,X_a),G),A_2)),Y_1) = hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co1399186613setsum(X_b,X_a),hAPP(X_a,fun(X_b,X_a),hAPP(fun(X_b,fun(X_a,X_a)),fun(X_a,fun(X_b,X_a)),combc(X_b,X_a,X_a),hAPP(fun(X_b,X_a),fun(X_b,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_b,X_a),fun(X_b,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),X_b),times_times(X_a)),G)),Y_1)),A_2)))) # label(fact_4190_mult__left_Osetsum) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.84 4123 (all X_b all X_a (real_normed_algebra(X_a) -> (all X_1 all G all A_2 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X_1),hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co1399186613setsum(X_b,X_a),G),A_2)) = hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co1399186613setsum(X_b,X_a),hAPP(fun(X_b,X_a),fun(X_b,X_a),hAPP(fun(X_a,X_a),fun(fun(X_b,X_a),fun(X_b,X_a)),combb(X_a,X_a,X_b),hAPP(X_a,fun(X_a,X_a),times_times(X_a),X_1)),G)),A_2)))) # label(fact_4191_mult__right_Osetsum) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.84 4124 (all F all N hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),F)),hAPP(real,fun(nat,real),power_power(real),zero_zero(real)))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),hAPP(nat,nat,suc,zero_zero(nat))),N)) = zero_zero(real)) # label(fact_4192_sumr__one__lb__realpow__zero) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.84 4125 (all P_1 all N ((all M_3 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_3),N)) -> hBOOL(hAPP(nat,bool,P_1,M_3)))) <-> (all X_2 (hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X_2),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),N))) -> hBOOL(hAPP(nat,bool,P_1,X_2)))))) # label(fact_4193_all__nat__less__eq) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.84 4126 (all P_1 all N ((exists M_3 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_3),N)) & hBOOL(hAPP(nat,bool,P_1,M_3)))) <-> (exists X_2 (hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X_2),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),N))) & hBOOL(hAPP(nat,bool,P_1,X_2)))))) # label(fact_4194_ex__nat__less__eq) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.84 4127 (all X_a (linorder(X_a) -> (all C_1 all D_1 all Aa all Ba (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),Ba)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),D_1)) -> (hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastLessThan(X_a),Aa),Ba) = hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastLessThan(X_a),C_1),D_1) <-> ti(X_a,Aa) = ti(X_a,C_1) & ti(X_a,Ba) = ti(X_a,D_1))))))) # label(fact_4195_atLeastLessThan__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.84 4128 (all X_a (linorder(X_a) -> (all Aa all Ba all C_1 all D_1 (hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastLessThan(X_a),Aa),Ba) = hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastLessThan(X_a),C_1),D_1) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),Ba)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),D_1)) -> ti(X_a,Aa) = ti(X_a,C_1))))))) # label(fact_4196_atLeastLessThan__inj_I1_J) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.84 4129 (all X_a (linorder(X_a) -> (all Aa all Ba all C_1 all D_1 (hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastLessThan(X_a),Aa),Ba) = hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastLessThan(X_a),C_1),D_1) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),Ba)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),D_1)) -> ti(X_a,Ba) = ti(X_a,D_1))))))) # label(fact_4197_atLeastLessThan__inj_I2_J) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.85 4130 (all X_a (comm_monoid_add(X_a) -> (all K all F (hAPP(nat,X_a,F,zero_zero(nat)) = zero_zero(X_a) -> hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),hAPP(nat,nat,suc,zero_zero(nat))),K)) = hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),K)))))) # label(fact_4198_setsum__shift__lb__Suc0__0__upt) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.85 4131 (all X_a (ab_group_add(X_a) -> (all F all Pa all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N),Pa)) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),M),Pa))),hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),M),N))) = hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),N),Pa))))))) # label(fact_4199_setsum__diff__nat__ivl) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.85 4132 (all X_a (comm_monoid_add(X_a) -> (all F all Pa all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N),Pa)) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),M),N))),hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),N),Pa))) = hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),M),Pa))))))) # label(fact_4200_setsum__add__nat__ivl) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.85 4133 (all L all U_1 hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),L),U_1)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1),L)) # label(fact_4201_card__atLeastLessThan) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.85 4134 (all X_a (linorder(X_a) -> (all Aa all Ba all C_1 all D_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastLessThan(X_a),Aa),Ba)),hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastLessThan(X_a),C_1),D_1))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Ba),Aa)) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C_1),Aa)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Ba),D_1)))))) # label(fact_4202_atLeastLessThan__subset__iff) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.85 4135 (all X_a (comm_monoid_add(X_a) -> (all F all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N)) -> hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),M),N)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(nat,X_a,F,M)),hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),hAPP(nat,nat,suc,M)),N))))))) # label(fact_4203_setsum__head__upt__Suc) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.85 4136 (all X_a (comm_monoid_add(X_a) -> (all F all N all M ((hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),M)) -> hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),M),hAPP(nat,nat,suc,N))) = zero_zero(X_a)) & (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),M)) -> hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),M),hAPP(nat,nat,suc,N))) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),M),N))),hAPP(nat,X_a,F,N))))))) # label(fact_4204_setsum__op__ivl__Suc) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.85 4137 (all X_a (linorder(X_a) -> (all M all I all N (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),I),N)) -> hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastLessThan(X_a),I),M)),hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastLessThan(X_a),I),N)) = hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastLessThan(X_a),N),M))))) # label(fact_4205_ivl__diff) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.85 4138 (all N all X_1 (X_1 != one_one(real) -> hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(real,fun(nat,real),power_power(real),X_1)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),N)) = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X_1),N)),one_one(real))),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),X_1),one_one(real))))) # label(fact_4206_sumr__geometric) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.85 4139 (all X_a all X_b (comm_monoid_add(X_b) -> (all G all A_2 (-hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2)) -> hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),G),A_2) = zero_zero(X_b))))) # label(fact_4207_setsum_Oinfinite) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.85 4140 (all X_a all X_b (comm_monoid_add(X_b) -> (all F all A_2 (-hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2)) -> hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),F),A_2) = zero_zero(X_b))))) # label(fact_4208_setsum__infinite) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.85 4141 (all X_b all X_a (ordere142940540dd_abs(X_a) -> (all F all A_2 hAPP(X_a,X_a,abs_abs(X_a),hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co1399186613setsum(X_b,X_a),hAPP(fun(X_b,X_a),fun(X_b,X_a),hAPP(fun(X_a,X_a),fun(fun(X_b,X_a),fun(X_b,X_a)),combb(X_a,X_a,X_b),abs_abs(X_a)),F)),A_2)) = hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co1399186613setsum(X_b,X_a),hAPP(fun(X_b,X_a),fun(X_b,X_a),hAPP(fun(X_a,X_a),fun(fun(X_b,X_a),fun(X_b,X_a)),combb(X_a,X_a,X_b),abs_abs(X_a)),F)),A_2)))) # label(fact_4209_abs__setsum__abs) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.85 4142 (all X_b all X_a (ab_group_add(X_a) -> (all F all A_2 hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co1399186613setsum(X_b,X_a),hAPP(fun(X_b,X_a),fun(X_b,X_a),hAPP(fun(X_a,X_a),fun(fun(X_b,X_a),fun(X_b,X_a)),combb(X_a,X_a,X_b),uminus_uminus(X_a)),F)),A_2) = hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co1399186613setsum(X_b,X_a),F),A_2))))) # label(fact_4210_setsum__negf) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.85 4143 (all X_b all X_a (semiring_0(X_a) -> (all R_1 all F all A_2 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),R_1),hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co1399186613setsum(X_b,X_a),F),A_2)) = hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co1399186613setsum(X_b,X_a),hAPP(fun(X_b,X_a),fun(X_b,X_a),hAPP(fun(X_a,X_a),fun(fun(X_b,X_a),fun(X_b,X_a)),combb(X_a,X_a,X_b),hAPP(X_a,fun(X_a,X_a),times_times(X_a),R_1)),F)),A_2)))) # label(fact_4211_setsum__right__distrib) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.85 4144 (all X_b all X_a (semiring_0(X_a) -> (all F all A_2 all R_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co1399186613setsum(X_b,X_a),F),A_2)),R_1) = hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co1399186613setsum(X_b,X_a),hAPP(X_a,fun(X_b,X_a),hAPP(fun(X_b,fun(X_a,X_a)),fun(X_a,fun(X_b,X_a)),combc(X_b,X_a,X_a),hAPP(fun(X_b,X_a),fun(X_b,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_b,X_a),fun(X_b,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),X_b),times_times(X_a)),F)),R_1)),A_2)))) # label(fact_4212_setsum__left__distrib) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.85 4145 (all X_b all X_c all X_a (semiring_0(X_a) -> (all F all A_2 all G all B_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co1399186613setsum(X_b,X_a),F),A_2)),hAPP(fun(X_c,bool),X_a,hAPP(fun(X_c,X_a),fun(fun(X_c,bool),X_a),big_co1399186613setsum(X_c,X_a),G),B_1)) = hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co1399186613setsum(X_b,X_a),hAPP(fun(X_c,bool),fun(X_b,X_a),hAPP(fun(X_b,fun(fun(X_c,bool),X_a)),fun(fun(X_c,bool),fun(X_b,X_a)),combc(X_b,fun(X_c,bool),X_a),hAPP(fun(X_b,fun(X_c,X_a)),fun(X_b,fun(fun(X_c,bool),X_a)),hAPP(fun(fun(X_c,X_a),fun(fun(X_c,bool),X_a)),fun(fun(X_b,fun(X_c,X_a)),fun(X_b,fun(fun(X_c,bool),X_a))),combb(fun(X_c,X_a),fun(fun(X_c,bool),X_a),X_b),big_co1399186613setsum(X_c,X_a)),hAPP(fun(X_c,X_a),fun(X_b,fun(X_c,X_a)),hAPP(fun(X_b,fun(fun(X_c,X_a),fun(X_c,X_a))),fun(fun(X_c,X_a),fun(X_b,fun(X_c,X_a))),combc(X_b,fun(X_c,X_a),fun(X_c,X_a)),hAPP(fun(X_b,fun(X_a,X_a)),fun(X_b,fun(fun(X_c,X_a),fun(X_c,X_a))),hAPP(fun(fun(X_a,X_a),fun(fun(X_c,X_a),fun(X_c,X_a))),fun(fun(X_b,fun(X_a,X_a)),fun(X_b,fun(fun(X_c,X_a),fun(X_c,X_a)))),combb(fun(X_a,X_a),fun(fun(X_c,X_a),fun(X_c,X_a)),X_b),combb(X_a,X_a,X_c)),hAPP(fun(X_b,X_a),fun(X_b,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_b,X_a),fun(X_b,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),X_b),times_times(X_a)),F))),G))),B_1)),A_2)))) # label(fact_4213_setsum__product) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.85 4146 (all X_b all X_c all X_a (comm_monoid_add(X_a) -> (all F all B_1 all A_2 hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co1399186613setsum(X_b,X_a),hAPP(fun(X_c,bool),fun(X_b,X_a),hAPP(fun(X_b,fun(fun(X_c,bool),X_a)),fun(fun(X_c,bool),fun(X_b,X_a)),combc(X_b,fun(X_c,bool),X_a),hAPP(fun(X_b,fun(X_c,X_a)),fun(X_b,fun(fun(X_c,bool),X_a)),hAPP(fun(fun(X_c,X_a),fun(fun(X_c,bool),X_a)),fun(fun(X_b,fun(X_c,X_a)),fun(X_b,fun(fun(X_c,bool),X_a))),combb(fun(X_c,X_a),fun(fun(X_c,bool),X_a),X_b),big_co1399186613setsum(X_c,X_a)),F)),B_1)),A_2) = hAPP(fun(X_c,bool),X_a,hAPP(fun(X_c,X_a),fun(fun(X_c,bool),X_a),big_co1399186613setsum(X_c,X_a),hAPP(fun(X_b,bool),fun(X_c,X_a),hAPP(fun(X_c,fun(fun(X_b,bool),X_a)),fun(fun(X_b,bool),fun(X_c,X_a)),combc(X_c,fun(X_b,bool),X_a),hAPP(fun(X_c,fun(X_b,X_a)),fun(X_c,fun(fun(X_b,bool),X_a)),hAPP(fun(fun(X_b,X_a),fun(fun(X_b,bool),X_a)),fun(fun(X_c,fun(X_b,X_a)),fun(X_c,fun(fun(X_b,bool),X_a))),combb(fun(X_b,X_a),fun(fun(X_b,bool),X_a),X_c),big_co1399186613setsum(X_b,X_a)),hAPP(fun(X_b,fun(X_c,X_a)),fun(X_c,fun(X_b,X_a)),combc(X_b,X_c,X_a),F))),A_2)),B_1)))) # label(fact_4214_setsum__commute) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.85 4147 (all X_a all X_b (comm_monoid_add(X_b) -> (all Ba all Aa all S (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),S)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Aa),S)) -> hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),hAPP(X_b,fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(X_b,fun(X_a,X_b)),combc(X_a,X_b,X_b),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,X_b)),hAPP(fun(X_a,fun(X_b,fun(X_b,X_b))),fun(fun(X_a,X_b),fun(X_a,fun(X_b,X_b))),combs(X_a,X_b,fun(X_b,X_b)),hAPP(fun(X_a,bool),fun(X_a,fun(X_b,fun(X_b,X_b))),hAPP(fun(bool,fun(X_b,fun(X_b,X_b))),fun(fun(X_a,bool),fun(X_a,fun(X_b,fun(X_b,X_b)))),combb(bool,fun(X_b,fun(X_b,X_b)),X_a),if(X_b)),hAPP(X_a,fun(X_a,bool),fequal(X_a),Aa))),Ba)),zero_zero(X_b))),S) = hAPP(X_a,X_b,Ba,Aa)) & (-hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Aa),S)) -> hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),hAPP(X_b,fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(X_b,fun(X_a,X_b)),combc(X_a,X_b,X_b),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,X_b)),hAPP(fun(X_a,fun(X_b,fun(X_b,X_b))),fun(fun(X_a,X_b),fun(X_a,fun(X_b,X_b))),combs(X_a,X_b,fun(X_b,X_b)),hAPP(fun(X_a,bool),fun(X_a,fun(X_b,fun(X_b,X_b))),hAPP(fun(bool,fun(X_b,fun(X_b,X_b))),fun(fun(X_a,bool),fun(X_a,fun(X_b,fun(X_b,X_b)))),combb(bool,fun(X_b,fun(X_b,X_b)),X_a),if(X_b)),hAPP(X_a,fun(X_a,bool),fequal(X_a),Aa))),Ba)),zero_zero(X_b))),S) = zero_zero(X_b)))))) # label(fact_4215_setsum__delta_H) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.85 4148 (all X_a all X_b (comm_monoid_add(X_b) -> (all Ba all Aa all S (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),S)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Aa),S)) -> hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),hAPP(X_b,fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(X_b,fun(X_a,X_b)),combc(X_a,X_b,X_b),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,X_b)),hAPP(fun(X_a,fun(X_b,fun(X_b,X_b))),fun(fun(X_a,X_b),fun(X_a,fun(X_b,X_b))),combs(X_a,X_b,fun(X_b,X_b)),hAPP(fun(X_a,bool),fun(X_a,fun(X_b,fun(X_b,X_b))),hAPP(fun(bool,fun(X_b,fun(X_b,X_b))),fun(fun(X_a,bool),fun(X_a,fun(X_b,fun(X_b,X_b)))),combb(bool,fun(X_b,fun(X_b,X_b)),X_a),if(X_b)),hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,fun(X_a,bool)),fun(X_a,fun(X_a,bool)),combc(X_a,X_a,bool),fequal(X_a)),Aa))),Ba)),zero_zero(X_b))),S) = hAPP(X_a,X_b,Ba,Aa)) & (-hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Aa),S)) -> hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),hAPP(X_b,fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(X_b,fun(X_a,X_b)),combc(X_a,X_b,X_b),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,X_b)),hAPP(fun(X_a,fun(X_b,fun(X_b,X_b))),fun(fun(X_a,X_b),fun(X_a,fun(X_b,X_b))),combs(X_a,X_b,fun(X_b,X_b)),hAPP(fun(X_a,bool),fun(X_a,fun(X_b,fun(X_b,X_b))),hAPP(fun(bool,fun(X_b,fun(X_b,X_b))),fun(fun(X_a,bool),fun(X_a,fun(X_b,fun(X_b,X_b)))),combb(bool,fun(X_b,fun(X_b,X_b)),X_a),if(X_b)),hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,fun(X_a,bool)),fun(X_a,fun(X_a,bool)),combc(X_a,X_a,bool),fequal(X_a)),Aa))),Ba)),zero_zero(X_b))),S) = zero_zero(X_b)))))) # label(fact_4216_setsum__delta) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.85 4149 (all X_b all X_a (field(X_a) -> (all F all A_2 all R_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co1399186613setsum(X_b,X_a),F),A_2)),R_1) = hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co1399186613setsum(X_b,X_a),hAPP(X_a,fun(X_b,X_a),hAPP(fun(X_b,fun(X_a,X_a)),fun(X_a,fun(X_b,X_a)),combc(X_b,X_a,X_a),hAPP(fun(X_b,X_a),fun(X_b,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_b,X_a),fun(X_b,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),X_b),inverse_divide(X_a)),F)),R_1)),A_2)))) # label(fact_4217_setsum__divide__distrib) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.85 4150 (all X_b all X_a (comm_monoid_add(X_a) -> (all A_2 hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co1399186613setsum(X_b,X_a),hAPP(X_a,fun(X_b,X_a),combk(X_a,X_b),zero_zero(X_a))),A_2) = zero_zero(X_a)))) # label(fact_4218_setsum__0) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.85 4151 (all X_a all X_b (comm_monoid_add(X_b) -> (all G all H all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2)) -> hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),hAPP(fun(X_a,X_b),fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,X_b)),combs(X_a,X_b,X_b),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,fun(X_b,X_b))),combb(X_b,fun(X_b,X_b),X_a),plus_plus(X_b)),G)),H)),A_2) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),G),A_2)),hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),H),A_2)))))) # label(fact_4219_setsum_Odistrib) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.85 4152 (all X_b all X_a (ab_group_add(X_a) -> (all F all G all A_2 hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co1399186613setsum(X_b,X_a),hAPP(fun(X_b,X_a),fun(X_b,X_a),hAPP(fun(X_b,fun(X_a,X_a)),fun(fun(X_b,X_a),fun(X_b,X_a)),combs(X_b,X_a,X_a),hAPP(fun(X_b,X_a),fun(X_b,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_b,X_a),fun(X_b,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),X_b),minus_minus(X_a)),F)),G)),A_2) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co1399186613setsum(X_b,X_a),F),A_2)),hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co1399186613setsum(X_b,X_a),G),A_2))))) # label(fact_4220_setsum__subtractf) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.85 4153 (all X_b all X_a (comm_monoid_add(X_a) -> (all F all G all A_2 hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co1399186613setsum(X_b,X_a),hAPP(fun(X_b,X_a),fun(X_b,X_a),hAPP(fun(X_b,fun(X_a,X_a)),fun(fun(X_b,X_a),fun(X_b,X_a)),combs(X_b,X_a,X_a),hAPP(fun(X_b,X_a),fun(X_b,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_b,X_a),fun(X_b,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),X_b),plus_plus(X_a)),F)),G)),A_2) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co1399186613setsum(X_b,X_a),F),A_2)),hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co1399186613setsum(X_b,X_a),G),A_2))))) # label(fact_4221_setsum__addf) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.85 4154 (all L all U_1 hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),hAPP(nat,nat,suc,L)),U_1) = hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_gr676655987ssThan(nat),L),U_1)) # label(fact_4222_atLeastSucLessThan__greaterThanLessThan) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.85 4155 (all K all I all J 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)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),I),J)) = hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(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_4223_image__add__atLeastLessThan) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.85 4156 (all X_c all X_a all X_b (comm_monoid_add(X_b) -> (all G all F all S (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),S)) -> hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),G),S) = 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,fun(X_a,bool)),fun(X_c,X_b),hAPP(fun(fun(X_a,bool),X_b),fun(fun(X_c,fun(X_a,bool)),fun(X_c,X_b)),combb(fun(X_a,bool),X_b,X_c),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),G)),hAPP(fun(X_c,fun(X_a,bool)),fun(X_c,fun(X_a,bool)),hAPP(fun(fun(X_a,bool),fun(X_a,bool)),fun(fun(X_c,fun(X_a,bool)),fun(X_c,fun(X_a,bool))),combb(fun(X_a,bool),fun(X_a,bool),X_c),collect(X_a)),hAPP(fun(X_c,fun(X_a,bool)),fun(X_c,fun(X_a,bool)),hAPP(fun(fun(X_a,bool),fun(X_a,bool)),fun(fun(X_c,fun(X_a,bool)),fun(X_c,fun(X_a,bool))),combb(fun(X_a,bool),fun(X_a,bool),X_c),hAPP(fun(X_a,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,bool)),combs(X_a,bool,bool),hAPP(fun(X_a,bool),fun(X_a,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,fun(bool,bool))),combb(bool,fun(bool,bool),X_a),fconj),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(X_a,bool)),combc(X_a,fun(X_a,bool),bool),member(X_a)),S)))),hAPP(fun(X_a,fun(X_c,bool)),fun(X_c,fun(X_a,bool)),combc(X_a,X_c,bool),hAPP(fun(X_a,X_c),fun(X_a,fun(X_c,bool)),hAPP(fun(X_c,fun(X_c,bool)),fun(fun(X_a,X_c),fun(X_a,fun(X_c,bool))),combb(X_c,fun(X_c,bool),X_a),fequal(X_c)),F)))))),hAPP(fun(X_a,bool),fun(X_c,bool),hAPP(fun(X_a,X_c),fun(fun(X_a,bool),fun(X_c,bool)),image(X_a,X_c),F),S)))))) # label(fact_4224_setsum__image__gen) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.85 4157 (all I all J hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,nat),fun(fun(nat,bool),fun(nat,bool)),image(nat,nat),suc),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),I),J)) = hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),hAPP(nat,nat,suc,I)),hAPP(nat,nat,suc,J))) # label(fact_4225_image__Suc__atLeastLessThan) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.85 4158 (all X_a (monoid_mult(X_a) & comm_ring(X_a) -> (all Z_1 all H all M hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),hAPP(X_a,fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(X_a,fun(nat,X_a)),combc(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),minus_minus(X_a)),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),times_times(X_a)),hAPP(fun(nat,nat),fun(nat,X_a),hAPP(fun(nat,X_a),fun(fun(nat,nat),fun(nat,X_a)),combb(nat,X_a,nat),hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Z_1),H))),hAPP(nat,fun(nat,nat),minus_minus(nat),M)))),hAPP(X_a,fun(nat,X_a),power_power(X_a),Z_1)))),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),Z_1),M))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),M)) = hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),times_times(X_a)),hAPP(X_a,fun(nat,X_a),power_power(X_a),Z_1))),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),minus_minus(X_a)),hAPP(fun(nat,nat),fun(nat,X_a),hAPP(fun(nat,X_a),fun(fun(nat,nat),fun(nat,X_a)),combb(nat,X_a,nat),hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Z_1),H))),hAPP(nat,fun(nat,nat),minus_minus(nat),M)))),hAPP(fun(nat,nat),fun(nat,X_a),hAPP(fun(nat,X_a),fun(fun(nat,nat),fun(nat,X_a)),combb(nat,X_a,nat),hAPP(X_a,fun(nat,X_a),power_power(X_a),Z_1)),hAPP(nat,fun(nat,nat),minus_minus(nat),M))))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),M))))) # label(fact_4226_lemma__termdiff1) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.85 4159 (all X_a (monoid_mult(X_a) & comm_ring(X_a) -> (all X_1 all N all Y_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X_1),hAPP(nat,nat,suc,N))),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),Y_1),hAPP(nat,nat,suc,N))) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),X_1),Y_1)),hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),times_times(X_a)),hAPP(X_a,fun(nat,X_a),power_power(X_a),X_1))),hAPP(fun(nat,nat),fun(nat,X_a),hAPP(fun(nat,X_a),fun(fun(nat,nat),fun(nat,X_a)),combb(nat,X_a,nat),hAPP(X_a,fun(nat,X_a),power_power(X_a),Y_1)),hAPP(nat,fun(nat,nat),minus_minus(nat),N)))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,suc,N))))))) # label(fact_4227_lemma__realpow__diff__sumr2) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.85 4160 (all X_b all X_a (semiring_1(X_a) -> (all Y_1 all A_2 hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co1399186613setsum(X_b,X_a),hAPP(X_a,fun(X_b,X_a),combk(X_a,X_b),Y_1)),A_2) = 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),hAPP(fun(X_b,bool),nat,finite_card(X_b),A_2))),Y_1)))) # label(fact_4228_setsum__constant) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.85 4161 (all X_a all A_2 hAPP(nat,real,real_1(nat),hAPP(fun(X_a,bool),nat,finite_card(X_a),A_2)) = hAPP(fun(X_a,bool),real,hAPP(fun(X_a,real),fun(fun(X_a,bool),real),big_co1399186613setsum(X_a,real),hAPP(real,fun(X_a,real),combk(real,X_a),one_one(real))),A_2)) # label(fact_4229_real__of__card) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.85 4162 (all Diff all N all X_1 (X_1 = zero_zero(real) -> (N != zero_zero(nat) -> hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),inverse_divide(real)),hAPP(real,fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(real,fun(nat,real)),combc(nat,real,real),Diff),zero_zero(real)))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),fact_fact(nat))))),hAPP(real,fun(nat,real),power_power(real),X_1))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),N)) = hAPP(real,real,hAPP(nat,fun(real,real),Diff,zero_zero(nat)),zero_zero(real))))) # label(fact_4230_Maclaurin__zero) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.85 4163 (all X_a (real_normed_field(X_a) -> (all K all F (hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),F)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K)) -> hBOOL(hAPP(X_a,bool,hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),hAPP(fun(nat,fun(nat,bool)),fun(nat,X_a),hAPP(fun(fun(nat,bool),X_a),fun(fun(nat,fun(nat,bool)),fun(nat,X_a)),combb(fun(nat,bool),X_a,nat),hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F)),hAPP(fun(nat,nat),fun(nat,fun(nat,bool)),hAPP(fun(nat,fun(nat,fun(nat,bool))),fun(fun(nat,nat),fun(nat,fun(nat,bool))),combs(nat,nat,fun(nat,bool)),hAPP(fun(nat,nat),fun(nat,fun(nat,fun(nat,bool))),hAPP(fun(nat,fun(nat,fun(nat,bool))),fun(fun(nat,nat),fun(nat,fun(nat,fun(nat,bool)))),combb(nat,fun(nat,fun(nat,bool)),nat),ord_atLeastLessThan(nat)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),times_times(nat)),K))),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),plus_plus(nat)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),times_times(nat)),K))),K)))),hAPP(fun(nat,X_a),X_a,suminf(X_a),F)))))))) # label(fact_4231_sums__group) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.85 4164 (all A_2 all K (hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,bool),fun(fun(nat,bool),bool),ord_less_eq(fun(nat,bool)),A_2),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),K),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K),hAPP(fun(nat,bool),nat,finite_card(nat),A_2))))) -> A_2 = hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),K),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K),hAPP(fun(nat,bool),nat,finite_card(nat),A_2))))) # label(fact_4232_subset__card__intvl__is__intvl) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.85 4165 (all X_a all X_b (ab_group_add(X_b) -> (all F all B_1 all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),B_1),A_2)) -> hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),F),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_2),B_1)) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),F),A_2)),hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),F),B_1))))))) # label(fact_4233_setsum__diff) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.85 4166 (all X_a (dense_linorder(X_a) -> (all Aa all Ba all C_1 all D_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_gr676655987ssThan(X_a),Aa),Ba)),hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastLessThan(X_a),C_1),D_1))) <-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),Ba)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C_1),Aa)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Ba),D_1))))))) # label(fact_4234_greaterThanLessThan__subseteq__atLeastLessThan__iff) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.85 4167 (all F all G all N hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(nat,fun(real,fun(real,real))),fun(fun(nat,real),fun(nat,fun(real,real))),combs(nat,real,fun(real,real)),hAPP(fun(nat,bool),fun(nat,fun(real,fun(real,real))),hAPP(fun(bool,fun(real,fun(real,real))),fun(fun(nat,bool),fun(nat,fun(real,fun(real,real)))),combb(bool,fun(real,fun(real,real)),nat),if(real)),even_odd_even(nat))),F)),G)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),N))) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),F),hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),N))),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),G),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),plus_plus(nat)),hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),one_one(nat)))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),N)))) # label(fact_4235_sum__split__even__odd) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.85 4168 (all X_a (zero(X_a) -> (all Diff all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> hAPP(X_a,real,hAPP(nat,fun(X_a,real),Diff,zero_zero(nat)),zero_zero(X_a)) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),inverse_divide(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(X_a,fun(nat,real),hAPP(fun(nat,fun(X_a,real)),fun(X_a,fun(nat,real)),combc(nat,X_a,real),Diff),zero_zero(X_a)))),hAPP(real,fun(nat,real),power_power(real),zero_zero(real))))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),fact_fact(nat)))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),N))),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(X_a,real,hAPP(nat,fun(X_a,real),Diff,N),zero_zero(X_a))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),zero_zero(real)),N))),hAPP(nat,real,real_1(nat),hAPP(nat,nat,fact_fact(nat),N)))))))) # label(fact_4236_Maclaurin__bi__le__lemma) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.85 4169 (all N hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),min))),suc)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),N))) = zero_zero(real)) # label(fact_4237_sumr__minus__one__realpow__zero) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.85 4170 (all X_a (field(X_a) -> (all Z_1 all N all H (ti(X_a,H) != zero_zero(X_a) -> 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),inverse_divide(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),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),plus_plus(X_a),Z_1),H)),N)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),Z_1),N))),H)),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),N)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),Z_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),hAPP(nat,nat,suc,zero_zero(nat)))))) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),H),hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),hAPP(fun(nat,fun(nat,bool)),fun(nat,X_a),hAPP(fun(fun(nat,bool),X_a),fun(fun(nat,fun(nat,bool)),fun(nat,X_a)),combb(fun(nat,bool),X_a,nat),hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),times_times(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),plus_plus(X_a),Z_1),H)))),hAPP(fun(nat,nat),fun(nat,X_a),hAPP(fun(nat,X_a),fun(fun(nat,nat),fun(nat,X_a)),combb(nat,X_a,nat),hAPP(X_a,fun(nat,X_a),power_power(X_a),Z_1)),hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))))),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),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat))),hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),hAPP(nat,nat,suc,zero_zero(nat))))))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),hAPP(nat,nat,suc,zero_zero(nat)))))))))) # label(fact_4238_lemma__termdiff2) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.85 4171 (all N hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(real,fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(real,fun(nat,real)),combc(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(nat,fun(real,fun(real,real))),fun(fun(nat,real),fun(nat,fun(real,real))),combs(nat,real,fun(real,real)),hAPP(fun(nat,bool),fun(nat,fun(real,fun(real,real))),hAPP(fun(bool,fun(real,fun(real,real))),fun(fun(nat,bool),fun(nat,fun(real,fun(real,real)))),combb(bool,fun(real,fun(real,real)),nat),if(real)),even_odd_even(nat))),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),inverse_divide(real)),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),min))),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),div_div(nat)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),fact_fact(nat))))),hAPP(real,fun(nat,real),power_power(real),zero_zero(real))))),zero_zero(real))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),one_one(nat)),N)) = zero_zero(real)) # label(fact_4239_lemma__STAR__cos2) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.85 4172 (all N hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(real,fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(real,fun(nat,real)),combc(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(nat,fun(real,fun(real,real))),fun(fun(nat,real),fun(nat,fun(real,real))),combs(nat,real,fun(real,real)),hAPP(fun(nat,bool),fun(nat,fun(real,fun(real,real))),hAPP(fun(bool,fun(real,fun(real,real))),fun(fun(nat,bool),fun(nat,fun(real,fun(real,real)))),combb(bool,fun(real,fun(real,real)),nat),if(real)),even_odd_even(nat))),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),inverse_divide(real)),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),min))),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),div_div(nat)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),fact_fact(nat))))),zero_zero(real)))),hAPP(real,fun(nat,real),power_power(real),zero_zero(real)))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,suc,N))) = one_one(real)) # label(fact_4240_sumr__cos__zero__one) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.85 4173 (all N all X_1 exists T_5 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),T_5)),hAPP(real,real,abs_abs(real),X_1))) & hAPP(real,real,sin,X_1) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(real,fun(nat,fun(real,real)),hAPP(fun(nat,fun(real,fun(real,real))),fun(real,fun(nat,fun(real,real))),combc(nat,real,fun(real,real)),hAPP(fun(nat,bool),fun(nat,fun(real,fun(real,real))),hAPP(fun(bool,fun(real,fun(real,real))),fun(fun(nat,bool),fun(nat,fun(real,fun(real,real)))),combb(bool,fun(real,fun(real,real)),nat),if(real)),even_odd_even(nat))),zero_zero(real))),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),inverse_divide(real)),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),min))),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),div_div(nat)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),minus_minus(nat)),hAPP(nat,nat,suc,zero_zero(nat))))),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),fact_fact(nat)))))),hAPP(real,fun(nat,real),power_power(real),X_1))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),N))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,sin,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),T_5),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),one_one(real)),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,real_1(nat),N))),pi)))),hAPP(nat,real,real_1(nat),hAPP(nat,nat,fact_fact(nat),N)))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X_1),N))))) # label(fact_4241_Maclaurin__sin__expansion2) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.85 4174 (all N all X_1 exists T_5 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),T_5)),hAPP(real,real,abs_abs(real),X_1))) & hAPP(real,real,cos,X_1) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(real,fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(real,fun(nat,real)),combc(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(nat,fun(real,fun(real,real))),fun(fun(nat,real),fun(nat,fun(real,real))),combs(nat,real,fun(real,real)),hAPP(fun(nat,bool),fun(nat,fun(real,fun(real,real))),hAPP(fun(bool,fun(real,fun(real,real))),fun(fun(nat,bool),fun(nat,fun(real,fun(real,real)))),combb(bool,fun(real,fun(real,real)),nat),if(real)),even_odd_even(nat))),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),inverse_divide(real)),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),min))),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),div_div(nat)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),fact_fact(nat))))),zero_zero(real)))),hAPP(real,fun(nat,real),power_power(real),X_1))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),N))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,cos,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),T_5),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),one_one(real)),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,real_1(nat),N))),pi)))),hAPP(nat,real,real_1(nat),hAPP(nat,nat,fact_fact(nat),N)))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X_1),N))))) # label(fact_4242_Maclaurin__cos__expansion) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.85 4175 (all L all U_1 hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastLessThan(int),L),U_1)))) # label(fact_4243_finite__atLeastLessThan__int) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.85 4176 (all X_a all F all A_2 hAPP(nat,int,semiring_1_of_nat(int),hAPP(fun(X_a,bool),nat,hAPP(fun(X_a,nat),fun(fun(X_a,bool),nat),big_co1399186613setsum(X_a,nat),F),A_2)) = hAPP(fun(X_a,bool),int,hAPP(fun(X_a,int),fun(fun(X_a,bool),int),big_co1399186613setsum(X_a,int),hAPP(fun(X_a,nat),fun(X_a,int),hAPP(fun(nat,int),fun(fun(X_a,nat),fun(X_a,int)),combb(nat,int,X_a),semiring_1_of_nat(int)),F)),A_2)) # label(fact_4244_int__setsum) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.85 4177 (all X_a all F all A_2 hAPP(fun(X_a,bool),nat,hAPP(fun(X_a,nat),fun(fun(X_a,bool),nat),big_co1399186613setsum(X_a,nat),F),A_2) = hAPP(int,nat,nat_1,hAPP(fun(X_a,bool),int,hAPP(fun(X_a,int),fun(fun(X_a,bool),int),big_co1399186613setsum(X_a,int),hAPP(fun(X_a,nat),fun(X_a,int),hAPP(fun(nat,int),fun(fun(X_a,nat),fun(X_a,int)),combb(nat,int,X_a),semiring_1_of_nat(int)),F)),A_2))) # label(fact_4245_transfer__nat__int__sum__prod2_I1_J) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.85 4178 (all X_a all F all A_2 hAPP(int,real,real_1(int),hAPP(fun(X_a,bool),int,hAPP(fun(X_a,int),fun(fun(X_a,bool),int),big_co1399186613setsum(X_a,int),F),A_2)) = hAPP(fun(X_a,bool),real,hAPP(fun(X_a,real),fun(fun(X_a,bool),real),big_co1399186613setsum(X_a,real),hAPP(fun(X_a,int),fun(X_a,real),hAPP(fun(int,real),fun(fun(X_a,int),fun(X_a,real)),combb(int,real,X_a),real_1(int)),F)),A_2)) # label(fact_4246_real__of__int__setsum) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.85 4179 (all X_a all F all A_2 hAPP(nat,real,real_1(nat),hAPP(fun(X_a,bool),nat,hAPP(fun(X_a,nat),fun(fun(X_a,bool),nat),big_co1399186613setsum(X_a,nat),F),A_2)) = hAPP(fun(X_a,bool),real,hAPP(fun(X_a,real),fun(fun(X_a,bool),real),big_co1399186613setsum(X_a,real),hAPP(fun(X_a,nat),fun(X_a,real),hAPP(fun(nat,real),fun(fun(X_a,nat),fun(X_a,real)),combb(nat,real,X_a),real_1(nat)),F)),A_2)) # label(fact_4247_real__of__nat__setsum) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.85 4180 (all X_a all G all A_2 hAPP(complex,complex,cnj,hAPP(fun(X_a,bool),complex,hAPP(fun(X_a,complex),fun(fun(X_a,bool),complex),big_co1399186613setsum(X_a,complex),G),A_2)) = hAPP(fun(X_a,bool),complex,hAPP(fun(X_a,complex),fun(fun(X_a,bool),complex),big_co1399186613setsum(X_a,complex),hAPP(fun(X_a,complex),fun(X_a,complex),hAPP(fun(complex,complex),fun(fun(X_a,complex),fun(X_a,complex)),combb(complex,complex,X_a),cnj),G)),A_2)) # label(fact_4248_cnj_Osetsum) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.85 4181 (all X_a all G all A_2 hAPP(complex,real,re,hAPP(fun(X_a,bool),complex,hAPP(fun(X_a,complex),fun(fun(X_a,bool),complex),big_co1399186613setsum(X_a,complex),G),A_2)) = hAPP(fun(X_a,bool),real,hAPP(fun(X_a,real),fun(fun(X_a,bool),real),big_co1399186613setsum(X_a,real),hAPP(fun(X_a,complex),fun(X_a,real),hAPP(fun(complex,real),fun(fun(X_a,complex),fun(X_a,real)),combb(complex,real,X_a),re),G)),A_2)) # label(fact_4249_Re_Osetsum) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.85 4182 (all X_a all G all A_2 hAPP(complex,real,im,hAPP(fun(X_a,bool),complex,hAPP(fun(X_a,complex),fun(fun(X_a,bool),complex),big_co1399186613setsum(X_a,complex),G),A_2)) = hAPP(fun(X_a,bool),real,hAPP(fun(X_a,real),fun(fun(X_a,bool),real),big_co1399186613setsum(X_a,real),hAPP(fun(X_a,complex),fun(X_a,real),hAPP(fun(complex,real),fun(fun(X_a,complex),fun(X_a,real)),combb(complex,real,X_a),im),G)),A_2)) # label(fact_4250_Im_Osetsum) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.85 4183 (all X_a all C_1 all F all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2)) -> hAPP(fun(X_a,bool),int,hAPP(fun(X_a,int),fun(fun(X_a,bool),int),big_co1399186613setsum(X_a,int),hAPP(fun(X_a,int),fun(X_a,int),hAPP(fun(int,int),fun(fun(X_a,int),fun(X_a,int)),combb(int,int,X_a),hAPP(int,fun(int,int),times_times(int),C_1)),F)),A_2) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C_1),hAPP(fun(X_a,bool),int,hAPP(fun(X_a,int),fun(fun(X_a,bool),int),big_co1399186613setsum(X_a,int),F),A_2)))) # label(fact_4251_setsum__const__mult) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.85 4184 (all U_1 hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastLessThan(int),zero_zero(int)),U_1)))) # label(fact_4252_finite__atLeastZeroLessThan__int) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.85 4185 (all X_a all F all F_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),F_1)) -> (hAPP(fun(X_a,bool),nat,hAPP(fun(X_a,nat),fun(fun(X_a,bool),nat),big_co1399186613setsum(X_a,nat),F),F_1) = zero_zero(nat) <-> (all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),F_1)) -> hAPP(X_a,nat,F,X_2) = zero_zero(nat)))))) # label(fact_4253_setsum__eq__0__iff) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.85 4186 (all X_a all A_2 hAPP(fun(X_a,bool),nat,finite_card(X_a),A_2) = hAPP(fun(X_a,bool),nat,hAPP(fun(X_a,nat),fun(fun(X_a,bool),nat),big_co1399186613setsum(X_a,nat),hAPP(nat,fun(X_a,nat),combk(nat,X_a),one_one(nat))),A_2)) # label(fact_4254_card__eq__setsum) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.85 4187 (all Y_1 all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),Y_1),X_1)) -> hAPP(fun(real,bool),real,complete_Sup_Sup(real),hAPP(real,fun(real,bool),hAPP(real,fun(real,fun(real,bool)),ord_atLeastLessThan(real),Y_1),X_1)) = X_1)) # label(fact_4255_Sup__atLeastLessThan) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.85 4188 (all X_a all F all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2)) -> (hAPP(fun(X_a,bool),nat,hAPP(fun(X_a,nat),fun(fun(X_a,bool),nat),big_co1399186613setsum(X_a,nat),F),A_2) = hAPP(nat,nat,suc,zero_zero(nat)) <-> (exists X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_2)) & hAPP(X_a,nat,F,X_2) = hAPP(nat,nat,suc,zero_zero(nat)) & (all Xa (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Xa),A_2)) -> (ti(X_a,X_2) != ti(X_a,Xa) -> hAPP(X_a,nat,F,Xa) = zero_zero(nat))))))))) # label(fact_4256_setsum__eq__Suc0__iff) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.85 4189 (all X_a all F all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2)) -> (hAPP(fun(X_a,bool),nat,hAPP(fun(X_a,nat),fun(fun(X_a,bool),nat),big_co1399186613setsum(X_a,nat),F),A_2) = one_one(nat) <-> (exists X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_2)) & hAPP(X_a,nat,F,X_2) = one_one(nat) & (all Xa (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Xa),A_2)) -> (ti(X_a,X_2) != ti(X_a,Xa) -> hAPP(X_a,nat,F,Xa) = zero_zero(nat))))))))) # label(fact_4257_setsum__eq__1__iff) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.85 4190 (all U_1 hAPP(fun(int,bool),nat,finite_card(int),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastLessThan(int),zero_zero(int)),U_1)) = hAPP(int,nat,nat_1,U_1)) # label(fact_4258_card__atLeastZeroLessThan__int) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.85 4191 (all L all U_1 hAPP(fun(int,bool),nat,finite_card(int),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastLessThan(int),L),U_1)) = hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),U_1),L))) # label(fact_4259_card__atLeastLessThan__int) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.85 4192 (all X_a all F all A_2 all B_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),B_1)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),B_1),A_2)) -> hAPP(fun(X_a,bool),nat,hAPP(fun(X_a,nat),fun(fun(X_a,bool),nat),big_co1399186613setsum(X_a,nat),F),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_2),B_1)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(fun(X_a,bool),nat,hAPP(fun(X_a,nat),fun(fun(X_a,bool),nat),big_co1399186613setsum(X_a,nat),F),A_2)),hAPP(fun(X_a,bool),nat,hAPP(fun(X_a,nat),fun(fun(X_a,bool),nat),big_co1399186613setsum(X_a,nat),F),B_1))))) # label(fact_4260_setsum__diff__nat) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.85 4193 (all L all U_1 hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastLessThan(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),L),one_one(int))),U_1) = hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_gr676655987ssThan(int),L),U_1)) # label(fact_4261_atLeastPlusOneLessThan__greaterThanLessThan__int) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.85 4194 (all X_a all C_1 all X_3 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),X_3)) -> hAPP(fun(X_a,bool),int,hAPP(fun(X_a,int),fun(fun(X_a,bool),int),big_co1399186613setsum(X_a,int),hAPP(int,fun(X_a,int),combk(int,X_a),C_1)),X_3) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C_1),hAPP(nat,int,semiring_1_of_nat(int),hAPP(fun(X_a,bool),nat,finite_card(X_a),X_3))))) # label(fact_4262_setsum__const) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.85 4195 (all X_a all C_1 all X_3 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),X_3)) -> hAPP(nat,int,semiring_1_of_nat(int),hAPP(fun(X_a,bool),nat,hAPP(fun(X_a,nat),fun(fun(X_a,bool),nat),big_co1399186613setsum(X_a,nat),hAPP(nat,fun(X_a,nat),combk(nat,X_a),C_1)),X_3)) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(nat,int,semiring_1_of_nat(int),C_1)),hAPP(nat,int,semiring_1_of_nat(int),hAPP(fun(X_a,bool),nat,finite_card(X_a),X_3))))) # label(fact_4263_setsum__const2) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.85 4196 (all X_a (comm_monoid_add(X_a) & comm_monoid_mult(X_a) -> (all F all A_2 hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),A_2) = hAPP(fun(int,bool),X_a,hAPP(fun(int,X_a),fun(fun(int,bool),X_a),big_co1399186613setsum(int,X_a),hAPP(fun(int,nat),fun(int,X_a),hAPP(fun(nat,X_a),fun(fun(int,nat),fun(int,X_a)),combb(nat,X_a,int),F),nat_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_2))))) # label(fact_4264_transfer__nat__int__sum__prod_I1_J) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.85 4197 (all L all U_1 hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,int),fun(fun(int,bool),fun(int,bool)),image(int,int),hAPP(int,fun(int,int),hAPP(fun(int,fun(int,int)),fun(int,fun(int,int)),combc(int,int,int),plus_plus(int)),L)),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastLessThan(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),U_1),L))) = hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastLessThan(int),L),U_1)) # label(fact_4265_image__add__int__atLeastLessThan) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.85 4198 (all X_a (comm_monoid_add(X_a) & comm_monoid_mult(X_a) -> (all F all A_2 (hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A_2)) -> hAPP(fun(int,bool),X_a,hAPP(fun(int,X_a),fun(fun(int,bool),X_a),big_co1399186613setsum(int,X_a),F),A_2) = hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),hAPP(fun(nat,int),fun(nat,X_a),hAPP(fun(int,X_a),fun(fun(nat,int),fun(nat,X_a)),combb(int,X_a,nat),F),semiring_1_of_nat(int))),hAPP(fun(int,bool),fun(nat,bool),hAPP(fun(int,nat),fun(fun(int,bool),fun(nat,bool)),image(int,nat),nat_1),A_2)))))) # label(fact_4266_transfer__int__nat__sum__prod_I1_J) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.85 4199 (all X_1 all N exists T_5 hAPP(real,real,sin,X_1) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(real,fun(nat,fun(real,real)),hAPP(fun(nat,fun(real,fun(real,real))),fun(real,fun(nat,fun(real,real))),combc(nat,real,fun(real,real)),hAPP(fun(nat,bool),fun(nat,fun(real,fun(real,real))),hAPP(fun(bool,fun(real,fun(real,real))),fun(fun(nat,bool),fun(nat,fun(real,fun(real,real)))),combb(bool,fun(real,fun(real,real)),nat),if(real)),even_odd_even(nat))),zero_zero(real))),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),inverse_divide(real)),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),min))),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),div_div(nat)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),minus_minus(nat)),hAPP(nat,nat,suc,zero_zero(nat))))),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),fact_fact(nat)))))),hAPP(real,fun(nat,real),power_power(real),X_1))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),N))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,sin,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),T_5),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),one_one(real)),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,real_1(nat),N))),pi)))),hAPP(nat,real,real_1(nat),hAPP(nat,nat,fact_fact(nat),N)))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X_1),N)))) # label(fact_4267_Maclaurin__sin__expansion) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.85 4200 (all B_1 all K all Diff all H all N ((all M_3 all T_5 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_3),N)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),T_5)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),T_5),H)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(nat,fun(real,real),Diff,M_3)),T_5),hAPP(real,real,hAPP(nat,fun(real,real),Diff,hAPP(nat,nat,suc,M_3)),T_5))))) -> (N = hAPP(nat,nat,suc,K) -> (all M_3 all T_5 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_3),N)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),T_5)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),T_5),H)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,real)),combs(real,real,real),hAPP(fun(real,real),fun(real,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,fun(real,real))),combb(real,fun(real,real),real),minus_minus(real)),hAPP(nat,fun(real,real),Diff,M_3))),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,real)),combs(real,real,real),hAPP(fun(real,real),fun(real,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,fun(real,real))),combb(real,fun(real,real),real),plus_plus(real)),hAPP(fun(nat,bool),fun(real,real),hAPP(fun(real,fun(fun(nat,bool),real)),fun(fun(nat,bool),fun(real,real)),combc(real,fun(nat,bool),real),hAPP(fun(real,fun(nat,real)),fun(real,fun(fun(nat,bool),real)),hAPP(fun(fun(nat,real),fun(fun(nat,bool),real)),fun(fun(real,fun(nat,real)),fun(real,fun(fun(nat,bool),real))),combb(fun(nat,real),fun(fun(nat,bool),real),real),big_co1399186613setsum(nat,real)),hAPP(fun(real,fun(nat,real)),fun(real,fun(nat,real)),hAPP(fun(fun(nat,real),fun(nat,real)),fun(fun(real,fun(nat,real)),fun(real,fun(nat,real))),combb(fun(nat,real),fun(nat,real),real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),inverse_divide(real)),hAPP(real,fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(real,fun(nat,real)),combc(nat,real,real),hAPP(fun(nat,nat),fun(nat,fun(real,real)),hAPP(fun(nat,fun(real,real)),fun(fun(nat,nat),fun(nat,fun(real,real))),combb(nat,fun(real,real),nat),Diff),hAPP(nat,fun(nat,nat),plus_plus(nat),M_3))),zero_zero(real)))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),fact_fact(nat)))))),power_power(real)))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),M_3))))),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,real),fun(fun(real,real),fun(real,real)),combb(real,real,real),hAPP(real,fun(real,real),times_times(real),B_1)),hAPP(real,fun(real,real),hAPP(fun(real,fun(real,real)),fun(real,fun(real,real)),combc(real,real,real),hAPP(fun(real,real),fun(real,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,fun(real,real))),combb(real,fun(real,real),real),inverse_divide(real)),hAPP(nat,fun(real,real),hAPP(fun(real,fun(nat,real)),fun(nat,fun(real,real)),combc(real,nat,real),power_power(real)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),M_3)))),hAPP(nat,real,real_1(nat),hAPP(nat,nat,fact_fact(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),M_3)))))))),T_5),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,hAPP(nat,fun(real,real),Diff,hAPP(nat,nat,suc,M_3)),T_5)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),inverse_divide(real)),hAPP(real,fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(real,fun(nat,real)),combc(nat,real,real),hAPP(fun(nat,nat),fun(nat,fun(real,real)),hAPP(fun(nat,fun(real,real)),fun(fun(nat,nat),fun(nat,fun(real,real))),combb(nat,fun(real,real),nat),Diff),hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,suc,M_3)))),zero_zero(real)))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),fact_fact(nat))))),hAPP(real,fun(nat,real),power_power(real),T_5))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),hAPP(nat,nat,suc,M_3))))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B_1),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),T_5),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),hAPP(nat,nat,suc,M_3)))),hAPP(nat,real,real_1(nat),hAPP(nat,nat,fact_fact(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),hAPP(nat,nat,suc,M_3))))))))))))))) # label(fact_4268_Maclaurin__lemma2) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.85 4201 (all N all X_1 (X_1 != zero_zero(real) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> (exists T_5 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,abs_abs(real),T_5))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,abs_abs(real),T_5)),hAPP(real,real,abs_abs(real),X_1))) & hAPP(real,real,exp(real),X_1) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),inverse_divide(real)),hAPP(real,fun(nat,real),power_power(real),X_1))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),fact_fact(nat)))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),N))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,exp(real),T_5)),hAPP(nat,real,real_1(nat),hAPP(nat,nat,fact_fact(nat),N)))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X_1),N)))))))) # label(fact_4269_Maclaurin__exp__lt) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.85 4202 (all N all X_1 exists T_5 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),T_5)),hAPP(real,real,abs_abs(real),X_1))) & hAPP(real,real,exp(real),X_1) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),inverse_divide(real)),hAPP(real,fun(nat,real),power_power(real),X_1))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),fact_fact(nat)))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),N))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,exp(real),T_5)),hAPP(nat,real,real_1(nat),hAPP(nat,nat,fact_fact(nat),N)))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X_1),N))))) # label(fact_4270_Maclaurin__exp__le) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.85 4203 (all K all F (hBOOL(hAPP(fun(nat,real),bool,summable(real),F)) -> ((all D_3 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,F,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat)))),D_3)))),hAPP(nat,real,F,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),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,suc,hAPP(nat,nat,suc,zero_zero(nat)))),D_3)),one_one(nat)))))))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),K))),hAPP(fun(nat,real),real,suminf(real),F)))))) # label(fact_4271_sumr__pos__lt__pair) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.85 4204 (all F all J all N all H (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),H)) -> (exists B_5 hAPP(real,real,F,H) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),inverse_divide(real)),J)),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),fact_fact(nat))))),hAPP(real,fun(nat,real),power_power(real),H))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),N))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B_5),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),H),N)),hAPP(nat,real,real_1(nat),hAPP(nat,nat,fact_fact(nat),N)))))))) # label(fact_4272_Maclaurin__lemma) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.86 4205 (all X_a (linordered_semidom(X_a) -> (all K all F all K_3 all N ((all P_5 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),P_5),N)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(nat,X_a,F,P_5)),K_3)))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),K_3)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),K)))),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),N)),K_3)))))))) # label(fact_4273_real__setsum__nat__ivl__bounded2) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.86 4206 (all N all F (hBOOL(hAPP(fun(nat,real),bool,summable(real),F)) -> ((all M_3 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N),M_3)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(nat,real,F,M_3))))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),N))),hAPP(fun(nat,real),real,suminf(real),F)))))) # label(fact_4274_series__pos__less) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.86 4207 (all N all F (hBOOL(hAPP(fun(nat,real),bool,summable(real),F)) -> ((all M_3 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N),M_3)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(nat,real,F,M_3))))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),N))),hAPP(fun(nat,real),real,suminf(real),F)))))) # label(fact_4275_series__pos__le) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.86 4208 (all N all X_1 all Diff all F (hAPP(nat,fun(real,real),Diff,zero_zero(nat)) = F & (all M_3 all X_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(nat,fun(real,real),Diff,M_3)),X_2),hAPP(real,real,hAPP(nat,fun(real,real),Diff,hAPP(nat,nat,suc,M_3)),X_2)))) & X_1 != zero_zero(real) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> (exists T_5 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,abs_abs(real),T_5))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,abs_abs(real),T_5)),hAPP(real,real,abs_abs(real),X_1))) & hAPP(real,real,F,X_1) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),inverse_divide(real)),hAPP(real,fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(real,fun(nat,real)),combc(nat,real,real),Diff),zero_zero(real)))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),fact_fact(nat))))),hAPP(real,fun(nat,real),power_power(real),X_1))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),N))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(nat,fun(real,real),Diff,N),T_5)),hAPP(nat,real,real_1(nat),hAPP(nat,nat,fact_fact(nat),N)))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X_1),N))))))) # label(fact_4276_Maclaurin__all__lt__objl) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.86 4209 (all X_1 all N all Diff all F (hAPP(nat,fun(real,real),Diff,zero_zero(nat)) = F -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> (X_1 != zero_zero(real) -> ((all M_3 all X_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(nat,fun(real,real),Diff,M_3)),X_2),hAPP(real,real,hAPP(nat,fun(real,real),Diff,hAPP(nat,nat,suc,M_3)),X_2)))) -> (exists T_5 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,abs_abs(real),T_5))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,abs_abs(real),T_5)),hAPP(real,real,abs_abs(real),X_1))) & hAPP(real,real,F,X_1) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),inverse_divide(real)),hAPP(real,fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(real,fun(nat,real)),combc(nat,real,real),Diff),zero_zero(real)))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),fact_fact(nat))))),hAPP(real,fun(nat,real),power_power(real),X_1))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),N))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(nat,fun(real,real),Diff,N),T_5)),hAPP(nat,real,real_1(nat),hAPP(nat,nat,fact_fact(nat),N)))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X_1),N)))))))))) # label(fact_4277_Maclaurin__all__lt) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.86 4210 (all X_1 all N all Diff all F (hAPP(nat,fun(real,real),Diff,zero_zero(nat)) = F -> ((all M_3 all T_5 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_3),N)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),T_5)),hAPP(real,real,abs_abs(real),X_1))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(nat,fun(real,real),Diff,M_3)),T_5),hAPP(real,real,hAPP(nat,fun(real,real),Diff,hAPP(nat,nat,suc,M_3)),T_5))))) -> (exists T_5 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),T_5)),hAPP(real,real,abs_abs(real),X_1))) & hAPP(real,real,F,X_1) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),inverse_divide(real)),hAPP(real,fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(real,fun(nat,real)),combc(nat,real,real),Diff),zero_zero(real)))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),fact_fact(nat))))),hAPP(real,fun(nat,real),power_power(real),X_1))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),N))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(nat,fun(real,real),Diff,N),T_5)),hAPP(nat,real,real_1(nat),hAPP(nat,nat,fact_fact(nat),N)))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X_1),N)))))))) # label(fact_4278_Maclaurin__bi__le) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.86 4211 (all Diff all F all N all H (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),H),zero_zero(real))) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> (hAPP(nat,fun(real,real),Diff,zero_zero(nat)) = F -> ((all M_3 all T_5 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_3),N)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),H),T_5)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),T_5),zero_zero(real))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(nat,fun(real,real),Diff,M_3)),T_5),hAPP(real,real,hAPP(nat,fun(real,real),Diff,hAPP(nat,nat,suc,M_3)),T_5))))) -> (exists T_5 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),H),T_5)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),T_5),zero_zero(real))) & hAPP(real,real,F,H) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),inverse_divide(real)),hAPP(real,fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(real,fun(nat,real)),combc(nat,real,real),Diff),zero_zero(real)))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),fact_fact(nat))))),hAPP(real,fun(nat,real),power_power(real),H))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),N))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(nat,fun(real,real),Diff,N),T_5)),hAPP(nat,real,real_1(nat),hAPP(nat,nat,fact_fact(nat),N)))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),H),N)))))))))) # label(fact_4279_Maclaurin__minus) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.86 4212 (all N all Diff all F all H (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),H)) -> (hAPP(nat,fun(real,real),Diff,zero_zero(nat)) = F -> ((all M_3 all T_5 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_3),N)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),T_5)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),T_5),H)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(nat,fun(real,real),Diff,M_3)),T_5),hAPP(real,real,hAPP(nat,fun(real,real),Diff,hAPP(nat,nat,suc,M_3)),T_5))))) -> (exists T_5 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),T_5)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),T_5),H)) & hAPP(real,real,F,H) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),inverse_divide(real)),hAPP(real,fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(real,fun(nat,real)),combc(nat,real,real),Diff),zero_zero(real)))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),fact_fact(nat))))),hAPP(real,fun(nat,real),power_power(real),H))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),N))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(nat,fun(real,real),Diff,N),T_5)),hAPP(nat,real,real_1(nat),hAPP(nat,nat,fact_fact(nat),N)))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),H),N))))))))) # label(fact_4280_Maclaurin2) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.86 4213 (all Diff all F all N all H (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),H)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) & hAPP(nat,fun(real,real),Diff,zero_zero(nat)) = F & (all M_3 all T_5 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_3),N)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),T_5)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),T_5),H)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(nat,fun(real,real),Diff,M_3)),T_5),hAPP(real,real,hAPP(nat,fun(real,real),Diff,hAPP(nat,nat,suc,M_3)),T_5))))) -> (exists T_5 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),T_5)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),T_5),H)) & hAPP(real,real,F,H) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),inverse_divide(real)),hAPP(real,fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(real,fun(nat,real)),combc(nat,real,real),Diff),zero_zero(real)))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),fact_fact(nat))))),hAPP(real,fun(nat,real),power_power(real),H))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),N))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(nat,fun(real,real),Diff,N),T_5)),hAPP(nat,real,real_1(nat),hAPP(nat,nat,fact_fact(nat),N)))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),H),N))))))) # label(fact_4281_Maclaurin__objl) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.86 4214 (all N all Diff all F all H (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),H)) & hAPP(nat,fun(real,real),Diff,zero_zero(nat)) = F & (all M_3 all T_5 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_3),N)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),T_5)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),T_5),H)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(nat,fun(real,real),Diff,M_3)),T_5),hAPP(real,real,hAPP(nat,fun(real,real),Diff,hAPP(nat,nat,suc,M_3)),T_5))))) -> (exists T_5 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),T_5)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),T_5),H)) & hAPP(real,real,F,H) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),inverse_divide(real)),hAPP(real,fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(real,fun(nat,real)),combc(nat,real,real),Diff),zero_zero(real)))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),fact_fact(nat))))),hAPP(real,fun(nat,real),power_power(real),H))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),N))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(nat,fun(real,real),Diff,N),T_5)),hAPP(nat,real,real_1(nat),hAPP(nat,nat,fact_fact(nat),N)))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),H),N))))))) # label(fact_4282_Maclaurin2__objl) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.86 4215 (all Diff all F all N all H (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),H)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> (hAPP(nat,fun(real,real),Diff,zero_zero(nat)) = F -> ((all M_3 all T_5 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_3),N)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),T_5)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),T_5),H)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(nat,fun(real,real),Diff,M_3)),T_5),hAPP(real,real,hAPP(nat,fun(real,real),Diff,hAPP(nat,nat,suc,M_3)),T_5))))) -> (exists T_5 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),T_5)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),T_5),H)) & hAPP(real,real,F,H) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),inverse_divide(real)),hAPP(real,fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(real,fun(nat,real)),combc(nat,real,real),Diff),zero_zero(real)))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),fact_fact(nat))))),hAPP(real,fun(nat,real),power_power(real),H))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),N))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(nat,fun(real,real),Diff,N),T_5)),hAPP(nat,real,real_1(nat),hAPP(nat,nat,fact_fact(nat),N)))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),H),N)))))))))) # label(fact_4283_Maclaurin) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.86 4216 (all Diff all F all N all H (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),H),zero_zero(real))) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) & hAPP(nat,fun(real,real),Diff,zero_zero(nat)) = F & (all M_3 all T_5 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_3),N)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),H),T_5)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),T_5),zero_zero(real))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(nat,fun(real,real),Diff,M_3)),T_5),hAPP(real,real,hAPP(nat,fun(real,real),Diff,hAPP(nat,nat,suc,M_3)),T_5))))) -> (exists T_5 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),H),T_5)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),T_5),zero_zero(real))) & hAPP(real,real,F,H) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),inverse_divide(real)),hAPP(real,fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(real,fun(nat,real)),combc(nat,real,real),Diff),zero_zero(real)))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),fact_fact(nat))))),hAPP(real,fun(nat,real),power_power(real),H))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),N))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(nat,fun(real,real),Diff,N),T_5)),hAPP(nat,real,real_1(nat),hAPP(nat,nat,fact_fact(nat),N)))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),H),N))))))) # label(fact_4284_Maclaurin__minus__objl) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.86 4217 (all N all X_1 all Diff all F (hAPP(nat,fun(real,real),Diff,zero_zero(nat)) = F & (all M_3 all X_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(nat,fun(real,real),Diff,M_3)),X_2),hAPP(real,real,hAPP(nat,fun(real,real),Diff,hAPP(nat,nat,suc,M_3)),X_2)))) -> (exists T_5 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),T_5)),hAPP(real,real,abs_abs(real),X_1))) & hAPP(real,real,F,X_1) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),inverse_divide(real)),hAPP(real,fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(real,fun(nat,real)),combc(nat,real,real),Diff),zero_zero(real)))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),fact_fact(nat))))),hAPP(real,fun(nat,real),power_power(real),X_1))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),N))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(nat,fun(real,real),Diff,N),T_5)),hAPP(nat,real,real_1(nat),hAPP(nat,nat,fact_fact(nat),N)))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X_1),N))))))) # label(fact_4285_Maclaurin__all__le__objl) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.86 4218 (all N all X_1 all Diff all F (hAPP(nat,fun(real,real),Diff,zero_zero(nat)) = F -> ((all M_3 all X_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(nat,fun(real,real),Diff,M_3)),X_2),hAPP(real,real,hAPP(nat,fun(real,real),Diff,hAPP(nat,nat,suc,M_3)),X_2)))) -> (exists T_5 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),T_5)),hAPP(real,real,abs_abs(real),X_1))) & hAPP(real,real,F,X_1) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),inverse_divide(real)),hAPP(real,fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(real,fun(nat,real)),combc(nat,real,real),Diff),zero_zero(real)))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),fact_fact(nat))))),hAPP(real,fun(nat,real),power_power(real),X_1))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),N))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(nat,fun(real,real),Diff,N),T_5)),hAPP(nat,real,real_1(nat),hAPP(nat,nat,fact_fact(nat),N)))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X_1),N)))))))) # label(fact_4286_Maclaurin__all__le) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.86 4219 (all X_a (banach(X_a) -> (all F (hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),F)) <-> (all E (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),E)) -> (exists N_3 all M_3 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_3),M_3)) -> (all N_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,norm_norm(X_a),hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),M_3),N_2)))),E))))))))))) # label(fact_4287_summable__Cauchy) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.86 4220 (all F all K_3 all N ((all P_5 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),P_5),N)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,F,P_5)),K_3)))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),N))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,real_1(nat),N)),K_3))))) # label(fact_4288_real__setsum__nat__ivl__bounded) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.86 4221 (all F all X_1 all F_2 all N all M ((all R_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),R_2)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),R_2),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(nat,fun(real,real),F,R_2)),X_1),hAPP(real,real,hAPP(nat,fun(real,real),F_2,R_2),X_1))))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(fun(nat,bool),fun(real,real),hAPP(fun(real,fun(fun(nat,bool),real)),fun(fun(nat,bool),fun(real,real)),combc(real,fun(nat,bool),real),hAPP(fun(real,fun(nat,real)),fun(real,fun(fun(nat,bool),real)),hAPP(fun(fun(nat,real),fun(fun(nat,bool),real)),fun(fun(real,fun(nat,real)),fun(real,fun(fun(nat,bool),real))),combb(fun(nat,real),fun(fun(nat,bool),real),real),big_co1399186613setsum(nat,real)),hAPP(fun(nat,fun(real,real)),fun(real,fun(nat,real)),combc(nat,real,real),F))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),M),N))),X_1),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(real,fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(real,fun(nat,real)),combc(nat,real,real),F_2),X_1)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),M),N)))))) # label(fact_4289_DERIV__sumr) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.86 4222 (all X_1 all F (hBOOL(hAPP(fun(nat,real),bool,summable(real),F)) -> ((all N_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),N_2))),X_1))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(fun(nat,real),real,suminf(real),F)),X_1))))) # label(fact_4290_suminf__le) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.86 4223 (all X_a (comm_monoid_add(X_a) & t2_space(X_a) -> (all F all N ((all M_3 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N),M_3)) -> hAPP(nat,X_a,F,M_3) = zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),F),hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),N)))))))) # label(fact_4291_series__zero) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.86 4224 (all X_a all X_b (comm_monoid_add(X_b) & ordere779506340up_add(X_b) -> (all F all A_2 all B_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),B_1)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_2),B_1)) -> ((all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),B_1),A_2))) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),zero_zero(X_b)),hAPP(X_a,X_b,F,X_2))))) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),F),A_2)),hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),F),B_1))))))))) # label(fact_4292_setsum__mono3) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.86 4225 (all X_a all X_b (ordere216010020id_add(X_b) -> (all F all A_2 all B_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),B_1)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_2),B_1)) -> ((all B_3 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),B_3),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),B_1),A_2))) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),zero_zero(X_b)),hAPP(X_a,X_b,F,B_3))))) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),F),A_2)),hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),F),B_1))))))))) # label(fact_4293_setsum__mono2) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.86 4226 (all X_a all X_b (comm_monoid_add(X_b) -> (all F all S all T_4 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),T_4)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),S),T_4)) -> ((all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),T_4),S))) -> hAPP(X_a,X_b,F,X_2) = zero_zero(X_b))) -> hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),F),S) = hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),F),T_4))))))) # label(fact_4294_setsum__mono__zero__left) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.86 4227 (all X_a all X_b (comm_monoid_add(X_b) -> (all F all S all T_4 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),T_4)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),S),T_4)) -> ((all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),T_4),S))) -> hAPP(X_a,X_b,F,X_2) = zero_zero(X_b))) -> hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),F),T_4) = hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),F),S))))))) # label(fact_4295_setsum__mono__zero__right) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.86 4228 (all X_a all X_b (ordere779506340up_add(X_b) & semiring_1(X_b) -> (all F all K_3 all A_2 ((all I_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),I_2),A_2)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_a,X_b,F,I_2)),K_3)))) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),F),A_2)),hAPP(X_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_a,bool),nat,finite_card(X_a),A_2))),K_3))))))) # label(fact_4296_setsum__bounded) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.86 4229 (all X_a (comm_monoid_add(X_a) & comm_monoid_mult(X_a) -> (all F all G all A_2 all B_1 (A_2 = B_1 -> (hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,B_1)) -> ((all X_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X_2)) -> hAPP(int,X_a,F,X_2) = hAPP(int,X_a,G,X_2))) -> hAPP(fun(int,bool),X_a,hAPP(fun(int,X_a),fun(fun(int,bool),X_a),big_co1399186613setsum(int,X_a),F),A_2) = hAPP(fun(int,bool),X_a,hAPP(fun(int,X_a),fun(fun(int,bool),X_a),big_co1399186613setsum(int,X_a),G),B_1))))))) # label(fact_4297_transfer__nat__int__sum__prod__cong_I1_J) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.86 4230 (all X_b all X_a all R_3 all K all T_4 all S (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),S)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),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),T_4)) -> hAPP(fun(X_a,bool),nat,finite_card(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,bool)),combs(X_a,bool,bool),hAPP(fun(X_a,bool),fun(X_a,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,fun(bool,bool))),combb(bool,fun(bool,bool),X_a),fconj),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(X_a,bool)),combc(X_a,fun(X_a,bool),bool),member(X_a)),S))),hAPP(X_b,fun(X_a,bool),hAPP(fun(X_a,fun(X_b,bool)),fun(X_b,fun(X_a,bool)),combc(X_a,X_b,bool),R_3),X_2)))) = K)) -> hAPP(fun(X_a,bool),nat,hAPP(fun(X_a,nat),fun(fun(X_a,bool),nat),big_co1399186613setsum(X_a,nat),hAPP(fun(X_a,fun(X_b,bool)),fun(X_a,nat),hAPP(fun(fun(X_b,bool),nat),fun(fun(X_a,fun(X_b,bool)),fun(X_a,nat)),combb(fun(X_b,bool),nat,X_a),finite_card(X_b)),hAPP(fun(X_a,fun(X_b,bool)),fun(X_a,fun(X_b,bool)),hAPP(fun(fun(X_b,bool),fun(X_b,bool)),fun(fun(X_a,fun(X_b,bool)),fun(X_a,fun(X_b,bool))),combb(fun(X_b,bool),fun(X_b,bool),X_a),collect(X_b)),hAPP(fun(X_a,fun(X_b,bool)),fun(X_a,fun(X_b,bool)),hAPP(fun(fun(X_b,bool),fun(X_b,bool)),fun(fun(X_a,fun(X_b,bool)),fun(X_a,fun(X_b,bool))),combb(fun(X_b,bool),fun(X_b,bool),X_a),hAPP(fun(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)),T_4)))),R_3)))),S) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),hAPP(fun(X_b,bool),nat,finite_card(X_b),T_4)))))) # label(fact_4298_setsum__multicount) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.86 4231 (all X_a all X_b (ordered_ab_group_add(X_b) -> (all I all B_1 all F all S_3 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),S_3)) -> ((all I_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),I_2),S_3)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),zero_zero(X_b)),hAPP(X_a,X_b,F,I_2))))) -> (hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),F),S_3) = B_1 -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),I),S_3)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_a,X_b,F,I)),B_1))))))))) # label(fact_4299_setsum__nonneg__leq__bound) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.86 4232 (all X_a all X_b (ordered_ab_group_add(X_b) -> (all I all F all S_3 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),S_3)) -> ((all I_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),I_2),S_3)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),zero_zero(X_b)),hAPP(X_a,X_b,F,I_2))))) -> (hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),F),S_3) = zero_zero(X_b) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),I),S_3)) -> hAPP(X_a,X_b,F,I) = zero_zero(X_b)))))))) # label(fact_4300_setsum__nonneg__0) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.86 4233 (all X_a all F all A_2 all N (hAPP(fun(X_a,bool),nat,hAPP(fun(X_a,nat),fun(fun(X_a,bool),nat),big_co1399186613setsum(X_a,nat),F),A_2) = hAPP(nat,nat,suc,N) -> (exists X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_2)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(X_a,nat,F,X_2))))))) # label(fact_4301_setsum__SucD) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.86 4234 (all X_b all X_a (ord(X_a) & comm_monoid_add(X_b) -> (all F all G all Ba all D_1 all Aa all C_1 (ti(X_a,Aa) = ti(X_a,C_1) -> (ti(X_a,Ba) = ti(X_a,D_1) -> ((all X_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C_1),X_2)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_2),D_1)) -> hAPP(X_a,X_b,F,X_2) = hAPP(X_a,X_b,G,X_2)))) -> hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),F),hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastLessThan(X_a),Aa),Ba)) = hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),G),hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastLessThan(X_a),C_1),D_1)))))))) # label(fact_4302_setsum__ivl__cong) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.86 4235 (all X_b all X_a all R_3 all K all T_3 all S_3 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),S_3)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),T_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),T_3)) -> hAPP(fun(X_a,bool),nat,finite_card(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,bool)),combs(X_a,bool,bool),hAPP(fun(X_a,bool),fun(X_a,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,fun(bool,bool))),combb(bool,fun(bool,bool),X_a),fconj),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(X_a,bool)),combc(X_a,fun(X_a,bool),bool),member(X_a)),S_3))),hAPP(X_b,fun(X_a,bool),hAPP(fun(X_a,fun(X_b,bool)),fun(X_b,fun(X_a,bool)),combc(X_a,X_b,bool),R_3),X_2)))) = hAPP(X_b,nat,K,X_2))) -> hAPP(fun(X_a,bool),nat,hAPP(fun(X_a,nat),fun(fun(X_a,bool),nat),big_co1399186613setsum(X_a,nat),hAPP(fun(X_a,fun(X_b,bool)),fun(X_a,nat),hAPP(fun(fun(X_b,bool),nat),fun(fun(X_a,fun(X_b,bool)),fun(X_a,nat)),combb(fun(X_b,bool),nat,X_a),finite_card(X_b)),hAPP(fun(X_a,fun(X_b,bool)),fun(X_a,fun(X_b,bool)),hAPP(fun(fun(X_b,bool),fun(X_b,bool)),fun(fun(X_a,fun(X_b,bool)),fun(X_a,fun(X_b,bool))),combb(fun(X_b,bool),fun(X_b,bool),X_a),collect(X_b)),hAPP(fun(X_a,fun(X_b,bool)),fun(X_a,fun(X_b,bool)),hAPP(fun(fun(X_b,bool),fun(X_b,bool)),fun(fun(X_a,fun(X_b,bool)),fun(X_a,fun(X_b,bool))),combb(fun(X_b,bool),fun(X_b,bool),X_a),hAPP(fun(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)),T_3)))),R_3)))),S_3) = hAPP(fun(X_b,bool),nat,hAPP(fun(X_b,nat),fun(fun(X_b,bool),nat),big_co1399186613setsum(X_b,nat),K),T_3))))) # label(fact_4303_setsum__multicount__gen) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.86 4236 (all X_a all X_b (real_normed_field(X_b) -> (all F all X_1 all F_2 all S (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),S)) -> ((all N_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),N_2),S)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),hAPP(fun(X_b,X_b),fun(X_b,fun(X_b,bool)),deriv(X_b),hAPP(X_a,fun(X_b,X_b),hAPP(fun(X_b,fun(X_a,X_b)),fun(X_a,fun(X_b,X_b)),combc(X_b,X_a,X_b),F),N_2)),X_1),hAPP(X_a,X_b,hAPP(X_b,fun(X_a,X_b),F_2,X_1),N_2))))) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),hAPP(fun(X_b,X_b),fun(X_b,fun(X_b,bool)),deriv(X_b),hAPP(fun(X_a,bool),fun(X_b,X_b),hAPP(fun(X_b,fun(fun(X_a,bool),X_b)),fun(fun(X_a,bool),fun(X_b,X_b)),combc(X_b,fun(X_a,bool),X_b),hAPP(fun(X_b,fun(X_a,X_b)),fun(X_b,fun(fun(X_a,bool),X_b)),hAPP(fun(fun(X_a,X_b),fun(fun(X_a,bool),X_b)),fun(fun(X_b,fun(X_a,X_b)),fun(X_b,fun(fun(X_a,bool),X_b))),combb(fun(X_a,X_b),fun(fun(X_a,bool),X_b),X_b),big_co1399186613setsum(X_a,X_b)),F)),S)),X_1),hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),hAPP(X_b,fun(X_a,X_b),F_2,X_1)),S)))))))) # label(fact_4304_DERIV__setsum) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.86 4237 (all F all A_2 (hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A_2)) -> ((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,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,F,X_2))))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(fun(int,bool),int,hAPP(fun(int,int),fun(fun(int,bool),int),big_co1399186613setsum(int,int),F),A_2)))))) # label(fact_4305_transfer__nat__int__sum__prod__closure_I1_J) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.86 4238 (all X_1 all F ((all N_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(nat,real,F,N_2)))) -> ((all N_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),N_2))),X_1))) -> hBOOL(hAPP(fun(nat,real),bool,summable(real),F))))) # label(fact_4306_pos__summable) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.86 4239 (all X_a all X_b (comm_monoid_add(X_b) -> (all G all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2)) -> ((all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_2)) -> hAPP(X_a,X_b,G,X_2) = zero_zero(X_b))) -> hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),G),A_2) = zero_zero(X_b)))))) # label(fact_4307_setsum_Oneutral) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.86 4240 (all X_a all X_b (comm_monoid_add(X_b) & ordere779506340up_add(X_b) -> (all F all A_2 ((all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_2)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_a,X_b,F,X_2)),zero_zero(X_b))))) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),F),A_2)),zero_zero(X_b))))))) # label(fact_4308_setsum__nonpos) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.86 4241 (all X_a all X_b (comm_monoid_add(X_b) & ordere779506340up_add(X_b) -> (all F all A_2 ((all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_2)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),zero_zero(X_b)),hAPP(X_a,X_b,F,X_2))))) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),zero_zero(X_b)),hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),F),A_2))))))) # label(fact_4309_setsum__nonneg) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.86 4242 (all X_a all X_b (comm_monoid_add(X_b) -> (all F all S (hBOOL(hAPP(fun(fun(X_a,bool),bool),bool,finite_finite_1(fun(X_a,bool)),S)) -> ((all X_2 (hBOOL(hAPP(fun(fun(X_a,bool),bool),bool,hAPP(fun(X_a,bool),fun(fun(fun(X_a,bool),bool),bool),member(fun(X_a,bool)),X_2),S)) -> hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),X_2)))) -> ((all T1 (hBOOL(hAPP(fun(fun(X_a,bool),bool),bool,hAPP(fun(X_a,bool),fun(fun(fun(X_a,bool),bool),bool),member(fun(X_a,bool)),T1),S)) -> (all T2 (hBOOL(hAPP(fun(fun(X_a,bool),bool),bool,hAPP(fun(X_a,bool),fun(fun(fun(X_a,bool),bool),bool),member(fun(X_a,bool)),T2),S)) -> (ti(fun(X_a,bool),T1) != ti(fun(X_a,bool),T2) -> (all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),T1)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),T2)) -> hAPP(X_a,X_b,F,X_2) = zero_zero(X_b))))))))) -> hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),F),hAPP(fun(fun(X_a,bool),bool),fun(X_a,bool),complete_Sup_Sup(fun(X_a,bool)),S)) = hAPP(fun(fun(X_a,bool),bool),X_b,hAPP(fun(fun(X_a,bool),X_b),fun(fun(fun(X_a,bool),bool),X_b),big_co1399186613setsum(fun(X_a,bool),X_b),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),F)),S))))))) # label(fact_4310_setsum__UNION__zero) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.86 4243 (all Aa all D_1 all N hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),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),Aa)),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))),D_1))),hAPP(nat,fun(nat,bool),ord_lessThan(nat),N))) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(nat,int,semiring_1_of_nat(int),N)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Aa),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Aa),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),N),one_one(nat)))),D_1))))) # label(fact_4311_arith__series__int) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.86 4244 (all K_3 all K all F ((all N_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),K),hAPP(nat,real,F,N_2))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,F,N_2)),K_3)))) -> hBOOL(hAPP(fun(nat,real),bool,bseq(real),F)))) # label(fact_4312_BseqI2) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.86 4245 (all K hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),hAPP(nat,fun(nat,bool),ord_lessThan(nat),K)))) # label(fact_4313_finite__lessThan) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.86 4246 (all X_a (ord(X_a) -> (all I all K (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),I),hAPP(X_a,fun(X_a,bool),ord_lessThan(X_a),K))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),I),K)))))) # label(fact_4314_lessThan__iff) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.86 4247 (all U_1 hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(nat,fun(nat,bool),ord_lessThan(nat),U_1)) = U_1) # label(fact_4315_card__lessThan) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.86 4248 (all X_a (linorder(X_a) -> (all X_1 all Y_1 (hAPP(X_a,fun(X_a,bool),ord_lessThan(X_a),X_1) = hAPP(X_a,fun(X_a,bool),ord_lessThan(X_a),Y_1) <-> ti(X_a,X_1) = ti(X_a,Y_1))))) # label(fact_4316_lessThan__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.86 4249 (all N hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),N) = hAPP(nat,fun(nat,bool),ord_lessThan(nat),N)) # label(fact_4317_atLeast0LessThan) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.86 4250 (all S (hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),S)) <-> (exists K_1 hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,bool),fun(fun(nat,bool),bool),ord_less_eq(fun(nat,bool)),S),hAPP(nat,fun(nat,bool),ord_lessThan(nat),K_1)))))) # label(fact_4318_finite__nat__iff__bounded) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.86 4251 (all X_a (linorder(X_a) -> (all X_1 all Y_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(X_a,fun(X_a,bool),ord_lessThan(X_a),X_1)),hAPP(X_a,fun(X_a,bool),ord_lessThan(X_a),Y_1))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),Y_1)))))) # label(fact_4319_lessThan__subset__iff) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.86 4252 (all X_a (linorder(X_a) -> (all M all N (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less(fun(X_a,bool)),hAPP(X_a,fun(X_a,bool),ord_lessThan(X_a),M)),hAPP(X_a,fun(X_a,bool),ord_lessThan(X_a),N))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),M),N)))))) # label(fact_4320_lessThan__strict__subset__iff) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.86 4253 (all X_a (comm_monoid_add(X_a) -> (all F all N hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),ord_lessThan(nat),hAPP(nat,nat,suc,N))) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),ord_lessThan(nat),N))),hAPP(nat,X_a,F,N))))) # label(fact_4321_setsum__lessThan__Suc) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.86 4254 (all Aa all D_1 all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(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),Aa)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),times_times(nat)),D_1))),hAPP(nat,fun(nat,bool),ord_lessThan(nat),N))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Aa),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Aa),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),one_one(nat))),D_1))))) # label(fact_4322_arith__series__nat) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.86 4255 (all U_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),U_1)) -> hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastLessThan(int),zero_zero(int)),U_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)),hAPP(nat,fun(nat,bool),ord_lessThan(nat),hAPP(int,nat,nat_1,U_1))))) # label(fact_4323_image__atLeastZeroLessThan__int) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.86 4256 (all X_a (comm_semiring_1(X_a) -> (all Aa all D_1 all N 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))),hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(X_a,X_a),fun(fun(nat,X_a),fun(nat,X_a)),combb(X_a,X_a,nat),hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Aa)),hAPP(X_a,fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(X_a,fun(nat,X_a)),combc(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),times_times(X_a)),semiring_1_of_nat(X_a))),D_1))),hAPP(nat,fun(nat,bool),ord_lessThan(nat),N))) = 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),N)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Aa),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Aa),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),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),one_one(nat)))),D_1))))))) # label(fact_4324_arith__series__general) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.86 4257 (all S (hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),S)) -> (exists K_1 hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,bool),fun(fun(nat,bool),bool),ord_less_eq(fun(nat,bool)),S),hAPP(nat,fun(nat,bool),ord_lessThan(nat),K_1)))))) # label(fact_4325_finite__nat__bounded) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.86 4258 (all N all Q_1 all P_1 ((all X_2 hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,Q_1,X_2)),hAPP(nat,nat,P_1,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),P_1),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_1),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)),P_1)),Q_1)),hAPP(nat,fun(nat,bool),ord_lessThan(nat),N)))) # label(fact_4326_sum__diff__distrib) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.86 4259 (all X_1 hAPP(fun(real,bool),real,complete_Sup_Sup(real),hAPP(real,fun(real,bool),ord_lessThan(real),X_1)) = X_1) # label(fact_4327_Sup__lessThan) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.86 4260 (all X_a (comm_monoid_add(X_a) & metric_space(X_a) -> (all F hAPP(fun(nat,X_a),X_a,suminf(X_a),F) = hAPP(fun(nat,X_a),X_a,lim(X_a),hAPP(fun(nat,fun(nat,bool)),fun(nat,X_a),hAPP(fun(fun(nat,bool),X_a),fun(fun(nat,fun(nat,bool)),fun(nat,X_a)),combb(fun(nat,bool),X_a,nat),hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F)),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat))))))) # label(fact_4328_suminf__eq__lim) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.86 4261 (all X_b all X_c all X_a all F all G ((all X_2 all Y_2 hAPP(X_b,X_c,hAPP(X_a,fun(X_b,X_c),F,X_2),Y_2) = hAPP(product_prod(X_a,X_b),X_c,G,hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),X_2),Y_2))) -> hAPP(fun(X_a,fun(X_b,X_c)),fun(product_prod(X_a,X_b),X_c),product_prod_case(X_a,X_b,X_c),F) = ti(fun(product_prod(X_a,X_b),X_c),G))) # label(fact_4329_cond__split__eta) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.86 4262 (all X_a all N all F all C_1 all H ((all N_2 hAPP(nat,X_a,F,N_2) = hAPP(nat,X_a,hAPP(fun(nat,fun(X_a,X_a)),fun(nat,X_a),hAPP(X_a,fun(fun(nat,fun(X_a,X_a)),fun(nat,X_a)),nat_rec(X_a),C_1),H),N_2)) -> hAPP(nat,X_a,F,hAPP(nat,nat,suc,N)) = hAPP(X_a,X_a,hAPP(nat,fun(X_a,X_a),H,N),hAPP(nat,X_a,F,N)))) # label(fact_4330_def__nat__rec__Suc) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.86 4263 (all X_b all X_a all F all A_2 (-hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),A_2))) -> (exists X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_2)) & -hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,bool)),combs(X_a,bool,bool),hAPP(fun(X_a,bool),fun(X_a,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,fun(bool,bool))),combb(bool,fun(bool,bool),X_a),fconj),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(X_a,bool)),combc(X_a,fun(X_a,bool),bool),member(X_a)),A_2))),hAPP(X_b,fun(X_a,bool),hAPP(fun(X_a,fun(X_b,bool)),fun(X_b,fun(X_a,bool)),combc(X_a,X_b,bool),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,bool)),hAPP(fun(X_b,fun(X_b,bool)),fun(fun(X_a,X_b),fun(X_a,fun(X_b,bool))),combb(X_b,fun(X_b,bool),X_a),fequal(X_b)),F)),hAPP(X_a,X_b,F,X_2))))))))))) # label(fact_4331_pigeonhole__infinite) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.86 4264 (all X_a all F all C_1 all H ((all N_2 hAPP(nat,X_a,F,N_2) = hAPP(nat,X_a,hAPP(fun(nat,fun(X_a,X_a)),fun(nat,X_a),hAPP(X_a,fun(fun(nat,fun(X_a,X_a)),fun(nat,X_a)),nat_rec(X_a),C_1),H),N_2)) -> hAPP(nat,X_a,F,zero_zero(nat)) = ti(X_a,C_1))) # label(fact_4332_def__nat__rec__0) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.86 4265 (all X_a all F all G all M all S ((all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),S)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(X_a,int,F,X_2)),hAPP(X_a,int,G,X_2)),M)))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(fun(X_a,bool),int,hAPP(fun(X_a,int),fun(fun(X_a,bool),int),big_co1399186613setsum(X_a,int),F),S)),hAPP(fun(X_a,bool),int,hAPP(fun(X_a,int),fun(fun(X_a,bool),int),big_co1399186613setsum(X_a,int),G),S)),M)))) # label(fact_4333_setsum__same__function__zcong) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.86 4266 (all P_2 all P_1 ((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,P_1,X_2)) <-> hBOOL(hAPP(int,bool,P_2,X_2))))) -> hAPP(fun(int,bool),fun(int,bool),collect(int),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),combs(int,bool,bool),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(int,fun(int,bool),ord_less_eq(int),zero_zero(int)))),P_1)) = hAPP(fun(int,bool),fun(int,bool),collect(int),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),combs(int,bool,bool),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(int,fun(int,bool),ord_less_eq(int),zero_zero(int)))),P_2)))) # label(fact_4334_transfer__nat__int__set__cong) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.87 4267 (all X_a all X_b all R_3 all S (hBOOL(hAPP(fun(X_a,fun(X_b,bool)),bool,hAPP(fun(X_a,fun(X_b,bool)),fun(fun(X_a,fun(X_b,bool)),bool),ord_less_eq(fun(X_a,fun(X_b,bool))),hAPP(fun(product_prod(X_a,X_b),bool),fun(X_a,fun(X_b,bool)),hAPP(fun(X_a,fun(fun(product_prod(X_a,X_b),bool),fun(X_b,bool))),fun(fun(product_prod(X_a,X_b),bool),fun(X_a,fun(X_b,bool))),combc(X_a,fun(product_prod(X_a,X_b),bool),fun(X_b,bool)),hAPP(fun(X_a,fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool))),fun(X_a,fun(fun(product_prod(X_a,X_b),bool),fun(X_b,bool))),hAPP(fun(fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool)),fun(fun(product_prod(X_a,X_b),bool),fun(X_b,bool))),fun(fun(X_a,fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool))),fun(X_a,fun(fun(product_prod(X_a,X_b),bool),fun(X_b,bool)))),combb(fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool)),fun(fun(product_prod(X_a,X_b),bool),fun(X_b,bool)),X_a),combc(X_b,fun(product_prod(X_a,X_b),bool),bool)),hAPP(fun(X_a,fun(X_b,product_prod(X_a,X_b))),fun(X_a,fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool))),hAPP(fun(fun(X_b,product_prod(X_a,X_b)),fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool))),fun(fun(X_a,fun(X_b,product_prod(X_a,X_b))),fun(X_a,fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool)))),combb(fun(X_b,product_prod(X_a,X_b)),fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool)),X_a),hAPP(fun(product_prod(X_a,X_b),fun(fun(product_prod(X_a,X_b),bool),bool)),fun(fun(X_b,product_prod(X_a,X_b)),fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool))),combb(product_prod(X_a,X_b),fun(fun(product_prod(X_a,X_b),bool),bool),X_b),member(product_prod(X_a,X_b)))),product_Pair(X_a,X_b)))),R_3)),hAPP(fun(product_prod(X_a,X_b),bool),fun(X_a,fun(X_b,bool)),hAPP(fun(X_a,fun(fun(product_prod(X_a,X_b),bool),fun(X_b,bool))),fun(fun(product_prod(X_a,X_b),bool),fun(X_a,fun(X_b,bool))),combc(X_a,fun(product_prod(X_a,X_b),bool),fun(X_b,bool)),hAPP(fun(X_a,fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool))),fun(X_a,fun(fun(product_prod(X_a,X_b),bool),fun(X_b,bool))),hAPP(fun(fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool)),fun(fun(product_prod(X_a,X_b),bool),fun(X_b,bool))),fun(fun(X_a,fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool))),fun(X_a,fun(fun(product_prod(X_a,X_b),bool),fun(X_b,bool)))),combb(fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool)),fun(fun(product_prod(X_a,X_b),bool),fun(X_b,bool)),X_a),combc(X_b,fun(product_prod(X_a,X_b),bool),bool)),hAPP(fun(X_a,fun(X_b,product_prod(X_a,X_b))),fun(X_a,fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool))),hAPP(fun(fun(X_b,product_prod(X_a,X_b)),fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool))),fun(fun(X_a,fun(X_b,product_prod(X_a,X_b))),fun(X_a,fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool)))),combb(fun(X_b,product_prod(X_a,X_b)),fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool)),X_a),hAPP(fun(product_prod(X_a,X_b),fun(fun(product_prod(X_a,X_b),bool),bool)),fun(fun(X_b,product_prod(X_a,X_b)),fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool))),combb(product_prod(X_a,X_b),fun(fun(product_prod(X_a,X_b),bool),bool),X_b),member(product_prod(X_a,X_b)))),product_Pair(X_a,X_b)))),S))) <-> hBOOL(hAPP(fun(product_prod(X_a,X_b),bool),bool,hAPP(fun(product_prod(X_a,X_b),bool),fun(fun(product_prod(X_a,X_b),bool),bool),ord_less_eq(fun(product_prod(X_a,X_b),bool)),R_3),S)))) # label(fact_4335_pred__subset__eq2) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.87 4268 (all X_a all Q_1 all P_1 all X_1 (hBOOL(hAPP(X_a,bool,P_1,X_1)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),P_1),Q_1)) -> hBOOL(hAPP(X_a,bool,Q_1,X_1))))) # label(fact_4336_rev__predicate1D) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.87 4269 (all X_a all X_1 all P_1 all Q_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),P_1),Q_1)) -> (hBOOL(hAPP(X_a,bool,P_1,X_1)) -> hBOOL(hAPP(X_a,bool,Q_1,X_1))))) # label(fact_4337_predicate1D) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.87 4270 (all X_a all X_b all S all R_3 ((all X_2 all Xa (hBOOL(hAPP(fun(product_prod(X_a,X_b),bool),bool,hAPP(product_prod(X_a,X_b),fun(fun(product_prod(X_a,X_b),bool),bool),member(product_prod(X_a,X_b)),hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),X_2),Xa)),R_3)) <-> hBOOL(hAPP(fun(product_prod(X_a,X_b),bool),bool,hAPP(product_prod(X_a,X_b),fun(fun(product_prod(X_a,X_b),bool),bool),member(product_prod(X_a,X_b)),hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),X_2),Xa)),S)))) <-> ti(fun(product_prod(X_a,X_b),bool),R_3) = ti(fun(product_prod(X_a,X_b),bool),S))) # label(fact_4338_pred__equals__eq2) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.87 4271 (all X_a all R_3 all S (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(X_a,bool)),combc(X_a,fun(X_a,bool),bool),member(X_a)),R_3)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(X_a,bool)),combc(X_a,fun(X_a,bool),bool),member(X_a)),S))) <-> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),R_3),S)))) # label(fact_4339_pred__subset__eq) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.87 4272 (all X_b all X_a all Q_1 all P_1 all X_1 all Y_1 (hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),P_1,X_1),Y_1)) -> (hBOOL(hAPP(fun(X_a,fun(X_b,bool)),bool,hAPP(fun(X_a,fun(X_b,bool)),fun(fun(X_a,fun(X_b,bool)),bool),ord_less_eq(fun(X_a,fun(X_b,bool))),P_1),Q_1)) -> hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),Q_1,X_1),Y_1))))) # label(fact_4340_rev__predicate2D) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.87 4273 (all X_a all X_b all X_1 all Y_1 all P_1 all Q_1 (hBOOL(hAPP(fun(X_a,fun(X_b,bool)),bool,hAPP(fun(X_a,fun(X_b,bool)),fun(fun(X_a,fun(X_b,bool)),bool),ord_less_eq(fun(X_a,fun(X_b,bool))),P_1),Q_1)) -> (hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),P_1,X_1),Y_1)) -> hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),Q_1,X_1),Y_1))))) # label(fact_4341_predicate2D) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.87 4274 (all X_b all X_a all Q_1 all P_1 ((all X_2 all Y_2 (hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),P_1,X_2),Y_2)) -> hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),Q_1,X_2),Y_2)))) -> hBOOL(hAPP(fun(X_a,fun(X_b,bool)),bool,hAPP(fun(X_a,fun(X_b,bool)),fun(fun(X_a,fun(X_b,bool)),bool),ord_less_eq(fun(X_a,fun(X_b,bool))),P_1),Q_1)))) # label(fact_4342_predicate2I) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.87 4275 (all X_a all X_b (comm_monoid_add(X_b) & ordere779506340up_add(X_b) -> (all F all G all K_3 ((all I_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),I_2),K_3)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_a,X_b,F,I_2)),hAPP(X_a,X_b,G,I_2))))) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),F),K_3)),hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),G),K_3))))))) # label(fact_4343_setsum__mono) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.87 4276 (all P_4 ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(product_prod(int,int),int,product_snd(int,int),P_4))) -> hAPP(product_prod(int,int),product_prod(int,int),normalize,P_4) = hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(product_prod(int,int),int,product_fst(int,int),P_4)),hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),hAPP(product_prod(int,int),int,product_fst(int,int),P_4)),hAPP(product_prod(int,int),int,product_snd(int,int),P_4)))),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(product_prod(int,int),int,product_snd(int,int),P_4)),hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),hAPP(product_prod(int,int),int,product_fst(int,int),P_4)),hAPP(product_prod(int,int),int,product_snd(int,int),P_4))))) & (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(product_prod(int,int),int,product_snd(int,int),P_4))) -> (hAPP(product_prod(int,int),int,product_snd(int,int),P_4) = zero_zero(int) -> hAPP(product_prod(int,int),product_prod(int,int),normalize,P_4) = hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),zero_zero(int)),one_one(int))) & (hAPP(product_prod(int,int),int,product_snd(int,int),P_4) != zero_zero(int) -> hAPP(product_prod(int,int),product_prod(int,int),normalize,P_4) = hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(product_prod(int,int),int,product_fst(int,int),P_4)),hAPP(int,int,uminus_uminus(int),hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),hAPP(product_prod(int,int),int,product_fst(int,int),P_4)),hAPP(product_prod(int,int),int,product_snd(int,int),P_4))))),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(product_prod(int,int),int,product_snd(int,int),P_4)),hAPP(int,int,uminus_uminus(int),hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),hAPP(product_prod(int,int),int,product_fst(int,int),P_4)),hAPP(product_prod(int,int),int,product_snd(int,int),P_4))))))))) # label(fact_4344_normalize__def) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.87 4277 (all X_a all X_b (comm_monoid_add(X_b) -> (all G all F all S all T_4 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),T_4)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),S),T_4)) -> ((all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),T_4),S))) -> hAPP(X_a,X_b,F,X_2) = zero_zero(X_b))) -> ((all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),S)) -> hAPP(X_a,X_b,F,X_2) = hAPP(X_a,X_b,G,X_2))) -> hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),F),T_4) = hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),G),S)))))))) # label(fact_4345_setsum__mono__zero__cong__right) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.87 4278 (all X all Y hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),X),Y)),X))) # label(fact_4346_gcd__dvd1__int) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.87 4279 (all X all Y hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),X),Y)),Y))) # label(fact_4347_gcd__dvd2__int) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.87 4280 (all N_1 all M_1 all A_1 all B (hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),A_1),B) = one_one(int) -> hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A_1),N_1)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),B),M_1)) = one_one(int))) # label(fact_4348_coprime__exp2__int) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.87 4281 (all X all Y all M_1 (hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X),Y)),M_1) = one_one(int) -> hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),X),M_1) = one_one(int))) # label(fact_4349_invertible__coprime__int) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.87 4282 (all M_1 all K_4 all N_1 (hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),K_4),N_1) = one_one(int) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),K_4),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),M_1),N_1))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),K_4),M_1))))) # label(fact_4350_coprime__dvd__mult__int) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.87 4283 (all M all K all N (hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),K),N) = one_one(int) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),K),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),M),N))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),K),M))))) # label(fact_4351_coprime__dvd__mult__iff__int) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.87 4284 (all N_1 all M_1 all R_4 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),M_1),R_4)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),N_1),R_4)) -> (hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),M_1),N_1) = one_one(int) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),M_1),N_1)),R_4)))))) # label(fact_4352_divides__mult__int) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.87 4285 (all B_4 all A_5 all A_1 all B (hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),A_1),B) != zero_zero(int) -> (A_1 = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_5),hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),A_1),B)) -> (B = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B_4),hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),A_1),B)) -> hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),A_5),B_4) = one_one(int))))) # label(fact_4353_gcd__coprime__int) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.87 4286 (all X all Y hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(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),gcd_gcd(nat),X),Y))) # label(fact_4354_transfer__int__nat__gcd_I1_J) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.87 4287 (all M_1 all K_4 all N_1 hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),M_1),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K_4),M_1)),N_1)) = hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),M_1),N_1)) # label(fact_4355_gcd__add__mult__int) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.87 4288 (all M_1 all N_1 hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),M_1),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),M_1),N_1)) = hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),M_1),N_1)) # label(fact_4356_gcd__add2__int) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.87 4289 (all M_1 all N_1 hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),M_1),N_1)),N_1) = hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),M_1),N_1)) # label(fact_4357_gcd__add1__int) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.87 4290 (all N_1 hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),N_1),one_one(int))),N_1) = one_one(int)) # label(fact_4358_coprime__minus__one__int) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.87 4291 (all N_1 hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),N_1),one_one(int))),N_1) = one_one(int)) # label(fact_4359_coprime__plus__one__int) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.87 4292 (all N_1 all D all A_1 (hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),D),A_1) = one_one(int) -> hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),D),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A_1),N_1)) = one_one(int))) # label(fact_4360_coprime__exp__int) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.87 4293 (all E_1 all B all D all A_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),D),A_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),E_1),B)) -> (hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),A_1),B) = one_one(int) -> hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),D),E_1) = one_one(int))))) # label(fact_4361_coprime__divisors__nat) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.87 4294 (all M_1 hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),M_1),one_one(int)) = one_one(int)) # label(fact_4362_gcd__1__int) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.87 4295 (all M all N (hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),M),N) = zero_zero(int) <-> M = zero_zero(int) & N = zero_zero(int))) # label(fact_4363_gcd__zero__int) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.87 4296 (all X all Y hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),X),Y) = hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),Y),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),X),Y))) # label(fact_4364_gcd__red__int) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.87 4297 (all K all M all N (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),K),hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),M),N))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),K),M)) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),K),N)))) # label(fact_4365_gcd__greatest__iff__int) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.87 4298 (all N_1 all K_4 all M_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),K_4),M_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),K_4),N_1)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),K_4),hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),M_1),N_1)))))) # label(fact_4366_gcd__greatest__int) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.87 4299 (all I_1 all M_1 all N_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),I_1),hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),M_1),N_1))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),I_1),M_1)))) # label(fact_4367_dvd__gcd__D1__int) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.87 4300 (all I_1 all M_1 all N_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),I_1),hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),M_1),N_1))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),I_1),N_1)))) # label(fact_4368_dvd__gcd__D2__int) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.87 4301 (all A_1 all B all C hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),A_1),B)),C) = hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),A_1),hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),B),C))) # label(fact_4369_gcd__assoc__int) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.87 4302 (all B all A_1 all C hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),B),hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),A_1),C)) = hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),A_1),hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),B),C))) # label(fact_4370_gcd__int_Oleft__commute) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.87 4303 (all A_1 all B hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),A_1),B) = hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),B),A_1)) # label(fact_4371_gcd__commute__int) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.87 4304 (all A_1 all N_1 all B hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A_1),N_1)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),B),N_1)) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),A_1),B)),N_1)) # label(fact_4372_gcd__exp__int) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.87 4305 (all K_4 all M_1 all N_1 hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,abs_abs(int),K_4)),hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),M_1),N_1)) = hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K_4),M_1)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K_4),N_1))) # label(fact_4373_gcd__mult__distrib__int) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.87 4306 (all X all Y hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),X),Y)) = hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),X),Y)) # label(fact_4374_abs__gcd__int) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.87 4307 (all X hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),X),X) = hAPP(int,int,abs_abs(int),X)) # label(fact_4375_gcd__idem__int) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.87 4308 (all X all Y hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),X),Y) = hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),hAPP(int,int,abs_abs(int),X)),hAPP(int,int,abs_abs(int),Y))) # label(fact_4376_gcd__abs__int) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.87 4309 (all X all Y hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),X),hAPP(int,int,abs_abs(int),Y)) = hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),X),Y)) # label(fact_4377_gcd__abs2__int) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.87 4310 (all X all Y hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),hAPP(int,int,abs_abs(int),X)),Y) = hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),X),Y)) # label(fact_4378_gcd__abs1__int) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.87 4311 (all X all Y hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),X),hAPP(int,int,uminus_uminus(int),Y)) = hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),X),Y)) # label(fact_4379_gcd__neg2__int) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.87 4312 (all X all Y hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),hAPP(int,int,uminus_uminus(int),X)),Y) = hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),X),Y)) # label(fact_4380_gcd__neg1__int) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.87 4313 (all Y all X (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),Y),X)) -> hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),X),Y) = hAPP(int,int,abs_abs(int),Y))) # label(fact_4381_gcd__proj2__if__dvd__int) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.87 4314 (all X all Y (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),X),Y)) -> hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),X),Y) = hAPP(int,int,abs_abs(int),X))) # label(fact_4382_gcd__proj1__if__dvd__int) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.87 4315 (all M all N (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),M),N))) <-> M != zero_zero(int) | N != zero_zero(int))) # label(fact_4383_gcd__pos__int) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.87 4316 (all X hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),zero_zero(int)),X) = hAPP(int,int,abs_abs(int),X)) # label(fact_4384_gcd__0__left__int) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.87 4317 (all X hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),X),zero_zero(int)) = hAPP(int,int,abs_abs(int),X)) # label(fact_4385_gcd__0__int) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.87 4318 (all D all A_1 all B (hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),D),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),B)) = one_one(int) -> hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),D),B) = one_one(int))) # label(fact_4386_coprime__rmult__int) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.87 4319 (all D all A_1 all B (hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),D),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),B)) = one_one(int) -> hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),D),A_1) = one_one(int))) # label(fact_4387_coprime__lmult__int) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.87 4320 (all B all D all A_1 (hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),D),A_1) = one_one(int) -> (hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),D),B) = one_one(int) -> hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),D),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),B)) = one_one(int)))) # label(fact_4388_coprime__mult__int) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.87 4321 (all M_1 all K_4 all N_1 (hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),K_4),N_1) = one_one(int) -> hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K_4),M_1)),N_1) = hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),M_1),N_1))) # label(fact_4389_gcd__mult__cancel__int) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.87 4322 (all D_1 all Aa all Ba (hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),D_1),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Aa),Ba)) = one_one(int) <-> hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),D_1),Aa) = one_one(int) & hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),D_1),Ba) = one_one(int))) # label(fact_4390_coprime__mul__eq__int) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.87 4323 (all A_1 all B hAPP(int,rat,hAPP(int,fun(int,rat),fract,hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_1),hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),A_1),B))),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),B),hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),A_1),B))) = hAPP(int,rat,hAPP(int,fun(int,rat),fract,A_1),B)) # label(fact_4391_Fract__coprime) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.87 4324 (all B all A_1 (A_1 != zero_zero(int) | B != zero_zero(int) -> hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_1),hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),A_1),B))),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),B),hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),A_1),B))) = one_one(int))) # label(fact_4392_div__gcd__coprime__int) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.87 4325 (all X all Y (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),Y)) -> hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),X),Y) = hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),Y),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),X),Y)))) # label(fact_4393_gcd__non__0__int) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.87 4326 (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),gcd_gcd(int),X),Y)))))) # label(fact_4394_transfer__nat__int__gcd__closures_I1_J) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.87 4327 (all X all 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),gcd_gcd(int),X),Y)))) # label(fact_4395_gcd__ge__0__int) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.87 4328 (all B all A_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A_1)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),A_1),B)),A_1)))) # label(fact_4396_gcd__le1__int) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.87 4329 (all A_1 all 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_eq(int),hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),A_1),B)),B)))) # label(fact_4397_gcd__le2__int) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.87 4330 (all Ba all Aa all D_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),D_1)) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),D_1),Aa)) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),D_1),Ba)) & (all E (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),E),Aa)) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),E),Ba)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),E),D_1)))) <-> D_1 = hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),Aa),Ba))) # label(fact_4398_gcd__unique__int) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.87 4331 (all P_1 all Y_1 all X_1 ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Y_1)) -> hBOOL(hAPP(int,bool,P_1,hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),X_1),Y_1))))) -> ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Y_1),zero_zero(int))) -> hBOOL(hAPP(int,bool,P_1,hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),X_1),hAPP(int,int,uminus_uminus(int),Y_1)))))) -> ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X_1),zero_zero(int))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Y_1)) -> hBOOL(hAPP(int,bool,P_1,hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),hAPP(int,int,uminus_uminus(int),X_1)),Y_1))))) -> ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X_1),zero_zero(int))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Y_1),zero_zero(int))) -> hBOOL(hAPP(int,bool,P_1,hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),hAPP(int,int,uminus_uminus(int),X_1)),hAPP(int,int,uminus_uminus(int),Y_1)))))) -> hBOOL(hAPP(int,bool,P_1,hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),X_1),Y_1)))))))) # label(fact_4399_gcd__cases__int) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.87 4332 (all Ba all C_1 all Aa all D_1 (hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),Aa),D_1) = one_one(int) -> (hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),Ba),C_1) = one_one(int) -> (hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,abs_abs(int),Aa)),hAPP(int,int,abs_abs(int),C_1)) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,abs_abs(int),Ba)),hAPP(int,int,abs_abs(int),D_1)) <-> hAPP(int,int,abs_abs(int),Aa) = hAPP(int,int,abs_abs(int),Ba) & hAPP(int,int,abs_abs(int),C_1) = hAPP(int,int,abs_abs(int),D_1))))) # label(fact_4400_coprime__crossproduct__int) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.87 4333 (all K all L hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),K),L) = hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),hAPP(bool,fun(int,fun(int,int)),if(int),hAPP(int,bool,hAPP(int,fun(int,bool),fequal(int),L),zero_zero(int))),K),hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),L),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,abs_abs(int),K)),hAPP(int,int,abs_abs(int),L)))))) # label(fact_4401_gcd__code__int) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.87 4334 (all X all A_1 all B (hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),A_1),B) = one_one(int) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),X),A_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),X),B)) -> hAPP(int,int,abs_abs(int),X) = one_one(int))))) # label(fact_4402_coprime__common__divisor__int) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.87 4335 (all R_4 all P_4 all Q_2 (hAPP(rat,product_prod(int,int),quotient_of,R_4) = hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),P_4),Q_2) -> hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),P_4),Q_2) = one_one(int))) # label(fact_4403_quotient__of__coprime) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.87 4336 (all R_4 all P_4 all Q_2 (hAPP(product_prod(int,int),product_prod(int,int),normalize,R_4) = hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),P_4),Q_2) -> hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),P_4),Q_2) = one_one(int))) # label(fact_4404_normalize__coprime) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.87 4337 (all Aa all Ba (hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),Aa),Ba) = one_one(int) <-> (all D_3 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),D_3)) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),D_3),Aa)) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),D_3),Ba)) <-> D_3 = one_one(int))))) # label(fact_4405_coprime__int) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.87 4338 (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)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),hAPP(int,nat,nat_1,X)),hAPP(int,nat,nat_1,Y)) = hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),X),Y))))) # label(fact_4406_transfer__nat__int__gcd_I1_J) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.87 4339 (all X all Y hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),X),Y) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),hAPP(int,nat,nat_1,hAPP(int,int,abs_abs(int),X))),hAPP(int,nat,nat_1,hAPP(int,int,abs_abs(int),Y))))) # label(fact_4407_gcd__int__def) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.87 4340 (all P_4 all Q_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),Q_2)) -> (hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),P_4),Q_2) = one_one(int) -> hAPP(product_prod(int,int),product_prod(int,int),normalize,hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),P_4),Q_2)) = hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),P_4),Q_2)))) # label(fact_4408_normalize__stable) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.87 4341 (all X_1 hAPP(rat,product_prod(int,int),quotient_of,X_1) = hAPP(fun(product_prod(int,int),bool),product_prod(int,int),the(product_prod(int,int)),hAPP(fun(product_prod(int,int),bool),fun(product_prod(int,int),bool),hAPP(fun(product_prod(int,int),fun(bool,bool)),fun(fun(product_prod(int,int),bool),fun(product_prod(int,int),bool)),combs(product_prod(int,int),bool,bool),hAPP(fun(product_prod(int,int),bool),fun(product_prod(int,int),fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(product_prod(int,int),bool),fun(product_prod(int,int),fun(bool,bool))),combb(bool,fun(bool,bool),product_prod(int,int)),fconj),hAPP(fun(product_prod(int,int),rat),fun(product_prod(int,int),bool),hAPP(fun(rat,bool),fun(fun(product_prod(int,int),rat),fun(product_prod(int,int),bool)),combb(rat,bool,product_prod(int,int)),hAPP(rat,fun(rat,bool),fequal(rat),X_1)),hAPP(fun(product_prod(int,int),int),fun(product_prod(int,int),rat),hAPP(fun(product_prod(int,int),fun(int,rat)),fun(fun(product_prod(int,int),int),fun(product_prod(int,int),rat)),combs(product_prod(int,int),int,rat),hAPP(fun(product_prod(int,int),int),fun(product_prod(int,int),fun(int,rat)),hAPP(fun(int,fun(int,rat)),fun(fun(product_prod(int,int),int),fun(product_prod(int,int),fun(int,rat))),combb(int,fun(int,rat),product_prod(int,int)),fract),product_fst(int,int))),product_snd(int,int))))),hAPP(fun(product_prod(int,int),bool),fun(product_prod(int,int),bool),hAPP(fun(product_prod(int,int),fun(bool,bool)),fun(fun(product_prod(int,int),bool),fun(product_prod(int,int),bool)),combs(product_prod(int,int),bool,bool),hAPP(fun(product_prod(int,int),bool),fun(product_prod(int,int),fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(product_prod(int,int),bool),fun(product_prod(int,int),fun(bool,bool))),combb(bool,fun(bool,bool),product_prod(int,int)),fconj),hAPP(fun(product_prod(int,int),int),fun(product_prod(int,int),bool),hAPP(fun(int,bool),fun(fun(product_prod(int,int),int),fun(product_prod(int,int),bool)),combb(int,bool,product_prod(int,int)),hAPP(int,fun(int,bool),ord_less(int),zero_zero(int))),product_snd(int,int)))),hAPP(int,fun(product_prod(int,int),bool),hAPP(fun(product_prod(int,int),fun(int,bool)),fun(int,fun(product_prod(int,int),bool)),combc(product_prod(int,int),int,bool),hAPP(fun(product_prod(int,int),int),fun(product_prod(int,int),fun(int,bool)),hAPP(fun(int,fun(int,bool)),fun(fun(product_prod(int,int),int),fun(product_prod(int,int),fun(int,bool))),combb(int,fun(int,bool),product_prod(int,int)),fequal(int)),hAPP(fun(product_prod(int,int),int),fun(product_prod(int,int),int),hAPP(fun(product_prod(int,int),fun(int,int)),fun(fun(product_prod(int,int),int),fun(product_prod(int,int),int)),combs(product_prod(int,int),int,int),hAPP(fun(product_prod(int,int),int),fun(product_prod(int,int),fun(int,int)),hAPP(fun(int,fun(int,int)),fun(fun(product_prod(int,int),int),fun(product_prod(int,int),fun(int,int))),combb(int,fun(int,int),product_prod(int,int)),gcd_gcd(int)),product_fst(int,int))),product_snd(int,int)))),one_one(int)))))) # label(fact_4409_quotient__of__def) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.87 4342 (all R_4 exists X_2 (R_4 = hAPP(int,rat,hAPP(int,fun(int,rat),fract,hAPP(product_prod(int,int),int,product_fst(int,int),X_2)),hAPP(product_prod(int,int),int,product_snd(int,int),X_2)) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(product_prod(int,int),int,product_snd(int,int),X_2))) & hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),hAPP(product_prod(int,int),int,product_fst(int,int),X_2)),hAPP(product_prod(int,int),int,product_snd(int,int),X_2)) = one_one(int) & (all Y_2 (R_4 = hAPP(int,rat,hAPP(int,fun(int,rat),fract,hAPP(product_prod(int,int),int,product_fst(int,int),Y_2)),hAPP(product_prod(int,int),int,product_snd(int,int),Y_2)) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(product_prod(int,int),int,product_snd(int,int),Y_2))) & hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),hAPP(product_prod(int,int),int,product_fst(int,int),Y_2)),hAPP(product_prod(int,int),int,product_snd(int,int),Y_2)) = one_one(int) -> Y_2 = X_2)))) # label(fact_4410_quotient__of__unique) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.87 4343 (all Q_2 ((all A_3 all B_3 (Q_2 = hAPP(int,rat,hAPP(int,fun(int,rat),fract,A_3),B_3) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B_3)) -> (A_3 != zero_zero(int) -> hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),A_3),B_3) != one_one(int))))) -> Q_2 = zero_zero(rat))) # label(fact_4411_Rat__cases__nonzero) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.87 4344 (all Qa all P_1 ((all A_3 all B_3 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B_3)) -> (hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),A_3),B_3) = one_one(int) -> hBOOL(hAPP(rat,bool,P_1,hAPP(int,rat,hAPP(int,fun(int,rat),fract,A_3),B_3)))))) -> hBOOL(hAPP(rat,bool,P_1,Qa)))) # label(fact_4412_Rat__induct) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.87 4345 (all Q_2 -(all A_3 all B_3 (Q_2 = hAPP(int,rat,hAPP(int,fun(int,rat),fract,A_3),B_3) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B_3)) -> hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),A_3),B_3) != one_one(int))))) # label(fact_4413_Rat__cases) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.87 4346 (all X_a all F all X_1 all A_2 ((all I_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),I_2),A_2)) -> hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),hAPP(X_a,int,F,I_2)),X_1) = one_one(int))) -> hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),hAPP(fun(X_a,bool),int,hAPP(fun(X_a,int),fun(fun(X_a,bool),int),big_co302546470etprod(X_a,int),F),A_2)),X_1) = one_one(int))) # label(fact_4414_setprod__coprime__int) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.87 4347 (all X_a all X_b (comm_monoid_add(X_b) -> (all F all G all S all T_4 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),T_4)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),S),T_4)) -> ((all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),T_4),S))) -> hAPP(X_a,X_b,G,X_2) = zero_zero(X_b))) -> ((all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),S)) -> hAPP(X_a,X_b,F,X_2) = hAPP(X_a,X_b,G,X_2))) -> hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),F),S) = hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),G),T_4)))))))) # label(fact_4415_setsum__mono__zero__cong__left) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.87 4348 (all N all S (hBOOL(hAPP(fun(fun(int,bool),bool),bool,finite_finite_1(fun(int,bool)),S)) -> ((all X_2 (hBOOL(hAPP(fun(fun(int,bool),bool),bool,hAPP(fun(int,bool),fun(fun(fun(int,bool),bool),bool),member(fun(int,bool)),X_2),S)) -> hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),X_2)))) -> ((all X_2 (hBOOL(hAPP(fun(fun(int,bool),bool),bool,hAPP(fun(int,bool),fun(fun(fun(int,bool),bool),bool),member(fun(int,bool)),X_2),S)) -> hAPP(fun(int,bool),nat,finite_card(int),X_2) = N)) -> hAPP(fun(fun(int,bool),bool),nat,hAPP(fun(fun(int,bool),nat),fun(fun(fun(int,bool),bool),nat),big_co1399186613setsum(fun(int,bool),nat),finite_card(int)),S) = hAPP(fun(fun(int,bool),bool),nat,hAPP(fun(fun(int,bool),nat),fun(fun(fun(int,bool),bool),nat),big_co1399186613setsum(fun(int,bool),nat),hAPP(nat,fun(fun(int,bool),nat),combk(nat,fun(int,bool)),N)),S))))) # label(fact_4416_card__setsum__aux) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.87 4349 (all X_a all F all G all M all S ((all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),S)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(X_a,int,F,X_2)),hAPP(X_a,int,G,X_2)),M)))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(fun(X_a,bool),int,hAPP(fun(X_a,int),fun(fun(X_a,bool),int),big_co302546470etprod(X_a,int),F),S)),hAPP(fun(X_a,bool),int,hAPP(fun(X_a,int),fun(fun(X_a,bool),int),big_co302546470etprod(X_a,int),G),S)),M)))) # label(fact_4417_setprod__same__function__zcong) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.87 4350 (all X_a all A_1 all B hAPP(int,X_a,hAPP(int,fun(int,X_a),frac(X_a),A_1),B) = hAPP(product_prod(int,int),X_a,abs_Frac(X_a),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),norm_frac,A_1),B))) # label(fact_4418_Nitpick_Ofrac__def) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.87 4351 (all X_b all X_a all Q_1 all P_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),P_1))) -> (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,fun(X_a,bool)),fun(X_b,bool),hAPP(fun(fun(X_a,bool),bool),fun(fun(X_b,fun(X_a,bool)),fun(X_b,bool)),combb(fun(X_a,bool),bool,X_b),fEx(X_a)),hAPP(fun(X_b,fun(X_a,bool)),fun(X_b,fun(X_a,bool)),hAPP(fun(fun(X_a,bool),fun(X_a,bool)),fun(fun(X_b,fun(X_a,bool)),fun(X_b,fun(X_a,bool))),combb(fun(X_a,bool),fun(X_a,bool),X_b),hAPP(fun(X_a,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,bool)),combs(X_a,bool,bool),hAPP(fun(X_a,bool),fun(X_a,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,fun(bool,bool))),combb(bool,fun(bool,bool),X_a),fconj),P_1))),Q_1))))) <-> (all Y_2 (hBOOL(hAPP(X_a,bool,P_1,Y_2)) -> 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(X_a,fun(X_b,bool),hAPP(fun(X_b,fun(X_a,bool)),fun(X_a,fun(X_b,bool)),combc(X_b,X_a,bool),Q_1),Y_2))))))))) # label(fact_4420_finite__Collect__bounded__ex) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.87 4352 (all X_b all X_a all F all P_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),P_1))) -> 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,fun(X_a,bool)),fun(X_b,bool),hAPP(fun(fun(X_a,bool),bool),fun(fun(X_b,fun(X_a,bool)),fun(X_b,bool)),combb(fun(X_a,bool),bool,X_b),fEx(X_a)),hAPP(fun(X_a,bool),fun(X_b,fun(X_a,bool)),hAPP(fun(X_b,fun(fun(X_a,bool),fun(X_a,bool))),fun(fun(X_a,bool),fun(X_b,fun(X_a,bool))),combc(X_b,fun(X_a,bool),fun(X_a,bool)),hAPP(fun(X_b,fun(X_a,fun(bool,bool))),fun(X_b,fun(fun(X_a,bool),fun(X_a,bool))),hAPP(fun(fun(X_a,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,bool))),fun(fun(X_b,fun(X_a,fun(bool,bool))),fun(X_b,fun(fun(X_a,bool),fun(X_a,bool)))),combb(fun(X_a,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,bool)),X_b),combs(X_a,bool,bool)),hAPP(fun(X_b,fun(X_a,bool)),fun(X_b,fun(X_a,fun(bool,bool))),hAPP(fun(fun(X_a,bool),fun(X_a,fun(bool,bool))),fun(fun(X_b,fun(X_a,bool)),fun(X_b,fun(X_a,fun(bool,bool)))),combb(fun(X_a,bool),fun(X_a,fun(bool,bool)),X_b),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,fun(bool,bool))),combb(bool,fun(bool,bool),X_a),fconj)),hAPP(fun(X_a,X_b),fun(X_b,fun(X_a,bool)),hAPP(fun(X_b,fun(fun(X_a,X_b),fun(X_a,bool))),fun(fun(X_a,X_b),fun(X_b,fun(X_a,bool))),combc(X_b,fun(X_a,X_b),fun(X_a,bool)),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(fun(X_a,X_b),fun(X_a,bool))),hAPP(fun(fun(X_b,bool),fun(fun(X_a,X_b),fun(X_a,bool))),fun(fun(X_b,fun(X_b,bool)),fun(X_b,fun(fun(X_a,X_b),fun(X_a,bool)))),combb(fun(X_b,bool),fun(fun(X_a,X_b),fun(X_a,bool)),X_b),combb(X_b,bool,X_a)),fequal(X_b))),F)))),P_1))))))) # label(fact_4421_finite__image__set) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.87 4353 (all Aa (hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),Aa),zero_zero(real)),sequentially)) -> (hBOOL(hAPP(fun(nat,real),bool,monoseq(real),Aa)) -> hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),hAPP(fun(nat,fun(nat,bool)),fun(nat,real),hAPP(fun(fun(nat,bool),real),fun(fun(nat,fun(nat,bool)),fun(nat,real)),combb(fun(nat,bool),real,nat),hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),min)))),Aa))),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),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat))),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),plus_plus(nat)),hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),one_one(nat))))),hAPP(fun(nat,real),real,suminf(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),min)))),Aa))),sequentially))))) # label(fact_4424_summable__Leibniz_I5_J) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.87 4354 (all X_a all X_b (comm_monoid_mult(X_b) & dvd(X_b) -> (all F all G all A_2 ((all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_2)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),dvd_dvd(X_b),hAPP(X_a,X_b,F,X_2)),hAPP(X_a,X_b,G,X_2))))) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),dvd_dvd(X_b),hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co302546470etprod(X_a,X_b),F),A_2)),hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co302546470etprod(X_a,X_b),G),A_2))))))) # label(fact_4425_setprod__dvd__setprod) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.87 4355 (all X_a all A_2 hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),pow(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),uminus_uminus(fun(X_a,bool)),A_2)) = hAPP(fun(fun(X_a,bool),bool),fun(fun(X_a,bool),bool),collect(fun(X_a,bool)),hAPP(fun(fun(X_a,bool),fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),bool),hAPP(fun(fun(fun(X_a,bool),bool),bool),fun(fun(fun(X_a,bool),fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),bool)),combb(fun(fun(X_a,bool),bool),bool,fun(X_a,bool)),fEx(fun(X_a,bool))),hAPP(fun(fun(X_a,bool),bool),fun(fun(X_a,bool),fun(fun(X_a,bool),bool)),hAPP(fun(fun(X_a,bool),fun(fun(fun(X_a,bool),bool),fun(fun(X_a,bool),bool))),fun(fun(fun(X_a,bool),bool),fun(fun(X_a,bool),fun(fun(X_a,bool),bool))),combc(fun(X_a,bool),fun(fun(X_a,bool),bool),fun(fun(X_a,bool),bool)),hAPP(fun(fun(X_a,bool),fun(fun(X_a,bool),fun(bool,bool))),fun(fun(X_a,bool),fun(fun(fun(X_a,bool),bool),fun(fun(X_a,bool),bool))),hAPP(fun(fun(fun(X_a,bool),fun(bool,bool)),fun(fun(fun(X_a,bool),bool),fun(fun(X_a,bool),bool))),fun(fun(fun(X_a,bool),fun(fun(X_a,bool),fun(bool,bool))),fun(fun(X_a,bool),fun(fun(fun(X_a,bool),bool),fun(fun(X_a,bool),bool)))),combb(fun(fun(X_a,bool),fun(bool,bool)),fun(fun(fun(X_a,bool),bool),fun(fun(X_a,bool),bool)),fun(X_a,bool)),combs(fun(X_a,bool),bool,bool)),hAPP(fun(fun(X_a,bool),fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(fun(X_a,bool),fun(bool,bool))),hAPP(fun(fun(fun(X_a,bool),bool),fun(fun(X_a,bool),fun(bool,bool))),fun(fun(fun(X_a,bool),fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(fun(X_a,bool),fun(bool,bool)))),combb(fun(fun(X_a,bool),bool),fun(fun(X_a,bool),fun(bool,bool)),fun(X_a,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(fun(X_a,bool),bool),fun(fun(X_a,bool),fun(bool,bool))),combb(bool,fun(bool,bool),fun(X_a,bool)),fconj)),hAPP(fun(fun(X_a,bool),fun(X_a,bool)),fun(fun(X_a,bool),fun(fun(X_a,bool),bool)),hAPP(fun(fun(X_a,bool),fun(fun(fun(X_a,bool),fun(X_a,bool)),fun(fun(X_a,bool),bool))),fun(fun(fun(X_a,bool),fun(X_a,bool)),fun(fun(X_a,bool),fun(fun(X_a,bool),bool))),combc(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),fun(fun(X_a,bool),bool)),hAPP(fun(fun(X_a,bool),fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(fun(fun(X_a,bool),fun(X_a,bool)),fun(fun(X_a,bool),bool))),hAPP(fun(fun(fun(X_a,bool),bool),fun(fun(fun(X_a,bool),fun(X_a,bool)),fun(fun(X_a,bool),bool))),fun(fun(fun(X_a,bool),fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(fun(fun(X_a,bool),fun(X_a,bool)),fun(fun(X_a,bool),bool)))),combb(fun(fun(X_a,bool),bool),fun(fun(fun(X_a,bool),fun(X_a,bool)),fun(fun(X_a,bool),bool)),fun(X_a,bool)),combb(fun(X_a,bool),bool,fun(X_a,bool))),fequal(fun(X_a,bool)))),uminus_uminus(fun(X_a,bool)))))),hAPP(fun(fun(X_a,bool),fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),bool),hAPP(fun(fun(fun(X_a,bool),bool),bool),fun(fun(fun(X_a,bool),fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),bool)),combb(fun(fun(X_a,bool),bool),bool,fun(X_a,bool)),hAPP(fun(X_a,bool),fun(fun(fun(X_a,bool),bool),bool),member(fun(X_a,bool)),A_2)),pow(X_a)))))) # label(fact_4426_Pow__Compl) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.87 4356 (all X_a (metric_space(X_a) -> (all X_3 hAPP(fun(nat,X_a),X_a,lim(X_a),X_3) = hAPP(fun(X_a,bool),X_a,the(X_a),hAPP(filter(nat),fun(X_a,bool),hAPP(fun(X_a,fun(filter(nat),bool)),fun(filter(nat),fun(X_a,bool)),combc(X_a,filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),X_3)),sequentially))))) # label(fact_4427_lim__def) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.87 4357 (all X_a (metric_space(X_a) -> (all X_3 all L_2 (hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),X_3),L_2),sequentially)) -> hAPP(fun(nat,X_a),X_a,lim(X_a),X_3) = ti(X_a,L_2))))) # label(fact_4428_limI) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.87 4358 (all S_3 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),S_3)) -> hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),hAPP(real,fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(real,fun(nat,real)),combc(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),powr),real_1(nat))),hAPP(real,real,uminus_uminus(real),S_3))),zero_zero(real)),sequentially)))) # label(fact_4429_LIMSEQ__neg__powr) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.87 4359 (all R_1 hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),hAPP(real,fun(real,real),plus_plus(real),R_1)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),uminus_uminus(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),inverse_inverse(real)),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),suc))))),R_1),sequentially))) # label(fact_4430_LIMSEQ__inverse__real__of__nat__add__minus) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.87 4360 (all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),X_1)) -> hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),inverse_inverse(real)),hAPP(real,fun(nat,real),power_power(real),X_1))),zero_zero(real)),sequentially)))) # label(fact_4431_LIMSEQ__inverse__realpow__zero) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.87 4361 (all X_a (real_n1866405975lgebra(X_a) -> (all X_3 all Aa (hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),X_3),Aa),sequentially)) -> (ti(X_a,Aa) != zero_zero(X_a) -> hBOOL(hAPP(fun(nat,X_a),bool,bseq(X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(X_a,X_a),fun(fun(nat,X_a),fun(nat,X_a)),combb(X_a,X_a,nat),inverse_inverse(X_a)),X_3)))))))) # label(fact_4432_Bseq__inverse) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.87 4362 (all X_a (metric_space(X_a) -> (all X_3 all Aa (hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),X_3),Aa),sequentially)) -> hBOOL(hAPP(fun(nat,X_a),bool,cauchy(X_a),X_3)))))) # label(fact_4433_LIMSEQ__imp__Cauchy) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.87 4363 (all X_a (real_n2089651433ebra_1(X_a) -> (all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,norm_norm(X_a),X_1)),one_one(real))) -> hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),hAPP(X_a,fun(nat,X_a),power_power(X_a),X_1)),zero_zero(X_a)),sequentially)))))) # label(fact_4434_LIMSEQ__power__zero) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.87 4364 (all Aa all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),X_1)) -> hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),hAPP(real,fun(real,real),inverse_divide(real),Aa)),hAPP(real,fun(nat,real),power_power(real),X_1))),zero_zero(real)),sequentially)))) # label(fact_4435_LIMSEQ__divide__realpow__zero) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.87 4365 (all X_a (metric_space(X_a) -> (all Ba all X_3 all Aa (hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),X_3),Aa),sequentially)) -> (hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),X_3),Ba),sequentially)) -> ti(X_a,Aa) = ti(X_a,Ba)))))) # label(fact_4436_LIMSEQ__unique) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.87 4366 (all X_a all X_b (real_n1866405975lgebra(X_b) -> (all F all Aa all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),Aa),A_2)) -> (ti(X_b,Aa) != zero_zero(X_b) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(fun(X_a,X_b),fun(X_a,X_b),hAPP(fun(X_b,X_b),fun(fun(X_a,X_b),fun(X_a,X_b)),combb(X_b,X_b,X_a),inverse_inverse(X_b)),F)),hAPP(X_b,X_b,inverse_inverse(X_b),Aa)),A_2))))))) # label(fact_4437_tendsto__inverse) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.87 4367 (all X_a (real_n1866405975lgebra(X_a) -> (all X_3 all Aa (hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),X_3),Aa),sequentially)) -> (ti(X_a,Aa) != zero_zero(X_a) -> hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(X_a,X_a),fun(fun(nat,X_a),fun(nat,X_a)),combb(X_a,X_a,nat),inverse_inverse(X_a)),X_3)),hAPP(X_a,X_a,inverse_inverse(X_a),Aa)),sequentially))))))) # label(fact_4439_LIMSEQ__inverse) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.87 4368 (all F (hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),abs_abs(real)),F)),zero_zero(real)),sequentially)) <-> hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),F),zero_zero(real)),sequentially)))) # label(fact_4440_LIMSEQ__rabs__zero) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.87 4369 (all X_a (topological_space(X_a) -> (all L all X_3 all X_1 (hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),X_3),X_1),sequentially)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),L)) -> hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),hAPP(fun(nat,nat),fun(nat,X_a),hAPP(fun(nat,X_a),fun(fun(nat,nat),fun(nat,X_a)),combb(nat,X_a,nat),X_3),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),times_times(nat)),L))),X_1),sequentially))))))) # label(fact_4441_LIMSEQ__linear) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.87 4370 (all F all L (hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),F),L),sequentially)) -> hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),abs_abs(real)),F)),hAPP(real,real,abs_abs(real),L)),sequentially)))) # label(fact_4442_LIMSEQ__imp__rabs) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.87 4371 (all X_a (real_normed_vector(X_a) -> (all X_3 all Aa (hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(X_a,X_a),fun(fun(nat,X_a),fun(nat,X_a)),combb(X_a,X_a,nat),uminus_uminus(X_a)),X_3)),hAPP(X_a,X_a,uminus_uminus(X_a),Aa)),sequentially)) -> hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),X_3),Aa),sequentially)))))) # label(fact_4443_LIMSEQ__minus__cancel) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.87 4372 (all X_a (real_normed_vector(X_a) -> (all X_3 all Aa (hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),X_3),Aa),sequentially)) -> hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(X_a,X_a),fun(fun(nat,X_a),fun(nat,X_a)),combb(X_a,X_a,nat),uminus_uminus(X_a)),X_3)),hAPP(X_a,X_a,uminus_uminus(X_a),Aa)),sequentially)))))) # label(fact_4444_LIMSEQ__minus) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.87 4373 (all X_a all X_b (real_normed_vector(X_b) -> (all F all Aa all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(fun(X_a,X_b),fun(X_a,X_b),hAPP(fun(X_b,X_b),fun(fun(X_a,X_b),fun(X_a,X_b)),combb(X_b,X_b,X_a),uminus_uminus(X_b)),F)),hAPP(X_b,X_b,uminus_uminus(X_b),Aa)),A_2)) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),Aa),A_2)))))) # label(fact_4445_tendsto__minus__cancel) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.87 4374 (all X_a all X_b (real_normed_vector(X_b) -> (all F all Aa all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),Aa),A_2)) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(fun(X_a,X_b),fun(X_a,X_b),hAPP(fun(X_b,X_b),fun(fun(X_a,X_b),fun(X_a,X_b)),combb(X_b,X_b,X_a),uminus_uminus(X_b)),F)),hAPP(X_b,X_b,uminus_uminus(X_b),Aa)),A_2)))))) # label(fact_4446_tendsto__minus) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.87 4375 (all X_a all X_b (real_normed_algebra(X_b) -> (all G all Ba all F all Aa all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),Aa),A_2)) -> (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),G),Ba),A_2)) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(fun(X_a,X_b),fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,X_b)),combs(X_a,X_b,X_b),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,fun(X_b,X_b))),combb(X_b,fun(X_b,X_b),X_a),times_times(X_b)),F)),G)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),Aa),Ba)),A_2))))))) # label(fact_4447_mult_Otendsto) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.87 4376 (all X_a all X_b (real_normed_algebra(X_b) -> (all Y_1 all G all Aa all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),G),Aa),A_2)) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(X_b,fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(X_b,fun(X_a,X_b)),combc(X_a,X_b,X_b),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,fun(X_b,X_b))),combb(X_b,fun(X_b,X_b),X_a),times_times(X_b)),G)),Y_1)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),Aa),Y_1)),A_2)))))) # label(fact_4448_mult__left_Otendsto) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.87 4377 (all X_a all X_b (real_normed_algebra(X_b) -> (all X_1 all G all Aa all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),G),Aa),A_2)) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(fun(X_a,X_b),fun(X_a,X_b),hAPP(fun(X_b,X_b),fun(fun(X_a,X_b),fun(X_a,X_b)),combb(X_b,X_b,X_a),hAPP(X_b,fun(X_b,X_b),times_times(X_b),X_1)),G)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),X_1),Aa)),A_2)))))) # label(fact_4449_mult__right_Otendsto) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.87 4378 (all X_a (real_normed_algebra(X_a) -> (all Y_3 all Ba all X_3 all Aa (hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),X_3),Aa),sequentially)) -> (hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),Y_3),Ba),sequentially)) -> hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),times_times(X_a)),X_3)),Y_3)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Aa),Ba)),sequentially))))))) # label(fact_4450_LIMSEQ__mult) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.87 4379 (all X_a (real_normed_algebra(X_a) -> (all Y_1 all X_3 all Aa (hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),X_3),Aa),sequentially)) -> hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),hAPP(X_a,fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(X_a,fun(nat,X_a)),combc(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),times_times(X_a)),X_3)),Y_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Aa),Y_1)),sequentially)))))) # label(fact_4451_mult__left_OLIMSEQ) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.87 4380 (all X_a (real_normed_algebra(X_a) -> (all X_1 all X_3 all Aa (hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),X_3),Aa),sequentially)) -> hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(X_a,X_a),fun(fun(nat,X_a),fun(nat,X_a)),combb(X_a,X_a,nat),hAPP(X_a,fun(X_a,X_a),times_times(X_a),X_1)),X_3)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X_1),Aa)),sequentially)))))) # label(fact_4452_mult__right_OLIMSEQ) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.87 4381 (all X_a all X_b (metric_space(X_b) -> (all G all M all F all L all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),L),A_2)) -> (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),G),M),A_2)) -> hBOOL(hAPP(filter(X_a),bool,hAPP(real,fun(filter(X_a),bool),hAPP(fun(X_a,real),fun(real,fun(filter(X_a),bool)),tendsto(X_a,real),hAPP(fun(X_a,X_b),fun(X_a,real),hAPP(fun(X_a,fun(X_b,real)),fun(fun(X_a,X_b),fun(X_a,real)),combs(X_a,X_b,real),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,real)),hAPP(fun(X_b,fun(X_b,real)),fun(fun(X_a,X_b),fun(X_a,fun(X_b,real))),combb(X_b,fun(X_b,real),X_a),dist_dist(X_b)),F)),G)),hAPP(X_b,real,hAPP(X_b,fun(X_b,real),dist_dist(X_b),L),M)),A_2))))))) # label(fact_4453_tendsto__dist) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.87 4382 (all X_a all X_b (real_algebra_1(X_b) & real_normed_vector(X_b) -> (all G all Aa all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(real,fun(filter(X_a),bool),hAPP(fun(X_a,real),fun(real,fun(filter(X_a),bool)),tendsto(X_a,real),G),Aa),A_2)) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(fun(X_a,real),fun(X_a,X_b),hAPP(fun(real,X_b),fun(fun(X_a,real),fun(X_a,X_b)),combb(real,X_b,X_a),of_real(X_b)),G)),hAPP(real,X_b,of_real(X_b),Aa)),A_2)))))) # label(fact_4454_of__real_Otendsto) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.87 4383 (all X_a all X_b (topological_space(X_b) -> (all K all A_2 hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(X_b,fun(X_a,X_b),combk(X_b,X_a),K)),K),A_2))))) # label(fact_4455_tendsto__const) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.87 4384 (all X_d all X_b all X_c all X_a (real_normed_vector(X_a) & real_normed_vector(X_c) & real_normed_vector(X_b) -> (all G all Ba all F all Aa all A_2 all Prod (hBOOL(hAPP(fun(X_a,fun(X_b,X_c)),bool,bounded_bilinear(X_a,X_b,X_c),Prod)) -> (hBOOL(hAPP(filter(X_d),bool,hAPP(X_a,fun(filter(X_d),bool),hAPP(fun(X_d,X_a),fun(X_a,fun(filter(X_d),bool)),tendsto(X_d,X_a),F),Aa),A_2)) -> (hBOOL(hAPP(filter(X_d),bool,hAPP(X_b,fun(filter(X_d),bool),hAPP(fun(X_d,X_b),fun(X_b,fun(filter(X_d),bool)),tendsto(X_d,X_b),G),Ba),A_2)) -> hBOOL(hAPP(filter(X_d),bool,hAPP(X_c,fun(filter(X_d),bool),hAPP(fun(X_d,X_c),fun(X_c,fun(filter(X_d),bool)),tendsto(X_d,X_c),hAPP(fun(X_d,X_b),fun(X_d,X_c),hAPP(fun(X_d,fun(X_b,X_c)),fun(fun(X_d,X_b),fun(X_d,X_c)),combs(X_d,X_b,X_c),hAPP(fun(X_d,X_a),fun(X_d,fun(X_b,X_c)),hAPP(fun(X_a,fun(X_b,X_c)),fun(fun(X_d,X_a),fun(X_d,fun(X_b,X_c))),combb(X_a,fun(X_b,X_c),X_d),Prod),F)),G)),hAPP(X_b,X_c,hAPP(X_a,fun(X_b,X_c),Prod,Aa),Ba)),A_2)))))))) # label(fact_4456_bounded__bilinear_Otendsto) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.87 4385 (all X_a all X_b (real_normed_vector(X_b) -> (all F all Aa all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),Aa),A_2)) -> hBOOL(hAPP(filter(X_a),bool,hAPP(real,fun(filter(X_a),bool),hAPP(fun(X_a,real),fun(real,fun(filter(X_a),bool)),tendsto(X_a,real),hAPP(fun(X_a,X_b),fun(X_a,real),hAPP(fun(X_b,real),fun(fun(X_a,X_b),fun(X_a,real)),combb(X_b,real,X_a),norm_norm(X_b)),F)),hAPP(X_b,real,norm_norm(X_b),Aa)),A_2)))))) # label(fact_4457_tendsto__norm) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.88 4386 (all X_a (real_normed_vector(X_a) -> (all X_3 all Aa (hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),X_3),Aa),sequentially)) -> hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),hAPP(fun(nat,X_a),fun(nat,real),hAPP(fun(X_a,real),fun(fun(nat,X_a),fun(nat,real)),combb(X_a,real,nat),norm_norm(X_a)),X_3)),hAPP(X_a,real,norm_norm(X_a),Aa)),sequentially)))))) # label(fact_4458_LIMSEQ__norm) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.88 4387 (all X_a (topological_space(X_a) -> (all F all L (hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),hAPP(fun(nat,nat),fun(nat,X_a),hAPP(fun(nat,X_a),fun(fun(nat,nat),fun(nat,X_a)),combb(nat,X_a,nat),F),suc)),L),sequentially)) <-> hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),F),L),sequentially)))))) # label(fact_4459_LIMSEQ__Suc__iff) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.88 4388 (all X_a (topological_space(X_a) -> (all F all L (hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),F),L),sequentially)) -> hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),hAPP(fun(nat,nat),fun(nat,X_a),hAPP(fun(nat,X_a),fun(fun(nat,nat),fun(nat,X_a)),combb(nat,X_a,nat),F),suc)),L),sequentially)))))) # label(fact_4460_LIMSEQ__Suc) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.88 4389 (all X_a (topological_space(X_a) -> (all F all L (hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),hAPP(fun(nat,nat),fun(nat,X_a),hAPP(fun(nat,X_a),fun(fun(nat,nat),fun(nat,X_a)),combb(nat,X_a,nat),F),suc)),L),sequentially)) -> hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),F),L),sequentially)))))) # label(fact_4461_LIMSEQ__imp__Suc) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.88 4390 (all X_a (topological_space(X_a) -> (all K hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),hAPP(X_a,fun(nat,X_a),combk(X_a,nat),K)),K),sequentially))))) # label(fact_4462_LIMSEQ__const) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.88 4391 (all X_a (metric_space(X_a) -> (all K all L (hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),hAPP(X_a,fun(nat,X_a),combk(X_a,nat),K)),L),sequentially)) <-> ti(X_a,K) = ti(X_a,L))))) # label(fact_4463_LIMSEQ__const__iff) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.88 4392 (all X_b all X_c all X_a (real_normed_vector(X_a) & real_normed_vector(X_c) & real_normed_vector(X_b) -> (all Y_3 all Ba all X_3 all Aa all Prod (hBOOL(hAPP(fun(X_a,fun(X_b,X_c)),bool,bounded_bilinear(X_a,X_b,X_c),Prod)) -> (hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),X_3),Aa),sequentially)) -> (hBOOL(hAPP(filter(nat),bool,hAPP(X_b,fun(filter(nat),bool),hAPP(fun(nat,X_b),fun(X_b,fun(filter(nat),bool)),tendsto(nat,X_b),Y_3),Ba),sequentially)) -> hBOOL(hAPP(filter(nat),bool,hAPP(X_c,fun(filter(nat),bool),hAPP(fun(nat,X_c),fun(X_c,fun(filter(nat),bool)),tendsto(nat,X_c),hAPP(fun(nat,X_b),fun(nat,X_c),hAPP(fun(nat,fun(X_b,X_c)),fun(fun(nat,X_b),fun(nat,X_c)),combs(nat,X_b,X_c),hAPP(fun(nat,X_a),fun(nat,fun(X_b,X_c)),hAPP(fun(X_a,fun(X_b,X_c)),fun(fun(nat,X_a),fun(nat,fun(X_b,X_c))),combb(X_a,fun(X_b,X_c),nat),Prod),X_3)),Y_3)),hAPP(X_b,X_c,hAPP(X_a,fun(X_b,X_c),Prod,Aa),Ba)),sequentially)))))))) # label(fact_4464_bounded__bilinear_OLIMSEQ) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.88 4393 (all X_a (power(X_a) & real_normed_algebra(X_a) -> (all M all X_3 all Aa (hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),X_3),Aa),sequentially)) -> hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),hAPP(nat,fun(nat,X_a),hAPP(fun(nat,fun(nat,X_a)),fun(nat,fun(nat,X_a)),combc(nat,nat,X_a),hAPP(fun(nat,X_a),fun(nat,fun(nat,X_a)),hAPP(fun(X_a,fun(nat,X_a)),fun(fun(nat,X_a),fun(nat,fun(nat,X_a))),combb(X_a,fun(nat,X_a),nat),power_power(X_a)),X_3)),M)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),Aa),M)),sequentially)))))) # label(fact_4465_LIMSEQ__pow) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.88 4394 (all X_a (real_algebra_1(X_a) & real_normed_vector(X_a) -> (all X_3 all Aa (hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),X_3),Aa),sequentially)) -> hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),hAPP(fun(nat,real),fun(nat,X_a),hAPP(fun(real,X_a),fun(fun(nat,real),fun(nat,X_a)),combb(real,X_a,nat),of_real(X_a)),X_3)),hAPP(real,X_a,of_real(X_a),Aa)),sequentially)))))) # label(fact_4466_of__real_OLIMSEQ) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.88 4395 (all X_a (real_normed_field(X_a) -> (all Y_1 all X_3 all Aa (hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),X_3),Aa),sequentially)) -> hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),hAPP(X_a,fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(X_a,fun(nat,X_a)),combc(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),inverse_divide(X_a)),X_3)),Y_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),Aa),Y_1)),sequentially)))))) # label(fact_4467_divide_OLIMSEQ) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.88 4396 (all X_a (real_normed_vector(X_a) -> (all X_3 (hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),hAPP(fun(nat,X_a),fun(nat,real),hAPP(fun(X_a,real),fun(fun(nat,X_a),fun(nat,real)),combb(X_a,real,nat),norm_norm(X_a)),X_3)),zero_zero(real)),sequentially)) <-> hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),X_3),zero_zero(X_a)),sequentially)))))) # label(fact_4468_LIMSEQ__norm__zero) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.88 4397 (all X_a (real_normed_field(X_a) -> (all Y_3 all Ba all X_3 all Aa (hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),X_3),Aa),sequentially)) -> (hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),Y_3),Ba),sequentially)) -> (ti(X_a,Ba) != zero_zero(X_a) -> hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),inverse_divide(X_a)),X_3)),Y_3)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),Aa),Ba)),sequentially)))))))) # label(fact_4469_LIMSEQ__divide) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.88 4398 (all X_a all X_b (real_normed_field(X_b) -> (all G all Ba all F all Aa all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),Aa),A_2)) -> (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),G),Ba),A_2)) -> (ti(X_b,Ba) != zero_zero(X_b) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(fun(X_a,X_b),fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,X_b)),combs(X_a,X_b,X_b),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,fun(X_b,X_b))),combb(X_b,fun(X_b,X_b),X_a),inverse_divide(X_b)),F)),G)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),inverse_divide(X_b),Aa),Ba)),A_2)))))))) # label(fact_4470_tendsto__divide) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.88 4399 (all X_a all X_b (real_normed_vector(X_b) -> (all F all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(real,fun(filter(X_a),bool),hAPP(fun(X_a,real),fun(real,fun(filter(X_a),bool)),tendsto(X_a,real),hAPP(fun(X_a,X_b),fun(X_a,real),hAPP(fun(X_b,real),fun(fun(X_a,X_b),fun(X_a,real)),combb(X_b,real,X_a),norm_norm(X_b)),F)),zero_zero(real)),A_2)) <-> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),zero_zero(X_b)),A_2)))))) # label(fact_4471_tendsto__norm__zero__iff) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.88 4400 (all X_a all X_b (real_normed_vector(X_b) -> (all F all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),zero_zero(X_b)),A_2)) -> hBOOL(hAPP(filter(X_a),bool,hAPP(real,fun(filter(X_a),bool),hAPP(fun(X_a,real),fun(real,fun(filter(X_a),bool)),tendsto(X_a,real),hAPP(fun(X_a,X_b),fun(X_a,real),hAPP(fun(X_b,real),fun(fun(X_a,X_b),fun(X_a,real)),combb(X_b,real,X_a),norm_norm(X_b)),F)),zero_zero(real)),A_2)))))) # label(fact_4472_tendsto__norm__zero) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.88 4401 (all X_a all X_b (real_normed_vector(X_b) -> (all F all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(real,fun(filter(X_a),bool),hAPP(fun(X_a,real),fun(real,fun(filter(X_a),bool)),tendsto(X_a,real),hAPP(fun(X_a,X_b),fun(X_a,real),hAPP(fun(X_b,real),fun(fun(X_a,X_b),fun(X_a,real)),combb(X_b,real,X_a),norm_norm(X_b)),F)),zero_zero(real)),A_2)) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),zero_zero(X_b)),A_2)))))) # label(fact_4473_tendsto__norm__zero__cancel) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.88 4402 (all X_a all X_b (real_normed_field(X_b) -> (all Y_1 all G all Aa all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),G),Aa),A_2)) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(X_b,fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(X_b,fun(X_a,X_b)),combc(X_a,X_b,X_b),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,fun(X_b,X_b))),combb(X_b,fun(X_b,X_b),X_a),inverse_divide(X_b)),G)),Y_1)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),inverse_divide(X_b),Aa),Y_1)),A_2)))))) # label(fact_4474_divide_Otendsto) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.88 4403 (all X_a (real_normed_vector(X_a) -> (all G all F all L_2 (hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),F),L_2),sequentially)) -> (hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),minus_minus(X_a)),F)),G)),zero_zero(X_a)),sequentially)) -> hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),G),L_2),sequentially))))))) # label(fact_4475_LIMSEQ__diff__approach__zero2) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.88 4404 (all X_a (real_normed_vector(X_a) -> (all F all G all L_2 (hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),G),L_2),sequentially)) -> (hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),minus_minus(X_a)),F)),G)),zero_zero(X_a)),sequentially)) -> hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),F),L_2),sequentially))))))) # label(fact_4476_LIMSEQ__diff__approach__zero) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.88 4405 (all X_a all X_b (real_normed_vector(X_b) -> (all G all Ba all F all Aa all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),Aa),A_2)) -> (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),G),Ba),A_2)) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(fun(X_a,X_b),fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,X_b)),combs(X_a,X_b,X_b),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,fun(X_b,X_b))),combb(X_b,fun(X_b,X_b),X_a),plus_plus(X_b)),F)),G)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),Aa),Ba)),A_2))))))) # label(fact_4477_tendsto__add) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.88 4406 (all X_a all X_b (real_normed_vector(X_b) -> (all G all Ba all F all Aa all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),Aa),A_2)) -> (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),G),Ba),A_2)) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(fun(X_a,X_b),fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,X_b)),combs(X_a,X_b,X_b),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,fun(X_b,X_b))),combb(X_b,fun(X_b,X_b),X_a),minus_minus(X_b)),F)),G)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),Aa),Ba)),A_2))))))) # label(fact_4478_tendsto__diff) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.88 4407 (all X_a (real_normed_vector(X_a) -> (all Ba all F all Aa (hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),F),Aa),sequentially)) -> hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),hAPP(X_a,fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(X_a,fun(nat,X_a)),combc(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),minus_minus(X_a)),F)),Ba)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),Aa),Ba)),sequentially)))))) # label(fact_4479_LIMSEQ__diff__const) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.88 4408 (all X_a (real_normed_vector(X_a) -> (all Y_3 all Ba all X_3 all Aa (hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),X_3),Aa),sequentially)) -> (hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),Y_3),Ba),sequentially)) -> hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),minus_minus(X_a)),X_3)),Y_3)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),Aa),Ba)),sequentially))))))) # label(fact_4480_LIMSEQ__diff) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.88 4409 (all X_a (topological_space(X_a) -> (all K all F all Aa (hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),F),Aa),sequentially)) -> hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),hAPP(fun(nat,nat),fun(nat,X_a),hAPP(fun(nat,X_a),fun(fun(nat,nat),fun(nat,X_a)),combb(nat,X_a,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))),Aa),sequentially)))))) # label(fact_4481_LIMSEQ__ignore__initial__segment) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.88 4410 (all X_a (real_normed_vector(X_a) -> (all Ba all F all Aa (hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),F),Aa),sequentially)) -> hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),hAPP(X_a,fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(X_a,fun(nat,X_a)),combc(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),plus_plus(X_a)),F)),Ba)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Aa),Ba)),sequentially)))))) # label(fact_4482_LIMSEQ__add__const) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.88 4411 (all X_a (real_normed_vector(X_a) -> (all Y_3 all Ba all X_3 all Aa (hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),X_3),Aa),sequentially)) -> (hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),Y_3),Ba),sequentially)) -> hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),plus_plus(X_a)),X_3)),Y_3)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Aa),Ba)),sequentially))))))) # label(fact_4483_LIMSEQ__add) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.88 4412 (all X_a (topological_space(X_a) -> (all F all K all Aa (hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),hAPP(fun(nat,nat),fun(nat,X_a),hAPP(fun(nat,X_a),fun(fun(nat,nat),fun(nat,X_a)),combb(nat,X_a,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))),Aa),sequentially)) -> hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),F),Aa),sequentially)))))) # label(fact_4484_LIMSEQ__offset) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.88 4413 (all R_1 hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),hAPP(real,fun(real,real),plus_plus(real),R_1)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),inverse_inverse(real)),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),suc)))),R_1),sequentially))) # label(fact_4485_LIMSEQ__inverse__real__of__nat__add) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.88 4414 (all X_a (real_normed_vector(X_a) -> (all Y_3 all Ba all X_3 all Aa (hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),X_3),Aa),sequentially)) -> (hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),Y_3),Ba),sequentially)) -> hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),plus_plus(X_a)),X_3)),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(X_a,X_a),fun(fun(nat,X_a),fun(nat,X_a)),combb(X_a,X_a,nat),uminus_uminus(X_a)),Y_3))),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Aa),hAPP(X_a,X_a,uminus_uminus(X_a),Ba))),sequentially))))))) # label(fact_4486_LIMSEQ__add__minus) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.88 4415 (all C_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,abs_abs(real),C_1)),one_one(real))) -> hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),hAPP(real,fun(nat,real),power_power(real),C_1)),zero_zero(real)),sequentially)))) # label(fact_4487_LIMSEQ__rabs__realpow__zero2) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.88 4416 (all C_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,abs_abs(real),C_1)),one_one(real))) -> hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,abs_abs(real),C_1))),zero_zero(real)),sequentially)))) # label(fact_4488_LIMSEQ__rabs__realpow__zero) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.88 4417 (all X_a (real_normed_field(X_a) -> (all F (hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),F)) -> hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),F),zero_zero(X_a)),sequentially)))))) # label(fact_4489_summable__LIMSEQ__zero) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.88 4418 (all X_1 all Aa (hBOOL(hAPP(fun(nat,real),bool,monoseq(real),Aa)) -> (hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),Aa),X_1),sequentially)) -> (all N_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,Aa,N_2)),X_1))) & (all M_3 all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_3),N_2)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,Aa,M_3)),hAPP(nat,real,Aa,N_2))))) | (all N_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_1),hAPP(nat,real,Aa,N_2)))) & (all M_3 all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_3),N_2)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,Aa,N_2)),hAPP(nat,real,Aa,M_3)))))))) # label(fact_4490_monoseq__le) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.88 4419 (all X_a all X_b (topological_space(X_b) -> (all F all L all A_2 all A_6 (hBOOL(hAPP(filter(X_a),bool,hAPP(filter(X_a),fun(filter(X_a),bool),ord_less_eq(filter(X_a)),A_2),A_6)) -> (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),L),A_6)) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),L),A_2))))))) # label(fact_4491_tendsto__mono) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.88 4420 (all Y_3 all Y_1 all X_3 all X_1 (hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),X_3),X_1),sequentially)) -> (hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),Y_3),Y_1),sequentially)) -> ((exists N_3 all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_3),N_2)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,X_3,N_2)),hAPP(nat,real,Y_3,N_2))))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_1),Y_1)))))) # label(fact_4492_LIMSEQ__le) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.88 4421 (all Aa all X_3 all X_1 (hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),X_3),X_1),sequentially)) -> ((exists N_3 all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_3),N_2)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,X_3,N_2)),Aa)))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_1),Aa))))) # label(fact_4493_LIMSEQ__le__const2) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.88 4422 (all Aa all X_3 all X_1 (hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),X_3),X_1),sequentially)) -> ((exists N_3 all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_3),N_2)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),Aa),hAPP(nat,real,X_3,N_2))))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),Aa),X_1))))) # label(fact_4494_LIMSEQ__le__const) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.88 4423 (all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_1),one_one(real))) -> hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),hAPP(real,fun(nat,real),power_power(real),X_1)),zero_zero(real)),sequentially))))) # label(fact_4495_LIMSEQ__realpow__zero) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.88 4424 (all X_a (comm_monoid_add(X_a) & t2_space(X_a) -> (all F (hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),F)) -> hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),hAPP(fun(nat,fun(nat,bool)),fun(nat,X_a),hAPP(fun(fun(nat,bool),X_a),fun(fun(nat,fun(nat,bool)),fun(nat,X_a)),combb(fun(nat,bool),X_a,nat),hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F)),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)))),hAPP(fun(nat,X_a),X_a,suminf(X_a),F)),sequentially)))))) # label(fact_4496_summable__sumr__LIMSEQ__suminf) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.88 4425 (all X_a (comm_monoid_add(X_a) & topological_space(X_a) -> (all F all S_3 (hBOOL(hAPP(X_a,bool,hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),F),S_3)) <-> hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),hAPP(fun(nat,fun(nat,bool)),fun(nat,X_a),hAPP(fun(fun(nat,bool),X_a),fun(fun(nat,fun(nat,bool)),fun(nat,X_a)),combb(fun(nat,bool),X_a,nat),hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F)),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)))),S_3),sequentially)))))) # label(fact_4497_sums__def) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.88 4426 (all R_1 hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),hAPP(real,fun(real,real),times_times(real),R_1)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),hAPP(real,fun(real,real),plus_plus(real),one_one(real))),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),uminus_uminus(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),inverse_inverse(real)),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),suc)))))),R_1),sequentially))) # label(fact_4498_LIMSEQ__inverse__real__of__nat__add__minus__mult) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.88 4427 (all Aa (hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),Aa),zero_zero(real)),sequentially)) -> (hBOOL(hAPP(fun(nat,real),bool,monoseq(real),Aa)) -> hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),min)))),Aa)))))) # label(fact_4499_summable__Leibniz_I1_J) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.88 4428 (all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),X_1)),one_one(real))) -> hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),hAPP(real,fun(real,real),inverse_divide(real),one_one(real))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),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),plus_plus(nat)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),times_times(nat)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),one_one(nat)))))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),hAPP(real,fun(nat,real),power_power(real),X_1)),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),plus_plus(nat)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),times_times(nat)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),one_one(nat))))),zero_zero(real)),sequentially)))) # label(fact_4500_zeroseq__arctan__series) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.88 4429 (all Aa (hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),Aa),zero_zero(real)),sequentially)) -> (hBOOL(hAPP(fun(nat,real),bool,monoseq(real),Aa)) -> hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),hAPP(fun(nat,fun(nat,bool)),fun(nat,real),hAPP(fun(fun(nat,bool),real),fun(fun(nat,fun(nat,bool)),fun(nat,real)),combb(fun(nat,bool),real,nat),hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),min)))),Aa))),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),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat))),hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))),hAPP(fun(nat,real),real,suminf(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),min)))),Aa))),sequentially))))) # label(fact_4502_summable__Leibniz_I4_J) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.88 4430 (all N all Aa (hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),Aa),zero_zero(real)),sequentially)) -> ((all N_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(nat,real,Aa,N_2)))) -> ((all N_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,Aa,hAPP(nat,nat,suc,N_2))),hAPP(nat,real,Aa,N_2)))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(fun(nat,real),real,suminf(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),min)))),Aa))),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),min)))),Aa)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),N)),one_one(nat)))))))))) # label(fact_4503_summable__Leibniz_H_I4_J) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.88 4431 (all Aa (hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),Aa),zero_zero(real)),sequentially)) -> ((all N_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(nat,real,Aa,N_2)))) -> ((all N_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,Aa,hAPP(nat,nat,suc,N_2))),hAPP(nat,real,Aa,N_2)))) -> hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),hAPP(fun(nat,fun(nat,bool)),fun(nat,real),hAPP(fun(fun(nat,bool),real),fun(fun(nat,fun(nat,bool)),fun(nat,real)),combb(fun(nat,bool),real,nat),hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),min)))),Aa))),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),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat))),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),plus_plus(nat)),hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),one_one(nat))))),hAPP(fun(nat,real),real,suminf(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),min)))),Aa))),sequentially)))))) # label(fact_4504_summable__Leibniz_H_I5_J) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.88 4432 (all X_a all G all Aa all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(complex,fun(filter(X_a),bool),hAPP(fun(X_a,complex),fun(complex,fun(filter(X_a),bool)),tendsto(X_a,complex),G),Aa),A_2)) -> hBOOL(hAPP(filter(X_a),bool,hAPP(real,fun(filter(X_a),bool),hAPP(fun(X_a,real),fun(real,fun(filter(X_a),bool)),tendsto(X_a,real),hAPP(fun(X_a,complex),fun(X_a,real),hAPP(fun(complex,real),fun(fun(X_a,complex),fun(X_a,real)),combb(complex,real,X_a),im),G)),hAPP(complex,real,im,Aa)),A_2)))) # label(fact_4505_Im_Otendsto) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.88 4433 (all X_a all G all Aa all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(complex,fun(filter(X_a),bool),hAPP(fun(X_a,complex),fun(complex,fun(filter(X_a),bool)),tendsto(X_a,complex),G),Aa),A_2)) -> hBOOL(hAPP(filter(X_a),bool,hAPP(real,fun(filter(X_a),bool),hAPP(fun(X_a,real),fun(real,fun(filter(X_a),bool)),tendsto(X_a,real),hAPP(fun(X_a,complex),fun(X_a,real),hAPP(fun(complex,real),fun(fun(X_a,complex),fun(X_a,real)),combb(complex,real,X_a),re),G)),hAPP(complex,real,re,Aa)),A_2)))) # label(fact_4506_Re_Otendsto) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.88 4434 (all X_3 all Aa (hBOOL(hAPP(filter(nat),bool,hAPP(complex,fun(filter(nat),bool),hAPP(fun(nat,complex),fun(complex,fun(filter(nat),bool)),tendsto(nat,complex),X_3),Aa),sequentially)) -> hBOOL(hAPP(filter(nat),bool,hAPP(complex,fun(filter(nat),bool),hAPP(fun(nat,complex),fun(complex,fun(filter(nat),bool)),tendsto(nat,complex),hAPP(fun(nat,complex),fun(nat,complex),hAPP(fun(complex,complex),fun(fun(nat,complex),fun(nat,complex)),combb(complex,complex,nat),cnj),X_3)),hAPP(complex,complex,cnj,Aa)),sequentially)))) # label(fact_4507_cnj_OLIMSEQ) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.88 4435 (all X_a all G all Aa all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(complex,fun(filter(X_a),bool),hAPP(fun(X_a,complex),fun(complex,fun(filter(X_a),bool)),tendsto(X_a,complex),G),Aa),A_2)) -> hBOOL(hAPP(filter(X_a),bool,hAPP(complex,fun(filter(X_a),bool),hAPP(fun(X_a,complex),fun(complex,fun(filter(X_a),bool)),tendsto(X_a,complex),hAPP(fun(X_a,complex),fun(X_a,complex),hAPP(fun(complex,complex),fun(fun(X_a,complex),fun(X_a,complex)),combb(complex,complex,X_a),cnj),G)),hAPP(complex,complex,cnj,Aa)),A_2)))) # label(fact_4508_cnj_Otendsto) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.88 4436 (all X_a all G all Ba all F all Aa all Net (hBOOL(hAPP(filter(X_a),bool,hAPP(real,fun(filter(X_a),bool),hAPP(fun(X_a,real),fun(real,fun(filter(X_a),bool)),tendsto(X_a,real),F),Aa),Net)) -> (hBOOL(hAPP(filter(X_a),bool,hAPP(real,fun(filter(X_a),bool),hAPP(fun(X_a,real),fun(real,fun(filter(X_a),bool)),tendsto(X_a,real),G),Ba),Net)) -> hBOOL(hAPP(filter(X_a),bool,hAPP(complex,fun(filter(X_a),bool),hAPP(fun(X_a,complex),fun(complex,fun(filter(X_a),bool)),tendsto(X_a,complex),hAPP(fun(X_a,real),fun(X_a,complex),hAPP(fun(X_a,fun(real,complex)),fun(fun(X_a,real),fun(X_a,complex)),combs(X_a,real,complex),hAPP(fun(X_a,real),fun(X_a,fun(real,complex)),hAPP(fun(real,fun(real,complex)),fun(fun(X_a,real),fun(X_a,fun(real,complex))),combb(real,fun(real,complex),X_a),complex_1),F)),G)),hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,Aa),Ba)),Net))))) # label(fact_4509_tendsto__Complex) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.88 4437 (all X_a all A_2 all B_1 (hBOOL(hAPP(filter(X_a),bool,hAPP(filter(X_a),fun(filter(X_a),bool),ord_less(filter(X_a)),A_2),B_1)) <-> hBOOL(hAPP(filter(X_a),bool,hAPP(filter(X_a),fun(filter(X_a),bool),ord_less_eq(filter(X_a)),A_2),B_1)) & -hBOOL(hAPP(filter(X_a),bool,hAPP(filter(X_a),fun(filter(X_a),bool),ord_less_eq(filter(X_a)),B_1),A_2)))) # label(fact_4510_less__filter__def) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.88 4438 (all X_3 all Aa (hBOOL(hAPP(filter(nat),bool,hAPP(complex,fun(filter(nat),bool),hAPP(fun(nat,complex),fun(complex,fun(filter(nat),bool)),tendsto(nat,complex),X_3),Aa),sequentially)) -> hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),hAPP(fun(nat,complex),fun(nat,real),hAPP(fun(complex,real),fun(fun(nat,complex),fun(nat,real)),combb(complex,real,nat),re),X_3)),hAPP(complex,real,re,Aa)),sequentially)))) # label(fact_4511_Re_OLIMSEQ) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.88 4439 (all X_3 all Aa (hBOOL(hAPP(filter(nat),bool,hAPP(complex,fun(filter(nat),bool),hAPP(fun(nat,complex),fun(complex,fun(filter(nat),bool)),tendsto(nat,complex),X_3),Aa),sequentially)) -> hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),hAPP(fun(nat,complex),fun(nat,real),hAPP(fun(complex,real),fun(fun(nat,complex),fun(nat,real)),combb(complex,real,nat),im),X_3)),hAPP(complex,real,im,Aa)),sequentially)))) # label(fact_4512_Im_OLIMSEQ) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.88 4440 (all Y_3 all Ba all X_3 all Aa (hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),X_3),Aa),sequentially)) -> (hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),Y_3),Ba),sequentially)) -> hBOOL(hAPP(filter(nat),bool,hAPP(complex,fun(filter(nat),bool),hAPP(fun(nat,complex),fun(complex,fun(filter(nat),bool)),tendsto(nat,complex),hAPP(fun(nat,real),fun(nat,complex),hAPP(fun(nat,fun(real,complex)),fun(fun(nat,real),fun(nat,complex)),combs(nat,real,complex),hAPP(fun(nat,real),fun(nat,fun(real,complex)),hAPP(fun(real,fun(real,complex)),fun(fun(nat,real),fun(nat,fun(real,complex))),combb(real,fun(real,complex),nat),complex_1),X_3)),Y_3)),hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,Aa),Ba)),sequentially))))) # label(fact_4513_LIMSEQ__Complex) # label(axiom) # label(non_clause). [assumption].
% 7.85/7.88 4441 (all P_1 all Aa all Ba (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),Aa),Ba)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),Aa),Ba)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),Aa),Ba)) -> (hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),minus_minus(real)),hAPP(fun(nat,product_prod(real,real)),fun(nat,real),hAPP(fun(product_prod(real,real),real),fun(fun(nat,product_prod(real,real)),fun(nat,real)),combb(product_prod(real,real),real,nat),product_fst(real,real)),hAPP(real,fun(nat,product_prod(real,real)),hAPP(real,fun(real,fun(nat,product_prod(real,real))),hAPP(fun(product_prod(real,real),bool),fun(real,fun(real,fun(nat,product_prod(real,real)))),bolzano_bisect,P_1),Aa),Ba)))),hAPP(fun(nat,product_prod(real,real)),fun(nat,real),hAPP(fun(product_prod(real,real),real),fun(fun(nat,product_prod(real,real)),fun(nat,real)),combb(product_prod(real,real),real,nat),product_snd(real,real)),hAPP(real,fun(nat,product_prod(real,real)),hAPP(real,fun(real,fun(nat,product_prod(real,real))),hAPP(fun(product_prod(real,real),bool),fun(real,fun(real,fun(nat,product_prod(real,real)))),bolzano_bisect,P_1),Aa),Ba)))),zero_zero(real)),sequentially)) -> (exists L_3 ((all N_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(product_prod(real,real),real,product_fst(real,real),hAPP(nat,product_prod(real,real),hAPP(real,fun(nat,product_prod(real,real)),hAPP(real,fun(real,fun(nat,product_prod(real,real))),hAPP(fun(product_prod(real,real),bool),fun(real,fun(real,fun(nat,product_prod(real,real)))),bolzano_bisect,P_1),Aa),Ba),N_2))),L_3))) & hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),hAPP(fun(nat,product_prod(real,real)),fun(nat,real),hAPP(fun(product_prod(real,real),real),fun(fun(nat,product_prod(real,real)),fun(nat,real)),combb(product_prod(real,real),real,nat),product_fst(real,real)),hAPP(real,fun(nat,product_prod(real,real)),hAPP(real,fun(real,fun(nat,product_prod(real,real))),hAPP(fun(product_prod(real,real),bool),fun(real,fun(real,fun(nat,product_prod(real,real)))),bolzano_bisect,P_1),Aa),Ba))),L_3),sequentially)) & (all N_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),L_3),hAPP(product_prod(real,real),real,product_snd(real,real),hAPP(nat,product_prod(real,real),hAPP(real,fun(nat,product_prod(real,real)),hAPP(real,fun(real,fun(nat,product_prod(real,real))),hAPP(fun(product_prod(real,real),bool),fun(real,fun(real,fun(nat,product_prod(real,real)))),bolzano_bisect,P_1),Aa),Ba),N_2))))) & hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),hAPP(fun(nat,product_prod(real,real)),fun(nat,real),hAPP(fun(product_prod(real,real),real),fun(fun(nat,product_prod(real,real)),fun(nat,real)),combb(product_prod(real,real),real,nat),product_snd(real,real)),hAPP(real,fun(nat,product_prod(real,real)),hAPP(real,fun(real,fun(nat,product_prod(real,real))),hAPP(fun(product_prod(real,real),bool),fun(real,fun(real,fun(nat,product_prod(real,real)))),bolzano_bisect,P_1),Aa),Ba))),L_3),sequentially))))))))) # label(fact_4514_Bolzano__nest__unique) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.88 4442 (all Aa (hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),Aa),zero_zero(real)),sequentially)) -> ((all N_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(nat,real,Aa,N_2)))) -> ((all N_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,Aa,hAPP(nat,nat,suc,N_2))),hAPP(nat,real,Aa,N_2)))) -> hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),hAPP(fun(nat,fun(nat,bool)),fun(nat,real),hAPP(fun(fun(nat,bool),real),fun(fun(nat,fun(nat,bool)),fun(nat,real)),combb(fun(nat,bool),real,nat),hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),min)))),Aa))),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),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat))),hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))),hAPP(fun(nat,real),real,suminf(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),min)))),Aa))),sequentially)))))) # label(fact_4515_summable__Leibniz_H_I3_J) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.88 4443 (all N all Aa (hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),Aa),zero_zero(real)),sequentially)) -> ((all N_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(nat,real,Aa,N_2)))) -> ((all N_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,Aa,hAPP(nat,nat,suc,N_2))),hAPP(nat,real,Aa,N_2)))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),min)))),Aa)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),N)))),hAPP(fun(nat,real),real,suminf(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),min)))),Aa)))))))) # label(fact_4516_summable__Leibniz_H_I2_J) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.88 4444 (all X_a (metric_space(X_a) -> (all X_3 all L_2 (hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),X_3),L_2),sequentially)) <-> (all R_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),R_2)) -> (exists No (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),No)) & (all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),No),N_2)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),hAPP(nat,X_a,X_3,N_2)),L_2)),R_2)))))))))))) # label(fact_4517_LIMSEQ__iff__nz) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.88 4445 (all X_a (real_normed_vector(X_a) -> (all R_1 all X_3 all L_2 (hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),X_3),L_2),sequentially)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),R_1)) -> (exists No all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),No),N_2)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(nat,X_a,X_3,N_2)),L_2))),R_1))))))))) # label(fact_4518_LIMSEQ__D) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.88 4446 (all X_a (real_normed_vector(X_a) -> (all X_3 all L_2 (hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),X_3),L_2),sequentially)) <-> (all R_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),R_2)) -> (exists No all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),No),N_2)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(nat,X_a,X_3,N_2)),L_2))),R_2)))))))))) # label(fact_4519_LIMSEQ__iff) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.88 4447 (all X_a (metric_space(X_a) -> (all R_1 all X_3 all L_2 (hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),X_3),L_2),sequentially)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),R_1)) -> (exists No all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),No),N_2)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),hAPP(nat,X_a,X_3,N_2)),L_2)),R_1))))))))) # label(fact_4520_metric__LIMSEQ__D) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.88 4448 (all X_a (metric_space(X_a) -> (all X_3 all L_2 (hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),X_3),L_2),sequentially)) <-> (all R_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),R_2)) -> (exists No all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),No),N_2)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),hAPP(nat,X_a,X_3,N_2)),L_2)),R_2)))))))))) # label(fact_4521_LIMSEQ__def) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.88 4449 (all Aa (hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),Aa),zero_zero(real)),sequentially)) -> (hBOOL(hAPP(fun(nat,real),bool,monoseq(real),Aa)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(nat,real,Aa,zero_zero(nat))),zero_zero(real))) -> (all N_2 hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),hAPP(fun(nat,real),real,suminf(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),min)))),Aa))),hAPP(real,fun(real,bool),hAPP(real,fun(real,fun(real,bool)),ord_atLeastAtMost(real),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),min)))),Aa)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),N_2)),one_one(nat))))),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),min)))),Aa)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),N_2))))))))))) # label(fact_4522_summable__Leibniz_I3_J) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.88 4450 (all Aa (hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),Aa),zero_zero(real)),sequentially)) -> (hBOOL(hAPP(fun(nat,real),bool,monoseq(real),Aa)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(nat,real,Aa,zero_zero(nat)))) -> (all N_2 hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),hAPP(fun(nat,real),real,suminf(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),min)))),Aa))),hAPP(real,fun(real,bool),hAPP(real,fun(real,fun(real,bool)),ord_atLeastAtMost(real),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),min)))),Aa)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),N_2)))),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),min)))),Aa)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),N_2)),one_one(nat)))))))))))) # label(fact_4523_summable__Leibniz_I2_J) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.88 4451 (all Y_1 all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),Y_1),X_1)) -> hAPP(fun(real,bool),real,complete_Sup_Sup(real),hAPP(real,fun(real,bool),hAPP(real,fun(real,fun(real,bool)),ord_atLeastAtMost(real),Y_1),X_1)) = X_1)) # label(fact_4524_Sup__atLeastAtMost) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.88 4452 (all X_a (order(X_a) -> (all Aa all Ba all C_1 all D_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastAtMost(X_a),Aa),Ba)),hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastAtMost(X_a),C_1),D_1))) <-> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Aa),Ba)) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C_1),Aa)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Ba),D_1)))))) # label(fact_4525_atLeastatMost__subset__iff) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.88 4453 (all X_a (ordered_ab_group_add(X_a) -> (all X_1 all Y_1 hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,X_a),fun(fun(X_a,bool),fun(X_a,bool)),image(X_a,X_a),uminus_uminus(X_a)),hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastAtMost(X_a),X_1),Y_1)) = hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastAtMost(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),Y_1)),hAPP(X_a,X_a,uminus_uminus(X_a),X_1))))) # label(fact_4526_image__uminus__atLeastAtMost) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.88 4454 (all X_a (order(X_a) -> (all Aa all Ba all C_1 all D_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less(fun(X_a,bool)),hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastAtMost(X_a),Aa),Ba)),hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastAtMost(X_a),C_1),D_1))) <-> (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Aa),Ba)) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C_1),Aa)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Ba),D_1)) & (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),Aa)) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Ba),D_1)))) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C_1),D_1)))))) # label(fact_4527_atLeastatMost__psubset__iff) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.88 4455 (all X_a (dense_linorder(X_a) -> (all Aa all Ba all C_1 all D_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastAtMost(X_a),Aa),Ba)),hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastLessThan(X_a),C_1),D_1))) <-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Aa),Ba)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C_1),Aa)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Ba),D_1))))))) # label(fact_4528_atLeastAtMost__subseteq__atLeastLessThan__iff) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.88 4456 (all X_a (dense_linorder(X_a) -> (all Aa all Ba all C_1 all D_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastLessThan(X_a),Aa),Ba)),hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastAtMost(X_a),C_1),D_1))) <-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),Ba)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C_1),Aa)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Ba),D_1))))))) # label(fact_4529_atLeastLessThan__subseteq__atLeastAtMost__iff) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.88 4457 (all X_a (dense_linorder(X_a) -> (all Aa all Ba all C_1 all D_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_gr676655987ssThan(X_a),Aa),Ba)),hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastAtMost(X_a),C_1),D_1))) <-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),Ba)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C_1),Aa)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Ba),D_1))))))) # label(fact_4530_greaterThanLessThan__subseteq__atLeastAtMost__iff) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.88 4458 (all Aa (hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),Aa),zero_zero(real)),sequentially)) -> ((all N_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(nat,real,Aa,N_2)))) -> ((all N_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,Aa,hAPP(nat,nat,suc,N_2))),hAPP(nat,real,Aa,N_2)))) -> hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),min)))),Aa))))))) # label(fact_4531_summable) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.88 4459 (all X_a (real_normed_field(X_a) & banach(X_a) -> (all X_1 all C_1 all K_3 (hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),times_times(X_a)),hAPP(fun(nat,X_a),fun(nat,X_a),diffs(X_a),hAPP(fun(nat,X_a),fun(nat,X_a),diffs(X_a),C_1)))),hAPP(X_a,fun(nat,X_a),power_power(X_a),K_3)))) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,norm_norm(X_a),X_1)),hAPP(X_a,real,norm_norm(X_a),K_3))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_a,fun(filter(X_a),bool),hAPP(fun(X_a,X_a),fun(X_a,fun(filter(X_a),bool)),tendsto(X_a,X_a),hAPP(fun(X_a,fun(nat,X_a)),fun(X_a,X_a),hAPP(fun(fun(nat,X_a),X_a),fun(fun(X_a,fun(nat,X_a)),fun(X_a,X_a)),combb(fun(nat,X_a),X_a,X_a),suminf(X_a)),hAPP(fun(X_a,fun(nat,X_a)),fun(X_a,fun(nat,X_a)),hAPP(fun(fun(nat,X_a),fun(nat,X_a)),fun(fun(X_a,fun(nat,X_a)),fun(X_a,fun(nat,X_a))),combb(fun(nat,X_a),fun(nat,X_a),X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),times_times(X_a)),C_1))),hAPP(fun(nat,X_a),fun(X_a,fun(nat,X_a)),hAPP(fun(X_a,fun(fun(nat,X_a),fun(nat,X_a))),fun(fun(nat,X_a),fun(X_a,fun(nat,X_a))),combc(X_a,fun(nat,X_a),fun(nat,X_a)),hAPP(fun(X_a,fun(nat,fun(X_a,X_a))),fun(X_a,fun(fun(nat,X_a),fun(nat,X_a))),hAPP(fun(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a))),fun(fun(X_a,fun(nat,fun(X_a,X_a))),fun(X_a,fun(fun(nat,X_a),fun(nat,X_a)))),combb(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),X_a),combs(nat,X_a,X_a)),hAPP(fun(X_a,fun(nat,X_a)),fun(X_a,fun(nat,fun(X_a,X_a))),hAPP(fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),fun(fun(X_a,fun(nat,X_a)),fun(X_a,fun(nat,fun(X_a,X_a)))),combb(fun(nat,X_a),fun(nat,fun(X_a,X_a)),X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),minus_minus(X_a))),hAPP(fun(X_a,X_a),fun(X_a,fun(nat,X_a)),hAPP(fun(X_a,fun(X_a,fun(nat,X_a))),fun(fun(X_a,X_a),fun(X_a,fun(nat,X_a))),combs(X_a,X_a,fun(nat,X_a)),hAPP(fun(X_a,fun(nat,fun(X_a,X_a))),fun(X_a,fun(X_a,fun(nat,X_a))),hAPP(fun(fun(nat,fun(X_a,X_a)),fun(X_a,fun(nat,X_a))),fun(fun(X_a,fun(nat,fun(X_a,X_a))),fun(X_a,fun(X_a,fun(nat,X_a)))),combb(fun(nat,fun(X_a,X_a)),fun(X_a,fun(nat,X_a)),X_a),combc(nat,X_a,X_a)),hAPP(fun(X_a,fun(nat,X_a)),fun(X_a,fun(nat,fun(X_a,X_a))),hAPP(fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),fun(fun(X_a,fun(nat,X_a)),fun(X_a,fun(nat,fun(X_a,X_a)))),combb(fun(nat,X_a),fun(nat,fun(X_a,X_a)),X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),inverse_divide(X_a))),hAPP(fun(nat,X_a),fun(X_a,fun(nat,X_a)),hAPP(fun(X_a,fun(fun(nat,X_a),fun(nat,X_a))),fun(fun(nat,X_a),fun(X_a,fun(nat,X_a))),combc(X_a,fun(nat,X_a),fun(nat,X_a)),hAPP(fun(X_a,fun(nat,fun(X_a,X_a))),fun(X_a,fun(fun(nat,X_a),fun(nat,X_a))),hAPP(fun(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a))),fun(fun(X_a,fun(nat,fun(X_a,X_a))),fun(X_a,fun(fun(nat,X_a),fun(nat,X_a)))),combb(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),X_a),combs(nat,X_a,X_a)),hAPP(fun(X_a,fun(nat,X_a)),fun(X_a,fun(nat,fun(X_a,X_a))),hAPP(fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),fun(fun(X_a,fun(nat,X_a)),fun(X_a,fun(nat,fun(X_a,X_a)))),combb(fun(nat,X_a),fun(nat,fun(X_a,X_a)),X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),minus_minus(X_a))),hAPP(fun(X_a,X_a),fun(X_a,fun(nat,X_a)),hAPP(fun(X_a,fun(nat,X_a)),fun(fun(X_a,X_a),fun(X_a,fun(nat,X_a))),combb(X_a,fun(nat,X_a),X_a),power_power(X_a)),hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X_1))))),hAPP(X_a,fun(nat,X_a),power_power(X_a),X_1))))),combi(X_a))))),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),times_times(X_a)),semiring_1_of_nat(X_a))),hAPP(fun(nat,nat),fun(nat,X_a),hAPP(fun(nat,X_a),fun(fun(nat,nat),fun(nat,X_a)),combb(nat,X_a,nat),hAPP(X_a,fun(nat,X_a),power_power(X_a),X_1)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),minus_minus(nat)),hAPP(nat,nat,suc,zero_zero(nat))))))))),zero_zero(X_a)),hAPP(X_a,filter(X_a),at(X_a),zero_zero(X_a))))))))) # label(fact_4532_termdiffs__aux) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.88 4460 (all L all U_1 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_1)))) # label(fact_4533_finite__atLeastAtMost) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.88 4461 (all L all U_1 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_1)))) # label(fact_4534_finite__atLeastAtMost__int) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.88 4462 (all P_1 all N ((exists M_3 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_3),N)) & hBOOL(hAPP(nat,bool,P_1,M_3)))) <-> (exists X_2 (hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X_2),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),zero_zero(nat)),N))) & hBOOL(hAPP(nat,bool,P_1,X_2)))))) # label(fact_4535_ex__nat__less) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.89 4463 (all P_1 all N ((all M_3 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_3),N)) -> hBOOL(hAPP(nat,bool,P_1,M_3)))) <-> (all X_2 (hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X_2),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),zero_zero(nat)),N))) -> hBOOL(hAPP(nat,bool,P_1,X_2)))))) # label(fact_4536_all__nat__less) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.89 4464 (all Y_1 all X_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X_1)) -> hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastAtMost(int),X_1),Y_1))))) # label(fact_4537_SetInterval_Otransfer__nat__int__set__function__closures) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.89 4465 (all L all U_1 hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),L),hAPP(nat,nat,suc,U_1)) = hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),L),U_1)) # label(fact_4538_atLeastLessThanSuc__atLeastAtMost) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.89 4466 (all N hAPP(nat,nat,fact_fact(nat),N) = hAPP(fun(nat,bool),nat,hAPP(fun(nat,nat),fun(fun(nat,bool),nat),big_co302546470etprod(nat,nat),combi(nat)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),one_one(nat)),N))) # label(fact_4539_fact__altdef__nat) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.89 4467 (all K all I all J 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)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),I),J)) = 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),K)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J),K))) # label(fact_4540_image__add__atLeastAtMost) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.89 4468 (all I all J hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,nat),fun(fun(nat,bool),fun(nat,bool)),image(nat,nat),suc),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),I),J)) = hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,suc,I)),hAPP(nat,nat,suc,J))) # label(fact_4541_image__Suc__atLeastAtMost) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.89 4469 (all M all N hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),M),N) = hAPP(fun(int,bool),fun(nat,bool),hAPP(fun(int,nat),fun(fun(int,bool),fun(nat,bool)),image(int,nat),nat_1),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastAtMost(int),hAPP(nat,int,semiring_1_of_nat(int),M)),hAPP(nat,int,semiring_1_of_nat(int),N)))) # label(fact_4542_SetInterval_Otransfer__nat__int__set__functions_I2_J) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.89 4470 (all X_a (comm_monoid_add(X_a) -> (all F all M all N hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,suc,M)),hAPP(nat,nat,suc,N))) = hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),hAPP(fun(nat,nat),fun(nat,X_a),hAPP(fun(nat,X_a),fun(fun(nat,nat),fun(nat,X_a)),combb(nat,X_a,nat),F),suc)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),M),N))))) # label(fact_4543_setsum__shift__bounds__cl__Suc__ivl) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.89 4471 (all X_a (comm_monoid_add(X_a) -> (all F all M all K all N hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),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),K)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),K))) = hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),hAPP(fun(nat,nat),fun(nat,X_a),hAPP(fun(nat,X_a),fun(fun(nat,nat),fun(nat,X_a)),combb(nat,X_a,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))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),M),N))))) # label(fact_4544_setsum__shift__bounds__cl__nat__ivl) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.89 4472 (all Aa hBOOL(hAPP(filter(complex),bool,hAPP(complex,fun(filter(complex),bool),hAPP(fun(complex,complex),fun(complex,fun(filter(complex),bool)),tendsto(complex,complex),cnj),hAPP(complex,complex,cnj,Aa)),hAPP(complex,filter(complex),at(complex),Aa)))) # label(fact_4545_cnj_Ocont) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.89 4473 (all Aa hBOOL(hAPP(filter(complex),bool,hAPP(real,fun(filter(complex),bool),hAPP(fun(complex,real),fun(real,fun(filter(complex),bool)),tendsto(complex,real),re),hAPP(complex,real,re,Aa)),hAPP(complex,filter(complex),at(complex),Aa)))) # label(fact_4546_Re_Ocont) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.89 4474 (all Aa hBOOL(hAPP(filter(complex),bool,hAPP(real,fun(filter(complex),bool),hAPP(fun(complex,real),fun(real,fun(filter(complex),bool)),tendsto(complex,real),im),hAPP(complex,real,im,Aa)),hAPP(complex,filter(complex),at(complex),Aa)))) # label(fact_4547_Im_Ocont) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.89 4475 (all X_a (topological_space(X_a) -> (all G all L all Aa (hBOOL(hAPP(filter(X_a),bool,hAPP(complex,fun(filter(X_a),bool),hAPP(fun(X_a,complex),fun(complex,fun(filter(X_a),bool)),tendsto(X_a,complex),G),L),hAPP(X_a,filter(X_a),at(X_a),Aa))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(complex,fun(filter(X_a),bool),hAPP(fun(X_a,complex),fun(complex,fun(filter(X_a),bool)),tendsto(X_a,complex),hAPP(fun(X_a,complex),fun(X_a,complex),hAPP(fun(complex,complex),fun(fun(X_a,complex),fun(X_a,complex)),combb(complex,complex,X_a),cnj),G)),hAPP(complex,complex,cnj,L)),hAPP(X_a,filter(X_a),at(X_a),Aa))))))) # label(fact_4548_cnj_OLIM) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.89 4476 (all X_b all X_a (topological_space(X_a) & real_normed_vector(X_b) -> (all G all M_2 all F all L_2 all Aa (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),L_2),hAPP(X_a,filter(X_a),at(X_a),Aa))) -> (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),G),M_2),hAPP(X_a,filter(X_a),at(X_a),Aa))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(fun(X_a,X_b),fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,X_b)),combs(X_a,X_b,X_b),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,fun(X_b,X_b))),combb(X_b,fun(X_b,X_b),X_a),plus_plus(X_b)),F)),G)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),L_2),M_2)),hAPP(X_a,filter(X_a),at(X_a),Aa)))))))) # label(fact_4549_LIM__add) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.89 4477 (all X_b all X_a (topological_space(X_a) & real_normed_vector(X_b) -> (all G all M all F all L all X_1 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),L),hAPP(X_a,filter(X_a),at(X_a),X_1))) -> (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),G),M),hAPP(X_a,filter(X_a),at(X_a),X_1))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(fun(X_a,X_b),fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,X_b)),combs(X_a,X_b,X_b),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,fun(X_b,X_b))),combb(X_b,fun(X_b,X_b),X_a),minus_minus(X_b)),F)),G)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),L),M)),hAPP(X_a,filter(X_a),at(X_a),X_1)))))))) # label(fact_4550_LIM__diff) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.89 4478 (all X_a all X_b (real_n2089651433ebra_1(X_b) & zero(X_a) & metric_space(X_a) -> (all Aa all K (ti(X_a,K) != zero_zero(X_a) -> -hBOOL(hAPP(filter(X_b),bool,hAPP(X_a,fun(filter(X_b),bool),hAPP(fun(X_b,X_a),fun(X_a,fun(filter(X_b),bool)),tendsto(X_b,X_a),hAPP(X_a,fun(X_b,X_a),combk(X_a,X_b),K)),zero_zero(X_a)),hAPP(X_b,filter(X_b),at(X_b),Aa))))))) # label(fact_4551_LIM__not__zero) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.89 4479 (all X_b all X_a (topological_space(X_a) & real_normed_field(X_b) -> (all Y_1 all G all L all Aa (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),G),L),hAPP(X_a,filter(X_a),at(X_a),Aa))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(X_b,fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(X_b,fun(X_a,X_b)),combc(X_a,X_b,X_b),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,fun(X_b,X_b))),combb(X_b,fun(X_b,X_b),X_a),inverse_divide(X_b)),G)),Y_1)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),inverse_divide(X_b),L),Y_1)),hAPP(X_a,filter(X_a),at(X_a),Aa))))))) # label(fact_4552_divide_OLIM) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.89 4480 (all X_a (real_normed_field(X_a) -> (all Y_1 all Aa hBOOL(hAPP(filter(X_a),bool,hAPP(X_a,fun(filter(X_a),bool),hAPP(fun(X_a,X_a),fun(X_a,fun(filter(X_a),bool)),tendsto(X_a,X_a),hAPP(X_a,fun(X_a,X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(X_a,X_a)),combc(X_a,X_a,X_a),inverse_divide(X_a)),Y_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),Aa),Y_1)),hAPP(X_a,filter(X_a),at(X_a),Aa)))))) # label(fact_4553_divide_Ocont) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.89 4481 (all X_a (real_algebra_1(X_a) & real_normed_vector(X_a) -> (all Aa hBOOL(hAPP(filter(real),bool,hAPP(X_a,fun(filter(real),bool),hAPP(fun(real,X_a),fun(X_a,fun(filter(real),bool)),tendsto(real,X_a),of_real(X_a)),hAPP(real,X_a,of_real(X_a),Aa)),hAPP(real,filter(real),at(real),Aa)))))) # label(fact_4554_of__real_Ocont) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.89 4482 (all X_b all X_a (topological_space(X_a) & power(X_b) & real_normed_algebra(X_b) -> (all N all F all L all Aa (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),L),hAPP(X_a,filter(X_a),at(X_a),Aa))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(nat,fun(X_a,X_b),hAPP(fun(X_a,fun(nat,X_b)),fun(nat,fun(X_a,X_b)),combc(X_a,nat,X_b),hAPP(fun(X_a,X_b),fun(X_a,fun(nat,X_b)),hAPP(fun(X_b,fun(nat,X_b)),fun(fun(X_a,X_b),fun(X_a,fun(nat,X_b))),combb(X_b,fun(nat,X_b),X_a),power_power(X_b)),F)),N)),hAPP(nat,X_b,hAPP(X_b,fun(nat,X_b),power_power(X_b),L),N)),hAPP(X_a,filter(X_a),at(X_a),Aa))))))) # label(fact_4555_LIM__power) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.89 4483 (all X_a all X_b (metric_space(X_b) & real_n2089651433ebra_1(X_a) -> (all K all L_2 all Aa (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(X_b,fun(X_a,X_b),combk(X_b,X_a),K)),L_2),hAPP(X_a,filter(X_a),at(X_a),Aa))) -> ti(X_b,K) = ti(X_b,L_2))))) # label(fact_4556_LIM__const__eq) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.89 4484 (all X_a all X_b all X_c (topological_space(X_c) & topological_space(X_b) & topological_space(X_a) -> (all F all Aa all G all L (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),G),hAPP(X_a,X_b,G,L)),hAPP(X_a,filter(X_a),at(X_a),L))) -> (hBOOL(hAPP(filter(X_c),bool,hAPP(X_a,fun(filter(X_c),bool),hAPP(fun(X_c,X_a),fun(X_a,fun(filter(X_c),bool)),tendsto(X_c,X_a),F),L),hAPP(X_c,filter(X_c),at(X_c),Aa))) -> hBOOL(hAPP(filter(X_c),bool,hAPP(X_b,fun(filter(X_c),bool),hAPP(fun(X_c,X_b),fun(X_b,fun(filter(X_c),bool)),tendsto(X_c,X_b),hAPP(fun(X_c,X_a),fun(X_c,X_b),hAPP(fun(X_a,X_b),fun(fun(X_c,X_a),fun(X_c,X_b)),combb(X_a,X_b,X_c),G),F)),hAPP(X_a,X_b,G,L)),hAPP(X_c,filter(X_c),at(X_c),Aa)))))))) # label(fact_4557_LIM__compose) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.89 4485 (all X_a all X_b (real_n2089651433ebra_1(X_b) & metric_space(X_a) -> (all Aa all K all L_2 (ti(X_a,K) != ti(X_a,L_2) -> -hBOOL(hAPP(filter(X_b),bool,hAPP(X_a,fun(filter(X_b),bool),hAPP(fun(X_b,X_a),fun(X_a,fun(filter(X_b),bool)),tendsto(X_b,X_a),hAPP(X_a,fun(X_b,X_a),combk(X_a,X_b),K)),L_2),hAPP(X_b,filter(X_b),at(X_b),Aa))))))) # label(fact_4558_LIM__const__not__eq) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.89 4486 (all X_a (topological_space(X_a) -> (all Aa hBOOL(hAPP(filter(X_a),bool,hAPP(X_a,fun(filter(X_a),bool),hAPP(fun(X_a,X_a),fun(X_a,fun(filter(X_a),bool)),tendsto(X_a,X_a),combi(X_a)),Aa),hAPP(X_a,filter(X_a),at(X_a),Aa)))))) # label(fact_4559_LIM__ident) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.89 4487 (all X_b all X_a (topological_space(X_a) & topological_space(X_b) -> (all K all X_1 hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(X_b,fun(X_a,X_b),combk(X_b,X_a),K)),K),hAPP(X_a,filter(X_a),at(X_a),X_1)))))) # label(fact_4560_LIM__const) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.89 4488 (all X_b all X_c all X_a all X_d (topological_space(X_d) & real_normed_vector(X_a) & real_normed_vector(X_c) & real_normed_vector(X_b) -> (all G all M_2 all F all L_2 all Aa all Prod (hBOOL(hAPP(fun(X_a,fun(X_b,X_c)),bool,bounded_bilinear(X_a,X_b,X_c),Prod)) -> (hBOOL(hAPP(filter(X_d),bool,hAPP(X_a,fun(filter(X_d),bool),hAPP(fun(X_d,X_a),fun(X_a,fun(filter(X_d),bool)),tendsto(X_d,X_a),F),L_2),hAPP(X_d,filter(X_d),at(X_d),Aa))) -> (hBOOL(hAPP(filter(X_d),bool,hAPP(X_b,fun(filter(X_d),bool),hAPP(fun(X_d,X_b),fun(X_b,fun(filter(X_d),bool)),tendsto(X_d,X_b),G),M_2),hAPP(X_d,filter(X_d),at(X_d),Aa))) -> hBOOL(hAPP(filter(X_d),bool,hAPP(X_c,fun(filter(X_d),bool),hAPP(fun(X_d,X_c),fun(X_c,fun(filter(X_d),bool)),tendsto(X_d,X_c),hAPP(fun(X_d,X_b),fun(X_d,X_c),hAPP(fun(X_d,fun(X_b,X_c)),fun(fun(X_d,X_b),fun(X_d,X_c)),combs(X_d,X_b,X_c),hAPP(fun(X_d,X_a),fun(X_d,fun(X_b,X_c)),hAPP(fun(X_a,fun(X_b,X_c)),fun(fun(X_d,X_a),fun(X_d,fun(X_b,X_c))),combb(X_a,fun(X_b,X_c),X_d),Prod),F)),G)),hAPP(X_b,X_c,hAPP(X_a,fun(X_b,X_c),Prod,L_2),M_2)),hAPP(X_d,filter(X_d),at(X_d),Aa))))))))) # label(fact_4561_bounded__bilinear_OLIM) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.89 4489 (all X_b all X_a (topological_space(X_a) & real_normed_algebra(X_b) -> (all G all M_2 all F all L_2 all Aa (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),L_2),hAPP(X_a,filter(X_a),at(X_a),Aa))) -> (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),G),M_2),hAPP(X_a,filter(X_a),at(X_a),Aa))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(fun(X_a,X_b),fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,X_b)),combs(X_a,X_b,X_b),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,fun(X_b,X_b))),combb(X_b,fun(X_b,X_b),X_a),times_times(X_b)),F)),G)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),L_2),M_2)),hAPP(X_a,filter(X_a),at(X_a),Aa)))))))) # label(fact_4562_LIM__mult) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.89 4490 (all X_b all X_a (topological_space(X_a) & real_normed_algebra(X_b) -> (all Y_1 all G all L all Aa (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),G),L),hAPP(X_a,filter(X_a),at(X_a),Aa))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(X_b,fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(X_b,fun(X_a,X_b)),combc(X_a,X_b,X_b),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,fun(X_b,X_b))),combb(X_b,fun(X_b,X_b),X_a),times_times(X_b)),G)),Y_1)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),L),Y_1)),hAPP(X_a,filter(X_a),at(X_a),Aa))))))) # label(fact_4563_mult__left_OLIM) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.89 4491 (all X_b all X_a (topological_space(X_a) & real_normed_algebra(X_b) -> (all X_1 all G all L all Aa (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),G),L),hAPP(X_a,filter(X_a),at(X_a),Aa))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(fun(X_a,X_b),fun(X_a,X_b),hAPP(fun(X_b,X_b),fun(fun(X_a,X_b),fun(X_a,X_b)),combb(X_b,X_b,X_a),hAPP(X_b,fun(X_b,X_b),times_times(X_b),X_1)),G)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),X_1),L)),hAPP(X_a,filter(X_a),at(X_a),Aa))))))) # label(fact_4564_mult__right_OLIM) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.89 4492 (all X_a (real_normed_algebra(X_a) -> (all Y_1 all Aa hBOOL(hAPP(filter(X_a),bool,hAPP(X_a,fun(filter(X_a),bool),hAPP(fun(X_a,X_a),fun(X_a,fun(filter(X_a),bool)),tendsto(X_a,X_a),hAPP(X_a,fun(X_a,X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(X_a,X_a)),combc(X_a,X_a,X_a),times_times(X_a)),Y_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Aa),Y_1)),hAPP(X_a,filter(X_a),at(X_a),Aa)))))) # label(fact_4565_mult__left_Ocont) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.89 4493 (all X_a (real_normed_algebra(X_a) -> (all X_1 all Aa hBOOL(hAPP(filter(X_a),bool,hAPP(X_a,fun(filter(X_a),bool),hAPP(fun(X_a,X_a),fun(X_a,fun(filter(X_a),bool)),tendsto(X_a,X_a),hAPP(X_a,fun(X_a,X_a),times_times(X_a),X_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X_1),Aa)),hAPP(X_a,filter(X_a),at(X_a),Aa)))))) # label(fact_4566_mult__right_Ocont) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.89 4494 (all X_b all X_a (topological_space(X_a) & real_normed_vector(X_b) -> (all F all L_2 all Aa (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),L_2),hAPP(X_a,filter(X_a),at(X_a),Aa))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(fun(X_a,X_b),fun(X_a,X_b),hAPP(fun(X_b,X_b),fun(fun(X_a,X_b),fun(X_a,X_b)),combb(X_b,X_b,X_a),uminus_uminus(X_b)),F)),hAPP(X_b,X_b,uminus_uminus(X_b),L_2)),hAPP(X_a,filter(X_a),at(X_a),Aa))))))) # label(fact_4567_LIM__minus) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.89 4495 (all X_a (topological_space(X_a) -> (all F all L all Aa (hBOOL(hAPP(filter(X_a),bool,hAPP(real,fun(filter(X_a),bool),hAPP(fun(X_a,real),fun(real,fun(filter(X_a),bool)),tendsto(X_a,real),F),L),hAPP(X_a,filter(X_a),at(X_a),Aa))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(real,fun(filter(X_a),bool),hAPP(fun(X_a,real),fun(real,fun(filter(X_a),bool)),tendsto(X_a,real),hAPP(fun(X_a,real),fun(X_a,real),hAPP(fun(real,real),fun(fun(X_a,real),fun(X_a,real)),combb(real,real,X_a),abs_abs(real)),F)),hAPP(real,real,abs_abs(real),L)),hAPP(X_a,filter(X_a),at(X_a),Aa))))))) # label(fact_4568_LIM__rabs) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.89 4496 (all X_a (real_n1866405975lgebra(X_a) -> (all Aa (ti(X_a,Aa) != zero_zero(X_a) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_a,fun(filter(X_a),bool),hAPP(fun(X_a,X_a),fun(X_a,fun(filter(X_a),bool)),tendsto(X_a,X_a),inverse_inverse(X_a)),hAPP(X_a,X_a,inverse_inverse(X_a),Aa)),hAPP(X_a,filter(X_a),at(X_a),Aa))))))) # label(fact_4569_LIM__inverse__fun) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.89 4497 (all X_b all X_a (topological_space(X_a) & topological_space(X_b) -> (all K_3 all F all L_2 all X_1 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),L_2),hAPP(X_a,filter(X_a),at(X_a),X_1))) -> (ti(X_b,K_3) = ti(X_b,L_2) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),K_3),hAPP(X_a,filter(X_a),at(X_a),X_1)))))))) # label(fact_4570_LIM__cong__limit) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.89 4498 (all X_a all X_b (metric_space(X_b) & real_n2089651433ebra_1(X_a) -> (all M_2 all F all L_2 all Aa (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),L_2),hAPP(X_a,filter(X_a),at(X_a),Aa))) -> (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),M_2),hAPP(X_a,filter(X_a),at(X_a),Aa))) -> ti(X_b,L_2) = ti(X_b,M_2)))))) # label(fact_4571_LIM__unique) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.89 4499 (all L all U_1 hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),L),U_1)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,U_1)),L)) # label(fact_4572_card__atLeastAtMost) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.89 4500 (all L all U_1 hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastLessThan(int),L),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),U_1),one_one(int))) = hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastAtMost(int),L),U_1)) # label(fact_4573_atLeastLessThanPlusOne__atLeastAtMost__int) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.89 4501 (all X_b all X_a (topological_space(X_a) & real_normed_algebra(X_b) -> (all C_1 all F all Aa (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),zero_zero(X_b)),hAPP(X_a,filter(X_a),at(X_a),Aa))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(fun(X_a,X_b),fun(X_a,X_b),hAPP(fun(X_b,X_b),fun(fun(X_a,X_b),fun(X_a,X_b)),combb(X_b,X_b,X_a),hAPP(X_b,fun(X_b,X_b),times_times(X_b),C_1)),F)),zero_zero(X_b)),hAPP(X_a,filter(X_a),at(X_a),Aa))))))) # label(fact_4574_LIM__mult__right__zero) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.89 4502 (all X_b all X_a (topological_space(X_a) & real_normed_algebra(X_b) -> (all X_1 all G all Aa (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),G),zero_zero(X_b)),hAPP(X_a,filter(X_a),at(X_a),Aa))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(fun(X_a,X_b),fun(X_a,X_b),hAPP(fun(X_b,X_b),fun(fun(X_a,X_b),fun(X_a,X_b)),combb(X_b,X_b,X_a),hAPP(X_b,fun(X_b,X_b),times_times(X_b),X_1)),G)),zero_zero(X_b)),hAPP(X_a,filter(X_a),at(X_a),Aa))))))) # label(fact_4575_mult__right_OLIM__zero) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.89 4503 (all X_b all X_a (topological_space(X_a) & real_normed_algebra(X_b) -> (all C_1 all F all Aa (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),zero_zero(X_b)),hAPP(X_a,filter(X_a),at(X_a),Aa))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(X_b,fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(X_b,fun(X_a,X_b)),combc(X_a,X_b,X_b),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,fun(X_b,X_b))),combb(X_b,fun(X_b,X_b),X_a),times_times(X_b)),F)),C_1)),zero_zero(X_b)),hAPP(X_a,filter(X_a),at(X_a),Aa))))))) # label(fact_4576_LIM__mult__left__zero) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.89 4504 (all X_b all X_a (topological_space(X_a) & real_normed_algebra(X_b) -> (all Y_1 all G all Aa (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),G),zero_zero(X_b)),hAPP(X_a,filter(X_a),at(X_a),Aa))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(X_b,fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(X_b,fun(X_a,X_b)),combc(X_a,X_b,X_b),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,fun(X_b,X_b))),combb(X_b,fun(X_b,X_b),X_a),times_times(X_b)),G)),Y_1)),zero_zero(X_b)),hAPP(X_a,filter(X_a),at(X_a),Aa))))))) # label(fact_4577_mult__left_OLIM__zero) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.89 4505 (all X_b all X_a (metric_space(X_a) & real_normed_algebra(X_b) -> (all G all F all Aa (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),zero_zero(X_b)),hAPP(X_a,filter(X_a),at(X_a),Aa))) -> (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),G),zero_zero(X_b)),hAPP(X_a,filter(X_a),at(X_a),Aa))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(fun(X_a,X_b),fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,X_b)),combs(X_a,X_b,X_b),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,fun(X_b,X_b))),combb(X_b,fun(X_b,X_b),X_a),times_times(X_b)),F)),G)),zero_zero(X_b)),hAPP(X_a,filter(X_a),at(X_a),Aa)))))))) # label(fact_4578_LIM__mult__zero) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.89 4506 (all X_b all X_a (real_normed_vector(X_a) & topological_space(X_b) -> (all F all Aa all L_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(fun(X_a,X_a),fun(X_a,X_b),hAPP(fun(X_a,X_b),fun(fun(X_a,X_a),fun(X_a,X_b)),combb(X_a,X_b,X_a),F),hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Aa))),L_2),hAPP(X_a,filter(X_a),at(X_a),zero_zero(X_a)))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),L_2),hAPP(X_a,filter(X_a),at(X_a),Aa))))))) # label(fact_4579_LIM__offset__zero__cancel) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.89 4507 (all X_b all X_a (real_normed_vector(X_a) & topological_space(X_b) -> (all F all L_2 all Aa (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),L_2),hAPP(X_a,filter(X_a),at(X_a),Aa))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(fun(X_a,X_a),fun(X_a,X_b),hAPP(fun(X_a,X_b),fun(fun(X_a,X_a),fun(X_a,X_b)),combb(X_a,X_b,X_a),F),hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Aa))),L_2),hAPP(X_a,filter(X_a),at(X_a),zero_zero(X_a)))))))) # label(fact_4580_LIM__offset__zero) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.89 4508 (all X_b all X_a (topological_space(X_a) & real_normed_vector(X_b) -> (all G all F all Aa (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),zero_zero(X_b)),hAPP(X_a,filter(X_a),at(X_a),Aa))) -> (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),G),zero_zero(X_b)),hAPP(X_a,filter(X_a),at(X_a),Aa))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(fun(X_a,X_b),fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,X_b)),combs(X_a,X_b,X_b),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,fun(X_b,X_b))),combb(X_b,fun(X_b,X_b),X_a),plus_plus(X_b)),F)),G)),zero_zero(X_b)),hAPP(X_a,filter(X_a),at(X_a),Aa)))))))) # label(fact_4581_LIM__add__zero) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.89 4509 (all X_b all X_a (real_normed_vector(X_a) & topological_space(X_b) -> (all F all Aa (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),hAPP(X_a,X_b,F,Aa)),hAPP(X_a,filter(X_a),at(X_a),Aa))) <-> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(fun(X_a,X_a),fun(X_a,X_b),hAPP(fun(X_a,X_b),fun(fun(X_a,X_a),fun(X_a,X_b)),combb(X_a,X_b,X_a),F),hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Aa))),hAPP(X_a,X_b,F,Aa)),hAPP(X_a,filter(X_a),at(X_a),zero_zero(X_a)))))))) # label(fact_4582_LIM__isCont__iff) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.89 4510 (all X_b all X_a (topological_space(X_a) & real_normed_vector(X_b) -> (all F all L all Aa (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(X_b,fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(X_b,fun(X_a,X_b)),combc(X_a,X_b,X_b),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,fun(X_b,X_b))),combb(X_b,fun(X_b,X_b),X_a),minus_minus(X_b)),F)),L)),zero_zero(X_b)),hAPP(X_a,filter(X_a),at(X_a),Aa))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),L),hAPP(X_a,filter(X_a),at(X_a),Aa))))))) # label(fact_4583_LIM__zero__cancel) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.89 4511 (all X_b all X_a (topological_space(X_a) & real_normed_vector(X_b) -> (all F all L all Aa (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),L),hAPP(X_a,filter(X_a),at(X_a),Aa))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(X_b,fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(X_b,fun(X_a,X_b)),combc(X_a,X_b,X_b),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,fun(X_b,X_b))),combb(X_b,fun(X_b,X_b),X_a),minus_minus(X_b)),F)),L)),zero_zero(X_b)),hAPP(X_a,filter(X_a),at(X_a),Aa))))))) # label(fact_4584_LIM__zero) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.89 4512 (all X_b all X_a (metric_space(X_a) & real_normed_vector(X_b) -> (all F all L all Aa (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(X_b,fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(X_b,fun(X_a,X_b)),combc(X_a,X_b,X_b),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,fun(X_b,X_b))),combb(X_b,fun(X_b,X_b),X_a),minus_minus(X_b)),F)),L)),zero_zero(X_b)),hAPP(X_a,filter(X_a),at(X_a),Aa))) <-> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),L),hAPP(X_a,filter(X_a),at(X_a),Aa))))))) # label(fact_4585_LIM__zero__iff) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.89 4513 (all X_b all X_a (real_normed_vector(X_a) & topological_space(X_b) -> (all K all F all L_2 all Aa (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),L_2),hAPP(X_a,filter(X_a),at(X_a),Aa))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(fun(X_a,X_a),fun(X_a,X_b),hAPP(fun(X_a,X_b),fun(fun(X_a,X_a),fun(X_a,X_b)),combb(X_a,X_b,X_a),F),hAPP(X_a,fun(X_a,X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(X_a,X_a)),combc(X_a,X_a,X_a),plus_plus(X_a)),K))),L_2),hAPP(X_a,filter(X_a),at(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),Aa),K)))))))) # label(fact_4586_LIM__offset) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.89 4514 (all X_b all X_a (topological_space(X_a) & real_normed_field(X_b) -> (all Y_1 all G all Aa (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),G),zero_zero(X_b)),hAPP(X_a,filter(X_a),at(X_a),Aa))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(X_b,fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(X_b,fun(X_a,X_b)),combc(X_a,X_b,X_b),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,fun(X_b,X_b))),combb(X_b,fun(X_b,X_b),X_a),inverse_divide(X_b)),G)),Y_1)),zero_zero(X_b)),hAPP(X_a,filter(X_a),at(X_a),Aa))))))) # label(fact_4587_divide_OLIM__zero) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.89 4515 (all X_b all X_a (topological_space(X_a) & real_normed_vector(X_b) -> (all G all M all F all L all X_1 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),L),hAPP(X_a,filter(X_a),at(X_a),X_1))) -> (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),G),M),hAPP(X_a,filter(X_a),at(X_a),X_1))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(fun(X_a,X_b),fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,X_b)),combs(X_a,X_b,X_b),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,fun(X_b,X_b))),combb(X_b,fun(X_b,X_b),X_a),plus_plus(X_b)),F)),hAPP(fun(X_a,X_b),fun(X_a,X_b),hAPP(fun(X_b,X_b),fun(fun(X_a,X_b),fun(X_a,X_b)),combb(X_b,X_b,X_a),uminus_uminus(X_b)),G))),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),L),hAPP(X_b,X_b,uminus_uminus(X_b),M))),hAPP(X_a,filter(X_a),at(X_a),X_1)))))))) # label(fact_4588_LIM__add__minus) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.89 4516 (all X_b all X_a (topological_space(X_a) & real_n1866405975lgebra(X_b) -> (all F all L_2 all Aa (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),L_2),hAPP(X_a,filter(X_a),at(X_a),Aa))) -> (ti(X_b,L_2) != zero_zero(X_b) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(fun(X_a,X_b),fun(X_a,X_b),hAPP(fun(X_b,X_b),fun(fun(X_a,X_b),fun(X_a,X_b)),combb(X_b,X_b,X_a),inverse_inverse(X_b)),F)),hAPP(X_b,X_b,inverse_inverse(X_b),L_2)),hAPP(X_a,filter(X_a),at(X_a),Aa)))))))) # label(fact_4589_LIM__inverse) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.89 4517 (all K all F (hAPP(nat,nat,F,zero_zero(nat)) = zero_zero(nat) -> hAPP(fun(nat,bool),nat,hAPP(fun(nat,nat),fun(fun(nat,bool),nat),big_co1399186613setsum(nat,nat),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,suc,zero_zero(nat))),K)) = hAPP(fun(nat,bool),nat,hAPP(fun(nat,nat),fun(fun(nat,bool),nat),big_co1399186613setsum(nat,nat),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),zero_zero(nat)),K)))) # label(fact_4590_setsum__shift__lb__Suc0__0) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.89 4518 (all X_b all X_a (topological_space(X_a) & real_normed_vector(X_b) -> (all F all L all Aa (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),L),hAPP(X_a,filter(X_a),at(X_a),Aa))) -> (ti(X_b,L) != zero_zero(X_b) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(fun(X_a,X_b),fun(X_a,X_b),hAPP(fun(X_b,X_b),fun(fun(X_a,X_b),fun(X_a,X_b)),combb(X_b,X_b,X_a),sgn_sgn(X_b)),F)),hAPP(X_b,X_b,sgn_sgn(X_b),L)),hAPP(X_a,filter(X_a),at(X_a),Aa)))))))) # label(fact_4591_LIM__sgn) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.89 4519 (all X_b all X_a (topological_space(X_a) & real_normed_vector(X_b) -> (all F all L all Aa (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),L),hAPP(X_a,filter(X_a),at(X_a),Aa))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(real,fun(filter(X_a),bool),hAPP(fun(X_a,real),fun(real,fun(filter(X_a),bool)),tendsto(X_a,real),hAPP(fun(X_a,X_b),fun(X_a,real),hAPP(fun(X_b,real),fun(fun(X_a,X_b),fun(X_a,real)),combb(X_b,real,X_a),norm_norm(X_b)),F)),hAPP(X_b,real,norm_norm(X_b),L)),hAPP(X_a,filter(X_a),at(X_a),Aa))))))) # label(fact_4592_LIM__norm) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.89 4520 (all X_c all X_a all X_b all X_d (metric_space(X_d) & real_normed_vector(X_b) & real_normed_vector(X_a) & real_normed_vector(X_c) -> (all G all F all Aa all Prod (hBOOL(hAPP(fun(X_a,fun(X_b,X_c)),bool,bounded_bilinear(X_a,X_b,X_c),Prod)) -> (hBOOL(hAPP(filter(X_d),bool,hAPP(X_a,fun(filter(X_d),bool),hAPP(fun(X_d,X_a),fun(X_a,fun(filter(X_d),bool)),tendsto(X_d,X_a),F),zero_zero(X_a)),hAPP(X_d,filter(X_d),at(X_d),Aa))) -> (hBOOL(hAPP(filter(X_d),bool,hAPP(X_b,fun(filter(X_d),bool),hAPP(fun(X_d,X_b),fun(X_b,fun(filter(X_d),bool)),tendsto(X_d,X_b),G),zero_zero(X_b)),hAPP(X_d,filter(X_d),at(X_d),Aa))) -> hBOOL(hAPP(filter(X_d),bool,hAPP(X_c,fun(filter(X_d),bool),hAPP(fun(X_d,X_c),fun(X_c,fun(filter(X_d),bool)),tendsto(X_d,X_c),hAPP(fun(X_d,X_b),fun(X_d,X_c),hAPP(fun(X_d,fun(X_b,X_c)),fun(fun(X_d,X_b),fun(X_d,X_c)),combs(X_d,X_b,X_c),hAPP(fun(X_d,X_a),fun(X_d,fun(X_b,X_c)),hAPP(fun(X_a,fun(X_b,X_c)),fun(fun(X_d,X_a),fun(X_d,fun(X_b,X_c))),combb(X_a,fun(X_b,X_c),X_d),Prod),F)),G)),zero_zero(X_c)),hAPP(X_d,filter(X_d),at(X_d),Aa))))))))) # label(fact_4593_bounded__bilinear_OLIM__prod__zero) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.89 4521 (all X_c all X_a all X_b all X_d (topological_space(X_d) & real_normed_vector(X_b) & real_normed_vector(X_a) & real_normed_vector(X_c) -> (all C_1 all F all Aa all Prod (hBOOL(hAPP(fun(X_a,fun(X_b,X_c)),bool,bounded_bilinear(X_a,X_b,X_c),Prod)) -> (hBOOL(hAPP(filter(X_d),bool,hAPP(X_a,fun(filter(X_d),bool),hAPP(fun(X_d,X_a),fun(X_a,fun(filter(X_d),bool)),tendsto(X_d,X_a),F),zero_zero(X_a)),hAPP(X_d,filter(X_d),at(X_d),Aa))) -> hBOOL(hAPP(filter(X_d),bool,hAPP(X_c,fun(filter(X_d),bool),hAPP(fun(X_d,X_c),fun(X_c,fun(filter(X_d),bool)),tendsto(X_d,X_c),hAPP(X_b,fun(X_d,X_c),hAPP(fun(X_d,fun(X_b,X_c)),fun(X_b,fun(X_d,X_c)),combc(X_d,X_b,X_c),hAPP(fun(X_d,X_a),fun(X_d,fun(X_b,X_c)),hAPP(fun(X_a,fun(X_b,X_c)),fun(fun(X_d,X_a),fun(X_d,fun(X_b,X_c))),combb(X_a,fun(X_b,X_c),X_d),Prod),F)),C_1)),zero_zero(X_c)),hAPP(X_d,filter(X_d),at(X_d),Aa)))))))) # label(fact_4594_bounded__bilinear_OLIM__left__zero) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.89 4522 (all X_c all X_a all X_b all X_d (topological_space(X_d) & real_normed_vector(X_b) & real_normed_vector(X_a) & real_normed_vector(X_c) -> (all C_1 all F all Aa all Prod (hBOOL(hAPP(fun(X_a,fun(X_b,X_c)),bool,bounded_bilinear(X_a,X_b,X_c),Prod)) -> (hBOOL(hAPP(filter(X_d),bool,hAPP(X_b,fun(filter(X_d),bool),hAPP(fun(X_d,X_b),fun(X_b,fun(filter(X_d),bool)),tendsto(X_d,X_b),F),zero_zero(X_b)),hAPP(X_d,filter(X_d),at(X_d),Aa))) -> hBOOL(hAPP(filter(X_d),bool,hAPP(X_c,fun(filter(X_d),bool),hAPP(fun(X_d,X_c),fun(X_c,fun(filter(X_d),bool)),tendsto(X_d,X_c),hAPP(fun(X_d,X_b),fun(X_d,X_c),hAPP(fun(X_b,X_c),fun(fun(X_d,X_b),fun(X_d,X_c)),combb(X_b,X_c,X_d),hAPP(X_a,fun(X_b,X_c),Prod,C_1)),F)),zero_zero(X_c)),hAPP(X_d,filter(X_d),at(X_d),Aa)))))))) # label(fact_4595_bounded__bilinear_OLIM__right__zero) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.89 4523 (all X_a (topological_space(X_a) -> (all F all Aa (hBOOL(hAPP(filter(X_a),bool,hAPP(real,fun(filter(X_a),bool),hAPP(fun(X_a,real),fun(real,fun(filter(X_a),bool)),tendsto(X_a,real),hAPP(fun(X_a,real),fun(X_a,real),hAPP(fun(real,real),fun(fun(X_a,real),fun(X_a,real)),combb(real,real,X_a),abs_abs(real)),F)),zero_zero(real)),hAPP(X_a,filter(X_a),at(X_a),Aa))) <-> hBOOL(hAPP(filter(X_a),bool,hAPP(real,fun(filter(X_a),bool),hAPP(fun(X_a,real),fun(real,fun(filter(X_a),bool)),tendsto(X_a,real),F),zero_zero(real)),hAPP(X_a,filter(X_a),at(X_a),Aa))))))) # label(fact_4596_LIM__rabs__zero__iff) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.89 4524 (all X_a (topological_space(X_a) -> (all F all Aa (hBOOL(hAPP(filter(X_a),bool,hAPP(real,fun(filter(X_a),bool),hAPP(fun(X_a,real),fun(real,fun(filter(X_a),bool)),tendsto(X_a,real),F),zero_zero(real)),hAPP(X_a,filter(X_a),at(X_a),Aa))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(real,fun(filter(X_a),bool),hAPP(fun(X_a,real),fun(real,fun(filter(X_a),bool)),tendsto(X_a,real),hAPP(fun(X_a,real),fun(X_a,real),hAPP(fun(real,real),fun(fun(X_a,real),fun(X_a,real)),combb(real,real,X_a),abs_abs(real)),F)),zero_zero(real)),hAPP(X_a,filter(X_a),at(X_a),Aa))))))) # label(fact_4597_LIM__rabs__zero) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.89 4525 (all X_a (topological_space(X_a) -> (all F all Aa (hBOOL(hAPP(filter(X_a),bool,hAPP(real,fun(filter(X_a),bool),hAPP(fun(X_a,real),fun(real,fun(filter(X_a),bool)),tendsto(X_a,real),hAPP(fun(X_a,real),fun(X_a,real),hAPP(fun(real,real),fun(fun(X_a,real),fun(X_a,real)),combb(real,real,X_a),abs_abs(real)),F)),zero_zero(real)),hAPP(X_a,filter(X_a),at(X_a),Aa))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(real,fun(filter(X_a),bool),hAPP(fun(X_a,real),fun(real,fun(filter(X_a),bool)),tendsto(X_a,real),F),zero_zero(real)),hAPP(X_a,filter(X_a),at(X_a),Aa))))))) # label(fact_4598_LIM__rabs__zero__cancel) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.89 4526 (all X_b all X_a (topological_space(X_a) & real_algebra_1(X_b) & real_normed_vector(X_b) -> (all G all L all Aa (hBOOL(hAPP(filter(X_a),bool,hAPP(real,fun(filter(X_a),bool),hAPP(fun(X_a,real),fun(real,fun(filter(X_a),bool)),tendsto(X_a,real),G),L),hAPP(X_a,filter(X_a),at(X_a),Aa))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(fun(X_a,real),fun(X_a,X_b),hAPP(fun(real,X_b),fun(fun(X_a,real),fun(X_a,X_b)),combb(real,X_b,X_a),of_real(X_b)),G)),hAPP(real,X_b,of_real(X_b),L)),hAPP(X_a,filter(X_a),at(X_a),Aa))))))) # label(fact_4599_LIM__of__real) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.89 4527 (all X_a (topological_space(X_a) -> (all G all L all Aa (hBOOL(hAPP(filter(X_a),bool,hAPP(complex,fun(filter(X_a),bool),hAPP(fun(X_a,complex),fun(complex,fun(filter(X_a),bool)),tendsto(X_a,complex),G),L),hAPP(X_a,filter(X_a),at(X_a),Aa))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(real,fun(filter(X_a),bool),hAPP(fun(X_a,real),fun(real,fun(filter(X_a),bool)),tendsto(X_a,real),hAPP(fun(X_a,complex),fun(X_a,real),hAPP(fun(complex,real),fun(fun(X_a,complex),fun(X_a,real)),combb(complex,real,X_a),re),G)),hAPP(complex,real,re,L)),hAPP(X_a,filter(X_a),at(X_a),Aa))))))) # label(fact_4600_Re_OLIM) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.89 4528 (all X_a (topological_space(X_a) -> (all G all L all Aa (hBOOL(hAPP(filter(X_a),bool,hAPP(complex,fun(filter(X_a),bool),hAPP(fun(X_a,complex),fun(complex,fun(filter(X_a),bool)),tendsto(X_a,complex),G),L),hAPP(X_a,filter(X_a),at(X_a),Aa))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(real,fun(filter(X_a),bool),hAPP(fun(X_a,real),fun(real,fun(filter(X_a),bool)),tendsto(X_a,real),hAPP(fun(X_a,complex),fun(X_a,real),hAPP(fun(complex,real),fun(fun(X_a,complex),fun(X_a,real)),combb(complex,real,X_a),im),G)),hAPP(complex,real,im,L)),hAPP(X_a,filter(X_a),at(X_a),Aa))))))) # label(fact_4601_Im_OLIM) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.89 4529 (all X_a (comm_monoid_add(X_a) -> (all F all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N)) -> hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),M),N)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(nat,X_a,F,M)),hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,suc,M)),N))))))) # label(fact_4602_setsum__head__Suc) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.89 4530 (all X_a (topological_space(X_a) -> (all G all Aa (hBOOL(hAPP(filter(X_a),bool,hAPP(complex,fun(filter(X_a),bool),hAPP(fun(X_a,complex),fun(complex,fun(filter(X_a),bool)),tendsto(X_a,complex),G),zero_zero(complex)),hAPP(X_a,filter(X_a),at(X_a),Aa))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(complex,fun(filter(X_a),bool),hAPP(fun(X_a,complex),fun(complex,fun(filter(X_a),bool)),tendsto(X_a,complex),hAPP(fun(X_a,complex),fun(X_a,complex),hAPP(fun(complex,complex),fun(fun(X_a,complex),fun(X_a,complex)),combb(complex,complex,X_a),cnj),G)),zero_zero(complex)),hAPP(X_a,filter(X_a),at(X_a),Aa))))))) # label(fact_4603_cnj_OLIM__zero) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.89 4531 (all X_b all X_a (metric_space(X_a) & real_normed_vector(X_b) -> (all L all F all G all Aa (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(fun(X_a,X_b),fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,X_b)),combs(X_a,X_b,X_b),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,fun(X_b,X_b))),combb(X_b,fun(X_b,X_b),X_a),plus_plus(X_b)),F)),hAPP(fun(X_a,X_b),fun(X_a,X_b),hAPP(fun(X_b,X_b),fun(fun(X_a,X_b),fun(X_a,X_b)),combb(X_b,X_b,X_a),uminus_uminus(X_b)),G))),zero_zero(X_b)),hAPP(X_a,filter(X_a),at(X_a),Aa))) -> (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),G),L),hAPP(X_a,filter(X_a),at(X_a),Aa))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),L),hAPP(X_a,filter(X_a),at(X_a),Aa)))))))) # label(fact_4604_LIM__trans) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.89 4532 (all X_a (real_normed_field(X_a) -> (all F all X_1 all D_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),F),X_1),D_2)) <-> hBOOL(hAPP(filter(X_a),bool,hAPP(X_a,fun(filter(X_a),bool),hAPP(fun(X_a,X_a),fun(X_a,fun(filter(X_a),bool)),tendsto(X_a,X_a),hAPP(fun(X_a,X_a),fun(X_a,X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,X_a),fun(X_a,X_a)),combs(X_a,X_a,X_a),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,X_a),fun(X_a,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),X_a),inverse_divide(X_a)),hAPP(X_a,fun(X_a,X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(X_a,X_a)),combc(X_a,X_a,X_a),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,X_a),fun(X_a,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),X_a),minus_minus(X_a)),F)),hAPP(X_a,X_a,F,X_1)))),hAPP(X_a,fun(X_a,X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(X_a,X_a)),combc(X_a,X_a,X_a),minus_minus(X_a)),X_1))),D_2),hAPP(X_a,filter(X_a),at(X_a),X_1))))))) # label(fact_4605_DERIV__iff2) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.89 4533 (all X_c all X_b all X_a (metric_space(X_a) & topological_space(X_b) & topological_space(X_c) -> (all G all C_1 all F all Ba all Aa (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),Ba),hAPP(X_a,filter(X_a),at(X_a),Aa))) -> (hBOOL(hAPP(filter(X_b),bool,hAPP(X_c,fun(filter(X_b),bool),hAPP(fun(X_b,X_c),fun(X_c,fun(filter(X_b),bool)),tendsto(X_b,X_c),G),C_1),hAPP(X_b,filter(X_b),at(X_b),Ba))) -> ((exists D_3 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),D_3)) & (all X_2 (ti(X_a,X_2) != ti(X_a,Aa) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),X_2),Aa)),D_3)) -> hAPP(X_a,X_b,F,X_2) != ti(X_b,Ba))))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_c,fun(filter(X_a),bool),hAPP(fun(X_a,X_c),fun(X_c,fun(filter(X_a),bool)),tendsto(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),G),F)),C_1),hAPP(X_a,filter(X_a),at(X_a),Aa))))))))) # label(fact_4606_metric__LIM__compose2) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.89 4534 (all X_a (comm_monoid_add(X_a) -> (all F all N all M ((hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,N)),M)) -> hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),M),hAPP(nat,nat,suc,N))) = zero_zero(X_a)) & (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,N)),M)) -> hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),M),hAPP(nat,nat,suc,N))) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),M),N))),hAPP(nat,X_a,F,hAPP(nat,nat,suc,N)))))))) # label(fact_4607_setsum__cl__ivl__Suc) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.89 4535 (all X_a (comm_monoid_add(X_a) -> (all F all Pa all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),one_one(nat)))) -> hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),M),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),Pa))) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),M),N))),hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),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),Pa)))))))) # label(fact_4608_setsum__ub__add__nat) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.89 4536 (all L all U_1 hAPP(fun(int,bool),nat,finite_card(int),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastAtMost(int),L),U_1)) = hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),U_1),L)),one_one(int)))) # label(fact_4609_card__atLeastAtMost__int) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.89 4537 (all X_a (comm_monoid_add(X_a) -> (all F all N all M ((hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,N)),M)) -> hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),M),hAPP(nat,nat,suc,N))) = zero_zero(X_a)) & (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,N)),M)) -> hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),M),hAPP(nat,nat,suc,N))) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(nat,X_a,F,M)),hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),hAPP(fun(nat,nat),fun(nat,X_a),hAPP(fun(nat,X_a),fun(fun(nat,nat),fun(nat,X_a)),combb(nat,X_a,nat),F),suc)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),M),N)))))))) # label(fact_4610_setsum__cl__ivl__Suc2) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.89 4538 (all X_a (inverse(X_a) & real_normed_vector(X_a) -> (all F all Aa all D_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_a,fun(filter(X_a),bool),hAPP(fun(X_a,X_a),fun(X_a,fun(filter(X_a),bool)),tendsto(X_a,X_a),hAPP(fun(X_a,X_a),fun(X_a,X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,X_a),fun(X_a,X_a)),combs(X_a,X_a,X_a),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,X_a),fun(X_a,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),X_a),inverse_divide(X_a)),hAPP(X_a,fun(X_a,X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(X_a,X_a)),combc(X_a,X_a,X_a),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,X_a),fun(X_a,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),X_a),minus_minus(X_a)),hAPP(fun(X_a,X_a),fun(X_a,X_a),hAPP(fun(X_a,X_a),fun(fun(X_a,X_a),fun(X_a,X_a)),combb(X_a,X_a,X_a),F),hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Aa)))),hAPP(X_a,X_a,F,Aa)))),combi(X_a))),D_2),hAPP(X_a,filter(X_a),at(X_a),zero_zero(X_a)))) <-> hBOOL(hAPP(filter(X_a),bool,hAPP(X_a,fun(filter(X_a),bool),hAPP(fun(X_a,X_a),fun(X_a,fun(filter(X_a),bool)),tendsto(X_a,X_a),hAPP(fun(X_a,X_a),fun(X_a,X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,X_a),fun(X_a,X_a)),combs(X_a,X_a,X_a),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,X_a),fun(X_a,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),X_a),inverse_divide(X_a)),hAPP(X_a,fun(X_a,X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(X_a,X_a)),combc(X_a,X_a,X_a),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,X_a),fun(X_a,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),X_a),minus_minus(X_a)),F)),hAPP(X_a,X_a,F,Aa)))),hAPP(X_a,fun(X_a,X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(X_a,X_a)),combc(X_a,X_a,X_a),minus_minus(X_a)),Aa))),D_2),hAPP(X_a,filter(X_a),at(X_a),Aa))))))) # label(fact_4611_DERIV__LIM__iff) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.89 4539 (all X_c all X_b all X_a (real_normed_vector(X_a) & topological_space(X_b) & topological_space(X_c) -> (all G all C_1 all F all Ba all Aa (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),Ba),hAPP(X_a,filter(X_a),at(X_a),Aa))) -> (hBOOL(hAPP(filter(X_b),bool,hAPP(X_c,fun(filter(X_b),bool),hAPP(fun(X_b,X_c),fun(X_c,fun(filter(X_b),bool)),tendsto(X_b,X_c),G),C_1),hAPP(X_b,filter(X_b),at(X_b),Ba))) -> ((exists D_3 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),D_3)) & (all X_2 (ti(X_a,X_2) != ti(X_a,Aa) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),X_2),Aa))),D_3)) -> hAPP(X_a,X_b,F,X_2) != ti(X_b,Ba))))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_c,fun(filter(X_a),bool),hAPP(fun(X_a,X_c),fun(X_c,fun(filter(X_a),bool)),tendsto(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),G),F)),C_1),hAPP(X_a,filter(X_a),at(X_a),Aa))))))))) # label(fact_4612_LIM__compose2) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.89 4540 (all X_b all X_a (topological_space(X_a) & real_normed_vector(X_b) -> (all F all Aa (hBOOL(hAPP(filter(X_a),bool,hAPP(real,fun(filter(X_a),bool),hAPP(fun(X_a,real),fun(real,fun(filter(X_a),bool)),tendsto(X_a,real),hAPP(fun(X_a,X_b),fun(X_a,real),hAPP(fun(X_b,real),fun(fun(X_a,X_b),fun(X_a,real)),combb(X_b,real,X_a),norm_norm(X_b)),F)),zero_zero(real)),hAPP(X_a,filter(X_a),at(X_a),Aa))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),zero_zero(X_b)),hAPP(X_a,filter(X_a),at(X_a),Aa))))))) # label(fact_4613_LIM__norm__zero__cancel) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.89 4541 (all X_b all X_a (topological_space(X_a) & real_normed_vector(X_b) -> (all F all Aa (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),zero_zero(X_b)),hAPP(X_a,filter(X_a),at(X_a),Aa))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(real,fun(filter(X_a),bool),hAPP(fun(X_a,real),fun(real,fun(filter(X_a),bool)),tendsto(X_a,real),hAPP(fun(X_a,X_b),fun(X_a,real),hAPP(fun(X_b,real),fun(fun(X_a,X_b),fun(X_a,real)),combb(X_b,real,X_a),norm_norm(X_b)),F)),zero_zero(real)),hAPP(X_a,filter(X_a),at(X_a),Aa))))))) # label(fact_4614_LIM__norm__zero) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.89 4542 (all X_b all X_a (topological_space(X_a) & real_normed_vector(X_b) -> (all F all Aa (hBOOL(hAPP(filter(X_a),bool,hAPP(real,fun(filter(X_a),bool),hAPP(fun(X_a,real),fun(real,fun(filter(X_a),bool)),tendsto(X_a,real),hAPP(fun(X_a,X_b),fun(X_a,real),hAPP(fun(X_b,real),fun(fun(X_a,X_b),fun(X_a,real)),combb(X_b,real,X_a),norm_norm(X_b)),F)),zero_zero(real)),hAPP(X_a,filter(X_a),at(X_a),Aa))) <-> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),zero_zero(X_b)),hAPP(X_a,filter(X_a),at(X_a),Aa))))))) # label(fact_4615_LIM__norm__zero__iff) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.89 4543 (all N all M (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N),M)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,fact_fact(nat),M)),hAPP(nat,nat,fact_fact(nat),N)) = hAPP(fun(nat,bool),nat,hAPP(fun(nat,nat),fun(fun(nat,bool),nat),big_co302546470etprod(nat,nat),combi(nat)),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))),M)))) # label(fact_4616_fact__div__fact) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.89 4544 (all X_b all X_a (topological_space(X_a) & real_algebra_1(X_b) & real_normed_vector(X_b) -> (all G all Aa (hBOOL(hAPP(filter(X_a),bool,hAPP(real,fun(filter(X_a),bool),hAPP(fun(X_a,real),fun(real,fun(filter(X_a),bool)),tendsto(X_a,real),G),zero_zero(real)),hAPP(X_a,filter(X_a),at(X_a),Aa))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(fun(X_a,real),fun(X_a,X_b),hAPP(fun(real,X_b),fun(fun(X_a,real),fun(X_a,X_b)),combb(real,X_b,X_a),of_real(X_b)),G)),zero_zero(X_b)),hAPP(X_a,filter(X_a),at(X_a),Aa))))))) # label(fact_4617_of__real_OLIM__zero) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.89 4545 (all N (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),N)) -> hAPP(int,int,fact_fact(int),N) = hAPP(fun(int,bool),int,hAPP(fun(int,int),fun(fun(int,bool),int),big_co302546470etprod(int,int),combi(int)),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastAtMost(int),one_one(int)),N)))) # label(fact_4618_fact__altdef__int) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.89 4546 (all X_a (topological_space(X_a) -> (all G all Aa (hBOOL(hAPP(filter(X_a),bool,hAPP(complex,fun(filter(X_a),bool),hAPP(fun(X_a,complex),fun(complex,fun(filter(X_a),bool)),tendsto(X_a,complex),G),zero_zero(complex)),hAPP(X_a,filter(X_a),at(X_a),Aa))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(real,fun(filter(X_a),bool),hAPP(fun(X_a,real),fun(real,fun(filter(X_a),bool)),tendsto(X_a,real),hAPP(fun(X_a,complex),fun(X_a,real),hAPP(fun(complex,real),fun(fun(X_a,complex),fun(X_a,real)),combb(complex,real,X_a),re),G)),zero_zero(real)),hAPP(X_a,filter(X_a),at(X_a),Aa))))))) # label(fact_4619_Re_OLIM__zero) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.89 4547 (all X_a (topological_space(X_a) -> (all G all Aa (hBOOL(hAPP(filter(X_a),bool,hAPP(complex,fun(filter(X_a),bool),hAPP(fun(X_a,complex),fun(complex,fun(filter(X_a),bool)),tendsto(X_a,complex),G),zero_zero(complex)),hAPP(X_a,filter(X_a),at(X_a),Aa))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(real,fun(filter(X_a),bool),hAPP(fun(X_a,real),fun(real,fun(filter(X_a),bool)),tendsto(X_a,real),hAPP(fun(X_a,complex),fun(X_a,real),hAPP(fun(complex,real),fun(fun(X_a,complex),fun(X_a,real)),combb(complex,real,X_a),im),G)),zero_zero(real)),hAPP(X_a,filter(X_a),at(X_a),Aa))))))) # label(fact_4620_Im_OLIM__zero) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.89 4548 (all X_a (comm_semiring_1(X_a) -> (all N 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))),hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),semiring_1_of_nat(X_a)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),one_one(nat)),N))) = 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),N)),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),N)),one_one(X_a)))))) # label(fact_4621_gauss__sum) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.89 4549 (all X_a (ab_group_add(X_a) -> (all F all M all N ((hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N)) -> hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),minus_minus(X_a)),F)),hAPP(fun(nat,nat),fun(nat,X_a),hAPP(fun(nat,X_a),fun(fun(nat,nat),fun(nat,X_a)),combb(nat,X_a,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),N)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(nat,X_a,F,M)),hAPP(nat,X_a,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),N)) -> hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),minus_minus(X_a)),F)),hAPP(fun(nat,nat),fun(nat,X_a),hAPP(fun(nat,X_a),fun(fun(nat,nat),fun(nat,X_a)),combb(nat,X_a,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),N)) = zero_zero(X_a)))))) # label(fact_4622_setsum__natinterval__difff) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.89 4550 (all X_a (real_normed_field(X_a) -> (all F all X_1 all D_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),F),X_1),D_2)) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_a,fun(filter(X_a),bool),hAPP(fun(X_a,X_a),fun(X_a,fun(filter(X_a),bool)),tendsto(X_a,X_a),hAPP(fun(X_a,X_a),fun(X_a,X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,X_a),fun(X_a,X_a)),combs(X_a,X_a,X_a),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,X_a),fun(X_a,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),X_a),inverse_divide(X_a)),hAPP(X_a,fun(X_a,X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(X_a,X_a)),combc(X_a,X_a,X_a),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,X_a),fun(X_a,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),X_a),minus_minus(X_a)),hAPP(fun(X_a,X_a),fun(X_a,X_a),hAPP(fun(X_a,X_a),fun(fun(X_a,X_a),fun(X_a,X_a)),combb(X_a,X_a,X_a),F),hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X_1)))),hAPP(X_a,X_a,F,X_1)))),combi(X_a))),D_2),hAPP(X_a,filter(X_a),at(X_a),zero_zero(X_a)))))))) # label(fact_4623_DERIV__D) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.89 4551 (all X_a (real_normed_field(X_a) -> (all F all X_1 all D_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),F),X_1),D_2)) <-> hBOOL(hAPP(filter(X_a),bool,hAPP(X_a,fun(filter(X_a),bool),hAPP(fun(X_a,X_a),fun(X_a,fun(filter(X_a),bool)),tendsto(X_a,X_a),hAPP(fun(X_a,X_a),fun(X_a,X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,X_a),fun(X_a,X_a)),combs(X_a,X_a,X_a),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,X_a),fun(X_a,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),X_a),inverse_divide(X_a)),hAPP(X_a,fun(X_a,X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(X_a,X_a)),combc(X_a,X_a,X_a),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,X_a),fun(X_a,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),X_a),minus_minus(X_a)),hAPP(fun(X_a,X_a),fun(X_a,X_a),hAPP(fun(X_a,X_a),fun(fun(X_a,X_a),fun(X_a,X_a)),combb(X_a,X_a,X_a),F),hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X_1)))),hAPP(X_a,X_a,F,X_1)))),combi(X_a))),D_2),hAPP(X_a,filter(X_a),at(X_a),zero_zero(X_a)))))))) # label(fact_4624_DERIV__iff) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.89 4552 (all X_a (real_normed_algebra(X_a) & banach(X_a) -> (all Ba all Aa (hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,X_a),fun(nat,real),hAPP(fun(X_a,real),fun(fun(nat,X_a),fun(nat,real)),combb(X_a,real,nat),norm_norm(X_a)),Aa))) -> (hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,X_a),fun(nat,real),hAPP(fun(X_a,real),fun(fun(nat,X_a),fun(nat,real)),combb(X_a,real,nat),norm_norm(X_a)),Ba))) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(fun(nat,X_a),X_a,suminf(X_a),Aa)),hAPP(fun(nat,X_a),X_a,suminf(X_a),Ba)) = hAPP(fun(nat,X_a),X_a,suminf(X_a),hAPP(fun(nat,fun(nat,bool)),fun(nat,X_a),hAPP(fun(nat,fun(fun(nat,bool),X_a)),fun(fun(nat,fun(nat,bool)),fun(nat,X_a)),combs(nat,fun(nat,bool),X_a),hAPP(fun(nat,fun(nat,X_a)),fun(nat,fun(fun(nat,bool),X_a)),hAPP(fun(fun(nat,X_a),fun(fun(nat,bool),X_a)),fun(fun(nat,fun(nat,X_a)),fun(nat,fun(fun(nat,bool),X_a))),combb(fun(nat,X_a),fun(fun(nat,bool),X_a),nat),big_co1399186613setsum(nat,X_a)),hAPP(fun(nat,fun(nat,X_a)),fun(nat,fun(nat,X_a)),hAPP(fun(fun(nat,X_a),fun(nat,X_a)),fun(fun(nat,fun(nat,X_a)),fun(nat,fun(nat,X_a))),combb(fun(nat,X_a),fun(nat,X_a),nat),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),times_times(X_a)),Aa))),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,X_a)),hAPP(fun(fun(nat,nat),fun(nat,X_a)),fun(fun(nat,fun(nat,nat)),fun(nat,fun(nat,X_a))),combb(fun(nat,nat),fun(nat,X_a),nat),hAPP(fun(nat,X_a),fun(fun(nat,nat),fun(nat,X_a)),combb(nat,X_a,nat),Ba)),minus_minus(nat))))),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),zero_zero(nat))))))))) # label(fact_4625_Cauchy__product) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.89 4553 (all X_a (comm_monoid_add(X_a) -> (all F all N hAPP(fun(product_prod(nat,nat),bool),X_a,hAPP(fun(product_prod(nat,nat),X_a),fun(fun(product_prod(nat,nat),bool),X_a),big_co1399186613setsum(product_prod(nat,nat),X_a),hAPP(fun(nat,fun(nat,X_a)),fun(product_prod(nat,nat),X_a),product_prod_case(nat,nat,X_a),F)),hAPP(fun(product_prod(nat,nat),bool),fun(product_prod(nat,nat),bool),collect(product_prod(nat,nat)),hAPP(fun(nat,fun(nat,bool)),fun(product_prod(nat,nat),bool),product_prod_case(nat,nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),hAPP(fun(nat,fun(nat,fun(nat,bool))),fun(nat,fun(nat,fun(nat,bool))),combc(nat,nat,fun(nat,bool)),hAPP(fun(nat,fun(nat,fun(nat,bool))),fun(nat,fun(nat,fun(nat,bool))),hAPP(fun(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool))),fun(fun(nat,fun(nat,fun(nat,bool))),fun(nat,fun(nat,fun(nat,bool)))),combb(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),nat),combc(nat,nat,bool)),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,fun(nat,bool))),hAPP(fun(fun(nat,nat),fun(nat,fun(nat,bool))),fun(fun(nat,fun(nat,nat)),fun(nat,fun(nat,fun(nat,bool)))),combb(fun(nat,nat),fun(nat,fun(nat,bool)),nat),hAPP(fun(nat,fun(nat,bool)),fun(fun(nat,nat),fun(nat,fun(nat,bool))),combb(nat,fun(nat,bool),nat),ord_less(nat))),plus_plus(nat)))),N)))) = hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),hAPP(fun(nat,fun(nat,bool)),fun(nat,X_a),hAPP(fun(nat,fun(fun(nat,bool),X_a)),fun(fun(nat,fun(nat,bool)),fun(nat,X_a)),combs(nat,fun(nat,bool),X_a),hAPP(fun(nat,fun(nat,X_a)),fun(nat,fun(fun(nat,bool),X_a)),hAPP(fun(fun(nat,X_a),fun(fun(nat,bool),X_a)),fun(fun(nat,fun(nat,X_a)),fun(nat,fun(fun(nat,bool),X_a))),combb(fun(nat,X_a),fun(fun(nat,bool),X_a),nat),big_co1399186613setsum(nat,X_a)),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,X_a)),hAPP(fun(fun(nat,nat),fun(nat,X_a)),fun(fun(nat,fun(nat,nat)),fun(nat,fun(nat,X_a))),combb(fun(nat,nat),fun(nat,X_a),nat),hAPP(fun(nat,fun(nat,X_a)),fun(fun(nat,nat),fun(nat,X_a)),combs(nat,nat,X_a),F)),minus_minus(nat)))),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),zero_zero(nat)))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),N))))) # label(fact_4626_setsum__triangle__reindex) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.89 4554 (all X_a (real_normed_algebra(X_a) & banach(X_a) -> (all Ba all Aa (hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,X_a),fun(nat,real),hAPP(fun(X_a,real),fun(fun(nat,X_a),fun(nat,real)),combb(X_a,real,nat),norm_norm(X_a)),Aa))) -> (hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,X_a),fun(nat,real),hAPP(fun(X_a,real),fun(fun(nat,X_a),fun(nat,real)),combb(X_a,real,nat),norm_norm(X_a)),Ba))) -> hBOOL(hAPP(X_a,bool,hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),hAPP(fun(nat,fun(nat,bool)),fun(nat,X_a),hAPP(fun(nat,fun(fun(nat,bool),X_a)),fun(fun(nat,fun(nat,bool)),fun(nat,X_a)),combs(nat,fun(nat,bool),X_a),hAPP(fun(nat,fun(nat,X_a)),fun(nat,fun(fun(nat,bool),X_a)),hAPP(fun(fun(nat,X_a),fun(fun(nat,bool),X_a)),fun(fun(nat,fun(nat,X_a)),fun(nat,fun(fun(nat,bool),X_a))),combb(fun(nat,X_a),fun(fun(nat,bool),X_a),nat),big_co1399186613setsum(nat,X_a)),hAPP(fun(nat,fun(nat,X_a)),fun(nat,fun(nat,X_a)),hAPP(fun(fun(nat,X_a),fun(nat,X_a)),fun(fun(nat,fun(nat,X_a)),fun(nat,fun(nat,X_a))),combb(fun(nat,X_a),fun(nat,X_a),nat),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),times_times(X_a)),Aa))),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,X_a)),hAPP(fun(fun(nat,nat),fun(nat,X_a)),fun(fun(nat,fun(nat,nat)),fun(nat,fun(nat,X_a))),combb(fun(nat,nat),fun(nat,X_a),nat),hAPP(fun(nat,X_a),fun(fun(nat,nat),fun(nat,X_a)),combb(nat,X_a,nat),Ba)),minus_minus(nat))))),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),zero_zero(nat)))),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(fun(nat,X_a),X_a,suminf(X_a),Aa)),hAPP(fun(nat,X_a),X_a,suminf(X_a),Ba))))))))) # label(fact_4627_Cauchy__product__sums) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.89 4555 (all X_b all X_a (real_normed_field(X_a) & banach(X_b) -> (all G all F all K (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),K)) -> (hBOOL(hAPP(fun(nat,real),bool,summable(real),F)) -> ((all H_1 all N_2 (ti(X_a,H_1) != zero_zero(X_a) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,norm_norm(X_a),H_1)),K)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_b,real,norm_norm(X_b),hAPP(nat,X_b,hAPP(X_a,fun(nat,X_b),G,H_1),N_2))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,F,N_2)),hAPP(X_a,real,norm_norm(X_a),H_1))))))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(fun(X_a,fun(nat,X_b)),fun(X_a,X_b),hAPP(fun(fun(nat,X_b),X_b),fun(fun(X_a,fun(nat,X_b)),fun(X_a,X_b)),combb(fun(nat,X_b),X_b,X_a),suminf(X_b)),G)),zero_zero(X_b)),hAPP(X_a,filter(X_a),at(X_a),zero_zero(X_a)))))))))) # label(fact_4629_lemma__termdiff5) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.89 4556 (all X_b all X_a (real_normed_field(X_a) & real_normed_vector(X_b) -> (all F all K_3 all K (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),K)) -> ((all H_1 (ti(X_a,H_1) != zero_zero(X_a) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,norm_norm(X_a),H_1)),K)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_b,real,norm_norm(X_b),hAPP(X_a,X_b,F,H_1))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),K_3),hAPP(X_a,real,norm_norm(X_a),H_1))))))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),zero_zero(X_b)),hAPP(X_a,filter(X_a),at(X_a),zero_zero(X_a))))))))) # label(fact_4630_lemma__termdiff4) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.89 4557 (all F all L all C_1 (hBOOL(hAPP(filter(real),bool,hAPP(real,fun(filter(real),bool),hAPP(fun(real,real),fun(real,fun(filter(real),bool)),tendsto(real,real),F),L),hAPP(real,filter(real),at(real),C_1))) -> (L != zero_zero(real) -> (exists R_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),R_2)) & (all X_2 (X_2 != C_1 & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),C_1),X_2))),R_2)) -> hAPP(real,real,F,X_2) != zero_zero(real)))))))) # label(fact_4631_LIM__fun__not__zero) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.89 4558 (all F all L all C_1 (hBOOL(hAPP(filter(real),bool,hAPP(real,fun(filter(real),bool),hAPP(fun(real,real),fun(real,fun(filter(real),bool)),tendsto(real,real),F),L),hAPP(real,filter(real),at(real),C_1))) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),L)) -> (exists R_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),R_2)) & (all X_2 (X_2 != C_1 & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),C_1),X_2))),R_2)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,F,X_2)))))))))) # label(fact_4632_LIM__fun__gt__zero) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.90 4559 (all F all L all C_1 (hBOOL(hAPP(filter(real),bool,hAPP(real,fun(filter(real),bool),hAPP(fun(real,real),fun(real,fun(filter(real),bool)),tendsto(real,real),F),L),hAPP(real,filter(real),at(real),C_1))) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),L),zero_zero(real))) -> (exists R_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),R_2)) & (all X_2 (X_2 != C_1 & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),C_1),X_2))),R_2)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,F,X_2)),zero_zero(real)))))))))) # label(fact_4633_LIM__fun__less__zero) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.90 4560 (all T_3 all A_2 all D_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D_2)) -> (all X_2 ((all Xa (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xa),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastAtMost(int),one_one(int)),D_2))) -> (all Xb (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xb),A_2)) -> X_2 != hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),Xb),Xa))))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),T_3),X_2)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),T_3),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X_2),D_2)))))))) # label(fact_4634_aset_I8_J) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.90 4561 (all T_3 all A_2 all D_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D_2)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),T_3),one_one(int))),A_2)) -> (all X_2 ((all Xa (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xa),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastAtMost(int),one_one(int)),D_2))) -> (all Xb (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xb),A_2)) -> X_2 != hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),Xb),Xa))))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X_2),T_3)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X_2),D_2)),T_3)))))))) # label(fact_4635_aset_I6_J) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.90 4562 (all T_3 all B_1 all D_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D_2)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),T_3),one_one(int))),B_1)) -> (all X_2 ((all Xa (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xa),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastAtMost(int),one_one(int)),D_2))) -> (all Xb (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xb),B_1)) -> X_2 != hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Xb),Xa))))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),T_3),X_2)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),T_3),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X_2),D_2))))))))) # label(fact_4636_bset_I8_J) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.90 4563 (all T_3 all B_1 all D_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D_2)) -> (all X_2 ((all Xa (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xa),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastAtMost(int),one_one(int)),D_2))) -> (all Xb (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xb),B_1)) -> X_2 != hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Xb),Xa))))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X_2),T_3)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X_2),D_2)),T_3))))))) # label(fact_4637_bset_I6_J) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.90 4564 (all X_a (metric_space(X_a) -> (all X_3 all L_2 all Aa ((all S_2 ((all N_2 hAPP(nat,real,S_2,N_2) != Aa) & hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),S_2),Aa),sequentially)) -> hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),hAPP(fun(nat,real),fun(nat,X_a),hAPP(fun(real,X_a),fun(fun(nat,real),fun(nat,X_a)),combb(real,X_a,nat),X_3),S_2)),L_2),sequentially)))) <-> hBOOL(hAPP(filter(real),bool,hAPP(X_a,fun(filter(real),bool),hAPP(fun(real,X_a),fun(X_a,fun(filter(real),bool)),tendsto(real,X_a),X_3),L_2),hAPP(real,filter(real),at(real),Aa))))))) # label(fact_4638_LIMSEQ__SEQ__conv) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.90 4565 (all T_3 all B_1 all D_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D_2)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),T_3),one_one(int))),B_1)) -> (all X_2 ((all Xa (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xa),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastAtMost(int),one_one(int)),D_2))) -> (all Xb (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xb),B_1)) -> X_2 != hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Xb),Xa))))) -> (X_2 = T_3 -> hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X_2),D_2) = T_3)))))) # label(fact_4639_bset_I3_J) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.90 4566 (all T_3 all A_2 all D_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D_2)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),T_3),one_one(int))),A_2)) -> (all X_2 ((all Xa (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xa),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastAtMost(int),one_one(int)),D_2))) -> (all Xb (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xb),A_2)) -> X_2 != hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),Xb),Xa))))) -> (X_2 = T_3 -> hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X_2),D_2) = T_3)))))) # label(fact_4640_aset_I3_J) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.90 4567 (all T_3 all A_2 all D_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D_2)) -> (all X_2 ((all Xa (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xa),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastAtMost(int),one_one(int)),D_2))) -> (all Xb (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xb),A_2)) -> X_2 != hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),Xb),Xa))))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),T_3),X_2)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),T_3),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X_2),D_2)))))))) # label(fact_4641_aset_I7_J) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.90 4568 (all T_3 all B_1 all D_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D_2)) -> (all X_2 ((all Xa (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xa),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastAtMost(int),one_one(int)),D_2))) -> (all Xb (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xb),B_1)) -> X_2 != hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Xb),Xa))))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X_2),T_3)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X_2),D_2)),T_3))))))) # label(fact_4642_bset_I5_J) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.90 4569 (all T_3 all A_2 all D_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D_2)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),T_3),A_2)) -> (all X_2 ((all Xa (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xa),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastAtMost(int),one_one(int)),D_2))) -> (all Xb (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xb),A_2)) -> X_2 != hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),Xb),Xa))))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X_2),T_3)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X_2),D_2)),T_3)))))))) # label(fact_4643_aset_I5_J) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.90 4570 (all T_3 all B_1 all D_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D_2)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),T_3),B_1)) -> (all X_2 ((all Xa (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xa),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastAtMost(int),one_one(int)),D_2))) -> (all Xb (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xb),B_1)) -> X_2 != hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Xb),Xa))))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),T_3),X_2)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),T_3),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X_2),D_2))))))))) # label(fact_4644_bset_I7_J) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.90 4571 (all T_3 all A_2 all D_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D_2)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),T_3),A_2)) -> (all X_2 ((all Xa (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xa),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastAtMost(int),one_one(int)),D_2))) -> (all Xb (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xb),A_2)) -> X_2 != hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),Xb),Xa))))) -> (X_2 != T_3 -> hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X_2),D_2) != T_3)))))) # label(fact_4645_aset_I4_J) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.90 4572 (all T_3 all B_1 all D_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D_2)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),T_3),B_1)) -> (all X_2 ((all Xa (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xa),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastAtMost(int),one_one(int)),D_2))) -> (all Xb (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xb),B_1)) -> X_2 != hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Xb),Xa))))) -> (X_2 != T_3 -> hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X_2),D_2) != T_3)))))) # label(fact_4646_bset_I4_J) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.90 4573 (all P_1 all D_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D_1)) -> ((all X_2 all K_1 (hBOOL(hAPP(int,bool,P_1,X_2)) <-> hBOOL(hAPP(int,bool,P_1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X_2),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K_1),D_1)))))) -> ((exists X1 hBOOL(hAPP(int,bool,P_1,X1))) <-> (exists X_2 (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_2),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastAtMost(int),one_one(int)),D_1))) & hBOOL(hAPP(int,bool,P_1,X_2)))))))) # label(fact_4647_periodic__finite__ex) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.90 4574 (all X_b all X_a (real_normed_vector(X_a) & real_normed_vector(X_b) -> (all F all L_2 all Aa (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),L_2),hAPP(X_a,filter(X_a),at(X_a),Aa))) <-> (all R_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),R_2)) -> (exists S_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),S_1)) & (all X_2 (ti(X_a,X_2) != ti(X_a,Aa) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),X_2),Aa))),S_1)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_b,real,norm_norm(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),hAPP(X_a,X_b,F,X_2)),L_2))),R_2)))))))))))) # label(fact_4648_LIM__eq) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.90 4575 (all X_b all X_a (real_normed_vector(X_a) & real_normed_vector(X_b) -> (all R_1 all F all L_2 all Aa (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),L_2),hAPP(X_a,filter(X_a),at(X_a),Aa))) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),R_1)) -> (exists S_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),S_1)) & (all X_2 (ti(X_a,X_2) != ti(X_a,Aa) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),X_2),Aa))),S_1)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_b,real,norm_norm(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),hAPP(X_a,X_b,F,X_2)),L_2))),R_1))))))))))) # label(fact_4649_LIM__D) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.90 4576 (all X_b all X_a (real_normed_vector(X_a) & topological_space(X_b) -> (all L all F all G all Aa all R_3 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),R_3)) -> ((all X_2 (ti(X_a,X_2) != ti(X_a,Aa) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),X_2),Aa))),R_3)) -> hAPP(X_a,X_b,F,X_2) = hAPP(X_a,X_b,G,X_2)))) -> (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),G),L),hAPP(X_a,filter(X_a),at(X_a),Aa))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),L),hAPP(X_a,filter(X_a),at(X_a),Aa))))))))) # label(fact_4650_LIM__equal2) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.90 4577 (all T_3 all A_2 all D_1 all D_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),D_1),D_2)) -> (all X_2 ((all Xa (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xa),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastAtMost(int),one_one(int)),D_2))) -> (all Xb (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xb),A_2)) -> X_2 != hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),Xb),Xa))))) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),D_1),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X_2),T_3))) -> -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),D_1),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X_2),D_2)),T_3)))))))) # label(fact_4651_aset_I10_J) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.90 4578 (all T_3 all B_1 all D_1 all D_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),D_1),D_2)) -> (all X_2 ((all Xa (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xa),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastAtMost(int),one_one(int)),D_2))) -> (all Xb (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xb),B_1)) -> X_2 != hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Xb),Xa))))) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),D_1),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X_2),T_3))) -> -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),D_1),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X_2),D_2)),T_3)))))))) # label(fact_4652_bset_I10_J) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.90 4579 (all T_3 all B_1 all D_1 all D_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),D_1),D_2)) -> (all X_2 ((all Xa (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xa),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastAtMost(int),one_one(int)),D_2))) -> (all Xb (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xb),B_1)) -> X_2 != hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Xb),Xa))))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),D_1),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X_2),T_3))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),D_1),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X_2),D_2)),T_3)))))))) # label(fact_4653_bset_I9_J) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.90 4580 (all T_3 all A_2 all D_1 all D_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),D_1),D_2)) -> (all X_2 ((all Xa (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xa),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastAtMost(int),one_one(int)),D_2))) -> (all Xb (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xb),A_2)) -> X_2 != hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),Xb),Xa))))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),D_1),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X_2),T_3))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),D_1),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X_2),D_2)),T_3)))))))) # label(fact_4654_aset_I9_J) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.90 4581 (all X_b all X_a (metric_space(X_a) & metric_space(X_b) -> (all R_1 all F all L_2 all Aa (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),L_2),hAPP(X_a,filter(X_a),at(X_a),Aa))) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),R_1)) -> (exists S_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),S_1)) & (all X_2 (ti(X_a,X_2) != ti(X_a,Aa) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),X_2),Aa)),S_1)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_b,real,hAPP(X_b,fun(X_b,real),dist_dist(X_b),hAPP(X_a,X_b,F,X_2)),L_2)),R_1))))))))))) # label(fact_4655_metric__LIM__D) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.90 4582 (all X_b all X_a (metric_space(X_a) & topological_space(X_b) -> (all L all F all G all Aa all R_3 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),R_3)) -> ((all X_2 (ti(X_a,X_2) != ti(X_a,Aa) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),X_2),Aa)),R_3)) -> hAPP(X_a,X_b,F,X_2) = hAPP(X_a,X_b,G,X_2)))) -> (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),G),L),hAPP(X_a,filter(X_a),at(X_a),Aa))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),L),hAPP(X_a,filter(X_a),at(X_a),Aa))))))))) # label(fact_4656_metric__LIM__equal2) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.90 4583 (all X_b all X_a (metric_space(X_a) & metric_space(X_b) -> (all F all L_2 all Aa (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),L_2),hAPP(X_a,filter(X_a),at(X_a),Aa))) <-> (all R_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),R_2)) -> (exists S_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),S_1)) & (all X_2 (ti(X_a,X_2) != ti(X_a,Aa) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),X_2),Aa)),S_1)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_b,real,hAPP(X_b,fun(X_b,real),dist_dist(X_b),hAPP(X_a,X_b,F,X_2)),L_2)),R_2)))))))))))) # label(fact_4657_LIM__def) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.90 4584 (all X_b all X_c all X_a (topological_space(X_a) & real_normed_vector(X_c) & real_normed_vector(X_b) -> (all G all M all F all L all Aa (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),L),hAPP(X_a,filter(X_a),at(X_a),Aa))) -> ((all X_2 (ti(X_a,X_2) != ti(X_a,Aa) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_c,real,norm_norm(X_c),hAPP(X_c,X_c,hAPP(X_c,fun(X_c,X_c),minus_minus(X_c),hAPP(X_a,X_c,G,X_2)),M))),hAPP(X_b,real,norm_norm(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),hAPP(X_a,X_b,F,X_2)),L)))))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_c,fun(filter(X_a),bool),hAPP(fun(X_a,X_c),fun(X_c,fun(filter(X_a),bool)),tendsto(X_a,X_c),G),M),hAPP(X_a,filter(X_a),at(X_a),Aa)))))))) # label(fact_4658_LIM__imp__LIM) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.90 4585 (all X_b all X_a (metric_space(X_a) & metric_space(X_b) -> (all X_3 all L_2 all Aa (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),X_3),L_2),hAPP(X_a,filter(X_a),at(X_a),Aa))) -> (all S_2 ((all N_2 hAPP(nat,X_a,S_2,N_2) != ti(X_a,Aa)) & hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),S_2),Aa),sequentially)) -> hBOOL(hAPP(filter(nat),bool,hAPP(X_b,fun(filter(nat),bool),hAPP(fun(nat,X_b),fun(X_b,fun(filter(nat),bool)),tendsto(nat,X_b),hAPP(fun(nat,X_a),fun(nat,X_b),hAPP(fun(X_a,X_b),fun(fun(nat,X_a),fun(nat,X_b)),combb(X_a,X_b,nat),X_3),S_2)),L_2),sequentially)))))))) # label(fact_4659_LIMSEQ__SEQ__conv1) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.90 4586 (all X_b all X_c all X_a (topological_space(X_a) & metric_space(X_c) & metric_space(X_b) -> (all G all M all F all L all Aa (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),L),hAPP(X_a,filter(X_a),at(X_a),Aa))) -> ((all X_2 (ti(X_a,X_2) != ti(X_a,Aa) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_c,real,hAPP(X_c,fun(X_c,real),dist_dist(X_c),hAPP(X_a,X_c,G,X_2)),M)),hAPP(X_b,real,hAPP(X_b,fun(X_b,real),dist_dist(X_b),hAPP(X_a,X_b,F,X_2)),L))))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_c,fun(filter(X_a),bool),hAPP(fun(X_a,X_c),fun(X_c,fun(filter(X_a),bool)),tendsto(X_a,X_c),G),M),hAPP(X_a,filter(X_a),at(X_a),Aa)))))))) # label(fact_4660_metric__LIM__imp__LIM) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.90 4587 (all X_a all X_b (real_normed_algebra(X_b) & comm_ring_1(X_b) -> (all X_3 all L_2 all S ((all N_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),N_2),S)) -> hBOOL(hAPP(filter(nat),bool,hAPP(X_b,fun(filter(nat),bool),hAPP(fun(nat,X_b),fun(X_b,fun(filter(nat),bool)),tendsto(nat,X_b),hAPP(X_a,fun(nat,X_b),X_3,N_2)),hAPP(X_a,X_b,L_2,N_2)),sequentially)))) -> hBOOL(hAPP(filter(nat),bool,hAPP(X_b,fun(filter(nat),bool),hAPP(fun(nat,X_b),fun(X_b,fun(filter(nat),bool)),tendsto(nat,X_b),hAPP(fun(X_a,bool),fun(nat,X_b),hAPP(fun(nat,fun(fun(X_a,bool),X_b)),fun(fun(X_a,bool),fun(nat,X_b)),combc(nat,fun(X_a,bool),X_b),hAPP(fun(nat,fun(X_a,X_b)),fun(nat,fun(fun(X_a,bool),X_b)),hAPP(fun(fun(X_a,X_b),fun(fun(X_a,bool),X_b)),fun(fun(nat,fun(X_a,X_b)),fun(nat,fun(fun(X_a,bool),X_b))),combb(fun(X_a,X_b),fun(fun(X_a,bool),X_b),nat),big_co302546470etprod(X_a,X_b)),hAPP(fun(X_a,fun(nat,X_b)),fun(nat,fun(X_a,X_b)),combc(X_a,nat,X_b),X_3))),S)),hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co302546470etprod(X_a,X_b),L_2),S)),sequentially)))))) # label(fact_4661_LIMSEQ__setprod) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.90 4588 (all X_a all X_b (real_normed_vector(X_b) -> (all X_3 all L_2 all S ((all N_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),N_2),S)) -> hBOOL(hAPP(filter(nat),bool,hAPP(X_b,fun(filter(nat),bool),hAPP(fun(nat,X_b),fun(X_b,fun(filter(nat),bool)),tendsto(nat,X_b),hAPP(X_a,fun(nat,X_b),X_3,N_2)),hAPP(X_a,X_b,L_2,N_2)),sequentially)))) -> hBOOL(hAPP(filter(nat),bool,hAPP(X_b,fun(filter(nat),bool),hAPP(fun(nat,X_b),fun(X_b,fun(filter(nat),bool)),tendsto(nat,X_b),hAPP(fun(X_a,bool),fun(nat,X_b),hAPP(fun(nat,fun(fun(X_a,bool),X_b)),fun(fun(X_a,bool),fun(nat,X_b)),combc(nat,fun(X_a,bool),X_b),hAPP(fun(nat,fun(X_a,X_b)),fun(nat,fun(fun(X_a,bool),X_b)),hAPP(fun(fun(X_a,X_b),fun(fun(X_a,bool),X_b)),fun(fun(nat,fun(X_a,X_b)),fun(nat,fun(fun(X_a,bool),X_b))),combb(fun(X_a,X_b),fun(fun(X_a,bool),X_b),nat),big_co1399186613setsum(X_a,X_b)),hAPP(fun(X_a,fun(nat,X_b)),fun(nat,fun(X_a,X_b)),combc(X_a,nat,X_b),X_3))),S)),hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),L_2),S)),sequentially)))))) # label(fact_4662_LIMSEQ__setsum) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.90 4589 (all X_a (real_normed_vector(X_a) -> (all X_3 all L_2 ((all R_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),R_2)) -> (exists No all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),No),N_2)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(nat,X_a,X_3,N_2)),L_2))),R_2)))))) -> hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),X_3),L_2),sequentially)))))) # label(fact_4663_LIMSEQ__I) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.90 4590 (all X_3 ((all R_2 exists N_3 all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_3),N_2)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),R_2),hAPP(nat,real,X_3,N_2))))) -> hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),inverse_inverse(real)),X_3)),zero_zero(real)),sequentially)))) # label(fact_4664_LIMSEQ__inverse__zero) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.90 4591 (all X_a (metric_space(X_a) -> (all X_3 all L_2 all Aa ((all S_2 ((all N_2 hAPP(nat,real,S_2,N_2) != Aa) & hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),S_2),Aa),sequentially)) -> hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),hAPP(fun(nat,real),fun(nat,X_a),hAPP(fun(real,X_a),fun(fun(nat,real),fun(nat,X_a)),combb(real,X_a,nat),X_3),S_2)),L_2),sequentially)))) -> hBOOL(hAPP(filter(real),bool,hAPP(X_a,fun(filter(real),bool),hAPP(fun(real,X_a),fun(X_a,fun(filter(real),bool)),tendsto(real,X_a),X_3),L_2),hAPP(real,filter(real),at(real),Aa))))))) # label(fact_4665_LIMSEQ__SEQ__conv2) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.90 4592 (all X_a (metric_space(X_a) -> (all X_3 all L_2 ((all R_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),R_2)) -> (exists No all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),No),N_2)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),hAPP(nat,X_a,X_3,N_2)),L_2)),R_2)))))) -> hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),X_3),L_2),sequentially)))))) # label(fact_4666_metric__LIMSEQ__I) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.90 4593 (all X_b all X_a (real_normed_vector(X_a) & real_normed_vector(X_b) -> (all F all L_2 all Aa ((all R_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),R_2)) -> (exists S_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),S_1)) & (all X_2 (ti(X_a,X_2) != ti(X_a,Aa) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),X_2),Aa))),S_1)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_b,real,norm_norm(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),hAPP(X_a,X_b,F,X_2)),L_2))),R_2)))))))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),L_2),hAPP(X_a,filter(X_a),at(X_a),Aa))))))) # label(fact_4667_LIM__I) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.90 4594 (all X_a (real_field(X_a) -> (all N all X_1 all Y_1 hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),hAPP(real,real,inverse_inverse(real),hAPP(nat,real,real_1(nat),hAPP(nat,nat,fact_fact(nat),N)))),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),plus_plus(X_a),X_1),Y_1)),N)) = hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),times_times(X_a)),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,real),fun(nat,fun(X_a,X_a)),hAPP(fun(real,fun(X_a,X_a)),fun(fun(nat,real),fun(nat,fun(X_a,X_a))),combb(real,fun(X_a,X_a),nat),scaleR_scaleR(X_a)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),inverse_inverse(real)),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),fact_fact(nat))))),hAPP(X_a,fun(nat,X_a),power_power(X_a),X_1)))),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,real),fun(nat,fun(X_a,X_a)),hAPP(fun(real,fun(X_a,X_a)),fun(fun(nat,real),fun(nat,fun(X_a,X_a))),combb(real,fun(X_a,X_a),nat),scaleR_scaleR(X_a)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),inverse_inverse(real)),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),hAPP(fun(nat,nat),fun(nat,nat),hAPP(fun(nat,nat),fun(fun(nat,nat),fun(nat,nat)),combb(nat,nat,nat),fact_fact(nat)),hAPP(nat,fun(nat,nat),minus_minus(nat),N)))))),hAPP(fun(nat,nat),fun(nat,X_a),hAPP(fun(nat,X_a),fun(fun(nat,nat),fun(nat,X_a)),combb(nat,X_a,nat),hAPP(X_a,fun(nat,X_a),power_power(X_a),Y_1)),hAPP(nat,fun(nat,nat),minus_minus(nat),N))))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),zero_zero(nat)),N))))) # label(fact_4668_exp__series__add) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.90 4595 (all X_a (real_normed_vector(X_a) -> (all A_1 all X hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_1),X)) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,abs_abs(real),A_1)),hAPP(X_a,real,norm_norm(X_a),X))))) # label(fact_4669_norm__scaleR) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.90 4596 (all X_a (real_vector(X_a) -> (all X hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),hAPP(int,real,number_number_of(real),min)),X) = hAPP(X_a,X_a,uminus_uminus(X_a),X)))) # label(fact_4670_scaleR__minus1__left) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.90 4597 (all X_a (real_normed_vector(X_a) -> (all X_1 all X_3 (hBOOL(hAPP(fun(nat,real),bool,cauchy(real),X_3)) -> hBOOL(hAPP(fun(nat,X_a),bool,cauchy(X_a),hAPP(X_a,fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(X_a,fun(nat,X_a)),combc(nat,X_a,X_a),hAPP(fun(nat,real),fun(nat,fun(X_a,X_a)),hAPP(fun(real,fun(X_a,X_a)),fun(fun(nat,real),fun(nat,fun(X_a,X_a))),combb(real,fun(X_a,X_a),nat),scaleR_scaleR(X_a)),X_3)),X_1))))))) # label(fact_4671_scaleR__left_OCauchy) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.90 4598 (all X_a (real_normed_vector(X_a) -> (all X all Y 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(real,fun(X_a,X_a),scaleR_scaleR(X_a),X),Y)),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(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,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),X),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),Y),B))),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),X),A_1)),B))),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),Y),B)))))) # label(fact_4672_scaleR_Oprod__diff__prod) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.90 4599 (all X_a (real_normed_vector(X_a) -> (all R_4 all X hAPP(X_a,X_a,sgn_sgn(X_a),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),R_4),X)) = hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),hAPP(real,real,sgn_sgn(real),R_4)),hAPP(X_a,X_a,sgn_sgn(X_a),X))))) # label(fact_4673_sgn__scaleR) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.90 4600 (all X_a (real_vector(X_a) -> (all X all Y all Xa_1 hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),X),Y)),Xa_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),X),Xa_1)),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),Y),Xa_1))))) # label(fact_4674_scaleR__left_Odiff) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.90 4601 (all X_a (real_normed_vector(X_a) -> (all A_1 all A_5 all B hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A_1),A_5)),B) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_1),B)),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_5),B))))) # label(fact_4675_scaleR_Odiff__left) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.90 4602 (all X_a (real_vector(X_a) -> (all A_1 all B all X hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A_1),B)),X) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_1),X)),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),B),X))))) # label(fact_4676_scaleR__left__diff__distrib) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.90 4603 (all X_a (real_vector(X_a) -> (all X all Y all Xa_1 hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),Y)),Xa_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),X),Xa_1)),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),Y),Xa_1))))) # label(fact_4677_scaleR__left_Oadd) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.90 4604 (all X_a (real_normed_vector(X_a) -> (all A_1 all A_5 all B hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A_1),A_5)),B) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_1),B)),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_5),B))))) # label(fact_4678_scaleR_Oadd__left) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.90 4605 (all X_a (real_vector(X_a) -> (all A_1 all B all X hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A_1),B)),X) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_1),X)),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),B),X))))) # label(fact_4679_real__vector_Oscale__left__distrib) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.90 4606 (all X_a (real_normed_vector(X_a) -> (all A_1 all B all B_4 hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B),B_4)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_1),B)),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_1),B_4))))) # label(fact_4680_scaleR_Oadd__right) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.90 4607 (all X_a (real_vector(X_a) -> (all A_1 all X all Y hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X),Y)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_1),X)),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_1),Y))))) # label(fact_4681_scaleR__right_Oadd) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.90 4608 (all X_a (real_normed_vector(X_a) -> (all A_1 all B all B_4 hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),B),B_4)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_1),B)),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_1),B_4))))) # label(fact_4682_scaleR_Odiff__right) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.90 4609 (all X_a (real_vector(X_a) -> (all A_1 all X all Y hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_1),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),minus_minus(X_a),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_1),X)),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_1),Y))))) # label(fact_4683_scaleR__right_Odiff) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.90 4610 (all X_a (real_vector(X_a) -> (all X hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),one_one(real)),X) = ti(X_a,X)))) # label(fact_4684_real__vector_Oscale__one) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.90 4611 (all X_a (real_vector(X_a) -> (all X all Y all A_1 (A_1 != zero_zero(real) -> (hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_1),X) = hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_1),Y) -> ti(X_a,X) = ti(X_a,Y)))))) # label(fact_4685_scaleR__left__imp__eq) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.90 4612 (all X_a (real_vector(X_a) -> (all Aa all X_1 all Y_1 (hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),Aa),X_1) = hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),Aa),Y_1) <-> ti(X_a,X_1) = ti(X_a,Y_1) | Aa = zero_zero(real))))) # label(fact_4686_scaleR__cancel__left) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.90 4613 (all X_a (real_vector(X_a) -> (all A_1 all B all X (ti(X_a,X) != zero_zero(X_a) -> (hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_1),X) = hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),B),X) -> A_1 = B))))) # label(fact_4687_scaleR__right__imp__eq) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.90 4614 (all X_a (real_vector(X_a) -> (all Aa all X_1 all Ba (hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),Aa),X_1) = hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),Ba),X_1) <-> Aa = Ba | ti(X_a,X_1) = zero_zero(X_a))))) # label(fact_4688_scaleR__cancel__right) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.90 4615 (all X_a (real_normed_vector(X_a) -> (all A_1 hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_1),zero_zero(X_a)) = zero_zero(X_a)))) # label(fact_4689_scaleR_Ozero__right) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.90 4616 (all X_a (real_vector(X_a) -> (all A_1 hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_1),zero_zero(X_a)) = zero_zero(X_a)))) # label(fact_4690_scaleR__right_Ozero) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.90 4617 (all X_a (real_vector(X_a) -> (all Aa all X_1 (hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),Aa),X_1) = zero_zero(X_a) <-> Aa = zero_zero(real) | ti(X_a,X_1) = zero_zero(X_a))))) # label(fact_4691_scaleR__eq__0__iff) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.90 4618 (all X_a (real_vector(X_a) -> (all X hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),zero_zero(real)),X) = zero_zero(X_a)))) # label(fact_4692_scaleR__left_Ozero) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.90 4619 (all X_a (real_normed_vector(X_a) -> (all B hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),zero_zero(real)),B) = zero_zero(X_a)))) # label(fact_4693_scaleR_Ozero__left) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.90 4620 (all X_a (real_normed_field(X_a) -> (all R_4 all X all Y hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),R_4),X)),Y) = hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),R_4),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),X),Y))))) # label(fact_4694_divide_OscaleR) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.90 4621 (all X_a (real_algebra_1(X_a) -> (all R_4 hAPP(real,X_a,of_real(X_a),R_4) = hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),R_4),one_one(X_a))))) # label(fact_4695_of__real__def) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.90 4622 (all X_a (real_algebra_1(X_a) & real_normed_vector(X_a) -> (all R_4 all X hAPP(real,X_a,of_real(X_a),hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),R_4),X)) = hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),R_4),hAPP(real,X_a,of_real(X_a),X))))) # label(fact_4696_of__real_OscaleR) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.90 4623 (all X_a (real_vector(X_a) -> (all A_1 all B all X hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_1),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),B),X)) = hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),B),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_1),X))))) # label(fact_4697_scaleR__left__commute) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.90 4624 (all X_a (real_normed_vector(X_a) -> (all A_1 all R_4 all B hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_1),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),R_4),B)) = hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),R_4),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_1),B))))) # label(fact_4698_scaleR_OscaleR__right) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.90 4625 (all X_a (real_normed_vector(X_a) -> (all Ra all R_4 all X hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),Ra),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),R_4),X)) = hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),R_4),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),Ra),X))))) # label(fact_4699_scaleR__right_OscaleR) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.90 4626 (all X_a (real_normed_vector(X_a) -> (all R_4 all A_1 all B hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),R_4),A_1)),B) = hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),R_4),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_1),B))))) # label(fact_4700_scaleR_OscaleR__left) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.90 4627 (all X_a (real_normed_vector(X_a) -> (all R_4 all X all Xa_1 hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),R_4),X)),Xa_1) = hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),R_4),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),X),Xa_1))))) # label(fact_4701_scaleR__left_OscaleR) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.90 4628 (all X_a all X_c all X_b (real_normed_vector(X_b) & real_normed_vector(X_c) & real_normed_vector(X_a) -> (all R_1 all Aa all Ba all Prod (hBOOL(hAPP(fun(X_a,fun(X_b,X_c)),bool,bounded_bilinear(X_a,X_b,X_c),Prod)) -> hAPP(X_b,X_c,hAPP(X_a,fun(X_b,X_c),Prod,hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),R_1),Aa)),Ba) = hAPP(X_c,X_c,hAPP(real,fun(X_c,X_c),scaleR_scaleR(X_c),R_1),hAPP(X_b,X_c,hAPP(X_a,fun(X_b,X_c),Prod,Aa),Ba)))))) # label(fact_4702_bounded__bilinear_OscaleR__left) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.90 4629 (all X_a all X_c all X_b (real_normed_vector(X_b) & real_normed_vector(X_c) & real_normed_vector(X_a) -> (all Aa all R_1 all Ba all Prod (hBOOL(hAPP(fun(X_a,fun(X_b,X_c)),bool,bounded_bilinear(X_a,X_b,X_c),Prod)) -> hAPP(X_b,X_c,hAPP(X_a,fun(X_b,X_c),Prod,Aa),hAPP(X_b,X_b,hAPP(real,fun(X_b,X_b),scaleR_scaleR(X_b),R_1),Ba)) = hAPP(X_c,X_c,hAPP(real,fun(X_c,X_c),scaleR_scaleR(X_c),R_1),hAPP(X_b,X_c,hAPP(X_a,fun(X_b,X_c),Prod,Aa),Ba)))))) # label(fact_4703_bounded__bilinear_OscaleR__right) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.90 4630 (all R_4 all X hAPP(complex,complex,cnj,hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),R_4),X)) = hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),R_4),hAPP(complex,complex,cnj,X))) # label(fact_4704_cnj_OscaleR) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.90 4631 (all R_4 all X hAPP(complex,real,re,hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),R_4),X)) = hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),R_4),hAPP(complex,real,re,X))) # label(fact_4705_Re_OscaleR) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.90 4632 (all R_4 all X hAPP(complex,real,im,hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),R_4),X)) = hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),R_4),hAPP(complex,real,im,X))) # label(fact_4706_Im_OscaleR) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.90 4633 (all X_a (real_normed_algebra(X_a) -> (all A_1 all R_4 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(real,fun(X_a,X_a),scaleR_scaleR(X_a),R_4),B)) = hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),R_4),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B))))) # label(fact_4707_mult_OscaleR__right) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.90 4634 (all X_a (real_algebra(X_a) -> (all X all A_1 all Y hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_1),Y)) = hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),Y))))) # label(fact_4708_mult__scaleR__right) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.90 4635 (all X_a (real_normed_algebra(X_a) -> (all Xa_1 all R_4 all X hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Xa_1),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),R_4),X)) = hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),R_4),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Xa_1),X))))) # label(fact_4709_mult__right_OscaleR) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.90 4636 (all X_a (real_algebra(X_a) -> (all A_1 all X all Y hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_1),X)),Y) = hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),Y))))) # label(fact_4710_mult__scaleR__left) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.90 4637 (all X_a (real_normed_algebra(X_a) -> (all R_4 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,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),R_4),A_1)),B) = hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),R_4),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B))))) # label(fact_4711_mult_OscaleR__left) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.90 4638 (all X_a (real_normed_algebra(X_a) -> (all R_4 all X all Y hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),R_4),X)),Y) = hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),R_4),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),Y))))) # label(fact_4712_mult__left_OscaleR) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.90 4639 (all A_1 all X hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),A_1),X) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A_1),X)) # label(fact_4713_real__scaleR__def) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.90 4640 (all X_a (real_vector(X_a) -> (all A_1 all B all X hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_1),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),B),X)) = hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A_1),B)),X)))) # label(fact_4714_real__vector_Oscale__scale) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.90 4641 (all X_a (real_algebra_1(X_a) -> (all R_4 all X hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),R_4),X) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(real,X_a,of_real(X_a),R_4)),X)))) # label(fact_4715_scaleR__conv__of__real) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.90 4642 (all R_4 all A_1 all B hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),R_4),hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,A_1),B)) = hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,hAPP(real,real,hAPP(real,fun(real,real),times_times(real),R_4),A_1)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),R_4),B))) # label(fact_4716_complex__scaleR) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.90 4643 (all R_4 all X hAPP(complex,real,im,hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),R_4),X)) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),R_4),hAPP(complex,real,im,X))) # label(fact_4717_complex__Im__scaleR) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.90 4644 (all R_4 all X hAPP(complex,real,re,hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),R_4),X)) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),R_4),hAPP(complex,real,re,X))) # label(fact_4718_complex__Re__scaleR) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.90 4645 (all X_a (real_normed_vector(X_a) -> (all A_1 all B hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_1),hAPP(X_a,X_a,uminus_uminus(X_a),B)) = hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_1),B))))) # label(fact_4719_scaleR_Ominus__right) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.90 4646 (all X_a (real_vector(X_a) -> (all A_1 all X hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_1),hAPP(X_a,X_a,uminus_uminus(X_a),X)) = hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_1),X))))) # label(fact_4720_scaleR__minus__right) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.90 4647 (all X_a (real_normed_vector(X_a) -> (all A_1 all B hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),hAPP(real,real,uminus_uminus(real),A_1)),B) = hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_1),B))))) # label(fact_4721_scaleR_Ominus__left) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.90 4648 (all X_a (real_vector(X_a) -> (all A_1 all X hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),hAPP(real,real,uminus_uminus(real),A_1)),X) = hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_1),X))))) # label(fact_4722_scaleR__minus__left) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.90 4649 (all X_a (real_vector(X_a) -> (all X all Xa_1 hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),hAPP(real,real,uminus_uminus(real),X)),Xa_1) = hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),X),Xa_1))))) # label(fact_4723_scaleR__left_Ominus) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.90 4650 (all X_a (divisi14063676e_zero(X_a) & real_div_algebra(X_a) -> (all A_1 all X hAPP(X_a,X_a,inverse_inverse(X_a),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_1),X)) = hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),hAPP(real,real,inverse_inverse(real),A_1)),hAPP(X_a,X_a,inverse_inverse(X_a),X))))) # label(fact_4724_inverse__scaleR__distrib) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.90 4651 (all X_a (real_normed_vector(X_a) -> hBOOL(hAPP(fun(X_a,fun(real,X_a)),bool,bounded_bilinear(X_a,real,X_a),hAPP(fun(real,fun(X_a,X_a)),fun(X_a,fun(real,X_a)),combc(real,X_a,X_a),scaleR_scaleR(X_a)))))) # label(fact_4725_scaleR_Oflip) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.90 4652 (all X_a (real_normed_vector(X_a) -> (all R_1 all X_3 (hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),X_3)) -> hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(X_a,X_a),fun(fun(nat,X_a),fun(nat,X_a)),combb(X_a,X_a,nat),hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),R_1)),X_3))))))) # label(fact_4726_scaleR__right_Osummable) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.90 4653 (all X_a (real_normed_vector(X_a) -> (all X_1 all X_3 (hBOOL(hAPP(fun(nat,real),bool,summable(real),X_3)) -> hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),hAPP(X_a,fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(X_a,fun(nat,X_a)),combc(nat,X_a,X_a),hAPP(fun(nat,real),fun(nat,fun(X_a,X_a)),hAPP(fun(real,fun(X_a,X_a)),fun(fun(nat,real),fun(nat,fun(X_a,X_a))),combb(real,fun(X_a,X_a),nat),scaleR_scaleR(X_a)),X_3)),X_1))))))) # label(fact_4727_scaleR__left_Osummable) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.90 4654 (all X_a (real_normed_vector(X_a) -> (all R_1 all X_3 (hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),X_3)) -> hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),R_1),hAPP(fun(nat,X_a),X_a,suminf(X_a),X_3)) = hAPP(fun(nat,X_a),X_a,suminf(X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(X_a,X_a),fun(fun(nat,X_a),fun(nat,X_a)),combb(X_a,X_a,nat),hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),R_1)),X_3)))))) # label(fact_4728_scaleR__right_Osuminf) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.90 4655 (all X_a (real_normed_vector(X_a) -> (all R_1 all X_3 (hBOOL(hAPP(fun(nat,X_a),bool,cauchy(X_a),X_3)) -> hBOOL(hAPP(fun(nat,X_a),bool,cauchy(X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(X_a,X_a),fun(fun(nat,X_a),fun(nat,X_a)),combb(X_a,X_a,nat),hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),R_1)),X_3))))))) # label(fact_4729_scaleR__right_OCauchy) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.90 4656 (all X_a (real_normed_vector(X_a) -> (all R_1 all X_3 all Aa (hBOOL(hAPP(X_a,bool,hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),X_3),Aa)) -> hBOOL(hAPP(X_a,bool,hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(X_a,X_a),fun(fun(nat,X_a),fun(nat,X_a)),combb(X_a,X_a,nat),hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),R_1)),X_3)),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),R_1),Aa))))))) # label(fact_4730_scaleR__right_Osums) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.90 4657 (all X_a (real_normed_vector(X_a) -> (all X_1 all X_3 all Aa (hBOOL(hAPP(real,bool,hAPP(fun(nat,real),fun(real,bool),sums(real),X_3),Aa)) -> hBOOL(hAPP(X_a,bool,hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),hAPP(X_a,fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(X_a,fun(nat,X_a)),combc(nat,X_a,X_a),hAPP(fun(nat,real),fun(nat,fun(X_a,X_a)),hAPP(fun(real,fun(X_a,X_a)),fun(fun(nat,real),fun(nat,fun(X_a,X_a))),combb(real,fun(X_a,X_a),nat),scaleR_scaleR(X_a)),X_3)),X_1)),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),Aa),X_1))))))) # label(fact_4731_scaleR__left_Osums) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.90 4658 (all X_a (sgn_div_norm(X_a) -> (all X hAPP(X_a,X_a,sgn_sgn(X_a),X) = hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),hAPP(real,real,inverse_inverse(real),hAPP(X_a,real,norm_norm(X_a),X))),X)))) # label(fact_4732_sgn__div__norm) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.90 4659 (all X_a all X_b (real_normed_vector(X_b) -> (all G all Ba all F all Aa all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(real,fun(filter(X_a),bool),hAPP(fun(X_a,real),fun(real,fun(filter(X_a),bool)),tendsto(X_a,real),F),Aa),A_2)) -> (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),G),Ba),A_2)) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(fun(X_a,X_b),fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,X_b)),combs(X_a,X_b,X_b),hAPP(fun(X_a,real),fun(X_a,fun(X_b,X_b)),hAPP(fun(real,fun(X_b,X_b)),fun(fun(X_a,real),fun(X_a,fun(X_b,X_b))),combb(real,fun(X_b,X_b),X_a),scaleR_scaleR(X_b)),F)),G)),hAPP(X_b,X_b,hAPP(real,fun(X_b,X_b),scaleR_scaleR(X_b),Aa),Ba)),A_2))))))) # label(fact_4733_scaleR_Otendsto) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.90 4660 (all X_a all X_b (real_normed_vector(X_b) -> (all X_1 all G all Aa all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(real,fun(filter(X_a),bool),hAPP(fun(X_a,real),fun(real,fun(filter(X_a),bool)),tendsto(X_a,real),G),Aa),A_2)) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(X_b,fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(X_b,fun(X_a,X_b)),combc(X_a,X_b,X_b),hAPP(fun(X_a,real),fun(X_a,fun(X_b,X_b)),hAPP(fun(real,fun(X_b,X_b)),fun(fun(X_a,real),fun(X_a,fun(X_b,X_b))),combb(real,fun(X_b,X_b),X_a),scaleR_scaleR(X_b)),G)),X_1)),hAPP(X_b,X_b,hAPP(real,fun(X_b,X_b),scaleR_scaleR(X_b),Aa),X_1)),A_2)))))) # label(fact_4734_scaleR__left_Otendsto) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.90 4661 (all X_a all X_b (real_normed_vector(X_b) -> (all R_1 all G all Aa all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),G),Aa),A_2)) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(fun(X_a,X_b),fun(X_a,X_b),hAPP(fun(X_b,X_b),fun(fun(X_a,X_b),fun(X_a,X_b)),combb(X_b,X_b,X_a),hAPP(real,fun(X_b,X_b),scaleR_scaleR(X_b),R_1)),G)),hAPP(X_b,X_b,hAPP(real,fun(X_b,X_b),scaleR_scaleR(X_b),R_1),Aa)),A_2)))))) # label(fact_4735_scaleR__right_Otendsto) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.90 4662 (all X_a (real_normed_vector(X_a) -> (all R_1 all X_3 all Aa (hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),X_3),Aa),sequentially)) -> hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(X_a,X_a),fun(fun(nat,X_a),fun(nat,X_a)),combb(X_a,X_a,nat),hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),R_1)),X_3)),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),R_1),Aa)),sequentially)))))) # label(fact_4736_scaleR__right_OLIMSEQ) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.90 4663 (all X_b all X_a (real_vector(X_a) -> (all Aa all G all A_2 hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),Aa),hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co1399186613setsum(X_b,X_a),G),A_2)) = hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co1399186613setsum(X_b,X_a),hAPP(fun(X_b,X_a),fun(X_b,X_a),hAPP(fun(X_a,X_a),fun(fun(X_b,X_a),fun(X_b,X_a)),combb(X_a,X_a,X_b),hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),Aa)),G)),A_2)))) # label(fact_4737_scaleR__right_Osetsum) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.90 4664 (all X_b all X_a (real_vector(X_a) -> (all G all A_2 all X_1 hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),hAPP(fun(X_b,bool),real,hAPP(fun(X_b,real),fun(fun(X_b,bool),real),big_co1399186613setsum(X_b,real),G),A_2)),X_1) = hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co1399186613setsum(X_b,X_a),hAPP(X_a,fun(X_b,X_a),hAPP(fun(X_b,fun(X_a,X_a)),fun(X_a,fun(X_b,X_a)),combc(X_b,X_a,X_a),hAPP(fun(X_b,real),fun(X_b,fun(X_a,X_a)),hAPP(fun(real,fun(X_a,X_a)),fun(fun(X_b,real),fun(X_b,fun(X_a,X_a))),combb(real,fun(X_a,X_a),X_b),scaleR_scaleR(X_a)),G)),X_1)),A_2)))) # label(fact_4738_scaleR__left_Osetsum) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.90 4665 (all X_a (real_normed_vector(X_a) -> (all R_1 all Aa hBOOL(hAPP(filter(X_a),bool,hAPP(X_a,fun(filter(X_a),bool),hAPP(fun(X_a,X_a),fun(X_a,fun(filter(X_a),bool)),tendsto(X_a,X_a),hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),R_1)),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),R_1),Aa)),hAPP(X_a,filter(X_a),at(X_a),Aa)))))) # label(fact_4739_scaleR__right_Ocont) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.90 4666 (all X_a (real_normed_vector(X_a) -> (all X_1 all Aa hBOOL(hAPP(filter(real),bool,hAPP(X_a,fun(filter(real),bool),hAPP(fun(real,X_a),fun(X_a,fun(filter(real),bool)),tendsto(real,X_a),hAPP(X_a,fun(real,X_a),hAPP(fun(real,fun(X_a,X_a)),fun(X_a,fun(real,X_a)),combc(real,X_a,X_a),scaleR_scaleR(X_a)),X_1)),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),Aa),X_1)),hAPP(real,filter(real),at(real),Aa)))))) # label(fact_4740_scaleR__left_Ocont) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.90 4667 (all X_b all X_a (topological_space(X_a) & real_normed_vector(X_b) -> (all R_1 all G all L all Aa (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),G),L),hAPP(X_a,filter(X_a),at(X_a),Aa))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(fun(X_a,X_b),fun(X_a,X_b),hAPP(fun(X_b,X_b),fun(fun(X_a,X_b),fun(X_a,X_b)),combb(X_b,X_b,X_a),hAPP(real,fun(X_b,X_b),scaleR_scaleR(X_b),R_1)),G)),hAPP(X_b,X_b,hAPP(real,fun(X_b,X_b),scaleR_scaleR(X_b),R_1),L)),hAPP(X_a,filter(X_a),at(X_a),Aa))))))) # label(fact_4741_scaleR__right_OLIM) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.90 4668 (all X_b all X_a (topological_space(X_a) & real_normed_vector(X_b) -> (all C_1 all F all Aa (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),zero_zero(X_b)),hAPP(X_a,filter(X_a),at(X_a),Aa))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(fun(X_a,X_b),fun(X_a,X_b),hAPP(fun(X_b,X_b),fun(fun(X_a,X_b),fun(X_a,X_b)),combb(X_b,X_b,X_a),hAPP(real,fun(X_b,X_b),scaleR_scaleR(X_b),C_1)),F)),zero_zero(X_b)),hAPP(X_a,filter(X_a),at(X_a),Aa))))))) # label(fact_4742_scaleR_OLIM__right__zero) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.90 4669 (all X_b all X_a (topological_space(X_a) & real_normed_vector(X_b) -> (all R_1 all G all Aa (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),G),zero_zero(X_b)),hAPP(X_a,filter(X_a),at(X_a),Aa))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(fun(X_a,X_b),fun(X_a,X_b),hAPP(fun(X_b,X_b),fun(fun(X_a,X_b),fun(X_a,X_b)),combb(X_b,X_b,X_a),hAPP(real,fun(X_b,X_b),scaleR_scaleR(X_b),R_1)),G)),zero_zero(X_b)),hAPP(X_a,filter(X_a),at(X_a),Aa))))))) # label(fact_4743_scaleR__right_OLIM__zero) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.90 4670 (all X_b all X_a (topological_space(X_a) & real_normed_vector(X_b) -> (all X_1 all G all L all Aa (hBOOL(hAPP(filter(X_a),bool,hAPP(real,fun(filter(X_a),bool),hAPP(fun(X_a,real),fun(real,fun(filter(X_a),bool)),tendsto(X_a,real),G),L),hAPP(X_a,filter(X_a),at(X_a),Aa))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(X_b,fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(X_b,fun(X_a,X_b)),combc(X_a,X_b,X_b),hAPP(fun(X_a,real),fun(X_a,fun(X_b,X_b)),hAPP(fun(real,fun(X_b,X_b)),fun(fun(X_a,real),fun(X_a,fun(X_b,X_b))),combb(real,fun(X_b,X_b),X_a),scaleR_scaleR(X_b)),G)),X_1)),hAPP(X_b,X_b,hAPP(real,fun(X_b,X_b),scaleR_scaleR(X_b),L),X_1)),hAPP(X_a,filter(X_a),at(X_a),Aa))))))) # label(fact_4744_scaleR__left_OLIM) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.90 4671 (all X_b all X_a (topological_space(X_a) & real_normed_vector(X_b) -> (all G all M_2 all F all L_2 all Aa (hBOOL(hAPP(filter(X_a),bool,hAPP(real,fun(filter(X_a),bool),hAPP(fun(X_a,real),fun(real,fun(filter(X_a),bool)),tendsto(X_a,real),F),L_2),hAPP(X_a,filter(X_a),at(X_a),Aa))) -> (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),G),M_2),hAPP(X_a,filter(X_a),at(X_a),Aa))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(fun(X_a,X_b),fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,X_b)),combs(X_a,X_b,X_b),hAPP(fun(X_a,real),fun(X_a,fun(X_b,X_b)),hAPP(fun(real,fun(X_b,X_b)),fun(fun(X_a,real),fun(X_a,fun(X_b,X_b))),combb(real,fun(X_b,X_b),X_a),scaleR_scaleR(X_b)),F)),G)),hAPP(X_b,X_b,hAPP(real,fun(X_b,X_b),scaleR_scaleR(X_b),L_2),M_2)),hAPP(X_a,filter(X_a),at(X_a),Aa)))))))) # label(fact_4745_LIM__scaleR) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.91 4672 (all X_a (real_normed_vector(X_a) -> (all Y_3 all Ba all X_3 all Aa (hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),X_3),Aa),sequentially)) -> (hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),Y_3),Ba),sequentially)) -> hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,real),fun(nat,fun(X_a,X_a)),hAPP(fun(real,fun(X_a,X_a)),fun(fun(nat,real),fun(nat,fun(X_a,X_a))),combb(real,fun(X_a,X_a),nat),scaleR_scaleR(X_a)),X_3)),Y_3)),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),Aa),Ba)),sequentially))))))) # label(fact_4746_scaleR_OLIMSEQ) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.91 4673 (all X_a (real_normed_vector(X_a) -> (all X_1 all X_3 all Aa (hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),X_3),Aa),sequentially)) -> hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),hAPP(X_a,fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(X_a,fun(nat,X_a)),combc(nat,X_a,X_a),hAPP(fun(nat,real),fun(nat,fun(X_a,X_a)),hAPP(fun(real,fun(X_a,X_a)),fun(fun(nat,real),fun(nat,fun(X_a,X_a))),combb(real,fun(X_a,X_a),nat),scaleR_scaleR(X_a)),X_3)),X_1)),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),Aa),X_1)),sequentially)))))) # label(fact_4747_scaleR__left_OLIMSEQ) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.91 4674 (all X_a (real_normed_vector(X_a) -> (all X_1 all X_3 (hBOOL(hAPP(fun(nat,real),bool,summable(real),X_3)) -> hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),hAPP(fun(nat,real),real,suminf(real),X_3)),X_1) = hAPP(fun(nat,X_a),X_a,suminf(X_a),hAPP(X_a,fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(X_a,fun(nat,X_a)),combc(nat,X_a,X_a),hAPP(fun(nat,real),fun(nat,fun(X_a,X_a)),hAPP(fun(real,fun(X_a,X_a)),fun(fun(nat,real),fun(nat,fun(X_a,X_a))),combb(real,fun(X_a,X_a),nat),scaleR_scaleR(X_a)),X_3)),X_1)))))) # label(fact_4748_scaleR__left_Osuminf) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.91 4675 (all X hAPP(complex,complex,sgn_sgn(complex),X) = hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),hAPP(real,real,inverse_inverse(real),hAPP(complex,real,norm_norm(complex),X))),X)) # label(fact_4749_complex__sgn__def) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.91 4676 (all X_a (real_div_algebra(X_a) -> (all X all A_1 (A_1 != zero_zero(real) -> (ti(X_a,X) != zero_zero(X_a) -> hAPP(X_a,X_a,inverse_inverse(X_a),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_1),X)) = hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),hAPP(real,real,inverse_inverse(real),A_1)),hAPP(X_a,X_a,inverse_inverse(X_a),X))))))) # label(fact_4750_nonzero__inverse__scaleR__distrib) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.91 4677 (all R_4 all X hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),R_4),X) = hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,hAPP(real,real,hAPP(real,fun(real,real),times_times(real),R_4),hAPP(complex,real,re,X))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),R_4),hAPP(complex,real,im,X)))) # label(fact_4751_complex__scaleR__def) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.91 4678 (all X_b all X_a (topological_space(X_a) & real_normed_vector(X_b) -> (all C_1 all F all Aa (hBOOL(hAPP(filter(X_a),bool,hAPP(real,fun(filter(X_a),bool),hAPP(fun(X_a,real),fun(real,fun(filter(X_a),bool)),tendsto(X_a,real),F),zero_zero(real)),hAPP(X_a,filter(X_a),at(X_a),Aa))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(X_b,fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(X_b,fun(X_a,X_b)),combc(X_a,X_b,X_b),hAPP(fun(X_a,real),fun(X_a,fun(X_b,X_b)),hAPP(fun(real,fun(X_b,X_b)),fun(fun(X_a,real),fun(X_a,fun(X_b,X_b))),combb(real,fun(X_b,X_b),X_a),scaleR_scaleR(X_b)),F)),C_1)),zero_zero(X_b)),hAPP(X_a,filter(X_a),at(X_a),Aa))))))) # label(fact_4752_scaleR_OLIM__left__zero) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.91 4679 (all X_b all X_a (topological_space(X_a) & real_normed_vector(X_b) -> (all X_1 all G all Aa (hBOOL(hAPP(filter(X_a),bool,hAPP(real,fun(filter(X_a),bool),hAPP(fun(X_a,real),fun(real,fun(filter(X_a),bool)),tendsto(X_a,real),G),zero_zero(real)),hAPP(X_a,filter(X_a),at(X_a),Aa))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(X_b,fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(X_b,fun(X_a,X_b)),combc(X_a,X_b,X_b),hAPP(fun(X_a,real),fun(X_a,fun(X_b,X_b)),hAPP(fun(real,fun(X_b,X_b)),fun(fun(X_a,real),fun(X_a,fun(X_b,X_b))),combb(real,fun(X_b,X_b),X_a),scaleR_scaleR(X_b)),G)),X_1)),zero_zero(X_b)),hAPP(X_a,filter(X_a),at(X_a),Aa))))))) # label(fact_4753_scaleR__left_OLIM__zero) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.91 4680 (all X_b all X_a (metric_space(X_a) & real_normed_vector(X_b) -> (all G all F all Aa (hBOOL(hAPP(filter(X_a),bool,hAPP(real,fun(filter(X_a),bool),hAPP(fun(X_a,real),fun(real,fun(filter(X_a),bool)),tendsto(X_a,real),F),zero_zero(real)),hAPP(X_a,filter(X_a),at(X_a),Aa))) -> (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),G),zero_zero(X_b)),hAPP(X_a,filter(X_a),at(X_a),Aa))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(fun(X_a,X_b),fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,X_b)),combs(X_a,X_b,X_b),hAPP(fun(X_a,real),fun(X_a,fun(X_b,X_b)),hAPP(fun(real,fun(X_b,X_b)),fun(fun(X_a,real),fun(X_a,fun(X_b,X_b))),combb(real,fun(X_b,X_b),X_a),scaleR_scaleR(X_b)),F)),G)),zero_zero(X_b)),hAPP(X_a,filter(X_a),at(X_a),Aa)))))))) # label(fact_4754_scaleR_OLIM__prod__zero) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.91 4681 (all X_a (real_n2089651433ebra_1(X_a) & banach(X_a) -> (all X_1 hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,real),fun(nat,fun(X_a,X_a)),hAPP(fun(real,fun(X_a,X_a)),fun(fun(nat,real),fun(nat,fun(X_a,X_a))),combb(real,fun(X_a,X_a),nat),scaleR_scaleR(X_a)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),inverse_inverse(real)),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),fact_fact(nat))))),hAPP(X_a,fun(nat,X_a),power_power(X_a),X_1))))))) # label(fact_4755_summable__exp__generic) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.91 4682 (all X_a (real_n2089651433ebra_1(X_a) & banach(X_a) -> (all X_1 hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,X_a),fun(nat,real),hAPP(fun(X_a,real),fun(fun(nat,X_a),fun(nat,real)),combb(X_a,real,nat),norm_norm(X_a)),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,real),fun(nat,fun(X_a,X_a)),hAPP(fun(real,fun(X_a,X_a)),fun(fun(nat,real),fun(nat,fun(X_a,X_a))),combb(real,fun(X_a,X_a),nat),scaleR_scaleR(X_a)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),inverse_inverse(real)),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),fact_fact(nat))))),hAPP(X_a,fun(nat,X_a),power_power(X_a),X_1)))))))) # label(fact_4756_summable__norm__exp) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.91 4683 (all X_a (real_normed_field(X_a) & banach(X_a) -> (all X_2 hAPP(X_a,X_a,exp(X_a),X_2) = hAPP(fun(nat,X_a),X_a,suminf(X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,real),fun(nat,fun(X_a,X_a)),hAPP(fun(real,fun(X_a,X_a)),fun(fun(nat,real),fun(nat,fun(X_a,X_a))),combb(real,fun(X_a,X_a),nat),scaleR_scaleR(X_a)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),inverse_inverse(real)),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),fact_fact(nat))))),hAPP(X_a,fun(nat,X_a),power_power(X_a),X_2)))))) # label(fact_4757_lemma__exp__ext) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.91 4684 (all X_a (real_normed_field(X_a) & banach(X_a) -> (all X_1 hAPP(X_a,X_a,exp(X_a),X_1) = hAPP(fun(nat,X_a),X_a,suminf(X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,real),fun(nat,fun(X_a,X_a)),hAPP(fun(real,fun(X_a,X_a)),fun(fun(nat,real),fun(nat,fun(X_a,X_a))),combb(real,fun(X_a,X_a),nat),scaleR_scaleR(X_a)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),inverse_inverse(real)),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),fact_fact(nat))))),hAPP(X_a,fun(nat,X_a),power_power(X_a),X_1)))))) # label(fact_4758_exp__def) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.91 4685 (all X_a (real_normed_field(X_a) & banach(X_a) -> (all X_1 hBOOL(hAPP(X_a,bool,hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,real),fun(nat,fun(X_a,X_a)),hAPP(fun(real,fun(X_a,X_a)),fun(fun(nat,real),fun(nat,fun(X_a,X_a))),combb(real,fun(X_a,X_a),nat),scaleR_scaleR(X_a)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),inverse_inverse(real)),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),fact_fact(nat))))),hAPP(X_a,fun(nat,X_a),power_power(X_a),X_1))),hAPP(X_a,X_a,exp(X_a),X_1)))))) # label(fact_4759_exp__converges) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.91 4686 (all X_a (real_normed_vector(X_a) -> (all X exists K_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),K_2)) & (all X_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),X_2),X))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,norm_norm(real),X_2)),K_2)))))))) # label(fact_4760_scaleR__left_Opos__bounded) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.91 4687 (all X_a (real_normed_vector(X_a) -> (exists K_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),K_2)) & (all A_3 all B_3 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_3),B_3))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,norm_norm(real),A_3)),hAPP(X_a,real,norm_norm(X_a),B_3))),K_2)))))))) # label(fact_4761_scaleR_Opos__bounded) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.91 4688 (all X_a (real_normed_vector(X_a) -> (exists K_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),K_2)) & (all A_3 all B_3 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_3),B_3))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,norm_norm(real),A_3)),hAPP(X_a,real,norm_norm(X_a),B_3))),K_2)))))))) # label(fact_4762_scaleR_Ononneg__bounded) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.91 4689 (all X_a (real_normed_vector(X_a) -> (all X exists K_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),K_2)) & (all X_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),X_2),X))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,norm_norm(real),X_2)),K_2)))))))) # label(fact_4763_scaleR__left_Ononneg__bounded) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.91 4690 (all X_a (real_normed_vector(X_a) -> (all R_4 exists K_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),K_2)) & (all X_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),R_4),X_2))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(X_a,real,norm_norm(X_a),X_2)),K_2)))))))) # label(fact_4764_scaleR__right_Opos__bounded) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.91 4691 (all X_a (real_normed_vector(X_a) -> (all X exists K_2 all X_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),X_2),X))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,norm_norm(real),X_2)),K_2)))))) # label(fact_4765_scaleR__left_Obounded) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.91 4692 (all X_a (real_normed_vector(X_a) -> (exists K_2 all A_3 all B_3 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_3),B_3))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,norm_norm(real),A_3)),hAPP(X_a,real,norm_norm(X_a),B_3))),K_2)))))) # label(fact_4766_scaleR_Obounded) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.91 4693 (all X_a (real_normed_vector(X_a) -> (all R_4 exists K_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),K_2)) & (all X_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),R_4),X_2))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(X_a,real,norm_norm(X_a),X_2)),K_2)))))))) # label(fact_4767_scaleR__right_Ononneg__bounded) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.91 4694 (all X_a (real_normed_vector(X_a) -> (all R_4 exists K_2 all X_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),R_4),X_2))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(X_a,real,norm_norm(X_a),X_2)),K_2)))))) # label(fact_4768_scaleR__right_Obounded) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.91 4695 (all X_b all X_a (topological_space(X_a) & topological_space(X_b) -> (all L all M all F all G all Aa all Ba (ti(X_a,Aa) = ti(X_a,Ba) -> ((all X_2 (ti(X_a,X_2) != ti(X_a,Ba) -> hAPP(X_a,X_b,F,X_2) = hAPP(X_a,X_b,G,X_2))) -> (ti(X_b,L) = ti(X_b,M) -> (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),L),hAPP(X_a,filter(X_a),at(X_a),Aa))) <-> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),G),M),hAPP(X_a,filter(X_a),at(X_a),Ba)))))))))) # label(fact_4769_LIM__cong) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.91 4696 (all X_b all X_a all X_c (real_normed_vector(X_c) -> (all F all Aa all A_2 all S ((all I_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),I_2),S)) -> hBOOL(hAPP(filter(X_b),bool,hAPP(X_c,fun(filter(X_b),bool),hAPP(fun(X_b,X_c),fun(X_c,fun(filter(X_b),bool)),tendsto(X_b,X_c),hAPP(X_a,fun(X_b,X_c),F,I_2)),hAPP(X_a,X_c,Aa,I_2)),A_2)))) -> hBOOL(hAPP(filter(X_b),bool,hAPP(X_c,fun(filter(X_b),bool),hAPP(fun(X_b,X_c),fun(X_c,fun(filter(X_b),bool)),tendsto(X_b,X_c),hAPP(fun(X_a,bool),fun(X_b,X_c),hAPP(fun(X_b,fun(fun(X_a,bool),X_c)),fun(fun(X_a,bool),fun(X_b,X_c)),combc(X_b,fun(X_a,bool),X_c),hAPP(fun(X_b,fun(X_a,X_c)),fun(X_b,fun(fun(X_a,bool),X_c)),hAPP(fun(fun(X_a,X_c),fun(fun(X_a,bool),X_c)),fun(fun(X_b,fun(X_a,X_c)),fun(X_b,fun(fun(X_a,bool),X_c))),combb(fun(X_a,X_c),fun(fun(X_a,bool),X_c),X_b),big_co1399186613setsum(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),F))),S)),hAPP(fun(X_a,bool),X_c,hAPP(fun(X_a,X_c),fun(fun(X_a,bool),X_c),big_co1399186613setsum(X_a,X_c),Aa),S)),A_2)))))) # label(fact_4770_tendsto__setsum) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.91 4697 (all X_b all X_a (metric_space(X_a) & metric_space(X_b) -> (all F all L_2 all Aa ((all R_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),R_2)) -> (exists S_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),S_1)) & (all X_2 (ti(X_a,X_2) != ti(X_a,Aa) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),X_2),Aa)),S_1)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_b,real,hAPP(X_b,fun(X_b,real),dist_dist(X_b),hAPP(X_a,X_b,F,X_2)),L_2)),R_2)))))))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),L_2),hAPP(X_a,filter(X_a),at(X_a),Aa))))))) # label(fact_4771_metric__LIM__I) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.91 4698 (all X_b all X_a (topological_space(X_a) & topological_space(X_b) -> (all L all F all G all Aa ((all X_2 (ti(X_a,X_2) != ti(X_a,Aa) -> hAPP(X_a,X_b,F,X_2) = hAPP(X_a,X_b,G,X_2))) -> (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),L),hAPP(X_a,filter(X_a),at(X_a),Aa))) <-> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),G),L),hAPP(X_a,filter(X_a),at(X_a),Aa)))))))) # label(fact_4773_LIM__equal) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.91 4699 (all X_a all X_b (t2_space(X_b) -> (all L_1 all F all L all A_2 (-hBOOL(hAPP(filter(X_a),bool,trivial_limit(X_a),A_2)) -> (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),L),A_2)) -> (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),L_1),A_2)) -> ti(X_b,L) = ti(X_b,L_1))))))) # label(fact_4774_tendsto__unique) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.91 4700 (all X_a all X_b (comm_monoid_mult(X_b) -> (all G all H all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2)) -> ((all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_2)) -> hAPP(X_a,X_b,G,X_2) = hAPP(X_a,X_b,H,X_2))) -> hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co302546470etprod(X_a,X_b),G),A_2) = hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co302546470etprod(X_a,X_b),H),A_2)))))) # label(fact_4776_setprod_Ocong) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.91 4701 (all X_a all X_b all X_c all Q_1 all P_1 all Z_1 (hBOOL(hAPP(X_a,bool,Q_1,hAPP(product_prod(X_b,X_c),X_a,hAPP(fun(X_b,fun(X_c,X_a)),fun(product_prod(X_b,X_c),X_a),product_prod_case(X_b,X_c,X_a),P_1),Z_1))) -> -(all X_2 all Y_2 (ti(product_prod(X_b,X_c),Z_1) = hAPP(X_c,product_prod(X_b,X_c),hAPP(X_b,fun(X_c,product_prod(X_b,X_c)),product_Pair(X_b,X_c),X_2),Y_2) -> -hBOOL(hAPP(X_a,bool,Q_1,hAPP(X_c,X_a,hAPP(X_b,fun(X_c,X_a),P_1,X_2),Y_2))))))) # label(fact_4777_splitE2) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.91 4702 (all X_c all X_b all X_a all Pa all F all G all Qa ((all X_2 all Y_2 (hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),X_2),Y_2) = ti(product_prod(X_a,X_b),Qa) -> hAPP(X_b,X_c,hAPP(X_a,fun(X_b,X_c),F,X_2),Y_2) = hAPP(X_b,X_c,hAPP(X_a,fun(X_b,X_c),G,X_2),Y_2))) -> (ti(product_prod(X_a,X_b),Pa) = ti(product_prod(X_a,X_b),Qa) -> hAPP(product_prod(X_a,X_b),X_c,hAPP(fun(X_a,fun(X_b,X_c)),fun(product_prod(X_a,X_b),X_c),product_prod_case(X_a,X_b,X_c),F),Pa) = hAPP(product_prod(X_a,X_b),X_c,hAPP(fun(X_a,fun(X_b,X_c)),fun(product_prod(X_a,X_b),X_c),product_prod_case(X_a,X_b,X_c),G),Qa)))) # label(fact_4778_split__cong) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.91 4703 (all X_a all X_b (comm_monoid_mult(X_b) -> (all F all F_1 ((all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),F_1)) -> hAPP(X_a,X_b,F,X_2) = one_one(X_b))) -> hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co302546470etprod(X_a,X_b),F),F_1) = one_one(X_b))))) # label(fact_4779_setprod__1_H) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.91 4704 (all X_a all X_b (comm_semiring_1(X_b) -> (all D_1 all F all A_2 ((all I_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),I_2),A_2)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),dvd_dvd(X_b),D_1),hAPP(X_a,X_b,F,I_2))))) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),dvd_dvd(X_b),D_1),hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),F),A_2))))))) # label(fact_4780_dvd__setsum) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.91 4705 (all X_a all X_b (comm_monoid_add(X_b) -> (all G all H all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2)) -> ((all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_2)) -> hAPP(X_a,X_b,G,X_2) = hAPP(X_a,X_b,H,X_2))) -> hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),G),A_2) = hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),H),A_2)))))) # label(fact_4781_setsum_Ocong) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.91 4706 (all X_a all X_b (comm_monoid_add(X_b) -> (all F all A_2 ((all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_2)) -> hAPP(X_a,X_b,F,X_2) = zero_zero(X_b))) -> hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),F),A_2) = zero_zero(X_b))))) # label(fact_4782_setsum__0_H) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.91 4707 (all X_a (topological_space(X_a) -> (all G all F all Aa (hBOOL(hAPP(filter(X_a),bool,hAPP(real,fun(filter(X_a),bool),hAPP(fun(X_a,real),fun(real,fun(filter(X_a),bool)),tendsto(X_a,real),F),zero_zero(real)),hAPP(X_a,filter(X_a),at(X_a),Aa))) -> ((all X_2 (ti(X_a,X_2) != ti(X_a,Aa) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(X_a,real,G,X_2))))) -> ((all X_2 (ti(X_a,X_2) != ti(X_a,Aa) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,G,X_2)),hAPP(X_a,real,F,X_2))))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(real,fun(filter(X_a),bool),hAPP(fun(X_a,real),fun(real,fun(filter(X_a),bool)),tendsto(X_a,real),G),zero_zero(real)),hAPP(X_a,filter(X_a),at(X_a),Aa))))))))) # label(fact_4783_real__LIM__sandwich__zero) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.91 4708 (all A_1 all B (hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),A_1),B) != zero_zero(int) -> (exists A_4 exists B_2 (A_1 = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_4),hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),A_1),B)) & B = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B_2),hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),A_1),B)) & hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),A_4),B_2) = one_one(int))))) # label(fact_4784_gcd__coprime__exists__int) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.91 4709 (all X_a all C_1 all P_1 ((exists X1 hBOOL(hAPP(X_a,bool,P_1,X1))) -> (ti(X_a,C_1) = hAPP(fun(X_a,bool),X_a,hilbert_Eps(X_a),P_1) -> hBOOL(hAPP(X_a,bool,P_1,C_1))))) # label(fact_4785_exE__some) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.91 4710 (all X_b all X_a (comm_monoid_mult(X_a) -> (all H all G all S all R_3 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),R_3,one_one(X_a)),one_one(X_a))) -> ((all X1 all Y1 all X2 all Y2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),R_3,X1),X2)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),R_3,Y1),Y2)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),R_3,hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X1),Y1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X2),Y2))))) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),S)) -> ((all X_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),S)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),R_3,hAPP(X_b,X_a,H,X_2)),hAPP(X_b,X_a,G,X_2))))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),R_3,hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co302546470etprod(X_b,X_a),H),S)),hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co302546470etprod(X_b,X_a),G),S)))))))))) # label(fact_4786_setprod_Orelated) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.91 4711 (all X_a all X_b all P_1 hAPP(fun(product_prod(X_a,X_b),bool),product_prod(X_a,X_b),hilbert_Eps(product_prod(X_a,X_b)),P_1) = hAPP(fun(product_prod(X_a,X_b),bool),product_prod(X_a,X_b),hilbert_Eps(product_prod(X_a,X_b)),hAPP(fun(X_a,fun(X_b,bool)),fun(product_prod(X_a,X_b),bool),product_prod_case(X_a,X_b,bool),hAPP(fun(X_a,fun(X_b,product_prod(X_a,X_b))),fun(X_a,fun(X_b,bool)),hAPP(fun(fun(X_b,product_prod(X_a,X_b)),fun(X_b,bool)),fun(fun(X_a,fun(X_b,product_prod(X_a,X_b))),fun(X_a,fun(X_b,bool))),combb(fun(X_b,product_prod(X_a,X_b)),fun(X_b,bool),X_a),hAPP(fun(product_prod(X_a,X_b),bool),fun(fun(X_b,product_prod(X_a,X_b)),fun(X_b,bool)),combb(product_prod(X_a,X_b),bool,X_b),P_1)),product_Pair(X_a,X_b))))) # label(fact_4787_split__paired__Eps) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.91 4712 (all X_a all X_b all X_1 all Y_1 hAPP(fun(product_prod(X_a,X_b),bool),product_prod(X_a,X_b),hilbert_Eps(product_prod(X_a,X_b)),hAPP(fun(X_a,fun(X_b,bool)),fun(product_prod(X_a,X_b),bool),product_prod_case(X_a,X_b,bool),hAPP(fun(X_b,bool),fun(X_a,fun(X_b,bool)),hAPP(fun(X_a,fun(fun(X_b,bool),fun(X_b,bool))),fun(fun(X_b,bool),fun(X_a,fun(X_b,bool))),combc(X_a,fun(X_b,bool),fun(X_b,bool)),hAPP(fun(X_a,fun(bool,bool)),fun(X_a,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_a,fun(bool,bool)),fun(X_a,fun(fun(X_b,bool),fun(X_b,bool)))),combb(fun(bool,bool),fun(fun(X_b,bool),fun(X_b,bool)),X_a),combb(bool,bool,X_b)),hAPP(fun(X_a,bool),fun(X_a,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,fun(bool,bool))),combb(bool,fun(bool,bool),X_a),fconj),hAPP(X_a,fun(X_a,bool),fequal(X_a),X_1)))),hAPP(X_b,fun(X_b,bool),fequal(X_b),Y_1)))) = hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),X_1),Y_1)) # label(fact_4788_Eps__split__eq) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.91 4713 (all X_a all X_b all P_1 hAPP(fun(product_prod(X_a,X_b),bool),product_prod(X_a,X_b),hilbert_Eps(product_prod(X_a,X_b)),hAPP(fun(X_a,fun(X_b,bool)),fun(product_prod(X_a,X_b),bool),product_prod_case(X_a,X_b,bool),P_1)) = hAPP(fun(product_prod(X_a,X_b),bool),product_prod(X_a,X_b),hilbert_Eps(product_prod(X_a,X_b)),hAPP(fun(product_prod(X_a,X_b),X_b),fun(product_prod(X_a,X_b),bool),hAPP(fun(product_prod(X_a,X_b),fun(X_b,bool)),fun(fun(product_prod(X_a,X_b),X_b),fun(product_prod(X_a,X_b),bool)),combs(product_prod(X_a,X_b),X_b,bool),hAPP(fun(product_prod(X_a,X_b),X_a),fun(product_prod(X_a,X_b),fun(X_b,bool)),hAPP(fun(X_a,fun(X_b,bool)),fun(fun(product_prod(X_a,X_b),X_a),fun(product_prod(X_a,X_b),fun(X_b,bool))),combb(X_a,fun(X_b,bool),product_prod(X_a,X_b)),P_1),product_fst(X_a,X_b))),product_snd(X_a,X_b)))) # label(fact_4789_Eps__split) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.91 4714 (all X_a all P_3 all X_2 (hBOOL(hAPP(X_a,bool,P_3,X_2)) -> hBOOL(hAPP(X_a,bool,P_3,hAPP(fun(X_a,bool),X_a,hilbert_Eps(X_a),P_3))))) # label(fact_4790_tfl__some) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.91 4715 (all X_a all P_1 all X_1 (hBOOL(hAPP(X_a,bool,P_1,X_1)) -> hBOOL(hAPP(X_a,bool,P_1,hAPP(fun(X_a,bool),X_a,hilbert_Eps(X_a),P_1))))) # label(fact_4791_someI) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.91 4716 (all X_a all P_1 ((exists X1 hBOOL(hAPP(X_a,bool,P_1,X1))) -> hBOOL(hAPP(X_a,bool,P_1,hAPP(fun(X_a,bool),X_a,hilbert_Eps(X_a),P_1))))) # label(fact_4792_someI__ex) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.91 4717 (all X_a all P_1 (hBOOL(hAPP(X_a,bool,P_1,hAPP(fun(X_a,bool),X_a,hilbert_Eps(X_a),P_1))) <-> (exists X1 hBOOL(hAPP(X_a,bool,P_1,X1))))) # label(fact_4793_some__eq__ex) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.91 4718 (all X_a all X_1 hAPP(fun(X_a,bool),X_a,hilbert_Eps(X_a),hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,fun(X_a,bool)),fun(X_a,fun(X_a,bool)),combc(X_a,X_a,bool),fequal(X_a)),X_1)) = ti(X_a,X_1)) # label(fact_4794_some__eq__trivial) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.91 4719 (all X_a all X_1 hAPP(fun(X_a,bool),X_a,hilbert_Eps(X_a),hAPP(X_a,fun(X_a,bool),fequal(X_a),X_1)) = ti(X_a,X_1)) # label(fact_4795_some__sym__eq__trivial) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.91 4720 (all X_a all P_1 all Aa (hBOOL(hAPP(X_a,bool,P_1,Aa)) -> ((all X_2 (hBOOL(hAPP(X_a,bool,P_1,X_2)) -> ti(X_a,X_2) = ti(X_a,Aa))) -> hAPP(fun(X_a,bool),X_a,hilbert_Eps(X_a),P_1) = ti(X_a,Aa)))) # label(fact_4796_some__equality) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.91 4721 (all X_a (order(X_a) -> (all X_1 all Y_1 all F (hBOOL(hAPP(fun(nat,X_a),bool,hAPP(fun(nat,fun(nat,bool)),fun(fun(nat,X_a),bool),strict_mono(nat,X_a),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),hAPP(fun(nat,fun(fun(nat,bool),fun(nat,bool))),fun(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool))),combs(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)),dvd_dvd(nat)))),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),hAPP(fun(fun(nat,bool),fun(nat,bool)),fun(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool))),combb(fun(nat,bool),fun(nat,bool),nat),hAPP(fun(bool,bool),fun(fun(nat,bool),fun(nat,bool)),combb(bool,bool,nat),fNot)),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),dvd_dvd(nat))))),F)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_1),Y_1)) & -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y_1),X_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,F,X_1)),hAPP(nat,X_a,F,Y_1)))))))) # label(fact_4797_dvd_Ostrict__monoD) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.91 4722 (all X_a (order(X_a) -> (all F ((all X_2 all Y_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_2),Y_2)) & -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y_2),X_2)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,F,X_2)),hAPP(nat,X_a,F,Y_2))))) -> hBOOL(hAPP(fun(nat,X_a),bool,hAPP(fun(nat,fun(nat,bool)),fun(fun(nat,X_a),bool),strict_mono(nat,X_a),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),hAPP(fun(nat,fun(fun(nat,bool),fun(nat,bool))),fun(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool))),combs(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)),dvd_dvd(nat)))),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),hAPP(fun(fun(nat,bool),fun(nat,bool)),fun(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool))),combb(fun(nat,bool),fun(nat,bool),nat),hAPP(fun(bool,bool),fun(fun(nat,bool),fun(nat,bool)),combb(bool,bool,nat),fNot)),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),dvd_dvd(nat))))),F)))))) # label(fact_4798_dvd_Ostrict__monoI) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.91 4723 (all X_a (order(X_a) -> (all F (hBOOL(hAPP(fun(nat,X_a),bool,hAPP(fun(nat,fun(nat,bool)),fun(fun(nat,X_a),bool),strict_mono(nat,X_a),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),hAPP(fun(nat,fun(fun(nat,bool),fun(nat,bool))),fun(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool))),combs(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)),dvd_dvd(nat)))),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),hAPP(fun(fun(nat,bool),fun(nat,bool)),fun(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool))),combb(fun(nat,bool),fun(nat,bool),nat),hAPP(fun(bool,bool),fun(fun(nat,bool),fun(nat,bool)),combb(bool,bool,nat),fNot)),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),dvd_dvd(nat))))),F)) -> hBOOL(hAPP(fun(nat,X_a),bool,hAPP(fun(nat,fun(nat,bool)),fun(fun(nat,X_a),bool),mono(nat,X_a),dvd_dvd(nat)),F)))))) # label(fact_4799_dvd_Ostrict__mono__mono) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.91 4724 (all X_a (order(X_a) -> (all X_1 all Y_1 all F (hBOOL(hAPP(fun(nat,X_a),bool,hAPP(fun(nat,fun(nat,bool)),fun(fun(nat,X_a),bool),mono(nat,X_a),dvd_dvd(nat)),F)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_1),Y_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(nat,X_a,F,X_1)),hAPP(nat,X_a,F,Y_1)))))))) # label(fact_4800_dvd_OmonoD) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.91 4725 (all X_a (order(X_a) -> (all F ((all X_2 all Y_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_2),Y_2)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(nat,X_a,F,X_2)),hAPP(nat,X_a,F,Y_2))))) -> hBOOL(hAPP(fun(nat,X_a),bool,hAPP(fun(nat,fun(nat,bool)),fun(fun(nat,X_a),bool),mono(nat,X_a),dvd_dvd(nat)),F)))))) # label(fact_4801_dvd_OmonoI) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.91 4726 (all X_b all X_a (comm_monoid_add(X_a) -> (all H all G all S all R_3 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),R_3,zero_zero(X_a)),zero_zero(X_a))) -> ((all X1 all Y1 all X2 all Y2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),R_3,X1),X2)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),R_3,Y1),Y2)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),R_3,hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X1),Y1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X2),Y2))))) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),S)) -> ((all X_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),S)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),R_3,hAPP(X_b,X_a,H,X_2)),hAPP(X_b,X_a,G,X_2))))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),R_3,hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co1399186613setsum(X_b,X_a),H),S)),hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co1399186613setsum(X_b,X_a),G),S)))))))))) # label(fact_4802_setsum_Orelated) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.91 4727 (all V_1 all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),hAPP(int,nat,number_number_of(nat),V_1)),hAPP(nat,nat,suc,N)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),hAPP(bool,fun(nat,fun(nat,nat)),if(nat),hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),hAPP(int,int,pred,V_1)))),zero_zero(nat)),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),hAPP(int,nat,nat_1,hAPP(int,int,number_number_of(int),hAPP(int,int,pred,V_1)))),N)))) # label(fact_4803_min__Suc__number__of) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.91 4728 (all N all V_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),hAPP(nat,nat,suc,N)),hAPP(int,nat,number_number_of(nat),V_1)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),hAPP(bool,fun(nat,fun(nat,nat)),if(nat),hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),hAPP(int,int,pred,V_1)))),zero_zero(nat)),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),N),hAPP(int,nat,nat_1,hAPP(int,int,number_number_of(int),hAPP(int,int,pred,V_1))))))) # label(fact_4804_min__number__of__Suc) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.91 4729 (all X_a (linorder(X_a) -> (all Z_1 all X_1 all Y_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X_1),Y_1))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z_1),X_1)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z_1),Y_1)))))) # label(fact_4805_min__less__iff__conj) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.91 4730 (all X_a (linorder(X_a) -> (all X_1 all Y_1 all Z_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X_1),Y_1)),Z_1)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Z_1)) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y_1),Z_1)))))) # label(fact_4806_min__less__iff__disj) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.91 4731 (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_4807_min__max_Oless__infI2) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.91 4732 (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_4808_min__max_Oless__infI1) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.91 4733 (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_4809_min__max_Oinf__assoc) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.91 4734 (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_4810_min__max_Oinf_Oassoc) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.91 4735 (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_4811_min__max_Oinf__left__commute) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.91 4736 (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_4812_min__max_Oinf_Oleft__commute) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.91 4737 (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_4813_min__max_Oinf__left__idem) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.91 4738 (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_4814_min__max_Oinf_Oleft__idem) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.91 4739 (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_4815_min__max_Oinf__commute) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.91 4740 (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_4816_min__max_Oinf_Ocommute) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.91 4741 (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_4817_min__max_Oinf_Oidem) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.91 4742 (all M_1 all N_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),hAPP(nat,nat,suc,M_1)),hAPP(nat,nat,suc,N_1)) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),M_1),N_1))) # label(fact_4818_min__Suc__Suc) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.91 4743 (all N_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),N_1),zero_zero(nat)) = zero_zero(nat)) # label(fact_4819_min__0R) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.91 4744 (all N_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),zero_zero(nat)),N_1) = zero_zero(nat)) # label(fact_4820_min__0L) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.91 4745 (all M_1 all I_1 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_1),I_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),I_1)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),M_1),N_1)),I_1)) # label(fact_4821_min__diff) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.91 4746 (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_4822_min__diff__distrib__left) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.91 4747 (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_4823_min__add__distrib__left) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.91 4748 (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_4824_Min_Oidem) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.91 4749 (all X_b (number(X_b) & ord(X_b) -> (all U all V ((hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(int,X_b,number_number_of(X_b),U)),hAPP(int,X_b,number_number_of(X_b),V))) -> hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),ord_min(X_b),hAPP(int,X_b,number_number_of(X_b),U)),hAPP(int,X_b,number_number_of(X_b),V)) = hAPP(int,X_b,number_number_of(X_b),U)) & (-hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(int,X_b,number_number_of(X_b),U)),hAPP(int,X_b,number_number_of(X_b),V))) -> hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),ord_min(X_b),hAPP(int,X_b,number_number_of(X_b),U)),hAPP(int,X_b,number_number_of(X_b),V)) = hAPP(int,X_b,number_number_of(X_b),V)))))) # label(fact_4825_min__number__of) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.91 4750 (all X_a (linorder(X_a) -> (all X_1 all Y_1 all Z_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X_1),Y_1)),Z_1)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),Z_1)) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y_1),Z_1)))))) # label(fact_4826_min__le__iff__disj) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.91 4751 (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_4827_min__max_Ole__infE) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.91 4752 (all X_a (linorder(X_a) -> (all B all D 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)) -> 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)))))))) # label(fact_4828_min__max_Oinf__mono) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.91 4753 (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_4829_min__max_Oinf__greatest) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.91 4754 (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_4830_min__max_Ole__infI) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.91 4755 (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_4831_min__max_Oinf__absorb2) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.91 4756 (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_4832_min__max_Oinf__absorb1) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.91 4757 (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_4833_min__max_Ole__infI2) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.91 4758 (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_4834_min__max_Ole__infI1) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.91 4759 (all X_a (linorder(X_a) -> (all X_1 all Y_1 all Z_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),Y_1),Z_1))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),Y_1)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),Z_1)))))) # label(fact_4835_min__max_Ole__inf__iff) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.91 4760 (all X_a (linorder(X_a) -> (all X_1 all Y_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),Y_1)) <-> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X_1),Y_1) = ti(X_a,X_1))))) # label(fact_4836_min__max_Ole__iff__inf) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.91 4761 (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_4837_min__max_Oinf__le2) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.91 4762 (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_4838_min__max_Oinf__le1) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.91 4763 (all M all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),M),hAPP(nat,nat,suc,N)) = hAPP(nat,nat,hAPP(fun(nat,nat),fun(nat,nat),hAPP(nat,fun(fun(nat,nat),fun(nat,nat)),nat_case(nat),zero_zero(nat)),hAPP(fun(nat,nat),fun(nat,nat),hAPP(fun(nat,nat),fun(fun(nat,nat),fun(nat,nat)),combb(nat,nat,nat),suc),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),ord_min(nat)),N))),M)) # label(fact_4839_min__Suc2) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.91 4764 (all N all M hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),hAPP(nat,nat,suc,N)),M) = hAPP(nat,nat,hAPP(fun(nat,nat),fun(nat,nat),hAPP(nat,fun(fun(nat,nat),fun(nat,nat)),nat_case(nat),zero_zero(nat)),hAPP(fun(nat,nat),fun(nat,nat),hAPP(fun(nat,nat),fun(fun(nat,nat),fun(nat,nat)),combb(nat,nat,nat),suc),hAPP(nat,fun(nat,nat),ord_min(nat),N))),M)) # label(fact_4840_min__Suc1) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.91 4765 (all X_a (linorder(X_a) -> hAPP(fun(X_a,fun(X_a,bool)),fun(X_a,fun(X_a,X_a)),max(X_a),hAPP(fun(X_a,fun(X_a,bool)),fun(X_a,fun(X_a,bool)),combc(X_a,X_a,bool),ord_less_eq(X_a))) = ord_min(X_a))) # label(fact_4841_dual__max) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.91 4766 (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_4842_min__leastL) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.91 4767 (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_4843_min__leastR) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.91 4768 (all X_a (ord(X_a) -> ord_min(X_a) = hAPP(fun(X_a,fun(X_a,bool)),fun(X_a,fun(X_a,X_a)),min_1(X_a),ord_less_eq(X_a)))) # label(fact_4844_min__ord__min) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.91 4769 (all Y_3 all X_3 ((exists A_3 (hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A_3)) & (all N_2 hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,abs_abs(rat),hAPP(nat,rat,X_3,N_2))),A_3))))) -> (hBOOL(hAPP(fun(nat,rat),bool,vanishes,Y_3)) -> hBOOL(hAPP(fun(nat,rat),bool,vanishes,hAPP(fun(nat,rat),fun(nat,rat),hAPP(fun(nat,fun(rat,rat)),fun(fun(nat,rat),fun(nat,rat)),combs(nat,rat,rat),hAPP(fun(nat,rat),fun(nat,fun(rat,rat)),hAPP(fun(rat,fun(rat,rat)),fun(fun(nat,rat),fun(nat,fun(rat,rat))),combb(rat,fun(rat,rat),nat),times_times(rat)),X_3)),Y_3)))))) # label(fact_4845_vanishes__mult__bounded) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.91 4770 (all N all M (hBOOL(hAPP(int,bool,nat_is_nat,M)) -> (hBOOL(hAPP(int,bool,nat_is_nat,N)) -> hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastAtMost(int),M),N) = 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)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(int,nat,nat_1,M)),hAPP(int,nat,nat_1,N)))))) # label(fact_4846_SetInterval_Otransfer__int__nat__set__functions) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.91 4771 (all X_1 (hBOOL(hAPP(int,bool,nat_is_nat,X_1)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X_1)))) # label(fact_4847_is__nat__def) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.91 4772 (all Z hBOOL(hAPP(int,bool,nat_is_nat,hAPP(nat,int,semiring_1_of_nat(int),Z)))) # label(fact_4848_Nat__Transfer_Otransfer__int__nat__function__closures_I9_J) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.91 4773 (all Y all X (hBOOL(hAPP(int,bool,nat_is_nat,X)) -> (hBOOL(hAPP(int,bool,nat_is_nat,Y)) -> hBOOL(hAPP(int,bool,nat_is_nat,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X),Y)))))) # label(fact_4849_Nat__Transfer_Otransfer__int__nat__function__closures_I1_J) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.91 4774 (all X_1 all A_2 (hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A_2)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),A_2)) -> hBOOL(hAPP(int,bool,nat_is_nat,X_1))))) # label(fact_4852_Nat__Transfer_Otransfer__int__nat__set__function__closures_I6_J) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.91 4775 (all N_1 all X (hBOOL(hAPP(int,bool,nat_is_nat,X)) -> hBOOL(hAPP(int,bool,nat_is_nat,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),X),N_1))))) # label(fact_4853_Nat__Transfer_Otransfer__int__nat__function__closures_I4_J) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.91 4776 (all Y all X (hBOOL(hAPP(int,bool,nat_is_nat,X)) -> (hBOOL(hAPP(int,bool,nat_is_nat,Y)) -> hBOOL(hAPP(int,bool,nat_is_nat,hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),X),Y)))))) # label(fact_4854_Divides_Otransfer__int__nat__function__closures_I2_J) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.91 4777 (all Y all X (hBOOL(hAPP(int,bool,nat_is_nat,X)) -> (hBOOL(hAPP(int,bool,nat_is_nat,Y)) -> hBOOL(hAPP(int,bool,nat_is_nat,hAPP(int,int,hAPP(int,fun(int,int),div_div(int),X),Y)))))) # label(fact_4855_Divides_Otransfer__int__nat__function__closures_I1_J) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.91 4778 (all Y all X (hBOOL(hAPP(int,bool,nat_is_nat,X)) -> (hBOOL(hAPP(int,bool,nat_is_nat,Y)) -> hBOOL(hAPP(int,bool,nat_is_nat,hAPP(int,int,hAPP(int,fun(int,int),nat_tsub,X),Y)))))) # label(fact_4856_Nat__Transfer_Otransfer__int__nat__function__closures_I3_J) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.91 4779 (all Y all X (hBOOL(hAPP(int,bool,nat_is_nat,X)) -> (hBOOL(hAPP(int,bool,nat_is_nat,Y)) -> hBOOL(hAPP(int,bool,nat_is_nat,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X),Y)))))) # label(fact_4857_Nat__Transfer_Otransfer__int__nat__function__closures_I2_J) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.91 4780 (all X_3 (hBOOL(hAPP(fun(nat,rat),bool,vanishes,X_3)) -> hBOOL(hAPP(fun(nat,rat),bool,vanishes,hAPP(fun(nat,rat),fun(nat,rat),hAPP(fun(rat,rat),fun(fun(nat,rat),fun(nat,rat)),combb(rat,rat,nat),uminus_uminus(rat)),X_3))))) # label(fact_4858_vanishes__minus) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.91 4781 (all C_1 (hBOOL(hAPP(fun(nat,rat),bool,vanishes,hAPP(rat,fun(nat,rat),combk(rat,nat),C_1))) <-> C_1 = zero_zero(rat))) # label(fact_4859_vanishes__const) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.91 4782 (all Y_3 all X_3 (hBOOL(hAPP(fun(nat,rat),bool,vanishes,X_3)) -> (hBOOL(hAPP(fun(nat,rat),bool,vanishes,Y_3)) -> hBOOL(hAPP(fun(nat,rat),bool,vanishes,hAPP(fun(nat,rat),fun(nat,rat),hAPP(fun(nat,fun(rat,rat)),fun(fun(nat,rat),fun(nat,rat)),combs(nat,rat,rat),hAPP(fun(nat,rat),fun(nat,fun(rat,rat)),hAPP(fun(rat,fun(rat,rat)),fun(fun(nat,rat),fun(nat,fun(rat,rat))),combb(rat,fun(rat,rat),nat),minus_minus(rat)),X_3)),Y_3)))))) # label(fact_4860_vanishes__diff) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.91 4783 (all Y_3 all X_3 (hBOOL(hAPP(fun(nat,rat),bool,vanishes,X_3)) -> (hBOOL(hAPP(fun(nat,rat),bool,vanishes,Y_3)) -> hBOOL(hAPP(fun(nat,rat),bool,vanishes,hAPP(fun(nat,rat),fun(nat,rat),hAPP(fun(nat,fun(rat,rat)),fun(fun(nat,rat),fun(nat,rat)),combs(nat,rat,rat),hAPP(fun(nat,rat),fun(nat,fun(rat,rat)),hAPP(fun(rat,fun(rat,rat)),fun(fun(nat,rat),fun(nat,fun(rat,rat))),combb(rat,fun(rat,rat),nat),plus_plus(rat)),X_3)),Y_3)))))) # label(fact_4861_vanishes__add) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.91 4784 (all Y_1 all X_1 (hBOOL(hAPP(int,bool,nat_is_nat,X_1)) -> hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastAtMost(int),X_1),Y_1))))) # label(fact_4862_SetInterval_Otransfer__int__nat__set__function__closures) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.91 4785 (all Y all X (hBOOL(hAPP(int,bool,nat_is_nat,X)) -> (hBOOL(hAPP(int,bool,nat_is_nat,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),gcd_gcd(int),X),Y)))))) # label(fact_4864_transfer__int__nat__gcd__closures_I1_J) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.91 4786 (all X (hBOOL(hAPP(int,bool,nat_is_nat,X)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,fact_fact(int),X))))) # label(fact_4865_transfer__int__nat__factorial__closure) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.91 4787 (all A_2 all X_1 (hBOOL(hAPP(int,bool,nat_is_nat,X_1)) -> (hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A_2)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),A_2)) <-> hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),hAPP(int,nat,nat_1,X_1)),hAPP(fun(int,bool),fun(nat,bool),hAPP(fun(int,nat),fun(fun(int,bool),fun(nat,bool)),image(int,nat),nat_1),A_2))))))) # label(fact_4866_transfer__int__nat__set__relations_I2_J) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.91 4788 (all X_a all F all A_2 ((all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_2)) -> hBOOL(hAPP(int,bool,nat_is_nat,hAPP(X_a,int,F,X_2))))) -> hAPP(fun(X_a,bool),int,hAPP(fun(X_a,int),fun(fun(X_a,bool),int),big_co302546470etprod(X_a,int),F),A_2) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(fun(X_a,bool),nat,hAPP(fun(X_a,nat),fun(fun(X_a,bool),nat),big_co302546470etprod(X_a,nat),hAPP(fun(X_a,int),fun(X_a,nat),hAPP(fun(int,nat),fun(fun(X_a,int),fun(X_a,nat)),combb(int,nat,X_a),nat_1),F)),A_2)))) # label(fact_4868_transfer__int__nat__sum__prod2_I2_J) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.91 4789 (all X_a all F all A_2 ((all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_2)) -> hBOOL(hAPP(int,bool,nat_is_nat,hAPP(X_a,int,F,X_2))))) -> hAPP(fun(X_a,bool),int,hAPP(fun(X_a,int),fun(fun(X_a,bool),int),big_co1399186613setsum(X_a,int),F),A_2) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(fun(X_a,bool),nat,hAPP(fun(X_a,nat),fun(fun(X_a,bool),nat),big_co1399186613setsum(X_a,nat),hAPP(fun(X_a,int),fun(X_a,nat),hAPP(fun(int,nat),fun(fun(X_a,int),fun(X_a,nat)),combb(int,nat,X_a),nat_1),F)),A_2)))) # label(fact_4869_transfer__int__nat__sum__prod2_I1_J) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.91 4790 (all R_1 all X_3 (hBOOL(hAPP(fun(nat,rat),bool,vanishes,X_3)) -> (hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),R_1)) -> (exists K_1 all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_1),N_2)) -> hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,abs_abs(rat),hAPP(nat,rat,X_3,N_2))),R_1))))))) # label(fact_4870_vanishesD) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.91 4791 (all X_3 (hBOOL(hAPP(fun(nat,rat),bool,vanishes,X_3)) <-> (all R_2 (hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),R_2)) -> (exists K_1 all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_1),N_2)) -> hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,abs_abs(rat),hAPP(nat,rat,X_3,N_2))),R_2)))))))) # label(fact_4871_vanishes__def) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.91 4792 (all X_3 ((all R_2 (hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),R_2)) -> (exists K_1 all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_1),N_2)) -> hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,abs_abs(rat),hAPP(nat,rat,X_3,N_2))),R_2)))))) -> hBOOL(hAPP(fun(nat,rat),bool,vanishes,X_3)))) # label(fact_4872_vanishesI) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.92 4793 (all X_a all Q_1 all P_1 (hBOOL(hAPP(X_a,bool,P_1,hAPP(fun(X_a,bool),X_a,hilbert_Eps(X_a),P_1))) -> (hBOOL(hAPP(X_a,bool,Q_1,hAPP(fun(X_a,bool),X_a,hilbert_Eps(X_a),Q_1))) -> (hAPP(fun(X_a,bool),X_a,hilbert_Eps(X_a),P_1) = hAPP(fun(X_a,bool),X_a,hilbert_Eps(X_a),Q_1) -> (exists A_3 (hBOOL(hAPP(X_a,bool,P_1,A_3)) & hBOOL(hAPP(X_a,bool,Q_1,A_3)))))))) # label(fact_4873_EulerFermat_Oaux) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.92 4794 (all X_a all Q_1 all P_1 all Aa (hBOOL(hAPP(X_a,bool,P_1,Aa)) -> ((all X_2 (hBOOL(hAPP(X_a,bool,P_1,X_2)) -> hBOOL(hAPP(X_a,bool,Q_1,X_2)))) -> hBOOL(hAPP(X_a,bool,Q_1,hAPP(fun(X_a,bool),X_a,hilbert_Eps(X_a),P_1)))))) # label(fact_4874_someI2) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.92 4795 (all X_a all Aa all P_1 ((exists X_2 (hBOOL(hAPP(X_a,bool,P_1,X_2)) & (all Y_2 (hBOOL(hAPP(X_a,bool,P_1,Y_2)) -> ti(X_a,Y_2) = ti(X_a,X_2))))) -> (hBOOL(hAPP(X_a,bool,P_1,Aa)) -> hAPP(fun(X_a,bool),X_a,hilbert_Eps(X_a),P_1) = ti(X_a,Aa)))) # label(fact_4875_some1__equality) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.92 4796 (all X_a all Q_1 all P_1 ((exists X1 hBOOL(hAPP(X_a,bool,P_1,X1))) -> ((all X_2 (hBOOL(hAPP(X_a,bool,P_1,X_2)) -> hBOOL(hAPP(X_a,bool,Q_1,X_2)))) -> hBOOL(hAPP(X_a,bool,Q_1,hAPP(fun(X_a,bool),X_a,hilbert_Eps(X_a),P_1)))))) # label(fact_4876_someI2__ex) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.92 4797 (all X_a all A_2 all B_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_2),B_1)) -> hBOOL(hAPP(fun(fun(X_a,bool),bool),bool,hAPP(fun(fun(X_a,bool),bool),fun(fun(fun(X_a,bool),bool),bool),ord_less_eq(fun(fun(X_a,bool),bool)),hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),powp(X_a),A_2)),hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),powp(X_a),B_1))))) # label(fact_4877_Powp__mono) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.92 4798 (all X_a all A_2 all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),powp(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(X_a,bool)),combc(X_a,fun(X_a,bool),bool),member(X_a)),A_2)),X_2)) <-> hBOOL(hAPP(fun(fun(X_a,bool),bool),bool,hAPP(fun(X_a,bool),fun(fun(fun(X_a,bool),bool),bool),member(fun(X_a,bool)),X_2),hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),pow(X_a),A_2))))) # label(fact_4878_Powp__Pow__eq) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.92 4799 (all M all X_2 all Xa (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcongm,M),X_2),Xa)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,X_2),Xa),M)))) # label(fact_4879_zcongm__def) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.92 4800 (all A_2 all P_2 all P_1 all D_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D_2)) -> ((exists Z_2 all X_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Z_2),X_2)) -> (hBOOL(hAPP(int,bool,P_1,X_2)) <-> hBOOL(hAPP(int,bool,P_2,X_2))))) -> ((all X_2 ((all Xa (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xa),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastAtMost(int),one_one(int)),D_2))) -> (all Xb (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xb),A_2)) -> X_2 != hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),Xb),Xa))))) -> (hBOOL(hAPP(int,bool,P_1,X_2)) -> hBOOL(hAPP(int,bool,P_1,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X_2),D_2)))))) -> ((all X_2 all K_1 (hBOOL(hAPP(int,bool,P_2,X_2)) <-> hBOOL(hAPP(int,bool,P_2,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X_2),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K_1),D_2)))))) -> ((exists X1 hBOOL(hAPP(int,bool,P_1,X1))) <-> (exists X_2 (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_2),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastAtMost(int),one_one(int)),D_2))) & hBOOL(hAPP(int,bool,P_2,X_2)))) | (exists X_2 (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_2),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastAtMost(int),one_one(int)),D_2))) & (exists Xa (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xa),A_2)) & hBOOL(hAPP(int,bool,P_1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),Xa),X_2))))))))))))) # label(fact_4880_cppi) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.92 4801 (all A_2 all B_1 all M (hBOOL(hAPP(fun(product_prod(fun(int,bool),fun(int,bool)),bool),bool,hAPP(product_prod(fun(int,bool),fun(int,bool)),fun(fun(product_prod(fun(int,bool),fun(int,bool)),bool),bool),member(product_prod(fun(int,bool),fun(int,bool))),hAPP(fun(int,bool),product_prod(fun(int,bool),fun(int,bool)),hAPP(fun(int,bool),fun(fun(int,bool),product_prod(fun(int,bool),fun(int,bool))),product_Pair(fun(int,bool),fun(int,bool)),A_2),B_1)),hAPP(fun(int,fun(int,bool)),fun(product_prod(fun(int,bool),fun(int,bool)),bool),bijR(int,int),hAPP(int,fun(int,fun(int,bool)),zcongm,M)))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(fun(int,bool),int,hAPP(fun(int,int),fun(fun(int,bool),int),big_co302546470etprod(int,int),combi(int)),A_2)),hAPP(fun(int,bool),int,hAPP(fun(int,int),fun(fun(int,bool),int),big_co302546470etprod(int,int),combi(int)),B_1)),M)))) # label(fact_4881_bijzcong__zcong__prod) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.92 4802 (all B_1 all P_2 all P_1 all D_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D_2)) -> ((exists Z_2 all X_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X_2),Z_2)) -> (hBOOL(hAPP(int,bool,P_1,X_2)) <-> hBOOL(hAPP(int,bool,P_2,X_2))))) -> ((all X_2 ((all Xa (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xa),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastAtMost(int),one_one(int)),D_2))) -> (all Xb (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xb),B_1)) -> X_2 != hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Xb),Xa))))) -> (hBOOL(hAPP(int,bool,P_1,X_2)) -> hBOOL(hAPP(int,bool,P_1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X_2),D_2)))))) -> ((all X_2 all K_1 (hBOOL(hAPP(int,bool,P_2,X_2)) <-> hBOOL(hAPP(int,bool,P_2,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X_2),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K_1),D_2)))))) -> ((exists X1 hBOOL(hAPP(int,bool,P_1,X1))) <-> (exists X_2 (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_2),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastAtMost(int),one_one(int)),D_2))) & hBOOL(hAPP(int,bool,P_2,X_2)))) | (exists X_2 (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_2),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastAtMost(int),one_one(int)),D_2))) & (exists Xa (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xa),B_1)) & hBOOL(hAPP(int,bool,P_1,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Xa),X_2))))))))))))) # label(fact_4882_cpmi) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.92 4803 (all X_a all X_b all A_2 all B_1 all P_1 (hBOOL(hAPP(fun(product_prod(fun(X_a,bool),fun(X_b,bool)),bool),bool,hAPP(product_prod(fun(X_a,bool),fun(X_b,bool)),fun(fun(product_prod(fun(X_a,bool),fun(X_b,bool)),bool),bool),member(product_prod(fun(X_a,bool),fun(X_b,bool))),hAPP(fun(X_b,bool),product_prod(fun(X_a,bool),fun(X_b,bool)),hAPP(fun(X_a,bool),fun(fun(X_b,bool),product_prod(fun(X_a,bool),fun(X_b,bool))),product_Pair(fun(X_a,bool),fun(X_b,bool)),A_2),B_1)),hAPP(fun(X_a,fun(X_b,bool)),fun(product_prod(fun(X_a,bool),fun(X_b,bool)),bool),bijR(X_a,X_b),P_1))) -> hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2)))) # label(fact_4883_fin__bijRl) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.92 4804 (all X_a all X_b all A_2 all B_1 all P_1 (hBOOL(hAPP(fun(product_prod(fun(X_a,bool),fun(X_b,bool)),bool),bool,hAPP(product_prod(fun(X_a,bool),fun(X_b,bool)),fun(fun(product_prod(fun(X_a,bool),fun(X_b,bool)),bool),bool),member(product_prod(fun(X_a,bool),fun(X_b,bool))),hAPP(fun(X_b,bool),product_prod(fun(X_a,bool),fun(X_b,bool)),hAPP(fun(X_a,bool),fun(fun(X_b,bool),product_prod(fun(X_a,bool),fun(X_b,bool))),product_Pair(fun(X_a,bool),fun(X_b,bool)),A_2),B_1)),hAPP(fun(X_a,fun(X_b,bool)),fun(product_prod(fun(X_a,bool),fun(X_b,bool)),bool),bijR(X_a,X_b),P_1))) -> hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),B_1)))) # label(fact_4884_fin__bijRr) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.92 4805 (all L all F ((all N_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,F,N_2)),hAPP(nat,real,F,hAPP(nat,nat,suc,N_2))))) -> ((all N_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,F,N_2)),L))) -> ((all E (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),E)) -> (exists N_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),L),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,F,N_2)),E)))))) -> hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),F),L),sequentially)))))) # label(fact_4885_increasing__LIMSEQ) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.92 4806 (all X_c all X_b all X_a (real_normed_vector(X_a) & topological_space(X_b) & topological_space(X_c) -> (all G all L all F all Aa (hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,X_b),fun(X_a,bool),isCont(X_a,X_b),F),Aa)) -> (hBOOL(hAPP(filter(X_b),bool,hAPP(X_c,fun(filter(X_b),bool),hAPP(fun(X_b,X_c),fun(X_c,fun(filter(X_b),bool)),tendsto(X_b,X_c),G),L),hAPP(X_b,filter(X_b),at(X_b),hAPP(X_a,X_b,F,Aa)))) -> ((exists D_3 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),D_3)) & (all X_2 (ti(X_a,X_2) != ti(X_a,Aa) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),X_2),Aa))),D_3)) -> hAPP(X_a,X_b,F,X_2) != hAPP(X_a,X_b,F,Aa))))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_c,fun(filter(X_a),bool),hAPP(fun(X_a,X_c),fun(X_c,fun(filter(X_a),bool)),tendsto(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),G),F)),L),hAPP(X_a,filter(X_a),at(X_a),Aa))))))))) # label(fact_4886_isCont__LIM__compose2) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.92 4807 (all X_a all X_b all X_c (topological_space(X_c) & topological_space(X_b) & topological_space(X_a) -> (all F all Aa all G all L (hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,X_b),fun(X_a,bool),isCont(X_a,X_b),G),L)) -> (hBOOL(hAPP(filter(X_c),bool,hAPP(X_a,fun(filter(X_c),bool),hAPP(fun(X_c,X_a),fun(X_a,fun(filter(X_c),bool)),tendsto(X_c,X_a),F),L),hAPP(X_c,filter(X_c),at(X_c),Aa))) -> hBOOL(hAPP(filter(X_c),bool,hAPP(X_b,fun(filter(X_c),bool),hAPP(fun(X_c,X_b),fun(X_b,fun(filter(X_c),bool)),tendsto(X_c,X_b),hAPP(fun(X_c,X_a),fun(X_c,X_b),hAPP(fun(X_a,X_b),fun(fun(X_c,X_a),fun(X_c,X_b)),combb(X_a,X_b,X_c),G),F)),hAPP(X_a,X_b,G,L)),hAPP(X_c,filter(X_c),at(X_c),Aa)))))))) # label(fact_4887_isCont__LIM__compose) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.92 4808 (all X_b all X_a (topological_space(X_a) & topological_space(X_b) -> (all F all Aa (hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,X_b),fun(X_a,bool),isCont(X_a,X_b),F),Aa)) <-> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),hAPP(X_a,X_b,F,Aa)),hAPP(X_a,filter(X_a),at(X_a),Aa))))))) # label(fact_4888_isCont__def) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.92 4809 (all X_a (real_normed_field(X_a) -> (all F all X_1 all L (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),F),X_1),L)) <-> (exists G_1 ((all Z_2 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_a,X_a,F,Z_2)),hAPP(X_a,X_a,F,X_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,G_1,Z_2)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),Z_2),X_1))) & hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,X_a),fun(X_a,bool),isCont(X_a,X_a),G_1),X_1)) & hAPP(X_a,X_a,G_1,X_1) = ti(X_a,L))))))) # label(fact_4889_CARAT__DERIV) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.92 4810 (all X_1 all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> hBOOL(hAPP(real,bool,hAPP(fun(real,real),fun(real,bool),isCont(real,real),hAPP(nat,fun(real,real),root,N)),X_1)))) # label(fact_4890_isCont__real__root) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.92 4811 (all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X_1)) -> hBOOL(hAPP(real,bool,hAPP(fun(real,real),fun(real,bool),isCont(real,real),ln),X_1)))) # label(fact_4891_isCont__ln) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.92 4812 (all Aa hBOOL(hAPP(real,bool,hAPP(fun(real,real),fun(real,bool),isCont(real,real),abs_abs(real)),Aa))) # label(fact_4892_isCont__abs) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.92 4813 (all X_b all X_a (topological_space(X_a) & real_normed_vector(X_b) -> (all F all Aa (hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,X_b),fun(X_a,bool),isCont(X_a,X_b),F),Aa)) -> (hAPP(X_a,X_b,F,Aa) != zero_zero(X_b) -> hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,X_b),fun(X_a,bool),isCont(X_a,X_b),hAPP(fun(X_a,X_b),fun(X_a,X_b),hAPP(fun(X_b,X_b),fun(fun(X_a,X_b),fun(X_a,X_b)),combb(X_b,X_b,X_a),sgn_sgn(X_b)),F)),Aa))))))) # label(fact_4893_isCont__sgn) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.92 4814 (all X_b all X_a (topological_space(X_a) & real_n1866405975lgebra(X_b) -> (all F all Aa (hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,X_b),fun(X_a,bool),isCont(X_a,X_b),F),Aa)) -> (hAPP(X_a,X_b,F,Aa) != zero_zero(X_b) -> hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,X_b),fun(X_a,bool),isCont(X_a,X_b),hAPP(fun(X_a,X_b),fun(X_a,X_b),hAPP(fun(X_b,X_b),fun(fun(X_a,X_b),fun(X_a,X_b)),combb(X_b,X_b,X_a),inverse_inverse(X_b)),F)),Aa))))))) # label(fact_4894_isCont__inverse) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.92 4815 (all X_a (topological_space(X_a) -> (all F all Aa (hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,real),fun(X_a,bool),isCont(X_a,real),F),Aa)) -> hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,real),fun(X_a,bool),isCont(X_a,real),hAPP(fun(X_a,real),fun(X_a,real),hAPP(fun(real,real),fun(fun(X_a,real),fun(X_a,real)),combb(real,real,X_a),abs_abs(real)),F)),Aa)))))) # label(fact_4895_isCont__rabs) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.92 4816 (all X_b all X_a (topological_space(X_a) & real_normed_vector(X_b) -> (all F all Aa (hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,X_b),fun(X_a,bool),isCont(X_a,X_b),F),Aa)) -> hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,X_b),fun(X_a,bool),isCont(X_a,X_b),hAPP(fun(X_a,X_b),fun(X_a,X_b),hAPP(fun(X_b,X_b),fun(fun(X_a,X_b),fun(X_a,X_b)),combb(X_b,X_b,X_a),uminus_uminus(X_b)),F)),Aa)))))) # label(fact_4896_isCont__minus) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.92 4817 (all X_a (real_normed_algebra(X_a) -> (all X_1 all Aa hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,X_a),fun(X_a,bool),isCont(X_a,X_a),hAPP(X_a,fun(X_a,X_a),times_times(X_a),X_1)),Aa))))) # label(fact_4897_mult__right_OisCont) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.92 4818 (all X_a (real_normed_algebra(X_a) -> (all Y_1 all Aa hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,X_a),fun(X_a,bool),isCont(X_a,X_a),hAPP(X_a,fun(X_a,X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(X_a,X_a)),combc(X_a,X_a,X_a),times_times(X_a)),Y_1)),Aa))))) # label(fact_4898_mult__left_OisCont) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.92 4819 (all X_b all X_a (topological_space(X_a) & real_normed_algebra(X_b) -> (all G all F all Aa (hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,X_b),fun(X_a,bool),isCont(X_a,X_b),F),Aa)) -> (hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,X_b),fun(X_a,bool),isCont(X_a,X_b),G),Aa)) -> hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,X_b),fun(X_a,bool),isCont(X_a,X_b),hAPP(fun(X_a,X_b),fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,X_b)),combs(X_a,X_b,X_b),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,fun(X_b,X_b))),combb(X_b,fun(X_b,X_b),X_a),times_times(X_b)),F)),G)),Aa))))))) # label(fact_4899_isCont__mult) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.92 4820 (all X_b all X_a (topological_space(X_a) & real_normed_algebra(X_b) -> (all G all F all Aa (hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,X_b),fun(X_a,bool),isCont(X_a,X_b),F),Aa)) -> (hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,X_b),fun(X_a,bool),isCont(X_a,X_b),G),Aa)) -> hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,X_b),fun(X_a,bool),isCont(X_a,X_b),hAPP(fun(X_a,X_b),fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,X_b)),combs(X_a,X_b,X_b),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,fun(X_b,X_b))),combb(X_b,fun(X_b,X_b),X_a),times_times(X_b)),F)),G)),Aa))))))) # label(fact_4900_mult_OisCont) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.92 4821 (all X_b all X_a (topological_space(X_a) & real_normed_vector(X_b) -> (all F all Aa (hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,X_b),fun(X_a,bool),isCont(X_a,X_b),F),Aa)) -> hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,real),fun(X_a,bool),isCont(X_a,real),hAPP(fun(X_a,X_b),fun(X_a,real),hAPP(fun(X_b,real),fun(fun(X_a,X_b),fun(X_a,real)),combb(X_b,real,X_a),norm_norm(X_b)),F)),Aa)))))) # label(fact_4901_isCont__norm) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.92 4822 (all X_b all X_a (topological_space(X_a) & topological_space(X_b) -> (all K all Aa hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,X_b),fun(X_a,bool),isCont(X_a,X_b),hAPP(X_b,fun(X_a,X_b),combk(X_b,X_a),K)),Aa))))) # label(fact_4902_isCont__const) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.92 4823 (all X_a (topological_space(X_a) -> (all Aa hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,X_a),fun(X_a,bool),isCont(X_a,X_a),combi(X_a)),Aa))))) # label(fact_4903_isCont__ident) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.92 4824 (all X_b all X_c all X_a (topological_space(X_a) & topological_space(X_c) & topological_space(X_b) -> (all G all F all Aa (hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,X_b),fun(X_a,bool),isCont(X_a,X_b),F),Aa)) -> (hBOOL(hAPP(X_b,bool,hAPP(fun(X_b,X_c),fun(X_b,bool),isCont(X_b,X_c),G),hAPP(X_a,X_b,F,Aa))) -> hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,X_c),fun(X_a,bool),isCont(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),G),F)),Aa))))))) # label(fact_4904_isCont__o2) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.92 4825 (all X_b all X_a (topological_space(X_a) & power(X_b) & real_normed_algebra(X_b) -> (all N all F all Aa (hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,X_b),fun(X_a,bool),isCont(X_a,X_b),F),Aa)) -> hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,X_b),fun(X_a,bool),isCont(X_a,X_b),hAPP(nat,fun(X_a,X_b),hAPP(fun(X_a,fun(nat,X_b)),fun(nat,fun(X_a,X_b)),combc(X_a,nat,X_b),hAPP(fun(X_a,X_b),fun(X_a,fun(nat,X_b)),hAPP(fun(X_b,fun(nat,X_b)),fun(fun(X_a,X_b),fun(X_a,fun(nat,X_b))),combb(X_b,fun(nat,X_b),X_a),power_power(X_b)),F)),N)),Aa)))))) # label(fact_4905_isCont__power) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.92 4826 (all X_a (real_algebra_1(X_a) & real_normed_vector(X_a) -> (all Aa hBOOL(hAPP(real,bool,hAPP(fun(real,X_a),fun(real,bool),isCont(real,X_a),of_real(X_a)),Aa))))) # label(fact_4906_of__real_OisCont) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.92 4827 (all X_b all X_a (topological_space(X_a) & real_n2089651433ebra_1(X_b) -> (all F all Aa (hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,real),fun(X_a,bool),isCont(X_a,real),F),Aa)) -> hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,X_b),fun(X_a,bool),isCont(X_a,X_b),hAPP(fun(X_a,real),fun(X_a,X_b),hAPP(fun(real,X_b),fun(fun(X_a,real),fun(X_a,X_b)),combb(real,X_b,X_a),of_real(X_b)),F)),Aa)))))) # label(fact_4907_isCont__of__real) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.92 4828 (all X_a (real_normed_field(X_a) -> (all Y_1 all Aa hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,X_a),fun(X_a,bool),isCont(X_a,X_a),hAPP(X_a,fun(X_a,X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(X_a,X_a)),combc(X_a,X_a,X_a),inverse_divide(X_a)),Y_1)),Aa))))) # label(fact_4908_divide_OisCont) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.92 4829 (all X_b all X_a (topological_space(X_a) & real_normed_vector(X_b) -> (all G all F all Aa (hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,X_b),fun(X_a,bool),isCont(X_a,X_b),F),Aa)) -> (hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,X_b),fun(X_a,bool),isCont(X_a,X_b),G),Aa)) -> hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,X_b),fun(X_a,bool),isCont(X_a,X_b),hAPP(fun(X_a,X_b),fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,X_b)),combs(X_a,X_b,X_b),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,fun(X_b,X_b))),combb(X_b,fun(X_b,X_b),X_a),minus_minus(X_b)),F)),G)),Aa))))))) # label(fact_4909_isCont__diff) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.92 4830 (all X_b all X_a (topological_space(X_a) & real_normed_vector(X_b) -> (all G all F all Aa (hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,X_b),fun(X_a,bool),isCont(X_a,X_b),F),Aa)) -> (hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,X_b),fun(X_a,bool),isCont(X_a,X_b),G),Aa)) -> hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,X_b),fun(X_a,bool),isCont(X_a,X_b),hAPP(fun(X_a,X_b),fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,X_b)),combs(X_a,X_b,X_b),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,fun(X_b,X_b))),combb(X_b,fun(X_b,X_b),X_a),plus_plus(X_b)),F)),G)),Aa))))))) # label(fact_4910_isCont__add) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.92 4831 (all Aa hBOOL(hAPP(complex,bool,hAPP(fun(complex,real),fun(complex,bool),isCont(complex,real),im),Aa))) # label(fact_4911_Im_OisCont) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.92 4832 (all Aa hBOOL(hAPP(complex,bool,hAPP(fun(complex,real),fun(complex,bool),isCont(complex,real),re),Aa))) # label(fact_4912_Re_OisCont) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.92 4833 (all Aa hBOOL(hAPP(complex,bool,hAPP(fun(complex,complex),fun(complex,bool),isCont(complex,complex),cnj),Aa))) # label(fact_4913_cnj_OisCont) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.92 4834 (all X_a (real_normed_field(X_a) -> (all F all X_1 all D_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),F),X_1),D_2)) -> hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,X_a),fun(X_a,bool),isCont(X_a,X_a),F),X_1)))))) # label(fact_4914_DERIV__isCont) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.92 4835 (all X_1 hBOOL(hAPP(real,bool,hAPP(fun(real,real),fun(real,bool),isCont(real,real),sqrt),X_1))) # label(fact_4915_isCont__real__sqrt) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.92 4836 (all X_1 hBOOL(hAPP(real,bool,hAPP(fun(real,real),fun(real,bool),isCont(real,real),cos),X_1))) # label(fact_4916_isCont__cos) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.92 4837 (all X_1 hBOOL(hAPP(real,bool,hAPP(fun(real,real),fun(real,bool),isCont(real,real),arctan),X_1))) # label(fact_4917_isCont__arctan) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.92 4838 (all X_1 hBOOL(hAPP(real,bool,hAPP(fun(real,real),fun(real,bool),isCont(real,real),sin),X_1))) # label(fact_4918_isCont__sin) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.92 4839 (all X_a (real_normed_field(X_a) & banach(X_a) -> (all X_1 hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,X_a),fun(X_a,bool),isCont(X_a,X_a),exp(X_a)),X_1))))) # label(fact_4919_isCont__exp) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.92 4840 (all X_1 (hAPP(real,real,cos,X_1) != zero_zero(real) -> hBOOL(hAPP(real,bool,hAPP(fun(real,real),fun(real,bool),isCont(real,real),tan),X_1)))) # label(fact_4920_isCont__tan) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.92 4841 (all X_b all X_c all X_a all X_d (topological_space(X_d) & real_normed_vector(X_a) & real_normed_vector(X_c) & real_normed_vector(X_b) -> (all G all F all Aa all Prod (hBOOL(hAPP(fun(X_a,fun(X_b,X_c)),bool,bounded_bilinear(X_a,X_b,X_c),Prod)) -> (hBOOL(hAPP(X_d,bool,hAPP(fun(X_d,X_a),fun(X_d,bool),isCont(X_d,X_a),F),Aa)) -> (hBOOL(hAPP(X_d,bool,hAPP(fun(X_d,X_b),fun(X_d,bool),isCont(X_d,X_b),G),Aa)) -> hBOOL(hAPP(X_d,bool,hAPP(fun(X_d,X_c),fun(X_d,bool),isCont(X_d,X_c),hAPP(fun(X_d,X_b),fun(X_d,X_c),hAPP(fun(X_d,fun(X_b,X_c)),fun(fun(X_d,X_b),fun(X_d,X_c)),combs(X_d,X_b,X_c),hAPP(fun(X_d,X_a),fun(X_d,fun(X_b,X_c)),hAPP(fun(X_a,fun(X_b,X_c)),fun(fun(X_d,X_a),fun(X_d,fun(X_b,X_c))),combb(X_a,fun(X_b,X_c),X_d),Prod),F)),G)),Aa)))))))) # label(fact_4921_bounded__bilinear_OisCont) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.92 4842 (all X_a (real_normed_vector(X_a) -> (all R_1 all Aa hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,X_a),fun(X_a,bool),isCont(X_a,X_a),hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),R_1)),Aa))))) # label(fact_4922_scaleR__right_OisCont) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.92 4843 (all X_a (real_normed_vector(X_a) -> (all X_1 all Aa hBOOL(hAPP(real,bool,hAPP(fun(real,X_a),fun(real,bool),isCont(real,X_a),hAPP(X_a,fun(real,X_a),hAPP(fun(real,fun(X_a,X_a)),fun(X_a,fun(real,X_a)),combc(real,X_a,X_a),scaleR_scaleR(X_a)),X_1)),Aa))))) # label(fact_4923_scaleR__left_OisCont) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.92 4844 (all X_b all X_a (topological_space(X_a) & real_normed_vector(X_b) -> (all G all F all Aa (hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,real),fun(X_a,bool),isCont(X_a,real),F),Aa)) -> (hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,X_b),fun(X_a,bool),isCont(X_a,X_b),G),Aa)) -> hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,X_b),fun(X_a,bool),isCont(X_a,X_b),hAPP(fun(X_a,X_b),fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,X_b)),combs(X_a,X_b,X_b),hAPP(fun(X_a,real),fun(X_a,fun(X_b,X_b)),hAPP(fun(real,fun(X_b,X_b)),fun(fun(X_a,real),fun(X_a,fun(X_b,X_b))),combb(real,fun(X_b,X_b),X_a),scaleR_scaleR(X_b)),F)),G)),Aa))))))) # label(fact_4924_isCont__scaleR) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.92 4845 (all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> hBOOL(hAPP(real,bool,hAPP(fun(real,real),fun(real,bool),isCont(real,real),hAPP(nat,fun(real,real),root,N)),zero_zero(real))))) # label(fact_4925_isCont__root__zero) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.92 4846 (all X_1 all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_1),zero_zero(real))) -> hBOOL(hAPP(real,bool,hAPP(fun(real,real),fun(real,bool),isCont(real,real),hAPP(nat,fun(real,real),root,N)),X_1))))) # label(fact_4926_isCont__root__neg) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.92 4847 (all X_1 all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X_1)) -> hBOOL(hAPP(real,bool,hAPP(fun(real,real),fun(real,bool),isCont(real,real),hAPP(nat,fun(real,real),root,N)),X_1))))) # label(fact_4927_isCont__root__pos) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.92 4848 (all X_b all X_a (real_normed_vector(X_a) & topological_space(X_b) -> (all F all X_1 (hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,X_b),fun(X_a,bool),isCont(X_a,X_b),F),X_1)) <-> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(fun(X_a,X_a),fun(X_a,X_b),hAPP(fun(X_a,X_b),fun(fun(X_a,X_a),fun(X_a,X_b)),combb(X_a,X_b,X_a),F),hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X_1))),hAPP(X_a,X_b,F,X_1)),hAPP(X_a,filter(X_a),at(X_a),zero_zero(X_a)))))))) # label(fact_4928_isCont__iff) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.92 4849 (all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,number_number_of(real),min)),X_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_1),one_one(real))) -> hBOOL(hAPP(real,bool,hAPP(fun(real,real),fun(real,bool),isCont(real,real),arccos),X_1))))) # label(fact_4929_isCont__arccos) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.92 4850 (all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,number_number_of(real),min)),X_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_1),one_one(real))) -> hBOOL(hAPP(real,bool,hAPP(fun(real,real),fun(real,bool),isCont(real,real),arcsin),X_1))))) # label(fact_4930_isCont__arcsin) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.92 4851 (all X_c all X_b all X_a (metric_space(X_a) & topological_space(X_b) & topological_space(X_c) -> (all G all L all F all Aa (hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,X_b),fun(X_a,bool),isCont(X_a,X_b),F),Aa)) -> (hBOOL(hAPP(filter(X_b),bool,hAPP(X_c,fun(filter(X_b),bool),hAPP(fun(X_b,X_c),fun(X_c,fun(filter(X_b),bool)),tendsto(X_b,X_c),G),L),hAPP(X_b,filter(X_b),at(X_b),hAPP(X_a,X_b,F,Aa)))) -> ((exists D_3 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),D_3)) & (all X_2 (ti(X_a,X_2) != ti(X_a,Aa) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),X_2),Aa)),D_3)) -> hAPP(X_a,X_b,F,X_2) != hAPP(X_a,X_b,F,Aa))))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_c,fun(filter(X_a),bool),hAPP(fun(X_a,X_c),fun(X_c,fun(filter(X_a),bool)),tendsto(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),G),F)),L),hAPP(X_a,filter(X_a),at(X_a),Aa))))))))) # label(fact_4931_metric__isCont__LIM__compose2) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.92 4852 (all F all Ba all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),Ba),X_1)) -> ((all X_2 (hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),X_2),hAPP(real,fun(real,bool),hAPP(real,fun(real,fun(real,bool)),ord_gr676655987ssThan(real),Ba),X_1))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(real,real,F,X_2))))) -> (hBOOL(hAPP(real,bool,hAPP(fun(real,real),fun(real,bool),isCont(real,real),F),X_1)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(real,real,F,X_1))))))) # label(fact_4932_LIM__less__bound) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.92 4853 (all Ba all Aa all F all G all X_1 all D_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),F),hAPP(real,real,G,X_1)),D_2)) -> (D_2 != zero_zero(real) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),Aa),X_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_1),Ba)) -> ((all Y_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),Aa),Y_2)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),Y_2),Ba)) -> hAPP(real,real,F,hAPP(real,real,G,Y_2)) = Y_2)) -> (hBOOL(hAPP(real,bool,hAPP(fun(real,real),fun(real,bool),isCont(real,real),G),X_1)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),G),X_1),hAPP(real,real,inverse_inverse(real),D_2)))))))))) # label(fact_4933_DERIV__inverse__function) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.92 4854 (all X_a all X_c all X_b (topological_space(X_b) & real_normed_vector(X_c) -> (all F all X_1 all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2)) -> ((all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_2)) -> hBOOL(hAPP(X_b,bool,hAPP(fun(X_b,X_c),fun(X_b,bool),isCont(X_b,X_c),hAPP(X_a,fun(X_b,X_c),F,X_2)),X_1)))) -> hBOOL(hAPP(X_b,bool,hAPP(fun(X_b,X_c),fun(X_b,bool),isCont(X_b,X_c),hAPP(fun(X_a,bool),fun(X_b,X_c),hAPP(fun(X_b,fun(fun(X_a,bool),X_c)),fun(fun(X_a,bool),fun(X_b,X_c)),combc(X_b,fun(X_a,bool),X_c),hAPP(fun(X_b,fun(X_a,X_c)),fun(X_b,fun(fun(X_a,bool),X_c)),hAPP(fun(fun(X_a,X_c),fun(fun(X_a,bool),X_c)),fun(fun(X_b,fun(X_a,X_c)),fun(X_b,fun(fun(X_a,bool),X_c))),combb(fun(X_a,X_c),fun(fun(X_a,bool),X_c),X_b),big_co1399186613setsum(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),F))),A_2)),X_1))))))) # label(fact_4934_isCont__setsum) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.92 4855 (all G all F all X_1 all D_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),D_1)) -> ((all Z_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),Z_2),X_1))),D_1)) -> hAPP(real,real,G,hAPP(real,real,F,Z_2)) = Z_2)) -> ((all Z_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),Z_2),X_1))),D_1)) -> hBOOL(hAPP(real,bool,hAPP(fun(real,real),fun(real,bool),isCont(real,real),F),Z_2)))) -> hBOOL(hAPP(real,bool,hAPP(fun(real,real),fun(real,bool),isCont(real,real),G),hAPP(real,real,F,X_1))))))) # label(fact_4935_isCont__inv__fun) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.92 4856 (all X_1 all F all Aa all Ba (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),Aa),Ba)) -> ((all X_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),Aa),X_2)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_2),Ba)) -> hBOOL(hAPP(real,bool,hAPP(fun(real,real),fun(real,bool),isCont(real,real),F),X_2)))) -> ((all X_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),Aa),X_2)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_2),Ba)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),F),X_2),zero_zero(real))))) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),Aa),X_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_1),Ba)) -> hAPP(real,real,F,X_1) = hAPP(real,real,F,Aa))))))) # label(fact_4936_DERIV__isconst2) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.92 4857 (all F all Aa all Ba (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),Aa),Ba)) -> ((all X_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),Aa),X_2)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_2),Ba)) -> hBOOL(hAPP(real,bool,hAPP(fun(real,real),fun(real,bool),isCont(real,real),F),X_2)))) -> ((all X_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),Aa),X_2)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_2),Ba)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),F),X_2),zero_zero(real))))) -> hAPP(real,real,F,Ba) = hAPP(real,real,F,Aa))))) # label(fact_4937_DERIV__isconst__end) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.92 4858 (all F all Aa all Ba (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),Aa),Ba)) -> ((all X_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),Aa),X_2)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_2),Ba)) -> hBOOL(hAPP(real,bool,hAPP(fun(real,real),fun(real,bool),isCont(real,real),F),X_2)))) -> ((all X_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),Aa),X_2)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_2),Ba)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),F),X_2),zero_zero(real))))) -> (all X_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),Aa),X_2)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_2),Ba)) -> hAPP(real,real,F,X_2) = hAPP(real,real,F,Aa))))))) # label(fact_4938_DERIV__isconst1) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.92 4859 (all G all F all X_1 all D_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),D_1)) -> ((all Z_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),Z_2),X_1))),D_1)) -> hAPP(real,real,G,hAPP(real,real,F,Z_2)) = Z_2)) -> ((all Z_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),Z_2),X_1))),D_1)) -> hBOOL(hAPP(real,bool,hAPP(fun(real,real),fun(real,bool),isCont(real,real),F),Z_2)))) -> (exists Z_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),Z_2),X_1))),D_1)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,F,Z_2)),hAPP(real,real,F,X_1))))))))) # label(fact_4939_lemma__isCont__inj2) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.92 4860 (all G all F all X_1 all D_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),D_1)) -> ((all Z_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),Z_2),X_1))),D_1)) -> hAPP(real,real,G,hAPP(real,real,F,Z_2)) = Z_2)) -> ((all Z_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),Z_2),X_1))),D_1)) -> hBOOL(hAPP(real,bool,hAPP(fun(real,real),fun(real,bool),isCont(real,real),F),Z_2)))) -> (exists E (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),E)) & (all Y_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),Y_2),hAPP(real,real,F,X_1))))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),Y_2),hAPP(real,real,F,X_1)))),E)) -> hAPP(real,real,F,hAPP(real,real,G,Y_2)) = Y_2)))))))) # label(fact_4940_isCont__inv__fun__inv) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.92 4861 (all G all F all X_1 all D_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),D_1)) -> ((all Z_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),Z_2),X_1))),D_1)) -> hAPP(real,real,G,hAPP(real,real,F,Z_2)) = Z_2)) -> ((all Z_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),Z_2),X_1))),D_1)) -> hBOOL(hAPP(real,bool,hAPP(fun(real,real),fun(real,bool),isCont(real,real),F),Z_2)))) -> (exists Z_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),Z_2),X_1))),D_1)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,F,X_1)),hAPP(real,real,F,Z_2))))))))) # label(fact_4941_lemma__isCont__inj) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.92 4862 (all N hAPP(nat,fun(nat,bool),ord_atMost(nat),N) = hAPP(fun(int,bool),fun(nat,bool),hAPP(fun(int,nat),fun(fun(int,bool),fun(nat,bool)),image(int,nat),nat_1),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastAtMost(int),zero_zero(int)),hAPP(nat,int,semiring_1_of_nat(int),N)))) # label(fact_4942_SetInterval_Otransfer__nat__int__set__functions_I1_J) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.92 4863 (all V_1 all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),hAPP(int,nat,number_number_of(nat),V_1)),hAPP(nat,nat,suc,N)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),hAPP(bool,fun(nat,fun(nat,nat)),if(nat),hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),hAPP(int,int,pred,V_1)))),hAPP(nat,nat,suc,N)),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),hAPP(int,nat,nat_1,hAPP(int,int,number_number_of(int),hAPP(int,int,pred,V_1)))),N)))) # label(fact_4943_max__Suc__number__of) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.92 4864 (all K hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),hAPP(nat,fun(nat,bool),ord_atMost(nat),K)))) # label(fact_4944_finite__atMost) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.92 4865 (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_4945_minus__min__eq__max) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.92 4866 (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_4946_minus__max__eq__min) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.93 4867 (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_4947_min__max_Oinf__sup__distrib2) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.93 4868 (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_4948_min__max_Osup__inf__distrib2) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.93 4869 (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_4949_min__max_Oinf__sup__distrib1) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.93 4870 (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_4950_min__max_Osup__inf__distrib1) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.93 4871 (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_4951_min__max_Oinf__sup__absorb) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.93 4872 (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_4952_min__max_Osup__inf__absorb) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.93 4873 (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_4953_min__max_Odistrib__inf__le) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.93 4874 (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_4954_min__max_Odistrib__sup__le) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.93 4875 (all X_a (ord(X_a) -> ord_max(X_a) = hAPP(fun(X_a,fun(X_a,bool)),fun(X_a,fun(X_a,X_a)),max(X_a),ord_less_eq(X_a)))) # label(fact_4955_max__ord__max) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.93 4876 (all N hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),zero_zero(nat)),N) = hAPP(nat,fun(nat,bool),ord_atMost(nat),N)) # label(fact_4956_atLeast0AtMost) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.93 4877 (all X_a (linorder(X_a) -> (all Z_1 all X_1 all Y_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X_1),Y_1))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z_1),X_1)) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z_1),Y_1)))))) # label(fact_4957_less__max__iff__disj) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.93 4878 (all X_a (linorder(X_a) -> (all X_1 all Y_1 all Z_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X_1),Y_1)),Z_1)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Z_1)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y_1),Z_1)))))) # label(fact_4958_max__less__iff__conj) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.93 4879 (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_4959_min__max_Oless__supI2) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.93 4880 (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_4960_min__max_Oless__supI1) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.93 4881 (all U_1 hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(nat,fun(nat,bool),ord_atMost(nat),U_1)) = hAPP(nat,nat,suc,U_1)) # label(fact_4961_card__atMost) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.93 4882 (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_4962_min__max_Osup__assoc) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.93 4883 (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_4963_min__max_Osup_Oassoc) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.93 4884 (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_4964_min__max_Osup__left__commute) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.93 4885 (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_4965_min__max_Osup_Oleft__commute) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.93 4886 (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_4966_min__max_Osup__left__idem) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.93 4887 (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_4967_min__max_Osup_Oleft__idem) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.93 4888 (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_4968_min__max_Osup__commute) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.93 4889 (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_4969_min__max_Osup_Ocommute) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.93 4890 (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_4970_min__max_Osup_Oidem) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.93 4891 (all M_1 all N_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),hAPP(nat,nat,suc,M_1)),hAPP(nat,nat,suc,N_1)) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),M_1),N_1))) # label(fact_4971_max__Suc__Suc) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.93 4892 (all X_a (linorder(X_a) -> (all X_1 all Y_1 (hAPP(X_a,fun(X_a,bool),ord_atMost(X_a),X_1) = hAPP(X_a,fun(X_a,bool),ord_atMost(X_a),Y_1) <-> ti(X_a,X_1) = ti(X_a,Y_1))))) # label(fact_4972_atMost__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.93 4893 (all N_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),N_1),zero_zero(nat)) = N_1) # label(fact_4973_max__0R) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.93 4894 (all N_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),zero_zero(nat)),N_1) = N_1) # label(fact_4974_max__0L) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.93 4895 (all N_1 all M_1 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_1)),M_1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),N_1),M_1)) # label(fact_4975_nat__minus__add__max) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.93 4896 (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_4976_max__diff__distrib__left) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.93 4897 (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_4977_max__add__distrib__left) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.93 4898 (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_4978_Max_Oidem) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.93 4899 (all N all M hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),hAPP(nat,nat,suc,N)),M) = hAPP(nat,nat,hAPP(fun(nat,nat),fun(nat,nat),hAPP(nat,fun(fun(nat,nat),fun(nat,nat)),nat_case(nat),hAPP(nat,nat,suc,N)),hAPP(fun(nat,nat),fun(nat,nat),hAPP(fun(nat,nat),fun(fun(nat,nat),fun(nat,nat)),combb(nat,nat,nat),suc),hAPP(nat,fun(nat,nat),ord_max(nat),N))),M)) # label(fact_4979_max__Suc1) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.93 4900 (all M all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),M),hAPP(nat,nat,suc,N)) = hAPP(nat,nat,hAPP(fun(nat,nat),fun(nat,nat),hAPP(nat,fun(fun(nat,nat),fun(nat,nat)),nat_case(nat),hAPP(nat,nat,suc,N)),hAPP(fun(nat,nat),fun(nat,nat),hAPP(fun(nat,nat),fun(fun(nat,nat),fun(nat,nat)),combb(nat,nat,nat),suc),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),ord_max(nat)),N))),M)) # label(fact_4980_max__Suc2) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.93 4901 (all K hAPP(nat,fun(nat,bool),ord_lessThan(nat),hAPP(nat,nat,suc,K)) = hAPP(nat,fun(nat,bool),ord_atMost(nat),K)) # label(fact_4981_lessThan__Suc__atMost) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.93 4902 (all S (hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),S)) <-> (exists K_1 hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,bool),fun(fun(nat,bool),bool),ord_less_eq(fun(nat,bool)),S),hAPP(nat,fun(nat,bool),ord_atMost(nat),K_1)))))) # label(fact_4982_finite__nat__iff__bounded__le) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.93 4903 (all X_a (order(X_a) -> (all X_1 all Y_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(X_a,fun(X_a,bool),ord_atMost(X_a),X_1)),hAPP(X_a,fun(X_a,bool),ord_atMost(X_a),Y_1))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),Y_1)))))) # label(fact_4983_atMost__subset__iff) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.93 4904 (all X_b (number(X_b) & ord(X_b) -> (all U all V ((hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(int,X_b,number_number_of(X_b),U)),hAPP(int,X_b,number_number_of(X_b),V))) -> hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),ord_max(X_b),hAPP(int,X_b,number_number_of(X_b),U)),hAPP(int,X_b,number_number_of(X_b),V)) = hAPP(int,X_b,number_number_of(X_b),V)) & (-hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(int,X_b,number_number_of(X_b),U)),hAPP(int,X_b,number_number_of(X_b),V))) -> hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),ord_max(X_b),hAPP(int,X_b,number_number_of(X_b),U)),hAPP(int,X_b,number_number_of(X_b),V)) = hAPP(int,X_b,number_number_of(X_b),U)))))) # label(fact_4984_max__number__of) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.93 4905 (all X_a (ord(X_a) -> (all I all K (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),I),hAPP(X_a,fun(X_a,bool),ord_atMost(X_a),K))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),I),K)))))) # label(fact_4985_atMost__iff) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.93 4906 (all X_a (linorder(X_a) -> (all Z_1 all X_1 all Y_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Z_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X_1),Y_1))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Z_1),X_1)) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Z_1),Y_1)))))) # label(fact_4986_le__max__iff__disj) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.93 4907 (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_4987_min__max_Ole__supE) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.93 4908 (all X_a (linorder(X_a) -> (all B all D 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)) -> 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)))))))) # label(fact_4988_min__max_Osup__mono) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.93 4909 (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_4989_min__max_Osup__least) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.93 4910 (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_4990_min__max_Ole__supI) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.93 4911 (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_4991_min__max_Osup__absorb1) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.93 4912 (all T_2 all T_1 (comple44059174attice(T_1) -> comple44059174attice(fun(T_2,T_1)))) # label(arity_fun___Complete__Lattice_Ocomplete__lattice) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.93 4913 (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].
% 7.93/7.93 4914 (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].
% 7.93/7.93 4915 (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].
% 7.93/7.93 4916 (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].
% 7.93/7.93 4917 (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].
% 7.93/7.93 4918 (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].
% 7.93/7.93 4919 (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].
% 7.93/7.93 4920 (all T_2 all T_1 (finite_finite(T_1) & finite_finite(T_2) -> finite_finite(sum_sum(T_2,T_1)))) # label(arity_sum___Finite__Set_Ofinite) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.93 4921 (all T_1 comple44059174attice(filter(T_1))) # label(arity_Limits_Ofilter___Complete__Lattice_Ocomplete__lattice) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.93 4922 (all T_1 preorder(filter(T_1))) # label(arity_Limits_Ofilter___Orderings_Opreorder) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.93 4923 (all T_1 order(filter(T_1))) # label(arity_Limits_Ofilter___Orderings_Oorder) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.93 4924 (all T_1 ord(filter(T_1))) # label(arity_Limits_Ofilter___Orderings_Oord) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.93 4925 (all T_2 all T_1 (finite_finite(T_1) & finite_finite(T_2) -> finite_finite(product_prod(T_2,T_1)))) # label(arity_prod___Finite__Set_Ofinite) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.93 4926 (all T all A ti(T,ti(T,A)) = ti(T,A)) # label(help_ti_idem) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.93 4927 (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].
% 7.93/7.93 4928 (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].
% 7.93/7.93 4929 (all P (ti(bool,P) = fTrue | ti(bool,P) = fFalse)) # label(help_If_3_1_T) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.93 4930 (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].
% 7.93/7.93 4931 (all P (-hBOOL(hAPP(bool,bool,fNot,P)) | -hBOOL(P))) # label(help_fNot_1_1_U) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.93 4932 (all P (hBOOL(P) | hBOOL(hAPP(bool,bool,fNot,P)))) # label(help_fNot_2_1_U) # label(axiom) # label(non_clause). [assumption].
% 7.93/7.93 4933 (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].
% 7.93/7.93 4934 (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].
% 7.93/7.93 4935 (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].
% 7.93/7.93 4936 (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].
% 7.93/7.93 4937 (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].
% 7.93/7.93 4938 (all P (ti(bool,P) = fTrue | ti(bool,P) = fFalse)) # label(help_fTrue_1_1_T) # label(axiom) # label(non_clause). [assumption].
% 10.54/10.51 4939 (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].
% 10.54/10.51 4940 (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].
% 10.54/10.51 4941 (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].
% 10.54/10.51 4942 (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].
% 10.54/10.51 4943 (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].
% 10.54/10.51 4944 (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].
% 10.54/10.51 4945 (all P (ti(bool,P) = fTrue | ti(bool,P) = fFalse)) # label(help_fFalse_1_1_T) # label(axiom) # label(non_clause). [assumption].
% 10.54/10.51 4946 (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].
% 10.54/10.51 4947 (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].
% 10.54/10.51 4948 (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].
% 10.54/10.51 4949 (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].
% 10.54/10.51 4950 (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].
% 10.54/10.51
% 10.54/10.51 ============================== end of process non-clausal formulas ===
% 10.54/10.51
% 10.54/10.51 ============================== PROCESS INITIAL CLAUSES ===============
% 10.54/10.51
% 10.54/10.51 ============================== PREDICATE ELIMINATION =================
% 10.54/10.51 4951 archim1727834104eiling(rat) # label(arity_Rat_Orat___Archimedean__Field_Ofloor__ceiling) # label(axiom). [assumption].
% 10.54/10.51 4952 -archim1727834104eiling(A) | ti(fun(A,int),archimedean_ceiling(A)) = archimedean_ceiling(A) # label(tsy_c_Archimedean__Field_Oceiling_res) # label(axiom). [clausify(1)].
% 10.54/10.51 4953 -archim1727834104eiling(A) | archim2085082626_floor(A) = ti(fun(A,int),archim2085082626_floor(A)) # label(tsy_c_Archimedean__Field_Ofloor__ceiling__class_Ofloor_res) # label(axiom). [clausify(2)].
% 10.54/10.51 4954 -archim1727834104eiling(A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),B)),hAPP(A,int,archimedean_ceiling(A),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(int,A,number_number_of(A),B)),one_one(A))),C)) # label(fact_246_number__of__le__ceiling) # label(axiom). [clausify(376)].
% 10.54/10.51 4955 -archim1727834104eiling(A) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),B)),hAPP(A,int,archimedean_ceiling(A),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(int,A,number_number_of(A),B)),one_one(A))),C)) # label(fact_246_number__of__le__ceiling) # label(axiom). [clausify(376)].
% 10.54/10.51 4956 -archim1727834104eiling(A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(A,int,archimedean_ceiling(A),B)),hAPP(int,int,number_number_of(int),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(int,A,number_number_of(A),C)),one_one(A)))) # label(fact_247_ceiling__less__number__of) # label(axiom). [clausify(377)].
% 10.54/10.51 4957 -archim1727834104eiling(A) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(A,int,archimedean_ceiling(A),B)),hAPP(int,int,number_number_of(int),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(int,A,number_number_of(A),C)),one_one(A)))) # label(fact_247_ceiling__less__number__of) # label(axiom). [clausify(377)].
% 10.54/10.51 4958 -archim1727834104eiling(A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(A,int,archimedean_ceiling(A),B))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) # label(fact_248_zero__less__ceiling) # label(axiom). [clausify(378)].
% 10.54/10.51 4959 -archim1727834104eiling(A) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(A,int,archimedean_ceiling(A),B))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) # label(fact_248_zero__less__ceiling) # label(axiom). [clausify(378)].
% 10.54/10.51 4960 -archim1727834104eiling(A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(A,int,archimedean_ceiling(A),B)),zero_zero(int))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),zero_zero(A))) # label(fact_249_ceiling__le__zero) # label(axiom). [clausify(379)].
% 10.54/10.51 4961 -archim1727834104eiling(A) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(A,int,archimedean_ceiling(A),B)),zero_zero(int))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),zero_zero(A))) # label(fact_249_ceiling__le__zero) # label(axiom). [clausify(379)].
% 10.54/10.51 4962 -archim1727834104eiling(A) | hAPP(A,int,archimedean_ceiling(A),zero_zero(A)) = zero_zero(int) # label(fact_250_ceiling__zero) # label(axiom). [clausify(380)].
% 10.54/10.51 4963 -archim1727834104eiling(A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(A,int,archimedean_ceiling(A),B)),one_one(int))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),zero_zero(A))) # label(fact_252_ceiling__less__one) # label(axiom). [clausify(382)].
% 10.54/10.51 4964 -archim1727834104eiling(A) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(A,int,archimedean_ceiling(A),B)),one_one(int))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),zero_zero(A))) # label(fact_252_ceiling__less__one) # label(axiom). [clausify(382)].
% 10.54/10.51 4965 -archim1727834104eiling(A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),hAPP(A,int,archimedean_ceiling(A),B))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) # label(fact_253_one__le__ceiling) # label(axiom). [clausify(383)].
% 10.54/10.51 4966 -archim1727834104eiling(A) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),hAPP(A,int,archimedean_ceiling(A),B))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) # label(fact_253_one__le__ceiling) # label(axiom). [clausify(383)].
% 10.54/10.51 4967 -archim1727834104eiling(A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(A,int,archimedean_ceiling(A),B)),hAPP(A,int,archimedean_ceiling(A),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) # label(fact_283_ceiling__less__cancel) # label(axiom). [clausify(412)].
% 10.54/10.51 4968 -archim1727834104eiling(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(A,int,archimedean_ceiling(A),B)),hAPP(A,int,archimedean_ceiling(A),C))) # label(fact_284_ceiling__mono) # label(axiom). [clausify(413)].
% 10.54/10.51 4969 -archim1727834104eiling(A) | hAPP(A,int,archimedean_ceiling(A),one_one(A)) = one_one(int) # label(fact_285_ceiling__one) # label(axiom). [clausify(414)].
% 10.54/10.51 4970 -archim1727834104eiling(A) | hAPP(int,int,number_number_of(int),B) = hAPP(A,int,archimedean_ceiling(A),hAPP(int,A,number_number_of(A),B)) # label(fact_288_ceiling__number__of) # label(axiom). [clausify(417)].
% 10.54/10.51 4971 -archim1727834104eiling(A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),hAPP(A,int,archimedean_ceiling(A),B))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),B)) # label(fact_348_one__less__ceiling) # label(axiom). [clausify(476)].
% 10.54/10.51 4972 -archim1727834104eiling(A) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),hAPP(A,int,archimedean_ceiling(A),B))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),B)) # label(fact_348_one__less__ceiling) # label(axiom). [clausify(476)].
% 10.54/10.51 4973 -archim1727834104eiling(A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(A,int,archimedean_ceiling(A),B)),one_one(int))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),one_one(A))) # label(fact_349_ceiling__le__one) # label(axiom). [clausify(477)].
% 10.54/10.51 4974 -archim1727834104eiling(A) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(A,int,archimedean_ceiling(A),B)),one_one(int))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),one_one(A))) # label(fact_349_ceiling__le__one) # label(axiom). [clausify(477)].
% 10.54/10.51 4975 -archim1727834104eiling(A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),B)),hAPP(A,int,archimedean_ceiling(A),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),B)),C)) # label(fact_350_number__of__less__ceiling) # label(axiom). [clausify(478)].
% 10.54/10.51 4976 -archim1727834104eiling(A) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),B)),hAPP(A,int,archimedean_ceiling(A),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),B)),C)) # label(fact_350_number__of__less__ceiling) # label(axiom). [clausify(478)].
% 10.54/10.51 4977 -archim1727834104eiling(A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(A,int,archimedean_ceiling(A),B)),hAPP(int,int,number_number_of(int),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(int,A,number_number_of(A),C))) # label(fact_351_ceiling__le__number__of) # label(axiom). [clausify(479)].
% 10.54/10.51 4978 -archim1727834104eiling(A) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(A,int,archimedean_ceiling(A),B)),hAPP(int,int,number_number_of(int),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(int,A,number_number_of(A),C))) # label(fact_351_ceiling__le__number__of) # label(axiom). [clausify(479)].
% 10.54/10.51 4979 -archim1727834104eiling(A) | hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(A,int,archimedean_ceiling(A),B)),one_one(int)) = hAPP(A,int,archimedean_ceiling(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),one_one(A))) # label(fact_352_ceiling__add__one) # label(axiom). [clausify(480)].
% 10.54/10.51 4980 -archim1727834104eiling(A) | hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(A,int,archimedean_ceiling(A),B)),hAPP(int,int,number_number_of(int),C)) = hAPP(A,int,archimedean_ceiling(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),hAPP(int,A,number_number_of(A),C))) # label(fact_353_ceiling__add__number__of) # label(axiom). [clausify(481)].
% 10.54/10.51 4981 -archim1727834104eiling(A) | hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(A,int,archimedean_ceiling(A),B)),one_one(int)) = hAPP(A,int,archimedean_ceiling(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),one_one(A))) # label(fact_354_ceiling__diff__one) # label(axiom). [clausify(482)].
% 10.54/10.51 4982 -archim1727834104eiling(A) | hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(A,int,archimedean_ceiling(A),B)),hAPP(int,int,number_number_of(int),C)) = hAPP(A,int,archimedean_ceiling(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),hAPP(int,A,number_number_of(A),C))) # label(fact_355_ceiling__diff__number__of) # label(axiom). [clausify(483)].
% 10.54/10.51 4983 -archim1727834104eiling(A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(A,int,archim2085082626_floor(A),B)),hAPP(int,int,number_number_of(int),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(int,A,number_number_of(A),C)),one_one(A)))) # label(fact_423_floor__le__number__of) # label(axiom). [clausify(549)].
% 10.54/10.51 4984 -archim1727834104eiling(A) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(A,int,archim2085082626_floor(A),B)),hAPP(int,int,number_number_of(int),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(int,A,number_number_of(A),C)),one_one(A)))) # label(fact_423_floor__le__number__of) # label(axiom). [clausify(549)].
% 10.57/10.51 4985 -archim1727834104eiling(A) | hAPP(A,int,archim2085082626_floor(A),zero_zero(A)) = zero_zero(int) # label(fact_424_floor__zero) # label(axiom). [clausify(550)].
% 10.57/10.51 4986 -archim1727834104eiling(A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(A,int,archim2085082626_floor(A),B)),hAPP(A,int,archim2085082626_floor(A),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) # label(fact_425_floor__less__cancel) # label(axiom). [clausify(551)].
% 10.57/10.51 4987 -archim1727834104eiling(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(A,int,archim2085082626_floor(A),B)),hAPP(A,int,archim2085082626_floor(A),C))) # label(fact_426_floor__mono) # label(axiom). [clausify(552)].
% 10.57/10.51 4988 -archim1727834104eiling(A) | hAPP(A,int,archim2085082626_floor(A),one_one(A)) = one_one(int) # label(fact_427_floor__one) # label(axiom). [clausify(553)].
% 10.57/10.51 4989 -archim1727834104eiling(A) | hAPP(int,int,number_number_of(int),B) = hAPP(A,int,archim2085082626_floor(A),hAPP(int,A,number_number_of(A),B)) # label(fact_428_floor__number__of) # label(axiom). [clausify(554)].
% 10.57/10.51 4990 -archim1727834104eiling(A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(A,int,archim2085082626_floor(A),B)),zero_zero(int))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) # label(fact_429_floor__less__zero) # label(axiom). [clausify(555)].
% 10.57/10.51 4991 -archim1727834104eiling(A) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(A,int,archim2085082626_floor(A),B)),zero_zero(int))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) # label(fact_429_floor__less__zero) # label(axiom). [clausify(555)].
% 10.57/10.51 4992 -archim1727834104eiling(A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(A,int,archim2085082626_floor(A),B))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) # label(fact_430_zero__le__floor) # label(axiom). [clausify(556)].
% 10.57/10.51 4993 -archim1727834104eiling(A) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(A,int,archim2085082626_floor(A),B))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) # label(fact_430_zero__le__floor) # label(axiom). [clausify(556)].
% 10.57/10.51 4994 -archim1727834104eiling(A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(A,int,archim2085082626_floor(A),B))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),one_one(A)),B)) # label(fact_431_zero__less__floor) # label(axiom). [clausify(557)].
% 10.57/10.51 4995 -archim1727834104eiling(A) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(A,int,archim2085082626_floor(A),B))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),one_one(A)),B)) # label(fact_431_zero__less__floor) # label(axiom). [clausify(557)].
% 10.57/10.51 4996 -archim1727834104eiling(A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(A,int,archim2085082626_floor(A),B)),zero_zero(int))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),one_one(A))) # label(fact_432_floor__le__zero) # label(axiom). [clausify(558)].
% 10.57/10.51 4997 -archim1727834104eiling(A) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(A,int,archim2085082626_floor(A),B)),zero_zero(int))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),one_one(A))) # label(fact_432_floor__le__zero) # label(axiom). [clausify(558)].
% 10.57/10.51 4998 -archim1727834104eiling(A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(A,int,archim2085082626_floor(A),B)),one_one(int))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),one_one(A))) # label(fact_433_floor__less__one) # label(axiom). [clausify(559)].
% 10.57/10.51 4999 -archim1727834104eiling(A) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(A,int,archim2085082626_floor(A),B)),one_one(int))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),one_one(A))) # label(fact_433_floor__less__one) # label(axiom). [clausify(559)].
% 10.57/10.51 5000 -archim1727834104eiling(A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),hAPP(A,int,archim2085082626_floor(A),B))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),one_one(A)),B)) # label(fact_434_one__le__floor) # label(axiom). [clausify(560)].
% 10.57/10.51 5001 -archim1727834104eiling(A) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),hAPP(A,int,archim2085082626_floor(A),B))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),one_one(A)),B)) # label(fact_434_one__le__floor) # label(axiom). [clausify(560)].
% 10.57/10.51 5002 -archim1727834104eiling(A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(A,int,archim2085082626_floor(A),B)),hAPP(int,int,number_number_of(int),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(int,A,number_number_of(A),C))) # label(fact_435_floor__less__number__of) # label(axiom). [clausify(561)].
% 10.57/10.51 5003 -archim1727834104eiling(A) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(A,int,archim2085082626_floor(A),B)),hAPP(int,int,number_number_of(int),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(int,A,number_number_of(A),C))) # label(fact_435_floor__less__number__of) # label(axiom). [clausify(561)].
% 10.57/10.51 5004 -archim1727834104eiling(A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),B)),hAPP(A,int,archim2085082626_floor(A),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(int,A,number_number_of(A),B)),C)) # label(fact_436_number__of__le__floor) # label(axiom). [clausify(562)].
% 10.57/10.51 5005 -archim1727834104eiling(A) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),B)),hAPP(A,int,archim2085082626_floor(A),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(int,A,number_number_of(A),B)),C)) # label(fact_436_number__of__le__floor) # label(axiom). [clausify(562)].
% 10.57/10.51 5006 -archim1727834104eiling(A) | hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(A,int,archim2085082626_floor(A),B)),one_one(int)) = hAPP(A,int,archim2085082626_floor(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),one_one(A))) # label(fact_437_floor__add__one) # label(axiom). [clausify(563)].
% 10.57/10.51 5007 -archim1727834104eiling(A) | hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(A,int,archim2085082626_floor(A),B)),hAPP(int,int,number_number_of(int),C)) = hAPP(A,int,archim2085082626_floor(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),hAPP(int,A,number_number_of(A),C))) # label(fact_438_floor__add__number__of) # label(axiom). [clausify(564)].
% 10.57/10.51 5008 -archim1727834104eiling(A) | hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(A,int,archim2085082626_floor(A),B)),one_one(int)) = hAPP(A,int,archim2085082626_floor(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),one_one(A))) # label(fact_439_floor__diff__one) # label(axiom). [clausify(565)].
% 10.57/10.51 5009 -archim1727834104eiling(A) | hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(A,int,archim2085082626_floor(A),B)),hAPP(int,int,number_number_of(int),C)) = hAPP(A,int,archim2085082626_floor(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),hAPP(int,A,number_number_of(A),C))) # label(fact_440_floor__diff__number__of) # label(axiom). [clausify(566)].
% 10.57/10.51 5010 -archim1727834104eiling(A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),B)),hAPP(A,int,archim2085082626_floor(A),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(int,A,number_number_of(A),B)),one_one(A))),C)) # label(fact_443_number__of__less__floor) # label(axiom). [clausify(569)].
% 10.57/10.51 5011 -archim1727834104eiling(A) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),B)),hAPP(A,int,archim2085082626_floor(A),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(int,A,number_number_of(A),B)),one_one(A))),C)) # label(fact_443_number__of__less__floor) # label(axiom). [clausify(569)].
% 10.57/10.51 5012 -archim1727834104eiling(A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(A,int,archimedean_ceiling(A),B))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),min)),B)) # label(fact_451_zero__le__ceiling) # label(axiom). [clausify(577)].
% 10.57/10.51 5013 -archim1727834104eiling(A) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(A,int,archimedean_ceiling(A),B))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),min)),B)) # label(fact_451_zero__le__ceiling) # label(axiom). [clausify(577)].
% 10.57/10.51 5014 -archim1727834104eiling(A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(A,int,archimedean_ceiling(A),B)),zero_zero(int))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(int,A,number_number_of(A),min))) # label(fact_452_ceiling__less__zero) # label(axiom). [clausify(578)].
% 10.57/10.51 5015 -archim1727834104eiling(A) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(A,int,archimedean_ceiling(A),B)),zero_zero(int))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(int,A,number_number_of(A),min))) # label(fact_452_ceiling__less__zero) # label(axiom). [clausify(578)].
% 10.57/10.51 5016 -archim1727834104eiling(A) | hAPP(int,int,uminus_uminus(int),hAPP(A,int,archimedean_ceiling(A),B)) = hAPP(A,int,archim2085082626_floor(A),hAPP(A,A,uminus_uminus(A),B)) # label(fact_550_floor__minus) # label(axiom). [clausify(674)].
% 10.57/10.51 5017 -archim1727834104eiling(A) | hAPP(int,int,uminus_uminus(int),hAPP(A,int,archim2085082626_floor(A),B)) = hAPP(A,int,archimedean_ceiling(A),hAPP(A,A,uminus_uminus(A),B)) # label(fact_551_ceiling__minus) # label(axiom). [clausify(675)].
% 10.57/10.51 5018 -archim1727834104eiling(A) | hAPP(int,int,uminus_uminus(int),hAPP(A,int,archim2085082626_floor(A),hAPP(A,A,uminus_uminus(A),B))) = hAPP(A,int,archimedean_ceiling(A),B) # label(fact_552_ceiling__def) # label(axiom). [clausify(676)].
% 10.57/10.51 5019 -archim1727834104eiling(A) | hAPP(real,int,archim2085082626_floor(real),hAPP(int,real,real_1(int),hAPP(A,int,archimedean_ceiling(A),B))) = hAPP(A,int,archimedean_ceiling(A),B) # label(fact_1530_floor__ceiling) # label(axiom). [clausify(1626)].
% 10.57/10.51 5020 -archim1727834104eiling(A) | hAPP(real,int,archimedean_ceiling(real),hAPP(int,real,real_1(int),hAPP(A,int,archim2085082626_floor(A),B))) = hAPP(A,int,archim2085082626_floor(A),B) # label(fact_1531_ceiling__floor) # label(axiom). [clausify(1627)].
% 10.57/10.51 5021 -archim1727834104eiling(A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),hAPP(A,int,archim2085082626_floor(A),B))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(int,A,number_number_of(A),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),B)) # label(fact_1896_one__less__floor) # label(axiom). [clausify(1941)].
% 10.57/10.51 5022 -archim1727834104eiling(A) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),hAPP(A,int,archim2085082626_floor(A),B))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(int,A,number_number_of(A),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),B)) # label(fact_1896_one__less__floor) # label(axiom). [clausify(1941)].
% 10.57/10.51 5023 -archim1727834104eiling(A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(A,int,archim2085082626_floor(A),B)),one_one(int))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(int,A,number_number_of(A),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) # label(fact_1897_floor__le__one) # label(axiom). [clausify(1942)].
% 10.57/10.51 5024 -archim1727834104eiling(A) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(A,int,archim2085082626_floor(A),B)),one_one(int))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(int,A,number_number_of(A),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) # label(fact_1897_floor__le__one) # label(axiom). [clausify(1942)].
% 10.57/10.51 5025 -archim1727834104eiling(A) | hAPP(nat,int,semiring_1_of_nat(int),B) = hAPP(A,int,archimedean_ceiling(A),hAPP(nat,A,semiring_1_of_nat(A),B)) # label(fact_2574_ceiling__of__nat) # label(axiom). [clausify(2574)].
% 10.57/10.51 5026 -archim1727834104eiling(A) | hAPP(nat,int,semiring_1_of_nat(int),B) = hAPP(A,int,archim2085082626_floor(A),hAPP(nat,A,semiring_1_of_nat(A),B)) # label(fact_2576_floor__of__nat) # label(axiom). [clausify(2576)].
% 10.57/10.51 5027 -archim1727834104eiling(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(int,A,ring_1_of_int(A),hAPP(A,int,archimedean_ceiling(A),B)))) # label(fact_3567_le__of__int__ceiling) # label(axiom). [clausify(3522)].
% 10.57/10.51 5028 -archim1727834104eiling(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(int,A,ring_1_of_int(A),hAPP(A,int,archim2085082626_floor(A),B))),B)) # label(fact_3568_of__int__floor__le) # label(axiom). [clausify(3523)].
% 10.57/10.51 5029 -archim1727834104eiling(A) | hAPP(A,int,archim2085082626_floor(A),hAPP(int,A,ring_1_of_int(A),B)) = B # label(fact_3577_floor__of__int) # label(axiom). [clausify(3530)].
% 10.57/10.51 5030 -archim1727834104eiling(A) | hAPP(A,int,archimedean_ceiling(A),hAPP(int,A,ring_1_of_int(A),B)) = B # label(fact_3579_ceiling__of__int) # label(axiom). [clausify(3532)].
% 10.57/10.51 5031 -archim1727834104eiling(A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(A,int,archim2085082626_floor(A),B)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(int,A,ring_1_of_int(A),C))) # label(fact_3599_floor__less__iff) # label(axiom). [clausify(3552)].
% 10.57/10.51 5032 -archim1727834104eiling(A) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(A,int,archim2085082626_floor(A),B)),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(int,A,ring_1_of_int(A),C))) # label(fact_3599_floor__less__iff) # label(axiom). [clausify(3552)].
% 10.57/10.51 5033 -archim1727834104eiling(A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),hAPP(A,int,archim2085082626_floor(A),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(int,A,ring_1_of_int(A),B)),C)) # label(fact_3600_le__floor__iff) # label(axiom). [clausify(3553)].
% 10.57/10.51 5034 -archim1727834104eiling(A) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),hAPP(A,int,archim2085082626_floor(A),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(int,A,ring_1_of_int(A),B)),C)) # label(fact_3600_le__floor__iff) # label(axiom). [clausify(3553)].
% 10.57/10.51 5035 -archim1727834104eiling(A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),hAPP(A,int,archimedean_ceiling(A),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,ring_1_of_int(A),B)),C)) # label(fact_3601_less__ceiling__iff) # label(axiom). [clausify(3554)].
% 10.57/10.51 5036 -archim1727834104eiling(A) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),hAPP(A,int,archimedean_ceiling(A),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,ring_1_of_int(A),B)),C)) # label(fact_3601_less__ceiling__iff) # label(axiom). [clausify(3554)].
% 10.57/10.51 5037 -archim1727834104eiling(A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(A,int,archimedean_ceiling(A),B)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(int,A,ring_1_of_int(A),C))) # label(fact_3602_ceiling__le__iff) # label(axiom). [clausify(3555)].
% 10.57/10.51 5038 -archim1727834104eiling(A) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(A,int,archimedean_ceiling(A),B)),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(int,A,ring_1_of_int(A),C))) # label(fact_3602_ceiling__le__iff) # label(axiom). [clausify(3555)].
% 10.57/10.51 5039 -archim1727834104eiling(A) | hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(A,int,archim2085082626_floor(A),B)),C) = hAPP(A,int,archim2085082626_floor(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),hAPP(int,A,ring_1_of_int(A),C))) # label(fact_3603_floor__add__of__int) # label(axiom). [clausify(3556)].
% 10.57/10.51 5040 -archim1727834104eiling(A) | hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(A,int,archimedean_ceiling(A),B)),C) = hAPP(A,int,archimedean_ceiling(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),hAPP(int,A,ring_1_of_int(A),C))) # label(fact_3604_ceiling__add__of__int) # label(axiom). [clausify(3557)].
% 10.57/10.51 5041 -archim1727834104eiling(A) | hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(A,int,archim2085082626_floor(A),B)),C) = hAPP(A,int,archim2085082626_floor(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),hAPP(int,A,ring_1_of_int(A),C))) # label(fact_3605_floor__diff__of__int) # label(axiom). [clausify(3558)].
% 10.57/10.51 5042 -archim1727834104eiling(A) | hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(A,int,archimedean_ceiling(A),B)),C) = hAPP(A,int,archimedean_ceiling(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),hAPP(int,A,ring_1_of_int(A),C))) # label(fact_3606_ceiling__diff__of__int) # label(axiom). [clausify(3559)].
% 10.57/10.51 5043 -archim1727834104eiling(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(int,A,ring_1_of_int(A),B)),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(int,A,ring_1_of_int(A),B)),one_one(A)))) | hAPP(A,int,archim2085082626_floor(A),C) = B # label(fact_3612_floor__unique) # label(axiom). [clausify(3565)].
% 10.57/10.51 5044 -archim1727834104eiling(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(int,A,ring_1_of_int(A),B)),one_one(A))),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),hAPP(int,A,ring_1_of_int(A),B))) | hAPP(A,int,archimedean_ceiling(A),C) = B # label(fact_3613_ceiling__unique) # label(axiom). [clausify(3566)].
% 10.57/10.51 5045 -archim1727834104eiling(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(int,A,ring_1_of_int(A),hAPP(A,int,archimedean_ceiling(A),B))),one_one(A))),B)) # label(fact_3614_ceiling__correct) # label(axiom). [clausify(3567)].
% 10.57/10.51 5046 -archim1727834104eiling(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(int,A,ring_1_of_int(A),hAPP(A,int,archimedean_ceiling(A),B)))) # label(fact_3614_ceiling__correct) # label(axiom). [clausify(3567)].
% 10.57/10.51 5047 -archim1727834104eiling(A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),hAPP(A,int,archim2085082626_floor(A),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(int,A,ring_1_of_int(A),B)),one_one(A))),C)) # label(fact_3615_less__floor__iff) # label(axiom). [clausify(3568)].
% 10.57/10.51 5048 -archim1727834104eiling(A) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),hAPP(A,int,archim2085082626_floor(A),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(int,A,ring_1_of_int(A),B)),one_one(A))),C)) # label(fact_3615_less__floor__iff) # label(axiom). [clausify(3568)].
% 10.57/10.51 5049 -archim1727834104eiling(A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(A,int,archim2085082626_floor(A),B)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(int,A,ring_1_of_int(A),C)),one_one(A)))) # label(fact_3616_floor__le__iff) # label(axiom). [clausify(3569)].
% 10.57/10.51 5050 -archim1727834104eiling(A) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(A,int,archim2085082626_floor(A),B)),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(int,A,ring_1_of_int(A),C)),one_one(A)))) # label(fact_3616_floor__le__iff) # label(axiom). [clausify(3569)].
% 10.57/10.51 5051 -archim1727834104eiling(A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(A,int,archimedean_ceiling(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),minus_minus(A),hAPP(int,A,ring_1_of_int(A),C)),one_one(A)))) # label(fact_3617_ceiling__less__iff) # label(axiom). [clausify(3570)].
% 10.57/10.51 5052 -archim1727834104eiling(A) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(A,int,archimedean_ceiling(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),minus_minus(A),hAPP(int,A,ring_1_of_int(A),C)),one_one(A)))) # label(fact_3617_ceiling__less__iff) # label(axiom). [clausify(3570)].
% 10.57/10.51 5053 -archim1727834104eiling(A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),hAPP(A,int,archimedean_ceiling(A),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(int,A,ring_1_of_int(A),B)),one_one(A))),C)) # label(fact_3618_le__ceiling__iff) # label(axiom). [clausify(3571)].
% 10.57/10.51 5054 -archim1727834104eiling(A) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),hAPP(A,int,archimedean_ceiling(A),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(int,A,ring_1_of_int(A),B)),one_one(A))),C)) # label(fact_3618_le__ceiling__iff) # label(axiom). [clausify(3571)].
% 10.57/10.51 5055 -archim1727834104eiling(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(int,A,ring_1_of_int(A),hAPP(A,int,archim2085082626_floor(A),B))),B)) # label(fact_3619_floor__correct) # label(axiom). [clausify(3572)].
% 10.57/10.51 5056 -archim1727834104eiling(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(int,A,ring_1_of_int(A),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(A,int,archim2085082626_floor(A),B)),one_one(int))))) # label(fact_3619_floor__correct) # label(axiom). [clausify(3572)].
% 10.57/10.51 Derived: ti(fun(rat,int),archimedean_ceiling(rat)) = archimedean_ceiling(rat). [resolve(4951,a,4952,a)].
% 10.57/10.51 Derived: archim2085082626_floor(rat) = ti(fun(rat,int),archim2085082626_floor(rat)). [resolve(4951,a,4953,a)].
% 10.57/10.51 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),A)),hAPP(rat,int,archimedean_ceiling(rat),B))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),hAPP(int,rat,number_number_of(rat),A)),one_one(rat))),B)). [resolve(4951,a,4954,a)].
% 10.57/10.51 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),A)),hAPP(rat,int,archimedean_ceiling(rat),B))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),hAPP(int,rat,number_number_of(rat),A)),one_one(rat))),B)). [resolve(4951,a,4955,a)].
% 10.57/10.51 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(rat,int,archimedean_ceiling(rat),A)),hAPP(int,int,number_number_of(int),B))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),hAPP(int,rat,number_number_of(rat),B)),one_one(rat)))). [resolve(4951,a,4956,a)].
% 10.57/10.51 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(rat,int,archimedean_ceiling(rat),A)),hAPP(int,int,number_number_of(int),B))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),hAPP(int,rat,number_number_of(rat),B)),one_one(rat)))). [resolve(4951,a,4957,a)].
% 10.57/10.51 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(rat,int,archimedean_ceiling(rat),A))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)). [resolve(4951,a,4958,a)].
% 10.57/10.51 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(rat,int,archimedean_ceiling(rat),A))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)). [resolve(4951,a,4959,a)].
% 10.57/10.51 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(rat,int,archimedean_ceiling(rat),A)),zero_zero(int))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),zero_zero(rat))). [resolve(4951,a,4960,a)].
% 10.57/10.51 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(rat,int,archimedean_ceiling(rat),A)),zero_zero(int))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),zero_zero(rat))). [resolve(4951,a,4961,a)].
% 10.57/10.51 Derived: hAPP(rat,int,archimedean_ceiling(rat),zero_zero(rat)) = zero_zero(int). [resolve(4951,a,4962,a)].
% 10.57/10.51 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(rat,int,archimedean_ceiling(rat),A)),one_one(int))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),zero_zero(rat))). [resolve(4951,a,4963,a)].
% 10.57/10.51 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(rat,int,archimedean_ceiling(rat),A)),one_one(int))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),zero_zero(rat))). [resolve(4951,a,4964,a)].
% 10.57/10.51 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),hAPP(rat,int,archimedean_ceiling(rat),A))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)). [resolve(4951,a,4965,a)].
% 10.57/10.51 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),hAPP(rat,int,archimedean_ceiling(rat),A))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)). [resolve(4951,a,4966,a)].
% 10.57/10.51 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(rat,int,archimedean_ceiling(rat),A)),hAPP(rat,int,archimedean_ceiling(rat),B))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),B)). [resolve(4951,a,4967,a)].
% 10.57/10.51 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(rat,int,archimedean_ceiling(rat),A)),hAPP(rat,int,archimedean_ceiling(rat),B))). [resolve(4951,a,4968,a)].
% 10.57/10.51 Derived: hAPP(rat,int,archimedean_ceiling(rat),one_one(rat)) = one_one(int). [resolve(4951,a,4969,a)].
% 10.57/10.51 Derived: hAPP(int,int,number_number_of(int),A) = hAPP(rat,int,archimedean_ceiling(rat),hAPP(int,rat,number_number_of(rat),A)). [resolve(4951,a,4970,a)].
% 10.57/10.51 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),hAPP(rat,int,archimedean_ceiling(rat),A))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),one_one(rat)),A)). [resolve(4951,a,4971,a)].
% 10.57/10.51 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),hAPP(rat,int,archimedean_ceiling(rat),A))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),one_one(rat)),A)). [resolve(4951,a,4972,a)].
% 10.57/10.51 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(rat,int,archimedean_ceiling(rat),A)),one_one(int))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),one_one(rat))). [resolve(4951,a,4973,a)].
% 10.57/10.51 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(rat,int,archimedean_ceiling(rat),A)),one_one(int))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),one_one(rat))). [resolve(4951,a,4974,a)].
% 10.57/10.51 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),A)),hAPP(rat,int,archimedean_ceiling(rat),B))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(int,rat,number_number_of(rat),A)),B)). [resolve(4951,a,4975,a)].
% 10.57/10.51 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),A)),hAPP(rat,int,archimedean_ceiling(rat),B))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(int,rat,number_number_of(rat),A)),B)). [resolve(4951,a,4976,a)].
% 10.57/10.51 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(rat,int,archimedean_ceiling(rat),A)),hAPP(int,int,number_number_of(int),B))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),hAPP(int,rat,number_number_of(rat),B))). [resolve(4951,a,4977,a)].
% 10.57/10.51 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(rat,int,archimedean_ceiling(rat),A)),hAPP(int,int,number_number_of(int),B))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),hAPP(int,rat,number_number_of(rat),B))). [resolve(4951,a,4978,a)].
% 10.57/10.51 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(rat,int,archimedean_ceiling(rat),A)),one_one(int)) = hAPP(rat,int,archimedean_ceiling(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),one_one(rat))). [resolve(4951,a,4979,a)].
% 10.57/10.51 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(rat,int,archimedean_ceiling(rat),A)),hAPP(int,int,number_number_of(int),B)) = hAPP(rat,int,archimedean_ceiling(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),hAPP(int,rat,number_number_of(rat),B))). [resolve(4951,a,4980,a)].
% 10.57/10.51 Derived: hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(rat,int,archimedean_ceiling(rat),A)),one_one(int)) = hAPP(rat,int,archimedean_ceiling(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),A),one_one(rat))). [resolve(4951,a,4981,a)].
% 10.57/10.52 Derived: hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(rat,int,archimedean_ceiling(rat),A)),hAPP(int,int,number_number_of(int),B)) = hAPP(rat,int,archimedean_ceiling(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),A),hAPP(int,rat,number_number_of(rat),B))). [resolve(4951,a,4982,a)].
% 10.57/10.52 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(rat,int,archim2085082626_floor(rat),A)),hAPP(int,int,number_number_of(int),B))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(int,rat,number_number_of(rat),B)),one_one(rat)))). [resolve(4951,a,4983,a)].
% 10.57/10.52 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(rat,int,archim2085082626_floor(rat),A)),hAPP(int,int,number_number_of(int),B))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(int,rat,number_number_of(rat),B)),one_one(rat)))). [resolve(4951,a,4984,a)].
% 10.57/10.52 Derived: hAPP(rat,int,archim2085082626_floor(rat),zero_zero(rat)) = zero_zero(int). [resolve(4951,a,4985,a)].
% 10.57/10.52 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(rat,int,archim2085082626_floor(rat),A)),hAPP(rat,int,archim2085082626_floor(rat),B))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),B)). [resolve(4951,a,4986,a)].
% 10.57/10.52 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(rat,int,archim2085082626_floor(rat),A)),hAPP(rat,int,archim2085082626_floor(rat),B))). [resolve(4951,a,4987,a)].
% 10.57/10.52 Derived: hAPP(rat,int,archim2085082626_floor(rat),one_one(rat)) = one_one(int). [resolve(4951,a,4988,a)].
% 10.57/10.52 Derived: hAPP(int,int,number_number_of(int),A) = hAPP(rat,int,archim2085082626_floor(rat),hAPP(int,rat,number_number_of(rat),A)). [resolve(4951,a,4989,a)].
% 10.57/10.52 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(rat,int,archim2085082626_floor(rat),A)),zero_zero(int))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),zero_zero(rat))). [resolve(4951,a,4990,a)].
% 10.57/10.52 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(rat,int,archim2085082626_floor(rat),A)),zero_zero(int))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),zero_zero(rat))). [resolve(4951,a,4991,a)].
% 10.57/10.52 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(rat,int,archim2085082626_floor(rat),A))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),A)). [resolve(4951,a,4992,a)].
% 10.57/10.52 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(rat,int,archim2085082626_floor(rat),A))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),A)). [resolve(4951,a,4993,a)].
% 10.57/10.52 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(rat,int,archim2085082626_floor(rat),A))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),one_one(rat)),A)). [resolve(4951,a,4994,a)].
% 10.57/10.52 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(rat,int,archim2085082626_floor(rat),A))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),one_one(rat)),A)). [resolve(4951,a,4995,a)].
% 10.57/10.52 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(rat,int,archim2085082626_floor(rat),A)),zero_zero(int))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),one_one(rat))). [resolve(4951,a,4996,a)].
% 10.57/10.52 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(rat,int,archim2085082626_floor(rat),A)),zero_zero(int))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),one_one(rat))). [resolve(4951,a,4997,a)].
% 10.57/10.52 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(rat,int,archim2085082626_floor(rat),A)),one_one(int))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),one_one(rat))). [resolve(4951,a,4998,a)].
% 10.57/10.52 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(rat,int,archim2085082626_floor(rat),A)),one_one(int))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),one_one(rat))). [resolve(4951,a,4999,a)].
% 10.57/10.52 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),hAPP(rat,int,archim2085082626_floor(rat),A))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),one_one(rat)),A)). [resolve(4951,a,5000,a)].
% 10.57/10.52 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),hAPP(rat,int,archim2085082626_floor(rat),A))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),one_one(rat)),A)). [resolve(4951,a,5001,a)].
% 10.57/10.52 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(rat,int,archim2085082626_floor(rat),A)),hAPP(int,int,number_number_of(int),B))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),hAPP(int,rat,number_number_of(rat),B))). [resolve(4951,a,5002,a)].
% 10.57/10.52 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(rat,int,archim2085082626_floor(rat),A)),hAPP(int,int,number_number_of(int),B))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),hAPP(int,rat,number_number_of(rat),B))). [resolve(4951,a,5003,a)].
% 10.57/10.52 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),A)),hAPP(rat,int,archim2085082626_floor(rat),B))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(int,rat,number_number_of(rat),A)),B)). [resolve(4951,a,5004,a)].
% 10.57/10.52 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),A)),hAPP(rat,int,archim2085082626_floor(rat),B))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(int,rat,number_number_of(rat),A)),B)). [resolve(4951,a,5005,a)].
% 10.57/10.52 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(rat,int,archim2085082626_floor(rat),A)),one_one(int)) = hAPP(rat,int,archim2085082626_floor(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),one_one(rat))). [resolve(4951,a,5006,a)].
% 10.57/10.52 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(rat,int,archim2085082626_floor(rat),A)),hAPP(int,int,number_number_of(int),B)) = hAPP(rat,int,archim2085082626_floor(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),hAPP(int,rat,number_number_of(rat),B))). [resolve(4951,a,5007,a)].
% 10.57/10.52 Derived: hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(rat,int,archim2085082626_floor(rat),A)),one_one(int)) = hAPP(rat,int,archim2085082626_floor(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),A),one_one(rat))). [resolve(4951,a,5008,a)].
% 10.57/10.52 Derived: hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(rat,int,archim2085082626_floor(rat),A)),hAPP(int,int,number_number_of(int),B)) = hAPP(rat,int,archim2085082626_floor(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),A),hAPP(int,rat,number_number_of(rat),B))). [resolve(4951,a,5009,a)].
% 10.57/10.52 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),A)),hAPP(rat,int,archim2085082626_floor(rat),B))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(int,rat,number_number_of(rat),A)),one_one(rat))),B)). [resolve(4951,a,5010,a)].
% 10.57/10.52 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),A)),hAPP(rat,int,archim2085082626_floor(rat),B))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(int,rat,number_number_of(rat),A)),one_one(rat))),B)). [resolve(4951,a,5011,a)].
% 10.57/10.52 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(rat,int,archimedean_ceiling(rat),A))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(int,rat,number_number_of(rat),min)),A)). [resolve(4951,a,5012,a)].
% 10.57/10.52 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(rat,int,archimedean_ceiling(rat),A))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(int,rat,number_number_of(rat),min)),A)). [resolve(4951,a,5013,a)].
% 10.57/10.52 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(rat,int,archimedean_ceiling(rat),A)),zero_zero(int))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),hAPP(int,rat,number_number_of(rat),min))). [resolve(4951,a,5014,a)].
% 10.57/10.52 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(rat,int,archimedean_ceiling(rat),A)),zero_zero(int))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),hAPP(int,rat,number_number_of(rat),min))). [resolve(4951,a,5015,a)].
% 10.57/10.52 Derived: hAPP(int,int,uminus_uminus(int),hAPP(rat,int,archimedean_ceiling(rat),A)) = hAPP(rat,int,archim2085082626_floor(rat),hAPP(rat,rat,uminus_uminus(rat),A)). [resolve(4951,a,5016,a)].
% 10.57/10.52 Derived: hAPP(int,int,uminus_uminus(int),hAPP(rat,int,archim2085082626_floor(rat),A)) = hAPP(rat,int,archimedean_ceiling(rat),hAPP(rat,rat,uminus_uminus(rat),A)). [resolve(4951,a,5017,a)].
% 10.57/10.52 Derived: hAPP(int,int,uminus_uminus(int),hAPP(rat,int,archim2085082626_floor(rat),hAPP(rat,rat,uminus_uminus(rat),A))) = hAPP(rat,int,archimedean_ceiling(rat),A). [resolve(4951,a,5018,a)].
% 10.57/10.52 Derived: hAPP(real,int,archim2085082626_floor(real),hAPP(int,real,real_1(int),hAPP(rat,int,archimedean_ceiling(rat),A))) = hAPP(rat,int,archimedean_ceiling(rat),A). [resolve(4951,a,5019,a)].
% 10.57/10.52 Derived: hAPP(real,int,archimedean_ceiling(real),hAPP(int,real,real_1(int),hAPP(rat,int,archim2085082626_floor(rat),A))) = hAPP(rat,int,archim2085082626_floor(rat),A). [resolve(4951,a,5020,a)].
% 10.57/10.52 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),hAPP(rat,int,archim2085082626_floor(rat),A))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(int,rat,number_number_of(rat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),A)). [resolve(4951,a,5021,a)].
% 10.57/10.52 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),hAPP(rat,int,archim2085082626_floor(rat),A))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(int,rat,number_number_of(rat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),A)). [resolve(4951,a,5022,a)].
% 10.57/10.52 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(rat,int,archim2085082626_floor(rat),A)),one_one(int))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),hAPP(int,rat,number_number_of(rat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))). [resolve(4951,a,5023,a)].
% 10.57/10.52 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(rat,int,archim2085082626_floor(rat),A)),one_one(int))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),hAPP(int,rat,number_number_of(rat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))). [resolve(4951,a,5024,a)].
% 10.57/10.52 Derived: hAPP(nat,int,semiring_1_of_nat(int),A) = hAPP(rat,int,archimedean_ceiling(rat),hAPP(nat,rat,semiring_1_of_nat(rat),A)). [resolve(4951,a,5025,a)].
% 10.57/10.52 Derived: hAPP(nat,int,semiring_1_of_nat(int),A) = hAPP(rat,int,archim2085082626_floor(rat),hAPP(nat,rat,semiring_1_of_nat(rat),A)). [resolve(4951,a,5026,a)].
% 10.57/10.52 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),hAPP(int,rat,ring_1_of_int(rat),hAPP(rat,int,archimedean_ceiling(rat),A)))). [resolve(4951,a,5027,a)].
% 10.57/10.52 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(int,rat,ring_1_of_int(rat),hAPP(rat,int,archim2085082626_floor(rat),A))),A)). [resolve(4951,a,5028,a)].
% 10.57/10.52 Derived: hAPP(rat,int,archim2085082626_floor(rat),hAPP(int,rat,ring_1_of_int(rat),A)) = A. [resolve(4951,a,5029,a)].
% 10.57/10.52 Derived: hAPP(rat,int,archimedean_ceiling(rat),hAPP(int,rat,ring_1_of_int(rat),A)) = A. [resolve(4951,a,5030,a)].
% 10.57/10.52 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(rat,int,archim2085082626_floor(rat),A)),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),hAPP(int,rat,ring_1_of_int(rat),B))). [resolve(4951,a,5031,a)].
% 10.57/10.52 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(rat,int,archim2085082626_floor(rat),A)),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),hAPP(int,rat,ring_1_of_int(rat),B))). [resolve(4951,a,5032,a)].
% 10.57/10.52 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),hAPP(rat,int,archim2085082626_floor(rat),B))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(int,rat,ring_1_of_int(rat),A)),B)). [resolve(4951,a,5033,a)].
% 10.57/10.52 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),hAPP(rat,int,archim2085082626_floor(rat),B))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(int,rat,ring_1_of_int(rat),A)),B)). [resolve(4951,a,5034,a)].
% 10.57/10.52 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),hAPP(rat,int,archimedean_ceiling(rat),B))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(int,rat,ring_1_of_int(rat),A)),B)). [resolve(4951,a,5035,a)].
% 10.57/10.52 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),hAPP(rat,int,archimedean_ceiling(rat),B))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(int,rat,ring_1_of_int(rat),A)),B)). [resolve(4951,a,5036,a)].
% 10.57/10.52 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(rat,int,archimedean_ceiling(rat),A)),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),hAPP(int,rat,ring_1_of_int(rat),B))). [resolve(4951,a,5037,a)].
% 10.57/10.52 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(rat,int,archimedean_ceiling(rat),A)),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),hAPP(int,rat,ring_1_of_int(rat),B))). [resolve(4951,a,5038,a)].
% 10.57/10.52 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(rat,int,archim2085082626_floor(rat),A)),B) = hAPP(rat,int,archim2085082626_floor(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),hAPP(int,rat,ring_1_of_int(rat),B))). [resolve(4951,a,5039,a)].
% 10.57/10.52 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(rat,int,archimedean_ceiling(rat),A)),B) = hAPP(rat,int,archimedean_ceiling(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),hAPP(int,rat,ring_1_of_int(rat),B))). [resolve(4951,a,5040,a)].
% 10.57/10.52 Derived: hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(rat,int,archim2085082626_floor(rat),A)),B) = hAPP(rat,int,archim2085082626_floor(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),A),hAPP(int,rat,ring_1_of_int(rat),B))). [resolve(4951,a,5041,a)].
% 10.57/10.52 Derived: hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(rat,int,archimedean_ceiling(rat),A)),B) = hAPP(rat,int,archimedean_ceiling(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),A),hAPP(int,rat,ring_1_of_int(rat),B))). [resolve(4951,a,5042,a)].
% 10.57/10.52 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(int,rat,ring_1_of_int(rat),A)),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(int,rat,ring_1_of_int(rat),A)),one_one(rat)))) | hAPP(rat,int,archim2085082626_floor(rat),B) = A. [resolve(4951,a,5043,a)].
% 10.57/10.52 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),hAPP(int,rat,ring_1_of_int(rat),A)),one_one(rat))),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),B),hAPP(int,rat,ring_1_of_int(rat),A))) | hAPP(rat,int,archimedean_ceiling(rat),B) = A. [resolve(4951,a,5044,a)].
% 10.57/10.52 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),hAPP(int,rat,ring_1_of_int(rat),hAPP(rat,int,archimedean_ceiling(rat),A))),one_one(rat))),A)). [resolve(4951,a,5045,a)].
% 10.57/10.52 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),hAPP(rat,int,archim2085082626_floor(rat),B))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(int,rat,ring_1_of_int(rat),A)),one_one(rat))),B)). [resolve(4951,a,5047,a)].
% 10.57/10.52 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),hAPP(rat,int,archim2085082626_floor(rat),B))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(int,rat,ring_1_of_int(rat),A)),one_one(rat))),B)). [resolve(4951,a,5048,a)].
% 10.60/10.56 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(rat,int,archim2085082626_floor(rat),A)),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(int,rat,ring_1_of_int(rat),B)),one_one(rat)))). [resolve(4951,a,5049,a)].
% 10.60/10.56 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(rat,int,archim2085082626_floor(rat),A)),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(int,rat,ring_1_of_int(rat),B)),one_one(rat)))). [resolve(4951,a,5050,a)].
% 10.60/10.56 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(rat,int,archimedean_ceiling(rat),A)),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),hAPP(int,rat,ring_1_of_int(rat),B)),one_one(rat)))). [resolve(4951,a,5051,a)].
% 10.60/10.56 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(rat,int,archimedean_ceiling(rat),A)),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),hAPP(int,rat,ring_1_of_int(rat),B)),one_one(rat)))). [resolve(4951,a,5052,a)].
% 10.60/10.56 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),hAPP(rat,int,archimedean_ceiling(rat),B))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),hAPP(int,rat,ring_1_of_int(rat),A)),one_one(rat))),B)). [resolve(4951,a,5053,a)].
% 10.60/10.56 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),hAPP(rat,int,archimedean_ceiling(rat),B))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),hAPP(int,rat,ring_1_of_int(rat),A)),one_one(rat))),B)). [resolve(4951,a,5054,a)].
% 10.60/10.56 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),hAPP(int,rat,ring_1_of_int(rat),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(rat,int,archim2085082626_floor(rat),A)),one_one(int))))). [resolve(4951,a,5056,a)].
% 10.60/10.56 5057 archim1727834104eiling(real) # label(arity_RealDef_Oreal___Archimedean__Field_Ofloor__ceiling) # label(axiom). [assumption].
% 10.60/10.56 Derived: ti(fun(real,int),archimedean_ceiling(real)) = archimedean_ceiling(real). [resolve(5057,a,4952,a)].
% 10.60/10.56 Derived: archim2085082626_floor(real) = ti(fun(real,int),archim2085082626_floor(real)). [resolve(5057,a,4953,a)].
% 10.60/10.56 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),A)),hAPP(real,int,archimedean_ceiling(real),B))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(int,real,number_number_of(real),A)),one_one(real))),B)). [resolve(5057,a,4954,a)].
% 10.60/10.56 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),A)),hAPP(real,int,archimedean_ceiling(real),B))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(int,real,number_number_of(real),A)),one_one(real))),B)). [resolve(5057,a,4955,a)].
% 10.60/10.56 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(real,int,archimedean_ceiling(real),A)),hAPP(int,int,number_number_of(int),B))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(int,real,number_number_of(real),B)),one_one(real)))). [resolve(5057,a,4956,a)].
% 10.60/10.56 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(real,int,archimedean_ceiling(real),A)),hAPP(int,int,number_number_of(int),B))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(int,real,number_number_of(real),B)),one_one(real)))). [resolve(5057,a,4957,a)].
% 10.60/10.56 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(real,int,archimedean_ceiling(real),A))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)). [resolve(5057,a,4958,a)].
% 10.60/10.56 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(real,int,archimedean_ceiling(real),A))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)). [resolve(5057,a,4959,a)].
% 10.60/10.56 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(real,int,archimedean_ceiling(real),A)),zero_zero(int))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),zero_zero(real))). [resolve(5057,a,4960,a)].
% 10.60/10.56 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(real,int,archimedean_ceiling(real),A)),zero_zero(int))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),zero_zero(real))). [resolve(5057,a,4961,a)].
% 10.60/10.56 Derived: hAPP(real,int,archimedean_ceiling(real),zero_zero(real)) = zero_zero(int). [resolve(5057,a,4962,a)].
% 10.60/10.56 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(real,int,archimedean_ceiling(real),A)),one_one(int))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),zero_zero(real))). [resolve(5057,a,4963,a)].
% 10.60/10.56 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(real,int,archimedean_ceiling(real),A)),one_one(int))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),zero_zero(real))). [resolve(5057,a,4964,a)].
% 10.60/10.56 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),hAPP(real,int,archimedean_ceiling(real),A))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)). [resolve(5057,a,4965,a)].
% 10.60/10.56 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),hAPP(real,int,archimedean_ceiling(real),A))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)). [resolve(5057,a,4966,a)].
% 10.60/10.56 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(real,int,archimedean_ceiling(real),A)),hAPP(real,int,archimedean_ceiling(real),B))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)). [resolve(5057,a,4967,a)].
% 10.60/10.56 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(real,int,archimedean_ceiling(real),A)),hAPP(real,int,archimedean_ceiling(real),B))). [resolve(5057,a,4968,a)].
% 10.60/10.56 Derived: hAPP(real,int,archimedean_ceiling(real),one_one(real)) = one_one(int). [resolve(5057,a,4969,a)].
% 10.60/10.56 Derived: hAPP(int,int,number_number_of(int),A) = hAPP(real,int,archimedean_ceiling(real),hAPP(int,real,number_number_of(real),A)). [resolve(5057,a,4970,a)].
% 10.60/10.56 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),hAPP(real,int,archimedean_ceiling(real),A))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),A)). [resolve(5057,a,4971,a)].
% 10.60/10.56 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),hAPP(real,int,archimedean_ceiling(real),A))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),A)). [resolve(5057,a,4972,a)].
% 10.60/10.56 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(real,int,archimedean_ceiling(real),A)),one_one(int))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),one_one(real))). [resolve(5057,a,4973,a)].
% 10.60/10.56 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(real,int,archimedean_ceiling(real),A)),one_one(int))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),one_one(real))). [resolve(5057,a,4974,a)].
% 10.60/10.56 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),A)),hAPP(real,int,archimedean_ceiling(real),B))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,number_number_of(real),A)),B)). [resolve(5057,a,4975,a)].
% 10.60/10.56 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),A)),hAPP(real,int,archimedean_ceiling(real),B))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,number_number_of(real),A)),B)). [resolve(5057,a,4976,a)].
% 10.60/10.56 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(real,int,archimedean_ceiling(real),A)),hAPP(int,int,number_number_of(int),B))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),hAPP(int,real,number_number_of(real),B))). [resolve(5057,a,4977,a)].
% 10.60/10.56 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(real,int,archimedean_ceiling(real),A)),hAPP(int,int,number_number_of(int),B))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),hAPP(int,real,number_number_of(real),B))). [resolve(5057,a,4978,a)].
% 10.60/10.56 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(real,int,archimedean_ceiling(real),A)),one_one(int)) = hAPP(real,int,archimedean_ceiling(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),one_one(real))). [resolve(5057,a,4979,a)].
% 10.60/10.56 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(real,int,archimedean_ceiling(real),A)),hAPP(int,int,number_number_of(int),B)) = hAPP(real,int,archimedean_ceiling(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),hAPP(int,real,number_number_of(real),B))). [resolve(5057,a,4980,a)].
% 10.60/10.56 Derived: hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(real,int,archimedean_ceiling(real),A)),one_one(int)) = hAPP(real,int,archimedean_ceiling(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),one_one(real))). [resolve(5057,a,4981,a)].
% 10.60/10.56 Derived: hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(real,int,archimedean_ceiling(real),A)),hAPP(int,int,number_number_of(int),B)) = hAPP(real,int,archimedean_ceiling(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),hAPP(int,real,number_number_of(real),B))). [resolve(5057,a,4982,a)].
% 10.60/10.56 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(real,int,archim2085082626_floor(real),A)),hAPP(int,int,number_number_of(int),B))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(int,real,number_number_of(real),B)),one_one(real)))). [resolve(5057,a,4983,a)].
% 10.60/10.56 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(real,int,archim2085082626_floor(real),A)),hAPP(int,int,number_number_of(int),B))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(int,real,number_number_of(real),B)),one_one(real)))). [resolve(5057,a,4984,a)].
% 10.60/10.56 Derived: hAPP(real,int,archim2085082626_floor(real),zero_zero(real)) = zero_zero(int). [resolve(5057,a,4985,a)].
% 10.60/10.56 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(real,int,archim2085082626_floor(real),A)),hAPP(real,int,archim2085082626_floor(real),B))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)). [resolve(5057,a,4986,a)].
% 10.60/10.56 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(real,int,archim2085082626_floor(real),A)),hAPP(real,int,archim2085082626_floor(real),B))). [resolve(5057,a,4987,a)].
% 10.60/10.56 Derived: hAPP(real,int,archim2085082626_floor(real),one_one(real)) = one_one(int). [resolve(5057,a,4988,a)].
% 10.60/10.56 Derived: hAPP(int,int,number_number_of(int),A) = hAPP(real,int,archim2085082626_floor(real),hAPP(int,real,number_number_of(real),A)). [resolve(5057,a,4989,a)].
% 10.60/10.56 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(real,int,archim2085082626_floor(real),A)),zero_zero(int))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))). [resolve(5057,a,4990,a)].
% 10.60/10.56 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(real,int,archim2085082626_floor(real),A)),zero_zero(int))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))). [resolve(5057,a,4991,a)].
% 10.60/10.56 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(real,int,archim2085082626_floor(real),A))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A)). [resolve(5057,a,4992,a)].
% 10.60/10.56 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(real,int,archim2085082626_floor(real),A))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A)). [resolve(5057,a,4993,a)].
% 10.60/10.56 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(real,int,archim2085082626_floor(real),A))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),one_one(real)),A)). [resolve(5057,a,4994,a)].
% 10.60/10.56 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(real,int,archim2085082626_floor(real),A))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),one_one(real)),A)). [resolve(5057,a,4995,a)].
% 10.60/10.56 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(real,int,archim2085082626_floor(real),A)),zero_zero(int))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),one_one(real))). [resolve(5057,a,4996,a)].
% 10.60/10.56 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(real,int,archim2085082626_floor(real),A)),zero_zero(int))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),one_one(real))). [resolve(5057,a,4997,a)].
% 10.60/10.56 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(real,int,archim2085082626_floor(real),A)),one_one(int))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),one_one(real))). [resolve(5057,a,4998,a)].
% 10.60/10.56 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(real,int,archim2085082626_floor(real),A)),one_one(int))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),one_one(real))). [resolve(5057,a,4999,a)].
% 10.60/10.56 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),hAPP(real,int,archim2085082626_floor(real),A))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),one_one(real)),A)). [resolve(5057,a,5000,a)].
% 10.60/10.56 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),hAPP(real,int,archim2085082626_floor(real),A))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),one_one(real)),A)). [resolve(5057,a,5001,a)].
% 10.60/10.56 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(real,int,archim2085082626_floor(real),A)),hAPP(int,int,number_number_of(int),B))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),hAPP(int,real,number_number_of(real),B))). [resolve(5057,a,5002,a)].
% 10.60/10.56 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(real,int,archim2085082626_floor(real),A)),hAPP(int,int,number_number_of(int),B))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),hAPP(int,real,number_number_of(real),B))). [resolve(5057,a,5003,a)].
% 10.60/10.56 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),A)),hAPP(real,int,archim2085082626_floor(real),B))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,number_number_of(real),A)),B)). [resolve(5057,a,5004,a)].
% 10.60/10.56 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),A)),hAPP(real,int,archim2085082626_floor(real),B))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,number_number_of(real),A)),B)). [resolve(5057,a,5005,a)].
% 10.60/10.56 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(real,int,archim2085082626_floor(real),A)),one_one(int)) = hAPP(real,int,archim2085082626_floor(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),one_one(real))). [resolve(5057,a,5006,a)].
% 10.60/10.56 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(real,int,archim2085082626_floor(real),A)),hAPP(int,int,number_number_of(int),B)) = hAPP(real,int,archim2085082626_floor(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),hAPP(int,real,number_number_of(real),B))). [resolve(5057,a,5007,a)].
% 10.60/10.57 Derived: hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(real,int,archim2085082626_floor(real),A)),one_one(int)) = hAPP(real,int,archim2085082626_floor(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),one_one(real))). [resolve(5057,a,5008,a)].
% 10.60/10.57 Derived: hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(real,int,archim2085082626_floor(real),A)),hAPP(int,int,number_number_of(int),B)) = hAPP(real,int,archim2085082626_floor(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),hAPP(int,real,number_number_of(real),B))). [resolve(5057,a,5009,a)].
% 10.60/10.57 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),A)),hAPP(real,int,archim2085082626_floor(real),B))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(int,real,number_number_of(real),A)),one_one(real))),B)). [resolve(5057,a,5010,a)].
% 10.60/10.57 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),A)),hAPP(real,int,archim2085082626_floor(real),B))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(int,real,number_number_of(real),A)),one_one(real))),B)). [resolve(5057,a,5011,a)].
% 10.60/10.57 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(real,int,archimedean_ceiling(real),A))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,number_number_of(real),min)),A)). [resolve(5057,a,5012,a)].
% 10.60/10.57 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(real,int,archimedean_ceiling(real),A))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,number_number_of(real),min)),A)). [resolve(5057,a,5013,a)].
% 10.60/10.57 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(real,int,archimedean_ceiling(real),A)),zero_zero(int))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),hAPP(int,real,number_number_of(real),min))). [resolve(5057,a,5014,a)].
% 10.60/10.57 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(real,int,archimedean_ceiling(real),A)),zero_zero(int))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),hAPP(int,real,number_number_of(real),min))). [resolve(5057,a,5015,a)].
% 10.60/10.57 Derived: hAPP(int,int,uminus_uminus(int),hAPP(real,int,archimedean_ceiling(real),A)) = hAPP(real,int,archim2085082626_floor(real),hAPP(real,real,uminus_uminus(real),A)). [resolve(5057,a,5016,a)].
% 10.60/10.57 Derived: hAPP(int,int,uminus_uminus(int),hAPP(real,int,archim2085082626_floor(real),A)) = hAPP(real,int,archimedean_ceiling(real),hAPP(real,real,uminus_uminus(real),A)). [resolve(5057,a,5017,a)].
% 10.60/10.57 Derived: hAPP(int,int,uminus_uminus(int),hAPP(real,int,archim2085082626_floor(real),hAPP(real,real,uminus_uminus(real),A))) = hAPP(real,int,archimedean_ceiling(real),A). [resolve(5057,a,5018,a)].
% 10.60/10.57 Derived: hAPP(real,int,archim2085082626_floor(real),hAPP(int,real,real_1(int),hAPP(real,int,archimedean_ceiling(real),A))) = hAPP(real,int,archimedean_ceiling(real),A). [resolve(5057,a,5019,a)].
% 10.60/10.57 Derived: hAPP(real,int,archimedean_ceiling(real),hAPP(int,real,real_1(int),hAPP(real,int,archim2085082626_floor(real),A))) = hAPP(real,int,archim2085082626_floor(real),A). [resolve(5057,a,5020,a)].
% 10.60/10.57 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),hAPP(real,int,archim2085082626_floor(real),A))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),A)). [resolve(5057,a,5021,a)].
% 10.60/10.57 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),hAPP(real,int,archim2085082626_floor(real),A))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),A)). [resolve(5057,a,5022,a)].
% 10.60/10.57 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(real,int,archim2085082626_floor(real),A)),one_one(int))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))). [resolve(5057,a,5023,a)].
% 10.60/10.57 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(real,int,archim2085082626_floor(real),A)),one_one(int))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))). [resolve(5057,a,5024,a)].
% 10.60/10.57 Derived: hAPP(nat,int,semiring_1_of_nat(int),A) = hAPP(real,int,archimedean_ceiling(real),hAPP(nat,real,semiring_1_of_nat(real),A)). [resolve(5057,a,5025,a)].
% 10.60/10.57 Derived: hAPP(nat,int,semiring_1_of_nat(int),A) = hAPP(real,int,archim2085082626_floor(real),hAPP(nat,real,semiring_1_of_nat(real),A)). [resolve(5057,a,5026,a)].
% 10.60/10.57 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),hAPP(int,real,ring_1_of_int(real),hAPP(real,int,archimedean_ceiling(real),A)))). [resolve(5057,a,5027,a)].
% 10.60/10.57 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,ring_1_of_int(real),hAPP(real,int,archim2085082626_floor(real),A))),A)). [resolve(5057,a,5028,a)].
% 10.60/10.57 Derived: hAPP(real,int,archim2085082626_floor(real),hAPP(int,real,ring_1_of_int(real),A)) = A. [resolve(5057,a,5029,a)].
% 10.60/10.57 Derived: hAPP(real,int,archimedean_ceiling(real),hAPP(int,real,ring_1_of_int(real),A)) = A. [resolve(5057,a,5030,a)].
% 10.60/10.57 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(real,int,archim2085082626_floor(real),A)),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),hAPP(int,real,ring_1_of_int(real),B))). [resolve(5057,a,5031,a)].
% 10.60/10.57 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(real,int,archim2085082626_floor(real),A)),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),hAPP(int,real,ring_1_of_int(real),B))). [resolve(5057,a,5032,a)].
% 10.60/10.57 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),hAPP(real,int,archim2085082626_floor(real),B))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,ring_1_of_int(real),A)),B)). [resolve(5057,a,5033,a)].
% 10.60/10.57 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),hAPP(real,int,archim2085082626_floor(real),B))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,ring_1_of_int(real),A)),B)). [resolve(5057,a,5034,a)].
% 10.60/10.57 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),hAPP(real,int,archimedean_ceiling(real),B))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,ring_1_of_int(real),A)),B)). [resolve(5057,a,5035,a)].
% 10.60/10.57 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),hAPP(real,int,archimedean_ceiling(real),B))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,ring_1_of_int(real),A)),B)). [resolve(5057,a,5036,a)].
% 10.60/10.57 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(real,int,archimedean_ceiling(real),A)),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),hAPP(int,real,ring_1_of_int(real),B))). [resolve(5057,a,5037,a)].
% 10.60/10.57 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(real,int,archimedean_ceiling(real),A)),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),hAPP(int,real,ring_1_of_int(real),B))). [resolve(5057,a,5038,a)].
% 10.60/10.57 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(real,int,archim2085082626_floor(real),A)),B) = hAPP(real,int,archim2085082626_floor(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),hAPP(int,real,ring_1_of_int(real),B))). [resolve(5057,a,5039,a)].
% 10.60/10.57 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(real,int,archimedean_ceiling(real),A)),B) = hAPP(real,int,archimedean_ceiling(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),hAPP(int,real,ring_1_of_int(real),B))). [resolve(5057,a,5040,a)].
% 10.60/10.57 Derived: hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(real,int,archim2085082626_floor(real),A)),B) = hAPP(real,int,archim2085082626_floor(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),hAPP(int,real,ring_1_of_int(real),B))). [resolve(5057,a,5041,a)].
% 10.60/10.57 Derived: hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(real,int,archimedean_ceiling(real),A)),B) = hAPP(real,int,archimedean_ceiling(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),hAPP(int,real,ring_1_of_int(real),B))). [resolve(5057,a,5042,a)].
% 10.60/10.57 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,ring_1_of_int(real),A)),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(int,real,ring_1_of_int(real),A)),one_one(real)))) | hAPP(real,int,archim2085082626_floor(real),B) = A. [resolve(5057,a,5043,a)].
% 10.60/10.57 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(int,real,ring_1_of_int(real),A)),one_one(real))),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),hAPP(int,real,ring_1_of_int(real),A))) | hAPP(real,int,archimedean_ceiling(real),B) = A. [resolve(5057,a,5044,a)].
% 10.60/10.57 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(int,real,ring_1_of_int(real),hAPP(real,int,archimedean_ceiling(real),A))),one_one(real))),A)). [resolve(5057,a,5045,a)].
% 10.60/10.57 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),hAPP(real,int,archim2085082626_floor(real),B))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(int,real,ring_1_of_int(real),A)),one_one(real))),B)). [resolve(5057,a,5047,a)].
% 10.60/10.57 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),hAPP(real,int,archim2085082626_floor(real),B))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(int,real,ring_1_of_int(real),A)),one_one(real))),B)). [resolve(5057,a,5048,a)].
% 10.60/10.57 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(real,int,archim2085082626_floor(real),A)),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(int,real,ring_1_of_int(real),B)),one_one(real)))). [resolve(5057,a,5049,a)].
% 10.60/10.57 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(real,int,archim2085082626_floor(real),A)),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(int,real,ring_1_of_int(real),B)),one_one(real)))). [resolve(5057,a,5050,a)].
% 10.60/10.57 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(real,int,archimedean_ceiling(real),A)),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(int,real,ring_1_of_int(real),B)),one_one(real)))). [resolve(5057,a,5051,a)].
% 10.60/10.57 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(real,int,archimedean_ceiling(real),A)),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(int,real,ring_1_of_int(real),B)),one_one(real)))). [resolve(5057,a,5052,a)].
% 10.60/10.57 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),hAPP(real,int,archimedean_ceiling(real),B))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(int,real,ring_1_of_int(real),A)),one_one(real))),B)). [resolve(5057,a,5053,a)].
% 10.60/10.57 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),hAPP(real,int,archimedean_ceiling(real),B))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(int,real,ring_1_of_int(real),A)),one_one(real))),B)). [resolve(5057,a,5054,a)].
% 13.27/13.23 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),hAPP(int,real,ring_1_of_int(real),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(real,int,archim2085082626_floor(real),A)),one_one(int))))). [resolve(5057,a,5056,a)].
% 13.27/13.23 5058 comm_monoid_add(int) # label(arity_Int_Oint___Groups_Ocomm__monoid__add) # label(axiom). [assumption].
% 13.27/13.23 5059 -comm_monoid_add(A) | big_co1399186613setsum(B,A) = ti(fun(fun(B,A),fun(fun(B,bool),A)),big_co1399186613setsum(B,A)) # label(tsy_c_Big__Operators_Ocomm__monoid__add__class_Osetsum_res) # label(axiom). [clausify(3)].
% 13.27/13.23 5060 -comm_monoid_add(A) | -topological_space(A) | the(A) = ti(fun(fun(A,bool),A),the(A)) # label(tsy_c_HOL_OThe_3_res) # label(axiom). [clausify(44)].
% 13.27/13.23 5061 -comm_monoid_add(A) | -topological_space(A) | suminf(A) = ti(fun(fun(nat,A),A),suminf(A)) # label(tsy_c_Series_Osuminf_res) # label(axiom). [clausify(103)].
% 13.27/13.23 5062 -comm_monoid_add(A) | -topological_space(A) | summable(A) = ti(fun(fun(nat,A),bool),summable(A)) # label(tsy_c_Series_Osummable_res) # label(axiom). [clausify(104)].
% 13.27/13.23 5063 -comm_monoid_add(A) | -topological_space(A) | sums(A) = ti(fun(fun(nat,A),fun(A,bool)),sums(A)) # label(tsy_c_Series_Osums_res) # label(axiom). [clausify(105)].
% 13.27/13.23 5064 -comm_monoid_add(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),zero_zero(A)) = ti(A,B) # label(fact_266_add_Ocomm__neutral) # label(axiom). [clausify(396)].
% 13.27/13.23 5065 -comm_monoid_add(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),zero_zero(A)),B) = ti(A,B) # label(fact_269_add__0) # label(axiom). [clausify(399)].
% 13.27/13.23 5066 -comm_monoid_add(A) | -comm_monoid_mult(A) | hAPP(fun(nat,bool),A,hAPP(fun(nat,A),fun(fun(nat,bool),A),big_co302546470etprod(nat,A),B),C) = hAPP(fun(int,bool),A,hAPP(fun(int,A),fun(fun(int,bool),A),big_co302546470etprod(int,A),hAPP(fun(int,nat),fun(int,A),hAPP(fun(nat,A),fun(fun(int,nat),fun(int,A)),combb(nat,A,int),B),nat_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)),C)) # label(fact_3941_transfer__nat__int__sum__prod_I2_J) # label(axiom). [clausify(3882)].
% 13.27/13.23 5067 -comm_monoid_add(A) | -comm_monoid_mult(A) | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,B)) | hAPP(fun(nat,bool),A,hAPP(fun(nat,A),fun(fun(nat,bool),A),big_co302546470etprod(nat,A),hAPP(fun(nat,int),fun(nat,A),hAPP(fun(int,A),fun(fun(nat,int),fun(nat,A)),combb(int,A,nat),C),semiring_1_of_nat(int))),hAPP(fun(int,bool),fun(nat,bool),hAPP(fun(int,nat),fun(fun(int,bool),fun(nat,bool)),image(int,nat),nat_1),B)) = hAPP(fun(int,bool),A,hAPP(fun(int,A),fun(fun(int,bool),A),big_co302546470etprod(int,A),C),B) # label(fact_3942_transfer__int__nat__sum__prod_I2_J) # label(axiom). [clausify(3883)].
% 13.27/13.23 5068 -comm_monoid_add(A) | -comm_monoid_mult(A) | B != C | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),f486(A,D,E,C,B))) | hAPP(fun(int,bool),A,hAPP(fun(int,A),fun(fun(int,bool),A),big_co302546470etprod(int,A),E),B) = hAPP(fun(int,bool),A,hAPP(fun(int,A),fun(fun(int,bool),A),big_co302546470etprod(int,A),D),C) # label(fact_3959_transfer__nat__int__sum__prod__cong_I2_J) # label(axiom). [clausify(3900)].
% 13.27/13.23 5069 -comm_monoid_add(A) | -comm_monoid_mult(A) | B != C | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,B)) | hAPP(int,A,D,f486(A,E,D,C,B)) != hAPP(int,A,E,f486(A,E,D,C,B)) | hAPP(fun(int,bool),A,hAPP(fun(int,A),fun(fun(int,bool),A),big_co302546470etprod(int,A),D),B) = hAPP(fun(int,bool),A,hAPP(fun(int,A),fun(fun(int,bool),A),big_co302546470etprod(int,A),E),C) # label(fact_3959_transfer__nat__int__sum__prod__cong_I2_J) # label(axiom). [clausify(3900)].
% 13.27/13.23 5070 -comm_monoid_add(A) | -t2_space(A) | hAPP(fun(nat,A),A,suminf(A),hAPP(A,fun(nat,A),combk(A,nat),zero_zero(A))) = zero_zero(A) # label(fact_3965_suminf__zero) # label(axiom). [clausify(3906)].
% 13.27/13.23 5071 -comm_monoid_add(A) | -topological_space(A) | hBOOL(hAPP(fun(nat,A),bool,summable(A),hAPP(A,fun(nat,A),combk(A,nat),zero_zero(A)))) # label(fact_3977_summable__zero) # label(axiom). [clausify(3917)].
% 13.27/13.23 5072 -comm_monoid_add(A) | -topological_space(A) | hBOOL(hAPP(A,bool,hAPP(fun(nat,A),fun(A,bool),sums(A),hAPP(A,fun(nat,A),combk(A,nat),zero_zero(A))),zero_zero(A))) # label(fact_4078_sums__zero) # label(axiom). [clausify(4014)].
% 13.27/13.23 5073 -comm_monoid_add(A) | -t2_space(A) | -hBOOL(hAPP(A,bool,hAPP(fun(nat,A),fun(A,bool),sums(A),B),C)) | hAPP(fun(nat,A),A,suminf(A),B) = ti(A,C) # label(fact_4089_sums__unique) # label(axiom). [clausify(4025)].
% 13.27/13.23 5074 -comm_monoid_add(A) | -topological_space(A) | -hBOOL(hAPP(A,bool,hAPP(fun(nat,A),fun(A,bool),sums(A),B),C)) | hBOOL(hAPP(fun(nat,A),bool,summable(A),B)) # label(fact_4090_sums__summable) # label(axiom). [clausify(4026)].
% 13.27/13.23 5075 -comm_monoid_add(A) | -topological_space(A) | -hBOOL(hAPP(fun(nat,A),bool,summable(A),B)) | hBOOL(hAPP(A,bool,hAPP(fun(nat,A),fun(A,bool),sums(A),B),f513(A,B))) # label(fact_4091_summable__def) # label(axiom). [clausify(4027)].
% 13.27/13.23 5076 -comm_monoid_add(A) | -topological_space(A) | hBOOL(hAPP(fun(nat,A),bool,summable(A),B)) | -hBOOL(hAPP(A,bool,hAPP(fun(nat,A),fun(A,bool),sums(A),B),C)) # label(fact_4091_summable__def) # label(axiom). [clausify(4027)].
% 13.27/13.23 5077 -comm_monoid_add(A) | -t2_space(A) | -hBOOL(hAPP(A,bool,hAPP(fun(nat,A),fun(A,bool),sums(A),B),C)) | hBOOL(hAPP(fun(nat,A),bool,summable(A),B)) # label(fact_4092_sums__iff) # label(axiom). [clausify(4028)].
% 13.27/13.23 5078 -comm_monoid_add(A) | -t2_space(A) | -hBOOL(hAPP(A,bool,hAPP(fun(nat,A),fun(A,bool),sums(A),B),C)) | hAPP(fun(nat,A),A,suminf(A),B) = ti(A,C) # label(fact_4092_sums__iff) # label(axiom). [clausify(4028)].
% 13.27/13.23 5079 -comm_monoid_add(A) | -t2_space(A) | hBOOL(hAPP(A,bool,hAPP(fun(nat,A),fun(A,bool),sums(A),B),C)) | -hBOOL(hAPP(fun(nat,A),bool,summable(A),B)) | hAPP(fun(nat,A),A,suminf(A),B) != ti(A,C) # label(fact_4092_sums__iff) # label(axiom). [clausify(4028)].
% 13.27/13.23 5080 -comm_monoid_add(A) | -t2_space(A) | -hBOOL(hAPP(fun(nat,A),bool,summable(A),B)) | hBOOL(hAPP(A,bool,hAPP(fun(nat,A),fun(A,bool),sums(A),B),hAPP(fun(nat,A),A,suminf(A),B))) # label(fact_4093_summable__sums) # label(axiom). [clausify(4029)].
% 13.27/13.23 5081 -comm_monoid_add(A) | -topological_space(A) | hAPP(nat,A,B,zero_zero(nat)) != zero_zero(A) | -hBOOL(hAPP(A,bool,hAPP(fun(nat,A),fun(A,bool),sums(A),hAPP(fun(nat,nat),fun(nat,A),hAPP(fun(nat,A),fun(fun(nat,nat),fun(nat,A)),combb(nat,A,nat),B),suc)),C)) | hBOOL(hAPP(A,bool,hAPP(fun(nat,A),fun(A,bool),sums(A),B),C)) # label(fact_4094_sums__Suc__imp) # label(axiom). [clausify(4030)].
% 13.27/13.23 5082 -comm_monoid_add(A) | -topological_space(A) | hAPP(fun(nat,A),A,suminf(A),B) = hAPP(fun(A,bool),A,the(A),hAPP(fun(nat,A),fun(A,bool),sums(A),B)) # label(fact_4135_suminf__def) # label(axiom). [clausify(4069)].
% 13.27/13.23 5083 -comm_monoid_add(A) | -power(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(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),times_times(A)),hAPP(fun(nat,nat),fun(nat,A),hAPP(fun(nat,A),fun(fun(nat,nat),fun(nat,A)),combb(nat,A,nat),hAPP(A,fun(nat,A),power_power(A),B)),hAPP(nat,fun(nat,nat),minus_minus(nat),C)))),hAPP(A,fun(nat,A),power_power(A),D))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,suc,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),times_times(A)),hAPP(A,fun(nat,A),power_power(A),B))),hAPP(fun(nat,nat),fun(nat,A),hAPP(fun(nat,A),fun(fun(nat,nat),fun(nat,A)),combb(nat,A,nat),hAPP(A,fun(nat,A),power_power(A),D)),hAPP(nat,fun(nat,nat),minus_minus(nat),C)))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,suc,C))) # label(fact_4174_lemma__realpow__rev__sumr) # label(axiom). [clausify(4106)].
% 13.27/13.23 5084 -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,fun(nat,bool)),fun(nat,A),hAPP(fun(fun(nat,bool),A),fun(fun(nat,fun(nat,bool)),fun(nat,A)),combb(fun(nat,bool),A,nat),hAPP(fun(nat,A),fun(fun(nat,bool),A),big_co1399186613setsum(nat,A),B)),hAPP(fun(nat,nat),fun(nat,fun(nat,bool)),hAPP(fun(nat,fun(nat,fun(nat,bool))),fun(fun(nat,nat),fun(nat,fun(nat,bool))),combs(nat,nat,fun(nat,bool)),hAPP(fun(nat,nat),fun(nat,fun(nat,fun(nat,bool))),hAPP(fun(nat,fun(nat,fun(nat,bool))),fun(fun(nat,nat),fun(nat,fun(nat,fun(nat,bool)))),combb(nat,fun(nat,fun(nat,bool)),nat),ord_atLeastLessThan(nat)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),times_times(nat)),C))),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),plus_plus(nat)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),times_times(nat)),C))),C)))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),D)) = 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_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),D),C))) # label(fact_4176_sumr__group) # label(axiom). [clausify(4108)].
% 13.27/13.23 5085 -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_atLeastLessThan(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_atLeastLessThan(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_4178_setsum__shift__bounds__nat__ivl) # label(axiom). [clausify(4110)].
% 13.27/13.23 5086 -comm_monoid_add(A) | 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_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),C),D))) = 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),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)),D))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),C))),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_atLeastLessThan(nat),zero_zero(nat)),D))) # label(fact_4180_sumr__offset3) # label(axiom). [clausify(4112)].
% 13.27/13.23 5087 -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(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)),D)),E)),zero_zero(A))),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),collect(B),hAPP(fun(B,bool),fun(B,bool),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))),D))) # label(fact_4185_setsum__restrict__set_H_H) # label(axiom). [clausify(4117)].
% 13.27/13.23 5088 -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(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(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)),D))),E)),zero_zero(A))),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),collect(B),hAPP(fun(B,bool),fun(B,bool),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,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)),D)))) # label(fact_4186_setsum__restrict__set_H) # label(axiom). [clausify(4118)].
% 13.27/13.23 5089 -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),suc)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),C),D)) = 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_atLeastLessThan(nat),hAPP(nat,nat,suc,C)),hAPP(nat,nat,suc,D))) # label(fact_4187_setsum__shift__bounds__Suc__ivl) # label(axiom). [clausify(4119)].
% 13.27/13.23 5090 -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(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) = 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) # label(fact_4188_setsum__setsum__restrict) # label(axiom). [clausify(4120)].
% 13.27/13.23 5091 -comm_monoid_add(A) | hAPP(nat,A,B,zero_zero(nat)) != zero_zero(A) | 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_atLeastLessThan(nat),hAPP(nat,nat,suc,zero_zero(nat))),C)) = 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_atLeastLessThan(nat),zero_zero(nat)),C)) # label(fact_4198_setsum__shift__lb__Suc0__0__upt) # label(axiom). [clausify(4130)].
% 13.27/13.23 5092 -comm_monoid_add(A) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),C)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),C),D)) | hAPP(fun(nat,bool),A,hAPP(fun(nat,A),fun(fun(nat,bool),A),big_co1399186613setsum(nat,A),E),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),B),D)) = 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),E),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),B),C))),hAPP(fun(nat,bool),A,hAPP(fun(nat,A),fun(fun(nat,bool),A),big_co1399186613setsum(nat,A),E),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),C),D))) # label(fact_4200_setsum__add__nat__ivl) # label(axiom). [clausify(4132)].
% 13.27/13.23 5093 -comm_monoid_add(A) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(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_atLeastLessThan(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_atLeastLessThan(nat),hAPP(nat,nat,suc,B)),C))) # label(fact_4203_setsum__head__upt__Suc) # label(axiom). [clausify(4135)].
% 13.27/13.23 5094 -comm_monoid_add(A) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(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_atLeastLessThan(nat),C),hAPP(nat,nat,suc,B))) = zero_zero(A) # label(fact_4204_setsum__op__ivl__Suc) # label(axiom). [clausify(4136)].
% 13.27/13.23 5095 -comm_monoid_add(A) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(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_atLeastLessThan(nat),C),hAPP(nat,nat,suc,B))) = 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_atLeastLessThan(nat),C),B))),hAPP(nat,A,D,B)) # label(fact_4204_setsum__op__ivl__Suc) # label(axiom). [clausify(4136)].
% 13.27/13.23 5096 -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),C) = zero_zero(A) # label(fact_4207_setsum_Oinfinite) # label(axiom). [clausify(4139)].
% 13.27/13.23 5097 -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),C) = zero_zero(A) # label(fact_4208_setsum__infinite) # label(axiom). [clausify(4140)].
% 13.27/13.23 5098 -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_4214_setsum__commute) # label(axiom). [clausify(4146)].
% 13.27/13.23 5099 -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),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)),zero_zero(A))),C) = hAPP(B,A,E,D) # label(fact_4215_setsum__delta_H) # label(axiom). [clausify(4147)].
% 13.27/13.23 5100 -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),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)),zero_zero(A))),C) = zero_zero(A) # label(fact_4215_setsum__delta_H) # label(axiom). [clausify(4147)].
% 13.27/13.23 5101 -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),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)),zero_zero(A))),C) = hAPP(B,A,E,D) # label(fact_4216_setsum__delta) # label(axiom). [clausify(4148)].
% 13.27/13.23 5102 -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),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)),zero_zero(A))),C) = zero_zero(A) # label(fact_4216_setsum__delta) # label(axiom). [clausify(4148)].
% 13.27/13.23 5103 -comm_monoid_add(A) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),hAPP(A,fun(B,A),combk(A,B),zero_zero(A))),C) = zero_zero(A) # label(fact_4218_setsum__0) # label(axiom). [clausify(4150)].
% 13.27/13.23 5104 -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_4219_setsum_Odistrib) # label(axiom). [clausify(4151)].
% 13.27/13.23 5105 -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_4221_setsum__addf) # label(axiom). [clausify(4153)].
% 13.27/13.23 5106 -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_4224_setsum__image__gen) # label(axiom). [clausify(4156)].
% 13.27/13.23 5107 -comm_monoid_add(A) | -comm_monoid_mult(A) | hAPP(fun(nat,bool),A,hAPP(fun(nat,A),fun(fun(nat,bool),A),big_co1399186613setsum(nat,A),B),C) = hAPP(fun(int,bool),A,hAPP(fun(int,A),fun(fun(int,bool),A),big_co1399186613setsum(int,A),hAPP(fun(int,nat),fun(int,A),hAPP(fun(nat,A),fun(fun(int,nat),fun(int,A)),combb(nat,A,int),B),nat_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)),C)) # label(fact_4264_transfer__nat__int__sum__prod_I1_J) # label(axiom). [clausify(4196)].
% 13.27/13.23 5108 -comm_monoid_add(A) | -comm_monoid_mult(A) | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,B)) | hAPP(fun(nat,bool),A,hAPP(fun(nat,A),fun(fun(nat,bool),A),big_co1399186613setsum(nat,A),hAPP(fun(nat,int),fun(nat,A),hAPP(fun(int,A),fun(fun(nat,int),fun(nat,A)),combb(int,A,nat),C),semiring_1_of_nat(int))),hAPP(fun(int,bool),fun(nat,bool),hAPP(fun(int,nat),fun(fun(int,bool),fun(nat,bool)),image(int,nat),nat_1),B)) = hAPP(fun(int,bool),A,hAPP(fun(int,A),fun(fun(int,bool),A),big_co1399186613setsum(int,A),C),B) # label(fact_4266_transfer__int__nat__sum__prod_I1_J) # label(axiom). [clausify(4198)].
% 13.27/13.23 5109 -comm_monoid_add(A) | -t2_space(A) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),f592(A,C,B))) | hBOOL(hAPP(A,bool,hAPP(fun(nat,A),fun(A,bool),sums(A),C),hAPP(fun(nat,bool),A,hAPP(fun(nat,A),fun(fun(nat,bool),A),big_co1399186613setsum(nat,A),C),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),B)))) # label(fact_4291_series__zero) # label(axiom). [clausify(4223)].
% 13.27/13.23 5110 -comm_monoid_add(A) | -t2_space(A) | hAPP(nat,A,B,f592(A,B,C)) != zero_zero(A) | hBOOL(hAPP(A,bool,hAPP(fun(nat,A),fun(A,bool),sums(A),B),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_atLeastLessThan(nat),zero_zero(nat)),C)))) # label(fact_4291_series__zero) # label(axiom). [clausify(4223)].
% 13.27/13.23 5111 -comm_monoid_add(A) | -ordere779506340up_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)) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f593(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))) | 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),E),D)),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),E),C))) # label(fact_4292_setsum__mono3) # label(axiom). [clausify(4224)].
% 13.27/13.23 5112 -comm_monoid_add(A) | -ordere779506340up_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)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(B,A,E,f593(B,A,E,D,C)))) | 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),E),D)),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),E),C))) # label(fact_4292_setsum__mono3) # label(axiom). [clausify(4224)].
% 13.27/13.23 5113 -comm_monoid_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)) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f595(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_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_4294_setsum__mono__zero__left) # label(axiom). [clausify(4226)].
% 13.27/13.23 5114 -comm_monoid_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(B,A,E,f595(B,A,E,D,C)) != zero_zero(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_4294_setsum__mono__zero__left) # label(axiom). [clausify(4226)].
% 13.27/13.23 5115 -comm_monoid_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)) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f596(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_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_4295_setsum__mono__zero__right) # label(axiom). [clausify(4227)].
% 13.27/13.23 5116 -comm_monoid_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(B,A,E,f596(B,A,E,D,C)) != zero_zero(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_4295_setsum__mono__zero__right) # label(axiom). [clausify(4227)].
% 13.27/13.23 5117 -comm_monoid_add(A) | -comm_monoid_mult(A) | B != C | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),f598(A,D,E,C,B))) | hAPP(fun(int,bool),A,hAPP(fun(int,A),fun(fun(int,bool),A),big_co1399186613setsum(int,A),E),B) = hAPP(fun(int,bool),A,hAPP(fun(int,A),fun(fun(int,bool),A),big_co1399186613setsum(int,A),D),C) # label(fact_4297_transfer__nat__int__sum__prod__cong_I1_J) # label(axiom). [clausify(4229)].
% 13.27/13.23 5118 -comm_monoid_add(A) | -comm_monoid_mult(A) | B != C | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,B)) | hAPP(int,A,D,f598(A,E,D,C,B)) != hAPP(int,A,E,f598(A,E,D,C,B)) | hAPP(fun(int,bool),A,hAPP(fun(int,A),fun(fun(int,bool),A),big_co1399186613setsum(int,A),D),B) = hAPP(fun(int,bool),A,hAPP(fun(int,A),fun(fun(int,bool),A),big_co1399186613setsum(int,A),E),C) # label(fact_4297_transfer__nat__int__sum__prod__cong_I1_J) # label(axiom). [clausify(4229)].
% 13.27/13.23 5119 -ord(A) | -comm_monoid_add(B) | ti(A,C) != ti(A,D) | ti(A,E) != ti(A,F) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),f603(B,A,V6,V7,F,E,D,C))) | hAPP(fun(A,bool),B,hAPP(fun(A,B),fun(fun(A,bool),B),big_co1399186613setsum(A,B),V7),hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_atLeastLessThan(A),C),E)) = hAPP(fun(A,bool),B,hAPP(fun(A,B),fun(fun(A,bool),B),big_co1399186613setsum(A,B),V6),hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_atLeastLessThan(A),D),F)) # label(fact_4302_setsum__ivl__cong) # label(axiom). [clausify(4234)].
% 13.27/13.23 5120 -ord(A) | -comm_monoid_add(B) | ti(A,C) != ti(A,D) | ti(A,E) != ti(A,F) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),f603(B,A,V6,V7,F,E,D,C)),E)) | hAPP(fun(A,bool),B,hAPP(fun(A,B),fun(fun(A,bool),B),big_co1399186613setsum(A,B),V7),hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_atLeastLessThan(A),C),E)) = hAPP(fun(A,bool),B,hAPP(fun(A,B),fun(fun(A,bool),B),big_co1399186613setsum(A,B),V6),hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_atLeastLessThan(A),D),F)) # label(fact_4302_setsum__ivl__cong) # label(axiom). [clausify(4234)].
% 13.27/13.23 5121 -ord(A) | -comm_monoid_add(B) | ti(A,C) != ti(A,D) | ti(A,E) != ti(A,F) | hAPP(A,B,V6,f603(B,A,V7,V6,F,E,D,C)) != hAPP(A,B,V7,f603(B,A,V7,V6,F,E,D,C)) | hAPP(fun(A,bool),B,hAPP(fun(A,B),fun(fun(A,bool),B),big_co1399186613setsum(A,B),V6),hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_atLeastLessThan(A),C),E)) = hAPP(fun(A,bool),B,hAPP(fun(A,B),fun(fun(A,bool),B),big_co1399186613setsum(A,B),V7),hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_atLeastLessThan(A),D),F)) # label(fact_4302_setsum__ivl__cong) # label(axiom). [clausify(4234)].
% 13.27/13.23 5122 -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),f609(B,A,D,C)),C)) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),D),C) = zero_zero(A) # label(fact_4307_setsum_Oneutral) # label(axiom). [clausify(4239)].
% 13.27/13.23 5123 -comm_monoid_add(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | hAPP(B,A,D,f609(B,A,D,C)) != zero_zero(A) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),D),C) = zero_zero(A) # label(fact_4307_setsum_Oneutral) # label(axiom). [clausify(4239)].
% 13.27/13.23 5124 -comm_monoid_add(A) | -ordere779506340up_add(A) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f610(B,A,C,D)),D)) | 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),D)),zero_zero(A))) # label(fact_4308_setsum__nonpos) # label(axiom). [clausify(4240)].
% 13.27/13.23 5125 -comm_monoid_add(A) | -ordere779506340up_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(B,A,C,f610(B,A,C,D))),zero_zero(A))) | 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),D)),zero_zero(A))) # label(fact_4308_setsum__nonpos) # label(axiom). [clausify(4240)].
% 13.27/13.23 5126 -comm_monoid_add(A) | -ordere779506340up_add(A) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f611(B,A,C,D)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),C),D))) # label(fact_4309_setsum__nonneg) # label(axiom). [clausify(4241)].
% 13.27/13.23 5127 -comm_monoid_add(A) | -ordere779506340up_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(B,A,C,f611(B,A,C,D)))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),C),D))) # label(fact_4309_setsum__nonneg) # label(axiom). [clausify(4241)].
% 13.27/13.23 5128 -comm_monoid_add(A) | -hBOOL(hAPP(fun(fun(B,bool),bool),bool,finite_finite_1(fun(B,bool)),C)) | hBOOL(hAPP(fun(fun(B,bool),bool),bool,hAPP(fun(B,bool),fun(fun(fun(B,bool),bool),bool),member(fun(B,bool)),f612(B,A,D,C)),C)) | hBOOL(hAPP(fun(fun(B,bool),bool),bool,hAPP(fun(B,bool),fun(fun(fun(B,bool),bool),bool),member(fun(B,bool)),f613(B,A,D,C)),C)) | hAPP(fun(fun(B,bool),bool),A,hAPP(fun(fun(B,bool),A),fun(fun(fun(B,bool),bool),A),big_co1399186613setsum(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),D),hAPP(fun(fun(B,bool),bool),fun(B,bool),complete_Sup_Sup(fun(B,bool)),C)) # label(fact_4310_setsum__UNION__zero) # label(axiom). [clausify(4242)].
% 13.27/13.23 5129 -comm_monoid_add(A) | -hBOOL(hAPP(fun(fun(B,bool),bool),bool,finite_finite_1(fun(B,bool)),C)) | hBOOL(hAPP(fun(fun(B,bool),bool),bool,hAPP(fun(B,bool),fun(fun(fun(B,bool),bool),bool),member(fun(B,bool)),f612(B,A,D,C)),C)) | hBOOL(hAPP(fun(fun(B,bool),bool),bool,hAPP(fun(B,bool),fun(fun(fun(B,bool),bool),bool),member(fun(B,bool)),f614(B,A,D,C)),C)) | hAPP(fun(fun(B,bool),bool),A,hAPP(fun(fun(B,bool),A),fun(fun(fun(B,bool),bool),A),big_co1399186613setsum(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),D),hAPP(fun(fun(B,bool),bool),fun(B,bool),complete_Sup_Sup(fun(B,bool)),C)) # label(fact_4310_setsum__UNION__zero) # label(axiom). [clausify(4242)].
% 13.27/13.23 5130 -comm_monoid_add(A) | -hBOOL(hAPP(fun(fun(B,bool),bool),bool,finite_finite_1(fun(B,bool)),C)) | hBOOL(hAPP(fun(fun(B,bool),bool),bool,hAPP(fun(B,bool),fun(fun(fun(B,bool),bool),bool),member(fun(B,bool)),f612(B,A,D,C)),C)) | ti(fun(B,bool),f614(B,A,D,C)) != ti(fun(B,bool),f613(B,A,D,C)) | hAPP(fun(fun(B,bool),bool),A,hAPP(fun(fun(B,bool),A),fun(fun(fun(B,bool),bool),A),big_co1399186613setsum(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),D),hAPP(fun(fun(B,bool),bool),fun(B,bool),complete_Sup_Sup(fun(B,bool)),C)) # label(fact_4310_setsum__UNION__zero) # label(axiom). [clausify(4242)].
% 13.27/13.23 5131 -comm_monoid_add(A) | -hBOOL(hAPP(fun(fun(B,bool),bool),bool,finite_finite_1(fun(B,bool)),C)) | hBOOL(hAPP(fun(fun(B,bool),bool),bool,hAPP(fun(B,bool),fun(fun(fun(B,bool),bool),bool),member(fun(B,bool)),f612(B,A,D,C)),C)) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f615(B,A,D,C)),f613(B,A,D,C))) | hAPP(fun(fun(B,bool),bool),A,hAPP(fun(fun(B,bool),A),fun(fun(fun(B,bool),bool),A),big_co1399186613setsum(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),D),hAPP(fun(fun(B,bool),bool),fun(B,bool),complete_Sup_Sup(fun(B,bool)),C)) # label(fact_4310_setsum__UNION__zero) # label(axiom). [clausify(4242)].
% 13.27/13.23 5132 -comm_monoid_add(A) | -hBOOL(hAPP(fun(fun(B,bool),bool),bool,finite_finite_1(fun(B,bool)),C)) | hBOOL(hAPP(fun(fun(B,bool),bool),bool,hAPP(fun(B,bool),fun(fun(fun(B,bool),bool),bool),member(fun(B,bool)),f612(B,A,D,C)),C)) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f615(B,A,D,C)),f614(B,A,D,C))) | hAPP(fun(fun(B,bool),bool),A,hAPP(fun(fun(B,bool),A),fun(fun(fun(B,bool),bool),A),big_co1399186613setsum(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),D),hAPP(fun(fun(B,bool),bool),fun(B,bool),complete_Sup_Sup(fun(B,bool)),C)) # label(fact_4310_setsum__UNION__zero) # label(axiom). [clausify(4242)].
% 13.27/13.23 5133 -comm_monoid_add(A) | -hBOOL(hAPP(fun(fun(B,bool),bool),bool,finite_finite_1(fun(B,bool)),C)) | hBOOL(hAPP(fun(fun(B,bool),bool),bool,hAPP(fun(B,bool),fun(fun(fun(B,bool),bool),bool),member(fun(B,bool)),f612(B,A,D,C)),C)) | hAPP(B,A,D,f615(B,A,D,C)) != zero_zero(A) | hAPP(fun(fun(B,bool),bool),A,hAPP(fun(fun(B,bool),A),fun(fun(fun(B,bool),bool),A),big_co1399186613setsum(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),D),hAPP(fun(fun(B,bool),bool),fun(B,bool),complete_Sup_Sup(fun(B,bool)),C)) # label(fact_4310_setsum__UNION__zero) # label(axiom). [clausify(4242)].
% 13.27/13.23 5134 -comm_monoid_add(A) | -hBOOL(hAPP(fun(fun(B,bool),bool),bool,finite_finite_1(fun(B,bool)),C)) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),f612(B,A,D,C))) | hBOOL(hAPP(fun(fun(B,bool),bool),bool,hAPP(fun(B,bool),fun(fun(fun(B,bool),bool),bool),member(fun(B,bool)),f613(B,A,D,C)),C)) | hAPP(fun(fun(B,bool),bool),A,hAPP(fun(fun(B,bool),A),fun(fun(fun(B,bool),bool),A),big_co1399186613setsum(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),D),hAPP(fun(fun(B,bool),bool),fun(B,bool),complete_Sup_Sup(fun(B,bool)),C)) # label(fact_4310_setsum__UNION__zero) # label(axiom). [clausify(4242)].
% 13.27/13.23 5135 -comm_monoid_add(A) | -hBOOL(hAPP(fun(fun(B,bool),bool),bool,finite_finite_1(fun(B,bool)),C)) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),f612(B,A,D,C))) | hBOOL(hAPP(fun(fun(B,bool),bool),bool,hAPP(fun(B,bool),fun(fun(fun(B,bool),bool),bool),member(fun(B,bool)),f614(B,A,D,C)),C)) | hAPP(fun(fun(B,bool),bool),A,hAPP(fun(fun(B,bool),A),fun(fun(fun(B,bool),bool),A),big_co1399186613setsum(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),D),hAPP(fun(fun(B,bool),bool),fun(B,bool),complete_Sup_Sup(fun(B,bool)),C)) # label(fact_4310_setsum__UNION__zero) # label(axiom). [clausify(4242)].
% 13.27/13.23 5136 -comm_monoid_add(A) | -hBOOL(hAPP(fun(fun(B,bool),bool),bool,finite_finite_1(fun(B,bool)),C)) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),f612(B,A,D,C))) | ti(fun(B,bool),f614(B,A,D,C)) != ti(fun(B,bool),f613(B,A,D,C)) | hAPP(fun(fun(B,bool),bool),A,hAPP(fun(fun(B,bool),A),fun(fun(fun(B,bool),bool),A),big_co1399186613setsum(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),D),hAPP(fun(fun(B,bool),bool),fun(B,bool),complete_Sup_Sup(fun(B,bool)),C)) # label(fact_4310_setsum__UNION__zero) # label(axiom). [clausify(4242)].
% 13.27/13.23 5137 -comm_monoid_add(A) | -hBOOL(hAPP(fun(fun(B,bool),bool),bool,finite_finite_1(fun(B,bool)),C)) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),f612(B,A,D,C))) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f615(B,A,D,C)),f613(B,A,D,C))) | hAPP(fun(fun(B,bool),bool),A,hAPP(fun(fun(B,bool),A),fun(fun(fun(B,bool),bool),A),big_co1399186613setsum(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),D),hAPP(fun(fun(B,bool),bool),fun(B,bool),complete_Sup_Sup(fun(B,bool)),C)) # label(fact_4310_setsum__UNION__zero) # label(axiom). [clausify(4242)].
% 13.27/13.23 5138 -comm_monoid_add(A) | -hBOOL(hAPP(fun(fun(B,bool),bool),bool,finite_finite_1(fun(B,bool)),C)) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),f612(B,A,D,C))) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f615(B,A,D,C)),f614(B,A,D,C))) | hAPP(fun(fun(B,bool),bool),A,hAPP(fun(fun(B,bool),A),fun(fun(fun(B,bool),bool),A),big_co1399186613setsum(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),D),hAPP(fun(fun(B,bool),bool),fun(B,bool),complete_Sup_Sup(fun(B,bool)),C)) # label(fact_4310_setsum__UNION__zero) # label(axiom). [clausify(4242)].
% 13.27/13.23 5139 -comm_monoid_add(A) | -hBOOL(hAPP(fun(fun(B,bool),bool),bool,finite_finite_1(fun(B,bool)),C)) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),f612(B,A,D,C))) | hAPP(B,A,D,f615(B,A,D,C)) != zero_zero(A) | hAPP(fun(fun(B,bool),bool),A,hAPP(fun(fun(B,bool),A),fun(fun(fun(B,bool),bool),A),big_co1399186613setsum(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),D),hAPP(fun(fun(B,bool),bool),fun(B,bool),complete_Sup_Sup(fun(B,bool)),C)) # label(fact_4310_setsum__UNION__zero) # label(axiom). [clausify(4242)].
% 13.27/13.23 5140 -comm_monoid_add(A) | hAPP(fun(nat,bool),A,hAPP(fun(nat,A),fun(fun(nat,bool),A),big_co1399186613setsum(nat,A),B),hAPP(nat,fun(nat,bool),ord_lessThan(nat),hAPP(nat,nat,suc,C))) = 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),B),hAPP(nat,fun(nat,bool),ord_lessThan(nat),C))),hAPP(nat,A,B,C)) # label(fact_4321_setsum__lessThan__Suc) # label(axiom). [clausify(4253)].
% 13.27/13.23 5141 -comm_monoid_add(A) | -metric_space(A) | hAPP(fun(nat,A),A,suminf(A),B) = hAPP(fun(nat,A),A,lim(A),hAPP(fun(nat,fun(nat,bool)),fun(nat,A),hAPP(fun(fun(nat,bool),A),fun(fun(nat,fun(nat,bool)),fun(nat,A)),combb(fun(nat,bool),A,nat),hAPP(fun(nat,A),fun(fun(nat,bool),A),big_co1399186613setsum(nat,A),B)),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)))) # label(fact_4328_suminf__eq__lim) # label(axiom). [clausify(4260)].
% 13.27/13.23 5142 -comm_monoid_add(A) | -ordere779506340up_add(A) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f631(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_4343_setsum__mono) # label(axiom). [clausify(4275)].
% 13.27/13.23 5143 -comm_monoid_add(A) | -ordere779506340up_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(B,A,C,f631(B,A,C,D,E))),hAPP(B,A,D,f631(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_4343_setsum__mono) # label(axiom). [clausify(4275)].
% 13.27/13.23 5144 -comm_monoid_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)) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f632(B,A,E,F,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))) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f633(B,A,E,F,D,C)),D)) | 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_4345_setsum__mono__zero__cong__right) # label(axiom). [clausify(4277)].
% 13.27/13.23 5145 -comm_monoid_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)) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f632(B,A,E,F,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(B,A,E,f633(B,A,E,F,D,C)) != hAPP(B,A,F,f633(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_4345_setsum__mono__zero__cong__right) # label(axiom). [clausify(4277)].
% 13.27/13.23 5146 -comm_monoid_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(B,A,E,f632(B,A,F,E,D,C)) != zero_zero(A) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f633(B,A,F,E,D,C)),D)) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),F),D) = hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),E),C) # label(fact_4345_setsum__mono__zero__cong__right) # label(axiom). [clausify(4277)].
% 13.27/13.23 5147 -comm_monoid_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(B,A,E,f632(B,A,F,E,D,C)) != zero_zero(A) | hAPP(B,A,F,f633(B,A,F,E,D,C)) != hAPP(B,A,E,f633(B,A,F,E,D,C)) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),F),D) = hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),E),C) # label(fact_4345_setsum__mono__zero__cong__right) # label(axiom). [clausify(4277)].
% 13.27/13.23 5148 -comm_monoid_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)) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f644(B,A,E,F,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))) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f645(B,A,E,F,D,C)),D)) | 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_4415_setsum__mono__zero__cong__left) # label(axiom). [clausify(4347)].
% 13.27/13.23 5149 -comm_monoid_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)) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f644(B,A,E,F,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(B,A,F,f645(B,A,E,F,D,C)) != hAPP(B,A,E,f645(B,A,E,F,D,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_4415_setsum__mono__zero__cong__left) # label(axiom). [clausify(4347)].
% 13.27/13.23 5150 -comm_monoid_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(B,A,E,f644(B,A,F,E,D,C)) != zero_zero(A) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f645(B,A,F,E,D,C)),D)) | 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_4415_setsum__mono__zero__cong__left) # label(axiom). [clausify(4347)].
% 13.27/13.23 5151 -comm_monoid_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(B,A,E,f644(B,A,F,E,D,C)) != zero_zero(A) | hAPP(B,A,E,f645(B,A,F,E,D,C)) != hAPP(B,A,F,f645(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_4415_setsum__mono__zero__cong__left) # label(axiom). [clausify(4347)].
% 13.27/13.23 5152 -comm_monoid_add(A) | -t2_space(A) | -hBOOL(hAPP(fun(nat,A),bool,summable(A),B)) | hBOOL(hAPP(filter(nat),bool,hAPP(A,fun(filter(nat),bool),hAPP(fun(nat,A),fun(A,fun(filter(nat),bool)),tendsto(nat,A),hAPP(fun(nat,fun(nat,bool)),fun(nat,A),hAPP(fun(fun(nat,bool),A),fun(fun(nat,fun(nat,bool)),fun(nat,A)),combb(fun(nat,bool),A,nat),hAPP(fun(nat,A),fun(fun(nat,bool),A),big_co1399186613setsum(nat,A),B)),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)))),hAPP(fun(nat,A),A,suminf(A),B)),sequentially)) # label(fact_4496_summable__sumr__LIMSEQ__suminf) # label(axiom). [clausify(4424)].
% 13.27/13.23 5153 -comm_monoid_add(A) | -topological_space(A) | -hBOOL(hAPP(A,bool,hAPP(fun(nat,A),fun(A,bool),sums(A),B),C)) | hBOOL(hAPP(filter(nat),bool,hAPP(A,fun(filter(nat),bool),hAPP(fun(nat,A),fun(A,fun(filter(nat),bool)),tendsto(nat,A),hAPP(fun(nat,fun(nat,bool)),fun(nat,A),hAPP(fun(fun(nat,bool),A),fun(fun(nat,fun(nat,bool)),fun(nat,A)),combb(fun(nat,bool),A,nat),hAPP(fun(nat,A),fun(fun(nat,bool),A),big_co1399186613setsum(nat,A),B)),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)))),C),sequentially)) # label(fact_4497_sums__def) # label(axiom). [clausify(4425)].
% 13.27/13.23 5154 -comm_monoid_add(A) | -topological_space(A) | hBOOL(hAPP(A,bool,hAPP(fun(nat,A),fun(A,bool),sums(A),B),C)) | -hBOOL(hAPP(filter(nat),bool,hAPP(A,fun(filter(nat),bool),hAPP(fun(nat,A),fun(A,fun(filter(nat),bool)),tendsto(nat,A),hAPP(fun(nat,fun(nat,bool)),fun(nat,A),hAPP(fun(fun(nat,bool),A),fun(fun(nat,fun(nat,bool)),fun(nat,A)),combb(fun(nat,bool),A,nat),hAPP(fun(nat,A),fun(fun(nat,bool),A),big_co1399186613setsum(nat,A),B)),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)))),C),sequentially)) # label(fact_4497_sums__def) # label(axiom). [clausify(4425)].
% 13.27/13.23 5155 -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),suc)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),C),D)) = 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,suc,C)),hAPP(nat,nat,suc,D))) # label(fact_4543_setsum__shift__bounds__cl__Suc__ivl) # label(axiom). [clausify(4470)].
% 13.27/13.23 5156 -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_4544_setsum__shift__bounds__cl__nat__ivl) # label(axiom). [clausify(4471)].
% 13.27/13.23 5157 -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_atLeastAtMost(nat),hAPP(nat,nat,suc,B)),C))) # label(fact_4602_setsum__head__Suc) # label(axiom). [clausify(4529)].
% 13.27/13.23 5158 -comm_monoid_add(A) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,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),C),hAPP(nat,nat,suc,B))) = zero_zero(A) # label(fact_4607_setsum__cl__ivl__Suc) # label(axiom). [clausify(4534)].
% 13.27/13.23 5159 -comm_monoid_add(A) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,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),C),hAPP(nat,nat,suc,B))) = 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),C),B))),hAPP(nat,A,D,hAPP(nat,nat,suc,B))) # label(fact_4607_setsum__cl__ivl__Suc) # label(axiom). [clausify(4534)].
% 13.27/13.23 5160 -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_4608_setsum__ub__add__nat) # label(axiom). [clausify(4535)].
% 13.27/13.23 5161 -comm_monoid_add(A) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,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),C),hAPP(nat,nat,suc,B))) = zero_zero(A) # label(fact_4610_setsum__cl__ivl__Suc2) # label(axiom). [clausify(4537)].
% 13.27/13.23 5162 -comm_monoid_add(A) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,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),C),hAPP(nat,nat,suc,B))) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(nat,A,D,C)),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),D),suc)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),C),B))) # label(fact_4610_setsum__cl__ivl__Suc2) # label(axiom). [clausify(4537)].
% 13.27/13.23 5163 -comm_monoid_add(A) | hAPP(fun(product_prod(nat,nat),bool),A,hAPP(fun(product_prod(nat,nat),A),fun(fun(product_prod(nat,nat),bool),A),big_co1399186613setsum(product_prod(nat,nat),A),hAPP(fun(nat,fun(nat,A)),fun(product_prod(nat,nat),A),product_prod_case(nat,nat,A),B)),hAPP(fun(product_prod(nat,nat),bool),fun(product_prod(nat,nat),bool),collect(product_prod(nat,nat)),hAPP(fun(nat,fun(nat,bool)),fun(product_prod(nat,nat),bool),product_prod_case(nat,nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),hAPP(fun(nat,fun(nat,fun(nat,bool))),fun(nat,fun(nat,fun(nat,bool))),combc(nat,nat,fun(nat,bool)),hAPP(fun(nat,fun(nat,fun(nat,bool))),fun(nat,fun(nat,fun(nat,bool))),hAPP(fun(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool))),fun(fun(nat,fun(nat,fun(nat,bool))),fun(nat,fun(nat,fun(nat,bool)))),combb(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),nat),combc(nat,nat,bool)),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,fun(nat,bool))),hAPP(fun(fun(nat,nat),fun(nat,fun(nat,bool))),fun(fun(nat,fun(nat,nat)),fun(nat,fun(nat,fun(nat,bool)))),combb(fun(nat,nat),fun(nat,fun(nat,bool)),nat),hAPP(fun(nat,fun(nat,bool)),fun(fun(nat,nat),fun(nat,fun(nat,bool))),combb(nat,fun(nat,bool),nat),ord_less(nat))),plus_plus(nat)))),C)))) = hAPP(fun(nat,bool),A,hAPP(fun(nat,A),fun(fun(nat,bool),A),big_co1399186613setsum(nat,A),hAPP(fun(nat,fun(nat,bool)),fun(nat,A),hAPP(fun(nat,fun(fun(nat,bool),A)),fun(fun(nat,fun(nat,bool)),fun(nat,A)),combs(nat,fun(nat,bool),A),hAPP(fun(nat,fun(nat,A)),fun(nat,fun(fun(nat,bool),A)),hAPP(fun(fun(nat,A),fun(fun(nat,bool),A)),fun(fun(nat,fun(nat,A)),fun(nat,fun(fun(nat,bool),A))),combb(fun(nat,A),fun(fun(nat,bool),A),nat),big_co1399186613setsum(nat,A)),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,A)),hAPP(fun(fun(nat,nat),fun(nat,A)),fun(fun(nat,fun(nat,nat)),fun(nat,fun(nat,A))),combb(fun(nat,nat),fun(nat,A),nat),hAPP(fun(nat,fun(nat,A)),fun(fun(nat,nat),fun(nat,A)),combs(nat,nat,A),B)),minus_minus(nat)))),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),zero_zero(nat)))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),C)) # label(fact_4626_setsum__triangle__reindex) # label(axiom). [clausify(4553)].
% 13.27/13.24 5164 -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),f771(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_4781_setsum_Ocong) # label(axiom). [clausify(4705)].
% 13.27/13.24 5165 -comm_monoid_add(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | hAPP(B,A,D,f771(B,A,E,D,C)) != hAPP(B,A,E,f771(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_4781_setsum_Ocong) # label(axiom). [clausify(4705)].
% 13.27/13.24 5166 -comm_monoid_add(A) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f772(B,A,C,D)),D)) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),C),D) = zero_zero(A) # label(fact_4782_setsum__0_H) # label(axiom). [clausify(4706)].
% 13.27/13.24 5167 -comm_monoid_add(A) | hAPP(B,A,C,f772(B,A,C,D)) != zero_zero(A) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),C),D) = zero_zero(A) # label(fact_4782_setsum__0_H) # label(axiom). [clausify(4706)].
% 13.27/13.24 5168 -comm_monoid_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),B,zero_zero(A)),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),B,f788(C,A,D,E,F,B)),f790(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),f792(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_co1399186613setsum(C,A),D),F)),hAPP(fun(C,bool),A,hAPP(fun(C,A),fun(fun(C,bool),A),big_co1399186613setsum(C,A),E),F))) # label(fact_4802_setsum_Orelated) # label(axiom). [clausify(4726)].
% 13.27/13.24 5169 -comm_monoid_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),B,zero_zero(A)),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),B,f788(C,A,D,E,F,B)),f790(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,f792(C,A,D,E,F,B))),hAPP(C,A,E,f792(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_co1399186613setsum(C,A),D),F)),hAPP(fun(C,bool),A,hAPP(fun(C,A),fun(fun(C,bool),A),big_co1399186613setsum(C,A),E),F))) # label(fact_4802_setsum_Orelated) # label(axiom). [clausify(4726)].
% 13.27/13.24 5170 -comm_monoid_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),B,zero_zero(A)),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),B,f789(C,A,D,E,F,B)),f791(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),f792(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_co1399186613setsum(C,A),D),F)),hAPP(fun(C,bool),A,hAPP(fun(C,A),fun(fun(C,bool),A),big_co1399186613setsum(C,A),E),F))) # label(fact_4802_setsum_Orelated) # label(axiom). [clausify(4726)].
% 13.27/13.24 5171 -comm_monoid_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),B,zero_zero(A)),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),B,f789(C,A,D,E,F,B)),f791(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,f792(C,A,D,E,F,B))),hAPP(C,A,E,f792(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_co1399186613setsum(C,A),D),F)),hAPP(fun(C,bool),A,hAPP(fun(C,A),fun(fun(C,bool),A),big_co1399186613setsum(C,A),E),F))) # label(fact_4802_setsum_Orelated) # label(axiom). [clausify(4726)].
% 13.27/13.24 5172 -comm_monoid_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),B,zero_zero(A)),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),B,hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),f788(C,A,D,E,F,B)),f789(C,A,D,E,F,B))),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),f790(C,A,D,E,F,B)),f791(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),f792(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_co1399186613setsum(C,A),D),F)),hAPP(fun(C,bool),A,hAPP(fun(C,A),fun(fun(C,bool),A),big_co1399186613setsum(C,A),E),F))) # label(fact_4802_setsum_Orelated) # label(axiom). [clausify(4726)].
% 13.27/13.24 5173 -comm_monoid_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),B,zero_zero(A)),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),B,hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),f788(C,A,D,E,F,B)),f789(C,A,D,E,F,B))),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),f790(C,A,D,E,F,B)),f791(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,f792(C,A,D,E,F,B))),hAPP(C,A,E,f792(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_co1399186613setsum(C,A),D),F)),hAPP(fun(C,bool),A,hAPP(fun(C,A),fun(fun(C,bool),A),big_co1399186613setsum(C,A),E),F))) # label(fact_4802_setsum_Orelated) # label(axiom). [clausify(4726)].
% 13.27/13.24 Derived: big_co1399186613setsum(A,int) = ti(fun(fun(A,int),fun(fun(A,bool),int)),big_co1399186613setsum(A,int)). [resolve(5058,a,5059,a)].
% 13.27/13.24 Derived: -topological_space(int) | the(int) = ti(fun(fun(int,bool),int),the(int)). [resolve(5058,a,5060,a)].
% 13.27/13.24 Derived: -topological_space(int) | suminf(int) = ti(fun(fun(nat,int),int),suminf(int)). [resolve(5058,a,5061,a)].
% 13.27/13.24 Derived: -topological_space(int) | summable(int) = ti(fun(fun(nat,int),bool),summable(int)). [resolve(5058,a,5062,a)].
% 13.27/13.24 Derived: -topological_space(int) | sums(int) = ti(fun(fun(nat,int),fun(int,bool)),sums(int)). [resolve(5058,a,5063,a)].
% 13.27/13.24 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),zero_zero(int)) = ti(int,A). [resolve(5058,a,5064,a)].
% 13.27/13.24 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),zero_zero(int)),A) = ti(int,A). [resolve(5058,a,5065,a)].
% 13.27/13.24 Derived: -comm_monoid_mult(int) | hAPP(fun(nat,bool),int,hAPP(fun(nat,int),fun(fun(nat,bool),int),big_co302546470etprod(nat,int),A),B) = hAPP(fun(int,bool),int,hAPP(fun(int,int),fun(fun(int,bool),int),big_co302546470etprod(int,int),hAPP(fun(int,nat),fun(int,int),hAPP(fun(nat,int),fun(fun(int,nat),fun(int,int)),combb(nat,int,int),A),nat_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)),B)). [resolve(5058,a,5066,a)].
% 13.27/13.24 Derived: -comm_monoid_mult(int) | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A)) | hAPP(fun(nat,bool),int,hAPP(fun(nat,int),fun(fun(nat,bool),int),big_co302546470etprod(nat,int),hAPP(fun(nat,int),fun(nat,int),hAPP(fun(int,int),fun(fun(nat,int),fun(nat,int)),combb(int,int,nat),B),semiring_1_of_nat(int))),hAPP(fun(int,bool),fun(nat,bool),hAPP(fun(int,nat),fun(fun(int,bool),fun(nat,bool)),image(int,nat),nat_1),A)) = hAPP(fun(int,bool),int,hAPP(fun(int,int),fun(fun(int,bool),int),big_co302546470etprod(int,int),B),A). [resolve(5058,a,5067,a)].
% 13.27/13.24 Derived: -comm_monoid_mult(int) | A != B | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),f486(int,C,D,B,A))) | hAPP(fun(int,bool),int,hAPP(fun(int,int),fun(fun(int,bool),int),big_co302546470etprod(int,int),D),A) = hAPP(fun(int,bool),int,hAPP(fun(int,int),fun(fun(int,bool),int),big_co302546470etprod(int,int),C),B). [resolve(5058,a,5068,a)].
% 13.27/13.24 Derived: -comm_monoid_mult(int) | A != B | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A)) | hAPP(int,int,C,f486(int,D,C,B,A)) != hAPP(int,int,D,f486(int,D,C,B,A)) | hAPP(fun(int,bool),int,hAPP(fun(int,int),fun(fun(int,bool),int),big_co302546470etprod(int,int),C),A) = hAPP(fun(int,bool),int,hAPP(fun(int,int),fun(fun(int,bool),int),big_co302546470etprod(int,int),D),B). [resolve(5058,a,5069,a)].
% 13.27/13.24 Derived: -t2_space(int) | hAPP(fun(nat,int),int,suminf(int),hAPP(int,fun(nat,int),combk(int,nat),zero_zero(int))) = zero_zero(int). [resolve(5058,a,5070,a)].
% 13.27/13.24 Derived: -topological_space(int) | hBOOL(hAPP(fun(nat,int),bool,summable(int),hAPP(int,fun(nat,int),combk(int,nat),zero_zero(int)))). [resolve(5058,a,5071,a)].
% 13.27/13.24 Derived: -topological_space(int) | hBOOL(hAPP(int,bool,hAPP(fun(nat,int),fun(int,bool),sums(int),hAPP(int,fun(nat,int),combk(int,nat),zero_zero(int))),zero_zero(int))). [resolve(5058,a,5072,a)].
% 13.27/13.24 Derived: -t2_space(int) | -hBOOL(hAPP(int,bool,hAPP(fun(nat,int),fun(int,bool),sums(int),A),B)) | hAPP(fun(nat,int),int,suminf(int),A) = ti(int,B). [resolve(5058,a,5073,a)].
% 13.27/13.24 Derived: -topological_space(int) | -hBOOL(hAPP(int,bool,hAPP(fun(nat,int),fun(int,bool),sums(int),A),B)) | hBOOL(hAPP(fun(nat,int),bool,summable(int),A)). [resolve(5058,a,5074,a)].
% 13.27/13.24 Derived: -topological_space(int) | -hBOOL(hAPP(fun(nat,int),bool,summable(int),A)) | hBOOL(hAPP(int,bool,hAPP(fun(nat,int),fun(int,bool),sums(int),A),f513(int,A))). [resolve(5058,a,5075,a)].
% 13.27/13.24 Derived: -t2_space(int) | -hBOOL(hAPP(int,bool,hAPP(fun(nat,int),fun(int,bool),sums(int),A),B)) | hBOOL(hAPP(fun(nat,int),bool,summable(int),A)). [resolve(5058,a,5077,a)].
% 13.27/13.24 Derived: -t2_space(int) | hBOOL(hAPP(int,bool,hAPP(fun(nat,int),fun(int,bool),sums(int),A),B)) | -hBOOL(hAPP(fun(nat,int),bool,summable(int),A)) | hAPP(fun(nat,int),int,suminf(int),A) != ti(int,B). [resolve(5058,a,5079,a)].
% 13.27/13.24 Derived: -t2_space(int) | -hBOOL(hAPP(fun(nat,int),bool,summable(int),A)) | hBOOL(hAPP(int,bool,hAPP(fun(nat,int),fun(int,bool),sums(int),A),hAPP(fun(nat,int),int,suminf(int),A))). [resolve(5058,a,5080,a)].
% 13.27/13.24 Derived: -topological_space(int) | hAPP(nat,int,A,zero_zero(nat)) != zero_zero(int) | -hBOOL(hAPP(int,bool,hAPP(fun(nat,int),fun(int,bool),sums(int),hAPP(fun(nat,nat),fun(nat,int),hAPP(fun(nat,int),fun(fun(nat,nat),fun(nat,int)),combb(nat,int,nat),A),suc)),B)) | hBOOL(hAPP(int,bool,hAPP(fun(nat,int),fun(int,bool),sums(int),A),B)). [resolve(5058,a,5081,a)].
% 13.27/13.24 Derived: -topological_space(int) | hAPP(fun(nat,int),int,suminf(int),A) = hAPP(fun(int,bool),int,the(int),hAPP(fun(nat,int),fun(int,bool),sums(int),A)). [resolve(5058,a,5082,a)].
% 13.27/13.24 Derived: -power(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(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),times_times(int)),hAPP(fun(nat,nat),fun(nat,int),hAPP(fun(nat,int),fun(fun(nat,nat),fun(nat,int)),combb(nat,int,nat),hAPP(int,fun(nat,int),power_power(int),A)),hAPP(nat,fun(nat,nat),minus_minus(nat),B)))),hAPP(int,fun(nat,int),power_power(int),C))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,suc,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),times_times(int)),hAPP(int,fun(nat,int),power_power(int),A))),hAPP(fun(nat,nat),fun(nat,int),hAPP(fun(nat,int),fun(fun(nat,nat),fun(nat,int)),combb(nat,int,nat),hAPP(int,fun(nat,int),power_power(int),C)),hAPP(nat,fun(nat,nat),minus_minus(nat),B)))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,suc,B))). [resolve(5058,a,5083,a)].
% 13.27/13.24 Derived: hAPP(fun(nat,bool),int,hAPP(fun(nat,int),fun(fun(nat,bool),int),big_co1399186613setsum(nat,int),hAPP(fun(nat,fun(nat,bool)),fun(nat,int),hAPP(fun(fun(nat,bool),int),fun(fun(nat,fun(nat,bool)),fun(nat,int)),combb(fun(nat,bool),int,nat),hAPP(fun(nat,int),fun(fun(nat,bool),int),big_co1399186613setsum(nat,int),A)),hAPP(fun(nat,nat),fun(nat,fun(nat,bool)),hAPP(fun(nat,fun(nat,fun(nat,bool))),fun(fun(nat,nat),fun(nat,fun(nat,bool))),combs(nat,nat,fun(nat,bool)),hAPP(fun(nat,nat),fun(nat,fun(nat,fun(nat,bool))),hAPP(fun(nat,fun(nat,fun(nat,bool))),fun(fun(nat,nat),fun(nat,fun(nat,fun(nat,bool)))),combb(nat,fun(nat,fun(nat,bool)),nat),ord_atLeastLessThan(nat)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),times_times(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),plus_plus(nat)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),times_times(nat)),B))),B)))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),C)) = 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_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),C),B))). [resolve(5058,a,5084,a)].
% 13.27/13.24 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_atLeastLessThan(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_atLeastLessThan(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(5058,a,5085,a)].
% 13.27/13.24 Derived: 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_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),C))) = 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),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)),C))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),B))),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_atLeastLessThan(nat),zero_zero(nat)),C))). [resolve(5058,a,5086,a)].
% 13.27/13.24 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),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)),C)),D)),zero_zero(int))),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),collect(A),hAPP(fun(A,bool),fun(A,bool),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))),C))). [resolve(5058,a,5087,a)].
% 13.27/13.24 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),suc)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),B),C)) = 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_atLeastLessThan(nat),hAPP(nat,nat,suc,B)),hAPP(nat,nat,suc,C))). [resolve(5058,a,5089,a)].
% 13.27/13.24 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(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) = 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). [resolve(5058,a,5090,a)].
% 13.27/13.24 Derived: hAPP(nat,int,A,zero_zero(nat)) != zero_zero(int) | 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_atLeastLessThan(nat),hAPP(nat,nat,suc,zero_zero(nat))),B)) = 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_atLeastLessThan(nat),zero_zero(nat)),B)). [resolve(5058,a,5091,a)].
% 13.27/13.24 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),C)) | hAPP(fun(nat,bool),int,hAPP(fun(nat,int),fun(fun(nat,bool),int),big_co1399186613setsum(nat,int),D),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),A),C)) = 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),D),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),A),B))),hAPP(fun(nat,bool),int,hAPP(fun(nat,int),fun(fun(nat,bool),int),big_co1399186613setsum(nat,int),D),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),B),C))). [resolve(5058,a,5092,a)].
% 13.27/13.24 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(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_atLeastLessThan(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_atLeastLessThan(nat),hAPP(nat,nat,suc,A)),B))). [resolve(5058,a,5093,a)].
% 13.27/13.24 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(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_atLeastLessThan(nat),B),hAPP(nat,nat,suc,A))) = zero_zero(int). [resolve(5058,a,5094,a)].
% 13.27/13.24 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(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_atLeastLessThan(nat),B),hAPP(nat,nat,suc,A))) = 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_atLeastLessThan(nat),B),A))),hAPP(nat,int,C,A)). [resolve(5058,a,5095,a)].
% 13.27/13.24 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),B) = zero_zero(int). [resolve(5058,a,5096,a)].
% 13.27/13.24 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(5058,a,5098,a)].
% 13.27/13.24 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),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)),zero_zero(int))),B) = hAPP(A,int,D,C). [resolve(5058,a,5099,a)].
% 13.27/13.24 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),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)),zero_zero(int))),B) = zero_zero(int). [resolve(5058,a,5100,a)].
% 13.27/13.24 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),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)),zero_zero(int))),B) = hAPP(A,int,D,C). [resolve(5058,a,5101,a)].
% 13.27/13.24 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),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)),zero_zero(int))),B) = zero_zero(int). [resolve(5058,a,5102,a)].
% 13.27/13.24 Derived: hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),hAPP(int,fun(A,int),combk(int,A),zero_zero(int))),B) = zero_zero(int). [resolve(5058,a,5103,a)].
% 13.27/13.24 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),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)),C)),D)),B) = 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),C),B)),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),D),B)). [resolve(5058,a,5104,a)].
% 13.27/13.24 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(5058,a,5105,a)].
% 13.27/13.24 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(5058,a,5106,a)].
% 13.27/13.24 Derived: -comm_monoid_mult(int) | hAPP(fun(nat,bool),int,hAPP(fun(nat,int),fun(fun(nat,bool),int),big_co1399186613setsum(nat,int),A),B) = hAPP(fun(int,bool),int,hAPP(fun(int,int),fun(fun(int,bool),int),big_co1399186613setsum(int,int),hAPP(fun(int,nat),fun(int,int),hAPP(fun(nat,int),fun(fun(int,nat),fun(int,int)),combb(nat,int,int),A),nat_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)),B)). [resolve(5058,a,5107,a)].
% 13.27/13.24 Derived: -comm_monoid_mult(int) | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A)) | 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),B),semiring_1_of_nat(int))),hAPP(fun(int,bool),fun(nat,bool),hAPP(fun(int,nat),fun(fun(int,bool),fun(nat,bool)),image(int,nat),nat_1),A)) = hAPP(fun(int,bool),int,hAPP(fun(int,int),fun(fun(int,bool),int),big_co1399186613setsum(int,int),B),A). [resolve(5058,a,5108,a)].
% 13.27/13.24 Derived: -t2_space(int) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),f592(int,B,A))) | hBOOL(hAPP(int,bool,hAPP(fun(nat,int),fun(int,bool),sums(int),B),hAPP(fun(nat,bool),int,hAPP(fun(nat,int),fun(fun(nat,bool),int),big_co1399186613setsum(nat,int),B),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),A)))). [resolve(5058,a,5109,a)].
% 13.27/13.24 Derived: -t2_space(int) | hAPP(nat,int,A,f592(int,A,B)) != zero_zero(int) | hBOOL(hAPP(int,bool,hAPP(fun(nat,int),fun(int,bool),sums(int),A),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_atLeastLessThan(nat),zero_zero(nat)),B)))). [resolve(5058,a,5110,a)].
% 13.27/13.24 Derived: -ordere779506340up_add(int) | -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),f593(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))) | 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),D),C)),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),D),B))). [resolve(5058,a,5111,a)].
% 13.27/13.24 Derived: -ordere779506340up_add(int) | -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(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(A,int,D,f593(A,int,D,C,B)))) | 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),D),C)),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),D),B))). [resolve(5058,a,5112,a)].
% 13.27/13.24 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),f595(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_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(5058,a,5113,a)].
% 13.27/13.24 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,f595(A,int,D,C,B)) != zero_zero(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(5058,a,5114,a)].
% 13.27/13.24 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),f596(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_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(5058,a,5115,a)].
% 13.27/13.24 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,f596(A,int,D,C,B)) != zero_zero(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(5058,a,5116,a)].
% 13.27/13.24 Derived: -comm_monoid_mult(int) | A != B | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),f598(int,C,D,B,A))) | hAPP(fun(int,bool),int,hAPP(fun(int,int),fun(fun(int,bool),int),big_co1399186613setsum(int,int),D),A) = hAPP(fun(int,bool),int,hAPP(fun(int,int),fun(fun(int,bool),int),big_co1399186613setsum(int,int),C),B). [resolve(5058,a,5117,a)].
% 13.27/13.24 Derived: -comm_monoid_mult(int) | A != B | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A)) | hAPP(int,int,C,f598(int,D,C,B,A)) != hAPP(int,int,D,f598(int,D,C,B,A)) | hAPP(fun(int,bool),int,hAPP(fun(int,int),fun(fun(int,bool),int),big_co1399186613setsum(int,int),C),A) = hAPP(fun(int,bool),int,hAPP(fun(int,int),fun(fun(int,bool),int),big_co1399186613setsum(int,int),D),B). [resolve(5058,a,5118,a)].
% 13.27/13.24 Derived: -ord(A) | ti(A,B) != ti(A,C) | ti(A,D) != ti(A,E) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),f603(int,A,F,V6,E,D,C,B))) | hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),V6),hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_atLeastLessThan(A),B),D)) = hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),F),hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_atLeastLessThan(A),C),E)). [resolve(5058,a,5119,b)].
% 13.27/13.24 Derived: -ord(A) | ti(A,B) != ti(A,C) | ti(A,D) != ti(A,E) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),f603(int,A,F,V6,E,D,C,B)),D)) | hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),V6),hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_atLeastLessThan(A),B),D)) = hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),F),hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_atLeastLessThan(A),C),E)). [resolve(5058,a,5120,b)].
% 13.27/13.24 Derived: -ord(A) | ti(A,B) != ti(A,C) | ti(A,D) != ti(A,E) | hAPP(A,int,F,f603(int,A,V6,F,E,D,C,B)) != hAPP(A,int,V6,f603(int,A,V6,F,E,D,C,B)) | hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),F),hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_atLeastLessThan(A),B),D)) = hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),V6),hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_atLeastLessThan(A),C),E)). [resolve(5058,a,5121,b)].
% 13.27/13.25 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),f609(A,int,C,B)),B)) | hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),C),B) = zero_zero(int). [resolve(5058,a,5122,a)].
% 13.27/13.25 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(A,int,C,f609(A,int,C,B)) != zero_zero(int) | hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),C),B) = zero_zero(int). [resolve(5058,a,5123,a)].
% 13.27/13.25 Derived: -ordere779506340up_add(int) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f610(A,int,B,C)),C)) | 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),C)),zero_zero(int))). [resolve(5058,a,5124,a)].
% 13.27/13.25 Derived: -ordere779506340up_add(int) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(A,int,B,f610(A,int,B,C))),zero_zero(int))) | 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),C)),zero_zero(int))). [resolve(5058,a,5125,a)].
% 13.27/13.25 Derived: -ordere779506340up_add(int) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f611(A,int,B,C)),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),B),C))). [resolve(5058,a,5126,a)].
% 13.27/13.25 Derived: -ordere779506340up_add(int) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(A,int,B,f611(A,int,B,C)))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),B),C))). [resolve(5058,a,5127,a)].
% 13.27/13.25 Derived: -hBOOL(hAPP(fun(fun(A,bool),bool),bool,finite_finite_1(fun(A,bool)),B)) | hBOOL(hAPP(fun(fun(A,bool),bool),bool,hAPP(fun(A,bool),fun(fun(fun(A,bool),bool),bool),member(fun(A,bool)),f612(A,int,C,B)),B)) | hBOOL(hAPP(fun(fun(A,bool),bool),bool,hAPP(fun(A,bool),fun(fun(fun(A,bool),bool),bool),member(fun(A,bool)),f613(A,int,C,B)),B)) | hAPP(fun(fun(A,bool),bool),int,hAPP(fun(fun(A,bool),int),fun(fun(fun(A,bool),bool),int),big_co1399186613setsum(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),C),hAPP(fun(fun(A,bool),bool),fun(A,bool),complete_Sup_Sup(fun(A,bool)),B)). [resolve(5058,a,5128,a)].
% 13.27/13.25 Derived: -hBOOL(hAPP(fun(fun(A,bool),bool),bool,finite_finite_1(fun(A,bool)),B)) | hBOOL(hAPP(fun(fun(A,bool),bool),bool,hAPP(fun(A,bool),fun(fun(fun(A,bool),bool),bool),member(fun(A,bool)),f612(A,int,C,B)),B)) | hBOOL(hAPP(fun(fun(A,bool),bool),bool,hAPP(fun(A,bool),fun(fun(fun(A,bool),bool),bool),member(fun(A,bool)),f614(A,int,C,B)),B)) | hAPP(fun(fun(A,bool),bool),int,hAPP(fun(fun(A,bool),int),fun(fun(fun(A,bool),bool),int),big_co1399186613setsum(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),C),hAPP(fun(fun(A,bool),bool),fun(A,bool),complete_Sup_Sup(fun(A,bool)),B)). [resolve(5058,a,5129,a)].
% 13.27/13.25 Derived: -hBOOL(hAPP(fun(fun(A,bool),bool),bool,finite_finite_1(fun(A,bool)),B)) | hBOOL(hAPP(fun(fun(A,bool),bool),bool,hAPP(fun(A,bool),fun(fun(fun(A,bool),bool),bool),member(fun(A,bool)),f612(A,int,C,B)),B)) | ti(fun(A,bool),f614(A,int,C,B)) != ti(fun(A,bool),f613(A,int,C,B)) | hAPP(fun(fun(A,bool),bool),int,hAPP(fun(fun(A,bool),int),fun(fun(fun(A,bool),bool),int),big_co1399186613setsum(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),C),hAPP(fun(fun(A,bool),bool),fun(A,bool),complete_Sup_Sup(fun(A,bool)),B)). [resolve(5058,a,5130,a)].
% 13.27/13.25 Derived: -hBOOL(hAPP(fun(fun(A,bool),bool),bool,finite_finite_1(fun(A,bool)),B)) | hBOOL(hAPP(fun(fun(A,bool),bool),bool,hAPP(fun(A,bool),fun(fun(fun(A,bool),bool),bool),member(fun(A,bool)),f612(A,int,C,B)),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f615(A,int,C,B)),f613(A,int,C,B))) | hAPP(fun(fun(A,bool),bool),int,hAPP(fun(fun(A,bool),int),fun(fun(fun(A,bool),bool),int),big_co1399186613setsum(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),C),hAPP(fun(fun(A,bool),bool),fun(A,bool),complete_Sup_Sup(fun(A,bool)),B)). [resolve(5058,a,5131,a)].
% 13.27/13.25 Derived: -hBOOL(hAPP(fun(fun(A,bool),bool),bool,finite_finite_1(fun(A,bool)),B)) | hBOOL(hAPP(fun(fun(A,bool),bool),bool,hAPP(fun(A,bool),fun(fun(fun(A,bool),bool),bool),member(fun(A,bool)),f612(A,int,C,B)),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f615(A,int,C,B)),f614(A,int,C,B))) | hAPP(fun(fun(A,bool),bool),int,hAPP(fun(fun(A,bool),int),fun(fun(fun(A,bool),bool),int),big_co1399186613setsum(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),C),hAPP(fun(fun(A,bool),bool),fun(A,bool),complete_Sup_Sup(fun(A,bool)),B)). [resolve(5058,a,5132,a)].
% 13.27/13.25 Derived: -hBOOL(hAPP(fun(fun(A,bool),bool),bool,finite_finite_1(fun(A,bool)),B)) | hBOOL(hAPP(fun(fun(A,bool),bool),bool,hAPP(fun(A,bool),fun(fun(fun(A,bool),bool),bool),member(fun(A,bool)),f612(A,int,C,B)),B)) | hAPP(A,int,C,f615(A,int,C,B)) != zero_zero(int) | hAPP(fun(fun(A,bool),bool),int,hAPP(fun(fun(A,bool),int),fun(fun(fun(A,bool),bool),int),big_co1399186613setsum(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),C),hAPP(fun(fun(A,bool),bool),fun(A,bool),complete_Sup_Sup(fun(A,bool)),B)). [resolve(5058,a,5133,a)].
% 13.27/13.25 Derived: -hBOOL(hAPP(fun(fun(A,bool),bool),bool,finite_finite_1(fun(A,bool)),B)) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),f612(A,int,C,B))) | hBOOL(hAPP(fun(fun(A,bool),bool),bool,hAPP(fun(A,bool),fun(fun(fun(A,bool),bool),bool),member(fun(A,bool)),f613(A,int,C,B)),B)) | hAPP(fun(fun(A,bool),bool),int,hAPP(fun(fun(A,bool),int),fun(fun(fun(A,bool),bool),int),big_co1399186613setsum(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),C),hAPP(fun(fun(A,bool),bool),fun(A,bool),complete_Sup_Sup(fun(A,bool)),B)). [resolve(5058,a,5134,a)].
% 13.27/13.25 Derived: -hBOOL(hAPP(fun(fun(A,bool),bool),bool,finite_finite_1(fun(A,bool)),B)) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),f612(A,int,C,B))) | hBOOL(hAPP(fun(fun(A,bool),bool),bool,hAPP(fun(A,bool),fun(fun(fun(A,bool),bool),bool),member(fun(A,bool)),f614(A,int,C,B)),B)) | hAPP(fun(fun(A,bool),bool),int,hAPP(fun(fun(A,bool),int),fun(fun(fun(A,bool),bool),int),big_co1399186613setsum(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),C),hAPP(fun(fun(A,bool),bool),fun(A,bool),complete_Sup_Sup(fun(A,bool)),B)). [resolve(5058,a,5135,a)].
% 13.27/13.25 Derived: -hBOOL(hAPP(fun(fun(A,bool),bool),bool,finite_finite_1(fun(A,bool)),B)) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),f612(A,int,C,B))) | ti(fun(A,bool),f614(A,int,C,B)) != ti(fun(A,bool),f613(A,int,C,B)) | hAPP(fun(fun(A,bool),bool),int,hAPP(fun(fun(A,bool),int),fun(fun(fun(A,bool),bool),int),big_co1399186613setsum(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),C),hAPP(fun(fun(A,bool),bool),fun(A,bool),complete_Sup_Sup(fun(A,bool)),B)). [resolve(5058,a,5136,a)].
% 13.27/13.25 Derived: -hBOOL(hAPP(fun(fun(A,bool),bool),bool,finite_finite_1(fun(A,bool)),B)) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),f612(A,int,C,B))) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f615(A,int,C,B)),f613(A,int,C,B))) | hAPP(fun(fun(A,bool),bool),int,hAPP(fun(fun(A,bool),int),fun(fun(fun(A,bool),bool),int),big_co1399186613setsum(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),C),hAPP(fun(fun(A,bool),bool),fun(A,bool),complete_Sup_Sup(fun(A,bool)),B)). [resolve(5058,a,5137,a)].
% 13.27/13.25 Derived: -hBOOL(hAPP(fun(fun(A,bool),bool),bool,finite_finite_1(fun(A,bool)),B)) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),f612(A,int,C,B))) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f615(A,int,C,B)),f614(A,int,C,B))) | hAPP(fun(fun(A,bool),bool),int,hAPP(fun(fun(A,bool),int),fun(fun(fun(A,bool),bool),int),big_co1399186613setsum(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),C),hAPP(fun(fun(A,bool),bool),fun(A,bool),complete_Sup_Sup(fun(A,bool)),B)). [resolve(5058,a,5138,a)].
% 13.27/13.25 Derived: -hBOOL(hAPP(fun(fun(A,bool),bool),bool,finite_finite_1(fun(A,bool)),B)) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),f612(A,int,C,B))) | hAPP(A,int,C,f615(A,int,C,B)) != zero_zero(int) | hAPP(fun(fun(A,bool),bool),int,hAPP(fun(fun(A,bool),int),fun(fun(fun(A,bool),bool),int),big_co1399186613setsum(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),C),hAPP(fun(fun(A,bool),bool),fun(A,bool),complete_Sup_Sup(fun(A,bool)),B)). [resolve(5058,a,5139,a)].
% 13.27/13.25 Derived: hAPP(fun(nat,bool),int,hAPP(fun(nat,int),fun(fun(nat,bool),int),big_co1399186613setsum(nat,int),A),hAPP(nat,fun(nat,bool),ord_lessThan(nat),hAPP(nat,nat,suc,B))) = 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),A),hAPP(nat,fun(nat,bool),ord_lessThan(nat),B))),hAPP(nat,int,A,B)). [resolve(5058,a,5140,a)].
% 13.27/13.25 Derived: -metric_space(int) | hAPP(fun(nat,int),int,suminf(int),A) = hAPP(fun(nat,int),int,lim(int),hAPP(fun(nat,fun(nat,bool)),fun(nat,int),hAPP(fun(fun(nat,bool),int),fun(fun(nat,fun(nat,bool)),fun(nat,int)),combb(fun(nat,bool),int,nat),hAPP(fun(nat,int),fun(fun(nat,bool),int),big_co1399186613setsum(nat,int),A)),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)))). [resolve(5058,a,5141,a)].
% 13.27/13.25 Derived: -ordere779506340up_add(int) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f631(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(5058,a,5142,a)].
% 13.27/13.25 Derived: -ordere779506340up_add(int) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(A,int,B,f631(A,int,B,C,D))),hAPP(A,int,C,f631(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(5058,a,5143,a)].
% 13.27/13.25 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),f632(A,int,D,E,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))) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f633(A,int,D,E,C,B)),C)) | 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(5058,a,5144,a)].
% 13.27/13.25 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),f632(A,int,D,E,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(A,int,D,f633(A,int,D,E,C,B)) != hAPP(A,int,E,f633(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(5058,a,5145,a)].
% 13.27/13.25 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,f632(A,int,E,D,C,B)) != zero_zero(int) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f633(A,int,E,D,C,B)),C)) | hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),E),C) = hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),D),B). [resolve(5058,a,5146,a)].
% 13.27/13.25 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,f632(A,int,E,D,C,B)) != zero_zero(int) | hAPP(A,int,E,f633(A,int,E,D,C,B)) != hAPP(A,int,D,f633(A,int,E,D,C,B)) | hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),E),C) = hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),D),B). [resolve(5058,a,5147,a)].
% 13.27/13.25 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),f644(A,int,D,E,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))) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f645(A,int,D,E,C,B)),C)) | 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(5058,a,5148,a)].
% 13.27/13.25 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),f644(A,int,D,E,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(A,int,E,f645(A,int,D,E,C,B)) != hAPP(A,int,D,f645(A,int,D,E,C,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(5058,a,5149,a)].
% 13.27/13.25 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,f644(A,int,E,D,C,B)) != zero_zero(int) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f645(A,int,E,D,C,B)),C)) | 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(5058,a,5150,a)].
% 13.27/13.25 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,f644(A,int,E,D,C,B)) != zero_zero(int) | hAPP(A,int,D,f645(A,int,E,D,C,B)) != hAPP(A,int,E,f645(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(5058,a,5151,a)].
% 13.27/13.25 Derived: -t2_space(int) | -hBOOL(hAPP(fun(nat,int),bool,summable(int),A)) | hBOOL(hAPP(filter(nat),bool,hAPP(int,fun(filter(nat),bool),hAPP(fun(nat,int),fun(int,fun(filter(nat),bool)),tendsto(nat,int),hAPP(fun(nat,fun(nat,bool)),fun(nat,int),hAPP(fun(fun(nat,bool),int),fun(fun(nat,fun(nat,bool)),fun(nat,int)),combb(fun(nat,bool),int,nat),hAPP(fun(nat,int),fun(fun(nat,bool),int),big_co1399186613setsum(nat,int),A)),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)))),hAPP(fun(nat,int),int,suminf(int),A)),sequentially)). [resolve(5058,a,5152,a)].
% 13.27/13.25 Derived: -topological_space(int) | -hBOOL(hAPP(int,bool,hAPP(fun(nat,int),fun(int,bool),sums(int),A),B)) | hBOOL(hAPP(filter(nat),bool,hAPP(int,fun(filter(nat),bool),hAPP(fun(nat,int),fun(int,fun(filter(nat),bool)),tendsto(nat,int),hAPP(fun(nat,fun(nat,bool)),fun(nat,int),hAPP(fun(fun(nat,bool),int),fun(fun(nat,fun(nat,bool)),fun(nat,int)),combb(fun(nat,bool),int,nat),hAPP(fun(nat,int),fun(fun(nat,bool),int),big_co1399186613setsum(nat,int),A)),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)))),B),sequentially)). [resolve(5058,a,5153,a)].
% 13.27/13.25 Derived: -topological_space(int) | hBOOL(hAPP(int,bool,hAPP(fun(nat,int),fun(int,bool),sums(int),A),B)) | -hBOOL(hAPP(filter(nat),bool,hAPP(int,fun(filter(nat),bool),hAPP(fun(nat,int),fun(int,fun(filter(nat),bool)),tendsto(nat,int),hAPP(fun(nat,fun(nat,bool)),fun(nat,int),hAPP(fun(fun(nat,bool),int),fun(fun(nat,fun(nat,bool)),fun(nat,int)),combb(fun(nat,bool),int,nat),hAPP(fun(nat,int),fun(fun(nat,bool),int),big_co1399186613setsum(nat,int),A)),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)))),B),sequentially)). [resolve(5058,a,5154,a)].
% 13.27/13.25 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),suc)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),B),C)) = 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,suc,B)),hAPP(nat,nat,suc,C))). [resolve(5058,a,5155,a)].
% 13.27/13.25 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(5058,a,5156,a)].
% 13.27/13.25 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_atLeastAtMost(nat),hAPP(nat,nat,suc,A)),B))). [resolve(5058,a,5157,a)].
% 13.27/13.25 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,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),B),hAPP(nat,nat,suc,A))) = zero_zero(int). [resolve(5058,a,5158,a)].
% 13.27/13.25 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,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),B),hAPP(nat,nat,suc,A))) = 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),B),A))),hAPP(nat,int,C,hAPP(nat,nat,suc,A))). [resolve(5058,a,5159,a)].
% 13.27/13.25 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(5058,a,5160,a)].
% 13.27/13.25 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,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),B),hAPP(nat,nat,suc,A))) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,C,B)),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),C),suc)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),B),A))). [resolve(5058,a,5162,a)].
% 13.27/13.25 Derived: hAPP(fun(product_prod(nat,nat),bool),int,hAPP(fun(product_prod(nat,nat),int),fun(fun(product_prod(nat,nat),bool),int),big_co1399186613setsum(product_prod(nat,nat),int),hAPP(fun(nat,fun(nat,int)),fun(product_prod(nat,nat),int),product_prod_case(nat,nat,int),A)),hAPP(fun(product_prod(nat,nat),bool),fun(product_prod(nat,nat),bool),collect(product_prod(nat,nat)),hAPP(fun(nat,fun(nat,bool)),fun(product_prod(nat,nat),bool),product_prod_case(nat,nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),hAPP(fun(nat,fun(nat,fun(nat,bool))),fun(nat,fun(nat,fun(nat,bool))),combc(nat,nat,fun(nat,bool)),hAPP(fun(nat,fun(nat,fun(nat,bool))),fun(nat,fun(nat,fun(nat,bool))),hAPP(fun(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool))),fun(fun(nat,fun(nat,fun(nat,bool))),fun(nat,fun(nat,fun(nat,bool)))),combb(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),nat),combc(nat,nat,bool)),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,fun(nat,bool))),hAPP(fun(fun(nat,nat),fun(nat,fun(nat,bool))),fun(fun(nat,fun(nat,nat)),fun(nat,fun(nat,fun(nat,bool)))),combb(fun(nat,nat),fun(nat,fun(nat,bool)),nat),hAPP(fun(nat,fun(nat,bool)),fun(fun(nat,nat),fun(nat,fun(nat,bool))),combb(nat,fun(nat,bool),nat),ord_less(nat))),plus_plus(nat)))),B)))) = hAPP(fun(nat,bool),int,hAPP(fun(nat,int),fun(fun(nat,bool),int),big_co1399186613setsum(nat,int),hAPP(fun(nat,fun(nat,bool)),fun(nat,int),hAPP(fun(nat,fun(fun(nat,bool),int)),fun(fun(nat,fun(nat,bool)),fun(nat,int)),combs(nat,fun(nat,bool),int),hAPP(fun(nat,fun(nat,int)),fun(nat,fun(fun(nat,bool),int)),hAPP(fun(fun(nat,int),fun(fun(nat,bool),int)),fun(fun(nat,fun(nat,int)),fun(nat,fun(fun(nat,bool),int))),combb(fun(nat,int),fun(fun(nat,bool),int),nat),big_co1399186613setsum(nat,int)),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,int)),hAPP(fun(fun(nat,nat),fun(nat,int)),fun(fun(nat,fun(nat,nat)),fun(nat,fun(nat,int))),combb(fun(nat,nat),fun(nat,int),nat),hAPP(fun(nat,fun(nat,int)),fun(fun(nat,nat),fun(nat,int)),combs(nat,nat,int),A)),minus_minus(nat)))),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),zero_zero(nat)))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),B)). [resolve(5058,a,5163,a)].
% 13.27/13.25 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),f771(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(5058,a,5164,a)].
% 13.27/13.25 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(A,int,C,f771(A,int,D,C,B)) != hAPP(A,int,D,f771(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(5058,a,5165,a)].
% 13.27/13.25 Derived: hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f772(A,int,B,C)),C)) | hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),B),C) = zero_zero(int). [resolve(5058,a,5166,a)].
% 13.27/13.25 Derived: hAPP(A,int,B,f772(A,int,B,C)) != zero_zero(int) | hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),B),C) = zero_zero(int). [resolve(5058,a,5167,a)].
% 13.27/13.25 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),A,zero_zero(int)),zero_zero(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),A,f788(B,int,C,D,E,A)),f790(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),f792(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_co1399186613setsum(B,int),C),E)),hAPP(fun(B,bool),int,hAPP(fun(B,int),fun(fun(B,bool),int),big_co1399186613setsum(B,int),D),E))). [resolve(5058,a,5168,a)].
% 13.27/13.25 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),A,zero_zero(int)),zero_zero(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),A,f788(B,int,C,D,E,A)),f790(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,f792(B,int,C,D,E,A))),hAPP(B,int,D,f792(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_co1399186613setsum(B,int),C),E)),hAPP(fun(B,bool),int,hAPP(fun(B,int),fun(fun(B,bool),int),big_co1399186613setsum(B,int),D),E))). [resolve(5058,a,5169,a)].
% 13.27/13.25 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),A,zero_zero(int)),zero_zero(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),A,f789(B,int,C,D,E,A)),f791(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),f792(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_co1399186613setsum(B,int),C),E)),hAPP(fun(B,bool),int,hAPP(fun(B,int),fun(fun(B,bool),int),big_co1399186613setsum(B,int),D),E))). [resolve(5058,a,5170,a)].
% 13.27/13.25 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),A,zero_zero(int)),zero_zero(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),A,f789(B,int,C,D,E,A)),f791(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,f792(B,int,C,D,E,A))),hAPP(B,int,D,f792(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_co1399186613setsum(B,int),C),E)),hAPP(fun(B,bool),int,hAPP(fun(B,int),fun(fun(B,bool),int),big_co1399186613setsum(B,int),D),E))). [resolve(5058,a,5171,a)].
% 13.27/13.25 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),A,zero_zero(int)),zero_zero(int))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),A,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),f788(B,int,C,D,E,A)),f789(B,int,C,D,E,A))),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),f790(B,int,C,D,E,A)),f791(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),f792(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_co1399186613setsum(B,int),C),E)),hAPP(fun(B,bool),int,hAPP(fun(B,int),fun(fun(B,bool),int),big_co1399186613setsum(B,int),D),E))). [resolve(5058,a,5172,a)].
% 13.27/13.28 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),A,zero_zero(int)),zero_zero(int))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),A,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),f788(B,int,C,D,E,A)),f789(B,int,C,D,E,A))),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),f790(B,int,C,D,E,A)),f791(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,f792(B,int,C,D,E,A))),hAPP(B,int,D,f792(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_co1399186613setsum(B,int),C),E)),hAPP(fun(B,bool),int,hAPP(fun(B,int),fun(fun(B,bool),int),big_co1399186613setsum(B,int),D),E))). [resolve(5058,a,5173,a)].
% 13.27/13.28 5174 comm_monoid_add(nat) # label(arity_Nat_Onat___Groups_Ocomm__monoid__add) # label(axiom). [assumption].
% 13.27/13.28 Derived: big_co1399186613setsum(A,nat) = ti(fun(fun(A,nat),fun(fun(A,bool),nat)),big_co1399186613setsum(A,nat)). [resolve(5174,a,5059,a)].
% 13.27/13.28 Derived: -topological_space(nat) | the(nat) = ti(fun(fun(nat,bool),nat),the(nat)). [resolve(5174,a,5060,a)].
% 13.27/13.28 Derived: -topological_space(nat) | suminf(nat) = ti(fun(fun(nat,nat),nat),suminf(nat)). [resolve(5174,a,5061,a)].
% 13.27/13.28 Derived: -topological_space(nat) | summable(nat) = ti(fun(fun(nat,nat),bool),summable(nat)). [resolve(5174,a,5062,a)].
% 13.27/13.28 Derived: -topological_space(nat) | sums(nat) = ti(fun(fun(nat,nat),fun(nat,bool)),sums(nat)). [resolve(5174,a,5063,a)].
% 13.27/13.28 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),zero_zero(nat)) = ti(nat,A). [resolve(5174,a,5064,a)].
% 13.27/13.28 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),zero_zero(nat)),A) = ti(nat,A). [resolve(5174,a,5065,a)].
% 13.27/13.28 Derived: -comm_monoid_mult(nat) | hAPP(fun(nat,bool),nat,hAPP(fun(nat,nat),fun(fun(nat,bool),nat),big_co302546470etprod(nat,nat),A),B) = hAPP(fun(int,bool),nat,hAPP(fun(int,nat),fun(fun(int,bool),nat),big_co302546470etprod(int,nat),hAPP(fun(int,nat),fun(int,nat),hAPP(fun(nat,nat),fun(fun(int,nat),fun(int,nat)),combb(nat,nat,int),A),nat_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)),B)). [resolve(5174,a,5066,a)].
% 13.27/13.28 Derived: -comm_monoid_mult(nat) | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A)) | hAPP(fun(nat,bool),nat,hAPP(fun(nat,nat),fun(fun(nat,bool),nat),big_co302546470etprod(nat,nat),hAPP(fun(nat,int),fun(nat,nat),hAPP(fun(int,nat),fun(fun(nat,int),fun(nat,nat)),combb(int,nat,nat),B),semiring_1_of_nat(int))),hAPP(fun(int,bool),fun(nat,bool),hAPP(fun(int,nat),fun(fun(int,bool),fun(nat,bool)),image(int,nat),nat_1),A)) = hAPP(fun(int,bool),nat,hAPP(fun(int,nat),fun(fun(int,bool),nat),big_co302546470etprod(int,nat),B),A). [resolve(5174,a,5067,a)].
% 13.27/13.28 Derived: -comm_monoid_mult(nat) | A != B | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),f486(nat,C,D,B,A))) | hAPP(fun(int,bool),nat,hAPP(fun(int,nat),fun(fun(int,bool),nat),big_co302546470etprod(int,nat),D),A) = hAPP(fun(int,bool),nat,hAPP(fun(int,nat),fun(fun(int,bool),nat),big_co302546470etprod(int,nat),C),B). [resolve(5174,a,5068,a)].
% 13.27/13.28 Derived: -comm_monoid_mult(nat) | A != B | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A)) | hAPP(int,nat,C,f486(nat,D,C,B,A)) != hAPP(int,nat,D,f486(nat,D,C,B,A)) | hAPP(fun(int,bool),nat,hAPP(fun(int,nat),fun(fun(int,bool),nat),big_co302546470etprod(int,nat),C),A) = hAPP(fun(int,bool),nat,hAPP(fun(int,nat),fun(fun(int,bool),nat),big_co302546470etprod(int,nat),D),B). [resolve(5174,a,5069,a)].
% 13.27/13.28 Derived: -t2_space(nat) | hAPP(fun(nat,nat),nat,suminf(nat),hAPP(nat,fun(nat,nat),combk(nat,nat),zero_zero(nat))) = zero_zero(nat). [resolve(5174,a,5070,a)].
% 13.27/13.28 Derived: -topological_space(nat) | hBOOL(hAPP(fun(nat,nat),bool,summable(nat),hAPP(nat,fun(nat,nat),combk(nat,nat),zero_zero(nat)))). [resolve(5174,a,5071,a)].
% 13.27/13.28 Derived: -topological_space(nat) | hBOOL(hAPP(nat,bool,hAPP(fun(nat,nat),fun(nat,bool),sums(nat),hAPP(nat,fun(nat,nat),combk(nat,nat),zero_zero(nat))),zero_zero(nat))). [resolve(5174,a,5072,a)].
% 13.27/13.28 Derived: -t2_space(nat) | -hBOOL(hAPP(nat,bool,hAPP(fun(nat,nat),fun(nat,bool),sums(nat),A),B)) | hAPP(fun(nat,nat),nat,suminf(nat),A) = ti(nat,B). [resolve(5174,a,5073,a)].
% 13.27/13.28 Derived: -topological_space(nat) | -hBOOL(hAPP(nat,bool,hAPP(fun(nat,nat),fun(nat,bool),sums(nat),A),B)) | hBOOL(hAPP(fun(nat,nat),bool,summable(nat),A)). [resolve(5174,a,5074,a)].
% 13.27/13.28 Derived: -topological_space(nat) | -hBOOL(hAPP(fun(nat,nat),bool,summable(nat),A)) | hBOOL(hAPP(nat,bool,hAPP(fun(nat,nat),fun(nat,bool),sums(nat),A),f513(nat,A))). [resolve(5174,a,5075,a)].
% 13.27/13.28 Derived: -t2_space(nat) | -hBOOL(hAPP(nat,bool,hAPP(fun(nat,nat),fun(nat,bool),sums(nat),A),B)) | hBOOL(hAPP(fun(nat,nat),bool,summable(nat),A)). [resolve(5174,a,5077,a)].
% 13.27/13.28 Derived: -t2_space(nat) | hBOOL(hAPP(nat,bool,hAPP(fun(nat,nat),fun(nat,bool),sums(nat),A),B)) | -hBOOL(hAPP(fun(nat,nat),bool,summable(nat),A)) | hAPP(fun(nat,nat),nat,suminf(nat),A) != ti(nat,B). [resolve(5174,a,5079,a)].
% 13.27/13.28 Derived: -t2_space(nat) | -hBOOL(hAPP(fun(nat,nat),bool,summable(nat),A)) | hBOOL(hAPP(nat,bool,hAPP(fun(nat,nat),fun(nat,bool),sums(nat),A),hAPP(fun(nat,nat),nat,suminf(nat),A))). [resolve(5174,a,5080,a)].
% 13.27/13.28 Derived: -topological_space(nat) | hAPP(nat,nat,A,zero_zero(nat)) != zero_zero(nat) | -hBOOL(hAPP(nat,bool,hAPP(fun(nat,nat),fun(nat,bool),sums(nat),hAPP(fun(nat,nat),fun(nat,nat),hAPP(fun(nat,nat),fun(fun(nat,nat),fun(nat,nat)),combb(nat,nat,nat),A),suc)),B)) | hBOOL(hAPP(nat,bool,hAPP(fun(nat,nat),fun(nat,bool),sums(nat),A),B)). [resolve(5174,a,5081,a)].
% 13.27/13.28 Derived: -topological_space(nat) | hAPP(fun(nat,nat),nat,suminf(nat),A) = hAPP(fun(nat,bool),nat,the(nat),hAPP(fun(nat,nat),fun(nat,bool),sums(nat),A)). [resolve(5174,a,5082,a)].
% 13.27/13.28 Derived: -power(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,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),times_times(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),power_power(nat),A)),hAPP(nat,fun(nat,nat),minus_minus(nat),B)))),hAPP(nat,fun(nat,nat),power_power(nat),C))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,suc,B))) = 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),times_times(nat)),hAPP(nat,fun(nat,nat),power_power(nat),A))),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),power_power(nat),C)),hAPP(nat,fun(nat,nat),minus_minus(nat),B)))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,suc,B))). [resolve(5174,a,5083,a)].
% 13.27/13.28 Derived: hAPP(fun(nat,bool),nat,hAPP(fun(nat,nat),fun(fun(nat,bool),nat),big_co1399186613setsum(nat,nat),hAPP(fun(nat,fun(nat,bool)),fun(nat,nat),hAPP(fun(fun(nat,bool),nat),fun(fun(nat,fun(nat,bool)),fun(nat,nat)),combb(fun(nat,bool),nat,nat),hAPP(fun(nat,nat),fun(fun(nat,bool),nat),big_co1399186613setsum(nat,nat),A)),hAPP(fun(nat,nat),fun(nat,fun(nat,bool)),hAPP(fun(nat,fun(nat,fun(nat,bool))),fun(fun(nat,nat),fun(nat,fun(nat,bool))),combs(nat,nat,fun(nat,bool)),hAPP(fun(nat,nat),fun(nat,fun(nat,fun(nat,bool))),hAPP(fun(nat,fun(nat,fun(nat,bool))),fun(fun(nat,nat),fun(nat,fun(nat,fun(nat,bool)))),combb(nat,fun(nat,fun(nat,bool)),nat),ord_atLeastLessThan(nat)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),times_times(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),plus_plus(nat)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),times_times(nat)),B))),B)))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),C)) = 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_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),C),B))). [resolve(5174,a,5084,a)].
% 13.27/13.28 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_atLeastLessThan(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_atLeastLessThan(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(5174,a,5085,a)].
% 13.27/13.28 Derived: 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_atLeastLessThan(nat),zero_zero(nat)),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(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)),C))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),B))),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_atLeastLessThan(nat),zero_zero(nat)),C))). [resolve(5174,a,5086,a)].
% 13.27/13.28 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),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)),C)),D)),zero_zero(nat))),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),collect(A),hAPP(fun(A,bool),fun(A,bool),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))),C))). [resolve(5174,a,5087,a)].
% 13.27/13.28 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),suc)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),B),C)) = 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_atLeastLessThan(nat),hAPP(nat,nat,suc,B)),hAPP(nat,nat,suc,C))). [resolve(5174,a,5089,a)].
% 13.27/13.28 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(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) = 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). [resolve(5174,a,5090,a)].
% 13.27/13.28 Derived: hAPP(nat,nat,A,zero_zero(nat)) != zero_zero(nat) | 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_atLeastLessThan(nat),hAPP(nat,nat,suc,zero_zero(nat))),B)) = 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_atLeastLessThan(nat),zero_zero(nat)),B)). [resolve(5174,a,5091,a)].
% 13.27/13.28 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),C)) | hAPP(fun(nat,bool),nat,hAPP(fun(nat,nat),fun(fun(nat,bool),nat),big_co1399186613setsum(nat,nat),D),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),A),C)) = 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),D),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),A),B))),hAPP(fun(nat,bool),nat,hAPP(fun(nat,nat),fun(fun(nat,bool),nat),big_co1399186613setsum(nat,nat),D),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),B),C))). [resolve(5174,a,5092,a)].
% 13.27/13.28 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(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_atLeastLessThan(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_atLeastLessThan(nat),hAPP(nat,nat,suc,A)),B))). [resolve(5174,a,5093,a)].
% 13.27/13.28 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(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_atLeastLessThan(nat),B),hAPP(nat,nat,suc,A))) = zero_zero(nat). [resolve(5174,a,5094,a)].
% 13.27/13.28 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(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_atLeastLessThan(nat),B),hAPP(nat,nat,suc,A))) = 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_atLeastLessThan(nat),B),A))),hAPP(nat,nat,C,A)). [resolve(5174,a,5095,a)].
% 13.27/13.28 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),B) = zero_zero(nat). [resolve(5174,a,5096,a)].
% 13.27/13.28 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(5174,a,5098,a)].
% 13.27/13.28 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),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)),zero_zero(nat))),B) = hAPP(A,nat,D,C). [resolve(5174,a,5099,a)].
% 13.27/13.28 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),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)),zero_zero(nat))),B) = zero_zero(nat). [resolve(5174,a,5100,a)].
% 13.27/13.28 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),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)),zero_zero(nat))),B) = hAPP(A,nat,D,C). [resolve(5174,a,5101,a)].
% 13.27/13.28 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),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)),zero_zero(nat))),B) = zero_zero(nat). [resolve(5174,a,5102,a)].
% 13.27/13.28 Derived: hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),hAPP(nat,fun(A,nat),combk(nat,A),zero_zero(nat))),B) = zero_zero(nat). [resolve(5174,a,5103,a)].
% 13.27/13.28 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),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)),C)),D)),B) = 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),C),B)),hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),D),B)). [resolve(5174,a,5104,a)].
% 13.27/13.28 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(5174,a,5105,a)].
% 13.27/13.28 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(5174,a,5106,a)].
% 13.27/13.28 Derived: -comm_monoid_mult(nat) | hAPP(fun(nat,bool),nat,hAPP(fun(nat,nat),fun(fun(nat,bool),nat),big_co1399186613setsum(nat,nat),A),B) = hAPP(fun(int,bool),nat,hAPP(fun(int,nat),fun(fun(int,bool),nat),big_co1399186613setsum(int,nat),hAPP(fun(int,nat),fun(int,nat),hAPP(fun(nat,nat),fun(fun(int,nat),fun(int,nat)),combb(nat,nat,int),A),nat_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)),B)). [resolve(5174,a,5107,a)].
% 13.27/13.28 Derived: -comm_monoid_mult(nat) | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A)) | hAPP(fun(nat,bool),nat,hAPP(fun(nat,nat),fun(fun(nat,bool),nat),big_co1399186613setsum(nat,nat),hAPP(fun(nat,int),fun(nat,nat),hAPP(fun(int,nat),fun(fun(nat,int),fun(nat,nat)),combb(int,nat,nat),B),semiring_1_of_nat(int))),hAPP(fun(int,bool),fun(nat,bool),hAPP(fun(int,nat),fun(fun(int,bool),fun(nat,bool)),image(int,nat),nat_1),A)) = hAPP(fun(int,bool),nat,hAPP(fun(int,nat),fun(fun(int,bool),nat),big_co1399186613setsum(int,nat),B),A). [resolve(5174,a,5108,a)].
% 13.27/13.28 Derived: -t2_space(nat) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),f592(nat,B,A))) | hBOOL(hAPP(nat,bool,hAPP(fun(nat,nat),fun(nat,bool),sums(nat),B),hAPP(fun(nat,bool),nat,hAPP(fun(nat,nat),fun(fun(nat,bool),nat),big_co1399186613setsum(nat,nat),B),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),A)))). [resolve(5174,a,5109,a)].
% 13.27/13.28 Derived: -t2_space(nat) | hAPP(nat,nat,A,f592(nat,A,B)) != zero_zero(nat) | hBOOL(hAPP(nat,bool,hAPP(fun(nat,nat),fun(nat,bool),sums(nat),A),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_atLeastLessThan(nat),zero_zero(nat)),B)))). [resolve(5174,a,5110,a)].
% 13.27/13.28 Derived: -ordere779506340up_add(nat) | -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),f593(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))) | 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),D),C)),hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),D),B))). [resolve(5174,a,5111,a)].
% 13.27/13.28 Derived: -ordere779506340up_add(nat) | -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(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),hAPP(A,nat,D,f593(A,nat,D,C,B)))) | 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),D),C)),hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),D),B))). [resolve(5174,a,5112,a)].
% 13.27/13.28 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),f595(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_co1399186613setsum(A,nat),D),B) = hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),D),C). [resolve(5174,a,5113,a)].
% 13.27/13.28 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,f595(A,nat,D,C,B)) != zero_zero(nat) | 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),D),C). [resolve(5174,a,5114,a)].
% 13.27/13.28 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),f596(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_co1399186613setsum(A,nat),D),B) = hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),D),C). [resolve(5174,a,5115,a)].
% 13.27/13.28 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,f596(A,nat,D,C,B)) != zero_zero(nat) | 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),D),C). [resolve(5174,a,5116,a)].
% 13.27/13.29 Derived: -comm_monoid_mult(nat) | A != B | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),f598(nat,C,D,B,A))) | hAPP(fun(int,bool),nat,hAPP(fun(int,nat),fun(fun(int,bool),nat),big_co1399186613setsum(int,nat),D),A) = hAPP(fun(int,bool),nat,hAPP(fun(int,nat),fun(fun(int,bool),nat),big_co1399186613setsum(int,nat),C),B). [resolve(5174,a,5117,a)].
% 13.27/13.29 Derived: -comm_monoid_mult(nat) | A != B | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A)) | hAPP(int,nat,C,f598(nat,D,C,B,A)) != hAPP(int,nat,D,f598(nat,D,C,B,A)) | hAPP(fun(int,bool),nat,hAPP(fun(int,nat),fun(fun(int,bool),nat),big_co1399186613setsum(int,nat),C),A) = hAPP(fun(int,bool),nat,hAPP(fun(int,nat),fun(fun(int,bool),nat),big_co1399186613setsum(int,nat),D),B). [resolve(5174,a,5118,a)].
% 13.27/13.29 Derived: -ord(A) | ti(A,B) != ti(A,C) | ti(A,D) != ti(A,E) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),f603(nat,A,F,V6,E,D,C,B))) | hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),V6),hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_atLeastLessThan(A),B),D)) = hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),F),hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_atLeastLessThan(A),C),E)). [resolve(5174,a,5119,b)].
% 13.27/13.29 Derived: -ord(A) | ti(A,B) != ti(A,C) | ti(A,D) != ti(A,E) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),f603(nat,A,F,V6,E,D,C,B)),D)) | hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),V6),hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_atLeastLessThan(A),B),D)) = hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),F),hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_atLeastLessThan(A),C),E)). [resolve(5174,a,5120,b)].
% 13.27/13.29 Derived: -ord(A) | ti(A,B) != ti(A,C) | ti(A,D) != ti(A,E) | hAPP(A,nat,F,f603(nat,A,V6,F,E,D,C,B)) != hAPP(A,nat,V6,f603(nat,A,V6,F,E,D,C,B)) | hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),F),hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_atLeastLessThan(A),B),D)) = hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),V6),hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_atLeastLessThan(A),C),E)). [resolve(5174,a,5121,b)].
% 13.27/13.29 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),f609(A,nat,C,B)),B)) | hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),C),B) = zero_zero(nat). [resolve(5174,a,5122,a)].
% 13.27/13.29 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(A,nat,C,f609(A,nat,C,B)) != zero_zero(nat) | hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),C),B) = zero_zero(nat). [resolve(5174,a,5123,a)].
% 13.27/13.29 Derived: -ordere779506340up_add(nat) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f610(A,nat,B,C)),C)) | 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),C)),zero_zero(nat))). [resolve(5174,a,5124,a)].
% 13.27/13.29 Derived: -ordere779506340up_add(nat) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(A,nat,B,f610(A,nat,B,C))),zero_zero(nat))) | 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),C)),zero_zero(nat))). [resolve(5174,a,5125,a)].
% 13.27/13.29 Derived: -ordere779506340up_add(nat) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f611(A,nat,B,C)),C)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),B),C))). [resolve(5174,a,5126,a)].
% 13.27/13.29 Derived: -ordere779506340up_add(nat) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),hAPP(A,nat,B,f611(A,nat,B,C)))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),B),C))). [resolve(5174,a,5127,a)].
% 13.27/13.29 Derived: -hBOOL(hAPP(fun(fun(A,bool),bool),bool,finite_finite_1(fun(A,bool)),B)) | hBOOL(hAPP(fun(fun(A,bool),bool),bool,hAPP(fun(A,bool),fun(fun(fun(A,bool),bool),bool),member(fun(A,bool)),f612(A,nat,C,B)),B)) | hBOOL(hAPP(fun(fun(A,bool),bool),bool,hAPP(fun(A,bool),fun(fun(fun(A,bool),bool),bool),member(fun(A,bool)),f613(A,nat,C,B)),B)) | hAPP(fun(fun(A,bool),bool),nat,hAPP(fun(fun(A,bool),nat),fun(fun(fun(A,bool),bool),nat),big_co1399186613setsum(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),C),hAPP(fun(fun(A,bool),bool),fun(A,bool),complete_Sup_Sup(fun(A,bool)),B)). [resolve(5174,a,5128,a)].
% 13.27/13.29 Derived: -hBOOL(hAPP(fun(fun(A,bool),bool),bool,finite_finite_1(fun(A,bool)),B)) | hBOOL(hAPP(fun(fun(A,bool),bool),bool,hAPP(fun(A,bool),fun(fun(fun(A,bool),bool),bool),member(fun(A,bool)),f612(A,nat,C,B)),B)) | hBOOL(hAPP(fun(fun(A,bool),bool),bool,hAPP(fun(A,bool),fun(fun(fun(A,bool),bool),bool),member(fun(A,bool)),f614(A,nat,C,B)),B)) | hAPP(fun(fun(A,bool),bool),nat,hAPP(fun(fun(A,bool),nat),fun(fun(fun(A,bool),bool),nat),big_co1399186613setsum(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),C),hAPP(fun(fun(A,bool),bool),fun(A,bool),complete_Sup_Sup(fun(A,bool)),B)). [resolve(5174,a,5129,a)].
% 13.27/13.29 Derived: -hBOOL(hAPP(fun(fun(A,bool),bool),bool,finite_finite_1(fun(A,bool)),B)) | hBOOL(hAPP(fun(fun(A,bool),bool),bool,hAPP(fun(A,bool),fun(fun(fun(A,bool),bool),bool),member(fun(A,bool)),f612(A,nat,C,B)),B)) | ti(fun(A,bool),f614(A,nat,C,B)) != ti(fun(A,bool),f613(A,nat,C,B)) | hAPP(fun(fun(A,bool),bool),nat,hAPP(fun(fun(A,bool),nat),fun(fun(fun(A,bool),bool),nat),big_co1399186613setsum(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),C),hAPP(fun(fun(A,bool),bool),fun(A,bool),complete_Sup_Sup(fun(A,bool)),B)). [resolve(5174,a,5130,a)].
% 13.27/13.29 Derived: -hBOOL(hAPP(fun(fun(A,bool),bool),bool,finite_finite_1(fun(A,bool)),B)) | hBOOL(hAPP(fun(fun(A,bool),bool),bool,hAPP(fun(A,bool),fun(fun(fun(A,bool),bool),bool),member(fun(A,bool)),f612(A,nat,C,B)),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f615(A,nat,C,B)),f613(A,nat,C,B))) | hAPP(fun(fun(A,bool),bool),nat,hAPP(fun(fun(A,bool),nat),fun(fun(fun(A,bool),bool),nat),big_co1399186613setsum(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),C),hAPP(fun(fun(A,bool),bool),fun(A,bool),complete_Sup_Sup(fun(A,bool)),B)). [resolve(5174,a,5131,a)].
% 13.27/13.29 Derived: -hBOOL(hAPP(fun(fun(A,bool),bool),bool,finite_finite_1(fun(A,bool)),B)) | hBOOL(hAPP(fun(fun(A,bool),bool),bool,hAPP(fun(A,bool),fun(fun(fun(A,bool),bool),bool),member(fun(A,bool)),f612(A,nat,C,B)),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f615(A,nat,C,B)),f614(A,nat,C,B))) | hAPP(fun(fun(A,bool),bool),nat,hAPP(fun(fun(A,bool),nat),fun(fun(fun(A,bool),bool),nat),big_co1399186613setsum(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),C),hAPP(fun(fun(A,bool),bool),fun(A,bool),complete_Sup_Sup(fun(A,bool)),B)). [resolve(5174,a,5132,a)].
% 13.27/13.29 Derived: -hBOOL(hAPP(fun(fun(A,bool),bool),bool,finite_finite_1(fun(A,bool)),B)) | hBOOL(hAPP(fun(fun(A,bool),bool),bool,hAPP(fun(A,bool),fun(fun(fun(A,bool),bool),bool),member(fun(A,bool)),f612(A,nat,C,B)),B)) | hAPP(A,nat,C,f615(A,nat,C,B)) != zero_zero(nat) | hAPP(fun(fun(A,bool),bool),nat,hAPP(fun(fun(A,bool),nat),fun(fun(fun(A,bool),bool),nat),big_co1399186613setsum(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),C),hAPP(fun(fun(A,bool),bool),fun(A,bool),complete_Sup_Sup(fun(A,bool)),B)). [resolve(5174,a,5133,a)].
% 13.27/13.29 Derived: -hBOOL(hAPP(fun(fun(A,bool),bool),bool,finite_finite_1(fun(A,bool)),B)) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),f612(A,nat,C,B))) | hBOOL(hAPP(fun(fun(A,bool),bool),bool,hAPP(fun(A,bool),fun(fun(fun(A,bool),bool),bool),member(fun(A,bool)),f613(A,nat,C,B)),B)) | hAPP(fun(fun(A,bool),bool),nat,hAPP(fun(fun(A,bool),nat),fun(fun(fun(A,bool),bool),nat),big_co1399186613setsum(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),C),hAPP(fun(fun(A,bool),bool),fun(A,bool),complete_Sup_Sup(fun(A,bool)),B)). [resolve(5174,a,5134,a)].
% 13.27/13.29 Derived: -hBOOL(hAPP(fun(fun(A,bool),bool),bool,finite_finite_1(fun(A,bool)),B)) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),f612(A,nat,C,B))) | hBOOL(hAPP(fun(fun(A,bool),bool),bool,hAPP(fun(A,bool),fun(fun(fun(A,bool),bool),bool),member(fun(A,bool)),f614(A,nat,C,B)),B)) | hAPP(fun(fun(A,bool),bool),nat,hAPP(fun(fun(A,bool),nat),fun(fun(fun(A,bool),bool),nat),big_co1399186613setsum(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),C),hAPP(fun(fun(A,bool),bool),fun(A,bool),complete_Sup_Sup(fun(A,bool)),B)). [resolve(5174,a,5135,a)].
% 13.27/13.29 Derived: -hBOOL(hAPP(fun(fun(A,bool),bool),bool,finite_finite_1(fun(A,bool)),B)) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),f612(A,nat,C,B))) | ti(fun(A,bool),f614(A,nat,C,B)) != ti(fun(A,bool),f613(A,nat,C,B)) | hAPP(fun(fun(A,bool),bool),nat,hAPP(fun(fun(A,bool),nat),fun(fun(fun(A,bool),bool),nat),big_co1399186613setsum(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),C),hAPP(fun(fun(A,bool),bool),fun(A,bool),complete_Sup_Sup(fun(A,bool)),B)). [resolve(5174,a,5136,a)].
% 13.27/13.29 Derived: -hBOOL(hAPP(fun(fun(A,bool),bool),bool,finite_finite_1(fun(A,bool)),B)) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),f612(A,nat,C,B))) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f615(A,nat,C,B)),f613(A,nat,C,B))) | hAPP(fun(fun(A,bool),bool),nat,hAPP(fun(fun(A,bool),nat),fun(fun(fun(A,bool),bool),nat),big_co1399186613setsum(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),C),hAPP(fun(fun(A,bool),bool),fun(A,bool),complete_Sup_Sup(fun(A,bool)),B)). [resolve(5174,a,5137,a)].
% 13.27/13.29 Derived: -hBOOL(hAPP(fun(fun(A,bool),bool),bool,finite_finite_1(fun(A,bool)),B)) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),f612(A,nat,C,B))) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f615(A,nat,C,B)),f614(A,nat,C,B))) | hAPP(fun(fun(A,bool),bool),nat,hAPP(fun(fun(A,bool),nat),fun(fun(fun(A,bool),bool),nat),big_co1399186613setsum(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),C),hAPP(fun(fun(A,bool),bool),fun(A,bool),complete_Sup_Sup(fun(A,bool)),B)). [resolve(5174,a,5138,a)].
% 13.27/13.29 Derived: -hBOOL(hAPP(fun(fun(A,bool),bool),bool,finite_finite_1(fun(A,bool)),B)) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),f612(A,nat,C,B))) | hAPP(A,nat,C,f615(A,nat,C,B)) != zero_zero(nat) | hAPP(fun(fun(A,bool),bool),nat,hAPP(fun(fun(A,bool),nat),fun(fun(fun(A,bool),bool),nat),big_co1399186613setsum(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),C),hAPP(fun(fun(A,bool),bool),fun(A,bool),complete_Sup_Sup(fun(A,bool)),B)). [resolve(5174,a,5139,a)].
% 13.27/13.29 Derived: hAPP(fun(nat,bool),nat,hAPP(fun(nat,nat),fun(fun(nat,bool),nat),big_co1399186613setsum(nat,nat),A),hAPP(nat,fun(nat,bool),ord_lessThan(nat),hAPP(nat,nat,suc,B))) = 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),A),hAPP(nat,fun(nat,bool),ord_lessThan(nat),B))),hAPP(nat,nat,A,B)). [resolve(5174,a,5140,a)].
% 13.27/13.29 Derived: -metric_space(nat) | hAPP(fun(nat,nat),nat,suminf(nat),A) = hAPP(fun(nat,nat),nat,lim(nat),hAPP(fun(nat,fun(nat,bool)),fun(nat,nat),hAPP(fun(fun(nat,bool),nat),fun(fun(nat,fun(nat,bool)),fun(nat,nat)),combb(fun(nat,bool),nat,nat),hAPP(fun(nat,nat),fun(fun(nat,bool),nat),big_co1399186613setsum(nat,nat),A)),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)))). [resolve(5174,a,5141,a)].
% 13.27/13.29 Derived: -ordere779506340up_add(nat) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f631(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(5174,a,5142,a)].
% 13.27/13.29 Derived: -ordere779506340up_add(nat) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(A,nat,B,f631(A,nat,B,C,D))),hAPP(A,nat,C,f631(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(5174,a,5143,a)].
% 13.27/13.29 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),f632(A,nat,D,E,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))) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f633(A,nat,D,E,C,B)),C)) | 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(5174,a,5144,a)].
% 13.27/13.29 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),f632(A,nat,D,E,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(A,nat,D,f633(A,nat,D,E,C,B)) != hAPP(A,nat,E,f633(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(5174,a,5145,a)].
% 13.27/13.29 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,f632(A,nat,E,D,C,B)) != zero_zero(nat) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f633(A,nat,E,D,C,B)),C)) | hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),E),C) = hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),D),B). [resolve(5174,a,5146,a)].
% 13.27/13.29 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,f632(A,nat,E,D,C,B)) != zero_zero(nat) | hAPP(A,nat,E,f633(A,nat,E,D,C,B)) != hAPP(A,nat,D,f633(A,nat,E,D,C,B)) | hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),E),C) = hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),D),B). [resolve(5174,a,5147,a)].
% 13.27/13.29 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),f644(A,nat,D,E,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))) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f645(A,nat,D,E,C,B)),C)) | 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(5174,a,5148,a)].
% 13.27/13.29 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),f644(A,nat,D,E,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(A,nat,E,f645(A,nat,D,E,C,B)) != hAPP(A,nat,D,f645(A,nat,D,E,C,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(5174,a,5149,a)].
% 13.27/13.29 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,f644(A,nat,E,D,C,B)) != zero_zero(nat) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f645(A,nat,E,D,C,B)),C)) | 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(5174,a,5150,a)].
% 13.27/13.29 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,f644(A,nat,E,D,C,B)) != zero_zero(nat) | hAPP(A,nat,D,f645(A,nat,E,D,C,B)) != hAPP(A,nat,E,f645(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(5174,a,5151,a)].
% 13.27/13.29 Derived: -t2_space(nat) | -hBOOL(hAPP(fun(nat,nat),bool,summable(nat),A)) | hBOOL(hAPP(filter(nat),bool,hAPP(nat,fun(filter(nat),bool),hAPP(fun(nat,nat),fun(nat,fun(filter(nat),bool)),tendsto(nat,nat),hAPP(fun(nat,fun(nat,bool)),fun(nat,nat),hAPP(fun(fun(nat,bool),nat),fun(fun(nat,fun(nat,bool)),fun(nat,nat)),combb(fun(nat,bool),nat,nat),hAPP(fun(nat,nat),fun(fun(nat,bool),nat),big_co1399186613setsum(nat,nat),A)),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)))),hAPP(fun(nat,nat),nat,suminf(nat),A)),sequentially)). [resolve(5174,a,5152,a)].
% 13.27/13.29 Derived: -topological_space(nat) | -hBOOL(hAPP(nat,bool,hAPP(fun(nat,nat),fun(nat,bool),sums(nat),A),B)) | hBOOL(hAPP(filter(nat),bool,hAPP(nat,fun(filter(nat),bool),hAPP(fun(nat,nat),fun(nat,fun(filter(nat),bool)),tendsto(nat,nat),hAPP(fun(nat,fun(nat,bool)),fun(nat,nat),hAPP(fun(fun(nat,bool),nat),fun(fun(nat,fun(nat,bool)),fun(nat,nat)),combb(fun(nat,bool),nat,nat),hAPP(fun(nat,nat),fun(fun(nat,bool),nat),big_co1399186613setsum(nat,nat),A)),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)))),B),sequentially)). [resolve(5174,a,5153,a)].
% 13.27/13.29 Derived: -topological_space(nat) | hBOOL(hAPP(nat,bool,hAPP(fun(nat,nat),fun(nat,bool),sums(nat),A),B)) | -hBOOL(hAPP(filter(nat),bool,hAPP(nat,fun(filter(nat),bool),hAPP(fun(nat,nat),fun(nat,fun(filter(nat),bool)),tendsto(nat,nat),hAPP(fun(nat,fun(nat,bool)),fun(nat,nat),hAPP(fun(fun(nat,bool),nat),fun(fun(nat,fun(nat,bool)),fun(nat,nat)),combb(fun(nat,bool),nat,nat),hAPP(fun(nat,nat),fun(fun(nat,bool),nat),big_co1399186613setsum(nat,nat),A)),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)))),B),sequentially)). [resolve(5174,a,5154,a)].
% 13.27/13.29 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),suc)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),B),C)) = 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,suc,B)),hAPP(nat,nat,suc,C))). [resolve(5174,a,5155,a)].
% 13.27/13.29 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(5174,a,5156,a)].
% 13.27/13.29 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_atLeastAtMost(nat),hAPP(nat,nat,suc,A)),B))). [resolve(5174,a,5157,a)].
% 13.27/13.29 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,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),B),hAPP(nat,nat,suc,A))) = zero_zero(nat). [resolve(5174,a,5158,a)].
% 13.27/13.29 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,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),B),hAPP(nat,nat,suc,A))) = 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),B),A))),hAPP(nat,nat,C,hAPP(nat,nat,suc,A))). [resolve(5174,a,5159,a)].
% 13.27/13.29 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(5174,a,5160,a)].
% 13.27/13.29 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,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),B),hAPP(nat,nat,suc,A))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,C,B)),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),C),suc)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),B),A))). [resolve(5174,a,5162,a)].
% 13.27/13.29 Derived: hAPP(fun(product_prod(nat,nat),bool),nat,hAPP(fun(product_prod(nat,nat),nat),fun(fun(product_prod(nat,nat),bool),nat),big_co1399186613setsum(product_prod(nat,nat),nat),hAPP(fun(nat,fun(nat,nat)),fun(product_prod(nat,nat),nat),product_prod_case(nat,nat,nat),A)),hAPP(fun(product_prod(nat,nat),bool),fun(product_prod(nat,nat),bool),collect(product_prod(nat,nat)),hAPP(fun(nat,fun(nat,bool)),fun(product_prod(nat,nat),bool),product_prod_case(nat,nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),hAPP(fun(nat,fun(nat,fun(nat,bool))),fun(nat,fun(nat,fun(nat,bool))),combc(nat,nat,fun(nat,bool)),hAPP(fun(nat,fun(nat,fun(nat,bool))),fun(nat,fun(nat,fun(nat,bool))),hAPP(fun(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool))),fun(fun(nat,fun(nat,fun(nat,bool))),fun(nat,fun(nat,fun(nat,bool)))),combb(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),nat),combc(nat,nat,bool)),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,fun(nat,bool))),hAPP(fun(fun(nat,nat),fun(nat,fun(nat,bool))),fun(fun(nat,fun(nat,nat)),fun(nat,fun(nat,fun(nat,bool)))),combb(fun(nat,nat),fun(nat,fun(nat,bool)),nat),hAPP(fun(nat,fun(nat,bool)),fun(fun(nat,nat),fun(nat,fun(nat,bool))),combb(nat,fun(nat,bool),nat),ord_less(nat))),plus_plus(nat)))),B)))) = hAPP(fun(nat,bool),nat,hAPP(fun(nat,nat),fun(fun(nat,bool),nat),big_co1399186613setsum(nat,nat),hAPP(fun(nat,fun(nat,bool)),fun(nat,nat),hAPP(fun(nat,fun(fun(nat,bool),nat)),fun(fun(nat,fun(nat,bool)),fun(nat,nat)),combs(nat,fun(nat,bool),nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(fun(nat,bool),nat)),hAPP(fun(fun(nat,nat),fun(fun(nat,bool),nat)),fun(fun(nat,fun(nat,nat)),fun(nat,fun(fun(nat,bool),nat))),combb(fun(nat,nat),fun(fun(nat,bool),nat),nat),big_co1399186613setsum(nat,nat)),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),hAPP(fun(fun(nat,nat),fun(nat,nat)),fun(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat))),combb(fun(nat,nat),fun(nat,nat),nat),hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,nat),fun(nat,nat)),combs(nat,nat,nat),A)),minus_minus(nat)))),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),zero_zero(nat)))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),B)). [resolve(5174,a,5163,a)].
% 13.27/13.29 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),f771(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(5174,a,5164,a)].
% 13.27/13.29 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(A,nat,C,f771(A,nat,D,C,B)) != hAPP(A,nat,D,f771(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(5174,a,5165,a)].
% 13.27/13.29 Derived: hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f772(A,nat,B,C)),C)) | hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),B),C) = zero_zero(nat). [resolve(5174,a,5166,a)].
% 13.27/13.29 Derived: hAPP(A,nat,B,f772(A,nat,B,C)) != zero_zero(nat) | hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),B),C) = zero_zero(nat). [resolve(5174,a,5167,a)].
% 13.27/13.29 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),A,zero_zero(nat)),zero_zero(nat))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),A,f788(B,nat,C,D,E,A)),f790(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),f792(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_co1399186613setsum(B,nat),C),E)),hAPP(fun(B,bool),nat,hAPP(fun(B,nat),fun(fun(B,bool),nat),big_co1399186613setsum(B,nat),D),E))). [resolve(5174,a,5168,a)].
% 13.27/13.29 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),A,zero_zero(nat)),zero_zero(nat))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),A,f788(B,nat,C,D,E,A)),f790(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,f792(B,nat,C,D,E,A))),hAPP(B,nat,D,f792(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_co1399186613setsum(B,nat),C),E)),hAPP(fun(B,bool),nat,hAPP(fun(B,nat),fun(fun(B,bool),nat),big_co1399186613setsum(B,nat),D),E))). [resolve(5174,a,5169,a)].
% 13.27/13.29 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),A,zero_zero(nat)),zero_zero(nat))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),A,f789(B,nat,C,D,E,A)),f791(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),f792(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_co1399186613setsum(B,nat),C),E)),hAPP(fun(B,bool),nat,hAPP(fun(B,nat),fun(fun(B,bool),nat),big_co1399186613setsum(B,nat),D),E))). [resolve(5174,a,5170,a)].
% 13.27/13.29 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),A,zero_zero(nat)),zero_zero(nat))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),A,f789(B,nat,C,D,E,A)),f791(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,f792(B,nat,C,D,E,A))),hAPP(B,nat,D,f792(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_co1399186613setsum(B,nat),C),E)),hAPP(fun(B,bool),nat,hAPP(fun(B,nat),fun(fun(B,bool),nat),big_co1399186613setsum(B,nat),D),E))). [resolve(5174,a,5171,a)].
% 13.27/13.29 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),A,zero_zero(nat)),zero_zero(nat))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),A,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),f788(B,nat,C,D,E,A)),f789(B,nat,C,D,E,A))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),f790(B,nat,C,D,E,A)),f791(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),f792(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_co1399186613setsum(B,nat),C),E)),hAPP(fun(B,bool),nat,hAPP(fun(B,nat),fun(fun(B,bool),nat),big_co1399186613setsum(B,nat),D),E))). [resolve(5174,a,5172,a)].
% 13.27/13.29 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),A,zero_zero(nat)),zero_zero(nat))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),A,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),f788(B,nat,C,D,E,A)),f789(B,nat,C,D,E,A))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),f790(B,nat,C,D,E,A)),f791(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,f792(B,nat,C,D,E,A))),hAPP(B,nat,D,f792(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_co1399186613setsum(B,nat),C),E)),hAPP(fun(B,bool),nat,hAPP(fun(B,nat),fun(fun(B,bool),nat),big_co1399186613setsum(B,nat),D),E))). [resolve(5174,a,5173,a)].
% 13.36/13.32 5175 comm_monoid_add(rat) # label(arity_Rat_Orat___Groups_Ocomm__monoid__add) # label(axiom). [assumption].
% 13.36/13.32 Derived: big_co1399186613setsum(A,rat) = ti(fun(fun(A,rat),fun(fun(A,bool),rat)),big_co1399186613setsum(A,rat)). [resolve(5175,a,5059,a)].
% 13.36/13.32 Derived: -topological_space(rat) | the(rat) = ti(fun(fun(rat,bool),rat),the(rat)). [resolve(5175,a,5060,a)].
% 13.36/13.32 Derived: -topological_space(rat) | suminf(rat) = ti(fun(fun(nat,rat),rat),suminf(rat)). [resolve(5175,a,5061,a)].
% 13.36/13.32 Derived: -topological_space(rat) | summable(rat) = ti(fun(fun(nat,rat),bool),summable(rat)). [resolve(5175,a,5062,a)].
% 13.36/13.32 Derived: -topological_space(rat) | sums(rat) = ti(fun(fun(nat,rat),fun(rat,bool)),sums(rat)). [resolve(5175,a,5063,a)].
% 13.36/13.32 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),zero_zero(rat)) = ti(rat,A). [resolve(5175,a,5064,a)].
% 13.36/13.32 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),zero_zero(rat)),A) = ti(rat,A). [resolve(5175,a,5065,a)].
% 13.36/13.32 Derived: -comm_monoid_mult(rat) | hAPP(fun(nat,bool),rat,hAPP(fun(nat,rat),fun(fun(nat,bool),rat),big_co302546470etprod(nat,rat),A),B) = hAPP(fun(int,bool),rat,hAPP(fun(int,rat),fun(fun(int,bool),rat),big_co302546470etprod(int,rat),hAPP(fun(int,nat),fun(int,rat),hAPP(fun(nat,rat),fun(fun(int,nat),fun(int,rat)),combb(nat,rat,int),A),nat_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)),B)). [resolve(5175,a,5066,a)].
% 13.36/13.32 Derived: -comm_monoid_mult(rat) | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A)) | hAPP(fun(nat,bool),rat,hAPP(fun(nat,rat),fun(fun(nat,bool),rat),big_co302546470etprod(nat,rat),hAPP(fun(nat,int),fun(nat,rat),hAPP(fun(int,rat),fun(fun(nat,int),fun(nat,rat)),combb(int,rat,nat),B),semiring_1_of_nat(int))),hAPP(fun(int,bool),fun(nat,bool),hAPP(fun(int,nat),fun(fun(int,bool),fun(nat,bool)),image(int,nat),nat_1),A)) = hAPP(fun(int,bool),rat,hAPP(fun(int,rat),fun(fun(int,bool),rat),big_co302546470etprod(int,rat),B),A). [resolve(5175,a,5067,a)].
% 13.36/13.32 Derived: -comm_monoid_mult(rat) | A != B | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),f486(rat,C,D,B,A))) | hAPP(fun(int,bool),rat,hAPP(fun(int,rat),fun(fun(int,bool),rat),big_co302546470etprod(int,rat),D),A) = hAPP(fun(int,bool),rat,hAPP(fun(int,rat),fun(fun(int,bool),rat),big_co302546470etprod(int,rat),C),B). [resolve(5175,a,5068,a)].
% 13.36/13.32 Derived: -comm_monoid_mult(rat) | A != B | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A)) | hAPP(int,rat,C,f486(rat,D,C,B,A)) != hAPP(int,rat,D,f486(rat,D,C,B,A)) | hAPP(fun(int,bool),rat,hAPP(fun(int,rat),fun(fun(int,bool),rat),big_co302546470etprod(int,rat),C),A) = hAPP(fun(int,bool),rat,hAPP(fun(int,rat),fun(fun(int,bool),rat),big_co302546470etprod(int,rat),D),B). [resolve(5175,a,5069,a)].
% 13.36/13.32 Derived: -t2_space(rat) | hAPP(fun(nat,rat),rat,suminf(rat),hAPP(rat,fun(nat,rat),combk(rat,nat),zero_zero(rat))) = zero_zero(rat). [resolve(5175,a,5070,a)].
% 13.36/13.32 Derived: -topological_space(rat) | hBOOL(hAPP(fun(nat,rat),bool,summable(rat),hAPP(rat,fun(nat,rat),combk(rat,nat),zero_zero(rat)))). [resolve(5175,a,5071,a)].
% 13.36/13.32 Derived: -topological_space(rat) | hBOOL(hAPP(rat,bool,hAPP(fun(nat,rat),fun(rat,bool),sums(rat),hAPP(rat,fun(nat,rat),combk(rat,nat),zero_zero(rat))),zero_zero(rat))). [resolve(5175,a,5072,a)].
% 13.36/13.32 Derived: -t2_space(rat) | -hBOOL(hAPP(rat,bool,hAPP(fun(nat,rat),fun(rat,bool),sums(rat),A),B)) | hAPP(fun(nat,rat),rat,suminf(rat),A) = ti(rat,B). [resolve(5175,a,5073,a)].
% 13.36/13.32 Derived: -topological_space(rat) | -hBOOL(hAPP(rat,bool,hAPP(fun(nat,rat),fun(rat,bool),sums(rat),A),B)) | hBOOL(hAPP(fun(nat,rat),bool,summable(rat),A)). [resolve(5175,a,5074,a)].
% 13.36/13.32 Derived: -topological_space(rat) | -hBOOL(hAPP(fun(nat,rat),bool,summable(rat),A)) | hBOOL(hAPP(rat,bool,hAPP(fun(nat,rat),fun(rat,bool),sums(rat),A),f513(rat,A))). [resolve(5175,a,5075,a)].
% 13.36/13.32 Derived: -t2_space(rat) | -hBOOL(hAPP(rat,bool,hAPP(fun(nat,rat),fun(rat,bool),sums(rat),A),B)) | hBOOL(hAPP(fun(nat,rat),bool,summable(rat),A)). [resolve(5175,a,5077,a)].
% 13.36/13.32 Derived: -t2_space(rat) | hBOOL(hAPP(rat,bool,hAPP(fun(nat,rat),fun(rat,bool),sums(rat),A),B)) | -hBOOL(hAPP(fun(nat,rat),bool,summable(rat),A)) | hAPP(fun(nat,rat),rat,suminf(rat),A) != ti(rat,B). [resolve(5175,a,5079,a)].
% 13.36/13.32 Derived: -t2_space(rat) | -hBOOL(hAPP(fun(nat,rat),bool,summable(rat),A)) | hBOOL(hAPP(rat,bool,hAPP(fun(nat,rat),fun(rat,bool),sums(rat),A),hAPP(fun(nat,rat),rat,suminf(rat),A))). [resolve(5175,a,5080,a)].
% 13.36/13.32 Derived: -topological_space(rat) | hAPP(nat,rat,A,zero_zero(nat)) != zero_zero(rat) | -hBOOL(hAPP(rat,bool,hAPP(fun(nat,rat),fun(rat,bool),sums(rat),hAPP(fun(nat,nat),fun(nat,rat),hAPP(fun(nat,rat),fun(fun(nat,nat),fun(nat,rat)),combb(nat,rat,nat),A),suc)),B)) | hBOOL(hAPP(rat,bool,hAPP(fun(nat,rat),fun(rat,bool),sums(rat),A),B)). [resolve(5175,a,5081,a)].
% 13.36/13.32 Derived: -topological_space(rat) | hAPP(fun(nat,rat),rat,suminf(rat),A) = hAPP(fun(rat,bool),rat,the(rat),hAPP(fun(nat,rat),fun(rat,bool),sums(rat),A)). [resolve(5175,a,5082,a)].
% 13.36/13.32 Derived: -power(rat) | hAPP(fun(nat,bool),rat,hAPP(fun(nat,rat),fun(fun(nat,bool),rat),big_co1399186613setsum(nat,rat),hAPP(fun(nat,rat),fun(nat,rat),hAPP(fun(nat,fun(rat,rat)),fun(fun(nat,rat),fun(nat,rat)),combs(nat,rat,rat),hAPP(fun(nat,rat),fun(nat,fun(rat,rat)),hAPP(fun(rat,fun(rat,rat)),fun(fun(nat,rat),fun(nat,fun(rat,rat))),combb(rat,fun(rat,rat),nat),times_times(rat)),hAPP(fun(nat,nat),fun(nat,rat),hAPP(fun(nat,rat),fun(fun(nat,nat),fun(nat,rat)),combb(nat,rat,nat),hAPP(rat,fun(nat,rat),power_power(rat),A)),hAPP(nat,fun(nat,nat),minus_minus(nat),B)))),hAPP(rat,fun(nat,rat),power_power(rat),C))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,suc,B))) = hAPP(fun(nat,bool),rat,hAPP(fun(nat,rat),fun(fun(nat,bool),rat),big_co1399186613setsum(nat,rat),hAPP(fun(nat,rat),fun(nat,rat),hAPP(fun(nat,fun(rat,rat)),fun(fun(nat,rat),fun(nat,rat)),combs(nat,rat,rat),hAPP(fun(nat,rat),fun(nat,fun(rat,rat)),hAPP(fun(rat,fun(rat,rat)),fun(fun(nat,rat),fun(nat,fun(rat,rat))),combb(rat,fun(rat,rat),nat),times_times(rat)),hAPP(rat,fun(nat,rat),power_power(rat),A))),hAPP(fun(nat,nat),fun(nat,rat),hAPP(fun(nat,rat),fun(fun(nat,nat),fun(nat,rat)),combb(nat,rat,nat),hAPP(rat,fun(nat,rat),power_power(rat),C)),hAPP(nat,fun(nat,nat),minus_minus(nat),B)))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,suc,B))). [resolve(5175,a,5083,a)].
% 13.36/13.32 Derived: hAPP(fun(nat,bool),rat,hAPP(fun(nat,rat),fun(fun(nat,bool),rat),big_co1399186613setsum(nat,rat),hAPP(fun(nat,fun(nat,bool)),fun(nat,rat),hAPP(fun(fun(nat,bool),rat),fun(fun(nat,fun(nat,bool)),fun(nat,rat)),combb(fun(nat,bool),rat,nat),hAPP(fun(nat,rat),fun(fun(nat,bool),rat),big_co1399186613setsum(nat,rat),A)),hAPP(fun(nat,nat),fun(nat,fun(nat,bool)),hAPP(fun(nat,fun(nat,fun(nat,bool))),fun(fun(nat,nat),fun(nat,fun(nat,bool))),combs(nat,nat,fun(nat,bool)),hAPP(fun(nat,nat),fun(nat,fun(nat,fun(nat,bool))),hAPP(fun(nat,fun(nat,fun(nat,bool))),fun(fun(nat,nat),fun(nat,fun(nat,fun(nat,bool)))),combb(nat,fun(nat,fun(nat,bool)),nat),ord_atLeastLessThan(nat)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),times_times(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),plus_plus(nat)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),times_times(nat)),B))),B)))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),C)) = hAPP(fun(nat,bool),rat,hAPP(fun(nat,rat),fun(fun(nat,bool),rat),big_co1399186613setsum(nat,rat),A),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),C),B))). [resolve(5175,a,5084,a)].
% 13.36/13.32 Derived: hAPP(fun(nat,bool),rat,hAPP(fun(nat,rat),fun(fun(nat,bool),rat),big_co1399186613setsum(nat,rat),hAPP(fun(nat,nat),fun(nat,rat),hAPP(fun(nat,rat),fun(fun(nat,nat),fun(nat,rat)),combb(nat,rat,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_atLeastLessThan(nat),C),D)) = hAPP(fun(nat,bool),rat,hAPP(fun(nat,rat),fun(fun(nat,bool),rat),big_co1399186613setsum(nat,rat),A),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(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(5175,a,5085,a)].
% 13.36/13.32 Derived: hAPP(fun(nat,bool),rat,hAPP(fun(nat,rat),fun(fun(nat,bool),rat),big_co1399186613setsum(nat,rat),A),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),C))) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(fun(nat,bool),rat,hAPP(fun(nat,rat),fun(fun(nat,bool),rat),big_co1399186613setsum(nat,rat),hAPP(fun(nat,nat),fun(nat,rat),hAPP(fun(nat,rat),fun(fun(nat,nat),fun(nat,rat)),combb(nat,rat,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)),C))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),B))),hAPP(fun(nat,bool),rat,hAPP(fun(nat,rat),fun(fun(nat,bool),rat),big_co1399186613setsum(nat,rat),A),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),C))). [resolve(5175,a,5086,a)].
% 13.36/13.32 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),hAPP(rat,fun(A,rat),hAPP(fun(A,fun(rat,rat)),fun(rat,fun(A,rat)),combc(A,rat,rat),hAPP(fun(A,rat),fun(A,fun(rat,rat)),hAPP(fun(A,fun(rat,fun(rat,rat))),fun(fun(A,rat),fun(A,fun(rat,rat))),combs(A,rat,fun(rat,rat)),hAPP(fun(A,bool),fun(A,fun(rat,fun(rat,rat))),hAPP(fun(bool,fun(rat,fun(rat,rat))),fun(fun(A,bool),fun(A,fun(rat,fun(rat,rat)))),combb(bool,fun(rat,fun(rat,rat)),A),if(rat)),C)),D)),zero_zero(rat))),B) = hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),D),hAPP(fun(A,bool),fun(A,bool),collect(A),hAPP(fun(A,bool),fun(A,bool),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))),C))). [resolve(5175,a,5087,a)].
% 13.36/13.32 Derived: hAPP(fun(nat,bool),rat,hAPP(fun(nat,rat),fun(fun(nat,bool),rat),big_co1399186613setsum(nat,rat),hAPP(fun(nat,nat),fun(nat,rat),hAPP(fun(nat,rat),fun(fun(nat,nat),fun(nat,rat)),combb(nat,rat,nat),A),suc)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),B),C)) = hAPP(fun(nat,bool),rat,hAPP(fun(nat,rat),fun(fun(nat,bool),rat),big_co1399186613setsum(nat,rat),A),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),hAPP(nat,nat,suc,B)),hAPP(nat,nat,suc,C))). [resolve(5175,a,5089,a)].
% 13.36/13.32 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(C,bool),rat,hAPP(fun(C,rat),fun(fun(C,bool),rat),big_co1399186613setsum(C,rat),hAPP(fun(C,fun(A,bool)),fun(C,rat),hAPP(fun(C,fun(fun(A,bool),rat)),fun(fun(C,fun(A,bool)),fun(C,rat)),combs(C,fun(A,bool),rat),hAPP(fun(C,fun(A,rat)),fun(C,fun(fun(A,bool),rat)),hAPP(fun(fun(A,rat),fun(fun(A,bool),rat)),fun(fun(C,fun(A,rat)),fun(C,fun(fun(A,bool),rat))),combb(fun(A,rat),fun(fun(A,bool),rat),C),big_co1399186613setsum(A,rat)),hAPP(fun(A,fun(C,rat)),fun(C,fun(A,rat)),combc(A,C,rat),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) = hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),hAPP(fun(A,fun(C,bool)),fun(A,rat),hAPP(fun(A,fun(fun(C,bool),rat)),fun(fun(A,fun(C,bool)),fun(A,rat)),combs(A,fun(C,bool),rat),hAPP(fun(A,fun(C,rat)),fun(A,fun(fun(C,bool),rat)),hAPP(fun(fun(C,rat),fun(fun(C,bool),rat)),fun(fun(A,fun(C,rat)),fun(A,fun(fun(C,bool),rat))),combb(fun(C,rat),fun(fun(C,bool),rat),A),big_co1399186613setsum(C,rat)),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). [resolve(5175,a,5090,a)].
% 13.36/13.32 Derived: hAPP(nat,rat,A,zero_zero(nat)) != zero_zero(rat) | hAPP(fun(nat,bool),rat,hAPP(fun(nat,rat),fun(fun(nat,bool),rat),big_co1399186613setsum(nat,rat),A),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),hAPP(nat,nat,suc,zero_zero(nat))),B)) = hAPP(fun(nat,bool),rat,hAPP(fun(nat,rat),fun(fun(nat,bool),rat),big_co1399186613setsum(nat,rat),A),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),B)). [resolve(5175,a,5091,a)].
% 13.36/13.32 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),C)) | hAPP(fun(nat,bool),rat,hAPP(fun(nat,rat),fun(fun(nat,bool),rat),big_co1399186613setsum(nat,rat),D),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),A),C)) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(fun(nat,bool),rat,hAPP(fun(nat,rat),fun(fun(nat,bool),rat),big_co1399186613setsum(nat,rat),D),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),A),B))),hAPP(fun(nat,bool),rat,hAPP(fun(nat,rat),fun(fun(nat,bool),rat),big_co1399186613setsum(nat,rat),D),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),B),C))). [resolve(5175,a,5092,a)].
% 13.36/13.32 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | hAPP(fun(nat,bool),rat,hAPP(fun(nat,rat),fun(fun(nat,bool),rat),big_co1399186613setsum(nat,rat),C),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),A),B)) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(nat,rat,C,A)),hAPP(fun(nat,bool),rat,hAPP(fun(nat,rat),fun(fun(nat,bool),rat),big_co1399186613setsum(nat,rat),C),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),hAPP(nat,nat,suc,A)),B))). [resolve(5175,a,5093,a)].
% 13.36/13.32 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | hAPP(fun(nat,bool),rat,hAPP(fun(nat,rat),fun(fun(nat,bool),rat),big_co1399186613setsum(nat,rat),C),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),B),hAPP(nat,nat,suc,A))) = zero_zero(rat). [resolve(5175,a,5094,a)].
% 13.36/13.32 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | hAPP(fun(nat,bool),rat,hAPP(fun(nat,rat),fun(fun(nat,bool),rat),big_co1399186613setsum(nat,rat),C),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),B),hAPP(nat,nat,suc,A))) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(fun(nat,bool),rat,hAPP(fun(nat,rat),fun(fun(nat,bool),rat),big_co1399186613setsum(nat,rat),C),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),B),A))),hAPP(nat,rat,C,A)). [resolve(5175,a,5095,a)].
% 13.36/13.32 Derived: hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),C),B) = zero_zero(rat). [resolve(5175,a,5096,a)].
% 13.36/13.32 Derived: hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),hAPP(fun(B,bool),fun(A,rat),hAPP(fun(A,fun(fun(B,bool),rat)),fun(fun(B,bool),fun(A,rat)),combc(A,fun(B,bool),rat),hAPP(fun(A,fun(B,rat)),fun(A,fun(fun(B,bool),rat)),hAPP(fun(fun(B,rat),fun(fun(B,bool),rat)),fun(fun(A,fun(B,rat)),fun(A,fun(fun(B,bool),rat))),combb(fun(B,rat),fun(fun(B,bool),rat),A),big_co1399186613setsum(B,rat)),hAPP(fun(B,fun(A,rat)),fun(A,fun(B,rat)),combc(B,A,rat),C))),D)),E) = hAPP(fun(B,bool),rat,hAPP(fun(B,rat),fun(fun(B,bool),rat),big_co1399186613setsum(B,rat),hAPP(fun(A,bool),fun(B,rat),hAPP(fun(B,fun(fun(A,bool),rat)),fun(fun(A,bool),fun(B,rat)),combc(B,fun(A,bool),rat),hAPP(fun(B,fun(A,rat)),fun(B,fun(fun(A,bool),rat)),hAPP(fun(fun(A,rat),fun(fun(A,bool),rat)),fun(fun(B,fun(A,rat)),fun(B,fun(fun(A,bool),rat))),combb(fun(A,rat),fun(fun(A,bool),rat),B),big_co1399186613setsum(A,rat)),C)),E)),D). [resolve(5175,a,5098,a)].
% 13.36/13.32 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),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),hAPP(rat,fun(A,rat),hAPP(fun(A,fun(rat,rat)),fun(rat,fun(A,rat)),combc(A,rat,rat),hAPP(fun(A,rat),fun(A,fun(rat,rat)),hAPP(fun(A,fun(rat,fun(rat,rat))),fun(fun(A,rat),fun(A,fun(rat,rat))),combs(A,rat,fun(rat,rat)),hAPP(fun(A,bool),fun(A,fun(rat,fun(rat,rat))),hAPP(fun(bool,fun(rat,fun(rat,rat))),fun(fun(A,bool),fun(A,fun(rat,fun(rat,rat)))),combb(bool,fun(rat,fun(rat,rat)),A),if(rat)),hAPP(A,fun(A,bool),fequal(A),C))),D)),zero_zero(rat))),B) = hAPP(A,rat,D,C). [resolve(5175,a,5099,a)].
% 13.36/13.32 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),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),hAPP(rat,fun(A,rat),hAPP(fun(A,fun(rat,rat)),fun(rat,fun(A,rat)),combc(A,rat,rat),hAPP(fun(A,rat),fun(A,fun(rat,rat)),hAPP(fun(A,fun(rat,fun(rat,rat))),fun(fun(A,rat),fun(A,fun(rat,rat))),combs(A,rat,fun(rat,rat)),hAPP(fun(A,bool),fun(A,fun(rat,fun(rat,rat))),hAPP(fun(bool,fun(rat,fun(rat,rat))),fun(fun(A,bool),fun(A,fun(rat,fun(rat,rat)))),combb(bool,fun(rat,fun(rat,rat)),A),if(rat)),hAPP(A,fun(A,bool),fequal(A),C))),D)),zero_zero(rat))),B) = zero_zero(rat). [resolve(5175,a,5100,a)].
% 13.36/13.32 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),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),hAPP(rat,fun(A,rat),hAPP(fun(A,fun(rat,rat)),fun(rat,fun(A,rat)),combc(A,rat,rat),hAPP(fun(A,rat),fun(A,fun(rat,rat)),hAPP(fun(A,fun(rat,fun(rat,rat))),fun(fun(A,rat),fun(A,fun(rat,rat))),combs(A,rat,fun(rat,rat)),hAPP(fun(A,bool),fun(A,fun(rat,fun(rat,rat))),hAPP(fun(bool,fun(rat,fun(rat,rat))),fun(fun(A,bool),fun(A,fun(rat,fun(rat,rat)))),combb(bool,fun(rat,fun(rat,rat)),A),if(rat)),hAPP(A,fun(A,bool),hAPP(fun(A,fun(A,bool)),fun(A,fun(A,bool)),combc(A,A,bool),fequal(A)),C))),D)),zero_zero(rat))),B) = hAPP(A,rat,D,C). [resolve(5175,a,5101,a)].
% 13.36/13.32 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),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),hAPP(rat,fun(A,rat),hAPP(fun(A,fun(rat,rat)),fun(rat,fun(A,rat)),combc(A,rat,rat),hAPP(fun(A,rat),fun(A,fun(rat,rat)),hAPP(fun(A,fun(rat,fun(rat,rat))),fun(fun(A,rat),fun(A,fun(rat,rat))),combs(A,rat,fun(rat,rat)),hAPP(fun(A,bool),fun(A,fun(rat,fun(rat,rat))),hAPP(fun(bool,fun(rat,fun(rat,rat))),fun(fun(A,bool),fun(A,fun(rat,fun(rat,rat)))),combb(bool,fun(rat,fun(rat,rat)),A),if(rat)),hAPP(A,fun(A,bool),hAPP(fun(A,fun(A,bool)),fun(A,fun(A,bool)),combc(A,A,bool),fequal(A)),C))),D)),zero_zero(rat))),B) = zero_zero(rat). [resolve(5175,a,5102,a)].
% 13.36/13.32 Derived: hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),hAPP(rat,fun(A,rat),combk(rat,A),zero_zero(rat))),B) = zero_zero(rat). [resolve(5175,a,5103,a)].
% 13.36/13.32 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),hAPP(fun(A,rat),fun(A,rat),hAPP(fun(A,fun(rat,rat)),fun(fun(A,rat),fun(A,rat)),combs(A,rat,rat),hAPP(fun(A,rat),fun(A,fun(rat,rat)),hAPP(fun(rat,fun(rat,rat)),fun(fun(A,rat),fun(A,fun(rat,rat))),combb(rat,fun(rat,rat),A),plus_plus(rat)),C)),D)),B) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),C),B)),hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),D),B)). [resolve(5175,a,5104,a)].
% 13.36/13.32 Derived: hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),hAPP(fun(A,rat),fun(A,rat),hAPP(fun(A,fun(rat,rat)),fun(fun(A,rat),fun(A,rat)),combs(A,rat,rat),hAPP(fun(A,rat),fun(A,fun(rat,rat)),hAPP(fun(rat,fun(rat,rat)),fun(fun(A,rat),fun(A,fun(rat,rat))),combb(rat,fun(rat,rat),A),plus_plus(rat)),B)),C)),D) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),B),D)),hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),C),D)). [resolve(5175,a,5105,a)].
% 13.36/13.32 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(fun(C,bool),rat,hAPP(fun(C,rat),fun(fun(C,bool),rat),big_co1399186613setsum(C,rat),hAPP(fun(C,fun(A,bool)),fun(C,rat),hAPP(fun(fun(A,bool),rat),fun(fun(C,fun(A,bool)),fun(C,rat)),combb(fun(A,bool),rat,C),hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),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),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),D),B). [resolve(5175,a,5106,a)].
% 13.36/13.32 Derived: -comm_monoid_mult(rat) | hAPP(fun(nat,bool),rat,hAPP(fun(nat,rat),fun(fun(nat,bool),rat),big_co1399186613setsum(nat,rat),A),B) = hAPP(fun(int,bool),rat,hAPP(fun(int,rat),fun(fun(int,bool),rat),big_co1399186613setsum(int,rat),hAPP(fun(int,nat),fun(int,rat),hAPP(fun(nat,rat),fun(fun(int,nat),fun(int,rat)),combb(nat,rat,int),A),nat_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)),B)). [resolve(5175,a,5107,a)].
% 13.36/13.33 Derived: -comm_monoid_mult(rat) | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A)) | hAPP(fun(nat,bool),rat,hAPP(fun(nat,rat),fun(fun(nat,bool),rat),big_co1399186613setsum(nat,rat),hAPP(fun(nat,int),fun(nat,rat),hAPP(fun(int,rat),fun(fun(nat,int),fun(nat,rat)),combb(int,rat,nat),B),semiring_1_of_nat(int))),hAPP(fun(int,bool),fun(nat,bool),hAPP(fun(int,nat),fun(fun(int,bool),fun(nat,bool)),image(int,nat),nat_1),A)) = hAPP(fun(int,bool),rat,hAPP(fun(int,rat),fun(fun(int,bool),rat),big_co1399186613setsum(int,rat),B),A). [resolve(5175,a,5108,a)].
% 13.36/13.33 Derived: -t2_space(rat) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),f592(rat,B,A))) | hBOOL(hAPP(rat,bool,hAPP(fun(nat,rat),fun(rat,bool),sums(rat),B),hAPP(fun(nat,bool),rat,hAPP(fun(nat,rat),fun(fun(nat,bool),rat),big_co1399186613setsum(nat,rat),B),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),A)))). [resolve(5175,a,5109,a)].
% 13.36/13.33 Derived: -t2_space(rat) | hAPP(nat,rat,A,f592(rat,A,B)) != zero_zero(rat) | hBOOL(hAPP(rat,bool,hAPP(fun(nat,rat),fun(rat,bool),sums(rat),A),hAPP(fun(nat,bool),rat,hAPP(fun(nat,rat),fun(fun(nat,bool),rat),big_co1399186613setsum(nat,rat),A),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),B)))). [resolve(5175,a,5110,a)].
% 13.36/13.33 Derived: -ordere779506340up_add(rat) | -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),f593(A,rat,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))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),D),C)),hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),D),B))). [resolve(5175,a,5111,a)].
% 13.36/13.33 Derived: -ordere779506340up_add(rat) | -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(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),hAPP(A,rat,D,f593(A,rat,D,C,B)))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),D),C)),hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),D),B))). [resolve(5175,a,5112,a)].
% 13.36/13.33 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),f595(A,rat,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),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),D),B) = hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),D),C). [resolve(5175,a,5113,a)].
% 13.36/13.33 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,rat,D,f595(A,rat,D,C,B)) != zero_zero(rat) | hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),D),B) = hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),D),C). [resolve(5175,a,5114,a)].
% 13.36/13.33 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),f596(A,rat,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),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),D),B) = hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),D),C). [resolve(5175,a,5115,a)].
% 13.36/13.33 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,rat,D,f596(A,rat,D,C,B)) != zero_zero(rat) | hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),D),B) = hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),D),C). [resolve(5175,a,5116,a)].
% 13.36/13.33 Derived: -comm_monoid_mult(rat) | A != B | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),f598(rat,C,D,B,A))) | hAPP(fun(int,bool),rat,hAPP(fun(int,rat),fun(fun(int,bool),rat),big_co1399186613setsum(int,rat),D),A) = hAPP(fun(int,bool),rat,hAPP(fun(int,rat),fun(fun(int,bool),rat),big_co1399186613setsum(int,rat),C),B). [resolve(5175,a,5117,a)].
% 13.36/13.33 Derived: -comm_monoid_mult(rat) | A != B | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A)) | hAPP(int,rat,C,f598(rat,D,C,B,A)) != hAPP(int,rat,D,f598(rat,D,C,B,A)) | hAPP(fun(int,bool),rat,hAPP(fun(int,rat),fun(fun(int,bool),rat),big_co1399186613setsum(int,rat),C),A) = hAPP(fun(int,bool),rat,hAPP(fun(int,rat),fun(fun(int,bool),rat),big_co1399186613setsum(int,rat),D),B). [resolve(5175,a,5118,a)].
% 13.36/13.33 Derived: -ord(A) | ti(A,B) != ti(A,C) | ti(A,D) != ti(A,E) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),f603(rat,A,F,V6,E,D,C,B))) | hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),V6),hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_atLeastLessThan(A),B),D)) = hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),F),hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_atLeastLessThan(A),C),E)). [resolve(5175,a,5119,b)].
% 13.36/13.33 Derived: -ord(A) | ti(A,B) != ti(A,C) | ti(A,D) != ti(A,E) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),f603(rat,A,F,V6,E,D,C,B)),D)) | hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),V6),hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_atLeastLessThan(A),B),D)) = hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),F),hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_atLeastLessThan(A),C),E)). [resolve(5175,a,5120,b)].
% 13.36/13.33 Derived: -ord(A) | ti(A,B) != ti(A,C) | ti(A,D) != ti(A,E) | hAPP(A,rat,F,f603(rat,A,V6,F,E,D,C,B)) != hAPP(A,rat,V6,f603(rat,A,V6,F,E,D,C,B)) | hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),F),hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_atLeastLessThan(A),B),D)) = hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),V6),hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_atLeastLessThan(A),C),E)). [resolve(5175,a,5121,b)].
% 13.36/13.33 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),f609(A,rat,C,B)),B)) | hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),C),B) = zero_zero(rat). [resolve(5175,a,5122,a)].
% 13.36/13.33 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(A,rat,C,f609(A,rat,C,B)) != zero_zero(rat) | hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),C),B) = zero_zero(rat). [resolve(5175,a,5123,a)].
% 13.36/13.33 Derived: -ordere779506340up_add(rat) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f610(A,rat,B,C)),C)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),B),C)),zero_zero(rat))). [resolve(5175,a,5124,a)].
% 13.36/13.33 Derived: -ordere779506340up_add(rat) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(A,rat,B,f610(A,rat,B,C))),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),B),C)),zero_zero(rat))). [resolve(5175,a,5125,a)].
% 13.36/13.33 Derived: -ordere779506340up_add(rat) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f611(A,rat,B,C)),C)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),B),C))). [resolve(5175,a,5126,a)].
% 13.36/13.33 Derived: -ordere779506340up_add(rat) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),hAPP(A,rat,B,f611(A,rat,B,C)))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),B),C))). [resolve(5175,a,5127,a)].
% 13.36/13.33 Derived: -hBOOL(hAPP(fun(fun(A,bool),bool),bool,finite_finite_1(fun(A,bool)),B)) | hBOOL(hAPP(fun(fun(A,bool),bool),bool,hAPP(fun(A,bool),fun(fun(fun(A,bool),bool),bool),member(fun(A,bool)),f612(A,rat,C,B)),B)) | hBOOL(hAPP(fun(fun(A,bool),bool),bool,hAPP(fun(A,bool),fun(fun(fun(A,bool),bool),bool),member(fun(A,bool)),f613(A,rat,C,B)),B)) | hAPP(fun(fun(A,bool),bool),rat,hAPP(fun(fun(A,bool),rat),fun(fun(fun(A,bool),bool),rat),big_co1399186613setsum(fun(A,bool),rat),hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),C)),B) = hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),C),hAPP(fun(fun(A,bool),bool),fun(A,bool),complete_Sup_Sup(fun(A,bool)),B)). [resolve(5175,a,5128,a)].
% 13.36/13.33 Derived: -hBOOL(hAPP(fun(fun(A,bool),bool),bool,finite_finite_1(fun(A,bool)),B)) | hBOOL(hAPP(fun(fun(A,bool),bool),bool,hAPP(fun(A,bool),fun(fun(fun(A,bool),bool),bool),member(fun(A,bool)),f612(A,rat,C,B)),B)) | hBOOL(hAPP(fun(fun(A,bool),bool),bool,hAPP(fun(A,bool),fun(fun(fun(A,bool),bool),bool),member(fun(A,bool)),f614(A,rat,C,B)),B)) | hAPP(fun(fun(A,bool),bool),rat,hAPP(fun(fun(A,bool),rat),fun(fun(fun(A,bool),bool),rat),big_co1399186613setsum(fun(A,bool),rat),hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),C)),B) = hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),C),hAPP(fun(fun(A,bool),bool),fun(A,bool),complete_Sup_Sup(fun(A,bool)),B)). [resolve(5175,a,5129,a)].
% 13.36/13.33 Derived: -hBOOL(hAPP(fun(fun(A,bool),bool),bool,finite_finite_1(fun(A,bool)),B)) | hBOOL(hAPP(fun(fun(A,bool),bool),bool,hAPP(fun(A,bool),fun(fun(fun(A,bool),bool),bool),member(fun(A,bool)),f612(A,rat,C,B)),B)) | ti(fun(A,bool),f614(A,rat,C,B)) != ti(fun(A,bool),f613(A,rat,C,B)) | hAPP(fun(fun(A,bool),bool),rat,hAPP(fun(fun(A,bool),rat),fun(fun(fun(A,bool),bool),rat),big_co1399186613setsum(fun(A,bool),rat),hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),C)),B) = hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),C),hAPP(fun(fun(A,bool),bool),fun(A,bool),complete_Sup_Sup(fun(A,bool)),B)). [resolve(5175,a,5130,a)].
% 13.36/13.33 Derived: -hBOOL(hAPP(fun(fun(A,bool),bool),bool,finite_finite_1(fun(A,bool)),B)) | hBOOL(hAPP(fun(fun(A,bool),bool),bool,hAPP(fun(A,bool),fun(fun(fun(A,bool),bool),bool),member(fun(A,bool)),f612(A,rat,C,B)),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f615(A,rat,C,B)),f613(A,rat,C,B))) | hAPP(fun(fun(A,bool),bool),rat,hAPP(fun(fun(A,bool),rat),fun(fun(fun(A,bool),bool),rat),big_co1399186613setsum(fun(A,bool),rat),hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),C)),B) = hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),C),hAPP(fun(fun(A,bool),bool),fun(A,bool),complete_Sup_Sup(fun(A,bool)),B)). [resolve(5175,a,5131,a)].
% 13.36/13.33 Derived: -hBOOL(hAPP(fun(fun(A,bool),bool),bool,finite_finite_1(fun(A,bool)),B)) | hBOOL(hAPP(fun(fun(A,bool),bool),bool,hAPP(fun(A,bool),fun(fun(fun(A,bool),bool),bool),member(fun(A,bool)),f612(A,rat,C,B)),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f615(A,rat,C,B)),f614(A,rat,C,B))) | hAPP(fun(fun(A,bool),bool),rat,hAPP(fun(fun(A,bool),rat),fun(fun(fun(A,bool),bool),rat),big_co1399186613setsum(fun(A,bool),rat),hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),C)),B) = hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),C),hAPP(fun(fun(A,bool),bool),fun(A,bool),complete_Sup_Sup(fun(A,bool)),B)). [resolve(5175,a,5132,a)].
% 13.36/13.33 Derived: -hBOOL(hAPP(fun(fun(A,bool),bool),bool,finite_finite_1(fun(A,bool)),B)) | hBOOL(hAPP(fun(fun(A,bool),bool),bool,hAPP(fun(A,bool),fun(fun(fun(A,bool),bool),bool),member(fun(A,bool)),f612(A,rat,C,B)),B)) | hAPP(A,rat,C,f615(A,rat,C,B)) != zero_zero(rat) | hAPP(fun(fun(A,bool),bool),rat,hAPP(fun(fun(A,bool),rat),fun(fun(fun(A,bool),bool),rat),big_co1399186613setsum(fun(A,bool),rat),hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),C)),B) = hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),C),hAPP(fun(fun(A,bool),bool),fun(A,bool),complete_Sup_Sup(fun(A,bool)),B)). [resolve(5175,a,5133,a)].
% 13.36/13.33 Derived: -hBOOL(hAPP(fun(fun(A,bool),bool),bool,finite_finite_1(fun(A,bool)),B)) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),f612(A,rat,C,B))) | hBOOL(hAPP(fun(fun(A,bool),bool),bool,hAPP(fun(A,bool),fun(fun(fun(A,bool),bool),bool),member(fun(A,bool)),f613(A,rat,C,B)),B)) | hAPP(fun(fun(A,bool),bool),rat,hAPP(fun(fun(A,bool),rat),fun(fun(fun(A,bool),bool),rat),big_co1399186613setsum(fun(A,bool),rat),hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),C)),B) = hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),C),hAPP(fun(fun(A,bool),bool),fun(A,bool),complete_Sup_Sup(fun(A,bool)),B)). [resolve(5175,a,5134,a)].
% 13.36/13.33 Derived: -hBOOL(hAPP(fun(fun(A,bool),bool),bool,finite_finite_1(fun(A,bool)),B)) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),f612(A,rat,C,B))) | hBOOL(hAPP(fun(fun(A,bool),bool),bool,hAPP(fun(A,bool),fun(fun(fun(A,bool),bool),bool),member(fun(A,bool)),f614(A,rat,C,B)),B)) | hAPP(fun(fun(A,bool),bool),rat,hAPP(fun(fun(A,bool),rat),fun(fun(fun(A,bool),bool),rat),big_co1399186613setsum(fun(A,bool),rat),hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),C)),B) = hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),C),hAPP(fun(fun(A,bool),bool),fun(A,bool),complete_Sup_Sup(fun(A,bool)),B)). [resolve(5175,a,5135,a)].
% 13.36/13.33 Derived: -hBOOL(hAPP(fun(fun(A,bool),bool),bool,finite_finite_1(fun(A,bool)),B)) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),f612(A,rat,C,B))) | ti(fun(A,bool),f614(A,rat,C,B)) != ti(fun(A,bool),f613(A,rat,C,B)) | hAPP(fun(fun(A,bool),bool),rat,hAPP(fun(fun(A,bool),rat),fun(fun(fun(A,bool),bool),rat),big_co1399186613setsum(fun(A,bool),rat),hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),C)),B) = hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),C),hAPP(fun(fun(A,bool),bool),fun(A,bool),complete_Sup_Sup(fun(A,bool)),B)). [resolve(5175,a,5136,a)].
% 13.36/13.33 Derived: -hBOOL(hAPP(fun(fun(A,bool),bool),bool,finite_finite_1(fun(A,bool)),B)) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),f612(A,rat,C,B))) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f615(A,rat,C,B)),f613(A,rat,C,B))) | hAPP(fun(fun(A,bool),bool),rat,hAPP(fun(fun(A,bool),rat),fun(fun(fun(A,bool),bool),rat),big_co1399186613setsum(fun(A,bool),rat),hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),C)),B) = hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),C),hAPP(fun(fun(A,bool),bool),fun(A,bool),complete_Sup_Sup(fun(A,bool)),B)). [resolve(5175,a,5137,a)].
% 13.36/13.33 Derived: -hBOOL(hAPP(fun(fun(A,bool),bool),bool,finite_finite_1(fun(A,bool)),B)) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),f612(A,rat,C,B))) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f615(A,rat,C,B)),f614(A,rat,C,B))) | hAPP(fun(fun(A,bool),bool),rat,hAPP(fun(fun(A,bool),rat),fun(fun(fun(A,bool),bool),rat),big_co1399186613setsum(fun(A,bool),rat),hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),C)),B) = hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),C),hAPP(fun(fun(A,bool),bool),fun(A,bool),complete_Sup_Sup(fun(A,bool)),B)). [resolve(5175,a,5138,a)].
% 13.36/13.33 Derived: -hBOOL(hAPP(fun(fun(A,bool),bool),bool,finite_finite_1(fun(A,bool)),B)) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),f612(A,rat,C,B))) | hAPP(A,rat,C,f615(A,rat,C,B)) != zero_zero(rat) | hAPP(fun(fun(A,bool),bool),rat,hAPP(fun(fun(A,bool),rat),fun(fun(fun(A,bool),bool),rat),big_co1399186613setsum(fun(A,bool),rat),hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),C)),B) = hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),C),hAPP(fun(fun(A,bool),bool),fun(A,bool),complete_Sup_Sup(fun(A,bool)),B)). [resolve(5175,a,5139,a)].
% 13.36/13.33 Derived: hAPP(fun(nat,bool),rat,hAPP(fun(nat,rat),fun(fun(nat,bool),rat),big_co1399186613setsum(nat,rat),A),hAPP(nat,fun(nat,bool),ord_lessThan(nat),hAPP(nat,nat,suc,B))) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(fun(nat,bool),rat,hAPP(fun(nat,rat),fun(fun(nat,bool),rat),big_co1399186613setsum(nat,rat),A),hAPP(nat,fun(nat,bool),ord_lessThan(nat),B))),hAPP(nat,rat,A,B)). [resolve(5175,a,5140,a)].
% 13.36/13.33 Derived: -metric_space(rat) | hAPP(fun(nat,rat),rat,suminf(rat),A) = hAPP(fun(nat,rat),rat,lim(rat),hAPP(fun(nat,fun(nat,bool)),fun(nat,rat),hAPP(fun(fun(nat,bool),rat),fun(fun(nat,fun(nat,bool)),fun(nat,rat)),combb(fun(nat,bool),rat,nat),hAPP(fun(nat,rat),fun(fun(nat,bool),rat),big_co1399186613setsum(nat,rat),A)),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)))). [resolve(5175,a,5141,a)].
% 13.36/13.33 Derived: -ordere779506340up_add(rat) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f631(A,rat,B,C,D)),D)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),B),D)),hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),C),D))). [resolve(5175,a,5142,a)].
% 13.36/13.33 Derived: -ordere779506340up_add(rat) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(A,rat,B,f631(A,rat,B,C,D))),hAPP(A,rat,C,f631(A,rat,B,C,D)))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),B),D)),hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),C),D))). [resolve(5175,a,5143,a)].
% 13.36/13.33 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),f632(A,rat,D,E,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))) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f633(A,rat,D,E,C,B)),C)) | hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),D),C) = hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),E),B). [resolve(5175,a,5144,a)].
% 13.36/13.33 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),f632(A,rat,D,E,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(A,rat,D,f633(A,rat,D,E,C,B)) != hAPP(A,rat,E,f633(A,rat,D,E,C,B)) | hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),D),C) = hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),E),B). [resolve(5175,a,5145,a)].
% 13.36/13.33 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,rat,D,f632(A,rat,E,D,C,B)) != zero_zero(rat) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f633(A,rat,E,D,C,B)),C)) | hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),E),C) = hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),D),B). [resolve(5175,a,5146,a)].
% 13.36/13.33 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,rat,D,f632(A,rat,E,D,C,B)) != zero_zero(rat) | hAPP(A,rat,E,f633(A,rat,E,D,C,B)) != hAPP(A,rat,D,f633(A,rat,E,D,C,B)) | hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),E),C) = hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),D),B). [resolve(5175,a,5147,a)].
% 13.36/13.33 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),f644(A,rat,D,E,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))) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f645(A,rat,D,E,C,B)),C)) | hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),E),B) = hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),D),C). [resolve(5175,a,5148,a)].
% 13.36/13.33 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),f644(A,rat,D,E,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(A,rat,E,f645(A,rat,D,E,C,B)) != hAPP(A,rat,D,f645(A,rat,D,E,C,B)) | hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),E),B) = hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),D),C). [resolve(5175,a,5149,a)].
% 13.36/13.33 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,rat,D,f644(A,rat,E,D,C,B)) != zero_zero(rat) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f645(A,rat,E,D,C,B)),C)) | hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),D),B) = hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),E),C). [resolve(5175,a,5150,a)].
% 13.36/13.33 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,rat,D,f644(A,rat,E,D,C,B)) != zero_zero(rat) | hAPP(A,rat,D,f645(A,rat,E,D,C,B)) != hAPP(A,rat,E,f645(A,rat,E,D,C,B)) | hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),D),B) = hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),E),C). [resolve(5175,a,5151,a)].
% 13.36/13.33 Derived: -t2_space(rat) | -hBOOL(hAPP(fun(nat,rat),bool,summable(rat),A)) | hBOOL(hAPP(filter(nat),bool,hAPP(rat,fun(filter(nat),bool),hAPP(fun(nat,rat),fun(rat,fun(filter(nat),bool)),tendsto(nat,rat),hAPP(fun(nat,fun(nat,bool)),fun(nat,rat),hAPP(fun(fun(nat,bool),rat),fun(fun(nat,fun(nat,bool)),fun(nat,rat)),combb(fun(nat,bool),rat,nat),hAPP(fun(nat,rat),fun(fun(nat,bool),rat),big_co1399186613setsum(nat,rat),A)),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)))),hAPP(fun(nat,rat),rat,suminf(rat),A)),sequentially)). [resolve(5175,a,5152,a)].
% 13.36/13.33 Derived: -topological_space(rat) | -hBOOL(hAPP(rat,bool,hAPP(fun(nat,rat),fun(rat,bool),sums(rat),A),B)) | hBOOL(hAPP(filter(nat),bool,hAPP(rat,fun(filter(nat),bool),hAPP(fun(nat,rat),fun(rat,fun(filter(nat),bool)),tendsto(nat,rat),hAPP(fun(nat,fun(nat,bool)),fun(nat,rat),hAPP(fun(fun(nat,bool),rat),fun(fun(nat,fun(nat,bool)),fun(nat,rat)),combb(fun(nat,bool),rat,nat),hAPP(fun(nat,rat),fun(fun(nat,bool),rat),big_co1399186613setsum(nat,rat),A)),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)))),B),sequentially)). [resolve(5175,a,5153,a)].
% 13.36/13.33 Derived: -topological_space(rat) | hBOOL(hAPP(rat,bool,hAPP(fun(nat,rat),fun(rat,bool),sums(rat),A),B)) | -hBOOL(hAPP(filter(nat),bool,hAPP(rat,fun(filter(nat),bool),hAPP(fun(nat,rat),fun(rat,fun(filter(nat),bool)),tendsto(nat,rat),hAPP(fun(nat,fun(nat,bool)),fun(nat,rat),hAPP(fun(fun(nat,bool),rat),fun(fun(nat,fun(nat,bool)),fun(nat,rat)),combb(fun(nat,bool),rat,nat),hAPP(fun(nat,rat),fun(fun(nat,bool),rat),big_co1399186613setsum(nat,rat),A)),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)))),B),sequentially)). [resolve(5175,a,5154,a)].
% 13.36/13.33 Derived: hAPP(fun(nat,bool),rat,hAPP(fun(nat,rat),fun(fun(nat,bool),rat),big_co1399186613setsum(nat,rat),hAPP(fun(nat,nat),fun(nat,rat),hAPP(fun(nat,rat),fun(fun(nat,nat),fun(nat,rat)),combb(nat,rat,nat),A),suc)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),B),C)) = hAPP(fun(nat,bool),rat,hAPP(fun(nat,rat),fun(fun(nat,bool),rat),big_co1399186613setsum(nat,rat),A),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,suc,B)),hAPP(nat,nat,suc,C))). [resolve(5175,a,5155,a)].
% 13.36/13.33 Derived: hAPP(fun(nat,bool),rat,hAPP(fun(nat,rat),fun(fun(nat,bool),rat),big_co1399186613setsum(nat,rat),hAPP(fun(nat,nat),fun(nat,rat),hAPP(fun(nat,rat),fun(fun(nat,nat),fun(nat,rat)),combb(nat,rat,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),rat,hAPP(fun(nat,rat),fun(fun(nat,bool),rat),big_co1399186613setsum(nat,rat),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(5175,a,5156,a)].
% 13.36/13.33 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | hAPP(fun(nat,bool),rat,hAPP(fun(nat,rat),fun(fun(nat,bool),rat),big_co1399186613setsum(nat,rat),C),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),A),B)) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(nat,rat,C,A)),hAPP(fun(nat,bool),rat,hAPP(fun(nat,rat),fun(fun(nat,bool),rat),big_co1399186613setsum(nat,rat),C),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,suc,A)),B))). [resolve(5175,a,5157,a)].
% 13.36/13.33 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,A)),B)) | hAPP(fun(nat,bool),rat,hAPP(fun(nat,rat),fun(fun(nat,bool),rat),big_co1399186613setsum(nat,rat),C),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),B),hAPP(nat,nat,suc,A))) = zero_zero(rat). [resolve(5175,a,5158,a)].
% 13.36/13.33 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,A)),B)) | hAPP(fun(nat,bool),rat,hAPP(fun(nat,rat),fun(fun(nat,bool),rat),big_co1399186613setsum(nat,rat),C),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),B),hAPP(nat,nat,suc,A))) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(fun(nat,bool),rat,hAPP(fun(nat,rat),fun(fun(nat,bool),rat),big_co1399186613setsum(nat,rat),C),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),B),A))),hAPP(nat,rat,C,hAPP(nat,nat,suc,A))). [resolve(5175,a,5159,a)].
% 13.36/13.33 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),rat,hAPP(fun(nat,rat),fun(fun(nat,bool),rat),big_co1399186613setsum(nat,rat),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(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(fun(nat,bool),rat,hAPP(fun(nat,rat),fun(fun(nat,bool),rat),big_co1399186613setsum(nat,rat),C),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),A),B))),hAPP(fun(nat,bool),rat,hAPP(fun(nat,rat),fun(fun(nat,bool),rat),big_co1399186613setsum(nat,rat),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(5175,a,5160,a)].
% 13.36/13.34 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,A)),B)) | hAPP(fun(nat,bool),rat,hAPP(fun(nat,rat),fun(fun(nat,bool),rat),big_co1399186613setsum(nat,rat),C),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),B),hAPP(nat,nat,suc,A))) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(nat,rat,C,B)),hAPP(fun(nat,bool),rat,hAPP(fun(nat,rat),fun(fun(nat,bool),rat),big_co1399186613setsum(nat,rat),hAPP(fun(nat,nat),fun(nat,rat),hAPP(fun(nat,rat),fun(fun(nat,nat),fun(nat,rat)),combb(nat,rat,nat),C),suc)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),B),A))). [resolve(5175,a,5162,a)].
% 13.36/13.34 Derived: hAPP(fun(product_prod(nat,nat),bool),rat,hAPP(fun(product_prod(nat,nat),rat),fun(fun(product_prod(nat,nat),bool),rat),big_co1399186613setsum(product_prod(nat,nat),rat),hAPP(fun(nat,fun(nat,rat)),fun(product_prod(nat,nat),rat),product_prod_case(nat,nat,rat),A)),hAPP(fun(product_prod(nat,nat),bool),fun(product_prod(nat,nat),bool),collect(product_prod(nat,nat)),hAPP(fun(nat,fun(nat,bool)),fun(product_prod(nat,nat),bool),product_prod_case(nat,nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),hAPP(fun(nat,fun(nat,fun(nat,bool))),fun(nat,fun(nat,fun(nat,bool))),combc(nat,nat,fun(nat,bool)),hAPP(fun(nat,fun(nat,fun(nat,bool))),fun(nat,fun(nat,fun(nat,bool))),hAPP(fun(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool))),fun(fun(nat,fun(nat,fun(nat,bool))),fun(nat,fun(nat,fun(nat,bool)))),combb(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),nat),combc(nat,nat,bool)),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,fun(nat,bool))),hAPP(fun(fun(nat,nat),fun(nat,fun(nat,bool))),fun(fun(nat,fun(nat,nat)),fun(nat,fun(nat,fun(nat,bool)))),combb(fun(nat,nat),fun(nat,fun(nat,bool)),nat),hAPP(fun(nat,fun(nat,bool)),fun(fun(nat,nat),fun(nat,fun(nat,bool))),combb(nat,fun(nat,bool),nat),ord_less(nat))),plus_plus(nat)))),B)))) = hAPP(fun(nat,bool),rat,hAPP(fun(nat,rat),fun(fun(nat,bool),rat),big_co1399186613setsum(nat,rat),hAPP(fun(nat,fun(nat,bool)),fun(nat,rat),hAPP(fun(nat,fun(fun(nat,bool),rat)),fun(fun(nat,fun(nat,bool)),fun(nat,rat)),combs(nat,fun(nat,bool),rat),hAPP(fun(nat,fun(nat,rat)),fun(nat,fun(fun(nat,bool),rat)),hAPP(fun(fun(nat,rat),fun(fun(nat,bool),rat)),fun(fun(nat,fun(nat,rat)),fun(nat,fun(fun(nat,bool),rat))),combb(fun(nat,rat),fun(fun(nat,bool),rat),nat),big_co1399186613setsum(nat,rat)),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,rat)),hAPP(fun(fun(nat,nat),fun(nat,rat)),fun(fun(nat,fun(nat,nat)),fun(nat,fun(nat,rat))),combb(fun(nat,nat),fun(nat,rat),nat),hAPP(fun(nat,fun(nat,rat)),fun(fun(nat,nat),fun(nat,rat)),combs(nat,nat,rat),A)),minus_minus(nat)))),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),zero_zero(nat)))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),B)). [resolve(5175,a,5163,a)].
% 13.36/13.34 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),f771(A,rat,C,D,B)),B)) | hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),D),B) = hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),C),B). [resolve(5175,a,5164,a)].
% 13.36/13.34 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(A,rat,C,f771(A,rat,D,C,B)) != hAPP(A,rat,D,f771(A,rat,D,C,B)) | hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),C),B) = hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),D),B). [resolve(5175,a,5165,a)].
% 13.36/13.34 Derived: hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f772(A,rat,B,C)),C)) | hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),B),C) = zero_zero(rat). [resolve(5175,a,5166,a)].
% 13.36/13.34 Derived: hAPP(A,rat,B,f772(A,rat,B,C)) != zero_zero(rat) | hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),B),C) = zero_zero(rat). [resolve(5175,a,5167,a)].
% 13.36/13.34 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),A,zero_zero(rat)),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),A,f788(B,rat,C,D,E,A)),f790(B,rat,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),f792(B,rat,C,D,E,A)),E)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),A,hAPP(fun(B,bool),rat,hAPP(fun(B,rat),fun(fun(B,bool),rat),big_co1399186613setsum(B,rat),C),E)),hAPP(fun(B,bool),rat,hAPP(fun(B,rat),fun(fun(B,bool),rat),big_co1399186613setsum(B,rat),D),E))). [resolve(5175,a,5168,a)].
% 13.36/13.34 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),A,zero_zero(rat)),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),A,f788(B,rat,C,D,E,A)),f790(B,rat,C,D,E,A))) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),E)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),A,hAPP(B,rat,C,f792(B,rat,C,D,E,A))),hAPP(B,rat,D,f792(B,rat,C,D,E,A)))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),A,hAPP(fun(B,bool),rat,hAPP(fun(B,rat),fun(fun(B,bool),rat),big_co1399186613setsum(B,rat),C),E)),hAPP(fun(B,bool),rat,hAPP(fun(B,rat),fun(fun(B,bool),rat),big_co1399186613setsum(B,rat),D),E))). [resolve(5175,a,5169,a)].
% 13.36/13.34 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),A,zero_zero(rat)),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),A,f789(B,rat,C,D,E,A)),f791(B,rat,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),f792(B,rat,C,D,E,A)),E)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),A,hAPP(fun(B,bool),rat,hAPP(fun(B,rat),fun(fun(B,bool),rat),big_co1399186613setsum(B,rat),C),E)),hAPP(fun(B,bool),rat,hAPP(fun(B,rat),fun(fun(B,bool),rat),big_co1399186613setsum(B,rat),D),E))). [resolve(5175,a,5170,a)].
% 13.36/13.34 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),A,zero_zero(rat)),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),A,f789(B,rat,C,D,E,A)),f791(B,rat,C,D,E,A))) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),E)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),A,hAPP(B,rat,C,f792(B,rat,C,D,E,A))),hAPP(B,rat,D,f792(B,rat,C,D,E,A)))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),A,hAPP(fun(B,bool),rat,hAPP(fun(B,rat),fun(fun(B,bool),rat),big_co1399186613setsum(B,rat),C),E)),hAPP(fun(B,bool),rat,hAPP(fun(B,rat),fun(fun(B,bool),rat),big_co1399186613setsum(B,rat),D),E))). [resolve(5175,a,5171,a)].
% 13.36/13.34 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),A,zero_zero(rat)),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),A,hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),f788(B,rat,C,D,E,A)),f789(B,rat,C,D,E,A))),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),f790(B,rat,C,D,E,A)),f791(B,rat,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),f792(B,rat,C,D,E,A)),E)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),A,hAPP(fun(B,bool),rat,hAPP(fun(B,rat),fun(fun(B,bool),rat),big_co1399186613setsum(B,rat),C),E)),hAPP(fun(B,bool),rat,hAPP(fun(B,rat),fun(fun(B,bool),rat),big_co1399186613setsum(B,rat),D),E))). [resolve(5175,a,5172,a)].
% 13.36/13.34 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),A,zero_zero(rat)),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),A,hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),f788(B,rat,C,D,E,A)),f789(B,rat,C,D,E,A))),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),f790(B,rat,C,D,E,A)),f791(B,rat,C,D,E,A)))) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),E)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),A,hAPP(B,rat,C,f792(B,rat,C,D,E,A))),hAPP(B,rat,D,f792(B,rat,C,D,E,A)))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),A,hAPP(fun(B,bool),rat,hAPP(fun(B,rat),fun(fun(B,bool),rat),big_co1399186613setsum(B,rat),C),E)),hAPP(fun(B,bool),rat,hAPP(fun(B,rat),fun(fun(B,bool),rat),big_co1399186613setsum(B,rat),D),E))). [resolve(5175,a,5173,a)].
% 13.36/13.38 5176 comm_monoid_add(real) # label(arity_RealDef_Oreal___Groups_Ocomm__monoid__add) # label(axiom). [assumption].
% 13.36/13.38 Derived: big_co1399186613setsum(A,real) = ti(fun(fun(A,real),fun(fun(A,bool),real)),big_co1399186613setsum(A,real)). [resolve(5176,a,5059,a)].
% 13.36/13.38 Derived: -topological_space(real) | the(real) = ti(fun(fun(real,bool),real),the(real)). [resolve(5176,a,5060,a)].
% 13.36/13.38 Derived: -topological_space(real) | suminf(real) = ti(fun(fun(nat,real),real),suminf(real)). [resolve(5176,a,5061,a)].
% 13.36/13.38 Derived: -topological_space(real) | summable(real) = ti(fun(fun(nat,real),bool),summable(real)). [resolve(5176,a,5062,a)].
% 13.36/13.38 Derived: -topological_space(real) | sums(real) = ti(fun(fun(nat,real),fun(real,bool)),sums(real)). [resolve(5176,a,5063,a)].
% 13.36/13.38 Derived: hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),zero_zero(real)) = ti(real,A). [resolve(5176,a,5064,a)].
% 13.36/13.38 Derived: hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),zero_zero(real)),A) = ti(real,A). [resolve(5176,a,5065,a)].
% 13.36/13.38 Derived: -comm_monoid_mult(real) | hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co302546470etprod(nat,real),A),B) = hAPP(fun(int,bool),real,hAPP(fun(int,real),fun(fun(int,bool),real),big_co302546470etprod(int,real),hAPP(fun(int,nat),fun(int,real),hAPP(fun(nat,real),fun(fun(int,nat),fun(int,real)),combb(nat,real,int),A),nat_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)),B)). [resolve(5176,a,5066,a)].
% 13.36/13.38 Derived: -comm_monoid_mult(real) | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A)) | hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co302546470etprod(nat,real),hAPP(fun(nat,int),fun(nat,real),hAPP(fun(int,real),fun(fun(nat,int),fun(nat,real)),combb(int,real,nat),B),semiring_1_of_nat(int))),hAPP(fun(int,bool),fun(nat,bool),hAPP(fun(int,nat),fun(fun(int,bool),fun(nat,bool)),image(int,nat),nat_1),A)) = hAPP(fun(int,bool),real,hAPP(fun(int,real),fun(fun(int,bool),real),big_co302546470etprod(int,real),B),A). [resolve(5176,a,5067,a)].
% 13.36/13.38 Derived: -comm_monoid_mult(real) | A != B | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),f486(real,C,D,B,A))) | hAPP(fun(int,bool),real,hAPP(fun(int,real),fun(fun(int,bool),real),big_co302546470etprod(int,real),D),A) = hAPP(fun(int,bool),real,hAPP(fun(int,real),fun(fun(int,bool),real),big_co302546470etprod(int,real),C),B). [resolve(5176,a,5068,a)].
% 13.36/13.38 Derived: -comm_monoid_mult(real) | A != B | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A)) | hAPP(int,real,C,f486(real,D,C,B,A)) != hAPP(int,real,D,f486(real,D,C,B,A)) | hAPP(fun(int,bool),real,hAPP(fun(int,real),fun(fun(int,bool),real),big_co302546470etprod(int,real),C),A) = hAPP(fun(int,bool),real,hAPP(fun(int,real),fun(fun(int,bool),real),big_co302546470etprod(int,real),D),B). [resolve(5176,a,5069,a)].
% 13.36/13.38 Derived: -t2_space(real) | hAPP(fun(nat,real),real,suminf(real),hAPP(real,fun(nat,real),combk(real,nat),zero_zero(real))) = zero_zero(real). [resolve(5176,a,5070,a)].
% 13.36/13.38 Derived: -topological_space(real) | hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(real,fun(nat,real),combk(real,nat),zero_zero(real)))). [resolve(5176,a,5071,a)].
% 13.36/13.38 Derived: -topological_space(real) | hBOOL(hAPP(real,bool,hAPP(fun(nat,real),fun(real,bool),sums(real),hAPP(real,fun(nat,real),combk(real,nat),zero_zero(real))),zero_zero(real))). [resolve(5176,a,5072,a)].
% 13.36/13.38 Derived: -t2_space(real) | -hBOOL(hAPP(real,bool,hAPP(fun(nat,real),fun(real,bool),sums(real),A),B)) | hAPP(fun(nat,real),real,suminf(real),A) = ti(real,B). [resolve(5176,a,5073,a)].
% 13.36/13.38 Derived: -topological_space(real) | -hBOOL(hAPP(real,bool,hAPP(fun(nat,real),fun(real,bool),sums(real),A),B)) | hBOOL(hAPP(fun(nat,real),bool,summable(real),A)). [resolve(5176,a,5074,a)].
% 13.36/13.38 Derived: -topological_space(real) | -hBOOL(hAPP(fun(nat,real),bool,summable(real),A)) | hBOOL(hAPP(real,bool,hAPP(fun(nat,real),fun(real,bool),sums(real),A),f513(real,A))). [resolve(5176,a,5075,a)].
% 13.36/13.38 Derived: -t2_space(real) | -hBOOL(hAPP(real,bool,hAPP(fun(nat,real),fun(real,bool),sums(real),A),B)) | hBOOL(hAPP(fun(nat,real),bool,summable(real),A)). [resolve(5176,a,5077,a)].
% 13.36/13.38 Derived: -t2_space(real) | hBOOL(hAPP(real,bool,hAPP(fun(nat,real),fun(real,bool),sums(real),A),B)) | -hBOOL(hAPP(fun(nat,real),bool,summable(real),A)) | hAPP(fun(nat,real),real,suminf(real),A) != ti(real,B). [resolve(5176,a,5079,a)].
% 13.36/13.38 Derived: -t2_space(real) | -hBOOL(hAPP(fun(nat,real),bool,summable(real),A)) | hBOOL(hAPP(real,bool,hAPP(fun(nat,real),fun(real,bool),sums(real),A),hAPP(fun(nat,real),real,suminf(real),A))). [resolve(5176,a,5080,a)].
% 13.36/13.38 Derived: -topological_space(real) | hAPP(nat,real,A,zero_zero(nat)) != zero_zero(real) | -hBOOL(hAPP(real,bool,hAPP(fun(nat,real),fun(real,bool),sums(real),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),A),suc)),B)) | hBOOL(hAPP(real,bool,hAPP(fun(nat,real),fun(real,bool),sums(real),A),B)). [resolve(5176,a,5081,a)].
% 13.36/13.38 Derived: -topological_space(real) | hAPP(fun(nat,real),real,suminf(real),A) = hAPP(fun(real,bool),real,the(real),hAPP(fun(nat,real),fun(real,bool),sums(real),A)). [resolve(5176,a,5082,a)].
% 13.36/13.38 Derived: -power(real) | hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),hAPP(real,fun(nat,real),power_power(real),A)),hAPP(nat,fun(nat,nat),minus_minus(nat),B)))),hAPP(real,fun(nat,real),power_power(real),C))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,suc,B))) = hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(real,fun(nat,real),power_power(real),A))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),hAPP(real,fun(nat,real),power_power(real),C)),hAPP(nat,fun(nat,nat),minus_minus(nat),B)))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,suc,B))). [resolve(5176,a,5083,a)].
% 13.36/13.38 Derived: hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,fun(nat,bool)),fun(nat,real),hAPP(fun(fun(nat,bool),real),fun(fun(nat,fun(nat,bool)),fun(nat,real)),combb(fun(nat,bool),real,nat),hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),A)),hAPP(fun(nat,nat),fun(nat,fun(nat,bool)),hAPP(fun(nat,fun(nat,fun(nat,bool))),fun(fun(nat,nat),fun(nat,fun(nat,bool))),combs(nat,nat,fun(nat,bool)),hAPP(fun(nat,nat),fun(nat,fun(nat,fun(nat,bool))),hAPP(fun(nat,fun(nat,fun(nat,bool))),fun(fun(nat,nat),fun(nat,fun(nat,fun(nat,bool)))),combb(nat,fun(nat,fun(nat,bool)),nat),ord_atLeastLessThan(nat)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),times_times(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),plus_plus(nat)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),times_times(nat)),B))),B)))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),C)) = hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),A),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),C),B))). [resolve(5176,a,5084,a)].
% 13.36/13.38 Derived: hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,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_atLeastLessThan(nat),C),D)) = hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),A),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(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(5176,a,5085,a)].
% 13.36/13.38 Derived: hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),A),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),C))) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,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)),C))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),B))),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),A),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),C))). [resolve(5176,a,5086,a)].
% 13.36/13.38 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),hAPP(real,fun(A,real),hAPP(fun(A,fun(real,real)),fun(real,fun(A,real)),combc(A,real,real),hAPP(fun(A,real),fun(A,fun(real,real)),hAPP(fun(A,fun(real,fun(real,real))),fun(fun(A,real),fun(A,fun(real,real))),combs(A,real,fun(real,real)),hAPP(fun(A,bool),fun(A,fun(real,fun(real,real))),hAPP(fun(bool,fun(real,fun(real,real))),fun(fun(A,bool),fun(A,fun(real,fun(real,real)))),combb(bool,fun(real,fun(real,real)),A),if(real)),C)),D)),zero_zero(real))),B) = hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),D),hAPP(fun(A,bool),fun(A,bool),collect(A),hAPP(fun(A,bool),fun(A,bool),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))),C))). [resolve(5176,a,5087,a)].
% 13.36/13.38 Derived: hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),A),suc)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),B),C)) = hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),A),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),hAPP(nat,nat,suc,B)),hAPP(nat,nat,suc,C))). [resolve(5176,a,5089,a)].
% 13.36/13.38 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(C,bool),real,hAPP(fun(C,real),fun(fun(C,bool),real),big_co1399186613setsum(C,real),hAPP(fun(C,fun(A,bool)),fun(C,real),hAPP(fun(C,fun(fun(A,bool),real)),fun(fun(C,fun(A,bool)),fun(C,real)),combs(C,fun(A,bool),real),hAPP(fun(C,fun(A,real)),fun(C,fun(fun(A,bool),real)),hAPP(fun(fun(A,real),fun(fun(A,bool),real)),fun(fun(C,fun(A,real)),fun(C,fun(fun(A,bool),real))),combb(fun(A,real),fun(fun(A,bool),real),C),big_co1399186613setsum(A,real)),hAPP(fun(A,fun(C,real)),fun(C,fun(A,real)),combc(A,C,real),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) = hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),hAPP(fun(A,fun(C,bool)),fun(A,real),hAPP(fun(A,fun(fun(C,bool),real)),fun(fun(A,fun(C,bool)),fun(A,real)),combs(A,fun(C,bool),real),hAPP(fun(A,fun(C,real)),fun(A,fun(fun(C,bool),real)),hAPP(fun(fun(C,real),fun(fun(C,bool),real)),fun(fun(A,fun(C,real)),fun(A,fun(fun(C,bool),real))),combb(fun(C,real),fun(fun(C,bool),real),A),big_co1399186613setsum(C,real)),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). [resolve(5176,a,5090,a)].
% 13.36/13.38 Derived: hAPP(nat,real,A,zero_zero(nat)) != zero_zero(real) | hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),A),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),hAPP(nat,nat,suc,zero_zero(nat))),B)) = hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),A),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),B)). [resolve(5176,a,5091,a)].
% 13.36/13.38 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),C)) | hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),D),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),A),C)) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),D),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),A),B))),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),D),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),B),C))). [resolve(5176,a,5092,a)].
% 13.36/13.38 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),C),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),A),B)) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,C,A)),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),C),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),hAPP(nat,nat,suc,A)),B))). [resolve(5176,a,5093,a)].
% 13.36/13.38 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),C),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),B),hAPP(nat,nat,suc,A))) = zero_zero(real). [resolve(5176,a,5094,a)].
% 13.36/13.38 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),C),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),B),hAPP(nat,nat,suc,A))) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),C),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),B),A))),hAPP(nat,real,C,A)). [resolve(5176,a,5095,a)].
% 13.36/13.38 Derived: hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),C),B) = zero_zero(real). [resolve(5176,a,5096,a)].
% 13.36/13.38 Derived: hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),hAPP(fun(B,bool),fun(A,real),hAPP(fun(A,fun(fun(B,bool),real)),fun(fun(B,bool),fun(A,real)),combc(A,fun(B,bool),real),hAPP(fun(A,fun(B,real)),fun(A,fun(fun(B,bool),real)),hAPP(fun(fun(B,real),fun(fun(B,bool),real)),fun(fun(A,fun(B,real)),fun(A,fun(fun(B,bool),real))),combb(fun(B,real),fun(fun(B,bool),real),A),big_co1399186613setsum(B,real)),hAPP(fun(B,fun(A,real)),fun(A,fun(B,real)),combc(B,A,real),C))),D)),E) = hAPP(fun(B,bool),real,hAPP(fun(B,real),fun(fun(B,bool),real),big_co1399186613setsum(B,real),hAPP(fun(A,bool),fun(B,real),hAPP(fun(B,fun(fun(A,bool),real)),fun(fun(A,bool),fun(B,real)),combc(B,fun(A,bool),real),hAPP(fun(B,fun(A,real)),fun(B,fun(fun(A,bool),real)),hAPP(fun(fun(A,real),fun(fun(A,bool),real)),fun(fun(B,fun(A,real)),fun(B,fun(fun(A,bool),real))),combb(fun(A,real),fun(fun(A,bool),real),B),big_co1399186613setsum(A,real)),C)),E)),D). [resolve(5176,a,5098,a)].
% 13.36/13.38 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),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),hAPP(real,fun(A,real),hAPP(fun(A,fun(real,real)),fun(real,fun(A,real)),combc(A,real,real),hAPP(fun(A,real),fun(A,fun(real,real)),hAPP(fun(A,fun(real,fun(real,real))),fun(fun(A,real),fun(A,fun(real,real))),combs(A,real,fun(real,real)),hAPP(fun(A,bool),fun(A,fun(real,fun(real,real))),hAPP(fun(bool,fun(real,fun(real,real))),fun(fun(A,bool),fun(A,fun(real,fun(real,real)))),combb(bool,fun(real,fun(real,real)),A),if(real)),hAPP(A,fun(A,bool),fequal(A),C))),D)),zero_zero(real))),B) = hAPP(A,real,D,C). [resolve(5176,a,5099,a)].
% 13.36/13.38 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),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),hAPP(real,fun(A,real),hAPP(fun(A,fun(real,real)),fun(real,fun(A,real)),combc(A,real,real),hAPP(fun(A,real),fun(A,fun(real,real)),hAPP(fun(A,fun(real,fun(real,real))),fun(fun(A,real),fun(A,fun(real,real))),combs(A,real,fun(real,real)),hAPP(fun(A,bool),fun(A,fun(real,fun(real,real))),hAPP(fun(bool,fun(real,fun(real,real))),fun(fun(A,bool),fun(A,fun(real,fun(real,real)))),combb(bool,fun(real,fun(real,real)),A),if(real)),hAPP(A,fun(A,bool),fequal(A),C))),D)),zero_zero(real))),B) = zero_zero(real). [resolve(5176,a,5100,a)].
% 13.36/13.38 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),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),hAPP(real,fun(A,real),hAPP(fun(A,fun(real,real)),fun(real,fun(A,real)),combc(A,real,real),hAPP(fun(A,real),fun(A,fun(real,real)),hAPP(fun(A,fun(real,fun(real,real))),fun(fun(A,real),fun(A,fun(real,real))),combs(A,real,fun(real,real)),hAPP(fun(A,bool),fun(A,fun(real,fun(real,real))),hAPP(fun(bool,fun(real,fun(real,real))),fun(fun(A,bool),fun(A,fun(real,fun(real,real)))),combb(bool,fun(real,fun(real,real)),A),if(real)),hAPP(A,fun(A,bool),hAPP(fun(A,fun(A,bool)),fun(A,fun(A,bool)),combc(A,A,bool),fequal(A)),C))),D)),zero_zero(real))),B) = hAPP(A,real,D,C). [resolve(5176,a,5101,a)].
% 13.36/13.38 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),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),hAPP(real,fun(A,real),hAPP(fun(A,fun(real,real)),fun(real,fun(A,real)),combc(A,real,real),hAPP(fun(A,real),fun(A,fun(real,real)),hAPP(fun(A,fun(real,fun(real,real))),fun(fun(A,real),fun(A,fun(real,real))),combs(A,real,fun(real,real)),hAPP(fun(A,bool),fun(A,fun(real,fun(real,real))),hAPP(fun(bool,fun(real,fun(real,real))),fun(fun(A,bool),fun(A,fun(real,fun(real,real)))),combb(bool,fun(real,fun(real,real)),A),if(real)),hAPP(A,fun(A,bool),hAPP(fun(A,fun(A,bool)),fun(A,fun(A,bool)),combc(A,A,bool),fequal(A)),C))),D)),zero_zero(real))),B) = zero_zero(real). [resolve(5176,a,5102,a)].
% 13.36/13.38 Derived: hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),hAPP(real,fun(A,real),combk(real,A),zero_zero(real))),B) = zero_zero(real). [resolve(5176,a,5103,a)].
% 13.36/13.38 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),hAPP(fun(A,real),fun(A,real),hAPP(fun(A,fun(real,real)),fun(fun(A,real),fun(A,real)),combs(A,real,real),hAPP(fun(A,real),fun(A,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(A,real),fun(A,fun(real,real))),combb(real,fun(real,real),A),plus_plus(real)),C)),D)),B) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),C),B)),hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),D),B)). [resolve(5176,a,5104,a)].
% 13.36/13.38 Derived: hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),hAPP(fun(A,real),fun(A,real),hAPP(fun(A,fun(real,real)),fun(fun(A,real),fun(A,real)),combs(A,real,real),hAPP(fun(A,real),fun(A,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(A,real),fun(A,fun(real,real))),combb(real,fun(real,real),A),plus_plus(real)),B)),C)),D) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),B),D)),hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),C),D)). [resolve(5176,a,5105,a)].
% 13.36/13.38 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(fun(C,bool),real,hAPP(fun(C,real),fun(fun(C,bool),real),big_co1399186613setsum(C,real),hAPP(fun(C,fun(A,bool)),fun(C,real),hAPP(fun(fun(A,bool),real),fun(fun(C,fun(A,bool)),fun(C,real)),combb(fun(A,bool),real,C),hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),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),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),D),B). [resolve(5176,a,5106,a)].
% 13.36/13.38 Derived: -comm_monoid_mult(real) | hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),A),B) = hAPP(fun(int,bool),real,hAPP(fun(int,real),fun(fun(int,bool),real),big_co1399186613setsum(int,real),hAPP(fun(int,nat),fun(int,real),hAPP(fun(nat,real),fun(fun(int,nat),fun(int,real)),combb(nat,real,int),A),nat_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)),B)). [resolve(5176,a,5107,a)].
% 13.36/13.38 Derived: -comm_monoid_mult(real) | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A)) | hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,int),fun(nat,real),hAPP(fun(int,real),fun(fun(nat,int),fun(nat,real)),combb(int,real,nat),B),semiring_1_of_nat(int))),hAPP(fun(int,bool),fun(nat,bool),hAPP(fun(int,nat),fun(fun(int,bool),fun(nat,bool)),image(int,nat),nat_1),A)) = hAPP(fun(int,bool),real,hAPP(fun(int,real),fun(fun(int,bool),real),big_co1399186613setsum(int,real),B),A). [resolve(5176,a,5108,a)].
% 13.36/13.38 Derived: -t2_space(real) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),f592(real,B,A))) | hBOOL(hAPP(real,bool,hAPP(fun(nat,real),fun(real,bool),sums(real),B),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),B),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),A)))). [resolve(5176,a,5109,a)].
% 13.36/13.38 Derived: -t2_space(real) | hAPP(nat,real,A,f592(real,A,B)) != zero_zero(real) | hBOOL(hAPP(real,bool,hAPP(fun(nat,real),fun(real,bool),sums(real),A),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),A),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),B)))). [resolve(5176,a,5110,a)].
% 13.36/13.38 Derived: -ordere779506340up_add(real) | -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),f593(A,real,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))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),D),C)),hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),D),B))). [resolve(5176,a,5111,a)].
% 13.36/13.38 Derived: -ordere779506340up_add(real) | -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(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(A,real,D,f593(A,real,D,C,B)))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),D),C)),hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),D),B))). [resolve(5176,a,5112,a)].
% 13.36/13.38 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),f595(A,real,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),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),D),B) = hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),D),C). [resolve(5176,a,5113,a)].
% 13.36/13.38 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,real,D,f595(A,real,D,C,B)) != zero_zero(real) | hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),D),B) = hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),D),C). [resolve(5176,a,5114,a)].
% 13.46/13.38 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),f596(A,real,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),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),D),B) = hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),D),C). [resolve(5176,a,5115,a)].
% 13.46/13.38 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,real,D,f596(A,real,D,C,B)) != zero_zero(real) | hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),D),B) = hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),D),C). [resolve(5176,a,5116,a)].
% 13.46/13.38 Derived: -comm_monoid_mult(real) | A != B | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),f598(real,C,D,B,A))) | hAPP(fun(int,bool),real,hAPP(fun(int,real),fun(fun(int,bool),real),big_co1399186613setsum(int,real),D),A) = hAPP(fun(int,bool),real,hAPP(fun(int,real),fun(fun(int,bool),real),big_co1399186613setsum(int,real),C),B). [resolve(5176,a,5117,a)].
% 13.46/13.38 Derived: -comm_monoid_mult(real) | A != B | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A)) | hAPP(int,real,C,f598(real,D,C,B,A)) != hAPP(int,real,D,f598(real,D,C,B,A)) | hAPP(fun(int,bool),real,hAPP(fun(int,real),fun(fun(int,bool),real),big_co1399186613setsum(int,real),C),A) = hAPP(fun(int,bool),real,hAPP(fun(int,real),fun(fun(int,bool),real),big_co1399186613setsum(int,real),D),B). [resolve(5176,a,5118,a)].
% 13.46/13.38 Derived: -ord(A) | ti(A,B) != ti(A,C) | ti(A,D) != ti(A,E) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),f603(real,A,F,V6,E,D,C,B))) | hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),V6),hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_atLeastLessThan(A),B),D)) = hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),F),hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_atLeastLessThan(A),C),E)). [resolve(5176,a,5119,b)].
% 13.46/13.38 Derived: -ord(A) | ti(A,B) != ti(A,C) | ti(A,D) != ti(A,E) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),f603(real,A,F,V6,E,D,C,B)),D)) | hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),V6),hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_atLeastLessThan(A),B),D)) = hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),F),hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_atLeastLessThan(A),C),E)). [resolve(5176,a,5120,b)].
% 13.46/13.38 Derived: -ord(A) | ti(A,B) != ti(A,C) | ti(A,D) != ti(A,E) | hAPP(A,real,F,f603(real,A,V6,F,E,D,C,B)) != hAPP(A,real,V6,f603(real,A,V6,F,E,D,C,B)) | hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),F),hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_atLeastLessThan(A),B),D)) = hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),V6),hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_atLeastLessThan(A),C),E)). [resolve(5176,a,5121,b)].
% 13.46/13.38 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),f609(A,real,C,B)),B)) | hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),C),B) = zero_zero(real). [resolve(5176,a,5122,a)].
% 13.46/13.38 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(A,real,C,f609(A,real,C,B)) != zero_zero(real) | hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),C),B) = zero_zero(real). [resolve(5176,a,5123,a)].
% 13.46/13.39 Derived: -ordere779506340up_add(real) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f610(A,real,B,C)),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),B),C)),zero_zero(real))). [resolve(5176,a,5124,a)].
% 13.46/13.39 Derived: -ordere779506340up_add(real) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(A,real,B,f610(A,real,B,C))),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),B),C)),zero_zero(real))). [resolve(5176,a,5125,a)].
% 13.46/13.39 Derived: -ordere779506340up_add(real) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f611(A,real,B,C)),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),B),C))). [resolve(5176,a,5126,a)].
% 13.46/13.39 Derived: -ordere779506340up_add(real) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(A,real,B,f611(A,real,B,C)))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),B),C))). [resolve(5176,a,5127,a)].
% 13.46/13.39 Derived: -hBOOL(hAPP(fun(fun(A,bool),bool),bool,finite_finite_1(fun(A,bool)),B)) | hBOOL(hAPP(fun(fun(A,bool),bool),bool,hAPP(fun(A,bool),fun(fun(fun(A,bool),bool),bool),member(fun(A,bool)),f612(A,real,C,B)),B)) | hBOOL(hAPP(fun(fun(A,bool),bool),bool,hAPP(fun(A,bool),fun(fun(fun(A,bool),bool),bool),member(fun(A,bool)),f613(A,real,C,B)),B)) | hAPP(fun(fun(A,bool),bool),real,hAPP(fun(fun(A,bool),real),fun(fun(fun(A,bool),bool),real),big_co1399186613setsum(fun(A,bool),real),hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),C)),B) = hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),C),hAPP(fun(fun(A,bool),bool),fun(A,bool),complete_Sup_Sup(fun(A,bool)),B)). [resolve(5176,a,5128,a)].
% 13.46/13.39 Derived: -hBOOL(hAPP(fun(fun(A,bool),bool),bool,finite_finite_1(fun(A,bool)),B)) | hBOOL(hAPP(fun(fun(A,bool),bool),bool,hAPP(fun(A,bool),fun(fun(fun(A,bool),bool),bool),member(fun(A,bool)),f612(A,real,C,B)),B)) | hBOOL(hAPP(fun(fun(A,bool),bool),bool,hAPP(fun(A,bool),fun(fun(fun(A,bool),bool),bool),member(fun(A,bool)),f614(A,real,C,B)),B)) | hAPP(fun(fun(A,bool),bool),real,hAPP(fun(fun(A,bool),real),fun(fun(fun(A,bool),bool),real),big_co1399186613setsum(fun(A,bool),real),hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),C)),B) = hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),C),hAPP(fun(fun(A,bool),bool),fun(A,bool),complete_Sup_Sup(fun(A,bool)),B)). [resolve(5176,a,5129,a)].
% 13.46/13.39 Derived: -hBOOL(hAPP(fun(fun(A,bool),bool),bool,finite_finite_1(fun(A,bool)),B)) | hBOOL(hAPP(fun(fun(A,bool),bool),bool,hAPP(fun(A,bool),fun(fun(fun(A,bool),bool),bool),member(fun(A,bool)),f612(A,real,C,B)),B)) | ti(fun(A,bool),f614(A,real,C,B)) != ti(fun(A,bool),f613(A,real,C,B)) | hAPP(fun(fun(A,bool),bool),real,hAPP(fun(fun(A,bool),real),fun(fun(fun(A,bool),bool),real),big_co1399186613setsum(fun(A,bool),real),hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),C)),B) = hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),C),hAPP(fun(fun(A,bool),bool),fun(A,bool),complete_Sup_Sup(fun(A,bool)),B)). [resolve(5176,a,5130,a)].
% 13.46/13.39 Derived: -hBOOL(hAPP(fun(fun(A,bool),bool),bool,finite_finite_1(fun(A,bool)),B)) | hBOOL(hAPP(fun(fun(A,bool),bool),bool,hAPP(fun(A,bool),fun(fun(fun(A,bool),bool),bool),member(fun(A,bool)),f612(A,real,C,B)),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f615(A,real,C,B)),f613(A,real,C,B))) | hAPP(fun(fun(A,bool),bool),real,hAPP(fun(fun(A,bool),real),fun(fun(fun(A,bool),bool),real),big_co1399186613setsum(fun(A,bool),real),hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),C)),B) = hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),C),hAPP(fun(fun(A,bool),bool),fun(A,bool),complete_Sup_Sup(fun(A,bool)),B)). [resolve(5176,a,5131,a)].
% 13.46/13.39 Derived: -hBOOL(hAPP(fun(fun(A,bool),bool),bool,finite_finite_1(fun(A,bool)),B)) | hBOOL(hAPP(fun(fun(A,bool),bool),bool,hAPP(fun(A,bool),fun(fun(fun(A,bool),bool),bool),member(fun(A,bool)),f612(A,real,C,B)),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f615(A,real,C,B)),f614(A,real,C,B))) | hAPP(fun(fun(A,bool),bool),real,hAPP(fun(fun(A,bool),real),fun(fun(fun(A,bool),bool),real),big_co1399186613setsum(fun(A,bool),real),hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),C)),B) = hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),C),hAPP(fun(fun(A,bool),bool),fun(A,bool),complete_Sup_Sup(fun(A,bool)),B)). [resolve(5176,a,5132,a)].
% 13.46/13.39 Derived: -hBOOL(hAPP(fun(fun(A,bool),bool),bool,finite_finite_1(fun(A,bool)),B)) | hBOOL(hAPP(fun(fun(A,bool),bool),bool,hAPP(fun(A,bool),fun(fun(fun(A,bool),bool),bool),member(fun(A,bool)),f612(A,real,C,B)),B)) | hAPP(A,real,C,f615(A,real,C,B)) != zero_zero(real) | hAPP(fun(fun(A,bool),bool),real,hAPP(fun(fun(A,bool),real),fun(fun(fun(A,bool),bool),real),big_co1399186613setsum(fun(A,bool),real),hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),C)),B) = hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),C),hAPP(fun(fun(A,bool),bool),fun(A,bool),complete_Sup_Sup(fun(A,bool)),B)). [resolve(5176,a,5133,a)].
% 13.46/13.39 Derived: -hBOOL(hAPP(fun(fun(A,bool),bool),bool,finite_finite_1(fun(A,bool)),B)) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),f612(A,real,C,B))) | hBOOL(hAPP(fun(fun(A,bool),bool),bool,hAPP(fun(A,bool),fun(fun(fun(A,bool),bool),bool),member(fun(A,bool)),f613(A,real,C,B)),B)) | hAPP(fun(fun(A,bool),bool),real,hAPP(fun(fun(A,bool),real),fun(fun(fun(A,bool),bool),real),big_co1399186613setsum(fun(A,bool),real),hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),C)),B) = hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),C),hAPP(fun(fun(A,bool),bool),fun(A,bool),complete_Sup_Sup(fun(A,bool)),B)). [resolve(5176,a,5134,a)].
% 13.46/13.39 Derived: -hBOOL(hAPP(fun(fun(A,bool),bool),bool,finite_finite_1(fun(A,bool)),B)) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),f612(A,real,C,B))) | hBOOL(hAPP(fun(fun(A,bool),bool),bool,hAPP(fun(A,bool),fun(fun(fun(A,bool),bool),bool),member(fun(A,bool)),f614(A,real,C,B)),B)) | hAPP(fun(fun(A,bool),bool),real,hAPP(fun(fun(A,bool),real),fun(fun(fun(A,bool),bool),real),big_co1399186613setsum(fun(A,bool),real),hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),C)),B) = hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),C),hAPP(fun(fun(A,bool),bool),fun(A,bool),complete_Sup_Sup(fun(A,bool)),B)). [resolve(5176,a,5135,a)].
% 13.46/13.39 Derived: -hBOOL(hAPP(fun(fun(A,bool),bool),bool,finite_finite_1(fun(A,bool)),B)) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),f612(A,real,C,B))) | ti(fun(A,bool),f614(A,real,C,B)) != ti(fun(A,bool),f613(A,real,C,B)) | hAPP(fun(fun(A,bool),bool),real,hAPP(fun(fun(A,bool),real),fun(fun(fun(A,bool),bool),real),big_co1399186613setsum(fun(A,bool),real),hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),C)),B) = hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),C),hAPP(fun(fun(A,bool),bool),fun(A,bool),complete_Sup_Sup(fun(A,bool)),B)). [resolve(5176,a,5136,a)].
% 13.46/13.39 Derived: -hBOOL(hAPP(fun(fun(A,bool),bool),bool,finite_finite_1(fun(A,bool)),B)) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),f612(A,real,C,B))) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f615(A,real,C,B)),f613(A,real,C,B))) | hAPP(fun(fun(A,bool),bool),real,hAPP(fun(fun(A,bool),real),fun(fun(fun(A,bool),bool),real),big_co1399186613setsum(fun(A,bool),real),hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),C)),B) = hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),C),hAPP(fun(fun(A,bool),bool),fun(A,bool),complete_Sup_Sup(fun(A,bool)),B)). [resolve(5176,a,5137,a)].
% 13.46/13.39 Derived: -hBOOL(hAPP(fun(fun(A,bool),bool),bool,finite_finite_1(fun(A,bool)),B)) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),f612(A,real,C,B))) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f615(A,real,C,B)),f614(A,real,C,B))) | hAPP(fun(fun(A,bool),bool),real,hAPP(fun(fun(A,bool),real),fun(fun(fun(A,bool),bool),real),big_co1399186613setsum(fun(A,bool),real),hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),C)),B) = hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),C),hAPP(fun(fun(A,bool),bool),fun(A,bool),complete_Sup_Sup(fun(A,bool)),B)). [resolve(5176,a,5138,a)].
% 13.46/13.39 Derived: -hBOOL(hAPP(fun(fun(A,bool),bool),bool,finite_finite_1(fun(A,bool)),B)) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),f612(A,real,C,B))) | hAPP(A,real,C,f615(A,real,C,B)) != zero_zero(real) | hAPP(fun(fun(A,bool),bool),real,hAPP(fun(fun(A,bool),real),fun(fun(fun(A,bool),bool),real),big_co1399186613setsum(fun(A,bool),real),hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),C)),B) = hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),C),hAPP(fun(fun(A,bool),bool),fun(A,bool),complete_Sup_Sup(fun(A,bool)),B)). [resolve(5176,a,5139,a)].
% 13.46/13.39 Derived: hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),A),hAPP(nat,fun(nat,bool),ord_lessThan(nat),hAPP(nat,nat,suc,B))) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),A),hAPP(nat,fun(nat,bool),ord_lessThan(nat),B))),hAPP(nat,real,A,B)). [resolve(5176,a,5140,a)].
% 13.46/13.39 Derived: -metric_space(real) | hAPP(fun(nat,real),real,suminf(real),A) = hAPP(fun(nat,real),real,lim(real),hAPP(fun(nat,fun(nat,bool)),fun(nat,real),hAPP(fun(fun(nat,bool),real),fun(fun(nat,fun(nat,bool)),fun(nat,real)),combb(fun(nat,bool),real,nat),hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),A)),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)))). [resolve(5176,a,5141,a)].
% 13.46/13.39 Derived: -ordere779506340up_add(real) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f631(A,real,B,C,D)),D)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),B),D)),hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),C),D))). [resolve(5176,a,5142,a)].
% 13.46/13.39 Derived: -ordere779506340up_add(real) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(A,real,B,f631(A,real,B,C,D))),hAPP(A,real,C,f631(A,real,B,C,D)))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),B),D)),hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),C),D))). [resolve(5176,a,5143,a)].
% 13.46/13.39 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),f632(A,real,D,E,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))) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f633(A,real,D,E,C,B)),C)) | hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),D),C) = hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),E),B). [resolve(5176,a,5144,a)].
% 13.46/13.39 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),f632(A,real,D,E,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(A,real,D,f633(A,real,D,E,C,B)) != hAPP(A,real,E,f633(A,real,D,E,C,B)) | hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),D),C) = hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),E),B). [resolve(5176,a,5145,a)].
% 13.46/13.39 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,real,D,f632(A,real,E,D,C,B)) != zero_zero(real) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f633(A,real,E,D,C,B)),C)) | hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),E),C) = hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),D),B). [resolve(5176,a,5146,a)].
% 13.46/13.39 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,real,D,f632(A,real,E,D,C,B)) != zero_zero(real) | hAPP(A,real,E,f633(A,real,E,D,C,B)) != hAPP(A,real,D,f633(A,real,E,D,C,B)) | hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),E),C) = hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),D),B). [resolve(5176,a,5147,a)].
% 13.46/13.39 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),f644(A,real,D,E,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))) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f645(A,real,D,E,C,B)),C)) | hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),E),B) = hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),D),C). [resolve(5176,a,5148,a)].
% 13.46/13.39 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),f644(A,real,D,E,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(A,real,E,f645(A,real,D,E,C,B)) != hAPP(A,real,D,f645(A,real,D,E,C,B)) | hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),E),B) = hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),D),C). [resolve(5176,a,5149,a)].
% 13.46/13.39 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,real,D,f644(A,real,E,D,C,B)) != zero_zero(real) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f645(A,real,E,D,C,B)),C)) | hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),D),B) = hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),E),C). [resolve(5176,a,5150,a)].
% 13.46/13.39 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,real,D,f644(A,real,E,D,C,B)) != zero_zero(real) | hAPP(A,real,D,f645(A,real,E,D,C,B)) != hAPP(A,real,E,f645(A,real,E,D,C,B)) | hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),D),B) = hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),E),C). [resolve(5176,a,5151,a)].
% 13.46/13.39 Derived: -t2_space(real) | -hBOOL(hAPP(fun(nat,real),bool,summable(real),A)) | hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),hAPP(fun(nat,fun(nat,bool)),fun(nat,real),hAPP(fun(fun(nat,bool),real),fun(fun(nat,fun(nat,bool)),fun(nat,real)),combb(fun(nat,bool),real,nat),hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),A)),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)))),hAPP(fun(nat,real),real,suminf(real),A)),sequentially)). [resolve(5176,a,5152,a)].
% 13.46/13.39 Derived: -topological_space(real) | -hBOOL(hAPP(real,bool,hAPP(fun(nat,real),fun(real,bool),sums(real),A),B)) | hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),hAPP(fun(nat,fun(nat,bool)),fun(nat,real),hAPP(fun(fun(nat,bool),real),fun(fun(nat,fun(nat,bool)),fun(nat,real)),combb(fun(nat,bool),real,nat),hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),A)),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)))),B),sequentially)). [resolve(5176,a,5153,a)].
% 13.46/13.39 Derived: -topological_space(real) | hBOOL(hAPP(real,bool,hAPP(fun(nat,real),fun(real,bool),sums(real),A),B)) | -hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),hAPP(fun(nat,fun(nat,bool)),fun(nat,real),hAPP(fun(fun(nat,bool),real),fun(fun(nat,fun(nat,bool)),fun(nat,real)),combb(fun(nat,bool),real,nat),hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),A)),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)))),B),sequentially)). [resolve(5176,a,5154,a)].
% 13.46/13.39 Derived: hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),A),suc)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),B),C)) = hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),A),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,suc,B)),hAPP(nat,nat,suc,C))). [resolve(5176,a,5155,a)].
% 13.46/13.39 Derived: hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,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),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),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(5176,a,5156,a)].
% 13.46/13.39 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),C),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),A),B)) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,C,A)),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),C),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,suc,A)),B))). [resolve(5176,a,5157,a)].
% 13.46/13.39 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,A)),B)) | hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),C),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),B),hAPP(nat,nat,suc,A))) = zero_zero(real). [resolve(5176,a,5158,a)].
% 13.46/13.39 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,A)),B)) | hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),C),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),B),hAPP(nat,nat,suc,A))) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),C),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),B),A))),hAPP(nat,real,C,hAPP(nat,nat,suc,A))). [resolve(5176,a,5159,a)].
% 13.46/13.39 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),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),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(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),C),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),A),B))),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),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(5176,a,5160,a)].
% 13.46/13.39 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,A)),B)) | hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),C),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),B),hAPP(nat,nat,suc,A))) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,C,B)),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),C),suc)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),B),A))). [resolve(5176,a,5162,a)].
% 13.46/13.39 Derived: hAPP(fun(product_prod(nat,nat),bool),real,hAPP(fun(product_prod(nat,nat),real),fun(fun(product_prod(nat,nat),bool),real),big_co1399186613setsum(product_prod(nat,nat),real),hAPP(fun(nat,fun(nat,real)),fun(product_prod(nat,nat),real),product_prod_case(nat,nat,real),A)),hAPP(fun(product_prod(nat,nat),bool),fun(product_prod(nat,nat),bool),collect(product_prod(nat,nat)),hAPP(fun(nat,fun(nat,bool)),fun(product_prod(nat,nat),bool),product_prod_case(nat,nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),hAPP(fun(nat,fun(nat,fun(nat,bool))),fun(nat,fun(nat,fun(nat,bool))),combc(nat,nat,fun(nat,bool)),hAPP(fun(nat,fun(nat,fun(nat,bool))),fun(nat,fun(nat,fun(nat,bool))),hAPP(fun(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool))),fun(fun(nat,fun(nat,fun(nat,bool))),fun(nat,fun(nat,fun(nat,bool)))),combb(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),nat),combc(nat,nat,bool)),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,fun(nat,bool))),hAPP(fun(fun(nat,nat),fun(nat,fun(nat,bool))),fun(fun(nat,fun(nat,nat)),fun(nat,fun(nat,fun(nat,bool)))),combb(fun(nat,nat),fun(nat,fun(nat,bool)),nat),hAPP(fun(nat,fun(nat,bool)),fun(fun(nat,nat),fun(nat,fun(nat,bool))),combb(nat,fun(nat,bool),nat),ord_less(nat))),plus_plus(nat)))),B)))) = hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,fun(nat,bool)),fun(nat,real),hAPP(fun(nat,fun(fun(nat,bool),real)),fun(fun(nat,fun(nat,bool)),fun(nat,real)),combs(nat,fun(nat,bool),real),hAPP(fun(nat,fun(nat,real)),fun(nat,fun(fun(nat,bool),real)),hAPP(fun(fun(nat,real),fun(fun(nat,bool),real)),fun(fun(nat,fun(nat,real)),fun(nat,fun(fun(nat,bool),real))),combb(fun(nat,real),fun(fun(nat,bool),real),nat),big_co1399186613setsum(nat,real)),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,real)),hAPP(fun(fun(nat,nat),fun(nat,real)),fun(fun(nat,fun(nat,nat)),fun(nat,fun(nat,real))),combb(fun(nat,nat),fun(nat,real),nat),hAPP(fun(nat,fun(nat,real)),fun(fun(nat,nat),fun(nat,real)),combs(nat,nat,real),A)),minus_minus(nat)))),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),zero_zero(nat)))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),B)). [resolve(5176,a,5163,a)].
% 13.46/13.39 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),f771(A,real,C,D,B)),B)) | hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),D),B) = hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),C),B). [resolve(5176,a,5164,a)].
% 13.46/13.39 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(A,real,C,f771(A,real,D,C,B)) != hAPP(A,real,D,f771(A,real,D,C,B)) | hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),C),B) = hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),D),B). [resolve(5176,a,5165,a)].
% 13.46/13.39 Derived: hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f772(A,real,B,C)),C)) | hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),B),C) = zero_zero(real). [resolve(5176,a,5166,a)].
% 13.46/13.39 Derived: hAPP(A,real,B,f772(A,real,B,C)) != zero_zero(real) | hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),B),C) = zero_zero(real). [resolve(5176,a,5167,a)].
% 13.46/13.39 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),A,zero_zero(real)),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),A,f788(B,real,C,D,E,A)),f790(B,real,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),f792(B,real,C,D,E,A)),E)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),A,hAPP(fun(B,bool),real,hAPP(fun(B,real),fun(fun(B,bool),real),big_co1399186613setsum(B,real),C),E)),hAPP(fun(B,bool),real,hAPP(fun(B,real),fun(fun(B,bool),real),big_co1399186613setsum(B,real),D),E))). [resolve(5176,a,5168,a)].
% 13.46/13.39 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),A,zero_zero(real)),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),A,f788(B,real,C,D,E,A)),f790(B,real,C,D,E,A))) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),E)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),A,hAPP(B,real,C,f792(B,real,C,D,E,A))),hAPP(B,real,D,f792(B,real,C,D,E,A)))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),A,hAPP(fun(B,bool),real,hAPP(fun(B,real),fun(fun(B,bool),real),big_co1399186613setsum(B,real),C),E)),hAPP(fun(B,bool),real,hAPP(fun(B,real),fun(fun(B,bool),real),big_co1399186613setsum(B,real),D),E))). [resolve(5176,a,5169,a)].
% 13.46/13.39 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),A,zero_zero(real)),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),A,f789(B,real,C,D,E,A)),f791(B,real,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),f792(B,real,C,D,E,A)),E)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),A,hAPP(fun(B,bool),real,hAPP(fun(B,real),fun(fun(B,bool),real),big_co1399186613setsum(B,real),C),E)),hAPP(fun(B,bool),real,hAPP(fun(B,real),fun(fun(B,bool),real),big_co1399186613setsum(B,real),D),E))). [resolve(5176,a,5170,a)].
% 13.46/13.39 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),A,zero_zero(real)),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),A,f789(B,real,C,D,E,A)),f791(B,real,C,D,E,A))) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),E)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),A,hAPP(B,real,C,f792(B,real,C,D,E,A))),hAPP(B,real,D,f792(B,real,C,D,E,A)))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),A,hAPP(fun(B,bool),real,hAPP(fun(B,real),fun(fun(B,bool),real),big_co1399186613setsum(B,real),C),E)),hAPP(fun(B,bool),real,hAPP(fun(B,real),fun(fun(B,bool),real),big_co1399186613setsum(B,real),D),E))). [resolve(5176,a,5171,a)].
% 13.46/13.39 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),A,zero_zero(real)),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),A,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),f788(B,real,C,D,E,A)),f789(B,real,C,D,E,A))),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),f790(B,real,C,D,E,A)),f791(B,real,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),f792(B,real,C,D,E,A)),E)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),A,hAPP(fun(B,bool),real,hAPP(fun(B,real),fun(fun(B,bool),real),big_co1399186613setsum(B,real),C),E)),hAPP(fun(B,bool),real,hAPP(fun(B,real),fun(fun(B,bool),real),big_co1399186613setsum(B,real),D),E))). [resolve(5176,a,5172,a)].
% 13.50/13.43 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),A,zero_zero(real)),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),A,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),f788(B,real,C,D,E,A)),f789(B,real,C,D,E,A))),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),f790(B,real,C,D,E,A)),f791(B,real,C,D,E,A)))) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),E)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),A,hAPP(B,real,C,f792(B,real,C,D,E,A))),hAPP(B,real,D,f792(B,real,C,D,E,A)))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),A,hAPP(fun(B,bool),real,hAPP(fun(B,real),fun(fun(B,bool),real),big_co1399186613setsum(B,real),C),E)),hAPP(fun(B,bool),real,hAPP(fun(B,real),fun(fun(B,bool),real),big_co1399186613setsum(B,real),D),E))). [resolve(5176,a,5173,a)].
% 13.50/13.43 5177 comm_monoid_add(complex) # label(arity_Complex_Ocomplex___Groups_Ocomm__monoid__add) # label(axiom). [assumption].
% 13.50/13.43 Derived: big_co1399186613setsum(A,complex) = ti(fun(fun(A,complex),fun(fun(A,bool),complex)),big_co1399186613setsum(A,complex)). [resolve(5177,a,5059,a)].
% 13.50/13.43 Derived: -topological_space(complex) | the(complex) = ti(fun(fun(complex,bool),complex),the(complex)). [resolve(5177,a,5060,a)].
% 13.50/13.43 Derived: -topological_space(complex) | suminf(complex) = ti(fun(fun(nat,complex),complex),suminf(complex)). [resolve(5177,a,5061,a)].
% 13.50/13.43 Derived: -topological_space(complex) | summable(complex) = ti(fun(fun(nat,complex),bool),summable(complex)). [resolve(5177,a,5062,a)].
% 13.50/13.43 Derived: -topological_space(complex) | sums(complex) = ti(fun(fun(nat,complex),fun(complex,bool)),sums(complex)). [resolve(5177,a,5063,a)].
% 13.50/13.43 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),A),zero_zero(complex)) = ti(complex,A). [resolve(5177,a,5064,a)].
% 13.50/13.43 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),zero_zero(complex)),A) = ti(complex,A). [resolve(5177,a,5065,a)].
% 13.50/13.43 Derived: -comm_monoid_mult(complex) | hAPP(fun(nat,bool),complex,hAPP(fun(nat,complex),fun(fun(nat,bool),complex),big_co302546470etprod(nat,complex),A),B) = hAPP(fun(int,bool),complex,hAPP(fun(int,complex),fun(fun(int,bool),complex),big_co302546470etprod(int,complex),hAPP(fun(int,nat),fun(int,complex),hAPP(fun(nat,complex),fun(fun(int,nat),fun(int,complex)),combb(nat,complex,int),A),nat_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)),B)). [resolve(5177,a,5066,a)].
% 13.50/13.43 Derived: -comm_monoid_mult(complex) | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A)) | hAPP(fun(nat,bool),complex,hAPP(fun(nat,complex),fun(fun(nat,bool),complex),big_co302546470etprod(nat,complex),hAPP(fun(nat,int),fun(nat,complex),hAPP(fun(int,complex),fun(fun(nat,int),fun(nat,complex)),combb(int,complex,nat),B),semiring_1_of_nat(int))),hAPP(fun(int,bool),fun(nat,bool),hAPP(fun(int,nat),fun(fun(int,bool),fun(nat,bool)),image(int,nat),nat_1),A)) = hAPP(fun(int,bool),complex,hAPP(fun(int,complex),fun(fun(int,bool),complex),big_co302546470etprod(int,complex),B),A). [resolve(5177,a,5067,a)].
% 13.50/13.43 Derived: -comm_monoid_mult(complex) | A != B | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),f486(complex,C,D,B,A))) | hAPP(fun(int,bool),complex,hAPP(fun(int,complex),fun(fun(int,bool),complex),big_co302546470etprod(int,complex),D),A) = hAPP(fun(int,bool),complex,hAPP(fun(int,complex),fun(fun(int,bool),complex),big_co302546470etprod(int,complex),C),B). [resolve(5177,a,5068,a)].
% 13.50/13.43 Derived: -comm_monoid_mult(complex) | A != B | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A)) | hAPP(int,complex,C,f486(complex,D,C,B,A)) != hAPP(int,complex,D,f486(complex,D,C,B,A)) | hAPP(fun(int,bool),complex,hAPP(fun(int,complex),fun(fun(int,bool),complex),big_co302546470etprod(int,complex),C),A) = hAPP(fun(int,bool),complex,hAPP(fun(int,complex),fun(fun(int,bool),complex),big_co302546470etprod(int,complex),D),B). [resolve(5177,a,5069,a)].
% 13.50/13.43 Derived: -t2_space(complex) | hAPP(fun(nat,complex),complex,suminf(complex),hAPP(complex,fun(nat,complex),combk(complex,nat),zero_zero(complex))) = zero_zero(complex). [resolve(5177,a,5070,a)].
% 13.50/13.43 Derived: -topological_space(complex) | hBOOL(hAPP(fun(nat,complex),bool,summable(complex),hAPP(complex,fun(nat,complex),combk(complex,nat),zero_zero(complex)))). [resolve(5177,a,5071,a)].
% 13.50/13.43 Derived: -topological_space(complex) | hBOOL(hAPP(complex,bool,hAPP(fun(nat,complex),fun(complex,bool),sums(complex),hAPP(complex,fun(nat,complex),combk(complex,nat),zero_zero(complex))),zero_zero(complex))). [resolve(5177,a,5072,a)].
% 13.50/13.43 Derived: -t2_space(complex) | -hBOOL(hAPP(complex,bool,hAPP(fun(nat,complex),fun(complex,bool),sums(complex),A),B)) | hAPP(fun(nat,complex),complex,suminf(complex),A) = ti(complex,B). [resolve(5177,a,5073,a)].
% 13.50/13.43 Derived: -topological_space(complex) | -hBOOL(hAPP(complex,bool,hAPP(fun(nat,complex),fun(complex,bool),sums(complex),A),B)) | hBOOL(hAPP(fun(nat,complex),bool,summable(complex),A)). [resolve(5177,a,5074,a)].
% 13.50/13.43 Derived: -topological_space(complex) | -hBOOL(hAPP(fun(nat,complex),bool,summable(complex),A)) | hBOOL(hAPP(complex,bool,hAPP(fun(nat,complex),fun(complex,bool),sums(complex),A),f513(complex,A))). [resolve(5177,a,5075,a)].
% 13.50/13.43 Derived: -t2_space(complex) | -hBOOL(hAPP(complex,bool,hAPP(fun(nat,complex),fun(complex,bool),sums(complex),A),B)) | hBOOL(hAPP(fun(nat,complex),bool,summable(complex),A)). [resolve(5177,a,5077,a)].
% 13.50/13.43 Derived: -t2_space(complex) | hBOOL(hAPP(complex,bool,hAPP(fun(nat,complex),fun(complex,bool),sums(complex),A),B)) | -hBOOL(hAPP(fun(nat,complex),bool,summable(complex),A)) | hAPP(fun(nat,complex),complex,suminf(complex),A) != ti(complex,B). [resolve(5177,a,5079,a)].
% 13.50/13.43 Derived: -t2_space(complex) | -hBOOL(hAPP(fun(nat,complex),bool,summable(complex),A)) | hBOOL(hAPP(complex,bool,hAPP(fun(nat,complex),fun(complex,bool),sums(complex),A),hAPP(fun(nat,complex),complex,suminf(complex),A))). [resolve(5177,a,5080,a)].
% 13.50/13.43 Derived: -topological_space(complex) | hAPP(nat,complex,A,zero_zero(nat)) != zero_zero(complex) | -hBOOL(hAPP(complex,bool,hAPP(fun(nat,complex),fun(complex,bool),sums(complex),hAPP(fun(nat,nat),fun(nat,complex),hAPP(fun(nat,complex),fun(fun(nat,nat),fun(nat,complex)),combb(nat,complex,nat),A),suc)),B)) | hBOOL(hAPP(complex,bool,hAPP(fun(nat,complex),fun(complex,bool),sums(complex),A),B)). [resolve(5177,a,5081,a)].
% 13.50/13.43 Derived: -topological_space(complex) | hAPP(fun(nat,complex),complex,suminf(complex),A) = hAPP(fun(complex,bool),complex,the(complex),hAPP(fun(nat,complex),fun(complex,bool),sums(complex),A)). [resolve(5177,a,5082,a)].
% 13.50/13.43 Derived: -power(complex) | hAPP(fun(nat,bool),complex,hAPP(fun(nat,complex),fun(fun(nat,bool),complex),big_co1399186613setsum(nat,complex),hAPP(fun(nat,complex),fun(nat,complex),hAPP(fun(nat,fun(complex,complex)),fun(fun(nat,complex),fun(nat,complex)),combs(nat,complex,complex),hAPP(fun(nat,complex),fun(nat,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(nat,complex),fun(nat,fun(complex,complex))),combb(complex,fun(complex,complex),nat),times_times(complex)),hAPP(fun(nat,nat),fun(nat,complex),hAPP(fun(nat,complex),fun(fun(nat,nat),fun(nat,complex)),combb(nat,complex,nat),hAPP(complex,fun(nat,complex),power_power(complex),A)),hAPP(nat,fun(nat,nat),minus_minus(nat),B)))),hAPP(complex,fun(nat,complex),power_power(complex),C))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,suc,B))) = hAPP(fun(nat,bool),complex,hAPP(fun(nat,complex),fun(fun(nat,bool),complex),big_co1399186613setsum(nat,complex),hAPP(fun(nat,complex),fun(nat,complex),hAPP(fun(nat,fun(complex,complex)),fun(fun(nat,complex),fun(nat,complex)),combs(nat,complex,complex),hAPP(fun(nat,complex),fun(nat,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(nat,complex),fun(nat,fun(complex,complex))),combb(complex,fun(complex,complex),nat),times_times(complex)),hAPP(complex,fun(nat,complex),power_power(complex),A))),hAPP(fun(nat,nat),fun(nat,complex),hAPP(fun(nat,complex),fun(fun(nat,nat),fun(nat,complex)),combb(nat,complex,nat),hAPP(complex,fun(nat,complex),power_power(complex),C)),hAPP(nat,fun(nat,nat),minus_minus(nat),B)))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,suc,B))). [resolve(5177,a,5083,a)].
% 13.50/13.43 Derived: hAPP(fun(nat,bool),complex,hAPP(fun(nat,complex),fun(fun(nat,bool),complex),big_co1399186613setsum(nat,complex),hAPP(fun(nat,fun(nat,bool)),fun(nat,complex),hAPP(fun(fun(nat,bool),complex),fun(fun(nat,fun(nat,bool)),fun(nat,complex)),combb(fun(nat,bool),complex,nat),hAPP(fun(nat,complex),fun(fun(nat,bool),complex),big_co1399186613setsum(nat,complex),A)),hAPP(fun(nat,nat),fun(nat,fun(nat,bool)),hAPP(fun(nat,fun(nat,fun(nat,bool))),fun(fun(nat,nat),fun(nat,fun(nat,bool))),combs(nat,nat,fun(nat,bool)),hAPP(fun(nat,nat),fun(nat,fun(nat,fun(nat,bool))),hAPP(fun(nat,fun(nat,fun(nat,bool))),fun(fun(nat,nat),fun(nat,fun(nat,fun(nat,bool)))),combb(nat,fun(nat,fun(nat,bool)),nat),ord_atLeastLessThan(nat)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),times_times(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),plus_plus(nat)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),times_times(nat)),B))),B)))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),C)) = hAPP(fun(nat,bool),complex,hAPP(fun(nat,complex),fun(fun(nat,bool),complex),big_co1399186613setsum(nat,complex),A),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),C),B))). [resolve(5177,a,5084,a)].
% 13.50/13.43 Derived: hAPP(fun(nat,bool),complex,hAPP(fun(nat,complex),fun(fun(nat,bool),complex),big_co1399186613setsum(nat,complex),hAPP(fun(nat,nat),fun(nat,complex),hAPP(fun(nat,complex),fun(fun(nat,nat),fun(nat,complex)),combb(nat,complex,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_atLeastLessThan(nat),C),D)) = hAPP(fun(nat,bool),complex,hAPP(fun(nat,complex),fun(fun(nat,bool),complex),big_co1399186613setsum(nat,complex),A),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(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(5177,a,5085,a)].
% 13.50/13.43 Derived: hAPP(fun(nat,bool),complex,hAPP(fun(nat,complex),fun(fun(nat,bool),complex),big_co1399186613setsum(nat,complex),A),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),C))) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(fun(nat,bool),complex,hAPP(fun(nat,complex),fun(fun(nat,bool),complex),big_co1399186613setsum(nat,complex),hAPP(fun(nat,nat),fun(nat,complex),hAPP(fun(nat,complex),fun(fun(nat,nat),fun(nat,complex)),combb(nat,complex,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)),C))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),B))),hAPP(fun(nat,bool),complex,hAPP(fun(nat,complex),fun(fun(nat,bool),complex),big_co1399186613setsum(nat,complex),A),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),C))). [resolve(5177,a,5086,a)].
% 13.50/13.43 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),hAPP(complex,fun(A,complex),hAPP(fun(A,fun(complex,complex)),fun(complex,fun(A,complex)),combc(A,complex,complex),hAPP(fun(A,complex),fun(A,fun(complex,complex)),hAPP(fun(A,fun(complex,fun(complex,complex))),fun(fun(A,complex),fun(A,fun(complex,complex))),combs(A,complex,fun(complex,complex)),hAPP(fun(A,bool),fun(A,fun(complex,fun(complex,complex))),hAPP(fun(bool,fun(complex,fun(complex,complex))),fun(fun(A,bool),fun(A,fun(complex,fun(complex,complex)))),combb(bool,fun(complex,fun(complex,complex)),A),if(complex)),C)),D)),zero_zero(complex))),B) = hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),D),hAPP(fun(A,bool),fun(A,bool),collect(A),hAPP(fun(A,bool),fun(A,bool),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))),C))). [resolve(5177,a,5087,a)].
% 13.50/13.43 Derived: hAPP(fun(nat,bool),complex,hAPP(fun(nat,complex),fun(fun(nat,bool),complex),big_co1399186613setsum(nat,complex),hAPP(fun(nat,nat),fun(nat,complex),hAPP(fun(nat,complex),fun(fun(nat,nat),fun(nat,complex)),combb(nat,complex,nat),A),suc)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),B),C)) = hAPP(fun(nat,bool),complex,hAPP(fun(nat,complex),fun(fun(nat,bool),complex),big_co1399186613setsum(nat,complex),A),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),hAPP(nat,nat,suc,B)),hAPP(nat,nat,suc,C))). [resolve(5177,a,5089,a)].
% 13.50/13.43 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(C,bool),complex,hAPP(fun(C,complex),fun(fun(C,bool),complex),big_co1399186613setsum(C,complex),hAPP(fun(C,fun(A,bool)),fun(C,complex),hAPP(fun(C,fun(fun(A,bool),complex)),fun(fun(C,fun(A,bool)),fun(C,complex)),combs(C,fun(A,bool),complex),hAPP(fun(C,fun(A,complex)),fun(C,fun(fun(A,bool),complex)),hAPP(fun(fun(A,complex),fun(fun(A,bool),complex)),fun(fun(C,fun(A,complex)),fun(C,fun(fun(A,bool),complex))),combb(fun(A,complex),fun(fun(A,bool),complex),C),big_co1399186613setsum(A,complex)),hAPP(fun(A,fun(C,complex)),fun(C,fun(A,complex)),combc(A,C,complex),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) = hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),hAPP(fun(A,fun(C,bool)),fun(A,complex),hAPP(fun(A,fun(fun(C,bool),complex)),fun(fun(A,fun(C,bool)),fun(A,complex)),combs(A,fun(C,bool),complex),hAPP(fun(A,fun(C,complex)),fun(A,fun(fun(C,bool),complex)),hAPP(fun(fun(C,complex),fun(fun(C,bool),complex)),fun(fun(A,fun(C,complex)),fun(A,fun(fun(C,bool),complex))),combb(fun(C,complex),fun(fun(C,bool),complex),A),big_co1399186613setsum(C,complex)),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). [resolve(5177,a,5090,a)].
% 13.50/13.43 Derived: hAPP(nat,complex,A,zero_zero(nat)) != zero_zero(complex) | hAPP(fun(nat,bool),complex,hAPP(fun(nat,complex),fun(fun(nat,bool),complex),big_co1399186613setsum(nat,complex),A),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),hAPP(nat,nat,suc,zero_zero(nat))),B)) = hAPP(fun(nat,bool),complex,hAPP(fun(nat,complex),fun(fun(nat,bool),complex),big_co1399186613setsum(nat,complex),A),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),B)). [resolve(5177,a,5091,a)].
% 13.50/13.43 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),C)) | hAPP(fun(nat,bool),complex,hAPP(fun(nat,complex),fun(fun(nat,bool),complex),big_co1399186613setsum(nat,complex),D),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),A),C)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(fun(nat,bool),complex,hAPP(fun(nat,complex),fun(fun(nat,bool),complex),big_co1399186613setsum(nat,complex),D),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),A),B))),hAPP(fun(nat,bool),complex,hAPP(fun(nat,complex),fun(fun(nat,bool),complex),big_co1399186613setsum(nat,complex),D),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),B),C))). [resolve(5177,a,5092,a)].
% 13.50/13.43 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | hAPP(fun(nat,bool),complex,hAPP(fun(nat,complex),fun(fun(nat,bool),complex),big_co1399186613setsum(nat,complex),C),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),A),B)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(nat,complex,C,A)),hAPP(fun(nat,bool),complex,hAPP(fun(nat,complex),fun(fun(nat,bool),complex),big_co1399186613setsum(nat,complex),C),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),hAPP(nat,nat,suc,A)),B))). [resolve(5177,a,5093,a)].
% 13.50/13.43 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | hAPP(fun(nat,bool),complex,hAPP(fun(nat,complex),fun(fun(nat,bool),complex),big_co1399186613setsum(nat,complex),C),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),B),hAPP(nat,nat,suc,A))) = zero_zero(complex). [resolve(5177,a,5094,a)].
% 13.50/13.43 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | hAPP(fun(nat,bool),complex,hAPP(fun(nat,complex),fun(fun(nat,bool),complex),big_co1399186613setsum(nat,complex),C),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),B),hAPP(nat,nat,suc,A))) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(fun(nat,bool),complex,hAPP(fun(nat,complex),fun(fun(nat,bool),complex),big_co1399186613setsum(nat,complex),C),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),B),A))),hAPP(nat,complex,C,A)). [resolve(5177,a,5095,a)].
% 13.50/13.43 Derived: hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),C),B) = zero_zero(complex). [resolve(5177,a,5096,a)].
% 13.50/13.43 Derived: hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),hAPP(fun(B,bool),fun(A,complex),hAPP(fun(A,fun(fun(B,bool),complex)),fun(fun(B,bool),fun(A,complex)),combc(A,fun(B,bool),complex),hAPP(fun(A,fun(B,complex)),fun(A,fun(fun(B,bool),complex)),hAPP(fun(fun(B,complex),fun(fun(B,bool),complex)),fun(fun(A,fun(B,complex)),fun(A,fun(fun(B,bool),complex))),combb(fun(B,complex),fun(fun(B,bool),complex),A),big_co1399186613setsum(B,complex)),hAPP(fun(B,fun(A,complex)),fun(A,fun(B,complex)),combc(B,A,complex),C))),D)),E) = hAPP(fun(B,bool),complex,hAPP(fun(B,complex),fun(fun(B,bool),complex),big_co1399186613setsum(B,complex),hAPP(fun(A,bool),fun(B,complex),hAPP(fun(B,fun(fun(A,bool),complex)),fun(fun(A,bool),fun(B,complex)),combc(B,fun(A,bool),complex),hAPP(fun(B,fun(A,complex)),fun(B,fun(fun(A,bool),complex)),hAPP(fun(fun(A,complex),fun(fun(A,bool),complex)),fun(fun(B,fun(A,complex)),fun(B,fun(fun(A,bool),complex))),combb(fun(A,complex),fun(fun(A,bool),complex),B),big_co1399186613setsum(A,complex)),C)),E)),D). [resolve(5177,a,5098,a)].
% 13.50/13.43 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),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),hAPP(complex,fun(A,complex),hAPP(fun(A,fun(complex,complex)),fun(complex,fun(A,complex)),combc(A,complex,complex),hAPP(fun(A,complex),fun(A,fun(complex,complex)),hAPP(fun(A,fun(complex,fun(complex,complex))),fun(fun(A,complex),fun(A,fun(complex,complex))),combs(A,complex,fun(complex,complex)),hAPP(fun(A,bool),fun(A,fun(complex,fun(complex,complex))),hAPP(fun(bool,fun(complex,fun(complex,complex))),fun(fun(A,bool),fun(A,fun(complex,fun(complex,complex)))),combb(bool,fun(complex,fun(complex,complex)),A),if(complex)),hAPP(A,fun(A,bool),fequal(A),C))),D)),zero_zero(complex))),B) = hAPP(A,complex,D,C). [resolve(5177,a,5099,a)].
% 13.50/13.43 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),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),hAPP(complex,fun(A,complex),hAPP(fun(A,fun(complex,complex)),fun(complex,fun(A,complex)),combc(A,complex,complex),hAPP(fun(A,complex),fun(A,fun(complex,complex)),hAPP(fun(A,fun(complex,fun(complex,complex))),fun(fun(A,complex),fun(A,fun(complex,complex))),combs(A,complex,fun(complex,complex)),hAPP(fun(A,bool),fun(A,fun(complex,fun(complex,complex))),hAPP(fun(bool,fun(complex,fun(complex,complex))),fun(fun(A,bool),fun(A,fun(complex,fun(complex,complex)))),combb(bool,fun(complex,fun(complex,complex)),A),if(complex)),hAPP(A,fun(A,bool),fequal(A),C))),D)),zero_zero(complex))),B) = zero_zero(complex). [resolve(5177,a,5100,a)].
% 13.50/13.43 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),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),hAPP(complex,fun(A,complex),hAPP(fun(A,fun(complex,complex)),fun(complex,fun(A,complex)),combc(A,complex,complex),hAPP(fun(A,complex),fun(A,fun(complex,complex)),hAPP(fun(A,fun(complex,fun(complex,complex))),fun(fun(A,complex),fun(A,fun(complex,complex))),combs(A,complex,fun(complex,complex)),hAPP(fun(A,bool),fun(A,fun(complex,fun(complex,complex))),hAPP(fun(bool,fun(complex,fun(complex,complex))),fun(fun(A,bool),fun(A,fun(complex,fun(complex,complex)))),combb(bool,fun(complex,fun(complex,complex)),A),if(complex)),hAPP(A,fun(A,bool),hAPP(fun(A,fun(A,bool)),fun(A,fun(A,bool)),combc(A,A,bool),fequal(A)),C))),D)),zero_zero(complex))),B) = hAPP(A,complex,D,C). [resolve(5177,a,5101,a)].
% 13.50/13.43 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),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),hAPP(complex,fun(A,complex),hAPP(fun(A,fun(complex,complex)),fun(complex,fun(A,complex)),combc(A,complex,complex),hAPP(fun(A,complex),fun(A,fun(complex,complex)),hAPP(fun(A,fun(complex,fun(complex,complex))),fun(fun(A,complex),fun(A,fun(complex,complex))),combs(A,complex,fun(complex,complex)),hAPP(fun(A,bool),fun(A,fun(complex,fun(complex,complex))),hAPP(fun(bool,fun(complex,fun(complex,complex))),fun(fun(A,bool),fun(A,fun(complex,fun(complex,complex)))),combb(bool,fun(complex,fun(complex,complex)),A),if(complex)),hAPP(A,fun(A,bool),hAPP(fun(A,fun(A,bool)),fun(A,fun(A,bool)),combc(A,A,bool),fequal(A)),C))),D)),zero_zero(complex))),B) = zero_zero(complex). [resolve(5177,a,5102,a)].
% 13.50/13.43 Derived: hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),hAPP(complex,fun(A,complex),combk(complex,A),zero_zero(complex))),B) = zero_zero(complex). [resolve(5177,a,5103,a)].
% 13.50/13.43 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),hAPP(fun(A,complex),fun(A,complex),hAPP(fun(A,fun(complex,complex)),fun(fun(A,complex),fun(A,complex)),combs(A,complex,complex),hAPP(fun(A,complex),fun(A,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(A,complex),fun(A,fun(complex,complex))),combb(complex,fun(complex,complex),A),plus_plus(complex)),C)),D)),B) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),C),B)),hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),D),B)). [resolve(5177,a,5104,a)].
% 13.50/13.43 Derived: hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),hAPP(fun(A,complex),fun(A,complex),hAPP(fun(A,fun(complex,complex)),fun(fun(A,complex),fun(A,complex)),combs(A,complex,complex),hAPP(fun(A,complex),fun(A,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(A,complex),fun(A,fun(complex,complex))),combb(complex,fun(complex,complex),A),plus_plus(complex)),B)),C)),D) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),B),D)),hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),C),D)). [resolve(5177,a,5105,a)].
% 13.50/13.43 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(fun(C,bool),complex,hAPP(fun(C,complex),fun(fun(C,bool),complex),big_co1399186613setsum(C,complex),hAPP(fun(C,fun(A,bool)),fun(C,complex),hAPP(fun(fun(A,bool),complex),fun(fun(C,fun(A,bool)),fun(C,complex)),combb(fun(A,bool),complex,C),hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),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),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),D),B). [resolve(5177,a,5106,a)].
% 13.50/13.43 Derived: -comm_monoid_mult(complex) | hAPP(fun(nat,bool),complex,hAPP(fun(nat,complex),fun(fun(nat,bool),complex),big_co1399186613setsum(nat,complex),A),B) = hAPP(fun(int,bool),complex,hAPP(fun(int,complex),fun(fun(int,bool),complex),big_co1399186613setsum(int,complex),hAPP(fun(int,nat),fun(int,complex),hAPP(fun(nat,complex),fun(fun(int,nat),fun(int,complex)),combb(nat,complex,int),A),nat_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)),B)). [resolve(5177,a,5107,a)].
% 13.50/13.44 Derived: -comm_monoid_mult(complex) | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A)) | hAPP(fun(nat,bool),complex,hAPP(fun(nat,complex),fun(fun(nat,bool),complex),big_co1399186613setsum(nat,complex),hAPP(fun(nat,int),fun(nat,complex),hAPP(fun(int,complex),fun(fun(nat,int),fun(nat,complex)),combb(int,complex,nat),B),semiring_1_of_nat(int))),hAPP(fun(int,bool),fun(nat,bool),hAPP(fun(int,nat),fun(fun(int,bool),fun(nat,bool)),image(int,nat),nat_1),A)) = hAPP(fun(int,bool),complex,hAPP(fun(int,complex),fun(fun(int,bool),complex),big_co1399186613setsum(int,complex),B),A). [resolve(5177,a,5108,a)].
% 13.50/13.44 Derived: -t2_space(complex) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),f592(complex,B,A))) | hBOOL(hAPP(complex,bool,hAPP(fun(nat,complex),fun(complex,bool),sums(complex),B),hAPP(fun(nat,bool),complex,hAPP(fun(nat,complex),fun(fun(nat,bool),complex),big_co1399186613setsum(nat,complex),B),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),A)))). [resolve(5177,a,5109,a)].
% 13.50/13.44 Derived: -t2_space(complex) | hAPP(nat,complex,A,f592(complex,A,B)) != zero_zero(complex) | hBOOL(hAPP(complex,bool,hAPP(fun(nat,complex),fun(complex,bool),sums(complex),A),hAPP(fun(nat,bool),complex,hAPP(fun(nat,complex),fun(fun(nat,bool),complex),big_co1399186613setsum(nat,complex),A),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),B)))). [resolve(5177,a,5110,a)].
% 13.50/13.44 Derived: -ordere779506340up_add(complex) | -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),f593(A,complex,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))) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less_eq(complex),hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),D),C)),hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),D),B))). [resolve(5177,a,5111,a)].
% 13.50/13.44 Derived: -ordere779506340up_add(complex) | -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(complex,bool,hAPP(complex,fun(complex,bool),ord_less_eq(complex),zero_zero(complex)),hAPP(A,complex,D,f593(A,complex,D,C,B)))) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less_eq(complex),hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),D),C)),hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),D),B))). [resolve(5177,a,5112,a)].
% 13.50/13.44 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),f595(A,complex,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),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),D),B) = hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),D),C). [resolve(5177,a,5113,a)].
% 13.50/13.44 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,complex,D,f595(A,complex,D,C,B)) != zero_zero(complex) | hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),D),B) = hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),D),C). [resolve(5177,a,5114,a)].
% 13.50/13.44 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),f596(A,complex,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),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),D),B) = hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),D),C). [resolve(5177,a,5115,a)].
% 13.50/13.44 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,complex,D,f596(A,complex,D,C,B)) != zero_zero(complex) | hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),D),B) = hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),D),C). [resolve(5177,a,5116,a)].
% 13.50/13.44 Derived: -comm_monoid_mult(complex) | A != B | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),f598(complex,C,D,B,A))) | hAPP(fun(int,bool),complex,hAPP(fun(int,complex),fun(fun(int,bool),complex),big_co1399186613setsum(int,complex),D),A) = hAPP(fun(int,bool),complex,hAPP(fun(int,complex),fun(fun(int,bool),complex),big_co1399186613setsum(int,complex),C),B). [resolve(5177,a,5117,a)].
% 13.50/13.44 Derived: -comm_monoid_mult(complex) | A != B | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A)) | hAPP(int,complex,C,f598(complex,D,C,B,A)) != hAPP(int,complex,D,f598(complex,D,C,B,A)) | hAPP(fun(int,bool),complex,hAPP(fun(int,complex),fun(fun(int,bool),complex),big_co1399186613setsum(int,complex),C),A) = hAPP(fun(int,bool),complex,hAPP(fun(int,complex),fun(fun(int,bool),complex),big_co1399186613setsum(int,complex),D),B). [resolve(5177,a,5118,a)].
% 13.50/13.44 Derived: -ord(A) | ti(A,B) != ti(A,C) | ti(A,D) != ti(A,E) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),f603(complex,A,F,V6,E,D,C,B))) | hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),V6),hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_atLeastLessThan(A),B),D)) = hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),F),hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_atLeastLessThan(A),C),E)). [resolve(5177,a,5119,b)].
% 13.50/13.44 Derived: -ord(A) | ti(A,B) != ti(A,C) | ti(A,D) != ti(A,E) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),f603(complex,A,F,V6,E,D,C,B)),D)) | hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),V6),hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_atLeastLessThan(A),B),D)) = hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),F),hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_atLeastLessThan(A),C),E)). [resolve(5177,a,5120,b)].
% 13.50/13.44 Derived: -ord(A) | ti(A,B) != ti(A,C) | ti(A,D) != ti(A,E) | hAPP(A,complex,F,f603(complex,A,V6,F,E,D,C,B)) != hAPP(A,complex,V6,f603(complex,A,V6,F,E,D,C,B)) | hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),F),hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_atLeastLessThan(A),B),D)) = hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),V6),hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_atLeastLessThan(A),C),E)). [resolve(5177,a,5121,b)].
% 13.50/13.44 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),f609(A,complex,C,B)),B)) | hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),C),B) = zero_zero(complex). [resolve(5177,a,5122,a)].
% 13.50/13.44 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(A,complex,C,f609(A,complex,C,B)) != zero_zero(complex) | hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),C),B) = zero_zero(complex). [resolve(5177,a,5123,a)].
% 13.50/13.44 Derived: -ordere779506340up_add(complex) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f610(A,complex,B,C)),C)) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less_eq(complex),hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),B),C)),zero_zero(complex))). [resolve(5177,a,5124,a)].
% 13.50/13.44 Derived: -ordere779506340up_add(complex) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less_eq(complex),hAPP(A,complex,B,f610(A,complex,B,C))),zero_zero(complex))) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less_eq(complex),hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),B),C)),zero_zero(complex))). [resolve(5177,a,5125,a)].
% 13.50/13.44 Derived: -ordere779506340up_add(complex) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f611(A,complex,B,C)),C)) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less_eq(complex),zero_zero(complex)),hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),B),C))). [resolve(5177,a,5126,a)].
% 13.50/13.44 Derived: -ordere779506340up_add(complex) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less_eq(complex),zero_zero(complex)),hAPP(A,complex,B,f611(A,complex,B,C)))) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less_eq(complex),zero_zero(complex)),hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),B),C))). [resolve(5177,a,5127,a)].
% 13.50/13.44 Derived: -hBOOL(hAPP(fun(fun(A,bool),bool),bool,finite_finite_1(fun(A,bool)),B)) | hBOOL(hAPP(fun(fun(A,bool),bool),bool,hAPP(fun(A,bool),fun(fun(fun(A,bool),bool),bool),member(fun(A,bool)),f612(A,complex,C,B)),B)) | hBOOL(hAPP(fun(fun(A,bool),bool),bool,hAPP(fun(A,bool),fun(fun(fun(A,bool),bool),bool),member(fun(A,bool)),f613(A,complex,C,B)),B)) | hAPP(fun(fun(A,bool),bool),complex,hAPP(fun(fun(A,bool),complex),fun(fun(fun(A,bool),bool),complex),big_co1399186613setsum(fun(A,bool),complex),hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),C)),B) = hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),C),hAPP(fun(fun(A,bool),bool),fun(A,bool),complete_Sup_Sup(fun(A,bool)),B)). [resolve(5177,a,5128,a)].
% 13.50/13.44 Derived: -hBOOL(hAPP(fun(fun(A,bool),bool),bool,finite_finite_1(fun(A,bool)),B)) | hBOOL(hAPP(fun(fun(A,bool),bool),bool,hAPP(fun(A,bool),fun(fun(fun(A,bool),bool),bool),member(fun(A,bool)),f612(A,complex,C,B)),B)) | hBOOL(hAPP(fun(fun(A,bool),bool),bool,hAPP(fun(A,bool),fun(fun(fun(A,bool),bool),bool),member(fun(A,bool)),f614(A,complex,C,B)),B)) | hAPP(fun(fun(A,bool),bool),complex,hAPP(fun(fun(A,bool),complex),fun(fun(fun(A,bool),bool),complex),big_co1399186613setsum(fun(A,bool),complex),hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),C)),B) = hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),C),hAPP(fun(fun(A,bool),bool),fun(A,bool),complete_Sup_Sup(fun(A,bool)),B)). [resolve(5177,a,5129,a)].
% 13.50/13.44 Derived: -hBOOL(hAPP(fun(fun(A,bool),bool),bool,finite_finite_1(fun(A,bool)),B)) | hBOOL(hAPP(fun(fun(A,bool),bool),bool,hAPP(fun(A,bool),fun(fun(fun(A,bool),bool),bool),member(fun(A,bool)),f612(A,complex,C,B)),B)) | ti(fun(A,bool),f614(A,complex,C,B)) != ti(fun(A,bool),f613(A,complex,C,B)) | hAPP(fun(fun(A,bool),bool),complex,hAPP(fun(fun(A,bool),complex),fun(fun(fun(A,bool),bool),complex),big_co1399186613setsum(fun(A,bool),complex),hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),C)),B) = hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),C),hAPP(fun(fun(A,bool),bool),fun(A,bool),complete_Sup_Sup(fun(A,bool)),B)). [resolve(5177,a,5130,a)].
% 13.50/13.44 Derived: -hBOOL(hAPP(fun(fun(A,bool),bool),bool,finite_finite_1(fun(A,bool)),B)) | hBOOL(hAPP(fun(fun(A,bool),bool),bool,hAPP(fun(A,bool),fun(fun(fun(A,bool),bool),bool),member(fun(A,bool)),f612(A,complex,C,B)),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f615(A,complex,C,B)),f613(A,complex,C,B))) | hAPP(fun(fun(A,bool),bool),complex,hAPP(fun(fun(A,bool),complex),fun(fun(fun(A,bool),bool),complex),big_co1399186613setsum(fun(A,bool),complex),hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),C)),B) = hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),C),hAPP(fun(fun(A,bool),bool),fun(A,bool),complete_Sup_Sup(fun(A,bool)),B)). [resolve(5177,a,5131,a)].
% 13.50/13.44 Derived: -hBOOL(hAPP(fun(fun(A,bool),bool),bool,finite_finite_1(fun(A,bool)),B)) | hBOOL(hAPP(fun(fun(A,bool),bool),bool,hAPP(fun(A,bool),fun(fun(fun(A,bool),bool),bool),member(fun(A,bool)),f612(A,complex,C,B)),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f615(A,complex,C,B)),f614(A,complex,C,B))) | hAPP(fun(fun(A,bool),bool),complex,hAPP(fun(fun(A,bool),complex),fun(fun(fun(A,bool),bool),complex),big_co1399186613setsum(fun(A,bool),complex),hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),C)),B) = hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),C),hAPP(fun(fun(A,bool),bool),fun(A,bool),complete_Sup_Sup(fun(A,bool)),B)). [resolve(5177,a,5132,a)].
% 13.50/13.44 Derived: -hBOOL(hAPP(fun(fun(A,bool),bool),bool,finite_finite_1(fun(A,bool)),B)) | hBOOL(hAPP(fun(fun(A,bool),bool),bool,hAPP(fun(A,bool),fun(fun(fun(A,bool),bool),bool),member(fun(A,bool)),f612(A,complex,C,B)),B)) | hAPP(A,complex,C,f615(A,complex,C,B)) != zero_zero(complex) | hAPP(fun(fun(A,bool),bool),complex,hAPP(fun(fun(A,bool),complex),fun(fun(fun(A,bool),bool),complex),big_co1399186613setsum(fun(A,bool),complex),hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),C)),B) = hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),C),hAPP(fun(fun(A,bool),bool),fun(A,bool),complete_Sup_Sup(fun(A,bool)),B)). [resolve(5177,a,5133,a)].
% 13.50/13.44 Derived: -hBOOL(hAPP(fun(fun(A,bool),bool),bool,finite_finite_1(fun(A,bool)),B)) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),f612(A,complex,C,B))) | hBOOL(hAPP(fun(fun(A,bool),bool),bool,hAPP(fun(A,bool),fun(fun(fun(A,bool),bool),bool),member(fun(A,bool)),f613(A,complex,C,B)),B)) | hAPP(fun(fun(A,bool),bool),complex,hAPP(fun(fun(A,bool),complex),fun(fun(fun(A,bool),bool),complex),big_co1399186613setsum(fun(A,bool),complex),hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),C)),B) = hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),C),hAPP(fun(fun(A,bool),bool),fun(A,bool),complete_Sup_Sup(fun(A,bool)),B)). [resolve(5177,a,5134,a)].
% 13.50/13.44 Derived: -hBOOL(hAPP(fun(fun(A,bool),bool),bool,finite_finite_1(fun(A,bool)),B)) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),f612(A,complex,C,B))) | hBOOL(hAPP(fun(fun(A,bool),bool),bool,hAPP(fun(A,bool),fun(fun(fun(A,bool),bool),bool),member(fun(A,bool)),f614(A,complex,C,B)),B)) | hAPP(fun(fun(A,bool),bool),complex,hAPP(fun(fun(A,bool),complex),fun(fun(fun(A,bool),bool),complex),big_co1399186613setsum(fun(A,bool),complex),hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),C)),B) = hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),C),hAPP(fun(fun(A,bool),bool),fun(A,bool),complete_Sup_Sup(fun(A,bool)),B)). [resolve(5177,a,5135,a)].
% 13.50/13.44 Derived: -hBOOL(hAPP(fun(fun(A,bool),bool),bool,finite_finite_1(fun(A,bool)),B)) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),f612(A,complex,C,B))) | ti(fun(A,bool),f614(A,complex,C,B)) != ti(fun(A,bool),f613(A,complex,C,B)) | hAPP(fun(fun(A,bool),bool),complex,hAPP(fun(fun(A,bool),complex),fun(fun(fun(A,bool),bool),complex),big_co1399186613setsum(fun(A,bool),complex),hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),C)),B) = hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),C),hAPP(fun(fun(A,bool),bool),fun(A,bool),complete_Sup_Sup(fun(A,bool)),B)). [resolve(5177,a,5136,a)].
% 13.50/13.44 Derived: -hBOOL(hAPP(fun(fun(A,bool),bool),bool,finite_finite_1(fun(A,bool)),B)) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),f612(A,complex,C,B))) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f615(A,complex,C,B)),f613(A,complex,C,B))) | hAPP(fun(fun(A,bool),bool),complex,hAPP(fun(fun(A,bool),complex),fun(fun(fun(A,bool),bool),complex),big_co1399186613setsum(fun(A,bool),complex),hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),C)),B) = hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),C),hAPP(fun(fun(A,bool),bool),fun(A,bool),complete_Sup_Sup(fun(A,bool)),B)). [resolve(5177,a,5137,a)].
% 13.50/13.44 Derived: -hBOOL(hAPP(fun(fun(A,bool),bool),bool,finite_finite_1(fun(A,bool)),B)) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),f612(A,complex,C,B))) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f615(A,complex,C,B)),f614(A,complex,C,B))) | hAPP(fun(fun(A,bool),bool),complex,hAPP(fun(fun(A,bool),complex),fun(fun(fun(A,bool),bool),complex),big_co1399186613setsum(fun(A,bool),complex),hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),C)),B) = hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),C),hAPP(fun(fun(A,bool),bool),fun(A,bool),complete_Sup_Sup(fun(A,bool)),B)). [resolve(5177,a,5138,a)].
% 13.50/13.44 Derived: -hBOOL(hAPP(fun(fun(A,bool),bool),bool,finite_finite_1(fun(A,bool)),B)) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),f612(A,complex,C,B))) | hAPP(A,complex,C,f615(A,complex,C,B)) != zero_zero(complex) | hAPP(fun(fun(A,bool),bool),complex,hAPP(fun(fun(A,bool),complex),fun(fun(fun(A,bool),bool),complex),big_co1399186613setsum(fun(A,bool),complex),hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),C)),B) = hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),C),hAPP(fun(fun(A,bool),bool),fun(A,bool),complete_Sup_Sup(fun(A,bool)),B)). [resolve(5177,a,5139,a)].
% 13.50/13.44 Derived: hAPP(fun(nat,bool),complex,hAPP(fun(nat,complex),fun(fun(nat,bool),complex),big_co1399186613setsum(nat,complex),A),hAPP(nat,fun(nat,bool),ord_lessThan(nat),hAPP(nat,nat,suc,B))) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(fun(nat,bool),complex,hAPP(fun(nat,complex),fun(fun(nat,bool),complex),big_co1399186613setsum(nat,complex),A),hAPP(nat,fun(nat,bool),ord_lessThan(nat),B))),hAPP(nat,complex,A,B)). [resolve(5177,a,5140,a)].
% 13.50/13.44 Derived: -metric_space(complex) | hAPP(fun(nat,complex),complex,suminf(complex),A) = hAPP(fun(nat,complex),complex,lim(complex),hAPP(fun(nat,fun(nat,bool)),fun(nat,complex),hAPP(fun(fun(nat,bool),complex),fun(fun(nat,fun(nat,bool)),fun(nat,complex)),combb(fun(nat,bool),complex,nat),hAPP(fun(nat,complex),fun(fun(nat,bool),complex),big_co1399186613setsum(nat,complex),A)),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)))). [resolve(5177,a,5141,a)].
% 13.50/13.44 Derived: -ordere779506340up_add(complex) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f631(A,complex,B,C,D)),D)) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less_eq(complex),hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),B),D)),hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),C),D))). [resolve(5177,a,5142,a)].
% 13.50/13.44 Derived: -ordere779506340up_add(complex) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less_eq(complex),hAPP(A,complex,B,f631(A,complex,B,C,D))),hAPP(A,complex,C,f631(A,complex,B,C,D)))) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less_eq(complex),hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),B),D)),hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),C),D))). [resolve(5177,a,5143,a)].
% 13.50/13.44 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),f632(A,complex,D,E,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))) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f633(A,complex,D,E,C,B)),C)) | hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),D),C) = hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),E),B). [resolve(5177,a,5144,a)].
% 13.50/13.44 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),f632(A,complex,D,E,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(A,complex,D,f633(A,complex,D,E,C,B)) != hAPP(A,complex,E,f633(A,complex,D,E,C,B)) | hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),D),C) = hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),E),B). [resolve(5177,a,5145,a)].
% 13.50/13.44 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,complex,D,f632(A,complex,E,D,C,B)) != zero_zero(complex) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f633(A,complex,E,D,C,B)),C)) | hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),E),C) = hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),D),B). [resolve(5177,a,5146,a)].
% 13.50/13.44 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,complex,D,f632(A,complex,E,D,C,B)) != zero_zero(complex) | hAPP(A,complex,E,f633(A,complex,E,D,C,B)) != hAPP(A,complex,D,f633(A,complex,E,D,C,B)) | hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),E),C) = hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),D),B). [resolve(5177,a,5147,a)].
% 13.50/13.44 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),f644(A,complex,D,E,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))) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f645(A,complex,D,E,C,B)),C)) | hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),E),B) = hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),D),C). [resolve(5177,a,5148,a)].
% 13.50/13.44 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),f644(A,complex,D,E,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(A,complex,E,f645(A,complex,D,E,C,B)) != hAPP(A,complex,D,f645(A,complex,D,E,C,B)) | hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),E),B) = hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),D),C). [resolve(5177,a,5149,a)].
% 13.50/13.44 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,complex,D,f644(A,complex,E,D,C,B)) != zero_zero(complex) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f645(A,complex,E,D,C,B)),C)) | hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),D),B) = hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),E),C). [resolve(5177,a,5150,a)].
% 13.50/13.44 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,complex,D,f644(A,complex,E,D,C,B)) != zero_zero(complex) | hAPP(A,complex,D,f645(A,complex,E,D,C,B)) != hAPP(A,complex,E,f645(A,complex,E,D,C,B)) | hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),D),B) = hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),E),C). [resolve(5177,a,5151,a)].
% 13.50/13.44 Derived: -t2_space(complex) | -hBOOL(hAPP(fun(nat,complex),bool,summable(complex),A)) | hBOOL(hAPP(filter(nat),bool,hAPP(complex,fun(filter(nat),bool),hAPP(fun(nat,complex),fun(complex,fun(filter(nat),bool)),tendsto(nat,complex),hAPP(fun(nat,fun(nat,bool)),fun(nat,complex),hAPP(fun(fun(nat,bool),complex),fun(fun(nat,fun(nat,bool)),fun(nat,complex)),combb(fun(nat,bool),complex,nat),hAPP(fun(nat,complex),fun(fun(nat,bool),complex),big_co1399186613setsum(nat,complex),A)),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)))),hAPP(fun(nat,complex),complex,suminf(complex),A)),sequentially)). [resolve(5177,a,5152,a)].
% 13.50/13.44 Derived: -topological_space(complex) | -hBOOL(hAPP(complex,bool,hAPP(fun(nat,complex),fun(complex,bool),sums(complex),A),B)) | hBOOL(hAPP(filter(nat),bool,hAPP(complex,fun(filter(nat),bool),hAPP(fun(nat,complex),fun(complex,fun(filter(nat),bool)),tendsto(nat,complex),hAPP(fun(nat,fun(nat,bool)),fun(nat,complex),hAPP(fun(fun(nat,bool),complex),fun(fun(nat,fun(nat,bool)),fun(nat,complex)),combb(fun(nat,bool),complex,nat),hAPP(fun(nat,complex),fun(fun(nat,bool),complex),big_co1399186613setsum(nat,complex),A)),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)))),B),sequentially)). [resolve(5177,a,5153,a)].
% 13.50/13.44 Derived: -topological_space(complex) | hBOOL(hAPP(complex,bool,hAPP(fun(nat,complex),fun(complex,bool),sums(complex),A),B)) | -hBOOL(hAPP(filter(nat),bool,hAPP(complex,fun(filter(nat),bool),hAPP(fun(nat,complex),fun(complex,fun(filter(nat),bool)),tendsto(nat,complex),hAPP(fun(nat,fun(nat,bool)),fun(nat,complex),hAPP(fun(fun(nat,bool),complex),fun(fun(nat,fun(nat,bool)),fun(nat,complex)),combb(fun(nat,bool),complex,nat),hAPP(fun(nat,complex),fun(fun(nat,bool),complex),big_co1399186613setsum(nat,complex),A)),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)))),B),sequentially)). [resolve(5177,a,5154,a)].
% 13.50/13.44 Derived: hAPP(fun(nat,bool),complex,hAPP(fun(nat,complex),fun(fun(nat,bool),complex),big_co1399186613setsum(nat,complex),hAPP(fun(nat,nat),fun(nat,complex),hAPP(fun(nat,complex),fun(fun(nat,nat),fun(nat,complex)),combb(nat,complex,nat),A),suc)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),B),C)) = hAPP(fun(nat,bool),complex,hAPP(fun(nat,complex),fun(fun(nat,bool),complex),big_co1399186613setsum(nat,complex),A),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,suc,B)),hAPP(nat,nat,suc,C))). [resolve(5177,a,5155,a)].
% 13.50/13.44 Derived: hAPP(fun(nat,bool),complex,hAPP(fun(nat,complex),fun(fun(nat,bool),complex),big_co1399186613setsum(nat,complex),hAPP(fun(nat,nat),fun(nat,complex),hAPP(fun(nat,complex),fun(fun(nat,nat),fun(nat,complex)),combb(nat,complex,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),complex,hAPP(fun(nat,complex),fun(fun(nat,bool),complex),big_co1399186613setsum(nat,complex),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(5177,a,5156,a)].
% 13.50/13.45 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | hAPP(fun(nat,bool),complex,hAPP(fun(nat,complex),fun(fun(nat,bool),complex),big_co1399186613setsum(nat,complex),C),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),A),B)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(nat,complex,C,A)),hAPP(fun(nat,bool),complex,hAPP(fun(nat,complex),fun(fun(nat,bool),complex),big_co1399186613setsum(nat,complex),C),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,suc,A)),B))). [resolve(5177,a,5157,a)].
% 13.50/13.45 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,A)),B)) | hAPP(fun(nat,bool),complex,hAPP(fun(nat,complex),fun(fun(nat,bool),complex),big_co1399186613setsum(nat,complex),C),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),B),hAPP(nat,nat,suc,A))) = zero_zero(complex). [resolve(5177,a,5158,a)].
% 13.50/13.45 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,A)),B)) | hAPP(fun(nat,bool),complex,hAPP(fun(nat,complex),fun(fun(nat,bool),complex),big_co1399186613setsum(nat,complex),C),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),B),hAPP(nat,nat,suc,A))) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(fun(nat,bool),complex,hAPP(fun(nat,complex),fun(fun(nat,bool),complex),big_co1399186613setsum(nat,complex),C),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),B),A))),hAPP(nat,complex,C,hAPP(nat,nat,suc,A))). [resolve(5177,a,5159,a)].
% 13.50/13.45 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),complex,hAPP(fun(nat,complex),fun(fun(nat,bool),complex),big_co1399186613setsum(nat,complex),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(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(fun(nat,bool),complex,hAPP(fun(nat,complex),fun(fun(nat,bool),complex),big_co1399186613setsum(nat,complex),C),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),A),B))),hAPP(fun(nat,bool),complex,hAPP(fun(nat,complex),fun(fun(nat,bool),complex),big_co1399186613setsum(nat,complex),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(5177,a,5160,a)].
% 13.50/13.45 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,A)),B)) | hAPP(fun(nat,bool),complex,hAPP(fun(nat,complex),fun(fun(nat,bool),complex),big_co1399186613setsum(nat,complex),C),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),B),hAPP(nat,nat,suc,A))) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(nat,complex,C,B)),hAPP(fun(nat,bool),complex,hAPP(fun(nat,complex),fun(fun(nat,bool),complex),big_co1399186613setsum(nat,complex),hAPP(fun(nat,nat),fun(nat,complex),hAPP(fun(nat,complex),fun(fun(nat,nat),fun(nat,complex)),combb(nat,complex,nat),C),suc)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),B),A))). [resolve(5177,a,5162,a)].
% 13.50/13.45 Derived: hAPP(fun(product_prod(nat,nat),bool),complex,hAPP(fun(product_prod(nat,nat),complex),fun(fun(product_prod(nat,nat),bool),complex),big_co1399186613setsum(product_prod(nat,nat),complex),hAPP(fun(nat,fun(nat,complex)),fun(product_prod(nat,nat),complex),product_prod_case(nat,nat,complex),A)),hAPP(fun(product_prod(nat,nat),bool),fun(product_prod(nat,nat),bool),collect(product_prod(nat,nat)),hAPP(fun(nat,fun(nat,bool)),fun(product_prod(nat,nat),bool),product_prod_case(nat,nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),hAPP(fun(nat,fun(nat,fun(nat,bool))),fun(nat,fun(nat,fun(nat,bool))),combc(nat,nat,fun(nat,bool)),hAPP(fun(nat,fun(nat,fun(nat,bool))),fun(nat,fun(nat,fun(nat,bool))),hAPP(fun(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool))),fun(fun(nat,fun(nat,fun(nat,bool))),fun(nat,fun(nat,fun(nat,bool)))),combb(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),nat),combc(nat,nat,bool)),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,fun(nat,bool))),hAPP(fun(fun(nat,nat),fun(nat,fun(nat,bool))),fun(fun(nat,fun(nat,nat)),fun(nat,fun(nat,fun(nat,bool)))),combb(fun(nat,nat),fun(nat,fun(nat,bool)),nat),hAPP(fun(nat,fun(nat,bool)),fun(fun(nat,nat),fun(nat,fun(nat,bool))),combb(nat,fun(nat,bool),nat),ord_less(nat))),plus_plus(nat)))),B)))) = hAPP(fun(nat,bool),complex,hAPP(fun(nat,complex),fun(fun(nat,bool),complex),big_co1399186613setsum(nat,complex),hAPP(fun(nat,fun(nat,bool)),fun(nat,complex),hAPP(fun(nat,fun(fun(nat,bool),complex)),fun(fun(nat,fun(nat,bool)),fun(nat,complex)),combs(nat,fun(nat,bool),complex),hAPP(fun(nat,fun(nat,complex)),fun(nat,fun(fun(nat,bool),complex)),hAPP(fun(fun(nat,complex),fun(fun(nat,bool),complex)),fun(fun(nat,fun(nat,complex)),fun(nat,fun(fun(nat,bool),complex))),combb(fun(nat,complex),fun(fun(nat,bool),complex),nat),big_co1399186613setsum(nat,complex)),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,complex)),hAPP(fun(fun(nat,nat),fun(nat,complex)),fun(fun(nat,fun(nat,nat)),fun(nat,fun(nat,complex))),combb(fun(nat,nat),fun(nat,complex),nat),hAPP(fun(nat,fun(nat,complex)),fun(fun(nat,nat),fun(nat,complex)),combs(nat,nat,complex),A)),minus_minus(nat)))),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),zero_zero(nat)))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),B)). [resolve(5177,a,5163,a)].
% 13.50/13.45 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),f771(A,complex,C,D,B)),B)) | hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),D),B) = hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),C),B). [resolve(5177,a,5164,a)].
% 13.50/13.45 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(A,complex,C,f771(A,complex,D,C,B)) != hAPP(A,complex,D,f771(A,complex,D,C,B)) | hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),C),B) = hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),D),B). [resolve(5177,a,5165,a)].
% 13.50/13.45 Derived: hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f772(A,complex,B,C)),C)) | hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),B),C) = zero_zero(complex). [resolve(5177,a,5166,a)].
% 13.50/13.45 Derived: hAPP(A,complex,B,f772(A,complex,B,C)) != zero_zero(complex) | hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),B),C) = zero_zero(complex). [resolve(5177,a,5167,a)].
% 13.50/13.45 Derived: -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),A,zero_zero(complex)),zero_zero(complex))) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),A,f788(B,complex,C,D,E,A)),f790(B,complex,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),f792(B,complex,C,D,E,A)),E)) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),A,hAPP(fun(B,bool),complex,hAPP(fun(B,complex),fun(fun(B,bool),complex),big_co1399186613setsum(B,complex),C),E)),hAPP(fun(B,bool),complex,hAPP(fun(B,complex),fun(fun(B,bool),complex),big_co1399186613setsum(B,complex),D),E))). [resolve(5177,a,5168,a)].
% 13.50/13.45 Derived: -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),A,zero_zero(complex)),zero_zero(complex))) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),A,f788(B,complex,C,D,E,A)),f790(B,complex,C,D,E,A))) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),E)) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),A,hAPP(B,complex,C,f792(B,complex,C,D,E,A))),hAPP(B,complex,D,f792(B,complex,C,D,E,A)))) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),A,hAPP(fun(B,bool),complex,hAPP(fun(B,complex),fun(fun(B,bool),complex),big_co1399186613setsum(B,complex),C),E)),hAPP(fun(B,bool),complex,hAPP(fun(B,complex),fun(fun(B,bool),complex),big_co1399186613setsum(B,complex),D),E))). [resolve(5177,a,5169,a)].
% 13.50/13.47 Derived: -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),A,zero_zero(complex)),zero_zero(complex))) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),A,f789(B,complex,C,D,E,A)),f791(B,complex,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),f792(B,complex,C,D,E,A)),E)) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),A,hAPP(fun(B,bool),complex,hAPP(fun(B,complex),fun(fun(B,bool),complex),big_co1399186613setsum(B,complex),C),E)),hAPP(fun(B,bool),complex,hAPP(fun(B,complex),fun(fun(B,bool),complex),big_co1399186613setsum(B,complex),D),E))). [resolve(5177,a,5170,a)].
% 13.50/13.47 Derived: -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),A,zero_zero(complex)),zero_zero(complex))) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),A,f789(B,complex,C,D,E,A)),f791(B,complex,C,D,E,A))) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),E)) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),A,hAPP(B,complex,C,f792(B,complex,C,D,E,A))),hAPP(B,complex,D,f792(B,complex,C,D,E,A)))) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),A,hAPP(fun(B,bool),complex,hAPP(fun(B,complex),fun(fun(B,bool),complex),big_co1399186613setsum(B,complex),C),E)),hAPP(fun(B,bool),complex,hAPP(fun(B,complex),fun(fun(B,bool),complex),big_co1399186613setsum(B,complex),D),E))). [resolve(5177,a,5171,a)].
% 13.50/13.47 Derived: -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),A,zero_zero(complex)),zero_zero(complex))) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),A,hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),f788(B,complex,C,D,E,A)),f789(B,complex,C,D,E,A))),hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),f790(B,complex,C,D,E,A)),f791(B,complex,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),f792(B,complex,C,D,E,A)),E)) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),A,hAPP(fun(B,bool),complex,hAPP(fun(B,complex),fun(fun(B,bool),complex),big_co1399186613setsum(B,complex),C),E)),hAPP(fun(B,bool),complex,hAPP(fun(B,complex),fun(fun(B,bool),complex),big_co1399186613setsum(B,complex),D),E))). [resolve(5177,a,5172,a)].
% 13.50/13.47 Derived: -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),A,zero_zero(complex)),zero_zero(complex))) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),A,hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),f788(B,complex,C,D,E,A)),f789(B,complex,C,D,E,A))),hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),f790(B,complex,C,D,E,A)),f791(B,complex,C,D,E,A)))) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),E)) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),A,hAPP(B,complex,C,f792(B,complex,C,D,E,A))),hAPP(B,complex,D,f792(B,complex,C,D,E,A)))) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),A,hAPP(fun(B,bool),complex,hAPP(fun(B,complex),fun(fun(B,bool),complex),big_co1399186613setsum(B,complex),C),E)),hAPP(fun(B,bool),complex,hAPP(fun(B,complex),fun(fun(B,bool),complex),big_co1399186613setsum(B,complex),D),E))). [resolve(5177,a,5173,a)].
% 13.50/13.47 5178 comm_monoid_add(code_code_numeral) # label(arity_Code__Numeral_Ocode__numeral___Groups_Ocomm__monoid__add) # label(axiom). [assumption].
% 13.50/13.47 Derived: big_co1399186613setsum(A,code_code_numeral) = ti(fun(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral)),big_co1399186613setsum(A,code_code_numeral)). [resolve(5178,a,5059,a)].
% 13.50/13.47 Derived: -topological_space(code_code_numeral) | the(code_code_numeral) = ti(fun(fun(code_code_numeral,bool),code_code_numeral),the(code_code_numeral)). [resolve(5178,a,5060,a)].
% 13.50/13.47 Derived: -topological_space(code_code_numeral) | suminf(code_code_numeral) = ti(fun(fun(nat,code_code_numeral),code_code_numeral),suminf(code_code_numeral)). [resolve(5178,a,5061,a)].
% 13.50/13.47 Derived: -topological_space(code_code_numeral) | summable(code_code_numeral) = ti(fun(fun(nat,code_code_numeral),bool),summable(code_code_numeral)). [resolve(5178,a,5062,a)].
% 13.50/13.47 Derived: -topological_space(code_code_numeral) | sums(code_code_numeral) = ti(fun(fun(nat,code_code_numeral),fun(code_code_numeral,bool)),sums(code_code_numeral)). [resolve(5178,a,5063,a)].
% 13.50/13.47 Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),A),zero_zero(code_code_numeral)) = ti(code_code_numeral,A). [resolve(5178,a,5064,a)].
% 13.50/13.47 Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),zero_zero(code_code_numeral)),A) = ti(code_code_numeral,A). [resolve(5178,a,5065,a)].
% 13.50/13.47 Derived: -comm_monoid_mult(code_code_numeral) | hAPP(fun(nat,bool),code_code_numeral,hAPP(fun(nat,code_code_numeral),fun(fun(nat,bool),code_code_numeral),big_co302546470etprod(nat,code_code_numeral),A),B) = hAPP(fun(int,bool),code_code_numeral,hAPP(fun(int,code_code_numeral),fun(fun(int,bool),code_code_numeral),big_co302546470etprod(int,code_code_numeral),hAPP(fun(int,nat),fun(int,code_code_numeral),hAPP(fun(nat,code_code_numeral),fun(fun(int,nat),fun(int,code_code_numeral)),combb(nat,code_code_numeral,int),A),nat_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)),B)). [resolve(5178,a,5066,a)].
% 13.50/13.47 Derived: -comm_monoid_mult(code_code_numeral) | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A)) | hAPP(fun(nat,bool),code_code_numeral,hAPP(fun(nat,code_code_numeral),fun(fun(nat,bool),code_code_numeral),big_co302546470etprod(nat,code_code_numeral),hAPP(fun(nat,int),fun(nat,code_code_numeral),hAPP(fun(int,code_code_numeral),fun(fun(nat,int),fun(nat,code_code_numeral)),combb(int,code_code_numeral,nat),B),semiring_1_of_nat(int))),hAPP(fun(int,bool),fun(nat,bool),hAPP(fun(int,nat),fun(fun(int,bool),fun(nat,bool)),image(int,nat),nat_1),A)) = hAPP(fun(int,bool),code_code_numeral,hAPP(fun(int,code_code_numeral),fun(fun(int,bool),code_code_numeral),big_co302546470etprod(int,code_code_numeral),B),A). [resolve(5178,a,5067,a)].
% 13.50/13.47 Derived: -comm_monoid_mult(code_code_numeral) | A != B | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),f486(code_code_numeral,C,D,B,A))) | hAPP(fun(int,bool),code_code_numeral,hAPP(fun(int,code_code_numeral),fun(fun(int,bool),code_code_numeral),big_co302546470etprod(int,code_code_numeral),D),A) = hAPP(fun(int,bool),code_code_numeral,hAPP(fun(int,code_code_numeral),fun(fun(int,bool),code_code_numeral),big_co302546470etprod(int,code_code_numeral),C),B). [resolve(5178,a,5068,a)].
% 13.50/13.47 Derived: -comm_monoid_mult(code_code_numeral) | A != B | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A)) | hAPP(int,code_code_numeral,C,f486(code_code_numeral,D,C,B,A)) != hAPP(int,code_code_numeral,D,f486(code_code_numeral,D,C,B,A)) | hAPP(fun(int,bool),code_code_numeral,hAPP(fun(int,code_code_numeral),fun(fun(int,bool),code_code_numeral),big_co302546470etprod(int,code_code_numeral),C),A) = hAPP(fun(int,bool),code_code_numeral,hAPP(fun(int,code_code_numeral),fun(fun(int,bool),code_code_numeral),big_co302546470etprod(int,code_code_numeral),D),B). [resolve(5178,a,5069,a)].
% 13.50/13.47 Derived: -t2_space(code_code_numeral) | hAPP(fun(nat,code_code_numeral),code_code_numeral,suminf(code_code_numeral),hAPP(code_code_numeral,fun(nat,code_code_numeral),combk(code_code_numeral,nat),zero_zero(code_code_numeral))) = zero_zero(code_code_numeral). [resolve(5178,a,5070,a)].
% 13.50/13.47 Derived: -topological_space(code_code_numeral) | hBOOL(hAPP(fun(nat,code_code_numeral),bool,summable(code_code_numeral),hAPP(code_code_numeral,fun(nat,code_code_numeral),combk(code_code_numeral,nat),zero_zero(code_code_numeral)))). [resolve(5178,a,5071,a)].
% 13.50/13.47 Derived: -topological_space(code_code_numeral) | hBOOL(hAPP(code_code_numeral,bool,hAPP(fun(nat,code_code_numeral),fun(code_code_numeral,bool),sums(code_code_numeral),hAPP(code_code_numeral,fun(nat,code_code_numeral),combk(code_code_numeral,nat),zero_zero(code_code_numeral))),zero_zero(code_code_numeral))). [resolve(5178,a,5072,a)].
% 13.50/13.47 Derived: -t2_space(code_code_numeral) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(fun(nat,code_code_numeral),fun(code_code_numeral,bool),sums(code_code_numeral),A),B)) | hAPP(fun(nat,code_code_numeral),code_code_numeral,suminf(code_code_numeral),A) = ti(code_code_numeral,B). [resolve(5178,a,5073,a)].
% 13.50/13.47 Derived: -topological_space(code_code_numeral) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(fun(nat,code_code_numeral),fun(code_code_numeral,bool),sums(code_code_numeral),A),B)) | hBOOL(hAPP(fun(nat,code_code_numeral),bool,summable(code_code_numeral),A)). [resolve(5178,a,5074,a)].
% 13.50/13.47 Derived: -topological_space(code_code_numeral) | -hBOOL(hAPP(fun(nat,code_code_numeral),bool,summable(code_code_numeral),A)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(fun(nat,code_code_numeral),fun(code_code_numeral,bool),sums(code_code_numeral),A),f513(code_code_numeral,A))). [resolve(5178,a,5075,a)].
% 13.50/13.47 Derived: -t2_space(code_code_numeral) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(fun(nat,code_code_numeral),fun(code_code_numeral,bool),sums(code_code_numeral),A),B)) | hBOOL(hAPP(fun(nat,code_code_numeral),bool,summable(code_code_numeral),A)). [resolve(5178,a,5077,a)].
% 13.50/13.47 Derived: -t2_space(code_code_numeral) | hBOOL(hAPP(code_code_numeral,bool,hAPP(fun(nat,code_code_numeral),fun(code_code_numeral,bool),sums(code_code_numeral),A),B)) | -hBOOL(hAPP(fun(nat,code_code_numeral),bool,summable(code_code_numeral),A)) | hAPP(fun(nat,code_code_numeral),code_code_numeral,suminf(code_code_numeral),A) != ti(code_code_numeral,B). [resolve(5178,a,5079,a)].
% 13.50/13.47 Derived: -t2_space(code_code_numeral) | -hBOOL(hAPP(fun(nat,code_code_numeral),bool,summable(code_code_numeral),A)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(fun(nat,code_code_numeral),fun(code_code_numeral,bool),sums(code_code_numeral),A),hAPP(fun(nat,code_code_numeral),code_code_numeral,suminf(code_code_numeral),A))). [resolve(5178,a,5080,a)].
% 13.50/13.47 Derived: -topological_space(code_code_numeral) | hAPP(nat,code_code_numeral,A,zero_zero(nat)) != zero_zero(code_code_numeral) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(fun(nat,code_code_numeral),fun(code_code_numeral,bool),sums(code_code_numeral),hAPP(fun(nat,nat),fun(nat,code_code_numeral),hAPP(fun(nat,code_code_numeral),fun(fun(nat,nat),fun(nat,code_code_numeral)),combb(nat,code_code_numeral,nat),A),suc)),B)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(fun(nat,code_code_numeral),fun(code_code_numeral,bool),sums(code_code_numeral),A),B)). [resolve(5178,a,5081,a)].
% 13.50/13.47 Derived: -topological_space(code_code_numeral) | hAPP(fun(nat,code_code_numeral),code_code_numeral,suminf(code_code_numeral),A) = hAPP(fun(code_code_numeral,bool),code_code_numeral,the(code_code_numeral),hAPP(fun(nat,code_code_numeral),fun(code_code_numeral,bool),sums(code_code_numeral),A)). [resolve(5178,a,5082,a)].
% 13.50/13.47 Derived: -power(code_code_numeral) | hAPP(fun(nat,bool),code_code_numeral,hAPP(fun(nat,code_code_numeral),fun(fun(nat,bool),code_code_numeral),big_co1399186613setsum(nat,code_code_numeral),hAPP(fun(nat,code_code_numeral),fun(nat,code_code_numeral),hAPP(fun(nat,fun(code_code_numeral,code_code_numeral)),fun(fun(nat,code_code_numeral),fun(nat,code_code_numeral)),combs(nat,code_code_numeral,code_code_numeral),hAPP(fun(nat,code_code_numeral),fun(nat,fun(code_code_numeral,code_code_numeral)),hAPP(fun(code_code_numeral,fun(code_code_numeral,code_code_numeral)),fun(fun(nat,code_code_numeral),fun(nat,fun(code_code_numeral,code_code_numeral))),combb(code_code_numeral,fun(code_code_numeral,code_code_numeral),nat),times_times(code_code_numeral)),hAPP(fun(nat,nat),fun(nat,code_code_numeral),hAPP(fun(nat,code_code_numeral),fun(fun(nat,nat),fun(nat,code_code_numeral)),combb(nat,code_code_numeral,nat),hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A)),hAPP(nat,fun(nat,nat),minus_minus(nat),B)))),hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),C))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,suc,B))) = hAPP(fun(nat,bool),code_code_numeral,hAPP(fun(nat,code_code_numeral),fun(fun(nat,bool),code_code_numeral),big_co1399186613setsum(nat,code_code_numeral),hAPP(fun(nat,code_code_numeral),fun(nat,code_code_numeral),hAPP(fun(nat,fun(code_code_numeral,code_code_numeral)),fun(fun(nat,code_code_numeral),fun(nat,code_code_numeral)),combs(nat,code_code_numeral,code_code_numeral),hAPP(fun(nat,code_code_numeral),fun(nat,fun(code_code_numeral,code_code_numeral)),hAPP(fun(code_code_numeral,fun(code_code_numeral,code_code_numeral)),fun(fun(nat,code_code_numeral),fun(nat,fun(code_code_numeral,code_code_numeral))),combb(code_code_numeral,fun(code_code_numeral,code_code_numeral),nat),times_times(code_code_numeral)),hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A))),hAPP(fun(nat,nat),fun(nat,code_code_numeral),hAPP(fun(nat,code_code_numeral),fun(fun(nat,nat),fun(nat,code_code_numeral)),combb(nat,code_code_numeral,nat),hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),C)),hAPP(nat,fun(nat,nat),minus_minus(nat),B)))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,suc,B))). [resolve(5178,a,5083,a)].
% 13.50/13.47 Derived: hAPP(fun(nat,bool),code_code_numeral,hAPP(fun(nat,code_code_numeral),fun(fun(nat,bool),code_code_numeral),big_co1399186613setsum(nat,code_code_numeral),hAPP(fun(nat,fun(nat,bool)),fun(nat,code_code_numeral),hAPP(fun(fun(nat,bool),code_code_numeral),fun(fun(nat,fun(nat,bool)),fun(nat,code_code_numeral)),combb(fun(nat,bool),code_code_numeral,nat),hAPP(fun(nat,code_code_numeral),fun(fun(nat,bool),code_code_numeral),big_co1399186613setsum(nat,code_code_numeral),A)),hAPP(fun(nat,nat),fun(nat,fun(nat,bool)),hAPP(fun(nat,fun(nat,fun(nat,bool))),fun(fun(nat,nat),fun(nat,fun(nat,bool))),combs(nat,nat,fun(nat,bool)),hAPP(fun(nat,nat),fun(nat,fun(nat,fun(nat,bool))),hAPP(fun(nat,fun(nat,fun(nat,bool))),fun(fun(nat,nat),fun(nat,fun(nat,fun(nat,bool)))),combb(nat,fun(nat,fun(nat,bool)),nat),ord_atLeastLessThan(nat)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),times_times(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),plus_plus(nat)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),times_times(nat)),B))),B)))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),C)) = hAPP(fun(nat,bool),code_code_numeral,hAPP(fun(nat,code_code_numeral),fun(fun(nat,bool),code_code_numeral),big_co1399186613setsum(nat,code_code_numeral),A),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),C),B))). [resolve(5178,a,5084,a)].
% 13.50/13.47 Derived: hAPP(fun(nat,bool),code_code_numeral,hAPP(fun(nat,code_code_numeral),fun(fun(nat,bool),code_code_numeral),big_co1399186613setsum(nat,code_code_numeral),hAPP(fun(nat,nat),fun(nat,code_code_numeral),hAPP(fun(nat,code_code_numeral),fun(fun(nat,nat),fun(nat,code_code_numeral)),combb(nat,code_code_numeral,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_atLeastLessThan(nat),C),D)) = hAPP(fun(nat,bool),code_code_numeral,hAPP(fun(nat,code_code_numeral),fun(fun(nat,bool),code_code_numeral),big_co1399186613setsum(nat,code_code_numeral),A),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(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(5178,a,5085,a)].
% 13.50/13.48 Derived: hAPP(fun(nat,bool),code_code_numeral,hAPP(fun(nat,code_code_numeral),fun(fun(nat,bool),code_code_numeral),big_co1399186613setsum(nat,code_code_numeral),A),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),C))) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),hAPP(fun(nat,bool),code_code_numeral,hAPP(fun(nat,code_code_numeral),fun(fun(nat,bool),code_code_numeral),big_co1399186613setsum(nat,code_code_numeral),hAPP(fun(nat,nat),fun(nat,code_code_numeral),hAPP(fun(nat,code_code_numeral),fun(fun(nat,nat),fun(nat,code_code_numeral)),combb(nat,code_code_numeral,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)),C))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),B))),hAPP(fun(nat,bool),code_code_numeral,hAPP(fun(nat,code_code_numeral),fun(fun(nat,bool),code_code_numeral),big_co1399186613setsum(nat,code_code_numeral),A),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),C))). [resolve(5178,a,5086,a)].
% 13.50/13.48 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),hAPP(code_code_numeral,fun(A,code_code_numeral),hAPP(fun(A,fun(code_code_numeral,code_code_numeral)),fun(code_code_numeral,fun(A,code_code_numeral)),combc(A,code_code_numeral,code_code_numeral),hAPP(fun(A,code_code_numeral),fun(A,fun(code_code_numeral,code_code_numeral)),hAPP(fun(A,fun(code_code_numeral,fun(code_code_numeral,code_code_numeral))),fun(fun(A,code_code_numeral),fun(A,fun(code_code_numeral,code_code_numeral))),combs(A,code_code_numeral,fun(code_code_numeral,code_code_numeral)),hAPP(fun(A,bool),fun(A,fun(code_code_numeral,fun(code_code_numeral,code_code_numeral))),hAPP(fun(bool,fun(code_code_numeral,fun(code_code_numeral,code_code_numeral))),fun(fun(A,bool),fun(A,fun(code_code_numeral,fun(code_code_numeral,code_code_numeral)))),combb(bool,fun(code_code_numeral,fun(code_code_numeral,code_code_numeral)),A),if(code_code_numeral)),C)),D)),zero_zero(code_code_numeral))),B) = hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),D),hAPP(fun(A,bool),fun(A,bool),collect(A),hAPP(fun(A,bool),fun(A,bool),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))),C))). [resolve(5178,a,5087,a)].
% 13.50/13.48 Derived: hAPP(fun(nat,bool),code_code_numeral,hAPP(fun(nat,code_code_numeral),fun(fun(nat,bool),code_code_numeral),big_co1399186613setsum(nat,code_code_numeral),hAPP(fun(nat,nat),fun(nat,code_code_numeral),hAPP(fun(nat,code_code_numeral),fun(fun(nat,nat),fun(nat,code_code_numeral)),combb(nat,code_code_numeral,nat),A),suc)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),B),C)) = hAPP(fun(nat,bool),code_code_numeral,hAPP(fun(nat,code_code_numeral),fun(fun(nat,bool),code_code_numeral),big_co1399186613setsum(nat,code_code_numeral),A),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),hAPP(nat,nat,suc,B)),hAPP(nat,nat,suc,C))). [resolve(5178,a,5089,a)].
% 13.50/13.48 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(C,bool),code_code_numeral,hAPP(fun(C,code_code_numeral),fun(fun(C,bool),code_code_numeral),big_co1399186613setsum(C,code_code_numeral),hAPP(fun(C,fun(A,bool)),fun(C,code_code_numeral),hAPP(fun(C,fun(fun(A,bool),code_code_numeral)),fun(fun(C,fun(A,bool)),fun(C,code_code_numeral)),combs(C,fun(A,bool),code_code_numeral),hAPP(fun(C,fun(A,code_code_numeral)),fun(C,fun(fun(A,bool),code_code_numeral)),hAPP(fun(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral)),fun(fun(C,fun(A,code_code_numeral)),fun(C,fun(fun(A,bool),code_code_numeral))),combb(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),C),big_co1399186613setsum(A,code_code_numeral)),hAPP(fun(A,fun(C,code_code_numeral)),fun(C,fun(A,code_code_numeral)),combc(A,C,code_code_numeral),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) = hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),hAPP(fun(A,fun(C,bool)),fun(A,code_code_numeral),hAPP(fun(A,fun(fun(C,bool),code_code_numeral)),fun(fun(A,fun(C,bool)),fun(A,code_code_numeral)),combs(A,fun(C,bool),code_code_numeral),hAPP(fun(A,fun(C,code_code_numeral)),fun(A,fun(fun(C,bool),code_code_numeral)),hAPP(fun(fun(C,code_code_numeral),fun(fun(C,bool),code_code_numeral)),fun(fun(A,fun(C,code_code_numeral)),fun(A,fun(fun(C,bool),code_code_numeral))),combb(fun(C,code_code_numeral),fun(fun(C,bool),code_code_numeral),A),big_co1399186613setsum(C,code_code_numeral)),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). [resolve(5178,a,5090,a)].
% 13.50/13.48 Derived: hAPP(nat,code_code_numeral,A,zero_zero(nat)) != zero_zero(code_code_numeral) | hAPP(fun(nat,bool),code_code_numeral,hAPP(fun(nat,code_code_numeral),fun(fun(nat,bool),code_code_numeral),big_co1399186613setsum(nat,code_code_numeral),A),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),hAPP(nat,nat,suc,zero_zero(nat))),B)) = hAPP(fun(nat,bool),code_code_numeral,hAPP(fun(nat,code_code_numeral),fun(fun(nat,bool),code_code_numeral),big_co1399186613setsum(nat,code_code_numeral),A),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),B)). [resolve(5178,a,5091,a)].
% 13.50/13.48 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),B),C)) | hAPP(fun(nat,bool),code_code_numeral,hAPP(fun(nat,code_code_numeral),fun(fun(nat,bool),code_code_numeral),big_co1399186613setsum(nat,code_code_numeral),D),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),A),C)) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),hAPP(fun(nat,bool),code_code_numeral,hAPP(fun(nat,code_code_numeral),fun(fun(nat,bool),code_code_numeral),big_co1399186613setsum(nat,code_code_numeral),D),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),A),B))),hAPP(fun(nat,bool),code_code_numeral,hAPP(fun(nat,code_code_numeral),fun(fun(nat,bool),code_code_numeral),big_co1399186613setsum(nat,code_code_numeral),D),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),B),C))). [resolve(5178,a,5092,a)].
% 13.50/13.48 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | hAPP(fun(nat,bool),code_code_numeral,hAPP(fun(nat,code_code_numeral),fun(fun(nat,bool),code_code_numeral),big_co1399186613setsum(nat,code_code_numeral),C),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),A),B)) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),hAPP(nat,code_code_numeral,C,A)),hAPP(fun(nat,bool),code_code_numeral,hAPP(fun(nat,code_code_numeral),fun(fun(nat,bool),code_code_numeral),big_co1399186613setsum(nat,code_code_numeral),C),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),hAPP(nat,nat,suc,A)),B))). [resolve(5178,a,5093,a)].
% 13.50/13.48 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | hAPP(fun(nat,bool),code_code_numeral,hAPP(fun(nat,code_code_numeral),fun(fun(nat,bool),code_code_numeral),big_co1399186613setsum(nat,code_code_numeral),C),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),B),hAPP(nat,nat,suc,A))) = zero_zero(code_code_numeral). [resolve(5178,a,5094,a)].
% 13.50/13.48 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | hAPP(fun(nat,bool),code_code_numeral,hAPP(fun(nat,code_code_numeral),fun(fun(nat,bool),code_code_numeral),big_co1399186613setsum(nat,code_code_numeral),C),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),B),hAPP(nat,nat,suc,A))) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),hAPP(fun(nat,bool),code_code_numeral,hAPP(fun(nat,code_code_numeral),fun(fun(nat,bool),code_code_numeral),big_co1399186613setsum(nat,code_code_numeral),C),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),B),A))),hAPP(nat,code_code_numeral,C,A)). [resolve(5178,a,5095,a)].
% 13.50/13.48 Derived: hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),C),B) = zero_zero(code_code_numeral). [resolve(5178,a,5096,a)].
% 13.50/13.48 Derived: hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),hAPP(fun(B,bool),fun(A,code_code_numeral),hAPP(fun(A,fun(fun(B,bool),code_code_numeral)),fun(fun(B,bool),fun(A,code_code_numeral)),combc(A,fun(B,bool),code_code_numeral),hAPP(fun(A,fun(B,code_code_numeral)),fun(A,fun(fun(B,bool),code_code_numeral)),hAPP(fun(fun(B,code_code_numeral),fun(fun(B,bool),code_code_numeral)),fun(fun(A,fun(B,code_code_numeral)),fun(A,fun(fun(B,bool),code_code_numeral))),combb(fun(B,code_code_numeral),fun(fun(B,bool),code_code_numeral),A),big_co1399186613setsum(B,code_code_numeral)),hAPP(fun(B,fun(A,code_code_numeral)),fun(A,fun(B,code_code_numeral)),combc(B,A,code_code_numeral),C))),D)),E) = hAPP(fun(B,bool),code_code_numeral,hAPP(fun(B,code_code_numeral),fun(fun(B,bool),code_code_numeral),big_co1399186613setsum(B,code_code_numeral),hAPP(fun(A,bool),fun(B,code_code_numeral),hAPP(fun(B,fun(fun(A,bool),code_code_numeral)),fun(fun(A,bool),fun(B,code_code_numeral)),combc(B,fun(A,bool),code_code_numeral),hAPP(fun(B,fun(A,code_code_numeral)),fun(B,fun(fun(A,bool),code_code_numeral)),hAPP(fun(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral)),fun(fun(B,fun(A,code_code_numeral)),fun(B,fun(fun(A,bool),code_code_numeral))),combb(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),B),big_co1399186613setsum(A,code_code_numeral)),C)),E)),D). [resolve(5178,a,5098,a)].
% 13.50/13.48 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),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),hAPP(code_code_numeral,fun(A,code_code_numeral),hAPP(fun(A,fun(code_code_numeral,code_code_numeral)),fun(code_code_numeral,fun(A,code_code_numeral)),combc(A,code_code_numeral,code_code_numeral),hAPP(fun(A,code_code_numeral),fun(A,fun(code_code_numeral,code_code_numeral)),hAPP(fun(A,fun(code_code_numeral,fun(code_code_numeral,code_code_numeral))),fun(fun(A,code_code_numeral),fun(A,fun(code_code_numeral,code_code_numeral))),combs(A,code_code_numeral,fun(code_code_numeral,code_code_numeral)),hAPP(fun(A,bool),fun(A,fun(code_code_numeral,fun(code_code_numeral,code_code_numeral))),hAPP(fun(bool,fun(code_code_numeral,fun(code_code_numeral,code_code_numeral))),fun(fun(A,bool),fun(A,fun(code_code_numeral,fun(code_code_numeral,code_code_numeral)))),combb(bool,fun(code_code_numeral,fun(code_code_numeral,code_code_numeral)),A),if(code_code_numeral)),hAPP(A,fun(A,bool),fequal(A),C))),D)),zero_zero(code_code_numeral))),B) = hAPP(A,code_code_numeral,D,C). [resolve(5178,a,5099,a)].
% 13.50/13.48 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),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),hAPP(code_code_numeral,fun(A,code_code_numeral),hAPP(fun(A,fun(code_code_numeral,code_code_numeral)),fun(code_code_numeral,fun(A,code_code_numeral)),combc(A,code_code_numeral,code_code_numeral),hAPP(fun(A,code_code_numeral),fun(A,fun(code_code_numeral,code_code_numeral)),hAPP(fun(A,fun(code_code_numeral,fun(code_code_numeral,code_code_numeral))),fun(fun(A,code_code_numeral),fun(A,fun(code_code_numeral,code_code_numeral))),combs(A,code_code_numeral,fun(code_code_numeral,code_code_numeral)),hAPP(fun(A,bool),fun(A,fun(code_code_numeral,fun(code_code_numeral,code_code_numeral))),hAPP(fun(bool,fun(code_code_numeral,fun(code_code_numeral,code_code_numeral))),fun(fun(A,bool),fun(A,fun(code_code_numeral,fun(code_code_numeral,code_code_numeral)))),combb(bool,fun(code_code_numeral,fun(code_code_numeral,code_code_numeral)),A),if(code_code_numeral)),hAPP(A,fun(A,bool),fequal(A),C))),D)),zero_zero(code_code_numeral))),B) = zero_zero(code_code_numeral). [resolve(5178,a,5100,a)].
% 13.50/13.48 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),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),hAPP(code_code_numeral,fun(A,code_code_numeral),hAPP(fun(A,fun(code_code_numeral,code_code_numeral)),fun(code_code_numeral,fun(A,code_code_numeral)),combc(A,code_code_numeral,code_code_numeral),hAPP(fun(A,code_code_numeral),fun(A,fun(code_code_numeral,code_code_numeral)),hAPP(fun(A,fun(code_code_numeral,fun(code_code_numeral,code_code_numeral))),fun(fun(A,code_code_numeral),fun(A,fun(code_code_numeral,code_code_numeral))),combs(A,code_code_numeral,fun(code_code_numeral,code_code_numeral)),hAPP(fun(A,bool),fun(A,fun(code_code_numeral,fun(code_code_numeral,code_code_numeral))),hAPP(fun(bool,fun(code_code_numeral,fun(code_code_numeral,code_code_numeral))),fun(fun(A,bool),fun(A,fun(code_code_numeral,fun(code_code_numeral,code_code_numeral)))),combb(bool,fun(code_code_numeral,fun(code_code_numeral,code_code_numeral)),A),if(code_code_numeral)),hAPP(A,fun(A,bool),hAPP(fun(A,fun(A,bool)),fun(A,fun(A,bool)),combc(A,A,bool),fequal(A)),C))),D)),zero_zero(code_code_numeral))),B) = hAPP(A,code_code_numeral,D,C). [resolve(5178,a,5101,a)].
% 13.50/13.48 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),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),hAPP(code_code_numeral,fun(A,code_code_numeral),hAPP(fun(A,fun(code_code_numeral,code_code_numeral)),fun(code_code_numeral,fun(A,code_code_numeral)),combc(A,code_code_numeral,code_code_numeral),hAPP(fun(A,code_code_numeral),fun(A,fun(code_code_numeral,code_code_numeral)),hAPP(fun(A,fun(code_code_numeral,fun(code_code_numeral,code_code_numeral))),fun(fun(A,code_code_numeral),fun(A,fun(code_code_numeral,code_code_numeral))),combs(A,code_code_numeral,fun(code_code_numeral,code_code_numeral)),hAPP(fun(A,bool),fun(A,fun(code_code_numeral,fun(code_code_numeral,code_code_numeral))),hAPP(fun(bool,fun(code_code_numeral,fun(code_code_numeral,code_code_numeral))),fun(fun(A,bool),fun(A,fun(code_code_numeral,fun(code_code_numeral,code_code_numeral)))),combb(bool,fun(code_code_numeral,fun(code_code_numeral,code_code_numeral)),A),if(code_code_numeral)),hAPP(A,fun(A,bool),hAPP(fun(A,fun(A,bool)),fun(A,fun(A,bool)),combc(A,A,bool),fequal(A)),C))),D)),zero_zero(code_code_numeral))),B) = zero_zero(code_code_numeral). [resolve(5178,a,5102,a)].
% 13.50/13.48 Derived: hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),hAPP(code_code_numeral,fun(A,code_code_numeral),combk(code_code_numeral,A),zero_zero(code_code_numeral))),B) = zero_zero(code_code_numeral). [resolve(5178,a,5103,a)].
% 13.50/13.48 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),hAPP(fun(A,code_code_numeral),fun(A,code_code_numeral),hAPP(fun(A,fun(code_code_numeral,code_code_numeral)),fun(fun(A,code_code_numeral),fun(A,code_code_numeral)),combs(A,code_code_numeral,code_code_numeral),hAPP(fun(A,code_code_numeral),fun(A,fun(code_code_numeral,code_code_numeral)),hAPP(fun(code_code_numeral,fun(code_code_numeral,code_code_numeral)),fun(fun(A,code_code_numeral),fun(A,fun(code_code_numeral,code_code_numeral))),combb(code_code_numeral,fun(code_code_numeral,code_code_numeral),A),plus_plus(code_code_numeral)),C)),D)),B) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),C),B)),hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),D),B)). [resolve(5178,a,5104,a)].
% 13.50/13.48 Derived: hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),hAPP(fun(A,code_code_numeral),fun(A,code_code_numeral),hAPP(fun(A,fun(code_code_numeral,code_code_numeral)),fun(fun(A,code_code_numeral),fun(A,code_code_numeral)),combs(A,code_code_numeral,code_code_numeral),hAPP(fun(A,code_code_numeral),fun(A,fun(code_code_numeral,code_code_numeral)),hAPP(fun(code_code_numeral,fun(code_code_numeral,code_code_numeral)),fun(fun(A,code_code_numeral),fun(A,fun(code_code_numeral,code_code_numeral))),combb(code_code_numeral,fun(code_code_numeral,code_code_numeral),A),plus_plus(code_code_numeral)),B)),C)),D) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),B),D)),hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),C),D)). [resolve(5178,a,5105,a)].
% 13.50/13.48 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(fun(C,bool),code_code_numeral,hAPP(fun(C,code_code_numeral),fun(fun(C,bool),code_code_numeral),big_co1399186613setsum(C,code_code_numeral),hAPP(fun(C,fun(A,bool)),fun(C,code_code_numeral),hAPP(fun(fun(A,bool),code_code_numeral),fun(fun(C,fun(A,bool)),fun(C,code_code_numeral)),combb(fun(A,bool),code_code_numeral,C),hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),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),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),D),B). [resolve(5178,a,5106,a)].
% 13.50/13.48 Derived: -comm_monoid_mult(code_code_numeral) | hAPP(fun(nat,bool),code_code_numeral,hAPP(fun(nat,code_code_numeral),fun(fun(nat,bool),code_code_numeral),big_co1399186613setsum(nat,code_code_numeral),A),B) = hAPP(fun(int,bool),code_code_numeral,hAPP(fun(int,code_code_numeral),fun(fun(int,bool),code_code_numeral),big_co1399186613setsum(int,code_code_numeral),hAPP(fun(int,nat),fun(int,code_code_numeral),hAPP(fun(nat,code_code_numeral),fun(fun(int,nat),fun(int,code_code_numeral)),combb(nat,code_code_numeral,int),A),nat_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)),B)). [resolve(5178,a,5107,a)].
% 13.50/13.48 Derived: -comm_monoid_mult(code_code_numeral) | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A)) | hAPP(fun(nat,bool),code_code_numeral,hAPP(fun(nat,code_code_numeral),fun(fun(nat,bool),code_code_numeral),big_co1399186613setsum(nat,code_code_numeral),hAPP(fun(nat,int),fun(nat,code_code_numeral),hAPP(fun(int,code_code_numeral),fun(fun(nat,int),fun(nat,code_code_numeral)),combb(int,code_code_numeral,nat),B),semiring_1_of_nat(int))),hAPP(fun(int,bool),fun(nat,bool),hAPP(fun(int,nat),fun(fun(int,bool),fun(nat,bool)),image(int,nat),nat_1),A)) = hAPP(fun(int,bool),code_code_numeral,hAPP(fun(int,code_code_numeral),fun(fun(int,bool),code_code_numeral),big_co1399186613setsum(int,code_code_numeral),B),A). [resolve(5178,a,5108,a)].
% 13.50/13.48 Derived: -t2_space(code_code_numeral) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),f592(code_code_numeral,B,A))) | hBOOL(hAPP(code_code_numeral,bool,hAPP(fun(nat,code_code_numeral),fun(code_code_numeral,bool),sums(code_code_numeral),B),hAPP(fun(nat,bool),code_code_numeral,hAPP(fun(nat,code_code_numeral),fun(fun(nat,bool),code_code_numeral),big_co1399186613setsum(nat,code_code_numeral),B),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),A)))). [resolve(5178,a,5109,a)].
% 13.50/13.48 Derived: -t2_space(code_code_numeral) | hAPP(nat,code_code_numeral,A,f592(code_code_numeral,A,B)) != zero_zero(code_code_numeral) | hBOOL(hAPP(code_code_numeral,bool,hAPP(fun(nat,code_code_numeral),fun(code_code_numeral,bool),sums(code_code_numeral),A),hAPP(fun(nat,bool),code_code_numeral,hAPP(fun(nat,code_code_numeral),fun(fun(nat,bool),code_code_numeral),big_co1399186613setsum(nat,code_code_numeral),A),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),B)))). [resolve(5178,a,5110,a)].
% 13.50/13.48 Derived: -ordere779506340up_add(code_code_numeral) | -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),f593(A,code_code_numeral,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))) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),D),C)),hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),D),B))). [resolve(5178,a,5111,a)].
% 13.50/13.48 Derived: -ordere779506340up_add(code_code_numeral) | -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(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),zero_zero(code_code_numeral)),hAPP(A,code_code_numeral,D,f593(A,code_code_numeral,D,C,B)))) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),D),C)),hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),D),B))). [resolve(5178,a,5112,a)].
% 13.50/13.48 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),f595(A,code_code_numeral,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),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),D),B) = hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),D),C). [resolve(5178,a,5113,a)].
% 13.50/13.48 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,code_code_numeral,D,f595(A,code_code_numeral,D,C,B)) != zero_zero(code_code_numeral) | hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),D),B) = hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),D),C). [resolve(5178,a,5114,a)].
% 13.50/13.48 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),f596(A,code_code_numeral,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),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),D),B) = hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),D),C). [resolve(5178,a,5115,a)].
% 13.50/13.48 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,code_code_numeral,D,f596(A,code_code_numeral,D,C,B)) != zero_zero(code_code_numeral) | hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),D),B) = hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),D),C). [resolve(5178,a,5116,a)].
% 13.50/13.48 Derived: -comm_monoid_mult(code_code_numeral) | A != B | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),f598(code_code_numeral,C,D,B,A))) | hAPP(fun(int,bool),code_code_numeral,hAPP(fun(int,code_code_numeral),fun(fun(int,bool),code_code_numeral),big_co1399186613setsum(int,code_code_numeral),D),A) = hAPP(fun(int,bool),code_code_numeral,hAPP(fun(int,code_code_numeral),fun(fun(int,bool),code_code_numeral),big_co1399186613setsum(int,code_code_numeral),C),B). [resolve(5178,a,5117,a)].
% 13.50/13.48 Derived: -comm_monoid_mult(code_code_numeral) | A != B | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A)) | hAPP(int,code_code_numeral,C,f598(code_code_numeral,D,C,B,A)) != hAPP(int,code_code_numeral,D,f598(code_code_numeral,D,C,B,A)) | hAPP(fun(int,bool),code_code_numeral,hAPP(fun(int,code_code_numeral),fun(fun(int,bool),code_code_numeral),big_co1399186613setsum(int,code_code_numeral),C),A) = hAPP(fun(int,bool),code_code_numeral,hAPP(fun(int,code_code_numeral),fun(fun(int,bool),code_code_numeral),big_co1399186613setsum(int,code_code_numeral),D),B). [resolve(5178,a,5118,a)].
% 13.50/13.48 Derived: -ord(A) | ti(A,B) != ti(A,C) | ti(A,D) != ti(A,E) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),f603(code_code_numeral,A,F,V6,E,D,C,B))) | hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),V6),hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_atLeastLessThan(A),B),D)) = hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),F),hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_atLeastLessThan(A),C),E)). [resolve(5178,a,5119,b)].
% 13.50/13.48 Derived: -ord(A) | ti(A,B) != ti(A,C) | ti(A,D) != ti(A,E) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),f603(code_code_numeral,A,F,V6,E,D,C,B)),D)) | hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),V6),hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_atLeastLessThan(A),B),D)) = hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),F),hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_atLeastLessThan(A),C),E)). [resolve(5178,a,5120,b)].
% 13.50/13.48 Derived: -ord(A) | ti(A,B) != ti(A,C) | ti(A,D) != ti(A,E) | hAPP(A,code_code_numeral,F,f603(code_code_numeral,A,V6,F,E,D,C,B)) != hAPP(A,code_code_numeral,V6,f603(code_code_numeral,A,V6,F,E,D,C,B)) | hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),F),hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_atLeastLessThan(A),B),D)) = hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),V6),hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_atLeastLessThan(A),C),E)). [resolve(5178,a,5121,b)].
% 13.50/13.48 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),f609(A,code_code_numeral,C,B)),B)) | hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),C),B) = zero_zero(code_code_numeral). [resolve(5178,a,5122,a)].
% 13.50/13.48 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(A,code_code_numeral,C,f609(A,code_code_numeral,C,B)) != zero_zero(code_code_numeral) | hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),C),B) = zero_zero(code_code_numeral). [resolve(5178,a,5123,a)].
% 13.50/13.48 Derived: -ordere779506340up_add(code_code_numeral) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f610(A,code_code_numeral,B,C)),C)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),B),C)),zero_zero(code_code_numeral))). [resolve(5178,a,5124,a)].
% 13.50/13.49 Derived: -ordere779506340up_add(code_code_numeral) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),hAPP(A,code_code_numeral,B,f610(A,code_code_numeral,B,C))),zero_zero(code_code_numeral))) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),B),C)),zero_zero(code_code_numeral))). [resolve(5178,a,5125,a)].
% 13.50/13.49 Derived: -ordere779506340up_add(code_code_numeral) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f611(A,code_code_numeral,B,C)),C)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),zero_zero(code_code_numeral)),hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),B),C))). [resolve(5178,a,5126,a)].
% 13.50/13.49 Derived: -ordere779506340up_add(code_code_numeral) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),zero_zero(code_code_numeral)),hAPP(A,code_code_numeral,B,f611(A,code_code_numeral,B,C)))) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),zero_zero(code_code_numeral)),hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),B),C))). [resolve(5178,a,5127,a)].
% 13.50/13.49 Derived: -hBOOL(hAPP(fun(fun(A,bool),bool),bool,finite_finite_1(fun(A,bool)),B)) | hBOOL(hAPP(fun(fun(A,bool),bool),bool,hAPP(fun(A,bool),fun(fun(fun(A,bool),bool),bool),member(fun(A,bool)),f612(A,code_code_numeral,C,B)),B)) | hBOOL(hAPP(fun(fun(A,bool),bool),bool,hAPP(fun(A,bool),fun(fun(fun(A,bool),bool),bool),member(fun(A,bool)),f613(A,code_code_numeral,C,B)),B)) | hAPP(fun(fun(A,bool),bool),code_code_numeral,hAPP(fun(fun(A,bool),code_code_numeral),fun(fun(fun(A,bool),bool),code_code_numeral),big_co1399186613setsum(fun(A,bool),code_code_numeral),hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),C)),B) = hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),C),hAPP(fun(fun(A,bool),bool),fun(A,bool),complete_Sup_Sup(fun(A,bool)),B)). [resolve(5178,a,5128,a)].
% 13.50/13.49 Derived: -hBOOL(hAPP(fun(fun(A,bool),bool),bool,finite_finite_1(fun(A,bool)),B)) | hBOOL(hAPP(fun(fun(A,bool),bool),bool,hAPP(fun(A,bool),fun(fun(fun(A,bool),bool),bool),member(fun(A,bool)),f612(A,code_code_numeral,C,B)),B)) | hBOOL(hAPP(fun(fun(A,bool),bool),bool,hAPP(fun(A,bool),fun(fun(fun(A,bool),bool),bool),member(fun(A,bool)),f614(A,code_code_numeral,C,B)),B)) | hAPP(fun(fun(A,bool),bool),code_code_numeral,hAPP(fun(fun(A,bool),code_code_numeral),fun(fun(fun(A,bool),bool),code_code_numeral),big_co1399186613setsum(fun(A,bool),code_code_numeral),hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),C)),B) = hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),C),hAPP(fun(fun(A,bool),bool),fun(A,bool),complete_Sup_Sup(fun(A,bool)),B)). [resolve(5178,a,5129,a)].
% 13.50/13.49 Derived: -hBOOL(hAPP(fun(fun(A,bool),bool),bool,finite_finite_1(fun(A,bool)),B)) | hBOOL(hAPP(fun(fun(A,bool),bool),bool,hAPP(fun(A,bool),fun(fun(fun(A,bool),bool),bool),member(fun(A,bool)),f612(A,code_code_numeral,C,B)),B)) | ti(fun(A,bool),f614(A,code_code_numeral,C,B)) != ti(fun(A,bool),f613(A,code_code_numeral,C,B)) | hAPP(fun(fun(A,bool),bool),code_code_numeral,hAPP(fun(fun(A,bool),code_code_numeral),fun(fun(fun(A,bool),bool),code_code_numeral),big_co1399186613setsum(fun(A,bool),code_code_numeral),hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),C)),B) = hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),C),hAPP(fun(fun(A,bool),bool),fun(A,bool),complete_Sup_Sup(fun(A,bool)),B)). [resolve(5178,a,5130,a)].
% 13.50/13.49 Derived: -hBOOL(hAPP(fun(fun(A,bool),bool),bool,finite_finite_1(fun(A,bool)),B)) | hBOOL(hAPP(fun(fun(A,bool),bool),bool,hAPP(fun(A,bool),fun(fun(fun(A,bool),bool),bool),member(fun(A,bool)),f612(A,code_code_numeral,C,B)),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f615(A,code_code_numeral,C,B)),f613(A,code_code_numeral,C,B))) | hAPP(fun(fun(A,bool),bool),code_code_numeral,hAPP(fun(fun(A,bool),code_code_numeral),fun(fun(fun(A,bool),bool),code_code_numeral),big_co1399186613setsum(fun(A,bool),code_code_numeral),hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),C)),B) = hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),C),hAPP(fun(fun(A,bool),bool),fun(A,bool),complete_Sup_Sup(fun(A,bool)),B)). [resolve(5178,a,5131,a)].
% 13.50/13.49 Derived: -hBOOL(hAPP(fun(fun(A,bool),bool),bool,finite_finite_1(fun(A,bool)),B)) | hBOOL(hAPP(fun(fun(A,bool),bool),bool,hAPP(fun(A,bool),fun(fun(fun(A,bool),bool),bool),member(fun(A,bool)),f612(A,code_code_numeral,C,B)),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f615(A,code_code_numeral,C,B)),f614(A,code_code_numeral,C,B))) | hAPP(fun(fun(A,bool),bool),code_code_numeral,hAPP(fun(fun(A,bool),code_code_numeral),fun(fun(fun(A,bool),bool),code_code_numeral),big_co1399186613setsum(fun(A,bool),code_code_numeral),hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),C)),B) = hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),C),hAPP(fun(fun(A,bool),bool),fun(A,bool),complete_Sup_Sup(fun(A,bool)),B)). [resolve(5178,a,5132,a)].
% 13.50/13.49 Derived: -hBOOL(hAPP(fun(fun(A,bool),bool),bool,finite_finite_1(fun(A,bool)),B)) | hBOOL(hAPP(fun(fun(A,bool),bool),bool,hAPP(fun(A,bool),fun(fun(fun(A,bool),bool),bool),member(fun(A,bool)),f612(A,code_code_numeral,C,B)),B)) | hAPP(A,code_code_numeral,C,f615(A,code_code_numeral,C,B)) != zero_zero(code_code_numeral) | hAPP(fun(fun(A,bool),bool),code_code_numeral,hAPP(fun(fun(A,bool),code_code_numeral),fun(fun(fun(A,bool),bool),code_code_numeral),big_co1399186613setsum(fun(A,bool),code_code_numeral),hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),C)),B) = hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),C),hAPP(fun(fun(A,bool),bool),fun(A,bool),complete_Sup_Sup(fun(A,bool)),B)). [resolve(5178,a,5133,a)].
% 13.50/13.49 Derived: -hBOOL(hAPP(fun(fun(A,bool),bool),bool,finite_finite_1(fun(A,bool)),B)) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),f612(A,code_code_numeral,C,B))) | hBOOL(hAPP(fun(fun(A,bool),bool),bool,hAPP(fun(A,bool),fun(fun(fun(A,bool),bool),bool),member(fun(A,bool)),f613(A,code_code_numeral,C,B)),B)) | hAPP(fun(fun(A,bool),bool),code_code_numeral,hAPP(fun(fun(A,bool),code_code_numeral),fun(fun(fun(A,bool),bool),code_code_numeral),big_co1399186613setsum(fun(A,bool),code_code_numeral),hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),C)),B) = hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),C),hAPP(fun(fun(A,bool),bool),fun(A,bool),complete_Sup_Sup(fun(A,bool)),B)). [resolve(5178,a,5134,a)].
% 13.50/13.49 Derived: -hBOOL(hAPP(fun(fun(A,bool),bool),bool,finite_finite_1(fun(A,bool)),B)) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),f612(A,code_code_numeral,C,B))) | hBOOL(hAPP(fun(fun(A,bool),bool),bool,hAPP(fun(A,bool),fun(fun(fun(A,bool),bool),bool),member(fun(A,bool)),f614(A,code_code_numeral,C,B)),B)) | hAPP(fun(fun(A,bool),bool),code_code_numeral,hAPP(fun(fun(A,bool),code_code_numeral),fun(fun(fun(A,bool),bool),code_code_numeral),big_co1399186613setsum(fun(A,bool),code_code_numeral),hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),C)),B) = hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),C),hAPP(fun(fun(A,bool),bool),fun(A,bool),complete_Sup_Sup(fun(A,bool)),B)). [resolve(5178,a,5135,a)].
% 13.50/13.49 Derived: -hBOOL(hAPP(fun(fun(A,bool),bool),bool,finite_finite_1(fun(A,bool)),B)) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),f612(A,code_code_numeral,C,B))) | ti(fun(A,bool),f614(A,code_code_numeral,C,B)) != ti(fun(A,bool),f613(A,code_code_numeral,C,B)) | hAPP(fun(fun(A,bool),bool),code_code_numeral,hAPP(fun(fun(A,bool),code_code_numeral),fun(fun(fun(A,bool),bool),code_code_numeral),big_co1399186613setsum(fun(A,bool),code_code_numeral),hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),C)),B) = hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),C),hAPP(fun(fun(A,bool),bool),fun(A,bool),complete_Sup_Sup(fun(A,bool)),B)). [resolve(5178,a,5136,a)].
% 13.50/13.49 Derived: -hBOOL(hAPP(fun(fun(A,bool),bool),bool,finite_finite_1(fun(A,bool)),B)) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),f612(A,code_code_numeral,C,B))) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f615(A,code_code_numeral,C,B)),f613(A,code_code_numeral,C,B))) | hAPP(fun(fun(A,bool),bool),code_code_numeral,hAPP(fun(fun(A,bool),code_code_numeral),fun(fun(fun(A,bool),bool),code_code_numeral),big_co1399186613setsum(fun(A,bool),code_code_numeral),hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),C)),B) = hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),C),hAPP(fun(fun(A,bool),bool),fun(A,bool),complete_Sup_Sup(fun(A,bool)),B)). [resolve(5178,a,5137,a)].
% 13.50/13.49 Derived: -hBOOL(hAPP(fun(fun(A,bool),bool),bool,finite_finite_1(fun(A,bool)),B)) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),f612(A,code_code_numeral,C,B))) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f615(A,code_code_numeral,C,B)),f614(A,code_code_numeral,C,B))) | hAPP(fun(fun(A,bool),bool),code_code_numeral,hAPP(fun(fun(A,bool),code_code_numeral),fun(fun(fun(A,bool),bool),code_code_numeral),big_co1399186613setsum(fun(A,bool),code_code_numeral),hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),C)),B) = hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),C),hAPP(fun(fun(A,bool),bool),fun(A,bool),complete_Sup_Sup(fun(A,bool)),B)). [resolve(5178,a,5138,a)].
% 13.50/13.49 Derived: -hBOOL(hAPP(fun(fun(A,bool),bool),bool,finite_finite_1(fun(A,bool)),B)) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),f612(A,code_code_numeral,C,B))) | hAPP(A,code_code_numeral,C,f615(A,code_code_numeral,C,B)) != zero_zero(code_code_numeral) | hAPP(fun(fun(A,bool),bool),code_code_numeral,hAPP(fun(fun(A,bool),code_code_numeral),fun(fun(fun(A,bool),bool),code_code_numeral),big_co1399186613setsum(fun(A,bool),code_code_numeral),hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),C)),B) = hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),C),hAPP(fun(fun(A,bool),bool),fun(A,bool),complete_Sup_Sup(fun(A,bool)),B)). [resolve(5178,a,5139,a)].
% 13.50/13.49 Derived: hAPP(fun(nat,bool),code_code_numeral,hAPP(fun(nat,code_code_numeral),fun(fun(nat,bool),code_code_numeral),big_co1399186613setsum(nat,code_code_numeral),A),hAPP(nat,fun(nat,bool),ord_lessThan(nat),hAPP(nat,nat,suc,B))) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),hAPP(fun(nat,bool),code_code_numeral,hAPP(fun(nat,code_code_numeral),fun(fun(nat,bool),code_code_numeral),big_co1399186613setsum(nat,code_code_numeral),A),hAPP(nat,fun(nat,bool),ord_lessThan(nat),B))),hAPP(nat,code_code_numeral,A,B)). [resolve(5178,a,5140,a)].
% 13.50/13.49 Derived: -metric_space(code_code_numeral) | hAPP(fun(nat,code_code_numeral),code_code_numeral,suminf(code_code_numeral),A) = hAPP(fun(nat,code_code_numeral),code_code_numeral,lim(code_code_numeral),hAPP(fun(nat,fun(nat,bool)),fun(nat,code_code_numeral),hAPP(fun(fun(nat,bool),code_code_numeral),fun(fun(nat,fun(nat,bool)),fun(nat,code_code_numeral)),combb(fun(nat,bool),code_code_numeral,nat),hAPP(fun(nat,code_code_numeral),fun(fun(nat,bool),code_code_numeral),big_co1399186613setsum(nat,code_code_numeral),A)),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)))). [resolve(5178,a,5141,a)].
% 13.50/13.49 Derived: -ordere779506340up_add(code_code_numeral) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f631(A,code_code_numeral,B,C,D)),D)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),B),D)),hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),C),D))). [resolve(5178,a,5142,a)].
% 13.50/13.49 Derived: -ordere779506340up_add(code_code_numeral) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),hAPP(A,code_code_numeral,B,f631(A,code_code_numeral,B,C,D))),hAPP(A,code_code_numeral,C,f631(A,code_code_numeral,B,C,D)))) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),B),D)),hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),C),D))). [resolve(5178,a,5143,a)].
% 13.50/13.49 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),f632(A,code_code_numeral,D,E,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))) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f633(A,code_code_numeral,D,E,C,B)),C)) | hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),D),C) = hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),E),B). [resolve(5178,a,5144,a)].
% 13.50/13.49 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),f632(A,code_code_numeral,D,E,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(A,code_code_numeral,D,f633(A,code_code_numeral,D,E,C,B)) != hAPP(A,code_code_numeral,E,f633(A,code_code_numeral,D,E,C,B)) | hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),D),C) = hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),E),B). [resolve(5178,a,5145,a)].
% 13.50/13.49 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,code_code_numeral,D,f632(A,code_code_numeral,E,D,C,B)) != zero_zero(code_code_numeral) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f633(A,code_code_numeral,E,D,C,B)),C)) | hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),E),C) = hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),D),B). [resolve(5178,a,5146,a)].
% 13.50/13.49 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,code_code_numeral,D,f632(A,code_code_numeral,E,D,C,B)) != zero_zero(code_code_numeral) | hAPP(A,code_code_numeral,E,f633(A,code_code_numeral,E,D,C,B)) != hAPP(A,code_code_numeral,D,f633(A,code_code_numeral,E,D,C,B)) | hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),E),C) = hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),D),B). [resolve(5178,a,5147,a)].
% 13.50/13.49 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),f644(A,code_code_numeral,D,E,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))) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f645(A,code_code_numeral,D,E,C,B)),C)) | hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),E),B) = hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),D),C). [resolve(5178,a,5148,a)].
% 13.50/13.49 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),f644(A,code_code_numeral,D,E,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(A,code_code_numeral,E,f645(A,code_code_numeral,D,E,C,B)) != hAPP(A,code_code_numeral,D,f645(A,code_code_numeral,D,E,C,B)) | hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),E),B) = hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),D),C). [resolve(5178,a,5149,a)].
% 13.50/13.49 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,code_code_numeral,D,f644(A,code_code_numeral,E,D,C,B)) != zero_zero(code_code_numeral) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f645(A,code_code_numeral,E,D,C,B)),C)) | hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),D),B) = hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),E),C). [resolve(5178,a,5150,a)].
% 13.50/13.49 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,code_code_numeral,D,f644(A,code_code_numeral,E,D,C,B)) != zero_zero(code_code_numeral) | hAPP(A,code_code_numeral,D,f645(A,code_code_numeral,E,D,C,B)) != hAPP(A,code_code_numeral,E,f645(A,code_code_numeral,E,D,C,B)) | hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),D),B) = hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),E),C). [resolve(5178,a,5151,a)].
% 13.50/13.49 Derived: -t2_space(code_code_numeral) | -hBOOL(hAPP(fun(nat,code_code_numeral),bool,summable(code_code_numeral),A)) | hBOOL(hAPP(filter(nat),bool,hAPP(code_code_numeral,fun(filter(nat),bool),hAPP(fun(nat,code_code_numeral),fun(code_code_numeral,fun(filter(nat),bool)),tendsto(nat,code_code_numeral),hAPP(fun(nat,fun(nat,bool)),fun(nat,code_code_numeral),hAPP(fun(fun(nat,bool),code_code_numeral),fun(fun(nat,fun(nat,bool)),fun(nat,code_code_numeral)),combb(fun(nat,bool),code_code_numeral,nat),hAPP(fun(nat,code_code_numeral),fun(fun(nat,bool),code_code_numeral),big_co1399186613setsum(nat,code_code_numeral),A)),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)))),hAPP(fun(nat,code_code_numeral),code_code_numeral,suminf(code_code_numeral),A)),sequentially)). [resolve(5178,a,5152,a)].
% 13.50/13.49 Derived: -topological_space(code_code_numeral) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(fun(nat,code_code_numeral),fun(code_code_numeral,bool),sums(code_code_numeral),A),B)) | hBOOL(hAPP(filter(nat),bool,hAPP(code_code_numeral,fun(filter(nat),bool),hAPP(fun(nat,code_code_numeral),fun(code_code_numeral,fun(filter(nat),bool)),tendsto(nat,code_code_numeral),hAPP(fun(nat,fun(nat,bool)),fun(nat,code_code_numeral),hAPP(fun(fun(nat,bool),code_code_numeral),fun(fun(nat,fun(nat,bool)),fun(nat,code_code_numeral)),combb(fun(nat,bool),code_code_numeral,nat),hAPP(fun(nat,code_code_numeral),fun(fun(nat,bool),code_code_numeral),big_co1399186613setsum(nat,code_code_numeral),A)),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)))),B),sequentially)). [resolve(5178,a,5153,a)].
% 13.50/13.49 Derived: -topological_space(code_code_numeral) | hBOOL(hAPP(code_code_numeral,bool,hAPP(fun(nat,code_code_numeral),fun(code_code_numeral,bool),sums(code_code_numeral),A),B)) | -hBOOL(hAPP(filter(nat),bool,hAPP(code_code_numeral,fun(filter(nat),bool),hAPP(fun(nat,code_code_numeral),fun(code_code_numeral,fun(filter(nat),bool)),tendsto(nat,code_code_numeral),hAPP(fun(nat,fun(nat,bool)),fun(nat,code_code_numeral),hAPP(fun(fun(nat,bool),code_code_numeral),fun(fun(nat,fun(nat,bool)),fun(nat,code_code_numeral)),combb(fun(nat,bool),code_code_numeral,nat),hAPP(fun(nat,code_code_numeral),fun(fun(nat,bool),code_code_numeral),big_co1399186613setsum(nat,code_code_numeral),A)),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)))),B),sequentially)). [resolve(5178,a,5154,a)].
% 13.50/13.49 Derived: hAPP(fun(nat,bool),code_code_numeral,hAPP(fun(nat,code_code_numeral),fun(fun(nat,bool),code_code_numeral),big_co1399186613setsum(nat,code_code_numeral),hAPP(fun(nat,nat),fun(nat,code_code_numeral),hAPP(fun(nat,code_code_numeral),fun(fun(nat,nat),fun(nat,code_code_numeral)),combb(nat,code_code_numeral,nat),A),suc)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),B),C)) = hAPP(fun(nat,bool),code_code_numeral,hAPP(fun(nat,code_code_numeral),fun(fun(nat,bool),code_code_numeral),big_co1399186613setsum(nat,code_code_numeral),A),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,suc,B)),hAPP(nat,nat,suc,C))). [resolve(5178,a,5155,a)].
% 13.50/13.49 Derived: hAPP(fun(nat,bool),code_code_numeral,hAPP(fun(nat,code_code_numeral),fun(fun(nat,bool),code_code_numeral),big_co1399186613setsum(nat,code_code_numeral),hAPP(fun(nat,nat),fun(nat,code_code_numeral),hAPP(fun(nat,code_code_numeral),fun(fun(nat,nat),fun(nat,code_code_numeral)),combb(nat,code_code_numeral,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),code_code_numeral,hAPP(fun(nat,code_code_numeral),fun(fun(nat,bool),code_code_numeral),big_co1399186613setsum(nat,code_code_numeral),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(5178,a,5156,a)].
% 13.50/13.49 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | hAPP(fun(nat,bool),code_code_numeral,hAPP(fun(nat,code_code_numeral),fun(fun(nat,bool),code_code_numeral),big_co1399186613setsum(nat,code_code_numeral),C),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),A),B)) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),hAPP(nat,code_code_numeral,C,A)),hAPP(fun(nat,bool),code_code_numeral,hAPP(fun(nat,code_code_numeral),fun(fun(nat,bool),code_code_numeral),big_co1399186613setsum(nat,code_code_numeral),C),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,suc,A)),B))). [resolve(5178,a,5157,a)].
% 13.50/13.49 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,A)),B)) | hAPP(fun(nat,bool),code_code_numeral,hAPP(fun(nat,code_code_numeral),fun(fun(nat,bool),code_code_numeral),big_co1399186613setsum(nat,code_code_numeral),C),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),B),hAPP(nat,nat,suc,A))) = zero_zero(code_code_numeral). [resolve(5178,a,5158,a)].
% 13.50/13.49 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,A)),B)) | hAPP(fun(nat,bool),code_code_numeral,hAPP(fun(nat,code_code_numeral),fun(fun(nat,bool),code_code_numeral),big_co1399186613setsum(nat,code_code_numeral),C),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),B),hAPP(nat,nat,suc,A))) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),hAPP(fun(nat,bool),code_code_numeral,hAPP(fun(nat,code_code_numeral),fun(fun(nat,bool),code_code_numeral),big_co1399186613setsum(nat,code_code_numeral),C),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),B),A))),hAPP(nat,code_code_numeral,C,hAPP(nat,nat,suc,A))). [resolve(5178,a,5159,a)].
% 13.50/13.49 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),code_code_numeral,hAPP(fun(nat,code_code_numeral),fun(fun(nat,bool),code_code_numeral),big_co1399186613setsum(nat,code_code_numeral),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(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),hAPP(fun(nat,bool),code_code_numeral,hAPP(fun(nat,code_code_numeral),fun(fun(nat,bool),code_code_numeral),big_co1399186613setsum(nat,code_code_numeral),C),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),A),B))),hAPP(fun(nat,bool),code_code_numeral,hAPP(fun(nat,code_code_numeral),fun(fun(nat,bool),code_code_numeral),big_co1399186613setsum(nat,code_code_numeral),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(5178,a,5160,a)].
% 13.50/13.49 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,A)),B)) | hAPP(fun(nat,bool),code_code_numeral,hAPP(fun(nat,code_code_numeral),fun(fun(nat,bool),code_code_numeral),big_co1399186613setsum(nat,code_code_numeral),C),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),B),hAPP(nat,nat,suc,A))) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),hAPP(nat,code_code_numeral,C,B)),hAPP(fun(nat,bool),code_code_numeral,hAPP(fun(nat,code_code_numeral),fun(fun(nat,bool),code_code_numeral),big_co1399186613setsum(nat,code_code_numeral),hAPP(fun(nat,nat),fun(nat,code_code_numeral),hAPP(fun(nat,code_code_numeral),fun(fun(nat,nat),fun(nat,code_code_numeral)),combb(nat,code_code_numeral,nat),C),suc)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),B),A))). [resolve(5178,a,5162,a)].
% 13.50/13.49 Derived: hAPP(fun(product_prod(nat,nat),bool),code_code_numeral,hAPP(fun(product_prod(nat,nat),code_code_numeral),fun(fun(product_prod(nat,nat),bool),code_code_numeral),big_co1399186613setsum(product_prod(nat,nat),code_code_numeral),hAPP(fun(nat,fun(nat,code_code_numeral)),fun(product_prod(nat,nat),code_code_numeral),product_prod_case(nat,nat,code_code_numeral),A)),hAPP(fun(product_prod(nat,nat),bool),fun(product_prod(nat,nat),bool),collect(product_prod(nat,nat)),hAPP(fun(nat,fun(nat,bool)),fun(product_prod(nat,nat),bool),product_prod_case(nat,nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),hAPP(fun(nat,fun(nat,fun(nat,bool))),fun(nat,fun(nat,fun(nat,bool))),combc(nat,nat,fun(nat,bool)),hAPP(fun(nat,fun(nat,fun(nat,bool))),fun(nat,fun(nat,fun(nat,bool))),hAPP(fun(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool))),fun(fun(nat,fun(nat,fun(nat,bool))),fun(nat,fun(nat,fun(nat,bool)))),combb(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),nat),combc(nat,nat,bool)),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,fun(nat,bool))),hAPP(fun(fun(nat,nat),fun(nat,fun(nat,bool))),fun(fun(nat,fun(nat,nat)),fun(nat,fun(nat,fun(nat,bool)))),combb(fun(nat,nat),fun(nat,fun(nat,bool)),nat),hAPP(fun(nat,fun(nat,bool)),fun(fun(nat,nat),fun(nat,fun(nat,bool))),combb(nat,fun(nat,bool),nat),ord_less(nat))),plus_plus(nat)))),B)))) = hAPP(fun(nat,bool),code_code_numeral,hAPP(fun(nat,code_code_numeral),fun(fun(nat,bool),code_code_numeral),big_co1399186613setsum(nat,code_code_numeral),hAPP(fun(nat,fun(nat,bool)),fun(nat,code_code_numeral),hAPP(fun(nat,fun(fun(nat,bool),code_code_numeral)),fun(fun(nat,fun(nat,bool)),fun(nat,code_code_numeral)),combs(nat,fun(nat,bool),code_code_numeral),hAPP(fun(nat,fun(nat,code_code_numeral)),fun(nat,fun(fun(nat,bool),code_code_numeral)),hAPP(fun(fun(nat,code_code_numeral),fun(fun(nat,bool),code_code_numeral)),fun(fun(nat,fun(nat,code_code_numeral)),fun(nat,fun(fun(nat,bool),code_code_numeral))),combb(fun(nat,code_code_numeral),fun(fun(nat,bool),code_code_numeral),nat),big_co1399186613setsum(nat,code_code_numeral)),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,code_code_numeral)),hAPP(fun(fun(nat,nat),fun(nat,code_code_numeral)),fun(fun(nat,fun(nat,nat)),fun(nat,fun(nat,code_code_numeral))),combb(fun(nat,nat),fun(nat,code_code_numeral),nat),hAPP(fun(nat,fun(nat,code_code_numeral)),fun(fun(nat,nat),fun(nat,code_code_numeral)),combs(nat,nat,code_code_numeral),A)),minus_minus(nat)))),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),zero_zero(nat)))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),B)). [resolve(5178,a,5163,a)].
% 13.50/13.49 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),f771(A,code_code_numeral,C,D,B)),B)) | hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),D),B) = hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),C),B). [resolve(5178,a,5164,a)].
% 13.50/13.49 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(A,code_code_numeral,C,f771(A,code_code_numeral,D,C,B)) != hAPP(A,code_code_numeral,D,f771(A,code_code_numeral,D,C,B)) | hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),C),B) = hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),D),B). [resolve(5178,a,5165,a)].
% 13.50/13.49 Derived: hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f772(A,code_code_numeral,B,C)),C)) | hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),B),C) = zero_zero(code_code_numeral). [resolve(5178,a,5166,a)].
% 13.50/13.50 Derived: hAPP(A,code_code_numeral,B,f772(A,code_code_numeral,B,C)) != zero_zero(code_code_numeral) | hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),B),C) = zero_zero(code_code_numeral). [resolve(5178,a,5167,a)].
% 13.50/13.50 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),A,zero_zero(code_code_numeral)),zero_zero(code_code_numeral))) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),A,f788(B,code_code_numeral,C,D,E,A)),f790(B,code_code_numeral,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),f792(B,code_code_numeral,C,D,E,A)),E)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),A,hAPP(fun(B,bool),code_code_numeral,hAPP(fun(B,code_code_numeral),fun(fun(B,bool),code_code_numeral),big_co1399186613setsum(B,code_code_numeral),C),E)),hAPP(fun(B,bool),code_code_numeral,hAPP(fun(B,code_code_numeral),fun(fun(B,bool),code_code_numeral),big_co1399186613setsum(B,code_code_numeral),D),E))). [resolve(5178,a,5168,a)].
% 13.50/13.50 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),A,zero_zero(code_code_numeral)),zero_zero(code_code_numeral))) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),A,f788(B,code_code_numeral,C,D,E,A)),f790(B,code_code_numeral,C,D,E,A))) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),E)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),A,hAPP(B,code_code_numeral,C,f792(B,code_code_numeral,C,D,E,A))),hAPP(B,code_code_numeral,D,f792(B,code_code_numeral,C,D,E,A)))) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),A,hAPP(fun(B,bool),code_code_numeral,hAPP(fun(B,code_code_numeral),fun(fun(B,bool),code_code_numeral),big_co1399186613setsum(B,code_code_numeral),C),E)),hAPP(fun(B,bool),code_code_numeral,hAPP(fun(B,code_code_numeral),fun(fun(B,bool),code_code_numeral),big_co1399186613setsum(B,code_code_numeral),D),E))). [resolve(5178,a,5169,a)].
% 13.50/13.50 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),A,zero_zero(code_code_numeral)),zero_zero(code_code_numeral))) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),A,f789(B,code_code_numeral,C,D,E,A)),f791(B,code_code_numeral,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),f792(B,code_code_numeral,C,D,E,A)),E)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),A,hAPP(fun(B,bool),code_code_numeral,hAPP(fun(B,code_code_numeral),fun(fun(B,bool),code_code_numeral),big_co1399186613setsum(B,code_code_numeral),C),E)),hAPP(fun(B,bool),code_code_numeral,hAPP(fun(B,code_code_numeral),fun(fun(B,bool),code_code_numeral),big_co1399186613setsum(B,code_code_numeral),D),E))). [resolve(5178,a,5170,a)].
% 13.50/13.50 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),A,zero_zero(code_code_numeral)),zero_zero(code_code_numeral))) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),A,f789(B,code_code_numeral,C,D,E,A)),f791(B,code_code_numeral,C,D,E,A))) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),E)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),A,hAPP(B,code_code_numeral,C,f792(B,code_code_numeral,C,D,E,A))),hAPP(B,code_code_numeral,D,f792(B,code_code_numeral,C,D,E,A)))) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),A,hAPP(fun(B,bool),code_code_numeral,hAPP(fun(B,code_code_numeral),fun(fun(B,bool),code_code_numeral),big_co1399186613setsum(B,code_code_numeral),C),E)),hAPP(fun(B,bool),code_code_numeral,hAPP(fun(B,code_code_numeral),fun(fun(B,bool),code_code_numeral),big_co1399186613setsum(B,code_code_numeral),D),E))). [resolve(5178,a,5171,a)].
% 13.50/13.51 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),A,zero_zero(code_code_numeral)),zero_zero(code_code_numeral))) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),A,hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),f788(B,code_code_numeral,C,D,E,A)),f789(B,code_code_numeral,C,D,E,A))),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),f790(B,code_code_numeral,C,D,E,A)),f791(B,code_code_numeral,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),f792(B,code_code_numeral,C,D,E,A)),E)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),A,hAPP(fun(B,bool),code_code_numeral,hAPP(fun(B,code_code_numeral),fun(fun(B,bool),code_code_numeral),big_co1399186613setsum(B,code_code_numeral),C),E)),hAPP(fun(B,bool),code_code_numeral,hAPP(fun(B,code_code_numeral),fun(fun(B,bool),code_code_numeral),big_co1399186613setsum(B,code_code_numeral),D),E))). [resolve(5178,a,5172,a)].
% 13.50/13.51 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),A,zero_zero(code_code_numeral)),zero_zero(code_code_numeral))) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),A,hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),f788(B,code_code_numeral,C,D,E,A)),f789(B,code_code_numeral,C,D,E,A))),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),f790(B,code_code_numeral,C,D,E,A)),f791(B,code_code_numeral,C,D,E,A)))) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),E)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),A,hAPP(B,code_code_numeral,C,f792(B,code_code_numeral,C,D,E,A))),hAPP(B,code_code_numeral,D,f792(B,code_code_numeral,C,D,E,A)))) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),A,hAPP(fun(B,bool),code_code_numeral,hAPP(fun(B,code_code_numeral),fun(fun(B,bool),code_code_numeral),big_co1399186613setsum(B,code_code_numeral),C),E)),hAPP(fun(B,bool),code_code_numeral,hAPP(fun(B,code_code_numeral),fun(fun(B,bool),code_code_numeral),big_co1399186613setsum(B,code_code_numeral),D),E))). [resolve(5178,a,5173,a)].
% 13.50/13.51 5179 comm_monoid_add(quickcheck_code_int) # label(arity_Quickcheck__Narrowing_Ocode__int___Groups_Ocomm__monoid__add) # label(axiom). [assumption].
% 13.50/13.51 Derived: big_co1399186613setsum(A,quickcheck_code_int) = ti(fun(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int)),big_co1399186613setsum(A,quickcheck_code_int)). [resolve(5179,a,5059,a)].
% 13.50/13.51 Derived: -topological_space(quickcheck_code_int) | the(quickcheck_code_int) = ti(fun(fun(quickcheck_code_int,bool),quickcheck_code_int),the(quickcheck_code_int)). [resolve(5179,a,5060,a)].
% 13.50/13.51 Derived: -topological_space(quickcheck_code_int) | suminf(quickcheck_code_int) = ti(fun(fun(nat,quickcheck_code_int),quickcheck_code_int),suminf(quickcheck_code_int)). [resolve(5179,a,5061,a)].
% 13.50/13.51 Derived: -topological_space(quickcheck_code_int) | summable(quickcheck_code_int) = ti(fun(fun(nat,quickcheck_code_int),bool),summable(quickcheck_code_int)). [resolve(5179,a,5062,a)].
% 13.50/13.51 Derived: -topological_space(quickcheck_code_int) | sums(quickcheck_code_int) = ti(fun(fun(nat,quickcheck_code_int),fun(quickcheck_code_int,bool)),sums(quickcheck_code_int)). [resolve(5179,a,5063,a)].
% 13.50/13.51 Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),A),zero_zero(quickcheck_code_int)) = ti(quickcheck_code_int,A). [resolve(5179,a,5064,a)].
% 13.50/13.52 Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),zero_zero(quickcheck_code_int)),A) = ti(quickcheck_code_int,A). [resolve(5179,a,5065,a)].
% 13.50/13.52 Derived: -comm_monoid_mult(quickcheck_code_int) | hAPP(fun(nat,bool),quickcheck_code_int,hAPP(fun(nat,quickcheck_code_int),fun(fun(nat,bool),quickcheck_code_int),big_co302546470etprod(nat,quickcheck_code_int),A),B) = hAPP(fun(int,bool),quickcheck_code_int,hAPP(fun(int,quickcheck_code_int),fun(fun(int,bool),quickcheck_code_int),big_co302546470etprod(int,quickcheck_code_int),hAPP(fun(int,nat),fun(int,quickcheck_code_int),hAPP(fun(nat,quickcheck_code_int),fun(fun(int,nat),fun(int,quickcheck_code_int)),combb(nat,quickcheck_code_int,int),A),nat_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)),B)). [resolve(5179,a,5066,a)].
% 13.50/13.52 Derived: -comm_monoid_mult(quickcheck_code_int) | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A)) | hAPP(fun(nat,bool),quickcheck_code_int,hAPP(fun(nat,quickcheck_code_int),fun(fun(nat,bool),quickcheck_code_int),big_co302546470etprod(nat,quickcheck_code_int),hAPP(fun(nat,int),fun(nat,quickcheck_code_int),hAPP(fun(int,quickcheck_code_int),fun(fun(nat,int),fun(nat,quickcheck_code_int)),combb(int,quickcheck_code_int,nat),B),semiring_1_of_nat(int))),hAPP(fun(int,bool),fun(nat,bool),hAPP(fun(int,nat),fun(fun(int,bool),fun(nat,bool)),image(int,nat),nat_1),A)) = hAPP(fun(int,bool),quickcheck_code_int,hAPP(fun(int,quickcheck_code_int),fun(fun(int,bool),quickcheck_code_int),big_co302546470etprod(int,quickcheck_code_int),B),A). [resolve(5179,a,5067,a)].
% 13.50/13.52 Derived: -comm_monoid_mult(quickcheck_code_int) | A != B | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),f486(quickcheck_code_int,C,D,B,A))) | hAPP(fun(int,bool),quickcheck_code_int,hAPP(fun(int,quickcheck_code_int),fun(fun(int,bool),quickcheck_code_int),big_co302546470etprod(int,quickcheck_code_int),D),A) = hAPP(fun(int,bool),quickcheck_code_int,hAPP(fun(int,quickcheck_code_int),fun(fun(int,bool),quickcheck_code_int),big_co302546470etprod(int,quickcheck_code_int),C),B). [resolve(5179,a,5068,a)].
% 13.50/13.52 Derived: -comm_monoid_mult(quickcheck_code_int) | A != B | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A)) | hAPP(int,quickcheck_code_int,C,f486(quickcheck_code_int,D,C,B,A)) != hAPP(int,quickcheck_code_int,D,f486(quickcheck_code_int,D,C,B,A)) | hAPP(fun(int,bool),quickcheck_code_int,hAPP(fun(int,quickcheck_code_int),fun(fun(int,bool),quickcheck_code_int),big_co302546470etprod(int,quickcheck_code_int),C),A) = hAPP(fun(int,bool),quickcheck_code_int,hAPP(fun(int,quickcheck_code_int),fun(fun(int,bool),quickcheck_code_int),big_co302546470etprod(int,quickcheck_code_int),D),B). [resolve(5179,a,5069,a)].
% 13.50/13.52 Derived: -t2_space(quickcheck_code_int) | hAPP(fun(nat,quickcheck_code_int),quickcheck_code_int,suminf(quickcheck_code_int),hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),combk(quickcheck_code_int,nat),zero_zero(quickcheck_code_int))) = zero_zero(quickcheck_code_int). [resolve(5179,a,5070,a)].
% 13.50/13.52 Derived: -topological_space(quickcheck_code_int) | hBOOL(hAPP(fun(nat,quickcheck_code_int),bool,summable(quickcheck_code_int),hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),combk(quickcheck_code_int,nat),zero_zero(quickcheck_code_int)))). [resolve(5179,a,5071,a)].
% 13.50/13.52 Derived: -topological_space(quickcheck_code_int) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(fun(nat,quickcheck_code_int),fun(quickcheck_code_int,bool),sums(quickcheck_code_int),hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),combk(quickcheck_code_int,nat),zero_zero(quickcheck_code_int))),zero_zero(quickcheck_code_int))). [resolve(5179,a,5072,a)].
% 13.50/13.52 Derived: -t2_space(quickcheck_code_int) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(fun(nat,quickcheck_code_int),fun(quickcheck_code_int,bool),sums(quickcheck_code_int),A),B)) | hAPP(fun(nat,quickcheck_code_int),quickcheck_code_int,suminf(quickcheck_code_int),A) = ti(quickcheck_code_int,B). [resolve(5179,a,5073,a)].
% 13.50/13.52 Derived: -topological_space(quickcheck_code_int) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(fun(nat,quickcheck_code_int),fun(quickcheck_code_int,bool),sums(quickcheck_code_int),A),B)) | hBOOL(hAPP(fun(nat,quickcheck_code_int),bool,summable(quickcheck_code_int),A)). [resolve(5179,a,5074,a)].
% 13.50/13.52 Derived: -topological_space(quickcheck_code_int) | -hBOOL(hAPP(fun(nat,quickcheck_code_int),bool,summable(quickcheck_code_int),A)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(fun(nat,quickcheck_code_int),fun(quickcheck_code_int,bool),sums(quickcheck_code_int),A),f513(quickcheck_code_int,A))). [resolve(5179,a,5075,a)].
% 13.50/13.52 Derived: -t2_space(quickcheck_code_int) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(fun(nat,quickcheck_code_int),fun(quickcheck_code_int,bool),sums(quickcheck_code_int),A),B)) | hBOOL(hAPP(fun(nat,quickcheck_code_int),bool,summable(quickcheck_code_int),A)). [resolve(5179,a,5077,a)].
% 13.50/13.52 Derived: -t2_space(quickcheck_code_int) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(fun(nat,quickcheck_code_int),fun(quickcheck_code_int,bool),sums(quickcheck_code_int),A),B)) | -hBOOL(hAPP(fun(nat,quickcheck_code_int),bool,summable(quickcheck_code_int),A)) | hAPP(fun(nat,quickcheck_code_int),quickcheck_code_int,suminf(quickcheck_code_int),A) != ti(quickcheck_code_int,B). [resolve(5179,a,5079,a)].
% 13.50/13.52 Derived: -t2_space(quickcheck_code_int) | -hBOOL(hAPP(fun(nat,quickcheck_code_int),bool,summable(quickcheck_code_int),A)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(fun(nat,quickcheck_code_int),fun(quickcheck_code_int,bool),sums(quickcheck_code_int),A),hAPP(fun(nat,quickcheck_code_int),quickcheck_code_int,suminf(quickcheck_code_int),A))). [resolve(5179,a,5080,a)].
% 13.50/13.52 Derived: -topological_space(quickcheck_code_int) | hAPP(nat,quickcheck_code_int,A,zero_zero(nat)) != zero_zero(quickcheck_code_int) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(fun(nat,quickcheck_code_int),fun(quickcheck_code_int,bool),sums(quickcheck_code_int),hAPP(fun(nat,nat),fun(nat,quickcheck_code_int),hAPP(fun(nat,quickcheck_code_int),fun(fun(nat,nat),fun(nat,quickcheck_code_int)),combb(nat,quickcheck_code_int,nat),A),suc)),B)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(fun(nat,quickcheck_code_int),fun(quickcheck_code_int,bool),sums(quickcheck_code_int),A),B)). [resolve(5179,a,5081,a)].
% 13.50/13.52 Derived: -topological_space(quickcheck_code_int) | hAPP(fun(nat,quickcheck_code_int),quickcheck_code_int,suminf(quickcheck_code_int),A) = hAPP(fun(quickcheck_code_int,bool),quickcheck_code_int,the(quickcheck_code_int),hAPP(fun(nat,quickcheck_code_int),fun(quickcheck_code_int,bool),sums(quickcheck_code_int),A)). [resolve(5179,a,5082,a)].
% 13.50/13.52 Derived: -power(quickcheck_code_int) | hAPP(fun(nat,bool),quickcheck_code_int,hAPP(fun(nat,quickcheck_code_int),fun(fun(nat,bool),quickcheck_code_int),big_co1399186613setsum(nat,quickcheck_code_int),hAPP(fun(nat,quickcheck_code_int),fun(nat,quickcheck_code_int),hAPP(fun(nat,fun(quickcheck_code_int,quickcheck_code_int)),fun(fun(nat,quickcheck_code_int),fun(nat,quickcheck_code_int)),combs(nat,quickcheck_code_int,quickcheck_code_int),hAPP(fun(nat,quickcheck_code_int),fun(nat,fun(quickcheck_code_int,quickcheck_code_int)),hAPP(fun(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int)),fun(fun(nat,quickcheck_code_int),fun(nat,fun(quickcheck_code_int,quickcheck_code_int))),combb(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),nat),times_times(quickcheck_code_int)),hAPP(fun(nat,nat),fun(nat,quickcheck_code_int),hAPP(fun(nat,quickcheck_code_int),fun(fun(nat,nat),fun(nat,quickcheck_code_int)),combb(nat,quickcheck_code_int,nat),hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A)),hAPP(nat,fun(nat,nat),minus_minus(nat),B)))),hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),C))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,suc,B))) = hAPP(fun(nat,bool),quickcheck_code_int,hAPP(fun(nat,quickcheck_code_int),fun(fun(nat,bool),quickcheck_code_int),big_co1399186613setsum(nat,quickcheck_code_int),hAPP(fun(nat,quickcheck_code_int),fun(nat,quickcheck_code_int),hAPP(fun(nat,fun(quickcheck_code_int,quickcheck_code_int)),fun(fun(nat,quickcheck_code_int),fun(nat,quickcheck_code_int)),combs(nat,quickcheck_code_int,quickcheck_code_int),hAPP(fun(nat,quickcheck_code_int),fun(nat,fun(quickcheck_code_int,quickcheck_code_int)),hAPP(fun(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int)),fun(fun(nat,quickcheck_code_int),fun(nat,fun(quickcheck_code_int,quickcheck_code_int))),combb(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),nat),times_times(quickcheck_code_int)),hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A))),hAPP(fun(nat,nat),fun(nat,quickcheck_code_int),hAPP(fun(nat,quickcheck_code_int),fun(fun(nat,nat),fun(nat,quickcheck_code_int)),combb(nat,quickcheck_code_int,nat),hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),C)),hAPP(nat,fun(nat,nat),minus_minus(nat),B)))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,suc,B))). [resolve(5179,a,5083,a)].
% 13.50/13.52 Derived: hAPP(fun(nat,bool),quickcheck_code_int,hAPP(fun(nat,quickcheck_code_int),fun(fun(nat,bool),quickcheck_code_int),big_co1399186613setsum(nat,quickcheck_code_int),hAPP(fun(nat,fun(nat,bool)),fun(nat,quickcheck_code_int),hAPP(fun(fun(nat,bool),quickcheck_code_int),fun(fun(nat,fun(nat,bool)),fun(nat,quickcheck_code_int)),combb(fun(nat,bool),quickcheck_code_int,nat),hAPP(fun(nat,quickcheck_code_int),fun(fun(nat,bool),quickcheck_code_int),big_co1399186613setsum(nat,quickcheck_code_int),A)),hAPP(fun(nat,nat),fun(nat,fun(nat,bool)),hAPP(fun(nat,fun(nat,fun(nat,bool))),fun(fun(nat,nat),fun(nat,fun(nat,bool))),combs(nat,nat,fun(nat,bool)),hAPP(fun(nat,nat),fun(nat,fun(nat,fun(nat,bool))),hAPP(fun(nat,fun(nat,fun(nat,bool))),fun(fun(nat,nat),fun(nat,fun(nat,fun(nat,bool)))),combb(nat,fun(nat,fun(nat,bool)),nat),ord_atLeastLessThan(nat)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),times_times(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),plus_plus(nat)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),times_times(nat)),B))),B)))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),C)) = hAPP(fun(nat,bool),quickcheck_code_int,hAPP(fun(nat,quickcheck_code_int),fun(fun(nat,bool),quickcheck_code_int),big_co1399186613setsum(nat,quickcheck_code_int),A),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),C),B))). [resolve(5179,a,5084,a)].
% 13.50/13.52 Derived: hAPP(fun(nat,bool),quickcheck_code_int,hAPP(fun(nat,quickcheck_code_int),fun(fun(nat,bool),quickcheck_code_int),big_co1399186613setsum(nat,quickcheck_code_int),hAPP(fun(nat,nat),fun(nat,quickcheck_code_int),hAPP(fun(nat,quickcheck_code_int),fun(fun(nat,nat),fun(nat,quickcheck_code_int)),combb(nat,quickcheck_code_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_atLeastLessThan(nat),C),D)) = hAPP(fun(nat,bool),quickcheck_code_int,hAPP(fun(nat,quickcheck_code_int),fun(fun(nat,bool),quickcheck_code_int),big_co1399186613setsum(nat,quickcheck_code_int),A),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(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(5179,a,5085,a)].
% 13.50/13.52 Derived: hAPP(fun(nat,bool),quickcheck_code_int,hAPP(fun(nat,quickcheck_code_int),fun(fun(nat,bool),quickcheck_code_int),big_co1399186613setsum(nat,quickcheck_code_int),A),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),C))) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),hAPP(fun(nat,bool),quickcheck_code_int,hAPP(fun(nat,quickcheck_code_int),fun(fun(nat,bool),quickcheck_code_int),big_co1399186613setsum(nat,quickcheck_code_int),hAPP(fun(nat,nat),fun(nat,quickcheck_code_int),hAPP(fun(nat,quickcheck_code_int),fun(fun(nat,nat),fun(nat,quickcheck_code_int)),combb(nat,quickcheck_code_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)),C))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),B))),hAPP(fun(nat,bool),quickcheck_code_int,hAPP(fun(nat,quickcheck_code_int),fun(fun(nat,bool),quickcheck_code_int),big_co1399186613setsum(nat,quickcheck_code_int),A),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),C))). [resolve(5179,a,5086,a)].
% 13.50/13.52 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),hAPP(quickcheck_code_int,fun(A,quickcheck_code_int),hAPP(fun(A,fun(quickcheck_code_int,quickcheck_code_int)),fun(quickcheck_code_int,fun(A,quickcheck_code_int)),combc(A,quickcheck_code_int,quickcheck_code_int),hAPP(fun(A,quickcheck_code_int),fun(A,fun(quickcheck_code_int,quickcheck_code_int)),hAPP(fun(A,fun(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int))),fun(fun(A,quickcheck_code_int),fun(A,fun(quickcheck_code_int,quickcheck_code_int))),combs(A,quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int)),hAPP(fun(A,bool),fun(A,fun(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int))),hAPP(fun(bool,fun(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int))),fun(fun(A,bool),fun(A,fun(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int)))),combb(bool,fun(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int)),A),if(quickcheck_code_int)),C)),D)),zero_zero(quickcheck_code_int))),B) = hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),D),hAPP(fun(A,bool),fun(A,bool),collect(A),hAPP(fun(A,bool),fun(A,bool),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))),C))). [resolve(5179,a,5087,a)].
% 13.50/13.52 Derived: hAPP(fun(nat,bool),quickcheck_code_int,hAPP(fun(nat,quickcheck_code_int),fun(fun(nat,bool),quickcheck_code_int),big_co1399186613setsum(nat,quickcheck_code_int),hAPP(fun(nat,nat),fun(nat,quickcheck_code_int),hAPP(fun(nat,quickcheck_code_int),fun(fun(nat,nat),fun(nat,quickcheck_code_int)),combb(nat,quickcheck_code_int,nat),A),suc)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),B),C)) = hAPP(fun(nat,bool),quickcheck_code_int,hAPP(fun(nat,quickcheck_code_int),fun(fun(nat,bool),quickcheck_code_int),big_co1399186613setsum(nat,quickcheck_code_int),A),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),hAPP(nat,nat,suc,B)),hAPP(nat,nat,suc,C))). [resolve(5179,a,5089,a)].
% 13.50/13.52 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(C,bool),quickcheck_code_int,hAPP(fun(C,quickcheck_code_int),fun(fun(C,bool),quickcheck_code_int),big_co1399186613setsum(C,quickcheck_code_int),hAPP(fun(C,fun(A,bool)),fun(C,quickcheck_code_int),hAPP(fun(C,fun(fun(A,bool),quickcheck_code_int)),fun(fun(C,fun(A,bool)),fun(C,quickcheck_code_int)),combs(C,fun(A,bool),quickcheck_code_int),hAPP(fun(C,fun(A,quickcheck_code_int)),fun(C,fun(fun(A,bool),quickcheck_code_int)),hAPP(fun(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int)),fun(fun(C,fun(A,quickcheck_code_int)),fun(C,fun(fun(A,bool),quickcheck_code_int))),combb(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),C),big_co1399186613setsum(A,quickcheck_code_int)),hAPP(fun(A,fun(C,quickcheck_code_int)),fun(C,fun(A,quickcheck_code_int)),combc(A,C,quickcheck_code_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) = hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),hAPP(fun(A,fun(C,bool)),fun(A,quickcheck_code_int),hAPP(fun(A,fun(fun(C,bool),quickcheck_code_int)),fun(fun(A,fun(C,bool)),fun(A,quickcheck_code_int)),combs(A,fun(C,bool),quickcheck_code_int),hAPP(fun(A,fun(C,quickcheck_code_int)),fun(A,fun(fun(C,bool),quickcheck_code_int)),hAPP(fun(fun(C,quickcheck_code_int),fun(fun(C,bool),quickcheck_code_int)),fun(fun(A,fun(C,quickcheck_code_int)),fun(A,fun(fun(C,bool),quickcheck_code_int))),combb(fun(C,quickcheck_code_int),fun(fun(C,bool),quickcheck_code_int),A),big_co1399186613setsum(C,quickcheck_code_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). [resolve(5179,a,5090,a)].
% 13.50/13.52 Derived: hAPP(nat,quickcheck_code_int,A,zero_zero(nat)) != zero_zero(quickcheck_code_int) | hAPP(fun(nat,bool),quickcheck_code_int,hAPP(fun(nat,quickcheck_code_int),fun(fun(nat,bool),quickcheck_code_int),big_co1399186613setsum(nat,quickcheck_code_int),A),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),hAPP(nat,nat,suc,zero_zero(nat))),B)) = hAPP(fun(nat,bool),quickcheck_code_int,hAPP(fun(nat,quickcheck_code_int),fun(fun(nat,bool),quickcheck_code_int),big_co1399186613setsum(nat,quickcheck_code_int),A),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),B)). [resolve(5179,a,5091,a)].
% 13.50/13.52 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),C)) | hAPP(fun(nat,bool),quickcheck_code_int,hAPP(fun(nat,quickcheck_code_int),fun(fun(nat,bool),quickcheck_code_int),big_co1399186613setsum(nat,quickcheck_code_int),D),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),A),C)) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),hAPP(fun(nat,bool),quickcheck_code_int,hAPP(fun(nat,quickcheck_code_int),fun(fun(nat,bool),quickcheck_code_int),big_co1399186613setsum(nat,quickcheck_code_int),D),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),A),B))),hAPP(fun(nat,bool),quickcheck_code_int,hAPP(fun(nat,quickcheck_code_int),fun(fun(nat,bool),quickcheck_code_int),big_co1399186613setsum(nat,quickcheck_code_int),D),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),B),C))). [resolve(5179,a,5092,a)].
% 13.50/13.52 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | hAPP(fun(nat,bool),quickcheck_code_int,hAPP(fun(nat,quickcheck_code_int),fun(fun(nat,bool),quickcheck_code_int),big_co1399186613setsum(nat,quickcheck_code_int),C),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),A),B)) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),hAPP(nat,quickcheck_code_int,C,A)),hAPP(fun(nat,bool),quickcheck_code_int,hAPP(fun(nat,quickcheck_code_int),fun(fun(nat,bool),quickcheck_code_int),big_co1399186613setsum(nat,quickcheck_code_int),C),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),hAPP(nat,nat,suc,A)),B))). [resolve(5179,a,5093,a)].
% 13.50/13.52 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | hAPP(fun(nat,bool),quickcheck_code_int,hAPP(fun(nat,quickcheck_code_int),fun(fun(nat,bool),quickcheck_code_int),big_co1399186613setsum(nat,quickcheck_code_int),C),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),B),hAPP(nat,nat,suc,A))) = zero_zero(quickcheck_code_int). [resolve(5179,a,5094,a)].
% 13.50/13.52 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | hAPP(fun(nat,bool),quickcheck_code_int,hAPP(fun(nat,quickcheck_code_int),fun(fun(nat,bool),quickcheck_code_int),big_co1399186613setsum(nat,quickcheck_code_int),C),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),B),hAPP(nat,nat,suc,A))) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),hAPP(fun(nat,bool),quickcheck_code_int,hAPP(fun(nat,quickcheck_code_int),fun(fun(nat,bool),quickcheck_code_int),big_co1399186613setsum(nat,quickcheck_code_int),C),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),B),A))),hAPP(nat,quickcheck_code_int,C,A)). [resolve(5179,a,5095,a)].
% 13.50/13.52 Derived: hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),C),B) = zero_zero(quickcheck_code_int). [resolve(5179,a,5096,a)].
% 13.50/13.52 Derived: hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),hAPP(fun(B,bool),fun(A,quickcheck_code_int),hAPP(fun(A,fun(fun(B,bool),quickcheck_code_int)),fun(fun(B,bool),fun(A,quickcheck_code_int)),combc(A,fun(B,bool),quickcheck_code_int),hAPP(fun(A,fun(B,quickcheck_code_int)),fun(A,fun(fun(B,bool),quickcheck_code_int)),hAPP(fun(fun(B,quickcheck_code_int),fun(fun(B,bool),quickcheck_code_int)),fun(fun(A,fun(B,quickcheck_code_int)),fun(A,fun(fun(B,bool),quickcheck_code_int))),combb(fun(B,quickcheck_code_int),fun(fun(B,bool),quickcheck_code_int),A),big_co1399186613setsum(B,quickcheck_code_int)),hAPP(fun(B,fun(A,quickcheck_code_int)),fun(A,fun(B,quickcheck_code_int)),combc(B,A,quickcheck_code_int),C))),D)),E) = hAPP(fun(B,bool),quickcheck_code_int,hAPP(fun(B,quickcheck_code_int),fun(fun(B,bool),quickcheck_code_int),big_co1399186613setsum(B,quickcheck_code_int),hAPP(fun(A,bool),fun(B,quickcheck_code_int),hAPP(fun(B,fun(fun(A,bool),quickcheck_code_int)),fun(fun(A,bool),fun(B,quickcheck_code_int)),combc(B,fun(A,bool),quickcheck_code_int),hAPP(fun(B,fun(A,quickcheck_code_int)),fun(B,fun(fun(A,bool),quickcheck_code_int)),hAPP(fun(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int)),fun(fun(B,fun(A,quickcheck_code_int)),fun(B,fun(fun(A,bool),quickcheck_code_int))),combb(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),B),big_co1399186613setsum(A,quickcheck_code_int)),C)),E)),D). [resolve(5179,a,5098,a)].
% 13.60/13.52 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),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),hAPP(quickcheck_code_int,fun(A,quickcheck_code_int),hAPP(fun(A,fun(quickcheck_code_int,quickcheck_code_int)),fun(quickcheck_code_int,fun(A,quickcheck_code_int)),combc(A,quickcheck_code_int,quickcheck_code_int),hAPP(fun(A,quickcheck_code_int),fun(A,fun(quickcheck_code_int,quickcheck_code_int)),hAPP(fun(A,fun(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int))),fun(fun(A,quickcheck_code_int),fun(A,fun(quickcheck_code_int,quickcheck_code_int))),combs(A,quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int)),hAPP(fun(A,bool),fun(A,fun(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int))),hAPP(fun(bool,fun(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int))),fun(fun(A,bool),fun(A,fun(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int)))),combb(bool,fun(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int)),A),if(quickcheck_code_int)),hAPP(A,fun(A,bool),fequal(A),C))),D)),zero_zero(quickcheck_code_int))),B) = hAPP(A,quickcheck_code_int,D,C). [resolve(5179,a,5099,a)].
% 13.60/13.52 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),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),hAPP(quickcheck_code_int,fun(A,quickcheck_code_int),hAPP(fun(A,fun(quickcheck_code_int,quickcheck_code_int)),fun(quickcheck_code_int,fun(A,quickcheck_code_int)),combc(A,quickcheck_code_int,quickcheck_code_int),hAPP(fun(A,quickcheck_code_int),fun(A,fun(quickcheck_code_int,quickcheck_code_int)),hAPP(fun(A,fun(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int))),fun(fun(A,quickcheck_code_int),fun(A,fun(quickcheck_code_int,quickcheck_code_int))),combs(A,quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int)),hAPP(fun(A,bool),fun(A,fun(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int))),hAPP(fun(bool,fun(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int))),fun(fun(A,bool),fun(A,fun(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int)))),combb(bool,fun(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int)),A),if(quickcheck_code_int)),hAPP(A,fun(A,bool),fequal(A),C))),D)),zero_zero(quickcheck_code_int))),B) = zero_zero(quickcheck_code_int). [resolve(5179,a,5100,a)].
% 13.60/13.52 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),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),hAPP(quickcheck_code_int,fun(A,quickcheck_code_int),hAPP(fun(A,fun(quickcheck_code_int,quickcheck_code_int)),fun(quickcheck_code_int,fun(A,quickcheck_code_int)),combc(A,quickcheck_code_int,quickcheck_code_int),hAPP(fun(A,quickcheck_code_int),fun(A,fun(quickcheck_code_int,quickcheck_code_int)),hAPP(fun(A,fun(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int))),fun(fun(A,quickcheck_code_int),fun(A,fun(quickcheck_code_int,quickcheck_code_int))),combs(A,quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int)),hAPP(fun(A,bool),fun(A,fun(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int))),hAPP(fun(bool,fun(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int))),fun(fun(A,bool),fun(A,fun(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int)))),combb(bool,fun(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int)),A),if(quickcheck_code_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)),zero_zero(quickcheck_code_int))),B) = hAPP(A,quickcheck_code_int,D,C). [resolve(5179,a,5101,a)].
% 13.60/13.52 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),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),hAPP(quickcheck_code_int,fun(A,quickcheck_code_int),hAPP(fun(A,fun(quickcheck_code_int,quickcheck_code_int)),fun(quickcheck_code_int,fun(A,quickcheck_code_int)),combc(A,quickcheck_code_int,quickcheck_code_int),hAPP(fun(A,quickcheck_code_int),fun(A,fun(quickcheck_code_int,quickcheck_code_int)),hAPP(fun(A,fun(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int))),fun(fun(A,quickcheck_code_int),fun(A,fun(quickcheck_code_int,quickcheck_code_int))),combs(A,quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int)),hAPP(fun(A,bool),fun(A,fun(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int))),hAPP(fun(bool,fun(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int))),fun(fun(A,bool),fun(A,fun(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int)))),combb(bool,fun(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int)),A),if(quickcheck_code_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)),zero_zero(quickcheck_code_int))),B) = zero_zero(quickcheck_code_int). [resolve(5179,a,5102,a)].
% 13.60/13.52 Derived: hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),hAPP(quickcheck_code_int,fun(A,quickcheck_code_int),combk(quickcheck_code_int,A),zero_zero(quickcheck_code_int))),B) = zero_zero(quickcheck_code_int). [resolve(5179,a,5103,a)].
% 13.60/13.52 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),hAPP(fun(A,quickcheck_code_int),fun(A,quickcheck_code_int),hAPP(fun(A,fun(quickcheck_code_int,quickcheck_code_int)),fun(fun(A,quickcheck_code_int),fun(A,quickcheck_code_int)),combs(A,quickcheck_code_int,quickcheck_code_int),hAPP(fun(A,quickcheck_code_int),fun(A,fun(quickcheck_code_int,quickcheck_code_int)),hAPP(fun(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int)),fun(fun(A,quickcheck_code_int),fun(A,fun(quickcheck_code_int,quickcheck_code_int))),combb(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),A),plus_plus(quickcheck_code_int)),C)),D)),B) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),C),B)),hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),D),B)). [resolve(5179,a,5104,a)].
% 13.60/13.52 Derived: hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),hAPP(fun(A,quickcheck_code_int),fun(A,quickcheck_code_int),hAPP(fun(A,fun(quickcheck_code_int,quickcheck_code_int)),fun(fun(A,quickcheck_code_int),fun(A,quickcheck_code_int)),combs(A,quickcheck_code_int,quickcheck_code_int),hAPP(fun(A,quickcheck_code_int),fun(A,fun(quickcheck_code_int,quickcheck_code_int)),hAPP(fun(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int)),fun(fun(A,quickcheck_code_int),fun(A,fun(quickcheck_code_int,quickcheck_code_int))),combb(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),A),plus_plus(quickcheck_code_int)),B)),C)),D) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),B),D)),hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),C),D)). [resolve(5179,a,5105,a)].
% 13.60/13.52 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(fun(C,bool),quickcheck_code_int,hAPP(fun(C,quickcheck_code_int),fun(fun(C,bool),quickcheck_code_int),big_co1399186613setsum(C,quickcheck_code_int),hAPP(fun(C,fun(A,bool)),fun(C,quickcheck_code_int),hAPP(fun(fun(A,bool),quickcheck_code_int),fun(fun(C,fun(A,bool)),fun(C,quickcheck_code_int)),combb(fun(A,bool),quickcheck_code_int,C),hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_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),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),D),B). [resolve(5179,a,5106,a)].
% 13.60/13.52 Derived: -comm_monoid_mult(quickcheck_code_int) | hAPP(fun(nat,bool),quickcheck_code_int,hAPP(fun(nat,quickcheck_code_int),fun(fun(nat,bool),quickcheck_code_int),big_co1399186613setsum(nat,quickcheck_code_int),A),B) = hAPP(fun(int,bool),quickcheck_code_int,hAPP(fun(int,quickcheck_code_int),fun(fun(int,bool),quickcheck_code_int),big_co1399186613setsum(int,quickcheck_code_int),hAPP(fun(int,nat),fun(int,quickcheck_code_int),hAPP(fun(nat,quickcheck_code_int),fun(fun(int,nat),fun(int,quickcheck_code_int)),combb(nat,quickcheck_code_int,int),A),nat_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)),B)). [resolve(5179,a,5107,a)].
% 13.60/13.52 Derived: -comm_monoid_mult(quickcheck_code_int) | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A)) | hAPP(fun(nat,bool),quickcheck_code_int,hAPP(fun(nat,quickcheck_code_int),fun(fun(nat,bool),quickcheck_code_int),big_co1399186613setsum(nat,quickcheck_code_int),hAPP(fun(nat,int),fun(nat,quickcheck_code_int),hAPP(fun(int,quickcheck_code_int),fun(fun(nat,int),fun(nat,quickcheck_code_int)),combb(int,quickcheck_code_int,nat),B),semiring_1_of_nat(int))),hAPP(fun(int,bool),fun(nat,bool),hAPP(fun(int,nat),fun(fun(int,bool),fun(nat,bool)),image(int,nat),nat_1),A)) = hAPP(fun(int,bool),quickcheck_code_int,hAPP(fun(int,quickcheck_code_int),fun(fun(int,bool),quickcheck_code_int),big_co1399186613setsum(int,quickcheck_code_int),B),A). [resolve(5179,a,5108,a)].
% 13.60/13.52 Derived: -t2_space(quickcheck_code_int) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),f592(quickcheck_code_int,B,A))) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(fun(nat,quickcheck_code_int),fun(quickcheck_code_int,bool),sums(quickcheck_code_int),B),hAPP(fun(nat,bool),quickcheck_code_int,hAPP(fun(nat,quickcheck_code_int),fun(fun(nat,bool),quickcheck_code_int),big_co1399186613setsum(nat,quickcheck_code_int),B),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),A)))). [resolve(5179,a,5109,a)].
% 13.60/13.52 Derived: -t2_space(quickcheck_code_int) | hAPP(nat,quickcheck_code_int,A,f592(quickcheck_code_int,A,B)) != zero_zero(quickcheck_code_int) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(fun(nat,quickcheck_code_int),fun(quickcheck_code_int,bool),sums(quickcheck_code_int),A),hAPP(fun(nat,bool),quickcheck_code_int,hAPP(fun(nat,quickcheck_code_int),fun(fun(nat,bool),quickcheck_code_int),big_co1399186613setsum(nat,quickcheck_code_int),A),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),B)))). [resolve(5179,a,5110,a)].
% 13.60/13.53 Derived: -ordere779506340up_add(quickcheck_code_int) | -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),f593(A,quickcheck_code_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))) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),D),C)),hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),D),B))). [resolve(5179,a,5111,a)].
% 13.60/13.53 Derived: -ordere779506340up_add(quickcheck_code_int) | -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(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),zero_zero(quickcheck_code_int)),hAPP(A,quickcheck_code_int,D,f593(A,quickcheck_code_int,D,C,B)))) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),D),C)),hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),D),B))). [resolve(5179,a,5112,a)].
% 13.60/13.53 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),f595(A,quickcheck_code_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),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),D),B) = hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),D),C). [resolve(5179,a,5113,a)].
% 13.60/13.53 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,quickcheck_code_int,D,f595(A,quickcheck_code_int,D,C,B)) != zero_zero(quickcheck_code_int) | hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),D),B) = hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),D),C). [resolve(5179,a,5114,a)].
% 13.60/13.53 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),f596(A,quickcheck_code_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),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),D),B) = hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),D),C). [resolve(5179,a,5115,a)].
% 13.60/13.53 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,quickcheck_code_int,D,f596(A,quickcheck_code_int,D,C,B)) != zero_zero(quickcheck_code_int) | hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),D),B) = hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),D),C). [resolve(5179,a,5116,a)].
% 13.60/13.53 Derived: -comm_monoid_mult(quickcheck_code_int) | A != B | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),f598(quickcheck_code_int,C,D,B,A))) | hAPP(fun(int,bool),quickcheck_code_int,hAPP(fun(int,quickcheck_code_int),fun(fun(int,bool),quickcheck_code_int),big_co1399186613setsum(int,quickcheck_code_int),D),A) = hAPP(fun(int,bool),quickcheck_code_int,hAPP(fun(int,quickcheck_code_int),fun(fun(int,bool),quickcheck_code_int),big_co1399186613setsum(int,quickcheck_code_int),C),B). [resolve(5179,a,5117,a)].
% 13.60/13.53 Derived: -comm_monoid_mult(quickcheck_code_int) | A != B | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A)) | hAPP(int,quickcheck_code_int,C,f598(quickcheck_code_int,D,C,B,A)) != hAPP(int,quickcheck_code_int,D,f598(quickcheck_code_int,D,C,B,A)) | hAPP(fun(int,bool),quickcheck_code_int,hAPP(fun(int,quickcheck_code_int),fun(fun(int,bool),quickcheck_code_int),big_co1399186613setsum(int,quickcheck_code_int),C),A) = hAPP(fun(int,bool),quickcheck_code_int,hAPP(fun(int,quickcheck_code_int),fun(fun(int,bool),quickcheck_code_int),big_co1399186613setsum(int,quickcheck_code_int),D),B). [resolve(5179,a,5118,a)].
% 13.60/13.53 Derived: -ord(A) | ti(A,B) != ti(A,C) | ti(A,D) != ti(A,E) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),f603(quickcheck_code_int,A,F,V6,E,D,C,B))) | hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),V6),hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_atLeastLessThan(A),B),D)) = hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),F),hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_atLeastLessThan(A),C),E)). [resolve(5179,a,5119,b)].
% 13.60/13.53 Derived: -ord(A) | ti(A,B) != ti(A,C) | ti(A,D) != ti(A,E) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),f603(quickcheck_code_int,A,F,V6,E,D,C,B)),D)) | hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),V6),hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_atLeastLessThan(A),B),D)) = hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),F),hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_atLeastLessThan(A),C),E)). [resolve(5179,a,5120,b)].
% 13.60/13.53 Derived: -ord(A) | ti(A,B) != ti(A,C) | ti(A,D) != ti(A,E) | hAPP(A,quickcheck_code_int,F,f603(quickcheck_code_int,A,V6,F,E,D,C,B)) != hAPP(A,quickcheck_code_int,V6,f603(quickcheck_code_int,A,V6,F,E,D,C,B)) | hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),F),hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_atLeastLessThan(A),B),D)) = hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),V6),hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_atLeastLessThan(A),C),E)). [resolve(5179,a,5121,b)].
% 13.60/13.53 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),f609(A,quickcheck_code_int,C,B)),B)) | hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),C),B) = zero_zero(quickcheck_code_int). [resolve(5179,a,5122,a)].
% 13.60/13.53 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(A,quickcheck_code_int,C,f609(A,quickcheck_code_int,C,B)) != zero_zero(quickcheck_code_int) | hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),C),B) = zero_zero(quickcheck_code_int). [resolve(5179,a,5123,a)].
% 13.60/13.53 Derived: -ordere779506340up_add(quickcheck_code_int) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f610(A,quickcheck_code_int,B,C)),C)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),B),C)),zero_zero(quickcheck_code_int))). [resolve(5179,a,5124,a)].
% 13.60/13.53 Derived: -ordere779506340up_add(quickcheck_code_int) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),hAPP(A,quickcheck_code_int,B,f610(A,quickcheck_code_int,B,C))),zero_zero(quickcheck_code_int))) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),B),C)),zero_zero(quickcheck_code_int))). [resolve(5179,a,5125,a)].
% 13.60/13.53 Derived: -ordere779506340up_add(quickcheck_code_int) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f611(A,quickcheck_code_int,B,C)),C)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),zero_zero(quickcheck_code_int)),hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),B),C))). [resolve(5179,a,5126,a)].
% 13.60/13.53 Derived: -ordere779506340up_add(quickcheck_code_int) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),zero_zero(quickcheck_code_int)),hAPP(A,quickcheck_code_int,B,f611(A,quickcheck_code_int,B,C)))) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),zero_zero(quickcheck_code_int)),hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),B),C))). [resolve(5179,a,5127,a)].
% 13.60/13.53 Derived: -hBOOL(hAPP(fun(fun(A,bool),bool),bool,finite_finite_1(fun(A,bool)),B)) | hBOOL(hAPP(fun(fun(A,bool),bool),bool,hAPP(fun(A,bool),fun(fun(fun(A,bool),bool),bool),member(fun(A,bool)),f612(A,quickcheck_code_int,C,B)),B)) | hBOOL(hAPP(fun(fun(A,bool),bool),bool,hAPP(fun(A,bool),fun(fun(fun(A,bool),bool),bool),member(fun(A,bool)),f613(A,quickcheck_code_int,C,B)),B)) | hAPP(fun(fun(A,bool),bool),quickcheck_code_int,hAPP(fun(fun(A,bool),quickcheck_code_int),fun(fun(fun(A,bool),bool),quickcheck_code_int),big_co1399186613setsum(fun(A,bool),quickcheck_code_int),hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),C)),B) = hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),C),hAPP(fun(fun(A,bool),bool),fun(A,bool),complete_Sup_Sup(fun(A,bool)),B)). [resolve(5179,a,5128,a)].
% 13.60/13.53 Derived: -hBOOL(hAPP(fun(fun(A,bool),bool),bool,finite_finite_1(fun(A,bool)),B)) | hBOOL(hAPP(fun(fun(A,bool),bool),bool,hAPP(fun(A,bool),fun(fun(fun(A,bool),bool),bool),member(fun(A,bool)),f612(A,quickcheck_code_int,C,B)),B)) | hBOOL(hAPP(fun(fun(A,bool),bool),bool,hAPP(fun(A,bool),fun(fun(fun(A,bool),bool),bool),member(fun(A,bool)),f614(A,quickcheck_code_int,C,B)),B)) | hAPP(fun(fun(A,bool),bool),quickcheck_code_int,hAPP(fun(fun(A,bool),quickcheck_code_int),fun(fun(fun(A,bool),bool),quickcheck_code_int),big_co1399186613setsum(fun(A,bool),quickcheck_code_int),hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),C)),B) = hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),C),hAPP(fun(fun(A,bool),bool),fun(A,bool),complete_Sup_Sup(fun(A,bool)),B)). [resolve(5179,a,5129,a)].
% 13.60/13.53 Derived: -hBOOL(hAPP(fun(fun(A,bool),bool),bool,finite_finite_1(fun(A,bool)),B)) | hBOOL(hAPP(fun(fun(A,bool),bool),bool,hAPP(fun(A,bool),fun(fun(fun(A,bool),bool),bool),member(fun(A,bool)),f612(A,quickcheck_code_int,C,B)),B)) | ti(fun(A,bool),f614(A,quickcheck_code_int,C,B)) != ti(fun(A,bool),f613(A,quickcheck_code_int,C,B)) | hAPP(fun(fun(A,bool),bool),quickcheck_code_int,hAPP(fun(fun(A,bool),quickcheck_code_int),fun(fun(fun(A,bool),bool),quickcheck_code_int),big_co1399186613setsum(fun(A,bool),quickcheck_code_int),hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),C)),B) = hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),C),hAPP(fun(fun(A,bool),bool),fun(A,bool),complete_Sup_Sup(fun(A,bool)),B)). [resolve(5179,a,5130,a)].
% 13.60/13.53 Derived: -hBOOL(hAPP(fun(fun(A,bool),bool),bool,finite_finite_1(fun(A,bool)),B)) | hBOOL(hAPP(fun(fun(A,bool),bool),bool,hAPP(fun(A,bool),fun(fun(fun(A,bool),bool),bool),member(fun(A,bool)),f612(A,quickcheck_code_int,C,B)),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f615(A,quickcheck_code_int,C,B)),f613(A,quickcheck_code_int,C,B))) | hAPP(fun(fun(A,bool),bool),quickcheck_code_int,hAPP(fun(fun(A,bool),quickcheck_code_int),fun(fun(fun(A,bool),bool),quickcheck_code_int),big_co1399186613setsum(fun(A,bool),quickcheck_code_int),hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),C)),B) = hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),C),hAPP(fun(fun(A,bool),bool),fun(A,bool),complete_Sup_Sup(fun(A,bool)),B)). [resolve(5179,a,5131,a)].
% 13.60/13.53 Derived: -hBOOL(hAPP(fun(fun(A,bool),bool),bool,finite_finite_1(fun(A,bool)),B)) | hBOOL(hAPP(fun(fun(A,bool),bool),bool,hAPP(fun(A,bool),fun(fun(fun(A,bool),bool),bool),member(fun(A,bool)),f612(A,quickcheck_code_int,C,B)),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f615(A,quickcheck_code_int,C,B)),f614(A,quickcheck_code_int,C,B))) | hAPP(fun(fun(A,bool),bool),quickcheck_code_int,hAPP(fun(fun(A,bool),quickcheck_code_int),fun(fun(fun(A,bool),bool),quickcheck_code_int),big_co1399186613setsum(fun(A,bool),quickcheck_code_int),hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),C)),B) = hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),C),hAPP(fun(fun(A,bool),bool),fun(A,bool),complete_Sup_Sup(fun(A,bool)),B)). [resolve(5179,a,5132,a)].
% 13.60/13.53 Derived: -hBOOL(hAPP(fun(fun(A,bool),bool),bool,finite_finite_1(fun(A,bool)),B)) | hBOOL(hAPP(fun(fun(A,bool),bool),bool,hAPP(fun(A,bool),fun(fun(fun(A,bool),bool),bool),member(fun(A,bool)),f612(A,quickcheck_code_int,C,B)),B)) | hAPP(A,quickcheck_code_int,C,f615(A,quickcheck_code_int,C,B)) != zero_zero(quickcheck_code_int) | hAPP(fun(fun(A,bool),bool),quickcheck_code_int,hAPP(fun(fun(A,bool),quickcheck_code_int),fun(fun(fun(A,bool),bool),quickcheck_code_int),big_co1399186613setsum(fun(A,bool),quickcheck_code_int),hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),C)),B) = hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),C),hAPP(fun(fun(A,bool),bool),fun(A,bool),complete_Sup_Sup(fun(A,bool)),B)). [resolve(5179,a,5133,a)].
% 13.60/13.53 Derived: -hBOOL(hAPP(fun(fun(A,bool),bool),bool,finite_finite_1(fun(A,bool)),B)) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),f612(A,quickcheck_code_int,C,B))) | hBOOL(hAPP(fun(fun(A,bool),bool),bool,hAPP(fun(A,bool),fun(fun(fun(A,bool),bool),bool),member(fun(A,bool)),f613(A,quickcheck_code_int,C,B)),B)) | hAPP(fun(fun(A,bool),bool),quickcheck_code_int,hAPP(fun(fun(A,bool),quickcheck_code_int),fun(fun(fun(A,bool),bool),quickcheck_code_int),big_co1399186613setsum(fun(A,bool),quickcheck_code_int),hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),C)),B) = hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),C),hAPP(fun(fun(A,bool),bool),fun(A,bool),complete_Sup_Sup(fun(A,bool)),B)). [resolve(5179,a,5134,a)].
% 13.60/13.53 Derived: -hBOOL(hAPP(fun(fun(A,bool),bool),bool,finite_finite_1(fun(A,bool)),B)) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),f612(A,quickcheck_code_int,C,B))) | hBOOL(hAPP(fun(fun(A,bool),bool),bool,hAPP(fun(A,bool),fun(fun(fun(A,bool),bool),bool),member(fun(A,bool)),f614(A,quickcheck_code_int,C,B)),B)) | hAPP(fun(fun(A,bool),bool),quickcheck_code_int,hAPP(fun(fun(A,bool),quickcheck_code_int),fun(fun(fun(A,bool),bool),quickcheck_code_int),big_co1399186613setsum(fun(A,bool),quickcheck_code_int),hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),C)),B) = hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),C),hAPP(fun(fun(A,bool),bool),fun(A,bool),complete_Sup_Sup(fun(A,bool)),B)). [resolve(5179,a,5135,a)].
% 13.60/13.53 Derived: -hBOOL(hAPP(fun(fun(A,bool),bool),bool,finite_finite_1(fun(A,bool)),B)) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),f612(A,quickcheck_code_int,C,B))) | ti(fun(A,bool),f614(A,quickcheck_code_int,C,B)) != ti(fun(A,bool),f613(A,quickcheck_code_int,C,B)) | hAPP(fun(fun(A,bool),bool),quickcheck_code_int,hAPP(fun(fun(A,bool),quickcheck_code_int),fun(fun(fun(A,bool),bool),quickcheck_code_int),big_co1399186613setsum(fun(A,bool),quickcheck_code_int),hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),C)),B) = hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),C),hAPP(fun(fun(A,bool),bool),fun(A,bool),complete_Sup_Sup(fun(A,bool)),B)). [resolve(5179,a,5136,a)].
% 13.60/13.53 Derived: -hBOOL(hAPP(fun(fun(A,bool),bool),bool,finite_finite_1(fun(A,bool)),B)) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),f612(A,quickcheck_code_int,C,B))) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f615(A,quickcheck_code_int,C,B)),f613(A,quickcheck_code_int,C,B))) | hAPP(fun(fun(A,bool),bool),quickcheck_code_int,hAPP(fun(fun(A,bool),quickcheck_code_int),fun(fun(fun(A,bool),bool),quickcheck_code_int),big_co1399186613setsum(fun(A,bool),quickcheck_code_int),hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),C)),B) = hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),C),hAPP(fun(fun(A,bool),bool),fun(A,bool),complete_Sup_Sup(fun(A,bool)),B)). [resolve(5179,a,5137,a)].
% 13.60/13.53 Derived: -hBOOL(hAPP(fun(fun(A,bool),bool),bool,finite_finite_1(fun(A,bool)),B)) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),f612(A,quickcheck_code_int,C,B))) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f615(A,quickcheck_code_int,C,B)),f614(A,quickcheck_code_int,C,B))) | hAPP(fun(fun(A,bool),bool),quickcheck_code_int,hAPP(fun(fun(A,bool),quickcheck_code_int),fun(fun(fun(A,bool),bool),quickcheck_code_int),big_co1399186613setsum(fun(A,bool),quickcheck_code_int),hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),C)),B) = hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),C),hAPP(fun(fun(A,bool),bool),fun(A,bool),complete_Sup_Sup(fun(A,bool)),B)). [resolve(5179,a,5138,a)].
% 13.60/13.53 Derived: -hBOOL(hAPP(fun(fun(A,bool),bool),bool,finite_finite_1(fun(A,bool)),B)) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),f612(A,quickcheck_code_int,C,B))) | hAPP(A,quickcheck_code_int,C,f615(A,quickcheck_code_int,C,B)) != zero_zero(quickcheck_code_int) | hAPP(fun(fun(A,bool),bool),quickcheck_code_int,hAPP(fun(fun(A,bool),quickcheck_code_int),fun(fun(fun(A,bool),bool),quickcheck_code_int),big_co1399186613setsum(fun(A,bool),quickcheck_code_int),hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),C)),B) = hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),C),hAPP(fun(fun(A,bool),bool),fun(A,bool),complete_Sup_Sup(fun(A,bool)),B)). [resolve(5179,a,5139,a)].
% 13.60/13.53 Derived: hAPP(fun(nat,bool),quickcheck_code_int,hAPP(fun(nat,quickcheck_code_int),fun(fun(nat,bool),quickcheck_code_int),big_co1399186613setsum(nat,quickcheck_code_int),A),hAPP(nat,fun(nat,bool),ord_lessThan(nat),hAPP(nat,nat,suc,B))) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),hAPP(fun(nat,bool),quickcheck_code_int,hAPP(fun(nat,quickcheck_code_int),fun(fun(nat,bool),quickcheck_code_int),big_co1399186613setsum(nat,quickcheck_code_int),A),hAPP(nat,fun(nat,bool),ord_lessThan(nat),B))),hAPP(nat,quickcheck_code_int,A,B)). [resolve(5179,a,5140,a)].
% 13.60/13.53 Derived: -metric_space(quickcheck_code_int) | hAPP(fun(nat,quickcheck_code_int),quickcheck_code_int,suminf(quickcheck_code_int),A) = hAPP(fun(nat,quickcheck_code_int),quickcheck_code_int,lim(quickcheck_code_int),hAPP(fun(nat,fun(nat,bool)),fun(nat,quickcheck_code_int),hAPP(fun(fun(nat,bool),quickcheck_code_int),fun(fun(nat,fun(nat,bool)),fun(nat,quickcheck_code_int)),combb(fun(nat,bool),quickcheck_code_int,nat),hAPP(fun(nat,quickcheck_code_int),fun(fun(nat,bool),quickcheck_code_int),big_co1399186613setsum(nat,quickcheck_code_int),A)),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)))). [resolve(5179,a,5141,a)].
% 13.60/13.53 Derived: -ordere779506340up_add(quickcheck_code_int) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f631(A,quickcheck_code_int,B,C,D)),D)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),B),D)),hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),C),D))). [resolve(5179,a,5142,a)].
% 13.60/13.53 Derived: -ordere779506340up_add(quickcheck_code_int) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),hAPP(A,quickcheck_code_int,B,f631(A,quickcheck_code_int,B,C,D))),hAPP(A,quickcheck_code_int,C,f631(A,quickcheck_code_int,B,C,D)))) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),B),D)),hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),C),D))). [resolve(5179,a,5143,a)].
% 13.60/13.54 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),f632(A,quickcheck_code_int,D,E,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))) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f633(A,quickcheck_code_int,D,E,C,B)),C)) | hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),D),C) = hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),E),B). [resolve(5179,a,5144,a)].
% 13.60/13.54 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),f632(A,quickcheck_code_int,D,E,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(A,quickcheck_code_int,D,f633(A,quickcheck_code_int,D,E,C,B)) != hAPP(A,quickcheck_code_int,E,f633(A,quickcheck_code_int,D,E,C,B)) | hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),D),C) = hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),E),B). [resolve(5179,a,5145,a)].
% 13.60/13.54 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,quickcheck_code_int,D,f632(A,quickcheck_code_int,E,D,C,B)) != zero_zero(quickcheck_code_int) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f633(A,quickcheck_code_int,E,D,C,B)),C)) | hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),E),C) = hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),D),B). [resolve(5179,a,5146,a)].
% 13.60/13.54 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,quickcheck_code_int,D,f632(A,quickcheck_code_int,E,D,C,B)) != zero_zero(quickcheck_code_int) | hAPP(A,quickcheck_code_int,E,f633(A,quickcheck_code_int,E,D,C,B)) != hAPP(A,quickcheck_code_int,D,f633(A,quickcheck_code_int,E,D,C,B)) | hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),E),C) = hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),D),B). [resolve(5179,a,5147,a)].
% 13.60/13.54 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),f644(A,quickcheck_code_int,D,E,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))) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f645(A,quickcheck_code_int,D,E,C,B)),C)) | hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),E),B) = hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),D),C). [resolve(5179,a,5148,a)].
% 13.60/13.54 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),f644(A,quickcheck_code_int,D,E,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(A,quickcheck_code_int,E,f645(A,quickcheck_code_int,D,E,C,B)) != hAPP(A,quickcheck_code_int,D,f645(A,quickcheck_code_int,D,E,C,B)) | hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),E),B) = hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),D),C). [resolve(5179,a,5149,a)].
% 13.60/13.54 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,quickcheck_code_int,D,f644(A,quickcheck_code_int,E,D,C,B)) != zero_zero(quickcheck_code_int) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f645(A,quickcheck_code_int,E,D,C,B)),C)) | hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),D),B) = hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),E),C). [resolve(5179,a,5150,a)].
% 13.60/13.54 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,quickcheck_code_int,D,f644(A,quickcheck_code_int,E,D,C,B)) != zero_zero(quickcheck_code_int) | hAPP(A,quickcheck_code_int,D,f645(A,quickcheck_code_int,E,D,C,B)) != hAPP(A,quickcheck_code_int,E,f645(A,quickcheck_code_int,E,D,C,B)) | hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),D),B) = hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),E),C). [resolve(5179,a,5151,a)].
% 13.60/13.54 Derived: -t2_space(quickcheck_code_int) | -hBOOL(hAPP(fun(nat,quickcheck_code_int),bool,summable(quickcheck_code_int),A)) | hBOOL(hAPP(filter(nat),bool,hAPP(quickcheck_code_int,fun(filter(nat),bool),hAPP(fun(nat,quickcheck_code_int),fun(quickcheck_code_int,fun(filter(nat),bool)),tendsto(nat,quickcheck_code_int),hAPP(fun(nat,fun(nat,bool)),fun(nat,quickcheck_code_int),hAPP(fun(fun(nat,bool),quickcheck_code_int),fun(fun(nat,fun(nat,bool)),fun(nat,quickcheck_code_int)),combb(fun(nat,bool),quickcheck_code_int,nat),hAPP(fun(nat,quickcheck_code_int),fun(fun(nat,bool),quickcheck_code_int),big_co1399186613setsum(nat,quickcheck_code_int),A)),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)))),hAPP(fun(nat,quickcheck_code_int),quickcheck_code_int,suminf(quickcheck_code_int),A)),sequentially)). [resolve(5179,a,5152,a)].
% 13.60/13.54 Derived: -topological_space(quickcheck_code_int) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(fun(nat,quickcheck_code_int),fun(quickcheck_code_int,bool),sums(quickcheck_code_int),A),B)) | hBOOL(hAPP(filter(nat),bool,hAPP(quickcheck_code_int,fun(filter(nat),bool),hAPP(fun(nat,quickcheck_code_int),fun(quickcheck_code_int,fun(filter(nat),bool)),tendsto(nat,quickcheck_code_int),hAPP(fun(nat,fun(nat,bool)),fun(nat,quickcheck_code_int),hAPP(fun(fun(nat,bool),quickcheck_code_int),fun(fun(nat,fun(nat,bool)),fun(nat,quickcheck_code_int)),combb(fun(nat,bool),quickcheck_code_int,nat),hAPP(fun(nat,quickcheck_code_int),fun(fun(nat,bool),quickcheck_code_int),big_co1399186613setsum(nat,quickcheck_code_int),A)),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)))),B),sequentially)). [resolve(5179,a,5153,a)].
% 13.60/13.54 Derived: -topological_space(quickcheck_code_int) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(fun(nat,quickcheck_code_int),fun(quickcheck_code_int,bool),sums(quickcheck_code_int),A),B)) | -hBOOL(hAPP(filter(nat),bool,hAPP(quickcheck_code_int,fun(filter(nat),bool),hAPP(fun(nat,quickcheck_code_int),fun(quickcheck_code_int,fun(filter(nat),bool)),tendsto(nat,quickcheck_code_int),hAPP(fun(nat,fun(nat,bool)),fun(nat,quickcheck_code_int),hAPP(fun(fun(nat,bool),quickcheck_code_int),fun(fun(nat,fun(nat,bool)),fun(nat,quickcheck_code_int)),combb(fun(nat,bool),quickcheck_code_int,nat),hAPP(fun(nat,quickcheck_code_int),fun(fun(nat,bool),quickcheck_code_int),big_co1399186613setsum(nat,quickcheck_code_int),A)),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)))),B),sequentially)). [resolve(5179,a,5154,a)].
% 13.60/13.54 Derived: hAPP(fun(nat,bool),quickcheck_code_int,hAPP(fun(nat,quickcheck_code_int),fun(fun(nat,bool),quickcheck_code_int),big_co1399186613setsum(nat,quickcheck_code_int),hAPP(fun(nat,nat),fun(nat,quickcheck_code_int),hAPP(fun(nat,quickcheck_code_int),fun(fun(nat,nat),fun(nat,quickcheck_code_int)),combb(nat,quickcheck_code_int,nat),A),suc)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),B),C)) = hAPP(fun(nat,bool),quickcheck_code_int,hAPP(fun(nat,quickcheck_code_int),fun(fun(nat,bool),quickcheck_code_int),big_co1399186613setsum(nat,quickcheck_code_int),A),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,suc,B)),hAPP(nat,nat,suc,C))). [resolve(5179,a,5155,a)].
% 13.60/13.54 Derived: hAPP(fun(nat,bool),quickcheck_code_int,hAPP(fun(nat,quickcheck_code_int),fun(fun(nat,bool),quickcheck_code_int),big_co1399186613setsum(nat,quickcheck_code_int),hAPP(fun(nat,nat),fun(nat,quickcheck_code_int),hAPP(fun(nat,quickcheck_code_int),fun(fun(nat,nat),fun(nat,quickcheck_code_int)),combb(nat,quickcheck_code_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),quickcheck_code_int,hAPP(fun(nat,quickcheck_code_int),fun(fun(nat,bool),quickcheck_code_int),big_co1399186613setsum(nat,quickcheck_code_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(5179,a,5156,a)].
% 13.60/13.54 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | hAPP(fun(nat,bool),quickcheck_code_int,hAPP(fun(nat,quickcheck_code_int),fun(fun(nat,bool),quickcheck_code_int),big_co1399186613setsum(nat,quickcheck_code_int),C),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),A),B)) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),hAPP(nat,quickcheck_code_int,C,A)),hAPP(fun(nat,bool),quickcheck_code_int,hAPP(fun(nat,quickcheck_code_int),fun(fun(nat,bool),quickcheck_code_int),big_co1399186613setsum(nat,quickcheck_code_int),C),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,suc,A)),B))). [resolve(5179,a,5157,a)].
% 13.60/13.54 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,A)),B)) | hAPP(fun(nat,bool),quickcheck_code_int,hAPP(fun(nat,quickcheck_code_int),fun(fun(nat,bool),quickcheck_code_int),big_co1399186613setsum(nat,quickcheck_code_int),C),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),B),hAPP(nat,nat,suc,A))) = zero_zero(quickcheck_code_int). [resolve(5179,a,5158,a)].
% 13.60/13.54 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,A)),B)) | hAPP(fun(nat,bool),quickcheck_code_int,hAPP(fun(nat,quickcheck_code_int),fun(fun(nat,bool),quickcheck_code_int),big_co1399186613setsum(nat,quickcheck_code_int),C),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),B),hAPP(nat,nat,suc,A))) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),hAPP(fun(nat,bool),quickcheck_code_int,hAPP(fun(nat,quickcheck_code_int),fun(fun(nat,bool),quickcheck_code_int),big_co1399186613setsum(nat,quickcheck_code_int),C),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),B),A))),hAPP(nat,quickcheck_code_int,C,hAPP(nat,nat,suc,A))). [resolve(5179,a,5159,a)].
% 13.60/13.54 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),quickcheck_code_int,hAPP(fun(nat,quickcheck_code_int),fun(fun(nat,bool),quickcheck_code_int),big_co1399186613setsum(nat,quickcheck_code_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(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),hAPP(fun(nat,bool),quickcheck_code_int,hAPP(fun(nat,quickcheck_code_int),fun(fun(nat,bool),quickcheck_code_int),big_co1399186613setsum(nat,quickcheck_code_int),C),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),A),B))),hAPP(fun(nat,bool),quickcheck_code_int,hAPP(fun(nat,quickcheck_code_int),fun(fun(nat,bool),quickcheck_code_int),big_co1399186613setsum(nat,quickcheck_code_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(5179,a,5160,a)].
% 13.60/13.54 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,A)),B)) | hAPP(fun(nat,bool),quickcheck_code_int,hAPP(fun(nat,quickcheck_code_int),fun(fun(nat,bool),quickcheck_code_int),big_co1399186613setsum(nat,quickcheck_code_int),C),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),B),hAPP(nat,nat,suc,A))) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),hAPP(nat,quickcheck_code_int,C,B)),hAPP(fun(nat,bool),quickcheck_code_int,hAPP(fun(nat,quickcheck_code_int),fun(fun(nat,bool),quickcheck_code_int),big_co1399186613setsum(nat,quickcheck_code_int),hAPP(fun(nat,nat),fun(nat,quickcheck_code_int),hAPP(fun(nat,quickcheck_code_int),fun(fun(nat,nat),fun(nat,quickcheck_code_int)),combb(nat,quickcheck_code_int,nat),C),suc)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),B),A))). [resolve(5179,a,5162,a)].
% 13.60/13.54 Derived: hAPP(fun(product_prod(nat,nat),bool),quickcheck_code_int,hAPP(fun(product_prod(nat,nat),quickcheck_code_int),fun(fun(product_prod(nat,nat),bool),quickcheck_code_int),big_co1399186613setsum(product_prod(nat,nat),quickcheck_code_int),hAPP(fun(nat,fun(nat,quickcheck_code_int)),fun(product_prod(nat,nat),quickcheck_code_int),product_prod_case(nat,nat,quickcheck_code_int),A)),hAPP(fun(product_prod(nat,nat),bool),fun(product_prod(nat,nat),bool),collect(product_prod(nat,nat)),hAPP(fun(nat,fun(nat,bool)),fun(product_prod(nat,nat),bool),product_prod_case(nat,nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),hAPP(fun(nat,fun(nat,fun(nat,bool))),fun(nat,fun(nat,fun(nat,bool))),combc(nat,nat,fun(nat,bool)),hAPP(fun(nat,fun(nat,fun(nat,bool))),fun(nat,fun(nat,fun(nat,bool))),hAPP(fun(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool))),fun(fun(nat,fun(nat,fun(nat,bool))),fun(nat,fun(nat,fun(nat,bool)))),combb(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),nat),combc(nat,nat,bool)),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,fun(nat,bool))),hAPP(fun(fun(nat,nat),fun(nat,fun(nat,bool))),fun(fun(nat,fun(nat,nat)),fun(nat,fun(nat,fun(nat,bool)))),combb(fun(nat,nat),fun(nat,fun(nat,bool)),nat),hAPP(fun(nat,fun(nat,bool)),fun(fun(nat,nat),fun(nat,fun(nat,bool))),combb(nat,fun(nat,bool),nat),ord_less(nat))),plus_plus(nat)))),B)))) = hAPP(fun(nat,bool),quickcheck_code_int,hAPP(fun(nat,quickcheck_code_int),fun(fun(nat,bool),quickcheck_code_int),big_co1399186613setsum(nat,quickcheck_code_int),hAPP(fun(nat,fun(nat,bool)),fun(nat,quickcheck_code_int),hAPP(fun(nat,fun(fun(nat,bool),quickcheck_code_int)),fun(fun(nat,fun(nat,bool)),fun(nat,quickcheck_code_int)),combs(nat,fun(nat,bool),quickcheck_code_int),hAPP(fun(nat,fun(nat,quickcheck_code_int)),fun(nat,fun(fun(nat,bool),quickcheck_code_int)),hAPP(fun(fun(nat,quickcheck_code_int),fun(fun(nat,bool),quickcheck_code_int)),fun(fun(nat,fun(nat,quickcheck_code_int)),fun(nat,fun(fun(nat,bool),quickcheck_code_int))),combb(fun(nat,quickcheck_code_int),fun(fun(nat,bool),quickcheck_code_int),nat),big_co1399186613setsum(nat,quickcheck_code_int)),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,quickcheck_code_int)),hAPP(fun(fun(nat,nat),fun(nat,quickcheck_code_int)),fun(fun(nat,fun(nat,nat)),fun(nat,fun(nat,quickcheck_code_int))),combb(fun(nat,nat),fun(nat,quickcheck_code_int),nat),hAPP(fun(nat,fun(nat,quickcheck_code_int)),fun(fun(nat,nat),fun(nat,quickcheck_code_int)),combs(nat,nat,quickcheck_code_int),A)),minus_minus(nat)))),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),zero_zero(nat)))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),B)). [resolve(5179,a,5163,a)].
% 13.60/13.54 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),f771(A,quickcheck_code_int,C,D,B)),B)) | hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),D),B) = hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),C),B). [resolve(5179,a,5164,a)].
% 13.60/13.54 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(A,quickcheck_code_int,C,f771(A,quickcheck_code_int,D,C,B)) != hAPP(A,quickcheck_code_int,D,f771(A,quickcheck_code_int,D,C,B)) | hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),C),B) = hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),D),B). [resolve(5179,a,5165,a)].
% 13.60/13.54 Derived: hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f772(A,quickcheck_code_int,B,C)),C)) | hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),B),C) = zero_zero(quickcheck_code_int). [resolve(5179,a,5166,a)].
% 13.60/13.54 Derived: hAPP(A,quickcheck_code_int,B,f772(A,quickcheck_code_int,B,C)) != zero_zero(quickcheck_code_int) | hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),B),C) = zero_zero(quickcheck_code_int). [resolve(5179,a,5167,a)].
% 13.60/13.54 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),A,zero_zero(quickcheck_code_int)),zero_zero(quickcheck_code_int))) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),A,f788(B,quickcheck_code_int,C,D,E,A)),f790(B,quickcheck_code_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),f792(B,quickcheck_code_int,C,D,E,A)),E)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),A,hAPP(fun(B,bool),quickcheck_code_int,hAPP(fun(B,quickcheck_code_int),fun(fun(B,bool),quickcheck_code_int),big_co1399186613setsum(B,quickcheck_code_int),C),E)),hAPP(fun(B,bool),quickcheck_code_int,hAPP(fun(B,quickcheck_code_int),fun(fun(B,bool),quickcheck_code_int),big_co1399186613setsum(B,quickcheck_code_int),D),E))). [resolve(5179,a,5168,a)].
% 13.60/13.54 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),A,zero_zero(quickcheck_code_int)),zero_zero(quickcheck_code_int))) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),A,f788(B,quickcheck_code_int,C,D,E,A)),f790(B,quickcheck_code_int,C,D,E,A))) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),E)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),A,hAPP(B,quickcheck_code_int,C,f792(B,quickcheck_code_int,C,D,E,A))),hAPP(B,quickcheck_code_int,D,f792(B,quickcheck_code_int,C,D,E,A)))) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),A,hAPP(fun(B,bool),quickcheck_code_int,hAPP(fun(B,quickcheck_code_int),fun(fun(B,bool),quickcheck_code_int),big_co1399186613setsum(B,quickcheck_code_int),C),E)),hAPP(fun(B,bool),quickcheck_code_int,hAPP(fun(B,quickcheck_code_int),fun(fun(B,bool),quickcheck_code_int),big_co1399186613setsum(B,quickcheck_code_int),D),E))). [resolve(5179,a,5169,a)].
% 13.60/13.54 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),A,zero_zero(quickcheck_code_int)),zero_zero(quickcheck_code_int))) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),A,f789(B,quickcheck_code_int,C,D,E,A)),f791(B,quickcheck_code_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),f792(B,quickcheck_code_int,C,D,E,A)),E)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),A,hAPP(fun(B,bool),quickcheck_code_int,hAPP(fun(B,quickcheck_code_int),fun(fun(B,bool),quickcheck_code_int),big_co1399186613setsum(B,quickcheck_code_int),C),E)),hAPP(fun(B,bool),quickcheck_code_int,hAPP(fun(B,quickcheck_code_int),fun(fun(B,bool),quickcheck_code_int),big_co1399186613setsum(B,quickcheck_code_int),D),E))). [resolve(5179,a,5170,a)].
% 13.60/13.54 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),A,zero_zero(quickcheck_code_int)),zero_zero(quickcheck_code_int))) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),A,f789(B,quickcheck_code_int,C,D,E,A)),f791(B,quickcheck_code_int,C,D,E,A))) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),E)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),A,hAPP(B,quickcheck_code_int,C,f792(B,quickcheck_code_int,C,D,E,A))),hAPP(B,quickcheck_code_int,D,f792(B,quickcheck_code_int,C,D,E,A)))) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),A,hAPP(fun(B,bool),quickcheck_code_int,hAPP(fun(B,quickcheck_code_int),fun(fun(B,bool),quickcheck_code_int),big_co1399186613setsum(B,quickcheck_code_int),C),E)),hAPP(fun(B,bool),quickcheck_code_int,hAPP(fun(B,quickcheck_code_int),fun(fun(B,bool),quickcheck_code_int),big_co1399186613setsum(B,quickcheck_code_int),D),E))). [resolve(5179,a,5171,a)].
% 13.60/13.54 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),A,zero_zero(quickcheck_code_int)),zero_zero(quickcheck_code_int))) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),A,hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),f788(B,quickcheck_code_int,C,D,E,A)),f789(B,quickcheck_code_int,C,D,E,A))),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),f790(B,quickcheck_code_int,C,D,E,A)),f791(B,quickcheck_code_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),f792(B,quickcheck_code_int,C,D,E,A)),E)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),A,hAPP(fun(B,bool),quickcheck_code_int,hAPP(fun(B,quickcheck_code_int),fun(fun(B,bool),quickcheck_code_int),big_co1399186613setsum(B,quickcheck_code_int),C),E)),hAPP(fun(B,bool),quickcheck_code_int,hAPP(fun(B,quickcheck_code_int),fun(fun(B,bool),quickcheck_code_int),big_co1399186613setsum(B,quickcheck_code_int),D),E))). [resolve(5179,a,5172,a)].
% 13.60/13.54 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),A,zero_zero(quickcheck_code_int)),zero_zero(quickcheck_code_int))) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),A,hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),f788(B,quickcheck_code_int,C,D,E,A)),f789(B,quickcheck_code_int,C,D,E,A))),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),f790(B,quickcheck_code_int,C,D,E,A)),f791(B,quickcheck_code_int,C,D,E,A)))) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),E)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),A,hAPP(B,quickcheck_code_int,C,f792(B,quickcheck_code_int,C,D,E,A))),hAPP(B,quickcheck_code_int,D,f792(B,quickcheck_code_int,C,D,E,A)))) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),A,hAPP(fun(B,bool),quickcheck_code_int,hAPP(fun(B,quickcheck_code_int),fun(fun(B,bool),quickcheck_code_int),big_co1399186613setsum(B,quickcheck_code_int),C),E)),hAPP(fun(B,bool),quickcheck_code_int,hAPP(fun(B,quickcheck_code_int),fun(fun(B,bool),quickcheck_code_int),big_co1399186613setsum(B,quickcheck_code_int),D),E))). [resolve(5179,a,5173,a)].
% 16.98/16.91 5180 real_normed_field(real) # label(arity_RealDef_Oreal___RealVector_Oreal__normed__field) # label(axiom). [assumption].
% 16.98/16.91 5181 -real_normed_field(A) | deriv(A) = ti(fun(fun(A,A),fun(A,fun(A,bool))),deriv(A)) # label(tsy_c_Deriv_Oderiv_res) # label(axiom). [clausify(15)].
% 16.98/16.91 5182 -real_normed_field(A) | -banach(A) | exp(A) = ti(fun(A,A),exp(A)) # label(tsy_c_Transcendental_Oexp_res) # label(axiom). [clausify(117)].
% 16.98/16.91 5183 -real_normed_field(A) | hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),zero_zero(A)),B) = zero_zero(A) # label(fact_1073_divide_Ozero) # label(axiom). [clausify(1184)].
% 16.98/16.91 5184 -real_normed_field(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),C)) = hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),D)),C) # label(fact_1077_divide_Oadd) # label(axiom). [clausify(1188)].
% 16.98/16.91 5185 -real_normed_field(A) | hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),C)) = hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),D)),C) # label(fact_1080_divide_Odiff) # label(axiom). [clausify(1191)].
% 16.98/16.91 5186 -real_normed_field(A) | hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),hAPP(A,A,uminus_uminus(A),B)),C) = hAPP(A,A,uminus_uminus(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)) # label(fact_1081_divide_Ominus) # label(axiom). [clausify(1192)].
% 16.98/16.91 5187 -real_normed_field(A) | zero_zero(A) = ti(A,B) | zero_zero(A) = ti(A,C) | hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(A,A,inverse_inverse(A),B)),hAPP(A,A,inverse_inverse(A),C))),D) = hAPP(A,A,uminus_uminus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,inverse_inverse(A),B)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C)),D))),hAPP(A,A,inverse_inverse(A),C))) # label(fact_2269_DERIV__inverse__lemma) # label(axiom). [clausify(2288)].
% 16.98/16.91 5188 -real_normed_field(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),hAPP(A,fun(A,A),times_times(A),B)),C),B)) # label(fact_2308_DERIV__cmult__Id) # label(axiom). [clausify(2318)].
% 16.98/16.91 5189 -real_normed_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),B),C),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),B),C),E)) | ti(A,D) = ti(A,E) # label(fact_2309_DERIV__unique) # label(axiom). [clausify(2319)].
% 16.98/16.91 5190 -real_normed_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),B),C),D)) | ti(A,D) != ti(A,E) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),B),C),E)) # label(fact_2310_DERIV__cong) # label(axiom). [clausify(2320)].
% 16.98/16.91 5191 -real_normed_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),B),C),D)) | ti(A,D) != ti(A,E) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),B),C),E)) # label(fact_2311_Deriv_Olemma__DERIV__subst) # label(axiom). [clausify(2321)].
% 16.98/16.91 5192 -real_normed_field(A) | -banach(A) | hAPP(A,A,exp(A),B) != zero_zero(A) # label(fact_2400_exp__not__eq__zero) # label(axiom). [clausify(2409)].
% 16.98/16.91 5193 -real_normed_field(A) | -banach(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),exp(A)),B),hAPP(A,A,exp(A),B))) # label(fact_2401_DERIV__exp) # label(axiom). [clausify(2410)].
% 16.98/16.91 5194 -real_normed_field(A) | -banach(A) | hAPP(A,A,exp(A),zero_zero(A)) = one_one(A) # label(fact_2407_exp__zero) # label(axiom). [clausify(2416)].
% 16.98/16.91 5195 -real_normed_field(A) | -banach(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,exp(A),B)),hAPP(A,A,exp(A),C)) = hAPP(A,A,exp(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)) # label(fact_2408_exp__add) # label(axiom). [clausify(2417)].
% 16.98/16.91 5196 -real_normed_field(A) | -banach(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,exp(A),B)),hAPP(A,A,exp(A),C)) = hAPP(A,A,exp(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)) # label(fact_2409_mult__exp__exp) # label(axiom). [clausify(2418)].
% 16.98/16.91 5197 -real_normed_field(A) | -banach(A) | hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),hAPP(A,A,exp(A),B)),hAPP(A,A,exp(A),C)) = hAPP(A,A,exp(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C)) # label(fact_2410_exp__diff) # label(axiom). [clausify(2419)].
% 16.98/16.91 5198 -real_normed_field(A) | -banach(A) | hAPP(A,A,exp(A),hAPP(A,A,uminus_uminus(A),B)) = hAPP(A,A,inverse_inverse(A),hAPP(A,A,exp(A),B)) # label(fact_2411_exp__minus) # label(axiom). [clausify(2420)].
% 16.98/16.91 5199 -real_normed_field(A) | zero_zero(A) = ti(A,B) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(A,real,norm_norm(A),C)),D)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(A,real,norm_norm(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),B))),D)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(A,real,norm_norm(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),B)),E)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),C),E))),B)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(nat,A,semiring_1_of_nat(A),E)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),C),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),E),hAPP(nat,nat,suc,zero_zero(nat)))))))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,semiring_1_of_nat(real),E)),hAPP(nat,real,semiring_1_of_nat(real),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),E),hAPP(nat,nat,suc,zero_zero(nat)))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),D),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),E),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))),hAPP(A,real,norm_norm(A),B)))) # label(fact_2685_lemma__termdiff3) # label(axiom). [clausify(2677)].
% 16.98/16.91 5200 -field_inverse_zero(A) | -real_normed_field(A) | hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(A,real,norm_norm(A),B)),hAPP(A,real,norm_norm(A),C)) = hAPP(A,real,norm_norm(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)) # label(fact_2703_norm__divide) # label(axiom). [clausify(2695)].
% 16.98/16.91 5201 -real_normed_field(A) | zero_zero(A) = ti(A,B) | hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(A,real,norm_norm(A),C)),hAPP(A,real,norm_norm(A),B)) = hAPP(A,real,norm_norm(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),B)) # label(fact_2712_nonzero__norm__divide) # label(axiom). [clausify(2704)].
% 16.98/16.91 5202 -real_normed_field(A) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),f257(A,B))) # label(fact_2737_divide_Opos__bounded) # label(axiom). [clausify(2729)].
% 16.98/16.91 5203 -real_normed_field(A) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(A,real,norm_norm(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(A,real,norm_norm(A),B)),f257(A,C)))) # label(fact_2737_divide_Opos__bounded) # label(axiom). [clausify(2729)].
% 16.98/16.91 5204 -real_normed_field(A) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),f264(A,B))) # label(fact_2744_divide_Ononneg__bounded) # label(axiom). [clausify(2736)].
% 16.98/16.91 5205 -real_normed_field(A) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(A,real,norm_norm(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(A,real,norm_norm(A),B)),f264(A,C)))) # label(fact_2744_divide_Ononneg__bounded) # label(axiom). [clausify(2736)].
% 16.98/16.91 5206 -real_normed_field(A) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(A,real,norm_norm(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(A,real,norm_norm(A),B)),f270(A,C)))) # label(fact_2750_divide_Obounded) # label(axiom). [clausify(2742)].
% 16.98/16.91 5207 -real_normed_field(A) | -banach(A) | hAPP(real,A,of_real(A),hAPP(real,real,exp(real),B)) = hAPP(A,A,exp(A),hAPP(real,A,of_real(A),B)) # label(fact_2805_exp__of__real) # label(axiom). [clausify(2790)].
% 16.98/16.91 5208 -real_normed_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),B),C),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),E),C),F)) | hAPP(A,A,E,C) = zero_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),hAPP(fun(A,A),fun(A,A),hAPP(fun(A,fun(A,A)),fun(fun(A,A),fun(A,A)),combs(A,A,A),hAPP(fun(A,A),fun(A,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(A,A),fun(A,fun(A,A))),combb(A,fun(A,A),A),inverse_divide(A)),B)),E)),C),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),hAPP(A,A,E,C))),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,B,C)),F))),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,E,C)),hAPP(A,A,E,C))))) # label(fact_3816_DERIV__divide) # label(axiom). [clausify(3758)].
% 16.98/16.91 5209 -real_normed_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),B),C),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),E),C),F)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),hAPP(fun(A,A),fun(A,A),hAPP(fun(A,fun(A,A)),fun(fun(A,A),fun(A,A)),combs(A,A,A),hAPP(fun(A,A),fun(A,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(A,A),fun(A,fun(A,A))),combb(A,fun(A,A),A),plus_plus(A)),B)),hAPP(fun(A,A),fun(A,A),hAPP(fun(A,A),fun(fun(A,A),fun(A,A)),combb(A,A,A),uminus_uminus(A)),E))),C),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),D),hAPP(A,A,uminus_uminus(A),F)))) # label(fact_3823_DERIV__add__minus) # label(axiom). [clausify(3765)].
% 16.98/16.91 5210 -real_normed_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),B),C),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),E),C),F)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),hAPP(fun(A,A),fun(A,A),hAPP(fun(A,fun(A,A)),fun(fun(A,A),fun(A,A)),combs(A,A,A),hAPP(fun(A,A),fun(A,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(A,A),fun(A,fun(A,A))),combb(A,fun(A,A),A),times_times(A)),B)),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),hAPP(A,A,E,C))),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),F),hAPP(A,A,B,C))))) # label(fact_3824_DERIV__mult) # label(axiom). [clausify(3766)].
% 16.98/16.91 5211 -real_normed_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),B),C),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),E),C),F)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),hAPP(fun(A,A),fun(A,A),hAPP(fun(A,fun(A,A)),fun(fun(A,A),fun(A,A)),combs(A,A,A),hAPP(fun(A,A),fun(A,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(A,A),fun(A,fun(A,A))),combb(A,fun(A,A),A),times_times(A)),B)),E)),C),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,B,C)),F)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),hAPP(A,A,E,C))))) # label(fact_3825_DERIV__mult_H) # label(axiom). [clausify(3767)].
% 16.98/16.91 5212 -real_normed_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),B),C),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),E),C),F)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),hAPP(fun(A,A),fun(A,A),hAPP(fun(A,fun(A,A)),fun(fun(A,A),fun(A,A)),combs(A,A,A),hAPP(fun(A,A),fun(A,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(A,A),fun(A,fun(A,A))),combb(A,fun(A,A),A),plus_plus(A)),B)),E)),C),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),D),F))) # label(fact_3828_DERIV__add) # label(axiom). [clausify(3770)].
% 16.98/16.91 5213 -real_normed_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),B),C),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),E),C),F)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),hAPP(fun(A,A),fun(A,A),hAPP(fun(A,fun(A,A)),fun(fun(A,A),fun(A,A)),combs(A,A,A),hAPP(fun(A,A),fun(A,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(A,A),fun(A,fun(A,A))),combb(A,fun(A,A),A),minus_minus(A)),B)),E)),C),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),D),F))) # label(fact_3829_DERIV__diff) # label(axiom). [clausify(3771)].
% 16.98/16.91 5214 -real_normed_field(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),combi(A)),B),one_one(A))) # label(fact_3842_DERIV__ident) # label(axiom). [clausify(3784)].
% 16.98/16.91 5215 -real_normed_field(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),hAPP(A,fun(A,A),combk(A,A),B)),C),zero_zero(A))) # label(fact_3843_DERIV__const) # label(axiom). [clausify(3785)].
% 16.98/16.91 5216 -real_normed_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),B),C),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),hAPP(A,fun(A,A),hAPP(fun(A,fun(A,A)),fun(A,fun(A,A)),combc(A,A,A),hAPP(fun(A,A),fun(A,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(A,A),fun(A,fun(A,A))),combb(A,fun(A,A),A),inverse_divide(A)),B)),E)),C),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),E))) # label(fact_3844_DERIV__cdivide) # label(axiom). [clausify(3786)].
% 16.98/16.91 5217 -real_normed_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),B),C),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),hAPP(fun(A,A),fun(A,A),hAPP(fun(A,A),fun(fun(A,A),fun(A,A)),combb(A,A,A),hAPP(A,fun(A,A),times_times(A),E)),B)),C),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),E),D))) # label(fact_3857_DERIV__cmult) # label(axiom). [clausify(3798)].
% 16.98/16.91 5218 -real_normed_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),B),C),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),E),hAPP(A,A,B,C)),F)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),hAPP(fun(A,A),fun(A,A),hAPP(fun(A,A),fun(fun(A,A),fun(A,A)),combb(A,A,A),E),B)),C),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),F),D))) # label(fact_3858_DERIV__chain_H) # label(axiom). [clausify(3799)].
% 16.98/16.91 5219 -real_normed_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),B),hAPP(A,A,C,D)),E)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),C),D),F)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),hAPP(fun(A,A),fun(A,A),hAPP(fun(A,A),fun(fun(A,A),fun(A,A)),combb(A,A,A),B),C)),D),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),E),F))) # label(fact_3859_DERIV__chain2) # label(axiom). [clausify(3800)].
% 16.98/16.91 5220 -real_normed_field(A) | -banach(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),B),C),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),hAPP(fun(A,A),fun(A,A),hAPP(fun(A,A),fun(fun(A,A),fun(A,A)),combb(A,A,A),exp(A)),B)),C),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,exp(A),hAPP(A,A,B,C))),D))) # label(fact_3860_DERIV__fun__exp) # label(axiom). [clausify(3801)].
% 16.98/16.91 5221 -real_normed_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),B),C),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),hAPP(fun(A,A),fun(A,A),hAPP(fun(A,A),fun(fun(A,A),fun(A,A)),combb(A,A,A),uminus_uminus(A)),B)),C),hAPP(A,A,uminus_uminus(A),D))) # label(fact_3864_DERIV__minus) # label(axiom). [clausify(3805)].
% 16.98/16.91 5222 -real_normed_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),B),C),D)) | hAPP(A,A,B,C) = zero_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),hAPP(fun(A,A),fun(A,A),hAPP(fun(A,A),fun(fun(A,A),fun(A,A)),combb(A,A,A),inverse_inverse(A)),B)),C),hAPP(A,A,uminus_uminus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,inverse_inverse(A),hAPP(A,A,B,C))),D)),hAPP(A,A,inverse_inverse(A),hAPP(A,A,B,C)))))) # label(fact_3877_DERIV__inverse_H) # label(axiom). [clausify(3818)].
% 16.98/16.91 5223 -real_normed_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),B),C),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),hAPP(nat,fun(A,A),hAPP(fun(A,fun(nat,A)),fun(nat,fun(A,A)),combc(A,nat,A),hAPP(fun(A,A),fun(A,fun(nat,A)),hAPP(fun(A,fun(nat,A)),fun(fun(A,A),fun(A,fun(nat,A))),combb(A,fun(nat,A),A),power_power(A)),B)),hAPP(nat,nat,suc,E))),C),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)),hAPP(nat,A,semiring_1_of_nat(A),E))),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),hAPP(A,A,B,C)),E))))) # label(fact_3886_DERIV__power__Suc) # label(axiom). [clausify(3827)].
% 16.98/16.91 5224 -real_normed_field(A) | zero_zero(A) = ti(A,B) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),inverse_inverse(A)),B),hAPP(A,A,uminus_uminus(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),hAPP(A,A,inverse_inverse(A),B)),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat))))))) # label(fact_3887_DERIV__inverse) # label(axiom). [clausify(3828)].
% 16.98/16.91 5225 -real_normed_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),B),C),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),hAPP(nat,fun(A,A),hAPP(fun(A,fun(nat,A)),fun(nat,fun(A,A)),combc(A,nat,A),hAPP(fun(A,A),fun(A,fun(nat,A)),hAPP(fun(A,fun(nat,A)),fun(fun(A,A),fun(A,fun(nat,A))),combb(A,fun(nat,A),A),power_power(A)),B)),E)),C),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(nat,A,semiring_1_of_nat(A),E)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),hAPP(A,A,B,C)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),E),hAPP(nat,nat,suc,zero_zero(nat)))))))) # label(fact_3888_DERIV__power) # label(axiom). [clausify(3829)].
% 16.98/16.91 5226 -real_normed_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),B),C),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),E),C),F)) | hAPP(A,A,E,C) = zero_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),hAPP(fun(A,A),fun(A,A),hAPP(fun(A,fun(A,A)),fun(fun(A,A),fun(A,A)),combs(A,A,A),hAPP(fun(A,A),fun(A,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(A,A),fun(A,fun(A,A))),combb(A,fun(A,A),A),inverse_divide(A)),B)),E)),C),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),hAPP(A,A,E,C))),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),F),hAPP(A,A,B,C)))),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),hAPP(A,A,E,C)),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat))))))) # label(fact_3897_DERIV__quotient) # label(axiom). [clausify(3838)].
% 16.98/16.91 5227 -real_normed_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),B),C),D)) | hAPP(A,A,B,C) = zero_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),hAPP(fun(A,A),fun(A,A),hAPP(fun(A,A),fun(fun(A,A),fun(A,A)),combb(A,A,A),inverse_inverse(A)),B)),C),hAPP(A,A,uminus_uminus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),hAPP(A,A,inverse_inverse(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),hAPP(A,A,B,C)),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat))))))))) # label(fact_3899_DERIV__inverse__fun) # label(axiom). [clausify(3840)].
% 16.98/16.91 5228 -real_normed_field(A) | -hBOOL(hAPP(fun(nat,A),bool,summable(A),B)) | -hBOOL(hAPP(fun(nat,A),bool,summable(A),C)) | hAPP(fun(nat,A),A,suminf(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),plus_plus(A)),B)),C)) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(fun(nat,A),A,suminf(A),B)),hAPP(fun(nat,A),A,suminf(A),C)) # label(fact_3979_suminf__add) # label(axiom). [clausify(3919)].
% 16.98/16.91 5229 -real_normed_field(A) | -hBOOL(hAPP(fun(nat,A),bool,summable(A),B)) | -hBOOL(hAPP(fun(nat,A),bool,summable(A),C)) | hAPP(fun(nat,A),A,suminf(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)),B)),C)) = hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(fun(nat,A),A,suminf(A),B)),hAPP(fun(nat,A),A,suminf(A),C)) # label(fact_3980_suminf__diff) # label(axiom). [clausify(3920)].
% 16.98/16.91 5230 -real_normed_field(A) | -hBOOL(hAPP(fun(nat,A),bool,summable(A),B)) | hAPP(fun(nat,A),A,suminf(A),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),inverse_divide(A)),B)),C)) = hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),hAPP(fun(nat,A),A,suminf(A),B)),C) # label(fact_3981_suminf__divide) # label(axiom). [clausify(3921)].
% 16.98/16.91 5231 -real_normed_field(A) | -hBOOL(hAPP(fun(nat,A),bool,summable(A),B)) | hAPP(fun(nat,A),A,suminf(A),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),inverse_divide(A)),B)),C)) = hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),hAPP(fun(nat,A),A,suminf(A),B)),C) # label(fact_3982_divide_Osuminf) # label(axiom). [clausify(3922)].
% 16.98/16.91 5232 -real_normed_field(A) | -hBOOL(hAPP(fun(nat,A),bool,summable(A),B)) | hAPP(fun(nat,A),A,suminf(A),hAPP(fun(nat,A),fun(nat,A),hAPP(fun(A,A),fun(fun(nat,A),fun(nat,A)),combb(A,A,nat),uminus_uminus(A)),B)) = hAPP(A,A,uminus_uminus(A),hAPP(fun(nat,A),A,suminf(A),B)) # label(fact_3987_suminf__minus) # label(axiom). [clausify(3927)].
% 16.98/16.91 5233 -real_normed_field(A) | -banach(A) | -hBOOL(hAPP(fun(nat,A),bool,summable(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),times_times(A)),B)),hAPP(A,fun(nat,A),power_power(A),C)))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(A,real,norm_norm(A),D)),hAPP(A,real,norm_norm(A),C))) | hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,A),fun(nat,real),hAPP(fun(A,real),fun(fun(nat,A),fun(nat,real)),combb(A,real,nat),norm_norm(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),times_times(A)),B)),hAPP(A,fun(nat,A),power_power(A),D))))) # label(fact_3996_powser__insidea) # label(axiom). [clausify(3936)].
% 16.98/16.91 5234 -real_normed_field(A) | -hBOOL(hAPP(fun(nat,A),bool,summable(A),B)) | hBOOL(hAPP(fun(nat,A),bool,summable(A),hAPP(fun(nat,A),fun(nat,A),hAPP(fun(A,A),fun(fun(nat,A),fun(nat,A)),combb(A,A,nat),uminus_uminus(A)),B))) # label(fact_3998_summable__minus) # label(axiom). [clausify(3938)].
% 16.98/16.91 5235 -real_normed_field(A) | -hBOOL(hAPP(fun(nat,A),bool,summable(A),B)) | hBOOL(hAPP(fun(nat,A),bool,summable(A),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),inverse_divide(A)),B)),C))) # label(fact_4008_divide_Osummable) # label(axiom). [clausify(3948)].
% 16.98/16.91 5236 -real_normed_field(A) | -hBOOL(hAPP(fun(nat,A),bool,summable(A),B)) | hBOOL(hAPP(fun(nat,A),bool,summable(A),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),inverse_divide(A)),B)),C))) # label(fact_4009_summable__divide) # label(axiom). [clausify(3949)].
% 16.98/16.91 5237 -real_normed_field(A) | -hBOOL(hAPP(fun(nat,A),bool,summable(A),B)) | -hBOOL(hAPP(fun(nat,A),bool,summable(A),C)) | hBOOL(hAPP(fun(nat,A),bool,summable(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)),B)),C))) # label(fact_4011_summable__diff) # label(axiom). [clausify(3951)].
% 16.98/16.91 5238 -real_normed_field(A) | -hBOOL(hAPP(fun(nat,A),bool,summable(A),B)) | -hBOOL(hAPP(fun(nat,A),bool,summable(A),C)) | hBOOL(hAPP(fun(nat,A),bool,summable(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),plus_plus(A)),B)),C))) # label(fact_4013_summable__add) # label(axiom). [clausify(3953)].
% 16.98/16.91 5239 -real_normed_field(A) | -banach(A) | -hBOOL(hAPP(fun(nat,A),bool,summable(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),times_times(A)),B)),hAPP(A,fun(nat,A),power_power(A),C)))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(A,real,norm_norm(A),D)),hAPP(A,real,norm_norm(A),C))) | hBOOL(hAPP(fun(nat,A),bool,summable(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),times_times(A)),B)),hAPP(A,fun(nat,A),power_power(A),D)))) # label(fact_4024_powser__inside) # label(axiom). [clausify(3964)].
% 16.98/16.91 5240 -real_normed_field(A) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(A,real,norm_norm(A),B)),one_one(real))) | hBOOL(hAPP(fun(nat,A),bool,summable(A),hAPP(A,fun(nat,A),power_power(A),B))) # label(fact_4026_summable__geometric) # label(axiom). [clausify(3966)].
% 16.98/16.91 5241 -real_normed_field(A) | -hBOOL(hAPP(A,bool,hAPP(fun(nat,A),fun(A,bool),sums(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(fun(nat,A),fun(A,bool),sums(A),hAPP(fun(nat,A),fun(nat,A),hAPP(fun(A,A),fun(fun(nat,A),fun(nat,A)),combb(A,A,nat),uminus_uminus(A)),B)),hAPP(A,A,uminus_uminus(A),C))) # label(fact_4079_sums__minus) # label(axiom). [clausify(4015)].
% 16.98/16.91 5242 -real_normed_field(A) | -hBOOL(hAPP(A,bool,hAPP(fun(nat,A),fun(A,bool),sums(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(fun(nat,A),fun(A,bool),sums(A),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),inverse_divide(A)),B)),D)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),D))) # label(fact_4085_divide_Osums) # label(axiom). [clausify(4021)].
% 16.98/16.91 5243 -real_normed_field(A) | -hBOOL(hAPP(A,bool,hAPP(fun(nat,A),fun(A,bool),sums(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(fun(nat,A),fun(A,bool),sums(A),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),inverse_divide(A)),B)),D)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),D))) # label(fact_4086_sums__divide) # label(axiom). [clausify(4022)].
% 16.98/16.91 5244 -real_normed_field(A) | -hBOOL(hAPP(A,bool,hAPP(fun(nat,A),fun(A,bool),sums(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(fun(nat,A),fun(A,bool),sums(A),D),E)) | hBOOL(hAPP(A,bool,hAPP(fun(nat,A),fun(A,bool),sums(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)),B)),D)),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),C),E))) # label(fact_4087_sums__diff) # label(axiom). [clausify(4023)].
% 16.98/16.91 5245 -real_normed_field(A) | -hBOOL(hAPP(A,bool,hAPP(fun(nat,A),fun(A,bool),sums(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(fun(nat,A),fun(A,bool),sums(A),D),E)) | hBOOL(hAPP(A,bool,hAPP(fun(nat,A),fun(A,bool),sums(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),plus_plus(A)),B)),D)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),E))) # label(fact_4088_sums__add) # label(axiom). [clausify(4024)].
% 16.98/16.91 5246 -real_normed_field(A) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(A,real,norm_norm(A),B)),one_one(real))) | hBOOL(hAPP(A,bool,hAPP(fun(nat,A),fun(A,bool),sums(A),hAPP(A,fun(nat,A),power_power(A),B)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),one_one(A)),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),one_one(A)),B)))) # label(fact_4098_geometric__sums) # label(axiom). [clausify(4034)].
% 16.98/16.91 5247 -real_normed_field(A) | -hBOOL(hAPP(fun(nat,A),bool,cauchy(A),B)) | hBOOL(hAPP(fun(nat,A),bool,cauchy(A),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),inverse_divide(A)),B)),C))) # label(fact_4102_divide_OCauchy) # label(axiom). [clausify(4037)].
% 16.98/16.91 5248 -real_normed_field(A) | -banach(A) | -hBOOL(hAPP(fun(nat,A),bool,summable(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),times_times(A)),B)),hAPP(A,fun(nat,A),power_power(A),C)))) | -hBOOL(hAPP(fun(nat,A),bool,summable(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),times_times(A)),hAPP(fun(nat,A),fun(nat,A),diffs(A),B))),hAPP(A,fun(nat,A),power_power(A),C)))) | -hBOOL(hAPP(fun(nat,A),bool,summable(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),times_times(A)),hAPP(fun(nat,A),fun(nat,A),diffs(A),hAPP(fun(nat,A),fun(nat,A),diffs(A),B)))),hAPP(A,fun(nat,A),power_power(A),C)))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(A,real,norm_norm(A),D)),hAPP(A,real,norm_norm(A),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),hAPP(fun(A,fun(nat,A)),fun(A,A),hAPP(fun(fun(nat,A),A),fun(fun(A,fun(nat,A)),fun(A,A)),combb(fun(nat,A),A,A),suminf(A)),hAPP(fun(A,fun(nat,A)),fun(A,fun(nat,A)),hAPP(fun(fun(nat,A),fun(nat,A)),fun(fun(A,fun(nat,A)),fun(A,fun(nat,A))),combb(fun(nat,A),fun(nat,A),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),times_times(A)),B))),power_power(A)))),D),hAPP(fun(nat,A),A,suminf(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),times_times(A)),hAPP(fun(nat,A),fun(nat,A),diffs(A),B))),hAPP(A,fun(nat,A),power_power(A),D))))) # label(fact_4124_termdiffs) # label(axiom). [clausify(4058)].
% 16.98/16.91 5249 -real_normed_field(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),inverse_divide(A)),C)),D)),E) = hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),C),E)),D) # label(fact_4184_divide_Osetsum) # label(axiom). [clausify(4116)].
% 16.98/16.91 5250 -real_normed_field(A) | -hBOOL(hAPP(fun(nat,A),bool,summable(A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),C)) | hBOOL(hAPP(A,bool,hAPP(fun(nat,A),fun(A,bool),sums(A),hAPP(fun(nat,fun(nat,bool)),fun(nat,A),hAPP(fun(fun(nat,bool),A),fun(fun(nat,fun(nat,bool)),fun(nat,A)),combb(fun(nat,bool),A,nat),hAPP(fun(nat,A),fun(fun(nat,bool),A),big_co1399186613setsum(nat,A),B)),hAPP(fun(nat,nat),fun(nat,fun(nat,bool)),hAPP(fun(nat,fun(nat,fun(nat,bool))),fun(fun(nat,nat),fun(nat,fun(nat,bool))),combs(nat,nat,fun(nat,bool)),hAPP(fun(nat,nat),fun(nat,fun(nat,fun(nat,bool))),hAPP(fun(nat,fun(nat,fun(nat,bool))),fun(fun(nat,nat),fun(nat,fun(nat,fun(nat,bool)))),combb(nat,fun(nat,fun(nat,bool)),nat),ord_atLeastLessThan(nat)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),times_times(nat)),C))),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),plus_plus(nat)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),times_times(nat)),C))),C)))),hAPP(fun(nat,A),A,suminf(A),B))) # label(fact_4231_sums__group) # label(axiom). [clausify(4163)].
% 16.98/16.91 5251 -real_normed_field(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),f605(B,A,D,E,F,C)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),hAPP(fun(B,bool),fun(A,A),hAPP(fun(A,fun(fun(B,bool),A)),fun(fun(B,bool),fun(A,A)),combc(A,fun(B,bool),A),hAPP(fun(A,fun(B,A)),fun(A,fun(fun(B,bool),A)),hAPP(fun(fun(B,A),fun(fun(B,bool),A)),fun(fun(A,fun(B,A)),fun(A,fun(fun(B,bool),A))),combb(fun(B,A),fun(fun(B,bool),A),A),big_co1399186613setsum(B,A)),D)),C)),E),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),hAPP(A,fun(B,A),F,E)),C))) # label(fact_4304_DERIV__setsum) # label(axiom). [clausify(4236)].
% 16.98/16.91 5252 -real_normed_field(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),hAPP(B,fun(A,A),hAPP(fun(A,fun(B,A)),fun(B,fun(A,A)),combc(A,B,A),D),f605(B,A,D,E,F,C))),E),hAPP(B,A,hAPP(A,fun(B,A),F,E),f605(B,A,D,E,F,C)))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),hAPP(fun(B,bool),fun(A,A),hAPP(fun(A,fun(fun(B,bool),A)),fun(fun(B,bool),fun(A,A)),combc(A,fun(B,bool),A),hAPP(fun(A,fun(B,A)),fun(A,fun(fun(B,bool),A)),hAPP(fun(fun(B,A),fun(fun(B,bool),A)),fun(fun(A,fun(B,A)),fun(A,fun(fun(B,bool),A))),combb(fun(B,A),fun(fun(B,bool),A),A),big_co1399186613setsum(B,A)),D)),C)),E),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),hAPP(A,fun(B,A),F,E)),C))) # label(fact_4304_DERIV__setsum) # label(axiom). [clausify(4236)].
% 16.98/16.91 5253 -real_normed_field(A) | -hBOOL(hAPP(filter(nat),bool,hAPP(A,fun(filter(nat),bool),hAPP(fun(nat,A),fun(A,fun(filter(nat),bool)),tendsto(nat,A),B),C),sequentially)) | hBOOL(hAPP(filter(nat),bool,hAPP(A,fun(filter(nat),bool),hAPP(fun(nat,A),fun(A,fun(filter(nat),bool)),tendsto(nat,A),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),inverse_divide(A)),B)),D)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),D)),sequentially)) # label(fact_4467_divide_OLIMSEQ) # label(axiom). [clausify(4395)].
% 16.98/16.91 5254 -real_normed_field(A) | -hBOOL(hAPP(filter(nat),bool,hAPP(A,fun(filter(nat),bool),hAPP(fun(nat,A),fun(A,fun(filter(nat),bool)),tendsto(nat,A),B),C),sequentially)) | -hBOOL(hAPP(filter(nat),bool,hAPP(A,fun(filter(nat),bool),hAPP(fun(nat,A),fun(A,fun(filter(nat),bool)),tendsto(nat,A),D),E),sequentially)) | zero_zero(A) = ti(A,E) | hBOOL(hAPP(filter(nat),bool,hAPP(A,fun(filter(nat),bool),hAPP(fun(nat,A),fun(A,fun(filter(nat),bool)),tendsto(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),inverse_divide(A)),B)),D)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),E)),sequentially)) # label(fact_4469_LIMSEQ__divide) # label(axiom). [clausify(4397)].
% 16.98/16.91 5255 -real_normed_field(A) | -hBOOL(hAPP(filter(B),bool,hAPP(A,fun(filter(B),bool),hAPP(fun(B,A),fun(A,fun(filter(B),bool)),tendsto(B,A),C),D),E)) | -hBOOL(hAPP(filter(B),bool,hAPP(A,fun(filter(B),bool),hAPP(fun(B,A),fun(A,fun(filter(B),bool)),tendsto(B,A),F),V6),E)) | zero_zero(A) = ti(A,V6) | hBOOL(hAPP(filter(B),bool,hAPP(A,fun(filter(B),bool),hAPP(fun(B,A),fun(A,fun(filter(B),bool)),tendsto(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),inverse_divide(A)),C)),F)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),V6)),E)) # label(fact_4470_tendsto__divide) # label(axiom). [clausify(4398)].
% 16.98/16.91 5256 -real_normed_field(A) | -hBOOL(hAPP(filter(B),bool,hAPP(A,fun(filter(B),bool),hAPP(fun(B,A),fun(A,fun(filter(B),bool)),tendsto(B,A),C),D),E)) | hBOOL(hAPP(filter(B),bool,hAPP(A,fun(filter(B),bool),hAPP(fun(B,A),fun(A,fun(filter(B),bool)),tendsto(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),inverse_divide(A)),C)),F)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),F)),E)) # label(fact_4474_divide_Otendsto) # label(axiom). [clausify(4402)].
% 16.98/16.91 5257 -real_normed_field(A) | -hBOOL(hAPP(fun(nat,A),bool,summable(A),B)) | hBOOL(hAPP(filter(nat),bool,hAPP(A,fun(filter(nat),bool),hAPP(fun(nat,A),fun(A,fun(filter(nat),bool)),tendsto(nat,A),B),zero_zero(A)),sequentially)) # label(fact_4489_summable__LIMSEQ__zero) # label(axiom). [clausify(4417)].
% 16.98/16.91 5258 -real_normed_field(A) | -banach(A) | -hBOOL(hAPP(fun(nat,A),bool,summable(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),times_times(A)),hAPP(fun(nat,A),fun(nat,A),diffs(A),hAPP(fun(nat,A),fun(nat,A),diffs(A),B)))),hAPP(A,fun(nat,A),power_power(A),C)))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(A,real,norm_norm(A),D)),hAPP(A,real,norm_norm(A),C))) | hBOOL(hAPP(filter(A),bool,hAPP(A,fun(filter(A),bool),hAPP(fun(A,A),fun(A,fun(filter(A),bool)),tendsto(A,A),hAPP(fun(A,fun(nat,A)),fun(A,A),hAPP(fun(fun(nat,A),A),fun(fun(A,fun(nat,A)),fun(A,A)),combb(fun(nat,A),A,A),suminf(A)),hAPP(fun(A,fun(nat,A)),fun(A,fun(nat,A)),hAPP(fun(fun(nat,A),fun(nat,A)),fun(fun(A,fun(nat,A)),fun(A,fun(nat,A))),combb(fun(nat,A),fun(nat,A),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),times_times(A)),B))),hAPP(fun(nat,A),fun(A,fun(nat,A)),hAPP(fun(A,fun(fun(nat,A),fun(nat,A))),fun(fun(nat,A),fun(A,fun(nat,A))),combc(A,fun(nat,A),fun(nat,A)),hAPP(fun(A,fun(nat,fun(A,A))),fun(A,fun(fun(nat,A),fun(nat,A))),hAPP(fun(fun(nat,fun(A,A)),fun(fun(nat,A),fun(nat,A))),fun(fun(A,fun(nat,fun(A,A))),fun(A,fun(fun(nat,A),fun(nat,A)))),combb(fun(nat,fun(A,A)),fun(fun(nat,A),fun(nat,A)),A),combs(nat,A,A)),hAPP(fun(A,fun(nat,A)),fun(A,fun(nat,fun(A,A))),hAPP(fun(fun(nat,A),fun(nat,fun(A,A))),fun(fun(A,fun(nat,A)),fun(A,fun(nat,fun(A,A)))),combb(fun(nat,A),fun(nat,fun(A,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))),hAPP(fun(A,A),fun(A,fun(nat,A)),hAPP(fun(A,fun(A,fun(nat,A))),fun(fun(A,A),fun(A,fun(nat,A))),combs(A,A,fun(nat,A)),hAPP(fun(A,fun(nat,fun(A,A))),fun(A,fun(A,fun(nat,A))),hAPP(fun(fun(nat,fun(A,A)),fun(A,fun(nat,A))),fun(fun(A,fun(nat,fun(A,A))),fun(A,fun(A,fun(nat,A)))),combb(fun(nat,fun(A,A)),fun(A,fun(nat,A)),A),combc(nat,A,A)),hAPP(fun(A,fun(nat,A)),fun(A,fun(nat,fun(A,A))),hAPP(fun(fun(nat,A),fun(nat,fun(A,A))),fun(fun(A,fun(nat,A)),fun(A,fun(nat,fun(A,A)))),combb(fun(nat,A),fun(nat,fun(A,A)),A),hAPP(fun(A,fun(A,A)),fun(fun(nat,A),fun(nat,fun(A,A))),combb(A,fun(A,A),nat),inverse_divide(A))),hAPP(fun(nat,A),fun(A,fun(nat,A)),hAPP(fun(A,fun(fun(nat,A),fun(nat,A))),fun(fun(nat,A),fun(A,fun(nat,A))),combc(A,fun(nat,A),fun(nat,A)),hAPP(fun(A,fun(nat,fun(A,A))),fun(A,fun(fun(nat,A),fun(nat,A))),hAPP(fun(fun(nat,fun(A,A)),fun(fun(nat,A),fun(nat,A))),fun(fun(A,fun(nat,fun(A,A))),fun(A,fun(fun(nat,A),fun(nat,A)))),combb(fun(nat,fun(A,A)),fun(fun(nat,A),fun(nat,A)),A),combs(nat,A,A)),hAPP(fun(A,fun(nat,A)),fun(A,fun(nat,fun(A,A))),hAPP(fun(fun(nat,A),fun(nat,fun(A,A))),fun(fun(A,fun(nat,A)),fun(A,fun(nat,fun(A,A)))),combb(fun(nat,A),fun(nat,fun(A,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))),hAPP(fun(A,A),fun(A,fun(nat,A)),hAPP(fun(A,fun(nat,A)),fun(fun(A,A),fun(A,fun(nat,A))),combb(A,fun(nat,A),A),power_power(A)),hAPP(A,fun(A,A),plus_plus(A),D))))),hAPP(A,fun(nat,A),power_power(A),D))))),combi(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),times_times(A)),semiring_1_of_nat(A))),hAPP(fun(nat,nat),fun(nat,A),hAPP(fun(nat,A),fun(fun(nat,nat),fun(nat,A)),combb(nat,A,nat),hAPP(A,fun(nat,A),power_power(A),D)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),minus_minus(nat)),hAPP(nat,nat,suc,zero_zero(nat))))))))),zero_zero(A)),hAPP(A,filter(A),at(A),zero_zero(A)))) # label(fact_4532_termdiffs__aux) # label(axiom). [clausify(4459)].
% 16.98/16.91 5259 -topological_space(A) | -real_normed_field(B) | -hBOOL(hAPP(filter(A),bool,hAPP(B,fun(filter(A),bool),hAPP(fun(A,B),fun(B,fun(filter(A),bool)),tendsto(A,B),C),D),hAPP(A,filter(A),at(A),E))) | hBOOL(hAPP(filter(A),bool,hAPP(B,fun(filter(A),bool),hAPP(fun(A,B),fun(B,fun(filter(A),bool)),tendsto(A,B),hAPP(B,fun(A,B),hAPP(fun(A,fun(B,B)),fun(B,fun(A,B)),combc(A,B,B),hAPP(fun(A,B),fun(A,fun(B,B)),hAPP(fun(B,fun(B,B)),fun(fun(A,B),fun(A,fun(B,B))),combb(B,fun(B,B),A),inverse_divide(B)),C)),F)),hAPP(B,B,hAPP(B,fun(B,B),inverse_divide(B),D),F)),hAPP(A,filter(A),at(A),E))) # label(fact_4552_divide_OLIM) # label(axiom). [clausify(4479)].
% 16.98/16.91 5260 -real_normed_field(A) | hBOOL(hAPP(filter(A),bool,hAPP(A,fun(filter(A),bool),hAPP(fun(A,A),fun(A,fun(filter(A),bool)),tendsto(A,A),hAPP(A,fun(A,A),hAPP(fun(A,fun(A,A)),fun(A,fun(A,A)),combc(A,A,A),inverse_divide(A)),B)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),B)),hAPP(A,filter(A),at(A),C))) # label(fact_4553_divide_Ocont) # label(axiom). [clausify(4480)].
% 16.98/16.91 5261 -topological_space(A) | -real_normed_field(B) | -hBOOL(hAPP(filter(A),bool,hAPP(B,fun(filter(A),bool),hAPP(fun(A,B),fun(B,fun(filter(A),bool)),tendsto(A,B),C),zero_zero(B)),hAPP(A,filter(A),at(A),D))) | hBOOL(hAPP(filter(A),bool,hAPP(B,fun(filter(A),bool),hAPP(fun(A,B),fun(B,fun(filter(A),bool)),tendsto(A,B),hAPP(B,fun(A,B),hAPP(fun(A,fun(B,B)),fun(B,fun(A,B)),combc(A,B,B),hAPP(fun(A,B),fun(A,fun(B,B)),hAPP(fun(B,fun(B,B)),fun(fun(A,B),fun(A,fun(B,B))),combb(B,fun(B,B),A),inverse_divide(B)),C)),E)),zero_zero(B)),hAPP(A,filter(A),at(A),D))) # label(fact_4587_divide_OLIM__zero) # label(axiom). [clausify(4514)].
% 16.98/16.91 5262 -real_normed_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),B),C),D)) | hBOOL(hAPP(filter(A),bool,hAPP(A,fun(filter(A),bool),hAPP(fun(A,A),fun(A,fun(filter(A),bool)),tendsto(A,A),hAPP(fun(A,A),fun(A,A),hAPP(fun(A,fun(A,A)),fun(fun(A,A),fun(A,A)),combs(A,A,A),hAPP(fun(A,A),fun(A,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(A,A),fun(A,fun(A,A))),combb(A,fun(A,A),A),inverse_divide(A)),hAPP(A,fun(A,A),hAPP(fun(A,fun(A,A)),fun(A,fun(A,A)),combc(A,A,A),hAPP(fun(A,A),fun(A,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(A,A),fun(A,fun(A,A))),combb(A,fun(A,A),A),minus_minus(A)),B)),hAPP(A,A,B,C)))),hAPP(A,fun(A,A),hAPP(fun(A,fun(A,A)),fun(A,fun(A,A)),combc(A,A,A),minus_minus(A)),C))),D),hAPP(A,filter(A),at(A),C))) # label(fact_4605_DERIV__iff2) # label(axiom). [clausify(4532)].
% 16.98/16.91 5263 -real_normed_field(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),B),C),D)) | -hBOOL(hAPP(filter(A),bool,hAPP(A,fun(filter(A),bool),hAPP(fun(A,A),fun(A,fun(filter(A),bool)),tendsto(A,A),hAPP(fun(A,A),fun(A,A),hAPP(fun(A,fun(A,A)),fun(fun(A,A),fun(A,A)),combs(A,A,A),hAPP(fun(A,A),fun(A,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(A,A),fun(A,fun(A,A))),combb(A,fun(A,A),A),inverse_divide(A)),hAPP(A,fun(A,A),hAPP(fun(A,fun(A,A)),fun(A,fun(A,A)),combc(A,A,A),hAPP(fun(A,A),fun(A,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(A,A),fun(A,fun(A,A))),combb(A,fun(A,A),A),minus_minus(A)),B)),hAPP(A,A,B,C)))),hAPP(A,fun(A,A),hAPP(fun(A,fun(A,A)),fun(A,fun(A,A)),combc(A,A,A),minus_minus(A)),C))),D),hAPP(A,filter(A),at(A),C))) # label(fact_4605_DERIV__iff2) # label(axiom). [clausify(4532)].
% 16.98/16.91 5264 -real_normed_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),B),C),D)) | hBOOL(hAPP(filter(A),bool,hAPP(A,fun(filter(A),bool),hAPP(fun(A,A),fun(A,fun(filter(A),bool)),tendsto(A,A),hAPP(fun(A,A),fun(A,A),hAPP(fun(A,fun(A,A)),fun(fun(A,A),fun(A,A)),combs(A,A,A),hAPP(fun(A,A),fun(A,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(A,A),fun(A,fun(A,A))),combb(A,fun(A,A),A),inverse_divide(A)),hAPP(A,fun(A,A),hAPP(fun(A,fun(A,A)),fun(A,fun(A,A)),combc(A,A,A),hAPP(fun(A,A),fun(A,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(A,A),fun(A,fun(A,A))),combb(A,fun(A,A),A),minus_minus(A)),hAPP(fun(A,A),fun(A,A),hAPP(fun(A,A),fun(fun(A,A),fun(A,A)),combb(A,A,A),B),hAPP(A,fun(A,A),plus_plus(A),C)))),hAPP(A,A,B,C)))),combi(A))),D),hAPP(A,filter(A),at(A),zero_zero(A)))) # label(fact_4623_DERIV__D) # label(axiom). [clausify(4550)].
% 16.98/16.91 5265 -real_normed_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),B),C),D)) | hBOOL(hAPP(filter(A),bool,hAPP(A,fun(filter(A),bool),hAPP(fun(A,A),fun(A,fun(filter(A),bool)),tendsto(A,A),hAPP(fun(A,A),fun(A,A),hAPP(fun(A,fun(A,A)),fun(fun(A,A),fun(A,A)),combs(A,A,A),hAPP(fun(A,A),fun(A,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(A,A),fun(A,fun(A,A))),combb(A,fun(A,A),A),inverse_divide(A)),hAPP(A,fun(A,A),hAPP(fun(A,fun(A,A)),fun(A,fun(A,A)),combc(A,A,A),hAPP(fun(A,A),fun(A,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(A,A),fun(A,fun(A,A))),combb(A,fun(A,A),A),minus_minus(A)),hAPP(fun(A,A),fun(A,A),hAPP(fun(A,A),fun(fun(A,A),fun(A,A)),combb(A,A,A),B),hAPP(A,fun(A,A),plus_plus(A),C)))),hAPP(A,A,B,C)))),combi(A))),D),hAPP(A,filter(A),at(A),zero_zero(A)))) # label(fact_4624_DERIV__iff) # label(axiom). [clausify(4551)].
% 16.98/16.91 5266 -real_normed_field(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),B),C),D)) | -hBOOL(hAPP(filter(A),bool,hAPP(A,fun(filter(A),bool),hAPP(fun(A,A),fun(A,fun(filter(A),bool)),tendsto(A,A),hAPP(fun(A,A),fun(A,A),hAPP(fun(A,fun(A,A)),fun(fun(A,A),fun(A,A)),combs(A,A,A),hAPP(fun(A,A),fun(A,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(A,A),fun(A,fun(A,A))),combb(A,fun(A,A),A),inverse_divide(A)),hAPP(A,fun(A,A),hAPP(fun(A,fun(A,A)),fun(A,fun(A,A)),combc(A,A,A),hAPP(fun(A,A),fun(A,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(A,A),fun(A,fun(A,A))),combb(A,fun(A,A),A),minus_minus(A)),hAPP(fun(A,A),fun(A,A),hAPP(fun(A,A),fun(fun(A,A),fun(A,A)),combb(A,A,A),B),hAPP(A,fun(A,A),plus_plus(A),C)))),hAPP(A,A,B,C)))),combi(A))),D),hAPP(A,filter(A),at(A),zero_zero(A)))) # label(fact_4624_DERIV__iff) # label(axiom). [clausify(4551)].
% 16.98/16.91 5267 -real_normed_field(A) | -banach(B) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),C)) | -hBOOL(hAPP(fun(nat,real),bool,summable(real),D)) | zero_zero(A) != ti(A,f682(B,A,E,D,C)) | hBOOL(hAPP(filter(A),bool,hAPP(B,fun(filter(A),bool),hAPP(fun(A,B),fun(B,fun(filter(A),bool)),tendsto(A,B),hAPP(fun(A,fun(nat,B)),fun(A,B),hAPP(fun(fun(nat,B),B),fun(fun(A,fun(nat,B)),fun(A,B)),combb(fun(nat,B),B,A),suminf(B)),E)),zero_zero(B)),hAPP(A,filter(A),at(A),zero_zero(A)))) # label(fact_4629_lemma__termdiff5) # label(axiom). [clausify(4555)].
% 16.98/16.91 5268 -real_normed_field(A) | -banach(B) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),C)) | -hBOOL(hAPP(fun(nat,real),bool,summable(real),D)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(A,real,norm_norm(A),f682(B,A,E,D,C))),C)) | hBOOL(hAPP(filter(A),bool,hAPP(B,fun(filter(A),bool),hAPP(fun(A,B),fun(B,fun(filter(A),bool)),tendsto(A,B),hAPP(fun(A,fun(nat,B)),fun(A,B),hAPP(fun(fun(nat,B),B),fun(fun(A,fun(nat,B)),fun(A,B)),combb(fun(nat,B),B,A),suminf(B)),E)),zero_zero(B)),hAPP(A,filter(A),at(A),zero_zero(A)))) # label(fact_4629_lemma__termdiff5) # label(axiom). [clausify(4555)].
% 16.98/16.91 5269 -real_normed_field(A) | -banach(B) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),C)) | -hBOOL(hAPP(fun(nat,real),bool,summable(real),D)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(B,real,norm_norm(B),hAPP(nat,B,hAPP(A,fun(nat,B),E,f682(B,A,E,D,C)),f683(B,A,E,D,C)))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,D,f683(B,A,E,D,C))),hAPP(A,real,norm_norm(A),f682(B,A,E,D,C))))) | hBOOL(hAPP(filter(A),bool,hAPP(B,fun(filter(A),bool),hAPP(fun(A,B),fun(B,fun(filter(A),bool)),tendsto(A,B),hAPP(fun(A,fun(nat,B)),fun(A,B),hAPP(fun(fun(nat,B),B),fun(fun(A,fun(nat,B)),fun(A,B)),combb(fun(nat,B),B,A),suminf(B)),E)),zero_zero(B)),hAPP(A,filter(A),at(A),zero_zero(A)))) # label(fact_4629_lemma__termdiff5) # label(axiom). [clausify(4555)].
% 16.98/16.91 5270 -real_normed_field(A) | -real_normed_vector(B) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),C)) | zero_zero(A) != ti(A,f684(B,A,D,E,C)) | hBOOL(hAPP(filter(A),bool,hAPP(B,fun(filter(A),bool),hAPP(fun(A,B),fun(B,fun(filter(A),bool)),tendsto(A,B),D),zero_zero(B)),hAPP(A,filter(A),at(A),zero_zero(A)))) # label(fact_4630_lemma__termdiff4) # label(axiom). [clausify(4556)].
% 16.98/16.91 5271 -real_normed_field(A) | -real_normed_vector(B) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(A,real,norm_norm(A),f684(B,A,D,E,C))),C)) | hBOOL(hAPP(filter(A),bool,hAPP(B,fun(filter(A),bool),hAPP(fun(A,B),fun(B,fun(filter(A),bool)),tendsto(A,B),D),zero_zero(B)),hAPP(A,filter(A),at(A),zero_zero(A)))) # label(fact_4630_lemma__termdiff4) # label(axiom). [clausify(4556)].
% 16.98/16.91 5272 -real_normed_field(A) | -real_normed_vector(B) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),C)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(B,real,norm_norm(B),hAPP(A,B,D,f684(B,A,D,E,C)))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),E),hAPP(A,real,norm_norm(A),f684(B,A,D,E,C))))) | hBOOL(hAPP(filter(A),bool,hAPP(B,fun(filter(A),bool),hAPP(fun(A,B),fun(B,fun(filter(A),bool)),tendsto(A,B),D),zero_zero(B)),hAPP(A,filter(A),at(A),zero_zero(A)))) # label(fact_4630_lemma__termdiff4) # label(axiom). [clausify(4556)].
% 16.98/16.91 5273 -real_normed_field(A) | hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),B),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),D)) = hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),B),C)),D) # label(fact_4694_divide_OscaleR) # label(axiom). [clausify(4620)].
% 16.98/16.91 5274 -real_normed_field(A) | -banach(A) | hAPP(fun(nat,A),A,suminf(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,real),fun(nat,fun(A,A)),hAPP(fun(real,fun(A,A)),fun(fun(nat,real),fun(nat,fun(A,A))),combb(real,fun(A,A),nat),scaleR_scaleR(A)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),inverse_inverse(real)),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),fact_fact(nat))))),hAPP(A,fun(nat,A),power_power(A),B))) = hAPP(A,A,exp(A),B) # label(fact_4757_lemma__exp__ext) # label(axiom). [clausify(4683)].
% 16.98/16.91 5275 -real_normed_field(A) | -banach(A) | hAPP(fun(nat,A),A,suminf(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,real),fun(nat,fun(A,A)),hAPP(fun(real,fun(A,A)),fun(fun(nat,real),fun(nat,fun(A,A))),combb(real,fun(A,A),nat),scaleR_scaleR(A)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),inverse_inverse(real)),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),fact_fact(nat))))),hAPP(A,fun(nat,A),power_power(A),B))) = hAPP(A,A,exp(A),B) # label(fact_4758_exp__def) # label(axiom). [clausify(4684)].
% 16.98/16.91 5276 -real_normed_field(A) | -banach(A) | hBOOL(hAPP(A,bool,hAPP(fun(nat,A),fun(A,bool),sums(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,real),fun(nat,fun(A,A)),hAPP(fun(real,fun(A,A)),fun(fun(nat,real),fun(nat,fun(A,A))),combb(real,fun(A,A),nat),scaleR_scaleR(A)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),inverse_inverse(real)),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),fact_fact(nat))))),hAPP(A,fun(nat,A),power_power(A),B))),hAPP(A,A,exp(A),B))) # label(fact_4759_exp__converges) # label(axiom). [clausify(4685)].
% 16.98/16.91 5277 -real_normed_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),B),C),D)) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,f828(A,B,C,D),E)),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),E),C)) = hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(A,A,B,E)),hAPP(A,A,B,C)) # label(fact_4889_CARAT__DERIV) # label(axiom). [clausify(4809)].
% 16.98/16.91 5278 -real_normed_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),B),C),D)) | hBOOL(hAPP(A,bool,hAPP(fun(A,A),fun(A,bool),isCont(A,A),f828(A,B,C,D)),C)) # label(fact_4889_CARAT__DERIV) # label(axiom). [clausify(4809)].
% 16.98/16.91 5279 -real_normed_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),B),C),D)) | hAPP(A,A,f828(A,B,C,D),C) = ti(A,D) # label(fact_4889_CARAT__DERIV) # label(axiom). [clausify(4809)].
% 16.98/16.91 5280 -real_normed_field(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),B),C),D)) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,E,f829(A,B,C,D,E))),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),f829(A,B,C,D,E)),C)) != hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(A,A,B,f829(A,B,C,D,E))),hAPP(A,A,B,C)) | -hBOOL(hAPP(A,bool,hAPP(fun(A,A),fun(A,bool),isCont(A,A),E),C)) | hAPP(A,A,E,C) != ti(A,D) # label(fact_4889_CARAT__DERIV) # label(axiom). [clausify(4809)].
% 16.98/16.91 5281 -real_normed_field(A) | hBOOL(hAPP(A,bool,hAPP(fun(A,A),fun(A,bool),isCont(A,A),hAPP(A,fun(A,A),hAPP(fun(A,fun(A,A)),fun(A,fun(A,A)),combc(A,A,A),inverse_divide(A)),B)),C)) # label(fact_4908_divide_OisCont) # label(axiom). [clausify(4828)].
% 16.98/16.91 5282 -real_normed_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),B),C),D)) | hBOOL(hAPP(A,bool,hAPP(fun(A,A),fun(A,bool),isCont(A,A),B),C)) # label(fact_4914_DERIV__isCont) # label(axiom). [clausify(4834)].
% 16.98/16.91 5283 -real_normed_field(A) | -banach(A) | hBOOL(hAPP(A,bool,hAPP(fun(A,A),fun(A,bool),isCont(A,A),exp(A)),B)) # label(fact_4919_isCont__exp) # label(axiom). [clausify(4839)].
% 16.98/16.92 Derived: deriv(real) = ti(fun(fun(real,real),fun(real,fun(real,bool))),deriv(real)). [resolve(5180,a,5181,a)].
% 16.98/16.92 Derived: -banach(real) | exp(real) = ti(fun(real,real),exp(real)). [resolve(5180,a,5182,a)].
% 16.98/16.92 Derived: hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),zero_zero(real)),A) = zero_zero(real). [resolve(5180,a,5183,a)].
% 16.98/16.92 Derived: hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),C),B)) = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),C)),B). [resolve(5180,a,5184,a)].
% 16.98/16.92 Derived: hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),C),B)) = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),C)),B). [resolve(5180,a,5185,a)].
% 16.98/16.92 Derived: hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,uminus_uminus(real),A)),B) = hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B)). [resolve(5180,a,5186,a)].
% 16.98/16.92 Derived: zero_zero(real) = ti(real,A) | zero_zero(real) = ti(real,B) | hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,inverse_inverse(real),A)),hAPP(real,real,inverse_inverse(real),B))),C) = hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,inverse_inverse(real),A)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),B)),C))),hAPP(real,real,inverse_inverse(real),B))). [resolve(5180,a,5187,a)].
% 16.98/16.92 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(real,fun(real,real),times_times(real),A)),B),A)). [resolve(5180,a,5188,a)].
% 16.98/16.92 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),A),B),C)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),A),B),D)) | ti(real,C) = ti(real,D). [resolve(5180,a,5189,a)].
% 16.98/16.92 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),A),B),C)) | ti(real,C) != ti(real,D) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),A),B),D)). [resolve(5180,a,5190,a)].
% 16.98/16.92 Derived: -banach(real) | hAPP(real,real,exp(real),A) != zero_zero(real). [resolve(5180,a,5192,a)].
% 16.98/16.92 Derived: -banach(real) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),exp(real)),A),hAPP(real,real,exp(real),A))). [resolve(5180,a,5193,a)].
% 16.98/16.92 Derived: -banach(real) | hAPP(real,real,exp(real),zero_zero(real)) = one_one(real). [resolve(5180,a,5194,a)].
% 16.98/16.92 Derived: -banach(real) | hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,exp(real),A)),hAPP(real,real,exp(real),B)) = hAPP(real,real,exp(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),B)). [resolve(5180,a,5195,a)].
% 16.98/16.92 Derived: -banach(real) | hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,exp(real),A)),hAPP(real,real,exp(real),B)) = hAPP(real,real,exp(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),B)). [resolve(5180,a,5197,a)].
% 16.98/16.92 Derived: -banach(real) | hAPP(real,real,exp(real),hAPP(real,real,uminus_uminus(real),A)) = hAPP(real,real,inverse_inverse(real),hAPP(real,real,exp(real),A)). [resolve(5180,a,5198,a)].
% 16.98/16.92 Derived: zero_zero(real) = ti(real,A) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,norm_norm(real),B)),C)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,norm_norm(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),B),A))),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,norm_norm(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),B),A)),D)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),B),D))),A)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,semiring_1_of_nat(real),D)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),D),hAPP(nat,nat,suc,zero_zero(nat)))))))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,semiring_1_of_nat(real),D)),hAPP(nat,real,semiring_1_of_nat(real),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),D),hAPP(nat,nat,suc,zero_zero(nat)))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),C),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),D),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))),hAPP(real,real,norm_norm(real),A)))). [resolve(5180,a,5199,a)].
% 16.98/16.92 Derived: -field_inverse_zero(real) | hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,norm_norm(real),A)),hAPP(real,real,norm_norm(real),B)) = hAPP(real,real,norm_norm(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B)). [resolve(5180,a,5200,b)].
% 16.98/16.92 Derived: zero_zero(real) = ti(real,A) | hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,norm_norm(real),B)),hAPP(real,real,norm_norm(real),A)) = hAPP(real,real,norm_norm(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),B),A)). [resolve(5180,a,5201,a)].
% 16.98/16.92 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),f257(real,A))). [resolve(5180,a,5202,a)].
% 16.98/16.92 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,norm_norm(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,norm_norm(real),A)),f257(real,B)))). [resolve(5180,a,5203,a)].
% 16.98/16.92 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),f264(real,A))). [resolve(5180,a,5204,a)].
% 16.98/16.92 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,norm_norm(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,norm_norm(real),A)),f264(real,B)))). [resolve(5180,a,5205,a)].
% 16.98/16.92 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,norm_norm(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,norm_norm(real),A)),f270(real,B)))). [resolve(5180,a,5206,a)].
% 16.98/16.92 Derived: -banach(real) | hAPP(real,real,of_real(real),hAPP(real,real,exp(real),A)) = hAPP(real,real,exp(real),hAPP(real,real,of_real(real),A)). [resolve(5180,a,5207,a)].
% 16.98/16.92 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),A),B),C)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),D),B),E)) | hAPP(real,real,D,B) = zero_zero(real) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,real)),combs(real,real,real),hAPP(fun(real,real),fun(real,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,fun(real,real))),combb(real,fun(real,real),real),inverse_divide(real)),A)),D)),B),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),hAPP(real,real,D,B))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,A,B)),E))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,D,B)),hAPP(real,real,D,B))))). [resolve(5180,a,5208,a)].
% 16.98/16.92 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),A),B),C)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),D),B),E)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,real)),combs(real,real,real),hAPP(fun(real,real),fun(real,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,fun(real,real))),combb(real,fun(real,real),real),plus_plus(real)),A)),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,real),fun(fun(real,real),fun(real,real)),combb(real,real,real),uminus_uminus(real)),D))),B),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),C),hAPP(real,real,uminus_uminus(real),E)))). [resolve(5180,a,5209,a)].
% 16.98/16.92 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),A),B),C)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),D),B),E)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,real)),combs(real,real,real),hAPP(fun(real,real),fun(real,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,fun(real,real))),combb(real,fun(real,real),real),times_times(real)),A)),D)),B),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),hAPP(real,real,D,B))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),E),hAPP(real,real,A,B))))). [resolve(5180,a,5210,a)].
% 16.98/16.92 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),A),B),C)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),D),B),E)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,real)),combs(real,real,real),hAPP(fun(real,real),fun(real,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,fun(real,real))),combb(real,fun(real,real),real),times_times(real)),A)),D)),B),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,A,B)),E)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),hAPP(real,real,D,B))))). [resolve(5180,a,5211,a)].
% 16.98/16.92 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),A),B),C)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),D),B),E)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,real)),combs(real,real,real),hAPP(fun(real,real),fun(real,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,fun(real,real))),combb(real,fun(real,real),real),plus_plus(real)),A)),D)),B),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),C),E))). [resolve(5180,a,5212,a)].
% 16.98/16.92 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),A),B),C)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),D),B),E)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,real)),combs(real,real,real),hAPP(fun(real,real),fun(real,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,fun(real,real))),combb(real,fun(real,real),real),minus_minus(real)),A)),D)),B),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),C),E))). [resolve(5180,a,5213,a)].
% 16.98/16.92 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),combi(real)),A),one_one(real))). [resolve(5180,a,5214,a)].
% 16.98/16.92 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(real,fun(real,real),combk(real,real),A)),B),zero_zero(real))). [resolve(5180,a,5215,a)].
% 16.98/16.92 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),A),B),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(real,fun(real,real),hAPP(fun(real,fun(real,real)),fun(real,fun(real,real)),combc(real,real,real),hAPP(fun(real,real),fun(real,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,fun(real,real))),combb(real,fun(real,real),real),inverse_divide(real)),A)),D)),B),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),C),D))). [resolve(5180,a,5216,a)].
% 16.98/16.92 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),A),B),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,real),fun(fun(real,real),fun(real,real)),combb(real,real,real),hAPP(real,fun(real,real),times_times(real),D)),A)),B),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),D),C))). [resolve(5180,a,5217,a)].
% 16.98/16.92 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),A),B),C)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),D),hAPP(real,real,A,B)),E)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,real),fun(fun(real,real),fun(real,real)),combb(real,real,real),D),A)),B),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),E),C))). [resolve(5180,a,5218,a)].
% 16.98/16.92 Derived: -banach(real) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),A),B),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,real),fun(fun(real,real),fun(real,real)),combb(real,real,real),exp(real)),A)),B),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,exp(real),hAPP(real,real,A,B))),C))). [resolve(5180,a,5220,a)].
% 16.98/16.92 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),A),B),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,real),fun(fun(real,real),fun(real,real)),combb(real,real,real),uminus_uminus(real)),A)),B),hAPP(real,real,uminus_uminus(real),C))). [resolve(5180,a,5221,a)].
% 16.98/16.92 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),A),B),C)) | hAPP(real,real,A,B) = zero_zero(real) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,real),fun(fun(real,real),fun(real,real)),combb(real,real,real),inverse_inverse(real)),A)),B),hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,inverse_inverse(real),hAPP(real,real,A,B))),C)),hAPP(real,real,inverse_inverse(real),hAPP(real,real,A,B)))))). [resolve(5180,a,5222,a)].
% 16.98/16.93 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),A),B),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(nat,fun(real,real),hAPP(fun(real,fun(nat,real)),fun(nat,fun(real,real)),combc(real,nat,real),hAPP(fun(real,real),fun(real,fun(nat,real)),hAPP(fun(real,fun(nat,real)),fun(fun(real,real),fun(real,fun(nat,real))),combb(real,fun(nat,real),real),power_power(real)),A)),hAPP(nat,nat,suc,D))),B),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),one_one(real)),hAPP(nat,real,semiring_1_of_nat(real),D))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,A,B)),D))))). [resolve(5180,a,5223,a)].
% 16.98/16.93 Derived: zero_zero(real) = ti(real,A) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),inverse_inverse(real)),A),hAPP(real,real,uminus_uminus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,inverse_inverse(real),A)),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat))))))). [resolve(5180,a,5224,a)].
% 16.98/16.93 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),A),B),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(nat,fun(real,real),hAPP(fun(real,fun(nat,real)),fun(nat,fun(real,real)),combc(real,nat,real),hAPP(fun(real,real),fun(real,fun(nat,real)),hAPP(fun(real,fun(nat,real)),fun(fun(real,real),fun(real,fun(nat,real))),combb(real,fun(nat,real),real),power_power(real)),A)),D)),B),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,semiring_1_of_nat(real),D)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,A,B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),D),hAPP(nat,nat,suc,zero_zero(nat)))))))). [resolve(5180,a,5225,a)].
% 16.98/16.93 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),A),B),C)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),D),B),E)) | hAPP(real,real,D,B) = zero_zero(real) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,real)),combs(real,real,real),hAPP(fun(real,real),fun(real,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,fun(real,real))),combb(real,fun(real,real),real),inverse_divide(real)),A)),D)),B),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),hAPP(real,real,D,B))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),E),hAPP(real,real,A,B)))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,D,B)),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat))))))). [resolve(5180,a,5226,a)].
% 16.98/16.93 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),A),B),C)) | hAPP(real,real,A,B) = zero_zero(real) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,real),fun(fun(real,real),fun(real,real)),combb(real,real,real),inverse_inverse(real)),A)),B),hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),hAPP(real,real,inverse_inverse(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,A,B)),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat))))))))). [resolve(5180,a,5227,a)].
% 16.98/16.93 Derived: -hBOOL(hAPP(fun(nat,real),bool,summable(real),A)) | -hBOOL(hAPP(fun(nat,real),bool,summable(real),B)) | hAPP(fun(nat,real),real,suminf(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),plus_plus(real)),A)),B)) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(fun(nat,real),real,suminf(real),A)),hAPP(fun(nat,real),real,suminf(real),B)). [resolve(5180,a,5228,a)].
% 16.98/16.93 Derived: -hBOOL(hAPP(fun(nat,real),bool,summable(real),A)) | -hBOOL(hAPP(fun(nat,real),bool,summable(real),B)) | hAPP(fun(nat,real),real,suminf(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),minus_minus(real)),A)),B)) = hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(fun(nat,real),real,suminf(real),A)),hAPP(fun(nat,real),real,suminf(real),B)). [resolve(5180,a,5229,a)].
% 16.98/16.93 Derived: -hBOOL(hAPP(fun(nat,real),bool,summable(real),A)) | hAPP(fun(nat,real),real,suminf(real),hAPP(real,fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(real,fun(nat,real)),combc(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),inverse_divide(real)),A)),B)) = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(fun(nat,real),real,suminf(real),A)),B). [resolve(5180,a,5230,a)].
% 16.98/16.93 Derived: -hBOOL(hAPP(fun(nat,real),bool,summable(real),A)) | hAPP(fun(nat,real),real,suminf(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),uminus_uminus(real)),A)) = hAPP(real,real,uminus_uminus(real),hAPP(fun(nat,real),real,suminf(real),A)). [resolve(5180,a,5232,a)].
% 16.98/16.93 Derived: -banach(real) | -hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),A)),hAPP(real,fun(nat,real),power_power(real),B)))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,norm_norm(real),C)),hAPP(real,real,norm_norm(real),B))) | hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),norm_norm(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),A)),hAPP(real,fun(nat,real),power_power(real),C))))). [resolve(5180,a,5233,a)].
% 16.98/16.93 Derived: -hBOOL(hAPP(fun(nat,real),bool,summable(real),A)) | hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),uminus_uminus(real)),A))). [resolve(5180,a,5234,a)].
% 16.98/16.93 Derived: -hBOOL(hAPP(fun(nat,real),bool,summable(real),A)) | hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(real,fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(real,fun(nat,real)),combc(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),inverse_divide(real)),A)),B))). [resolve(5180,a,5235,a)].
% 16.98/16.93 Derived: -hBOOL(hAPP(fun(nat,real),bool,summable(real),A)) | -hBOOL(hAPP(fun(nat,real),bool,summable(real),B)) | hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),minus_minus(real)),A)),B))). [resolve(5180,a,5237,a)].
% 16.98/16.93 Derived: -hBOOL(hAPP(fun(nat,real),bool,summable(real),A)) | -hBOOL(hAPP(fun(nat,real),bool,summable(real),B)) | hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),plus_plus(real)),A)),B))). [resolve(5180,a,5238,a)].
% 16.98/16.93 Derived: -banach(real) | -hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),A)),hAPP(real,fun(nat,real),power_power(real),B)))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,norm_norm(real),C)),hAPP(real,real,norm_norm(real),B))) | hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),A)),hAPP(real,fun(nat,real),power_power(real),C)))). [resolve(5180,a,5239,a)].
% 16.98/16.93 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,norm_norm(real),A)),one_one(real))) | hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(real,fun(nat,real),power_power(real),A))). [resolve(5180,a,5240,a)].
% 16.98/16.93 Derived: -hBOOL(hAPP(real,bool,hAPP(fun(nat,real),fun(real,bool),sums(real),A),B)) | hBOOL(hAPP(real,bool,hAPP(fun(nat,real),fun(real,bool),sums(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),uminus_uminus(real)),A)),hAPP(real,real,uminus_uminus(real),B))). [resolve(5180,a,5241,a)].
% 16.98/16.93 Derived: -hBOOL(hAPP(real,bool,hAPP(fun(nat,real),fun(real,bool),sums(real),A),B)) | hBOOL(hAPP(real,bool,hAPP(fun(nat,real),fun(real,bool),sums(real),hAPP(real,fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(real,fun(nat,real)),combc(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),inverse_divide(real)),A)),C)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),B),C))). [resolve(5180,a,5242,a)].
% 16.98/16.93 Derived: -hBOOL(hAPP(real,bool,hAPP(fun(nat,real),fun(real,bool),sums(real),A),B)) | -hBOOL(hAPP(real,bool,hAPP(fun(nat,real),fun(real,bool),sums(real),C),D)) | hBOOL(hAPP(real,bool,hAPP(fun(nat,real),fun(real,bool),sums(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),minus_minus(real)),A)),C)),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),B),D))). [resolve(5180,a,5244,a)].
% 16.98/16.93 Derived: -hBOOL(hAPP(real,bool,hAPP(fun(nat,real),fun(real,bool),sums(real),A),B)) | -hBOOL(hAPP(real,bool,hAPP(fun(nat,real),fun(real,bool),sums(real),C),D)) | hBOOL(hAPP(real,bool,hAPP(fun(nat,real),fun(real,bool),sums(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),plus_plus(real)),A)),C)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),B),D))). [resolve(5180,a,5245,a)].
% 16.98/16.93 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,norm_norm(real),A)),one_one(real))) | hBOOL(hAPP(real,bool,hAPP(fun(nat,real),fun(real,bool),sums(real),hAPP(real,fun(nat,real),power_power(real),A)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),one_one(real)),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),one_one(real)),A)))). [resolve(5180,a,5246,a)].
% 16.98/16.93 Derived: -hBOOL(hAPP(fun(nat,real),bool,cauchy(real),A)) | hBOOL(hAPP(fun(nat,real),bool,cauchy(real),hAPP(real,fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(real,fun(nat,real)),combc(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),inverse_divide(real)),A)),B))). [resolve(5180,a,5247,a)].
% 16.98/16.93 Derived: -banach(real) | -hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),A)),hAPP(real,fun(nat,real),power_power(real),B)))) | -hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(fun(nat,real),fun(nat,real),diffs(real),A))),hAPP(real,fun(nat,real),power_power(real),B)))) | -hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(fun(nat,real),fun(nat,real),diffs(real),hAPP(fun(nat,real),fun(nat,real),diffs(real),A)))),hAPP(real,fun(nat,real),power_power(real),B)))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,norm_norm(real),C)),hAPP(real,real,norm_norm(real),B))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(fun(real,fun(nat,real)),fun(real,real),hAPP(fun(fun(nat,real),real),fun(fun(real,fun(nat,real)),fun(real,real)),combb(fun(nat,real),real,real),suminf(real)),hAPP(fun(real,fun(nat,real)),fun(real,fun(nat,real)),hAPP(fun(fun(nat,real),fun(nat,real)),fun(fun(real,fun(nat,real)),fun(real,fun(nat,real))),combb(fun(nat,real),fun(nat,real),real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),A))),power_power(real)))),C),hAPP(fun(nat,real),real,suminf(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(fun(nat,real),fun(nat,real),diffs(real),A))),hAPP(real,fun(nat,real),power_power(real),C))))). [resolve(5180,a,5248,a)].
% 16.98/16.93 Derived: hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),hAPP(real,fun(A,real),hAPP(fun(A,fun(real,real)),fun(real,fun(A,real)),combc(A,real,real),hAPP(fun(A,real),fun(A,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(A,real),fun(A,fun(real,real))),combb(real,fun(real,real),A),inverse_divide(real)),B)),C)),D) = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),B),D)),C). [resolve(5180,a,5249,a)].
% 16.98/16.93 Derived: -hBOOL(hAPP(fun(nat,real),bool,summable(real),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),B)) | hBOOL(hAPP(real,bool,hAPP(fun(nat,real),fun(real,bool),sums(real),hAPP(fun(nat,fun(nat,bool)),fun(nat,real),hAPP(fun(fun(nat,bool),real),fun(fun(nat,fun(nat,bool)),fun(nat,real)),combb(fun(nat,bool),real,nat),hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),A)),hAPP(fun(nat,nat),fun(nat,fun(nat,bool)),hAPP(fun(nat,fun(nat,fun(nat,bool))),fun(fun(nat,nat),fun(nat,fun(nat,bool))),combs(nat,nat,fun(nat,bool)),hAPP(fun(nat,nat),fun(nat,fun(nat,fun(nat,bool))),hAPP(fun(nat,fun(nat,fun(nat,bool))),fun(fun(nat,nat),fun(nat,fun(nat,fun(nat,bool)))),combb(nat,fun(nat,fun(nat,bool)),nat),ord_atLeastLessThan(nat)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),times_times(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),plus_plus(nat)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),times_times(nat)),B))),B)))),hAPP(fun(nat,real),real,suminf(real),A))). [resolve(5180,a,5250,a)].
% 16.98/16.93 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),f605(A,real,C,D,E,B)),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(fun(A,bool),fun(real,real),hAPP(fun(real,fun(fun(A,bool),real)),fun(fun(A,bool),fun(real,real)),combc(real,fun(A,bool),real),hAPP(fun(real,fun(A,real)),fun(real,fun(fun(A,bool),real)),hAPP(fun(fun(A,real),fun(fun(A,bool),real)),fun(fun(real,fun(A,real)),fun(real,fun(fun(A,bool),real))),combb(fun(A,real),fun(fun(A,bool),real),real),big_co1399186613setsum(A,real)),C)),B)),D),hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),hAPP(real,fun(A,real),E,D)),B))). [resolve(5180,a,5251,a)].
% 16.98/16.93 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(A,fun(real,real),hAPP(fun(real,fun(A,real)),fun(A,fun(real,real)),combc(real,A,real),C),f605(A,real,C,D,E,B))),D),hAPP(A,real,hAPP(real,fun(A,real),E,D),f605(A,real,C,D,E,B)))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(fun(A,bool),fun(real,real),hAPP(fun(real,fun(fun(A,bool),real)),fun(fun(A,bool),fun(real,real)),combc(real,fun(A,bool),real),hAPP(fun(real,fun(A,real)),fun(real,fun(fun(A,bool),real)),hAPP(fun(fun(A,real),fun(fun(A,bool),real)),fun(fun(real,fun(A,real)),fun(real,fun(fun(A,bool),real))),combb(fun(A,real),fun(fun(A,bool),real),real),big_co1399186613setsum(A,real)),C)),B)),D),hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),hAPP(real,fun(A,real),E,D)),B))). [resolve(5180,a,5252,a)].
% 16.98/16.93 Derived: -hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),A),B),sequentially)) | hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),hAPP(real,fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(real,fun(nat,real)),combc(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),inverse_divide(real)),A)),C)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),B),C)),sequentially)). [resolve(5180,a,5253,a)].
% 16.98/16.93 Derived: -hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),A),B),sequentially)) | -hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),C),D),sequentially)) | zero_zero(real) = ti(real,D) | hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),inverse_divide(real)),A)),C)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),B),D)),sequentially)). [resolve(5180,a,5254,a)].
% 16.98/16.93 Derived: -hBOOL(hAPP(filter(A),bool,hAPP(real,fun(filter(A),bool),hAPP(fun(A,real),fun(real,fun(filter(A),bool)),tendsto(A,real),B),C),D)) | -hBOOL(hAPP(filter(A),bool,hAPP(real,fun(filter(A),bool),hAPP(fun(A,real),fun(real,fun(filter(A),bool)),tendsto(A,real),E),F),D)) | zero_zero(real) = ti(real,F) | hBOOL(hAPP(filter(A),bool,hAPP(real,fun(filter(A),bool),hAPP(fun(A,real),fun(real,fun(filter(A),bool)),tendsto(A,real),hAPP(fun(A,real),fun(A,real),hAPP(fun(A,fun(real,real)),fun(fun(A,real),fun(A,real)),combs(A,real,real),hAPP(fun(A,real),fun(A,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(A,real),fun(A,fun(real,real))),combb(real,fun(real,real),A),inverse_divide(real)),B)),E)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),C),F)),D)). [resolve(5180,a,5255,a)].
% 16.98/16.93 Derived: -hBOOL(hAPP(filter(A),bool,hAPP(real,fun(filter(A),bool),hAPP(fun(A,real),fun(real,fun(filter(A),bool)),tendsto(A,real),B),C),D)) | hBOOL(hAPP(filter(A),bool,hAPP(real,fun(filter(A),bool),hAPP(fun(A,real),fun(real,fun(filter(A),bool)),tendsto(A,real),hAPP(real,fun(A,real),hAPP(fun(A,fun(real,real)),fun(real,fun(A,real)),combc(A,real,real),hAPP(fun(A,real),fun(A,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(A,real),fun(A,fun(real,real))),combb(real,fun(real,real),A),inverse_divide(real)),B)),E)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),C),E)),D)). [resolve(5180,a,5256,a)].
% 16.98/16.93 Derived: -hBOOL(hAPP(fun(nat,real),bool,summable(real),A)) | hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),A),zero_zero(real)),sequentially)). [resolve(5180,a,5257,a)].
% 16.98/16.93 Derived: -banach(real) | -hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(fun(nat,real),fun(nat,real),diffs(real),hAPP(fun(nat,real),fun(nat,real),diffs(real),A)))),hAPP(real,fun(nat,real),power_power(real),B)))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,norm_norm(real),C)),hAPP(real,real,norm_norm(real),B))) | hBOOL(hAPP(filter(real),bool,hAPP(real,fun(filter(real),bool),hAPP(fun(real,real),fun(real,fun(filter(real),bool)),tendsto(real,real),hAPP(fun(real,fun(nat,real)),fun(real,real),hAPP(fun(fun(nat,real),real),fun(fun(real,fun(nat,real)),fun(real,real)),combb(fun(nat,real),real,real),suminf(real)),hAPP(fun(real,fun(nat,real)),fun(real,fun(nat,real)),hAPP(fun(fun(nat,real),fun(nat,real)),fun(fun(real,fun(nat,real)),fun(real,fun(nat,real))),combb(fun(nat,real),fun(nat,real),real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),A))),hAPP(fun(nat,real),fun(real,fun(nat,real)),hAPP(fun(real,fun(fun(nat,real),fun(nat,real))),fun(fun(nat,real),fun(real,fun(nat,real))),combc(real,fun(nat,real),fun(nat,real)),hAPP(fun(real,fun(nat,fun(real,real))),fun(real,fun(fun(nat,real),fun(nat,real))),hAPP(fun(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real))),fun(fun(real,fun(nat,fun(real,real))),fun(real,fun(fun(nat,real),fun(nat,real)))),combb(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),real),combs(nat,real,real)),hAPP(fun(real,fun(nat,real)),fun(real,fun(nat,fun(real,real))),hAPP(fun(fun(nat,real),fun(nat,fun(real,real))),fun(fun(real,fun(nat,real)),fun(real,fun(nat,fun(real,real)))),combb(fun(nat,real),fun(nat,fun(real,real)),real),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),minus_minus(real))),hAPP(fun(real,real),fun(real,fun(nat,real)),hAPP(fun(real,fun(real,fun(nat,real))),fun(fun(real,real),fun(real,fun(nat,real))),combs(real,real,fun(nat,real)),hAPP(fun(real,fun(nat,fun(real,real))),fun(real,fun(real,fun(nat,real))),hAPP(fun(fun(nat,fun(real,real)),fun(real,fun(nat,real))),fun(fun(real,fun(nat,fun(real,real))),fun(real,fun(real,fun(nat,real)))),combb(fun(nat,fun(real,real)),fun(real,fun(nat,real)),real),combc(nat,real,real)),hAPP(fun(real,fun(nat,real)),fun(real,fun(nat,fun(real,real))),hAPP(fun(fun(nat,real),fun(nat,fun(real,real))),fun(fun(real,fun(nat,real)),fun(real,fun(nat,fun(real,real)))),combb(fun(nat,real),fun(nat,fun(real,real)),real),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),inverse_divide(real))),hAPP(fun(nat,real),fun(real,fun(nat,real)),hAPP(fun(real,fun(fun(nat,real),fun(nat,real))),fun(fun(nat,real),fun(real,fun(nat,real))),combc(real,fun(nat,real),fun(nat,real)),hAPP(fun(real,fun(nat,fun(real,real))),fun(real,fun(fun(nat,real),fun(nat,real))),hAPP(fun(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real))),fun(fun(real,fun(nat,fun(real,real))),fun(real,fun(fun(nat,real),fun(nat,real)))),combb(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),real),combs(nat,real,real)),hAPP(fun(real,fun(nat,real)),fun(real,fun(nat,fun(real,real))),hAPP(fun(fun(nat,real),fun(nat,fun(real,real))),fun(fun(real,fun(nat,real)),fun(real,fun(nat,fun(real,real)))),combb(fun(nat,real),fun(nat,fun(real,real)),real),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),minus_minus(real))),hAPP(fun(real,real),fun(real,fun(nat,real)),hAPP(fun(real,fun(nat,real)),fun(fun(real,real),fun(real,fun(nat,real))),combb(real,fun(nat,real),real),power_power(real)),hAPP(real,fun(real,real),plus_plus(real),C))))),hAPP(real,fun(nat,real),power_power(real),C))))),combi(real))))),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),semiring_1_of_nat(real))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),hAPP(real,fun(nat,real),power_power(real),C)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),minus_minus(nat)),hAPP(nat,nat,suc,zero_zero(nat))))))))),zero_zero(real)),hAPP(real,filter(real),at(real),zero_zero(real)))). [resolve(5180,a,5258,a)].
% 16.98/16.94 Derived: hBOOL(hAPP(filter(real),bool,hAPP(real,fun(filter(real),bool),hAPP(fun(real,real),fun(real,fun(filter(real),bool)),tendsto(real,real),hAPP(real,fun(real,real),hAPP(fun(real,fun(real,real)),fun(real,fun(real,real)),combc(real,real,real),inverse_divide(real)),A)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),B),A)),hAPP(real,filter(real),at(real),B))). [resolve(5180,a,5260,a)].
% 16.98/16.94 Derived: -topological_space(A) | -hBOOL(hAPP(filter(A),bool,hAPP(real,fun(filter(A),bool),hAPP(fun(A,real),fun(real,fun(filter(A),bool)),tendsto(A,real),B),zero_zero(real)),hAPP(A,filter(A),at(A),C))) | hBOOL(hAPP(filter(A),bool,hAPP(real,fun(filter(A),bool),hAPP(fun(A,real),fun(real,fun(filter(A),bool)),tendsto(A,real),hAPP(real,fun(A,real),hAPP(fun(A,fun(real,real)),fun(real,fun(A,real)),combc(A,real,real),hAPP(fun(A,real),fun(A,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(A,real),fun(A,fun(real,real))),combb(real,fun(real,real),A),inverse_divide(real)),B)),D)),zero_zero(real)),hAPP(A,filter(A),at(A),C))). [resolve(5180,a,5261,b)].
% 16.98/16.94 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),A),B),C)) | hBOOL(hAPP(filter(real),bool,hAPP(real,fun(filter(real),bool),hAPP(fun(real,real),fun(real,fun(filter(real),bool)),tendsto(real,real),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,real)),combs(real,real,real),hAPP(fun(real,real),fun(real,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,fun(real,real))),combb(real,fun(real,real),real),inverse_divide(real)),hAPP(real,fun(real,real),hAPP(fun(real,fun(real,real)),fun(real,fun(real,real)),combc(real,real,real),hAPP(fun(real,real),fun(real,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,fun(real,real))),combb(real,fun(real,real),real),minus_minus(real)),A)),hAPP(real,real,A,B)))),hAPP(real,fun(real,real),hAPP(fun(real,fun(real,real)),fun(real,fun(real,real)),combc(real,real,real),minus_minus(real)),B))),C),hAPP(real,filter(real),at(real),B))). [resolve(5180,a,5262,a)].
% 16.98/16.94 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),A),B),C)) | -hBOOL(hAPP(filter(real),bool,hAPP(real,fun(filter(real),bool),hAPP(fun(real,real),fun(real,fun(filter(real),bool)),tendsto(real,real),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,real)),combs(real,real,real),hAPP(fun(real,real),fun(real,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,fun(real,real))),combb(real,fun(real,real),real),inverse_divide(real)),hAPP(real,fun(real,real),hAPP(fun(real,fun(real,real)),fun(real,fun(real,real)),combc(real,real,real),hAPP(fun(real,real),fun(real,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,fun(real,real))),combb(real,fun(real,real),real),minus_minus(real)),A)),hAPP(real,real,A,B)))),hAPP(real,fun(real,real),hAPP(fun(real,fun(real,real)),fun(real,fun(real,real)),combc(real,real,real),minus_minus(real)),B))),C),hAPP(real,filter(real),at(real),B))). [resolve(5180,a,5263,a)].
% 16.98/16.94 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),A),B),C)) | hBOOL(hAPP(filter(real),bool,hAPP(real,fun(filter(real),bool),hAPP(fun(real,real),fun(real,fun(filter(real),bool)),tendsto(real,real),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,real)),combs(real,real,real),hAPP(fun(real,real),fun(real,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,fun(real,real))),combb(real,fun(real,real),real),inverse_divide(real)),hAPP(real,fun(real,real),hAPP(fun(real,fun(real,real)),fun(real,fun(real,real)),combc(real,real,real),hAPP(fun(real,real),fun(real,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,fun(real,real))),combb(real,fun(real,real),real),minus_minus(real)),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,real),fun(fun(real,real),fun(real,real)),combb(real,real,real),A),hAPP(real,fun(real,real),plus_plus(real),B)))),hAPP(real,real,A,B)))),combi(real))),C),hAPP(real,filter(real),at(real),zero_zero(real)))). [resolve(5180,a,5264,a)].
% 16.98/16.94 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),A),B),C)) | -hBOOL(hAPP(filter(real),bool,hAPP(real,fun(filter(real),bool),hAPP(fun(real,real),fun(real,fun(filter(real),bool)),tendsto(real,real),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,real)),combs(real,real,real),hAPP(fun(real,real),fun(real,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,fun(real,real))),combb(real,fun(real,real),real),inverse_divide(real)),hAPP(real,fun(real,real),hAPP(fun(real,fun(real,real)),fun(real,fun(real,real)),combc(real,real,real),hAPP(fun(real,real),fun(real,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,fun(real,real))),combb(real,fun(real,real),real),minus_minus(real)),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,real),fun(fun(real,real),fun(real,real)),combb(real,real,real),A),hAPP(real,fun(real,real),plus_plus(real),B)))),hAPP(real,real,A,B)))),combi(real))),C),hAPP(real,filter(real),at(real),zero_zero(real)))). [resolve(5180,a,5266,a)].
% 16.98/16.94 Derived: -banach(A) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B)) | -hBOOL(hAPP(fun(nat,real),bool,summable(real),C)) | zero_zero(real) != ti(real,f682(A,real,D,C,B)) | hBOOL(hAPP(filter(real),bool,hAPP(A,fun(filter(real),bool),hAPP(fun(real,A),fun(A,fun(filter(real),bool)),tendsto(real,A),hAPP(fun(real,fun(nat,A)),fun(real,A),hAPP(fun(fun(nat,A),A),fun(fun(real,fun(nat,A)),fun(real,A)),combb(fun(nat,A),A,real),suminf(A)),D)),zero_zero(A)),hAPP(real,filter(real),at(real),zero_zero(real)))). [resolve(5180,a,5267,a)].
% 16.98/16.94 Derived: -banach(A) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B)) | -hBOOL(hAPP(fun(nat,real),bool,summable(real),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,norm_norm(real),f682(A,real,D,C,B))),B)) | hBOOL(hAPP(filter(real),bool,hAPP(A,fun(filter(real),bool),hAPP(fun(real,A),fun(A,fun(filter(real),bool)),tendsto(real,A),hAPP(fun(real,fun(nat,A)),fun(real,A),hAPP(fun(fun(nat,A),A),fun(fun(real,fun(nat,A)),fun(real,A)),combb(fun(nat,A),A,real),suminf(A)),D)),zero_zero(A)),hAPP(real,filter(real),at(real),zero_zero(real)))). [resolve(5180,a,5268,a)].
% 16.98/16.94 Derived: -banach(A) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B)) | -hBOOL(hAPP(fun(nat,real),bool,summable(real),C)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(A,real,norm_norm(A),hAPP(nat,A,hAPP(real,fun(nat,A),D,f682(A,real,D,C,B)),f683(A,real,D,C,B)))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,C,f683(A,real,D,C,B))),hAPP(real,real,norm_norm(real),f682(A,real,D,C,B))))) | hBOOL(hAPP(filter(real),bool,hAPP(A,fun(filter(real),bool),hAPP(fun(real,A),fun(A,fun(filter(real),bool)),tendsto(real,A),hAPP(fun(real,fun(nat,A)),fun(real,A),hAPP(fun(fun(nat,A),A),fun(fun(real,fun(nat,A)),fun(real,A)),combb(fun(nat,A),A,real),suminf(A)),D)),zero_zero(A)),hAPP(real,filter(real),at(real),zero_zero(real)))). [resolve(5180,a,5269,a)].
% 16.98/16.94 Derived: -real_normed_vector(A) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B)) | zero_zero(real) != ti(real,f684(A,real,C,D,B)) | hBOOL(hAPP(filter(real),bool,hAPP(A,fun(filter(real),bool),hAPP(fun(real,A),fun(A,fun(filter(real),bool)),tendsto(real,A),C),zero_zero(A)),hAPP(real,filter(real),at(real),zero_zero(real)))). [resolve(5180,a,5270,a)].
% 16.98/16.94 Derived: -real_normed_vector(A) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,norm_norm(real),f684(A,real,C,D,B))),B)) | hBOOL(hAPP(filter(real),bool,hAPP(A,fun(filter(real),bool),hAPP(fun(real,A),fun(A,fun(filter(real),bool)),tendsto(real,A),C),zero_zero(A)),hAPP(real,filter(real),at(real),zero_zero(real)))). [resolve(5180,a,5271,a)].
% 16.98/16.94 Derived: -real_normed_vector(A) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(A,real,norm_norm(A),hAPP(real,A,C,f684(A,real,C,D,B)))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),D),hAPP(real,real,norm_norm(real),f684(A,real,C,D,B))))) | hBOOL(hAPP(filter(real),bool,hAPP(A,fun(filter(real),bool),hAPP(fun(real,A),fun(A,fun(filter(real),bool)),tendsto(real,A),C),zero_zero(A)),hAPP(real,filter(real),at(real),zero_zero(real)))). [resolve(5180,a,5272,a)].
% 16.98/16.94 Derived: hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),A),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),B),C)) = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),A),B)),C). [resolve(5180,a,5273,a)].
% 16.98/16.94 Derived: -banach(real) | hAPP(fun(nat,real),real,suminf(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),scaleR_scaleR(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),inverse_inverse(real)),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),fact_fact(nat))))),hAPP(real,fun(nat,real),power_power(real),A))) = hAPP(real,real,exp(real),A). [resolve(5180,a,5274,a)].
% 16.98/16.98 Derived: -banach(real) | hBOOL(hAPP(real,bool,hAPP(fun(nat,real),fun(real,bool),sums(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),scaleR_scaleR(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),inverse_inverse(real)),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),fact_fact(nat))))),hAPP(real,fun(nat,real),power_power(real),A))),hAPP(real,real,exp(real),A))). [resolve(5180,a,5276,a)].
% 16.98/16.98 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),A),B),C)) | hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,f828(real,A,B,C),D)),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),D),B)) = hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,A,D)),hAPP(real,real,A,B)). [resolve(5180,a,5277,a)].
% 16.98/16.98 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),A),B),C)) | hBOOL(hAPP(real,bool,hAPP(fun(real,real),fun(real,bool),isCont(real,real),f828(real,A,B,C)),B)). [resolve(5180,a,5278,a)].
% 16.98/16.98 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),A),B),C)) | hAPP(real,real,f828(real,A,B,C),B) = ti(real,C). [resolve(5180,a,5279,a)].
% 16.98/16.98 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),A),B),C)) | hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,D,f829(real,A,B,C,D))),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),f829(real,A,B,C,D)),B)) != hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,A,f829(real,A,B,C,D))),hAPP(real,real,A,B)) | -hBOOL(hAPP(real,bool,hAPP(fun(real,real),fun(real,bool),isCont(real,real),D),B)) | hAPP(real,real,D,B) != ti(real,C). [resolve(5180,a,5280,a)].
% 16.98/16.98 Derived: hBOOL(hAPP(real,bool,hAPP(fun(real,real),fun(real,bool),isCont(real,real),hAPP(real,fun(real,real),hAPP(fun(real,fun(real,real)),fun(real,fun(real,real)),combc(real,real,real),inverse_divide(real)),A)),B)). [resolve(5180,a,5281,a)].
% 16.98/16.98 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),A),B),C)) | hBOOL(hAPP(real,bool,hAPP(fun(real,real),fun(real,bool),isCont(real,real),A),B)). [resolve(5180,a,5282,a)].
% 16.98/16.98 Derived: -banach(real) | hBOOL(hAPP(real,bool,hAPP(fun(real,real),fun(real,bool),isCont(real,real),exp(real)),A)). [resolve(5180,a,5283,a)].
% 16.98/16.98 5284 real_normed_field(complex) # label(arity_Complex_Ocomplex___RealVector_Oreal__normed__field) # label(axiom). [assumption].
% 16.98/16.98 Derived: deriv(complex) = ti(fun(fun(complex,complex),fun(complex,fun(complex,bool))),deriv(complex)). [resolve(5284,a,5181,a)].
% 16.98/16.98 Derived: -banach(complex) | exp(complex) = ti(fun(complex,complex),exp(complex)). [resolve(5284,a,5182,a)].
% 16.98/16.98 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),zero_zero(complex)),A) = zero_zero(complex). [resolve(5284,a,5183,a)].
% 16.98/16.98 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),A),B)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),C),B)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),A),C)),B). [resolve(5284,a,5184,a)].
% 16.98/16.98 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),A),B)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),C),B)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),A),C)),B). [resolve(5284,a,5185,a)].
% 16.98/16.98 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),hAPP(complex,complex,uminus_uminus(complex),A)),B) = hAPP(complex,complex,uminus_uminus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),A),B)). [resolve(5284,a,5186,a)].
% 16.98/16.98 Derived: zero_zero(complex) = ti(complex,A) | zero_zero(complex) = ti(complex,B) | hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),hAPP(complex,complex,inverse_inverse(complex),A)),hAPP(complex,complex,inverse_inverse(complex),B))),C) = hAPP(complex,complex,uminus_uminus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,inverse_inverse(complex),A)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),A),B)),C))),hAPP(complex,complex,inverse_inverse(complex),B))). [resolve(5284,a,5187,a)].
% 16.98/16.98 Derived: hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),hAPP(complex,fun(complex,complex),times_times(complex),A)),B),A)). [resolve(5284,a,5188,a)].
% 16.98/16.98 Derived: -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),A),B),C)) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),A),B),D)) | ti(complex,C) = ti(complex,D). [resolve(5284,a,5189,a)].
% 16.98/16.98 Derived: -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),A),B),C)) | ti(complex,C) != ti(complex,D) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),A),B),D)). [resolve(5284,a,5190,a)].
% 16.98/16.98 Derived: -banach(complex) | hAPP(complex,complex,exp(complex),A) != zero_zero(complex). [resolve(5284,a,5192,a)].
% 16.98/16.98 Derived: -banach(complex) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),exp(complex)),A),hAPP(complex,complex,exp(complex),A))). [resolve(5284,a,5193,a)].
% 16.98/16.98 Derived: -banach(complex) | hAPP(complex,complex,exp(complex),zero_zero(complex)) = one_one(complex). [resolve(5284,a,5194,a)].
% 16.98/16.98 Derived: -banach(complex) | hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,exp(complex),A)),hAPP(complex,complex,exp(complex),B)) = hAPP(complex,complex,exp(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),A),B)). [resolve(5284,a,5195,a)].
% 16.98/16.98 Derived: -banach(complex) | hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),hAPP(complex,complex,exp(complex),A)),hAPP(complex,complex,exp(complex),B)) = hAPP(complex,complex,exp(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),A),B)). [resolve(5284,a,5197,a)].
% 16.98/16.98 Derived: -banach(complex) | hAPP(complex,complex,exp(complex),hAPP(complex,complex,uminus_uminus(complex),A)) = hAPP(complex,complex,inverse_inverse(complex),hAPP(complex,complex,exp(complex),A)). [resolve(5284,a,5198,a)].
% 16.98/16.98 Derived: zero_zero(complex) = ti(complex,A) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(complex,real,norm_norm(complex),B)),C)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),B),A))),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),B),A)),D)),hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),B),D))),A)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(nat,complex,semiring_1_of_nat(complex),D)),hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),D),hAPP(nat,nat,suc,zero_zero(nat)))))))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,semiring_1_of_nat(real),D)),hAPP(nat,real,semiring_1_of_nat(real),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),D),hAPP(nat,nat,suc,zero_zero(nat)))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),C),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),D),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))),hAPP(complex,real,norm_norm(complex),A)))). [resolve(5284,a,5199,a)].
% 16.98/16.98 Derived: -field_inverse_zero(complex) | hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(complex,real,norm_norm(complex),A)),hAPP(complex,real,norm_norm(complex),B)) = hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),A),B)). [resolve(5284,a,5200,b)].
% 16.98/16.98 Derived: zero_zero(complex) = ti(complex,A) | hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(complex,real,norm_norm(complex),B)),hAPP(complex,real,norm_norm(complex),A)) = hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),B),A)). [resolve(5284,a,5201,a)].
% 16.98/16.98 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),f257(complex,A))). [resolve(5284,a,5202,a)].
% 16.98/16.98 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),A),B))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(complex,real,norm_norm(complex),A)),f257(complex,B)))). [resolve(5284,a,5203,a)].
% 16.98/16.98 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),f264(complex,A))). [resolve(5284,a,5204,a)].
% 16.98/16.98 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),A),B))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(complex,real,norm_norm(complex),A)),f264(complex,B)))). [resolve(5284,a,5205,a)].
% 16.98/16.98 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),A),B))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(complex,real,norm_norm(complex),A)),f270(complex,B)))). [resolve(5284,a,5206,a)].
% 16.98/16.98 Derived: -banach(complex) | hAPP(real,complex,of_real(complex),hAPP(real,real,exp(real),A)) = hAPP(complex,complex,exp(complex),hAPP(real,complex,of_real(complex),A)). [resolve(5284,a,5207,a)].
% 16.98/16.98 Derived: -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),A),B),C)) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),D),B),E)) | hAPP(complex,complex,D,B) = zero_zero(complex) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),hAPP(fun(complex,complex),fun(complex,complex),hAPP(fun(complex,fun(complex,complex)),fun(fun(complex,complex),fun(complex,complex)),combs(complex,complex,complex),hAPP(fun(complex,complex),fun(complex,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(complex,complex),fun(complex,fun(complex,complex))),combb(complex,fun(complex,complex),complex),inverse_divide(complex)),A)),D)),B),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),C),hAPP(complex,complex,D,B))),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,A,B)),E))),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,D,B)),hAPP(complex,complex,D,B))))). [resolve(5284,a,5208,a)].
% 16.98/16.98 Derived: -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),A),B),C)) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),D),B),E)) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),hAPP(fun(complex,complex),fun(complex,complex),hAPP(fun(complex,fun(complex,complex)),fun(fun(complex,complex),fun(complex,complex)),combs(complex,complex,complex),hAPP(fun(complex,complex),fun(complex,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(complex,complex),fun(complex,fun(complex,complex))),combb(complex,fun(complex,complex),complex),plus_plus(complex)),A)),hAPP(fun(complex,complex),fun(complex,complex),hAPP(fun(complex,complex),fun(fun(complex,complex),fun(complex,complex)),combb(complex,complex,complex),uminus_uminus(complex)),D))),B),hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),C),hAPP(complex,complex,uminus_uminus(complex),E)))). [resolve(5284,a,5209,a)].
% 16.98/16.98 Derived: -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),A),B),C)) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),D),B),E)) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),hAPP(fun(complex,complex),fun(complex,complex),hAPP(fun(complex,fun(complex,complex)),fun(fun(complex,complex),fun(complex,complex)),combs(complex,complex,complex),hAPP(fun(complex,complex),fun(complex,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(complex,complex),fun(complex,fun(complex,complex))),combb(complex,fun(complex,complex),complex),times_times(complex)),A)),D)),B),hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),C),hAPP(complex,complex,D,B))),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),E),hAPP(complex,complex,A,B))))). [resolve(5284,a,5210,a)].
% 16.98/16.98 Derived: -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),A),B),C)) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),D),B),E)) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),hAPP(fun(complex,complex),fun(complex,complex),hAPP(fun(complex,fun(complex,complex)),fun(fun(complex,complex),fun(complex,complex)),combs(complex,complex,complex),hAPP(fun(complex,complex),fun(complex,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(complex,complex),fun(complex,fun(complex,complex))),combb(complex,fun(complex,complex),complex),times_times(complex)),A)),D)),B),hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,A,B)),E)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),C),hAPP(complex,complex,D,B))))). [resolve(5284,a,5211,a)].
% 16.98/16.98 Derived: -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),A),B),C)) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),D),B),E)) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),hAPP(fun(complex,complex),fun(complex,complex),hAPP(fun(complex,fun(complex,complex)),fun(fun(complex,complex),fun(complex,complex)),combs(complex,complex,complex),hAPP(fun(complex,complex),fun(complex,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(complex,complex),fun(complex,fun(complex,complex))),combb(complex,fun(complex,complex),complex),plus_plus(complex)),A)),D)),B),hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),C),E))). [resolve(5284,a,5212,a)].
% 16.98/16.98 Derived: -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),A),B),C)) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),D),B),E)) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),hAPP(fun(complex,complex),fun(complex,complex),hAPP(fun(complex,fun(complex,complex)),fun(fun(complex,complex),fun(complex,complex)),combs(complex,complex,complex),hAPP(fun(complex,complex),fun(complex,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(complex,complex),fun(complex,fun(complex,complex))),combb(complex,fun(complex,complex),complex),minus_minus(complex)),A)),D)),B),hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),C),E))). [resolve(5284,a,5213,a)].
% 16.98/16.98 Derived: hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),combi(complex)),A),one_one(complex))). [resolve(5284,a,5214,a)].
% 16.98/16.98 Derived: hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),hAPP(complex,fun(complex,complex),combk(complex,complex),A)),B),zero_zero(complex))). [resolve(5284,a,5215,a)].
% 16.98/16.98 Derived: -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),A),B),C)) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),hAPP(complex,fun(complex,complex),hAPP(fun(complex,fun(complex,complex)),fun(complex,fun(complex,complex)),combc(complex,complex,complex),hAPP(fun(complex,complex),fun(complex,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(complex,complex),fun(complex,fun(complex,complex))),combb(complex,fun(complex,complex),complex),inverse_divide(complex)),A)),D)),B),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),C),D))). [resolve(5284,a,5216,a)].
% 16.98/16.98 Derived: -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),A),B),C)) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),hAPP(fun(complex,complex),fun(complex,complex),hAPP(fun(complex,complex),fun(fun(complex,complex),fun(complex,complex)),combb(complex,complex,complex),hAPP(complex,fun(complex,complex),times_times(complex),D)),A)),B),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),D),C))). [resolve(5284,a,5217,a)].
% 16.98/16.98 Derived: -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),A),B),C)) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),D),hAPP(complex,complex,A,B)),E)) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),hAPP(fun(complex,complex),fun(complex,complex),hAPP(fun(complex,complex),fun(fun(complex,complex),fun(complex,complex)),combb(complex,complex,complex),D),A)),B),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),E),C))). [resolve(5284,a,5218,a)].
% 16.98/16.98 Derived: -banach(complex) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),A),B),C)) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),hAPP(fun(complex,complex),fun(complex,complex),hAPP(fun(complex,complex),fun(fun(complex,complex),fun(complex,complex)),combb(complex,complex,complex),exp(complex)),A)),B),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,exp(complex),hAPP(complex,complex,A,B))),C))). [resolve(5284,a,5220,a)].
% 16.98/16.98 Derived: -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),A),B),C)) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),hAPP(fun(complex,complex),fun(complex,complex),hAPP(fun(complex,complex),fun(fun(complex,complex),fun(complex,complex)),combb(complex,complex,complex),uminus_uminus(complex)),A)),B),hAPP(complex,complex,uminus_uminus(complex),C))). [resolve(5284,a,5221,a)].
% 16.98/16.98 Derived: -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),A),B),C)) | hAPP(complex,complex,A,B) = zero_zero(complex) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),hAPP(fun(complex,complex),fun(complex,complex),hAPP(fun(complex,complex),fun(fun(complex,complex),fun(complex,complex)),combb(complex,complex,complex),inverse_inverse(complex)),A)),B),hAPP(complex,complex,uminus_uminus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,inverse_inverse(complex),hAPP(complex,complex,A,B))),C)),hAPP(complex,complex,inverse_inverse(complex),hAPP(complex,complex,A,B)))))). [resolve(5284,a,5222,a)].
% 16.98/16.98 Derived: -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),A),B),C)) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),hAPP(nat,fun(complex,complex),hAPP(fun(complex,fun(nat,complex)),fun(nat,fun(complex,complex)),combc(complex,nat,complex),hAPP(fun(complex,complex),fun(complex,fun(nat,complex)),hAPP(fun(complex,fun(nat,complex)),fun(fun(complex,complex),fun(complex,fun(nat,complex))),combb(complex,fun(nat,complex),complex),power_power(complex)),A)),hAPP(nat,nat,suc,D))),B),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),one_one(complex)),hAPP(nat,complex,semiring_1_of_nat(complex),D))),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),C),hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),hAPP(complex,complex,A,B)),D))))). [resolve(5284,a,5223,a)].
% 16.98/16.98 Derived: zero_zero(complex) = ti(complex,A) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),inverse_inverse(complex)),A),hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),hAPP(complex,complex,inverse_inverse(complex),A)),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat))))))). [resolve(5284,a,5224,a)].
% 16.98/16.99 Derived: -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),A),B),C)) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),hAPP(nat,fun(complex,complex),hAPP(fun(complex,fun(nat,complex)),fun(nat,fun(complex,complex)),combc(complex,nat,complex),hAPP(fun(complex,complex),fun(complex,fun(nat,complex)),hAPP(fun(complex,fun(nat,complex)),fun(fun(complex,complex),fun(complex,fun(nat,complex))),combb(complex,fun(nat,complex),complex),power_power(complex)),A)),D)),B),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(nat,complex,semiring_1_of_nat(complex),D)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),C),hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),hAPP(complex,complex,A,B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),D),hAPP(nat,nat,suc,zero_zero(nat)))))))). [resolve(5284,a,5225,a)].
% 16.98/16.99 Derived: -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),A),B),C)) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),D),B),E)) | hAPP(complex,complex,D,B) = zero_zero(complex) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),hAPP(fun(complex,complex),fun(complex,complex),hAPP(fun(complex,fun(complex,complex)),fun(fun(complex,complex),fun(complex,complex)),combs(complex,complex,complex),hAPP(fun(complex,complex),fun(complex,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(complex,complex),fun(complex,fun(complex,complex))),combb(complex,fun(complex,complex),complex),inverse_divide(complex)),A)),D)),B),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),C),hAPP(complex,complex,D,B))),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),E),hAPP(complex,complex,A,B)))),hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),hAPP(complex,complex,D,B)),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat))))))). [resolve(5284,a,5226,a)].
% 16.98/16.99 Derived: -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),A),B),C)) | hAPP(complex,complex,A,B) = zero_zero(complex) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),hAPP(fun(complex,complex),fun(complex,complex),hAPP(fun(complex,complex),fun(fun(complex,complex),fun(complex,complex)),combb(complex,complex,complex),inverse_inverse(complex)),A)),B),hAPP(complex,complex,uminus_uminus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),C),hAPP(complex,complex,inverse_inverse(complex),hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),hAPP(complex,complex,A,B)),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat))))))))). [resolve(5284,a,5227,a)].
% 16.98/16.99 Derived: -hBOOL(hAPP(fun(nat,complex),bool,summable(complex),A)) | -hBOOL(hAPP(fun(nat,complex),bool,summable(complex),B)) | hAPP(fun(nat,complex),complex,suminf(complex),hAPP(fun(nat,complex),fun(nat,complex),hAPP(fun(nat,fun(complex,complex)),fun(fun(nat,complex),fun(nat,complex)),combs(nat,complex,complex),hAPP(fun(nat,complex),fun(nat,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(nat,complex),fun(nat,fun(complex,complex))),combb(complex,fun(complex,complex),nat),plus_plus(complex)),A)),B)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(fun(nat,complex),complex,suminf(complex),A)),hAPP(fun(nat,complex),complex,suminf(complex),B)). [resolve(5284,a,5228,a)].
% 16.98/16.99 Derived: -hBOOL(hAPP(fun(nat,complex),bool,summable(complex),A)) | -hBOOL(hAPP(fun(nat,complex),bool,summable(complex),B)) | hAPP(fun(nat,complex),complex,suminf(complex),hAPP(fun(nat,complex),fun(nat,complex),hAPP(fun(nat,fun(complex,complex)),fun(fun(nat,complex),fun(nat,complex)),combs(nat,complex,complex),hAPP(fun(nat,complex),fun(nat,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(nat,complex),fun(nat,fun(complex,complex))),combb(complex,fun(complex,complex),nat),minus_minus(complex)),A)),B)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),hAPP(fun(nat,complex),complex,suminf(complex),A)),hAPP(fun(nat,complex),complex,suminf(complex),B)). [resolve(5284,a,5229,a)].
% 16.98/16.99 Derived: -hBOOL(hAPP(fun(nat,complex),bool,summable(complex),A)) | hAPP(fun(nat,complex),complex,suminf(complex),hAPP(complex,fun(nat,complex),hAPP(fun(nat,fun(complex,complex)),fun(complex,fun(nat,complex)),combc(nat,complex,complex),hAPP(fun(nat,complex),fun(nat,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(nat,complex),fun(nat,fun(complex,complex))),combb(complex,fun(complex,complex),nat),inverse_divide(complex)),A)),B)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),hAPP(fun(nat,complex),complex,suminf(complex),A)),B). [resolve(5284,a,5230,a)].
% 16.98/16.99 Derived: -hBOOL(hAPP(fun(nat,complex),bool,summable(complex),A)) | hAPP(fun(nat,complex),complex,suminf(complex),hAPP(fun(nat,complex),fun(nat,complex),hAPP(fun(complex,complex),fun(fun(nat,complex),fun(nat,complex)),combb(complex,complex,nat),uminus_uminus(complex)),A)) = hAPP(complex,complex,uminus_uminus(complex),hAPP(fun(nat,complex),complex,suminf(complex),A)). [resolve(5284,a,5232,a)].
% 16.98/16.99 Derived: -banach(complex) | -hBOOL(hAPP(fun(nat,complex),bool,summable(complex),hAPP(fun(nat,complex),fun(nat,complex),hAPP(fun(nat,fun(complex,complex)),fun(fun(nat,complex),fun(nat,complex)),combs(nat,complex,complex),hAPP(fun(nat,complex),fun(nat,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(nat,complex),fun(nat,fun(complex,complex))),combb(complex,fun(complex,complex),nat),times_times(complex)),A)),hAPP(complex,fun(nat,complex),power_power(complex),B)))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(complex,real,norm_norm(complex),C)),hAPP(complex,real,norm_norm(complex),B))) | hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,complex),fun(nat,real),hAPP(fun(complex,real),fun(fun(nat,complex),fun(nat,real)),combb(complex,real,nat),norm_norm(complex)),hAPP(fun(nat,complex),fun(nat,complex),hAPP(fun(nat,fun(complex,complex)),fun(fun(nat,complex),fun(nat,complex)),combs(nat,complex,complex),hAPP(fun(nat,complex),fun(nat,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(nat,complex),fun(nat,fun(complex,complex))),combb(complex,fun(complex,complex),nat),times_times(complex)),A)),hAPP(complex,fun(nat,complex),power_power(complex),C))))). [resolve(5284,a,5233,a)].
% 16.98/16.99 Derived: -hBOOL(hAPP(fun(nat,complex),bool,summable(complex),A)) | hBOOL(hAPP(fun(nat,complex),bool,summable(complex),hAPP(fun(nat,complex),fun(nat,complex),hAPP(fun(complex,complex),fun(fun(nat,complex),fun(nat,complex)),combb(complex,complex,nat),uminus_uminus(complex)),A))). [resolve(5284,a,5234,a)].
% 16.98/16.99 Derived: -hBOOL(hAPP(fun(nat,complex),bool,summable(complex),A)) | hBOOL(hAPP(fun(nat,complex),bool,summable(complex),hAPP(complex,fun(nat,complex),hAPP(fun(nat,fun(complex,complex)),fun(complex,fun(nat,complex)),combc(nat,complex,complex),hAPP(fun(nat,complex),fun(nat,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(nat,complex),fun(nat,fun(complex,complex))),combb(complex,fun(complex,complex),nat),inverse_divide(complex)),A)),B))). [resolve(5284,a,5235,a)].
% 16.98/16.99 Derived: -hBOOL(hAPP(fun(nat,complex),bool,summable(complex),A)) | -hBOOL(hAPP(fun(nat,complex),bool,summable(complex),B)) | hBOOL(hAPP(fun(nat,complex),bool,summable(complex),hAPP(fun(nat,complex),fun(nat,complex),hAPP(fun(nat,fun(complex,complex)),fun(fun(nat,complex),fun(nat,complex)),combs(nat,complex,complex),hAPP(fun(nat,complex),fun(nat,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(nat,complex),fun(nat,fun(complex,complex))),combb(complex,fun(complex,complex),nat),minus_minus(complex)),A)),B))). [resolve(5284,a,5237,a)].
% 16.98/16.99 Derived: -hBOOL(hAPP(fun(nat,complex),bool,summable(complex),A)) | -hBOOL(hAPP(fun(nat,complex),bool,summable(complex),B)) | hBOOL(hAPP(fun(nat,complex),bool,summable(complex),hAPP(fun(nat,complex),fun(nat,complex),hAPP(fun(nat,fun(complex,complex)),fun(fun(nat,complex),fun(nat,complex)),combs(nat,complex,complex),hAPP(fun(nat,complex),fun(nat,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(nat,complex),fun(nat,fun(complex,complex))),combb(complex,fun(complex,complex),nat),plus_plus(complex)),A)),B))). [resolve(5284,a,5238,a)].
% 16.98/16.99 Derived: -banach(complex) | -hBOOL(hAPP(fun(nat,complex),bool,summable(complex),hAPP(fun(nat,complex),fun(nat,complex),hAPP(fun(nat,fun(complex,complex)),fun(fun(nat,complex),fun(nat,complex)),combs(nat,complex,complex),hAPP(fun(nat,complex),fun(nat,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(nat,complex),fun(nat,fun(complex,complex))),combb(complex,fun(complex,complex),nat),times_times(complex)),A)),hAPP(complex,fun(nat,complex),power_power(complex),B)))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(complex,real,norm_norm(complex),C)),hAPP(complex,real,norm_norm(complex),B))) | hBOOL(hAPP(fun(nat,complex),bool,summable(complex),hAPP(fun(nat,complex),fun(nat,complex),hAPP(fun(nat,fun(complex,complex)),fun(fun(nat,complex),fun(nat,complex)),combs(nat,complex,complex),hAPP(fun(nat,complex),fun(nat,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(nat,complex),fun(nat,fun(complex,complex))),combb(complex,fun(complex,complex),nat),times_times(complex)),A)),hAPP(complex,fun(nat,complex),power_power(complex),C)))). [resolve(5284,a,5239,a)].
% 16.98/16.99 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(complex,real,norm_norm(complex),A)),one_one(real))) | hBOOL(hAPP(fun(nat,complex),bool,summable(complex),hAPP(complex,fun(nat,complex),power_power(complex),A))). [resolve(5284,a,5240,a)].
% 16.98/16.99 Derived: -hBOOL(hAPP(complex,bool,hAPP(fun(nat,complex),fun(complex,bool),sums(complex),A),B)) | hBOOL(hAPP(complex,bool,hAPP(fun(nat,complex),fun(complex,bool),sums(complex),hAPP(fun(nat,complex),fun(nat,complex),hAPP(fun(complex,complex),fun(fun(nat,complex),fun(nat,complex)),combb(complex,complex,nat),uminus_uminus(complex)),A)),hAPP(complex,complex,uminus_uminus(complex),B))). [resolve(5284,a,5241,a)].
% 16.98/16.99 Derived: -hBOOL(hAPP(complex,bool,hAPP(fun(nat,complex),fun(complex,bool),sums(complex),A),B)) | hBOOL(hAPP(complex,bool,hAPP(fun(nat,complex),fun(complex,bool),sums(complex),hAPP(complex,fun(nat,complex),hAPP(fun(nat,fun(complex,complex)),fun(complex,fun(nat,complex)),combc(nat,complex,complex),hAPP(fun(nat,complex),fun(nat,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(nat,complex),fun(nat,fun(complex,complex))),combb(complex,fun(complex,complex),nat),inverse_divide(complex)),A)),C)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),B),C))). [resolve(5284,a,5242,a)].
% 16.98/16.99 Derived: -hBOOL(hAPP(complex,bool,hAPP(fun(nat,complex),fun(complex,bool),sums(complex),A),B)) | -hBOOL(hAPP(complex,bool,hAPP(fun(nat,complex),fun(complex,bool),sums(complex),C),D)) | hBOOL(hAPP(complex,bool,hAPP(fun(nat,complex),fun(complex,bool),sums(complex),hAPP(fun(nat,complex),fun(nat,complex),hAPP(fun(nat,fun(complex,complex)),fun(fun(nat,complex),fun(nat,complex)),combs(nat,complex,complex),hAPP(fun(nat,complex),fun(nat,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(nat,complex),fun(nat,fun(complex,complex))),combb(complex,fun(complex,complex),nat),minus_minus(complex)),A)),C)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),B),D))). [resolve(5284,a,5244,a)].
% 16.98/16.99 Derived: -hBOOL(hAPP(complex,bool,hAPP(fun(nat,complex),fun(complex,bool),sums(complex),A),B)) | -hBOOL(hAPP(complex,bool,hAPP(fun(nat,complex),fun(complex,bool),sums(complex),C),D)) | hBOOL(hAPP(complex,bool,hAPP(fun(nat,complex),fun(complex,bool),sums(complex),hAPP(fun(nat,complex),fun(nat,complex),hAPP(fun(nat,fun(complex,complex)),fun(fun(nat,complex),fun(nat,complex)),combs(nat,complex,complex),hAPP(fun(nat,complex),fun(nat,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(nat,complex),fun(nat,fun(complex,complex))),combb(complex,fun(complex,complex),nat),plus_plus(complex)),A)),C)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),B),D))). [resolve(5284,a,5245,a)].
% 16.98/16.99 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(complex,real,norm_norm(complex),A)),one_one(real))) | hBOOL(hAPP(complex,bool,hAPP(fun(nat,complex),fun(complex,bool),sums(complex),hAPP(complex,fun(nat,complex),power_power(complex),A)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),one_one(complex)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),one_one(complex)),A)))). [resolve(5284,a,5246,a)].
% 16.98/16.99 Derived: -hBOOL(hAPP(fun(nat,complex),bool,cauchy(complex),A)) | hBOOL(hAPP(fun(nat,complex),bool,cauchy(complex),hAPP(complex,fun(nat,complex),hAPP(fun(nat,fun(complex,complex)),fun(complex,fun(nat,complex)),combc(nat,complex,complex),hAPP(fun(nat,complex),fun(nat,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(nat,complex),fun(nat,fun(complex,complex))),combb(complex,fun(complex,complex),nat),inverse_divide(complex)),A)),B))). [resolve(5284,a,5247,a)].
% 16.98/16.99 Derived: -banach(complex) | -hBOOL(hAPP(fun(nat,complex),bool,summable(complex),hAPP(fun(nat,complex),fun(nat,complex),hAPP(fun(nat,fun(complex,complex)),fun(fun(nat,complex),fun(nat,complex)),combs(nat,complex,complex),hAPP(fun(nat,complex),fun(nat,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(nat,complex),fun(nat,fun(complex,complex))),combb(complex,fun(complex,complex),nat),times_times(complex)),A)),hAPP(complex,fun(nat,complex),power_power(complex),B)))) | -hBOOL(hAPP(fun(nat,complex),bool,summable(complex),hAPP(fun(nat,complex),fun(nat,complex),hAPP(fun(nat,fun(complex,complex)),fun(fun(nat,complex),fun(nat,complex)),combs(nat,complex,complex),hAPP(fun(nat,complex),fun(nat,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(nat,complex),fun(nat,fun(complex,complex))),combb(complex,fun(complex,complex),nat),times_times(complex)),hAPP(fun(nat,complex),fun(nat,complex),diffs(complex),A))),hAPP(complex,fun(nat,complex),power_power(complex),B)))) | -hBOOL(hAPP(fun(nat,complex),bool,summable(complex),hAPP(fun(nat,complex),fun(nat,complex),hAPP(fun(nat,fun(complex,complex)),fun(fun(nat,complex),fun(nat,complex)),combs(nat,complex,complex),hAPP(fun(nat,complex),fun(nat,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(nat,complex),fun(nat,fun(complex,complex))),combb(complex,fun(complex,complex),nat),times_times(complex)),hAPP(fun(nat,complex),fun(nat,complex),diffs(complex),hAPP(fun(nat,complex),fun(nat,complex),diffs(complex),A)))),hAPP(complex,fun(nat,complex),power_power(complex),B)))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(complex,real,norm_norm(complex),C)),hAPP(complex,real,norm_norm(complex),B))) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),hAPP(fun(complex,fun(nat,complex)),fun(complex,complex),hAPP(fun(fun(nat,complex),complex),fun(fun(complex,fun(nat,complex)),fun(complex,complex)),combb(fun(nat,complex),complex,complex),suminf(complex)),hAPP(fun(complex,fun(nat,complex)),fun(complex,fun(nat,complex)),hAPP(fun(fun(nat,complex),fun(nat,complex)),fun(fun(complex,fun(nat,complex)),fun(complex,fun(nat,complex))),combb(fun(nat,complex),fun(nat,complex),complex),hAPP(fun(nat,fun(complex,complex)),fun(fun(nat,complex),fun(nat,complex)),combs(nat,complex,complex),hAPP(fun(nat,complex),fun(nat,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(nat,complex),fun(nat,fun(complex,complex))),combb(complex,fun(complex,complex),nat),times_times(complex)),A))),power_power(complex)))),C),hAPP(fun(nat,complex),complex,suminf(complex),hAPP(fun(nat,complex),fun(nat,complex),hAPP(fun(nat,fun(complex,complex)),fun(fun(nat,complex),fun(nat,complex)),combs(nat,complex,complex),hAPP(fun(nat,complex),fun(nat,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(nat,complex),fun(nat,fun(complex,complex))),combb(complex,fun(complex,complex),nat),times_times(complex)),hAPP(fun(nat,complex),fun(nat,complex),diffs(complex),A))),hAPP(complex,fun(nat,complex),power_power(complex),C))))). [resolve(5284,a,5248,a)].
% 16.98/16.99 Derived: hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),hAPP(complex,fun(A,complex),hAPP(fun(A,fun(complex,complex)),fun(complex,fun(A,complex)),combc(A,complex,complex),hAPP(fun(A,complex),fun(A,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(A,complex),fun(A,fun(complex,complex))),combb(complex,fun(complex,complex),A),inverse_divide(complex)),B)),C)),D) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),B),D)),C). [resolve(5284,a,5249,a)].
% 16.98/16.99 Derived: -hBOOL(hAPP(fun(nat,complex),bool,summable(complex),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),B)) | hBOOL(hAPP(complex,bool,hAPP(fun(nat,complex),fun(complex,bool),sums(complex),hAPP(fun(nat,fun(nat,bool)),fun(nat,complex),hAPP(fun(fun(nat,bool),complex),fun(fun(nat,fun(nat,bool)),fun(nat,complex)),combb(fun(nat,bool),complex,nat),hAPP(fun(nat,complex),fun(fun(nat,bool),complex),big_co1399186613setsum(nat,complex),A)),hAPP(fun(nat,nat),fun(nat,fun(nat,bool)),hAPP(fun(nat,fun(nat,fun(nat,bool))),fun(fun(nat,nat),fun(nat,fun(nat,bool))),combs(nat,nat,fun(nat,bool)),hAPP(fun(nat,nat),fun(nat,fun(nat,fun(nat,bool))),hAPP(fun(nat,fun(nat,fun(nat,bool))),fun(fun(nat,nat),fun(nat,fun(nat,fun(nat,bool)))),combb(nat,fun(nat,fun(nat,bool)),nat),ord_atLeastLessThan(nat)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),times_times(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),plus_plus(nat)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),times_times(nat)),B))),B)))),hAPP(fun(nat,complex),complex,suminf(complex),A))). [resolve(5284,a,5250,a)].
% 16.98/16.99 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),f605(A,complex,C,D,E,B)),B)) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),hAPP(fun(A,bool),fun(complex,complex),hAPP(fun(complex,fun(fun(A,bool),complex)),fun(fun(A,bool),fun(complex,complex)),combc(complex,fun(A,bool),complex),hAPP(fun(complex,fun(A,complex)),fun(complex,fun(fun(A,bool),complex)),hAPP(fun(fun(A,complex),fun(fun(A,bool),complex)),fun(fun(complex,fun(A,complex)),fun(complex,fun(fun(A,bool),complex))),combb(fun(A,complex),fun(fun(A,bool),complex),complex),big_co1399186613setsum(A,complex)),C)),B)),D),hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),hAPP(complex,fun(A,complex),E,D)),B))). [resolve(5284,a,5251,a)].
% 16.98/16.99 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),hAPP(A,fun(complex,complex),hAPP(fun(complex,fun(A,complex)),fun(A,fun(complex,complex)),combc(complex,A,complex),C),f605(A,complex,C,D,E,B))),D),hAPP(A,complex,hAPP(complex,fun(A,complex),E,D),f605(A,complex,C,D,E,B)))) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),hAPP(fun(A,bool),fun(complex,complex),hAPP(fun(complex,fun(fun(A,bool),complex)),fun(fun(A,bool),fun(complex,complex)),combc(complex,fun(A,bool),complex),hAPP(fun(complex,fun(A,complex)),fun(complex,fun(fun(A,bool),complex)),hAPP(fun(fun(A,complex),fun(fun(A,bool),complex)),fun(fun(complex,fun(A,complex)),fun(complex,fun(fun(A,bool),complex))),combb(fun(A,complex),fun(fun(A,bool),complex),complex),big_co1399186613setsum(A,complex)),C)),B)),D),hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),hAPP(complex,fun(A,complex),E,D)),B))). [resolve(5284,a,5252,a)].
% 16.98/16.99 Derived: -hBOOL(hAPP(filter(nat),bool,hAPP(complex,fun(filter(nat),bool),hAPP(fun(nat,complex),fun(complex,fun(filter(nat),bool)),tendsto(nat,complex),A),B),sequentially)) | hBOOL(hAPP(filter(nat),bool,hAPP(complex,fun(filter(nat),bool),hAPP(fun(nat,complex),fun(complex,fun(filter(nat),bool)),tendsto(nat,complex),hAPP(complex,fun(nat,complex),hAPP(fun(nat,fun(complex,complex)),fun(complex,fun(nat,complex)),combc(nat,complex,complex),hAPP(fun(nat,complex),fun(nat,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(nat,complex),fun(nat,fun(complex,complex))),combb(complex,fun(complex,complex),nat),inverse_divide(complex)),A)),C)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),B),C)),sequentially)). [resolve(5284,a,5253,a)].
% 16.98/16.99 Derived: -hBOOL(hAPP(filter(nat),bool,hAPP(complex,fun(filter(nat),bool),hAPP(fun(nat,complex),fun(complex,fun(filter(nat),bool)),tendsto(nat,complex),A),B),sequentially)) | -hBOOL(hAPP(filter(nat),bool,hAPP(complex,fun(filter(nat),bool),hAPP(fun(nat,complex),fun(complex,fun(filter(nat),bool)),tendsto(nat,complex),C),D),sequentially)) | zero_zero(complex) = ti(complex,D) | hBOOL(hAPP(filter(nat),bool,hAPP(complex,fun(filter(nat),bool),hAPP(fun(nat,complex),fun(complex,fun(filter(nat),bool)),tendsto(nat,complex),hAPP(fun(nat,complex),fun(nat,complex),hAPP(fun(nat,fun(complex,complex)),fun(fun(nat,complex),fun(nat,complex)),combs(nat,complex,complex),hAPP(fun(nat,complex),fun(nat,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(nat,complex),fun(nat,fun(complex,complex))),combb(complex,fun(complex,complex),nat),inverse_divide(complex)),A)),C)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),B),D)),sequentially)). [resolve(5284,a,5254,a)].
% 16.98/16.99 Derived: -hBOOL(hAPP(filter(A),bool,hAPP(complex,fun(filter(A),bool),hAPP(fun(A,complex),fun(complex,fun(filter(A),bool)),tendsto(A,complex),B),C),D)) | -hBOOL(hAPP(filter(A),bool,hAPP(complex,fun(filter(A),bool),hAPP(fun(A,complex),fun(complex,fun(filter(A),bool)),tendsto(A,complex),E),F),D)) | zero_zero(complex) = ti(complex,F) | hBOOL(hAPP(filter(A),bool,hAPP(complex,fun(filter(A),bool),hAPP(fun(A,complex),fun(complex,fun(filter(A),bool)),tendsto(A,complex),hAPP(fun(A,complex),fun(A,complex),hAPP(fun(A,fun(complex,complex)),fun(fun(A,complex),fun(A,complex)),combs(A,complex,complex),hAPP(fun(A,complex),fun(A,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(A,complex),fun(A,fun(complex,complex))),combb(complex,fun(complex,complex),A),inverse_divide(complex)),B)),E)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),C),F)),D)). [resolve(5284,a,5255,a)].
% 16.98/16.99 Derived: -hBOOL(hAPP(filter(A),bool,hAPP(complex,fun(filter(A),bool),hAPP(fun(A,complex),fun(complex,fun(filter(A),bool)),tendsto(A,complex),B),C),D)) | hBOOL(hAPP(filter(A),bool,hAPP(complex,fun(filter(A),bool),hAPP(fun(A,complex),fun(complex,fun(filter(A),bool)),tendsto(A,complex),hAPP(complex,fun(A,complex),hAPP(fun(A,fun(complex,complex)),fun(complex,fun(A,complex)),combc(A,complex,complex),hAPP(fun(A,complex),fun(A,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(A,complex),fun(A,fun(complex,complex))),combb(complex,fun(complex,complex),A),inverse_divide(complex)),B)),E)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),C),E)),D)). [resolve(5284,a,5256,a)].
% 16.98/16.99 Derived: -hBOOL(hAPP(fun(nat,complex),bool,summable(complex),A)) | hBOOL(hAPP(filter(nat),bool,hAPP(complex,fun(filter(nat),bool),hAPP(fun(nat,complex),fun(complex,fun(filter(nat),bool)),tendsto(nat,complex),A),zero_zero(complex)),sequentially)). [resolve(5284,a,5257,a)].
% 16.98/17.00 Derived: -banach(complex) | -hBOOL(hAPP(fun(nat,complex),bool,summable(complex),hAPP(fun(nat,complex),fun(nat,complex),hAPP(fun(nat,fun(complex,complex)),fun(fun(nat,complex),fun(nat,complex)),combs(nat,complex,complex),hAPP(fun(nat,complex),fun(nat,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(nat,complex),fun(nat,fun(complex,complex))),combb(complex,fun(complex,complex),nat),times_times(complex)),hAPP(fun(nat,complex),fun(nat,complex),diffs(complex),hAPP(fun(nat,complex),fun(nat,complex),diffs(complex),A)))),hAPP(complex,fun(nat,complex),power_power(complex),B)))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(complex,real,norm_norm(complex),C)),hAPP(complex,real,norm_norm(complex),B))) | hBOOL(hAPP(filter(complex),bool,hAPP(complex,fun(filter(complex),bool),hAPP(fun(complex,complex),fun(complex,fun(filter(complex),bool)),tendsto(complex,complex),hAPP(fun(complex,fun(nat,complex)),fun(complex,complex),hAPP(fun(fun(nat,complex),complex),fun(fun(complex,fun(nat,complex)),fun(complex,complex)),combb(fun(nat,complex),complex,complex),suminf(complex)),hAPP(fun(complex,fun(nat,complex)),fun(complex,fun(nat,complex)),hAPP(fun(fun(nat,complex),fun(nat,complex)),fun(fun(complex,fun(nat,complex)),fun(complex,fun(nat,complex))),combb(fun(nat,complex),fun(nat,complex),complex),hAPP(fun(nat,fun(complex,complex)),fun(fun(nat,complex),fun(nat,complex)),combs(nat,complex,complex),hAPP(fun(nat,complex),fun(nat,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(nat,complex),fun(nat,fun(complex,complex))),combb(complex,fun(complex,complex),nat),times_times(complex)),A))),hAPP(fun(nat,complex),fun(complex,fun(nat,complex)),hAPP(fun(complex,fun(fun(nat,complex),fun(nat,complex))),fun(fun(nat,complex),fun(complex,fun(nat,complex))),combc(complex,fun(nat,complex),fun(nat,complex)),hAPP(fun(complex,fun(nat,fun(complex,complex))),fun(complex,fun(fun(nat,complex),fun(nat,complex))),hAPP(fun(fun(nat,fun(complex,complex)),fun(fun(nat,complex),fun(nat,complex))),fun(fun(complex,fun(nat,fun(complex,complex))),fun(complex,fun(fun(nat,complex),fun(nat,complex)))),combb(fun(nat,fun(complex,complex)),fun(fun(nat,complex),fun(nat,complex)),complex),combs(nat,complex,complex)),hAPP(fun(complex,fun(nat,complex)),fun(complex,fun(nat,fun(complex,complex))),hAPP(fun(fun(nat,complex),fun(nat,fun(complex,complex))),fun(fun(complex,fun(nat,complex)),fun(complex,fun(nat,fun(complex,complex)))),combb(fun(nat,complex),fun(nat,fun(complex,complex)),complex),hAPP(fun(complex,fun(complex,complex)),fun(fun(nat,complex),fun(nat,fun(complex,complex))),combb(complex,fun(complex,complex),nat),minus_minus(complex))),hAPP(fun(complex,complex),fun(complex,fun(nat,complex)),hAPP(fun(complex,fun(complex,fun(nat,complex))),fun(fun(complex,complex),fun(complex,fun(nat,complex))),combs(complex,complex,fun(nat,complex)),hAPP(fun(complex,fun(nat,fun(complex,complex))),fun(complex,fun(complex,fun(nat,complex))),hAPP(fun(fun(nat,fun(complex,complex)),fun(complex,fun(nat,complex))),fun(fun(complex,fun(nat,fun(complex,complex))),fun(complex,fun(complex,fun(nat,complex)))),combb(fun(nat,fun(complex,complex)),fun(complex,fun(nat,complex)),complex),combc(nat,complex,complex)),hAPP(fun(complex,fun(nat,complex)),fun(complex,fun(nat,fun(complex,complex))),hAPP(fun(fun(nat,complex),fun(nat,fun(complex,complex))),fun(fun(complex,fun(nat,complex)),fun(complex,fun(nat,fun(complex,complex)))),combb(fun(nat,complex),fun(nat,fun(complex,complex)),complex),hAPP(fun(complex,fun(complex,complex)),fun(fun(nat,complex),fun(nat,fun(complex,complex))),combb(complex,fun(complex,complex),nat),inverse_divide(complex))),hAPP(fun(nat,complex),fun(complex,fun(nat,complex)),hAPP(fun(complex,fun(fun(nat,complex),fun(nat,complex))),fun(fun(nat,complex),fun(complex,fun(nat,complex))),combc(complex,fun(nat,complex),fun(nat,complex)),hAPP(fun(complex,fun(nat,fun(complex,complex))),fun(complex,fun(fun(nat,complex),fun(nat,complex))),hAPP(fun(fun(nat,fun(complex,complex)),fun(fun(nat,complex),fun(nat,complex))),fun(fun(complex,fun(nat,fun(complex,complex))),fun(complex,fun(fun(nat,complex),fun(nat,complex)))),combb(fun(nat,fun(complex,complex)),fun(fun(nat,complex),fun(nat,complex)),complex),combs(nat,complex,complex)),hAPP(fun(complex,fun(nat,complex)),fun(complex,fun(nat,fun(complex,complex))),hAPP(fun(fun(nat,complex),fun(nat,fun(complex,complex))),fun(fun(complex,fun(nat,complex)),fun(complex,fun(nat,fun(complex,complex)))),combb(fun(nat,complex),fun(nat,fun(complex,complex)),complex),hAPP(fun(complex,fun(complex,complex)),fun(fun(nat,complex),fun(nat,fun(complex,complex))),combb(complex,fun(complex,complex),nat),minus_minus(complex))),hAPP(fun(complex,complex),fun(complex,fun(nat,complex)),hAPP(fun(complex,fun(nat,complex)),fun(fun(complex,complex),fun(complex,fun(nat,complex))),combb(complex,fun(nat,complex),complex),power_power(complex)),hAPP(complex,fun(complex,complex),plus_plus(complex),C))))),hAPP(complex,fun(nat,complex),power_power(complex),C))))),combi(complex))))),hAPP(fun(nat,complex),fun(nat,complex),hAPP(fun(nat,fun(complex,complex)),fun(fun(nat,complex),fun(nat,complex)),combs(nat,complex,complex),hAPP(fun(nat,complex),fun(nat,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(nat,complex),fun(nat,fun(complex,complex))),combb(complex,fun(complex,complex),nat),times_times(complex)),semiring_1_of_nat(complex))),hAPP(fun(nat,nat),fun(nat,complex),hAPP(fun(nat,complex),fun(fun(nat,nat),fun(nat,complex)),combb(nat,complex,nat),hAPP(complex,fun(nat,complex),power_power(complex),C)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),minus_minus(nat)),hAPP(nat,nat,suc,zero_zero(nat))))))))),zero_zero(complex)),hAPP(complex,filter(complex),at(complex),zero_zero(complex)))). [resolve(5284,a,5258,a)].
% 17.08/17.00 Derived: hBOOL(hAPP(filter(complex),bool,hAPP(complex,fun(filter(complex),bool),hAPP(fun(complex,complex),fun(complex,fun(filter(complex),bool)),tendsto(complex,complex),hAPP(complex,fun(complex,complex),hAPP(fun(complex,fun(complex,complex)),fun(complex,fun(complex,complex)),combc(complex,complex,complex),inverse_divide(complex)),A)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),B),A)),hAPP(complex,filter(complex),at(complex),B))). [resolve(5284,a,5260,a)].
% 17.08/17.00 Derived: -topological_space(A) | -hBOOL(hAPP(filter(A),bool,hAPP(complex,fun(filter(A),bool),hAPP(fun(A,complex),fun(complex,fun(filter(A),bool)),tendsto(A,complex),B),zero_zero(complex)),hAPP(A,filter(A),at(A),C))) | hBOOL(hAPP(filter(A),bool,hAPP(complex,fun(filter(A),bool),hAPP(fun(A,complex),fun(complex,fun(filter(A),bool)),tendsto(A,complex),hAPP(complex,fun(A,complex),hAPP(fun(A,fun(complex,complex)),fun(complex,fun(A,complex)),combc(A,complex,complex),hAPP(fun(A,complex),fun(A,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(A,complex),fun(A,fun(complex,complex))),combb(complex,fun(complex,complex),A),inverse_divide(complex)),B)),D)),zero_zero(complex)),hAPP(A,filter(A),at(A),C))). [resolve(5284,a,5261,b)].
% 17.08/17.00 Derived: -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),A),B),C)) | hBOOL(hAPP(filter(complex),bool,hAPP(complex,fun(filter(complex),bool),hAPP(fun(complex,complex),fun(complex,fun(filter(complex),bool)),tendsto(complex,complex),hAPP(fun(complex,complex),fun(complex,complex),hAPP(fun(complex,fun(complex,complex)),fun(fun(complex,complex),fun(complex,complex)),combs(complex,complex,complex),hAPP(fun(complex,complex),fun(complex,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(complex,complex),fun(complex,fun(complex,complex))),combb(complex,fun(complex,complex),complex),inverse_divide(complex)),hAPP(complex,fun(complex,complex),hAPP(fun(complex,fun(complex,complex)),fun(complex,fun(complex,complex)),combc(complex,complex,complex),hAPP(fun(complex,complex),fun(complex,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(complex,complex),fun(complex,fun(complex,complex))),combb(complex,fun(complex,complex),complex),minus_minus(complex)),A)),hAPP(complex,complex,A,B)))),hAPP(complex,fun(complex,complex),hAPP(fun(complex,fun(complex,complex)),fun(complex,fun(complex,complex)),combc(complex,complex,complex),minus_minus(complex)),B))),C),hAPP(complex,filter(complex),at(complex),B))). [resolve(5284,a,5262,a)].
% 17.08/17.00 Derived: hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),A),B),C)) | -hBOOL(hAPP(filter(complex),bool,hAPP(complex,fun(filter(complex),bool),hAPP(fun(complex,complex),fun(complex,fun(filter(complex),bool)),tendsto(complex,complex),hAPP(fun(complex,complex),fun(complex,complex),hAPP(fun(complex,fun(complex,complex)),fun(fun(complex,complex),fun(complex,complex)),combs(complex,complex,complex),hAPP(fun(complex,complex),fun(complex,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(complex,complex),fun(complex,fun(complex,complex))),combb(complex,fun(complex,complex),complex),inverse_divide(complex)),hAPP(complex,fun(complex,complex),hAPP(fun(complex,fun(complex,complex)),fun(complex,fun(complex,complex)),combc(complex,complex,complex),hAPP(fun(complex,complex),fun(complex,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(complex,complex),fun(complex,fun(complex,complex))),combb(complex,fun(complex,complex),complex),minus_minus(complex)),A)),hAPP(complex,complex,A,B)))),hAPP(complex,fun(complex,complex),hAPP(fun(complex,fun(complex,complex)),fun(complex,fun(complex,complex)),combc(complex,complex,complex),minus_minus(complex)),B))),C),hAPP(complex,filter(complex),at(complex),B))). [resolve(5284,a,5263,a)].
% 17.08/17.00 Derived: -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),A),B),C)) | hBOOL(hAPP(filter(complex),bool,hAPP(complex,fun(filter(complex),bool),hAPP(fun(complex,complex),fun(complex,fun(filter(complex),bool)),tendsto(complex,complex),hAPP(fun(complex,complex),fun(complex,complex),hAPP(fun(complex,fun(complex,complex)),fun(fun(complex,complex),fun(complex,complex)),combs(complex,complex,complex),hAPP(fun(complex,complex),fun(complex,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(complex,complex),fun(complex,fun(complex,complex))),combb(complex,fun(complex,complex),complex),inverse_divide(complex)),hAPP(complex,fun(complex,complex),hAPP(fun(complex,fun(complex,complex)),fun(complex,fun(complex,complex)),combc(complex,complex,complex),hAPP(fun(complex,complex),fun(complex,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(complex,complex),fun(complex,fun(complex,complex))),combb(complex,fun(complex,complex),complex),minus_minus(complex)),hAPP(fun(complex,complex),fun(complex,complex),hAPP(fun(complex,complex),fun(fun(complex,complex),fun(complex,complex)),combb(complex,complex,complex),A),hAPP(complex,fun(complex,complex),plus_plus(complex),B)))),hAPP(complex,complex,A,B)))),combi(complex))),C),hAPP(complex,filter(complex),at(complex),zero_zero(complex)))). [resolve(5284,a,5264,a)].
% 17.08/17.00 Derived: hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),A),B),C)) | -hBOOL(hAPP(filter(complex),bool,hAPP(complex,fun(filter(complex),bool),hAPP(fun(complex,complex),fun(complex,fun(filter(complex),bool)),tendsto(complex,complex),hAPP(fun(complex,complex),fun(complex,complex),hAPP(fun(complex,fun(complex,complex)),fun(fun(complex,complex),fun(complex,complex)),combs(complex,complex,complex),hAPP(fun(complex,complex),fun(complex,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(complex,complex),fun(complex,fun(complex,complex))),combb(complex,fun(complex,complex),complex),inverse_divide(complex)),hAPP(complex,fun(complex,complex),hAPP(fun(complex,fun(complex,complex)),fun(complex,fun(complex,complex)),combc(complex,complex,complex),hAPP(fun(complex,complex),fun(complex,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(complex,complex),fun(complex,fun(complex,complex))),combb(complex,fun(complex,complex),complex),minus_minus(complex)),hAPP(fun(complex,complex),fun(complex,complex),hAPP(fun(complex,complex),fun(fun(complex,complex),fun(complex,complex)),combb(complex,complex,complex),A),hAPP(complex,fun(complex,complex),plus_plus(complex),B)))),hAPP(complex,complex,A,B)))),combi(complex))),C),hAPP(complex,filter(complex),at(complex),zero_zero(complex)))). [resolve(5284,a,5266,a)].
% 17.08/17.00 Derived: -banach(A) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B)) | -hBOOL(hAPP(fun(nat,real),bool,summable(real),C)) | zero_zero(complex) != ti(complex,f682(A,complex,D,C,B)) | hBOOL(hAPP(filter(complex),bool,hAPP(A,fun(filter(complex),bool),hAPP(fun(complex,A),fun(A,fun(filter(complex),bool)),tendsto(complex,A),hAPP(fun(complex,fun(nat,A)),fun(complex,A),hAPP(fun(fun(nat,A),A),fun(fun(complex,fun(nat,A)),fun(complex,A)),combb(fun(nat,A),A,complex),suminf(A)),D)),zero_zero(A)),hAPP(complex,filter(complex),at(complex),zero_zero(complex)))). [resolve(5284,a,5267,a)].
% 17.08/17.00 Derived: -banach(A) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B)) | -hBOOL(hAPP(fun(nat,real),bool,summable(real),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(complex,real,norm_norm(complex),f682(A,complex,D,C,B))),B)) | hBOOL(hAPP(filter(complex),bool,hAPP(A,fun(filter(complex),bool),hAPP(fun(complex,A),fun(A,fun(filter(complex),bool)),tendsto(complex,A),hAPP(fun(complex,fun(nat,A)),fun(complex,A),hAPP(fun(fun(nat,A),A),fun(fun(complex,fun(nat,A)),fun(complex,A)),combb(fun(nat,A),A,complex),suminf(A)),D)),zero_zero(A)),hAPP(complex,filter(complex),at(complex),zero_zero(complex)))). [resolve(5284,a,5268,a)].
% 17.08/17.00 Derived: -banach(A) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B)) | -hBOOL(hAPP(fun(nat,real),bool,summable(real),C)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(A,real,norm_norm(A),hAPP(nat,A,hAPP(complex,fun(nat,A),D,f682(A,complex,D,C,B)),f683(A,complex,D,C,B)))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,C,f683(A,complex,D,C,B))),hAPP(complex,real,norm_norm(complex),f682(A,complex,D,C,B))))) | hBOOL(hAPP(filter(complex),bool,hAPP(A,fun(filter(complex),bool),hAPP(fun(complex,A),fun(A,fun(filter(complex),bool)),tendsto(complex,A),hAPP(fun(complex,fun(nat,A)),fun(complex,A),hAPP(fun(fun(nat,A),A),fun(fun(complex,fun(nat,A)),fun(complex,A)),combb(fun(nat,A),A,complex),suminf(A)),D)),zero_zero(A)),hAPP(complex,filter(complex),at(complex),zero_zero(complex)))). [resolve(5284,a,5269,a)].
% 17.08/17.00 Derived: -real_normed_vector(A) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B)) | zero_zero(complex) != ti(complex,f684(A,complex,C,D,B)) | hBOOL(hAPP(filter(complex),bool,hAPP(A,fun(filter(complex),bool),hAPP(fun(complex,A),fun(A,fun(filter(complex),bool)),tendsto(complex,A),C),zero_zero(A)),hAPP(complex,filter(complex),at(complex),zero_zero(complex)))). [resolve(5284,a,5270,a)].
% 17.08/17.00 Derived: -real_normed_vector(A) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(complex,real,norm_norm(complex),f684(A,complex,C,D,B))),B)) | hBOOL(hAPP(filter(complex),bool,hAPP(A,fun(filter(complex),bool),hAPP(fun(complex,A),fun(A,fun(filter(complex),bool)),tendsto(complex,A),C),zero_zero(A)),hAPP(complex,filter(complex),at(complex),zero_zero(complex)))). [resolve(5284,a,5271,a)].
% 17.08/17.00 Derived: -real_normed_vector(A) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(A,real,norm_norm(A),hAPP(complex,A,C,f684(A,complex,C,D,B)))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),D),hAPP(complex,real,norm_norm(complex),f684(A,complex,C,D,B))))) | hBOOL(hAPP(filter(complex),bool,hAPP(A,fun(filter(complex),bool),hAPP(fun(complex,A),fun(A,fun(filter(complex),bool)),tendsto(complex,A),C),zero_zero(A)),hAPP(complex,filter(complex),at(complex),zero_zero(complex)))). [resolve(5284,a,5272,a)].
% 17.08/17.00 Derived: hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),A),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),B),C)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),A),B)),C). [resolve(5284,a,5273,a)].
% 17.08/17.00 Derived: -banach(complex) | hAPP(fun(nat,complex),complex,suminf(complex),hAPP(fun(nat,complex),fun(nat,complex),hAPP(fun(nat,fun(complex,complex)),fun(fun(nat,complex),fun(nat,complex)),combs(nat,complex,complex),hAPP(fun(nat,real),fun(nat,fun(complex,complex)),hAPP(fun(real,fun(complex,complex)),fun(fun(nat,real),fun(nat,fun(complex,complex))),combb(real,fun(complex,complex),nat),scaleR_scaleR(complex)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),inverse_inverse(real)),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),fact_fact(nat))))),hAPP(complex,fun(nat,complex),power_power(complex),A))) = hAPP(complex,complex,exp(complex),A). [resolve(5284,a,5274,a)].
% 17.08/17.00 Derived: -banach(complex) | hBOOL(hAPP(complex,bool,hAPP(fun(nat,complex),fun(complex,bool),sums(complex),hAPP(fun(nat,complex),fun(nat,complex),hAPP(fun(nat,fun(complex,complex)),fun(fun(nat,complex),fun(nat,complex)),combs(nat,complex,complex),hAPP(fun(nat,real),fun(nat,fun(complex,complex)),hAPP(fun(real,fun(complex,complex)),fun(fun(nat,real),fun(nat,fun(complex,complex))),combb(real,fun(complex,complex),nat),scaleR_scaleR(complex)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),inverse_inverse(real)),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),fact_fact(nat))))),hAPP(complex,fun(nat,complex),power_power(complex),A))),hAPP(complex,complex,exp(complex),A))). [resolve(5284,a,5276,a)].
% 17.08/17.00 Derived: -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),A),B),C)) | hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,f828(complex,A,B,C),D)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),D),B)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),hAPP(complex,complex,A,D)),hAPP(complex,complex,A,B)). [resolve(5284,a,5277,a)].
% 17.08/17.00 Derived: -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),A),B),C)) | hBOOL(hAPP(complex,bool,hAPP(fun(complex,complex),fun(complex,bool),isCont(complex,complex),f828(complex,A,B,C)),B)). [resolve(5284,a,5278,a)].
% 17.08/17.00 Derived: -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),A),B),C)) | hAPP(complex,complex,f828(complex,A,B,C),B) = ti(complex,C). [resolve(5284,a,5279,a)].
% 17.08/17.00 Derived: hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),A),B),C)) | hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,D,f829(complex,A,B,C,D))),hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),f829(complex,A,B,C,D)),B)) != hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),hAPP(complex,complex,A,f829(complex,A,B,C,D))),hAPP(complex,complex,A,B)) | -hBOOL(hAPP(complex,bool,hAPP(fun(complex,complex),fun(complex,bool),isCont(complex,complex),D),B)) | hAPP(complex,complex,D,B) != ti(complex,C). [resolve(5284,a,5280,a)].
% 17.08/17.00 Derived: hBOOL(hAPP(complex,bool,hAPP(fun(complex,complex),fun(complex,bool),isCont(complex,complex),hAPP(complex,fun(complex,complex),hAPP(fun(complex,fun(complex,complex)),fun(complex,fun(complex,complex)),combc(complex,complex,complex),inverse_divide(complex)),A)),B)). [resolve(5284,a,5281,a)].
% 20.20/20.11 Derived: -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),A),B),C)) | hBOOL(hAPP(complex,bool,hAPP(fun(complex,complex),fun(complex,bool),isCont(complex,complex),A),B)). [resolve(5284,a,5282,a)].
% 20.20/20.11 Derived: -banach(complex) | hBOOL(hAPP(complex,bool,hAPP(fun(complex,complex),fun(complex,bool),isCont(complex,complex),exp(complex)),A)). [resolve(5284,a,5283,a)].
% 20.20/20.11 5285 semiring_div(int) # label(arity_Int_Oint___Divides_Osemiring__div) # label(axiom). [assumption].
% 20.20/20.11 5286 -semiring_div(A) | div_div(A) = ti(fun(A,fun(A,A)),div_div(A)) # label(tsy_c_Divides_Odiv__class_Odiv_res) # label(axiom). [clausify(16)].
% 20.20/20.11 5287 -semiring_div(A) | div_mod(A) = ti(fun(A,fun(A,A)),div_mod(A)) # label(tsy_c_Divides_Odiv__class_Omod_res) # label(axiom). [clausify(17)].
% 20.20/20.11 5288 -semiring_div(A) | hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),B),C)),C) = hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),B),C) # label(fact_467_mod__mod__trivial) # label(axiom). [clausify(592)].
% 20.20/20.11 5289 -semiring_div(A) | hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),zero_zero(A)),B) = zero_zero(A) # label(fact_519_mod__0) # label(axiom). [clausify(643)].
% 20.20/20.11 5290 -semiring_div(A) | hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),B),zero_zero(A)) = ti(A,B) # label(fact_520_mod__by__0) # label(axiom). [clausify(644)].
% 20.20/20.11 5291 -semiring_div(A) | hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),B),B) = zero_zero(A) # label(fact_521_mod__self) # label(axiom). [clausify(645)].
% 20.20/20.11 5292 -semiring_div(A) | hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),B),C) != hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),D),C) | hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),E),C) != hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),F),C) | hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),E)),C) = hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),F)),C) # label(fact_526_mod__mult__cong) # label(axiom). [clausify(650)].
% 20.20/20.11 5293 -semiring_div(A) | hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),B),C)),D)),C) = hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D)),C) # label(fact_527_zmod__simps_I4_J) # label(axiom). [clausify(651)].
% 20.20/20.11 5294 -semiring_div(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),B),C)),D) = hAPP(A,A,hAPP(A,fun(A,A),div_mod(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_528_mod__mult__mult2) # label(axiom). [clausify(652)].
% 20.20/20.11 5295 -semiring_div(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),C),D)) = hAPP(A,A,hAPP(A,fun(A,A),div_mod(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_529_mod__mult__mult1) # label(axiom). [clausify(653)].
% 20.20/20.11 5296 -semiring_div(A) | hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),D),C))),C) = hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D)),C) # label(fact_530_mod__mult__eq) # label(axiom). [clausify(654)].
% 20.20/20.11 5297 -semiring_div(A) | hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),B),C)),D)),C) = hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D)),C) # label(fact_531_mod__mult__left__eq) # label(axiom). [clausify(655)].
% 20.20/20.11 5298 -semiring_div(A) | hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),C),D))),D) = hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),D) # label(fact_532_mod__mult__right__eq) # label(axiom). [clausify(656)].
% 20.20/20.11 5299 -semiring_div(A) | hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),B),C) != hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),D),C) | hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),E),C) != hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),F),C) | hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),E)),C) = hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),D),F)),C) # label(fact_533_mod__add__cong) # label(axiom). [clausify(657)].
% 20.20/20.11 5300 -semiring_div(A) | hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),B),C)),D)),C) = hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),D)),C) # label(fact_534_zmod__simps_I1_J) # label(axiom). [clausify(658)].
% 20.20/20.11 5301 -semiring_div(A) | hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),C),D))),D) = hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),D) # label(fact_535_zmod__simps_I2_J) # label(axiom). [clausify(659)].
% 20.20/20.11 5302 -semiring_div(A) | hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),D),C))),C) = hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),D)),C) # label(fact_536_mod__add__eq) # label(axiom). [clausify(660)].
% 20.20/20.11 5303 -semiring_div(A) | hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),B),C)),D)),C) = hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),D)),C) # label(fact_537_mod__add__left__eq) # label(axiom). [clausify(661)].
% 20.20/20.11 5304 -semiring_div(A) | hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),C),D))),D) = hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),D) # label(fact_538_mod__add__right__eq) # label(axiom). [clausify(662)].
% 20.20/20.11 5305 -semiring_div(A) | hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),B) = hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),C),B) # label(fact_539_mod__add__self1) # label(axiom). [clausify(663)].
% 20.20/20.11 5306 -semiring_div(A) | hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),C) = hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),B),C) # label(fact_540_mod__add__self2) # label(axiom). [clausify(664)].
% 20.20/20.11 5307 -semiring_div(A) | hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),B) = zero_zero(A) # label(fact_608_mod__mult__self1__is__0) # label(axiom). [clausify(729)].
% 20.20/20.11 5308 -semiring_div(A) | hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),C) = zero_zero(A) # label(fact_609_mod__mult__self2__is__0) # label(axiom). [clausify(730)].
% 20.20/20.11 5309 -semiring_div(A) | hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),B),one_one(A)) = zero_zero(A) # label(fact_616_mod__by__1) # label(axiom). [clausify(737)].
% 20.20/20.11 5310 -semiring_div(A) | hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),D))),D) = hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),B),D) # label(fact_618_mod__mult__self1) # label(axiom). [clausify(739)].
% 20.20/20.11 5311 -semiring_div(A) | hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),D))),C) = hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),B),C) # label(fact_619_mod__mult__self2) # label(axiom). [clausify(740)].
% 20.20/20.11 5312 -semiring_div(A) | hAPP(A,A,hAPP(A,fun(A,A),div_div(A),B),zero_zero(A)) = zero_zero(A) # label(fact_729_div__by__0) # label(axiom). [clausify(849)].
% 20.20/20.11 5313 -semiring_div(A) | hAPP(A,A,hAPP(A,fun(A,A),div_div(A),zero_zero(A)),B) = zero_zero(A) # label(fact_730_div__0) # label(axiom). [clausify(850)].
% 20.20/20.11 5314 -semiring_div(A) | hAPP(A,A,hAPP(A,fun(A,A),div_div(A),B),one_one(A)) = ti(A,B) # label(fact_731_div__by__1) # label(axiom). [clausify(851)].
% 20.20/20.11 5315 -semiring_div(A) | zero_zero(A) != ti(A,B) | hAPP(A,A,hAPP(A,fun(A,A),div_div(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)) = zero_zero(A) # label(fact_744_div__mult__mult1__if) # label(axiom). [clausify(864)].
% 20.20/20.11 5316 -semiring_div(A) | zero_zero(A) = ti(A,B) | hAPP(A,A,hAPP(A,fun(A,A),div_div(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)) = hAPP(A,A,hAPP(A,fun(A,A),div_div(A),C),D) # label(fact_744_div__mult__mult1__if) # label(axiom). [clausify(864)].
% 20.20/20.11 5317 -semiring_div(A) | zero_zero(A) = ti(A,B) | hAPP(A,A,hAPP(A,fun(A,A),div_div(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),B)),B) = ti(A,C) # label(fact_745_div__mult__self2__is__id) # label(axiom). [clausify(865)].
% 20.20/20.11 5318 -semiring_div(A) | zero_zero(A) = ti(A,B) | hAPP(A,A,hAPP(A,fun(A,A),div_div(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),B) = ti(A,C) # label(fact_746_div__mult__self1__is__id) # label(axiom). [clausify(866)].
% 20.20/20.11 5319 -semiring_div(A) | zero_zero(A) = ti(A,B) | hAPP(A,A,hAPP(A,fun(A,A),div_div(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),B)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),B)) = hAPP(A,A,hAPP(A,fun(A,A),div_div(A),C),D) # label(fact_747_div__mult__mult2) # label(axiom). [clausify(867)].
% 20.20/20.11 5320 -semiring_div(A) | zero_zero(A) = ti(A,B) | hAPP(A,A,hAPP(A,fun(A,A),div_div(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)) = hAPP(A,A,hAPP(A,fun(A,A),div_div(A),C),D) # label(fact_748_div__mult__mult1) # label(axiom). [clausify(868)].
% 20.20/20.11 5321 -semiring_div(A) | zero_zero(A) = ti(A,B) | hAPP(A,A,hAPP(A,fun(A,A),div_div(A),B),B) = one_one(A) # label(fact_749_div__self) # label(axiom). [clausify(869)].
% 20.20/20.11 5322 -semiring_div(A) | hAPP(A,A,hAPP(A,fun(A,A),div_div(A),hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),B),C)),C) = zero_zero(A) # label(fact_750_mod__div__trivial) # label(axiom). [clausify(870)].
% 20.20/20.11 5323 -semiring_div(A) | zero_zero(A) = ti(A,B) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),hAPP(A,A,hAPP(A,fun(A,A),div_div(A),D),B)) = hAPP(A,A,hAPP(A,fun(A,A),div_div(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),D),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C))),B) # label(fact_775_div__mult__self2) # label(axiom). [clausify(895)].
% 20.20/20.11 5324 -semiring_div(A) | zero_zero(A) = ti(A,B) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),hAPP(A,A,hAPP(A,fun(A,A),div_div(A),D),B)) = hAPP(A,A,hAPP(A,fun(A,A),div_div(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),D),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),B))),B) # label(fact_776_div__mult__self1) # label(axiom). [clausify(896)].
% 20.20/20.11 5325 -semiring_div(A) | zero_zero(A) = ti(A,B) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),div_div(A),C),B)),one_one(A)) = hAPP(A,A,hAPP(A,fun(A,A),div_div(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),B)),B) # label(fact_778_div__add__self2) # label(axiom). [clausify(898)].
% 20.20/20.11 5326 -semiring_div(A) | zero_zero(A) = ti(A,B) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),div_div(A),C),B)),one_one(A)) = hAPP(A,A,hAPP(A,fun(A,A),div_div(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),B) # label(fact_779_div__add__self1) # label(axiom). [clausify(899)].
% 20.20/20.11 5327 -semiring_div(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),div_div(A),B),C)),C)) = ti(A,B) # label(fact_780_semiring__div__class_Omod__div__equality_H) # label(axiom). [clausify(900)].
% 20.20/20.11 5328 -semiring_div(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(A,A,hAPP(A,fun(A,A),div_div(A),C),B))),hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),C),B)) = ti(A,C) # label(fact_781_mod__div__equality2) # label(axiom). [clausify(901)].
% 20.20/20.11 5329 -semiring_div(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),div_div(A),B),C)),C)),hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),B),C)) = ti(A,B) # label(fact_782_mod__div__equality) # label(axiom). [clausify(902)].
% 20.20/20.11 5330 -semiring_div(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(A,A,hAPP(A,fun(A,A),div_div(A),C),B))),hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),C),B))),D) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),D) # label(fact_783_div__mod__equality2) # label(axiom). [clausify(903)].
% 20.20/20.11 5331 -semiring_div(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(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),div_div(A),B),C)),C)),hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),B),C))),D) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),D) # label(fact_784_div__mod__equality) # label(axiom). [clausify(904)].
% 20.20/20.11 5332 -semiring_div(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),div_div(A),B),C)),C)),hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),B),C)) = ti(A,B) # label(fact_806_mod__div__decomp) # label(axiom). [clausify(926)].
% 20.20/20.11 5333 -semiring_div(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),D),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),D)) # label(fact_3079_dvd__mod__iff) # label(axiom). [clausify(3046)].
% 20.20/20.11 5334 -semiring_div(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),D),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),D)) # label(fact_3079_dvd__mod__iff) # label(axiom). [clausify(3046)].
% 20.20/20.11 5335 -semiring_div(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),C)) | hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),D),C)),B) = hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),D),B) # label(fact_3080_mod__mod__cancel) # label(axiom). [clausify(3047)].
% 20.20/20.11 5336 -semiring_div(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),C),D))) # label(fact_3081_dvd__mod) # label(axiom). [clausify(3048)].
% 20.20/20.11 5337 -semiring_div(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),C),D))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),C)) # label(fact_3082_dvd__mod__imp__dvd) # label(axiom). [clausify(3049)].
% 20.20/20.11 5338 -semiring_div(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),hAPP(A,A,hAPP(A,fun(A,A),div_div(A),C),B)),hAPP(A,A,hAPP(A,fun(A,A),div_div(A),D),B))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),C),D)) # label(fact_3083_div__dvd__div) # label(axiom). [clausify(3050)].
% 20.20/20.11 5339 -semiring_div(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),hAPP(A,A,hAPP(A,fun(A,A),div_div(A),C),B)),hAPP(A,A,hAPP(A,fun(A,A),div_div(A),D),B))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),C),D)) # label(fact_3083_div__dvd__div) # label(axiom). [clausify(3050)].
% 20.20/20.11 5340 -semiring_div(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),C)) | hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),C),B) = zero_zero(A) # label(fact_3125_dvd__imp__mod__0) # label(axiom). [clausify(3092)].
% 20.20/20.11 5341 -semiring_div(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),C)) | hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),C),B) = zero_zero(A) # label(fact_3126_dvd__eq__mod__eq__0) # label(axiom). [clausify(3093)].
% 20.20/20.11 5342 -semiring_div(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),C)) | hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),C),B) != zero_zero(A) # label(fact_3126_dvd__eq__mod__eq__0) # label(axiom). [clausify(3093)].
% 20.20/20.11 5343 -semiring_div(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),C)) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(A,A,hAPP(A,fun(A,A),div_div(A),C),B)) = ti(A,C) # label(fact_3127_dvd__mult__div__cancel) # label(axiom). [clausify(3094)].
% 20.20/20.11 5344 -semiring_div(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),C)) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),hAPP(A,A,hAPP(A,fun(A,A),div_div(A),C),B)) = hAPP(A,A,hAPP(A,fun(A,A),div_div(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),C)),B) # label(fact_3128_div__mult__swap) # label(axiom). [clausify(3095)].
% 20.20/20.11 5345 -semiring_div(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),C)) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),div_div(A),C),B)),B) = ti(A,C) # label(fact_3129_dvd__div__mult__self) # label(axiom). [clausify(3096)].
% 20.20/20.11 5346 -semiring_div(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),C)) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),div_div(A),C),B)),D) = hAPP(A,A,hAPP(A,fun(A,A),div_div(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),D)),B) # label(fact_3130_dvd__div__mult) # label(axiom). [clausify(3097)].
% 20.20/20.11 5347 -semiring_div(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),D),E)) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),div_div(A),C),B)),hAPP(A,A,hAPP(A,fun(A,A),div_div(A),E),D)) = hAPP(A,A,hAPP(A,fun(A,A),div_div(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_3131_div__mult__div__if__dvd) # label(axiom). [clausify(3098)].
% 20.20/20.11 5348 -semiring_div(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),D)) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),div_div(A),C),B)),hAPP(A,A,hAPP(A,fun(A,A),div_div(A),D),B)) = hAPP(A,A,hAPP(A,fun(A,A),div_div(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),D)),B) # label(fact_3132_div__add) # label(axiom). [clausify(3099)].
% 20.20/20.11 5349 -semiring_div(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),C)) | hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),hAPP(A,A,hAPP(A,fun(A,A),div_div(A),C),B)),D) = hAPP(A,A,hAPP(A,fun(A,A),div_div(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),C),D)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),D)) # label(fact_3136_div__power) # label(axiom). [clausify(3103)].
% 20.20/20.11 5350 -semiring_div(A) | zero_zero(A) = ti(A,B) | zero_zero(A) = ti(A,C) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),C),E)) | hAPP(A,A,hAPP(A,fun(A,A),div_div(A),E),C) != hAPP(A,A,hAPP(A,fun(A,A),div_div(A),D),B) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),C) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),E) # label(fact_3159_dvd__div__div__eq__mult) # label(axiom). [clausify(3126)].
% 20.20/20.11 5351 -semiring_div(A) | zero_zero(A) = ti(A,B) | zero_zero(A) = ti(A,C) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),C),E)) | hAPP(A,A,hAPP(A,fun(A,A),div_div(A),E),C) = hAPP(A,A,hAPP(A,fun(A,A),div_div(A),D),B) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),C) != hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),E) # label(fact_3159_dvd__div__div__eq__mult) # label(axiom). [clausify(3126)].
% 20.20/20.11 5352 -semiring_div(A) | zero_zero(A) = ti(A,B) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),C)) | hAPP(A,A,hAPP(A,fun(A,A),div_div(A),C),B) != ti(A,D) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),B) = ti(A,C) # label(fact_3160_dvd__div__eq__mult) # label(axiom). [clausify(3127)].
% 20.20/20.11 5353 -semiring_div(A) | zero_zero(A) = ti(A,B) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),C)) | hAPP(A,A,hAPP(A,fun(A,A),div_div(A),C),B) = ti(A,D) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),B) != ti(A,C) # label(fact_3160_dvd__div__eq__mult) # label(axiom). [clausify(3127)].
% 20.20/20.11 5354 -semiring_div(A) | -number(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),hAPP(int,A,number_number_of(A),B)),hAPP(int,A,number_number_of(A),C))) | hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),hAPP(int,A,number_number_of(A),C)),hAPP(int,A,number_number_of(A),B)) = zero_zero(A) # label(fact_3161_dvd__eq__mod__eq__0__number__of) # label(axiom). [clausify(3128)].
% 20.20/20.11 5355 -semiring_div(A) | -number(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),hAPP(int,A,number_number_of(A),B)),hAPP(int,A,number_number_of(A),C))) | hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),hAPP(int,A,number_number_of(A),C)),hAPP(int,A,number_number_of(A),B)) != zero_zero(A) # label(fact_3161_dvd__eq__mod__eq__0__number__of) # label(axiom). [clausify(3128)].
% 20.20/20.12 Derived: div_div(int) = ti(fun(int,fun(int,int)),div_div(int)). [resolve(5285,a,5286,a)].
% 20.20/20.12 Derived: div_mod(int) = ti(fun(int,fun(int,int)),div_mod(int)). [resolve(5285,a,5287,a)].
% 20.20/20.12 Derived: hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A),B)),B) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A),B). [resolve(5285,a,5288,a)].
% 20.20/20.12 Derived: hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),zero_zero(int)),A) = zero_zero(int). [resolve(5285,a,5289,a)].
% 20.20/20.12 Derived: hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A),zero_zero(int)) = ti(int,A). [resolve(5285,a,5290,a)].
% 20.20/20.12 Derived: hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A),A) = zero_zero(int). [resolve(5285,a,5291,a)].
% 20.20/20.12 Derived: hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A),B) != hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),C),B) | hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),D),B) != hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),E),B) | hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),D)),B) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),E)),B). [resolve(5285,a,5292,a)].
% 20.20/20.12 Derived: hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A),B)),C)),B) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),C)),B). [resolve(5285,a,5293,a)].
% 20.20/20.12 Derived: hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A),B)),C) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(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(5285,a,5294,a)].
% 20.20/20.12 Derived: hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),B),C)) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(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(5285,a,5295,a)].
% 20.20/20.12 Derived: hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),C),B))),B) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),C)),B). [resolve(5285,a,5296,a)].
% 20.20/20.12 Derived: hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),B),C))),C) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),C). [resolve(5285,a,5298,a)].
% 20.20/20.12 Derived: hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A),B) != hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),C),B) | hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),D),B) != hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),E),B) | hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),D)),B) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),C),E)),B). [resolve(5285,a,5299,a)].
% 20.20/20.12 Derived: hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A),B)),C)),B) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),C)),B). [resolve(5285,a,5300,a)].
% 20.20/20.12 Derived: hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),B),C))),C) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B)),C). [resolve(5285,a,5301,a)].
% 20.20/20.12 Derived: hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),C),B))),B) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),C)),B). [resolve(5285,a,5302,a)].
% 20.20/20.12 Derived: hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B)),A) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),B),A). [resolve(5285,a,5305,a)].
% 20.20/20.12 Derived: hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B)),B) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A),B). [resolve(5285,a,5306,a)].
% 20.20/20.12 Derived: hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),A) = zero_zero(int). [resolve(5285,a,5307,a)].
% 20.20/20.12 Derived: hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),B) = zero_zero(int). [resolve(5285,a,5308,a)].
% 20.20/20.12 Derived: hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A),one_one(int)) = zero_zero(int). [resolve(5285,a,5309,a)].
% 20.20/20.12 Derived: hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),C))),C) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A),C). [resolve(5285,a,5310,a)].
% 20.20/20.12 Derived: hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),C))),B) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A),B). [resolve(5285,a,5311,a)].
% 20.20/20.12 Derived: hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A),zero_zero(int)) = zero_zero(int). [resolve(5285,a,5312,a)].
% 20.20/20.12 Derived: hAPP(int,int,hAPP(int,fun(int,int),div_div(int),zero_zero(int)),A) = zero_zero(int). [resolve(5285,a,5313,a)].
% 20.20/20.12 Derived: hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A),one_one(int)) = ti(int,A). [resolve(5285,a,5314,a)].
% 20.20/20.12 Derived: zero_zero(int) != ti(int,A) | hAPP(int,int,hAPP(int,fun(int,int),div_div(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)) = zero_zero(int). [resolve(5285,a,5315,a)].
% 20.20/20.12 Derived: zero_zero(int) = ti(int,A) | hAPP(int,int,hAPP(int,fun(int,int),div_div(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)) = hAPP(int,int,hAPP(int,fun(int,int),div_div(int),B),C). [resolve(5285,a,5316,a)].
% 20.20/20.12 Derived: zero_zero(int) = ti(int,A) | hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),A)),A) = ti(int,B). [resolve(5285,a,5317,a)].
% 20.20/20.12 Derived: zero_zero(int) = ti(int,A) | hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),A) = ti(int,B). [resolve(5285,a,5318,a)].
% 20.20/20.12 Derived: zero_zero(int) = ti(int,A) | hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),A)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),A)) = hAPP(int,int,hAPP(int,fun(int,int),div_div(int),B),C). [resolve(5285,a,5319,a)].
% 20.20/20.12 Derived: zero_zero(int) = ti(int,A) | hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A),A) = one_one(int). [resolve(5285,a,5321,a)].
% 20.20/20.12 Derived: hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A),B)),B) = zero_zero(int). [resolve(5285,a,5322,a)].
% 20.20/20.12 Derived: zero_zero(int) = ti(int,A) | hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),B),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),C),A)) = hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),C),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B))),A). [resolve(5285,a,5323,a)].
% 20.20/20.12 Derived: zero_zero(int) = ti(int,A) | hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),B),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),C),A)) = hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),C),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),A))),A). [resolve(5285,a,5324,a)].
% 20.20/20.13 Derived: zero_zero(int) = ti(int,A) | hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),B),A)),one_one(int)) = hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),B),A)),A). [resolve(5285,a,5325,a)].
% 20.20/20.13 Derived: zero_zero(int) = ti(int,A) | hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),B),A)),one_one(int)) = hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B)),A). [resolve(5285,a,5326,a)].
% 20.20/20.13 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A),B)),B)) = ti(int,A). [resolve(5285,a,5327,a)].
% 20.20/20.13 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),B),A))),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),B),A)) = ti(int,B). [resolve(5285,a,5328,a)].
% 20.20/20.13 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),div_div(int),A),B)),B)),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A),B)) = ti(int,A). [resolve(5285,a,5329,a)].
% 20.20/20.13 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),B),A))),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),B),A))),C) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),B),C). [resolve(5285,a,5330,a)].
% 20.20/20.13 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(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),div_div(int),A),B)),B)),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A),B))),C) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),C). [resolve(5285,a,5331,a)].
% 20.20/20.13 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),C),B))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),C)). [resolve(5285,a,5333,a)].
% 20.20/20.13 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),C),B))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),C)). [resolve(5285,a,5334,a)].
% 20.20/20.13 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),B)) | hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),C),B)),A) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),C),A). [resolve(5285,a,5335,a)].
% 20.20/20.13 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),C)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),B),A)),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),C),A))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),B),C)). [resolve(5285,a,5338,a)].
% 20.20/20.13 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),B),A)),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),C),A))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),B),C)). [resolve(5285,a,5339,a)].
% 20.20/20.13 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),B)) | hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),B),A) = zero_zero(int). [resolve(5285,a,5340,a)].
% 20.20/20.13 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),B)) | hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),B),A) != zero_zero(int). [resolve(5285,a,5342,a)].
% 20.20/20.15 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),B)) | hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),B),A)) = ti(int,B). [resolve(5285,a,5343,a)].
% 20.20/20.15 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),B)) | hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),B),A)) = hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),B)),A). [resolve(5285,a,5344,a)].
% 20.20/20.15 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),B)) | hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),B),A)),A) = ti(int,B). [resolve(5285,a,5345,a)].
% 20.20/20.15 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),B)) | hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),B),A)),C) = hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),C)),A). [resolve(5285,a,5346,a)].
% 20.20/20.15 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),C),D)) | hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),B),A)),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),D),C)) = hAPP(int,int,hAPP(int,fun(int,int),div_div(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(5285,a,5347,a)].
% 20.20/20.15 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),C)) | hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),B),A)),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),C),A)) = hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),B),C)),A). [resolve(5285,a,5348,a)].
% 20.20/20.15 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),B)) | hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),B),A)),C) = hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),B),C)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),C)). [resolve(5285,a,5349,a)].
% 20.20/20.15 Derived: zero_zero(int) = ti(int,A) | zero_zero(int) = ti(int,B) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),C)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),B),D)) | hAPP(int,int,hAPP(int,fun(int,int),div_div(int),D),B) != hAPP(int,int,hAPP(int,fun(int,int),div_div(int),C),A) | hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),B) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),D). [resolve(5285,a,5350,a)].
% 20.20/20.15 Derived: zero_zero(int) = ti(int,A) | zero_zero(int) = ti(int,B) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),C)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),B),D)) | hAPP(int,int,hAPP(int,fun(int,int),div_div(int),D),B) = hAPP(int,int,hAPP(int,fun(int,int),div_div(int),C),A) | hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),B) != hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),D). [resolve(5285,a,5351,a)].
% 20.20/20.15 Derived: zero_zero(int) = ti(int,A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),B)) | hAPP(int,int,hAPP(int,fun(int,int),div_div(int),B),A) != ti(int,C) | hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),A) = ti(int,B). [resolve(5285,a,5352,a)].
% 20.20/20.15 Derived: zero_zero(int) = ti(int,A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),B)) | hAPP(int,int,hAPP(int,fun(int,int),div_div(int),B),A) = ti(int,C) | hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),A) != ti(int,B). [resolve(5285,a,5353,a)].
% 20.20/20.15 5356 semiring_div(nat) # label(arity_Nat_Onat___Divides_Osemiring__div) # label(axiom). [assumption].
% 20.20/20.15 Derived: div_div(nat) = ti(fun(nat,fun(nat,nat)),div_div(nat)). [resolve(5356,a,5286,a)].
% 20.20/20.16 Derived: div_mod(nat) = ti(fun(nat,fun(nat,nat)),div_mod(nat)). [resolve(5356,a,5287,a)].
% 20.20/20.16 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),A),B)),B) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),A),B). [resolve(5356,a,5288,a)].
% 20.20/20.16 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),zero_zero(nat)),A) = zero_zero(nat). [resolve(5356,a,5289,a)].
% 20.20/20.16 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),A),zero_zero(nat)) = ti(nat,A). [resolve(5356,a,5290,a)].
% 20.20/20.16 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),A),A) = zero_zero(nat). [resolve(5356,a,5291,a)].
% 20.20/20.16 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),A),B) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),C),B) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),D),B) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),E),B) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),D)),B) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),C),E)),B). [resolve(5356,a,5292,a)].
% 20.20/20.16 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),A),B)),C)),B) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),C)),B). [resolve(5356,a,5293,a)].
% 20.20/20.16 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),A),B)),C) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(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(5356,a,5294,a)].
% 20.20/20.16 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),B),C)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(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(5356,a,5295,a)].
% 20.20/20.16 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),A),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),C),B))),B) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),C)),B). [resolve(5356,a,5296,a)].
% 20.20/20.16 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),B),C))),C) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),B)),C). [resolve(5356,a,5298,a)].
% 20.20/20.16 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),A),B) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),C),B) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),D),B) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),E),B) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),D)),B) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),C),E)),B). [resolve(5356,a,5299,a)].
% 20.20/20.16 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),A),B)),C)),B) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),C)),B). [resolve(5356,a,5300,a)].
% 20.20/20.16 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),B),C))),C) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B)),C). [resolve(5356,a,5301,a)].
% 20.20/20.16 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),A),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),C),B))),B) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),C)),B). [resolve(5356,a,5302,a)].
% 20.20/20.16 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B)),A) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),B),A). [resolve(5356,a,5305,a)].
% 20.20/20.16 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B)),B) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),A),B). [resolve(5356,a,5306,a)].
% 20.20/20.16 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),B)),A) = zero_zero(nat). [resolve(5356,a,5307,a)].
% 20.20/20.16 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),B)),B) = zero_zero(nat). [resolve(5356,a,5308,a)].
% 20.20/20.16 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),A),one_one(nat)) = zero_zero(nat). [resolve(5356,a,5309,a)].
% 20.20/20.16 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),C))),C) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),A),C). [resolve(5356,a,5310,a)].
% 20.20/20.16 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),C))),B) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),A),B). [resolve(5356,a,5311,a)].
% 20.20/20.16 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),A),zero_zero(nat)) = zero_zero(nat). [resolve(5356,a,5312,a)].
% 20.20/20.16 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),zero_zero(nat)),A) = zero_zero(nat). [resolve(5356,a,5313,a)].
% 20.20/20.16 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),A),one_one(nat)) = ti(nat,A). [resolve(5356,a,5314,a)].
% 20.20/20.16 Derived: zero_zero(nat) != ti(nat,A) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(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)) = zero_zero(nat). [resolve(5356,a,5315,a)].
% 20.20/20.16 Derived: zero_zero(nat) = ti(nat,A) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(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)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),B),C). [resolve(5356,a,5316,a)].
% 20.20/20.16 Derived: zero_zero(nat) = ti(nat,A) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),A)),A) = ti(nat,B). [resolve(5356,a,5317,a)].
% 20.20/20.16 Derived: zero_zero(nat) = ti(nat,A) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),B)),A) = ti(nat,B). [resolve(5356,a,5318,a)].
% 20.20/20.16 Derived: zero_zero(nat) = ti(nat,A) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),A)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),C),A)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),B),C). [resolve(5356,a,5319,a)].
% 20.20/20.16 Derived: zero_zero(nat) = ti(nat,A) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),A),A) = one_one(nat). [resolve(5356,a,5321,a)].
% 20.20/20.16 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),A),B)),B) = zero_zero(nat). [resolve(5356,a,5322,a)].
% 20.20/20.16 Derived: zero_zero(nat) = ti(nat,A) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),C),A)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),C),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),B))),A). [resolve(5356,a,5323,a)].
% 20.20/20.16 Derived: zero_zero(nat) = ti(nat,A) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),C),A)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),C),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),A))),A). [resolve(5356,a,5324,a)].
% 20.20/20.16 Derived: zero_zero(nat) = ti(nat,A) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),B),A)),one_one(nat)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),A)),A). [resolve(5356,a,5325,a)].
% 20.20/20.17 Derived: zero_zero(nat) = ti(nat,A) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),B),A)),one_one(nat)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B)),A). [resolve(5356,a,5326,a)].
% 20.20/20.17 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),A),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),A),B)),B)) = ti(nat,A). [resolve(5356,a,5327,a)].
% 20.20/20.17 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),B),A))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),B),A)) = ti(nat,B). [resolve(5356,a,5328,a)].
% 20.20/20.17 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),div_div(nat),A),B)),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),A),B)) = ti(nat,A). [resolve(5356,a,5329,a)].
% 20.20/20.17 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),B),A))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),B),A))),C) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),C). [resolve(5356,a,5330,a)].
% 20.20/20.17 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(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),div_div(nat),A),B)),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),A),B))),C) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),C). [resolve(5356,a,5331,a)].
% 20.20/20.17 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),C),B))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A),C)). [resolve(5356,a,5333,a)].
% 20.20/20.17 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),C),B))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A),C)). [resolve(5356,a,5334,a)].
% 20.20/20.17 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A),B)) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),C),B)),A) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),C),A). [resolve(5356,a,5335,a)].
% 20.20/20.17 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A),C)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),B),A)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),C),A))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),B),C)). [resolve(5356,a,5338,a)].
% 20.20/20.17 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A),C)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),B),A)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),C),A))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),B),C)). [resolve(5356,a,5339,a)].
% 20.20/20.17 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A),B)) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),B),A) = zero_zero(nat). [resolve(5356,a,5340,a)].
% 20.20/20.17 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A),B)) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),B),A) != zero_zero(nat). [resolve(5356,a,5342,a)].
% 20.20/20.17 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A),B)) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),B),A)) = ti(nat,B). [resolve(5356,a,5343,a)].
% 20.31/20.27 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A),B)) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),C),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),B),A)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),C),B)),A). [resolve(5356,a,5344,a)].
% 20.31/20.27 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A),B)) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),B),A)),A) = ti(nat,B). [resolve(5356,a,5345,a)].
% 20.31/20.27 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A),B)) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),B),A)),C) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),C)),A). [resolve(5356,a,5346,a)].
% 20.31/20.27 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),C),D)) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),B),A)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),D),C)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(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(5356,a,5347,a)].
% 20.31/20.27 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A),C)) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),B),A)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),C),A)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),C)),A). [resolve(5356,a,5348,a)].
% 20.31/20.27 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A),B)) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),B),A)),C) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),B),C)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),C)). [resolve(5356,a,5349,a)].
% 20.31/20.27 Derived: zero_zero(nat) = ti(nat,A) | zero_zero(nat) = ti(nat,B) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A),C)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),B),D)) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),D),B) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),C),A) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),C),B) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),D). [resolve(5356,a,5350,a)].
% 20.31/20.27 Derived: zero_zero(nat) = ti(nat,A) | zero_zero(nat) = ti(nat,B) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A),C)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),B),D)) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),D),B) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),C),A) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),C),B) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),D). [resolve(5356,a,5351,a)].
% 20.31/20.27 Derived: zero_zero(nat) = ti(nat,A) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A),B)) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),B),A) != ti(nat,C) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),C),A) = ti(nat,B). [resolve(5356,a,5352,a)].
% 20.31/20.27 Derived: zero_zero(nat) = ti(nat,A) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A),B)) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),B),A) = ti(nat,C) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),C),A) != ti(nat,B). [resolve(5356,a,5353,a)].
% 20.31/20.27 5357 semiring_div(code_code_numeral) # label(arity_Code__Numeral_Ocode__numeral___Divides_Osemiring__div) # label(axiom). [assumption].
% 20.31/20.27 Derived: div_div(code_code_numeral) = ti(fun(code_code_numeral,fun(code_code_numeral,code_code_numeral)),div_div(code_code_numeral)). [resolve(5357,a,5286,a)].
% 20.31/20.27 Derived: div_mod(code_code_numeral) = ti(fun(code_code_numeral,fun(code_code_numeral,code_code_numeral)),div_mod(code_code_numeral)). [resolve(5357,a,5287,a)].
% 20.31/20.27 Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),A),B)),B) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),A),B). [resolve(5357,a,5288,a)].
% 20.31/20.27 Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),zero_zero(code_code_numeral)),A) = zero_zero(code_code_numeral). [resolve(5357,a,5289,a)].
% 20.31/20.27 Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),A),zero_zero(code_code_numeral)) = ti(code_code_numeral,A). [resolve(5357,a,5290,a)].
% 20.31/20.27 Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),A),A) = zero_zero(code_code_numeral). [resolve(5357,a,5291,a)].
% 20.31/20.27 Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),A),B) != hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),C),B) | hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),D),B) != hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),E),B) | hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),D)),B) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),C),E)),B). [resolve(5357,a,5292,a)].
% 20.31/20.27 Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),A),B)),C)),B) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),C)),B). [resolve(5357,a,5293,a)].
% 20.31/20.27 Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),A),B)),C) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),C)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),B),C)). [resolve(5357,a,5294,a)].
% 20.31/20.27 Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),B),C)) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),B)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),C)). [resolve(5357,a,5295,a)].
% 20.31/20.27 Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),A),B)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),C),B))),B) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),C)),B). [resolve(5357,a,5296,a)].
% 20.31/20.27 Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),B),C))),C) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),B)),C). [resolve(5357,a,5298,a)].
% 20.31/20.27 Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),A),B) != hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),C),B) | hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),D),B) != hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),E),B) | hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),A),D)),B) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),C),E)),B). [resolve(5357,a,5299,a)].
% 20.31/20.27 Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),A),B)),C)),B) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),A),C)),B). [resolve(5357,a,5300,a)].
% 20.31/20.27 Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),A),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),B),C))),C) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),A),B)),C). [resolve(5357,a,5301,a)].
% 20.31/20.27 Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),A),B)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),C),B))),B) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),A),C)),B). [resolve(5357,a,5302,a)].
% 20.31/20.27 Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),A),B)),A) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),B),A). [resolve(5357,a,5305,a)].
% 20.31/20.27 Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),A),B)),B) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),A),B). [resolve(5357,a,5306,a)].
% 20.31/20.27 Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),B)),A) = zero_zero(code_code_numeral). [resolve(5357,a,5307,a)].
% 20.31/20.27 Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),B)),B) = zero_zero(code_code_numeral). [resolve(5357,a,5308,a)].
% 20.31/20.27 Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),A),one_one(code_code_numeral)) = zero_zero(code_code_numeral). [resolve(5357,a,5309,a)].
% 20.31/20.27 Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),A),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),B),C))),C) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),A),C). [resolve(5357,a,5310,a)].
% 20.31/20.27 Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),A),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),B),C))),B) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),A),B). [resolve(5357,a,5311,a)].
% 20.31/20.28 Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),A),zero_zero(code_code_numeral)) = zero_zero(code_code_numeral). [resolve(5357,a,5312,a)].
% 20.31/20.28 Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),zero_zero(code_code_numeral)),A) = zero_zero(code_code_numeral). [resolve(5357,a,5313,a)].
% 20.31/20.28 Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),A),one_one(code_code_numeral)) = ti(code_code_numeral,A). [resolve(5357,a,5314,a)].
% 20.31/20.28 Derived: zero_zero(code_code_numeral) != ti(code_code_numeral,A) | hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),B)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),C)) = zero_zero(code_code_numeral). [resolve(5357,a,5315,a)].
% 20.31/20.28 Derived: zero_zero(code_code_numeral) = ti(code_code_numeral,A) | hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),B)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),C)) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),B),C). [resolve(5357,a,5316,a)].
% 20.31/20.28 Derived: zero_zero(code_code_numeral) = ti(code_code_numeral,A) | hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),B),A)),A) = ti(code_code_numeral,B). [resolve(5357,a,5317,a)].
% 20.31/20.28 Derived: zero_zero(code_code_numeral) = ti(code_code_numeral,A) | hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),B)),A) = ti(code_code_numeral,B). [resolve(5357,a,5318,a)].
% 20.31/20.28 Derived: zero_zero(code_code_numeral) = ti(code_code_numeral,A) | hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),B),A)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),C),A)) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),B),C). [resolve(5357,a,5319,a)].
% 20.31/20.28 Derived: zero_zero(code_code_numeral) = ti(code_code_numeral,A) | hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),A),A) = one_one(code_code_numeral). [resolve(5357,a,5321,a)].
% 20.31/20.28 Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),A),B)),B) = zero_zero(code_code_numeral). [resolve(5357,a,5322,a)].
% 20.31/20.28 Derived: zero_zero(code_code_numeral) = ti(code_code_numeral,A) | hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),B),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),C),A)) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),C),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),B))),A). [resolve(5357,a,5323,a)].
% 20.31/20.28 Derived: zero_zero(code_code_numeral) = ti(code_code_numeral,A) | hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),B),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),C),A)) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),C),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),B),A))),A). [resolve(5357,a,5324,a)].
% 20.31/20.28 Derived: zero_zero(code_code_numeral) = ti(code_code_numeral,A) | hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),B),A)),one_one(code_code_numeral)) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),B),A)),A). [resolve(5357,a,5325,a)].
% 20.31/20.28 Derived: zero_zero(code_code_numeral) = ti(code_code_numeral,A) | hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),B),A)),one_one(code_code_numeral)) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),A),B)),A). [resolve(5357,a,5326,a)].
% 20.31/20.28 Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),A),B)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),A),B)),B)) = ti(code_code_numeral,A). [resolve(5357,a,5327,a)].
% 20.31/20.28 Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),B),A))),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),B),A)) = ti(code_code_numeral,B). [resolve(5357,a,5328,a)].
% 20.31/20.28 Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),A),B)),B)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),A),B)) = ti(code_code_numeral,A). [resolve(5357,a,5329,a)].
% 20.31/20.28 Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),B),A))),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),B),A))),C) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),B),C). [resolve(5357,a,5330,a)].
% 20.31/20.28 Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),A),B)),B)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),A),B))),C) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),A),C). [resolve(5357,a,5331,a)].
% 20.31/20.28 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),A),B)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),A),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),C),B))) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),A),C)). [resolve(5357,a,5333,a)].
% 20.31/20.28 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),A),B)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),A),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),C),B))) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),A),C)). [resolve(5357,a,5334,a)].
% 20.31/20.28 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),A),B)) | hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),C),B)),A) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),C),A). [resolve(5357,a,5335,a)].
% 20.31/20.28 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),A),B)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),A),C)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),B),A)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),C),A))) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),B),C)). [resolve(5357,a,5338,a)].
% 20.31/20.28 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),A),B)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),A),C)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),B),A)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),C),A))) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),B),C)). [resolve(5357,a,5339,a)].
% 20.31/20.28 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),A),B)) | hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),B),A) = zero_zero(code_code_numeral). [resolve(5357,a,5340,a)].
% 20.31/20.28 Derived: hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),A),B)) | hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),B),A) != zero_zero(code_code_numeral). [resolve(5357,a,5342,a)].
% 20.31/20.28 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),A),B)) | hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),B),A)) = ti(code_code_numeral,B). [resolve(5357,a,5343,a)].
% 20.31/20.28 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),A),B)) | hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),C),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),B),A)) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),C),B)),A). [resolve(5357,a,5344,a)].
% 20.31/20.28 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),A),B)) | hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),B),A)),A) = ti(code_code_numeral,B). [resolve(5357,a,5345,a)].
% 20.31/20.28 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),A),B)) | hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),B),A)),C) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),B),C)),A). [resolve(5357,a,5346,a)].
% 20.31/20.28 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),A),B)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),C),D)) | hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),B),A)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),D),C)) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),B),D)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),C)). [resolve(5357,a,5347,a)].
% 20.31/20.28 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),A),B)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),A),C)) | hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),B),A)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),C),A)) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),B),C)),A). [resolve(5357,a,5348,a)].
% 20.31/20.28 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),A),B)) | hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),B),A)),C) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),B),C)),hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A),C)). [resolve(5357,a,5349,a)].
% 20.31/20.28 Derived: zero_zero(code_code_numeral) = ti(code_code_numeral,A) | zero_zero(code_code_numeral) = ti(code_code_numeral,B) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),A),C)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),B),D)) | hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),D),B) != hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),C),A) | hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),C),B) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),D). [resolve(5357,a,5350,a)].
% 20.31/20.30 Derived: zero_zero(code_code_numeral) = ti(code_code_numeral,A) | zero_zero(code_code_numeral) = ti(code_code_numeral,B) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),A),C)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),B),D)) | hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),D),B) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),C),A) | hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),C),B) != hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),D). [resolve(5357,a,5351,a)].
% 20.31/20.30 Derived: zero_zero(code_code_numeral) = ti(code_code_numeral,A) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),A),B)) | hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),B),A) != ti(code_code_numeral,C) | hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),C),A) = ti(code_code_numeral,B). [resolve(5357,a,5352,a)].
% 20.31/20.30 Derived: zero_zero(code_code_numeral) = ti(code_code_numeral,A) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),A),B)) | hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),B),A) = ti(code_code_numeral,C) | hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),C),A) != ti(code_code_numeral,B). [resolve(5357,a,5353,a)].
% 20.31/20.30 5358 semiring_div(quickcheck_code_int) # label(arity_Quickcheck__Narrowing_Ocode__int___Divides_Osemiring__div) # label(axiom). [assumption].
% 20.31/20.30 Derived: div_div(quickcheck_code_int) = ti(fun(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int)),div_div(quickcheck_code_int)). [resolve(5358,a,5286,a)].
% 20.31/20.30 Derived: div_mod(quickcheck_code_int) = ti(fun(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int)),div_mod(quickcheck_code_int)). [resolve(5358,a,5287,a)].
% 20.31/20.30 Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),A),B)),B) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),A),B). [resolve(5358,a,5288,a)].
% 20.31/20.30 Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),zero_zero(quickcheck_code_int)),A) = zero_zero(quickcheck_code_int). [resolve(5358,a,5289,a)].
% 20.31/20.30 Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),A),zero_zero(quickcheck_code_int)) = ti(quickcheck_code_int,A). [resolve(5358,a,5290,a)].
% 20.31/20.30 Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),A),A) = zero_zero(quickcheck_code_int). [resolve(5358,a,5291,a)].
% 20.31/20.30 Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),A),B) != hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),C),B) | hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),D),B) != hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),E),B) | hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),D)),B) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),C),E)),B). [resolve(5358,a,5292,a)].
% 20.31/20.30 Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),A),B)),C)),B) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),C)),B). [resolve(5358,a,5293,a)].
% 20.31/20.30 Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),A),B)),C) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),C)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),B),C)). [resolve(5358,a,5294,a)].
% 20.31/20.30 Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),B),C)) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),B)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),C)). [resolve(5358,a,5295,a)].
% 20.31/20.30 Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),A),B)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),C),B))),B) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),C)),B). [resolve(5358,a,5296,a)].
% 20.31/20.30 Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),B),C))),C) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),B)),C). [resolve(5358,a,5298,a)].
% 20.31/20.30 Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),A),B) != hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),C),B) | hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),D),B) != hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),E),B) | hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),A),D)),B) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),C),E)),B). [resolve(5358,a,5299,a)].
% 20.31/20.30 Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),A),B)),C)),B) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),A),C)),B). [resolve(5358,a,5300,a)].
% 20.31/20.30 Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),A),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),B),C))),C) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),A),B)),C). [resolve(5358,a,5301,a)].
% 20.31/20.31 Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),A),B)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),C),B))),B) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),A),C)),B). [resolve(5358,a,5302,a)].
% 20.31/20.31 Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),A),B)),A) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),B),A). [resolve(5358,a,5305,a)].
% 20.31/20.31 Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),A),B)),B) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),A),B). [resolve(5358,a,5306,a)].
% 20.31/20.31 Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),B)),A) = zero_zero(quickcheck_code_int). [resolve(5358,a,5307,a)].
% 20.31/20.31 Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),B)),B) = zero_zero(quickcheck_code_int). [resolve(5358,a,5308,a)].
% 20.31/20.31 Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),A),one_one(quickcheck_code_int)) = zero_zero(quickcheck_code_int). [resolve(5358,a,5309,a)].
% 20.31/20.31 Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),A),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),B),C))),C) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),A),C). [resolve(5358,a,5310,a)].
% 20.31/20.31 Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),A),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),B),C))),B) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),A),B). [resolve(5358,a,5311,a)].
% 20.39/20.31 Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),A),zero_zero(quickcheck_code_int)) = zero_zero(quickcheck_code_int). [resolve(5358,a,5312,a)].
% 20.39/20.31 Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),zero_zero(quickcheck_code_int)),A) = zero_zero(quickcheck_code_int). [resolve(5358,a,5313,a)].
% 20.39/20.31 Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),A),one_one(quickcheck_code_int)) = ti(quickcheck_code_int,A). [resolve(5358,a,5314,a)].
% 20.39/20.31 Derived: zero_zero(quickcheck_code_int) != ti(quickcheck_code_int,A) | hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),B)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),C)) = zero_zero(quickcheck_code_int). [resolve(5358,a,5315,a)].
% 20.39/20.31 Derived: zero_zero(quickcheck_code_int) = ti(quickcheck_code_int,A) | hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),B)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),C)) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),B),C). [resolve(5358,a,5316,a)].
% 20.39/20.31 Derived: zero_zero(quickcheck_code_int) = ti(quickcheck_code_int,A) | hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),B),A)),A) = ti(quickcheck_code_int,B). [resolve(5358,a,5317,a)].
% 20.39/20.31 Derived: zero_zero(quickcheck_code_int) = ti(quickcheck_code_int,A) | hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),B)),A) = ti(quickcheck_code_int,B). [resolve(5358,a,5318,a)].
% 20.39/20.31 Derived: zero_zero(quickcheck_code_int) = ti(quickcheck_code_int,A) | hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),B),A)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),C),A)) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),B),C). [resolve(5358,a,5319,a)].
% 20.39/20.31 Derived: zero_zero(quickcheck_code_int) = ti(quickcheck_code_int,A) | hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),A),A) = one_one(quickcheck_code_int). [resolve(5358,a,5321,a)].
% 20.39/20.31 Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),A),B)),B) = zero_zero(quickcheck_code_int). [resolve(5358,a,5322,a)].
% 20.39/20.31 Derived: zero_zero(quickcheck_code_int) = ti(quickcheck_code_int,A) | hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),B),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),C),A)) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),C),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),B))),A). [resolve(5358,a,5323,a)].
% 20.39/20.31 Derived: zero_zero(quickcheck_code_int) = ti(quickcheck_code_int,A) | hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),B),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),C),A)) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),C),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),B),A))),A). [resolve(5358,a,5324,a)].
% 20.39/20.31 Derived: zero_zero(quickcheck_code_int) = ti(quickcheck_code_int,A) | hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),B),A)),one_one(quickcheck_code_int)) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),B),A)),A). [resolve(5358,a,5325,a)].
% 20.39/20.31 Derived: zero_zero(quickcheck_code_int) = ti(quickcheck_code_int,A) | hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),B),A)),one_one(quickcheck_code_int)) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),A),B)),A). [resolve(5358,a,5326,a)].
% 20.39/20.31 Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),A),B)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),A),B)),B)) = ti(quickcheck_code_int,A). [resolve(5358,a,5327,a)].
% 20.39/20.31 Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),B),A))),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),B),A)) = ti(quickcheck_code_int,B). [resolve(5358,a,5328,a)].
% 20.39/20.31 Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),A),B)),B)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),A),B)) = ti(quickcheck_code_int,A). [resolve(5358,a,5329,a)].
% 20.39/20.31 Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),B),A))),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),B),A))),C) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),B),C). [resolve(5358,a,5330,a)].
% 20.39/20.31 Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),A),B)),B)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),A),B))),C) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),A),C). [resolve(5358,a,5331,a)].
% 20.39/20.31 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),A),B)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),A),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),C),B))) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),A),C)). [resolve(5358,a,5333,a)].
% 20.39/20.31 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),A),B)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),A),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),C),B))) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),A),C)). [resolve(5358,a,5334,a)].
% 20.39/20.31 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),A),B)) | hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),C),B)),A) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),C),A). [resolve(5358,a,5335,a)].
% 20.39/20.31 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),A),B)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),A),C)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),B),A)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),C),A))) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),B),C)). [resolve(5358,a,5338,a)].
% 20.39/20.32 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),A),B)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),A),C)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),B),A)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),C),A))) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),B),C)). [resolve(5358,a,5339,a)].
% 20.39/20.32 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),A),B)) | hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),B),A) = zero_zero(quickcheck_code_int). [resolve(5358,a,5340,a)].
% 20.39/20.32 Derived: hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),A),B)) | hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),B),A) != zero_zero(quickcheck_code_int). [resolve(5358,a,5342,a)].
% 20.39/20.32 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),A),B)) | hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),B),A)) = ti(quickcheck_code_int,B). [resolve(5358,a,5343,a)].
% 20.39/20.32 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),A),B)) | hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),C),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),B),A)) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),C),B)),A). [resolve(5358,a,5344,a)].
% 20.39/20.32 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),A),B)) | hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),B),A)),A) = ti(quickcheck_code_int,B). [resolve(5358,a,5345,a)].
% 20.39/20.32 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),A),B)) | hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),B),A)),C) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),B),C)),A). [resolve(5358,a,5346,a)].
% 20.39/20.32 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),A),B)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),C),D)) | hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),B),A)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),D),C)) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),B),D)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),C)). [resolve(5358,a,5347,a)].
% 20.39/20.32 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),A),B)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),A),C)) | hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),B),A)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),C),A)) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),B),C)),A). [resolve(5358,a,5348,a)].
% 20.39/20.32 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),A),B)) | hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),B),A)),C) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),B),C)),hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A),C)). [resolve(5358,a,5349,a)].
% 23.59/23.57 Derived: zero_zero(quickcheck_code_int) = ti(quickcheck_code_int,A) | zero_zero(quickcheck_code_int) = ti(quickcheck_code_int,B) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),A),C)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),B),D)) | hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),D),B) != hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),C),A) | hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),C),B) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),D). [resolve(5358,a,5350,a)].
% 23.59/23.57 Derived: zero_zero(quickcheck_code_int) = ti(quickcheck_code_int,A) | zero_zero(quickcheck_code_int) = ti(quickcheck_code_int,B) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),A),C)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),B),D)) | hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),D),B) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),C),A) | hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),C),B) != hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),D). [resolve(5358,a,5351,a)].
% 23.59/23.57 Derived: zero_zero(quickcheck_code_int) = ti(quickcheck_code_int,A) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),A),B)) | hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),B),A) != ti(quickcheck_code_int,C) | hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),C),A) = ti(quickcheck_code_int,B). [resolve(5358,a,5352,a)].
% 23.59/23.57 Derived: zero_zero(quickcheck_code_int) = ti(quickcheck_code_int,A) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),A),B)) | hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),B),A) = ti(quickcheck_code_int,C) | hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),C),A) != ti(quickcheck_code_int,B). [resolve(5358,a,5353,a)].
% 23.59/23.57 5359 inverse(rat) # label(arity_Rat_Orat___Fields_Oinverse) # label(axiom). [assumption].
% 23.59/23.57 5360 -inverse(A) | -real_normed_vector(A) | inverse_divide(A) = ti(fun(A,fun(A,A)),inverse_divide(A)) # label(tsy_c_Fields_Oinverse__class_Odivide_0_res) # label(axiom). [clausify(18)].
% 23.59/23.57 5361 -inverse(A) | -real_normed_vector(A) | -hBOOL(hAPP(filter(A),bool,hAPP(A,fun(filter(A),bool),hAPP(fun(A,A),fun(A,fun(filter(A),bool)),tendsto(A,A),hAPP(fun(A,A),fun(A,A),hAPP(fun(A,fun(A,A)),fun(fun(A,A),fun(A,A)),combs(A,A,A),hAPP(fun(A,A),fun(A,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(A,A),fun(A,fun(A,A))),combb(A,fun(A,A),A),inverse_divide(A)),hAPP(A,fun(A,A),hAPP(fun(A,fun(A,A)),fun(A,fun(A,A)),combc(A,A,A),hAPP(fun(A,A),fun(A,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(A,A),fun(A,fun(A,A))),combb(A,fun(A,A),A),minus_minus(A)),hAPP(fun(A,A),fun(A,A),hAPP(fun(A,A),fun(fun(A,A),fun(A,A)),combb(A,A,A),B),hAPP(A,fun(A,A),plus_plus(A),C)))),hAPP(A,A,B,C)))),combi(A))),D),hAPP(A,filter(A),at(A),zero_zero(A)))) | hBOOL(hAPP(filter(A),bool,hAPP(A,fun(filter(A),bool),hAPP(fun(A,A),fun(A,fun(filter(A),bool)),tendsto(A,A),hAPP(fun(A,A),fun(A,A),hAPP(fun(A,fun(A,A)),fun(fun(A,A),fun(A,A)),combs(A,A,A),hAPP(fun(A,A),fun(A,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(A,A),fun(A,fun(A,A))),combb(A,fun(A,A),A),inverse_divide(A)),hAPP(A,fun(A,A),hAPP(fun(A,fun(A,A)),fun(A,fun(A,A)),combc(A,A,A),hAPP(fun(A,A),fun(A,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(A,A),fun(A,fun(A,A))),combb(A,fun(A,A),A),minus_minus(A)),B)),hAPP(A,A,B,C)))),hAPP(A,fun(A,A),hAPP(fun(A,fun(A,A)),fun(A,fun(A,A)),combc(A,A,A),minus_minus(A)),C))),D),hAPP(A,filter(A),at(A),C))) # label(fact_4611_DERIV__LIM__iff) # label(axiom). [clausify(4538)].
% 23.59/23.57 5362 -inverse(A) | -real_normed_vector(A) | hBOOL(hAPP(filter(A),bool,hAPP(A,fun(filter(A),bool),hAPP(fun(A,A),fun(A,fun(filter(A),bool)),tendsto(A,A),hAPP(fun(A,A),fun(A,A),hAPP(fun(A,fun(A,A)),fun(fun(A,A),fun(A,A)),combs(A,A,A),hAPP(fun(A,A),fun(A,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(A,A),fun(A,fun(A,A))),combb(A,fun(A,A),A),inverse_divide(A)),hAPP(A,fun(A,A),hAPP(fun(A,fun(A,A)),fun(A,fun(A,A)),combc(A,A,A),hAPP(fun(A,A),fun(A,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(A,A),fun(A,fun(A,A))),combb(A,fun(A,A),A),minus_minus(A)),hAPP(fun(A,A),fun(A,A),hAPP(fun(A,A),fun(fun(A,A),fun(A,A)),combb(A,A,A),B),hAPP(A,fun(A,A),plus_plus(A),C)))),hAPP(A,A,B,C)))),combi(A))),D),hAPP(A,filter(A),at(A),zero_zero(A)))) | -hBOOL(hAPP(filter(A),bool,hAPP(A,fun(filter(A),bool),hAPP(fun(A,A),fun(A,fun(filter(A),bool)),tendsto(A,A),hAPP(fun(A,A),fun(A,A),hAPP(fun(A,fun(A,A)),fun(fun(A,A),fun(A,A)),combs(A,A,A),hAPP(fun(A,A),fun(A,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(A,A),fun(A,fun(A,A))),combb(A,fun(A,A),A),inverse_divide(A)),hAPP(A,fun(A,A),hAPP(fun(A,fun(A,A)),fun(A,fun(A,A)),combc(A,A,A),hAPP(fun(A,A),fun(A,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(A,A),fun(A,fun(A,A))),combb(A,fun(A,A),A),minus_minus(A)),B)),hAPP(A,A,B,C)))),hAPP(A,fun(A,A),hAPP(fun(A,fun(A,A)),fun(A,fun(A,A)),combc(A,A,A),minus_minus(A)),C))),D),hAPP(A,filter(A),at(A),C))) # label(fact_4611_DERIV__LIM__iff) # label(axiom). [clausify(4538)].
% 23.59/23.57 Derived: -real_normed_vector(rat) | inverse_divide(rat) = ti(fun(rat,fun(rat,rat)),inverse_divide(rat)). [resolve(5359,a,5360,a)].
% 23.59/23.57 Derived: -real_normed_vector(rat) | -hBOOL(hAPP(filter(rat),bool,hAPP(rat,fun(filter(rat),bool),hAPP(fun(rat,rat),fun(rat,fun(filter(rat),bool)),tendsto(rat,rat),hAPP(fun(rat,rat),fun(rat,rat),hAPP(fun(rat,fun(rat,rat)),fun(fun(rat,rat),fun(rat,rat)),combs(rat,rat,rat),hAPP(fun(rat,rat),fun(rat,fun(rat,rat)),hAPP(fun(rat,fun(rat,rat)),fun(fun(rat,rat),fun(rat,fun(rat,rat))),combb(rat,fun(rat,rat),rat),inverse_divide(rat)),hAPP(rat,fun(rat,rat),hAPP(fun(rat,fun(rat,rat)),fun(rat,fun(rat,rat)),combc(rat,rat,rat),hAPP(fun(rat,rat),fun(rat,fun(rat,rat)),hAPP(fun(rat,fun(rat,rat)),fun(fun(rat,rat),fun(rat,fun(rat,rat))),combb(rat,fun(rat,rat),rat),minus_minus(rat)),hAPP(fun(rat,rat),fun(rat,rat),hAPP(fun(rat,rat),fun(fun(rat,rat),fun(rat,rat)),combb(rat,rat,rat),A),hAPP(rat,fun(rat,rat),plus_plus(rat),B)))),hAPP(rat,rat,A,B)))),combi(rat))),C),hAPP(rat,filter(rat),at(rat),zero_zero(rat)))) | hBOOL(hAPP(filter(rat),bool,hAPP(rat,fun(filter(rat),bool),hAPP(fun(rat,rat),fun(rat,fun(filter(rat),bool)),tendsto(rat,rat),hAPP(fun(rat,rat),fun(rat,rat),hAPP(fun(rat,fun(rat,rat)),fun(fun(rat,rat),fun(rat,rat)),combs(rat,rat,rat),hAPP(fun(rat,rat),fun(rat,fun(rat,rat)),hAPP(fun(rat,fun(rat,rat)),fun(fun(rat,rat),fun(rat,fun(rat,rat))),combb(rat,fun(rat,rat),rat),inverse_divide(rat)),hAPP(rat,fun(rat,rat),hAPP(fun(rat,fun(rat,rat)),fun(rat,fun(rat,rat)),combc(rat,rat,rat),hAPP(fun(rat,rat),fun(rat,fun(rat,rat)),hAPP(fun(rat,fun(rat,rat)),fun(fun(rat,rat),fun(rat,fun(rat,rat))),combb(rat,fun(rat,rat),rat),minus_minus(rat)),A)),hAPP(rat,rat,A,B)))),hAPP(rat,fun(rat,rat),hAPP(fun(rat,fun(rat,rat)),fun(rat,fun(rat,rat)),combc(rat,rat,rat),minus_minus(rat)),B))),C),hAPP(rat,filter(rat),at(rat),B))). [resolve(5359,a,5361,a)].
% 23.68/23.61 Derived: -real_normed_vector(rat) | hBOOL(hAPP(filter(rat),bool,hAPP(rat,fun(filter(rat),bool),hAPP(fun(rat,rat),fun(rat,fun(filter(rat),bool)),tendsto(rat,rat),hAPP(fun(rat,rat),fun(rat,rat),hAPP(fun(rat,fun(rat,rat)),fun(fun(rat,rat),fun(rat,rat)),combs(rat,rat,rat),hAPP(fun(rat,rat),fun(rat,fun(rat,rat)),hAPP(fun(rat,fun(rat,rat)),fun(fun(rat,rat),fun(rat,fun(rat,rat))),combb(rat,fun(rat,rat),rat),inverse_divide(rat)),hAPP(rat,fun(rat,rat),hAPP(fun(rat,fun(rat,rat)),fun(rat,fun(rat,rat)),combc(rat,rat,rat),hAPP(fun(rat,rat),fun(rat,fun(rat,rat)),hAPP(fun(rat,fun(rat,rat)),fun(fun(rat,rat),fun(rat,fun(rat,rat))),combb(rat,fun(rat,rat),rat),minus_minus(rat)),hAPP(fun(rat,rat),fun(rat,rat),hAPP(fun(rat,rat),fun(fun(rat,rat),fun(rat,rat)),combb(rat,rat,rat),A),hAPP(rat,fun(rat,rat),plus_plus(rat),B)))),hAPP(rat,rat,A,B)))),combi(rat))),C),hAPP(rat,filter(rat),at(rat),zero_zero(rat)))) | -hBOOL(hAPP(filter(rat),bool,hAPP(rat,fun(filter(rat),bool),hAPP(fun(rat,rat),fun(rat,fun(filter(rat),bool)),tendsto(rat,rat),hAPP(fun(rat,rat),fun(rat,rat),hAPP(fun(rat,fun(rat,rat)),fun(fun(rat,rat),fun(rat,rat)),combs(rat,rat,rat),hAPP(fun(rat,rat),fun(rat,fun(rat,rat)),hAPP(fun(rat,fun(rat,rat)),fun(fun(rat,rat),fun(rat,fun(rat,rat))),combb(rat,fun(rat,rat),rat),inverse_divide(rat)),hAPP(rat,fun(rat,rat),hAPP(fun(rat,fun(rat,rat)),fun(rat,fun(rat,rat)),combc(rat,rat,rat),hAPP(fun(rat,rat),fun(rat,fun(rat,rat)),hAPP(fun(rat,fun(rat,rat)),fun(fun(rat,rat),fun(rat,fun(rat,rat))),combb(rat,fun(rat,rat),rat),minus_minus(rat)),A)),hAPP(rat,rat,A,B)))),hAPP(rat,fun(rat,rat),hAPP(fun(rat,fun(rat,rat)),fun(rat,fun(rat,rat)),combc(rat,rat,rat),minus_minus(rat)),B))),C),hAPP(rat,filter(rat),at(rat),B))). [resolve(5359,a,5362,a)].
% 23.68/23.61 5363 inverse(real) # label(arity_RealDef_Oreal___Fields_Oinverse) # label(axiom). [assumption].
% 23.68/23.61 Derived: -real_normed_vector(real) | inverse_divide(real) = ti(fun(real,fun(real,real)),inverse_divide(real)). [resolve(5363,a,5360,a)].
% 23.68/23.61 Derived: -real_normed_vector(real) | -hBOOL(hAPP(filter(real),bool,hAPP(real,fun(filter(real),bool),hAPP(fun(real,real),fun(real,fun(filter(real),bool)),tendsto(real,real),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,real)),combs(real,real,real),hAPP(fun(real,real),fun(real,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,fun(real,real))),combb(real,fun(real,real),real),inverse_divide(real)),hAPP(real,fun(real,real),hAPP(fun(real,fun(real,real)),fun(real,fun(real,real)),combc(real,real,real),hAPP(fun(real,real),fun(real,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,fun(real,real))),combb(real,fun(real,real),real),minus_minus(real)),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,real),fun(fun(real,real),fun(real,real)),combb(real,real,real),A),hAPP(real,fun(real,real),plus_plus(real),B)))),hAPP(real,real,A,B)))),combi(real))),C),hAPP(real,filter(real),at(real),zero_zero(real)))) | hBOOL(hAPP(filter(real),bool,hAPP(real,fun(filter(real),bool),hAPP(fun(real,real),fun(real,fun(filter(real),bool)),tendsto(real,real),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,real)),combs(real,real,real),hAPP(fun(real,real),fun(real,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,fun(real,real))),combb(real,fun(real,real),real),inverse_divide(real)),hAPP(real,fun(real,real),hAPP(fun(real,fun(real,real)),fun(real,fun(real,real)),combc(real,real,real),hAPP(fun(real,real),fun(real,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,fun(real,real))),combb(real,fun(real,real),real),minus_minus(real)),A)),hAPP(real,real,A,B)))),hAPP(real,fun(real,real),hAPP(fun(real,fun(real,real)),fun(real,fun(real,real)),combc(real,real,real),minus_minus(real)),B))),C),hAPP(real,filter(real),at(real),B))). [resolve(5363,a,5361,a)].
% 23.68/23.63 Derived: -real_normed_vector(real) | hBOOL(hAPP(filter(real),bool,hAPP(real,fun(filter(real),bool),hAPP(fun(real,real),fun(real,fun(filter(real),bool)),tendsto(real,real),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,real)),combs(real,real,real),hAPP(fun(real,real),fun(real,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,fun(real,real))),combb(real,fun(real,real),real),inverse_divide(real)),hAPP(real,fun(real,real),hAPP(fun(real,fun(real,real)),fun(real,fun(real,real)),combc(real,real,real),hAPP(fun(real,real),fun(real,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,fun(real,real))),combb(real,fun(real,real),real),minus_minus(real)),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,real),fun(fun(real,real),fun(real,real)),combb(real,real,real),A),hAPP(real,fun(real,real),plus_plus(real),B)))),hAPP(real,real,A,B)))),combi(real))),C),hAPP(real,filter(real),at(real),zero_zero(real)))) | -hBOOL(hAPP(filter(real),bool,hAPP(real,fun(filter(real),bool),hAPP(fun(real,real),fun(real,fun(filter(real),bool)),tendsto(real,real),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,real)),combs(real,real,real),hAPP(fun(real,real),fun(real,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,fun(real,real))),combb(real,fun(real,real),real),inverse_divide(real)),hAPP(real,fun(real,real),hAPP(fun(real,fun(real,real)),fun(real,fun(real,real)),combc(real,real,real),hAPP(fun(real,real),fun(real,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,fun(real,real))),combb(real,fun(real,real),real),minus_minus(real)),A)),hAPP(real,real,A,B)))),hAPP(real,fun(real,real),hAPP(fun(real,fun(real,real)),fun(real,fun(real,real)),combc(real,real,real),minus_minus(real)),B))),C),hAPP(real,filter(real),at(real),B))). [resolve(5363,a,5362,a)].
% 23.68/23.63 5364 inverse(complex) # label(arity_Complex_Ocomplex___Fields_Oinverse) # label(axiom). [assumption].
% 23.68/23.63 Derived: -real_normed_vector(complex) | inverse_divide(complex) = ti(fun(complex,fun(complex,complex)),inverse_divide(complex)). [resolve(5364,a,5360,a)].
% 23.68/23.63 Derived: -real_normed_vector(complex) | -hBOOL(hAPP(filter(complex),bool,hAPP(complex,fun(filter(complex),bool),hAPP(fun(complex,complex),fun(complex,fun(filter(complex),bool)),tendsto(complex,complex),hAPP(fun(complex,complex),fun(complex,complex),hAPP(fun(complex,fun(complex,complex)),fun(fun(complex,complex),fun(complex,complex)),combs(complex,complex,complex),hAPP(fun(complex,complex),fun(complex,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(complex,complex),fun(complex,fun(complex,complex))),combb(complex,fun(complex,complex),complex),inverse_divide(complex)),hAPP(complex,fun(complex,complex),hAPP(fun(complex,fun(complex,complex)),fun(complex,fun(complex,complex)),combc(complex,complex,complex),hAPP(fun(complex,complex),fun(complex,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(complex,complex),fun(complex,fun(complex,complex))),combb(complex,fun(complex,complex),complex),minus_minus(complex)),hAPP(fun(complex,complex),fun(complex,complex),hAPP(fun(complex,complex),fun(fun(complex,complex),fun(complex,complex)),combb(complex,complex,complex),A),hAPP(complex,fun(complex,complex),plus_plus(complex),B)))),hAPP(complex,complex,A,B)))),combi(complex))),C),hAPP(complex,filter(complex),at(complex),zero_zero(complex)))) | hBOOL(hAPP(filter(complex),bool,hAPP(complex,fun(filter(complex),bool),hAPP(fun(complex,complex),fun(complex,fun(filter(complex),bool)),tendsto(complex,complex),hAPP(fun(complex,complex),fun(complex,complex),hAPP(fun(complex,fun(complex,complex)),fun(fun(complex,complex),fun(complex,complex)),combs(complex,complex,complex),hAPP(fun(complex,complex),fun(complex,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(complex,complex),fun(complex,fun(complex,complex))),combb(complex,fun(complex,complex),complex),inverse_divide(complex)),hAPP(complex,fun(complex,complex),hAPP(fun(complex,fun(complex,complex)),fun(complex,fun(complex,complex)),combc(complex,complex,complex),hAPP(fun(complex,complex),fun(complex,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(complex,complex),fun(complex,fun(complex,complex))),combb(complex,fun(complex,complex),complex),minus_minus(complex)),A)),hAPP(complex,complex,A,B)))),hAPP(complex,fun(complex,complex),hAPP(fun(complex,fun(complex,complex)),fun(complex,fun(complex,complex)),combc(complex,complex,complex),minus_minus(complex)),B))),C),hAPP(complex,filter(complex),at(complex),B))). [resolve(5364,a,5361,a)].
% 26.91/26.88 Derived: -real_normed_vector(complex) | hBOOL(hAPP(filter(complex),bool,hAPP(complex,fun(filter(complex),bool),hAPP(fun(complex,complex),fun(complex,fun(filter(complex),bool)),tendsto(complex,complex),hAPP(fun(complex,complex),fun(complex,complex),hAPP(fun(complex,fun(complex,complex)),fun(fun(complex,complex),fun(complex,complex)),combs(complex,complex,complex),hAPP(fun(complex,complex),fun(complex,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(complex,complex),fun(complex,fun(complex,complex))),combb(complex,fun(complex,complex),complex),inverse_divide(complex)),hAPP(complex,fun(complex,complex),hAPP(fun(complex,fun(complex,complex)),fun(complex,fun(complex,complex)),combc(complex,complex,complex),hAPP(fun(complex,complex),fun(complex,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(complex,complex),fun(complex,fun(complex,complex))),combb(complex,fun(complex,complex),complex),minus_minus(complex)),hAPP(fun(complex,complex),fun(complex,complex),hAPP(fun(complex,complex),fun(fun(complex,complex),fun(complex,complex)),combb(complex,complex,complex),A),hAPP(complex,fun(complex,complex),plus_plus(complex),B)))),hAPP(complex,complex,A,B)))),combi(complex))),C),hAPP(complex,filter(complex),at(complex),zero_zero(complex)))) | -hBOOL(hAPP(filter(complex),bool,hAPP(complex,fun(filter(complex),bool),hAPP(fun(complex,complex),fun(complex,fun(filter(complex),bool)),tendsto(complex,complex),hAPP(fun(complex,complex),fun(complex,complex),hAPP(fun(complex,fun(complex,complex)),fun(fun(complex,complex),fun(complex,complex)),combs(complex,complex,complex),hAPP(fun(complex,complex),fun(complex,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(complex,complex),fun(complex,fun(complex,complex))),combb(complex,fun(complex,complex),complex),inverse_divide(complex)),hAPP(complex,fun(complex,complex),hAPP(fun(complex,fun(complex,complex)),fun(complex,fun(complex,complex)),combc(complex,complex,complex),hAPP(fun(complex,complex),fun(complex,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(complex,complex),fun(complex,fun(complex,complex))),combb(complex,fun(complex,complex),complex),minus_minus(complex)),A)),hAPP(complex,complex,A,B)))),hAPP(complex,fun(complex,complex),hAPP(fun(complex,fun(complex,complex)),fun(complex,fun(complex,complex)),combc(complex,complex,complex),minus_minus(complex)),B))),C),hAPP(complex,filter(complex),at(complex),B))). [resolve(5364,a,5362,a)].
% 26.91/26.88 5365 division_ring(rat) # label(arity_Rat_Orat___Fields_Odivision__ring) # label(axiom). [assumption].
% 26.91/26.88 5366 -division_ring(A) | inverse_divide(A) = ti(fun(A,fun(A,A)),inverse_divide(A)) # label(tsy_c_Fields_Oinverse__class_Odivide_1_res) # label(axiom). [clausify(19)].
% 26.91/26.88 5367 -division_ring(A) | inverse_inverse(A) = ti(fun(A,A),inverse_inverse(A)) # label(tsy_c_Fields_Oinverse__class_Oinverse_res) # label(axiom). [clausify(20)].
% 26.91/26.88 5368 -division_ring(A) | hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),zero_zero(A)),B) = zero_zero(A) # label(fact_1071_divide__zero__left) # label(axiom). [clausify(1182)].
% 26.91/26.88 5369 -division_ring(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),D)) = hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),D) # label(fact_1075_times__divide__eq__right) # label(axiom). [clausify(1186)].
% 26.91/26.88 5370 -division_ring(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),C)) = hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),D)),C) # label(fact_1076_add__divide__distrib) # label(axiom). [clausify(1187)].
% 26.91/26.88 5371 -division_ring(A) | hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),one_one(A)) = ti(A,B) # label(fact_1078_divide__1) # label(axiom). [clausify(1189)].
% 26.91/26.88 5372 -division_ring(A) | hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),C)) = hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),D)),C) # label(fact_1079_diff__divide__distrib) # label(axiom). [clausify(1190)].
% 26.91/26.88 5373 -division_ring(A) | hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),hAPP(A,A,uminus_uminus(A),B)),C) = hAPP(A,A,uminus_uminus(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)) # label(fact_1083_minus__divide__left) # label(axiom). [clausify(1194)].
% 26.91/26.88 5374 -division_ring(A) | zero_zero(A) = ti(A,B) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),B) != ti(A,D) | hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),B) = ti(A,C) # label(fact_1104_eq__divide__imp) # label(axiom). [clausify(1215)].
% 26.91/26.88 5375 -division_ring(A) | zero_zero(A) = ti(A,B) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),B) != ti(A,D) | hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),B) = ti(A,C) # label(fact_1105_divide__eq__imp) # label(axiom). [clausify(1216)].
% 26.91/26.88 5376 -division_ring(A) | zero_zero(A) = ti(A,B) | hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),B) != ti(A,D) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),B) = ti(A,C) # label(fact_1109_nonzero__divide__eq__eq) # label(axiom). [clausify(1220)].
% 26.91/26.88 5377 -division_ring(A) | zero_zero(A) = ti(A,B) | hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),B) = ti(A,D) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),B) != ti(A,C) # label(fact_1109_nonzero__divide__eq__eq) # label(axiom). [clausify(1220)].
% 26.91/26.88 5378 -division_ring(A) | zero_zero(A) = ti(A,B) | hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),B) != ti(A,D) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),B) = ti(A,C) # label(fact_1110_nonzero__eq__divide__eq) # label(axiom). [clausify(1221)].
% 26.91/26.88 5379 -division_ring(A) | zero_zero(A) = ti(A,B) | hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),B) = ti(A,D) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),B) != ti(A,C) # label(fact_1110_nonzero__eq__divide__eq) # label(axiom). [clausify(1221)].
% 26.91/26.88 5380 -division_ring(A) | zero_zero(A) = ti(A,B) | hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),B) = one_one(A) # label(fact_1114_divide__self) # label(axiom). [clausify(1225)].
% 26.91/26.88 5381 -division_ring(A) | zero_zero(A) = ti(A,B) | hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),B) != one_one(A) | ti(A,B) = ti(A,C) # label(fact_1115_right__inverse__eq) # label(axiom). [clausify(1226)].
% 26.91/26.88 5382 -division_ring(A) | zero_zero(A) = ti(A,B) | hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),B) = one_one(A) | ti(A,B) != ti(A,C) # label(fact_1115_right__inverse__eq) # label(axiom). [clausify(1226)].
% 26.91/26.88 5383 -division_ring(A) | zero_zero(A) = ti(A,B) | hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),hAPP(A,A,uminus_uminus(A),C)),hAPP(A,A,uminus_uminus(A),B)) = hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),B) # label(fact_1116_nonzero__minus__divide__divide) # label(axiom). [clausify(1227)].
% 26.91/26.88 5384 -division_ring(A) | zero_zero(A) = ti(A,B) | hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),hAPP(A,A,uminus_uminus(A),B)) = hAPP(A,A,uminus_uminus(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),B)) # label(fact_1117_nonzero__minus__divide__right) # label(axiom). [clausify(1228)].
% 26.91/26.88 5385 -division_ring(A) | hAPP(A,A,inverse_inverse(A),B) != hAPP(A,A,inverse_inverse(A),C) | zero_zero(A) = ti(A,C) | zero_zero(A) = ti(A,B) | ti(A,B) = ti(A,C) # label(fact_2171_nonzero__inverse__eq__imp__eq) # label(axiom). [clausify(2192)].
% 26.91/26.88 5386 -division_ring(A) | hAPP(A,A,inverse_inverse(A),B) != zero_zero(A) | zero_zero(A) = ti(A,B) # label(fact_2172_inverse__zero__imp__zero) # label(axiom). [clausify(2193)].
% 26.91/26.88 5387 -division_ring(A) | zero_zero(A) = ti(A,B) | hAPP(A,A,inverse_inverse(A),hAPP(A,A,inverse_inverse(A),B)) = ti(A,B) # label(fact_2173_nonzero__inverse__inverse__eq) # label(axiom). [clausify(2194)].
% 26.91/26.88 5388 -division_ring(A) | zero_zero(A) = ti(A,B) | hAPP(A,A,inverse_inverse(A),B) != zero_zero(A) # label(fact_2174_nonzero__imp__inverse__nonzero) # label(axiom). [clausify(2195)].
% 26.91/26.88 5389 -division_ring(A) | hAPP(A,A,inverse_inverse(A),one_one(A)) = one_one(A) # label(fact_2196_inverse__1) # label(axiom). [clausify(2215)].
% 26.91/26.88 5390 -division_ring(A) | zero_zero(A) = ti(A,B) | zero_zero(A) = ti(A,C) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,inverse_inverse(A),C)),hAPP(A,A,inverse_inverse(A),B)) = hAPP(A,A,inverse_inverse(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)) # label(fact_2213_nonzero__inverse__mult__distrib) # label(axiom). [clausify(2232)].
% 26.91/26.88 5391 -division_ring(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C) != one_one(A) | hAPP(A,A,inverse_inverse(A),B) = ti(A,C) # label(fact_2214_inverse__unique) # label(axiom). [clausify(2233)].
% 26.91/26.88 5392 -division_ring(A) | zero_zero(A) = ti(A,B) | hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),hAPP(A,A,inverse_inverse(A),B)),C) = hAPP(A,A,inverse_inverse(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C)) # label(fact_2215_nonzero__power__inverse) # label(axiom). [clausify(2234)].
% 26.91/26.88 5393 -division_ring(A) | zero_zero(A) = ti(A,B) | hAPP(A,A,uminus_uminus(A),hAPP(A,A,inverse_inverse(A),B)) = hAPP(A,A,inverse_inverse(A),hAPP(A,A,uminus_uminus(A),B)) # label(fact_2224_nonzero__inverse__minus__eq) # label(axiom). [clausify(2243)].
% 26.91/26.88 5394 -division_ring(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(A,A,inverse_inverse(A),C)) = hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C) # label(fact_2225_divide__inverse) # label(axiom). [clausify(2244)].
% 26.91/26.88 5395 -division_ring(A) | hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),one_one(A)),B) = hAPP(A,A,inverse_inverse(A),B) # label(fact_2234_inverse__eq__divide) # label(axiom). [clausify(2253)].
% 26.91/26.88 5396 -division_ring(A) | zero_zero(A) = ti(A,B) | zero_zero(A) = ti(A,C) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,inverse_inverse(A),B)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C))),hAPP(A,A,inverse_inverse(A),C)) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,inverse_inverse(A),B)),hAPP(A,A,inverse_inverse(A),C)) # label(fact_2245_division__ring__inverse__add) # label(axiom). [clausify(2264)].
% 26.91/26.88 5397 -division_ring(A) | zero_zero(A) = ti(A,B) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(A,A,inverse_inverse(A),B)) = one_one(A) # label(fact_2247_right__inverse) # label(axiom). [clausify(2266)].
% 26.91/26.88 5398 -division_ring(A) | zero_zero(A) = ti(A,B) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,inverse_inverse(A),B)),B) = one_one(A) # label(fact_2249_left__inverse) # label(axiom). [clausify(2268)].
% 26.91/26.88 5399 -division_ring(A) | zero_zero(A) = ti(A,B) | zero_zero(A) = ti(A,C) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,inverse_inverse(A),B)),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),C),B))),hAPP(A,A,inverse_inverse(A),C)) = hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(A,A,inverse_inverse(A),B)),hAPP(A,A,inverse_inverse(A),C)) # label(fact_2250_division__ring__inverse__diff) # label(axiom). [clausify(2269)].
% 26.91/26.88 5400 -division_ring(A) | zero_zero(A) = ti(A,B) | hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),one_one(A)),B) = hAPP(A,A,inverse_inverse(A),B) # label(fact_2251_nonzero__inverse__eq__divide) # label(axiom). [clausify(2270)].
% 26.91/26.88 5401 -division_ring(A) | -number(A) | hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),one_one(A)),hAPP(int,A,number_number_of(A),B)) = hAPP(A,A,inverse_inverse(A),hAPP(int,A,number_number_of(A),B)) # label(fact_2253_inverse__eq__divide__number__of) # label(axiom). [clausify(2272)].
% 26.91/26.89 5402 -division_ring(A) | zero_zero(A) = ti(A,B) | zero_zero(A) = ti(A,C) | hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(A,A,inverse_inverse(A),B)),hAPP(A,A,inverse_inverse(A),C)) = hAPP(A,A,uminus_uminus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,inverse_inverse(A),B)),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C))),hAPP(A,A,inverse_inverse(A),C))) # label(fact_2264_inverse__diff__inverse) # label(axiom). [clausify(2283)].
% 26.91/26.89 Derived: inverse_divide(rat) = ti(fun(rat,fun(rat,rat)),inverse_divide(rat)). [resolve(5365,a,5366,a)].
% 26.91/26.89 Derived: inverse_inverse(rat) = ti(fun(rat,rat),inverse_inverse(rat)). [resolve(5365,a,5367,a)].
% 26.91/26.89 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),zero_zero(rat)),A) = zero_zero(rat). [resolve(5365,a,5368,a)].
% 26.91/26.89 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),B),C)) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B)),C). [resolve(5365,a,5369,a)].
% 26.91/26.89 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),B)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),C),B)) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),C)),B). [resolve(5365,a,5370,a)].
% 26.91/26.89 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),one_one(rat)) = ti(rat,A). [resolve(5365,a,5371,a)].
% 26.91/26.89 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),B)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),C),B)) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),A),C)),B). [resolve(5365,a,5372,a)].
% 26.91/26.89 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),hAPP(rat,rat,uminus_uminus(rat),A)),B) = hAPP(rat,rat,uminus_uminus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),B)). [resolve(5365,a,5373,a)].
% 26.91/26.89 Derived: zero_zero(rat) = ti(rat,A) | hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),B),A) != ti(rat,C) | hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),C),A) = ti(rat,B). [resolve(5365,a,5374,a)].
% 26.91/26.89 Derived: zero_zero(rat) = ti(rat,A) | hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),B),A) != ti(rat,C) | hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),C),A) = ti(rat,B). [resolve(5365,a,5376,a)].
% 26.91/26.89 Derived: zero_zero(rat) = ti(rat,A) | hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),A) = one_one(rat). [resolve(5365,a,5380,a)].
% 26.91/26.89 Derived: zero_zero(rat) = ti(rat,A) | hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),B),A) != one_one(rat) | ti(rat,A) = ti(rat,B). [resolve(5365,a,5381,a)].
% 26.91/26.89 Derived: zero_zero(rat) = ti(rat,A) | hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),B),A) = one_one(rat) | ti(rat,A) != ti(rat,B). [resolve(5365,a,5382,a)].
% 26.91/26.89 Derived: zero_zero(rat) = ti(rat,A) | hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),hAPP(rat,rat,uminus_uminus(rat),B)),hAPP(rat,rat,uminus_uminus(rat),A)) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),B),A). [resolve(5365,a,5383,a)].
% 26.91/26.89 Derived: zero_zero(rat) = ti(rat,A) | hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),B),hAPP(rat,rat,uminus_uminus(rat),A)) = hAPP(rat,rat,uminus_uminus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),B),A)). [resolve(5365,a,5384,a)].
% 26.91/26.89 Derived: hAPP(rat,rat,inverse_inverse(rat),A) != hAPP(rat,rat,inverse_inverse(rat),B) | zero_zero(rat) = ti(rat,B) | zero_zero(rat) = ti(rat,A) | ti(rat,A) = ti(rat,B). [resolve(5365,a,5385,a)].
% 26.91/26.89 Derived: hAPP(rat,rat,inverse_inverse(rat),A) != zero_zero(rat) | zero_zero(rat) = ti(rat,A). [resolve(5365,a,5386,a)].
% 26.91/26.89 Derived: zero_zero(rat) = ti(rat,A) | hAPP(rat,rat,inverse_inverse(rat),hAPP(rat,rat,inverse_inverse(rat),A)) = ti(rat,A). [resolve(5365,a,5387,a)].
% 27.01/26.93 Derived: hAPP(rat,rat,inverse_inverse(rat),one_one(rat)) = one_one(rat). [resolve(5365,a,5389,a)].
% 27.01/26.93 Derived: zero_zero(rat) = ti(rat,A) | zero_zero(rat) = ti(rat,B) | hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(rat,rat,inverse_inverse(rat),B)),hAPP(rat,rat,inverse_inverse(rat),A)) = hAPP(rat,rat,inverse_inverse(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B)). [resolve(5365,a,5390,a)].
% 27.01/26.93 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B) != one_one(rat) | hAPP(rat,rat,inverse_inverse(rat),A) = ti(rat,B). [resolve(5365,a,5391,a)].
% 27.01/26.93 Derived: zero_zero(rat) = ti(rat,A) | hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),hAPP(rat,rat,inverse_inverse(rat),A)),B) = hAPP(rat,rat,inverse_inverse(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),B)). [resolve(5365,a,5392,a)].
% 27.01/26.93 Derived: zero_zero(rat) = ti(rat,A) | hAPP(rat,rat,uminus_uminus(rat),hAPP(rat,rat,inverse_inverse(rat),A)) = hAPP(rat,rat,inverse_inverse(rat),hAPP(rat,rat,uminus_uminus(rat),A)). [resolve(5365,a,5393,a)].
% 27.01/26.93 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),hAPP(rat,rat,inverse_inverse(rat),B)) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),B). [resolve(5365,a,5394,a)].
% 27.01/26.93 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),one_one(rat)),A) = hAPP(rat,rat,inverse_inverse(rat),A). [resolve(5365,a,5395,a)].
% 27.01/26.93 Derived: zero_zero(rat) = ti(rat,A) | zero_zero(rat) = ti(rat,B) | hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(rat,rat,inverse_inverse(rat),A)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),B))),hAPP(rat,rat,inverse_inverse(rat),B)) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(rat,rat,inverse_inverse(rat),A)),hAPP(rat,rat,inverse_inverse(rat),B)). [resolve(5365,a,5396,a)].
% 27.01/26.93 Derived: zero_zero(rat) = ti(rat,A) | hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),hAPP(rat,rat,inverse_inverse(rat),A)) = one_one(rat). [resolve(5365,a,5397,a)].
% 27.01/26.93 Derived: zero_zero(rat) = ti(rat,A) | hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(rat,rat,inverse_inverse(rat),A)),A) = one_one(rat). [resolve(5365,a,5398,a)].
% 27.01/26.93 Derived: zero_zero(rat) = ti(rat,A) | zero_zero(rat) = ti(rat,B) | hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(rat,rat,inverse_inverse(rat),A)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),B),A))),hAPP(rat,rat,inverse_inverse(rat),B)) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),hAPP(rat,rat,inverse_inverse(rat),A)),hAPP(rat,rat,inverse_inverse(rat),B)). [resolve(5365,a,5399,a)].
% 27.01/26.93 Derived: zero_zero(rat) = ti(rat,A) | zero_zero(rat) = ti(rat,B) | hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),hAPP(rat,rat,inverse_inverse(rat),A)),hAPP(rat,rat,inverse_inverse(rat),B)) = hAPP(rat,rat,uminus_uminus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(rat,rat,inverse_inverse(rat),A)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),A),B))),hAPP(rat,rat,inverse_inverse(rat),B))). [resolve(5365,a,5402,a)].
% 27.01/26.93 5403 division_ring(real) # label(arity_RealDef_Oreal___Fields_Odivision__ring) # label(axiom). [assumption].
% 27.01/26.93 Derived: inverse_divide(real) = ti(fun(real,fun(real,real)),inverse_divide(real)). [resolve(5403,a,5366,a)].
% 27.01/26.93 Derived: inverse_inverse(real) = ti(fun(real,real),inverse_inverse(real)). [resolve(5403,a,5367,a)].
% 27.01/26.93 Derived: hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),B),C)) = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),C). [resolve(5403,a,5369,a)].
% 27.01/26.93 Derived: hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),one_one(real)) = ti(real,A). [resolve(5403,a,5371,a)].
% 27.01/26.93 Derived: zero_zero(real) = ti(real,A) | hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),A) != ti(real,C) | hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),C),A) = ti(real,B). [resolve(5403,a,5374,a)].
% 27.01/26.93 Derived: zero_zero(real) = ti(real,A) | hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),B),A) != ti(real,C) | hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),A) = ti(real,B). [resolve(5403,a,5376,a)].
% 27.01/26.93 Derived: zero_zero(real) = ti(real,A) | hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),A) = one_one(real). [resolve(5403,a,5380,a)].
% 27.01/26.93 Derived: zero_zero(real) = ti(real,A) | hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),B),A) != one_one(real) | ti(real,A) = ti(real,B). [resolve(5403,a,5381,a)].
% 27.01/26.93 Derived: zero_zero(real) = ti(real,A) | hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),B),A) = one_one(real) | ti(real,A) != ti(real,B). [resolve(5403,a,5382,a)].
% 27.01/26.93 Derived: zero_zero(real) = ti(real,A) | hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,uminus_uminus(real),B)),hAPP(real,real,uminus_uminus(real),A)) = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),B),A). [resolve(5403,a,5383,a)].
% 27.01/26.93 Derived: zero_zero(real) = ti(real,A) | hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),B),hAPP(real,real,uminus_uminus(real),A)) = hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),B),A)). [resolve(5403,a,5384,a)].
% 27.01/26.93 Derived: hAPP(real,real,inverse_inverse(real),A) != hAPP(real,real,inverse_inverse(real),B) | zero_zero(real) = ti(real,B) | zero_zero(real) = ti(real,A) | ti(real,A) = ti(real,B). [resolve(5403,a,5385,a)].
% 27.01/26.93 Derived: hAPP(real,real,inverse_inverse(real),A) != zero_zero(real) | zero_zero(real) = ti(real,A). [resolve(5403,a,5386,a)].
% 27.01/26.93 Derived: zero_zero(real) = ti(real,A) | hAPP(real,real,inverse_inverse(real),hAPP(real,real,inverse_inverse(real),A)) = ti(real,A). [resolve(5403,a,5387,a)].
% 27.01/26.93 Derived: hAPP(real,real,inverse_inverse(real),one_one(real)) = one_one(real). [resolve(5403,a,5389,a)].
% 27.01/26.93 Derived: zero_zero(real) = ti(real,A) | zero_zero(real) = ti(real,B) | hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,inverse_inverse(real),B)),hAPP(real,real,inverse_inverse(real),A)) = hAPP(real,real,inverse_inverse(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)). [resolve(5403,a,5390,a)].
% 27.01/26.93 Derived: hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B) != one_one(real) | hAPP(real,real,inverse_inverse(real),A) = ti(real,B). [resolve(5403,a,5391,a)].
% 27.01/26.93 Derived: zero_zero(real) = ti(real,A) | hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,inverse_inverse(real),A)),B) = hAPP(real,real,inverse_inverse(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),B)). [resolve(5403,a,5392,a)].
% 27.01/26.93 Derived: zero_zero(real) = ti(real,A) | hAPP(real,real,uminus_uminus(real),hAPP(real,real,inverse_inverse(real),A)) = hAPP(real,real,inverse_inverse(real),hAPP(real,real,uminus_uminus(real),A)). [resolve(5403,a,5393,a)].
% 27.01/26.93 Derived: hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),hAPP(real,real,inverse_inverse(real),B)) = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B). [resolve(5403,a,5394,a)].
% 27.01/26.93 Derived: hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),one_one(real)),A) = hAPP(real,real,inverse_inverse(real),A). [resolve(5403,a,5395,a)].
% 27.01/26.93 Derived: zero_zero(real) = ti(real,A) | zero_zero(real) = ti(real,B) | hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,inverse_inverse(real),A)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),B))),hAPP(real,real,inverse_inverse(real),B)) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,inverse_inverse(real),A)),hAPP(real,real,inverse_inverse(real),B)). [resolve(5403,a,5396,a)].
% 27.01/26.93 Derived: zero_zero(real) = ti(real,A) | hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),hAPP(real,real,inverse_inverse(real),A)) = one_one(real). [resolve(5403,a,5397,a)].
% 27.01/26.93 Derived: zero_zero(real) = ti(real,A) | hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,inverse_inverse(real),A)),A) = one_one(real). [resolve(5403,a,5398,a)].
% 27.01/26.96 Derived: zero_zero(real) = ti(real,A) | zero_zero(real) = ti(real,B) | hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,inverse_inverse(real),A)),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),B),A))),hAPP(real,real,inverse_inverse(real),B)) = hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,inverse_inverse(real),A)),hAPP(real,real,inverse_inverse(real),B)). [resolve(5403,a,5399,a)].
% 27.01/26.96 Derived: zero_zero(real) = ti(real,A) | zero_zero(real) = ti(real,B) | hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,inverse_inverse(real),A)),hAPP(real,real,inverse_inverse(real),B)) = hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,inverse_inverse(real),A)),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),B))),hAPP(real,real,inverse_inverse(real),B))). [resolve(5403,a,5402,a)].
% 27.01/26.96 5404 division_ring(complex) # label(arity_Complex_Ocomplex___Fields_Odivision__ring) # label(axiom). [assumption].
% 27.01/26.96 Derived: inverse_divide(complex) = ti(fun(complex,fun(complex,complex)),inverse_divide(complex)). [resolve(5404,a,5366,a)].
% 27.01/26.96 Derived: inverse_inverse(complex) = ti(fun(complex,complex),inverse_inverse(complex)). [resolve(5404,a,5367,a)].
% 27.01/26.96 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),B),C)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),B)),C). [resolve(5404,a,5369,a)].
% 27.01/26.96 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),A),one_one(complex)) = ti(complex,A). [resolve(5404,a,5371,a)].
% 27.01/26.96 Derived: zero_zero(complex) = ti(complex,A) | hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),B),A) != ti(complex,C) | hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),C),A) = ti(complex,B). [resolve(5404,a,5374,a)].
% 27.01/26.96 Derived: zero_zero(complex) = ti(complex,A) | hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),B),A) != ti(complex,C) | hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),C),A) = ti(complex,B). [resolve(5404,a,5376,a)].
% 27.01/26.96 Derived: zero_zero(complex) = ti(complex,A) | hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),A),A) = one_one(complex). [resolve(5404,a,5380,a)].
% 27.01/26.96 Derived: zero_zero(complex) = ti(complex,A) | hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),B),A) != one_one(complex) | ti(complex,A) = ti(complex,B). [resolve(5404,a,5381,a)].
% 27.01/26.96 Derived: zero_zero(complex) = ti(complex,A) | hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),B),A) = one_one(complex) | ti(complex,A) != ti(complex,B). [resolve(5404,a,5382,a)].
% 27.01/26.96 Derived: zero_zero(complex) = ti(complex,A) | hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),hAPP(complex,complex,uminus_uminus(complex),B)),hAPP(complex,complex,uminus_uminus(complex),A)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),B),A). [resolve(5404,a,5383,a)].
% 27.01/26.96 Derived: zero_zero(complex) = ti(complex,A) | hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),B),hAPP(complex,complex,uminus_uminus(complex),A)) = hAPP(complex,complex,uminus_uminus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),B),A)). [resolve(5404,a,5384,a)].
% 27.01/26.96 Derived: hAPP(complex,complex,inverse_inverse(complex),A) != hAPP(complex,complex,inverse_inverse(complex),B) | zero_zero(complex) = ti(complex,B) | zero_zero(complex) = ti(complex,A) | ti(complex,A) = ti(complex,B). [resolve(5404,a,5385,a)].
% 27.01/26.97 Derived: hAPP(complex,complex,inverse_inverse(complex),A) != zero_zero(complex) | zero_zero(complex) = ti(complex,A). [resolve(5404,a,5386,a)].
% 27.01/26.97 Derived: zero_zero(complex) = ti(complex,A) | hAPP(complex,complex,inverse_inverse(complex),hAPP(complex,complex,inverse_inverse(complex),A)) = ti(complex,A). [resolve(5404,a,5387,a)].
% 27.01/26.97 Derived: hAPP(complex,complex,inverse_inverse(complex),one_one(complex)) = one_one(complex). [resolve(5404,a,5389,a)].
% 27.01/26.97 Derived: zero_zero(complex) = ti(complex,A) | zero_zero(complex) = ti(complex,B) | hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,inverse_inverse(complex),B)),hAPP(complex,complex,inverse_inverse(complex),A)) = hAPP(complex,complex,inverse_inverse(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),B)). [resolve(5404,a,5390,a)].
% 27.01/26.97 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),B) != one_one(complex) | hAPP(complex,complex,inverse_inverse(complex),A) = ti(complex,B). [resolve(5404,a,5391,a)].
% 27.01/26.97 Derived: zero_zero(complex) = ti(complex,A) | hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),hAPP(complex,complex,inverse_inverse(complex),A)),B) = hAPP(complex,complex,inverse_inverse(complex),hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),A),B)). [resolve(5404,a,5392,a)].
% 27.01/26.97 Derived: zero_zero(complex) = ti(complex,A) | hAPP(complex,complex,uminus_uminus(complex),hAPP(complex,complex,inverse_inverse(complex),A)) = hAPP(complex,complex,inverse_inverse(complex),hAPP(complex,complex,uminus_uminus(complex),A)). [resolve(5404,a,5393,a)].
% 27.01/26.97 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),hAPP(complex,complex,inverse_inverse(complex),B)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),A),B). [resolve(5404,a,5394,a)].
% 27.01/26.97 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),one_one(complex)),A) = hAPP(complex,complex,inverse_inverse(complex),A). [resolve(5404,a,5395,a)].
% 27.01/26.97 Derived: zero_zero(complex) = ti(complex,A) | zero_zero(complex) = ti(complex,B) | hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,inverse_inverse(complex),A)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),A),B))),hAPP(complex,complex,inverse_inverse(complex),B)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(complex,complex,inverse_inverse(complex),A)),hAPP(complex,complex,inverse_inverse(complex),B)). [resolve(5404,a,5396,a)].
% 27.01/26.97 Derived: zero_zero(complex) = ti(complex,A) | hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),hAPP(complex,complex,inverse_inverse(complex),A)) = one_one(complex). [resolve(5404,a,5397,a)].
% 27.01/26.97 Derived: zero_zero(complex) = ti(complex,A) | hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,inverse_inverse(complex),A)),A) = one_one(complex). [resolve(5404,a,5398,a)].
% 27.01/26.97 Derived: zero_zero(complex) = ti(complex,A) | zero_zero(complex) = ti(complex,B) | hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,inverse_inverse(complex),A)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),B),A))),hAPP(complex,complex,inverse_inverse(complex),B)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),hAPP(complex,complex,inverse_inverse(complex),A)),hAPP(complex,complex,inverse_inverse(complex),B)). [resolve(5404,a,5399,a)].
% 27.01/26.97 Derived: zero_zero(complex) = ti(complex,A) | zero_zero(complex) = ti(complex,B) | hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),hAPP(complex,complex,inverse_inverse(complex),A)),hAPP(complex,complex,inverse_inverse(complex),B)) = hAPP(complex,complex,uminus_uminus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,inverse_inverse(complex),A)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),A),B))),hAPP(complex,complex,inverse_inverse(complex),B))). [resolve(5404,a,5402,a)].
% 33.86/33.78 5405 abs_if(int) # label(arity_Int_Oint___Groups_Oabs__if) # label(axiom). [assumption].
% 33.86/33.78 5406 -abs_if(A) | abs_abs(A) = ti(fun(A,A),abs_abs(A)) # label(tsy_c_Groups_Oabs__class_Oabs_0_res) # label(axiom). [clausify(24)].
% 33.86/33.78 5407 -abs_if(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | hAPP(A,A,uminus_uminus(A),B) = hAPP(A,A,abs_abs(A),B) # label(fact_507_abs__if) # label(axiom). [clausify(631)].
% 33.86/33.78 5408 -abs_if(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | hAPP(A,A,abs_abs(A),B) = ti(A,B) # label(fact_507_abs__if) # label(axiom). [clausify(631)].
% 33.86/33.78 Derived: abs_abs(int) = ti(fun(int,int),abs_abs(int)). [resolve(5405,a,5406,a)].
% 33.86/33.78 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),zero_zero(int))) | hAPP(int,int,uminus_uminus(int),A) = hAPP(int,int,abs_abs(int),A). [resolve(5405,a,5407,a)].
% 33.86/33.78 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),zero_zero(int))) | hAPP(int,int,abs_abs(int),A) = ti(int,A). [resolve(5405,a,5408,a)].
% 33.86/33.78 5409 abs_if(rat) # label(arity_Rat_Orat___Groups_Oabs__if) # label(axiom). [assumption].
% 33.86/33.78 Derived: abs_abs(rat) = ti(fun(rat,rat),abs_abs(rat)). [resolve(5409,a,5406,a)].
% 33.86/33.78 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),zero_zero(rat))) | hAPP(rat,rat,uminus_uminus(rat),A) = hAPP(rat,rat,abs_abs(rat),A). [resolve(5409,a,5407,a)].
% 33.86/33.78 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),zero_zero(rat))) | hAPP(rat,rat,abs_abs(rat),A) = ti(rat,A). [resolve(5409,a,5408,a)].
% 33.86/33.78 5410 abs_if(real) # label(arity_RealDef_Oreal___Groups_Oabs__if) # label(axiom). [assumption].
% 33.86/33.78 Derived: abs_abs(real) = ti(fun(real,real),abs_abs(real)). [resolve(5410,a,5406,a)].
% 33.86/33.78 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))) | hAPP(real,real,uminus_uminus(real),A) = hAPP(real,real,abs_abs(real),A). [resolve(5410,a,5407,a)].
% 33.86/33.78 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))) | hAPP(real,real,abs_abs(real),A) = ti(real,A). [resolve(5410,a,5408,a)].
% 33.86/33.78 5411 ordere142940540dd_abs(int) # label(arity_Int_Oint___Groups_Oordered__ab__group__add__abs) # label(axiom). [assumption].
% 33.86/33.78 5412 -ordere142940540dd_abs(A) | abs_abs(A) = ti(fun(A,A),abs_abs(A)) # label(tsy_c_Groups_Oabs__class_Oabs_1_res) # label(axiom). [clausify(25)].
% 33.86/33.78 5413 -ordere142940540dd_abs(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,uminus_uminus(A),B)),hAPP(A,A,abs_abs(A),B))) # label(fact_481_abs__ge__minus__self) # label(axiom). [clausify(605)].
% 33.86/33.78 5414 -ordere142940540dd_abs(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,abs_abs(A),B)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) # label(fact_482_abs__le__iff) # label(axiom). [clausify(606)].
% 33.86/33.78 5415 -ordere142940540dd_abs(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,abs_abs(A),B)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,uminus_uminus(A),B)),C)) # label(fact_482_abs__le__iff) # label(axiom). [clausify(606)].
% 33.86/33.78 5416 -ordere142940540dd_abs(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,abs_abs(A),B)),C)) | -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),B)),C)) # label(fact_482_abs__le__iff) # label(axiom). [clausify(606)].
% 33.86/33.78 5417 -ordere142940540dd_abs(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),B)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,abs_abs(A),B)),C)) # label(fact_483_abs__leI) # label(axiom). [clausify(607)].
% 33.86/33.78 5418 -ordere142940540dd_abs(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,abs_abs(A),B)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,uminus_uminus(A),B)),C)) # label(fact_484_abs__le__D2) # label(axiom). [clausify(608)].
% 33.86/33.78 5419 -ordere142940540dd_abs(A) | hAPP(A,A,abs_abs(A),hAPP(A,A,uminus_uminus(A),B)) = hAPP(A,A,abs_abs(A),B) # label(fact_496_abs__minus__cancel) # label(axiom). [clausify(620)].
% 33.86/33.78 5420 -ordere142940540dd_abs(A) | hAPP(A,A,abs_abs(A),hAPP(A,A,abs_abs(A),B)) = hAPP(A,A,abs_abs(A),B) # label(fact_497_abs__idempotent) # label(axiom). [clausify(621)].
% 33.86/33.78 5421 -ordere142940540dd_abs(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,uminus_uminus(A),hAPP(A,A,abs_abs(A),B))),zero_zero(A))) # label(fact_504_abs__minus__le__zero) # label(axiom). [clausify(628)].
% 33.86/33.78 5422 -ordere142940540dd_abs(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),zero_zero(A))) | hAPP(A,A,uminus_uminus(A),B) = hAPP(A,A,abs_abs(A),B) # label(fact_505_abs__of__nonpos) # label(axiom). [clausify(629)].
% 33.86/33.78 5423 -ordere142940540dd_abs(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | hAPP(A,A,uminus_uminus(A),B) = hAPP(A,A,abs_abs(A),B) # label(fact_506_abs__of__neg) # label(axiom). [clausify(630)].
% 33.86/33.78 5424 -ordere142940540dd_abs(A) | hAPP(A,A,abs_abs(A),B) != zero_zero(A) | zero_zero(A) = ti(A,B) # label(fact_522_abs__eq__0) # label(axiom). [clausify(646)].
% 33.86/33.78 5425 -ordere142940540dd_abs(A) | hAPP(A,A,abs_abs(A),B) = zero_zero(A) | zero_zero(A) != ti(A,B) # label(fact_522_abs__eq__0) # label(axiom). [clausify(646)].
% 33.86/33.78 5426 -ordere142940540dd_abs(A) | hAPP(A,A,abs_abs(A),zero_zero(A)) = zero_zero(A) # label(fact_523_abs__zero) # label(axiom). [clausify(647)].
% 33.86/33.78 5427 -ordere142940540dd_abs(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,abs_abs(A),B)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) # label(fact_524_abs__le__D1) # label(axiom). [clausify(648)].
% 33.86/33.78 5428 -ordere142940540dd_abs(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,abs_abs(A),B))) # label(fact_525_abs__ge__self) # label(axiom). [clausify(649)].
% 33.86/33.78 5429 -ordere142940540dd_abs(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,abs_abs(A),B)),hAPP(A,A,abs_abs(A),C)) = hAPP(A,A,abs_abs(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,abs_abs(A),B)),hAPP(A,A,abs_abs(A),C))) # label(fact_543_abs__add__abs) # label(axiom). [clausify(667)].
% 33.86/33.78 5430 -ordere142940540dd_abs(A) | hAPP(A,A,abs_abs(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C)) = hAPP(A,A,abs_abs(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),C),B)) # label(fact_549_abs__minus__commute) # label(axiom). [clausify(673)].
% 33.86/33.78 5431 -ordere142940540dd_abs(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) | hAPP(A,A,abs_abs(A),B) = ti(A,B) # label(fact_610_abs__of__nonneg) # label(axiom). [clausify(731)].
% 33.86/33.78 5432 -ordere142940540dd_abs(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,abs_abs(A),B)),zero_zero(A))) | zero_zero(A) = ti(A,B) # label(fact_611_abs__le__zero__iff) # label(axiom). [clausify(732)].
% 33.86/33.78 5433 -ordere142940540dd_abs(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,abs_abs(A),B)),zero_zero(A))) | zero_zero(A) != ti(A,B) # label(fact_611_abs__le__zero__iff) # label(axiom). [clausify(732)].
% 33.86/33.78 5434 -ordere142940540dd_abs(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(A,A,abs_abs(A),B))) # label(fact_612_abs__ge__zero) # label(axiom). [clausify(733)].
% 33.86/33.78 5435 -ordere142940540dd_abs(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | hAPP(A,A,abs_abs(A),B) = ti(A,B) # label(fact_613_abs__of__pos) # label(axiom). [clausify(734)].
% 33.86/33.78 5436 -ordere142940540dd_abs(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,abs_abs(A),B))) | zero_zero(A) != ti(A,B) # label(fact_614_zero__less__abs__iff) # label(axiom). [clausify(735)].
% 33.86/33.78 5437 -ordere142940540dd_abs(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,abs_abs(A),B))) | zero_zero(A) = ti(A,B) # label(fact_614_zero__less__abs__iff) # label(axiom). [clausify(735)].
% 33.86/33.78 5438 -ordere142940540dd_abs(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,abs_abs(A),B)),zero_zero(A))) # label(fact_615_abs__not__less__zero) # label(axiom). [clausify(736)].
% 33.86/33.78 5439 -ordere142940540dd_abs(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,abs_abs(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),hAPP(A,A,abs_abs(A),B)),hAPP(A,A,abs_abs(A),C)))) # label(fact_620_abs__triangle__ineq) # label(axiom). [clausify(741)].
% 33.86/33.78 5440 -ordere142940540dd_abs(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,abs_abs(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(A,A,abs_abs(A),B)),hAPP(A,A,abs_abs(A),C)))),hAPP(A,A,abs_abs(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C)))) # label(fact_621_abs__triangle__ineq3) # label(axiom). [clausify(742)].
% 33.86/33.78 5441 -ordere142940540dd_abs(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(A,A,abs_abs(A),B)),hAPP(A,A,abs_abs(A),C))),hAPP(A,A,abs_abs(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C)))) # label(fact_622_abs__triangle__ineq2) # label(axiom). [clausify(743)].
% 33.86/33.78 5442 -ordere142940540dd_abs(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(A,A,abs_abs(A),B)),hAPP(A,A,abs_abs(A),C))),hAPP(A,A,abs_abs(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),C),B)))) # label(fact_623_abs__triangle__ineq2__sym) # label(axiom). [clausify(744)].
% 33.86/33.78 5443 -ordere142940540dd_abs(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,abs_abs(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)),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,abs_abs(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),D))),hAPP(A,A,abs_abs(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),C),E))))) # label(fact_661_abs__diff__triangle__ineq) # label(axiom). [clausify(781)].
% 33.86/33.78 5444 -ordere142940540dd_abs(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,abs_abs(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C))),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,abs_abs(A),B)),hAPP(A,A,abs_abs(A),C)))) # label(fact_662_abs__triangle__ineq4) # label(axiom). [clausify(782)].
% 33.86/33.78 5445 -ordere142940540dd_abs(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,abs_abs(A),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),C),D))),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),abs_abs(A)),C)),D))) # label(fact_4165_setsum__abs) # label(axiom). [clausify(4097)].
% 33.86/33.78 5446 -ordere142940540dd_abs(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(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),abs_abs(A)),C)),D))) # label(fact_4166_setsum__abs__ge__zero) # label(axiom). [clausify(4098)].
% 33.86/33.78 5447 -ordere142940540dd_abs(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),abs_abs(A)),C)),D) = hAPP(A,A,abs_abs(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),abs_abs(A)),C)),D)) # label(fact_4209_abs__setsum__abs) # label(axiom). [clausify(4141)].
% 33.86/33.78 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,uminus_uminus(int),A)),hAPP(int,int,abs_abs(int),A))). [resolve(5411,a,5413,a)].
% 33.86/33.78 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,abs_abs(int),A)),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)). [resolve(5411,a,5414,a)].
% 33.86/33.78 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,abs_abs(int),A)),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,uminus_uminus(int),A)),B)). [resolve(5411,a,5415,a)].
% 33.86/33.79 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,abs_abs(int),A)),B)) | -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),A)),B)). [resolve(5411,a,5416,a)].
% 33.86/33.79 Derived: hAPP(int,int,abs_abs(int),hAPP(int,int,uminus_uminus(int),A)) = hAPP(int,int,abs_abs(int),A). [resolve(5411,a,5419,a)].
% 33.86/33.79 Derived: hAPP(int,int,abs_abs(int),hAPP(int,int,abs_abs(int),A)) = hAPP(int,int,abs_abs(int),A). [resolve(5411,a,5420,a)].
% 33.86/33.79 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,uminus_uminus(int),hAPP(int,int,abs_abs(int),A))),zero_zero(int))). [resolve(5411,a,5421,a)].
% 33.86/33.79 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),zero_zero(int))) | hAPP(int,int,uminus_uminus(int),A) = hAPP(int,int,abs_abs(int),A). [resolve(5411,a,5422,a)].
% 33.86/33.79 Derived: hAPP(int,int,abs_abs(int),A) != zero_zero(int) | zero_zero(int) = ti(int,A). [resolve(5411,a,5424,a)].
% 33.86/33.79 Derived: hAPP(int,int,abs_abs(int),A) = zero_zero(int) | zero_zero(int) != ti(int,A). [resolve(5411,a,5425,a)].
% 33.86/33.79 Derived: hAPP(int,int,abs_abs(int),zero_zero(int)) = zero_zero(int). [resolve(5411,a,5426,a)].
% 33.86/33.79 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),hAPP(int,int,abs_abs(int),A))). [resolve(5411,a,5428,a)].
% 33.86/33.79 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,abs_abs(int),A)),hAPP(int,int,abs_abs(int),B)) = hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,abs_abs(int),A)),hAPP(int,int,abs_abs(int),B))). [resolve(5411,a,5429,a)].
% 33.86/33.79 Derived: hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),B)) = hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),B),A)). [resolve(5411,a,5430,a)].
% 33.86/33.79 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A)) | hAPP(int,int,abs_abs(int),A) = ti(int,A). [resolve(5411,a,5431,a)].
% 33.86/33.79 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,abs_abs(int),A)),zero_zero(int))) | zero_zero(int) = ti(int,A). [resolve(5411,a,5432,a)].
% 33.86/33.79 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,abs_abs(int),A)),zero_zero(int))) | zero_zero(int) != ti(int,A). [resolve(5411,a,5433,a)].
% 33.86/33.79 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,abs_abs(int),A))). [resolve(5411,a,5434,a)].
% 33.86/33.79 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A)) | hAPP(int,int,abs_abs(int),A) = ti(int,A). [resolve(5411,a,5435,a)].
% 33.86/33.79 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,abs_abs(int),A))) | zero_zero(int) != ti(int,A). [resolve(5411,a,5436,a)].
% 33.86/33.79 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,abs_abs(int),A))) | zero_zero(int) = ti(int,A). [resolve(5411,a,5437,a)].
% 33.86/33.79 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,abs_abs(int),A)),zero_zero(int))). [resolve(5411,a,5438,a)].
% 33.86/33.79 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,abs_abs(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),hAPP(int,int,abs_abs(int),A)),hAPP(int,int,abs_abs(int),B)))). [resolve(5411,a,5439,a)].
% 33.86/33.79 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,abs_abs(int),A)),hAPP(int,int,abs_abs(int),B)))),hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),B)))). [resolve(5411,a,5440,a)].
% 33.86/33.79 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,abs_abs(int),A)),hAPP(int,int,abs_abs(int),B))),hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),B)))). [resolve(5411,a,5441,a)].
% 33.92/33.83 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,abs_abs(int),A)),hAPP(int,int,abs_abs(int),B))),hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),B),A)))). [resolve(5411,a,5442,a)].
% 33.92/33.83 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(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,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),C))),hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),B),D))))). [resolve(5411,a,5443,a)].
% 33.92/33.83 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),B))),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,abs_abs(int),A)),hAPP(int,int,abs_abs(int),B)))). [resolve(5411,a,5444,a)].
% 33.92/33.83 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,abs_abs(int),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),B),C))),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),abs_abs(int)),B)),C))). [resolve(5411,a,5445,a)].
% 33.92/33.83 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),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),abs_abs(int)),B)),C))). [resolve(5411,a,5446,a)].
% 33.92/33.83 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),abs_abs(int)),B)),C) = hAPP(int,int,abs_abs(int),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),abs_abs(int)),B)),C)). [resolve(5411,a,5447,a)].
% 33.92/33.83 5448 ordere142940540dd_abs(rat) # label(arity_Rat_Orat___Groups_Oordered__ab__group__add__abs) # label(axiom). [assumption].
% 33.92/33.83 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,uminus_uminus(rat),A)),hAPP(rat,rat,abs_abs(rat),A))). [resolve(5448,a,5413,a)].
% 33.92/33.83 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,abs_abs(rat),A)),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),B)). [resolve(5448,a,5414,a)].
% 33.92/33.83 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,abs_abs(rat),A)),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,uminus_uminus(rat),A)),B)). [resolve(5448,a,5415,a)].
% 33.92/33.84 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,abs_abs(rat),A)),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,uminus_uminus(rat),A)),B)). [resolve(5448,a,5416,a)].
% 33.92/33.84 Derived: hAPP(rat,rat,abs_abs(rat),hAPP(rat,rat,uminus_uminus(rat),A)) = hAPP(rat,rat,abs_abs(rat),A). [resolve(5448,a,5419,a)].
% 33.92/33.84 Derived: hAPP(rat,rat,abs_abs(rat),hAPP(rat,rat,abs_abs(rat),A)) = hAPP(rat,rat,abs_abs(rat),A). [resolve(5448,a,5420,a)].
% 33.92/33.84 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,uminus_uminus(rat),hAPP(rat,rat,abs_abs(rat),A))),zero_zero(rat))). [resolve(5448,a,5421,a)].
% 33.92/33.84 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),zero_zero(rat))) | hAPP(rat,rat,uminus_uminus(rat),A) = hAPP(rat,rat,abs_abs(rat),A). [resolve(5448,a,5422,a)].
% 33.92/33.84 Derived: hAPP(rat,rat,abs_abs(rat),A) != zero_zero(rat) | zero_zero(rat) = ti(rat,A). [resolve(5448,a,5424,a)].
% 33.92/33.84 Derived: hAPP(rat,rat,abs_abs(rat),A) = zero_zero(rat) | zero_zero(rat) != ti(rat,A). [resolve(5448,a,5425,a)].
% 33.92/33.84 Derived: hAPP(rat,rat,abs_abs(rat),zero_zero(rat)) = zero_zero(rat). [resolve(5448,a,5426,a)].
% 33.92/33.84 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),hAPP(rat,rat,abs_abs(rat),A))). [resolve(5448,a,5428,a)].
% 33.92/33.84 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(rat,rat,abs_abs(rat),A)),hAPP(rat,rat,abs_abs(rat),B)) = hAPP(rat,rat,abs_abs(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(rat,rat,abs_abs(rat),A)),hAPP(rat,rat,abs_abs(rat),B))). [resolve(5448,a,5429,a)].
% 33.92/33.84 Derived: hAPP(rat,rat,abs_abs(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),A),B)) = hAPP(rat,rat,abs_abs(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),B),A)). [resolve(5448,a,5430,a)].
% 33.92/33.84 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),A)) | hAPP(rat,rat,abs_abs(rat),A) = ti(rat,A). [resolve(5448,a,5431,a)].
% 33.92/33.84 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,abs_abs(rat),A)),zero_zero(rat))) | zero_zero(rat) = ti(rat,A). [resolve(5448,a,5432,a)].
% 33.92/33.84 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,abs_abs(rat),A)),zero_zero(rat))) | zero_zero(rat) != ti(rat,A). [resolve(5448,a,5433,a)].
% 33.92/33.84 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),hAPP(rat,rat,abs_abs(rat),A))). [resolve(5448,a,5434,a)].
% 33.92/33.84 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)) | hAPP(rat,rat,abs_abs(rat),A) = ti(rat,A). [resolve(5448,a,5435,a)].
% 33.92/33.84 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(rat,rat,abs_abs(rat),A))) | zero_zero(rat) != ti(rat,A). [resolve(5448,a,5436,a)].
% 33.92/33.84 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(rat,rat,abs_abs(rat),A))) | zero_zero(rat) = ti(rat,A). [resolve(5448,a,5437,a)].
% 33.92/33.84 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,abs_abs(rat),A)),zero_zero(rat))). [resolve(5448,a,5438,a)].
% 33.92/33.84 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,abs_abs(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),B))),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(rat,rat,abs_abs(rat),A)),hAPP(rat,rat,abs_abs(rat),B)))). [resolve(5448,a,5439,a)].
% 33.92/33.84 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,abs_abs(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),hAPP(rat,rat,abs_abs(rat),A)),hAPP(rat,rat,abs_abs(rat),B)))),hAPP(rat,rat,abs_abs(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),A),B)))). [resolve(5448,a,5440,a)].
% 33.92/33.84 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),hAPP(rat,rat,abs_abs(rat),A)),hAPP(rat,rat,abs_abs(rat),B))),hAPP(rat,rat,abs_abs(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),A),B)))). [resolve(5448,a,5441,a)].
% 33.92/33.84 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),hAPP(rat,rat,abs_abs(rat),A)),hAPP(rat,rat,abs_abs(rat),B))),hAPP(rat,rat,abs_abs(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),B),A)))). [resolve(5448,a,5442,a)].
% 33.92/33.84 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,abs_abs(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),B)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),C),D)))),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(rat,rat,abs_abs(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),A),C))),hAPP(rat,rat,abs_abs(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),B),D))))). [resolve(5448,a,5443,a)].
% 33.92/33.84 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,abs_abs(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),A),B))),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(rat,rat,abs_abs(rat),A)),hAPP(rat,rat,abs_abs(rat),B)))). [resolve(5448,a,5444,a)].
% 33.92/33.88 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,abs_abs(rat),hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),B),C))),hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),hAPP(fun(A,rat),fun(A,rat),hAPP(fun(rat,rat),fun(fun(A,rat),fun(A,rat)),combb(rat,rat,A),abs_abs(rat)),B)),C))). [resolve(5448,a,5445,a)].
% 33.92/33.88 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),hAPP(fun(A,rat),fun(A,rat),hAPP(fun(rat,rat),fun(fun(A,rat),fun(A,rat)),combb(rat,rat,A),abs_abs(rat)),B)),C))). [resolve(5448,a,5446,a)].
% 33.92/33.88 Derived: hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),hAPP(fun(A,rat),fun(A,rat),hAPP(fun(rat,rat),fun(fun(A,rat),fun(A,rat)),combb(rat,rat,A),abs_abs(rat)),B)),C) = hAPP(rat,rat,abs_abs(rat),hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),hAPP(fun(A,rat),fun(A,rat),hAPP(fun(rat,rat),fun(fun(A,rat),fun(A,rat)),combb(rat,rat,A),abs_abs(rat)),B)),C)). [resolve(5448,a,5447,a)].
% 33.92/33.88 5449 ordere142940540dd_abs(real) # label(arity_RealDef_Oreal___Groups_Oordered__ab__group__add__abs) # label(axiom). [assumption].
% 33.92/33.88 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,uminus_uminus(real),A)),hAPP(real,real,abs_abs(real),A))). [resolve(5449,a,5413,a)].
% 33.92/33.88 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),A)),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),B)). [resolve(5449,a,5414,a)].
% 33.92/33.88 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),A)),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,uminus_uminus(real),A)),B)). [resolve(5449,a,5415,a)].
% 33.92/33.88 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),A)),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,uminus_uminus(real),A)),B)). [resolve(5449,a,5416,a)].
% 33.92/33.88 Derived: hAPP(real,real,abs_abs(real),hAPP(real,real,uminus_uminus(real),A)) = hAPP(real,real,abs_abs(real),A). [resolve(5449,a,5419,a)].
% 33.92/33.88 Derived: hAPP(real,real,abs_abs(real),hAPP(real,real,abs_abs(real),A)) = hAPP(real,real,abs_abs(real),A). [resolve(5449,a,5420,a)].
% 33.92/33.88 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,uminus_uminus(real),hAPP(real,real,abs_abs(real),A))),zero_zero(real))). [resolve(5449,a,5421,a)].
% 33.92/33.88 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),zero_zero(real))) | hAPP(real,real,uminus_uminus(real),A) = hAPP(real,real,abs_abs(real),A). [resolve(5449,a,5422,a)].
% 33.92/33.88 Derived: hAPP(real,real,abs_abs(real),A) != zero_zero(real) | zero_zero(real) = ti(real,A). [resolve(5449,a,5424,a)].
% 33.92/33.88 Derived: hAPP(real,real,abs_abs(real),A) = zero_zero(real) | zero_zero(real) != ti(real,A). [resolve(5449,a,5425,a)].
% 33.92/33.88 Derived: hAPP(real,real,abs_abs(real),zero_zero(real)) = zero_zero(real). [resolve(5449,a,5426,a)].
% 33.92/33.88 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),hAPP(real,real,abs_abs(real),A))). [resolve(5449,a,5428,a)].
% 33.92/33.88 Derived: hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,abs_abs(real),A)),hAPP(real,real,abs_abs(real),B)) = hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,abs_abs(real),A)),hAPP(real,real,abs_abs(real),B))). [resolve(5449,a,5429,a)].
% 33.92/33.88 Derived: hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),B)) = hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),B),A)). [resolve(5449,a,5430,a)].
% 33.92/33.88 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A)) | hAPP(real,real,abs_abs(real),A) = ti(real,A). [resolve(5449,a,5431,a)].
% 33.92/33.88 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),A)),zero_zero(real))) | zero_zero(real) = ti(real,A). [resolve(5449,a,5432,a)].
% 33.92/33.88 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),A)),zero_zero(real))) | zero_zero(real) != ti(real,A). [resolve(5449,a,5433,a)].
% 33.92/33.88 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(real,real,abs_abs(real),A))). [resolve(5449,a,5434,a)].
% 33.92/33.88 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | hAPP(real,real,abs_abs(real),A) = ti(real,A). [resolve(5449,a,5435,a)].
% 33.92/33.88 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,abs_abs(real),A))) | zero_zero(real) != ti(real,A). [resolve(5449,a,5436,a)].
% 33.92/33.88 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,abs_abs(real),A))) | zero_zero(real) = ti(real,A). [resolve(5449,a,5437,a)].
% 33.92/33.88 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,abs_abs(real),A)),zero_zero(real))). [resolve(5449,a,5438,a)].
% 33.92/33.88 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),B))),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,abs_abs(real),A)),hAPP(real,real,abs_abs(real),B)))). [resolve(5449,a,5439,a)].
% 33.92/33.88 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,abs_abs(real),A)),hAPP(real,real,abs_abs(real),B)))),hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),B)))). [resolve(5449,a,5440,a)].
% 33.92/33.88 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,abs_abs(real),A)),hAPP(real,real,abs_abs(real),B))),hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),B)))). [resolve(5449,a,5441,a)].
% 33.92/33.88 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,abs_abs(real),A)),hAPP(real,real,abs_abs(real),B))),hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),B),A)))). [resolve(5449,a,5442,a)].
% 33.92/33.88 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),C),D)))),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),C))),hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),B),D))))). [resolve(5449,a,5443,a)].
% 33.92/33.88 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),B))),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,abs_abs(real),A)),hAPP(real,real,abs_abs(real),B)))). [resolve(5449,a,5444,a)].
% 33.92/33.88 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),B),C))),hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),hAPP(fun(A,real),fun(A,real),hAPP(fun(real,real),fun(fun(A,real),fun(A,real)),combb(real,real,A),abs_abs(real)),B)),C))). [resolve(5449,a,5445,a)].
% 33.92/33.88 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),hAPP(fun(A,real),fun(A,real),hAPP(fun(real,real),fun(fun(A,real),fun(A,real)),combb(real,real,A),abs_abs(real)),B)),C))). [resolve(5449,a,5446,a)].
% 40.79/40.71 Derived: hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),hAPP(fun(A,real),fun(A,real),hAPP(fun(real,real),fun(fun(A,real),fun(A,real)),combb(real,real,A),abs_abs(real)),B)),C) = hAPP(real,real,abs_abs(real),hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),hAPP(fun(A,real),fun(A,real),hAPP(fun(real,real),fun(fun(A,real),fun(A,real)),combb(real,real,A),abs_abs(real)),B)),C)). [resolve(5449,a,5447,a)].
% 40.79/40.71 5450 one(int) # label(arity_Int_Oint___Groups_Oone) # label(axiom). [assumption].
% 40.79/40.71 5451 -one(A) | one_one(A) = ti(A,one_one(A)) # label(tsy_c_Groups_Oone__class_Oone_res) # label(axiom). [clausify(27)].
% 40.79/40.71 Derived: one_one(int) = ti(int,one_one(int)). [resolve(5450,a,5451,a)].
% 40.79/40.71 5452 one(nat) # label(arity_Nat_Onat___Groups_Oone) # label(axiom). [assumption].
% 40.79/40.71 Derived: one_one(nat) = ti(nat,one_one(nat)). [resolve(5452,a,5451,a)].
% 40.79/40.71 5453 one(rat) # label(arity_Rat_Orat___Groups_Oone) # label(axiom). [assumption].
% 40.79/40.71 Derived: one_one(rat) = ti(rat,one_one(rat)). [resolve(5453,a,5451,a)].
% 40.79/40.71 5454 one(real) # label(arity_RealDef_Oreal___Groups_Oone) # label(axiom). [assumption].
% 40.79/40.71 Derived: one_one(real) = ti(real,one_one(real)). [resolve(5454,a,5451,a)].
% 40.79/40.71 5455 one(complex) # label(arity_Complex_Ocomplex___Groups_Oone) # label(axiom). [assumption].
% 40.79/40.71 Derived: one_one(complex) = ti(complex,one_one(complex)). [resolve(5455,a,5451,a)].
% 40.79/40.71 5456 one(code_code_numeral) # label(arity_Code__Numeral_Ocode__numeral___Groups_Oone) # label(axiom). [assumption].
% 40.79/40.71 Derived: one_one(code_code_numeral) = ti(code_code_numeral,one_one(code_code_numeral)). [resolve(5456,a,5451,a)].
% 40.79/40.71 5457 one(quickcheck_code_int) # label(arity_Quickcheck__Narrowing_Ocode__int___Groups_Oone) # label(axiom). [assumption].
% 40.79/40.71 Derived: one_one(quickcheck_code_int) = ti(quickcheck_code_int,one_one(quickcheck_code_int)). [resolve(5457,a,5451,a)].
% 40.79/40.71 5458 plus(int) # label(arity_Int_Oint___Groups_Oplus) # label(axiom). [assumption].
% 40.79/40.71 5459 -plus(A) | -linorder(A) | -dvd(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(28)].
% 40.79/40.71 Derived: -linorder(int) | -dvd(int) | plus_plus(int) = ti(fun(int,fun(int,int)),plus_plus(int)). [resolve(5458,a,5459,a)].
% 40.79/40.71 5460 plus(nat) # label(arity_Nat_Onat___Groups_Oplus) # label(axiom). [assumption].
% 40.79/40.71 Derived: -linorder(nat) | -dvd(nat) | plus_plus(nat) = ti(fun(nat,fun(nat,nat)),plus_plus(nat)). [resolve(5460,a,5459,a)].
% 40.79/40.71 5461 plus(rat) # label(arity_Rat_Orat___Groups_Oplus) # label(axiom). [assumption].
% 40.79/40.71 Derived: -linorder(rat) | -dvd(rat) | plus_plus(rat) = ti(fun(rat,fun(rat,rat)),plus_plus(rat)). [resolve(5461,a,5459,a)].
% 40.79/40.71 5462 plus(real) # label(arity_RealDef_Oreal___Groups_Oplus) # label(axiom). [assumption].
% 40.79/40.71 Derived: -linorder(real) | -dvd(real) | plus_plus(real) = ti(fun(real,fun(real,real)),plus_plus(real)). [resolve(5462,a,5459,a)].
% 40.79/40.71 5463 plus(complex) # label(arity_Complex_Ocomplex___Groups_Oplus) # label(axiom). [assumption].
% 40.79/40.71 Derived: -linorder(complex) | -dvd(complex) | plus_plus(complex) = ti(fun(complex,fun(complex,complex)),plus_plus(complex)). [resolve(5463,a,5459,a)].
% 40.79/40.71 5464 plus(code_code_numeral) # label(arity_Code__Numeral_Ocode__numeral___Groups_Oplus) # label(axiom). [assumption].
% 40.79/40.71 Derived: -linorder(code_code_numeral) | -dvd(code_code_numeral) | plus_plus(code_code_numeral) = ti(fun(code_code_numeral,fun(code_code_numeral,code_code_numeral)),plus_plus(code_code_numeral)). [resolve(5464,a,5459,a)].
% 40.79/40.71 5465 plus(quickcheck_code_int) # label(arity_Quickcheck__Narrowing_Ocode__int___Groups_Oplus) # label(axiom). [assumption].
% 40.79/40.71 Derived: -linorder(quickcheck_code_int) | -dvd(quickcheck_code_int) | plus_plus(quickcheck_code_int) = ti(fun(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int)),plus_plus(quickcheck_code_int)). [resolve(5465,a,5459,a)].
% 47.64/47.60 5466 monoid_add(int) # label(arity_Int_Oint___Groups_Omonoid__add) # label(axiom). [assumption].
% 47.64/47.60 5467 -monoid_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(29)].
% 47.64/47.60 5468 -monoid_add(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),zero_zero(A)) = ti(A,B) # label(fact_267_add__0__right) # label(axiom). [clausify(397)].
% 47.64/47.60 5469 -monoid_add(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),zero_zero(A)),B) = ti(A,B) # label(fact_270_add__0__left) # label(axiom). [clausify(400)].
% 47.64/47.60 Derived: plus_plus(int) = ti(fun(int,fun(int,int)),plus_plus(int)). [resolve(5466,a,5467,a)].
% 47.64/47.60 5470 monoid_add(nat) # label(arity_Nat_Onat___Groups_Omonoid__add) # label(axiom). [assumption].
% 47.64/47.60 Derived: plus_plus(nat) = ti(fun(nat,fun(nat,nat)),plus_plus(nat)). [resolve(5470,a,5467,a)].
% 47.64/47.60 5471 monoid_add(rat) # label(arity_Rat_Orat___Groups_Omonoid__add) # label(axiom). [assumption].
% 47.64/47.60 Derived: plus_plus(rat) = ti(fun(rat,fun(rat,rat)),plus_plus(rat)). [resolve(5471,a,5467,a)].
% 47.64/47.60 5472 monoid_add(real) # label(arity_RealDef_Oreal___Groups_Omonoid__add) # label(axiom). [assumption].
% 47.64/47.60 Derived: plus_plus(real) = ti(fun(real,fun(real,real)),plus_plus(real)). [resolve(5472,a,5467,a)].
% 47.64/47.60 5473 monoid_add(complex) # label(arity_Complex_Ocomplex___Groups_Omonoid__add) # label(axiom). [assumption].
% 47.64/47.60 Derived: plus_plus(complex) = ti(fun(complex,fun(complex,complex)),plus_plus(complex)). [resolve(5473,a,5467,a)].
% 47.64/47.60 5474 monoid_add(code_code_numeral) # label(arity_Code__Numeral_Ocode__numeral___Groups_Omonoid__add) # label(axiom). [assumption].
% 47.64/47.60 Derived: plus_plus(code_code_numeral) = ti(fun(code_code_numeral,fun(code_code_numeral,code_code_numeral)),plus_plus(code_code_numeral)). [resolve(5474,a,5467,a)].
% 47.64/47.60 5475 monoid_add(quickcheck_code_int) # label(arity_Quickcheck__Narrowing_Ocode__int___Groups_Omonoid__add) # label(axiom). [assumption].
% 47.64/47.60 Derived: plus_plus(quickcheck_code_int) = ti(fun(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int)),plus_plus(quickcheck_code_int)). [resolve(5475,a,5467,a)].
% 47.64/47.60 5476 ab_semigroup_add(int) # label(arity_Int_Oint___Groups_Oab__semigroup__add) # label(axiom). [assumption].
% 47.64/47.60 5477 -ab_semigroup_add(A) | plus_plus(A) = ti(fun(A,fun(A,A)),plus_plus(A)) # label(tsy_c_Groups_Oplus__class_Oplus_2_res) # label(axiom). [clausify(30)].
% 47.64/47.60 5478 -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_18_ab__semigroup__add__class_Oadd__ac_I1_J) # label(axiom). [clausify(148)].
% 47.64/47.60 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(5476,a,5478,a)].
% 47.64/47.60 5479 ab_semigroup_add(nat) # label(arity_Nat_Onat___Groups_Oab__semigroup__add) # label(axiom). [assumption].
% 47.64/47.60 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(5479,a,5478,a)].
% 47.64/47.60 5480 ab_semigroup_add(rat) # label(arity_Rat_Orat___Groups_Oab__semigroup__add) # label(axiom). [assumption].
% 47.64/47.60 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),B)),C) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),B),C)). [resolve(5480,a,5478,a)].
% 47.64/47.60 5481 ab_semigroup_add(real) # label(arity_RealDef_Oreal___Groups_Oab__semigroup__add) # label(axiom). [assumption].
% 47.64/47.60 Derived: hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),B)),C) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),B),C)). [resolve(5481,a,5478,a)].
% 51.00/50.91 5482 ab_semigroup_add(complex) # label(arity_Complex_Ocomplex___Groups_Oab__semigroup__add) # label(axiom). [assumption].
% 51.00/50.91 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),A),B)),C) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),A),hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),B),C)). [resolve(5482,a,5478,a)].
% 51.00/50.91 5483 ab_semigroup_add(code_code_numeral) # label(arity_Code__Numeral_Ocode__numeral___Groups_Oab__semigroup__add) # label(axiom). [assumption].
% 51.00/50.91 Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),A),B)),C) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),A),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),B),C)). [resolve(5483,a,5478,a)].
% 51.00/50.91 5484 ab_semigroup_add(quickcheck_code_int) # label(arity_Quickcheck__Narrowing_Ocode__int___Groups_Oab__semigroup__add) # label(axiom). [assumption].
% 51.00/50.91 Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),A),B)),C) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),A),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),B),C)). [resolve(5484,a,5478,a)].
% 51.00/50.91 5485 cancel_semigroup_add(int) # label(arity_Int_Oint___Groups_Ocancel__semigroup__add) # label(axiom). [assumption].
% 51.00/50.91 5486 -cancel_semigroup_add(A) | plus_plus(A) = ti(fun(A,fun(A,A)),plus_plus(A)) # label(tsy_c_Groups_Oplus__class_Oplus_3_res) # label(axiom). [clausify(31)].
% 51.00/50.91 5487 -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_13_add__right__imp__eq) # label(axiom). [clausify(143)].
% 51.00/50.91 5488 -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_15_add__left__imp__eq) # label(axiom). [clausify(145)].
% 51.00/50.91 5489 -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_16_add__right__cancel) # label(axiom). [clausify(146)].
% 51.00/50.91 5490 -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_16_add__right__cancel) # label(axiom). [clausify(146)].
% 51.00/50.91 5491 -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_17_add__left__cancel) # label(axiom). [clausify(147)].
% 51.00/50.91 5492 -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_17_add__left__cancel) # label(axiom). [clausify(147)].
% 51.00/50.91 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(5485,a,5487,a)].
% 51.00/50.91 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(5485,a,5488,a)].
% 51.00/50.91 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(5485,a,5490,a)].
% 51.13/51.03 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(5485,a,5492,a)].
% 51.13/51.03 5493 cancel_semigroup_add(nat) # label(arity_Nat_Onat___Groups_Ocancel__semigroup__add) # label(axiom). [assumption].
% 51.13/51.03 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(5493,a,5487,a)].
% 51.13/51.03 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(5493,a,5488,a)].
% 51.13/51.03 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(5493,a,5490,a)].
% 51.13/51.03 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(5493,a,5492,a)].
% 51.13/51.03 5494 cancel_semigroup_add(rat) # label(arity_Rat_Orat___Groups_Ocancel__semigroup__add) # label(axiom). [assumption].
% 51.13/51.03 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),B) != hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),C),B) | ti(rat,A) = ti(rat,C). [resolve(5494,a,5487,a)].
% 51.13/51.03 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),B) != hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),C) | ti(rat,B) = ti(rat,C). [resolve(5494,a,5488,a)].
% 51.13/51.03 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),B) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),C),B) | ti(rat,A) != ti(rat,C). [resolve(5494,a,5490,a)].
% 51.13/51.03 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),B) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),C) | ti(rat,B) != ti(rat,C). [resolve(5494,a,5492,a)].
% 51.13/51.03 5495 cancel_semigroup_add(real) # label(arity_RealDef_Oreal___Groups_Ocancel__semigroup__add) # label(axiom). [assumption].
% 51.13/51.03 Derived: hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),B) != hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),C),B) | ti(real,A) = ti(real,C). [resolve(5495,a,5487,a)].
% 51.13/51.03 Derived: hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),B) != hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),C) | ti(real,B) = ti(real,C). [resolve(5495,a,5488,a)].
% 51.13/51.03 Derived: hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),B) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),C),B) | ti(real,A) != ti(real,C). [resolve(5495,a,5490,a)].
% 51.13/51.03 Derived: hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),B) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),C) | ti(real,B) != ti(real,C). [resolve(5495,a,5492,a)].
% 51.13/51.03 5496 cancel_semigroup_add(complex) # label(arity_Complex_Ocomplex___Groups_Ocancel__semigroup__add) # label(axiom). [assumption].
% 51.13/51.03 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),A),B) != hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),C),B) | ti(complex,A) = ti(complex,C). [resolve(5496,a,5487,a)].
% 51.13/51.03 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),A),B) != hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),A),C) | ti(complex,B) = ti(complex,C). [resolve(5496,a,5488,a)].
% 51.13/51.03 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),A),B) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),C),B) | ti(complex,A) != ti(complex,C). [resolve(5496,a,5490,a)].
% 51.13/51.03 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),A),B) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),A),C) | ti(complex,B) != ti(complex,C). [resolve(5496,a,5492,a)].
% 51.13/51.03 5497 cancel_semigroup_add(code_code_numeral) # label(arity_Code__Numeral_Ocode__numeral___Groups_Ocancel__semigroup__add) # label(axiom). [assumption].
% 51.13/51.03 Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),A),B) != hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),C),B) | ti(code_code_numeral,A) = ti(code_code_numeral,C). [resolve(5497,a,5487,a)].
% 54.43/54.38 Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),A),B) != hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),A),C) | ti(code_code_numeral,B) = ti(code_code_numeral,C). [resolve(5497,a,5488,a)].
% 54.43/54.38 Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),A),B) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),C),B) | ti(code_code_numeral,A) != ti(code_code_numeral,C). [resolve(5497,a,5490,a)].
% 54.43/54.38 Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),A),B) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),A),C) | ti(code_code_numeral,B) != ti(code_code_numeral,C). [resolve(5497,a,5492,a)].
% 54.43/54.38 5498 cancel_semigroup_add(quickcheck_code_int) # label(arity_Quickcheck__Narrowing_Ocode__int___Groups_Ocancel__semigroup__add) # label(axiom). [assumption].
% 54.43/54.38 Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),A),B) != hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),C),B) | ti(quickcheck_code_int,A) = ti(quickcheck_code_int,C). [resolve(5498,a,5487,a)].
% 54.43/54.38 Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),A),B) != hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),A),C) | ti(quickcheck_code_int,B) = ti(quickcheck_code_int,C). [resolve(5498,a,5488,a)].
% 54.43/54.38 Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),A),B) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),C),B) | ti(quickcheck_code_int,A) != ti(quickcheck_code_int,C). [resolve(5498,a,5490,a)].
% 54.43/54.38 Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),A),B) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),A),C) | ti(quickcheck_code_int,B) != ti(quickcheck_code_int,C). [resolve(5498,a,5492,a)].
% 54.43/54.38 5499 sgn_div_norm(real) # label(arity_RealDef_Oreal___RealVector_Osgn__div__norm) # label(axiom). [assumption].
% 54.43/54.38 5500 -sgn_div_norm(A) | sgn_sgn(A) = ti(fun(A,A),sgn_sgn(A)) # label(tsy_c_Groups_Osgn__class_Osgn_0_res) # label(axiom). [clausify(32)].
% 54.43/54.38 5501 -sgn_div_norm(A) | norm_norm(A) = ti(fun(A,real),norm_norm(A)) # label(tsy_c_RealVector_Onorm__class_Onorm_0_res) # label(axiom). [clausify(93)].
% 54.43/54.38 5502 -sgn_div_norm(A) | scaleR_scaleR(A) = ti(fun(real,fun(A,A)),scaleR_scaleR(A)) # label(tsy_c_RealVector_OscaleR__class_OscaleR_0_res) # label(axiom). [clausify(96)].
% 54.43/54.38 5503 -sgn_div_norm(A) | hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),hAPP(real,real,inverse_inverse(real),hAPP(A,real,norm_norm(A),B))),B) = hAPP(A,A,sgn_sgn(A),B) # label(fact_4732_sgn__div__norm) # label(axiom). [clausify(4658)].
% 54.43/54.38 Derived: sgn_sgn(real) = ti(fun(real,real),sgn_sgn(real)). [resolve(5499,a,5500,a)].
% 54.43/54.38 Derived: norm_norm(real) = ti(fun(real,real),norm_norm(real)). [resolve(5499,a,5501,a)].
% 54.43/54.38 Derived: scaleR_scaleR(real) = ti(fun(real,fun(real,real)),scaleR_scaleR(real)). [resolve(5499,a,5502,a)].
% 58.03/57.98 Derived: hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),hAPP(real,real,inverse_inverse(real),hAPP(real,real,norm_norm(real),A))),A) = hAPP(real,real,sgn_sgn(real),A). [resolve(5499,a,5503,a)].
% 58.03/57.98 5504 sgn_div_norm(complex) # label(arity_Complex_Ocomplex___RealVector_Osgn__div__norm) # label(axiom). [assumption].
% 58.03/57.98 Derived: sgn_sgn(complex) = ti(fun(complex,complex),sgn_sgn(complex)). [resolve(5504,a,5500,a)].
% 58.03/57.98 Derived: norm_norm(complex) = ti(fun(complex,real),norm_norm(complex)). [resolve(5504,a,5501,a)].
% 58.03/57.98 Derived: scaleR_scaleR(complex) = ti(fun(real,fun(complex,complex)),scaleR_scaleR(complex)). [resolve(5504,a,5502,a)].
% 58.03/57.98 Derived: hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),hAPP(real,real,inverse_inverse(real),hAPP(complex,real,norm_norm(complex),A))),A) = hAPP(complex,complex,sgn_sgn(complex),A). [resolve(5504,a,5503,a)].
% 58.03/57.98 5505 sgn_if(int) # label(arity_Int_Oint___Groups_Osgn__if) # label(axiom). [assumption].
% 58.03/57.98 5506 -sgn_if(A) | sgn_sgn(A) = ti(fun(A,A),sgn_sgn(A)) # label(tsy_c_Groups_Osgn__class_Osgn_1_res) # label(axiom). [clausify(33)].
% 58.03/57.98 5507 -sgn_if(A) | hAPP(A,A,sgn_sgn(A),zero_zero(A)) = zero_zero(A) # label(fact_2067_sgn0) # label(axiom). [clausify(2095)].
% 58.03/57.98 5508 -sgn_if(A) | zero_zero(A) != ti(A,B) | hAPP(A,A,sgn_sgn(A),B) = zero_zero(A) # label(fact_2127_sgn__if) # label(axiom). [clausify(2153)].
% 58.03/57.98 5509 -sgn_if(A) | zero_zero(A) = ti(A,B) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | hAPP(A,A,sgn_sgn(A),B) = one_one(A) # label(fact_2127_sgn__if) # label(axiom). [clausify(2153)].
% 58.03/57.98 5510 -sgn_if(A) | zero_zero(A) = ti(A,B) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | hAPP(A,A,uminus_uminus(A),one_one(A)) = hAPP(A,A,sgn_sgn(A),B) # label(fact_2127_sgn__if) # label(axiom). [clausify(2153)].
% 58.03/57.98 Derived: sgn_sgn(int) = ti(fun(int,int),sgn_sgn(int)). [resolve(5505,a,5506,a)].
% 58.03/57.98 Derived: hAPP(int,int,sgn_sgn(int),zero_zero(int)) = zero_zero(int). [resolve(5505,a,5507,a)].
% 58.03/57.98 Derived: zero_zero(int) != ti(int,A) | hAPP(int,int,sgn_sgn(int),A) = zero_zero(int). [resolve(5505,a,5508,a)].
% 58.03/57.98 Derived: zero_zero(int) = ti(int,A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A)) | hAPP(int,int,sgn_sgn(int),A) = one_one(int). [resolve(5505,a,5509,a)].
% 58.03/57.98 Derived: zero_zero(int) = ti(int,A) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A)) | hAPP(int,int,uminus_uminus(int),one_one(int)) = hAPP(int,int,sgn_sgn(int),A). [resolve(5505,a,5510,a)].
% 58.03/57.98 5511 sgn_if(rat) # label(arity_Rat_Orat___Groups_Osgn__if) # label(axiom). [assumption].
% 58.03/57.98 Derived: sgn_sgn(rat) = ti(fun(rat,rat),sgn_sgn(rat)). [resolve(5511,a,5506,a)].
% 58.03/57.98 Derived: hAPP(rat,rat,sgn_sgn(rat),zero_zero(rat)) = zero_zero(rat). [resolve(5511,a,5507,a)].
% 58.03/57.98 Derived: zero_zero(rat) != ti(rat,A) | hAPP(rat,rat,sgn_sgn(rat),A) = zero_zero(rat). [resolve(5511,a,5508,a)].
% 58.03/57.98 Derived: zero_zero(rat) = ti(rat,A) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)) | hAPP(rat,rat,sgn_sgn(rat),A) = one_one(rat). [resolve(5511,a,5509,a)].
% 58.03/57.98 Derived: zero_zero(rat) = ti(rat,A) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)) | hAPP(rat,rat,uminus_uminus(rat),one_one(rat)) = hAPP(rat,rat,sgn_sgn(rat),A). [resolve(5511,a,5510,a)].
% 58.03/57.98 5512 sgn_if(real) # label(arity_RealDef_Oreal___Groups_Osgn__if) # label(axiom). [assumption].
% 58.03/57.98 Derived: hAPP(real,real,sgn_sgn(real),zero_zero(real)) = zero_zero(real). [resolve(5512,a,5507,a)].
% 58.03/57.98 Derived: zero_zero(real) != ti(real,A) | hAPP(real,real,sgn_sgn(real),A) = zero_zero(real). [resolve(5512,a,5508,a)].
% 58.03/57.98 Derived: zero_zero(real) = ti(real,A) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | hAPP(real,real,sgn_sgn(real),A) = one_one(real). [resolve(5512,a,5509,a)].
% 58.03/57.98 Derived: zero_zero(real) = ti(real,A) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | hAPP(real,real,uminus_uminus(real),one_one(real)) = hAPP(real,real,sgn_sgn(real),A). [resolve(5512,a,5510,a)].
% 61.38/61.31 5513 mult_zero(int) # label(arity_Int_Oint___Rings_Omult__zero) # label(axiom). [assumption].
% 61.38/61.31 5514 -mult_zero(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(36)].
% 61.38/61.31 5515 -mult_zero(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),zero_zero(A)) = zero_zero(A) # label(fact_259_mult__zero__right) # label(axiom). [clausify(389)].
% 61.38/61.31 5516 -mult_zero(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),zero_zero(A)),B) = zero_zero(A) # label(fact_262_mult__zero__left) # label(axiom). [clausify(392)].
% 61.38/61.31 5517 -power(A) | -mult_zero(A) | -no_zero_divisors(A) | -zero_neq_one(A) | hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(int,nat,number_number_of(nat),C)) != zero_zero(A) | zero_zero(A) = ti(A,B) # label(fact_1393_power__eq__0__iff__number__of) # label(axiom). [clausify(1496)].
% 61.38/61.31 5518 -power(A) | -mult_zero(A) | -no_zero_divisors(A) | -zero_neq_one(A) | hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(int,nat,number_number_of(nat),C)) != zero_zero(A) | hAPP(int,nat,number_number_of(nat),C) != zero_zero(nat) # label(fact_1393_power__eq__0__iff__number__of) # label(axiom). [clausify(1496)].
% 61.38/61.31 5519 -power(A) | -mult_zero(A) | -no_zero_divisors(A) | -zero_neq_one(A) | hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(int,nat,number_number_of(nat),C)) = zero_zero(A) | zero_zero(A) != ti(A,B) | hAPP(int,nat,number_number_of(nat),C) = zero_zero(nat) # label(fact_1393_power__eq__0__iff__number__of) # label(axiom). [clausify(1496)].
% 61.38/61.31 5520 -power(A) | -mult_zero(A) | -no_zero_divisors(A) | -zero_neq_one(A) | hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C) != zero_zero(A) | zero_zero(A) = ti(A,B) # label(fact_1445_power__eq__0__iff) # label(axiom). [clausify(1548)].
% 61.38/61.31 5521 -power(A) | -mult_zero(A) | -no_zero_divisors(A) | -zero_neq_one(A) | hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C) != zero_zero(A) | zero_zero(nat) != C # label(fact_1445_power__eq__0__iff) # label(axiom). [clausify(1548)].
% 61.38/61.31 5522 -power(A) | -mult_zero(A) | -no_zero_divisors(A) | -zero_neq_one(A) | hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C) = zero_zero(A) | zero_zero(A) != ti(A,B) | zero_zero(nat) = C # label(fact_1445_power__eq__0__iff) # label(axiom). [clausify(1548)].
% 61.38/61.31 Derived: times_times(int) = ti(fun(int,fun(int,int)),times_times(int)). [resolve(5513,a,5514,a)].
% 61.38/61.31 Derived: hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),zero_zero(int)) = zero_zero(int). [resolve(5513,a,5515,a)].
% 61.38/61.31 Derived: hAPP(int,int,hAPP(int,fun(int,int),times_times(int),zero_zero(int)),A) = zero_zero(int). [resolve(5513,a,5516,a)].
% 61.38/61.31 Derived: -power(int) | -no_zero_divisors(int) | -zero_neq_one(int) | hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),hAPP(int,nat,number_number_of(nat),B)) != zero_zero(int) | zero_zero(int) = ti(int,A). [resolve(5513,a,5517,b)].
% 61.38/61.31 Derived: -power(int) | -no_zero_divisors(int) | -zero_neq_one(int) | hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),hAPP(int,nat,number_number_of(nat),B)) != zero_zero(int) | hAPP(int,nat,number_number_of(nat),B) != zero_zero(nat). [resolve(5513,a,5518,b)].
% 61.38/61.31 Derived: -power(int) | -no_zero_divisors(int) | -zero_neq_one(int) | hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),hAPP(int,nat,number_number_of(nat),B)) = zero_zero(int) | zero_zero(int) != ti(int,A) | hAPP(int,nat,number_number_of(nat),B) = zero_zero(nat). [resolve(5513,a,5519,b)].
% 61.38/61.31 Derived: -power(int) | -no_zero_divisors(int) | -zero_neq_one(int) | hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),B) != zero_zero(int) | zero_zero(int) = ti(int,A). [resolve(5513,a,5520,b)].
% 61.38/61.31 Derived: -power(int) | -no_zero_divisors(int) | -zero_neq_one(int) | hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),B) != zero_zero(int) | zero_zero(nat) != B. [resolve(5513,a,5521,b)].
% 61.38/61.31 Derived: -power(int) | -no_zero_divisors(int) | -zero_neq_one(int) | hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),B) = zero_zero(int) | zero_zero(int) != ti(int,A) | zero_zero(nat) = B. [resolve(5513,a,5522,b)].
% 61.38/61.31 5523 mult_zero(nat) # label(arity_Nat_Onat___Rings_Omult__zero) # label(axiom). [assumption].
% 61.47/61.37 Derived: times_times(nat) = ti(fun(nat,fun(nat,nat)),times_times(nat)). [resolve(5523,a,5514,a)].
% 61.47/61.37 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),zero_zero(nat)) = zero_zero(nat). [resolve(5523,a,5515,a)].
% 61.47/61.37 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),zero_zero(nat)),A) = zero_zero(nat). [resolve(5523,a,5516,a)].
% 61.47/61.37 Derived: -power(nat) | -no_zero_divisors(nat) | -zero_neq_one(nat) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),hAPP(int,nat,number_number_of(nat),B)) != zero_zero(nat) | zero_zero(nat) = ti(nat,A). [resolve(5523,a,5517,b)].
% 61.47/61.37 Derived: -power(nat) | -no_zero_divisors(nat) | -zero_neq_one(nat) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),hAPP(int,nat,number_number_of(nat),B)) != zero_zero(nat) | hAPP(int,nat,number_number_of(nat),B) != zero_zero(nat). [resolve(5523,a,5518,b)].
% 61.47/61.37 Derived: -power(nat) | -no_zero_divisors(nat) | -zero_neq_one(nat) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),hAPP(int,nat,number_number_of(nat),B)) = zero_zero(nat) | zero_zero(nat) != ti(nat,A) | hAPP(int,nat,number_number_of(nat),B) = zero_zero(nat). [resolve(5523,a,5519,b)].
% 61.47/61.37 Derived: -power(nat) | -no_zero_divisors(nat) | -zero_neq_one(nat) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),B) != zero_zero(nat) | zero_zero(nat) = ti(nat,A). [resolve(5523,a,5520,b)].
% 61.47/61.37 Derived: -power(nat) | -no_zero_divisors(nat) | -zero_neq_one(nat) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),B) != zero_zero(nat) | zero_zero(nat) != B. [resolve(5523,a,5521,b)].
% 61.47/61.37 Derived: -power(nat) | -no_zero_divisors(nat) | -zero_neq_one(nat) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),B) = zero_zero(nat) | zero_zero(nat) != ti(nat,A) | zero_zero(nat) = B. [resolve(5523,a,5522,b)].
% 61.47/61.37 5524 mult_zero(rat) # label(arity_Rat_Orat___Rings_Omult__zero) # label(axiom). [assumption].
% 61.47/61.37 Derived: times_times(rat) = ti(fun(rat,fun(rat,rat)),times_times(rat)). [resolve(5524,a,5514,a)].
% 61.47/61.37 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),zero_zero(rat)) = zero_zero(rat). [resolve(5524,a,5515,a)].
% 61.47/61.37 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),zero_zero(rat)),A) = zero_zero(rat). [resolve(5524,a,5516,a)].
% 61.47/61.37 Derived: -power(rat) | -no_zero_divisors(rat) | -zero_neq_one(rat) | hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),hAPP(int,nat,number_number_of(nat),B)) != zero_zero(rat) | zero_zero(rat) = ti(rat,A). [resolve(5524,a,5517,b)].
% 61.47/61.37 Derived: -power(rat) | -no_zero_divisors(rat) | -zero_neq_one(rat) | hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),hAPP(int,nat,number_number_of(nat),B)) != zero_zero(rat) | hAPP(int,nat,number_number_of(nat),B) != zero_zero(nat). [resolve(5524,a,5518,b)].
% 61.47/61.37 Derived: -power(rat) | -no_zero_divisors(rat) | -zero_neq_one(rat) | hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),hAPP(int,nat,number_number_of(nat),B)) = zero_zero(rat) | zero_zero(rat) != ti(rat,A) | hAPP(int,nat,number_number_of(nat),B) = zero_zero(nat). [resolve(5524,a,5519,b)].
% 61.47/61.37 Derived: -power(rat) | -no_zero_divisors(rat) | -zero_neq_one(rat) | hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),B) != zero_zero(rat) | zero_zero(rat) = ti(rat,A). [resolve(5524,a,5520,b)].
% 61.47/61.37 Derived: -power(rat) | -no_zero_divisors(rat) | -zero_neq_one(rat) | hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),B) != zero_zero(rat) | zero_zero(nat) != B. [resolve(5524,a,5521,b)].
% 61.47/61.37 Derived: -power(rat) | -no_zero_divisors(rat) | -zero_neq_one(rat) | hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),B) = zero_zero(rat) | zero_zero(rat) != ti(rat,A) | zero_zero(nat) = B. [resolve(5524,a,5522,b)].
% 61.47/61.37 5525 mult_zero(real) # label(arity_RealDef_Oreal___Rings_Omult__zero) # label(axiom). [assumption].
% 61.47/61.37 Derived: times_times(real) = ti(fun(real,fun(real,real)),times_times(real)). [resolve(5525,a,5514,a)].
% 61.47/61.37 Derived: hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),zero_zero(real)) = zero_zero(real). [resolve(5525,a,5515,a)].
% 61.47/61.37 Derived: hAPP(real,real,hAPP(real,fun(real,real),times_times(real),zero_zero(real)),A) = zero_zero(real). [resolve(5525,a,5516,a)].
% 61.50/61.41 Derived: -power(real) | -no_zero_divisors(real) | -zero_neq_one(real) | hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),hAPP(int,nat,number_number_of(nat),B)) != zero_zero(real) | zero_zero(real) = ti(real,A). [resolve(5525,a,5517,b)].
% 61.50/61.41 Derived: -power(real) | -no_zero_divisors(real) | -zero_neq_one(real) | hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),hAPP(int,nat,number_number_of(nat),B)) != zero_zero(real) | hAPP(int,nat,number_number_of(nat),B) != zero_zero(nat). [resolve(5525,a,5518,b)].
% 61.50/61.41 Derived: -power(real) | -no_zero_divisors(real) | -zero_neq_one(real) | hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),hAPP(int,nat,number_number_of(nat),B)) = zero_zero(real) | zero_zero(real) != ti(real,A) | hAPP(int,nat,number_number_of(nat),B) = zero_zero(nat). [resolve(5525,a,5519,b)].
% 61.50/61.41 Derived: -power(real) | -no_zero_divisors(real) | -zero_neq_one(real) | hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),B) != zero_zero(real) | zero_zero(real) = ti(real,A). [resolve(5525,a,5520,b)].
% 61.50/61.41 Derived: -power(real) | -no_zero_divisors(real) | -zero_neq_one(real) | hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),B) != zero_zero(real) | zero_zero(nat) != B. [resolve(5525,a,5521,b)].
% 61.50/61.41 Derived: -power(real) | -no_zero_divisors(real) | -zero_neq_one(real) | hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),B) = zero_zero(real) | zero_zero(real) != ti(real,A) | zero_zero(nat) = B. [resolve(5525,a,5522,b)].
% 61.50/61.41 5526 mult_zero(complex) # label(arity_Complex_Ocomplex___Rings_Omult__zero) # label(axiom). [assumption].
% 61.50/61.41 Derived: times_times(complex) = ti(fun(complex,fun(complex,complex)),times_times(complex)). [resolve(5526,a,5514,a)].
% 61.50/61.41 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),zero_zero(complex)) = zero_zero(complex). [resolve(5526,a,5515,a)].
% 61.50/61.41 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),zero_zero(complex)),A) = zero_zero(complex). [resolve(5526,a,5516,a)].
% 61.50/61.41 Derived: -power(complex) | -no_zero_divisors(complex) | -zero_neq_one(complex) | hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),A),hAPP(int,nat,number_number_of(nat),B)) != zero_zero(complex) | zero_zero(complex) = ti(complex,A). [resolve(5526,a,5517,b)].
% 61.50/61.41 Derived: -power(complex) | -no_zero_divisors(complex) | -zero_neq_one(complex) | hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),A),hAPP(int,nat,number_number_of(nat),B)) != zero_zero(complex) | hAPP(int,nat,number_number_of(nat),B) != zero_zero(nat). [resolve(5526,a,5518,b)].
% 61.50/61.41 Derived: -power(complex) | -no_zero_divisors(complex) | -zero_neq_one(complex) | hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),A),hAPP(int,nat,number_number_of(nat),B)) = zero_zero(complex) | zero_zero(complex) != ti(complex,A) | hAPP(int,nat,number_number_of(nat),B) = zero_zero(nat). [resolve(5526,a,5519,b)].
% 61.50/61.41 Derived: -power(complex) | -no_zero_divisors(complex) | -zero_neq_one(complex) | hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),A),B) != zero_zero(complex) | zero_zero(complex) = ti(complex,A). [resolve(5526,a,5520,b)].
% 61.50/61.41 Derived: -power(complex) | -no_zero_divisors(complex) | -zero_neq_one(complex) | hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),A),B) != zero_zero(complex) | zero_zero(nat) != B. [resolve(5526,a,5521,b)].
% 61.50/61.41 Derived: -power(complex) | -no_zero_divisors(complex) | -zero_neq_one(complex) | hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),A),B) = zero_zero(complex) | zero_zero(complex) != ti(complex,A) | zero_zero(nat) = B. [resolve(5526,a,5522,b)].
% 61.50/61.41 5527 mult_zero(code_code_numeral) # label(arity_Code__Numeral_Ocode__numeral___Rings_Omult__zero) # label(axiom). [assumption].
% 61.50/61.41 Derived: times_times(code_code_numeral) = ti(fun(code_code_numeral,fun(code_code_numeral,code_code_numeral)),times_times(code_code_numeral)). [resolve(5527,a,5514,a)].
% 61.50/61.41 Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),zero_zero(code_code_numeral)) = zero_zero(code_code_numeral). [resolve(5527,a,5515,a)].
% 61.50/61.43 Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),zero_zero(code_code_numeral)),A) = zero_zero(code_code_numeral). [resolve(5527,a,5516,a)].
% 61.50/61.43 Derived: -power(code_code_numeral) | -no_zero_divisors(code_code_numeral) | -zero_neq_one(code_code_numeral) | hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A),hAPP(int,nat,number_number_of(nat),B)) != zero_zero(code_code_numeral) | zero_zero(code_code_numeral) = ti(code_code_numeral,A). [resolve(5527,a,5517,b)].
% 61.50/61.43 Derived: -power(code_code_numeral) | -no_zero_divisors(code_code_numeral) | -zero_neq_one(code_code_numeral) | hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A),hAPP(int,nat,number_number_of(nat),B)) != zero_zero(code_code_numeral) | hAPP(int,nat,number_number_of(nat),B) != zero_zero(nat). [resolve(5527,a,5518,b)].
% 61.50/61.43 Derived: -power(code_code_numeral) | -no_zero_divisors(code_code_numeral) | -zero_neq_one(code_code_numeral) | hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A),hAPP(int,nat,number_number_of(nat),B)) = zero_zero(code_code_numeral) | zero_zero(code_code_numeral) != ti(code_code_numeral,A) | hAPP(int,nat,number_number_of(nat),B) = zero_zero(nat). [resolve(5527,a,5519,b)].
% 61.50/61.43 Derived: -power(code_code_numeral) | -no_zero_divisors(code_code_numeral) | -zero_neq_one(code_code_numeral) | hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A),B) != zero_zero(code_code_numeral) | zero_zero(code_code_numeral) = ti(code_code_numeral,A). [resolve(5527,a,5520,b)].
% 61.50/61.43 Derived: -power(code_code_numeral) | -no_zero_divisors(code_code_numeral) | -zero_neq_one(code_code_numeral) | hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A),B) != zero_zero(code_code_numeral) | zero_zero(nat) != B. [resolve(5527,a,5521,b)].
% 61.50/61.43 Derived: -power(code_code_numeral) | -no_zero_divisors(code_code_numeral) | -zero_neq_one(code_code_numeral) | hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A),B) = zero_zero(code_code_numeral) | zero_zero(code_code_numeral) != ti(code_code_numeral,A) | zero_zero(nat) = B. [resolve(5527,a,5522,b)].
% 61.50/61.43 5528 mult_zero(quickcheck_code_int) # label(arity_Quickcheck__Narrowing_Ocode__int___Rings_Omult__zero) # label(axiom). [assumption].
% 61.50/61.43 Derived: times_times(quickcheck_code_int) = ti(fun(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int)),times_times(quickcheck_code_int)). [resolve(5528,a,5514,a)].
% 61.50/61.43 Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),zero_zero(quickcheck_code_int)) = zero_zero(quickcheck_code_int). [resolve(5528,a,5515,a)].
% 61.50/61.43 Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),zero_zero(quickcheck_code_int)),A) = zero_zero(quickcheck_code_int). [resolve(5528,a,5516,a)].
% 61.50/61.43 Derived: -power(quickcheck_code_int) | -no_zero_divisors(quickcheck_code_int) | -zero_neq_one(quickcheck_code_int) | hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A),hAPP(int,nat,number_number_of(nat),B)) != zero_zero(quickcheck_code_int) | zero_zero(quickcheck_code_int) = ti(quickcheck_code_int,A). [resolve(5528,a,5517,b)].
% 61.50/61.43 Derived: -power(quickcheck_code_int) | -no_zero_divisors(quickcheck_code_int) | -zero_neq_one(quickcheck_code_int) | hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A),hAPP(int,nat,number_number_of(nat),B)) != zero_zero(quickcheck_code_int) | hAPP(int,nat,number_number_of(nat),B) != zero_zero(nat). [resolve(5528,a,5518,b)].
% 64.78/64.75 Derived: -power(quickcheck_code_int) | -no_zero_divisors(quickcheck_code_int) | -zero_neq_one(quickcheck_code_int) | hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A),hAPP(int,nat,number_number_of(nat),B)) = zero_zero(quickcheck_code_int) | zero_zero(quickcheck_code_int) != ti(quickcheck_code_int,A) | hAPP(int,nat,number_number_of(nat),B) = zero_zero(nat). [resolve(5528,a,5519,b)].
% 64.78/64.75 Derived: -power(quickcheck_code_int) | -no_zero_divisors(quickcheck_code_int) | -zero_neq_one(quickcheck_code_int) | hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A),B) != zero_zero(quickcheck_code_int) | zero_zero(quickcheck_code_int) = ti(quickcheck_code_int,A). [resolve(5528,a,5520,b)].
% 64.78/64.75 Derived: -power(quickcheck_code_int) | -no_zero_divisors(quickcheck_code_int) | -zero_neq_one(quickcheck_code_int) | hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A),B) != zero_zero(quickcheck_code_int) | zero_zero(nat) != B. [resolve(5528,a,5521,b)].
% 64.78/64.75 Derived: -power(quickcheck_code_int) | -no_zero_divisors(quickcheck_code_int) | -zero_neq_one(quickcheck_code_int) | hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A),B) = zero_zero(quickcheck_code_int) | zero_zero(quickcheck_code_int) != ti(quickcheck_code_int,A) | zero_zero(nat) = B. [resolve(5528,a,5522,b)].
% 64.78/64.75 5529 semiring(int) # label(arity_Int_Oint___Rings_Osemiring) # label(axiom). [assumption].
% 64.78/64.75 5530 -semiring(A) | times_times(A) = ti(fun(A,fun(A,A)),times_times(A)) # label(tsy_c_Groups_Otimes__class_Otimes_4_res) # label(axiom). [clausify(38)].
% 64.78/64.75 5531 -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_25_combine__common__factor) # label(axiom). [clausify(155)].
% 64.78/64.75 5532 -number(A) | -semiring(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(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),hAPP(int,A,number_number_of(A),B)),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),B)),D)) # label(fact_141_right__distrib__number__of) # label(axiom). [clausify(271)].
% 64.78/64.75 5533 -number(A) | -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)),hAPP(int,A,number_number_of(A),D)) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(int,A,number_number_of(A),D))),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),hAPP(int,A,number_number_of(A),D))) # label(fact_142_left__distrib__number__of) # label(axiom). [clausify(272)].
% 64.78/64.75 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(5529,a,5531,a)].
% 64.78/64.75 Derived: -number(int) | hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(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),hAPP(int,int,number_number_of(int),A)),B)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),A)),C)). [resolve(5529,a,5532,b)].
% 64.78/64.75 Derived: -number(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)),hAPP(int,int,number_number_of(int),C)) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),hAPP(int,int,number_number_of(int),C))),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),hAPP(int,int,number_number_of(int),C))). [resolve(5529,a,5533,b)].
% 64.90/64.83 5534 semiring(nat) # label(arity_Nat_Onat___Rings_Osemiring) # label(axiom). [assumption].
% 64.90/64.83 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(5534,a,5531,a)].
% 64.90/64.83 Derived: -number(nat) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(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),hAPP(int,nat,number_number_of(nat),A)),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),A)),C)). [resolve(5534,a,5532,b)].
% 64.90/64.83 Derived: -number(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)),hAPP(int,nat,number_number_of(nat),C)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),hAPP(int,nat,number_number_of(nat),C))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),hAPP(int,nat,number_number_of(nat),C))). [resolve(5534,a,5533,b)].
% 64.90/64.83 5535 semiring(rat) # label(arity_Rat_Orat___Rings_Osemiring) # label(axiom). [assumption].
% 64.90/64.83 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),B)),C)),D) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),C)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),B),C)),D)). [resolve(5535,a,5531,a)].
% 64.90/64.83 Derived: -number(rat) | hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(int,rat,number_number_of(rat),A)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),B),C)) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(int,rat,number_number_of(rat),A)),B)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(int,rat,number_number_of(rat),A)),C)). [resolve(5535,a,5532,b)].
% 64.90/64.83 Derived: -number(rat) | hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),B)),hAPP(int,rat,number_number_of(rat),C)) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),hAPP(int,rat,number_number_of(rat),C))),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),B),hAPP(int,rat,number_number_of(rat),C))). [resolve(5535,a,5533,b)].
% 64.90/64.83 5536 semiring(real) # label(arity_RealDef_Oreal___Rings_Osemiring) # label(axiom). [assumption].
% 64.90/64.83 Derived: hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),B)),C)),D) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),C)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),C)),D)). [resolve(5536,a,5531,a)].
% 64.90/64.83 Derived: -number(real) | hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),A)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),B),C)) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),A)),B)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),A)),C)). [resolve(5536,a,5532,b)].
% 64.93/64.87 Derived: -number(real) | hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),B)),hAPP(int,real,number_number_of(real),C)) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),hAPP(int,real,number_number_of(real),C))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),hAPP(int,real,number_number_of(real),C))). [resolve(5536,a,5533,b)].
% 64.93/64.87 5537 semiring(complex) # label(arity_Complex_Ocomplex___Rings_Osemiring) # label(axiom). [assumption].
% 64.93/64.87 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),A),B)),C)),D) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),C)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),B),C)),D)). [resolve(5537,a,5531,a)].
% 64.93/64.87 Derived: -number(complex) | hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(int,complex,number_number_of(complex),A)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),B),C)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(int,complex,number_number_of(complex),A)),B)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(int,complex,number_number_of(complex),A)),C)). [resolve(5537,a,5532,b)].
% 64.93/64.87 Derived: -number(complex) | hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),A),B)),hAPP(int,complex,number_number_of(complex),C)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),hAPP(int,complex,number_number_of(complex),C))),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),B),hAPP(int,complex,number_number_of(complex),C))). [resolve(5537,a,5533,b)].
% 64.93/64.87 5538 semiring(code_code_numeral) # label(arity_Code__Numeral_Ocode__numeral___Rings_Osemiring) # label(axiom). [assumption].
% 64.93/64.87 Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),A),B)),C)),D) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),C)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),B),C)),D)). [resolve(5538,a,5531,a)].
% 64.93/64.87 Derived: -number(code_code_numeral) | hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),A)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),B),C)) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),A)),B)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),A)),C)). [resolve(5538,a,5532,b)].
% 64.93/64.88 Derived: -number(code_code_numeral) | hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),A),B)),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),C)) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),C))),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),B),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),C))). [resolve(5538,a,5533,b)].
% 64.93/64.88 5539 semiring(quickcheck_code_int) # label(arity_Quickcheck__Narrowing_Ocode__int___Rings_Osemiring) # label(axiom). [assumption].
% 64.93/64.88 Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),A),B)),C)),D) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),C)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),B),C)),D)). [resolve(5539,a,5531,a)].
% 64.93/64.88 Derived: -number(quickcheck_code_int) | hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),A)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),B),C)) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),A)),B)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),A)),C)). [resolve(5539,a,5532,b)].
% 64.93/64.88 Derived: -number(quickcheck_code_int) | hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),A),B)),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),C)) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),C))),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),B),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),C))). [resolve(5539,a,5533,b)].
% 68.41/68.31 5540 ab_semigroup_mult(int) # label(arity_Int_Oint___Groups_Oab__semigroup__mult) # label(axiom). [assumption].
% 68.41/68.31 5541 -ab_semigroup_mult(A) | times_times(A) = ti(fun(A,fun(A,A)),times_times(A)) # label(tsy_c_Groups_Otimes__class_Otimes_5_res) # label(axiom). [clausify(39)].
% 68.41/68.31 5542 -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_12_ab__semigroup__mult__class_Omult__ac_I1_J) # label(axiom). [clausify(142)].
% 68.41/68.31 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(5540,a,5542,a)].
% 68.41/68.31 5543 ab_semigroup_mult(nat) # label(arity_Nat_Onat___Groups_Oab__semigroup__mult) # label(axiom). [assumption].
% 68.41/68.31 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(5543,a,5542,a)].
% 68.41/68.31 5544 ab_semigroup_mult(rat) # label(arity_Rat_Orat___Groups_Oab__semigroup__mult) # label(axiom). [assumption].
% 68.41/68.31 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B)),C) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),B),C)). [resolve(5544,a,5542,a)].
% 68.41/68.31 5545 ab_semigroup_mult(real) # label(arity_RealDef_Oreal___Groups_Oab__semigroup__mult) # label(axiom). [assumption].
% 68.41/68.31 Derived: hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),C) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),C)). [resolve(5545,a,5542,a)].
% 68.41/68.31 5546 ab_semigroup_mult(complex) # label(arity_Complex_Ocomplex___Groups_Oab__semigroup__mult) # label(axiom). [assumption].
% 68.41/68.31 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),B)),C) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),B),C)). [resolve(5546,a,5542,a)].
% 68.41/68.31 5547 ab_semigroup_mult(code_code_numeral) # label(arity_Code__Numeral_Ocode__numeral___Groups_Oab__semigroup__mult) # label(axiom). [assumption].
% 68.41/68.31 Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),B)),C) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),B),C)). [resolve(5547,a,5542,a)].
% 68.41/68.31 5548 ab_semigroup_mult(quickcheck_code_int) # label(arity_Quickcheck__Narrowing_Ocode__int___Groups_Oab__semigroup__mult) # label(axiom). [assumption].
% 68.41/68.31 Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),B)),C) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),B),C)). [resolve(5548,a,5542,a)].
% 71.86/71.84 5549 zero(int) # label(arity_Int_Oint___Groups_Ozero) # label(axiom). [assumption].
% 71.86/71.84 5550 -zero(A) | zero_zero(A) = ti(A,zero_zero(A)) # label(tsy_c_Groups_Ozero__class_Ozero_res) # label(axiom). [clausify(41)].
% 71.86/71.84 5551 -zero(A) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),B)) | hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),inverse_divide(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(A,fun(nat,real),hAPP(fun(nat,fun(A,real)),fun(A,fun(nat,real)),combc(nat,A,real),C),zero_zero(A)))),hAPP(real,fun(nat,real),power_power(real),zero_zero(real))))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),fact_fact(nat)))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),B))),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(A,real,hAPP(nat,fun(A,real),C,B),zero_zero(A))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),zero_zero(real)),B))),hAPP(nat,real,real_1(nat),hAPP(nat,nat,fact_fact(nat),B)))) = hAPP(A,real,hAPP(nat,fun(A,real),C,zero_zero(nat)),zero_zero(A)) # label(fact_4236_Maclaurin__bi__le__lemma) # label(axiom). [clausify(4168)].
% 71.86/71.84 5552 -real_n2089651433ebra_1(A) | -zero(B) | -metric_space(B) | zero_zero(B) = ti(B,C) | -hBOOL(hAPP(filter(A),bool,hAPP(B,fun(filter(A),bool),hAPP(fun(A,B),fun(B,fun(filter(A),bool)),tendsto(A,B),hAPP(B,fun(A,B),combk(B,A),C)),zero_zero(B)),hAPP(A,filter(A),at(A),D))) # label(fact_4551_LIM__not__zero) # label(axiom). [clausify(4478)].
% 71.86/71.84 Derived: zero_zero(int) = ti(int,zero_zero(int)). [resolve(5549,a,5550,a)].
% 71.86/71.84 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A)) | hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),inverse_divide(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(int,fun(nat,real),hAPP(fun(nat,fun(int,real)),fun(int,fun(nat,real)),combc(nat,int,real),B),zero_zero(int)))),hAPP(real,fun(nat,real),power_power(real),zero_zero(real))))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),fact_fact(nat)))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),A))),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,hAPP(nat,fun(int,real),B,A),zero_zero(int))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),zero_zero(real)),A))),hAPP(nat,real,real_1(nat),hAPP(nat,nat,fact_fact(nat),A)))) = hAPP(int,real,hAPP(nat,fun(int,real),B,zero_zero(nat)),zero_zero(int)). [resolve(5549,a,5551,a)].
% 71.95/71.87 Derived: -real_n2089651433ebra_1(A) | -metric_space(int) | zero_zero(int) = ti(int,B) | -hBOOL(hAPP(filter(A),bool,hAPP(int,fun(filter(A),bool),hAPP(fun(A,int),fun(int,fun(filter(A),bool)),tendsto(A,int),hAPP(int,fun(A,int),combk(int,A),B)),zero_zero(int)),hAPP(A,filter(A),at(A),C))). [resolve(5549,a,5552,b)].
% 71.95/71.87 5553 zero(nat) # label(arity_Nat_Onat___Groups_Ozero) # label(axiom). [assumption].
% 71.95/71.87 Derived: zero_zero(nat) = ti(nat,zero_zero(nat)). [resolve(5553,a,5550,a)].
% 71.95/71.87 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A)) | hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),inverse_divide(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(nat,fun(nat,real),hAPP(fun(nat,fun(nat,real)),fun(nat,fun(nat,real)),combc(nat,nat,real),B),zero_zero(nat)))),hAPP(real,fun(nat,real),power_power(real),zero_zero(real))))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),fact_fact(nat)))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),A))),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,hAPP(nat,fun(nat,real),B,A),zero_zero(nat))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),zero_zero(real)),A))),hAPP(nat,real,real_1(nat),hAPP(nat,nat,fact_fact(nat),A)))) = hAPP(nat,real,hAPP(nat,fun(nat,real),B,zero_zero(nat)),zero_zero(nat)). [resolve(5553,a,5551,a)].
% 71.95/71.87 Derived: -real_n2089651433ebra_1(A) | -metric_space(nat) | zero_zero(nat) = ti(nat,B) | -hBOOL(hAPP(filter(A),bool,hAPP(nat,fun(filter(A),bool),hAPP(fun(A,nat),fun(nat,fun(filter(A),bool)),tendsto(A,nat),hAPP(nat,fun(A,nat),combk(nat,A),B)),zero_zero(nat)),hAPP(A,filter(A),at(A),C))). [resolve(5553,a,5552,b)].
% 71.95/71.87 5554 zero(rat) # label(arity_Rat_Orat___Groups_Ozero) # label(axiom). [assumption].
% 71.95/71.87 Derived: zero_zero(rat) = ti(rat,zero_zero(rat)). [resolve(5554,a,5550,a)].
% 71.95/71.87 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A)) | hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),inverse_divide(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(rat,fun(nat,real),hAPP(fun(nat,fun(rat,real)),fun(rat,fun(nat,real)),combc(nat,rat,real),B),zero_zero(rat)))),hAPP(real,fun(nat,real),power_power(real),zero_zero(real))))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),fact_fact(nat)))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),A))),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(rat,real,hAPP(nat,fun(rat,real),B,A),zero_zero(rat))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),zero_zero(real)),A))),hAPP(nat,real,real_1(nat),hAPP(nat,nat,fact_fact(nat),A)))) = hAPP(rat,real,hAPP(nat,fun(rat,real),B,zero_zero(nat)),zero_zero(rat)). [resolve(5554,a,5551,a)].
% 71.99/71.93 Derived: -real_n2089651433ebra_1(A) | -metric_space(rat) | zero_zero(rat) = ti(rat,B) | -hBOOL(hAPP(filter(A),bool,hAPP(rat,fun(filter(A),bool),hAPP(fun(A,rat),fun(rat,fun(filter(A),bool)),tendsto(A,rat),hAPP(rat,fun(A,rat),combk(rat,A),B)),zero_zero(rat)),hAPP(A,filter(A),at(A),C))). [resolve(5554,a,5552,b)].
% 71.99/71.93 5555 zero(real) # label(arity_RealDef_Oreal___Groups_Ozero) # label(axiom). [assumption].
% 71.99/71.93 Derived: zero_zero(real) = ti(real,zero_zero(real)). [resolve(5555,a,5550,a)].
% 71.99/71.93 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A)) | hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),inverse_divide(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(real,fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(real,fun(nat,real)),combc(nat,real,real),B),zero_zero(real)))),hAPP(real,fun(nat,real),power_power(real),zero_zero(real))))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),fact_fact(nat)))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),A))),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(nat,fun(real,real),B,A),zero_zero(real))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),zero_zero(real)),A))),hAPP(nat,real,real_1(nat),hAPP(nat,nat,fact_fact(nat),A)))) = hAPP(real,real,hAPP(nat,fun(real,real),B,zero_zero(nat)),zero_zero(real)). [resolve(5555,a,5551,a)].
% 71.99/71.93 Derived: -real_n2089651433ebra_1(A) | -metric_space(real) | zero_zero(real) = ti(real,B) | -hBOOL(hAPP(filter(A),bool,hAPP(real,fun(filter(A),bool),hAPP(fun(A,real),fun(real,fun(filter(A),bool)),tendsto(A,real),hAPP(real,fun(A,real),combk(real,A),B)),zero_zero(real)),hAPP(A,filter(A),at(A),C))). [resolve(5555,a,5552,b)].
% 71.99/71.93 5556 zero(complex) # label(arity_Complex_Ocomplex___Groups_Ozero) # label(axiom). [assumption].
% 71.99/71.93 Derived: zero_zero(complex) = ti(complex,zero_zero(complex)). [resolve(5556,a,5550,a)].
% 71.99/71.93 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A)) | hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),inverse_divide(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(complex,fun(nat,real),hAPP(fun(nat,fun(complex,real)),fun(complex,fun(nat,real)),combc(nat,complex,real),B),zero_zero(complex)))),hAPP(real,fun(nat,real),power_power(real),zero_zero(real))))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),fact_fact(nat)))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),A))),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(complex,real,hAPP(nat,fun(complex,real),B,A),zero_zero(complex))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),zero_zero(real)),A))),hAPP(nat,real,real_1(nat),hAPP(nat,nat,fact_fact(nat),A)))) = hAPP(complex,real,hAPP(nat,fun(complex,real),B,zero_zero(nat)),zero_zero(complex)). [resolve(5556,a,5551,a)].
% 72.05/71.96 Derived: -real_n2089651433ebra_1(A) | -metric_space(complex) | zero_zero(complex) = ti(complex,B) | -hBOOL(hAPP(filter(A),bool,hAPP(complex,fun(filter(A),bool),hAPP(fun(A,complex),fun(complex,fun(filter(A),bool)),tendsto(A,complex),hAPP(complex,fun(A,complex),combk(complex,A),B)),zero_zero(complex)),hAPP(A,filter(A),at(A),C))). [resolve(5556,a,5552,b)].
% 72.05/71.96 5557 zero(code_code_numeral) # label(arity_Code__Numeral_Ocode__numeral___Groups_Ozero) # label(axiom). [assumption].
% 72.05/71.96 Derived: zero_zero(code_code_numeral) = ti(code_code_numeral,zero_zero(code_code_numeral)). [resolve(5557,a,5550,a)].
% 72.05/71.96 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A)) | hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),inverse_divide(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(code_code_numeral,fun(nat,real),hAPP(fun(nat,fun(code_code_numeral,real)),fun(code_code_numeral,fun(nat,real)),combc(nat,code_code_numeral,real),B),zero_zero(code_code_numeral)))),hAPP(real,fun(nat,real),power_power(real),zero_zero(real))))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),fact_fact(nat)))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),A))),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(code_code_numeral,real,hAPP(nat,fun(code_code_numeral,real),B,A),zero_zero(code_code_numeral))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),zero_zero(real)),A))),hAPP(nat,real,real_1(nat),hAPP(nat,nat,fact_fact(nat),A)))) = hAPP(code_code_numeral,real,hAPP(nat,fun(code_code_numeral,real),B,zero_zero(nat)),zero_zero(code_code_numeral)). [resolve(5557,a,5551,a)].
% 72.05/71.96 Derived: -real_n2089651433ebra_1(A) | -metric_space(code_code_numeral) | zero_zero(code_code_numeral) = ti(code_code_numeral,B) | -hBOOL(hAPP(filter(A),bool,hAPP(code_code_numeral,fun(filter(A),bool),hAPP(fun(A,code_code_numeral),fun(code_code_numeral,fun(filter(A),bool)),tendsto(A,code_code_numeral),hAPP(code_code_numeral,fun(A,code_code_numeral),combk(code_code_numeral,A),B)),zero_zero(code_code_numeral)),hAPP(A,filter(A),at(A),C))). [resolve(5557,a,5552,b)].
% 72.05/71.96 5558 zero(quickcheck_code_int) # label(arity_Quickcheck__Narrowing_Ocode__int___Groups_Ozero) # label(axiom). [assumption].
% 72.05/71.96 Derived: zero_zero(quickcheck_code_int) = ti(quickcheck_code_int,zero_zero(quickcheck_code_int)). [resolve(5558,a,5550,a)].
% 72.05/71.96 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A)) | hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),inverse_divide(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(quickcheck_code_int,fun(nat,real),hAPP(fun(nat,fun(quickcheck_code_int,real)),fun(quickcheck_code_int,fun(nat,real)),combc(nat,quickcheck_code_int,real),B),zero_zero(quickcheck_code_int)))),hAPP(real,fun(nat,real),power_power(real),zero_zero(real))))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),fact_fact(nat)))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),A))),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(quickcheck_code_int,real,hAPP(nat,fun(quickcheck_code_int,real),B,A),zero_zero(quickcheck_code_int))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),zero_zero(real)),A))),hAPP(nat,real,real_1(nat),hAPP(nat,nat,fact_fact(nat),A)))) = hAPP(quickcheck_code_int,real,hAPP(nat,fun(quickcheck_code_int,real),B,zero_zero(nat)),zero_zero(quickcheck_code_int)). [resolve(5558,a,5551,a)].
% 75.36/75.29 Derived: -real_n2089651433ebra_1(A) | -metric_space(quickcheck_code_int) | zero_zero(quickcheck_code_int) = ti(quickcheck_code_int,B) | -hBOOL(hAPP(filter(A),bool,hAPP(quickcheck_code_int,fun(filter(A),bool),hAPP(fun(A,quickcheck_code_int),fun(quickcheck_code_int,fun(filter(A),bool)),tendsto(A,quickcheck_code_int),hAPP(quickcheck_code_int,fun(A,quickcheck_code_int),combk(quickcheck_code_int,A),B)),zero_zero(quickcheck_code_int)),hAPP(A,filter(A),at(A),C))). [resolve(5558,a,5552,b)].
% 75.36/75.29 5559 semiring_1(int) # label(arity_Int_Oint___Rings_Osemiring__1) # label(axiom). [assumption].
% 75.36/75.29 5560 -semiring_1(A) | iszero(A) = ti(fun(A,bool),iszero(A)) # label(tsy_c_Int_Oiszero_res) # label(axiom). [clausify(48)].
% 75.36/75.29 5561 -semiring_1(A) | semiring_1_of_nat(A) = ti(fun(nat,A),semiring_1_of_nat(A)) # label(tsy_c_Nat_Osemiring__1__class_Oof__nat_res) # label(axiom). [clausify(58)].
% 75.36/75.29 5562 -semiring_1(A) | semiri532925092at_aux(A) = ti(fun(fun(A,A),fun(nat,fun(A,A))),semiri532925092at_aux(A)) # label(tsy_c_Nat_Osemiring__1__class_Oof__nat__aux_res) # label(axiom). [clausify(59)].
% 75.36/75.29 5563 -semiring_1(A) | -hBOOL(hAPP(A,bool,iszero(A),B)) | zero_zero(A) = ti(A,B) # label(fact_1682_iszero__def) # label(axiom). [clausify(1755)].
% 75.36/75.29 5564 -semiring_1(A) | hBOOL(hAPP(A,bool,iszero(A),B)) | zero_zero(A) != ti(A,B) # label(fact_1682_iszero__def) # label(axiom). [clausify(1755)].
% 75.36/75.29 5565 -semiring_1(A) | hBOOL(hAPP(A,bool,iszero(A),zero_zero(A))) # label(fact_1683_iszero__0) # label(axiom). [clausify(1756)].
% 75.36/75.29 5566 -semiring_1(A) | -hBOOL(hAPP(A,bool,iszero(A),one_one(A))) # label(fact_1684_not__iszero__1) # label(axiom). [clausify(1757)].
% 75.36/75.29 5567 -semiring_1(A) | hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),zero_zero(A)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = zero_zero(A) # label(fact_1812_zero__power2) # label(axiom). [clausify(1873)].
% 75.36/75.29 5568 -semiring_1(A) | hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),one_one(A)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = one_one(A) # label(fact_1815_one__power2) # label(axiom). [clausify(1876)].
% 75.36/75.29 5569 -semiring_1(A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),B)) | hAPP(nat,A,semiring_1_of_nat(A),hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),B))) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(nat,A,semiring_1_of_nat(A),hAPP(int,nat,nat_1,B))),hAPP(nat,A,semiring_1_of_nat(A),hAPP(int,nat,nat_1,B))) # label(fact_2561_of__nat__double) # label(axiom). [clausify(2564)].
% 75.36/75.29 5570 -semiring_1(A) | hAPP(nat,A,semiring_1_of_nat(A),zero_zero(nat)) = zero_zero(A) # label(fact_2589_of__nat__0) # label(axiom). [clausify(2589)].
% 75.36/75.29 5571 -semiring_1(A) | hAPP(nat,A,semiring_1_of_nat(A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),C)) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(nat,A,semiring_1_of_nat(A),B)),hAPP(nat,A,semiring_1_of_nat(A),C)) # label(fact_2594_of__nat__add) # label(axiom). [clausify(2594)].
% 75.36/75.29 5572 -semiring_1(A) | hAPP(nat,A,semiring_1_of_nat(A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),C)) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(nat,A,semiring_1_of_nat(A),B)),hAPP(nat,A,semiring_1_of_nat(A),C)) # label(fact_2595_of__nat__mult) # label(axiom). [clausify(2595)].
% 75.36/75.29 5573 -semiring_1(A) | hAPP(nat,A,semiring_1_of_nat(A),one_one(nat)) = one_one(A) # label(fact_2596_of__nat__1) # label(axiom). [clausify(2596)].
% 75.36/75.29 5574 -semiring_1(A) | hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),hAPP(nat,A,semiring_1_of_nat(A),B)),C) = hAPP(nat,A,semiring_1_of_nat(A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),B),C)) # label(fact_2601_of__nat__power) # label(axiom). [clausify(2599)].
% 75.36/75.29 5575 -semiring_1(A) | hAPP(nat,A,semiring_1_of_nat(A),hAPP(nat,nat,suc,B)) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),one_one(A)),hAPP(nat,A,semiring_1_of_nat(A),B)) # label(fact_2639_of__nat__Suc) # label(axiom). [clausify(2634)].
% 75.36/75.29 5576 -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_3926_of__nat__setprod) # label(axiom). [clausify(3867)].
% 75.36/75.29 5577 -semiring_1(A) | hAPP(nat,A,semiring_1_of_nat(A),B) = hAPP(A,A,hAPP(nat,fun(A,A),hAPP(fun(A,A),fun(nat,fun(A,A)),semiri532925092at_aux(A),hAPP(A,fun(A,A),hAPP(fun(A,fun(A,A)),fun(A,fun(A,A)),combc(A,A,A),plus_plus(A)),one_one(A))),B),zero_zero(A)) # label(fact_4158_semiring__1__class_Oof__nat__code) # label(axiom). [clausify(4090)].
% 75.36/75.29 5578 -semiring_1(A) | hAPP(A,A,hAPP(nat,fun(A,A),hAPP(fun(A,A),fun(nat,fun(A,A)),semiri532925092at_aux(A),B),zero_zero(nat)),C) = ti(A,C) # label(fact_4160_of__nat__aux_Osimps_I1_J) # label(axiom). [clausify(4092)].
% 75.36/75.29 5579 -semiring_1(A) | hAPP(A,A,hAPP(nat,fun(A,A),hAPP(fun(A,A),fun(nat,fun(A,A)),semiri532925092at_aux(A),B),hAPP(nat,nat,suc,C)),D) = hAPP(A,A,hAPP(nat,fun(A,A),hAPP(fun(A,A),fun(nat,fun(A,A)),semiri532925092at_aux(A),B),C),hAPP(A,A,B,D)) # label(fact_4161_of__nat__aux_Osimps_I2_J) # label(axiom). [clausify(4093)].
% 75.36/75.29 5580 -semiring_1(A) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(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_co1399186613setsum(B,nat),C),D)) # label(fact_4170_of__nat__setsum) # label(axiom). [clausify(4102)].
% 75.36/75.29 5581 -semiring_1(A) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),hAPP(A,fun(B,A),combk(A,B),C)),D) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(nat,A,semiring_1_of_nat(A),hAPP(fun(B,bool),nat,finite_card(B),D))),C) # label(fact_4228_setsum__constant) # label(axiom). [clausify(4160)].
% 75.36/75.29 5582 -ordere779506340up_add(A) | -semiring_1(A) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f597(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(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(nat,A,semiring_1_of_nat(A),hAPP(fun(B,bool),nat,finite_card(B),E))),D))) # label(fact_4296_setsum__bounded) # label(axiom). [clausify(4228)].
% 75.36/75.29 5583 -ordere779506340up_add(A) | -semiring_1(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(B,A,C,f597(B,A,C,D,E))),D)) | 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(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(nat,A,semiring_1_of_nat(A),hAPP(fun(B,bool),nat,finite_card(B),E))),D))) # label(fact_4296_setsum__bounded) # label(axiom). [clausify(4228)].
% 75.41/75.30 Derived: iszero(int) = ti(fun(int,bool),iszero(int)). [resolve(5559,a,5560,a)].
% 75.41/75.30 Derived: semiring_1_of_nat(int) = ti(fun(nat,int),semiring_1_of_nat(int)). [resolve(5559,a,5561,a)].
% 75.41/75.30 Derived: semiri532925092at_aux(int) = ti(fun(fun(int,int),fun(nat,fun(int,int))),semiri532925092at_aux(int)). [resolve(5559,a,5562,a)].
% 75.41/75.30 Derived: -hBOOL(hAPP(int,bool,iszero(int),A)) | zero_zero(int) = ti(int,A). [resolve(5559,a,5563,a)].
% 75.41/75.30 Derived: hBOOL(hAPP(int,bool,iszero(int),A)) | zero_zero(int) != ti(int,A). [resolve(5559,a,5564,a)].
% 75.41/75.30 Derived: hBOOL(hAPP(int,bool,iszero(int),zero_zero(int))). [resolve(5559,a,5565,a)].
% 75.41/75.30 Derived: -hBOOL(hAPP(int,bool,iszero(int),one_one(int))). [resolve(5559,a,5566,a)].
% 75.41/75.30 Derived: hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),zero_zero(int)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = zero_zero(int). [resolve(5559,a,5567,a)].
% 75.41/75.30 Derived: hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),one_one(int)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = one_one(int). [resolve(5559,a,5568,a)].
% 75.41/75.30 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A)) | hAPP(nat,int,semiring_1_of_nat(int),hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),A))) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,semiring_1_of_nat(int),hAPP(int,nat,nat_1,A))),hAPP(nat,int,semiring_1_of_nat(int),hAPP(int,nat,nat_1,A))). [resolve(5559,a,5569,a)].
% 75.41/75.30 Derived: hAPP(nat,int,semiring_1_of_nat(int),zero_zero(nat)) = zero_zero(int). [resolve(5559,a,5570,a)].
% 75.41/75.30 Derived: hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B)) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,semiring_1_of_nat(int),A)),hAPP(nat,int,semiring_1_of_nat(int),B)). [resolve(5559,a,5571,a)].
% 75.41/75.30 Derived: hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),B)) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(nat,int,semiring_1_of_nat(int),A)),hAPP(nat,int,semiring_1_of_nat(int),B)). [resolve(5559,a,5572,a)].
% 75.41/75.30 Derived: hAPP(nat,int,semiring_1_of_nat(int),one_one(nat)) = one_one(int). [resolve(5559,a,5573,a)].
% 75.41/75.30 Derived: hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(nat,int,semiring_1_of_nat(int),A)),B) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),B)). [resolve(5559,a,5574,a)].
% 75.41/75.30 Derived: hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,A)) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),A)). [resolve(5559,a,5575,a)].
% 75.41/75.30 Derived: -comm_monoid_mult(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(5559,a,5576,b)].
% 75.41/75.30 Derived: hAPP(nat,int,semiring_1_of_nat(int),A) = hAPP(int,int,hAPP(nat,fun(int,int),hAPP(fun(int,int),fun(nat,fun(int,int)),semiri532925092at_aux(int),hAPP(int,fun(int,int),hAPP(fun(int,fun(int,int)),fun(int,fun(int,int)),combc(int,int,int),plus_plus(int)),one_one(int))),A),zero_zero(int)). [resolve(5559,a,5577,a)].
% 75.41/75.30 Derived: hAPP(int,int,hAPP(nat,fun(int,int),hAPP(fun(int,int),fun(nat,fun(int,int)),semiri532925092at_aux(int),A),zero_zero(nat)),B) = ti(int,B). [resolve(5559,a,5578,a)].
% 75.41/75.32 Derived: hAPP(int,int,hAPP(nat,fun(int,int),hAPP(fun(int,int),fun(nat,fun(int,int)),semiri532925092at_aux(int),A),hAPP(nat,nat,suc,B)),C) = hAPP(int,int,hAPP(nat,fun(int,int),hAPP(fun(int,int),fun(nat,fun(int,int)),semiri532925092at_aux(int),A),B),hAPP(int,int,A,C)). [resolve(5559,a,5579,a)].
% 75.41/75.32 Derived: hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(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_co1399186613setsum(A,nat),B),C)). [resolve(5559,a,5580,a)].
% 75.41/75.32 Derived: hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),hAPP(int,fun(A,int),combk(int,A),B)),C) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(nat,int,semiring_1_of_nat(int),hAPP(fun(A,bool),nat,finite_card(A),C))),B). [resolve(5559,a,5581,a)].
% 75.41/75.32 Derived: -ordere779506340up_add(int) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f597(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(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(nat,int,semiring_1_of_nat(int),hAPP(fun(A,bool),nat,finite_card(A),D))),C))). [resolve(5559,a,5582,b)].
% 75.41/75.32 Derived: -ordere779506340up_add(int) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(A,int,B,f597(A,int,B,C,D))),C)) | 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(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(nat,int,semiring_1_of_nat(int),hAPP(fun(A,bool),nat,finite_card(A),D))),C))). [resolve(5559,a,5583,b)].
% 75.41/75.32 5584 semiring_1(nat) # label(arity_Nat_Onat___Rings_Osemiring__1) # label(axiom). [assumption].
% 75.41/75.32 Derived: iszero(nat) = ti(fun(nat,bool),iszero(nat)). [resolve(5584,a,5560,a)].
% 75.41/75.32 Derived: semiring_1_of_nat(nat) = ti(fun(nat,nat),semiring_1_of_nat(nat)). [resolve(5584,a,5561,a)].
% 75.41/75.32 Derived: semiri532925092at_aux(nat) = ti(fun(fun(nat,nat),fun(nat,fun(nat,nat))),semiri532925092at_aux(nat)). [resolve(5584,a,5562,a)].
% 75.41/75.32 Derived: -hBOOL(hAPP(nat,bool,iszero(nat),A)) | zero_zero(nat) = ti(nat,A). [resolve(5584,a,5563,a)].
% 75.41/75.32 Derived: hBOOL(hAPP(nat,bool,iszero(nat),A)) | zero_zero(nat) != ti(nat,A). [resolve(5584,a,5564,a)].
% 75.41/75.32 Derived: hBOOL(hAPP(nat,bool,iszero(nat),zero_zero(nat))). [resolve(5584,a,5565,a)].
% 75.41/75.32 Derived: -hBOOL(hAPP(nat,bool,iszero(nat),one_one(nat))). [resolve(5584,a,5566,a)].
% 75.41/75.32 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),zero_zero(nat)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = zero_zero(nat). [resolve(5584,a,5567,a)].
% 75.41/75.32 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),one_one(nat)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = one_one(nat). [resolve(5584,a,5568,a)].
% 75.41/75.32 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A)) | hAPP(nat,nat,semiring_1_of_nat(nat),hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),A))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,semiring_1_of_nat(nat),hAPP(int,nat,nat_1,A))),hAPP(nat,nat,semiring_1_of_nat(nat),hAPP(int,nat,nat_1,A))). [resolve(5584,a,5569,a)].
% 75.41/75.32 Derived: hAPP(nat,nat,semiring_1_of_nat(nat),zero_zero(nat)) = zero_zero(nat). [resolve(5584,a,5570,a)].
% 75.41/75.32 Derived: hAPP(nat,nat,semiring_1_of_nat(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),hAPP(nat,nat,semiring_1_of_nat(nat),A)),hAPP(nat,nat,semiring_1_of_nat(nat),B)). [resolve(5584,a,5571,a)].
% 75.41/75.32 Derived: hAPP(nat,nat,semiring_1_of_nat(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),hAPP(nat,nat,semiring_1_of_nat(nat),A)),hAPP(nat,nat,semiring_1_of_nat(nat),B)). [resolve(5584,a,5572,a)].
% 75.45/75.34 Derived: hAPP(nat,nat,semiring_1_of_nat(nat),one_one(nat)) = one_one(nat). [resolve(5584,a,5573,a)].
% 75.45/75.34 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),hAPP(nat,nat,semiring_1_of_nat(nat),A)),B) = hAPP(nat,nat,semiring_1_of_nat(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),B)). [resolve(5584,a,5574,a)].
% 75.45/75.34 Derived: hAPP(nat,nat,semiring_1_of_nat(nat),hAPP(nat,nat,suc,A)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),hAPP(nat,nat,semiring_1_of_nat(nat),A)). [resolve(5584,a,5575,a)].
% 75.45/75.34 Derived: -comm_monoid_mult(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(5584,a,5576,b)].
% 75.45/75.34 Derived: hAPP(nat,nat,semiring_1_of_nat(nat),A) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),hAPP(fun(nat,nat),fun(nat,fun(nat,nat)),semiri532925092at_aux(nat),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))),A),zero_zero(nat)). [resolve(5584,a,5577,a)].
% 75.45/75.34 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),hAPP(fun(nat,nat),fun(nat,fun(nat,nat)),semiri532925092at_aux(nat),A),zero_zero(nat)),B) = ti(nat,B). [resolve(5584,a,5578,a)].
% 75.45/75.34 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),hAPP(fun(nat,nat),fun(nat,fun(nat,nat)),semiri532925092at_aux(nat),A),hAPP(nat,nat,suc,B)),C) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),hAPP(fun(nat,nat),fun(nat,fun(nat,nat)),semiri532925092at_aux(nat),A),B),hAPP(nat,nat,A,C)). [resolve(5584,a,5579,a)].
% 75.45/75.34 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),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_co1399186613setsum(A,nat),B),C)). [resolve(5584,a,5580,a)].
% 75.45/75.34 Derived: hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),hAPP(nat,fun(A,nat),combk(nat,A),B)),C) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,semiring_1_of_nat(nat),hAPP(fun(A,bool),nat,finite_card(A),C))),B). [resolve(5584,a,5581,a)].
% 75.45/75.34 Derived: -ordere779506340up_add(nat) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f597(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(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,semiring_1_of_nat(nat),hAPP(fun(A,bool),nat,finite_card(A),D))),C))). [resolve(5584,a,5582,b)].
% 75.45/75.34 Derived: -ordere779506340up_add(nat) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(A,nat,B,f597(A,nat,B,C,D))),C)) | 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(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,semiring_1_of_nat(nat),hAPP(fun(A,bool),nat,finite_card(A),D))),C))). [resolve(5584,a,5583,b)].
% 75.45/75.34 5585 semiring_1(rat) # label(arity_Rat_Orat___Rings_Osemiring__1) # label(axiom). [assumption].
% 75.45/75.34 Derived: iszero(rat) = ti(fun(rat,bool),iszero(rat)). [resolve(5585,a,5560,a)].
% 75.45/75.34 Derived: semiring_1_of_nat(rat) = ti(fun(nat,rat),semiring_1_of_nat(rat)). [resolve(5585,a,5561,a)].
% 75.45/75.34 Derived: semiri532925092at_aux(rat) = ti(fun(fun(rat,rat),fun(nat,fun(rat,rat))),semiri532925092at_aux(rat)). [resolve(5585,a,5562,a)].
% 75.45/75.34 Derived: -hBOOL(hAPP(rat,bool,iszero(rat),A)) | zero_zero(rat) = ti(rat,A). [resolve(5585,a,5563,a)].
% 75.45/75.34 Derived: hBOOL(hAPP(rat,bool,iszero(rat),A)) | zero_zero(rat) != ti(rat,A). [resolve(5585,a,5564,a)].
% 75.45/75.34 Derived: hBOOL(hAPP(rat,bool,iszero(rat),zero_zero(rat))). [resolve(5585,a,5565,a)].
% 75.46/75.35 Derived: -hBOOL(hAPP(rat,bool,iszero(rat),one_one(rat))). [resolve(5585,a,5566,a)].
% 75.46/75.35 Derived: hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),zero_zero(rat)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = zero_zero(rat). [resolve(5585,a,5567,a)].
% 75.46/75.35 Derived: hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),one_one(rat)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = one_one(rat). [resolve(5585,a,5568,a)].
% 75.46/75.35 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A)) | hAPP(nat,rat,semiring_1_of_nat(rat),hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),A))) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(nat,rat,semiring_1_of_nat(rat),hAPP(int,nat,nat_1,A))),hAPP(nat,rat,semiring_1_of_nat(rat),hAPP(int,nat,nat_1,A))). [resolve(5585,a,5569,a)].
% 75.46/75.35 Derived: hAPP(nat,rat,semiring_1_of_nat(rat),zero_zero(nat)) = zero_zero(rat). [resolve(5585,a,5570,a)].
% 75.46/75.35 Derived: hAPP(nat,rat,semiring_1_of_nat(rat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B)) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(nat,rat,semiring_1_of_nat(rat),A)),hAPP(nat,rat,semiring_1_of_nat(rat),B)). [resolve(5585,a,5571,a)].
% 75.46/75.35 Derived: hAPP(nat,rat,semiring_1_of_nat(rat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),B)) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(nat,rat,semiring_1_of_nat(rat),A)),hAPP(nat,rat,semiring_1_of_nat(rat),B)). [resolve(5585,a,5572,a)].
% 75.46/75.35 Derived: hAPP(nat,rat,semiring_1_of_nat(rat),one_one(nat)) = one_one(rat). [resolve(5585,a,5573,a)].
% 75.46/75.35 Derived: hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),hAPP(nat,rat,semiring_1_of_nat(rat),A)),B) = hAPP(nat,rat,semiring_1_of_nat(rat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),B)). [resolve(5585,a,5574,a)].
% 75.46/75.35 Derived: hAPP(nat,rat,semiring_1_of_nat(rat),hAPP(nat,nat,suc,A)) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),one_one(rat)),hAPP(nat,rat,semiring_1_of_nat(rat),A)). [resolve(5585,a,5575,a)].
% 75.46/75.35 Derived: -comm_monoid_mult(rat) | hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co302546470etprod(A,rat),hAPP(fun(A,nat),fun(A,rat),hAPP(fun(nat,rat),fun(fun(A,nat),fun(A,rat)),combb(nat,rat,A),semiring_1_of_nat(rat)),B)),C) = hAPP(nat,rat,semiring_1_of_nat(rat),hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),B),C)). [resolve(5585,a,5576,b)].
% 75.46/75.35 Derived: hAPP(nat,rat,semiring_1_of_nat(rat),A) = hAPP(rat,rat,hAPP(nat,fun(rat,rat),hAPP(fun(rat,rat),fun(nat,fun(rat,rat)),semiri532925092at_aux(rat),hAPP(rat,fun(rat,rat),hAPP(fun(rat,fun(rat,rat)),fun(rat,fun(rat,rat)),combc(rat,rat,rat),plus_plus(rat)),one_one(rat))),A),zero_zero(rat)). [resolve(5585,a,5577,a)].
% 75.46/75.35 Derived: hAPP(rat,rat,hAPP(nat,fun(rat,rat),hAPP(fun(rat,rat),fun(nat,fun(rat,rat)),semiri532925092at_aux(rat),A),zero_zero(nat)),B) = ti(rat,B). [resolve(5585,a,5578,a)].
% 75.46/75.35 Derived: hAPP(rat,rat,hAPP(nat,fun(rat,rat),hAPP(fun(rat,rat),fun(nat,fun(rat,rat)),semiri532925092at_aux(rat),A),hAPP(nat,nat,suc,B)),C) = hAPP(rat,rat,hAPP(nat,fun(rat,rat),hAPP(fun(rat,rat),fun(nat,fun(rat,rat)),semiri532925092at_aux(rat),A),B),hAPP(rat,rat,A,C)). [resolve(5585,a,5579,a)].
% 75.46/75.35 Derived: hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),hAPP(fun(A,nat),fun(A,rat),hAPP(fun(nat,rat),fun(fun(A,nat),fun(A,rat)),combb(nat,rat,A),semiring_1_of_nat(rat)),B)),C) = hAPP(nat,rat,semiring_1_of_nat(rat),hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),B),C)). [resolve(5585,a,5580,a)].
% 75.46/75.35 Derived: hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),hAPP(rat,fun(A,rat),combk(rat,A),B)),C) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(nat,rat,semiring_1_of_nat(rat),hAPP(fun(A,bool),nat,finite_card(A),C))),B). [resolve(5585,a,5581,a)].
% 75.46/75.35 Derived: -ordere779506340up_add(rat) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f597(A,rat,B,C,D)),D)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),B),D)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(nat,rat,semiring_1_of_nat(rat),hAPP(fun(A,bool),nat,finite_card(A),D))),C))). [resolve(5585,a,5582,b)].
% 75.46/75.38 Derived: -ordere779506340up_add(rat) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(A,rat,B,f597(A,rat,B,C,D))),C)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),B),D)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(nat,rat,semiring_1_of_nat(rat),hAPP(fun(A,bool),nat,finite_card(A),D))),C))). [resolve(5585,a,5583,b)].
% 75.46/75.38 5586 semiring_1(real) # label(arity_RealDef_Oreal___Rings_Osemiring__1) # label(axiom). [assumption].
% 75.46/75.38 Derived: iszero(real) = ti(fun(real,bool),iszero(real)). [resolve(5586,a,5560,a)].
% 75.46/75.38 Derived: semiring_1_of_nat(real) = ti(fun(nat,real),semiring_1_of_nat(real)). [resolve(5586,a,5561,a)].
% 75.46/75.38 Derived: semiri532925092at_aux(real) = ti(fun(fun(real,real),fun(nat,fun(real,real))),semiri532925092at_aux(real)). [resolve(5586,a,5562,a)].
% 75.46/75.38 Derived: -hBOOL(hAPP(real,bool,iszero(real),A)) | zero_zero(real) = ti(real,A). [resolve(5586,a,5563,a)].
% 75.46/75.38 Derived: hBOOL(hAPP(real,bool,iszero(real),A)) | zero_zero(real) != ti(real,A). [resolve(5586,a,5564,a)].
% 75.46/75.38 Derived: hBOOL(hAPP(real,bool,iszero(real),zero_zero(real))). [resolve(5586,a,5565,a)].
% 75.46/75.38 Derived: -hBOOL(hAPP(real,bool,iszero(real),one_one(real))). [resolve(5586,a,5566,a)].
% 75.46/75.38 Derived: hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),zero_zero(real)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = zero_zero(real). [resolve(5586,a,5567,a)].
% 75.46/75.38 Derived: hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),one_one(real)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = one_one(real). [resolve(5586,a,5568,a)].
% 75.46/75.38 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A)) | hAPP(nat,real,semiring_1_of_nat(real),hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),A))) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,semiring_1_of_nat(real),hAPP(int,nat,nat_1,A))),hAPP(nat,real,semiring_1_of_nat(real),hAPP(int,nat,nat_1,A))). [resolve(5586,a,5569,a)].
% 75.46/75.38 Derived: hAPP(nat,real,semiring_1_of_nat(real),zero_zero(nat)) = zero_zero(real). [resolve(5586,a,5570,a)].
% 75.46/75.38 Derived: hAPP(nat,real,semiring_1_of_nat(real),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B)) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,semiring_1_of_nat(real),A)),hAPP(nat,real,semiring_1_of_nat(real),B)). [resolve(5586,a,5571,a)].
% 75.46/75.38 Derived: hAPP(nat,real,semiring_1_of_nat(real),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),B)) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,semiring_1_of_nat(real),A)),hAPP(nat,real,semiring_1_of_nat(real),B)). [resolve(5586,a,5572,a)].
% 75.46/75.38 Derived: hAPP(nat,real,semiring_1_of_nat(real),one_one(nat)) = one_one(real). [resolve(5586,a,5573,a)].
% 75.46/75.38 Derived: hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(nat,real,semiring_1_of_nat(real),A)),B) = hAPP(nat,real,semiring_1_of_nat(real),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),B)). [resolve(5586,a,5574,a)].
% 75.46/75.38 Derived: hAPP(nat,real,semiring_1_of_nat(real),hAPP(nat,nat,suc,A)) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),one_one(real)),hAPP(nat,real,semiring_1_of_nat(real),A)). [resolve(5586,a,5575,a)].
% 75.46/75.38 Derived: -comm_monoid_mult(real) | hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co302546470etprod(A,real),hAPP(fun(A,nat),fun(A,real),hAPP(fun(nat,real),fun(fun(A,nat),fun(A,real)),combb(nat,real,A),semiring_1_of_nat(real)),B)),C) = hAPP(nat,real,semiring_1_of_nat(real),hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),B),C)). [resolve(5586,a,5576,b)].
% 75.51/75.41 Derived: hAPP(nat,real,semiring_1_of_nat(real),A) = hAPP(real,real,hAPP(nat,fun(real,real),hAPP(fun(real,real),fun(nat,fun(real,real)),semiri532925092at_aux(real),hAPP(real,fun(real,real),hAPP(fun(real,fun(real,real)),fun(real,fun(real,real)),combc(real,real,real),plus_plus(real)),one_one(real))),A),zero_zero(real)). [resolve(5586,a,5577,a)].
% 75.51/75.41 Derived: hAPP(real,real,hAPP(nat,fun(real,real),hAPP(fun(real,real),fun(nat,fun(real,real)),semiri532925092at_aux(real),A),zero_zero(nat)),B) = ti(real,B). [resolve(5586,a,5578,a)].
% 75.51/75.41 Derived: hAPP(real,real,hAPP(nat,fun(real,real),hAPP(fun(real,real),fun(nat,fun(real,real)),semiri532925092at_aux(real),A),hAPP(nat,nat,suc,B)),C) = hAPP(real,real,hAPP(nat,fun(real,real),hAPP(fun(real,real),fun(nat,fun(real,real)),semiri532925092at_aux(real),A),B),hAPP(real,real,A,C)). [resolve(5586,a,5579,a)].
% 75.51/75.41 Derived: hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),hAPP(fun(A,nat),fun(A,real),hAPP(fun(nat,real),fun(fun(A,nat),fun(A,real)),combb(nat,real,A),semiring_1_of_nat(real)),B)),C) = hAPP(nat,real,semiring_1_of_nat(real),hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),B),C)). [resolve(5586,a,5580,a)].
% 75.51/75.41 Derived: hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),hAPP(real,fun(A,real),combk(real,A),B)),C) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,semiring_1_of_nat(real),hAPP(fun(A,bool),nat,finite_card(A),C))),B). [resolve(5586,a,5581,a)].
% 75.51/75.41 Derived: -ordere779506340up_add(real) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f597(A,real,B,C,D)),D)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),B),D)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,semiring_1_of_nat(real),hAPP(fun(A,bool),nat,finite_card(A),D))),C))). [resolve(5586,a,5582,b)].
% 75.51/75.41 Derived: -ordere779506340up_add(real) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(A,real,B,f597(A,real,B,C,D))),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),B),D)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,semiring_1_of_nat(real),hAPP(fun(A,bool),nat,finite_card(A),D))),C))). [resolve(5586,a,5583,b)].
% 75.51/75.41 5587 semiring_1(complex) # label(arity_Complex_Ocomplex___Rings_Osemiring__1) # label(axiom). [assumption].
% 75.51/75.41 Derived: iszero(complex) = ti(fun(complex,bool),iszero(complex)). [resolve(5587,a,5560,a)].
% 75.51/75.41 Derived: semiring_1_of_nat(complex) = ti(fun(nat,complex),semiring_1_of_nat(complex)). [resolve(5587,a,5561,a)].
% 75.51/75.41 Derived: semiri532925092at_aux(complex) = ti(fun(fun(complex,complex),fun(nat,fun(complex,complex))),semiri532925092at_aux(complex)). [resolve(5587,a,5562,a)].
% 75.51/75.41 Derived: -hBOOL(hAPP(complex,bool,iszero(complex),A)) | zero_zero(complex) = ti(complex,A). [resolve(5587,a,5563,a)].
% 75.51/75.41 Derived: hBOOL(hAPP(complex,bool,iszero(complex),A)) | zero_zero(complex) != ti(complex,A). [resolve(5587,a,5564,a)].
% 75.51/75.41 Derived: hBOOL(hAPP(complex,bool,iszero(complex),zero_zero(complex))). [resolve(5587,a,5565,a)].
% 75.51/75.41 Derived: -hBOOL(hAPP(complex,bool,iszero(complex),one_one(complex))). [resolve(5587,a,5566,a)].
% 75.51/75.41 Derived: hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),zero_zero(complex)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = zero_zero(complex). [resolve(5587,a,5567,a)].
% 75.51/75.41 Derived: hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),one_one(complex)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = one_one(complex). [resolve(5587,a,5568,a)].
% 75.51/75.41 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A)) | hAPP(nat,complex,semiring_1_of_nat(complex),hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),A))) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),hAPP(int,nat,nat_1,A))),hAPP(nat,complex,semiring_1_of_nat(complex),hAPP(int,nat,nat_1,A))). [resolve(5587,a,5569,a)].
% 75.51/75.41 Derived: hAPP(nat,complex,semiring_1_of_nat(complex),zero_zero(nat)) = zero_zero(complex). [resolve(5587,a,5570,a)].
% 75.51/75.41 Derived: hAPP(nat,complex,semiring_1_of_nat(complex),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),A)),hAPP(nat,complex,semiring_1_of_nat(complex),B)). [resolve(5587,a,5571,a)].
% 75.51/75.41 Derived: hAPP(nat,complex,semiring_1_of_nat(complex),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),B)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(nat,complex,semiring_1_of_nat(complex),A)),hAPP(nat,complex,semiring_1_of_nat(complex),B)). [resolve(5587,a,5572,a)].
% 75.51/75.41 Derived: hAPP(nat,complex,semiring_1_of_nat(complex),one_one(nat)) = one_one(complex). [resolve(5587,a,5573,a)].
% 75.51/75.41 Derived: hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),hAPP(nat,complex,semiring_1_of_nat(complex),A)),B) = hAPP(nat,complex,semiring_1_of_nat(complex),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),B)). [resolve(5587,a,5574,a)].
% 75.51/75.41 Derived: hAPP(nat,complex,semiring_1_of_nat(complex),hAPP(nat,nat,suc,A)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),one_one(complex)),hAPP(nat,complex,semiring_1_of_nat(complex),A)). [resolve(5587,a,5575,a)].
% 75.51/75.41 Derived: -comm_monoid_mult(complex) | hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co302546470etprod(A,complex),hAPP(fun(A,nat),fun(A,complex),hAPP(fun(nat,complex),fun(fun(A,nat),fun(A,complex)),combb(nat,complex,A),semiring_1_of_nat(complex)),B)),C) = hAPP(nat,complex,semiring_1_of_nat(complex),hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),B),C)). [resolve(5587,a,5576,b)].
% 75.51/75.41 Derived: hAPP(nat,complex,semiring_1_of_nat(complex),A) = hAPP(complex,complex,hAPP(nat,fun(complex,complex),hAPP(fun(complex,complex),fun(nat,fun(complex,complex)),semiri532925092at_aux(complex),hAPP(complex,fun(complex,complex),hAPP(fun(complex,fun(complex,complex)),fun(complex,fun(complex,complex)),combc(complex,complex,complex),plus_plus(complex)),one_one(complex))),A),zero_zero(complex)). [resolve(5587,a,5577,a)].
% 75.51/75.41 Derived: hAPP(complex,complex,hAPP(nat,fun(complex,complex),hAPP(fun(complex,complex),fun(nat,fun(complex,complex)),semiri532925092at_aux(complex),A),zero_zero(nat)),B) = ti(complex,B). [resolve(5587,a,5578,a)].
% 75.51/75.41 Derived: hAPP(complex,complex,hAPP(nat,fun(complex,complex),hAPP(fun(complex,complex),fun(nat,fun(complex,complex)),semiri532925092at_aux(complex),A),hAPP(nat,nat,suc,B)),C) = hAPP(complex,complex,hAPP(nat,fun(complex,complex),hAPP(fun(complex,complex),fun(nat,fun(complex,complex)),semiri532925092at_aux(complex),A),B),hAPP(complex,complex,A,C)). [resolve(5587,a,5579,a)].
% 75.51/75.41 Derived: hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),hAPP(fun(A,nat),fun(A,complex),hAPP(fun(nat,complex),fun(fun(A,nat),fun(A,complex)),combb(nat,complex,A),semiring_1_of_nat(complex)),B)),C) = hAPP(nat,complex,semiring_1_of_nat(complex),hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),B),C)). [resolve(5587,a,5580,a)].
% 75.51/75.41 Derived: hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),hAPP(complex,fun(A,complex),combk(complex,A),B)),C) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(nat,complex,semiring_1_of_nat(complex),hAPP(fun(A,bool),nat,finite_card(A),C))),B). [resolve(5587,a,5581,a)].
% 75.51/75.41 Derived: -ordere779506340up_add(complex) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f597(A,complex,B,C,D)),D)) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less_eq(complex),hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),B),D)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(nat,complex,semiring_1_of_nat(complex),hAPP(fun(A,bool),nat,finite_card(A),D))),C))). [resolve(5587,a,5582,b)].
% 75.51/75.43 Derived: -ordere779506340up_add(complex) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less_eq(complex),hAPP(A,complex,B,f597(A,complex,B,C,D))),C)) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less_eq(complex),hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),B),D)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(nat,complex,semiring_1_of_nat(complex),hAPP(fun(A,bool),nat,finite_card(A),D))),C))). [resolve(5587,a,5583,b)].
% 75.51/75.43 5588 semiring_1(code_code_numeral) # label(arity_Code__Numeral_Ocode__numeral___Rings_Osemiring__1) # label(axiom). [assumption].
% 75.51/75.43 Derived: iszero(code_code_numeral) = ti(fun(code_code_numeral,bool),iszero(code_code_numeral)). [resolve(5588,a,5560,a)].
% 75.51/75.43 Derived: semiring_1_of_nat(code_code_numeral) = ti(fun(nat,code_code_numeral),semiring_1_of_nat(code_code_numeral)). [resolve(5588,a,5561,a)].
% 75.51/75.43 Derived: semiri532925092at_aux(code_code_numeral) = ti(fun(fun(code_code_numeral,code_code_numeral),fun(nat,fun(code_code_numeral,code_code_numeral))),semiri532925092at_aux(code_code_numeral)). [resolve(5588,a,5562,a)].
% 75.51/75.43 Derived: -hBOOL(hAPP(code_code_numeral,bool,iszero(code_code_numeral),A)) | zero_zero(code_code_numeral) = ti(code_code_numeral,A). [resolve(5588,a,5563,a)].
% 75.51/75.43 Derived: hBOOL(hAPP(code_code_numeral,bool,iszero(code_code_numeral),A)) | zero_zero(code_code_numeral) != ti(code_code_numeral,A). [resolve(5588,a,5564,a)].
% 75.51/75.43 Derived: hBOOL(hAPP(code_code_numeral,bool,iszero(code_code_numeral),zero_zero(code_code_numeral))). [resolve(5588,a,5565,a)].
% 75.51/75.43 Derived: -hBOOL(hAPP(code_code_numeral,bool,iszero(code_code_numeral),one_one(code_code_numeral))). [resolve(5588,a,5566,a)].
% 75.51/75.43 Derived: hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),zero_zero(code_code_numeral)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = zero_zero(code_code_numeral). [resolve(5588,a,5567,a)].
% 75.51/75.43 Derived: hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),one_one(code_code_numeral)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = one_one(code_code_numeral). [resolve(5588,a,5568,a)].
% 75.51/75.43 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A)) | hAPP(nat,code_code_numeral,semiring_1_of_nat(code_code_numeral),hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),A))) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),hAPP(nat,code_code_numeral,semiring_1_of_nat(code_code_numeral),hAPP(int,nat,nat_1,A))),hAPP(nat,code_code_numeral,semiring_1_of_nat(code_code_numeral),hAPP(int,nat,nat_1,A))). [resolve(5588,a,5569,a)].
% 75.51/75.43 Derived: hAPP(nat,code_code_numeral,semiring_1_of_nat(code_code_numeral),zero_zero(nat)) = zero_zero(code_code_numeral). [resolve(5588,a,5570,a)].
% 75.51/75.43 Derived: hAPP(nat,code_code_numeral,semiring_1_of_nat(code_code_numeral),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B)) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),hAPP(nat,code_code_numeral,semiring_1_of_nat(code_code_numeral),A)),hAPP(nat,code_code_numeral,semiring_1_of_nat(code_code_numeral),B)). [resolve(5588,a,5571,a)].
% 75.51/75.43 Derived: hAPP(nat,code_code_numeral,semiring_1_of_nat(code_code_numeral),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),B)) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),hAPP(nat,code_code_numeral,semiring_1_of_nat(code_code_numeral),A)),hAPP(nat,code_code_numeral,semiring_1_of_nat(code_code_numeral),B)). [resolve(5588,a,5572,a)].
% 75.51/75.43 Derived: hAPP(nat,code_code_numeral,semiring_1_of_nat(code_code_numeral),one_one(nat)) = one_one(code_code_numeral). [resolve(5588,a,5573,a)].
% 75.51/75.43 Derived: hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),hAPP(nat,code_code_numeral,semiring_1_of_nat(code_code_numeral),A)),B) = hAPP(nat,code_code_numeral,semiring_1_of_nat(code_code_numeral),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),B)). [resolve(5588,a,5574,a)].
% 75.51/75.43 Derived: hAPP(nat,code_code_numeral,semiring_1_of_nat(code_code_numeral),hAPP(nat,nat,suc,A)) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),one_one(code_code_numeral)),hAPP(nat,code_code_numeral,semiring_1_of_nat(code_code_numeral),A)). [resolve(5588,a,5575,a)].
% 75.51/75.43 Derived: -comm_monoid_mult(code_code_numeral) | hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co302546470etprod(A,code_code_numeral),hAPP(fun(A,nat),fun(A,code_code_numeral),hAPP(fun(nat,code_code_numeral),fun(fun(A,nat),fun(A,code_code_numeral)),combb(nat,code_code_numeral,A),semiring_1_of_nat(code_code_numeral)),B)),C) = hAPP(nat,code_code_numeral,semiring_1_of_nat(code_code_numeral),hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),B),C)). [resolve(5588,a,5576,b)].
% 75.51/75.43 Derived: hAPP(nat,code_code_numeral,semiring_1_of_nat(code_code_numeral),A) = hAPP(code_code_numeral,code_code_numeral,hAPP(nat,fun(code_code_numeral,code_code_numeral),hAPP(fun(code_code_numeral,code_code_numeral),fun(nat,fun(code_code_numeral,code_code_numeral)),semiri532925092at_aux(code_code_numeral),hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),hAPP(fun(code_code_numeral,fun(code_code_numeral,code_code_numeral)),fun(code_code_numeral,fun(code_code_numeral,code_code_numeral)),combc(code_code_numeral,code_code_numeral,code_code_numeral),plus_plus(code_code_numeral)),one_one(code_code_numeral))),A),zero_zero(code_code_numeral)). [resolve(5588,a,5577,a)].
% 75.51/75.43 Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(nat,fun(code_code_numeral,code_code_numeral),hAPP(fun(code_code_numeral,code_code_numeral),fun(nat,fun(code_code_numeral,code_code_numeral)),semiri532925092at_aux(code_code_numeral),A),zero_zero(nat)),B) = ti(code_code_numeral,B). [resolve(5588,a,5578,a)].
% 75.51/75.43 Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(nat,fun(code_code_numeral,code_code_numeral),hAPP(fun(code_code_numeral,code_code_numeral),fun(nat,fun(code_code_numeral,code_code_numeral)),semiri532925092at_aux(code_code_numeral),A),hAPP(nat,nat,suc,B)),C) = hAPP(code_code_numeral,code_code_numeral,hAPP(nat,fun(code_code_numeral,code_code_numeral),hAPP(fun(code_code_numeral,code_code_numeral),fun(nat,fun(code_code_numeral,code_code_numeral)),semiri532925092at_aux(code_code_numeral),A),B),hAPP(code_code_numeral,code_code_numeral,A,C)). [resolve(5588,a,5579,a)].
% 75.51/75.43 Derived: hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),hAPP(fun(A,nat),fun(A,code_code_numeral),hAPP(fun(nat,code_code_numeral),fun(fun(A,nat),fun(A,code_code_numeral)),combb(nat,code_code_numeral,A),semiring_1_of_nat(code_code_numeral)),B)),C) = hAPP(nat,code_code_numeral,semiring_1_of_nat(code_code_numeral),hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),B),C)). [resolve(5588,a,5580,a)].
% 75.51/75.43 Derived: hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),hAPP(code_code_numeral,fun(A,code_code_numeral),combk(code_code_numeral,A),B)),C) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),hAPP(nat,code_code_numeral,semiring_1_of_nat(code_code_numeral),hAPP(fun(A,bool),nat,finite_card(A),C))),B). [resolve(5588,a,5581,a)].
% 75.51/75.45 Derived: -ordere779506340up_add(code_code_numeral) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f597(A,code_code_numeral,B,C,D)),D)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),B),D)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),hAPP(nat,code_code_numeral,semiring_1_of_nat(code_code_numeral),hAPP(fun(A,bool),nat,finite_card(A),D))),C))). [resolve(5588,a,5582,b)].
% 75.51/75.45 Derived: -ordere779506340up_add(code_code_numeral) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),hAPP(A,code_code_numeral,B,f597(A,code_code_numeral,B,C,D))),C)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),B),D)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),hAPP(nat,code_code_numeral,semiring_1_of_nat(code_code_numeral),hAPP(fun(A,bool),nat,finite_card(A),D))),C))). [resolve(5588,a,5583,b)].
% 75.51/75.45 5589 semiring_1(quickcheck_code_int) # label(arity_Quickcheck__Narrowing_Ocode__int___Rings_Osemiring__1) # label(axiom). [assumption].
% 75.51/75.45 Derived: iszero(quickcheck_code_int) = ti(fun(quickcheck_code_int,bool),iszero(quickcheck_code_int)). [resolve(5589,a,5560,a)].
% 75.51/75.45 Derived: semiring_1_of_nat(quickcheck_code_int) = ti(fun(nat,quickcheck_code_int),semiring_1_of_nat(quickcheck_code_int)). [resolve(5589,a,5561,a)].
% 75.51/75.45 Derived: semiri532925092at_aux(quickcheck_code_int) = ti(fun(fun(quickcheck_code_int,quickcheck_code_int),fun(nat,fun(quickcheck_code_int,quickcheck_code_int))),semiri532925092at_aux(quickcheck_code_int)). [resolve(5589,a,5562,a)].
% 75.51/75.45 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,iszero(quickcheck_code_int),A)) | zero_zero(quickcheck_code_int) = ti(quickcheck_code_int,A). [resolve(5589,a,5563,a)].
% 75.51/75.45 Derived: hBOOL(hAPP(quickcheck_code_int,bool,iszero(quickcheck_code_int),A)) | zero_zero(quickcheck_code_int) != ti(quickcheck_code_int,A). [resolve(5589,a,5564,a)].
% 75.51/75.45 Derived: hBOOL(hAPP(quickcheck_code_int,bool,iszero(quickcheck_code_int),zero_zero(quickcheck_code_int))). [resolve(5589,a,5565,a)].
% 75.51/75.45 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,iszero(quickcheck_code_int),one_one(quickcheck_code_int))). [resolve(5589,a,5566,a)].
% 75.51/75.45 Derived: hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),zero_zero(quickcheck_code_int)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = zero_zero(quickcheck_code_int). [resolve(5589,a,5567,a)].
% 75.51/75.45 Derived: hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),one_one(quickcheck_code_int)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = one_one(quickcheck_code_int). [resolve(5589,a,5568,a)].
% 75.51/75.45 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A)) | hAPP(nat,quickcheck_code_int,semiring_1_of_nat(quickcheck_code_int),hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),A))) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),hAPP(nat,quickcheck_code_int,semiring_1_of_nat(quickcheck_code_int),hAPP(int,nat,nat_1,A))),hAPP(nat,quickcheck_code_int,semiring_1_of_nat(quickcheck_code_int),hAPP(int,nat,nat_1,A))). [resolve(5589,a,5569,a)].
% 75.51/75.45 Derived: hAPP(nat,quickcheck_code_int,semiring_1_of_nat(quickcheck_code_int),zero_zero(nat)) = zero_zero(quickcheck_code_int). [resolve(5589,a,5570,a)].
% 75.51/75.45 Derived: hAPP(nat,quickcheck_code_int,semiring_1_of_nat(quickcheck_code_int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B)) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),hAPP(nat,quickcheck_code_int,semiring_1_of_nat(quickcheck_code_int),A)),hAPP(nat,quickcheck_code_int,semiring_1_of_nat(quickcheck_code_int),B)). [resolve(5589,a,5571,a)].
% 75.51/75.45 Derived: hAPP(nat,quickcheck_code_int,semiring_1_of_nat(quickcheck_code_int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),B)) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),hAPP(nat,quickcheck_code_int,semiring_1_of_nat(quickcheck_code_int),A)),hAPP(nat,quickcheck_code_int,semiring_1_of_nat(quickcheck_code_int),B)). [resolve(5589,a,5572,a)].
% 75.51/75.45 Derived: hAPP(nat,quickcheck_code_int,semiring_1_of_nat(quickcheck_code_int),one_one(nat)) = one_one(quickcheck_code_int). [resolve(5589,a,5573,a)].
% 75.51/75.45 Derived: hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),hAPP(nat,quickcheck_code_int,semiring_1_of_nat(quickcheck_code_int),A)),B) = hAPP(nat,quickcheck_code_int,semiring_1_of_nat(quickcheck_code_int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),B)). [resolve(5589,a,5574,a)].
% 75.51/75.45 Derived: hAPP(nat,quickcheck_code_int,semiring_1_of_nat(quickcheck_code_int),hAPP(nat,nat,suc,A)) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),one_one(quickcheck_code_int)),hAPP(nat,quickcheck_code_int,semiring_1_of_nat(quickcheck_code_int),A)). [resolve(5589,a,5575,a)].
% 75.51/75.45 Derived: -comm_monoid_mult(quickcheck_code_int) | hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co302546470etprod(A,quickcheck_code_int),hAPP(fun(A,nat),fun(A,quickcheck_code_int),hAPP(fun(nat,quickcheck_code_int),fun(fun(A,nat),fun(A,quickcheck_code_int)),combb(nat,quickcheck_code_int,A),semiring_1_of_nat(quickcheck_code_int)),B)),C) = hAPP(nat,quickcheck_code_int,semiring_1_of_nat(quickcheck_code_int),hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),B),C)). [resolve(5589,a,5576,b)].
% 75.51/75.45 Derived: hAPP(nat,quickcheck_code_int,semiring_1_of_nat(quickcheck_code_int),A) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(nat,fun(quickcheck_code_int,quickcheck_code_int),hAPP(fun(quickcheck_code_int,quickcheck_code_int),fun(nat,fun(quickcheck_code_int,quickcheck_code_int)),semiri532925092at_aux(quickcheck_code_int),hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),hAPP(fun(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int)),fun(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int)),combc(quickcheck_code_int,quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int)),one_one(quickcheck_code_int))),A),zero_zero(quickcheck_code_int)). [resolve(5589,a,5577,a)].
% 75.51/75.45 Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(nat,fun(quickcheck_code_int,quickcheck_code_int),hAPP(fun(quickcheck_code_int,quickcheck_code_int),fun(nat,fun(quickcheck_code_int,quickcheck_code_int)),semiri532925092at_aux(quickcheck_code_int),A),zero_zero(nat)),B) = ti(quickcheck_code_int,B). [resolve(5589,a,5578,a)].
% 75.51/75.45 Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(nat,fun(quickcheck_code_int,quickcheck_code_int),hAPP(fun(quickcheck_code_int,quickcheck_code_int),fun(nat,fun(quickcheck_code_int,quickcheck_code_int)),semiri532925092at_aux(quickcheck_code_int),A),hAPP(nat,nat,suc,B)),C) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(nat,fun(quickcheck_code_int,quickcheck_code_int),hAPP(fun(quickcheck_code_int,quickcheck_code_int),fun(nat,fun(quickcheck_code_int,quickcheck_code_int)),semiri532925092at_aux(quickcheck_code_int),A),B),hAPP(quickcheck_code_int,quickcheck_code_int,A,C)). [resolve(5589,a,5579,a)].
% 79.01/78.94 Derived: hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),hAPP(fun(A,nat),fun(A,quickcheck_code_int),hAPP(fun(nat,quickcheck_code_int),fun(fun(A,nat),fun(A,quickcheck_code_int)),combb(nat,quickcheck_code_int,A),semiring_1_of_nat(quickcheck_code_int)),B)),C) = hAPP(nat,quickcheck_code_int,semiring_1_of_nat(quickcheck_code_int),hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),B),C)). [resolve(5589,a,5580,a)].
% 79.01/78.94 Derived: hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),hAPP(quickcheck_code_int,fun(A,quickcheck_code_int),combk(quickcheck_code_int,A),B)),C) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),hAPP(nat,quickcheck_code_int,semiring_1_of_nat(quickcheck_code_int),hAPP(fun(A,bool),nat,finite_card(A),C))),B). [resolve(5589,a,5581,a)].
% 79.01/78.94 Derived: -ordere779506340up_add(quickcheck_code_int) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f597(A,quickcheck_code_int,B,C,D)),D)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),B),D)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),hAPP(nat,quickcheck_code_int,semiring_1_of_nat(quickcheck_code_int),hAPP(fun(A,bool),nat,finite_card(A),D))),C))). [resolve(5589,a,5582,b)].
% 79.01/78.94 Derived: -ordere779506340up_add(quickcheck_code_int) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),hAPP(A,quickcheck_code_int,B,f597(A,quickcheck_code_int,B,C,D))),C)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),B),D)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),hAPP(nat,quickcheck_code_int,semiring_1_of_nat(quickcheck_code_int),hAPP(fun(A,bool),nat,finite_card(A),D))),C))). [resolve(5589,a,5583,b)].
% 79.01/78.94 5590 ring_1(int) # label(arity_Int_Oint___Rings_Oring__1) # label(axiom). [assumption].
% 79.01/78.94 5591 -ring_1(A) | ring_1_Ints(A) = ti(fun(A,bool),ring_1_Ints(A)) # label(tsy_c_Int_Oring__1__class_OInts_res) # label(axiom). [clausify(50)].
% 79.01/78.94 5592 -ring_1(A) | ring_1_of_int(A) = ti(fun(int,A),ring_1_of_int(A)) # label(tsy_c_Int_Oring__1__class_Oof__int_res) # label(axiom). [clausify(51)].
% 79.01/78.94 5593 -ring_1(A) | diffs(A) = ti(fun(fun(nat,A),fun(nat,A)),diffs(A)) # label(tsy_c_Transcendental_Odiffs_res) # label(axiom). [clausify(116)].
% 79.01/78.94 5594 -ring_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))),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),one_one(A))) = hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),B)),one_one(A)) # label(fact_83_real__squared__diff__one__factored) # label(axiom). [clausify(213)].
% 79.01/78.94 5595 -ring_1(A) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),B),ring_1_Ints(A))) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),hAPP(A,A,uminus_uminus(A),B)),ring_1_Ints(A))) # label(fact_489_Ints__minus) # label(axiom). [clausify(613)].
% 79.01/78.94 5596 -ring_1(A) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),zero_zero(A)),ring_1_Ints(A))) # label(fact_602_Ints__0) # label(axiom). [clausify(723)].
% 79.01/78.94 5597 -ring_1(A) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),B),ring_1_Ints(A))) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),ring_1_Ints(A))) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),ring_1_Ints(A))) # label(fact_603_Ints__mult) # label(axiom). [clausify(724)].
% 79.01/78.94 5598 -ring_1(A) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),B),ring_1_Ints(A))) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),ring_1_Ints(A))) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),ring_1_Ints(A))) # label(fact_604_Ints__add) # label(axiom). [clausify(725)].
% 79.01/78.94 5599 -ring_1(A) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),one_one(A)),ring_1_Ints(A))) # label(fact_606_Ints__1) # label(axiom). [clausify(727)].
% 79.01/78.94 5600 -ring_1(A) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),B),ring_1_Ints(A))) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),ring_1_Ints(A))) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C)),ring_1_Ints(A))) # label(fact_607_Ints__diff) # label(axiom). [clausify(728)].
% 79.01/78.94 5601 -ring_1(A) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),B),ring_1_Ints(A))) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C)),ring_1_Ints(A))) # label(fact_1385_Ints__power) # label(axiom). [clausify(1488)].
% 79.01/78.94 5602 -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_1465_power__minus) # label(axiom). [clausify(1568)].
% 79.01/78.94 5603 -ring_1(A) | hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),hAPP(A,A,uminus_uminus(A),B)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) # label(fact_1819_power2__minus) # label(axiom). [clausify(1877)].
% 79.01/78.94 5604 -ring_1(A) | hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),hAPP(A,A,uminus_uminus(A),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),C)) = hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),C)) # label(fact_1857_ring__1__class_Opower__minus__even) # label(axiom). [clausify(1908)].
% 79.01/78.94 5605 -ring_1(A) | hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),hAPP(A,A,uminus_uminus(A),one_one(A))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),B)) = one_one(A) # label(fact_1892_power__minus1__even) # label(axiom). [clausify(1937)].
% 79.01/78.94 5606 -ring_1(A) | hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),hAPP(A,A,uminus_uminus(A),one_one(A))),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),B))) = hAPP(A,A,uminus_uminus(A),one_one(A)) # label(fact_1922_power__minus1__odd) # label(axiom). [clausify(1959)].
% 79.01/78.94 5607 -ring_1(A) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),hAPP(nat,A,semiring_1_of_nat(A),B)),ring_1_Ints(A))) # label(fact_2580_Ints__of__nat) # label(axiom). [clausify(2580)].
% 79.01/78.94 5608 -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_2643_of__nat__diff) # label(axiom). [clausify(2638)].
% 79.01/78.94 5609 -ring_1(A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),zero_zero(int))) | hAPP(int,A,ring_1_of_int(A),B) = hAPP(A,A,uminus_uminus(A),hAPP(nat,A,semiring_1_of_nat(A),hAPP(int,nat,nat_1,hAPP(int,int,uminus_uminus(int),B)))) # label(fact_3565_of__int__of__nat) # label(axiom). [clausify(3520)].
% 79.01/78.94 5610 -ring_1(A) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),zero_zero(int))) | hAPP(nat,A,semiring_1_of_nat(A),hAPP(int,nat,nat_1,B)) = hAPP(int,A,ring_1_of_int(A),B) # label(fact_3565_of__int__of__nat) # label(axiom). [clausify(3520)].
% 79.01/78.94 5611 -ring_1(A) | hAPP(int,A,ring_1_of_int(A),hAPP(int,int,uminus_uminus(int),B)) = hAPP(A,A,uminus_uminus(A),hAPP(int,A,ring_1_of_int(A),B)) # label(fact_3569_of__int__minus) # label(axiom). [clausify(3524)].
% 79.01/78.94 5612 -ring_1(A) | hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),hAPP(int,A,ring_1_of_int(A),B)),C) = hAPP(int,A,ring_1_of_int(A),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),B),C)) # label(fact_3570_of__int__power) # label(axiom). [clausify(3525)].
% 79.01/78.94 5613 -ring_1(A) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),hAPP(int,A,ring_1_of_int(A),B)),ring_1_Ints(A))) # label(fact_3580_Ints__of__int) # label(axiom). [clausify(3533)].
% 79.01/78.94 5614 -ring_1(A) | hAPP(int,A,ring_1_of_int(A),one_one(int)) = one_one(A) # label(fact_3584_of__int__1) # label(axiom). [clausify(3537)].
% 79.01/78.94 5615 -ring_1(A) | hAPP(int,A,ring_1_of_int(A),zero_zero(int)) = zero_zero(A) # label(fact_3590_of__int__0) # label(axiom). [clausify(3543)].
% 79.01/78.94 5616 -ring_1(A) | hAPP(nat,A,semiring_1_of_nat(A),B) = hAPP(int,A,ring_1_of_int(A),hAPP(nat,int,semiring_1_of_nat(int),B)) # label(fact_3593_of__int__of__nat__eq) # label(axiom). [clausify(3546)].
% 79.01/78.94 5617 -ring_1(A) | hAPP(int,A,ring_1_of_int(A),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),C)) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,ring_1_of_int(A),B)),hAPP(int,A,ring_1_of_int(A),C)) # label(fact_3595_of__int__mult) # label(axiom). [clausify(3548)].
% 79.01/78.94 5618 -ring_1(A) | hAPP(int,A,ring_1_of_int(A),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),B),C)) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(int,A,ring_1_of_int(A),B)),hAPP(int,A,ring_1_of_int(A),C)) # label(fact_3596_of__int__add) # label(axiom). [clausify(3549)].
% 79.01/78.94 5619 -ring_1(A) | hAPP(int,A,ring_1_of_int(A),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),B),C)) = hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(int,A,ring_1_of_int(A),B)),hAPP(int,A,ring_1_of_int(A),C)) # label(fact_3597_of__int__diff) # label(axiom). [clausify(3550)].
% 79.01/78.94 5620 -ring_1(A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),B)) | hAPP(nat,A,semiring_1_of_nat(A),hAPP(int,nat,nat_1,B)) = hAPP(int,A,ring_1_of_int(A),B) # label(fact_3611_of__nat__nat) # label(axiom). [clausify(3564)].
% 79.01/78.94 5621 -ring_1(A) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),B),ring_1_Ints(A))) | -hBOOL(hAPP(A,bool,C,hAPP(int,A,ring_1_of_int(A),f438(A,C,B)))) | hBOOL(hAPP(A,bool,C,B)) # label(fact_3631_Ints__induct) # label(axiom). [clausify(3584)].
% 79.01/78.94 5622 -ring_1(A) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),B),ring_1_Ints(A))) | hAPP(int,A,ring_1_of_int(A),f439(A,B)) = ti(A,B) # label(fact_3632_Ints__cases) # label(axiom). [clausify(3585)].
% 79.01/78.94 5623 -comm_monoid_mult(A) | -ring_1(A) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),hAPP(fun(B,int),fun(B,A),hAPP(fun(int,A),fun(fun(B,int),fun(B,A)),combb(int,A,B),ring_1_of_int(A)),C)),D) = hAPP(int,A,ring_1_of_int(A),hAPP(fun(B,bool),int,hAPP(fun(B,int),fun(fun(B,bool),int),big_co302546470etprod(B,int),C),D)) # label(fact_3925_of__int__setprod) # label(axiom). [clausify(3866)].
% 79.01/78.94 5624 -ring_1(A) | zero_zero(int) != B | hAPP(int,A,ring_1_of_int(A),B) = zero_zero(A) # label(fact_3975_of__int__num) # label(axiom). [clausify(3915)].
% 79.01/78.94 5625 -ring_1(A) | zero_zero(int) = B | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),zero_zero(int))) | hAPP(int,A,ring_1_of_int(A),B) = hAPP(A,A,uminus_uminus(A),hAPP(int,A,ring_1_of_int(A),hAPP(int,int,uminus_uminus(int),B))) # label(fact_3975_of__int__num) # label(axiom). [clausify(3915)].
% 79.01/78.94 5626 -ring_1(A) | zero_zero(int) = B | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),zero_zero(int))) | hAPP(product_prod(int,int),A,hAPP(fun(int,fun(int,A)),fun(product_prod(int,int),A),product_prod_case(int,int,A),hAPP(fun(int,A),fun(int,fun(int,A)),hAPP(fun(int,fun(A,fun(int,A))),fun(fun(int,A),fun(int,fun(int,A))),combs(int,A,fun(int,A)),hAPP(fun(int,fun(int,fun(A,A))),fun(int,fun(A,fun(int,A))),hAPP(fun(fun(int,fun(A,A)),fun(A,fun(int,A))),fun(fun(int,fun(int,fun(A,A))),fun(int,fun(A,fun(int,A)))),combb(fun(int,fun(A,A)),fun(A,fun(int,A)),int),combc(int,A,A)),hAPP(fun(int,A),fun(int,fun(int,fun(A,A))),hAPP(fun(A,fun(int,fun(A,A))),fun(fun(int,A),fun(int,fun(int,fun(A,A)))),combb(A,fun(int,fun(A,A)),int),hAPP(fun(int,fun(A,fun(A,A))),fun(A,fun(int,fun(A,A))),combc(int,A,fun(A,A)),hAPP(fun(int,bool),fun(int,fun(A,fun(A,A))),hAPP(fun(bool,fun(A,fun(A,A))),fun(fun(int,bool),fun(int,fun(A,fun(A,A)))),combb(bool,fun(A,fun(A,A)),int),if(A)),hAPP(int,fun(int,bool),hAPP(fun(int,fun(int,bool)),fun(int,fun(int,bool)),combc(int,int,bool),fequal(int)),zero_zero(int))))),hAPP(fun(int,A),fun(int,A),hAPP(fun(int,fun(A,A)),fun(fun(int,A),fun(int,A)),combs(int,A,A),hAPP(fun(int,A),fun(int,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(int,A),fun(int,fun(A,A))),combb(A,fun(A,A),int),plus_plus(A)),ring_1_of_int(A))),ring_1_of_int(A))))),hAPP(A,fun(int,A),hAPP(fun(int,fun(A,A)),fun(A,fun(int,A)),combc(int,A,A),hAPP(fun(int,A),fun(int,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(int,A),fun(int,fun(A,A))),combb(A,fun(A,A),int),plus_plus(A)),hAPP(fun(int,A),fun(int,A),hAPP(fun(int,fun(A,A)),fun(fun(int,A),fun(int,A)),combs(int,A,A),hAPP(fun(int,A),fun(int,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(int,A),fun(int,fun(A,A))),combb(A,fun(A,A),int),plus_plus(A)),ring_1_of_int(A))),ring_1_of_int(A)))),one_one(A)))),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),divmod_int,B),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) = hAPP(int,A,ring_1_of_int(A),B) # label(fact_3975_of__int__num) # label(axiom). [clausify(3915)].
% 79.01/78.94 5627 -real_normed_vector(A) | -ring_1(A) | -hBOOL(hAPP(fun(nat,A),bool,summable(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),times_times(A)),hAPP(fun(nat,A),fun(nat,A),diffs(A),B))),hAPP(A,fun(nat,A),power_power(A),C)))) | hBOOL(hAPP(A,bool,hAPP(fun(nat,A),fun(A,bool),sums(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),times_times(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),times_times(A)),semiring_1_of_nat(A))),B))),hAPP(fun(nat,nat),fun(nat,A),hAPP(fun(nat,A),fun(fun(nat,nat),fun(nat,A)),combb(nat,A,nat),hAPP(A,fun(nat,A),power_power(A),C)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),minus_minus(nat)),hAPP(nat,nat,suc,zero_zero(nat)))))),hAPP(fun(nat,A),A,suminf(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),times_times(A)),hAPP(fun(nat,A),fun(nat,A),diffs(A),B))),hAPP(A,fun(nat,A),power_power(A),C))))) # label(fact_4107_diffs__equiv) # label(axiom). [clausify(4042)].
% 79.01/78.94 5628 -ring_1(A) | hAPP(nat,A,hAPP(fun(nat,A),fun(nat,A),diffs(A),hAPP(fun(nat,A),fun(nat,A),hAPP(fun(A,A),fun(fun(nat,A),fun(nat,A)),combb(A,A,nat),uminus_uminus(A)),B)),C) = hAPP(A,A,uminus_uminus(A),hAPP(nat,A,hAPP(fun(nat,A),fun(nat,A),diffs(A),B),C)) # label(fact_4113_diffs__minus) # label(axiom). [clausify(4048)].
% 79.01/78.94 5629 -ring_1(A) | hAPP(nat,A,hAPP(fun(nat,A),fun(nat,A),diffs(A),B),C) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(nat,A,semiring_1_of_nat(A),hAPP(nat,nat,suc,C))),hAPP(nat,A,B,hAPP(nat,nat,suc,C))) # label(fact_4118_diffs__def) # label(axiom). [clausify(4052)].
% 79.01/78.94 5630 -ring_1(A) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),hAPP(fun(B,int),fun(B,A),hAPP(fun(int,A),fun(fun(B,int),fun(B,A)),combb(int,A,B),ring_1_of_int(A)),C)),D) = hAPP(int,A,ring_1_of_int(A),hAPP(fun(B,bool),int,hAPP(fun(B,int),fun(fun(B,bool),int),big_co1399186613setsum(B,int),C),D)) # label(fact_4171_of__int__setsum) # label(axiom). [clausify(4103)].
% 79.01/78.94 5631 -ring_1(A) | hAPP(fun(nat,bool),A,hAPP(fun(nat,A),fun(fun(nat,bool),A),big_co1399186613setsum(nat,A),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),minus_minus(A)),B)),C)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),D)) = hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),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_atLeastLessThan(nat),zero_zero(nat)),D))),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(nat,A,semiring_1_of_nat(A),D)),C)) # label(fact_4172_sumr__diff__mult__const2) # label(axiom). [clausify(4104)].
% 79.01/78.94 Derived: ring_1_Ints(int) = ti(fun(int,bool),ring_1_Ints(int)). [resolve(5590,a,5591,a)].
% 79.01/78.94 Derived: ring_1_of_int(int) = ti(fun(int,int),ring_1_of_int(int)). [resolve(5590,a,5592,a)].
% 79.01/78.94 Derived: diffs(int) = ti(fun(fun(nat,int),fun(nat,int)),diffs(int)). [resolve(5590,a,5593,a)].
% 79.01/78.94 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))),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),one_one(int))) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),A)),one_one(int)). [resolve(5590,a,5594,a)].
% 79.01/78.94 Derived: -hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),A),ring_1_Ints(int))) | hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),hAPP(int,int,uminus_uminus(int),A)),ring_1_Ints(int))). [resolve(5590,a,5595,a)].
% 79.01/78.94 Derived: hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),zero_zero(int)),ring_1_Ints(int))). [resolve(5590,a,5596,a)].
% 79.01/78.94 Derived: -hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),A),ring_1_Ints(int))) | -hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),B),ring_1_Ints(int))) | hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),ring_1_Ints(int))). [resolve(5590,a,5597,a)].
% 79.01/78.94 Derived: -hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),A),ring_1_Ints(int))) | -hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),B),ring_1_Ints(int))) | hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B)),ring_1_Ints(int))). [resolve(5590,a,5598,a)].
% 79.01/78.94 Derived: hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),one_one(int)),ring_1_Ints(int))). [resolve(5590,a,5599,a)].
% 79.01/78.94 Derived: -hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),A),ring_1_Ints(int))) | -hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),B),ring_1_Ints(int))) | hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),B)),ring_1_Ints(int))). [resolve(5590,a,5600,a)].
% 79.01/78.94 Derived: -hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),A),ring_1_Ints(int))) | hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),B)),ring_1_Ints(int))). [resolve(5590,a,5601,a)].
% 79.01/78.95 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(5590,a,5602,a)].
% 79.01/78.95 Derived: hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,uminus_uminus(int),A)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))). [resolve(5590,a,5603,a)].
% 79.01/78.95 Derived: hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,uminus_uminus(int),A)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),B)) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),B)). [resolve(5590,a,5604,a)].
% 79.01/78.95 Derived: hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,uminus_uminus(int),one_one(int))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),A)) = one_one(int). [resolve(5590,a,5605,a)].
% 79.01/78.95 Derived: hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,uminus_uminus(int),one_one(int))),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),A))) = hAPP(int,int,uminus_uminus(int),one_one(int)). [resolve(5590,a,5606,a)].
% 79.01/78.95 Derived: hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),hAPP(nat,int,semiring_1_of_nat(int),A)),ring_1_Ints(int))). [resolve(5590,a,5607,a)].
% 79.01/78.95 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(5590,a,5608,a)].
% 79.01/78.95 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),zero_zero(int))) | hAPP(int,int,ring_1_of_int(int),A) = hAPP(int,int,uminus_uminus(int),hAPP(nat,int,semiring_1_of_nat(int),hAPP(int,nat,nat_1,hAPP(int,int,uminus_uminus(int),A)))). [resolve(5590,a,5609,a)].
% 79.01/78.95 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),zero_zero(int))) | hAPP(nat,int,semiring_1_of_nat(int),hAPP(int,nat,nat_1,A)) = hAPP(int,int,ring_1_of_int(int),A). [resolve(5590,a,5610,a)].
% 79.01/78.95 Derived: hAPP(int,int,ring_1_of_int(int),hAPP(int,int,uminus_uminus(int),A)) = hAPP(int,int,uminus_uminus(int),hAPP(int,int,ring_1_of_int(int),A)). [resolve(5590,a,5611,a)].
% 79.01/78.95 Derived: hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,ring_1_of_int(int),A)),B) = hAPP(int,int,ring_1_of_int(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),B)). [resolve(5590,a,5612,a)].
% 79.01/78.95 Derived: hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),hAPP(int,int,ring_1_of_int(int),A)),ring_1_Ints(int))). [resolve(5590,a,5613,a)].
% 79.01/78.95 Derived: hAPP(int,int,ring_1_of_int(int),one_one(int)) = one_one(int). [resolve(5590,a,5614,a)].
% 79.01/78.95 Derived: hAPP(int,int,ring_1_of_int(int),zero_zero(int)) = zero_zero(int). [resolve(5590,a,5615,a)].
% 79.01/78.95 Derived: hAPP(nat,int,semiring_1_of_nat(int),A) = hAPP(int,int,ring_1_of_int(int),hAPP(nat,int,semiring_1_of_nat(int),A)). [resolve(5590,a,5616,a)].
% 79.01/78.95 Derived: hAPP(int,int,ring_1_of_int(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),hAPP(int,int,ring_1_of_int(int),A)),hAPP(int,int,ring_1_of_int(int),B)). [resolve(5590,a,5617,a)].
% 79.01/78.95 Derived: hAPP(int,int,ring_1_of_int(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),hAPP(int,int,ring_1_of_int(int),A)),hAPP(int,int,ring_1_of_int(int),B)). [resolve(5590,a,5618,a)].
% 79.01/78.95 Derived: hAPP(int,int,ring_1_of_int(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),B)) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,ring_1_of_int(int),A)),hAPP(int,int,ring_1_of_int(int),B)). [resolve(5590,a,5619,a)].
% 79.01/78.95 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A)) | hAPP(nat,int,semiring_1_of_nat(int),hAPP(int,nat,nat_1,A)) = hAPP(int,int,ring_1_of_int(int),A). [resolve(5590,a,5620,a)].
% 79.01/78.95 Derived: -hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),A),ring_1_Ints(int))) | -hBOOL(hAPP(int,bool,B,hAPP(int,int,ring_1_of_int(int),f438(int,B,A)))) | hBOOL(hAPP(int,bool,B,A)). [resolve(5590,a,5621,a)].
% 79.01/78.95 Derived: -hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),A),ring_1_Ints(int))) | hAPP(int,int,ring_1_of_int(int),f439(int,A)) = ti(int,A). [resolve(5590,a,5622,a)].
% 79.01/78.95 Derived: -comm_monoid_mult(int) | 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(int,int),fun(fun(A,int),fun(A,int)),combb(int,int,A),ring_1_of_int(int)),B)),C) = hAPP(int,int,ring_1_of_int(int),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),B),C)). [resolve(5590,a,5623,b)].
% 79.01/78.95 Derived: zero_zero(int) != A | hAPP(int,int,ring_1_of_int(int),A) = zero_zero(int). [resolve(5590,a,5624,a)].
% 79.01/78.95 Derived: zero_zero(int) = A | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),zero_zero(int))) | hAPP(int,int,ring_1_of_int(int),A) = hAPP(int,int,uminus_uminus(int),hAPP(int,int,ring_1_of_int(int),hAPP(int,int,uminus_uminus(int),A))). [resolve(5590,a,5625,a)].
% 79.01/78.95 Derived: zero_zero(int) = A | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),zero_zero(int))) | hAPP(product_prod(int,int),int,hAPP(fun(int,fun(int,int)),fun(product_prod(int,int),int),product_prod_case(int,int,int),hAPP(fun(int,int),fun(int,fun(int,int)),hAPP(fun(int,fun(int,fun(int,int))),fun(fun(int,int),fun(int,fun(int,int))),combs(int,int,fun(int,int)),hAPP(fun(int,fun(int,fun(int,int))),fun(int,fun(int,fun(int,int))),hAPP(fun(fun(int,fun(int,int)),fun(int,fun(int,int))),fun(fun(int,fun(int,fun(int,int))),fun(int,fun(int,fun(int,int)))),combb(fun(int,fun(int,int)),fun(int,fun(int,int)),int),combc(int,int,int)),hAPP(fun(int,int),fun(int,fun(int,fun(int,int))),hAPP(fun(int,fun(int,fun(int,int))),fun(fun(int,int),fun(int,fun(int,fun(int,int)))),combb(int,fun(int,fun(int,int)),int),hAPP(fun(int,fun(int,fun(int,int))),fun(int,fun(int,fun(int,int))),combc(int,int,fun(int,int)),hAPP(fun(int,bool),fun(int,fun(int,fun(int,int))),hAPP(fun(bool,fun(int,fun(int,int))),fun(fun(int,bool),fun(int,fun(int,fun(int,int)))),combb(bool,fun(int,fun(int,int)),int),if(int)),hAPP(int,fun(int,bool),hAPP(fun(int,fun(int,bool)),fun(int,fun(int,bool)),combc(int,int,bool),fequal(int)),zero_zero(int))))),hAPP(fun(int,int),fun(int,int),hAPP(fun(int,fun(int,int)),fun(fun(int,int),fun(int,int)),combs(int,int,int),hAPP(fun(int,int),fun(int,fun(int,int)),hAPP(fun(int,fun(int,int)),fun(fun(int,int),fun(int,fun(int,int))),combb(int,fun(int,int),int),plus_plus(int)),ring_1_of_int(int))),ring_1_of_int(int))))),hAPP(int,fun(int,int),hAPP(fun(int,fun(int,int)),fun(int,fun(int,int)),combc(int,int,int),hAPP(fun(int,int),fun(int,fun(int,int)),hAPP(fun(int,fun(int,int)),fun(fun(int,int),fun(int,fun(int,int))),combb(int,fun(int,int),int),plus_plus(int)),hAPP(fun(int,int),fun(int,int),hAPP(fun(int,fun(int,int)),fun(fun(int,int),fun(int,int)),combs(int,int,int),hAPP(fun(int,int),fun(int,fun(int,int)),hAPP(fun(int,fun(int,int)),fun(fun(int,int),fun(int,fun(int,int))),combb(int,fun(int,int),int),plus_plus(int)),ring_1_of_int(int))),ring_1_of_int(int)))),one_one(int)))),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),divmod_int,A),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) = hAPP(int,int,ring_1_of_int(int),A). [resolve(5590,a,5626,a)].
% 79.08/78.99 Derived: -real_normed_vector(int) | -hBOOL(hAPP(fun(nat,int),bool,summable(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),times_times(int)),hAPP(fun(nat,int),fun(nat,int),diffs(int),A))),hAPP(int,fun(nat,int),power_power(int),B)))) | hBOOL(hAPP(int,bool,hAPP(fun(nat,int),fun(int,bool),sums(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),times_times(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),times_times(int)),semiring_1_of_nat(int))),A))),hAPP(fun(nat,nat),fun(nat,int),hAPP(fun(nat,int),fun(fun(nat,nat),fun(nat,int)),combb(nat,int,nat),hAPP(int,fun(nat,int),power_power(int),B)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),minus_minus(nat)),hAPP(nat,nat,suc,zero_zero(nat)))))),hAPP(fun(nat,int),int,suminf(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),times_times(int)),hAPP(fun(nat,int),fun(nat,int),diffs(int),A))),hAPP(int,fun(nat,int),power_power(int),B))))). [resolve(5590,a,5627,b)].
% 79.08/78.99 Derived: hAPP(nat,int,hAPP(fun(nat,int),fun(nat,int),diffs(int),hAPP(fun(nat,int),fun(nat,int),hAPP(fun(int,int),fun(fun(nat,int),fun(nat,int)),combb(int,int,nat),uminus_uminus(int)),A)),B) = hAPP(int,int,uminus_uminus(int),hAPP(nat,int,hAPP(fun(nat,int),fun(nat,int),diffs(int),A),B)). [resolve(5590,a,5628,a)].
% 79.08/78.99 Derived: hAPP(nat,int,hAPP(fun(nat,int),fun(nat,int),diffs(int),A),B) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,B))),hAPP(nat,int,A,hAPP(nat,nat,suc,B))). [resolve(5590,a,5629,a)].
% 79.08/78.99 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),ring_1_of_int(int)),B)),C) = hAPP(int,int,ring_1_of_int(int),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),B),C)). [resolve(5590,a,5630,a)].
% 79.08/78.99 Derived: hAPP(fun(nat,bool),int,hAPP(fun(nat,int),fun(fun(nat,bool),int),big_co1399186613setsum(nat,int),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),minus_minus(int)),A)),B)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),C)) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),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_atLeastLessThan(nat),zero_zero(nat)),C))),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(nat,int,semiring_1_of_nat(int),C)),B)). [resolve(5590,a,5631,a)].
% 79.08/78.99 5632 ring_1(rat) # label(arity_Rat_Orat___Rings_Oring__1) # label(axiom). [assumption].
% 79.08/78.99 Derived: ring_1_Ints(rat) = ti(fun(rat,bool),ring_1_Ints(rat)). [resolve(5632,a,5591,a)].
% 79.08/78.99 Derived: ring_1_of_int(rat) = ti(fun(int,rat),ring_1_of_int(rat)). [resolve(5632,a,5592,a)].
% 79.08/78.99 Derived: diffs(rat) = ti(fun(fun(nat,rat),fun(nat,rat)),diffs(rat)). [resolve(5632,a,5593,a)].
% 79.08/78.99 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),one_one(rat))),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),A),one_one(rat))) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),A)),one_one(rat)). [resolve(5632,a,5594,a)].
% 79.08/79.00 Derived: -hBOOL(hAPP(fun(rat,bool),bool,hAPP(rat,fun(fun(rat,bool),bool),member(rat),A),ring_1_Ints(rat))) | hBOOL(hAPP(fun(rat,bool),bool,hAPP(rat,fun(fun(rat,bool),bool),member(rat),hAPP(rat,rat,uminus_uminus(rat),A)),ring_1_Ints(rat))). [resolve(5632,a,5595,a)].
% 79.08/79.00 Derived: hBOOL(hAPP(fun(rat,bool),bool,hAPP(rat,fun(fun(rat,bool),bool),member(rat),zero_zero(rat)),ring_1_Ints(rat))). [resolve(5632,a,5596,a)].
% 79.08/79.00 Derived: -hBOOL(hAPP(fun(rat,bool),bool,hAPP(rat,fun(fun(rat,bool),bool),member(rat),A),ring_1_Ints(rat))) | -hBOOL(hAPP(fun(rat,bool),bool,hAPP(rat,fun(fun(rat,bool),bool),member(rat),B),ring_1_Ints(rat))) | hBOOL(hAPP(fun(rat,bool),bool,hAPP(rat,fun(fun(rat,bool),bool),member(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B)),ring_1_Ints(rat))). [resolve(5632,a,5597,a)].
% 79.08/79.00 Derived: -hBOOL(hAPP(fun(rat,bool),bool,hAPP(rat,fun(fun(rat,bool),bool),member(rat),A),ring_1_Ints(rat))) | -hBOOL(hAPP(fun(rat,bool),bool,hAPP(rat,fun(fun(rat,bool),bool),member(rat),B),ring_1_Ints(rat))) | hBOOL(hAPP(fun(rat,bool),bool,hAPP(rat,fun(fun(rat,bool),bool),member(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),B)),ring_1_Ints(rat))). [resolve(5632,a,5598,a)].
% 79.08/79.00 Derived: hBOOL(hAPP(fun(rat,bool),bool,hAPP(rat,fun(fun(rat,bool),bool),member(rat),one_one(rat)),ring_1_Ints(rat))). [resolve(5632,a,5599,a)].
% 79.08/79.00 Derived: -hBOOL(hAPP(fun(rat,bool),bool,hAPP(rat,fun(fun(rat,bool),bool),member(rat),A),ring_1_Ints(rat))) | -hBOOL(hAPP(fun(rat,bool),bool,hAPP(rat,fun(fun(rat,bool),bool),member(rat),B),ring_1_Ints(rat))) | hBOOL(hAPP(fun(rat,bool),bool,hAPP(rat,fun(fun(rat,bool),bool),member(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),A),B)),ring_1_Ints(rat))). [resolve(5632,a,5600,a)].
% 79.08/79.00 Derived: -hBOOL(hAPP(fun(rat,bool),bool,hAPP(rat,fun(fun(rat,bool),bool),member(rat),A),ring_1_Ints(rat))) | hBOOL(hAPP(fun(rat,bool),bool,hAPP(rat,fun(fun(rat,bool),bool),member(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),B)),ring_1_Ints(rat))). [resolve(5632,a,5601,a)].
% 79.08/79.00 Derived: hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),hAPP(rat,rat,uminus_uminus(rat),A)),B) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),hAPP(rat,rat,uminus_uminus(rat),one_one(rat))),B)),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),B)). [resolve(5632,a,5602,a)].
% 79.08/79.00 Derived: hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),hAPP(rat,rat,uminus_uminus(rat),A)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))). [resolve(5632,a,5603,a)].
% 79.08/79.00 Derived: hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),hAPP(rat,rat,uminus_uminus(rat),A)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),B)) = hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),B)). [resolve(5632,a,5604,a)].
% 79.08/79.00 Derived: hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),hAPP(rat,rat,uminus_uminus(rat),one_one(rat))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),A)) = one_one(rat). [resolve(5632,a,5605,a)].
% 79.08/79.00 Derived: hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),hAPP(rat,rat,uminus_uminus(rat),one_one(rat))),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),A))) = hAPP(rat,rat,uminus_uminus(rat),one_one(rat)). [resolve(5632,a,5606,a)].
% 79.08/79.00 Derived: hBOOL(hAPP(fun(rat,bool),bool,hAPP(rat,fun(fun(rat,bool),bool),member(rat),hAPP(nat,rat,semiring_1_of_nat(rat),A)),ring_1_Ints(rat))). [resolve(5632,a,5607,a)].
% 79.08/79.00 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | hAPP(nat,rat,semiring_1_of_nat(rat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),B),A)) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),hAPP(nat,rat,semiring_1_of_nat(rat),B)),hAPP(nat,rat,semiring_1_of_nat(rat),A)). [resolve(5632,a,5608,a)].
% 79.08/79.00 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),zero_zero(int))) | hAPP(int,rat,ring_1_of_int(rat),A) = hAPP(rat,rat,uminus_uminus(rat),hAPP(nat,rat,semiring_1_of_nat(rat),hAPP(int,nat,nat_1,hAPP(int,int,uminus_uminus(int),A)))). [resolve(5632,a,5609,a)].
% 79.08/79.00 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),zero_zero(int))) | hAPP(nat,rat,semiring_1_of_nat(rat),hAPP(int,nat,nat_1,A)) = hAPP(int,rat,ring_1_of_int(rat),A). [resolve(5632,a,5610,a)].
% 79.08/79.00 Derived: hAPP(int,rat,ring_1_of_int(rat),hAPP(int,int,uminus_uminus(int),A)) = hAPP(rat,rat,uminus_uminus(rat),hAPP(int,rat,ring_1_of_int(rat),A)). [resolve(5632,a,5611,a)].
% 79.08/79.00 Derived: hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),hAPP(int,rat,ring_1_of_int(rat),A)),B) = hAPP(int,rat,ring_1_of_int(rat),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),B)). [resolve(5632,a,5612,a)].
% 79.08/79.00 Derived: hBOOL(hAPP(fun(rat,bool),bool,hAPP(rat,fun(fun(rat,bool),bool),member(rat),hAPP(int,rat,ring_1_of_int(rat),A)),ring_1_Ints(rat))). [resolve(5632,a,5613,a)].
% 79.08/79.00 Derived: hAPP(int,rat,ring_1_of_int(rat),one_one(int)) = one_one(rat). [resolve(5632,a,5614,a)].
% 79.08/79.00 Derived: hAPP(int,rat,ring_1_of_int(rat),zero_zero(int)) = zero_zero(rat). [resolve(5632,a,5615,a)].
% 79.08/79.00 Derived: hAPP(nat,rat,semiring_1_of_nat(rat),A) = hAPP(int,rat,ring_1_of_int(rat),hAPP(nat,int,semiring_1_of_nat(int),A)). [resolve(5632,a,5616,a)].
% 79.08/79.00 Derived: hAPP(int,rat,ring_1_of_int(rat),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(int,rat,ring_1_of_int(rat),A)),hAPP(int,rat,ring_1_of_int(rat),B)). [resolve(5632,a,5617,a)].
% 79.08/79.00 Derived: hAPP(int,rat,ring_1_of_int(rat),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B)) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(int,rat,ring_1_of_int(rat),A)),hAPP(int,rat,ring_1_of_int(rat),B)). [resolve(5632,a,5618,a)].
% 79.08/79.00 Derived: hAPP(int,rat,ring_1_of_int(rat),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),B)) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),hAPP(int,rat,ring_1_of_int(rat),A)),hAPP(int,rat,ring_1_of_int(rat),B)). [resolve(5632,a,5619,a)].
% 79.08/79.00 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A)) | hAPP(nat,rat,semiring_1_of_nat(rat),hAPP(int,nat,nat_1,A)) = hAPP(int,rat,ring_1_of_int(rat),A). [resolve(5632,a,5620,a)].
% 79.08/79.00 Derived: -hBOOL(hAPP(fun(rat,bool),bool,hAPP(rat,fun(fun(rat,bool),bool),member(rat),A),ring_1_Ints(rat))) | -hBOOL(hAPP(rat,bool,B,hAPP(int,rat,ring_1_of_int(rat),f438(rat,B,A)))) | hBOOL(hAPP(rat,bool,B,A)). [resolve(5632,a,5621,a)].
% 79.08/79.00 Derived: -hBOOL(hAPP(fun(rat,bool),bool,hAPP(rat,fun(fun(rat,bool),bool),member(rat),A),ring_1_Ints(rat))) | hAPP(int,rat,ring_1_of_int(rat),f439(rat,A)) = ti(rat,A). [resolve(5632,a,5622,a)].
% 79.08/79.00 Derived: -comm_monoid_mult(rat) | hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co302546470etprod(A,rat),hAPP(fun(A,int),fun(A,rat),hAPP(fun(int,rat),fun(fun(A,int),fun(A,rat)),combb(int,rat,A),ring_1_of_int(rat)),B)),C) = hAPP(int,rat,ring_1_of_int(rat),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),B),C)). [resolve(5632,a,5623,b)].
% 79.08/79.00 Derived: zero_zero(int) != A | hAPP(int,rat,ring_1_of_int(rat),A) = zero_zero(rat). [resolve(5632,a,5624,a)].
% 79.08/79.00 Derived: zero_zero(int) = A | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),zero_zero(int))) | hAPP(int,rat,ring_1_of_int(rat),A) = hAPP(rat,rat,uminus_uminus(rat),hAPP(int,rat,ring_1_of_int(rat),hAPP(int,int,uminus_uminus(int),A))). [resolve(5632,a,5625,a)].
% 79.08/79.00 Derived: zero_zero(int) = A | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),zero_zero(int))) | hAPP(product_prod(int,int),rat,hAPP(fun(int,fun(int,rat)),fun(product_prod(int,int),rat),product_prod_case(int,int,rat),hAPP(fun(int,rat),fun(int,fun(int,rat)),hAPP(fun(int,fun(rat,fun(int,rat))),fun(fun(int,rat),fun(int,fun(int,rat))),combs(int,rat,fun(int,rat)),hAPP(fun(int,fun(int,fun(rat,rat))),fun(int,fun(rat,fun(int,rat))),hAPP(fun(fun(int,fun(rat,rat)),fun(rat,fun(int,rat))),fun(fun(int,fun(int,fun(rat,rat))),fun(int,fun(rat,fun(int,rat)))),combb(fun(int,fun(rat,rat)),fun(rat,fun(int,rat)),int),combc(int,rat,rat)),hAPP(fun(int,rat),fun(int,fun(int,fun(rat,rat))),hAPP(fun(rat,fun(int,fun(rat,rat))),fun(fun(int,rat),fun(int,fun(int,fun(rat,rat)))),combb(rat,fun(int,fun(rat,rat)),int),hAPP(fun(int,fun(rat,fun(rat,rat))),fun(rat,fun(int,fun(rat,rat))),combc(int,rat,fun(rat,rat)),hAPP(fun(int,bool),fun(int,fun(rat,fun(rat,rat))),hAPP(fun(bool,fun(rat,fun(rat,rat))),fun(fun(int,bool),fun(int,fun(rat,fun(rat,rat)))),combb(bool,fun(rat,fun(rat,rat)),int),if(rat)),hAPP(int,fun(int,bool),hAPP(fun(int,fun(int,bool)),fun(int,fun(int,bool)),combc(int,int,bool),fequal(int)),zero_zero(int))))),hAPP(fun(int,rat),fun(int,rat),hAPP(fun(int,fun(rat,rat)),fun(fun(int,rat),fun(int,rat)),combs(int,rat,rat),hAPP(fun(int,rat),fun(int,fun(rat,rat)),hAPP(fun(rat,fun(rat,rat)),fun(fun(int,rat),fun(int,fun(rat,rat))),combb(rat,fun(rat,rat),int),plus_plus(rat)),ring_1_of_int(rat))),ring_1_of_int(rat))))),hAPP(rat,fun(int,rat),hAPP(fun(int,fun(rat,rat)),fun(rat,fun(int,rat)),combc(int,rat,rat),hAPP(fun(int,rat),fun(int,fun(rat,rat)),hAPP(fun(rat,fun(rat,rat)),fun(fun(int,rat),fun(int,fun(rat,rat))),combb(rat,fun(rat,rat),int),plus_plus(rat)),hAPP(fun(int,rat),fun(int,rat),hAPP(fun(int,fun(rat,rat)),fun(fun(int,rat),fun(int,rat)),combs(int,rat,rat),hAPP(fun(int,rat),fun(int,fun(rat,rat)),hAPP(fun(rat,fun(rat,rat)),fun(fun(int,rat),fun(int,fun(rat,rat))),combb(rat,fun(rat,rat),int),plus_plus(rat)),ring_1_of_int(rat))),ring_1_of_int(rat)))),one_one(rat)))),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),divmod_int,A),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) = hAPP(int,rat,ring_1_of_int(rat),A). [resolve(5632,a,5626,a)].
% 79.08/79.00 Derived: -real_normed_vector(rat) | -hBOOL(hAPP(fun(nat,rat),bool,summable(rat),hAPP(fun(nat,rat),fun(nat,rat),hAPP(fun(nat,fun(rat,rat)),fun(fun(nat,rat),fun(nat,rat)),combs(nat,rat,rat),hAPP(fun(nat,rat),fun(nat,fun(rat,rat)),hAPP(fun(rat,fun(rat,rat)),fun(fun(nat,rat),fun(nat,fun(rat,rat))),combb(rat,fun(rat,rat),nat),times_times(rat)),hAPP(fun(nat,rat),fun(nat,rat),diffs(rat),A))),hAPP(rat,fun(nat,rat),power_power(rat),B)))) | hBOOL(hAPP(rat,bool,hAPP(fun(nat,rat),fun(rat,bool),sums(rat),hAPP(fun(nat,rat),fun(nat,rat),hAPP(fun(nat,fun(rat,rat)),fun(fun(nat,rat),fun(nat,rat)),combs(nat,rat,rat),hAPP(fun(nat,rat),fun(nat,fun(rat,rat)),hAPP(fun(rat,fun(rat,rat)),fun(fun(nat,rat),fun(nat,fun(rat,rat))),combb(rat,fun(rat,rat),nat),times_times(rat)),hAPP(fun(nat,rat),fun(nat,rat),hAPP(fun(nat,fun(rat,rat)),fun(fun(nat,rat),fun(nat,rat)),combs(nat,rat,rat),hAPP(fun(nat,rat),fun(nat,fun(rat,rat)),hAPP(fun(rat,fun(rat,rat)),fun(fun(nat,rat),fun(nat,fun(rat,rat))),combb(rat,fun(rat,rat),nat),times_times(rat)),semiring_1_of_nat(rat))),A))),hAPP(fun(nat,nat),fun(nat,rat),hAPP(fun(nat,rat),fun(fun(nat,nat),fun(nat,rat)),combb(nat,rat,nat),hAPP(rat,fun(nat,rat),power_power(rat),B)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),minus_minus(nat)),hAPP(nat,nat,suc,zero_zero(nat)))))),hAPP(fun(nat,rat),rat,suminf(rat),hAPP(fun(nat,rat),fun(nat,rat),hAPP(fun(nat,fun(rat,rat)),fun(fun(nat,rat),fun(nat,rat)),combs(nat,rat,rat),hAPP(fun(nat,rat),fun(nat,fun(rat,rat)),hAPP(fun(rat,fun(rat,rat)),fun(fun(nat,rat),fun(nat,fun(rat,rat))),combb(rat,fun(rat,rat),nat),times_times(rat)),hAPP(fun(nat,rat),fun(nat,rat),diffs(rat),A))),hAPP(rat,fun(nat,rat),power_power(rat),B))))). [resolve(5632,a,5627,b)].
% 79.08/79.00 Derived: hAPP(nat,rat,hAPP(fun(nat,rat),fun(nat,rat),diffs(rat),hAPP(fun(nat,rat),fun(nat,rat),hAPP(fun(rat,rat),fun(fun(nat,rat),fun(nat,rat)),combb(rat,rat,nat),uminus_uminus(rat)),A)),B) = hAPP(rat,rat,uminus_uminus(rat),hAPP(nat,rat,hAPP(fun(nat,rat),fun(nat,rat),diffs(rat),A),B)). [resolve(5632,a,5628,a)].
% 79.13/79.04 Derived: hAPP(nat,rat,hAPP(fun(nat,rat),fun(nat,rat),diffs(rat),A),B) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(nat,rat,semiring_1_of_nat(rat),hAPP(nat,nat,suc,B))),hAPP(nat,rat,A,hAPP(nat,nat,suc,B))). [resolve(5632,a,5629,a)].
% 79.13/79.04 Derived: hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),hAPP(fun(A,int),fun(A,rat),hAPP(fun(int,rat),fun(fun(A,int),fun(A,rat)),combb(int,rat,A),ring_1_of_int(rat)),B)),C) = hAPP(int,rat,ring_1_of_int(rat),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),B),C)). [resolve(5632,a,5630,a)].
% 79.13/79.04 Derived: hAPP(fun(nat,bool),rat,hAPP(fun(nat,rat),fun(fun(nat,bool),rat),big_co1399186613setsum(nat,rat),hAPP(rat,fun(nat,rat),hAPP(fun(nat,fun(rat,rat)),fun(rat,fun(nat,rat)),combc(nat,rat,rat),hAPP(fun(nat,rat),fun(nat,fun(rat,rat)),hAPP(fun(rat,fun(rat,rat)),fun(fun(nat,rat),fun(nat,fun(rat,rat))),combb(rat,fun(rat,rat),nat),minus_minus(rat)),A)),B)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),C)) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),hAPP(fun(nat,bool),rat,hAPP(fun(nat,rat),fun(fun(nat,bool),rat),big_co1399186613setsum(nat,rat),A),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),C))),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(nat,rat,semiring_1_of_nat(rat),C)),B)). [resolve(5632,a,5631,a)].
% 79.13/79.04 5633 ring_1(real) # label(arity_RealDef_Oreal___Rings_Oring__1) # label(axiom). [assumption].
% 79.13/79.04 Derived: ring_1_Ints(real) = ti(fun(real,bool),ring_1_Ints(real)). [resolve(5633,a,5591,a)].
% 79.13/79.04 Derived: ring_1_of_int(real) = ti(fun(int,real),ring_1_of_int(real)). [resolve(5633,a,5592,a)].
% 79.13/79.04 Derived: diffs(real) = ti(fun(fun(nat,real),fun(nat,real)),diffs(real)). [resolve(5633,a,5593,a)].
% 79.13/79.04 Derived: hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),one_one(real))),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),one_one(real))) = hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),A)),one_one(real)). [resolve(5633,a,5594,a)].
% 79.13/79.04 Derived: -hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),A),ring_1_Ints(real))) | hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),hAPP(real,real,uminus_uminus(real),A)),ring_1_Ints(real))). [resolve(5633,a,5595,a)].
% 79.13/79.04 Derived: hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),zero_zero(real)),ring_1_Ints(real))). [resolve(5633,a,5596,a)].
% 79.13/79.04 Derived: -hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),A),ring_1_Ints(real))) | -hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),B),ring_1_Ints(real))) | hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),ring_1_Ints(real))). [resolve(5633,a,5597,a)].
% 79.13/79.04 Derived: -hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),A),ring_1_Ints(real))) | -hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),B),ring_1_Ints(real))) | hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),B)),ring_1_Ints(real))). [resolve(5633,a,5598,a)].
% 79.13/79.04 Derived: hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),one_one(real)),ring_1_Ints(real))). [resolve(5633,a,5599,a)].
% 79.13/79.04 Derived: -hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),A),ring_1_Ints(real))) | -hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),B),ring_1_Ints(real))) | hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),B)),ring_1_Ints(real))). [resolve(5633,a,5600,a)].
% 79.16/79.05 Derived: -hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),A),ring_1_Ints(real))) | hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),B)),ring_1_Ints(real))). [resolve(5633,a,5601,a)].
% 79.16/79.05 Derived: hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,uminus_uminus(real),A)),B) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,uminus_uminus(real),one_one(real))),B)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),B)). [resolve(5633,a,5602,a)].
% 79.16/79.05 Derived: hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,uminus_uminus(real),A)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))). [resolve(5633,a,5603,a)].
% 79.16/79.05 Derived: hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,uminus_uminus(real),A)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),B)) = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),B)). [resolve(5633,a,5604,a)].
% 79.16/79.05 Derived: hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,uminus_uminus(real),one_one(real))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),A)) = one_one(real). [resolve(5633,a,5605,a)].
% 79.16/79.05 Derived: hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,uminus_uminus(real),one_one(real))),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),A))) = hAPP(real,real,uminus_uminus(real),one_one(real)). [resolve(5633,a,5606,a)].
% 79.16/79.05 Derived: hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),hAPP(nat,real,semiring_1_of_nat(real),A)),ring_1_Ints(real))). [resolve(5633,a,5607,a)].
% 79.16/79.05 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | hAPP(nat,real,semiring_1_of_nat(real),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),B),A)) = hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(nat,real,semiring_1_of_nat(real),B)),hAPP(nat,real,semiring_1_of_nat(real),A)). [resolve(5633,a,5608,a)].
% 79.16/79.05 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),zero_zero(int))) | hAPP(int,real,ring_1_of_int(real),A) = hAPP(real,real,uminus_uminus(real),hAPP(nat,real,semiring_1_of_nat(real),hAPP(int,nat,nat_1,hAPP(int,int,uminus_uminus(int),A)))). [resolve(5633,a,5609,a)].
% 79.16/79.05 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),zero_zero(int))) | hAPP(nat,real,semiring_1_of_nat(real),hAPP(int,nat,nat_1,A)) = hAPP(int,real,ring_1_of_int(real),A). [resolve(5633,a,5610,a)].
% 79.16/79.05 Derived: hAPP(int,real,ring_1_of_int(real),hAPP(int,int,uminus_uminus(int),A)) = hAPP(real,real,uminus_uminus(real),hAPP(int,real,ring_1_of_int(real),A)). [resolve(5633,a,5611,a)].
% 79.16/79.05 Derived: hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,ring_1_of_int(real),A)),B) = hAPP(int,real,ring_1_of_int(real),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),B)). [resolve(5633,a,5612,a)].
% 79.16/79.05 Derived: hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),hAPP(int,real,ring_1_of_int(real),A)),ring_1_Ints(real))). [resolve(5633,a,5613,a)].
% 79.16/79.05 Derived: hAPP(int,real,ring_1_of_int(real),one_one(int)) = one_one(real). [resolve(5633,a,5614,a)].
% 79.16/79.05 Derived: hAPP(int,real,ring_1_of_int(real),zero_zero(int)) = zero_zero(real). [resolve(5633,a,5615,a)].
% 79.16/79.05 Derived: hAPP(nat,real,semiring_1_of_nat(real),A) = hAPP(int,real,ring_1_of_int(real),hAPP(nat,int,semiring_1_of_nat(int),A)). [resolve(5633,a,5616,a)].
% 79.16/79.05 Derived: hAPP(int,real,ring_1_of_int(real),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,ring_1_of_int(real),A)),hAPP(int,real,ring_1_of_int(real),B)). [resolve(5633,a,5617,a)].
% 79.16/79.05 Derived: hAPP(int,real,ring_1_of_int(real),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B)) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(int,real,ring_1_of_int(real),A)),hAPP(int,real,ring_1_of_int(real),B)). [resolve(5633,a,5618,a)].
% 79.16/79.05 Derived: hAPP(int,real,ring_1_of_int(real),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),B)) = hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(int,real,ring_1_of_int(real),A)),hAPP(int,real,ring_1_of_int(real),B)). [resolve(5633,a,5619,a)].
% 79.16/79.05 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A)) | hAPP(nat,real,semiring_1_of_nat(real),hAPP(int,nat,nat_1,A)) = hAPP(int,real,ring_1_of_int(real),A). [resolve(5633,a,5620,a)].
% 79.16/79.05 Derived: -hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),A),ring_1_Ints(real))) | -hBOOL(hAPP(real,bool,B,hAPP(int,real,ring_1_of_int(real),f438(real,B,A)))) | hBOOL(hAPP(real,bool,B,A)). [resolve(5633,a,5621,a)].
% 79.16/79.05 Derived: -hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),A),ring_1_Ints(real))) | hAPP(int,real,ring_1_of_int(real),f439(real,A)) = ti(real,A). [resolve(5633,a,5622,a)].
% 79.16/79.05 Derived: -comm_monoid_mult(real) | hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co302546470etprod(A,real),hAPP(fun(A,int),fun(A,real),hAPP(fun(int,real),fun(fun(A,int),fun(A,real)),combb(int,real,A),ring_1_of_int(real)),B)),C) = hAPP(int,real,ring_1_of_int(real),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),B),C)). [resolve(5633,a,5623,b)].
% 79.16/79.05 Derived: zero_zero(int) != A | hAPP(int,real,ring_1_of_int(real),A) = zero_zero(real). [resolve(5633,a,5624,a)].
% 79.16/79.05 Derived: zero_zero(int) = A | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),zero_zero(int))) | hAPP(int,real,ring_1_of_int(real),A) = hAPP(real,real,uminus_uminus(real),hAPP(int,real,ring_1_of_int(real),hAPP(int,int,uminus_uminus(int),A))). [resolve(5633,a,5625,a)].
% 79.16/79.05 Derived: zero_zero(int) = A | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),zero_zero(int))) | hAPP(product_prod(int,int),real,hAPP(fun(int,fun(int,real)),fun(product_prod(int,int),real),product_prod_case(int,int,real),hAPP(fun(int,real),fun(int,fun(int,real)),hAPP(fun(int,fun(real,fun(int,real))),fun(fun(int,real),fun(int,fun(int,real))),combs(int,real,fun(int,real)),hAPP(fun(int,fun(int,fun(real,real))),fun(int,fun(real,fun(int,real))),hAPP(fun(fun(int,fun(real,real)),fun(real,fun(int,real))),fun(fun(int,fun(int,fun(real,real))),fun(int,fun(real,fun(int,real)))),combb(fun(int,fun(real,real)),fun(real,fun(int,real)),int),combc(int,real,real)),hAPP(fun(int,real),fun(int,fun(int,fun(real,real))),hAPP(fun(real,fun(int,fun(real,real))),fun(fun(int,real),fun(int,fun(int,fun(real,real)))),combb(real,fun(int,fun(real,real)),int),hAPP(fun(int,fun(real,fun(real,real))),fun(real,fun(int,fun(real,real))),combc(int,real,fun(real,real)),hAPP(fun(int,bool),fun(int,fun(real,fun(real,real))),hAPP(fun(bool,fun(real,fun(real,real))),fun(fun(int,bool),fun(int,fun(real,fun(real,real)))),combb(bool,fun(real,fun(real,real)),int),if(real)),hAPP(int,fun(int,bool),hAPP(fun(int,fun(int,bool)),fun(int,fun(int,bool)),combc(int,int,bool),fequal(int)),zero_zero(int))))),hAPP(fun(int,real),fun(int,real),hAPP(fun(int,fun(real,real)),fun(fun(int,real),fun(int,real)),combs(int,real,real),hAPP(fun(int,real),fun(int,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(int,real),fun(int,fun(real,real))),combb(real,fun(real,real),int),plus_plus(real)),ring_1_of_int(real))),ring_1_of_int(real))))),hAPP(real,fun(int,real),hAPP(fun(int,fun(real,real)),fun(real,fun(int,real)),combc(int,real,real),hAPP(fun(int,real),fun(int,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(int,real),fun(int,fun(real,real))),combb(real,fun(real,real),int),plus_plus(real)),hAPP(fun(int,real),fun(int,real),hAPP(fun(int,fun(real,real)),fun(fun(int,real),fun(int,real)),combs(int,real,real),hAPP(fun(int,real),fun(int,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(int,real),fun(int,fun(real,real))),combb(real,fun(real,real),int),plus_plus(real)),ring_1_of_int(real))),ring_1_of_int(real)))),one_one(real)))),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),divmod_int,A),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) = hAPP(int,real,ring_1_of_int(real),A). [resolve(5633,a,5626,a)].
% 79.16/79.05 Derived: -real_normed_vector(real) | -hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(fun(nat,real),fun(nat,real),diffs(real),A))),hAPP(real,fun(nat,real),power_power(real),B)))) | hBOOL(hAPP(real,bool,hAPP(fun(nat,real),fun(real,bool),sums(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),semiring_1_of_nat(real))),A))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),hAPP(real,fun(nat,real),power_power(real),B)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),minus_minus(nat)),hAPP(nat,nat,suc,zero_zero(nat)))))),hAPP(fun(nat,real),real,suminf(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(fun(nat,real),fun(nat,real),diffs(real),A))),hAPP(real,fun(nat,real),power_power(real),B))))). [resolve(5633,a,5627,b)].
% 79.16/79.05 Derived: hAPP(nat,real,hAPP(fun(nat,real),fun(nat,real),diffs(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),uminus_uminus(real)),A)),B) = hAPP(real,real,uminus_uminus(real),hAPP(nat,real,hAPP(fun(nat,real),fun(nat,real),diffs(real),A),B)). [resolve(5633,a,5628,a)].
% 79.16/79.05 Derived: hAPP(nat,real,hAPP(fun(nat,real),fun(nat,real),diffs(real),A),B) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,semiring_1_of_nat(real),hAPP(nat,nat,suc,B))),hAPP(nat,real,A,hAPP(nat,nat,suc,B))). [resolve(5633,a,5629,a)].
% 79.16/79.05 Derived: hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),hAPP(fun(A,int),fun(A,real),hAPP(fun(int,real),fun(fun(A,int),fun(A,real)),combb(int,real,A),ring_1_of_int(real)),B)),C) = hAPP(int,real,ring_1_of_int(real),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),B),C)). [resolve(5633,a,5630,a)].
% 79.16/79.05 Derived: hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(real,fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(real,fun(nat,real)),combc(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),minus_minus(real)),A)),B)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),C)) = hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),A),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),C))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,semiring_1_of_nat(real),C)),B)). [resolve(5633,a,5631,a)].
% 79.16/79.08 5634 ring_1(complex) # label(arity_Complex_Ocomplex___Rings_Oring__1) # label(axiom). [assumption].
% 79.16/79.08 Derived: ring_1_Ints(complex) = ti(fun(complex,bool),ring_1_Ints(complex)). [resolve(5634,a,5591,a)].
% 79.16/79.08 Derived: ring_1_of_int(complex) = ti(fun(int,complex),ring_1_of_int(complex)). [resolve(5634,a,5592,a)].
% 79.16/79.08 Derived: diffs(complex) = ti(fun(fun(nat,complex),fun(nat,complex)),diffs(complex)). [resolve(5634,a,5593,a)].
% 79.16/79.08 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),A),one_one(complex))),hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),A),one_one(complex))) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),A)),one_one(complex)). [resolve(5634,a,5594,a)].
% 79.16/79.08 Derived: -hBOOL(hAPP(fun(complex,bool),bool,hAPP(complex,fun(fun(complex,bool),bool),member(complex),A),ring_1_Ints(complex))) | hBOOL(hAPP(fun(complex,bool),bool,hAPP(complex,fun(fun(complex,bool),bool),member(complex),hAPP(complex,complex,uminus_uminus(complex),A)),ring_1_Ints(complex))). [resolve(5634,a,5595,a)].
% 79.16/79.08 Derived: hBOOL(hAPP(fun(complex,bool),bool,hAPP(complex,fun(fun(complex,bool),bool),member(complex),zero_zero(complex)),ring_1_Ints(complex))). [resolve(5634,a,5596,a)].
% 79.16/79.08 Derived: -hBOOL(hAPP(fun(complex,bool),bool,hAPP(complex,fun(fun(complex,bool),bool),member(complex),A),ring_1_Ints(complex))) | -hBOOL(hAPP(fun(complex,bool),bool,hAPP(complex,fun(fun(complex,bool),bool),member(complex),B),ring_1_Ints(complex))) | hBOOL(hAPP(fun(complex,bool),bool,hAPP(complex,fun(fun(complex,bool),bool),member(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),B)),ring_1_Ints(complex))). [resolve(5634,a,5597,a)].
% 79.16/79.08 Derived: -hBOOL(hAPP(fun(complex,bool),bool,hAPP(complex,fun(fun(complex,bool),bool),member(complex),A),ring_1_Ints(complex))) | -hBOOL(hAPP(fun(complex,bool),bool,hAPP(complex,fun(fun(complex,bool),bool),member(complex),B),ring_1_Ints(complex))) | hBOOL(hAPP(fun(complex,bool),bool,hAPP(complex,fun(fun(complex,bool),bool),member(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),A),B)),ring_1_Ints(complex))). [resolve(5634,a,5598,a)].
% 79.16/79.08 Derived: hBOOL(hAPP(fun(complex,bool),bool,hAPP(complex,fun(fun(complex,bool),bool),member(complex),one_one(complex)),ring_1_Ints(complex))). [resolve(5634,a,5599,a)].
% 79.16/79.08 Derived: -hBOOL(hAPP(fun(complex,bool),bool,hAPP(complex,fun(fun(complex,bool),bool),member(complex),A),ring_1_Ints(complex))) | -hBOOL(hAPP(fun(complex,bool),bool,hAPP(complex,fun(fun(complex,bool),bool),member(complex),B),ring_1_Ints(complex))) | hBOOL(hAPP(fun(complex,bool),bool,hAPP(complex,fun(fun(complex,bool),bool),member(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),A),B)),ring_1_Ints(complex))). [resolve(5634,a,5600,a)].
% 79.16/79.08 Derived: -hBOOL(hAPP(fun(complex,bool),bool,hAPP(complex,fun(fun(complex,bool),bool),member(complex),A),ring_1_Ints(complex))) | hBOOL(hAPP(fun(complex,bool),bool,hAPP(complex,fun(fun(complex,bool),bool),member(complex),hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),A),B)),ring_1_Ints(complex))). [resolve(5634,a,5601,a)].
% 79.16/79.08 Derived: hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),hAPP(complex,complex,uminus_uminus(complex),A)),B) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),hAPP(complex,complex,uminus_uminus(complex),one_one(complex))),B)),hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),A),B)). [resolve(5634,a,5602,a)].
% 79.16/79.08 Derived: hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),hAPP(complex,complex,uminus_uminus(complex),A)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))). [resolve(5634,a,5603,a)].
% 79.16/79.08 Derived: hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),hAPP(complex,complex,uminus_uminus(complex),A)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),B)) = hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),B)). [resolve(5634,a,5604,a)].
% 79.16/79.08 Derived: hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),hAPP(complex,complex,uminus_uminus(complex),one_one(complex))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),A)) = one_one(complex). [resolve(5634,a,5605,a)].
% 79.16/79.08 Derived: hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),hAPP(complex,complex,uminus_uminus(complex),one_one(complex))),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),A))) = hAPP(complex,complex,uminus_uminus(complex),one_one(complex)). [resolve(5634,a,5606,a)].
% 79.16/79.08 Derived: hBOOL(hAPP(fun(complex,bool),bool,hAPP(complex,fun(fun(complex,bool),bool),member(complex),hAPP(nat,complex,semiring_1_of_nat(complex),A)),ring_1_Ints(complex))). [resolve(5634,a,5607,a)].
% 79.16/79.08 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | hAPP(nat,complex,semiring_1_of_nat(complex),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),B),A)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),B)),hAPP(nat,complex,semiring_1_of_nat(complex),A)). [resolve(5634,a,5608,a)].
% 79.16/79.08 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),zero_zero(int))) | hAPP(int,complex,ring_1_of_int(complex),A) = hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),hAPP(int,nat,nat_1,hAPP(int,int,uminus_uminus(int),A)))). [resolve(5634,a,5609,a)].
% 79.16/79.08 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),zero_zero(int))) | hAPP(nat,complex,semiring_1_of_nat(complex),hAPP(int,nat,nat_1,A)) = hAPP(int,complex,ring_1_of_int(complex),A). [resolve(5634,a,5610,a)].
% 79.16/79.08 Derived: hAPP(int,complex,ring_1_of_int(complex),hAPP(int,int,uminus_uminus(int),A)) = hAPP(complex,complex,uminus_uminus(complex),hAPP(int,complex,ring_1_of_int(complex),A)). [resolve(5634,a,5611,a)].
% 79.16/79.08 Derived: hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),hAPP(int,complex,ring_1_of_int(complex),A)),B) = hAPP(int,complex,ring_1_of_int(complex),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),B)). [resolve(5634,a,5612,a)].
% 79.16/79.08 Derived: hBOOL(hAPP(fun(complex,bool),bool,hAPP(complex,fun(fun(complex,bool),bool),member(complex),hAPP(int,complex,ring_1_of_int(complex),A)),ring_1_Ints(complex))). [resolve(5634,a,5613,a)].
% 79.16/79.08 Derived: hAPP(int,complex,ring_1_of_int(complex),one_one(int)) = one_one(complex). [resolve(5634,a,5614,a)].
% 79.16/79.08 Derived: hAPP(int,complex,ring_1_of_int(complex),zero_zero(int)) = zero_zero(complex). [resolve(5634,a,5615,a)].
% 79.16/79.08 Derived: hAPP(nat,complex,semiring_1_of_nat(complex),A) = hAPP(int,complex,ring_1_of_int(complex),hAPP(nat,int,semiring_1_of_nat(int),A)). [resolve(5634,a,5616,a)].
% 79.16/79.08 Derived: hAPP(int,complex,ring_1_of_int(complex),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(int,complex,ring_1_of_int(complex),A)),hAPP(int,complex,ring_1_of_int(complex),B)). [resolve(5634,a,5617,a)].
% 79.16/79.09 Derived: hAPP(int,complex,ring_1_of_int(complex),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(int,complex,ring_1_of_int(complex),A)),hAPP(int,complex,ring_1_of_int(complex),B)). [resolve(5634,a,5618,a)].
% 79.16/79.09 Derived: hAPP(int,complex,ring_1_of_int(complex),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),B)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),hAPP(int,complex,ring_1_of_int(complex),A)),hAPP(int,complex,ring_1_of_int(complex),B)). [resolve(5634,a,5619,a)].
% 79.16/79.09 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A)) | hAPP(nat,complex,semiring_1_of_nat(complex),hAPP(int,nat,nat_1,A)) = hAPP(int,complex,ring_1_of_int(complex),A). [resolve(5634,a,5620,a)].
% 79.16/79.09 Derived: -hBOOL(hAPP(fun(complex,bool),bool,hAPP(complex,fun(fun(complex,bool),bool),member(complex),A),ring_1_Ints(complex))) | -hBOOL(hAPP(complex,bool,B,hAPP(int,complex,ring_1_of_int(complex),f438(complex,B,A)))) | hBOOL(hAPP(complex,bool,B,A)). [resolve(5634,a,5621,a)].
% 79.16/79.09 Derived: -hBOOL(hAPP(fun(complex,bool),bool,hAPP(complex,fun(fun(complex,bool),bool),member(complex),A),ring_1_Ints(complex))) | hAPP(int,complex,ring_1_of_int(complex),f439(complex,A)) = ti(complex,A). [resolve(5634,a,5622,a)].
% 79.16/79.09 Derived: -comm_monoid_mult(complex) | hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co302546470etprod(A,complex),hAPP(fun(A,int),fun(A,complex),hAPP(fun(int,complex),fun(fun(A,int),fun(A,complex)),combb(int,complex,A),ring_1_of_int(complex)),B)),C) = hAPP(int,complex,ring_1_of_int(complex),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),B),C)). [resolve(5634,a,5623,b)].
% 79.16/79.09 Derived: zero_zero(int) != A | hAPP(int,complex,ring_1_of_int(complex),A) = zero_zero(complex). [resolve(5634,a,5624,a)].
% 79.16/79.09 Derived: zero_zero(int) = A | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),zero_zero(int))) | hAPP(int,complex,ring_1_of_int(complex),A) = hAPP(complex,complex,uminus_uminus(complex),hAPP(int,complex,ring_1_of_int(complex),hAPP(int,int,uminus_uminus(int),A))). [resolve(5634,a,5625,a)].
% 79.16/79.09 Derived: zero_zero(int) = A | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),zero_zero(int))) | hAPP(product_prod(int,int),complex,hAPP(fun(int,fun(int,complex)),fun(product_prod(int,int),complex),product_prod_case(int,int,complex),hAPP(fun(int,complex),fun(int,fun(int,complex)),hAPP(fun(int,fun(complex,fun(int,complex))),fun(fun(int,complex),fun(int,fun(int,complex))),combs(int,complex,fun(int,complex)),hAPP(fun(int,fun(int,fun(complex,complex))),fun(int,fun(complex,fun(int,complex))),hAPP(fun(fun(int,fun(complex,complex)),fun(complex,fun(int,complex))),fun(fun(int,fun(int,fun(complex,complex))),fun(int,fun(complex,fun(int,complex)))),combb(fun(int,fun(complex,complex)),fun(complex,fun(int,complex)),int),combc(int,complex,complex)),hAPP(fun(int,complex),fun(int,fun(int,fun(complex,complex))),hAPP(fun(complex,fun(int,fun(complex,complex))),fun(fun(int,complex),fun(int,fun(int,fun(complex,complex)))),combb(complex,fun(int,fun(complex,complex)),int),hAPP(fun(int,fun(complex,fun(complex,complex))),fun(complex,fun(int,fun(complex,complex))),combc(int,complex,fun(complex,complex)),hAPP(fun(int,bool),fun(int,fun(complex,fun(complex,complex))),hAPP(fun(bool,fun(complex,fun(complex,complex))),fun(fun(int,bool),fun(int,fun(complex,fun(complex,complex)))),combb(bool,fun(complex,fun(complex,complex)),int),if(complex)),hAPP(int,fun(int,bool),hAPP(fun(int,fun(int,bool)),fun(int,fun(int,bool)),combc(int,int,bool),fequal(int)),zero_zero(int))))),hAPP(fun(int,complex),fun(int,complex),hAPP(fun(int,fun(complex,complex)),fun(fun(int,complex),fun(int,complex)),combs(int,complex,complex),hAPP(fun(int,complex),fun(int,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(int,complex),fun(int,fun(complex,complex))),combb(complex,fun(complex,complex),int),plus_plus(complex)),ring_1_of_int(complex))),ring_1_of_int(complex))))),hAPP(complex,fun(int,complex),hAPP(fun(int,fun(complex,complex)),fun(complex,fun(int,complex)),combc(int,complex,complex),hAPP(fun(int,complex),fun(int,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(int,complex),fun(int,fun(complex,complex))),combb(complex,fun(complex,complex),int),plus_plus(complex)),hAPP(fun(int,complex),fun(int,complex),hAPP(fun(int,fun(complex,complex)),fun(fun(int,complex),fun(int,complex)),combs(int,complex,complex),hAPP(fun(int,complex),fun(int,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(int,complex),fun(int,fun(complex,complex))),combb(complex,fun(complex,complex),int),plus_plus(complex)),ring_1_of_int(complex))),ring_1_of_int(complex)))),one_one(complex)))),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),divmod_int,A),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) = hAPP(int,complex,ring_1_of_int(complex),A). [resolve(5634,a,5626,a)].
% 79.16/79.09 Derived: -real_normed_vector(complex) | -hBOOL(hAPP(fun(nat,complex),bool,summable(complex),hAPP(fun(nat,complex),fun(nat,complex),hAPP(fun(nat,fun(complex,complex)),fun(fun(nat,complex),fun(nat,complex)),combs(nat,complex,complex),hAPP(fun(nat,complex),fun(nat,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(nat,complex),fun(nat,fun(complex,complex))),combb(complex,fun(complex,complex),nat),times_times(complex)),hAPP(fun(nat,complex),fun(nat,complex),diffs(complex),A))),hAPP(complex,fun(nat,complex),power_power(complex),B)))) | hBOOL(hAPP(complex,bool,hAPP(fun(nat,complex),fun(complex,bool),sums(complex),hAPP(fun(nat,complex),fun(nat,complex),hAPP(fun(nat,fun(complex,complex)),fun(fun(nat,complex),fun(nat,complex)),combs(nat,complex,complex),hAPP(fun(nat,complex),fun(nat,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(nat,complex),fun(nat,fun(complex,complex))),combb(complex,fun(complex,complex),nat),times_times(complex)),hAPP(fun(nat,complex),fun(nat,complex),hAPP(fun(nat,fun(complex,complex)),fun(fun(nat,complex),fun(nat,complex)),combs(nat,complex,complex),hAPP(fun(nat,complex),fun(nat,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(nat,complex),fun(nat,fun(complex,complex))),combb(complex,fun(complex,complex),nat),times_times(complex)),semiring_1_of_nat(complex))),A))),hAPP(fun(nat,nat),fun(nat,complex),hAPP(fun(nat,complex),fun(fun(nat,nat),fun(nat,complex)),combb(nat,complex,nat),hAPP(complex,fun(nat,complex),power_power(complex),B)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),minus_minus(nat)),hAPP(nat,nat,suc,zero_zero(nat)))))),hAPP(fun(nat,complex),complex,suminf(complex),hAPP(fun(nat,complex),fun(nat,complex),hAPP(fun(nat,fun(complex,complex)),fun(fun(nat,complex),fun(nat,complex)),combs(nat,complex,complex),hAPP(fun(nat,complex),fun(nat,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(nat,complex),fun(nat,fun(complex,complex))),combb(complex,fun(complex,complex),nat),times_times(complex)),hAPP(fun(nat,complex),fun(nat,complex),diffs(complex),A))),hAPP(complex,fun(nat,complex),power_power(complex),B))))). [resolve(5634,a,5627,b)].
% 79.16/79.09 Derived: hAPP(nat,complex,hAPP(fun(nat,complex),fun(nat,complex),diffs(complex),hAPP(fun(nat,complex),fun(nat,complex),hAPP(fun(complex,complex),fun(fun(nat,complex),fun(nat,complex)),combb(complex,complex,nat),uminus_uminus(complex)),A)),B) = hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,hAPP(fun(nat,complex),fun(nat,complex),diffs(complex),A),B)). [resolve(5634,a,5628,a)].
% 79.16/79.09 Derived: hAPP(nat,complex,hAPP(fun(nat,complex),fun(nat,complex),diffs(complex),A),B) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(nat,complex,semiring_1_of_nat(complex),hAPP(nat,nat,suc,B))),hAPP(nat,complex,A,hAPP(nat,nat,suc,B))). [resolve(5634,a,5629,a)].
% 79.16/79.09 Derived: hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),hAPP(fun(A,int),fun(A,complex),hAPP(fun(int,complex),fun(fun(A,int),fun(A,complex)),combb(int,complex,A),ring_1_of_int(complex)),B)),C) = hAPP(int,complex,ring_1_of_int(complex),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),B),C)). [resolve(5634,a,5630,a)].
% 82.69/82.64 Derived: hAPP(fun(nat,bool),complex,hAPP(fun(nat,complex),fun(fun(nat,bool),complex),big_co1399186613setsum(nat,complex),hAPP(complex,fun(nat,complex),hAPP(fun(nat,fun(complex,complex)),fun(complex,fun(nat,complex)),combc(nat,complex,complex),hAPP(fun(nat,complex),fun(nat,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(nat,complex),fun(nat,fun(complex,complex))),combb(complex,fun(complex,complex),nat),minus_minus(complex)),A)),B)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),C)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),hAPP(fun(nat,bool),complex,hAPP(fun(nat,complex),fun(fun(nat,bool),complex),big_co1399186613setsum(nat,complex),A),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),C))),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(nat,complex,semiring_1_of_nat(complex),C)),B)). [resolve(5634,a,5631,a)].
% 82.69/82.64 5635 field_char_0(rat) # label(arity_Rat_Orat___Rat_Ofield__char__0) # label(axiom). [assumption].
% 82.69/82.64 5636 -field_char_0(A) | field_char_0_Rats(A) = ti(fun(A,bool),field_char_0_Rats(A)) # label(tsy_c_Rat_Ofield__char__0__class_ORats_res) # label(axiom). [clausify(89)].
% 82.69/82.64 5637 -field_char_0(A) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),B),field_char_0_Rats(A))) | zero_zero(A) = ti(A,B) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),hAPP(A,A,inverse_inverse(A),B)),field_char_0_Rats(A))) # label(fact_3697_nonzero__Rats__inverse) # label(axiom). [clausify(3650)].
% 82.69/82.64 5638 -field_char_0(A) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),B),field_char_0_Rats(A))) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),field_char_0_Rats(A))) | zero_zero(A) = ti(A,C) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)),field_char_0_Rats(A))) # label(fact_3698_nonzero__Rats__divide) # label(axiom). [clausify(3651)].
% 82.69/82.64 5639 -field_char_0(A) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),zero_zero(A)),field_char_0_Rats(A))) # label(fact_3700_Rats__0) # label(axiom). [clausify(3653)].
% 82.69/82.64 5640 -field_char_0(A) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),B),field_char_0_Rats(A))) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),field_char_0_Rats(A))) | 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),B),C)),field_char_0_Rats(A))) # label(fact_3701_Rats__mult) # label(axiom). [clausify(3654)].
% 82.69/82.64 5641 -field_char_0(A) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),B),field_char_0_Rats(A))) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),field_char_0_Rats(A))) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),field_char_0_Rats(A))) # label(fact_3702_Rats__add) # label(axiom). [clausify(3655)].
% 82.69/82.64 5642 -number_ring(A) | -field_char_0(A) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),hAPP(int,A,number_number_of(A),B)),field_char_0_Rats(A))) # label(fact_3703_Rats__number__of) # label(axiom). [clausify(3656)].
% 82.69/82.64 5643 -field_char_0(A) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),one_one(A)),field_char_0_Rats(A))) # label(fact_3704_Rats__1) # label(axiom). [clausify(3657)].
% 82.69/82.64 5644 -field_char_0(A) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),B),field_char_0_Rats(A))) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),field_char_0_Rats(A))) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C)),field_char_0_Rats(A))) # label(fact_3705_Rats__diff) # label(axiom). [clausify(3658)].
% 82.69/82.64 5645 -field_char_0(A) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),B),field_char_0_Rats(A))) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C)),field_char_0_Rats(A))) # label(fact_3706_Rats__power) # label(axiom). [clausify(3659)].
% 82.69/82.64 5646 -field_char_0(A) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),B),field_char_0_Rats(A))) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),hAPP(A,A,uminus_uminus(A),B)),field_char_0_Rats(A))) # label(fact_3707_Rats__minus) # label(axiom). [clausify(3660)].
% 82.69/82.64 5647 -field_inverse_zero(A) | -field_char_0(A) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),B),field_char_0_Rats(A))) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),field_char_0_Rats(A))) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)),field_char_0_Rats(A))) # label(fact_3708_Rats__divide) # label(axiom). [clausify(3661)].
% 82.69/82.64 5648 -field_char_0(A) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),hAPP(nat,A,semiring_1_of_nat(A),B)),field_char_0_Rats(A))) # label(fact_3709_Rats__of__nat) # label(axiom). [clausify(3662)].
% 82.69/82.64 5649 -field_inverse_zero(A) | -field_char_0(A) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),B),field_char_0_Rats(A))) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),hAPP(A,A,inverse_inverse(A),B)),field_char_0_Rats(A))) # label(fact_3710_Rats__inverse) # label(axiom). [clausify(3663)].
% 82.69/82.64 5650 -field_char_0(A) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),hAPP(int,A,ring_1_of_int(A),B)),field_char_0_Rats(A))) # label(fact_3711_Rats__of__int) # label(axiom). [clausify(3664)].
% 82.69/82.64 Derived: field_char_0_Rats(rat) = ti(fun(rat,bool),field_char_0_Rats(rat)). [resolve(5635,a,5636,a)].
% 82.69/82.64 Derived: -hBOOL(hAPP(fun(rat,bool),bool,hAPP(rat,fun(fun(rat,bool),bool),member(rat),A),field_char_0_Rats(rat))) | zero_zero(rat) = ti(rat,A) | hBOOL(hAPP(fun(rat,bool),bool,hAPP(rat,fun(fun(rat,bool),bool),member(rat),hAPP(rat,rat,inverse_inverse(rat),A)),field_char_0_Rats(rat))). [resolve(5635,a,5637,a)].
% 82.69/82.64 Derived: -hBOOL(hAPP(fun(rat,bool),bool,hAPP(rat,fun(fun(rat,bool),bool),member(rat),A),field_char_0_Rats(rat))) | -hBOOL(hAPP(fun(rat,bool),bool,hAPP(rat,fun(fun(rat,bool),bool),member(rat),B),field_char_0_Rats(rat))) | zero_zero(rat) = ti(rat,B) | hBOOL(hAPP(fun(rat,bool),bool,hAPP(rat,fun(fun(rat,bool),bool),member(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),B)),field_char_0_Rats(rat))). [resolve(5635,a,5638,a)].
% 82.69/82.64 Derived: hBOOL(hAPP(fun(rat,bool),bool,hAPP(rat,fun(fun(rat,bool),bool),member(rat),zero_zero(rat)),field_char_0_Rats(rat))). [resolve(5635,a,5639,a)].
% 82.69/82.64 Derived: -hBOOL(hAPP(fun(rat,bool),bool,hAPP(rat,fun(fun(rat,bool),bool),member(rat),A),field_char_0_Rats(rat))) | -hBOOL(hAPP(fun(rat,bool),bool,hAPP(rat,fun(fun(rat,bool),bool),member(rat),B),field_char_0_Rats(rat))) | hBOOL(hAPP(fun(rat,bool),bool,hAPP(rat,fun(fun(rat,bool),bool),member(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B)),field_char_0_Rats(rat))). [resolve(5635,a,5640,a)].
% 82.69/82.64 Derived: -hBOOL(hAPP(fun(rat,bool),bool,hAPP(rat,fun(fun(rat,bool),bool),member(rat),A),field_char_0_Rats(rat))) | -hBOOL(hAPP(fun(rat,bool),bool,hAPP(rat,fun(fun(rat,bool),bool),member(rat),B),field_char_0_Rats(rat))) | hBOOL(hAPP(fun(rat,bool),bool,hAPP(rat,fun(fun(rat,bool),bool),member(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),B)),field_char_0_Rats(rat))). [resolve(5635,a,5641,a)].
% 82.69/82.64 Derived: -number_ring(rat) | hBOOL(hAPP(fun(rat,bool),bool,hAPP(rat,fun(fun(rat,bool),bool),member(rat),hAPP(int,rat,number_number_of(rat),A)),field_char_0_Rats(rat))). [resolve(5635,a,5642,b)].
% 82.69/82.64 Derived: hBOOL(hAPP(fun(rat,bool),bool,hAPP(rat,fun(fun(rat,bool),bool),member(rat),one_one(rat)),field_char_0_Rats(rat))). [resolve(5635,a,5643,a)].
% 82.69/82.64 Derived: -hBOOL(hAPP(fun(rat,bool),bool,hAPP(rat,fun(fun(rat,bool),bool),member(rat),A),field_char_0_Rats(rat))) | -hBOOL(hAPP(fun(rat,bool),bool,hAPP(rat,fun(fun(rat,bool),bool),member(rat),B),field_char_0_Rats(rat))) | hBOOL(hAPP(fun(rat,bool),bool,hAPP(rat,fun(fun(rat,bool),bool),member(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),A),B)),field_char_0_Rats(rat))). [resolve(5635,a,5644,a)].
% 82.78/82.67 Derived: -hBOOL(hAPP(fun(rat,bool),bool,hAPP(rat,fun(fun(rat,bool),bool),member(rat),A),field_char_0_Rats(rat))) | hBOOL(hAPP(fun(rat,bool),bool,hAPP(rat,fun(fun(rat,bool),bool),member(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),B)),field_char_0_Rats(rat))). [resolve(5635,a,5645,a)].
% 82.78/82.67 Derived: -hBOOL(hAPP(fun(rat,bool),bool,hAPP(rat,fun(fun(rat,bool),bool),member(rat),A),field_char_0_Rats(rat))) | hBOOL(hAPP(fun(rat,bool),bool,hAPP(rat,fun(fun(rat,bool),bool),member(rat),hAPP(rat,rat,uminus_uminus(rat),A)),field_char_0_Rats(rat))). [resolve(5635,a,5646,a)].
% 82.78/82.67 Derived: -field_inverse_zero(rat) | -hBOOL(hAPP(fun(rat,bool),bool,hAPP(rat,fun(fun(rat,bool),bool),member(rat),A),field_char_0_Rats(rat))) | -hBOOL(hAPP(fun(rat,bool),bool,hAPP(rat,fun(fun(rat,bool),bool),member(rat),B),field_char_0_Rats(rat))) | hBOOL(hAPP(fun(rat,bool),bool,hAPP(rat,fun(fun(rat,bool),bool),member(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),B)),field_char_0_Rats(rat))). [resolve(5635,a,5647,b)].
% 82.78/82.67 Derived: hBOOL(hAPP(fun(rat,bool),bool,hAPP(rat,fun(fun(rat,bool),bool),member(rat),hAPP(nat,rat,semiring_1_of_nat(rat),A)),field_char_0_Rats(rat))). [resolve(5635,a,5648,a)].
% 82.78/82.67 Derived: -field_inverse_zero(rat) | -hBOOL(hAPP(fun(rat,bool),bool,hAPP(rat,fun(fun(rat,bool),bool),member(rat),A),field_char_0_Rats(rat))) | hBOOL(hAPP(fun(rat,bool),bool,hAPP(rat,fun(fun(rat,bool),bool),member(rat),hAPP(rat,rat,inverse_inverse(rat),A)),field_char_0_Rats(rat))). [resolve(5635,a,5649,b)].
% 82.78/82.67 Derived: hBOOL(hAPP(fun(rat,bool),bool,hAPP(rat,fun(fun(rat,bool),bool),member(rat),hAPP(int,rat,ring_1_of_int(rat),A)),field_char_0_Rats(rat))). [resolve(5635,a,5650,a)].
% 82.78/82.67 5651 field_char_0(real) # label(arity_RealDef_Oreal___Rat_Ofield__char__0) # label(axiom). [assumption].
% 82.78/82.67 Derived: field_char_0_Rats(real) = ti(fun(real,bool),field_char_0_Rats(real)). [resolve(5651,a,5636,a)].
% 82.78/82.67 Derived: -hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),A),field_char_0_Rats(real))) | zero_zero(real) = ti(real,A) | hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),hAPP(real,real,inverse_inverse(real),A)),field_char_0_Rats(real))). [resolve(5651,a,5637,a)].
% 82.78/82.67 Derived: -hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),A),field_char_0_Rats(real))) | -hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),B),field_char_0_Rats(real))) | zero_zero(real) = ti(real,B) | hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B)),field_char_0_Rats(real))). [resolve(5651,a,5638,a)].
% 82.78/82.67 Derived: hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),zero_zero(real)),field_char_0_Rats(real))). [resolve(5651,a,5639,a)].
% 82.78/82.67 Derived: -hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),A),field_char_0_Rats(real))) | -hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),B),field_char_0_Rats(real))) | hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),field_char_0_Rats(real))). [resolve(5651,a,5640,a)].
% 82.78/82.67 Derived: -hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),A),field_char_0_Rats(real))) | -hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),B),field_char_0_Rats(real))) | hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),B)),field_char_0_Rats(real))). [resolve(5651,a,5641,a)].
% 82.78/82.67 Derived: -number_ring(real) | hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),hAPP(int,real,number_number_of(real),A)),field_char_0_Rats(real))). [resolve(5651,a,5642,b)].
% 82.78/82.70 Derived: hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),one_one(real)),field_char_0_Rats(real))). [resolve(5651,a,5643,a)].
% 82.78/82.70 Derived: -hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),A),field_char_0_Rats(real))) | -hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),B),field_char_0_Rats(real))) | hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),B)),field_char_0_Rats(real))). [resolve(5651,a,5644,a)].
% 82.78/82.70 Derived: -hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),A),field_char_0_Rats(real))) | hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),B)),field_char_0_Rats(real))). [resolve(5651,a,5645,a)].
% 82.78/82.70 Derived: -hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),A),field_char_0_Rats(real))) | hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),hAPP(real,real,uminus_uminus(real),A)),field_char_0_Rats(real))). [resolve(5651,a,5646,a)].
% 82.78/82.70 Derived: -field_inverse_zero(real) | -hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),A),field_char_0_Rats(real))) | -hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),B),field_char_0_Rats(real))) | hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B)),field_char_0_Rats(real))). [resolve(5651,a,5647,b)].
% 82.78/82.70 Derived: hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),hAPP(nat,real,semiring_1_of_nat(real),A)),field_char_0_Rats(real))). [resolve(5651,a,5648,a)].
% 82.78/82.70 Derived: -field_inverse_zero(real) | -hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),A),field_char_0_Rats(real))) | hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),hAPP(real,real,inverse_inverse(real),A)),field_char_0_Rats(real))). [resolve(5651,a,5649,b)].
% 82.78/82.70 Derived: hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),hAPP(int,real,ring_1_of_int(real),A)),field_char_0_Rats(real))). [resolve(5651,a,5650,a)].
% 82.78/82.70 5652 field_char_0(complex) # label(arity_Complex_Ocomplex___Rat_Ofield__char__0) # label(axiom). [assumption].
% 82.78/82.70 Derived: field_char_0_Rats(complex) = ti(fun(complex,bool),field_char_0_Rats(complex)). [resolve(5652,a,5636,a)].
% 82.78/82.70 Derived: -hBOOL(hAPP(fun(complex,bool),bool,hAPP(complex,fun(fun(complex,bool),bool),member(complex),A),field_char_0_Rats(complex))) | zero_zero(complex) = ti(complex,A) | hBOOL(hAPP(fun(complex,bool),bool,hAPP(complex,fun(fun(complex,bool),bool),member(complex),hAPP(complex,complex,inverse_inverse(complex),A)),field_char_0_Rats(complex))). [resolve(5652,a,5637,a)].
% 82.78/82.70 Derived: -hBOOL(hAPP(fun(complex,bool),bool,hAPP(complex,fun(fun(complex,bool),bool),member(complex),A),field_char_0_Rats(complex))) | -hBOOL(hAPP(fun(complex,bool),bool,hAPP(complex,fun(fun(complex,bool),bool),member(complex),B),field_char_0_Rats(complex))) | zero_zero(complex) = ti(complex,B) | hBOOL(hAPP(fun(complex,bool),bool,hAPP(complex,fun(fun(complex,bool),bool),member(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),A),B)),field_char_0_Rats(complex))). [resolve(5652,a,5638,a)].
% 82.78/82.70 Derived: hBOOL(hAPP(fun(complex,bool),bool,hAPP(complex,fun(fun(complex,bool),bool),member(complex),zero_zero(complex)),field_char_0_Rats(complex))). [resolve(5652,a,5639,a)].
% 82.78/82.70 Derived: -hBOOL(hAPP(fun(complex,bool),bool,hAPP(complex,fun(fun(complex,bool),bool),member(complex),A),field_char_0_Rats(complex))) | -hBOOL(hAPP(fun(complex,bool),bool,hAPP(complex,fun(fun(complex,bool),bool),member(complex),B),field_char_0_Rats(complex))) | hBOOL(hAPP(fun(complex,bool),bool,hAPP(complex,fun(fun(complex,bool),bool),member(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),B)),field_char_0_Rats(complex))). [resolve(5652,a,5640,a)].
% 86.55/86.44 Derived: -hBOOL(hAPP(fun(complex,bool),bool,hAPP(complex,fun(fun(complex,bool),bool),member(complex),A),field_char_0_Rats(complex))) | -hBOOL(hAPP(fun(complex,bool),bool,hAPP(complex,fun(fun(complex,bool),bool),member(complex),B),field_char_0_Rats(complex))) | hBOOL(hAPP(fun(complex,bool),bool,hAPP(complex,fun(fun(complex,bool),bool),member(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),A),B)),field_char_0_Rats(complex))). [resolve(5652,a,5641,a)].
% 86.55/86.44 Derived: -number_ring(complex) | hBOOL(hAPP(fun(complex,bool),bool,hAPP(complex,fun(fun(complex,bool),bool),member(complex),hAPP(int,complex,number_number_of(complex),A)),field_char_0_Rats(complex))). [resolve(5652,a,5642,b)].
% 86.55/86.44 Derived: hBOOL(hAPP(fun(complex,bool),bool,hAPP(complex,fun(fun(complex,bool),bool),member(complex),one_one(complex)),field_char_0_Rats(complex))). [resolve(5652,a,5643,a)].
% 86.55/86.44 Derived: -hBOOL(hAPP(fun(complex,bool),bool,hAPP(complex,fun(fun(complex,bool),bool),member(complex),A),field_char_0_Rats(complex))) | -hBOOL(hAPP(fun(complex,bool),bool,hAPP(complex,fun(fun(complex,bool),bool),member(complex),B),field_char_0_Rats(complex))) | hBOOL(hAPP(fun(complex,bool),bool,hAPP(complex,fun(fun(complex,bool),bool),member(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),A),B)),field_char_0_Rats(complex))). [resolve(5652,a,5644,a)].
% 86.55/86.44 Derived: -hBOOL(hAPP(fun(complex,bool),bool,hAPP(complex,fun(fun(complex,bool),bool),member(complex),A),field_char_0_Rats(complex))) | hBOOL(hAPP(fun(complex,bool),bool,hAPP(complex,fun(fun(complex,bool),bool),member(complex),hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),A),B)),field_char_0_Rats(complex))). [resolve(5652,a,5645,a)].
% 86.55/86.44 Derived: -hBOOL(hAPP(fun(complex,bool),bool,hAPP(complex,fun(fun(complex,bool),bool),member(complex),A),field_char_0_Rats(complex))) | hBOOL(hAPP(fun(complex,bool),bool,hAPP(complex,fun(fun(complex,bool),bool),member(complex),hAPP(complex,complex,uminus_uminus(complex),A)),field_char_0_Rats(complex))). [resolve(5652,a,5646,a)].
% 86.55/86.44 Derived: -field_inverse_zero(complex) | -hBOOL(hAPP(fun(complex,bool),bool,hAPP(complex,fun(fun(complex,bool),bool),member(complex),A),field_char_0_Rats(complex))) | -hBOOL(hAPP(fun(complex,bool),bool,hAPP(complex,fun(fun(complex,bool),bool),member(complex),B),field_char_0_Rats(complex))) | hBOOL(hAPP(fun(complex,bool),bool,hAPP(complex,fun(fun(complex,bool),bool),member(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),A),B)),field_char_0_Rats(complex))). [resolve(5652,a,5647,b)].
% 86.55/86.44 Derived: hBOOL(hAPP(fun(complex,bool),bool,hAPP(complex,fun(fun(complex,bool),bool),member(complex),hAPP(nat,complex,semiring_1_of_nat(complex),A)),field_char_0_Rats(complex))). [resolve(5652,a,5648,a)].
% 86.55/86.44 Derived: -field_inverse_zero(complex) | -hBOOL(hAPP(fun(complex,bool),bool,hAPP(complex,fun(fun(complex,bool),bool),member(complex),A),field_char_0_Rats(complex))) | hBOOL(hAPP(fun(complex,bool),bool,hAPP(complex,fun(fun(complex,bool),bool),member(complex),hAPP(complex,complex,inverse_inverse(complex),A)),field_char_0_Rats(complex))). [resolve(5652,a,5649,b)].
% 86.55/86.44 Derived: hBOOL(hAPP(fun(complex,bool),bool,hAPP(complex,fun(fun(complex,bool),bool),member(complex),hAPP(int,complex,ring_1_of_int(complex),A)),field_char_0_Rats(complex))). [resolve(5652,a,5650,a)].
% 86.55/86.44 5653 dist_norm(real) # label(arity_RealDef_Oreal___RealVector_Odist__norm) # label(axiom). [assumption].
% 86.55/86.44 5654 -dist_norm(A) | dist_dist(A) = ti(fun(A,fun(A,real)),dist_dist(A)) # label(tsy_c_RealVector_Odist__class_Odist_0_res) # label(axiom). [clausify(91)].
% 86.55/86.44 5655 -dist_norm(A) | norm_norm(A) = ti(fun(A,real),norm_norm(A)) # label(tsy_c_RealVector_Onorm__class_Onorm_1_res) # label(axiom). [clausify(94)].
% 86.55/86.44 5656 -dist_norm(A) | hAPP(A,real,hAPP(A,fun(A,real),dist_dist(A),B),C) = hAPP(A,real,norm_norm(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C)) # label(fact_3514_dist__norm) # label(axiom). [clausify(3473)].
% 90.10/90.02 Derived: dist_dist(real) = ti(fun(real,fun(real,real)),dist_dist(real)). [resolve(5653,a,5654,a)].
% 90.10/90.02 Derived: hAPP(real,real,hAPP(real,fun(real,real),dist_dist(real),A),B) = hAPP(real,real,norm_norm(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),B)). [resolve(5653,a,5656,a)].
% 90.10/90.02 5657 dist_norm(complex) # label(arity_Complex_Ocomplex___RealVector_Odist__norm) # label(axiom). [assumption].
% 90.10/90.02 Derived: dist_dist(complex) = ti(fun(complex,fun(complex,real)),dist_dist(complex)). [resolve(5657,a,5654,a)].
% 90.10/90.02 Derived: hAPP(complex,real,hAPP(complex,fun(complex,real),dist_dist(complex),A),B) = hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),A),B)). [resolve(5657,a,5656,a)].
% 90.10/90.02 5658 real_algebra_1(real) # label(arity_RealDef_Oreal___RealVector_Oreal__algebra__1) # label(axiom). [assumption].
% 90.10/90.02 5659 -real_algebra_1(A) | of_real(A) = ti(fun(real,A),of_real(A)) # label(tsy_c_RealVector_Oof__real_res) # label(axiom). [clausify(95)].
% 90.10/90.02 5660 -real_algebra_1(A) | hAPP(real,A,of_real(A),B) != hAPP(real,A,of_real(A),C) | B = C # label(fact_2786_of__real__eq__iff) # label(axiom). [clausify(2771)].
% 90.10/90.02 5661 -real_algebra_1(A) | hAPP(real,A,of_real(A),B) = hAPP(real,A,of_real(A),C) | B != C # label(fact_2786_of__real__eq__iff) # label(axiom). [clausify(2771)].
% 90.10/90.02 5662 -real_algebra_1(A) | hAPP(real,A,of_real(A),zero_zero(real)) = zero_zero(A) # label(fact_2787_of__real__0) # label(axiom). [clausify(2772)].
% 90.10/90.02 5663 -real_algebra_1(A) | -real_normed_vector(A) | hAPP(real,A,of_real(A),zero_zero(real)) = zero_zero(A) # label(fact_2788_of__real_Ozero) # label(axiom). [clausify(2773)].
% 90.10/90.02 5664 -real_algebra_1(A) | hAPP(real,A,of_real(A),B) != zero_zero(A) | zero_zero(real) = B # label(fact_2789_of__real__eq__0__iff) # label(axiom). [clausify(2774)].
% 90.10/90.02 5665 -real_algebra_1(A) | hAPP(real,A,of_real(A),B) = zero_zero(A) | zero_zero(real) != B # label(fact_2789_of__real__eq__0__iff) # label(axiom). [clausify(2774)].
% 90.10/90.02 5666 -real_algebra_1(A) | hAPP(real,A,of_real(A),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),C)) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(real,A,of_real(A),B)),hAPP(real,A,of_real(A),C)) # label(fact_2790_of__real__mult) # label(axiom). [clausify(2775)].
% 90.10/90.02 5667 -number_ring(A) | -real_algebra_1(A) | hAPP(real,A,of_real(A),hAPP(int,real,number_number_of(real),B)) = hAPP(int,A,number_number_of(A),B) # label(fact_2791_of__real__number__of__eq) # label(axiom). [clausify(2776)].
% 90.10/90.02 5668 -real_algebra_1(A) | hAPP(real,A,of_real(A),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),B),C)) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(real,A,of_real(A),B)),hAPP(real,A,of_real(A),C)) # label(fact_2792_of__real__add) # label(axiom). [clausify(2777)].
% 90.10/90.02 5669 -real_algebra_1(A) | -real_normed_vector(A) | hAPP(real,A,of_real(A),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),B),C)) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(real,A,of_real(A),B)),hAPP(real,A,of_real(A),C)) # label(fact_2793_of__real_Oadd) # label(axiom). [clausify(2778)].
% 90.10/90.02 5670 -real_algebra_1(A) | hAPP(real,A,of_real(A),one_one(real)) = one_one(A) # label(fact_2794_of__real__1) # label(axiom). [clausify(2779)].
% 90.10/90.02 5671 -real_algebra_1(A) | hAPP(real,A,of_real(A),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),B),C)) = hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),hAPP(real,A,of_real(A),B)),C) # label(fact_2795_of__real__power) # label(axiom). [clausify(2780)].
% 90.10/90.02 5672 -real_algebra_1(A) | hAPP(real,A,of_real(A),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),B),C)) = hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(real,A,of_real(A),B)),hAPP(real,A,of_real(A),C)) # label(fact_2799_of__real__diff) # label(axiom). [clausify(2784)].
% 90.10/90.02 5673 -real_algebra_1(A) | -real_normed_vector(A) | hAPP(real,A,of_real(A),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),B),C)) = hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(real,A,of_real(A),B)),hAPP(real,A,of_real(A),C)) # label(fact_2800_of__real_Odiff) # label(axiom). [clausify(2785)].
% 90.10/90.02 5674 -real_algebra_1(A) | hAPP(real,A,of_real(A),hAPP(real,real,uminus_uminus(real),B)) = hAPP(A,A,uminus_uminus(A),hAPP(real,A,of_real(A),B)) # label(fact_2801_of__real__minus) # label(axiom). [clausify(2786)].
% 90.10/90.02 5675 -real_algebra_1(A) | -real_normed_vector(A) | hAPP(real,A,of_real(A),hAPP(real,real,uminus_uminus(real),B)) = hAPP(A,A,uminus_uminus(A),hAPP(real,A,of_real(A),B)) # label(fact_2802_of__real_Ominus) # label(axiom). [clausify(2787)].
% 90.10/90.02 5676 -real_algebra_1(A) | hAPP(real,A,of_real(A),hAPP(nat,real,semiring_1_of_nat(real),B)) = hAPP(nat,A,semiring_1_of_nat(A),B) # label(fact_2806_of__real__of__nat__eq) # label(axiom). [clausify(2791)].
% 90.10/90.02 5677 -real_algebra_1(A) | -real_normed_vector(A) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),f280(A))) # label(fact_2820_of__real_Opos__bounded) # label(axiom). [clausify(2803)].
% 90.10/90.02 5678 -real_algebra_1(A) | -real_normed_vector(A) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(A,real,norm_norm(A),hAPP(real,A,of_real(A),B))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,norm_norm(real),B)),f280(A)))) # label(fact_2820_of__real_Opos__bounded) # label(axiom). [clausify(2803)].
% 90.10/90.02 5679 -real_algebra_1(A) | -real_normed_vector(A) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),f281(A))) # label(fact_2821_of__real_Ononneg__bounded) # label(axiom). [clausify(2804)].
% 90.10/90.02 5680 -real_algebra_1(A) | -real_normed_vector(A) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(A,real,norm_norm(A),hAPP(real,A,of_real(A),B))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,norm_norm(real),B)),f281(A)))) # label(fact_2821_of__real_Ononneg__bounded) # label(axiom). [clausify(2804)].
% 90.10/90.02 5681 -real_algebra_1(A) | -real_normed_vector(A) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(A,real,norm_norm(A),hAPP(real,A,of_real(A),B))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,norm_norm(real),B)),f282(A)))) # label(fact_2825_of__real_Obounded) # label(axiom). [clausify(2806)].
% 90.10/90.02 5682 -real_algebra_1(A) | hAPP(real,A,of_real(A),hAPP(int,real,ring_1_of_int(real),B)) = hAPP(int,A,ring_1_of_int(A),B) # label(fact_3574_of__real__of__int__eq) # label(axiom). [clausify(3529)].
% 90.10/90.02 5683 -real_algebra_1(A) | -real_normed_vector(A) | -hBOOL(hAPP(fun(nat,real),bool,summable(real),B)) | hBOOL(hAPP(fun(nat,A),bool,summable(A),hAPP(fun(nat,real),fun(nat,A),hAPP(fun(real,A),fun(fun(nat,real),fun(nat,A)),combb(real,A,nat),of_real(A)),B))) # label(fact_4007_of__real_Osummable) # label(axiom). [clausify(3947)].
% 90.10/90.02 5684 -real_algebra_1(A) | -real_normed_vector(A) | -hBOOL(hAPP(fun(nat,real),bool,summable(real),B)) | hAPP(fun(nat,A),A,suminf(A),hAPP(fun(nat,real),fun(nat,A),hAPP(fun(real,A),fun(fun(nat,real),fun(nat,A)),combb(real,A,nat),of_real(A)),B)) = hAPP(real,A,of_real(A),hAPP(fun(nat,real),real,suminf(real),B)) # label(fact_4020_of__real_Osuminf) # label(axiom). [clausify(3960)].
% 90.10/90.02 5685 -real_algebra_1(A) | -real_normed_vector(A) | -hBOOL(hAPP(fun(nat,real),bool,cauchy(real),B)) | hBOOL(hAPP(fun(nat,A),bool,cauchy(A),hAPP(fun(nat,real),fun(nat,A),hAPP(fun(real,A),fun(fun(nat,real),fun(nat,A)),combb(real,A,nat),of_real(A)),B))) # label(fact_4077_of__real_OCauchy) # label(axiom). [clausify(4013)].
% 90.10/90.02 5686 -real_algebra_1(A) | -real_normed_vector(A) | -hBOOL(hAPP(real,bool,hAPP(fun(nat,real),fun(real,bool),sums(real),B),C)) | hBOOL(hAPP(A,bool,hAPP(fun(nat,A),fun(A,bool),sums(A),hAPP(fun(nat,real),fun(nat,A),hAPP(fun(real,A),fun(fun(nat,real),fun(nat,A)),combb(real,A,nat),of_real(A)),B)),hAPP(real,A,of_real(A),C))) # label(fact_4084_of__real_Osums) # label(axiom). [clausify(4020)].
% 90.10/90.02 5687 -real_algebra_1(A) | hAPP(real,A,of_real(A),hAPP(nat,real,hAPP(fun(nat,real),fun(nat,real),diffs(real),B),C)) = hAPP(nat,A,hAPP(fun(nat,A),fun(nat,A),diffs(A),hAPP(fun(nat,real),fun(nat,A),hAPP(fun(real,A),fun(fun(nat,real),fun(nat,A)),combb(real,A,nat),of_real(A)),B)),C) # label(fact_4111_diffs__of__real) # label(axiom). [clausify(4046)].
% 90.10/90.02 5688 -real_algebra_1(A) | -real_normed_vector(A) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),hAPP(fun(B,real),fun(B,A),hAPP(fun(real,A),fun(fun(B,real),fun(B,A)),combb(real,A,B),of_real(A)),C)),D) = hAPP(real,A,of_real(A),hAPP(fun(B,bool),real,hAPP(fun(B,real),fun(fun(B,bool),real),big_co1399186613setsum(B,real),C),D)) # label(fact_4189_of__real_Osetsum) # label(axiom). [clausify(4121)].
% 90.10/90.02 5689 -real_algebra_1(A) | -real_normed_vector(A) | -hBOOL(hAPP(filter(B),bool,hAPP(real,fun(filter(B),bool),hAPP(fun(B,real),fun(real,fun(filter(B),bool)),tendsto(B,real),C),D),E)) | hBOOL(hAPP(filter(B),bool,hAPP(A,fun(filter(B),bool),hAPP(fun(B,A),fun(A,fun(filter(B),bool)),tendsto(B,A),hAPP(fun(B,real),fun(B,A),hAPP(fun(real,A),fun(fun(B,real),fun(B,A)),combb(real,A,B),of_real(A)),C)),hAPP(real,A,of_real(A),D)),E)) # label(fact_4454_of__real_Otendsto) # label(axiom). [clausify(4382)].
% 90.10/90.02 5690 -real_algebra_1(A) | -real_normed_vector(A) | -hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),B),C),sequentially)) | hBOOL(hAPP(filter(nat),bool,hAPP(A,fun(filter(nat),bool),hAPP(fun(nat,A),fun(A,fun(filter(nat),bool)),tendsto(nat,A),hAPP(fun(nat,real),fun(nat,A),hAPP(fun(real,A),fun(fun(nat,real),fun(nat,A)),combb(real,A,nat),of_real(A)),B)),hAPP(real,A,of_real(A),C)),sequentially)) # label(fact_4466_of__real_OLIMSEQ) # label(axiom). [clausify(4394)].
% 90.10/90.02 5691 -real_algebra_1(A) | -real_normed_vector(A) | hBOOL(hAPP(filter(real),bool,hAPP(A,fun(filter(real),bool),hAPP(fun(real,A),fun(A,fun(filter(real),bool)),tendsto(real,A),of_real(A)),hAPP(real,A,of_real(A),B)),hAPP(real,filter(real),at(real),B))) # label(fact_4554_of__real_Ocont) # label(axiom). [clausify(4481)].
% 90.10/90.02 5692 -topological_space(A) | -real_algebra_1(B) | -real_normed_vector(B) | -hBOOL(hAPP(filter(A),bool,hAPP(real,fun(filter(A),bool),hAPP(fun(A,real),fun(real,fun(filter(A),bool)),tendsto(A,real),C),D),hAPP(A,filter(A),at(A),E))) | hBOOL(hAPP(filter(A),bool,hAPP(B,fun(filter(A),bool),hAPP(fun(A,B),fun(B,fun(filter(A),bool)),tendsto(A,B),hAPP(fun(A,real),fun(A,B),hAPP(fun(real,B),fun(fun(A,real),fun(A,B)),combb(real,B,A),of_real(B)),C)),hAPP(real,B,of_real(B),D)),hAPP(A,filter(A),at(A),E))) # label(fact_4599_LIM__of__real) # label(axiom). [clausify(4526)].
% 90.10/90.02 5693 -topological_space(A) | -real_algebra_1(B) | -real_normed_vector(B) | -hBOOL(hAPP(filter(A),bool,hAPP(real,fun(filter(A),bool),hAPP(fun(A,real),fun(real,fun(filter(A),bool)),tendsto(A,real),C),zero_zero(real)),hAPP(A,filter(A),at(A),D))) | hBOOL(hAPP(filter(A),bool,hAPP(B,fun(filter(A),bool),hAPP(fun(A,B),fun(B,fun(filter(A),bool)),tendsto(A,B),hAPP(fun(A,real),fun(A,B),hAPP(fun(real,B),fun(fun(A,real),fun(A,B)),combb(real,B,A),of_real(B)),C)),zero_zero(B)),hAPP(A,filter(A),at(A),D))) # label(fact_4617_of__real_OLIM__zero) # label(axiom). [clausify(4544)].
% 90.10/90.02 5694 -real_algebra_1(A) | hAPP(real,A,of_real(A),B) = hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),B),one_one(A)) # label(fact_4695_of__real__def) # label(axiom). [clausify(4621)].
% 90.10/90.02 5695 -real_algebra_1(A) | -real_normed_vector(A) | hAPP(real,A,of_real(A),hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),B),C)) = hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),B),hAPP(real,A,of_real(A),C)) # label(fact_4696_of__real_OscaleR) # label(axiom). [clausify(4622)].
% 90.10/90.02 5696 -real_algebra_1(A) | hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),B),C) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(real,A,of_real(A),B)),C) # label(fact_4715_scaleR__conv__of__real) # label(axiom). [clausify(4641)].
% 90.10/90.02 5697 -real_algebra_1(A) | -real_normed_vector(A) | hBOOL(hAPP(real,bool,hAPP(fun(real,A),fun(real,bool),isCont(real,A),of_real(A)),B)) # label(fact_4906_of__real_OisCont) # label(axiom). [clausify(4826)].
% 90.10/90.02 Derived: of_real(real) = ti(fun(real,real),of_real(real)). [resolve(5658,a,5659,a)].
% 90.10/90.02 Derived: hAPP(real,real,of_real(real),A) != hAPP(real,real,of_real(real),B) | A = B. [resolve(5658,a,5660,a)].
% 90.10/90.02 Derived: hAPP(real,real,of_real(real),A) = hAPP(real,real,of_real(real),B) | A != B. [resolve(5658,a,5661,a)].
% 90.10/90.03 Derived: hAPP(real,real,of_real(real),zero_zero(real)) = zero_zero(real). [resolve(5658,a,5662,a)].
% 90.10/90.03 Derived: hAPP(real,real,of_real(real),A) != zero_zero(real) | zero_zero(real) = A. [resolve(5658,a,5664,a)].
% 90.10/90.03 Derived: hAPP(real,real,of_real(real),A) = zero_zero(real) | zero_zero(real) != A. [resolve(5658,a,5665,a)].
% 90.10/90.03 Derived: hAPP(real,real,of_real(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,of_real(real),A)),hAPP(real,real,of_real(real),B)). [resolve(5658,a,5666,a)].
% 90.10/90.03 Derived: -number_ring(real) | hAPP(real,real,of_real(real),hAPP(int,real,number_number_of(real),A)) = hAPP(int,real,number_number_of(real),A). [resolve(5658,a,5667,b)].
% 90.10/90.03 Derived: hAPP(real,real,of_real(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),B)) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,of_real(real),A)),hAPP(real,real,of_real(real),B)). [resolve(5658,a,5668,a)].
% 90.10/90.03 Derived: hAPP(real,real,of_real(real),one_one(real)) = one_one(real). [resolve(5658,a,5670,a)].
% 90.10/90.03 Derived: hAPP(real,real,of_real(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),B)) = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,of_real(real),A)),B). [resolve(5658,a,5671,a)].
% 90.10/90.03 Derived: hAPP(real,real,of_real(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),B)) = hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,of_real(real),A)),hAPP(real,real,of_real(real),B)). [resolve(5658,a,5672,a)].
% 90.10/90.03 Derived: hAPP(real,real,of_real(real),hAPP(real,real,uminus_uminus(real),A)) = hAPP(real,real,uminus_uminus(real),hAPP(real,real,of_real(real),A)). [resolve(5658,a,5674,a)].
% 90.10/90.03 Derived: hAPP(real,real,of_real(real),hAPP(nat,real,semiring_1_of_nat(real),A)) = hAPP(nat,real,semiring_1_of_nat(real),A). [resolve(5658,a,5676,a)].
% 90.10/90.03 Derived: -real_normed_vector(real) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),f280(real))). [resolve(5658,a,5677,a)].
% 90.10/90.03 Derived: -real_normed_vector(real) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,norm_norm(real),hAPP(real,real,of_real(real),A))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,norm_norm(real),A)),f280(real)))). [resolve(5658,a,5678,a)].
% 90.10/90.03 Derived: -real_normed_vector(real) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),f281(real))). [resolve(5658,a,5679,a)].
% 90.10/90.03 Derived: -real_normed_vector(real) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,norm_norm(real),hAPP(real,real,of_real(real),A))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,norm_norm(real),A)),f281(real)))). [resolve(5658,a,5680,a)].
% 90.10/90.03 Derived: -real_normed_vector(real) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,norm_norm(real),hAPP(real,real,of_real(real),A))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,norm_norm(real),A)),f282(real)))). [resolve(5658,a,5681,a)].
% 90.10/90.03 Derived: hAPP(real,real,of_real(real),hAPP(int,real,ring_1_of_int(real),A)) = hAPP(int,real,ring_1_of_int(real),A). [resolve(5658,a,5682,a)].
% 90.10/90.03 Derived: -real_normed_vector(real) | -hBOOL(hAPP(fun(nat,real),bool,summable(real),A)) | hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),of_real(real)),A))). [resolve(5658,a,5683,a)].
% 90.10/90.03 Derived: -real_normed_vector(real) | -hBOOL(hAPP(fun(nat,real),bool,summable(real),A)) | hAPP(fun(nat,real),real,suminf(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),of_real(real)),A)) = hAPP(real,real,of_real(real),hAPP(fun(nat,real),real,suminf(real),A)). [resolve(5658,a,5684,a)].
% 90.10/90.03 Derived: -real_normed_vector(real) | -hBOOL(hAPP(fun(nat,real),bool,cauchy(real),A)) | hBOOL(hAPP(fun(nat,real),bool,cauchy(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),of_real(real)),A))). [resolve(5658,a,5685,a)].
% 90.18/90.06 Derived: -real_normed_vector(real) | -hBOOL(hAPP(real,bool,hAPP(fun(nat,real),fun(real,bool),sums(real),A),B)) | hBOOL(hAPP(real,bool,hAPP(fun(nat,real),fun(real,bool),sums(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),of_real(real)),A)),hAPP(real,real,of_real(real),B))). [resolve(5658,a,5686,a)].
% 90.18/90.06 Derived: hAPP(real,real,of_real(real),hAPP(nat,real,hAPP(fun(nat,real),fun(nat,real),diffs(real),A),B)) = hAPP(nat,real,hAPP(fun(nat,real),fun(nat,real),diffs(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),of_real(real)),A)),B). [resolve(5658,a,5687,a)].
% 90.18/90.06 Derived: -real_normed_vector(real) | hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),hAPP(fun(A,real),fun(A,real),hAPP(fun(real,real),fun(fun(A,real),fun(A,real)),combb(real,real,A),of_real(real)),B)),C) = hAPP(real,real,of_real(real),hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),B),C)). [resolve(5658,a,5688,a)].
% 90.18/90.06 Derived: -real_normed_vector(real) | -hBOOL(hAPP(filter(A),bool,hAPP(real,fun(filter(A),bool),hAPP(fun(A,real),fun(real,fun(filter(A),bool)),tendsto(A,real),B),C),D)) | hBOOL(hAPP(filter(A),bool,hAPP(real,fun(filter(A),bool),hAPP(fun(A,real),fun(real,fun(filter(A),bool)),tendsto(A,real),hAPP(fun(A,real),fun(A,real),hAPP(fun(real,real),fun(fun(A,real),fun(A,real)),combb(real,real,A),of_real(real)),B)),hAPP(real,real,of_real(real),C)),D)). [resolve(5658,a,5689,a)].
% 90.18/90.06 Derived: -real_normed_vector(real) | hBOOL(hAPP(filter(real),bool,hAPP(real,fun(filter(real),bool),hAPP(fun(real,real),fun(real,fun(filter(real),bool)),tendsto(real,real),of_real(real)),hAPP(real,real,of_real(real),A)),hAPP(real,filter(real),at(real),A))). [resolve(5658,a,5691,a)].
% 90.18/90.06 Derived: -topological_space(A) | -real_normed_vector(real) | -hBOOL(hAPP(filter(A),bool,hAPP(real,fun(filter(A),bool),hAPP(fun(A,real),fun(real,fun(filter(A),bool)),tendsto(A,real),B),zero_zero(real)),hAPP(A,filter(A),at(A),C))) | hBOOL(hAPP(filter(A),bool,hAPP(real,fun(filter(A),bool),hAPP(fun(A,real),fun(real,fun(filter(A),bool)),tendsto(A,real),hAPP(fun(A,real),fun(A,real),hAPP(fun(real,real),fun(fun(A,real),fun(A,real)),combb(real,real,A),of_real(real)),B)),zero_zero(real)),hAPP(A,filter(A),at(A),C))). [resolve(5658,a,5693,b)].
% 90.18/90.06 Derived: hAPP(real,real,of_real(real),A) = hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),A),one_one(real)). [resolve(5658,a,5694,a)].
% 90.18/90.06 Derived: -real_normed_vector(real) | hAPP(real,real,of_real(real),hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),A),B)) = hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),A),hAPP(real,real,of_real(real),B)). [resolve(5658,a,5695,a)].
% 90.18/90.06 Derived: hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),A),B) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,of_real(real),A)),B). [resolve(5658,a,5696,a)].
% 90.18/90.06 Derived: -real_normed_vector(real) | hBOOL(hAPP(real,bool,hAPP(fun(real,real),fun(real,bool),isCont(real,real),of_real(real)),A)). [resolve(5658,a,5697,a)].
% 90.18/90.06 5698 real_algebra_1(complex) # label(arity_Complex_Ocomplex___RealVector_Oreal__algebra__1) # label(axiom). [assumption].
% 90.18/90.06 Derived: of_real(complex) = ti(fun(real,complex),of_real(complex)). [resolve(5698,a,5659,a)].
% 90.18/90.06 Derived: hAPP(real,complex,of_real(complex),A) != hAPP(real,complex,of_real(complex),B) | A = B. [resolve(5698,a,5660,a)].
% 90.18/90.06 Derived: hAPP(real,complex,of_real(complex),A) = hAPP(real,complex,of_real(complex),B) | A != B. [resolve(5698,a,5661,a)].
% 90.18/90.06 Derived: hAPP(real,complex,of_real(complex),zero_zero(real)) = zero_zero(complex). [resolve(5698,a,5662,a)].
% 90.18/90.06 Derived: hAPP(real,complex,of_real(complex),A) != zero_zero(complex) | zero_zero(real) = A. [resolve(5698,a,5664,a)].
% 90.18/90.06 Derived: hAPP(real,complex,of_real(complex),A) = zero_zero(complex) | zero_zero(real) != A. [resolve(5698,a,5665,a)].
% 90.18/90.07 Derived: hAPP(real,complex,of_real(complex),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(real,complex,of_real(complex),A)),hAPP(real,complex,of_real(complex),B)). [resolve(5698,a,5666,a)].
% 90.18/90.07 Derived: -number_ring(complex) | hAPP(real,complex,of_real(complex),hAPP(int,real,number_number_of(real),A)) = hAPP(int,complex,number_number_of(complex),A). [resolve(5698,a,5667,b)].
% 90.18/90.07 Derived: hAPP(real,complex,of_real(complex),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),B)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(real,complex,of_real(complex),A)),hAPP(real,complex,of_real(complex),B)). [resolve(5698,a,5668,a)].
% 90.18/90.07 Derived: hAPP(real,complex,of_real(complex),one_one(real)) = one_one(complex). [resolve(5698,a,5670,a)].
% 90.18/90.07 Derived: hAPP(real,complex,of_real(complex),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),B)) = hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),hAPP(real,complex,of_real(complex),A)),B). [resolve(5698,a,5671,a)].
% 90.18/90.07 Derived: hAPP(real,complex,of_real(complex),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),B)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),hAPP(real,complex,of_real(complex),A)),hAPP(real,complex,of_real(complex),B)). [resolve(5698,a,5672,a)].
% 90.18/90.07 Derived: hAPP(real,complex,of_real(complex),hAPP(real,real,uminus_uminus(real),A)) = hAPP(complex,complex,uminus_uminus(complex),hAPP(real,complex,of_real(complex),A)). [resolve(5698,a,5674,a)].
% 90.18/90.07 Derived: hAPP(real,complex,of_real(complex),hAPP(nat,real,semiring_1_of_nat(real),A)) = hAPP(nat,complex,semiring_1_of_nat(complex),A). [resolve(5698,a,5676,a)].
% 90.18/90.07 Derived: -real_normed_vector(complex) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),f280(complex))). [resolve(5698,a,5677,a)].
% 90.18/90.07 Derived: -real_normed_vector(complex) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(complex,real,norm_norm(complex),hAPP(real,complex,of_real(complex),A))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,norm_norm(real),A)),f280(complex)))). [resolve(5698,a,5678,a)].
% 90.18/90.07 Derived: -real_normed_vector(complex) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),f281(complex))). [resolve(5698,a,5679,a)].
% 90.18/90.07 Derived: -real_normed_vector(complex) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(complex,real,norm_norm(complex),hAPP(real,complex,of_real(complex),A))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,norm_norm(real),A)),f281(complex)))). [resolve(5698,a,5680,a)].
% 90.18/90.07 Derived: -real_normed_vector(complex) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(complex,real,norm_norm(complex),hAPP(real,complex,of_real(complex),A))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,norm_norm(real),A)),f282(complex)))). [resolve(5698,a,5681,a)].
% 90.18/90.07 Derived: hAPP(real,complex,of_real(complex),hAPP(int,real,ring_1_of_int(real),A)) = hAPP(int,complex,ring_1_of_int(complex),A). [resolve(5698,a,5682,a)].
% 90.18/90.07 Derived: -real_normed_vector(complex) | -hBOOL(hAPP(fun(nat,real),bool,summable(real),A)) | hBOOL(hAPP(fun(nat,complex),bool,summable(complex),hAPP(fun(nat,real),fun(nat,complex),hAPP(fun(real,complex),fun(fun(nat,real),fun(nat,complex)),combb(real,complex,nat),of_real(complex)),A))). [resolve(5698,a,5683,a)].
% 90.18/90.07 Derived: -real_normed_vector(complex) | -hBOOL(hAPP(fun(nat,real),bool,summable(real),A)) | hAPP(fun(nat,complex),complex,suminf(complex),hAPP(fun(nat,real),fun(nat,complex),hAPP(fun(real,complex),fun(fun(nat,real),fun(nat,complex)),combb(real,complex,nat),of_real(complex)),A)) = hAPP(real,complex,of_real(complex),hAPP(fun(nat,real),real,suminf(real),A)). [resolve(5698,a,5684,a)].
% 90.18/90.07 Derived: -real_normed_vector(complex) | -hBOOL(hAPP(fun(nat,real),bool,cauchy(real),A)) | hBOOL(hAPP(fun(nat,complex),bool,cauchy(complex),hAPP(fun(nat,real),fun(nat,complex),hAPP(fun(real,complex),fun(fun(nat,real),fun(nat,complex)),combb(real,complex,nat),of_real(complex)),A))). [resolve(5698,a,5685,a)].
% 93.82/93.73 Derived: -real_normed_vector(complex) | -hBOOL(hAPP(real,bool,hAPP(fun(nat,real),fun(real,bool),sums(real),A),B)) | hBOOL(hAPP(complex,bool,hAPP(fun(nat,complex),fun(complex,bool),sums(complex),hAPP(fun(nat,real),fun(nat,complex),hAPP(fun(real,complex),fun(fun(nat,real),fun(nat,complex)),combb(real,complex,nat),of_real(complex)),A)),hAPP(real,complex,of_real(complex),B))). [resolve(5698,a,5686,a)].
% 93.82/93.73 Derived: hAPP(real,complex,of_real(complex),hAPP(nat,real,hAPP(fun(nat,real),fun(nat,real),diffs(real),A),B)) = hAPP(nat,complex,hAPP(fun(nat,complex),fun(nat,complex),diffs(complex),hAPP(fun(nat,real),fun(nat,complex),hAPP(fun(real,complex),fun(fun(nat,real),fun(nat,complex)),combb(real,complex,nat),of_real(complex)),A)),B). [resolve(5698,a,5687,a)].
% 93.82/93.73 Derived: -real_normed_vector(complex) | hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),hAPP(fun(A,real),fun(A,complex),hAPP(fun(real,complex),fun(fun(A,real),fun(A,complex)),combb(real,complex,A),of_real(complex)),B)),C) = hAPP(real,complex,of_real(complex),hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),B),C)). [resolve(5698,a,5688,a)].
% 93.82/93.73 Derived: -real_normed_vector(complex) | -hBOOL(hAPP(filter(A),bool,hAPP(real,fun(filter(A),bool),hAPP(fun(A,real),fun(real,fun(filter(A),bool)),tendsto(A,real),B),C),D)) | hBOOL(hAPP(filter(A),bool,hAPP(complex,fun(filter(A),bool),hAPP(fun(A,complex),fun(complex,fun(filter(A),bool)),tendsto(A,complex),hAPP(fun(A,real),fun(A,complex),hAPP(fun(real,complex),fun(fun(A,real),fun(A,complex)),combb(real,complex,A),of_real(complex)),B)),hAPP(real,complex,of_real(complex),C)),D)). [resolve(5698,a,5689,a)].
% 93.82/93.73 Derived: -real_normed_vector(complex) | hBOOL(hAPP(filter(real),bool,hAPP(complex,fun(filter(real),bool),hAPP(fun(real,complex),fun(complex,fun(filter(real),bool)),tendsto(real,complex),of_real(complex)),hAPP(real,complex,of_real(complex),A)),hAPP(real,filter(real),at(real),A))). [resolve(5698,a,5691,a)].
% 93.82/93.73 Derived: -topological_space(A) | -real_normed_vector(complex) | -hBOOL(hAPP(filter(A),bool,hAPP(real,fun(filter(A),bool),hAPP(fun(A,real),fun(real,fun(filter(A),bool)),tendsto(A,real),B),zero_zero(real)),hAPP(A,filter(A),at(A),C))) | hBOOL(hAPP(filter(A),bool,hAPP(complex,fun(filter(A),bool),hAPP(fun(A,complex),fun(complex,fun(filter(A),bool)),tendsto(A,complex),hAPP(fun(A,real),fun(A,complex),hAPP(fun(real,complex),fun(fun(A,real),fun(A,complex)),combb(real,complex,A),of_real(complex)),B)),zero_zero(complex)),hAPP(A,filter(A),at(A),C))). [resolve(5698,a,5693,b)].
% 93.82/93.73 Derived: hAPP(real,complex,of_real(complex),A) = hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),A),one_one(complex)). [resolve(5698,a,5694,a)].
% 93.82/93.73 Derived: -real_normed_vector(complex) | hAPP(real,complex,of_real(complex),hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),A),B)) = hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),A),hAPP(real,complex,of_real(complex),B)). [resolve(5698,a,5695,a)].
% 93.82/93.73 Derived: hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),A),B) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(real,complex,of_real(complex),A)),B). [resolve(5698,a,5696,a)].
% 93.82/93.73 Derived: -real_normed_vector(complex) | hBOOL(hAPP(real,bool,hAPP(fun(real,complex),fun(real,bool),isCont(real,complex),of_real(complex)),A)). [resolve(5698,a,5697,a)].
% 93.82/93.73 5699 real_vector(real) # label(arity_RealDef_Oreal___RealVector_Oreal__vector) # label(axiom). [assumption].
% 93.82/93.73 5700 -real_vector(A) | scaleR_scaleR(A) = ti(fun(real,fun(A,A)),scaleR_scaleR(A)) # label(tsy_c_RealVector_OscaleR__class_OscaleR_1_res) # label(axiom). [clausify(97)].
% 93.82/93.73 5701 -real_vector(A) | hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),hAPP(int,real,number_number_of(real),min)),B) = hAPP(A,A,uminus_uminus(A),B) # label(fact_4670_scaleR__minus1__left) # label(axiom). [clausify(4596)].
% 93.82/93.73 5702 -real_vector(A) | hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),B),C)),D) = hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),B),D)),hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),C),D)) # label(fact_4674_scaleR__left_Odiff) # label(axiom). [clausify(4600)].
% 93.82/93.73 5703 -real_vector(A) | hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),B),C)),D) = hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),B),D)),hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),C),D)) # label(fact_4676_scaleR__left__diff__distrib) # label(axiom). [clausify(4602)].
% 93.82/93.73 5704 -real_vector(A) | hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),B),C)),D) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),B),D)),hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),C),D)) # label(fact_4677_scaleR__left_Oadd) # label(axiom). [clausify(4603)].
% 93.82/93.73 5705 -real_vector(A) | hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),B),C)),D) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),B),D)),hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),C),D)) # label(fact_4679_real__vector_Oscale__left__distrib) # label(axiom). [clausify(4605)].
% 93.82/93.73 5706 -real_vector(A) | hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(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(real,fun(A,A),scaleR_scaleR(A),B),C)),hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),B),D)) # label(fact_4681_scaleR__right_Oadd) # label(axiom). [clausify(4607)].
% 93.82/93.73 5707 -real_vector(A) | hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),B),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),C),D)) = hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),B),C)),hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),B),D)) # label(fact_4683_scaleR__right_Odiff) # label(axiom). [clausify(4609)].
% 93.82/93.73 5708 -real_vector(A) | hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),one_one(real)),B) = ti(A,B) # label(fact_4684_real__vector_Oscale__one) # label(axiom). [clausify(4610)].
% 93.82/93.73 5709 -real_vector(A) | zero_zero(real) = B | hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),B),C) != hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),B),D) | ti(A,C) = ti(A,D) # label(fact_4685_scaleR__left__imp__eq) # label(axiom). [clausify(4611)].
% 93.82/93.73 5710 -real_vector(A) | hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),B),C) != hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),B),D) | ti(A,C) = ti(A,D) | zero_zero(real) = B # label(fact_4686_scaleR__cancel__left) # label(axiom). [clausify(4612)].
% 93.82/93.73 5711 -real_vector(A) | hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),B),C) = hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),B),D) | ti(A,C) != ti(A,D) # label(fact_4686_scaleR__cancel__left) # label(axiom). [clausify(4612)].
% 93.82/93.73 5712 -real_vector(A) | hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),B),C) = hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),B),D) | zero_zero(real) != B # label(fact_4686_scaleR__cancel__left) # label(axiom). [clausify(4612)].
% 93.82/93.73 5713 -real_vector(A) | zero_zero(A) = ti(A,B) | hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),C),B) != hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),D),B) | C = D # label(fact_4687_scaleR__right__imp__eq) # label(axiom). [clausify(4613)].
% 93.82/93.73 5714 -real_vector(A) | hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),B),C) != hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),D),C) | B = D | zero_zero(A) = ti(A,C) # label(fact_4688_scaleR__cancel__right) # label(axiom). [clausify(4614)].
% 93.82/93.73 5715 -real_vector(A) | hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),B),C) = hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),D),C) | B != D # label(fact_4688_scaleR__cancel__right) # label(axiom). [clausify(4614)].
% 93.82/93.73 5716 -real_vector(A) | hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),B),C) = hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),D),C) | zero_zero(A) != ti(A,C) # label(fact_4688_scaleR__cancel__right) # label(axiom). [clausify(4614)].
% 93.82/93.74 5717 -real_vector(A) | hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),B),zero_zero(A)) = zero_zero(A) # label(fact_4690_scaleR__right_Ozero) # label(axiom). [clausify(4616)].
% 93.82/93.74 5718 -real_vector(A) | hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),B),C) != zero_zero(A) | zero_zero(real) = B | zero_zero(A) = ti(A,C) # label(fact_4691_scaleR__eq__0__iff) # label(axiom). [clausify(4617)].
% 93.82/93.74 5719 -real_vector(A) | hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),B),C) = zero_zero(A) | zero_zero(real) != B # label(fact_4691_scaleR__eq__0__iff) # label(axiom). [clausify(4617)].
% 93.82/93.74 5720 -real_vector(A) | hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),B),C) = zero_zero(A) | zero_zero(A) != ti(A,C) # label(fact_4691_scaleR__eq__0__iff) # label(axiom). [clausify(4617)].
% 93.82/93.74 5721 -real_vector(A) | hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),zero_zero(real)),B) = zero_zero(A) # label(fact_4692_scaleR__left_Ozero) # label(axiom). [clausify(4618)].
% 93.82/93.74 5722 -real_vector(A) | hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),B),hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),C),D)) = hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),C),hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),B),D)) # label(fact_4697_scaleR__left__commute) # label(axiom). [clausify(4623)].
% 93.82/93.74 5723 -real_vector(A) | hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),C)),D) = hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),B),hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),C),D)) # label(fact_4714_real__vector_Oscale__scale) # label(axiom). [clausify(4640)].
% 93.82/93.74 5724 -real_vector(A) | hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),B),hAPP(A,A,uminus_uminus(A),C)) = hAPP(A,A,uminus_uminus(A),hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),B),C)) # label(fact_4720_scaleR__minus__right) # label(axiom). [clausify(4646)].
% 93.82/93.74 5725 -real_vector(A) | hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),hAPP(real,real,uminus_uminus(real),B)),C) = hAPP(A,A,uminus_uminus(A),hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),B),C)) # label(fact_4722_scaleR__minus__left) # label(axiom). [clausify(4648)].
% 93.82/93.74 5726 -real_vector(A) | hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),hAPP(real,real,uminus_uminus(real),B)),C) = hAPP(A,A,uminus_uminus(A),hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),B),C)) # label(fact_4723_scaleR__left_Ominus) # label(axiom). [clausify(4649)].
% 93.82/93.74 5727 -real_vector(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(real,fun(A,A),scaleR_scaleR(A),C)),D)),E) = hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),C),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),D),E)) # label(fact_4737_scaleR__right_Osetsum) # label(axiom). [clausify(4663)].
% 93.82/93.74 5728 -real_vector(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,real),fun(B,fun(A,A)),hAPP(fun(real,fun(A,A)),fun(fun(B,real),fun(B,fun(A,A))),combb(real,fun(A,A),B),scaleR_scaleR(A)),C)),D)),E) = hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),hAPP(fun(B,bool),real,hAPP(fun(B,real),fun(fun(B,bool),real),big_co1399186613setsum(B,real),C),E)),D) # label(fact_4738_scaleR__left_Osetsum) # label(axiom). [clausify(4664)].
% 93.82/93.74 Derived: hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),hAPP(int,real,number_number_of(real),min)),A) = hAPP(real,real,uminus_uminus(real),A). [resolve(5699,a,5701,a)].
% 93.82/93.74 Derived: hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),B)),C) = hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),A),C)),hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),B),C)). [resolve(5699,a,5702,a)].
% 93.82/93.74 Derived: hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),B)),C) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),A),C)),hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),B),C)). [resolve(5699,a,5704,a)].
% 93.82/93.74 Derived: hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),A),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),B),C)) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),A),C)). [resolve(5699,a,5706,a)].
% 93.82/93.74 Derived: hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),A),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),B),C)) = hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),A),C)). [resolve(5699,a,5707,a)].
% 93.82/93.74 Derived: hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),one_one(real)),A) = ti(real,A). [resolve(5699,a,5708,a)].
% 93.82/93.74 Derived: zero_zero(real) = A | hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),A),B) != hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),A),C) | ti(real,B) = ti(real,C). [resolve(5699,a,5709,a)].
% 93.82/93.74 Derived: hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),A),B) = hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),A),C) | ti(real,B) != ti(real,C). [resolve(5699,a,5711,a)].
% 93.82/93.74 Derived: hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),A),B) = hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),A),C) | zero_zero(real) != A. [resolve(5699,a,5712,a)].
% 93.82/93.74 Derived: zero_zero(real) = ti(real,A) | hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),B),A) != hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),C),A) | B = C. [resolve(5699,a,5713,a)].
% 93.82/93.74 Derived: hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),A),B) = hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),C),B) | A != C. [resolve(5699,a,5715,a)].
% 93.82/93.74 Derived: hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),A),B) = hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),C),B) | zero_zero(real) != ti(real,B). [resolve(5699,a,5716,a)].
% 93.82/93.74 Derived: hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),A),zero_zero(real)) = zero_zero(real). [resolve(5699,a,5717,a)].
% 93.82/93.74 Derived: hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),A),B) != zero_zero(real) | zero_zero(real) = A | zero_zero(real) = ti(real,B). [resolve(5699,a,5718,a)].
% 93.82/93.74 Derived: hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),A),B) = zero_zero(real) | zero_zero(real) != A. [resolve(5699,a,5719,a)].
% 93.82/93.74 Derived: hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),A),B) = zero_zero(real) | zero_zero(real) != ti(real,B). [resolve(5699,a,5720,a)].
% 93.82/93.74 Derived: hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),zero_zero(real)),A) = zero_zero(real). [resolve(5699,a,5721,a)].
% 93.82/93.74 Derived: hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),A),hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),B),C)) = hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),B),hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),A),C)). [resolve(5699,a,5722,a)].
% 93.82/93.74 Derived: hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),C) = hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),A),hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),B),C)). [resolve(5699,a,5723,a)].
% 93.82/93.74 Derived: hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),A),hAPP(real,real,uminus_uminus(real),B)) = hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),A),B)). [resolve(5699,a,5724,a)].
% 93.82/93.74 Derived: hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),hAPP(real,real,uminus_uminus(real),A)),B) = hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),A),B)). [resolve(5699,a,5725,a)].
% 93.82/93.74 Derived: hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),hAPP(fun(A,real),fun(A,real),hAPP(fun(real,real),fun(fun(A,real),fun(A,real)),combb(real,real,A),hAPP(real,fun(real,real),scaleR_scaleR(real),B)),C)),D) = hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),B),hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),C),D)). [resolve(5699,a,5727,a)].
% 93.82/93.77 Derived: hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),hAPP(real,fun(A,real),hAPP(fun(A,fun(real,real)),fun(real,fun(A,real)),combc(A,real,real),hAPP(fun(A,real),fun(A,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(A,real),fun(A,fun(real,real))),combb(real,fun(real,real),A),scaleR_scaleR(real)),B)),C)),D) = hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),B),D)),C). [resolve(5699,a,5728,a)].
% 93.82/93.77 5729 real_vector(complex) # label(arity_Complex_Ocomplex___RealVector_Oreal__vector) # label(axiom). [assumption].
% 93.82/93.77 Derived: hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),hAPP(int,real,number_number_of(real),min)),A) = hAPP(complex,complex,uminus_uminus(complex),A). [resolve(5729,a,5701,a)].
% 93.82/93.77 Derived: hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),B)),C) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),A),C)),hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),B),C)). [resolve(5729,a,5702,a)].
% 93.82/93.77 Derived: hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),B)),C) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),A),C)),hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),B),C)). [resolve(5729,a,5704,a)].
% 93.82/93.77 Derived: hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),A),hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),B),C)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),A),B)),hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),A),C)). [resolve(5729,a,5706,a)].
% 93.82/93.77 Derived: hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),A),hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),B),C)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),A),B)),hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),A),C)). [resolve(5729,a,5707,a)].
% 93.82/93.77 Derived: hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),one_one(real)),A) = ti(complex,A). [resolve(5729,a,5708,a)].
% 93.82/93.77 Derived: zero_zero(real) = A | hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),A),B) != hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),A),C) | ti(complex,B) = ti(complex,C). [resolve(5729,a,5709,a)].
% 93.82/93.77 Derived: hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),A),B) = hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),A),C) | ti(complex,B) != ti(complex,C). [resolve(5729,a,5711,a)].
% 93.82/93.77 Derived: hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),A),B) = hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),A),C) | zero_zero(real) != A. [resolve(5729,a,5712,a)].
% 93.82/93.77 Derived: zero_zero(complex) = ti(complex,A) | hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),B),A) != hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),C),A) | B = C. [resolve(5729,a,5713,a)].
% 93.82/93.77 Derived: hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),A),B) = hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),C),B) | A != C. [resolve(5729,a,5715,a)].
% 97.43/97.35 Derived: hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),A),B) = hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),C),B) | zero_zero(complex) != ti(complex,B). [resolve(5729,a,5716,a)].
% 97.43/97.35 Derived: hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),A),zero_zero(complex)) = zero_zero(complex). [resolve(5729,a,5717,a)].
% 97.43/97.35 Derived: hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),A),B) != zero_zero(complex) | zero_zero(real) = A | zero_zero(complex) = ti(complex,B). [resolve(5729,a,5718,a)].
% 97.43/97.35 Derived: hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),A),B) = zero_zero(complex) | zero_zero(real) != A. [resolve(5729,a,5719,a)].
% 97.43/97.35 Derived: hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),A),B) = zero_zero(complex) | zero_zero(complex) != ti(complex,B). [resolve(5729,a,5720,a)].
% 97.43/97.35 Derived: hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),zero_zero(real)),A) = zero_zero(complex). [resolve(5729,a,5721,a)].
% 97.43/97.35 Derived: hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),A),hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),B),C)) = hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),B),hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),A),C)). [resolve(5729,a,5722,a)].
% 97.43/97.35 Derived: hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),C) = hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),A),hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),B),C)). [resolve(5729,a,5723,a)].
% 97.43/97.35 Derived: hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),A),hAPP(complex,complex,uminus_uminus(complex),B)) = hAPP(complex,complex,uminus_uminus(complex),hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),A),B)). [resolve(5729,a,5724,a)].
% 97.43/97.35 Derived: hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),hAPP(real,real,uminus_uminus(real),A)),B) = hAPP(complex,complex,uminus_uminus(complex),hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),A),B)). [resolve(5729,a,5725,a)].
% 97.43/97.35 Derived: hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),hAPP(fun(A,complex),fun(A,complex),hAPP(fun(complex,complex),fun(fun(A,complex),fun(A,complex)),combb(complex,complex,A),hAPP(real,fun(complex,complex),scaleR_scaleR(complex),B)),C)),D) = hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),B),hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),C),D)). [resolve(5729,a,5727,a)].
% 97.43/97.35 Derived: hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),hAPP(complex,fun(A,complex),hAPP(fun(A,fun(complex,complex)),fun(complex,fun(A,complex)),combc(A,complex,complex),hAPP(fun(A,real),fun(A,fun(complex,complex)),hAPP(fun(real,fun(complex,complex)),fun(fun(A,real),fun(A,fun(complex,complex))),combb(real,fun(complex,complex),A),scaleR_scaleR(complex)),B)),C)),D) = hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),B),D)),C). [resolve(5729,a,5728,a)].
% 97.43/97.35 5730 dense_linorder(rat) # label(arity_Rat_Orat___Orderings_Odense__linorder) # label(axiom). [assumption].
% 97.43/97.35 5731 -dense_linorder(A) | ord_gr676655987ssThan(A) = ti(fun(A,fun(A,fun(A,bool))),ord_gr676655987ssThan(A)) # label(tsy_c_SetInterval_Oord__class_OgreaterThanLessThan_0_res) # label(axiom). [clausify(109)].
% 97.43/97.35 5732 -dense_linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),f55(A,B,C)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),B)) # label(fact_230_dense__le) # label(axiom). [clausify(360)].
% 97.43/97.35 5733 -dense_linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),f55(A,B,C)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),B)) # label(fact_230_dense__le) # label(axiom). [clausify(360)].
% 97.43/97.35 5734 -dense_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),f56(A,D,B,C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),D)) # label(fact_231_dense__le__bounded) # label(axiom). [clausify(361)].
% 97.43/97.35 5735 -dense_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),f56(A,D,B,C)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),D)) # label(fact_231_dense__le__bounded) # label(axiom). [clausify(361)].
% 97.43/97.35 5736 -dense_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),f56(A,D,B,C)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),D)) # label(fact_231_dense__le__bounded) # label(axiom). [clausify(361)].
% 97.43/97.35 5737 -dense_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),hAPP(A,fun(A,fun(A,bool)),ord_gr676655987ssThan(A),B),C)),hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_atLeastLessThan(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_eq(A),D),B)) # label(fact_4234_greaterThanLessThan__subseteq__atLeastLessThan__iff) # label(axiom). [clausify(4166)].
% 97.43/97.35 5738 -dense_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),hAPP(A,fun(A,fun(A,bool)),ord_gr676655987ssThan(A),B),C)),hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_atLeastLessThan(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_eq(A),C),E)) # label(fact_4234_greaterThanLessThan__subseteq__atLeastLessThan__iff) # label(axiom). [clausify(4166)].
% 97.43/97.35 5739 -dense_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),hAPP(A,fun(A,fun(A,bool)),ord_gr676655987ssThan(A),B),C)),hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_atLeastLessThan(A),D),E))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) # label(fact_4234_greaterThanLessThan__subseteq__atLeastLessThan__iff) # label(axiom). [clausify(4166)].
% 97.43/97.35 5740 -dense_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),hAPP(A,fun(A,fun(A,bool)),ord_gr676655987ssThan(A),B),C)),hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_atLeastLessThan(A),D),E))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),D),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),E)) # label(fact_4234_greaterThanLessThan__subseteq__atLeastLessThan__iff) # label(axiom). [clausify(4166)].
% 97.43/97.35 5741 -dense_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),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_atLeastLessThan(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),B)) # label(fact_4528_atLeastAtMost__subseteq__atLeastLessThan__iff) # label(axiom). [clausify(4455)].
% 97.43/97.35 5742 -dense_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),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_atLeastLessThan(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(A),C),E)) # label(fact_4528_atLeastAtMost__subseteq__atLeastLessThan__iff) # label(axiom). [clausify(4455)].
% 97.43/97.35 5743 -dense_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),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_atLeastLessThan(A),D),E))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) # label(fact_4528_atLeastAtMost__subseteq__atLeastLessThan__iff) # label(axiom). [clausify(4455)].
% 97.43/97.35 5744 -dense_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),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_atLeastLessThan(A),D),E))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),D),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),E)) # label(fact_4528_atLeastAtMost__subseteq__atLeastLessThan__iff) # label(axiom). [clausify(4455)].
% 97.43/97.35 5745 -dense_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),hAPP(A,fun(A,fun(A,bool)),ord_atLeastLessThan(A),B),C)),hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_atLeastAtMost(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_eq(A),D),B)) # label(fact_4529_atLeastLessThan__subseteq__atLeastAtMost__iff) # label(axiom). [clausify(4456)].
% 97.43/97.35 5746 -dense_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),hAPP(A,fun(A,fun(A,bool)),ord_atLeastLessThan(A),B),C)),hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_atLeastAtMost(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_eq(A),C),E)) # label(fact_4529_atLeastLessThan__subseteq__atLeastAtMost__iff) # label(axiom). [clausify(4456)].
% 97.43/97.35 5747 -dense_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),hAPP(A,fun(A,fun(A,bool)),ord_atLeastLessThan(A),B),C)),hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_atLeastAtMost(A),D),E))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) # label(fact_4529_atLeastLessThan__subseteq__atLeastAtMost__iff) # label(axiom). [clausify(4456)].
% 97.43/97.35 5748 -dense_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),hAPP(A,fun(A,fun(A,bool)),ord_atLeastLessThan(A),B),C)),hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_atLeastAtMost(A),D),E))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),D),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),E)) # label(fact_4529_atLeastLessThan__subseteq__atLeastAtMost__iff) # label(axiom). [clausify(4456)].
% 97.43/97.35 5749 -dense_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),hAPP(A,fun(A,fun(A,bool)),ord_gr676655987ssThan(A),B),C)),hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_atLeastAtMost(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_eq(A),D),B)) # label(fact_4530_greaterThanLessThan__subseteq__atLeastAtMost__iff) # label(axiom). [clausify(4457)].
% 97.43/97.35 5750 -dense_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),hAPP(A,fun(A,fun(A,bool)),ord_gr676655987ssThan(A),B),C)),hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_atLeastAtMost(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_eq(A),C),E)) # label(fact_4530_greaterThanLessThan__subseteq__atLeastAtMost__iff) # label(axiom). [clausify(4457)].
% 97.43/97.35 5751 -dense_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),hAPP(A,fun(A,fun(A,bool)),ord_gr676655987ssThan(A),B),C)),hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_atLeastAtMost(A),D),E))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) # label(fact_4530_greaterThanLessThan__subseteq__atLeastAtMost__iff) # label(axiom). [clausify(4457)].
% 97.43/97.36 5752 -dense_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),hAPP(A,fun(A,fun(A,bool)),ord_gr676655987ssThan(A),B),C)),hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_atLeastAtMost(A),D),E))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),D),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),E)) # label(fact_4530_greaterThanLessThan__subseteq__atLeastAtMost__iff) # label(axiom). [clausify(4457)].
% 97.43/97.36 Derived: ord_gr676655987ssThan(rat) = ti(fun(rat,fun(rat,fun(rat,bool))),ord_gr676655987ssThan(rat)). [resolve(5730,a,5731,a)].
% 97.43/97.36 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),f55(rat,A,B)),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),B),A)). [resolve(5730,a,5732,a)].
% 97.43/97.36 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),f55(rat,A,B)),A)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),B),A)). [resolve(5730,a,5733,a)].
% 97.43/97.36 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),f56(rat,C,A,B))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),B),C)). [resolve(5730,a,5734,a)].
% 97.43/97.36 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),f56(rat,C,A,B)),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),B),C)). [resolve(5730,a,5735,a)].
% 97.43/97.36 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),f56(rat,C,A,B)),C)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),B),C)). [resolve(5730,a,5736,a)].
% 97.43/97.36 Derived: -hBOOL(hAPP(fun(rat,bool),bool,hAPP(fun(rat,bool),fun(fun(rat,bool),bool),ord_less_eq(fun(rat,bool)),hAPP(rat,fun(rat,bool),hAPP(rat,fun(rat,fun(rat,bool)),ord_gr676655987ssThan(rat),A),B)),hAPP(rat,fun(rat,bool),hAPP(rat,fun(rat,fun(rat,bool)),ord_atLeastLessThan(rat),C),D))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),C),A)). [resolve(5730,a,5737,a)].
% 97.43/97.36 Derived: -hBOOL(hAPP(fun(rat,bool),bool,hAPP(fun(rat,bool),fun(fun(rat,bool),bool),ord_less_eq(fun(rat,bool)),hAPP(rat,fun(rat,bool),hAPP(rat,fun(rat,fun(rat,bool)),ord_gr676655987ssThan(rat),A),B)),hAPP(rat,fun(rat,bool),hAPP(rat,fun(rat,fun(rat,bool)),ord_atLeastLessThan(rat),C),D))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),B),D)). [resolve(5730,a,5738,a)].
% 97.43/97.36 Derived: hBOOL(hAPP(fun(rat,bool),bool,hAPP(fun(rat,bool),fun(fun(rat,bool),bool),ord_less_eq(fun(rat,bool)),hAPP(rat,fun(rat,bool),hAPP(rat,fun(rat,fun(rat,bool)),ord_gr676655987ssThan(rat),A),B)),hAPP(rat,fun(rat,bool),hAPP(rat,fun(rat,fun(rat,bool)),ord_atLeastLessThan(rat),C),D))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),B)). [resolve(5730,a,5739,a)].
% 97.43/97.36 Derived: hBOOL(hAPP(fun(rat,bool),bool,hAPP(fun(rat,bool),fun(fun(rat,bool),bool),ord_less_eq(fun(rat,bool)),hAPP(rat,fun(rat,bool),hAPP(rat,fun(rat,fun(rat,bool)),ord_gr676655987ssThan(rat),A),B)),hAPP(rat,fun(rat,bool),hAPP(rat,fun(rat,fun(rat,bool)),ord_atLeastLessThan(rat),C),D))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),C),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),B),D)). [resolve(5730,a,5740,a)].
% 97.43/97.36 Derived: -hBOOL(hAPP(fun(rat,bool),bool,hAPP(fun(rat,bool),fun(fun(rat,bool),bool),ord_less_eq(fun(rat,bool)),hAPP(rat,fun(rat,bool),hAPP(rat,fun(rat,fun(rat,bool)),ord_atLeastAtMost(rat),A),B)),hAPP(rat,fun(rat,bool),hAPP(rat,fun(rat,fun(rat,bool)),ord_atLeastLessThan(rat),C),D))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),C),A)). [resolve(5730,a,5741,a)].
% 97.43/97.36 Derived: -hBOOL(hAPP(fun(rat,bool),bool,hAPP(fun(rat,bool),fun(fun(rat,bool),bool),ord_less_eq(fun(rat,bool)),hAPP(rat,fun(rat,bool),hAPP(rat,fun(rat,fun(rat,bool)),ord_atLeastAtMost(rat),A),B)),hAPP(rat,fun(rat,bool),hAPP(rat,fun(rat,fun(rat,bool)),ord_atLeastLessThan(rat),C),D))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),D)). [resolve(5730,a,5742,a)].
% 97.43/97.36 Derived: hBOOL(hAPP(fun(rat,bool),bool,hAPP(fun(rat,bool),fun(fun(rat,bool),bool),ord_less_eq(fun(rat,bool)),hAPP(rat,fun(rat,bool),hAPP(rat,fun(rat,fun(rat,bool)),ord_atLeastAtMost(rat),A),B)),hAPP(rat,fun(rat,bool),hAPP(rat,fun(rat,fun(rat,bool)),ord_atLeastLessThan(rat),C),D))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),B)). [resolve(5730,a,5743,a)].
% 97.43/97.36 Derived: hBOOL(hAPP(fun(rat,bool),bool,hAPP(fun(rat,bool),fun(fun(rat,bool),bool),ord_less_eq(fun(rat,bool)),hAPP(rat,fun(rat,bool),hAPP(rat,fun(rat,fun(rat,bool)),ord_atLeastAtMost(rat),A),B)),hAPP(rat,fun(rat,bool),hAPP(rat,fun(rat,fun(rat,bool)),ord_atLeastLessThan(rat),C),D))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),C),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),D)). [resolve(5730,a,5744,a)].
% 97.43/97.36 Derived: -hBOOL(hAPP(fun(rat,bool),bool,hAPP(fun(rat,bool),fun(fun(rat,bool),bool),ord_less_eq(fun(rat,bool)),hAPP(rat,fun(rat,bool),hAPP(rat,fun(rat,fun(rat,bool)),ord_atLeastLessThan(rat),A),B)),hAPP(rat,fun(rat,bool),hAPP(rat,fun(rat,fun(rat,bool)),ord_atLeastAtMost(rat),C),D))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),C),A)). [resolve(5730,a,5745,a)].
% 97.43/97.36 Derived: -hBOOL(hAPP(fun(rat,bool),bool,hAPP(fun(rat,bool),fun(fun(rat,bool),bool),ord_less_eq(fun(rat,bool)),hAPP(rat,fun(rat,bool),hAPP(rat,fun(rat,fun(rat,bool)),ord_atLeastLessThan(rat),A),B)),hAPP(rat,fun(rat,bool),hAPP(rat,fun(rat,fun(rat,bool)),ord_atLeastAtMost(rat),C),D))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),B),D)). [resolve(5730,a,5746,a)].
% 97.43/97.36 Derived: hBOOL(hAPP(fun(rat,bool),bool,hAPP(fun(rat,bool),fun(fun(rat,bool),bool),ord_less_eq(fun(rat,bool)),hAPP(rat,fun(rat,bool),hAPP(rat,fun(rat,fun(rat,bool)),ord_atLeastLessThan(rat),A),B)),hAPP(rat,fun(rat,bool),hAPP(rat,fun(rat,fun(rat,bool)),ord_atLeastAtMost(rat),C),D))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),B)). [resolve(5730,a,5747,a)].
% 97.43/97.36 Derived: hBOOL(hAPP(fun(rat,bool),bool,hAPP(fun(rat,bool),fun(fun(rat,bool),bool),ord_less_eq(fun(rat,bool)),hAPP(rat,fun(rat,bool),hAPP(rat,fun(rat,fun(rat,bool)),ord_atLeastLessThan(rat),A),B)),hAPP(rat,fun(rat,bool),hAPP(rat,fun(rat,fun(rat,bool)),ord_atLeastAtMost(rat),C),D))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),C),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),B),D)). [resolve(5730,a,5748,a)].
% 97.43/97.36 Derived: -hBOOL(hAPP(fun(rat,bool),bool,hAPP(fun(rat,bool),fun(fun(rat,bool),bool),ord_less_eq(fun(rat,bool)),hAPP(rat,fun(rat,bool),hAPP(rat,fun(rat,fun(rat,bool)),ord_gr676655987ssThan(rat),A),B)),hAPP(rat,fun(rat,bool),hAPP(rat,fun(rat,fun(rat,bool)),ord_atLeastAtMost(rat),C),D))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),C),A)). [resolve(5730,a,5749,a)].
% 97.43/97.36 Derived: -hBOOL(hAPP(fun(rat,bool),bool,hAPP(fun(rat,bool),fun(fun(rat,bool),bool),ord_less_eq(fun(rat,bool)),hAPP(rat,fun(rat,bool),hAPP(rat,fun(rat,fun(rat,bool)),ord_gr676655987ssThan(rat),A),B)),hAPP(rat,fun(rat,bool),hAPP(rat,fun(rat,fun(rat,bool)),ord_atLeastAtMost(rat),C),D))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),B),D)). [resolve(5730,a,5750,a)].
% 97.43/97.36 Derived: hBOOL(hAPP(fun(rat,bool),bool,hAPP(fun(rat,bool),fun(fun(rat,bool),bool),ord_less_eq(fun(rat,bool)),hAPP(rat,fun(rat,bool),hAPP(rat,fun(rat,fun(rat,bool)),ord_gr676655987ssThan(rat),A),B)),hAPP(rat,fun(rat,bool),hAPP(rat,fun(rat,fun(rat,bool)),ord_atLeastAtMost(rat),C),D))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),B)). [resolve(5730,a,5751,a)].
% 97.43/97.39 Derived: hBOOL(hAPP(fun(rat,bool),bool,hAPP(fun(rat,bool),fun(fun(rat,bool),bool),ord_less_eq(fun(rat,bool)),hAPP(rat,fun(rat,bool),hAPP(rat,fun(rat,fun(rat,bool)),ord_gr676655987ssThan(rat),A),B)),hAPP(rat,fun(rat,bool),hAPP(rat,fun(rat,fun(rat,bool)),ord_atLeastAtMost(rat),C),D))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),C),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),B),D)). [resolve(5730,a,5752,a)].
% 97.43/97.39 5753 dense_linorder(real) # label(arity_RealDef_Oreal___Orderings_Odense__linorder) # label(axiom). [assumption].
% 97.43/97.39 Derived: ord_gr676655987ssThan(real) = ti(fun(real,fun(real,fun(real,bool))),ord_gr676655987ssThan(real)). [resolve(5753,a,5731,a)].
% 97.43/97.39 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),f55(real,A,B)),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),A)). [resolve(5753,a,5732,a)].
% 97.43/97.39 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),f55(real,A,B)),A)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),A)). [resolve(5753,a,5733,a)].
% 97.43/97.39 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),f56(real,C,A,B))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),C)). [resolve(5753,a,5734,a)].
% 97.43/97.39 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),f56(real,C,A,B)),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),C)). [resolve(5753,a,5735,a)].
% 97.43/97.39 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),f56(real,C,A,B)),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),C)). [resolve(5753,a,5736,a)].
% 97.43/97.39 Derived: -hBOOL(hAPP(fun(real,bool),bool,hAPP(fun(real,bool),fun(fun(real,bool),bool),ord_less_eq(fun(real,bool)),hAPP(real,fun(real,bool),hAPP(real,fun(real,fun(real,bool)),ord_gr676655987ssThan(real),A),B)),hAPP(real,fun(real,bool),hAPP(real,fun(real,fun(real,bool)),ord_atLeastLessThan(real),C),D))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),C),A)). [resolve(5753,a,5737,a)].
% 97.43/97.39 Derived: -hBOOL(hAPP(fun(real,bool),bool,hAPP(fun(real,bool),fun(fun(real,bool),bool),ord_less_eq(fun(real,bool)),hAPP(real,fun(real,bool),hAPP(real,fun(real,fun(real,bool)),ord_gr676655987ssThan(real),A),B)),hAPP(real,fun(real,bool),hAPP(real,fun(real,fun(real,bool)),ord_atLeastLessThan(real),C),D))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),D)). [resolve(5753,a,5738,a)].
% 97.43/97.39 Derived: hBOOL(hAPP(fun(real,bool),bool,hAPP(fun(real,bool),fun(fun(real,bool),bool),ord_less_eq(fun(real,bool)),hAPP(real,fun(real,bool),hAPP(real,fun(real,fun(real,bool)),ord_gr676655987ssThan(real),A),B)),hAPP(real,fun(real,bool),hAPP(real,fun(real,fun(real,bool)),ord_atLeastLessThan(real),C),D))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)). [resolve(5753,a,5739,a)].
% 97.43/97.39 Derived: hBOOL(hAPP(fun(real,bool),bool,hAPP(fun(real,bool),fun(fun(real,bool),bool),ord_less_eq(fun(real,bool)),hAPP(real,fun(real,bool),hAPP(real,fun(real,fun(real,bool)),ord_gr676655987ssThan(real),A),B)),hAPP(real,fun(real,bool),hAPP(real,fun(real,fun(real,bool)),ord_atLeastLessThan(real),C),D))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),C),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),D)). [resolve(5753,a,5740,a)].
% 97.43/97.39 Derived: -hBOOL(hAPP(fun(real,bool),bool,hAPP(fun(real,bool),fun(fun(real,bool),bool),ord_less_eq(fun(real,bool)),hAPP(real,fun(real,bool),hAPP(real,fun(real,fun(real,bool)),ord_atLeastAtMost(real),A),B)),hAPP(real,fun(real,bool),hAPP(real,fun(real,fun(real,bool)),ord_atLeastLessThan(real),C),D))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),C),A)). [resolve(5753,a,5741,a)].
% 97.52/97.40 Derived: -hBOOL(hAPP(fun(real,bool),bool,hAPP(fun(real,bool),fun(fun(real,bool),bool),ord_less_eq(fun(real,bool)),hAPP(real,fun(real,bool),hAPP(real,fun(real,fun(real,bool)),ord_atLeastAtMost(real),A),B)),hAPP(real,fun(real,bool),hAPP(real,fun(real,fun(real,bool)),ord_atLeastLessThan(real),C),D))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),D)). [resolve(5753,a,5742,a)].
% 97.52/97.40 Derived: hBOOL(hAPP(fun(real,bool),bool,hAPP(fun(real,bool),fun(fun(real,bool),bool),ord_less_eq(fun(real,bool)),hAPP(real,fun(real,bool),hAPP(real,fun(real,fun(real,bool)),ord_atLeastAtMost(real),A),B)),hAPP(real,fun(real,bool),hAPP(real,fun(real,fun(real,bool)),ord_atLeastLessThan(real),C),D))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),B)). [resolve(5753,a,5743,a)].
% 97.52/97.40 Derived: hBOOL(hAPP(fun(real,bool),bool,hAPP(fun(real,bool),fun(fun(real,bool),bool),ord_less_eq(fun(real,bool)),hAPP(real,fun(real,bool),hAPP(real,fun(real,fun(real,bool)),ord_atLeastAtMost(real),A),B)),hAPP(real,fun(real,bool),hAPP(real,fun(real,fun(real,bool)),ord_atLeastLessThan(real),C),D))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),C),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),D)). [resolve(5753,a,5744,a)].
% 97.52/97.40 Derived: -hBOOL(hAPP(fun(real,bool),bool,hAPP(fun(real,bool),fun(fun(real,bool),bool),ord_less_eq(fun(real,bool)),hAPP(real,fun(real,bool),hAPP(real,fun(real,fun(real,bool)),ord_atLeastLessThan(real),A),B)),hAPP(real,fun(real,bool),hAPP(real,fun(real,fun(real,bool)),ord_atLeastAtMost(real),C),D))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),C),A)). [resolve(5753,a,5745,a)].
% 97.52/97.40 Derived: -hBOOL(hAPP(fun(real,bool),bool,hAPP(fun(real,bool),fun(fun(real,bool),bool),ord_less_eq(fun(real,bool)),hAPP(real,fun(real,bool),hAPP(real,fun(real,fun(real,bool)),ord_atLeastLessThan(real),A),B)),hAPP(real,fun(real,bool),hAPP(real,fun(real,fun(real,bool)),ord_atLeastAtMost(real),C),D))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),D)). [resolve(5753,a,5746,a)].
% 97.52/97.40 Derived: hBOOL(hAPP(fun(real,bool),bool,hAPP(fun(real,bool),fun(fun(real,bool),bool),ord_less_eq(fun(real,bool)),hAPP(real,fun(real,bool),hAPP(real,fun(real,fun(real,bool)),ord_atLeastLessThan(real),A),B)),hAPP(real,fun(real,bool),hAPP(real,fun(real,fun(real,bool)),ord_atLeastAtMost(real),C),D))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)). [resolve(5753,a,5747,a)].
% 97.52/97.40 Derived: hBOOL(hAPP(fun(real,bool),bool,hAPP(fun(real,bool),fun(fun(real,bool),bool),ord_less_eq(fun(real,bool)),hAPP(real,fun(real,bool),hAPP(real,fun(real,fun(real,bool)),ord_atLeastLessThan(real),A),B)),hAPP(real,fun(real,bool),hAPP(real,fun(real,fun(real,bool)),ord_atLeastAtMost(real),C),D))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),C),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),D)). [resolve(5753,a,5748,a)].
% 97.52/97.40 Derived: -hBOOL(hAPP(fun(real,bool),bool,hAPP(fun(real,bool),fun(fun(real,bool),bool),ord_less_eq(fun(real,bool)),hAPP(real,fun(real,bool),hAPP(real,fun(real,fun(real,bool)),ord_gr676655987ssThan(real),A),B)),hAPP(real,fun(real,bool),hAPP(real,fun(real,fun(real,bool)),ord_atLeastAtMost(real),C),D))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),C),A)). [resolve(5753,a,5749,a)].
% 97.52/97.40 Derived: -hBOOL(hAPP(fun(real,bool),bool,hAPP(fun(real,bool),fun(fun(real,bool),bool),ord_less_eq(fun(real,bool)),hAPP(real,fun(real,bool),hAPP(real,fun(real,fun(real,bool)),ord_gr676655987ssThan(real),A),B)),hAPP(real,fun(real,bool),hAPP(real,fun(real,fun(real,bool)),ord_atLeastAtMost(real),C),D))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),D)). [resolve(5753,a,5750,a)].
% 101.23/101.11 Derived: hBOOL(hAPP(fun(real,bool),bool,hAPP(fun(real,bool),fun(fun(real,bool),bool),ord_less_eq(fun(real,bool)),hAPP(real,fun(real,bool),hAPP(real,fun(real,fun(real,bool)),ord_gr676655987ssThan(real),A),B)),hAPP(real,fun(real,bool),hAPP(real,fun(real,fun(real,bool)),ord_atLeastAtMost(real),C),D))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)). [resolve(5753,a,5751,a)].
% 101.23/101.11 Derived: hBOOL(hAPP(fun(real,bool),bool,hAPP(fun(real,bool),fun(fun(real,bool),bool),ord_less_eq(fun(real,bool)),hAPP(real,fun(real,bool),hAPP(real,fun(real,fun(real,bool)),ord_gr676655987ssThan(real),A),B)),hAPP(real,fun(real,bool),hAPP(real,fun(real,fun(real,bool)),ord_atLeastAtMost(real),C),D))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),C),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),D)). [resolve(5753,a,5752,a)].
% 101.23/101.11 5754 ordered_ab_group_add(int) # label(arity_Int_Oint___Groups_Oordered__ab__group__add) # label(axiom). [assumption].
% 101.23/101.11 5755 -ordered_ab_group_add(A) | ord_gr676655987ssThan(A) = ti(fun(A,fun(A,fun(A,bool))),ord_gr676655987ssThan(A)) # label(tsy_c_SetInterval_Oord__class_OgreaterThanLessThan_2_res) # label(axiom). [clausify(110)].
% 101.23/101.11 5756 -ordered_ab_group_add(A) | hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C) != hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),D),E) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),E)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) # label(fact_122_diff__eq__diff__less) # label(axiom). [clausify(252)].
% 101.23/101.11 5757 -ordered_ab_group_add(A) | hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C) != hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),D),E) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),E)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) # label(fact_122_diff__eq__diff__less) # label(axiom). [clausify(252)].
% 101.23/101.11 5758 -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),D),E)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) # label(fact_130_diff__eq__diff__less__eq) # label(axiom). [clausify(260)].
% 101.23/101.11 5759 -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),D),E)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) # label(fact_130_diff__eq__diff__less__eq) # label(axiom). [clausify(260)].
% 101.23/101.11 5760 -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,hAPP(A,fun(A,A),minus_minus(A),B),C)),zero_zero(A))) # label(fact_340_le__iff__diff__le__0) # label(axiom). [clausify(469)].
% 101.23/101.11 5761 -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,hAPP(A,fun(A,A),minus_minus(A),B),C)),zero_zero(A))) # label(fact_340_le__iff__diff__le__0) # label(axiom). [clausify(469)].
% 101.23/101.11 5762 -ordered_ab_group_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C)),zero_zero(A))) # label(fact_342_less__iff__diff__less__0) # label(axiom). [clausify(471)].
% 101.23/101.11 5763 -ordered_ab_group_add(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C)),zero_zero(A))) # label(fact_342_less__iff__diff__less__0) # label(axiom). [clausify(471)].
% 101.23/101.11 5764 -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_562_le__imp__neg__le) # label(axiom). [clausify(686)].
% 101.23/101.11 5765 -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_563_neg__le__iff__le) # label(axiom). [clausify(687)].
% 101.23/101.11 5766 -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_563_neg__le__iff__le) # label(axiom). [clausify(687)].
% 101.23/101.11 5767 -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_564_minus__le__iff) # label(axiom). [clausify(688)].
% 101.23/101.11 5768 -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_564_minus__le__iff) # label(axiom). [clausify(688)].
% 101.23/101.11 5769 -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_565_le__minus__iff) # label(axiom). [clausify(689)].
% 101.23/101.11 5770 -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_565_le__minus__iff) # label(axiom). [clausify(689)].
% 101.23/101.11 5771 -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_569_neg__less__iff__less) # label(axiom). [clausify(693)].
% 101.23/101.11 5772 -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_569_neg__less__iff__less) # label(axiom). [clausify(693)].
% 101.23/101.11 5773 -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_570_minus__less__iff) # label(axiom). [clausify(694)].
% 101.23/101.11 5774 -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_570_minus__less__iff) # label(axiom). [clausify(694)].
% 101.23/101.11 5775 -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_571_less__minus__iff) # label(axiom). [clausify(695)].
% 101.23/101.11 5776 -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_571_less__minus__iff) # label(axiom). [clausify(695)].
% 101.23/101.11 5777 -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)),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) # label(fact_627_neg__le__0__iff__le) # label(axiom). [clausify(748)].
% 101.23/101.11 5778 -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)),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) # label(fact_627_neg__le__0__iff__le) # label(axiom). [clausify(748)].
% 101.23/101.11 5779 -ordered_ab_group_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(A,A,uminus_uminus(A),B))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),zero_zero(A))) # label(fact_629_neg__0__le__iff__le) # label(axiom). [clausify(750)].
% 101.23/101.11 5780 -ordered_ab_group_add(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(A,A,uminus_uminus(A),B))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),zero_zero(A))) # label(fact_629_neg__0__le__iff__le) # label(axiom). [clausify(750)].
% 101.23/101.11 5781 -ordered_ab_group_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,uminus_uminus(A),B)),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) # label(fact_632_neg__less__0__iff__less) # label(axiom). [clausify(753)].
% 101.23/101.11 5782 -ordered_ab_group_add(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,uminus_uminus(A),B)),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) # label(fact_632_neg__less__0__iff__less) # label(axiom). [clausify(753)].
% 101.23/101.11 5783 -ordered_ab_group_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,uminus_uminus(A),B))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) # label(fact_634_neg__0__less__iff__less) # label(axiom). [clausify(755)].
% 101.23/101.11 5784 -ordered_ab_group_add(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,uminus_uminus(A),B))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) # label(fact_634_neg__0__less__iff__less) # label(axiom). [clausify(755)].
% 101.23/101.11 5785 -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_gr676655987ssThan(A),B),C)) = hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_gr676655987ssThan(A),hAPP(A,A,uminus_uminus(A),C)),hAPP(A,A,uminus_uminus(A),B)) # label(fact_3687_image__uminus__greaterThanLessThan) # label(axiom). [clausify(3640)].
% 101.23/101.11 5786 -ordered_ab_group_add(A) | -hBOOL(hAPP(fun(nat,A),bool,monoseq(A),B)) | hBOOL(hAPP(fun(nat,A),bool,monoseq(A),hAPP(fun(nat,A),fun(nat,A),hAPP(fun(A,A),fun(fun(nat,A),fun(nat,A)),combb(A,A,nat),uminus_uminus(A)),B))) # label(fact_3918_monoseq__minus) # label(axiom). [clausify(3859)].
% 101.23/101.11 5787 -ordered_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),f600(B,A,D,E,F,C)),C)) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),F),C) != E | -hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),D),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(B,A,F,D)),E)) # label(fact_4299_setsum__nonneg__leq__bound) # label(axiom). [clausify(4231)].
% 101.23/101.11 5788 -ordered_ab_group_add(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(B,A,D,f600(B,A,E,F,D,C)))) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),D),C) != F | -hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),E),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(B,A,D,E)),F)) # label(fact_4299_setsum__nonneg__leq__bound) # label(axiom). [clausify(4231)].
% 101.23/101.11 5789 -ordered_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),f601(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) != zero_zero(A) | -hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),D),C)) | hAPP(B,A,E,D) = zero_zero(A) # label(fact_4300_setsum__nonneg__0) # label(axiom). [clausify(4232)].
% 101.23/101.11 5790 -ordered_ab_group_add(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(B,A,D,f601(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) != zero_zero(A) | -hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),E),C)) | hAPP(B,A,D,E) = zero_zero(A) # label(fact_4300_setsum__nonneg__0) # label(axiom). [clausify(4232)].
% 101.23/101.11 5791 -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_4526_image__uminus__atLeastAtMost) # label(axiom). [clausify(4453)].
% 101.23/101.12 5792 -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_4822_min__diff__distrib__left) # label(axiom). [clausify(4746)].
% 101.23/101.12 5793 -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_4976_max__diff__distrib__left) # label(axiom). [clausify(4896)].
% 101.23/101.12 Derived: ord_gr676655987ssThan(int) = ti(fun(int,fun(int,fun(int,bool))),ord_gr676655987ssThan(int)). [resolve(5754,a,5755,a)].
% 101.23/101.12 Derived: hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),B) != hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),C),D) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),C),D)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)). [resolve(5754,a,5756,a)].
% 101.23/101.12 Derived: hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),B) != hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),C),D) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),C),D)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)). [resolve(5754,a,5757,a)].
% 101.23/101.12 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),C),D)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)). [resolve(5754,a,5758,a)].
% 101.23/101.12 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),C),D)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)). [resolve(5754,a,5759,a)].
% 101.23/101.12 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,hAPP(int,fun(int,int),minus_minus(int),A),B)),zero_zero(int))). [resolve(5754,a,5760,a)].
% 101.23/101.12 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,hAPP(int,fun(int,int),minus_minus(int),A),B)),zero_zero(int))). [resolve(5754,a,5761,a)].
% 101.23/101.12 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),B)),zero_zero(int))). [resolve(5754,a,5762,a)].
% 101.23/101.12 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),B)),zero_zero(int))). [resolve(5754,a,5763,a)].
% 101.23/101.12 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(5754,a,5764,a)].
% 101.23/101.12 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(5754,a,5765,a)].
% 101.23/101.12 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(5754,a,5767,a)].
% 101.23/101.12 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(5754,a,5769,a)].
% 101.23/101.13 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(5754,a,5771,a)].
% 101.23/101.13 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(5754,a,5772,a)].
% 101.23/101.13 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(5754,a,5773,a)].
% 101.23/101.13 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(5754,a,5775,a)].
% 101.23/101.13 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,uminus_uminus(int),A)),zero_zero(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A)). [resolve(5754,a,5777,a)].
% 101.23/101.13 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,uminus_uminus(int),A)),zero_zero(int))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A)). [resolve(5754,a,5778,a)].
% 101.23/101.13 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,uminus_uminus(int),A))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),zero_zero(int))). [resolve(5754,a,5779,a)].
% 101.23/101.13 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,uminus_uminus(int),A))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),zero_zero(int))). [resolve(5754,a,5780,a)].
% 101.23/101.13 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,uminus_uminus(int),A)),zero_zero(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A)). [resolve(5754,a,5781,a)].
% 101.23/101.13 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,uminus_uminus(int),A)),zero_zero(int))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A)). [resolve(5754,a,5782,a)].
% 101.23/101.13 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,uminus_uminus(int),A))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),zero_zero(int))). [resolve(5754,a,5783,a)].
% 101.23/101.13 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,uminus_uminus(int),A))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),zero_zero(int))). [resolve(5754,a,5784,a)].
% 101.23/101.13 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_gr676655987ssThan(int),A),B)) = hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_gr676655987ssThan(int),hAPP(int,int,uminus_uminus(int),B)),hAPP(int,int,uminus_uminus(int),A)). [resolve(5754,a,5785,a)].
% 101.23/101.13 Derived: -hBOOL(hAPP(fun(nat,int),bool,monoseq(int),A)) | hBOOL(hAPP(fun(nat,int),bool,monoseq(int),hAPP(fun(nat,int),fun(nat,int),hAPP(fun(int,int),fun(fun(nat,int),fun(nat,int)),combb(int,int,nat),uminus_uminus(int)),A))). [resolve(5754,a,5786,a)].
% 101.23/101.13 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),f600(A,int,C,D,E,B)),B)) | hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),E),B) != D | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(A,int,E,C)),D)). [resolve(5754,a,5787,a)].
% 101.23/101.13 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(A,int,C,f600(A,int,D,E,C,B)))) | hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),C),B) != E | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),D),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(A,int,C,D)),E)). [resolve(5754,a,5788,a)].
% 101.23/101.17 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),f601(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) != zero_zero(int) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | hAPP(A,int,D,C) = zero_zero(int). [resolve(5754,a,5789,a)].
% 101.23/101.17 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(A,int,C,f601(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) != zero_zero(int) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),D),B)) | hAPP(A,int,C,D) = zero_zero(int). [resolve(5754,a,5790,a)].
% 101.23/101.17 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(5754,a,5791,a)].
% 101.23/101.17 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(5754,a,5792,a)].
% 101.23/101.17 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(5754,a,5793,a)].
% 101.23/101.17 5794 ordered_ab_group_add(rat) # label(arity_Rat_Orat___Groups_Oordered__ab__group__add) # label(axiom). [assumption].
% 101.23/101.17 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),A),B) != hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),C),D) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),C),D)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),B)). [resolve(5794,a,5756,a)].
% 101.23/101.17 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),A),B) != hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),C),D) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),C),D)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),B)). [resolve(5794,a,5757,a)].
% 101.23/101.17 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),A),B) != hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),C),D) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),C),D)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),B)). [resolve(5794,a,5758,a)].
% 101.23/101.17 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),A),B) != hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),C),D) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),C),D)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),B)). [resolve(5794,a,5759,a)].
% 101.23/101.17 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),A),B)),zero_zero(rat))). [resolve(5794,a,5760,a)].
% 101.23/101.17 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),A),B)),zero_zero(rat))). [resolve(5794,a,5761,a)].
% 101.23/101.17 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),A),B)),zero_zero(rat))). [resolve(5794,a,5762,a)].
% 101.23/101.18 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),A),B)),zero_zero(rat))). [resolve(5794,a,5763,a)].
% 101.23/101.18 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,uminus_uminus(rat),B)),hAPP(rat,rat,uminus_uminus(rat),A))). [resolve(5794,a,5764,a)].
% 101.23/101.18 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,uminus_uminus(rat),A)),hAPP(rat,rat,uminus_uminus(rat),B))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),B),A)). [resolve(5794,a,5765,a)].
% 101.23/101.18 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,uminus_uminus(rat),A)),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,uminus_uminus(rat),B)),A)). [resolve(5794,a,5767,a)].
% 101.23/101.18 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),hAPP(rat,rat,uminus_uminus(rat),B))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),B),hAPP(rat,rat,uminus_uminus(rat),A))). [resolve(5794,a,5769,a)].
% 101.23/101.18 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,uminus_uminus(rat),A)),hAPP(rat,rat,uminus_uminus(rat),B))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),A)). [resolve(5794,a,5771,a)].
% 101.23/101.18 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,uminus_uminus(rat),A)),hAPP(rat,rat,uminus_uminus(rat),B))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),A)). [resolve(5794,a,5772,a)].
% 101.23/101.18 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,uminus_uminus(rat),A)),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,uminus_uminus(rat),B)),A)). [resolve(5794,a,5773,a)].
% 101.23/101.18 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),hAPP(rat,rat,uminus_uminus(rat),B))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),hAPP(rat,rat,uminus_uminus(rat),A))). [resolve(5794,a,5775,a)].
% 101.23/101.18 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,uminus_uminus(rat),A)),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),A)). [resolve(5794,a,5777,a)].
% 101.23/101.18 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,uminus_uminus(rat),A)),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),A)). [resolve(5794,a,5778,a)].
% 101.23/101.18 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),hAPP(rat,rat,uminus_uminus(rat),A))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),zero_zero(rat))). [resolve(5794,a,5779,a)].
% 101.23/101.18 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),hAPP(rat,rat,uminus_uminus(rat),A))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),zero_zero(rat))). [resolve(5794,a,5780,a)].
% 101.23/101.18 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,uminus_uminus(rat),A)),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)). [resolve(5794,a,5781,a)].
% 101.23/101.18 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,uminus_uminus(rat),A)),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)). [resolve(5794,a,5782,a)].
% 101.23/101.18 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(rat,rat,uminus_uminus(rat),A))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),zero_zero(rat))). [resolve(5794,a,5783,a)].
% 101.23/101.18 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(rat,rat,uminus_uminus(rat),A))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),zero_zero(rat))). [resolve(5794,a,5784,a)].
% 101.30/101.21 Derived: hAPP(fun(rat,bool),fun(rat,bool),hAPP(fun(rat,rat),fun(fun(rat,bool),fun(rat,bool)),image(rat,rat),uminus_uminus(rat)),hAPP(rat,fun(rat,bool),hAPP(rat,fun(rat,fun(rat,bool)),ord_gr676655987ssThan(rat),A),B)) = hAPP(rat,fun(rat,bool),hAPP(rat,fun(rat,fun(rat,bool)),ord_gr676655987ssThan(rat),hAPP(rat,rat,uminus_uminus(rat),B)),hAPP(rat,rat,uminus_uminus(rat),A)). [resolve(5794,a,5785,a)].
% 101.30/101.21 Derived: -hBOOL(hAPP(fun(nat,rat),bool,monoseq(rat),A)) | hBOOL(hAPP(fun(nat,rat),bool,monoseq(rat),hAPP(fun(nat,rat),fun(nat,rat),hAPP(fun(rat,rat),fun(fun(nat,rat),fun(nat,rat)),combb(rat,rat,nat),uminus_uminus(rat)),A))). [resolve(5794,a,5786,a)].
% 101.30/101.21 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),f600(A,rat,C,D,E,B)),B)) | hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),E),B) != D | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(A,rat,E,C)),D)). [resolve(5794,a,5787,a)].
% 101.30/101.21 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),hAPP(A,rat,C,f600(A,rat,D,E,C,B)))) | hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),C),B) != E | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),D),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(A,rat,C,D)),E)). [resolve(5794,a,5788,a)].
% 101.30/101.21 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),f601(A,rat,C,D,B)),B)) | hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),D),B) != zero_zero(rat) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | hAPP(A,rat,D,C) = zero_zero(rat). [resolve(5794,a,5789,a)].
% 101.30/101.21 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),hAPP(A,rat,C,f601(A,rat,D,C,B)))) | hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),C),B) != zero_zero(rat) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),D),B)) | hAPP(A,rat,C,D) = zero_zero(rat). [resolve(5794,a,5790,a)].
% 101.30/101.21 Derived: hAPP(fun(rat,bool),fun(rat,bool),hAPP(fun(rat,rat),fun(fun(rat,bool),fun(rat,bool)),image(rat,rat),uminus_uminus(rat)),hAPP(rat,fun(rat,bool),hAPP(rat,fun(rat,fun(rat,bool)),ord_atLeastAtMost(rat),A),B)) = hAPP(rat,fun(rat,bool),hAPP(rat,fun(rat,fun(rat,bool)),ord_atLeastAtMost(rat),hAPP(rat,rat,uminus_uminus(rat),B)),hAPP(rat,rat,uminus_uminus(rat),A)). [resolve(5794,a,5791,a)].
% 101.30/101.21 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_min(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),A),B)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),C),B)) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_min(rat),A),C)),B). [resolve(5794,a,5792,a)].
% 101.30/101.21 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_max(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),A),B)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),C),B)) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_max(rat),A),C)),B). [resolve(5794,a,5793,a)].
% 101.30/101.21 5795 ordered_ab_group_add(real) # label(arity_RealDef_Oreal___Groups_Oordered__ab__group__add) # label(axiom). [assumption].
% 101.30/101.21 Derived: hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),B) != hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),C),D) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),C),D)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)). [resolve(5795,a,5756,a)].
% 101.30/101.21 Derived: hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),B) != hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),C),D) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),C),D)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)). [resolve(5795,a,5757,a)].
% 101.30/101.22 Derived: hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),B) != hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),C),D) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),C),D)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),B)). [resolve(5795,a,5758,a)].
% 101.30/101.22 Derived: hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),B) != hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),C),D) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),C),D)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),B)). [resolve(5795,a,5759,a)].
% 101.30/101.22 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),B)),zero_zero(real))). [resolve(5795,a,5760,a)].
% 101.30/101.22 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),B)),zero_zero(real))). [resolve(5795,a,5761,a)].
% 101.30/101.22 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),B)),zero_zero(real))). [resolve(5795,a,5762,a)].
% 101.30/101.22 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),B)),zero_zero(real))). [resolve(5795,a,5763,a)].
% 101.30/101.22 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,uminus_uminus(real),B)),hAPP(real,real,uminus_uminus(real),A))). [resolve(5795,a,5764,a)].
% 101.30/101.22 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,uminus_uminus(real),A)),hAPP(real,real,uminus_uminus(real),B))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),A)). [resolve(5795,a,5765,a)].
% 101.30/101.22 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,uminus_uminus(real),A)),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,uminus_uminus(real),B)),A)). [resolve(5795,a,5767,a)].
% 101.30/101.22 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),hAPP(real,real,uminus_uminus(real),B))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),hAPP(real,real,uminus_uminus(real),A))). [resolve(5795,a,5769,a)].
% 101.30/101.22 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,uminus_uminus(real),A)),hAPP(real,real,uminus_uminus(real),B))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),A)). [resolve(5795,a,5771,a)].
% 101.30/101.22 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,uminus_uminus(real),A)),hAPP(real,real,uminus_uminus(real),B))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),A)). [resolve(5795,a,5772,a)].
% 101.30/101.22 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,uminus_uminus(real),A)),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,uminus_uminus(real),B)),A)). [resolve(5795,a,5773,a)].
% 101.30/101.22 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),hAPP(real,real,uminus_uminus(real),B))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),hAPP(real,real,uminus_uminus(real),A))). [resolve(5795,a,5775,a)].
% 101.30/101.22 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,uminus_uminus(real),A)),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A)). [resolve(5795,a,5777,a)].
% 101.30/101.22 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,uminus_uminus(real),A)),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A)). [resolve(5795,a,5778,a)].
% 101.30/101.22 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(real,real,uminus_uminus(real),A))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),zero_zero(real))). [resolve(5795,a,5779,a)].
% 101.30/101.22 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(real,real,uminus_uminus(real),A))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),zero_zero(real))). [resolve(5795,a,5780,a)].
% 101.30/101.22 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,uminus_uminus(real),A)),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)). [resolve(5795,a,5781,a)].
% 101.30/101.22 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,uminus_uminus(real),A)),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)). [resolve(5795,a,5782,a)].
% 101.30/101.22 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,uminus_uminus(real),A))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))). [resolve(5795,a,5783,a)].
% 101.30/101.22 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,uminus_uminus(real),A))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))). [resolve(5795,a,5784,a)].
% 101.30/101.22 Derived: hAPP(fun(real,bool),fun(real,bool),hAPP(fun(real,real),fun(fun(real,bool),fun(real,bool)),image(real,real),uminus_uminus(real)),hAPP(real,fun(real,bool),hAPP(real,fun(real,fun(real,bool)),ord_gr676655987ssThan(real),A),B)) = hAPP(real,fun(real,bool),hAPP(real,fun(real,fun(real,bool)),ord_gr676655987ssThan(real),hAPP(real,real,uminus_uminus(real),B)),hAPP(real,real,uminus_uminus(real),A)). [resolve(5795,a,5785,a)].
% 101.30/101.22 Derived: -hBOOL(hAPP(fun(nat,real),bool,monoseq(real),A)) | hBOOL(hAPP(fun(nat,real),bool,monoseq(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),uminus_uminus(real)),A))). [resolve(5795,a,5786,a)].
% 101.30/101.22 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),f600(A,real,C,D,E,B)),B)) | hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),E),B) != D | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(A,real,E,C)),D)). [resolve(5795,a,5787,a)].
% 101.30/101.22 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(A,real,C,f600(A,real,D,E,C,B)))) | hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),C),B) != E | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),D),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(A,real,C,D)),E)). [resolve(5795,a,5788,a)].
% 101.30/101.22 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),f601(A,real,C,D,B)),B)) | hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),D),B) != zero_zero(real) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | hAPP(A,real,D,C) = zero_zero(real). [resolve(5795,a,5789,a)].
% 101.30/101.22 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(A,real,C,f601(A,real,D,C,B)))) | hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),C),B) != zero_zero(real) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),D),B)) | hAPP(A,real,C,D) = zero_zero(real). [resolve(5795,a,5790,a)].
% 104.93/104.86 Derived: hAPP(fun(real,bool),fun(real,bool),hAPP(fun(real,real),fun(fun(real,bool),fun(real,bool)),image(real,real),uminus_uminus(real)),hAPP(real,fun(real,bool),hAPP(real,fun(real,fun(real,bool)),ord_atLeastAtMost(real),A),B)) = hAPP(real,fun(real,bool),hAPP(real,fun(real,fun(real,bool)),ord_atLeastAtMost(real),hAPP(real,real,uminus_uminus(real),B)),hAPP(real,real,uminus_uminus(real),A)). [resolve(5795,a,5791,a)].
% 104.93/104.86 Derived: hAPP(real,real,hAPP(real,fun(real,real),ord_min(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),C),B)) = hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,hAPP(real,fun(real,real),ord_min(real),A),C)),B). [resolve(5795,a,5792,a)].
% 104.93/104.86 Derived: hAPP(real,real,hAPP(real,fun(real,real),ord_max(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),C),B)) = hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,hAPP(real,fun(real,real),ord_max(real),A),C)),B). [resolve(5795,a,5793,a)].
% 104.93/104.86 5796 ring(int) # label(arity_Int_Oint___Rings_Oring) # label(axiom). [assumption].
% 104.93/104.86 5797 -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),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),C),D))),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),E)),D)) = hAPP(A,A,hAPP(A,fun(A,A),minus_minus(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),E),D)) # label(fact_1_mult__diff__mult) # label(axiom). [clausify(131)].
% 104.93/104.86 5798 -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_3_eq__add__iff2) # label(axiom). [clausify(133)].
% 104.93/104.86 5799 -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_3_eq__add__iff2) # label(axiom). [clausify(133)].
% 104.93/104.86 5800 -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_4_eq__add__iff1) # label(axiom). [clausify(134)].
% 104.93/104.86 5801 -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_4_eq__add__iff1) # label(axiom). [clausify(134)].
% 104.93/104.86 5802 -number(A) | -ring(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),B)),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),C),D)) = hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),B)),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),B)),D)) # label(fact_143_right__diff__distrib__number__of) # label(axiom). [clausify(273)].
% 104.93/104.86 5803 -number(A) | -ring(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C)),hAPP(int,A,number_number_of(A),D)) = hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(int,A,number_number_of(A),D))),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),hAPP(int,A,number_number_of(A),D))) # label(fact_144_left__diff__distrib__number__of) # label(axiom). [clausify(274)].
% 104.93/104.86 5804 -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_573_minus__mult__minus) # label(axiom). [clausify(697)].
% 104.93/104.86 5805 -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_574_minus__mult__commute) # label(axiom). [clausify(698)].
% 104.93/104.86 5806 -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_579_minus__mult__left) # label(axiom). [clausify(703)].
% 104.93/104.86 5807 -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_580_minus__mult__right) # label(axiom). [clausify(704)].
% 104.93/104.86 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),B),C))),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),D)),C)) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(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),D),C)). [resolve(5796,a,5797,a)].
% 104.93/104.86 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(5796,a,5798,a)].
% 104.93/104.86 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(5796,a,5799,a)].
% 104.93/104.86 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(5796,a,5800,a)].
% 104.93/104.86 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(5796,a,5801,a)].
% 104.93/104.86 Derived: -number(int) | hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),A)),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),B),C)) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),A)),B)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),A)),C)). [resolve(5796,a,5802,b)].
% 104.93/104.86 Derived: -number(int) | hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),B)),hAPP(int,int,number_number_of(int),C)) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),hAPP(int,int,number_number_of(int),C))),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),hAPP(int,int,number_number_of(int),C))). [resolve(5796,a,5803,b)].
% 105.02/104.90 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(5796,a,5804,a)].
% 105.02/104.90 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(5796,a,5805,a)].
% 105.02/104.90 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(5796,a,5806,a)].
% 105.02/104.90 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(5796,a,5807,a)].
% 105.02/104.90 5808 ring(rat) # label(arity_Rat_Orat___Rings_Oring) # label(axiom). [assumption].
% 105.02/104.90 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),B),C))),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),A),D)),C)) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),D),C)). [resolve(5808,a,5797,a)].
% 105.02/104.90 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B)),C) != hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),D),B)),E) | hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),A),D)),B)),C) = ti(rat,E). [resolve(5808,a,5798,a)].
% 105.02/104.90 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B)),C) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),D),B)),E) | hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),A),D)),B)),C) != ti(rat,E). [resolve(5808,a,5799,a)].
% 105.02/104.90 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B)),C) != hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),D),B)),E) | hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),D),A)),B)),E) = ti(rat,C). [resolve(5808,a,5800,a)].
% 105.02/104.90 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B)),C) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),D),B)),E) | hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),D),A)),B)),E) != ti(rat,C). [resolve(5808,a,5801,a)].
% 105.02/104.90 Derived: -number(rat) | hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(int,rat,number_number_of(rat),A)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),B),C)) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(int,rat,number_number_of(rat),A)),B)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(int,rat,number_number_of(rat),A)),C)). [resolve(5808,a,5802,b)].
% 105.02/104.90 Derived: -number(rat) | hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),A),B)),hAPP(int,rat,number_number_of(rat),C)) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),hAPP(int,rat,number_number_of(rat),C))),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),B),hAPP(int,rat,number_number_of(rat),C))). [resolve(5808,a,5803,b)].
% 105.06/104.93 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(rat,rat,uminus_uminus(rat),A)),hAPP(rat,rat,uminus_uminus(rat),B)) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B). [resolve(5808,a,5804,a)].
% 105.06/104.93 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(rat,rat,uminus_uminus(rat),A)),B) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),hAPP(rat,rat,uminus_uminus(rat),B)). [resolve(5808,a,5805,a)].
% 105.06/104.93 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(rat,rat,uminus_uminus(rat),A)),B) = hAPP(rat,rat,uminus_uminus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B)). [resolve(5808,a,5806,a)].
% 105.06/104.93 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),hAPP(rat,rat,uminus_uminus(rat),B)) = hAPP(rat,rat,uminus_uminus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B)). [resolve(5808,a,5807,a)].
% 105.06/104.93 5809 ring(real) # label(arity_RealDef_Oreal___Rings_Oring) # label(axiom). [assumption].
% 105.06/104.93 Derived: hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),B),C))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),D)),C)) = hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),D),C)). [resolve(5809,a,5797,a)].
% 105.06/104.93 Derived: hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),C) != hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),D),B)),E) | hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),D)),B)),C) = ti(real,E). [resolve(5809,a,5798,a)].
% 105.06/104.93 Derived: hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),C) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),D),B)),E) | hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),D)),B)),C) != ti(real,E). [resolve(5809,a,5799,a)].
% 105.06/104.93 Derived: hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),C) != hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),D),B)),E) | hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),D),A)),B)),E) = ti(real,C). [resolve(5809,a,5800,a)].
% 105.06/104.93 Derived: hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),C) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),D),B)),E) | hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),D),A)),B)),E) != ti(real,C). [resolve(5809,a,5801,a)].
% 105.06/104.93 Derived: -number(real) | hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),A)),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),B),C)) = hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),A)),B)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),A)),C)). [resolve(5809,a,5802,b)].
% 105.06/104.93 Derived: -number(real) | hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),B)),hAPP(int,real,number_number_of(real),C)) = hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),hAPP(int,real,number_number_of(real),C))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),hAPP(int,real,number_number_of(real),C))). [resolve(5809,a,5803,b)].
% 105.06/104.95 Derived: hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,uminus_uminus(real),A)),hAPP(real,real,uminus_uminus(real),B)) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B). [resolve(5809,a,5804,a)].
% 105.06/104.95 Derived: hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,uminus_uminus(real),A)),B) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),hAPP(real,real,uminus_uminus(real),B)). [resolve(5809,a,5805,a)].
% 105.06/104.95 Derived: hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,uminus_uminus(real),A)),B) = hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)). [resolve(5809,a,5806,a)].
% 105.06/104.95 Derived: hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),hAPP(real,real,uminus_uminus(real),B)) = hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)). [resolve(5809,a,5807,a)].
% 105.06/104.95 5810 ring(complex) # label(arity_Complex_Ocomplex___Rings_Oring) # label(axiom). [assumption].
% 105.06/104.95 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),B),C))),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),A),D)),C)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),B)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),D),C)). [resolve(5810,a,5797,a)].
% 105.06/104.95 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),B)),C) != hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),D),B)),E) | hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),A),D)),B)),C) = ti(complex,E). [resolve(5810,a,5798,a)].
% 105.06/104.95 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),B)),C) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),D),B)),E) | hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),A),D)),B)),C) != ti(complex,E). [resolve(5810,a,5799,a)].
% 105.06/104.95 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),B)),C) != hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),D),B)),E) | hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),D),A)),B)),E) = ti(complex,C). [resolve(5810,a,5800,a)].
% 105.06/104.95 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),B)),C) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),D),B)),E) | hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),D),A)),B)),E) != ti(complex,C). [resolve(5810,a,5801,a)].
% 108.76/108.66 Derived: -number(complex) | hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(int,complex,number_number_of(complex),A)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),B),C)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(int,complex,number_number_of(complex),A)),B)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(int,complex,number_number_of(complex),A)),C)). [resolve(5810,a,5802,b)].
% 108.76/108.66 Derived: -number(complex) | hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),A),B)),hAPP(int,complex,number_number_of(complex),C)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),hAPP(int,complex,number_number_of(complex),C))),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),B),hAPP(int,complex,number_number_of(complex),C))). [resolve(5810,a,5803,b)].
% 108.76/108.66 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,uminus_uminus(complex),A)),hAPP(complex,complex,uminus_uminus(complex),B)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),B). [resolve(5810,a,5804,a)].
% 108.76/108.66 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,uminus_uminus(complex),A)),B) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),hAPP(complex,complex,uminus_uminus(complex),B)). [resolve(5810,a,5805,a)].
% 108.76/108.66 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,uminus_uminus(complex),A)),B) = hAPP(complex,complex,uminus_uminus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),B)). [resolve(5810,a,5806,a)].
% 108.76/108.66 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),hAPP(complex,complex,uminus_uminus(complex),B)) = hAPP(complex,complex,uminus_uminus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),B)). [resolve(5810,a,5807,a)].
% 108.76/108.66 5811 real_normed_algebra(real) # label(arity_RealDef_Oreal___RealVector_Oreal__normed__algebra) # label(axiom). [assumption].
% 108.76/108.66 5812 -real_normed_algebra(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(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),C)),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),D),E))),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C)),E))),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),D),E))) = hAPP(A,A,hAPP(A,fun(A,A),minus_minus(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_2_mult_Oprod__diff__prod) # label(axiom). [clausify(132)].
% 108.76/108.66 5813 -real_normed_algebra(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_26_mult__left_Oadd) # label(axiom). [clausify(156)].
% 108.76/108.66 5814 -real_normed_algebra(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_27_mult_Oadd__left) # label(axiom). [clausify(157)].
% 108.76/108.66 5815 -real_normed_algebra(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_29_mult__right_Oadd) # label(axiom). [clausify(159)].
% 108.76/108.66 5816 -real_normed_algebra(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_30_mult_Oadd__right) # label(axiom). [clausify(160)].
% 108.76/108.66 5817 -real_normed_algebra(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C)),D) = hAPP(A,A,hAPP(A,fun(A,A),minus_minus(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_31_mult__left_Odiff) # label(axiom). [clausify(161)].
% 108.76/108.66 5818 -real_normed_algebra(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C)),D) = hAPP(A,A,hAPP(A,fun(A,A),minus_minus(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_32_mult_Odiff__left) # label(axiom). [clausify(162)].
% 108.76/108.66 5819 -real_normed_algebra(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),C),D)) = hAPP(A,A,hAPP(A,fun(A,A),minus_minus(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_33_mult__right_Odiff) # label(axiom). [clausify(163)].
% 108.76/108.66 5820 -real_normed_algebra(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),C),D)) = hAPP(A,A,hAPP(A,fun(A,A),minus_minus(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_34_mult_Odiff__right) # label(axiom). [clausify(164)].
% 108.76/108.66 5821 -real_normed_algebra(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),zero_zero(A)) = zero_zero(A) # label(fact_257_mult__right_Ozero) # label(axiom). [clausify(387)].
% 108.76/108.66 5822 -real_normed_algebra(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),zero_zero(A)) = zero_zero(A) # label(fact_258_mult_Ozero__right) # label(axiom). [clausify(388)].
% 108.76/108.66 5823 -real_normed_algebra(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),zero_zero(A)),B) = zero_zero(A) # label(fact_260_mult__left_Ozero) # label(axiom). [clausify(390)].
% 108.76/108.66 5824 -real_normed_algebra(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),zero_zero(A)),B) = zero_zero(A) # label(fact_261_mult_Ozero__left) # label(axiom). [clausify(391)].
% 108.76/108.66 5825 -real_normed_algebra(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_575_mult__left_Ominus) # label(axiom). [clausify(699)].
% 108.76/108.66 5826 -real_normed_algebra(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_576_mult_Ominus__left) # label(axiom). [clausify(700)].
% 108.76/108.66 5827 -real_normed_algebra(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_577_mult__right_Ominus) # label(axiom). [clausify(701)].
% 108.76/108.66 5828 -real_normed_algebra(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_578_mult_Ominus__right) # label(axiom). [clausify(702)].
% 108.76/108.66 5829 -real_normed_algebra(A) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(A,real,norm_norm(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(A,real,norm_norm(A),B)),hAPP(A,real,norm_norm(A),C)))) # label(fact_2710_norm__mult__ineq) # label(axiom). [clausify(2702)].
% 108.76/108.66 5830 -real_normed_algebra(A) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(A,real,norm_norm(A),B)),C)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(A,real,norm_norm(A),D)),E)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(A,real,norm_norm(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),E))) # label(fact_2711_norm__mult__less) # label(axiom). [clausify(2703)].
% 108.76/108.66 5831 -real_normed_algebra(A) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),f259(A))) # label(fact_2739_mult_Opos__bounded) # label(axiom). [clausify(2731)].
% 108.76/108.66 5832 -real_normed_algebra(A) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(A,real,norm_norm(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(A,real,norm_norm(A),B)),hAPP(A,real,norm_norm(A),C))),f259(A)))) # label(fact_2739_mult_Opos__bounded) # label(axiom). [clausify(2731)].
% 108.76/108.66 5833 -real_normed_algebra(A) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),f260(A,B))) # label(fact_2740_mult__left_Opos__bounded) # label(axiom). [clausify(2732)].
% 108.76/108.66 5834 -real_normed_algebra(A) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(A,real,norm_norm(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(A,real,norm_norm(A),B)),f260(A,C)))) # label(fact_2740_mult__left_Opos__bounded) # label(axiom). [clausify(2732)].
% 108.76/108.66 5835 -real_normed_algebra(A) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),f261(A,B))) # label(fact_2741_mult__right_Opos__bounded) # label(axiom). [clausify(2733)].
% 108.76/108.66 5836 -real_normed_algebra(A) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(A,real,norm_norm(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(A,real,norm_norm(A),C)),f261(A,B)))) # label(fact_2741_mult__right_Opos__bounded) # label(axiom). [clausify(2733)].
% 108.76/108.66 5837 -real_normed_algebra(A) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),f266(A))) # label(fact_2746_mult_Ononneg__bounded) # label(axiom). [clausify(2738)].
% 108.76/108.66 5838 -real_normed_algebra(A) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(A,real,norm_norm(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(A,real,norm_norm(A),B)),hAPP(A,real,norm_norm(A),C))),f266(A)))) # label(fact_2746_mult_Ononneg__bounded) # label(axiom). [clausify(2738)].
% 108.76/108.66 5839 -real_normed_algebra(A) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),f267(A,B))) # label(fact_2747_mult__right_Ononneg__bounded) # label(axiom). [clausify(2739)].
% 108.76/108.66 5840 -real_normed_algebra(A) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(A,real,norm_norm(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(A,real,norm_norm(A),C)),f267(A,B)))) # label(fact_2747_mult__right_Ononneg__bounded) # label(axiom). [clausify(2739)].
% 108.76/108.66 5841 -real_normed_algebra(A) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),f268(A,B))) # label(fact_2748_mult__left_Ononneg__bounded) # label(axiom). [clausify(2740)].
% 108.76/108.66 5842 -real_normed_algebra(A) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(A,real,norm_norm(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(A,real,norm_norm(A),B)),f268(A,C)))) # label(fact_2748_mult__left_Ononneg__bounded) # label(axiom). [clausify(2740)].
% 108.76/108.66 5843 -real_normed_algebra(A) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(A,real,norm_norm(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(A,real,norm_norm(A),B)),f271(A,C)))) # label(fact_2751_mult__left_Obounded) # label(axiom). [clausify(2743)].
% 108.76/108.66 5844 -real_normed_algebra(A) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(A,real,norm_norm(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(A,real,norm_norm(A),C)),f272(A,B)))) # label(fact_2752_mult__right_Obounded) # label(axiom). [clausify(2744)].
% 108.76/108.66 5845 -real_normed_algebra(A) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(A,real,norm_norm(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(A,real,norm_norm(A),B)),hAPP(A,real,norm_norm(A),C))),f273(A)))) # label(fact_2753_mult_Obounded) # label(axiom). [clausify(2745)].
% 108.76/108.66 5846 -real_normed_algebra(A) | hBOOL(hAPP(fun(A,fun(A,A)),bool,bounded_bilinear(A,A,A),hAPP(fun(A,fun(A,A)),fun(A,fun(A,A)),combc(A,A,A),times_times(A)))) # label(fact_3861_mult_Oflip) # label(axiom). [clausify(3802)].
% 108.76/108.66 5847 -real_normed_algebra(A) | -hBOOL(hAPP(fun(nat,A),bool,summable(A),B)) | hAPP(fun(nat,A),A,suminf(A),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)),B)),C)) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(fun(nat,A),A,suminf(A),B)),C) # label(fact_3983_mult__left_Osuminf) # label(axiom). [clausify(3923)].
% 108.76/108.66 5848 -real_normed_algebra(A) | -hBOOL(hAPP(fun(nat,A),bool,summable(A),B)) | hAPP(fun(nat,A),A,suminf(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),times_times(A),C)),B)) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),hAPP(fun(nat,A),A,suminf(A),B)) # label(fact_3984_mult__right_Osuminf) # label(axiom). [clausify(3924)].
% 108.76/108.66 5849 -real_normed_algebra(A) | -hBOOL(hAPP(fun(nat,A),bool,summable(A),B)) | hAPP(fun(nat,A),A,suminf(A),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)),B)),C)) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(fun(nat,A),A,suminf(A),B)),C) # label(fact_3985_suminf__mult2) # label(axiom). [clausify(3925)].
% 108.76/108.66 5850 -real_normed_algebra(A) | -hBOOL(hAPP(fun(nat,A),bool,summable(A),B)) | hAPP(fun(nat,A),A,suminf(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),times_times(A),C)),B)) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),hAPP(fun(nat,A),A,suminf(A),B)) # label(fact_3986_suminf__mult) # label(axiom). [clausify(3926)].
% 108.76/108.66 5851 -real_normed_algebra(A) | -hBOOL(hAPP(fun(nat,A),bool,summable(A),B)) | hBOOL(hAPP(fun(nat,A),bool,summable(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),times_times(A),C)),B))) # label(fact_3999_summable__mult) # label(axiom). [clausify(3939)].
% 108.76/108.66 5852 -real_normed_algebra(A) | -hBOOL(hAPP(fun(nat,A),bool,summable(A),B)) | hBOOL(hAPP(fun(nat,A),bool,summable(A),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)),B)),C))) # label(fact_4000_summable__mult2) # label(axiom). [clausify(3940)].
% 108.76/108.66 5853 -real_normed_algebra(A) | -hBOOL(hAPP(fun(nat,A),bool,summable(A),B)) | hBOOL(hAPP(fun(nat,A),bool,summable(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),times_times(A),C)),B))) # label(fact_4001_mult__right_Osummable) # label(axiom). [clausify(3941)].
% 108.76/108.66 5854 -real_normed_algebra(A) | -hBOOL(hAPP(fun(nat,A),bool,summable(A),B)) | hBOOL(hAPP(fun(nat,A),bool,summable(A),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)),B)),C))) # label(fact_4002_mult__left_Osummable) # label(axiom). [clausify(3942)].
% 108.76/108.67 5855 -real_normed_algebra(A) | -hBOOL(hAPP(A,bool,hAPP(fun(nat,A),fun(A,bool),sums(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(fun(nat,A),fun(A,bool),sums(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),times_times(A),D)),B)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),C))) # label(fact_4080_sums__mult) # label(axiom). [clausify(4016)].
% 108.76/108.67 5856 -real_normed_algebra(A) | -hBOOL(hAPP(A,bool,hAPP(fun(nat,A),fun(A,bool),sums(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(fun(nat,A),fun(A,bool),sums(A),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)),B)),D)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),D))) # label(fact_4081_sums__mult2) # label(axiom). [clausify(4017)].
% 108.76/108.67 5857 -real_normed_algebra(A) | -hBOOL(hAPP(A,bool,hAPP(fun(nat,A),fun(A,bool),sums(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(fun(nat,A),fun(A,bool),sums(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),times_times(A),D)),B)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),C))) # label(fact_4082_mult__right_Osums) # label(axiom). [clausify(4018)].
% 108.76/108.67 5858 -real_normed_algebra(A) | -hBOOL(hAPP(A,bool,hAPP(fun(nat,A),fun(A,bool),sums(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(fun(nat,A),fun(A,bool),sums(A),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)),B)),D)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),D))) # label(fact_4083_mult__left_Osums) # label(axiom). [clausify(4019)].
% 108.76/108.67 5859 -real_normed_algebra(A) | -hBOOL(hAPP(fun(nat,A),bool,cauchy(A),B)) | hBOOL(hAPP(fun(nat,A),bool,cauchy(A),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)),B)),C))) # label(fact_4100_mult__left_OCauchy) # label(axiom). [clausify(4035)].
% 108.76/108.67 5860 -real_normed_algebra(A) | -hBOOL(hAPP(fun(nat,A),bool,cauchy(A),B)) | hBOOL(hAPP(fun(nat,A),bool,cauchy(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),times_times(A),C)),B))) # label(fact_4101_mult__right_OCauchy) # label(axiom). [clausify(4036)].
% 108.76/108.67 5861 -real_normed_algebra(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_4190_mult__left_Osetsum) # label(axiom). [clausify(4122)].
% 108.76/108.67 5862 -real_normed_algebra(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_4191_mult__right_Osetsum) # label(axiom). [clausify(4123)].
% 108.76/108.67 5863 -real_normed_algebra(A) | -hBOOL(hAPP(filter(B),bool,hAPP(A,fun(filter(B),bool),hAPP(fun(B,A),fun(A,fun(filter(B),bool)),tendsto(B,A),C),D),E)) | -hBOOL(hAPP(filter(B),bool,hAPP(A,fun(filter(B),bool),hAPP(fun(B,A),fun(A,fun(filter(B),bool)),tendsto(B,A),F),V6),E)) | hBOOL(hAPP(filter(B),bool,hAPP(A,fun(filter(B),bool),hAPP(fun(B,A),fun(A,fun(filter(B),bool)),tendsto(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)),F)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),V6)),E)) # label(fact_4447_mult_Otendsto) # label(axiom). [clausify(4375)].
% 108.76/108.67 5864 -real_normed_algebra(A) | -hBOOL(hAPP(filter(B),bool,hAPP(A,fun(filter(B),bool),hAPP(fun(B,A),fun(A,fun(filter(B),bool)),tendsto(B,A),C),D),E)) | hBOOL(hAPP(filter(B),bool,hAPP(A,fun(filter(B),bool),hAPP(fun(B,A),fun(A,fun(filter(B),bool)),tendsto(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)),F)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),F)),E)) # label(fact_4448_mult__left_Otendsto) # label(axiom). [clausify(4376)].
% 108.76/108.67 5865 -real_normed_algebra(A) | -hBOOL(hAPP(filter(B),bool,hAPP(A,fun(filter(B),bool),hAPP(fun(B,A),fun(A,fun(filter(B),bool)),tendsto(B,A),C),D),E)) | hBOOL(hAPP(filter(B),bool,hAPP(A,fun(filter(B),bool),hAPP(fun(B,A),fun(A,fun(filter(B),bool)),tendsto(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),F)),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),F),D)),E)) # label(fact_4449_mult__right_Otendsto) # label(axiom). [clausify(4377)].
% 108.76/108.67 5866 -real_normed_algebra(A) | -hBOOL(hAPP(filter(nat),bool,hAPP(A,fun(filter(nat),bool),hAPP(fun(nat,A),fun(A,fun(filter(nat),bool)),tendsto(nat,A),B),C),sequentially)) | -hBOOL(hAPP(filter(nat),bool,hAPP(A,fun(filter(nat),bool),hAPP(fun(nat,A),fun(A,fun(filter(nat),bool)),tendsto(nat,A),D),E),sequentially)) | hBOOL(hAPP(filter(nat),bool,hAPP(A,fun(filter(nat),bool),hAPP(fun(nat,A),fun(A,fun(filter(nat),bool)),tendsto(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),times_times(A)),B)),D)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),E)),sequentially)) # label(fact_4450_LIMSEQ__mult) # label(axiom). [clausify(4378)].
% 108.76/108.67 5867 -real_normed_algebra(A) | -hBOOL(hAPP(filter(nat),bool,hAPP(A,fun(filter(nat),bool),hAPP(fun(nat,A),fun(A,fun(filter(nat),bool)),tendsto(nat,A),B),C),sequentially)) | hBOOL(hAPP(filter(nat),bool,hAPP(A,fun(filter(nat),bool),hAPP(fun(nat,A),fun(A,fun(filter(nat),bool)),tendsto(nat,A),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)),B)),D)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),D)),sequentially)) # label(fact_4451_mult__left_OLIMSEQ) # label(axiom). [clausify(4379)].
% 108.76/108.67 5868 -real_normed_algebra(A) | -hBOOL(hAPP(filter(nat),bool,hAPP(A,fun(filter(nat),bool),hAPP(fun(nat,A),fun(A,fun(filter(nat),bool)),tendsto(nat,A),B),C),sequentially)) | hBOOL(hAPP(filter(nat),bool,hAPP(A,fun(filter(nat),bool),hAPP(fun(nat,A),fun(A,fun(filter(nat),bool)),tendsto(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),times_times(A),D)),B)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),C)),sequentially)) # label(fact_4452_mult__right_OLIMSEQ) # label(axiom). [clausify(4380)].
% 108.76/108.67 5869 -power(A) | -real_normed_algebra(A) | -hBOOL(hAPP(filter(nat),bool,hAPP(A,fun(filter(nat),bool),hAPP(fun(nat,A),fun(A,fun(filter(nat),bool)),tendsto(nat,A),B),C),sequentially)) | hBOOL(hAPP(filter(nat),bool,hAPP(A,fun(filter(nat),bool),hAPP(fun(nat,A),fun(A,fun(filter(nat),bool)),tendsto(nat,A),hAPP(nat,fun(nat,A),hAPP(fun(nat,fun(nat,A)),fun(nat,fun(nat,A)),combc(nat,nat,A),hAPP(fun(nat,A),fun(nat,fun(nat,A)),hAPP(fun(A,fun(nat,A)),fun(fun(nat,A),fun(nat,fun(nat,A))),combb(A,fun(nat,A),nat),power_power(A)),B)),D)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),C),D)),sequentially)) # label(fact_4465_LIMSEQ__pow) # label(axiom). [clausify(4393)].
% 108.76/108.67 5870 -topological_space(A) | -power(B) | -real_normed_algebra(B) | -hBOOL(hAPP(filter(A),bool,hAPP(B,fun(filter(A),bool),hAPP(fun(A,B),fun(B,fun(filter(A),bool)),tendsto(A,B),C),D),hAPP(A,filter(A),at(A),E))) | hBOOL(hAPP(filter(A),bool,hAPP(B,fun(filter(A),bool),hAPP(fun(A,B),fun(B,fun(filter(A),bool)),tendsto(A,B),hAPP(nat,fun(A,B),hAPP(fun(A,fun(nat,B)),fun(nat,fun(A,B)),combc(A,nat,B),hAPP(fun(A,B),fun(A,fun(nat,B)),hAPP(fun(B,fun(nat,B)),fun(fun(A,B),fun(A,fun(nat,B))),combb(B,fun(nat,B),A),power_power(B)),C)),F)),hAPP(nat,B,hAPP(B,fun(nat,B),power_power(B),D),F)),hAPP(A,filter(A),at(A),E))) # label(fact_4555_LIM__power) # label(axiom). [clausify(4482)].
% 108.76/108.67 5871 -topological_space(A) | -real_normed_algebra(B) | -hBOOL(hAPP(filter(A),bool,hAPP(B,fun(filter(A),bool),hAPP(fun(A,B),fun(B,fun(filter(A),bool)),tendsto(A,B),C),D),hAPP(A,filter(A),at(A),E))) | -hBOOL(hAPP(filter(A),bool,hAPP(B,fun(filter(A),bool),hAPP(fun(A,B),fun(B,fun(filter(A),bool)),tendsto(A,B),F),V6),hAPP(A,filter(A),at(A),E))) | hBOOL(hAPP(filter(A),bool,hAPP(B,fun(filter(A),bool),hAPP(fun(A,B),fun(B,fun(filter(A),bool)),tendsto(A,B),hAPP(fun(A,B),fun(A,B),hAPP(fun(A,fun(B,B)),fun(fun(A,B),fun(A,B)),combs(A,B,B),hAPP(fun(A,B),fun(A,fun(B,B)),hAPP(fun(B,fun(B,B)),fun(fun(A,B),fun(A,fun(B,B))),combb(B,fun(B,B),A),times_times(B)),C)),F)),hAPP(B,B,hAPP(B,fun(B,B),times_times(B),D),V6)),hAPP(A,filter(A),at(A),E))) # label(fact_4562_LIM__mult) # label(axiom). [clausify(4489)].
% 108.76/108.67 5872 -topological_space(A) | -real_normed_algebra(B) | -hBOOL(hAPP(filter(A),bool,hAPP(B,fun(filter(A),bool),hAPP(fun(A,B),fun(B,fun(filter(A),bool)),tendsto(A,B),C),D),hAPP(A,filter(A),at(A),E))) | hBOOL(hAPP(filter(A),bool,hAPP(B,fun(filter(A),bool),hAPP(fun(A,B),fun(B,fun(filter(A),bool)),tendsto(A,B),hAPP(B,fun(A,B),hAPP(fun(A,fun(B,B)),fun(B,fun(A,B)),combc(A,B,B),hAPP(fun(A,B),fun(A,fun(B,B)),hAPP(fun(B,fun(B,B)),fun(fun(A,B),fun(A,fun(B,B))),combb(B,fun(B,B),A),times_times(B)),C)),F)),hAPP(B,B,hAPP(B,fun(B,B),times_times(B),D),F)),hAPP(A,filter(A),at(A),E))) # label(fact_4563_mult__left_OLIM) # label(axiom). [clausify(4490)].
% 108.76/108.67 5873 -topological_space(A) | -real_normed_algebra(B) | -hBOOL(hAPP(filter(A),bool,hAPP(B,fun(filter(A),bool),hAPP(fun(A,B),fun(B,fun(filter(A),bool)),tendsto(A,B),C),D),hAPP(A,filter(A),at(A),E))) | hBOOL(hAPP(filter(A),bool,hAPP(B,fun(filter(A),bool),hAPP(fun(A,B),fun(B,fun(filter(A),bool)),tendsto(A,B),hAPP(fun(A,B),fun(A,B),hAPP(fun(B,B),fun(fun(A,B),fun(A,B)),combb(B,B,A),hAPP(B,fun(B,B),times_times(B),F)),C)),hAPP(B,B,hAPP(B,fun(B,B),times_times(B),F),D)),hAPP(A,filter(A),at(A),E))) # label(fact_4564_mult__right_OLIM) # label(axiom). [clausify(4491)].
% 108.76/108.67 5874 -real_normed_algebra(A) | hBOOL(hAPP(filter(A),bool,hAPP(A,fun(filter(A),bool),hAPP(fun(A,A),fun(A,fun(filter(A),bool)),tendsto(A,A),hAPP(A,fun(A,A),hAPP(fun(A,fun(A,A)),fun(A,fun(A,A)),combc(A,A,A),times_times(A)),B)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),B)),hAPP(A,filter(A),at(A),C))) # label(fact_4565_mult__left_Ocont) # label(axiom). [clausify(4492)].
% 108.76/108.67 5875 -real_normed_algebra(A) | hBOOL(hAPP(filter(A),bool,hAPP(A,fun(filter(A),bool),hAPP(fun(A,A),fun(A,fun(filter(A),bool)),tendsto(A,A),hAPP(A,fun(A,A),times_times(A),B)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),hAPP(A,filter(A),at(A),C))) # label(fact_4566_mult__right_Ocont) # label(axiom). [clausify(4493)].
% 108.76/108.67 5876 -topological_space(A) | -real_normed_algebra(B) | -hBOOL(hAPP(filter(A),bool,hAPP(B,fun(filter(A),bool),hAPP(fun(A,B),fun(B,fun(filter(A),bool)),tendsto(A,B),C),zero_zero(B)),hAPP(A,filter(A),at(A),D))) | hBOOL(hAPP(filter(A),bool,hAPP(B,fun(filter(A),bool),hAPP(fun(A,B),fun(B,fun(filter(A),bool)),tendsto(A,B),hAPP(fun(A,B),fun(A,B),hAPP(fun(B,B),fun(fun(A,B),fun(A,B)),combb(B,B,A),hAPP(B,fun(B,B),times_times(B),E)),C)),zero_zero(B)),hAPP(A,filter(A),at(A),D))) # label(fact_4574_LIM__mult__right__zero) # label(axiom). [clausify(4501)].
% 108.76/108.67 5877 -topological_space(A) | -real_normed_algebra(B) | -hBOOL(hAPP(filter(A),bool,hAPP(B,fun(filter(A),bool),hAPP(fun(A,B),fun(B,fun(filter(A),bool)),tendsto(A,B),C),zero_zero(B)),hAPP(A,filter(A),at(A),D))) | hBOOL(hAPP(filter(A),bool,hAPP(B,fun(filter(A),bool),hAPP(fun(A,B),fun(B,fun(filter(A),bool)),tendsto(A,B),hAPP(fun(A,B),fun(A,B),hAPP(fun(B,B),fun(fun(A,B),fun(A,B)),combb(B,B,A),hAPP(B,fun(B,B),times_times(B),E)),C)),zero_zero(B)),hAPP(A,filter(A),at(A),D))) # label(fact_4575_mult__right_OLIM__zero) # label(axiom). [clausify(4502)].
% 108.76/108.67 5878 -topological_space(A) | -real_normed_algebra(B) | -hBOOL(hAPP(filter(A),bool,hAPP(B,fun(filter(A),bool),hAPP(fun(A,B),fun(B,fun(filter(A),bool)),tendsto(A,B),C),zero_zero(B)),hAPP(A,filter(A),at(A),D))) | hBOOL(hAPP(filter(A),bool,hAPP(B,fun(filter(A),bool),hAPP(fun(A,B),fun(B,fun(filter(A),bool)),tendsto(A,B),hAPP(B,fun(A,B),hAPP(fun(A,fun(B,B)),fun(B,fun(A,B)),combc(A,B,B),hAPP(fun(A,B),fun(A,fun(B,B)),hAPP(fun(B,fun(B,B)),fun(fun(A,B),fun(A,fun(B,B))),combb(B,fun(B,B),A),times_times(B)),C)),E)),zero_zero(B)),hAPP(A,filter(A),at(A),D))) # label(fact_4576_LIM__mult__left__zero) # label(axiom). [clausify(4503)].
% 108.76/108.67 5879 -topological_space(A) | -real_normed_algebra(B) | -hBOOL(hAPP(filter(A),bool,hAPP(B,fun(filter(A),bool),hAPP(fun(A,B),fun(B,fun(filter(A),bool)),tendsto(A,B),C),zero_zero(B)),hAPP(A,filter(A),at(A),D))) | hBOOL(hAPP(filter(A),bool,hAPP(B,fun(filter(A),bool),hAPP(fun(A,B),fun(B,fun(filter(A),bool)),tendsto(A,B),hAPP(B,fun(A,B),hAPP(fun(A,fun(B,B)),fun(B,fun(A,B)),combc(A,B,B),hAPP(fun(A,B),fun(A,fun(B,B)),hAPP(fun(B,fun(B,B)),fun(fun(A,B),fun(A,fun(B,B))),combb(B,fun(B,B),A),times_times(B)),C)),E)),zero_zero(B)),hAPP(A,filter(A),at(A),D))) # label(fact_4577_mult__left_OLIM__zero) # label(axiom). [clausify(4504)].
% 108.76/108.67 5880 -metric_space(A) | -real_normed_algebra(B) | -hBOOL(hAPP(filter(A),bool,hAPP(B,fun(filter(A),bool),hAPP(fun(A,B),fun(B,fun(filter(A),bool)),tendsto(A,B),C),zero_zero(B)),hAPP(A,filter(A),at(A),D))) | -hBOOL(hAPP(filter(A),bool,hAPP(B,fun(filter(A),bool),hAPP(fun(A,B),fun(B,fun(filter(A),bool)),tendsto(A,B),E),zero_zero(B)),hAPP(A,filter(A),at(A),D))) | hBOOL(hAPP(filter(A),bool,hAPP(B,fun(filter(A),bool),hAPP(fun(A,B),fun(B,fun(filter(A),bool)),tendsto(A,B),hAPP(fun(A,B),fun(A,B),hAPP(fun(A,fun(B,B)),fun(fun(A,B),fun(A,B)),combs(A,B,B),hAPP(fun(A,B),fun(A,fun(B,B)),hAPP(fun(B,fun(B,B)),fun(fun(A,B),fun(A,fun(B,B))),combb(B,fun(B,B),A),times_times(B)),C)),E)),zero_zero(B)),hAPP(A,filter(A),at(A),D))) # label(fact_4578_LIM__mult__zero) # label(axiom). [clausify(4505)].
% 108.76/108.67 5881 -real_normed_algebra(A) | -banach(A) | -hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,A),fun(nat,real),hAPP(fun(A,real),fun(fun(nat,A),fun(nat,real)),combb(A,real,nat),norm_norm(A)),B))) | -hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,A),fun(nat,real),hAPP(fun(A,real),fun(fun(nat,A),fun(nat,real)),combb(A,real,nat),norm_norm(A)),C))) | hAPP(fun(nat,A),A,suminf(A),hAPP(fun(nat,fun(nat,bool)),fun(nat,A),hAPP(fun(nat,fun(fun(nat,bool),A)),fun(fun(nat,fun(nat,bool)),fun(nat,A)),combs(nat,fun(nat,bool),A),hAPP(fun(nat,fun(nat,A)),fun(nat,fun(fun(nat,bool),A)),hAPP(fun(fun(nat,A),fun(fun(nat,bool),A)),fun(fun(nat,fun(nat,A)),fun(nat,fun(fun(nat,bool),A))),combb(fun(nat,A),fun(fun(nat,bool),A),nat),big_co1399186613setsum(nat,A)),hAPP(fun(nat,fun(nat,A)),fun(nat,fun(nat,A)),hAPP(fun(fun(nat,A),fun(nat,A)),fun(fun(nat,fun(nat,A)),fun(nat,fun(nat,A))),combb(fun(nat,A),fun(nat,A),nat),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),times_times(A)),B))),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,A)),hAPP(fun(fun(nat,nat),fun(nat,A)),fun(fun(nat,fun(nat,nat)),fun(nat,fun(nat,A))),combb(fun(nat,nat),fun(nat,A),nat),hAPP(fun(nat,A),fun(fun(nat,nat),fun(nat,A)),combb(nat,A,nat),C)),minus_minus(nat))))),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),zero_zero(nat)))) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(fun(nat,A),A,suminf(A),B)),hAPP(fun(nat,A),A,suminf(A),C)) # label(fact_4625_Cauchy__product) # label(axiom). [clausify(4552)].
% 108.76/108.67 5882 -real_normed_algebra(A) | -banach(A) | -hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,A),fun(nat,real),hAPP(fun(A,real),fun(fun(nat,A),fun(nat,real)),combb(A,real,nat),norm_norm(A)),B))) | -hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,A),fun(nat,real),hAPP(fun(A,real),fun(fun(nat,A),fun(nat,real)),combb(A,real,nat),norm_norm(A)),C))) | hBOOL(hAPP(A,bool,hAPP(fun(nat,A),fun(A,bool),sums(A),hAPP(fun(nat,fun(nat,bool)),fun(nat,A),hAPP(fun(nat,fun(fun(nat,bool),A)),fun(fun(nat,fun(nat,bool)),fun(nat,A)),combs(nat,fun(nat,bool),A),hAPP(fun(nat,fun(nat,A)),fun(nat,fun(fun(nat,bool),A)),hAPP(fun(fun(nat,A),fun(fun(nat,bool),A)),fun(fun(nat,fun(nat,A)),fun(nat,fun(fun(nat,bool),A))),combb(fun(nat,A),fun(fun(nat,bool),A),nat),big_co1399186613setsum(nat,A)),hAPP(fun(nat,fun(nat,A)),fun(nat,fun(nat,A)),hAPP(fun(fun(nat,A),fun(nat,A)),fun(fun(nat,fun(nat,A)),fun(nat,fun(nat,A))),combb(fun(nat,A),fun(nat,A),nat),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),times_times(A)),B))),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,A)),hAPP(fun(fun(nat,nat),fun(nat,A)),fun(fun(nat,fun(nat,nat)),fun(nat,fun(nat,A))),combb(fun(nat,nat),fun(nat,A),nat),hAPP(fun(nat,A),fun(fun(nat,nat),fun(nat,A)),combb(nat,A,nat),C)),minus_minus(nat))))),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),zero_zero(nat)))),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(fun(nat,A),A,suminf(A),B)),hAPP(fun(nat,A),A,suminf(A),C)))) # label(fact_4627_Cauchy__product__sums) # label(axiom). [clausify(4554)].
% 108.76/108.67 5883 -real_normed_algebra(A) | -comm_ring_1(A) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f739(B,A,C,D,E)),E)) | hBOOL(hAPP(filter(nat),bool,hAPP(A,fun(filter(nat),bool),hAPP(fun(nat,A),fun(A,fun(filter(nat),bool)),tendsto(nat,A),hAPP(fun(B,bool),fun(nat,A),hAPP(fun(nat,fun(fun(B,bool),A)),fun(fun(B,bool),fun(nat,A)),combc(nat,fun(B,bool),A),hAPP(fun(nat,fun(B,A)),fun(nat,fun(fun(B,bool),A)),hAPP(fun(fun(B,A),fun(fun(B,bool),A)),fun(fun(nat,fun(B,A)),fun(nat,fun(fun(B,bool),A))),combb(fun(B,A),fun(fun(B,bool),A),nat),big_co302546470etprod(B,A)),hAPP(fun(B,fun(nat,A)),fun(nat,fun(B,A)),combc(B,nat,A),C))),E)),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),D),E)),sequentially)) # label(fact_4661_LIMSEQ__setprod) # label(axiom). [clausify(4587)].
% 108.76/108.67 5884 -real_normed_algebra(A) | -comm_ring_1(A) | -hBOOL(hAPP(filter(nat),bool,hAPP(A,fun(filter(nat),bool),hAPP(fun(nat,A),fun(A,fun(filter(nat),bool)),tendsto(nat,A),hAPP(B,fun(nat,A),C,f739(B,A,C,D,E))),hAPP(B,A,D,f739(B,A,C,D,E))),sequentially)) | hBOOL(hAPP(filter(nat),bool,hAPP(A,fun(filter(nat),bool),hAPP(fun(nat,A),fun(A,fun(filter(nat),bool)),tendsto(nat,A),hAPP(fun(B,bool),fun(nat,A),hAPP(fun(nat,fun(fun(B,bool),A)),fun(fun(B,bool),fun(nat,A)),combc(nat,fun(B,bool),A),hAPP(fun(nat,fun(B,A)),fun(nat,fun(fun(B,bool),A)),hAPP(fun(fun(B,A),fun(fun(B,bool),A)),fun(fun(nat,fun(B,A)),fun(nat,fun(fun(B,bool),A))),combb(fun(B,A),fun(fun(B,bool),A),nat),big_co302546470etprod(B,A)),hAPP(fun(B,fun(nat,A)),fun(nat,fun(B,A)),combc(B,nat,A),C))),E)),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),D),E)),sequentially)) # label(fact_4661_LIMSEQ__setprod) # label(axiom). [clausify(4587)].
% 108.76/108.67 5885 -real_normed_algebra(A) | hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(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(real,fun(A,A),scaleR_scaleR(A),B),D)) # label(fact_4707_mult_OscaleR__right) # label(axiom). [clausify(4633)].
% 108.76/108.67 5886 -real_normed_algebra(A) | hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(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(real,fun(A,A),scaleR_scaleR(A),B),D)) # label(fact_4709_mult__right_OscaleR) # label(axiom). [clausify(4635)].
% 108.76/108.67 5887 -real_normed_algebra(A) | hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(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),hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),B),C)),D) # label(fact_4711_mult_OscaleR__left) # label(axiom). [clausify(4637)].
% 108.76/108.67 5888 -real_normed_algebra(A) | hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(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),hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),B),C)),D) # label(fact_4712_mult__left_OscaleR) # label(axiom). [clausify(4638)].
% 108.76/108.67 5889 -real_normed_algebra(A) | hBOOL(hAPP(A,bool,hAPP(fun(A,A),fun(A,bool),isCont(A,A),hAPP(A,fun(A,A),times_times(A),B)),C)) # label(fact_4897_mult__right_OisCont) # label(axiom). [clausify(4817)].
% 108.76/108.67 5890 -real_normed_algebra(A) | hBOOL(hAPP(A,bool,hAPP(fun(A,A),fun(A,bool),isCont(A,A),hAPP(A,fun(A,A),hAPP(fun(A,fun(A,A)),fun(A,fun(A,A)),combc(A,A,A),times_times(A)),B)),C)) # label(fact_4898_mult__left_OisCont) # label(axiom). [clausify(4818)].
% 108.76/108.67 5891 -topological_space(A) | -real_normed_algebra(B) | -hBOOL(hAPP(A,bool,hAPP(fun(A,B),fun(A,bool),isCont(A,B),C),D)) | -hBOOL(hAPP(A,bool,hAPP(fun(A,B),fun(A,bool),isCont(A,B),E),D)) | hBOOL(hAPP(A,bool,hAPP(fun(A,B),fun(A,bool),isCont(A,B),hAPP(fun(A,B),fun(A,B),hAPP(fun(A,fun(B,B)),fun(fun(A,B),fun(A,B)),combs(A,B,B),hAPP(fun(A,B),fun(A,fun(B,B)),hAPP(fun(B,fun(B,B)),fun(fun(A,B),fun(A,fun(B,B))),combb(B,fun(B,B),A),times_times(B)),C)),E)),D)) # label(fact_4899_isCont__mult) # label(axiom). [clausify(4819)].
% 108.76/108.67 5892 -topological_space(A) | -real_normed_algebra(B) | -hBOOL(hAPP(A,bool,hAPP(fun(A,B),fun(A,bool),isCont(A,B),C),D)) | -hBOOL(hAPP(A,bool,hAPP(fun(A,B),fun(A,bool),isCont(A,B),E),D)) | hBOOL(hAPP(A,bool,hAPP(fun(A,B),fun(A,bool),isCont(A,B),hAPP(fun(A,B),fun(A,B),hAPP(fun(A,fun(B,B)),fun(fun(A,B),fun(A,B)),combs(A,B,B),hAPP(fun(A,B),fun(A,fun(B,B)),hAPP(fun(B,fun(B,B)),fun(fun(A,B),fun(A,fun(B,B))),combb(B,fun(B,B),A),times_times(B)),C)),E)),D)) # label(fact_4900_mult_OisCont) # label(axiom). [clausify(4820)].
% 108.76/108.67 5893 -topological_space(A) | -power(B) | -real_normed_algebra(B) | -hBOOL(hAPP(A,bool,hAPP(fun(A,B),fun(A,bool),isCont(A,B),C),D)) | hBOOL(hAPP(A,bool,hAPP(fun(A,B),fun(A,bool),isCont(A,B),hAPP(nat,fun(A,B),hAPP(fun(A,fun(nat,B)),fun(nat,fun(A,B)),combc(A,nat,B),hAPP(fun(A,B),fun(A,fun(nat,B)),hAPP(fun(B,fun(nat,B)),fun(fun(A,B),fun(A,fun(nat,B))),combb(B,fun(nat,B),A),power_power(B)),C)),E)),D)) # label(fact_4905_isCont__power) # label(axiom). [clausify(4825)].
% 108.76/108.67 Derived: hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),C),D))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),B)),D))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),C),D))) = hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),C)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),D)). [resolve(5811,a,5812,a)].
% 108.76/108.67 Derived: hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),B)),C) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),C)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),C)). [resolve(5811,a,5813,a)].
% 108.76/108.67 Derived: hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),B),C)) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),C)). [resolve(5811,a,5815,a)].
% 108.76/108.67 Derived: hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),B)),C) = hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),C)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),C)). [resolve(5811,a,5817,a)].
% 108.76/108.67 Derived: hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),B),C)) = hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),C)). [resolve(5811,a,5819,a)].
% 108.76/108.68 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,norm_norm(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,norm_norm(real),A)),hAPP(real,real,norm_norm(real),B)))). [resolve(5811,a,5829,a)].
% 108.76/108.68 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,norm_norm(real),A)),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,norm_norm(real),C)),D)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,norm_norm(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),C))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),D))). [resolve(5811,a,5830,a)].
% 108.76/108.68 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),f259(real))). [resolve(5811,a,5831,a)].
% 108.76/108.68 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,norm_norm(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,norm_norm(real),A)),hAPP(real,real,norm_norm(real),B))),f259(real)))). [resolve(5811,a,5832,a)].
% 108.76/108.68 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),f260(real,A))). [resolve(5811,a,5833,a)].
% 108.76/108.68 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,norm_norm(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,norm_norm(real),A)),f260(real,B)))). [resolve(5811,a,5834,a)].
% 108.76/108.68 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),f261(real,A))). [resolve(5811,a,5835,a)].
% 108.76/108.68 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,norm_norm(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,norm_norm(real),B)),f261(real,A)))). [resolve(5811,a,5836,a)].
% 108.76/108.68 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),f266(real))). [resolve(5811,a,5837,a)].
% 108.76/108.68 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,norm_norm(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,norm_norm(real),A)),hAPP(real,real,norm_norm(real),B))),f266(real)))). [resolve(5811,a,5838,a)].
% 108.76/108.68 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),f267(real,A))). [resolve(5811,a,5839,a)].
% 108.76/108.68 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,norm_norm(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,norm_norm(real),B)),f267(real,A)))). [resolve(5811,a,5840,a)].
% 108.76/108.68 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),f268(real,A))). [resolve(5811,a,5841,a)].
% 108.76/108.68 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,norm_norm(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,norm_norm(real),A)),f268(real,B)))). [resolve(5811,a,5842,a)].
% 108.76/108.68 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,norm_norm(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,norm_norm(real),A)),f271(real,B)))). [resolve(5811,a,5843,a)].
% 108.76/108.69 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,norm_norm(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,norm_norm(real),B)),f272(real,A)))). [resolve(5811,a,5844,a)].
% 108.76/108.69 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,norm_norm(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,norm_norm(real),A)),hAPP(real,real,norm_norm(real),B))),f273(real)))). [resolve(5811,a,5845,a)].
% 108.76/108.69 Derived: hBOOL(hAPP(fun(real,fun(real,real)),bool,bounded_bilinear(real,real,real),hAPP(fun(real,fun(real,real)),fun(real,fun(real,real)),combc(real,real,real),times_times(real)))). [resolve(5811,a,5846,a)].
% 108.76/108.69 Derived: -hBOOL(hAPP(fun(nat,real),bool,summable(real),A)) | hAPP(fun(nat,real),real,suminf(real),hAPP(real,fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(real,fun(nat,real)),combc(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),A)),B)) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(fun(nat,real),real,suminf(real),A)),B). [resolve(5811,a,5847,a)].
% 108.76/108.69 Derived: -hBOOL(hAPP(fun(nat,real),bool,summable(real),A)) | hAPP(fun(nat,real),real,suminf(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),hAPP(real,fun(real,real),times_times(real),B)),A)) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),hAPP(fun(nat,real),real,suminf(real),A)). [resolve(5811,a,5848,a)].
% 108.76/108.69 Derived: -hBOOL(hAPP(fun(nat,real),bool,summable(real),A)) | hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),hAPP(real,fun(real,real),times_times(real),B)),A))). [resolve(5811,a,5851,a)].
% 108.76/108.69 Derived: -hBOOL(hAPP(fun(nat,real),bool,summable(real),A)) | hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(real,fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(real,fun(nat,real)),combc(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),A)),B))). [resolve(5811,a,5852,a)].
% 108.76/108.69 Derived: -hBOOL(hAPP(real,bool,hAPP(fun(nat,real),fun(real,bool),sums(real),A),B)) | hBOOL(hAPP(real,bool,hAPP(fun(nat,real),fun(real,bool),sums(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),hAPP(real,fun(real,real),times_times(real),C)),A)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),B))). [resolve(5811,a,5855,a)].
% 108.76/108.69 Derived: -hBOOL(hAPP(real,bool,hAPP(fun(nat,real),fun(real,bool),sums(real),A),B)) | hBOOL(hAPP(real,bool,hAPP(fun(nat,real),fun(real,bool),sums(real),hAPP(real,fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(real,fun(nat,real)),combc(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),A)),C)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),C))). [resolve(5811,a,5856,a)].
% 108.76/108.69 Derived: -hBOOL(hAPP(fun(nat,real),bool,cauchy(real),A)) | hBOOL(hAPP(fun(nat,real),bool,cauchy(real),hAPP(real,fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(real,fun(nat,real)),combc(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),A)),B))). [resolve(5811,a,5859,a)].
% 108.76/108.69 Derived: -hBOOL(hAPP(fun(nat,real),bool,cauchy(real),A)) | hBOOL(hAPP(fun(nat,real),bool,cauchy(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),hAPP(real,fun(real,real),times_times(real),B)),A))). [resolve(5811,a,5860,a)].
% 108.76/108.69 Derived: hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),hAPP(real,fun(A,real),hAPP(fun(A,fun(real,real)),fun(real,fun(A,real)),combc(A,real,real),hAPP(fun(A,real),fun(A,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(A,real),fun(A,fun(real,real))),combb(real,fun(real,real),A),times_times(real)),B)),C)),D) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),B),D)),C). [resolve(5811,a,5861,a)].
% 108.76/108.69 Derived: hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),hAPP(fun(A,real),fun(A,real),hAPP(fun(real,real),fun(fun(A,real),fun(A,real)),combb(real,real,A),hAPP(real,fun(real,real),times_times(real),B)),C)),D) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),C),D)). [resolve(5811,a,5862,a)].
% 108.76/108.69 Derived: -hBOOL(hAPP(filter(A),bool,hAPP(real,fun(filter(A),bool),hAPP(fun(A,real),fun(real,fun(filter(A),bool)),tendsto(A,real),B),C),D)) | -hBOOL(hAPP(filter(A),bool,hAPP(real,fun(filter(A),bool),hAPP(fun(A,real),fun(real,fun(filter(A),bool)),tendsto(A,real),E),F),D)) | hBOOL(hAPP(filter(A),bool,hAPP(real,fun(filter(A),bool),hAPP(fun(A,real),fun(real,fun(filter(A),bool)),tendsto(A,real),hAPP(fun(A,real),fun(A,real),hAPP(fun(A,fun(real,real)),fun(fun(A,real),fun(A,real)),combs(A,real,real),hAPP(fun(A,real),fun(A,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(A,real),fun(A,fun(real,real))),combb(real,fun(real,real),A),times_times(real)),B)),E)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),F)),D)). [resolve(5811,a,5863,a)].
% 108.76/108.69 Derived: -hBOOL(hAPP(filter(A),bool,hAPP(real,fun(filter(A),bool),hAPP(fun(A,real),fun(real,fun(filter(A),bool)),tendsto(A,real),B),C),D)) | hBOOL(hAPP(filter(A),bool,hAPP(real,fun(filter(A),bool),hAPP(fun(A,real),fun(real,fun(filter(A),bool)),tendsto(A,real),hAPP(real,fun(A,real),hAPP(fun(A,fun(real,real)),fun(real,fun(A,real)),combc(A,real,real),hAPP(fun(A,real),fun(A,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(A,real),fun(A,fun(real,real))),combb(real,fun(real,real),A),times_times(real)),B)),E)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),E)),D)). [resolve(5811,a,5864,a)].
% 108.76/108.69 Derived: -hBOOL(hAPP(filter(A),bool,hAPP(real,fun(filter(A),bool),hAPP(fun(A,real),fun(real,fun(filter(A),bool)),tendsto(A,real),B),C),D)) | hBOOL(hAPP(filter(A),bool,hAPP(real,fun(filter(A),bool),hAPP(fun(A,real),fun(real,fun(filter(A),bool)),tendsto(A,real),hAPP(fun(A,real),fun(A,real),hAPP(fun(real,real),fun(fun(A,real),fun(A,real)),combb(real,real,A),hAPP(real,fun(real,real),times_times(real),E)),B)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),E),C)),D)). [resolve(5811,a,5865,a)].
% 108.76/108.69 Derived: -power(real) | -hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),A),B),sequentially)) | hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),hAPP(nat,fun(nat,real),hAPP(fun(nat,fun(nat,real)),fun(nat,fun(nat,real)),combc(nat,nat,real),hAPP(fun(nat,real),fun(nat,fun(nat,real)),hAPP(fun(real,fun(nat,real)),fun(fun(nat,real),fun(nat,fun(nat,real))),combb(real,fun(nat,real),nat),power_power(real)),A)),C)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),B),C)),sequentially)). [resolve(5811,a,5869,b)].
% 108.76/108.69 Derived: -topological_space(A) | -power(real) | -hBOOL(hAPP(filter(A),bool,hAPP(real,fun(filter(A),bool),hAPP(fun(A,real),fun(real,fun(filter(A),bool)),tendsto(A,real),B),C),hAPP(A,filter(A),at(A),D))) | hBOOL(hAPP(filter(A),bool,hAPP(real,fun(filter(A),bool),hAPP(fun(A,real),fun(real,fun(filter(A),bool)),tendsto(A,real),hAPP(nat,fun(A,real),hAPP(fun(A,fun(nat,real)),fun(nat,fun(A,real)),combc(A,nat,real),hAPP(fun(A,real),fun(A,fun(nat,real)),hAPP(fun(real,fun(nat,real)),fun(fun(A,real),fun(A,fun(nat,real))),combb(real,fun(nat,real),A),power_power(real)),B)),E)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),C),E)),hAPP(A,filter(A),at(A),D))). [resolve(5811,a,5870,c)].
% 108.84/108.70 Derived: hBOOL(hAPP(filter(real),bool,hAPP(real,fun(filter(real),bool),hAPP(fun(real,real),fun(real,fun(filter(real),bool)),tendsto(real,real),hAPP(real,fun(real,real),hAPP(fun(real,fun(real,real)),fun(real,fun(real,real)),combc(real,real,real),times_times(real)),A)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),A)),hAPP(real,filter(real),at(real),B))). [resolve(5811,a,5874,a)].
% 108.84/108.70 Derived: hBOOL(hAPP(filter(real),bool,hAPP(real,fun(filter(real),bool),hAPP(fun(real,real),fun(real,fun(filter(real),bool)),tendsto(real,real),hAPP(real,fun(real,real),times_times(real),A)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),hAPP(real,filter(real),at(real),B))). [resolve(5811,a,5875,a)].
% 108.84/108.70 Derived: -topological_space(A) | -hBOOL(hAPP(filter(A),bool,hAPP(real,fun(filter(A),bool),hAPP(fun(A,real),fun(real,fun(filter(A),bool)),tendsto(A,real),B),zero_zero(real)),hAPP(A,filter(A),at(A),C))) | hBOOL(hAPP(filter(A),bool,hAPP(real,fun(filter(A),bool),hAPP(fun(A,real),fun(real,fun(filter(A),bool)),tendsto(A,real),hAPP(fun(A,real),fun(A,real),hAPP(fun(real,real),fun(fun(A,real),fun(A,real)),combb(real,real,A),hAPP(real,fun(real,real),times_times(real),D)),B)),zero_zero(real)),hAPP(A,filter(A),at(A),C))). [resolve(5811,a,5876,b)].
% 108.84/108.70 Derived: -topological_space(A) | -hBOOL(hAPP(filter(A),bool,hAPP(real,fun(filter(A),bool),hAPP(fun(A,real),fun(real,fun(filter(A),bool)),tendsto(A,real),B),zero_zero(real)),hAPP(A,filter(A),at(A),C))) | hBOOL(hAPP(filter(A),bool,hAPP(real,fun(filter(A),bool),hAPP(fun(A,real),fun(real,fun(filter(A),bool)),tendsto(A,real),hAPP(real,fun(A,real),hAPP(fun(A,fun(real,real)),fun(real,fun(A,real)),combc(A,real,real),hAPP(fun(A,real),fun(A,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(A,real),fun(A,fun(real,real))),combb(real,fun(real,real),A),times_times(real)),B)),D)),zero_zero(real)),hAPP(A,filter(A),at(A),C))). [resolve(5811,a,5878,b)].
% 108.84/108.70 Derived: -metric_space(A) | -hBOOL(hAPP(filter(A),bool,hAPP(real,fun(filter(A),bool),hAPP(fun(A,real),fun(real,fun(filter(A),bool)),tendsto(A,real),B),zero_zero(real)),hAPP(A,filter(A),at(A),C))) | -hBOOL(hAPP(filter(A),bool,hAPP(real,fun(filter(A),bool),hAPP(fun(A,real),fun(real,fun(filter(A),bool)),tendsto(A,real),D),zero_zero(real)),hAPP(A,filter(A),at(A),C))) | hBOOL(hAPP(filter(A),bool,hAPP(real,fun(filter(A),bool),hAPP(fun(A,real),fun(real,fun(filter(A),bool)),tendsto(A,real),hAPP(fun(A,real),fun(A,real),hAPP(fun(A,fun(real,real)),fun(fun(A,real),fun(A,real)),combs(A,real,real),hAPP(fun(A,real),fun(A,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(A,real),fun(A,fun(real,real))),combb(real,fun(real,real),A),times_times(real)),B)),D)),zero_zero(real)),hAPP(A,filter(A),at(A),C))). [resolve(5811,a,5880,b)].
% 108.84/108.70 Derived: -banach(real) | -hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),norm_norm(real)),A))) | -hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),norm_norm(real)),B))) | hAPP(fun(nat,real),real,suminf(real),hAPP(fun(nat,fun(nat,bool)),fun(nat,real),hAPP(fun(nat,fun(fun(nat,bool),real)),fun(fun(nat,fun(nat,bool)),fun(nat,real)),combs(nat,fun(nat,bool),real),hAPP(fun(nat,fun(nat,real)),fun(nat,fun(fun(nat,bool),real)),hAPP(fun(fun(nat,real),fun(fun(nat,bool),real)),fun(fun(nat,fun(nat,real)),fun(nat,fun(fun(nat,bool),real))),combb(fun(nat,real),fun(fun(nat,bool),real),nat),big_co1399186613setsum(nat,real)),hAPP(fun(nat,fun(nat,real)),fun(nat,fun(nat,real)),hAPP(fun(fun(nat,real),fun(nat,real)),fun(fun(nat,fun(nat,real)),fun(nat,fun(nat,real))),combb(fun(nat,real),fun(nat,real),nat),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),A))),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,real)),hAPP(fun(fun(nat,nat),fun(nat,real)),fun(fun(nat,fun(nat,nat)),fun(nat,fun(nat,real))),combb(fun(nat,nat),fun(nat,real),nat),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),B)),minus_minus(nat))))),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),zero_zero(nat)))) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(fun(nat,real),real,suminf(real),A)),hAPP(fun(nat,real),real,suminf(real),B)). [resolve(5811,a,5881,a)].
% 108.84/108.70 Derived: -banach(real) | -hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),norm_norm(real)),A))) | -hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),norm_norm(real)),B))) | hBOOL(hAPP(real,bool,hAPP(fun(nat,real),fun(real,bool),sums(real),hAPP(fun(nat,fun(nat,bool)),fun(nat,real),hAPP(fun(nat,fun(fun(nat,bool),real)),fun(fun(nat,fun(nat,bool)),fun(nat,real)),combs(nat,fun(nat,bool),real),hAPP(fun(nat,fun(nat,real)),fun(nat,fun(fun(nat,bool),real)),hAPP(fun(fun(nat,real),fun(fun(nat,bool),real)),fun(fun(nat,fun(nat,real)),fun(nat,fun(fun(nat,bool),real))),combb(fun(nat,real),fun(fun(nat,bool),real),nat),big_co1399186613setsum(nat,real)),hAPP(fun(nat,fun(nat,real)),fun(nat,fun(nat,real)),hAPP(fun(fun(nat,real),fun(nat,real)),fun(fun(nat,fun(nat,real)),fun(nat,fun(nat,real))),combb(fun(nat,real),fun(nat,real),nat),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),A))),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,real)),hAPP(fun(fun(nat,nat),fun(nat,real)),fun(fun(nat,fun(nat,nat)),fun(nat,fun(nat,real))),combb(fun(nat,nat),fun(nat,real),nat),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),B)),minus_minus(nat))))),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),zero_zero(nat)))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(fun(nat,real),real,suminf(real),A)),hAPP(fun(nat,real),real,suminf(real),B)))). [resolve(5811,a,5882,a)].
% 108.84/108.70 Derived: -comm_ring_1(real) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f739(A,real,B,C,D)),D)) | hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),hAPP(fun(A,bool),fun(nat,real),hAPP(fun(nat,fun(fun(A,bool),real)),fun(fun(A,bool),fun(nat,real)),combc(nat,fun(A,bool),real),hAPP(fun(nat,fun(A,real)),fun(nat,fun(fun(A,bool),real)),hAPP(fun(fun(A,real),fun(fun(A,bool),real)),fun(fun(nat,fun(A,real)),fun(nat,fun(fun(A,bool),real))),combb(fun(A,real),fun(fun(A,bool),real),nat),big_co302546470etprod(A,real)),hAPP(fun(A,fun(nat,real)),fun(nat,fun(A,real)),combc(A,nat,real),B))),D)),hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co302546470etprod(A,real),C),D)),sequentially)). [resolve(5811,a,5883,a)].
% 108.84/108.70 Derived: -comm_ring_1(real) | -hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),hAPP(A,fun(nat,real),B,f739(A,real,B,C,D))),hAPP(A,real,C,f739(A,real,B,C,D))),sequentially)) | hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),hAPP(fun(A,bool),fun(nat,real),hAPP(fun(nat,fun(fun(A,bool),real)),fun(fun(A,bool),fun(nat,real)),combc(nat,fun(A,bool),real),hAPP(fun(nat,fun(A,real)),fun(nat,fun(fun(A,bool),real)),hAPP(fun(fun(A,real),fun(fun(A,bool),real)),fun(fun(nat,fun(A,real)),fun(nat,fun(fun(A,bool),real))),combb(fun(A,real),fun(fun(A,bool),real),nat),big_co302546470etprod(A,real)),hAPP(fun(A,fun(nat,real)),fun(nat,fun(A,real)),combc(A,nat,real),B))),D)),hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co302546470etprod(A,real),C),D)),sequentially)). [resolve(5811,a,5884,a)].
% 108.84/108.73 Derived: hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),A),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),C)) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),A),C)). [resolve(5811,a,5885,a)].
% 108.84/108.73 Derived: hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),A),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),C)) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),A),B)),C). [resolve(5811,a,5887,a)].
% 108.84/108.73 Derived: hBOOL(hAPP(real,bool,hAPP(fun(real,real),fun(real,bool),isCont(real,real),hAPP(real,fun(real,real),times_times(real),A)),B)). [resolve(5811,a,5889,a)].
% 108.84/108.73 Derived: hBOOL(hAPP(real,bool,hAPP(fun(real,real),fun(real,bool),isCont(real,real),hAPP(real,fun(real,real),hAPP(fun(real,fun(real,real)),fun(real,fun(real,real)),combc(real,real,real),times_times(real)),A)),B)). [resolve(5811,a,5890,a)].
% 108.84/108.73 Derived: -topological_space(A) | -hBOOL(hAPP(A,bool,hAPP(fun(A,real),fun(A,bool),isCont(A,real),B),C)) | -hBOOL(hAPP(A,bool,hAPP(fun(A,real),fun(A,bool),isCont(A,real),D),C)) | hBOOL(hAPP(A,bool,hAPP(fun(A,real),fun(A,bool),isCont(A,real),hAPP(fun(A,real),fun(A,real),hAPP(fun(A,fun(real,real)),fun(fun(A,real),fun(A,real)),combs(A,real,real),hAPP(fun(A,real),fun(A,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(A,real),fun(A,fun(real,real))),combb(real,fun(real,real),A),times_times(real)),B)),D)),C)). [resolve(5811,a,5891,b)].
% 108.84/108.73 Derived: -topological_space(A) | -power(real) | -hBOOL(hAPP(A,bool,hAPP(fun(A,real),fun(A,bool),isCont(A,real),B),C)) | hBOOL(hAPP(A,bool,hAPP(fun(A,real),fun(A,bool),isCont(A,real),hAPP(nat,fun(A,real),hAPP(fun(A,fun(nat,real)),fun(nat,fun(A,real)),combc(A,nat,real),hAPP(fun(A,real),fun(A,fun(nat,real)),hAPP(fun(real,fun(nat,real)),fun(fun(A,real),fun(A,fun(nat,real))),combb(real,fun(nat,real),A),power_power(real)),B)),D)),C)). [resolve(5811,a,5893,c)].
% 108.84/108.73 5894 real_normed_algebra(complex) # label(arity_Complex_Ocomplex___RealVector_Oreal__normed__algebra) # label(axiom). [assumption].
% 108.84/108.73 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),A),B)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),C),D))),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),A),B)),D))),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),B),hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),C),D))) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),C)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),B),D)). [resolve(5894,a,5812,a)].
% 108.84/108.73 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),A),B)),C) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),C)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),B),C)). [resolve(5894,a,5813,a)].
% 108.84/108.73 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),B),C)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),B)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),C)). [resolve(5894,a,5815,a)].
% 108.84/108.74 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),A),B)),C) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),C)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),B),C)). [resolve(5894,a,5817,a)].
% 108.84/108.74 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),B),C)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),B)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),C)). [resolve(5894,a,5819,a)].
% 108.84/108.74 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),B))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(complex,real,norm_norm(complex),A)),hAPP(complex,real,norm_norm(complex),B)))). [resolve(5894,a,5829,a)].
% 108.84/108.74 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(complex,real,norm_norm(complex),A)),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(complex,real,norm_norm(complex),C)),D)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),C))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),D))). [resolve(5894,a,5830,a)].
% 108.84/108.74 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),f259(complex))). [resolve(5894,a,5831,a)].
% 108.84/108.74 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),B))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(complex,real,norm_norm(complex),A)),hAPP(complex,real,norm_norm(complex),B))),f259(complex)))). [resolve(5894,a,5832,a)].
% 108.84/108.74 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),f260(complex,A))). [resolve(5894,a,5833,a)].
% 108.84/108.74 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),B))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(complex,real,norm_norm(complex),A)),f260(complex,B)))). [resolve(5894,a,5834,a)].
% 108.84/108.74 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),f261(complex,A))). [resolve(5894,a,5835,a)].
% 108.84/108.74 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),B))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(complex,real,norm_norm(complex),B)),f261(complex,A)))). [resolve(5894,a,5836,a)].
% 108.84/108.74 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),f266(complex))). [resolve(5894,a,5837,a)].
% 108.84/108.74 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),B))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(complex,real,norm_norm(complex),A)),hAPP(complex,real,norm_norm(complex),B))),f266(complex)))). [resolve(5894,a,5838,a)].
% 108.84/108.74 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),f267(complex,A))). [resolve(5894,a,5839,a)].
% 108.84/108.74 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),B))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(complex,real,norm_norm(complex),B)),f267(complex,A)))). [resolve(5894,a,5840,a)].
% 108.84/108.75 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),f268(complex,A))). [resolve(5894,a,5841,a)].
% 108.84/108.75 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),B))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(complex,real,norm_norm(complex),A)),f268(complex,B)))). [resolve(5894,a,5842,a)].
% 108.84/108.75 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),B))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(complex,real,norm_norm(complex),A)),f271(complex,B)))). [resolve(5894,a,5843,a)].
% 108.84/108.75 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),B))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(complex,real,norm_norm(complex),B)),f272(complex,A)))). [resolve(5894,a,5844,a)].
% 108.84/108.75 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),B))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(complex,real,norm_norm(complex),A)),hAPP(complex,real,norm_norm(complex),B))),f273(complex)))). [resolve(5894,a,5845,a)].
% 108.84/108.75 Derived: hBOOL(hAPP(fun(complex,fun(complex,complex)),bool,bounded_bilinear(complex,complex,complex),hAPP(fun(complex,fun(complex,complex)),fun(complex,fun(complex,complex)),combc(complex,complex,complex),times_times(complex)))). [resolve(5894,a,5846,a)].
% 108.84/108.75 Derived: -hBOOL(hAPP(fun(nat,complex),bool,summable(complex),A)) | hAPP(fun(nat,complex),complex,suminf(complex),hAPP(complex,fun(nat,complex),hAPP(fun(nat,fun(complex,complex)),fun(complex,fun(nat,complex)),combc(nat,complex,complex),hAPP(fun(nat,complex),fun(nat,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(nat,complex),fun(nat,fun(complex,complex))),combb(complex,fun(complex,complex),nat),times_times(complex)),A)),B)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(fun(nat,complex),complex,suminf(complex),A)),B). [resolve(5894,a,5847,a)].
% 108.84/108.75 Derived: -hBOOL(hAPP(fun(nat,complex),bool,summable(complex),A)) | hAPP(fun(nat,complex),complex,suminf(complex),hAPP(fun(nat,complex),fun(nat,complex),hAPP(fun(complex,complex),fun(fun(nat,complex),fun(nat,complex)),combb(complex,complex,nat),hAPP(complex,fun(complex,complex),times_times(complex),B)),A)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),B),hAPP(fun(nat,complex),complex,suminf(complex),A)). [resolve(5894,a,5848,a)].
% 108.84/108.75 Derived: -hBOOL(hAPP(fun(nat,complex),bool,summable(complex),A)) | hBOOL(hAPP(fun(nat,complex),bool,summable(complex),hAPP(fun(nat,complex),fun(nat,complex),hAPP(fun(complex,complex),fun(fun(nat,complex),fun(nat,complex)),combb(complex,complex,nat),hAPP(complex,fun(complex,complex),times_times(complex),B)),A))). [resolve(5894,a,5851,a)].
% 108.84/108.75 Derived: -hBOOL(hAPP(fun(nat,complex),bool,summable(complex),A)) | hBOOL(hAPP(fun(nat,complex),bool,summable(complex),hAPP(complex,fun(nat,complex),hAPP(fun(nat,fun(complex,complex)),fun(complex,fun(nat,complex)),combc(nat,complex,complex),hAPP(fun(nat,complex),fun(nat,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(nat,complex),fun(nat,fun(complex,complex))),combb(complex,fun(complex,complex),nat),times_times(complex)),A)),B))). [resolve(5894,a,5852,a)].
% 108.84/108.75 Derived: -hBOOL(hAPP(complex,bool,hAPP(fun(nat,complex),fun(complex,bool),sums(complex),A),B)) | hBOOL(hAPP(complex,bool,hAPP(fun(nat,complex),fun(complex,bool),sums(complex),hAPP(fun(nat,complex),fun(nat,complex),hAPP(fun(complex,complex),fun(fun(nat,complex),fun(nat,complex)),combb(complex,complex,nat),hAPP(complex,fun(complex,complex),times_times(complex),C)),A)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),C),B))). [resolve(5894,a,5855,a)].
% 108.84/108.75 Derived: -hBOOL(hAPP(complex,bool,hAPP(fun(nat,complex),fun(complex,bool),sums(complex),A),B)) | hBOOL(hAPP(complex,bool,hAPP(fun(nat,complex),fun(complex,bool),sums(complex),hAPP(complex,fun(nat,complex),hAPP(fun(nat,fun(complex,complex)),fun(complex,fun(nat,complex)),combc(nat,complex,complex),hAPP(fun(nat,complex),fun(nat,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(nat,complex),fun(nat,fun(complex,complex))),combb(complex,fun(complex,complex),nat),times_times(complex)),A)),C)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),B),C))). [resolve(5894,a,5856,a)].
% 108.84/108.75 Derived: -hBOOL(hAPP(fun(nat,complex),bool,cauchy(complex),A)) | hBOOL(hAPP(fun(nat,complex),bool,cauchy(complex),hAPP(complex,fun(nat,complex),hAPP(fun(nat,fun(complex,complex)),fun(complex,fun(nat,complex)),combc(nat,complex,complex),hAPP(fun(nat,complex),fun(nat,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(nat,complex),fun(nat,fun(complex,complex))),combb(complex,fun(complex,complex),nat),times_times(complex)),A)),B))). [resolve(5894,a,5859,a)].
% 108.84/108.75 Derived: -hBOOL(hAPP(fun(nat,complex),bool,cauchy(complex),A)) | hBOOL(hAPP(fun(nat,complex),bool,cauchy(complex),hAPP(fun(nat,complex),fun(nat,complex),hAPP(fun(complex,complex),fun(fun(nat,complex),fun(nat,complex)),combb(complex,complex,nat),hAPP(complex,fun(complex,complex),times_times(complex),B)),A))). [resolve(5894,a,5860,a)].
% 108.84/108.75 Derived: hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),hAPP(complex,fun(A,complex),hAPP(fun(A,fun(complex,complex)),fun(complex,fun(A,complex)),combc(A,complex,complex),hAPP(fun(A,complex),fun(A,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(A,complex),fun(A,fun(complex,complex))),combb(complex,fun(complex,complex),A),times_times(complex)),B)),C)),D) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),B),D)),C). [resolve(5894,a,5861,a)].
% 108.84/108.75 Derived: hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),hAPP(fun(A,complex),fun(A,complex),hAPP(fun(complex,complex),fun(fun(A,complex),fun(A,complex)),combb(complex,complex,A),hAPP(complex,fun(complex,complex),times_times(complex),B)),C)),D) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),B),hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),C),D)). [resolve(5894,a,5862,a)].
% 108.84/108.75 Derived: -hBOOL(hAPP(filter(A),bool,hAPP(complex,fun(filter(A),bool),hAPP(fun(A,complex),fun(complex,fun(filter(A),bool)),tendsto(A,complex),B),C),D)) | -hBOOL(hAPP(filter(A),bool,hAPP(complex,fun(filter(A),bool),hAPP(fun(A,complex),fun(complex,fun(filter(A),bool)),tendsto(A,complex),E),F),D)) | hBOOL(hAPP(filter(A),bool,hAPP(complex,fun(filter(A),bool),hAPP(fun(A,complex),fun(complex,fun(filter(A),bool)),tendsto(A,complex),hAPP(fun(A,complex),fun(A,complex),hAPP(fun(A,fun(complex,complex)),fun(fun(A,complex),fun(A,complex)),combs(A,complex,complex),hAPP(fun(A,complex),fun(A,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(A,complex),fun(A,fun(complex,complex))),combb(complex,fun(complex,complex),A),times_times(complex)),B)),E)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),C),F)),D)). [resolve(5894,a,5863,a)].
% 108.84/108.75 Derived: -hBOOL(hAPP(filter(A),bool,hAPP(complex,fun(filter(A),bool),hAPP(fun(A,complex),fun(complex,fun(filter(A),bool)),tendsto(A,complex),B),C),D)) | hBOOL(hAPP(filter(A),bool,hAPP(complex,fun(filter(A),bool),hAPP(fun(A,complex),fun(complex,fun(filter(A),bool)),tendsto(A,complex),hAPP(complex,fun(A,complex),hAPP(fun(A,fun(complex,complex)),fun(complex,fun(A,complex)),combc(A,complex,complex),hAPP(fun(A,complex),fun(A,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(A,complex),fun(A,fun(complex,complex))),combb(complex,fun(complex,complex),A),times_times(complex)),B)),E)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),C),E)),D)). [resolve(5894,a,5864,a)].
% 108.84/108.76 Derived: -hBOOL(hAPP(filter(A),bool,hAPP(complex,fun(filter(A),bool),hAPP(fun(A,complex),fun(complex,fun(filter(A),bool)),tendsto(A,complex),B),C),D)) | hBOOL(hAPP(filter(A),bool,hAPP(complex,fun(filter(A),bool),hAPP(fun(A,complex),fun(complex,fun(filter(A),bool)),tendsto(A,complex),hAPP(fun(A,complex),fun(A,complex),hAPP(fun(complex,complex),fun(fun(A,complex),fun(A,complex)),combb(complex,complex,A),hAPP(complex,fun(complex,complex),times_times(complex),E)),B)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),E),C)),D)). [resolve(5894,a,5865,a)].
% 108.84/108.76 Derived: -power(complex) | -hBOOL(hAPP(filter(nat),bool,hAPP(complex,fun(filter(nat),bool),hAPP(fun(nat,complex),fun(complex,fun(filter(nat),bool)),tendsto(nat,complex),A),B),sequentially)) | hBOOL(hAPP(filter(nat),bool,hAPP(complex,fun(filter(nat),bool),hAPP(fun(nat,complex),fun(complex,fun(filter(nat),bool)),tendsto(nat,complex),hAPP(nat,fun(nat,complex),hAPP(fun(nat,fun(nat,complex)),fun(nat,fun(nat,complex)),combc(nat,nat,complex),hAPP(fun(nat,complex),fun(nat,fun(nat,complex)),hAPP(fun(complex,fun(nat,complex)),fun(fun(nat,complex),fun(nat,fun(nat,complex))),combb(complex,fun(nat,complex),nat),power_power(complex)),A)),C)),hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),B),C)),sequentially)). [resolve(5894,a,5869,b)].
% 108.84/108.76 Derived: -topological_space(A) | -power(complex) | -hBOOL(hAPP(filter(A),bool,hAPP(complex,fun(filter(A),bool),hAPP(fun(A,complex),fun(complex,fun(filter(A),bool)),tendsto(A,complex),B),C),hAPP(A,filter(A),at(A),D))) | hBOOL(hAPP(filter(A),bool,hAPP(complex,fun(filter(A),bool),hAPP(fun(A,complex),fun(complex,fun(filter(A),bool)),tendsto(A,complex),hAPP(nat,fun(A,complex),hAPP(fun(A,fun(nat,complex)),fun(nat,fun(A,complex)),combc(A,nat,complex),hAPP(fun(A,complex),fun(A,fun(nat,complex)),hAPP(fun(complex,fun(nat,complex)),fun(fun(A,complex),fun(A,fun(nat,complex))),combb(complex,fun(nat,complex),A),power_power(complex)),B)),E)),hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),C),E)),hAPP(A,filter(A),at(A),D))). [resolve(5894,a,5870,c)].
% 108.84/108.76 Derived: hBOOL(hAPP(filter(complex),bool,hAPP(complex,fun(filter(complex),bool),hAPP(fun(complex,complex),fun(complex,fun(filter(complex),bool)),tendsto(complex,complex),hAPP(complex,fun(complex,complex),hAPP(fun(complex,fun(complex,complex)),fun(complex,fun(complex,complex)),combc(complex,complex,complex),times_times(complex)),A)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),B),A)),hAPP(complex,filter(complex),at(complex),B))). [resolve(5894,a,5874,a)].
% 108.84/108.76 Derived: hBOOL(hAPP(filter(complex),bool,hAPP(complex,fun(filter(complex),bool),hAPP(fun(complex,complex),fun(complex,fun(filter(complex),bool)),tendsto(complex,complex),hAPP(complex,fun(complex,complex),times_times(complex),A)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),B)),hAPP(complex,filter(complex),at(complex),B))). [resolve(5894,a,5875,a)].
% 108.84/108.76 Derived: -topological_space(A) | -hBOOL(hAPP(filter(A),bool,hAPP(complex,fun(filter(A),bool),hAPP(fun(A,complex),fun(complex,fun(filter(A),bool)),tendsto(A,complex),B),zero_zero(complex)),hAPP(A,filter(A),at(A),C))) | hBOOL(hAPP(filter(A),bool,hAPP(complex,fun(filter(A),bool),hAPP(fun(A,complex),fun(complex,fun(filter(A),bool)),tendsto(A,complex),hAPP(fun(A,complex),fun(A,complex),hAPP(fun(complex,complex),fun(fun(A,complex),fun(A,complex)),combb(complex,complex,A),hAPP(complex,fun(complex,complex),times_times(complex),D)),B)),zero_zero(complex)),hAPP(A,filter(A),at(A),C))). [resolve(5894,a,5876,b)].
% 108.84/108.76 Derived: -topological_space(A) | -hBOOL(hAPP(filter(A),bool,hAPP(complex,fun(filter(A),bool),hAPP(fun(A,complex),fun(complex,fun(filter(A),bool)),tendsto(A,complex),B),zero_zero(complex)),hAPP(A,filter(A),at(A),C))) | hBOOL(hAPP(filter(A),bool,hAPP(complex,fun(filter(A),bool),hAPP(fun(A,complex),fun(complex,fun(filter(A),bool)),tendsto(A,complex),hAPP(complex,fun(A,complex),hAPP(fun(A,fun(complex,complex)),fun(complex,fun(A,complex)),combc(A,complex,complex),hAPP(fun(A,complex),fun(A,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(A,complex),fun(A,fun(complex,complex))),combb(complex,fun(complex,complex),A),times_times(complex)),B)),D)),zero_zero(complex)),hAPP(A,filter(A),at(A),C))). [resolve(5894,a,5878,b)].
% 108.84/108.76 Derived: -metric_space(A) | -hBOOL(hAPP(filter(A),bool,hAPP(complex,fun(filter(A),bool),hAPP(fun(A,complex),fun(complex,fun(filter(A),bool)),tendsto(A,complex),B),zero_zero(complex)),hAPP(A,filter(A),at(A),C))) | -hBOOL(hAPP(filter(A),bool,hAPP(complex,fun(filter(A),bool),hAPP(fun(A,complex),fun(complex,fun(filter(A),bool)),tendsto(A,complex),D),zero_zero(complex)),hAPP(A,filter(A),at(A),C))) | hBOOL(hAPP(filter(A),bool,hAPP(complex,fun(filter(A),bool),hAPP(fun(A,complex),fun(complex,fun(filter(A),bool)),tendsto(A,complex),hAPP(fun(A,complex),fun(A,complex),hAPP(fun(A,fun(complex,complex)),fun(fun(A,complex),fun(A,complex)),combs(A,complex,complex),hAPP(fun(A,complex),fun(A,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(A,complex),fun(A,fun(complex,complex))),combb(complex,fun(complex,complex),A),times_times(complex)),B)),D)),zero_zero(complex)),hAPP(A,filter(A),at(A),C))). [resolve(5894,a,5880,b)].
% 108.84/108.76 Derived: -banach(complex) | -hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,complex),fun(nat,real),hAPP(fun(complex,real),fun(fun(nat,complex),fun(nat,real)),combb(complex,real,nat),norm_norm(complex)),A))) | -hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,complex),fun(nat,real),hAPP(fun(complex,real),fun(fun(nat,complex),fun(nat,real)),combb(complex,real,nat),norm_norm(complex)),B))) | hAPP(fun(nat,complex),complex,suminf(complex),hAPP(fun(nat,fun(nat,bool)),fun(nat,complex),hAPP(fun(nat,fun(fun(nat,bool),complex)),fun(fun(nat,fun(nat,bool)),fun(nat,complex)),combs(nat,fun(nat,bool),complex),hAPP(fun(nat,fun(nat,complex)),fun(nat,fun(fun(nat,bool),complex)),hAPP(fun(fun(nat,complex),fun(fun(nat,bool),complex)),fun(fun(nat,fun(nat,complex)),fun(nat,fun(fun(nat,bool),complex))),combb(fun(nat,complex),fun(fun(nat,bool),complex),nat),big_co1399186613setsum(nat,complex)),hAPP(fun(nat,fun(nat,complex)),fun(nat,fun(nat,complex)),hAPP(fun(fun(nat,complex),fun(nat,complex)),fun(fun(nat,fun(nat,complex)),fun(nat,fun(nat,complex))),combb(fun(nat,complex),fun(nat,complex),nat),hAPP(fun(nat,fun(complex,complex)),fun(fun(nat,complex),fun(nat,complex)),combs(nat,complex,complex),hAPP(fun(nat,complex),fun(nat,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(nat,complex),fun(nat,fun(complex,complex))),combb(complex,fun(complex,complex),nat),times_times(complex)),A))),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,complex)),hAPP(fun(fun(nat,nat),fun(nat,complex)),fun(fun(nat,fun(nat,nat)),fun(nat,fun(nat,complex))),combb(fun(nat,nat),fun(nat,complex),nat),hAPP(fun(nat,complex),fun(fun(nat,nat),fun(nat,complex)),combb(nat,complex,nat),B)),minus_minus(nat))))),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),zero_zero(nat)))) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(fun(nat,complex),complex,suminf(complex),A)),hAPP(fun(nat,complex),complex,suminf(complex),B)). [resolve(5894,a,5881,a)].
% 108.84/108.76 Derived: -banach(complex) | -hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,complex),fun(nat,real),hAPP(fun(complex,real),fun(fun(nat,complex),fun(nat,real)),combb(complex,real,nat),norm_norm(complex)),A))) | -hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,complex),fun(nat,real),hAPP(fun(complex,real),fun(fun(nat,complex),fun(nat,real)),combb(complex,real,nat),norm_norm(complex)),B))) | hBOOL(hAPP(complex,bool,hAPP(fun(nat,complex),fun(complex,bool),sums(complex),hAPP(fun(nat,fun(nat,bool)),fun(nat,complex),hAPP(fun(nat,fun(fun(nat,bool),complex)),fun(fun(nat,fun(nat,bool)),fun(nat,complex)),combs(nat,fun(nat,bool),complex),hAPP(fun(nat,fun(nat,complex)),fun(nat,fun(fun(nat,bool),complex)),hAPP(fun(fun(nat,complex),fun(fun(nat,bool),complex)),fun(fun(nat,fun(nat,complex)),fun(nat,fun(fun(nat,bool),complex))),combb(fun(nat,complex),fun(fun(nat,bool),complex),nat),big_co1399186613setsum(nat,complex)),hAPP(fun(nat,fun(nat,complex)),fun(nat,fun(nat,complex)),hAPP(fun(fun(nat,complex),fun(nat,complex)),fun(fun(nat,fun(nat,complex)),fun(nat,fun(nat,complex))),combb(fun(nat,complex),fun(nat,complex),nat),hAPP(fun(nat,fun(complex,complex)),fun(fun(nat,complex),fun(nat,complex)),combs(nat,complex,complex),hAPP(fun(nat,complex),fun(nat,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(nat,complex),fun(nat,fun(complex,complex))),combb(complex,fun(complex,complex),nat),times_times(complex)),A))),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,complex)),hAPP(fun(fun(nat,nat),fun(nat,complex)),fun(fun(nat,fun(nat,nat)),fun(nat,fun(nat,complex))),combb(fun(nat,nat),fun(nat,complex),nat),hAPP(fun(nat,complex),fun(fun(nat,nat),fun(nat,complex)),combb(nat,complex,nat),B)),minus_minus(nat))))),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),zero_zero(nat)))),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(fun(nat,complex),complex,suminf(complex),A)),hAPP(fun(nat,complex),complex,suminf(complex),B)))). [resolve(5894,a,5882,a)].
% 108.84/108.76 Derived: -comm_ring_1(complex) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f739(A,complex,B,C,D)),D)) | hBOOL(hAPP(filter(nat),bool,hAPP(complex,fun(filter(nat),bool),hAPP(fun(nat,complex),fun(complex,fun(filter(nat),bool)),tendsto(nat,complex),hAPP(fun(A,bool),fun(nat,complex),hAPP(fun(nat,fun(fun(A,bool),complex)),fun(fun(A,bool),fun(nat,complex)),combc(nat,fun(A,bool),complex),hAPP(fun(nat,fun(A,complex)),fun(nat,fun(fun(A,bool),complex)),hAPP(fun(fun(A,complex),fun(fun(A,bool),complex)),fun(fun(nat,fun(A,complex)),fun(nat,fun(fun(A,bool),complex))),combb(fun(A,complex),fun(fun(A,bool),complex),nat),big_co302546470etprod(A,complex)),hAPP(fun(A,fun(nat,complex)),fun(nat,fun(A,complex)),combc(A,nat,complex),B))),D)),hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co302546470etprod(A,complex),C),D)),sequentially)). [resolve(5894,a,5883,a)].
% 108.84/108.76 Derived: -comm_ring_1(complex) | -hBOOL(hAPP(filter(nat),bool,hAPP(complex,fun(filter(nat),bool),hAPP(fun(nat,complex),fun(complex,fun(filter(nat),bool)),tendsto(nat,complex),hAPP(A,fun(nat,complex),B,f739(A,complex,B,C,D))),hAPP(A,complex,C,f739(A,complex,B,C,D))),sequentially)) | hBOOL(hAPP(filter(nat),bool,hAPP(complex,fun(filter(nat),bool),hAPP(fun(nat,complex),fun(complex,fun(filter(nat),bool)),tendsto(nat,complex),hAPP(fun(A,bool),fun(nat,complex),hAPP(fun(nat,fun(fun(A,bool),complex)),fun(fun(A,bool),fun(nat,complex)),combc(nat,fun(A,bool),complex),hAPP(fun(nat,fun(A,complex)),fun(nat,fun(fun(A,bool),complex)),hAPP(fun(fun(A,complex),fun(fun(A,bool),complex)),fun(fun(nat,fun(A,complex)),fun(nat,fun(fun(A,bool),complex))),combb(fun(A,complex),fun(fun(A,bool),complex),nat),big_co302546470etprod(A,complex)),hAPP(fun(A,fun(nat,complex)),fun(nat,fun(A,complex)),combc(A,nat,complex),B))),D)),hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co302546470etprod(A,complex),C),D)),sequentially)). [resolve(5894,a,5884,a)].
% 108.84/108.76 Derived: hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),A),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),B),C)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),B),hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),A),C)). [resolve(5894,a,5885,a)].
% 108.84/108.76 Derived: hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),A),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),B),C)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),A),B)),C). [resolve(5894,a,5887,a)].
% 112.56/112.43 Derived: hBOOL(hAPP(complex,bool,hAPP(fun(complex,complex),fun(complex,bool),isCont(complex,complex),hAPP(complex,fun(complex,complex),times_times(complex),A)),B)). [resolve(5894,a,5889,a)].
% 112.56/112.43 Derived: hBOOL(hAPP(complex,bool,hAPP(fun(complex,complex),fun(complex,bool),isCont(complex,complex),hAPP(complex,fun(complex,complex),hAPP(fun(complex,fun(complex,complex)),fun(complex,fun(complex,complex)),combc(complex,complex,complex),times_times(complex)),A)),B)). [resolve(5894,a,5890,a)].
% 112.56/112.43 Derived: -topological_space(A) | -hBOOL(hAPP(A,bool,hAPP(fun(A,complex),fun(A,bool),isCont(A,complex),B),C)) | -hBOOL(hAPP(A,bool,hAPP(fun(A,complex),fun(A,bool),isCont(A,complex),D),C)) | hBOOL(hAPP(A,bool,hAPP(fun(A,complex),fun(A,bool),isCont(A,complex),hAPP(fun(A,complex),fun(A,complex),hAPP(fun(A,fun(complex,complex)),fun(fun(A,complex),fun(A,complex)),combs(A,complex,complex),hAPP(fun(A,complex),fun(A,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(A,complex),fun(A,fun(complex,complex))),combb(complex,fun(complex,complex),A),times_times(complex)),B)),D)),C)). [resolve(5894,a,5891,b)].
% 112.56/112.43 Derived: -topological_space(A) | -power(complex) | -hBOOL(hAPP(A,bool,hAPP(fun(A,complex),fun(A,bool),isCont(A,complex),B),C)) | hBOOL(hAPP(A,bool,hAPP(fun(A,complex),fun(A,bool),isCont(A,complex),hAPP(nat,fun(A,complex),hAPP(fun(A,fun(nat,complex)),fun(nat,fun(A,complex)),combc(A,nat,complex),hAPP(fun(A,complex),fun(A,fun(nat,complex)),hAPP(fun(complex,fun(nat,complex)),fun(fun(A,complex),fun(A,fun(nat,complex))),combb(complex,fun(nat,complex),A),power_power(complex)),B)),D)),C)). [resolve(5894,a,5893,c)].
% 112.56/112.43 5895 group_add(int) # label(arity_Int_Oint___Groups_Ogroup__add) # label(axiom). [assumption].
% 112.56/112.43 5896 -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_11_diff__add__cancel) # label(axiom). [clausify(141)].
% 112.56/112.43 5897 -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_36_add__diff__cancel) # label(axiom). [clausify(166)].
% 112.56/112.43 5898 -group_add(A) | hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C) != zero_zero(A) | ti(A,C) = ti(A,B) # label(fact_276_right__minus__eq) # label(axiom). [clausify(406)].
% 112.56/112.43 5899 -group_add(A) | hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C) = zero_zero(A) | ti(A,C) != ti(A,B) # label(fact_276_right__minus__eq) # label(axiom). [clausify(406)].
% 112.56/112.43 5900 -group_add(A) | hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),B) = zero_zero(A) # label(fact_278_diff__self) # label(axiom). [clausify(408)].
% 112.56/112.43 5901 -group_add(A) | hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),zero_zero(A)) = ti(A,B) # label(fact_279_diff__0__right) # label(axiom). [clausify(409)].
% 112.56/112.43 5902 -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_492_neg__equal__iff__equal) # label(axiom). [clausify(616)].
% 112.56/112.43 5903 -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_492_neg__equal__iff__equal) # label(axiom). [clausify(616)].
% 112.56/112.43 5904 -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_493_minus__equation__iff) # label(axiom). [clausify(617)].
% 112.56/112.43 5905 -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_493_minus__equation__iff) # label(axiom). [clausify(617)].
% 112.56/112.43 5906 -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_494_equation__minus__iff) # label(axiom). [clausify(618)].
% 112.56/112.43 5907 -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_494_equation__minus__iff) # label(axiom). [clausify(618)].
% 112.56/112.43 5908 -group_add(A) | hAPP(A,A,uminus_uminus(A),hAPP(A,A,uminus_uminus(A),B)) = ti(A,B) # label(fact_499_minus__minus) # label(axiom). [clausify(623)].
% 112.56/112.43 5909 -group_add(A) | hAPP(A,A,uminus_uminus(A),B) != zero_zero(A) | zero_zero(A) = ti(A,B) # label(fact_554_neg__equal__0__iff__equal) # label(axiom). [clausify(678)].
% 112.56/112.43 5910 -group_add(A) | hAPP(A,A,uminus_uminus(A),B) = zero_zero(A) | zero_zero(A) != ti(A,B) # label(fact_554_neg__equal__0__iff__equal) # label(axiom). [clausify(678)].
% 112.56/112.43 5911 -group_add(A) | hAPP(A,A,uminus_uminus(A),B) != zero_zero(A) | zero_zero(A) = ti(A,B) # label(fact_556_neg__0__equal__iff__equal) # label(axiom). [clausify(680)].
% 112.56/112.43 5912 -group_add(A) | hAPP(A,A,uminus_uminus(A),B) = zero_zero(A) | zero_zero(A) != ti(A,B) # label(fact_556_neg__0__equal__iff__equal) # label(axiom). [clausify(680)].
% 112.56/112.43 5913 -group_add(A) | hAPP(A,A,uminus_uminus(A),zero_zero(A)) = zero_zero(A) # label(fact_557_minus__zero) # label(axiom). [clausify(681)].
% 112.56/112.43 5914 -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_581_minus__add__cancel) # label(axiom). [clausify(705)].
% 112.56/112.43 5915 -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_582_add__minus__cancel) # label(axiom). [clausify(706)].
% 112.56/112.43 5916 -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_583_minus__add) # label(axiom). [clausify(707)].
% 112.56/112.43 5917 -group_add(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),hAPP(A,A,uminus_uminus(A),B)) = zero_zero(A) # label(fact_635_right__minus) # label(axiom). [clausify(756)].
% 112.56/112.43 5918 -group_add(A) | hAPP(A,A,uminus_uminus(A),B) != ti(A,C) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),B) = zero_zero(A) # label(fact_636_eq__neg__iff__add__eq__0) # label(axiom). [clausify(757)].
% 112.56/112.43 5919 -group_add(A) | hAPP(A,A,uminus_uminus(A),B) = ti(A,C) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),B) != zero_zero(A) # label(fact_636_eq__neg__iff__add__eq__0) # label(axiom). [clausify(757)].
% 112.56/112.43 5920 -group_add(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,uminus_uminus(A),B)),B) = zero_zero(A) # label(fact_637_left__minus) # label(axiom). [clausify(758)].
% 112.56/112.43 5921 -group_add(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C) != zero_zero(A) | hAPP(A,A,uminus_uminus(A),B) = ti(A,C) # label(fact_639_add__eq__0__iff) # label(axiom). [clausify(760)].
% 112.56/112.43 5922 -group_add(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C) = zero_zero(A) | hAPP(A,A,uminus_uminus(A),B) != ti(A,C) # label(fact_639_add__eq__0__iff) # label(axiom). [clausify(760)].
% 112.56/112.43 5923 -group_add(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C) != zero_zero(A) | hAPP(A,A,uminus_uminus(A),B) = ti(A,C) # label(fact_640_minus__unique) # label(axiom). [clausify(761)].
% 112.56/112.43 5924 -group_add(A) | hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),zero_zero(A)),B) = hAPP(A,A,uminus_uminus(A),B) # label(fact_641_diff__0) # label(axiom). [clausify(762)].
% 112.56/112.43 5925 -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_644_diff__minus__eq__add) # label(axiom). [clausify(765)].
% 112.56/112.43 5926 -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_646_Groups_Odiff__def) # label(axiom). [clausify(767)].
% 112.56/112.43 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(5895,a,5896,a)].
% 112.56/112.43 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(5895,a,5897,a)].
% 112.56/112.43 Derived: hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),B) != zero_zero(int) | ti(int,B) = ti(int,A). [resolve(5895,a,5898,a)].
% 112.56/112.43 Derived: hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),B) = zero_zero(int) | ti(int,B) != ti(int,A). [resolve(5895,a,5899,a)].
% 112.56/112.43 Derived: hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),A) = zero_zero(int). [resolve(5895,a,5900,a)].
% 112.59/112.48 Derived: hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),zero_zero(int)) = ti(int,A). [resolve(5895,a,5901,a)].
% 112.59/112.48 Derived: hAPP(int,int,uminus_uminus(int),A) != hAPP(int,int,uminus_uminus(int),B) | ti(int,A) = ti(int,B). [resolve(5895,a,5902,a)].
% 112.59/112.48 Derived: hAPP(int,int,uminus_uminus(int),A) = hAPP(int,int,uminus_uminus(int),B) | ti(int,A) != ti(int,B). [resolve(5895,a,5903,a)].
% 112.59/112.48 Derived: hAPP(int,int,uminus_uminus(int),A) != ti(int,B) | hAPP(int,int,uminus_uminus(int),B) = ti(int,A). [resolve(5895,a,5904,a)].
% 112.59/112.48 Derived: hAPP(int,int,uminus_uminus(int),hAPP(int,int,uminus_uminus(int),A)) = ti(int,A). [resolve(5895,a,5908,a)].
% 112.59/112.48 Derived: hAPP(int,int,uminus_uminus(int),A) != zero_zero(int) | zero_zero(int) = ti(int,A). [resolve(5895,a,5909,a)].
% 112.59/112.48 Derived: hAPP(int,int,uminus_uminus(int),A) = zero_zero(int) | zero_zero(int) != ti(int,A). [resolve(5895,a,5910,a)].
% 112.59/112.48 Derived: hAPP(int,int,uminus_uminus(int),zero_zero(int)) = zero_zero(int). [resolve(5895,a,5913,a)].
% 112.59/112.48 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(5895,a,5914,a)].
% 112.59/112.48 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(5895,a,5915,a)].
% 112.59/112.48 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(5895,a,5916,a)].
% 112.59/112.48 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),hAPP(int,int,uminus_uminus(int),A)) = zero_zero(int). [resolve(5895,a,5917,a)].
% 112.59/112.48 Derived: hAPP(int,int,uminus_uminus(int),A) != ti(int,B) | hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),B),A) = zero_zero(int). [resolve(5895,a,5918,a)].
% 112.59/112.48 Derived: hAPP(int,int,uminus_uminus(int),A) = ti(int,B) | hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),B),A) != zero_zero(int). [resolve(5895,a,5919,a)].
% 112.59/112.48 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,uminus_uminus(int),A)),A) = zero_zero(int). [resolve(5895,a,5920,a)].
% 112.59/112.48 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B) != zero_zero(int) | hAPP(int,int,uminus_uminus(int),A) = ti(int,B). [resolve(5895,a,5921,a)].
% 112.59/112.48 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B) = zero_zero(int) | hAPP(int,int,uminus_uminus(int),A) != ti(int,B). [resolve(5895,a,5922,a)].
% 112.59/112.48 Derived: hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),zero_zero(int)),A) = hAPP(int,int,uminus_uminus(int),A). [resolve(5895,a,5924,a)].
% 112.59/112.48 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(5895,a,5925,a)].
% 112.59/112.48 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(5895,a,5926,a)].
% 112.59/112.48 5927 group_add(rat) # label(arity_Rat_Orat___Groups_Ogroup__add) # label(axiom). [assumption].
% 112.59/112.48 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),A),B)),B) = ti(rat,A). [resolve(5927,a,5896,a)].
% 112.59/112.48 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),B)),B) = ti(rat,A). [resolve(5927,a,5897,a)].
% 112.59/112.48 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),A),B) != zero_zero(rat) | ti(rat,B) = ti(rat,A). [resolve(5927,a,5898,a)].
% 112.59/112.48 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),A),B) = zero_zero(rat) | ti(rat,B) != ti(rat,A). [resolve(5927,a,5899,a)].
% 112.59/112.48 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),A),A) = zero_zero(rat). [resolve(5927,a,5900,a)].
% 112.59/112.48 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),A),zero_zero(rat)) = ti(rat,A). [resolve(5927,a,5901,a)].
% 112.59/112.48 Derived: hAPP(rat,rat,uminus_uminus(rat),A) != hAPP(rat,rat,uminus_uminus(rat),B) | ti(rat,A) = ti(rat,B). [resolve(5927,a,5902,a)].
% 112.59/112.52 Derived: hAPP(rat,rat,uminus_uminus(rat),A) = hAPP(rat,rat,uminus_uminus(rat),B) | ti(rat,A) != ti(rat,B). [resolve(5927,a,5903,a)].
% 112.59/112.52 Derived: hAPP(rat,rat,uminus_uminus(rat),A) != ti(rat,B) | hAPP(rat,rat,uminus_uminus(rat),B) = ti(rat,A). [resolve(5927,a,5904,a)].
% 112.59/112.52 Derived: hAPP(rat,rat,uminus_uminus(rat),hAPP(rat,rat,uminus_uminus(rat),A)) = ti(rat,A). [resolve(5927,a,5908,a)].
% 112.59/112.52 Derived: hAPP(rat,rat,uminus_uminus(rat),A) != zero_zero(rat) | zero_zero(rat) = ti(rat,A). [resolve(5927,a,5909,a)].
% 112.59/112.52 Derived: hAPP(rat,rat,uminus_uminus(rat),A) = zero_zero(rat) | zero_zero(rat) != ti(rat,A). [resolve(5927,a,5910,a)].
% 112.59/112.52 Derived: hAPP(rat,rat,uminus_uminus(rat),zero_zero(rat)) = zero_zero(rat). [resolve(5927,a,5913,a)].
% 112.59/112.52 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(rat,rat,uminus_uminus(rat),A)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),B)) = ti(rat,B). [resolve(5927,a,5914,a)].
% 112.59/112.52 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(rat,rat,uminus_uminus(rat),A)),B)) = ti(rat,B). [resolve(5927,a,5915,a)].
% 112.59/112.52 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(rat,rat,uminus_uminus(rat),A)),hAPP(rat,rat,uminus_uminus(rat),B)) = hAPP(rat,rat,uminus_uminus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),B),A)). [resolve(5927,a,5916,a)].
% 112.59/112.52 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),hAPP(rat,rat,uminus_uminus(rat),A)) = zero_zero(rat). [resolve(5927,a,5917,a)].
% 112.59/112.52 Derived: hAPP(rat,rat,uminus_uminus(rat),A) != ti(rat,B) | hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),B),A) = zero_zero(rat). [resolve(5927,a,5918,a)].
% 112.59/112.52 Derived: hAPP(rat,rat,uminus_uminus(rat),A) = ti(rat,B) | hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),B),A) != zero_zero(rat). [resolve(5927,a,5919,a)].
% 112.59/112.52 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(rat,rat,uminus_uminus(rat),A)),A) = zero_zero(rat). [resolve(5927,a,5920,a)].
% 112.59/112.52 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),B) != zero_zero(rat) | hAPP(rat,rat,uminus_uminus(rat),A) = ti(rat,B). [resolve(5927,a,5921,a)].
% 112.59/112.52 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),B) = zero_zero(rat) | hAPP(rat,rat,uminus_uminus(rat),A) != ti(rat,B). [resolve(5927,a,5922,a)].
% 112.59/112.52 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),zero_zero(rat)),A) = hAPP(rat,rat,uminus_uminus(rat),A). [resolve(5927,a,5924,a)].
% 112.59/112.52 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),B) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),A),hAPP(rat,rat,uminus_uminus(rat),B)). [resolve(5927,a,5925,a)].
% 112.59/112.52 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),hAPP(rat,rat,uminus_uminus(rat),B)) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),A),B). [resolve(5927,a,5926,a)].
% 112.59/112.52 5928 group_add(real) # label(arity_RealDef_Oreal___Groups_Ogroup__add) # label(axiom). [assumption].
% 112.59/112.52 Derived: hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),B)),B) = ti(real,A). [resolve(5928,a,5896,a)].
% 112.59/112.52 Derived: hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),B)),B) = ti(real,A). [resolve(5928,a,5897,a)].
% 112.59/112.52 Derived: hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),B) != zero_zero(real) | ti(real,B) = ti(real,A). [resolve(5928,a,5898,a)].
% 112.59/112.52 Derived: hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),B) = zero_zero(real) | ti(real,B) != ti(real,A). [resolve(5928,a,5899,a)].
% 112.59/112.52 Derived: hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),A) = zero_zero(real). [resolve(5928,a,5900,a)].
% 112.59/112.52 Derived: hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),zero_zero(real)) = ti(real,A). [resolve(5928,a,5901,a)].
% 112.59/112.52 Derived: hAPP(real,real,uminus_uminus(real),A) != hAPP(real,real,uminus_uminus(real),B) | ti(real,A) = ti(real,B). [resolve(5928,a,5902,a)].
% 112.59/112.52 Derived: hAPP(real,real,uminus_uminus(real),A) = hAPP(real,real,uminus_uminus(real),B) | ti(real,A) != ti(real,B). [resolve(5928,a,5903,a)].
% 112.69/112.55 Derived: hAPP(real,real,uminus_uminus(real),A) != ti(real,B) | hAPP(real,real,uminus_uminus(real),B) = ti(real,A). [resolve(5928,a,5904,a)].
% 112.69/112.55 Derived: hAPP(real,real,uminus_uminus(real),hAPP(real,real,uminus_uminus(real),A)) = ti(real,A). [resolve(5928,a,5908,a)].
% 112.69/112.55 Derived: hAPP(real,real,uminus_uminus(real),A) != zero_zero(real) | zero_zero(real) = ti(real,A). [resolve(5928,a,5909,a)].
% 112.69/112.55 Derived: hAPP(real,real,uminus_uminus(real),A) = zero_zero(real) | zero_zero(real) != ti(real,A). [resolve(5928,a,5910,a)].
% 112.69/112.55 Derived: hAPP(real,real,uminus_uminus(real),zero_zero(real)) = zero_zero(real). [resolve(5928,a,5913,a)].
% 112.69/112.55 Derived: hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,uminus_uminus(real),A)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),B)) = ti(real,B). [resolve(5928,a,5914,a)].
% 112.69/112.55 Derived: hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,uminus_uminus(real),A)),B)) = ti(real,B). [resolve(5928,a,5915,a)].
% 112.69/112.55 Derived: hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,uminus_uminus(real),A)),hAPP(real,real,uminus_uminus(real),B)) = hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),B),A)). [resolve(5928,a,5916,a)].
% 112.69/112.55 Derived: hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),hAPP(real,real,uminus_uminus(real),A)) = zero_zero(real). [resolve(5928,a,5917,a)].
% 112.69/112.55 Derived: hAPP(real,real,uminus_uminus(real),A) != ti(real,B) | hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),B),A) = zero_zero(real). [resolve(5928,a,5918,a)].
% 112.69/112.55 Derived: hAPP(real,real,uminus_uminus(real),A) = ti(real,B) | hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),B),A) != zero_zero(real). [resolve(5928,a,5919,a)].
% 112.69/112.55 Derived: hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,uminus_uminus(real),A)),A) = zero_zero(real). [resolve(5928,a,5920,a)].
% 112.69/112.55 Derived: hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),B) != zero_zero(real) | hAPP(real,real,uminus_uminus(real),A) = ti(real,B). [resolve(5928,a,5921,a)].
% 112.69/112.55 Derived: hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),B) = zero_zero(real) | hAPP(real,real,uminus_uminus(real),A) != ti(real,B). [resolve(5928,a,5922,a)].
% 112.69/112.55 Derived: hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),zero_zero(real)),A) = hAPP(real,real,uminus_uminus(real),A). [resolve(5928,a,5924,a)].
% 112.69/112.55 Derived: hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),B) = hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),hAPP(real,real,uminus_uminus(real),B)). [resolve(5928,a,5925,a)].
% 112.69/112.55 Derived: hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),hAPP(real,real,uminus_uminus(real),B)) = hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),B). [resolve(5928,a,5926,a)].
% 112.69/112.55 5929 group_add(complex) # label(arity_Complex_Ocomplex___Groups_Ogroup__add) # label(axiom). [assumption].
% 112.69/112.55 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),A),B)),B) = ti(complex,A). [resolve(5929,a,5896,a)].
% 112.69/112.55 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),A),B)),B) = ti(complex,A). [resolve(5929,a,5897,a)].
% 112.69/112.55 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),A),B) != zero_zero(complex) | ti(complex,B) = ti(complex,A). [resolve(5929,a,5898,a)].
% 112.69/112.55 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),A),B) = zero_zero(complex) | ti(complex,B) != ti(complex,A). [resolve(5929,a,5899,a)].
% 112.69/112.55 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),A),A) = zero_zero(complex). [resolve(5929,a,5900,a)].
% 112.69/112.55 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),A),zero_zero(complex)) = ti(complex,A). [resolve(5929,a,5901,a)].
% 112.69/112.55 Derived: hAPP(complex,complex,uminus_uminus(complex),A) != hAPP(complex,complex,uminus_uminus(complex),B) | ti(complex,A) = ti(complex,B). [resolve(5929,a,5902,a)].
% 116.51/116.38 Derived: hAPP(complex,complex,uminus_uminus(complex),A) = hAPP(complex,complex,uminus_uminus(complex),B) | ti(complex,A) != ti(complex,B). [resolve(5929,a,5903,a)].
% 116.51/116.38 Derived: hAPP(complex,complex,uminus_uminus(complex),A) != ti(complex,B) | hAPP(complex,complex,uminus_uminus(complex),B) = ti(complex,A). [resolve(5929,a,5904,a)].
% 116.51/116.38 Derived: hAPP(complex,complex,uminus_uminus(complex),hAPP(complex,complex,uminus_uminus(complex),A)) = ti(complex,A). [resolve(5929,a,5908,a)].
% 116.51/116.38 Derived: hAPP(complex,complex,uminus_uminus(complex),A) != zero_zero(complex) | zero_zero(complex) = ti(complex,A). [resolve(5929,a,5909,a)].
% 116.51/116.38 Derived: hAPP(complex,complex,uminus_uminus(complex),A) = zero_zero(complex) | zero_zero(complex) != ti(complex,A). [resolve(5929,a,5910,a)].
% 116.51/116.38 Derived: hAPP(complex,complex,uminus_uminus(complex),zero_zero(complex)) = zero_zero(complex). [resolve(5929,a,5913,a)].
% 116.51/116.38 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(complex,complex,uminus_uminus(complex),A)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),A),B)) = ti(complex,B). [resolve(5929,a,5914,a)].
% 116.51/116.38 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),A),hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(complex,complex,uminus_uminus(complex),A)),B)) = ti(complex,B). [resolve(5929,a,5915,a)].
% 116.51/116.38 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(complex,complex,uminus_uminus(complex),A)),hAPP(complex,complex,uminus_uminus(complex),B)) = hAPP(complex,complex,uminus_uminus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),B),A)). [resolve(5929,a,5916,a)].
% 116.51/116.38 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),A),hAPP(complex,complex,uminus_uminus(complex),A)) = zero_zero(complex). [resolve(5929,a,5917,a)].
% 116.51/116.38 Derived: hAPP(complex,complex,uminus_uminus(complex),A) != ti(complex,B) | hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),B),A) = zero_zero(complex). [resolve(5929,a,5918,a)].
% 116.51/116.38 Derived: hAPP(complex,complex,uminus_uminus(complex),A) = ti(complex,B) | hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),B),A) != zero_zero(complex). [resolve(5929,a,5919,a)].
% 116.51/116.38 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(complex,complex,uminus_uminus(complex),A)),A) = zero_zero(complex). [resolve(5929,a,5920,a)].
% 116.51/116.38 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),A),B) != zero_zero(complex) | hAPP(complex,complex,uminus_uminus(complex),A) = ti(complex,B). [resolve(5929,a,5921,a)].
% 116.51/116.38 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),A),B) = zero_zero(complex) | hAPP(complex,complex,uminus_uminus(complex),A) != ti(complex,B). [resolve(5929,a,5922,a)].
% 116.51/116.38 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),zero_zero(complex)),A) = hAPP(complex,complex,uminus_uminus(complex),A). [resolve(5929,a,5924,a)].
% 116.51/116.38 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),A),B) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),A),hAPP(complex,complex,uminus_uminus(complex),B)). [resolve(5929,a,5925,a)].
% 116.51/116.38 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),A),hAPP(complex,complex,uminus_uminus(complex),B)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),A),B). [resolve(5929,a,5926,a)].
% 116.51/116.38 5930 cancel146912293up_add(int) # label(arity_Int_Oint___Groups_Ocancel__ab__semigroup__add) # label(axiom). [assumption].
% 116.51/116.38 5931 -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_14_add__imp__eq) # label(axiom). [clausify(144)].
% 116.51/116.38 5932 cancel146912293up_add(nat) # label(arity_Nat_Onat___Groups_Ocancel__ab__semigroup__add) # label(axiom). [assumption].
% 120.28/120.13 5933 cancel146912293up_add(rat) # label(arity_Rat_Orat___Groups_Ocancel__ab__semigroup__add) # label(axiom). [assumption].
% 120.28/120.13 5934 cancel146912293up_add(real) # label(arity_RealDef_Oreal___Groups_Ocancel__ab__semigroup__add) # label(axiom). [assumption].
% 120.28/120.13 5935 cancel146912293up_add(complex) # label(arity_Complex_Ocomplex___Groups_Ocancel__ab__semigroup__add) # label(axiom). [assumption].
% 120.28/120.13 5936 cancel146912293up_add(code_code_numeral) # label(arity_Code__Numeral_Ocode__numeral___Groups_Ocancel__ab__semigroup__add) # label(axiom). [assumption].
% 120.28/120.13 5937 cancel146912293up_add(quickcheck_code_int) # label(arity_Quickcheck__Narrowing_Ocode__int___Groups_Ocancel__ab__semigroup__add) # label(axiom). [assumption].
% 120.28/120.13 5938 ab_group_add(int) # label(arity_Int_Oint___Groups_Oab__group__add) # label(axiom). [assumption].
% 120.28/120.13 5939 -ab_group_add(A) | hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C) != hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),D),E) | ti(A,E) != ti(A,D) | ti(A,C) = ti(A,B) # label(fact_19_diff__eq__diff__eq) # label(axiom). [clausify(149)].
% 120.28/120.13 5940 -ab_group_add(A) | hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C) != hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),D),E) | ti(A,E) = ti(A,D) | ti(A,C) != ti(A,B) # label(fact_19_diff__eq__diff__eq) # label(axiom). [clausify(149)].
% 120.28/120.13 5941 -ab_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)),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),D),E)) = hAPP(A,A,hAPP(A,fun(A,A),minus_minus(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_35_add__diff__add) # label(axiom). [clausify(165)].
% 120.28/120.13 5942 -ab_group_add(A) | ti(A,B) != ti(A,C) | hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),C),B) = zero_zero(A) # label(fact_277_eq__iff__diff__eq__0) # label(axiom). [clausify(407)].
% 120.28/120.13 5943 -ab_group_add(A) | ti(A,B) = ti(A,C) | hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),C),B) != zero_zero(A) # label(fact_277_eq__iff__diff__eq__0) # label(axiom). [clausify(407)].
% 120.28/120.13 5944 -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_584_minus__add__distrib) # label(axiom). [clausify(708)].
% 120.28/120.13 5945 -ab_group_add(A) | hAPP(A,A,hAPP(A,fun(A,A),minus_minus(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),minus_minus(A),B),C)) # label(fact_587_minus__diff__minus) # label(axiom). [clausify(711)].
% 120.28/120.13 5946 -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_588_minus__diff__eq) # label(axiom). [clausify(712)].
% 120.28/120.13 5947 -ab_group_add(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,uminus_uminus(A),B)),B) = zero_zero(A) # label(fact_638_ab__left__minus) # label(axiom). [clausify(759)].
% 120.28/120.13 5948 -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_645_ab__diff__minus) # label(axiom). [clausify(766)].
% 120.28/120.13 5949 -ab_group_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_atLeastLessThan(nat),zero_zero(nat)),D)) = hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),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_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),D),C)))),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_atLeastLessThan(nat),zero_zero(nat)),C))) # label(fact_4183_sumr__offset) # label(axiom). [clausify(4115)].
% 120.28/120.13 5950 -ab_group_add(A) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),C)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),C),D)) | hAPP(fun(nat,bool),A,hAPP(fun(nat,A),fun(fun(nat,bool),A),big_co1399186613setsum(nat,A),E),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),C),D)) = hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(fun(nat,bool),A,hAPP(fun(nat,A),fun(fun(nat,bool),A),big_co1399186613setsum(nat,A),E),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),B),D))),hAPP(fun(nat,bool),A,hAPP(fun(nat,A),fun(fun(nat,bool),A),big_co1399186613setsum(nat,A),E),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),B),C))) # label(fact_4199_setsum__diff__nat__ivl) # label(axiom). [clausify(4131)].
% 120.28/120.13 5951 -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_4210_setsum__negf) # label(axiom). [clausify(4142)].
% 120.28/120.13 5952 -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_4220_setsum__subtractf) # label(axiom). [clausify(4152)].
% 120.28/120.13 5953 -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_4233_setsum__diff) # label(axiom). [clausify(4165)].
% 120.28/120.13 5954 -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_4622_setsum__natinterval__difff) # label(axiom). [clausify(4549)].
% 120.28/120.13 5955 -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_4622_setsum__natinterval__difff) # label(axiom). [clausify(4549)].
% 120.28/120.14 Derived: hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),B) != hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),C),D) | ti(int,D) != ti(int,C) | ti(int,B) = ti(int,A). [resolve(5938,a,5939,a)].
% 120.28/120.14 Derived: hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),B) != hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),C),D) | ti(int,D) = ti(int,C) | ti(int,B) != ti(int,A). [resolve(5938,a,5940,a)].
% 120.28/120.14 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)),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),C),D)) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(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(5938,a,5941,a)].
% 120.28/120.14 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(5938,a,5944,a)].
% 120.28/120.14 Derived: hAPP(int,int,hAPP(int,fun(int,int),minus_minus(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),minus_minus(int),A),B)). [resolve(5938,a,5945,a)].
% 120.28/120.14 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(5938,a,5946,a)].
% 120.28/120.14 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_atLeastLessThan(nat),zero_zero(nat)),C)) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),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_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),C),B)))),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_atLeastLessThan(nat),zero_zero(nat)),B))). [resolve(5938,a,5949,a)].
% 120.28/120.14 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),C)) | hAPP(fun(nat,bool),int,hAPP(fun(nat,int),fun(fun(nat,bool),int),big_co1399186613setsum(nat,int),D),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),B),C)) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(fun(nat,bool),int,hAPP(fun(nat,int),fun(fun(nat,bool),int),big_co1399186613setsum(nat,int),D),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),A),C))),hAPP(fun(nat,bool),int,hAPP(fun(nat,int),fun(fun(nat,bool),int),big_co1399186613setsum(nat,int),D),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),A),B))). [resolve(5938,a,5950,a)].
% 120.28/120.14 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(5938,a,5951,a)].
% 120.28/120.14 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(5938,a,5952,a)].
% 120.33/120.17 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(5938,a,5953,a)].
% 120.33/120.17 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(5938,a,5954,a)].
% 120.33/120.17 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(5938,a,5955,a)].
% 120.33/120.17 5956 ab_group_add(rat) # label(arity_Rat_Orat___Groups_Oab__group__add) # label(axiom). [assumption].
% 120.33/120.17 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),A),B) != hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),C),D) | ti(rat,D) != ti(rat,C) | ti(rat,B) = ti(rat,A). [resolve(5956,a,5939,a)].
% 120.33/120.17 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),A),B) != hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),C),D) | ti(rat,D) = ti(rat,C) | ti(rat,B) != ti(rat,A). [resolve(5956,a,5940,a)].
% 120.33/120.17 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),A),B)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),C),D)) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),C)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),B),D)). [resolve(5956,a,5941,a)].
% 120.33/120.17 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(rat,rat,uminus_uminus(rat),A)),hAPP(rat,rat,uminus_uminus(rat),B)) = hAPP(rat,rat,uminus_uminus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),B)). [resolve(5956,a,5944,a)].
% 120.33/120.17 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),hAPP(rat,rat,uminus_uminus(rat),A)),hAPP(rat,rat,uminus_uminus(rat),B)) = hAPP(rat,rat,uminus_uminus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),A),B)). [resolve(5956,a,5945,a)].
% 120.33/120.17 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),A),B) = hAPP(rat,rat,uminus_uminus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),B),A)). [resolve(5956,a,5946,a)].
% 120.33/120.18 Derived: hAPP(fun(nat,bool),rat,hAPP(fun(nat,rat),fun(fun(nat,bool),rat),big_co1399186613setsum(nat,rat),hAPP(fun(nat,nat),fun(nat,rat),hAPP(fun(nat,rat),fun(fun(nat,nat),fun(nat,rat)),combb(nat,rat,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_atLeastLessThan(nat),zero_zero(nat)),C)) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),hAPP(fun(nat,bool),rat,hAPP(fun(nat,rat),fun(fun(nat,bool),rat),big_co1399186613setsum(nat,rat),A),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),C),B)))),hAPP(fun(nat,bool),rat,hAPP(fun(nat,rat),fun(fun(nat,bool),rat),big_co1399186613setsum(nat,rat),A),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),B))). [resolve(5956,a,5949,a)].
% 120.33/120.18 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),C)) | hAPP(fun(nat,bool),rat,hAPP(fun(nat,rat),fun(fun(nat,bool),rat),big_co1399186613setsum(nat,rat),D),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),B),C)) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),hAPP(fun(nat,bool),rat,hAPP(fun(nat,rat),fun(fun(nat,bool),rat),big_co1399186613setsum(nat,rat),D),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),A),C))),hAPP(fun(nat,bool),rat,hAPP(fun(nat,rat),fun(fun(nat,bool),rat),big_co1399186613setsum(nat,rat),D),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),A),B))). [resolve(5956,a,5950,a)].
% 120.33/120.18 Derived: hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),hAPP(fun(A,rat),fun(A,rat),hAPP(fun(rat,rat),fun(fun(A,rat),fun(A,rat)),combb(rat,rat,A),uminus_uminus(rat)),B)),C) = hAPP(rat,rat,uminus_uminus(rat),hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),B),C)). [resolve(5956,a,5951,a)].
% 120.33/120.18 Derived: hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),hAPP(fun(A,rat),fun(A,rat),hAPP(fun(A,fun(rat,rat)),fun(fun(A,rat),fun(A,rat)),combs(A,rat,rat),hAPP(fun(A,rat),fun(A,fun(rat,rat)),hAPP(fun(rat,fun(rat,rat)),fun(fun(A,rat),fun(A,fun(rat,rat))),combb(rat,fun(rat,rat),A),minus_minus(rat)),B)),C)),D) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),B),D)),hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),C),D)). [resolve(5956,a,5952,a)].
% 120.33/120.18 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),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),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(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),D),B)),hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),D),C)). [resolve(5956,a,5953,a)].
% 120.33/120.18 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | hAPP(fun(nat,bool),rat,hAPP(fun(nat,rat),fun(fun(nat,bool),rat),big_co1399186613setsum(nat,rat),hAPP(fun(nat,rat),fun(nat,rat),hAPP(fun(nat,fun(rat,rat)),fun(fun(nat,rat),fun(nat,rat)),combs(nat,rat,rat),hAPP(fun(nat,rat),fun(nat,fun(rat,rat)),hAPP(fun(rat,fun(rat,rat)),fun(fun(nat,rat),fun(nat,fun(rat,rat))),combb(rat,fun(rat,rat),nat),minus_minus(rat)),C)),hAPP(fun(nat,nat),fun(nat,rat),hAPP(fun(nat,rat),fun(fun(nat,nat),fun(nat,rat)),combb(nat,rat,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(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),hAPP(nat,rat,C,A)),hAPP(nat,rat,C,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),one_one(nat)))). [resolve(5956,a,5954,a)].
% 120.33/120.21 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | hAPP(fun(nat,bool),rat,hAPP(fun(nat,rat),fun(fun(nat,bool),rat),big_co1399186613setsum(nat,rat),hAPP(fun(nat,rat),fun(nat,rat),hAPP(fun(nat,fun(rat,rat)),fun(fun(nat,rat),fun(nat,rat)),combs(nat,rat,rat),hAPP(fun(nat,rat),fun(nat,fun(rat,rat)),hAPP(fun(rat,fun(rat,rat)),fun(fun(nat,rat),fun(nat,fun(rat,rat))),combb(rat,fun(rat,rat),nat),minus_minus(rat)),C)),hAPP(fun(nat,nat),fun(nat,rat),hAPP(fun(nat,rat),fun(fun(nat,nat),fun(nat,rat)),combb(nat,rat,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(rat). [resolve(5956,a,5955,a)].
% 120.33/120.21 5957 ab_group_add(real) # label(arity_RealDef_Oreal___Groups_Oab__group__add) # label(axiom). [assumption].
% 120.33/120.21 Derived: hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),B) != hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),C),D) | ti(real,D) != ti(real,C) | ti(real,B) = ti(real,A). [resolve(5957,a,5939,a)].
% 120.33/120.21 Derived: hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),B) != hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),C),D) | ti(real,D) = ti(real,C) | ti(real,B) != ti(real,A). [resolve(5957,a,5940,a)].
% 120.33/120.21 Derived: hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),C),D)) = hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),C)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),B),D)). [resolve(5957,a,5941,a)].
% 120.33/120.21 Derived: hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,uminus_uminus(real),A)),hAPP(real,real,uminus_uminus(real),B)) = hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),B)). [resolve(5957,a,5944,a)].
% 120.33/120.21 Derived: hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,uminus_uminus(real),A)),hAPP(real,real,uminus_uminus(real),B)) = hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),B)). [resolve(5957,a,5945,a)].
% 120.33/120.21 Derived: hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),B) = hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),B),A)). [resolve(5957,a,5946,a)].
% 120.33/120.21 Derived: hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,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_atLeastLessThan(nat),zero_zero(nat)),C)) = hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),A),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),C),B)))),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),A),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),B))). [resolve(5957,a,5949,a)].
% 120.33/120.21 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),C)) | hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),D),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),B),C)) = hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),D),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),A),C))),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),D),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),A),B))). [resolve(5957,a,5950,a)].
% 120.33/120.22 Derived: hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),hAPP(fun(A,real),fun(A,real),hAPP(fun(real,real),fun(fun(A,real),fun(A,real)),combb(real,real,A),uminus_uminus(real)),B)),C) = hAPP(real,real,uminus_uminus(real),hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),B),C)). [resolve(5957,a,5951,a)].
% 120.33/120.22 Derived: hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),hAPP(fun(A,real),fun(A,real),hAPP(fun(A,fun(real,real)),fun(fun(A,real),fun(A,real)),combs(A,real,real),hAPP(fun(A,real),fun(A,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(A,real),fun(A,fun(real,real))),combb(real,fun(real,real),A),minus_minus(real)),B)),C)),D) = hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),B),D)),hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),C),D)). [resolve(5957,a,5952,a)].
% 120.33/120.22 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),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),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(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),D),B)),hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),D),C)). [resolve(5957,a,5953,a)].
% 120.33/120.22 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),minus_minus(real)),C)),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,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(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(nat,real,C,A)),hAPP(nat,real,C,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),one_one(nat)))). [resolve(5957,a,5954,a)].
% 120.33/120.22 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),minus_minus(real)),C)),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,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(real). [resolve(5957,a,5955,a)].
% 120.33/120.22 5958 ab_group_add(complex) # label(arity_Complex_Ocomplex___Groups_Oab__group__add) # label(axiom). [assumption].
% 120.33/120.23 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),A),B) != hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),C),D) | ti(complex,D) != ti(complex,C) | ti(complex,B) = ti(complex,A). [resolve(5958,a,5939,a)].
% 120.33/120.23 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),A),B) != hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),C),D) | ti(complex,D) = ti(complex,C) | ti(complex,B) != ti(complex,A). [resolve(5958,a,5940,a)].
% 120.33/120.23 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),A),B)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),C),D)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),A),C)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),B),D)). [resolve(5958,a,5941,a)].
% 120.33/120.23 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(complex,complex,uminus_uminus(complex),A)),hAPP(complex,complex,uminus_uminus(complex),B)) = hAPP(complex,complex,uminus_uminus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),A),B)). [resolve(5958,a,5944,a)].
% 120.33/120.23 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),hAPP(complex,complex,uminus_uminus(complex),A)),hAPP(complex,complex,uminus_uminus(complex),B)) = hAPP(complex,complex,uminus_uminus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),A),B)). [resolve(5958,a,5945,a)].
% 120.33/120.23 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),A),B) = hAPP(complex,complex,uminus_uminus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),B),A)). [resolve(5958,a,5946,a)].
% 120.33/120.23 Derived: hAPP(fun(nat,bool),complex,hAPP(fun(nat,complex),fun(fun(nat,bool),complex),big_co1399186613setsum(nat,complex),hAPP(fun(nat,nat),fun(nat,complex),hAPP(fun(nat,complex),fun(fun(nat,nat),fun(nat,complex)),combb(nat,complex,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_atLeastLessThan(nat),zero_zero(nat)),C)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),hAPP(fun(nat,bool),complex,hAPP(fun(nat,complex),fun(fun(nat,bool),complex),big_co1399186613setsum(nat,complex),A),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),C),B)))),hAPP(fun(nat,bool),complex,hAPP(fun(nat,complex),fun(fun(nat,bool),complex),big_co1399186613setsum(nat,complex),A),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),B))). [resolve(5958,a,5949,a)].
% 120.33/120.23 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),C)) | hAPP(fun(nat,bool),complex,hAPP(fun(nat,complex),fun(fun(nat,bool),complex),big_co1399186613setsum(nat,complex),D),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),B),C)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),hAPP(fun(nat,bool),complex,hAPP(fun(nat,complex),fun(fun(nat,bool),complex),big_co1399186613setsum(nat,complex),D),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),A),C))),hAPP(fun(nat,bool),complex,hAPP(fun(nat,complex),fun(fun(nat,bool),complex),big_co1399186613setsum(nat,complex),D),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),A),B))). [resolve(5958,a,5950,a)].
% 120.33/120.23 Derived: hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),hAPP(fun(A,complex),fun(A,complex),hAPP(fun(complex,complex),fun(fun(A,complex),fun(A,complex)),combb(complex,complex,A),uminus_uminus(complex)),B)),C) = hAPP(complex,complex,uminus_uminus(complex),hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),B),C)). [resolve(5958,a,5951,a)].
% 124.04/123.95 Derived: hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),hAPP(fun(A,complex),fun(A,complex),hAPP(fun(A,fun(complex,complex)),fun(fun(A,complex),fun(A,complex)),combs(A,complex,complex),hAPP(fun(A,complex),fun(A,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(A,complex),fun(A,fun(complex,complex))),combb(complex,fun(complex,complex),A),minus_minus(complex)),B)),C)),D) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),B),D)),hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),C),D)). [resolve(5958,a,5952,a)].
% 124.04/123.95 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),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),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(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),D),B)),hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),D),C)). [resolve(5958,a,5953,a)].
% 124.04/123.95 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | hAPP(fun(nat,bool),complex,hAPP(fun(nat,complex),fun(fun(nat,bool),complex),big_co1399186613setsum(nat,complex),hAPP(fun(nat,complex),fun(nat,complex),hAPP(fun(nat,fun(complex,complex)),fun(fun(nat,complex),fun(nat,complex)),combs(nat,complex,complex),hAPP(fun(nat,complex),fun(nat,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(nat,complex),fun(nat,fun(complex,complex))),combb(complex,fun(complex,complex),nat),minus_minus(complex)),C)),hAPP(fun(nat,nat),fun(nat,complex),hAPP(fun(nat,complex),fun(fun(nat,nat),fun(nat,complex)),combb(nat,complex,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(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),hAPP(nat,complex,C,A)),hAPP(nat,complex,C,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),one_one(nat)))). [resolve(5958,a,5954,a)].
% 124.04/123.95 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | hAPP(fun(nat,bool),complex,hAPP(fun(nat,complex),fun(fun(nat,bool),complex),big_co1399186613setsum(nat,complex),hAPP(fun(nat,complex),fun(nat,complex),hAPP(fun(nat,fun(complex,complex)),fun(fun(nat,complex),fun(nat,complex)),combs(nat,complex,complex),hAPP(fun(nat,complex),fun(nat,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(nat,complex),fun(nat,fun(complex,complex))),combb(complex,fun(complex,complex),nat),minus_minus(complex)),C)),hAPP(fun(nat,nat),fun(nat,complex),hAPP(fun(nat,complex),fun(fun(nat,nat),fun(nat,complex)),combb(nat,complex,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(complex). [resolve(5958,a,5955,a)].
% 124.04/123.95 5959 comm_semiring(int) # label(arity_Int_Oint___Rings_Ocomm__semiring) # label(axiom). [assumption].
% 124.04/123.95 5960 -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_28_comm__semiring__class_Odistrib) # label(axiom). [clausify(158)].
% 127.85/127.73 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(5959,a,5960,a)].
% 127.85/127.73 5961 comm_semiring(nat) # label(arity_Nat_Onat___Rings_Ocomm__semiring) # label(axiom). [assumption].
% 127.85/127.73 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(5961,a,5960,a)].
% 127.85/127.73 5962 comm_semiring(rat) # label(arity_Rat_Orat___Rings_Ocomm__semiring) # label(axiom). [assumption].
% 127.85/127.73 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),B)),C) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),C)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),B),C)). [resolve(5962,a,5960,a)].
% 127.85/127.73 5963 comm_semiring(real) # label(arity_RealDef_Oreal___Rings_Ocomm__semiring) # label(axiom). [assumption].
% 127.85/127.73 5964 comm_semiring(complex) # label(arity_Complex_Ocomplex___Rings_Ocomm__semiring) # label(axiom). [assumption].
% 127.85/127.73 5965 comm_semiring(code_code_numeral) # label(arity_Code__Numeral_Ocode__numeral___Rings_Ocomm__semiring) # label(axiom). [assumption].
% 127.85/127.73 Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),A),B)),C) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),C)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),B),C)). [resolve(5965,a,5960,a)].
% 127.85/127.73 5966 comm_semiring(quickcheck_code_int) # label(arity_Quickcheck__Narrowing_Ocode__int___Rings_Ocomm__semiring) # label(axiom). [assumption].
% 127.85/127.73 Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),A),B)),C) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),C)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),B),C)). [resolve(5966,a,5960,a)].
% 127.85/127.73 5967 semiri456707255roduct(int) # label(arity_Int_Oint___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduc) # label(axiom). [assumption].
% 127.85/127.73 5968 -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_37_crossproduct__eq) # label(axiom). [clausify(167)].
% 127.85/127.73 5969 -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_37_crossproduct__eq) # label(axiom). [clausify(167)].
% 127.85/127.73 5970 -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_37_crossproduct__eq) # label(axiom). [clausify(167)].
% 127.85/127.73 5971 -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_40_crossproduct__noteq) # label(axiom). [clausify(170)].
% 127.85/127.73 5972 -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_40_crossproduct__noteq) # label(axiom). [clausify(170)].
% 127.85/127.73 5973 -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_40_crossproduct__noteq) # label(axiom). [clausify(170)].
% 127.85/127.73 5974 -semiri456707255roduct(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C) != ti(A,B) | zero_zero(A) = ti(A,C) # label(fact_271_add__0__iff) # label(axiom). [clausify(401)].
% 127.85/127.73 5975 -semiri456707255roduct(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C) = ti(A,B) | zero_zero(A) != ti(A,C) # label(fact_271_add__0__iff) # label(axiom). [clausify(401)].
% 127.85/127.73 5976 -semiri456707255roduct(A) | zero_zero(A) = ti(A,B) | ti(A,C) != ti(A,D) | ti(A,E) = ti(A,F) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),E)) != hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),D),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),F)) # label(fact_341_add__scale__eq__noteq) # label(axiom). [clausify(470)].
% 127.85/127.73 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(5967,a,5968,a)].
% 127.85/127.73 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(5967,a,5969,a)].
% 127.85/127.73 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(5967,a,5970,a)].
% 127.85/127.73 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(5967,a,5971,a)].
% 127.85/127.76 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(5967,a,5972,a)].
% 127.85/127.76 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B) != ti(int,A) | zero_zero(int) = ti(int,B). [resolve(5967,a,5974,a)].
% 127.85/127.76 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B) = ti(int,A) | zero_zero(int) != ti(int,B). [resolve(5967,a,5975,a)].
% 127.85/127.76 Derived: zero_zero(int) = ti(int,A) | ti(int,B) != ti(int,C) | ti(int,D) = ti(int,E) | hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),B),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),D)) != hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),C),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),E)). [resolve(5967,a,5976,a)].
% 127.85/127.76 5977 semiri456707255roduct(nat) # label(arity_Nat_Onat___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduc) # label(axiom). [assumption].
% 127.85/127.76 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(5977,a,5968,a)].
% 127.85/127.76 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(5977,a,5969,a)].
% 127.85/127.76 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(5977,a,5970,a)].
% 127.85/127.76 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(5977,a,5971,a)].
% 127.85/127.76 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(5977,a,5972,a)].
% 127.85/127.76 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B) != ti(nat,A) | zero_zero(nat) = ti(nat,B). [resolve(5977,a,5974,a)].
% 127.85/127.76 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B) = ti(nat,A) | zero_zero(nat) != ti(nat,B). [resolve(5977,a,5975,a)].
% 127.85/127.76 Derived: zero_zero(nat) = ti(nat,A) | ti(nat,B) != ti(nat,C) | ti(nat,D) = ti(nat,E) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),D)) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),C),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),E)). [resolve(5977,a,5976,a)].
% 127.85/127.76 5978 semiri456707255roduct(rat) # label(arity_Rat_Orat___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduc) # label(axiom). [assumption].
% 127.85/127.76 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),C),D)) != hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),D)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),C),B)) | ti(rat,A) = ti(rat,C) | ti(rat,B) = ti(rat,D). [resolve(5978,a,5968,a)].
% 127.93/127.79 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),C),D)) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),D)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),C),B)) | ti(rat,A) != ti(rat,C). [resolve(5978,a,5969,a)].
% 127.93/127.79 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),C),D)) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),D)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),C),B)) | ti(rat,B) != ti(rat,D). [resolve(5978,a,5970,a)].
% 127.93/127.79 Derived: ti(rat,A) = ti(rat,B) | ti(rat,C) = ti(rat,D) | hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),B),C)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),D)) != hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),B),D)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),C)). [resolve(5978,a,5971,a)].
% 127.93/127.79 Derived: ti(rat,A) != ti(rat,B) | hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),B),C)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),D)) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),B),D)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),C)). [resolve(5978,a,5972,a)].
% 127.93/127.79 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),B) != ti(rat,A) | zero_zero(rat) = ti(rat,B). [resolve(5978,a,5974,a)].
% 127.93/127.79 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),B) = ti(rat,A) | zero_zero(rat) != ti(rat,B). [resolve(5978,a,5975,a)].
% 127.93/127.79 Derived: zero_zero(rat) = ti(rat,A) | ti(rat,B) != ti(rat,C) | ti(rat,D) = ti(rat,E) | hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),B),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),D)) != hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),C),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),E)). [resolve(5978,a,5976,a)].
% 127.93/127.79 5979 semiri456707255roduct(real) # label(arity_RealDef_Oreal___Semiring__Normalization_Ocomm__semiring__1__cancel__crossp) # label(axiom). [assumption].
% 127.93/127.79 Derived: hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),D)) != hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),D)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),B)) | ti(real,A) = ti(real,C) | ti(real,B) = ti(real,D). [resolve(5979,a,5968,a)].
% 127.93/127.79 Derived: hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),D)) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),D)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),B)) | ti(real,A) != ti(real,C). [resolve(5979,a,5969,a)].
% 127.93/127.79 Derived: hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),D)) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),D)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),B)) | ti(real,B) != ti(real,D). [resolve(5979,a,5970,a)].
% 127.93/127.79 Derived: ti(real,A) = ti(real,B) | ti(real,C) = ti(real,D) | hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),C)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),D)) != hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),D)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),C)). [resolve(5979,a,5971,a)].
% 127.96/127.82 Derived: ti(real,A) != ti(real,B) | hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),C)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),D)) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),D)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),C)). [resolve(5979,a,5972,a)].
% 127.96/127.82 Derived: hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),B) != ti(real,A) | zero_zero(real) = ti(real,B). [resolve(5979,a,5974,a)].
% 127.96/127.82 Derived: hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),B) = ti(real,A) | zero_zero(real) != ti(real,B). [resolve(5979,a,5975,a)].
% 127.96/127.82 Derived: zero_zero(real) = ti(real,A) | ti(real,B) != ti(real,C) | ti(real,D) = ti(real,E) | hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),B),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),D)) != hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),C),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),E)). [resolve(5979,a,5976,a)].
% 127.96/127.82 5980 semiri456707255roduct(complex) # label(arity_Complex_Ocomplex___Semiring__Normalization_Ocomm__semiring__1__cancel__cro) # label(axiom). [assumption].
% 127.96/127.82 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),B)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),C),D)) != hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),D)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),C),B)) | ti(complex,A) = ti(complex,C) | ti(complex,B) = ti(complex,D). [resolve(5980,a,5968,a)].
% 127.96/127.82 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),B)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),C),D)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),D)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),C),B)) | ti(complex,A) != ti(complex,C). [resolve(5980,a,5969,a)].
% 127.96/127.82 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),B)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),C),D)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),D)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),C),B)) | ti(complex,B) != ti(complex,D). [resolve(5980,a,5970,a)].
% 127.96/127.82 Derived: ti(complex,A) = ti(complex,B) | ti(complex,C) = ti(complex,D) | hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),B),C)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),D)) != hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),B),D)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),C)). [resolve(5980,a,5971,a)].
% 127.96/127.82 Derived: ti(complex,A) != ti(complex,B) | hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),B),C)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),D)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),B),D)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),C)). [resolve(5980,a,5972,a)].
% 131.73/131.66 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),A),B) != ti(complex,A) | zero_zero(complex) = ti(complex,B). [resolve(5980,a,5974,a)].
% 131.73/131.66 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),A),B) = ti(complex,A) | zero_zero(complex) != ti(complex,B). [resolve(5980,a,5975,a)].
% 131.73/131.66 Derived: zero_zero(complex) = ti(complex,A) | ti(complex,B) != ti(complex,C) | ti(complex,D) = ti(complex,E) | hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),B),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),D)) != hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),C),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),E)). [resolve(5980,a,5976,a)].
% 131.73/131.66 5981 comm_semiring_1(int) # label(arity_Int_Oint___Rings_Ocomm__semiring__1) # label(axiom). [assumption].
% 131.73/131.66 5982 -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_38_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J) # label(axiom). [clausify(168)].
% 131.73/131.66 5983 -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_39_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J) # label(axiom). [clausify(169)].
% 131.73/131.66 5984 -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_41_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J) # label(axiom). [clausify(171)].
% 131.73/131.66 5985 -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_47_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) # label(axiom). [clausify(177)].
% 131.73/131.66 5986 -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_48_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) # label(axiom). [clausify(178)].
% 131.73/131.66 5987 -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_51_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) # label(axiom). [clausify(181)].
% 131.73/131.66 5988 -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_53_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J) # label(axiom). [clausify(183)].
% 131.73/131.66 5989 -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_54_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J) # label(axiom). [clausify(184)].
% 131.73/131.66 5990 -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_55_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J) # label(axiom). [clausify(185)].
% 131.73/131.66 5991 -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_56_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J) # label(axiom). [clausify(186)].
% 131.73/131.66 5992 -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_57_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J) # label(axiom). [clausify(187)].
% 131.73/131.66 5993 -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_58_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J) # label(axiom). [clausify(188)].
% 131.73/131.66 5994 -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_59_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J) # label(axiom). [clausify(189)].
% 131.73/131.66 5995 -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_60_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) # label(axiom). [clausify(190)].
% 131.73/131.66 5996 -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_61_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) # label(axiom). [clausify(191)].
% 131.73/131.66 5997 -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_62_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) # label(axiom). [clausify(192)].
% 131.73/131.66 5998 -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_63_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) # label(axiom). [clausify(193)].
% 131.73/131.66 5999 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),one_one(A)),B) = ti(A,B) # label(fact_116_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J) # label(axiom). [clausify(246)].
% 131.73/131.66 6000 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),one_one(A)) = ti(A,B) # label(fact_117_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J) # label(axiom). [clausify(247)].
% 131.73/131.66 6001 -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_152_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J) # label(axiom). [clausify(282)].
% 131.73/131.66 6002 -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_153_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J) # label(axiom). [clausify(283)].
% 131.73/131.66 6003 -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_154_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J) # label(axiom). [clausify(284)].
% 131.73/131.66 6004 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),zero_zero(A)) = zero_zero(A) # label(fact_263_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J) # label(axiom). [clausify(393)].
% 131.73/131.66 6005 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),zero_zero(A)),B) = zero_zero(A) # label(fact_264_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J) # label(axiom). [clausify(394)].
% 131.73/131.66 6006 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),zero_zero(A)) = ti(A,B) # label(fact_272_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) # label(axiom). [clausify(402)].
% 131.73/131.66 6007 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),zero_zero(A)),B) = ti(A,B) # label(fact_273_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) # label(axiom). [clausify(403)].
% 131.73/131.66 6008 -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_1380_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J) # label(axiom). [clausify(1483)].
% 131.73/131.66 6009 -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_1381_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J) # label(axiom). [clausify(1484)].
% 131.73/131.66 6010 -comm_semiring_1(A) | hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),one_one(nat)) = ti(A,B) # label(fact_1382_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J) # label(axiom). [clausify(1485)].
% 131.73/131.66 6011 -comm_semiring_1(A) | hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),zero_zero(nat)) = one_one(A) # label(fact_1386_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J) # label(axiom). [clausify(1489)].
% 131.73/131.66 6012 -comm_semiring_1(A) | hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(nat,nat,suc,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_1387_comm__semiring__1__class_Onormalizing__semiring__rules_I35_J) # label(axiom). [clausify(1490)].
% 131.73/131.66 6013 -comm_semiring_1(A) | hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(nat,nat,suc,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_1388_comm__semiring__1__class_Onormalizing__semiring__rules_I27_J) # label(axiom). [clausify(1491)].
% 131.73/131.66 6014 -comm_semiring_1(A) | hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(nat,nat,suc,C)) = 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) # label(fact_1389_comm__semiring__1__class_Onormalizing__semiring__rules_I28_J) # label(axiom). [clausify(1492)].
% 131.73/131.66 6015 -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_1390_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J) # label(axiom). [clausify(1493)].
% 131.73/131.66 6016 -comm_semiring_1(A) | hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),B) # label(fact_1813_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J) # label(axiom). [clausify(1874)].
% 131.73/131.66 6017 -comm_semiring_1(A) | hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),C)) = 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),C)) # label(fact_1855_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J) # label(axiom). [clausify(1906)].
% 131.73/131.66 6018 -comm_semiring_1(A) | hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),C))) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),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),C))) # label(fact_1890_comm__semiring__1__class_Onormalizing__semiring__rules_I37_J) # label(axiom). [clausify(1935)].
% 131.73/131.66 6019 -comm_semiring_1(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),zero_zero(A))) # label(fact_3048_dvd__0__right) # label(axiom). [clausify(3015)].
% 131.73/131.66 6020 -comm_semiring_1(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(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_3052_dvd__power__same) # label(axiom). [clausify(3019)].
% 131.73/131.66 6021 -comm_semiring_1(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),one_one(A)),B)) # label(fact_3063_one__dvd) # label(axiom). [clausify(3030)].
% 131.73/131.66 6022 -comm_semiring_1(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),D))) # label(fact_3065_dvd__add) # label(axiom). [clausify(3032)].
% 131.73/131.66 6023 -comm_semiring_1(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C))) # label(fact_3066_dvd__triv__left) # label(axiom). [clausify(3033)].
% 131.73/131.66 6024 -comm_semiring_1(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),B))) # label(fact_3067_dvd__triv__right) # label(axiom). [clausify(3034)].
% 131.73/131.66 6025 -comm_semiring_1(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),D))) # label(fact_3068_dvd__mult2) # label(axiom). [clausify(3035)].
% 131.73/131.66 6026 -comm_semiring_1(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),C))) # label(fact_3069_dvd__mult) # label(axiom). [clausify(3036)].
% 131.73/131.66 6027 -comm_semiring_1(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),D),E)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(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_3070_mult__dvd__mono) # label(axiom). [clausify(3037)].
% 131.73/131.66 6028 -comm_semiring_1(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),D)) # label(fact_3072_dvd__mult__left) # label(axiom). [clausify(3039)].
% 131.73/131.66 6029 -comm_semiring_1(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),C),D)) # label(fact_3073_dvd__mult__right) # label(axiom). [clausify(3040)].
% 131.73/131.66 6030 -comm_semiring_1(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),zero_zero(A)),B)) | zero_zero(A) = ti(A,B) # label(fact_3078_dvd__0__left) # label(axiom). [clausify(3045)].
% 131.73/131.66 6031 -comm_semiring_1(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),B)) # label(fact_3113_dvd__refl) # label(axiom). [clausify(3080)].
% 131.73/131.66 6032 -comm_semiring_1(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),C),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),D)) # label(fact_3114_dvd__trans) # label(axiom). [clausify(3081)].
% 131.73/131.66 6033 -comm_semiring_1(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),dvd_dvd(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_3133_le__imp__power__dvd) # label(axiom). [clausify(3100)].
% 131.73/131.66 6034 -comm_semiring_1(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),C)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),D),E)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(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),E))) # label(fact_3134_dvd__power__le) # label(axiom). [clausify(3101)].
% 131.73/131.66 6035 -comm_semiring_1(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C)),D)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),E),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),E)),D)) # label(fact_3135_power__le__dvd) # label(axiom). [clausify(3102)].
% 131.73/131.66 6036 -comm_semiring_1(A) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),C),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),C),B))) # label(fact_3166_dvd__power) # label(axiom). [clausify(3133)].
% 131.73/131.66 6037 -comm_semiring_1(A) | one_one(A) != ti(A,B) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C))) # label(fact_3166_dvd__power) # label(axiom). [clausify(3133)].
% 131.73/131.66 6038 -comm_semiring_1(A) | -no_zero_divisors(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) != zero_zero(A) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f483(B,A,D,C)),C)) # label(fact_3946_setprod__zero__iff) # label(axiom). [clausify(3887)].
% 131.73/131.66 6039 -comm_semiring_1(A) | -no_zero_divisors(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) != zero_zero(A) | hAPP(B,A,D,f483(B,A,D,C)) = zero_zero(A) # label(fact_3946_setprod__zero__iff) # label(axiom). [clausify(3887)].
% 131.73/131.66 6040 -comm_semiring_1(A) | -no_zero_divisors(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) = zero_zero(A) | -hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),E),C)) | hAPP(B,A,D,E) != zero_zero(A) # label(fact_3946_setprod__zero__iff) # label(axiom). [clausify(3887)].
% 131.73/131.66 6041 -comm_semiring_1(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(B,A,E,D) != zero_zero(A) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),E),C) = zero_zero(A) # label(fact_3947_setprod__zero) # label(axiom). [clausify(3888)].
% 131.73/131.66 6042 -comm_semiring_1(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)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(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_3950_dvd__setprod) # label(axiom). [clausify(3891)].
% 131.73/131.66 6043 -comm_semiring_1(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),f489(B,A,E,F,D,C)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),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_3962_setprod__dvd__setprod__subset2) # label(axiom). [clausify(3903)].
% 131.73/131.66 6044 -comm_semiring_1(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(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),hAPP(B,A,E,f489(B,A,E,F,D,C))),hAPP(B,A,F,f489(B,A,E,F,D,C)))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),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_3962_setprod__dvd__setprod__subset2) # label(axiom). [clausify(3903)].
% 131.83/131.67 6045 -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_4324_arith__series__general) # label(axiom). [clausify(4256)].
% 131.83/131.67 6046 -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_4621_gauss__sum) # label(axiom). [clausify(4548)].
% 131.83/131.67 6047 -comm_semiring_1(A) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f770(B,A,C,D,E)),E)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),C),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),D),E))) # label(fact_4780_dvd__setsum) # label(axiom). [clausify(4704)].
% 131.83/131.67 6048 -comm_semiring_1(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),hAPP(C,A,D,f770(C,A,B,D,E)))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),hAPP(fun(C,bool),A,hAPP(fun(C,A),fun(fun(C,bool),A),big_co1399186613setsum(C,A),D),E))) # label(fact_4780_dvd__setsum) # label(axiom). [clausify(4704)].
% 131.83/131.67 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(5981,a,5984,a)].
% 131.83/131.67 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(5981,a,5985,a)].
% 131.83/131.67 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(5981,a,5986,a)].
% 131.83/131.67 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(5981,a,5987,a)].
% 131.83/131.67 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(5981,a,5988,a)].
% 131.83/131.67 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(5981,a,5991,a)].
% 131.83/131.68 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(5981,a,5994,a)].
% 131.83/131.68 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(5981,a,5995,a)].
% 131.83/131.68 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(5981,a,5996,a)].
% 131.83/131.68 Derived: hAPP(int,int,hAPP(int,fun(int,int),times_times(int),one_one(int)),A) = ti(int,A). [resolve(5981,a,5999,a)].
% 131.83/131.68 Derived: hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),one_one(int)) = ti(int,A). [resolve(5981,a,6000,a)].
% 131.83/131.68 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(5981,a,6001,a)].
% 131.83/131.68 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(5981,a,6002,a)].
% 131.83/131.68 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(5981,a,6003,a)].
% 131.83/131.68 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(5981,a,6008,a)].
% 131.83/131.68 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(5981,a,6009,a)].
% 131.83/131.68 Derived: hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),one_one(nat)) = ti(int,A). [resolve(5981,a,6010,a)].
% 131.83/131.68 Derived: hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),zero_zero(nat)) = one_one(int). [resolve(5981,a,6011,a)].
% 131.83/131.68 Derived: hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),hAPP(nat,nat,suc,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(5981,a,6012,a)].
% 131.83/131.68 Derived: hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),hAPP(nat,nat,suc,B)) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),B)),A). [resolve(5981,a,6014,a)].
% 131.83/131.68 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(5981,a,6015,a)].
% 131.83/131.68 Derived: hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),A). [resolve(5981,a,6016,a)].
% 131.83/131.68 Derived: hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),B)) = 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),B)). [resolve(5981,a,6017,a)].
% 131.83/131.69 Derived: hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),B))) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),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),B))). [resolve(5981,a,6018,a)].
% 131.83/131.69 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),zero_zero(int))). [resolve(5981,a,6019,a)].
% 131.83/131.69 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(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(5981,a,6020,a)].
% 131.83/131.69 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),one_one(int)),A)). [resolve(5981,a,6021,a)].
% 131.83/131.69 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),B),C))). [resolve(5981,a,6022,a)].
% 131.83/131.69 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B))). [resolve(5981,a,6023,a)].
% 131.83/131.69 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),A))). [resolve(5981,a,6024,a)].
% 131.83/131.69 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),C))). [resolve(5981,a,6025,a)].
% 131.83/131.69 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),B))). [resolve(5981,a,6026,a)].
% 131.83/131.69 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),C),D)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(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(5981,a,6027,a)].
% 131.83/131.69 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),C)). [resolve(5981,a,6028,a)].
% 131.83/131.69 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),B),C)). [resolve(5981,a,6029,a)].
% 131.83/131.69 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),zero_zero(int)),A)) | zero_zero(int) = ti(int,A). [resolve(5981,a,6030,a)].
% 131.83/131.69 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),A)). [resolve(5981,a,6031,a)].
% 131.83/131.69 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),B),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),C)). [resolve(5981,a,6032,a)].
% 131.83/131.69 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),dvd_dvd(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(5981,a,6033,a)].
% 131.83/131.69 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),C),D)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(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),D))). [resolve(5981,a,6034,a)].
% 131.83/131.69 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),B)),C)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),D),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),D)),C)). [resolve(5981,a,6035,a)].
% 131.86/131.70 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),B),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),B),A))). [resolve(5981,a,6036,a)].
% 131.86/131.70 Derived: one_one(int) != ti(int,A) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),B))). [resolve(5981,a,6037,a)].
% 131.86/131.70 Derived: -no_zero_divisors(int) | -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) != zero_zero(int) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f483(A,int,C,B)),B)). [resolve(5981,a,6038,a)].
% 131.86/131.70 Derived: -no_zero_divisors(int) | -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) != zero_zero(int) | hAPP(A,int,C,f483(A,int,C,B)) = zero_zero(int). [resolve(5981,a,6039,a)].
% 131.86/131.70 Derived: -no_zero_divisors(int) | -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) = zero_zero(int) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),D),B)) | hAPP(A,int,C,D) != zero_zero(int). [resolve(5981,a,6040,a)].
% 131.86/131.70 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(A,int,D,C) != zero_zero(int) | hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),D),B) = zero_zero(int). [resolve(5981,a,6041,a)].
% 131.86/131.70 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)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(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(5981,a,6042,a)].
% 131.86/131.70 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),f489(A,int,D,E,C,B)),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),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(5981,a,6043,a)].
% 131.86/131.70 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(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(A,int,D,f489(A,int,D,E,C,B))),hAPP(A,int,E,f489(A,int,D,E,C,B)))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),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(5981,a,6044,a)].
% 131.86/131.70 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(5981,a,6045,a)].
% 131.86/131.72 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(5981,a,6046,a)].
% 131.86/131.72 Derived: hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f770(A,int,B,C,D)),D)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),B),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),C),D))). [resolve(5981,a,6047,a)].
% 131.86/131.72 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),hAPP(B,int,C,f770(B,int,A,C,D)))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),hAPP(fun(B,bool),int,hAPP(fun(B,int),fun(fun(B,bool),int),big_co1399186613setsum(B,int),C),D))). [resolve(5981,a,6048,a)].
% 131.86/131.72 6049 comm_semiring_1(nat) # label(arity_Nat_Onat___Rings_Ocomm__semiring__1) # label(axiom). [assumption].
% 131.86/131.72 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(6049,a,5984,a)].
% 131.86/131.72 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),C),D)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),C)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),D)). [resolve(6049,a,5985,a)].
% 131.86/131.72 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B)),C) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),C)),B). [resolve(6049,a,5986,a)].
% 131.86/131.72 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(6049,a,5987,a)].
% 131.86/131.72 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(6049,a,5988,a)].
% 131.86/131.72 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(6049,a,5991,a)].
% 131.86/131.72 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(6049,a,5994,a)].
% 131.86/131.72 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(6049,a,5995,a)].
% 131.86/131.72 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(6049,a,5996,a)].
% 131.86/131.72 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),one_one(nat)),A) = ti(nat,A). [resolve(6049,a,5999,a)].
% 131.86/131.72 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),one_one(nat)) = ti(nat,A). [resolve(6049,a,6000,a)].
% 131.89/131.73 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(6049,a,6001,a)].
% 131.89/131.73 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(6049,a,6002,a)].
% 131.89/131.73 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(6049,a,6003,a)].
% 131.89/131.73 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(6049,a,6008,a)].
% 131.89/131.73 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(6049,a,6009,a)].
% 131.89/131.73 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),one_one(nat)) = ti(nat,A). [resolve(6049,a,6010,a)].
% 131.89/131.73 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),zero_zero(nat)) = one_one(nat). [resolve(6049,a,6011,a)].
% 131.89/131.73 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),hAPP(nat,nat,suc,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(6049,a,6012,a)].
% 131.89/131.73 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),hAPP(nat,nat,suc,B)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),B)),A). [resolve(6049,a,6014,a)].
% 131.89/131.73 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(6049,a,6015,a)].
% 131.89/131.73 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),A). [resolve(6049,a,6016,a)].
% 131.89/131.73 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),B)) = 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),B)). [resolve(6049,a,6017,a)].
% 131.89/131.73 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),B))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),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),B))). [resolve(6049,a,6018,a)].
% 131.89/131.73 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A),zero_zero(nat))). [resolve(6049,a,6019,a)].
% 131.89/131.73 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(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(6049,a,6020,a)].
% 131.89/131.73 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),one_one(nat)),A)). [resolve(6049,a,6021,a)].
% 131.89/131.73 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A),C)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),C))). [resolve(6049,a,6022,a)].
% 131.89/131.74 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),B))). [resolve(6049,a,6023,a)].
% 131.89/131.74 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),A))). [resolve(6049,a,6024,a)].
% 131.89/131.74 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),C))). [resolve(6049,a,6025,a)].
% 131.89/131.74 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),C),B))). [resolve(6049,a,6026,a)].
% 131.89/131.74 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),C),D)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(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(6049,a,6027,a)].
% 131.89/131.74 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),B)),C)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A),C)). [resolve(6049,a,6028,a)].
% 131.89/131.74 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),B)),C)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),B),C)). [resolve(6049,a,6029,a)].
% 131.89/131.74 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),zero_zero(nat)),A)) | zero_zero(nat) = ti(nat,A). [resolve(6049,a,6030,a)].
% 131.89/131.74 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A),A)). [resolve(6049,a,6031,a)].
% 131.89/131.74 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),B),C)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A),C)). [resolve(6049,a,6032,a)].
% 131.89/131.74 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),dvd_dvd(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(6049,a,6033,a)].
% 131.89/131.74 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(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),dvd_dvd(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),D))). [resolve(6049,a,6034,a)].
% 131.89/131.74 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),B)),C)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),D),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),D)),C)). [resolve(6049,a,6035,a)].
% 131.89/131.74 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),dvd_dvd(nat),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),B),A))). [resolve(6049,a,6036,a)].
% 131.89/131.74 Derived: one_one(nat) != ti(nat,A) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),B))). [resolve(6049,a,6037,a)].
% 131.89/131.74 Derived: -no_zero_divisors(nat) | -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) != zero_zero(nat) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f483(A,nat,C,B)),B)). [resolve(6049,a,6038,a)].
% 131.89/131.74 Derived: -no_zero_divisors(nat) | -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) != zero_zero(nat) | hAPP(A,nat,C,f483(A,nat,C,B)) = zero_zero(nat). [resolve(6049,a,6039,a)].
% 131.89/131.74 Derived: -no_zero_divisors(nat) | -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) = zero_zero(nat) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),D),B)) | hAPP(A,nat,C,D) != zero_zero(nat). [resolve(6049,a,6040,a)].
% 131.89/131.74 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(A,nat,D,C) != zero_zero(nat) | hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),D),B) = zero_zero(nat). [resolve(6049,a,6041,a)].
% 131.89/131.74 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)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(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(6049,a,6042,a)].
% 131.89/131.74 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),f489(A,nat,D,E,C,B)),C)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),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(6049,a,6043,a)].
% 131.89/131.74 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(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(A,nat,D,f489(A,nat,D,E,C,B))),hAPP(A,nat,E,f489(A,nat,D,E,C,B)))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),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(6049,a,6044,a)].
% 131.89/131.74 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(6049,a,6045,a)].
% 131.89/131.74 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(6049,a,6046,a)].
% 131.89/131.74 Derived: hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f770(A,nat,B,C,D)),D)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),B),hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),C),D))). [resolve(6049,a,6047,a)].
% 131.89/131.77 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A),hAPP(B,nat,C,f770(B,nat,A,C,D)))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A),hAPP(fun(B,bool),nat,hAPP(fun(B,nat),fun(fun(B,bool),nat),big_co1399186613setsum(B,nat),C),D))). [resolve(6049,a,6048,a)].
% 131.89/131.77 6050 comm_semiring_1(rat) # label(arity_Rat_Orat___Rings_Ocomm__semiring__1) # label(axiom). [assumption].
% 131.89/131.77 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),B),C)) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),C)). [resolve(6050,a,5984,a)].
% 131.89/131.77 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),B)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),C),D)) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),C)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),B),D)). [resolve(6050,a,5985,a)].
% 131.89/131.77 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),B)),C) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),C)),B). [resolve(6050,a,5986,a)].
% 131.89/131.77 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),B),A). [resolve(6050,a,5987,a)].
% 131.89/131.77 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),B),C)) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),B),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),C)). [resolve(6050,a,5988,a)].
% 131.89/131.77 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B)),C) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),C)),B). [resolve(6050,a,5991,a)].
% 131.89/131.77 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),C),D)) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),C)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),B),D)). [resolve(6050,a,5994,a)].
% 131.89/131.77 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),B) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),B),A). [resolve(6050,a,5995,a)].
% 131.89/131.77 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),B),C)) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),B),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),C)). [resolve(6050,a,5996,a)].
% 131.89/131.77 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),one_one(rat)),A) = ti(rat,A). [resolve(6050,a,5999,a)].
% 131.89/131.77 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),one_one(rat)) = ti(rat,A). [resolve(6050,a,6000,a)].
% 131.89/131.77 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),one_one(rat)),one_one(rat))),A) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),A). [resolve(6050,a,6001,a)].
% 131.89/131.77 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),one_one(rat))),B) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),B),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B)). [resolve(6050,a,6002,a)].
% 131.89/131.77 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),one_one(rat))),B) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B)),B). [resolve(6050,a,6003,a)].
% 131.89/131.77 Derived: hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B)),C) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),C)),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),B),C)). [resolve(6050,a,6008,a)].
% 131.89/131.78 Derived: hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),B)),C) = hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),C)). [resolve(6050,a,6009,a)].
% 131.89/131.78 Derived: hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),one_one(nat)) = ti(rat,A). [resolve(6050,a,6010,a)].
% 131.89/131.78 Derived: hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),zero_zero(nat)) = one_one(rat). [resolve(6050,a,6011,a)].
% 131.89/131.78 Derived: hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),hAPP(nat,nat,suc,B)) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),B)). [resolve(6050,a,6012,a)].
% 131.89/131.78 Derived: hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),hAPP(nat,nat,suc,B)) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),B)),A). [resolve(6050,a,6014,a)].
% 131.89/131.78 Derived: hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),C)) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),B)),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),C)). [resolve(6050,a,6015,a)].
% 131.89/131.78 Derived: hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),A). [resolve(6050,a,6016,a)].
% 131.89/131.78 Derived: hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),B)) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),B)),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),B)). [resolve(6050,a,6017,a)].
% 131.89/131.78 Derived: hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),B))) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),B)),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),B))). [resolve(6050,a,6018,a)].
% 131.89/131.78 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),dvd_dvd(rat),A),zero_zero(rat))). [resolve(6050,a,6019,a)].
% 131.89/131.78 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),dvd_dvd(rat),A),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),dvd_dvd(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),C)),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),B),C))). [resolve(6050,a,6020,a)].
% 131.89/131.78 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),dvd_dvd(rat),one_one(rat)),A)). [resolve(6050,a,6021,a)].
% 131.89/131.78 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),dvd_dvd(rat),A),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),dvd_dvd(rat),A),C)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),dvd_dvd(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),B),C))). [resolve(6050,a,6022,a)].
% 131.89/131.78 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),dvd_dvd(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B))). [resolve(6050,a,6023,a)].
% 131.89/131.78 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),dvd_dvd(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),B),A))). [resolve(6050,a,6024,a)].
% 131.89/131.78 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),dvd_dvd(rat),A),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),dvd_dvd(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),B),C))). [resolve(6050,a,6025,a)].
% 131.89/131.78 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),dvd_dvd(rat),A),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),dvd_dvd(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),C),B))). [resolve(6050,a,6026,a)].
% 131.89/131.79 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),dvd_dvd(rat),A),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),dvd_dvd(rat),C),D)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),dvd_dvd(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),C)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),B),D))). [resolve(6050,a,6027,a)].
% 131.89/131.79 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),dvd_dvd(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B)),C)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),dvd_dvd(rat),A),C)). [resolve(6050,a,6028,a)].
% 131.89/131.79 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),dvd_dvd(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B)),C)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),dvd_dvd(rat),B),C)). [resolve(6050,a,6029,a)].
% 131.89/131.79 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),dvd_dvd(rat),zero_zero(rat)),A)) | zero_zero(rat) = ti(rat,A). [resolve(6050,a,6030,a)].
% 131.89/131.79 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),dvd_dvd(rat),A),A)). [resolve(6050,a,6031,a)].
% 131.89/131.79 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),dvd_dvd(rat),A),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),dvd_dvd(rat),B),C)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),dvd_dvd(rat),A),C)). [resolve(6050,a,6032,a)].
% 131.89/131.79 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),dvd_dvd(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),C),A)),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),C),B))). [resolve(6050,a,6033,a)].
% 131.89/131.79 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),dvd_dvd(rat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),C),D)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),dvd_dvd(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),C)),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),B),D))). [resolve(6050,a,6034,a)].
% 131.89/131.79 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),dvd_dvd(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),B)),C)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),D),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),dvd_dvd(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),D)),C)). [resolve(6050,a,6035,a)].
% 131.89/131.79 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),dvd_dvd(rat),B),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),B),A))). [resolve(6050,a,6036,a)].
% 131.89/131.79 Derived: one_one(rat) != ti(rat,A) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),dvd_dvd(rat),A),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),B))). [resolve(6050,a,6037,a)].
% 131.89/131.79 Derived: -no_zero_divisors(rat) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co302546470etprod(A,rat),C),B) != zero_zero(rat) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f483(A,rat,C,B)),B)). [resolve(6050,a,6038,a)].
% 131.89/131.79 Derived: -no_zero_divisors(rat) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co302546470etprod(A,rat),C),B) != zero_zero(rat) | hAPP(A,rat,C,f483(A,rat,C,B)) = zero_zero(rat). [resolve(6050,a,6039,a)].
% 131.89/131.79 Derived: -no_zero_divisors(rat) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co302546470etprod(A,rat),C),B) = zero_zero(rat) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),D),B)) | hAPP(A,rat,C,D) != zero_zero(rat). [resolve(6050,a,6040,a)].
% 131.89/131.79 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(A,rat,D,C) != zero_zero(rat) | hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co302546470etprod(A,rat),D),B) = zero_zero(rat). [resolve(6050,a,6041,a)].
% 131.89/131.79 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)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),dvd_dvd(rat),hAPP(A,rat,D,C)),hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co302546470etprod(A,rat),D),B))). [resolve(6050,a,6042,a)].
% 131.89/131.82 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),f489(A,rat,D,E,C,B)),C)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),dvd_dvd(rat),hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co302546470etprod(A,rat),D),C)),hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co302546470etprod(A,rat),E),B))). [resolve(6050,a,6043,a)].
% 131.89/131.82 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(rat,bool,hAPP(rat,fun(rat,bool),dvd_dvd(rat),hAPP(A,rat,D,f489(A,rat,D,E,C,B))),hAPP(A,rat,E,f489(A,rat,D,E,C,B)))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),dvd_dvd(rat),hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co302546470etprod(A,rat),D),C)),hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co302546470etprod(A,rat),E),B))). [resolve(6050,a,6044,a)].
% 131.89/131.82 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(nat,rat,semiring_1_of_nat(rat),A)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),B),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),B),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(nat,rat,semiring_1_of_nat(rat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),A),one_one(nat)))),C)))) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),one_one(rat)),one_one(rat))),hAPP(fun(nat,bool),rat,hAPP(fun(nat,rat),fun(fun(nat,bool),rat),big_co1399186613setsum(nat,rat),hAPP(fun(nat,rat),fun(nat,rat),hAPP(fun(rat,rat),fun(fun(nat,rat),fun(nat,rat)),combb(rat,rat,nat),hAPP(rat,fun(rat,rat),plus_plus(rat),B)),hAPP(rat,fun(nat,rat),hAPP(fun(nat,fun(rat,rat)),fun(rat,fun(nat,rat)),combc(nat,rat,rat),hAPP(fun(nat,rat),fun(nat,fun(rat,rat)),hAPP(fun(rat,fun(rat,rat)),fun(fun(nat,rat),fun(nat,fun(rat,rat))),combb(rat,fun(rat,rat),nat),times_times(rat)),semiring_1_of_nat(rat))),C))),hAPP(nat,fun(nat,bool),ord_lessThan(nat),A))). [resolve(6050,a,6045,a)].
% 131.89/131.82 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(nat,rat,semiring_1_of_nat(rat),A)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(nat,rat,semiring_1_of_nat(rat),A)),one_one(rat))) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),one_one(rat)),one_one(rat))),hAPP(fun(nat,bool),rat,hAPP(fun(nat,rat),fun(fun(nat,bool),rat),big_co1399186613setsum(nat,rat),semiring_1_of_nat(rat)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),one_one(nat)),A))). [resolve(6050,a,6046,a)].
% 131.89/131.82 Derived: hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f770(A,rat,B,C,D)),D)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),dvd_dvd(rat),B),hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),C),D))). [resolve(6050,a,6047,a)].
% 131.89/131.82 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),dvd_dvd(rat),A),hAPP(B,rat,C,f770(B,rat,A,C,D)))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),dvd_dvd(rat),A),hAPP(fun(B,bool),rat,hAPP(fun(B,rat),fun(fun(B,bool),rat),big_co1399186613setsum(B,rat),C),D))). [resolve(6050,a,6048,a)].
% 131.89/131.82 6051 comm_semiring_1(real) # label(arity_RealDef_Oreal___Rings_Ocomm__semiring__1) # label(axiom). [assumption].
% 131.89/131.82 Derived: hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),C),D)) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),C)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),B),D)). [resolve(6051,a,5985,a)].
% 131.89/131.82 Derived: hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),B)),C) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),C)),B). [resolve(6051,a,5986,a)].
% 131.99/131.83 Derived: hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),A). [resolve(6051,a,5987,a)].
% 131.99/131.83 Derived: hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),C)) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),C)). [resolve(6051,a,5988,a)].
% 131.99/131.83 Derived: hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),C) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),C)),B). [resolve(6051,a,5991,a)].
% 131.99/131.83 Derived: hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),D)) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),C)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),D)). [resolve(6051,a,5994,a)].
% 131.99/131.83 Derived: hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),B) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),B),A). [resolve(6051,a,5995,a)].
% 131.99/131.83 Derived: hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),B),C)) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),B),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),C)). [resolve(6051,a,5996,a)].
% 131.99/131.83 Derived: hAPP(real,real,hAPP(real,fun(real,real),times_times(real),one_one(real)),A) = ti(real,A). [resolve(6051,a,5999,a)].
% 131.99/131.83 Derived: hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),one_one(real)) = ti(real,A). [resolve(6051,a,6000,a)].
% 131.99/131.83 Derived: hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),one_one(real)),one_one(real))),A) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),A). [resolve(6051,a,6001,a)].
% 131.99/131.83 Derived: hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),one_one(real))),B) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),B),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)). [resolve(6051,a,6002,a)].
% 131.99/131.83 Derived: hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),one_one(real))),B) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),B). [resolve(6051,a,6003,a)].
% 131.99/131.83 Derived: hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),C) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),C)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),B),C)). [resolve(6051,a,6008,a)].
% 131.99/131.83 Derived: hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),B)),C) = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),C)). [resolve(6051,a,6009,a)].
% 131.99/131.83 Derived: hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),one_one(nat)) = ti(real,A). [resolve(6051,a,6010,a)].
% 131.99/131.83 Derived: hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),zero_zero(nat)) = one_one(real). [resolve(6051,a,6011,a)].
% 131.99/131.83 Derived: hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),hAPP(nat,nat,suc,B)) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),B)). [resolve(6051,a,6012,a)].
% 131.99/131.83 Derived: hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),hAPP(nat,nat,suc,B)) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),B)),A). [resolve(6051,a,6014,a)].
% 131.99/131.84 Derived: hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),C)) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),B)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),C)). [resolve(6051,a,6015,a)].
% 131.99/131.84 Derived: hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),A). [resolve(6051,a,6016,a)].
% 131.99/131.84 Derived: hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),B)) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),B)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),B)). [resolve(6051,a,6017,a)].
% 131.99/131.84 Derived: hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),B))) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),B)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),B))). [resolve(6051,a,6018,a)].
% 131.99/131.84 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),dvd_dvd(real),A),zero_zero(real))). [resolve(6051,a,6019,a)].
% 131.99/131.84 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),dvd_dvd(real),A),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),dvd_dvd(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),C)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),B),C))). [resolve(6051,a,6020,a)].
% 131.99/131.84 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),dvd_dvd(real),one_one(real)),A)). [resolve(6051,a,6021,a)].
% 131.99/131.84 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),dvd_dvd(real),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),dvd_dvd(real),A),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),dvd_dvd(real),A),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),B),C))). [resolve(6051,a,6022,a)].
% 131.99/131.84 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),dvd_dvd(real),A),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B))). [resolve(6051,a,6023,a)].
% 131.99/131.84 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),dvd_dvd(real),A),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),A))). [resolve(6051,a,6024,a)].
% 131.99/131.84 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),dvd_dvd(real),A),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),dvd_dvd(real),A),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),C))). [resolve(6051,a,6025,a)].
% 131.99/131.84 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),dvd_dvd(real),A),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),dvd_dvd(real),A),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),B))). [resolve(6051,a,6026,a)].
% 131.99/131.84 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),dvd_dvd(real),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),dvd_dvd(real),C),D)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),dvd_dvd(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),C)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),D))). [resolve(6051,a,6027,a)].
% 131.99/131.84 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),dvd_dvd(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),dvd_dvd(real),A),C)). [resolve(6051,a,6028,a)].
% 131.99/131.84 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),dvd_dvd(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),dvd_dvd(real),B),C)). [resolve(6051,a,6029,a)].
% 131.99/131.85 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),dvd_dvd(real),zero_zero(real)),A)) | zero_zero(real) = ti(real,A). [resolve(6051,a,6030,a)].
% 131.99/131.85 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),dvd_dvd(real),A),A)). [resolve(6051,a,6031,a)].
% 131.99/131.85 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),dvd_dvd(real),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),dvd_dvd(real),B),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),dvd_dvd(real),A),C)). [resolve(6051,a,6032,a)].
% 131.99/131.85 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),dvd_dvd(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),C),A)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),C),B))). [resolve(6051,a,6033,a)].
% 131.99/131.85 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),dvd_dvd(real),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),C),D)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),dvd_dvd(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),C)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),B),D))). [resolve(6051,a,6034,a)].
% 131.99/131.85 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),dvd_dvd(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),B)),C)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),D),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),dvd_dvd(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),D)),C)). [resolve(6051,a,6035,a)].
% 131.99/131.85 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),dvd_dvd(real),B),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),B),A))). [resolve(6051,a,6036,a)].
% 131.99/131.85 Derived: one_one(real) != ti(real,A) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),dvd_dvd(real),A),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),B))). [resolve(6051,a,6037,a)].
% 131.99/131.85 Derived: -no_zero_divisors(real) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co302546470etprod(A,real),C),B) != zero_zero(real) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f483(A,real,C,B)),B)). [resolve(6051,a,6038,a)].
% 131.99/131.85 Derived: -no_zero_divisors(real) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co302546470etprod(A,real),C),B) != zero_zero(real) | hAPP(A,real,C,f483(A,real,C,B)) = zero_zero(real). [resolve(6051,a,6039,a)].
% 131.99/131.85 Derived: -no_zero_divisors(real) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co302546470etprod(A,real),C),B) = zero_zero(real) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),D),B)) | hAPP(A,real,C,D) != zero_zero(real). [resolve(6051,a,6040,a)].
% 131.99/131.85 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(A,real,D,C) != zero_zero(real) | hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co302546470etprod(A,real),D),B) = zero_zero(real). [resolve(6051,a,6041,a)].
% 131.99/131.85 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)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),dvd_dvd(real),hAPP(A,real,D,C)),hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co302546470etprod(A,real),D),B))). [resolve(6051,a,6042,a)].
% 131.99/131.85 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),f489(A,real,D,E,C,B)),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),dvd_dvd(real),hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co302546470etprod(A,real),D),C)),hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co302546470etprod(A,real),E),B))). [resolve(6051,a,6043,a)].
% 131.99/131.87 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(real,bool,hAPP(real,fun(real,bool),dvd_dvd(real),hAPP(A,real,D,f489(A,real,D,E,C,B))),hAPP(A,real,E,f489(A,real,D,E,C,B)))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),dvd_dvd(real),hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co302546470etprod(A,real),D),C)),hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co302546470etprod(A,real),E),B))). [resolve(6051,a,6044,a)].
% 131.99/131.87 Derived: hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,semiring_1_of_nat(real),A)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),B),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),B),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,semiring_1_of_nat(real),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),A),one_one(nat)))),C)))) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),one_one(real)),one_one(real))),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),hAPP(real,fun(real,real),plus_plus(real),B)),hAPP(real,fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(real,fun(nat,real)),combc(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),semiring_1_of_nat(real))),C))),hAPP(nat,fun(nat,bool),ord_lessThan(nat),A))). [resolve(6051,a,6045,a)].
% 131.99/131.87 Derived: hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,semiring_1_of_nat(real),A)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,semiring_1_of_nat(real),A)),one_one(real))) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),one_one(real)),one_one(real))),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),semiring_1_of_nat(real)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),one_one(nat)),A))). [resolve(6051,a,6046,a)].
% 131.99/131.87 Derived: hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f770(A,real,B,C,D)),D)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),dvd_dvd(real),B),hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),C),D))). [resolve(6051,a,6047,a)].
% 131.99/131.87 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),dvd_dvd(real),A),hAPP(B,real,C,f770(B,real,A,C,D)))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),dvd_dvd(real),A),hAPP(fun(B,bool),real,hAPP(fun(B,real),fun(fun(B,bool),real),big_co1399186613setsum(B,real),C),D))). [resolve(6051,a,6048,a)].
% 131.99/131.87 6052 comm_semiring_1(complex) # label(arity_Complex_Ocomplex___Rings_Ocomm__semiring__1) # label(axiom). [assumption].
% 131.99/131.87 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),A),B)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),C),D)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),A),C)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),B),D)). [resolve(6052,a,5985,a)].
% 131.99/131.87 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),A),B)),C) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),A),C)),B). [resolve(6052,a,5986,a)].
% 131.99/131.87 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),B) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),B),A). [resolve(6052,a,5987,a)].
% 131.99/131.88 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),B),C)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),B),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),C)). [resolve(6052,a,5988,a)].
% 131.99/131.88 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),B)),C) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),C)),B). [resolve(6052,a,5991,a)].
% 131.99/131.88 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),B)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),C),D)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),C)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),B),D)). [resolve(6052,a,5994,a)].
% 131.99/131.88 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),A),B) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),B),A). [resolve(6052,a,5995,a)].
% 131.99/131.88 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),A),hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),B),C)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),B),hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),A),C)). [resolve(6052,a,5996,a)].
% 131.99/131.88 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),one_one(complex)),A) = ti(complex,A). [resolve(6052,a,5999,a)].
% 131.99/131.88 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),one_one(complex)) = ti(complex,A). [resolve(6052,a,6000,a)].
% 131.99/131.88 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),one_one(complex)),one_one(complex))),A) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),A),A). [resolve(6052,a,6001,a)].
% 131.99/131.88 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),A),one_one(complex))),B) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),B),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),B)). [resolve(6052,a,6002,a)].
% 131.99/131.88 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),A),one_one(complex))),B) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),B)),B). [resolve(6052,a,6003,a)].
% 131.99/131.88 Derived: hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),B)),C) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),A),C)),hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),B),C)). [resolve(6052,a,6008,a)].
% 131.99/131.88 Derived: hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),A),B)),C) = hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),C)). [resolve(6052,a,6009,a)].
% 131.99/131.88 Derived: hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),A),one_one(nat)) = ti(complex,A). [resolve(6052,a,6010,a)].
% 131.99/131.89 Derived: hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),A),zero_zero(nat)) = one_one(complex). [resolve(6052,a,6011,a)].
% 131.99/131.89 Derived: hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),A),hAPP(nat,nat,suc,B)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),A),B)). [resolve(6052,a,6012,a)].
% 131.99/131.89 Derived: hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),A),hAPP(nat,nat,suc,B)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),A),B)),A). [resolve(6052,a,6014,a)].
% 131.99/131.89 Derived: hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),C)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),A),B)),hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),A),C)). [resolve(6052,a,6015,a)].
% 131.99/131.89 Derived: hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),A). [resolve(6052,a,6016,a)].
% 131.99/131.89 Derived: hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),B)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),A),B)),hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),A),B)). [resolve(6052,a,6017,a)].
% 131.99/131.89 Derived: hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),A),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),B))) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),A),B)),hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),A),B))). [resolve(6052,a,6018,a)].
% 131.99/131.89 Derived: hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),dvd_dvd(complex),A),zero_zero(complex))). [resolve(6052,a,6019,a)].
% 131.99/131.89 Derived: -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),dvd_dvd(complex),A),B)) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),dvd_dvd(complex),hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),A),C)),hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),B),C))). [resolve(6052,a,6020,a)].
% 131.99/131.89 Derived: hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),dvd_dvd(complex),one_one(complex)),A)). [resolve(6052,a,6021,a)].
% 131.99/131.89 Derived: -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),dvd_dvd(complex),A),B)) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),dvd_dvd(complex),A),C)) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),dvd_dvd(complex),A),hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),B),C))). [resolve(6052,a,6022,a)].
% 131.99/131.89 Derived: hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),dvd_dvd(complex),A),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),B))). [resolve(6052,a,6023,a)].
% 131.99/131.89 Derived: hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),dvd_dvd(complex),A),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),B),A))). [resolve(6052,a,6024,a)].
% 131.99/131.89 Derived: -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),dvd_dvd(complex),A),B)) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),dvd_dvd(complex),A),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),B),C))). [resolve(6052,a,6025,a)].
% 131.99/131.89 Derived: -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),dvd_dvd(complex),A),B)) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),dvd_dvd(complex),A),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),C),B))). [resolve(6052,a,6026,a)].
% 131.99/131.89 Derived: -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),dvd_dvd(complex),A),B)) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),dvd_dvd(complex),C),D)) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),dvd_dvd(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),C)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),B),D))). [resolve(6052,a,6027,a)].
% 131.99/131.89 Derived: -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),dvd_dvd(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),B)),C)) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),dvd_dvd(complex),A),C)). [resolve(6052,a,6028,a)].
% 131.99/131.89 Derived: -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),dvd_dvd(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),B)),C)) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),dvd_dvd(complex),B),C)). [resolve(6052,a,6029,a)].
% 131.99/131.89 Derived: -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),dvd_dvd(complex),zero_zero(complex)),A)) | zero_zero(complex) = ti(complex,A). [resolve(6052,a,6030,a)].
% 131.99/131.89 Derived: hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),dvd_dvd(complex),A),A)). [resolve(6052,a,6031,a)].
% 131.99/131.89 Derived: -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),dvd_dvd(complex),A),B)) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),dvd_dvd(complex),B),C)) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),dvd_dvd(complex),A),C)). [resolve(6052,a,6032,a)].
% 131.99/131.89 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),dvd_dvd(complex),hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),C),A)),hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),C),B))). [resolve(6052,a,6033,a)].
% 131.99/131.89 Derived: -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),dvd_dvd(complex),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),C),D)) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),dvd_dvd(complex),hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),A),C)),hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),B),D))). [resolve(6052,a,6034,a)].
% 131.99/131.89 Derived: -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),dvd_dvd(complex),hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),A),B)),C)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),D),B)) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),dvd_dvd(complex),hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),A),D)),C)). [resolve(6052,a,6035,a)].
% 131.99/131.89 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A)) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),dvd_dvd(complex),B),hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),B),A))). [resolve(6052,a,6036,a)].
% 131.99/131.89 Derived: one_one(complex) != ti(complex,A) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),dvd_dvd(complex),A),hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),A),B))). [resolve(6052,a,6037,a)].
% 131.99/131.89 Derived: -no_zero_divisors(complex) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co302546470etprod(A,complex),C),B) != zero_zero(complex) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f483(A,complex,C,B)),B)). [resolve(6052,a,6038,a)].
% 131.99/131.89 Derived: -no_zero_divisors(complex) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co302546470etprod(A,complex),C),B) != zero_zero(complex) | hAPP(A,complex,C,f483(A,complex,C,B)) = zero_zero(complex). [resolve(6052,a,6039,a)].
% 131.99/131.90 Derived: -no_zero_divisors(complex) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co302546470etprod(A,complex),C),B) = zero_zero(complex) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),D),B)) | hAPP(A,complex,C,D) != zero_zero(complex). [resolve(6052,a,6040,a)].
% 131.99/131.90 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(A,complex,D,C) != zero_zero(complex) | hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co302546470etprod(A,complex),D),B) = zero_zero(complex). [resolve(6052,a,6041,a)].
% 131.99/131.90 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)) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),dvd_dvd(complex),hAPP(A,complex,D,C)),hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co302546470etprod(A,complex),D),B))). [resolve(6052,a,6042,a)].
% 131.99/131.90 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),f489(A,complex,D,E,C,B)),C)) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),dvd_dvd(complex),hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co302546470etprod(A,complex),D),C)),hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co302546470etprod(A,complex),E),B))). [resolve(6052,a,6043,a)].
% 131.99/131.90 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(complex,bool,hAPP(complex,fun(complex,bool),dvd_dvd(complex),hAPP(A,complex,D,f489(A,complex,D,E,C,B))),hAPP(A,complex,E,f489(A,complex,D,E,C,B)))) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),dvd_dvd(complex),hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co302546470etprod(A,complex),D),C)),hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co302546470etprod(A,complex),E),B))). [resolve(6052,a,6044,a)].
% 131.99/131.90 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(nat,complex,semiring_1_of_nat(complex),A)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),B),hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),B),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(nat,complex,semiring_1_of_nat(complex),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),A),one_one(nat)))),C)))) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),one_one(complex)),one_one(complex))),hAPP(fun(nat,bool),complex,hAPP(fun(nat,complex),fun(fun(nat,bool),complex),big_co1399186613setsum(nat,complex),hAPP(fun(nat,complex),fun(nat,complex),hAPP(fun(complex,complex),fun(fun(nat,complex),fun(nat,complex)),combb(complex,complex,nat),hAPP(complex,fun(complex,complex),plus_plus(complex),B)),hAPP(complex,fun(nat,complex),hAPP(fun(nat,fun(complex,complex)),fun(complex,fun(nat,complex)),combc(nat,complex,complex),hAPP(fun(nat,complex),fun(nat,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(nat,complex),fun(nat,fun(complex,complex))),combb(complex,fun(complex,complex),nat),times_times(complex)),semiring_1_of_nat(complex))),C))),hAPP(nat,fun(nat,bool),ord_lessThan(nat),A))). [resolve(6052,a,6045,a)].
% 131.99/131.90 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(nat,complex,semiring_1_of_nat(complex),A)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),A)),one_one(complex))) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),one_one(complex)),one_one(complex))),hAPP(fun(nat,bool),complex,hAPP(fun(nat,complex),fun(fun(nat,bool),complex),big_co1399186613setsum(nat,complex),semiring_1_of_nat(complex)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),one_one(nat)),A))). [resolve(6052,a,6046,a)].
% 132.08/131.92 Derived: hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f770(A,complex,B,C,D)),D)) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),dvd_dvd(complex),B),hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),C),D))). [resolve(6052,a,6047,a)].
% 132.08/131.92 Derived: -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),dvd_dvd(complex),A),hAPP(B,complex,C,f770(B,complex,A,C,D)))) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),dvd_dvd(complex),A),hAPP(fun(B,bool),complex,hAPP(fun(B,complex),fun(fun(B,bool),complex),big_co1399186613setsum(B,complex),C),D))). [resolve(6052,a,6048,a)].
% 132.08/131.92 6053 comm_semiring_1(code_code_numeral) # label(arity_Code__Numeral_Ocode__numeral___Rings_Ocomm__semiring__1) # label(axiom). [assumption].
% 132.08/131.92 Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),B),C)) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),B)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),C)). [resolve(6053,a,5984,a)].
% 132.08/131.92 Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),A),B)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),C),D)) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),A),C)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),B),D)). [resolve(6053,a,5985,a)].
% 132.08/131.92 Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),A),B)),C) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),A),C)),B). [resolve(6053,a,5986,a)].
% 132.08/131.92 Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),B) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),B),A). [resolve(6053,a,5987,a)].
% 132.08/131.92 Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),B),C)) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),B),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),C)). [resolve(6053,a,5988,a)].
% 132.08/131.92 Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),B)),C) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),C)),B). [resolve(6053,a,5991,a)].
% 132.08/131.92 Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),B)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),C),D)) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),C)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),B),D)). [resolve(6053,a,5994,a)].
% 132.08/131.92 Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),A),B) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),B),A). [resolve(6053,a,5995,a)].
% 132.08/131.92 Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),A),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),B),C)) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),B),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),A),C)). [resolve(6053,a,5996,a)].
% 132.08/131.92 Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),one_one(code_code_numeral)),A) = ti(code_code_numeral,A). [resolve(6053,a,5999,a)].
% 132.08/131.92 Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),one_one(code_code_numeral)) = ti(code_code_numeral,A). [resolve(6053,a,6000,a)].
% 132.08/131.92 Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),one_one(code_code_numeral)),one_one(code_code_numeral))),A) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),A),A). [resolve(6053,a,6001,a)].
% 132.08/131.92 Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),A),one_one(code_code_numeral))),B) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),B),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),B)). [resolve(6053,a,6002,a)].
% 132.08/131.93 Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),A),one_one(code_code_numeral))),B) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),B)),B). [resolve(6053,a,6003,a)].
% 132.08/131.93 Derived: hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),B)),C) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A),C)),hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),B),C)). [resolve(6053,a,6008,a)].
% 132.08/131.93 Derived: hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A),B)),C) = hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),C)). [resolve(6053,a,6009,a)].
% 132.08/131.93 Derived: hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A),one_one(nat)) = ti(code_code_numeral,A). [resolve(6053,a,6010,a)].
% 132.08/131.93 Derived: hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A),zero_zero(nat)) = one_one(code_code_numeral). [resolve(6053,a,6011,a)].
% 132.08/131.93 Derived: hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A),hAPP(nat,nat,suc,B)) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A),B)). [resolve(6053,a,6012,a)].
% 132.08/131.93 Derived: hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A),hAPP(nat,nat,suc,B)) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A),B)),A). [resolve(6053,a,6014,a)].
% 132.08/131.93 Derived: hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),C)) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A),B)),hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A),C)). [resolve(6053,a,6015,a)].
% 132.08/131.93 Derived: hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),A). [resolve(6053,a,6016,a)].
% 132.08/131.94 Derived: hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),B)) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A),B)),hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A),B)). [resolve(6053,a,6017,a)].
% 132.08/131.94 Derived: hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),B))) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A),B)),hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A),B))). [resolve(6053,a,6018,a)].
% 132.08/131.94 Derived: hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),A),zero_zero(code_code_numeral))). [resolve(6053,a,6019,a)].
% 132.08/131.94 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),A),B)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A),C)),hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),B),C))). [resolve(6053,a,6020,a)].
% 132.08/131.94 Derived: hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),one_one(code_code_numeral)),A)). [resolve(6053,a,6021,a)].
% 132.08/131.94 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),A),B)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),A),C)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),A),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),B),C))). [resolve(6053,a,6022,a)].
% 132.08/131.94 Derived: hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),A),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),B))). [resolve(6053,a,6023,a)].
% 132.08/131.94 Derived: hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),A),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),B),A))). [resolve(6053,a,6024,a)].
% 132.08/131.94 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),A),B)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),A),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),B),C))). [resolve(6053,a,6025,a)].
% 132.08/131.94 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),A),B)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),A),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),C),B))). [resolve(6053,a,6026,a)].
% 132.08/131.94 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),A),B)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),C),D)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),C)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),B),D))). [resolve(6053,a,6027,a)].
% 132.08/131.94 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),B)),C)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),A),C)). [resolve(6053,a,6028,a)].
% 132.08/131.94 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),B)),C)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),B),C)). [resolve(6053,a,6029,a)].
% 132.08/131.94 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),zero_zero(code_code_numeral)),A)) | zero_zero(code_code_numeral) = ti(code_code_numeral,A). [resolve(6053,a,6030,a)].
% 132.08/131.94 Derived: hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),A),A)). [resolve(6053,a,6031,a)].
% 132.08/131.94 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),A),B)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),B),C)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),A),C)). [resolve(6053,a,6032,a)].
% 132.08/131.94 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),C),A)),hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),C),B))). [resolve(6053,a,6033,a)].
% 132.08/131.94 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),C),D)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A),C)),hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),B),D))). [resolve(6053,a,6034,a)].
% 132.08/131.94 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A),B)),C)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),D),B)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A),D)),C)). [resolve(6053,a,6035,a)].
% 132.08/131.95 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),B),hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),B),A))). [resolve(6053,a,6036,a)].
% 132.08/131.95 Derived: one_one(code_code_numeral) != ti(code_code_numeral,A) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),A),hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A),B))). [resolve(6053,a,6037,a)].
% 132.08/131.95 Derived: -no_zero_divisors(code_code_numeral) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co302546470etprod(A,code_code_numeral),C),B) != zero_zero(code_code_numeral) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f483(A,code_code_numeral,C,B)),B)). [resolve(6053,a,6038,a)].
% 132.08/131.95 Derived: -no_zero_divisors(code_code_numeral) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co302546470etprod(A,code_code_numeral),C),B) != zero_zero(code_code_numeral) | hAPP(A,code_code_numeral,C,f483(A,code_code_numeral,C,B)) = zero_zero(code_code_numeral). [resolve(6053,a,6039,a)].
% 132.08/131.95 Derived: -no_zero_divisors(code_code_numeral) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co302546470etprod(A,code_code_numeral),C),B) = zero_zero(code_code_numeral) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),D),B)) | hAPP(A,code_code_numeral,C,D) != zero_zero(code_code_numeral). [resolve(6053,a,6040,a)].
% 132.08/131.95 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(A,code_code_numeral,D,C) != zero_zero(code_code_numeral) | hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co302546470etprod(A,code_code_numeral),D),B) = zero_zero(code_code_numeral). [resolve(6053,a,6041,a)].
% 132.08/131.95 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)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),hAPP(A,code_code_numeral,D,C)),hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co302546470etprod(A,code_code_numeral),D),B))). [resolve(6053,a,6042,a)].
% 132.08/131.95 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),f489(A,code_code_numeral,D,E,C,B)),C)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co302546470etprod(A,code_code_numeral),D),C)),hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co302546470etprod(A,code_code_numeral),E),B))). [resolve(6053,a,6043,a)].
% 132.08/131.95 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(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),hAPP(A,code_code_numeral,D,f489(A,code_code_numeral,D,E,C,B))),hAPP(A,code_code_numeral,E,f489(A,code_code_numeral,D,E,C,B)))) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co302546470etprod(A,code_code_numeral),D),C)),hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co302546470etprod(A,code_code_numeral),E),B))). [resolve(6053,a,6044,a)].
% 132.08/131.95 Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),hAPP(nat,code_code_numeral,semiring_1_of_nat(code_code_numeral),A)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),B),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),B),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),hAPP(nat,code_code_numeral,semiring_1_of_nat(code_code_numeral),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),A),one_one(nat)))),C)))) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),one_one(code_code_numeral)),one_one(code_code_numeral))),hAPP(fun(nat,bool),code_code_numeral,hAPP(fun(nat,code_code_numeral),fun(fun(nat,bool),code_code_numeral),big_co1399186613setsum(nat,code_code_numeral),hAPP(fun(nat,code_code_numeral),fun(nat,code_code_numeral),hAPP(fun(code_code_numeral,code_code_numeral),fun(fun(nat,code_code_numeral),fun(nat,code_code_numeral)),combb(code_code_numeral,code_code_numeral,nat),hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),B)),hAPP(code_code_numeral,fun(nat,code_code_numeral),hAPP(fun(nat,fun(code_code_numeral,code_code_numeral)),fun(code_code_numeral,fun(nat,code_code_numeral)),combc(nat,code_code_numeral,code_code_numeral),hAPP(fun(nat,code_code_numeral),fun(nat,fun(code_code_numeral,code_code_numeral)),hAPP(fun(code_code_numeral,fun(code_code_numeral,code_code_numeral)),fun(fun(nat,code_code_numeral),fun(nat,fun(code_code_numeral,code_code_numeral))),combb(code_code_numeral,fun(code_code_numeral,code_code_numeral),nat),times_times(code_code_numeral)),semiring_1_of_nat(code_code_numeral))),C))),hAPP(nat,fun(nat,bool),ord_lessThan(nat),A))). [resolve(6053,a,6045,a)].
% 132.08/131.95 Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),hAPP(nat,code_code_numeral,semiring_1_of_nat(code_code_numeral),A)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),hAPP(nat,code_code_numeral,semiring_1_of_nat(code_code_numeral),A)),one_one(code_code_numeral))) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),one_one(code_code_numeral)),one_one(code_code_numeral))),hAPP(fun(nat,bool),code_code_numeral,hAPP(fun(nat,code_code_numeral),fun(fun(nat,bool),code_code_numeral),big_co1399186613setsum(nat,code_code_numeral),semiring_1_of_nat(code_code_numeral)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),one_one(nat)),A))). [resolve(6053,a,6046,a)].
% 132.08/131.95 Derived: hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f770(A,code_code_numeral,B,C,D)),D)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),B),hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),C),D))). [resolve(6053,a,6047,a)].
% 132.08/131.95 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),A),hAPP(B,code_code_numeral,C,f770(B,code_code_numeral,A,C,D)))) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),A),hAPP(fun(B,bool),code_code_numeral,hAPP(fun(B,code_code_numeral),fun(fun(B,bool),code_code_numeral),big_co1399186613setsum(B,code_code_numeral),C),D))). [resolve(6053,a,6048,a)].
% 132.08/131.96 6054 comm_semiring_1(quickcheck_code_int) # label(arity_Quickcheck__Narrowing_Ocode__int___Rings_Ocomm__semiring__1) # label(axiom). [assumption].
% 132.08/131.96 Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),B),C)) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),B)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),C)). [resolve(6054,a,5984,a)].
% 132.08/131.96 Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),A),B)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),C),D)) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),A),C)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),B),D)). [resolve(6054,a,5985,a)].
% 132.08/131.96 Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),A),B)),C) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),A),C)),B). [resolve(6054,a,5986,a)].
% 132.08/131.96 Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),B) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),B),A). [resolve(6054,a,5987,a)].
% 132.08/131.96 Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),B),C)) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),B),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),C)). [resolve(6054,a,5988,a)].
% 132.08/131.96 Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),B)),C) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),C)),B). [resolve(6054,a,5991,a)].
% 132.08/131.97 Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),B)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),C),D)) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),C)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),B),D)). [resolve(6054,a,5994,a)].
% 132.08/131.97 Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),A),B) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),B),A). [resolve(6054,a,5995,a)].
% 132.08/131.97 Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),A),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),B),C)) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),B),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),A),C)). [resolve(6054,a,5996,a)].
% 132.08/131.97 Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),one_one(quickcheck_code_int)),A) = ti(quickcheck_code_int,A). [resolve(6054,a,5999,a)].
% 132.08/131.97 Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),one_one(quickcheck_code_int)) = ti(quickcheck_code_int,A). [resolve(6054,a,6000,a)].
% 132.08/131.97 Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),one_one(quickcheck_code_int)),one_one(quickcheck_code_int))),A) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),A),A). [resolve(6054,a,6001,a)].
% 132.08/131.97 Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),A),one_one(quickcheck_code_int))),B) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),B),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),B)). [resolve(6054,a,6002,a)].
% 132.08/131.97 Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),A),one_one(quickcheck_code_int))),B) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),B)),B). [resolve(6054,a,6003,a)].
% 132.08/131.97 Derived: hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),B)),C) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A),C)),hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),B),C)). [resolve(6054,a,6008,a)].
% 132.08/131.97 Derived: hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A),B)),C) = hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),C)). [resolve(6054,a,6009,a)].
% 132.08/131.97 Derived: hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A),one_one(nat)) = ti(quickcheck_code_int,A). [resolve(6054,a,6010,a)].
% 132.08/131.97 Derived: hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A),zero_zero(nat)) = one_one(quickcheck_code_int). [resolve(6054,a,6011,a)].
% 132.08/131.97 Derived: hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A),hAPP(nat,nat,suc,B)) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A),B)). [resolve(6054,a,6012,a)].
% 132.08/131.97 Derived: hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A),hAPP(nat,nat,suc,B)) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A),B)),A). [resolve(6054,a,6014,a)].
% 132.08/131.97 Derived: hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),C)) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A),B)),hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A),C)). [resolve(6054,a,6015,a)].
% 132.08/131.97 Derived: hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),A). [resolve(6054,a,6016,a)].
% 132.08/131.98 Derived: hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),B)) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A),B)),hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A),B)). [resolve(6054,a,6017,a)].
% 132.08/131.98 Derived: hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),B))) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A),B)),hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A),B))). [resolve(6054,a,6018,a)].
% 132.08/131.98 Derived: hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),A),zero_zero(quickcheck_code_int))). [resolve(6054,a,6019,a)].
% 132.08/131.98 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),A),B)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A),C)),hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),B),C))). [resolve(6054,a,6020,a)].
% 132.08/131.98 Derived: hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),one_one(quickcheck_code_int)),A)). [resolve(6054,a,6021,a)].
% 132.08/131.98 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),A),B)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),A),C)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),A),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),B),C))). [resolve(6054,a,6022,a)].
% 132.08/131.98 Derived: hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),A),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),B))). [resolve(6054,a,6023,a)].
% 132.08/131.98 Derived: hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),A),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),B),A))). [resolve(6054,a,6024,a)].
% 132.08/131.98 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),A),B)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),A),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),B),C))). [resolve(6054,a,6025,a)].
% 132.16/131.98 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),A),B)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),A),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),C),B))). [resolve(6054,a,6026,a)].
% 132.16/131.98 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),A),B)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),C),D)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),C)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),B),D))). [resolve(6054,a,6027,a)].
% 132.16/131.98 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),B)),C)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),A),C)). [resolve(6054,a,6028,a)].
% 132.16/131.98 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),B)),C)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),B),C)). [resolve(6054,a,6029,a)].
% 132.16/131.98 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),zero_zero(quickcheck_code_int)),A)) | zero_zero(quickcheck_code_int) = ti(quickcheck_code_int,A). [resolve(6054,a,6030,a)].
% 132.16/131.98 Derived: hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),A),A)). [resolve(6054,a,6031,a)].
% 132.16/131.98 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),A),B)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),B),C)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),A),C)). [resolve(6054,a,6032,a)].
% 132.16/131.98 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),C),A)),hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),C),B))). [resolve(6054,a,6033,a)].
% 132.16/131.98 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),C),D)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A),C)),hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),B),D))). [resolve(6054,a,6034,a)].
% 132.16/131.98 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A),B)),C)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),D),B)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A),D)),C)). [resolve(6054,a,6035,a)].
% 132.16/131.99 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),B),hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),B),A))). [resolve(6054,a,6036,a)].
% 132.16/131.99 Derived: one_one(quickcheck_code_int) != ti(quickcheck_code_int,A) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),A),hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A),B))). [resolve(6054,a,6037,a)].
% 132.16/131.99 Derived: -no_zero_divisors(quickcheck_code_int) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co302546470etprod(A,quickcheck_code_int),C),B) != zero_zero(quickcheck_code_int) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f483(A,quickcheck_code_int,C,B)),B)). [resolve(6054,a,6038,a)].
% 132.16/131.99 Derived: -no_zero_divisors(quickcheck_code_int) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co302546470etprod(A,quickcheck_code_int),C),B) != zero_zero(quickcheck_code_int) | hAPP(A,quickcheck_code_int,C,f483(A,quickcheck_code_int,C,B)) = zero_zero(quickcheck_code_int). [resolve(6054,a,6039,a)].
% 132.16/131.99 Derived: -no_zero_divisors(quickcheck_code_int) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co302546470etprod(A,quickcheck_code_int),C),B) = zero_zero(quickcheck_code_int) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),D),B)) | hAPP(A,quickcheck_code_int,C,D) != zero_zero(quickcheck_code_int). [resolve(6054,a,6040,a)].
% 132.16/131.99 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(A,quickcheck_code_int,D,C) != zero_zero(quickcheck_code_int) | hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co302546470etprod(A,quickcheck_code_int),D),B) = zero_zero(quickcheck_code_int). [resolve(6054,a,6041,a)].
% 132.16/131.99 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)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),hAPP(A,quickcheck_code_int,D,C)),hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co302546470etprod(A,quickcheck_code_int),D),B))). [resolve(6054,a,6042,a)].
% 132.16/131.99 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),f489(A,quickcheck_code_int,D,E,C,B)),C)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co302546470etprod(A,quickcheck_code_int),D),C)),hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co302546470etprod(A,quickcheck_code_int),E),B))). [resolve(6054,a,6043,a)].
% 132.16/131.99 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(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),hAPP(A,quickcheck_code_int,D,f489(A,quickcheck_code_int,D,E,C,B))),hAPP(A,quickcheck_code_int,E,f489(A,quickcheck_code_int,D,E,C,B)))) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co302546470etprod(A,quickcheck_code_int),D),C)),hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co302546470etprod(A,quickcheck_code_int),E),B))). [resolve(6054,a,6044,a)].
% 132.16/131.99 Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),hAPP(nat,quickcheck_code_int,semiring_1_of_nat(quickcheck_code_int),A)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),B),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),B),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),hAPP(nat,quickcheck_code_int,semiring_1_of_nat(quickcheck_code_int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),A),one_one(nat)))),C)))) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),one_one(quickcheck_code_int)),one_one(quickcheck_code_int))),hAPP(fun(nat,bool),quickcheck_code_int,hAPP(fun(nat,quickcheck_code_int),fun(fun(nat,bool),quickcheck_code_int),big_co1399186613setsum(nat,quickcheck_code_int),hAPP(fun(nat,quickcheck_code_int),fun(nat,quickcheck_code_int),hAPP(fun(quickcheck_code_int,quickcheck_code_int),fun(fun(nat,quickcheck_code_int),fun(nat,quickcheck_code_int)),combb(quickcheck_code_int,quickcheck_code_int,nat),hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),B)),hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),hAPP(fun(nat,fun(quickcheck_code_int,quickcheck_code_int)),fun(quickcheck_code_int,fun(nat,quickcheck_code_int)),combc(nat,quickcheck_code_int,quickcheck_code_int),hAPP(fun(nat,quickcheck_code_int),fun(nat,fun(quickcheck_code_int,quickcheck_code_int)),hAPP(fun(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int)),fun(fun(nat,quickcheck_code_int),fun(nat,fun(quickcheck_code_int,quickcheck_code_int))),combb(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),nat),times_times(quickcheck_code_int)),semiring_1_of_nat(quickcheck_code_int))),C))),hAPP(nat,fun(nat,bool),ord_lessThan(nat),A))). [resolve(6054,a,6045,a)].
% 132.16/131.99 Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),hAPP(nat,quickcheck_code_int,semiring_1_of_nat(quickcheck_code_int),A)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),hAPP(nat,quickcheck_code_int,semiring_1_of_nat(quickcheck_code_int),A)),one_one(quickcheck_code_int))) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),one_one(quickcheck_code_int)),one_one(quickcheck_code_int))),hAPP(fun(nat,bool),quickcheck_code_int,hAPP(fun(nat,quickcheck_code_int),fun(fun(nat,bool),quickcheck_code_int),big_co1399186613setsum(nat,quickcheck_code_int),semiring_1_of_nat(quickcheck_code_int)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),one_one(nat)),A))). [resolve(6054,a,6046,a)].
% 139.98/139.81 Derived: hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f770(A,quickcheck_code_int,B,C,D)),D)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),B),hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),C),D))). [resolve(6054,a,6047,a)].
% 139.98/139.81 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),A),hAPP(B,quickcheck_code_int,C,f770(B,quickcheck_code_int,A,C,D)))) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),A),hAPP(fun(B,bool),quickcheck_code_int,hAPP(fun(B,quickcheck_code_int),fun(fun(B,bool),quickcheck_code_int),big_co1399186613setsum(B,quickcheck_code_int),C),D))). [resolve(6054,a,6048,a)].
% 139.98/139.81 6055 ordered_ring(int) # label(arity_Int_Oint___Rings_Oordered__ring) # label(axiom). [assumption].
% 139.98/139.81 6056 -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_81_le__add__iff1) # label(axiom). [clausify(211)].
% 139.98/139.81 6057 -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_81_le__add__iff1) # label(axiom). [clausify(211)].
% 139.98/139.81 6058 -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_82_le__add__iff2) # label(axiom). [clausify(212)].
% 139.98/139.81 6059 -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_82_le__add__iff2) # label(axiom). [clausify(212)].
% 139.98/139.81 6060 -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_84_less__add__iff1) # label(axiom). [clausify(214)].
% 139.98/139.81 6061 -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_84_less__add__iff1) # label(axiom). [clausify(214)].
% 139.98/139.82 6062 -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_85_less__add__iff2) # label(axiom). [clausify(215)].
% 139.98/139.82 6063 -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_85_less__add__iff2) # label(axiom). [clausify(215)].
% 139.98/139.82 6064 -ordered_ring(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C))) # label(fact_296_mult__nonpos__nonpos) # label(axiom). [clausify(425)].
% 139.98/139.82 6065 -ordered_ring(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),zero_zero(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),D)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D))) # label(fact_300_mult__right__mono__neg) # label(axiom). [clausify(429)].
% 139.98/139.82 6066 -ordered_ring(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),zero_zero(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),D),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),B))) # label(fact_301_mult__left__mono__neg) # label(axiom). [clausify(430)].
% 139.98/139.82 6067 -ordered_ring(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C))) # label(fact_304_split__mult__pos__le) # label(axiom). [clausify(433)].
% 139.98/139.82 6068 -ordered_ring(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C))) # label(fact_304_split__mult__pos__le) # label(axiom). [clausify(433)].
% 139.98/139.82 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(6055,a,6056,a)].
% 139.98/139.82 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(6055,a,6057,a)].
% 139.98/139.82 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(6055,a,6058,a)].
% 139.98/139.82 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(6055,a,6059,a)].
% 139.98/139.82 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(6055,a,6060,a)].
% 139.98/139.82 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(6055,a,6061,a)].
% 139.98/139.82 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(6055,a,6062,a)].
% 139.98/139.82 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(6055,a,6063,a)].
% 139.98/139.82 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_eq(int),B),zero_zero(int))) | 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),A),B))). [resolve(6055,a,6064,a)].
% 139.98/139.82 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),zero_zero(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),C)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),C))). [resolve(6055,a,6065,a)].
% 140.01/139.85 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),zero_zero(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),C),B)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),A))). [resolve(6055,a,6066,a)].
% 140.01/139.85 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),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B))). [resolve(6055,a,6067,a)].
% 140.01/139.85 6069 ordered_ring(rat) # label(arity_Rat_Orat___Rings_Oordered__ring) # label(axiom). [assumption].
% 140.01/139.85 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B)),C)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),D),B)),E))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),A),D)),B)),C)),E)). [resolve(6069,a,6056,a)].
% 140.01/139.85 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B)),C)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),D),B)),E))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),A),D)),B)),C)),E)). [resolve(6069,a,6057,a)].
% 140.01/139.85 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B)),C)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),D),B)),E))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),C),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),D),A)),B)),E))). [resolve(6069,a,6058,a)].
% 140.01/139.85 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B)),C)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),D),B)),E))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),C),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),D),A)),B)),E))). [resolve(6069,a,6059,a)].
% 140.01/139.85 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B)),C)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),D),B)),E))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),A),D)),B)),C)),E)). [resolve(6069,a,6060,a)].
% 140.01/139.85 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B)),C)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),D),B)),E))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),A),D)),B)),C)),E)). [resolve(6069,a,6061,a)].
% 140.01/139.88 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B)),C)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),D),B)),E))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),C),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),D),A)),B)),E))). [resolve(6069,a,6062,a)].
% 140.01/139.88 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B)),C)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),D),B)),E))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),C),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),D),A)),B)),E))). [resolve(6069,a,6063,a)].
% 140.01/139.88 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),B),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B))). [resolve(6069,a,6064,a)].
% 140.01/139.88 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),C),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),B),C)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),C))). [resolve(6069,a,6065,a)].
% 140.01/139.88 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),C),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),C),B)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),C),A))). [resolve(6069,a,6066,a)].
% 140.01/139.88 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B))). [resolve(6069,a,6067,a)].
% 140.01/139.88 6070 ordered_ring(real) # label(arity_RealDef_Oreal___Rings_Oordered__ring) # label(axiom). [assumption].
% 140.01/139.88 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),C)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),D),B)),E))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),D)),B)),C)),E)). [resolve(6070,a,6056,a)].
% 140.01/139.88 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),C)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),D),B)),E))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),D)),B)),C)),E)). [resolve(6070,a,6057,a)].
% 140.01/139.89 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),C)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),D),B)),E))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),C),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),D),A)),B)),E))). [resolve(6070,a,6058,a)].
% 140.01/139.89 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),C)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),D),B)),E))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),C),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),D),A)),B)),E))). [resolve(6070,a,6059,a)].
% 140.01/139.89 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),C)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),D),B)),E))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),D)),B)),C)),E)). [resolve(6070,a,6060,a)].
% 140.01/139.89 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),C)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),D),B)),E))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),D)),B)),C)),E)). [resolve(6070,a,6061,a)].
% 140.01/139.89 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),C)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),D),B)),E))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),C),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),D),A)),B)),E))). [resolve(6070,a,6062,a)].
% 140.01/139.89 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),C)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),D),B)),E))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),C),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),D),A)),B)),E))). [resolve(6070,a,6063,a)].
% 140.01/139.89 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B))). [resolve(6070,a,6064,a)].
% 143.95/143.83 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),C),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),C)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),C))). [resolve(6070,a,6065,a)].
% 143.95/143.83 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),C),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),B)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),A))). [resolve(6070,a,6066,a)].
% 143.95/143.83 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B))). [resolve(6070,a,6067,a)].
% 143.95/143.83 6071 ring_char_0(int) # label(arity_Int_Oint___Int_Oring__char__0) # label(axiom). [assumption].
% 143.95/143.83 6072 -number_ring(A) | -ring_char_0(A) | hAPP(int,A,number_number_of(A),B) != hAPP(int,A,number_number_of(A),C) | B = C # label(fact_95_eq__number__of) # label(axiom). [clausify(225)].
% 143.95/143.83 6073 -number_ring(A) | -ring_char_0(A) | hAPP(int,A,number_number_of(A),B) = hAPP(int,A,number_number_of(A),C) | B != C # label(fact_95_eq__number__of) # label(axiom). [clausify(225)].
% 143.95/143.83 6074 -ring_char_0(A) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),B),ring_1_Ints(A))) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),B) != zero_zero(A) | zero_zero(A) = ti(A,B) # label(fact_663_Ints__double__eq__0__iff) # label(axiom). [clausify(783)].
% 143.95/143.83 6075 -ring_char_0(A) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),B),ring_1_Ints(A))) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),B) = zero_zero(A) | zero_zero(A) != ti(A,B) # label(fact_663_Ints__double__eq__0__iff) # label(axiom). [clausify(783)].
% 143.95/143.83 6076 -ring_char_0(A) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),B),ring_1_Ints(A))) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),one_one(A)),B)),B) != zero_zero(A) # label(fact_680_Ints__odd__nonzero) # label(axiom). [clausify(800)].
% 143.95/143.83 6077 -number_ring(A) | -ring_char_0(A) | -hBOOL(hAPP(A,bool,iszero(A),hAPP(int,A,number_number_of(A),hAPP(int,int,bit1,B)))) # label(fact_1668_iszero__number__of__Bit1) # label(axiom). [clausify(1742)].
% 143.95/143.83 6078 -number_ring(A) | -ring_char_0(A) | -hBOOL(hAPP(A,bool,iszero(A),hAPP(int,A,number_number_of(A),hAPP(int,int,bit0,B)))) | hBOOL(hAPP(A,bool,iszero(A),hAPP(int,A,number_number_of(A),B))) # label(fact_1787_iszero__number__of__Bit0) # label(axiom). [clausify(1848)].
% 143.95/143.83 6079 -number_ring(A) | -ring_char_0(A) | hBOOL(hAPP(A,bool,iszero(A),hAPP(int,A,number_number_of(A),hAPP(int,int,bit0,B)))) | -hBOOL(hAPP(A,bool,iszero(A),hAPP(int,A,number_number_of(A),B))) # label(fact_1787_iszero__number__of__Bit0) # label(axiom). [clausify(1848)].
% 143.95/143.83 6080 -ring_char_0(A) | hAPP(int,A,ring_1_of_int(A),B) != hAPP(int,A,ring_1_of_int(A),C) | B = C # label(fact_3578_of__int__eq__iff) # label(axiom). [clausify(3531)].
% 143.95/143.83 6081 -ring_char_0(A) | hAPP(int,A,ring_1_of_int(A),B) = hAPP(int,A,ring_1_of_int(A),C) | B != C # label(fact_3578_of__int__eq__iff) # label(axiom). [clausify(3531)].
% 143.95/143.83 6082 -ring_char_0(A) | hAPP(int,A,ring_1_of_int(A),B) != zero_zero(A) | zero_zero(int) = B # label(fact_3591_of__int__0__eq__iff) # label(axiom). [clausify(3544)].
% 143.95/143.83 6083 -ring_char_0(A) | hAPP(int,A,ring_1_of_int(A),B) = zero_zero(A) | zero_zero(int) != B # label(fact_3591_of__int__0__eq__iff) # label(axiom). [clausify(3544)].
% 143.95/143.83 6084 -ring_char_0(A) | hAPP(int,A,ring_1_of_int(A),B) != zero_zero(A) | zero_zero(int) = B # label(fact_3592_of__int__eq__0__iff) # label(axiom). [clausify(3545)].
% 143.95/143.83 6085 -ring_char_0(A) | hAPP(int,A,ring_1_of_int(A),B) = zero_zero(A) | zero_zero(int) != B # label(fact_3592_of__int__eq__0__iff) # label(axiom). [clausify(3545)].
% 144.05/143.87 Derived: -number_ring(int) | hAPP(int,int,number_number_of(int),A) != hAPP(int,int,number_number_of(int),B) | A = B. [resolve(6071,a,6072,b)].
% 144.05/143.87 Derived: -number_ring(int) | hAPP(int,int,number_number_of(int),A) = hAPP(int,int,number_number_of(int),B) | A != B. [resolve(6071,a,6073,b)].
% 144.05/143.87 Derived: -hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),A),ring_1_Ints(int))) | hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),A) != zero_zero(int) | zero_zero(int) = ti(int,A). [resolve(6071,a,6074,a)].
% 144.05/143.87 Derived: -hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),A),ring_1_Ints(int))) | hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),A) = zero_zero(int) | zero_zero(int) != ti(int,A). [resolve(6071,a,6075,a)].
% 144.05/143.87 Derived: -hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),A),ring_1_Ints(int))) | hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),A)),A) != zero_zero(int). [resolve(6071,a,6076,a)].
% 144.05/143.87 Derived: -number_ring(int) | -hBOOL(hAPP(int,bool,iszero(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit1,A)))). [resolve(6071,a,6077,b)].
% 144.05/143.87 Derived: -number_ring(int) | -hBOOL(hAPP(int,bool,iszero(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,A)))) | hBOOL(hAPP(int,bool,iszero(int),hAPP(int,int,number_number_of(int),A))). [resolve(6071,a,6078,b)].
% 144.05/143.87 Derived: -number_ring(int) | hBOOL(hAPP(int,bool,iszero(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,A)))) | -hBOOL(hAPP(int,bool,iszero(int),hAPP(int,int,number_number_of(int),A))). [resolve(6071,a,6079,b)].
% 144.05/143.87 Derived: hAPP(int,int,ring_1_of_int(int),A) != hAPP(int,int,ring_1_of_int(int),B) | A = B. [resolve(6071,a,6080,a)].
% 144.05/143.87 Derived: hAPP(int,int,ring_1_of_int(int),A) = hAPP(int,int,ring_1_of_int(int),B) | A != B. [resolve(6071,a,6081,a)].
% 144.05/143.87 Derived: hAPP(int,int,ring_1_of_int(int),A) != zero_zero(int) | zero_zero(int) = A. [resolve(6071,a,6082,a)].
% 144.05/143.87 6086 ring_char_0(rat) # label(arity_Rat_Orat___Int_Oring__char__0) # label(axiom). [assumption].
% 144.05/143.87 Derived: -number_ring(rat) | hAPP(int,rat,number_number_of(rat),A) != hAPP(int,rat,number_number_of(rat),B) | A = B. [resolve(6086,a,6072,b)].
% 144.05/143.87 Derived: -number_ring(rat) | hAPP(int,rat,number_number_of(rat),A) = hAPP(int,rat,number_number_of(rat),B) | A != B. [resolve(6086,a,6073,b)].
% 144.05/143.87 Derived: -hBOOL(hAPP(fun(rat,bool),bool,hAPP(rat,fun(fun(rat,bool),bool),member(rat),A),ring_1_Ints(rat))) | hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),A) != zero_zero(rat) | zero_zero(rat) = ti(rat,A). [resolve(6086,a,6074,a)].
% 144.05/143.87 Derived: -hBOOL(hAPP(fun(rat,bool),bool,hAPP(rat,fun(fun(rat,bool),bool),member(rat),A),ring_1_Ints(rat))) | hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),A) = zero_zero(rat) | zero_zero(rat) != ti(rat,A). [resolve(6086,a,6075,a)].
% 144.05/143.87 Derived: -hBOOL(hAPP(fun(rat,bool),bool,hAPP(rat,fun(fun(rat,bool),bool),member(rat),A),ring_1_Ints(rat))) | hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),one_one(rat)),A)),A) != zero_zero(rat). [resolve(6086,a,6076,a)].
% 144.05/143.87 Derived: -number_ring(rat) | -hBOOL(hAPP(rat,bool,iszero(rat),hAPP(int,rat,number_number_of(rat),hAPP(int,int,bit1,A)))). [resolve(6086,a,6077,b)].
% 144.05/143.87 Derived: -number_ring(rat) | -hBOOL(hAPP(rat,bool,iszero(rat),hAPP(int,rat,number_number_of(rat),hAPP(int,int,bit0,A)))) | hBOOL(hAPP(rat,bool,iszero(rat),hAPP(int,rat,number_number_of(rat),A))). [resolve(6086,a,6078,b)].
% 144.05/143.87 Derived: -number_ring(rat) | hBOOL(hAPP(rat,bool,iszero(rat),hAPP(int,rat,number_number_of(rat),hAPP(int,int,bit0,A)))) | -hBOOL(hAPP(rat,bool,iszero(rat),hAPP(int,rat,number_number_of(rat),A))). [resolve(6086,a,6079,b)].
% 144.05/143.87 Derived: hAPP(int,rat,ring_1_of_int(rat),A) != hAPP(int,rat,ring_1_of_int(rat),B) | A = B. [resolve(6086,a,6080,a)].
% 144.05/143.87 Derived: hAPP(int,rat,ring_1_of_int(rat),A) = hAPP(int,rat,ring_1_of_int(rat),B) | A != B. [resolve(6086,a,6081,a)].
% 144.08/143.92 Derived: hAPP(int,rat,ring_1_of_int(rat),A) != zero_zero(rat) | zero_zero(int) = A. [resolve(6086,a,6082,a)].
% 144.08/143.92 6087 ring_char_0(real) # label(arity_RealDef_Oreal___Int_Oring__char__0) # label(axiom). [assumption].
% 144.08/143.92 Derived: -number_ring(real) | hAPP(int,real,number_number_of(real),A) != hAPP(int,real,number_number_of(real),B) | A = B. [resolve(6087,a,6072,b)].
% 144.08/143.92 Derived: -number_ring(real) | hAPP(int,real,number_number_of(real),A) = hAPP(int,real,number_number_of(real),B) | A != B. [resolve(6087,a,6073,b)].
% 144.08/143.92 Derived: -hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),A),ring_1_Ints(real))) | hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),A) != zero_zero(real) | zero_zero(real) = ti(real,A). [resolve(6087,a,6074,a)].
% 144.08/143.92 Derived: -hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),A),ring_1_Ints(real))) | hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),A) = zero_zero(real) | zero_zero(real) != ti(real,A). [resolve(6087,a,6075,a)].
% 144.08/143.92 Derived: -hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),A),ring_1_Ints(real))) | hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),one_one(real)),A)),A) != zero_zero(real). [resolve(6087,a,6076,a)].
% 144.08/143.92 Derived: -number_ring(real) | -hBOOL(hAPP(real,bool,iszero(real),hAPP(int,real,number_number_of(real),hAPP(int,int,bit1,A)))). [resolve(6087,a,6077,b)].
% 144.08/143.92 Derived: -number_ring(real) | -hBOOL(hAPP(real,bool,iszero(real),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,A)))) | hBOOL(hAPP(real,bool,iszero(real),hAPP(int,real,number_number_of(real),A))). [resolve(6087,a,6078,b)].
% 144.08/143.92 Derived: -number_ring(real) | hBOOL(hAPP(real,bool,iszero(real),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,A)))) | -hBOOL(hAPP(real,bool,iszero(real),hAPP(int,real,number_number_of(real),A))). [resolve(6087,a,6079,b)].
% 144.08/143.92 Derived: hAPP(int,real,ring_1_of_int(real),A) != hAPP(int,real,ring_1_of_int(real),B) | A = B. [resolve(6087,a,6080,a)].
% 144.08/143.92 Derived: hAPP(int,real,ring_1_of_int(real),A) = hAPP(int,real,ring_1_of_int(real),B) | A != B. [resolve(6087,a,6081,a)].
% 144.08/143.92 Derived: hAPP(int,real,ring_1_of_int(real),A) != zero_zero(real) | zero_zero(int) = A. [resolve(6087,a,6082,a)].
% 144.08/143.92 6088 ring_char_0(complex) # label(arity_Complex_Ocomplex___Int_Oring__char__0) # label(axiom). [assumption].
% 144.08/143.92 Derived: -number_ring(complex) | hAPP(int,complex,number_number_of(complex),A) != hAPP(int,complex,number_number_of(complex),B) | A = B. [resolve(6088,a,6072,b)].
% 144.08/143.92 Derived: -number_ring(complex) | hAPP(int,complex,number_number_of(complex),A) = hAPP(int,complex,number_number_of(complex),B) | A != B. [resolve(6088,a,6073,b)].
% 144.08/143.92 Derived: -hBOOL(hAPP(fun(complex,bool),bool,hAPP(complex,fun(fun(complex,bool),bool),member(complex),A),ring_1_Ints(complex))) | hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),A),A) != zero_zero(complex) | zero_zero(complex) = ti(complex,A). [resolve(6088,a,6074,a)].
% 144.08/143.92 Derived: -hBOOL(hAPP(fun(complex,bool),bool,hAPP(complex,fun(fun(complex,bool),bool),member(complex),A),ring_1_Ints(complex))) | hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),A),A) = zero_zero(complex) | zero_zero(complex) != ti(complex,A). [resolve(6088,a,6075,a)].
% 144.08/143.92 Derived: -hBOOL(hAPP(fun(complex,bool),bool,hAPP(complex,fun(fun(complex,bool),bool),member(complex),A),ring_1_Ints(complex))) | hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),one_one(complex)),A)),A) != zero_zero(complex). [resolve(6088,a,6076,a)].
% 144.08/143.92 Derived: -number_ring(complex) | -hBOOL(hAPP(complex,bool,iszero(complex),hAPP(int,complex,number_number_of(complex),hAPP(int,int,bit1,A)))). [resolve(6088,a,6077,b)].
% 144.08/143.92 Derived: -number_ring(complex) | -hBOOL(hAPP(complex,bool,iszero(complex),hAPP(int,complex,number_number_of(complex),hAPP(int,int,bit0,A)))) | hBOOL(hAPP(complex,bool,iszero(complex),hAPP(int,complex,number_number_of(complex),A))). [resolve(6088,a,6078,b)].
% 148.12/147.98 Derived: -number_ring(complex) | hBOOL(hAPP(complex,bool,iszero(complex),hAPP(int,complex,number_number_of(complex),hAPP(int,int,bit0,A)))) | -hBOOL(hAPP(complex,bool,iszero(complex),hAPP(int,complex,number_number_of(complex),A))). [resolve(6088,a,6079,b)].
% 148.12/147.98 Derived: hAPP(int,complex,ring_1_of_int(complex),A) != hAPP(int,complex,ring_1_of_int(complex),B) | A = B. [resolve(6088,a,6080,a)].
% 148.12/147.98 Derived: hAPP(int,complex,ring_1_of_int(complex),A) = hAPP(int,complex,ring_1_of_int(complex),B) | A != B. [resolve(6088,a,6081,a)].
% 148.12/147.98 Derived: hAPP(int,complex,ring_1_of_int(complex),A) != zero_zero(complex) | zero_zero(int) = A. [resolve(6088,a,6082,a)].
% 148.12/147.98 6089 linordered_idom(int) # label(arity_Int_Oint___Rings_Olinordered__idom) # label(axiom). [assumption].
% 148.12/147.98 6090 -number_ring(A) | -linordered_idom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),B)),hAPP(int,A,number_number_of(A),C))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),C)) # label(fact_96_less__number__of) # label(axiom). [clausify(226)].
% 148.12/147.98 6091 -number_ring(A) | -linordered_idom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),B)),hAPP(int,A,number_number_of(A),C))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),C)) # label(fact_96_less__number__of) # label(axiom). [clausify(226)].
% 148.12/147.98 6092 -number_ring(A) | -linordered_idom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(int,A,number_number_of(A),B)),hAPP(int,A,number_number_of(A),C))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),C)) # label(fact_97_le__number__of) # label(axiom). [clausify(227)].
% 148.12/147.98 6093 -number_ring(A) | -linordered_idom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(int,A,number_number_of(A),B)),hAPP(int,A,number_number_of(A),C))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),C)) # label(fact_97_le__number__of) # label(axiom). [clausify(227)].
% 148.12/147.98 6094 -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_99_linorder__neqE__linordered__idom) # label(axiom). [clausify(229)].
% 148.12/147.98 6095 -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_331_even__less__0__iff) # label(axiom). [clausify(460)].
% 148.12/147.98 6096 -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_331_even__less__0__iff) # label(axiom). [clausify(460)].
% 148.12/147.98 6097 -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_374_mult__left__le__one__le) # label(axiom). [clausify(502)].
% 148.12/147.98 6098 -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_375_mult__right__le__one__le) # label(axiom). [clausify(503)].
% 148.12/147.98 6099 -linordered_idom(A) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),B),ring_1_Ints(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),one_one(A)),B)),B)),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) # label(fact_448_Ints__odd__less__0) # label(axiom). [clausify(574)].
% 148.12/147.98 6100 -linordered_idom(A) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),B),ring_1_Ints(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),one_one(A)),B)),B)),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) # label(fact_448_Ints__odd__less__0) # label(axiom). [clausify(574)].
% 148.12/147.98 6101 -linordered_idom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,abs_abs(A),B)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) # label(fact_501_abs__less__iff) # label(axiom). [clausify(625)].
% 148.12/147.98 6102 -linordered_idom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,abs_abs(A),B)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,uminus_uminus(A),B)),C)) # label(fact_501_abs__less__iff) # label(axiom). [clausify(625)].
% 148.12/147.98 6103 -linordered_idom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,abs_abs(A),B)),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,uminus_uminus(A),B)),C)) # label(fact_501_abs__less__iff) # label(axiom). [clausify(625)].
% 148.12/147.98 6104 -number_ring(A) | -linordered_idom(A) | hAPP(A,A,abs_abs(A),hAPP(int,A,number_number_of(A),min)) = one_one(A) # label(fact_508_abs__minus__one) # label(axiom). [clausify(632)].
% 148.12/147.98 6105 -linordered_idom(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,abs_abs(A),B)),hAPP(A,A,abs_abs(A),B)) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),B) # label(fact_541_abs__mult__self) # label(axiom). [clausify(665)].
% 148.12/147.98 6106 -linordered_idom(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,abs_abs(A),B)),hAPP(A,A,abs_abs(A),C)) = hAPP(A,A,abs_abs(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)) # label(fact_542_abs__mult) # label(axiom). [clausify(666)].
% 148.12/147.98 6107 -linordered_idom(A) | hAPP(A,A,abs_abs(A),one_one(A)) = one_one(A) # label(fact_548_abs__one) # label(axiom). [clausify(672)].
% 148.12/147.98 6108 -number_ring(A) | -linordered_idom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),B)),zero_zero(A))) | hAPP(A,A,uminus_uminus(A),hAPP(int,A,number_number_of(A),B)) = hAPP(A,A,abs_abs(A),hAPP(int,A,number_number_of(A),B)) # label(fact_601_abs__number__of) # label(axiom). [clausify(722)].
% 148.12/147.98 6109 -number_ring(A) | -linordered_idom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),B)),zero_zero(A))) | hAPP(int,A,number_number_of(A),B) = hAPP(A,A,abs_abs(A),hAPP(int,A,number_number_of(A),B)) # label(fact_601_abs__number__of) # label(axiom). [clausify(722)].
% 148.12/147.98 6110 -linordered_idom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,abs_abs(A),B)),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,abs_abs(A),D)),E)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,abs_abs(A),B)),hAPP(A,A,abs_abs(A),D))),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),E))) # label(fact_617_abs__mult__less) # label(axiom). [clausify(738)].
% 148.12/147.98 6111 -linordered_idom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,abs_abs(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C))),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),C),D)),B)) # label(fact_624_abs__diff__less__iff) # label(axiom). [clausify(745)].
% 148.12/147.98 6112 -linordered_idom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,abs_abs(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C))),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),D))) # label(fact_624_abs__diff__less__iff) # label(axiom). [clausify(745)].
% 148.12/147.98 6113 -linordered_idom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,abs_abs(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C))),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),C),D)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),D))) # label(fact_624_abs__diff__less__iff) # label(axiom). [clausify(745)].
% 148.12/147.98 6114 -linordered_idom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(A,A,uminus_uminus(A),B))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) # label(fact_633_less__minus__self__iff) # label(axiom). [clausify(754)].
% 148.12/147.98 6115 -linordered_idom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(A,A,uminus_uminus(A),B))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) # label(fact_633_less__minus__self__iff) # label(axiom). [clausify(754)].
% 148.12/147.98 6116 -linordered_idom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,abs_abs(A),C)),B) = hAPP(A,A,abs_abs(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),B)) # label(fact_660_abs__mult__pos) # label(axiom). [clausify(780)].
% 148.12/147.98 6117 -number_ring(A) | -linordered_idom(A) | hAPP(A,A,abs_abs(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),hAPP(int,A,number_number_of(A),min)),B)) = one_one(A) # label(fact_1399_abs__power__minus__one) # label(axiom). [clausify(1502)].
% 148.12/147.98 6118 -linordered_idom(A) | hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),hAPP(A,A,abs_abs(A),B)),C) = hAPP(A,A,abs_abs(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C)) # label(fact_1438_power__abs) # label(axiom). [clausify(1541)].
% 148.12/147.98 6119 -linordered_idom(A) | hAPP(A,A,abs_abs(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),hAPP(A,A,uminus_uminus(A),B)),C)) = hAPP(A,A,abs_abs(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C)) # label(fact_1453_abs__power__minus) # label(axiom). [clausify(1556)].
% 148.12/147.98 6120 -linordered_idom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),hAPP(A,A,abs_abs(A),B)),C))) # label(fact_1460_zero__le__power__abs) # label(axiom). [clausify(1563)].
% 148.12/147.98 6121 -number_ring(A) | -linordered_idom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(int,A,number_number_of(A),B))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),B)) # label(fact_1647_less__special_I1_J) # label(axiom). [clausify(1721)].
% 148.12/147.98 6122 -number_ring(A) | -linordered_idom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(int,A,number_number_of(A),B))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),B)) # label(fact_1647_less__special_I1_J) # label(axiom). [clausify(1721)].
% 148.12/147.98 6123 -number_ring(A) | -linordered_idom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),B)),zero_zero(A))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),pls)) # label(fact_1648_less__special_I3_J) # label(axiom). [clausify(1722)].
% 148.12/147.98 6124 -number_ring(A) | -linordered_idom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),B)),zero_zero(A))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),pls)) # label(fact_1648_less__special_I3_J) # label(axiom). [clausify(1722)].
% 148.12/147.98 6125 -number_ring(A) | -linordered_idom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(int,A,number_number_of(A),B))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),B)) # label(fact_1649_le__special_I1_J) # label(axiom). [clausify(1723)].
% 148.12/147.98 6126 -number_ring(A) | -linordered_idom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(int,A,number_number_of(A),B))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),B)) # label(fact_1649_le__special_I1_J) # label(axiom). [clausify(1723)].
% 148.12/147.98 6127 -number_ring(A) | -linordered_idom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(int,A,number_number_of(A),B)),zero_zero(A))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),pls)) # label(fact_1650_le__special_I3_J) # label(axiom). [clausify(1724)].
% 148.12/147.98 6128 -number_ring(A) | -linordered_idom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(int,A,number_number_of(A),B)),zero_zero(A))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),pls)) # label(fact_1650_le__special_I3_J) # label(axiom). [clausify(1724)].
% 148.12/147.98 6129 -number_ring(A) | -linordered_idom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),B)),one_one(A))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),hAPP(int,int,bit1,pls))) # label(fact_1728_less__special_I4_J) # label(axiom). [clausify(1791)].
% 148.12/147.98 6130 -number_ring(A) | -linordered_idom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),B)),one_one(A))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),hAPP(int,int,bit1,pls))) # label(fact_1728_less__special_I4_J) # label(axiom). [clausify(1791)].
% 148.12/147.98 6131 -number_ring(A) | -linordered_idom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),hAPP(int,A,number_number_of(A),B))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,pls)),B)) # label(fact_1729_less__special_I2_J) # label(axiom). [clausify(1792)].
% 148.12/147.98 6132 -number_ring(A) | -linordered_idom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),hAPP(int,A,number_number_of(A),B))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,pls)),B)) # label(fact_1729_less__special_I2_J) # label(axiom). [clausify(1792)].
% 148.12/147.98 6133 -number_ring(A) | -linordered_idom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(int,A,number_number_of(A),B)),one_one(A))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),hAPP(int,int,bit1,pls))) # label(fact_1730_le__special_I4_J) # label(axiom). [clausify(1793)].
% 148.12/147.98 6134 -number_ring(A) | -linordered_idom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(int,A,number_number_of(A),B)),one_one(A))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),hAPP(int,int,bit1,pls))) # label(fact_1730_le__special_I4_J) # label(axiom). [clausify(1793)].
% 148.12/147.98 6135 -number_ring(A) | -linordered_idom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),one_one(A)),hAPP(int,A,number_number_of(A),B))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,pls)),B)) # label(fact_1731_le__special_I2_J) # label(axiom). [clausify(1794)].
% 148.12/147.98 6136 -number_ring(A) | -linordered_idom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),one_one(A)),hAPP(int,A,number_number_of(A),B))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,pls)),B)) # label(fact_1731_le__special_I2_J) # label(axiom). [clausify(1794)].
% 148.12/147.98 6137 -linordered_idom(A) | hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),hAPP(A,A,abs_abs(A),B)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) # label(fact_1824_power2__abs) # label(axiom). [clausify(1881)].
% 148.12/147.98 6138 -linordered_idom(A) | hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(A,A,abs_abs(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) # label(fact_1825_abs__power2) # label(axiom). [clausify(1882)].
% 148.12/147.98 6139 -linordered_idom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) # label(fact_1849_zero__le__power2) # label(axiom). [clausify(1900)].
% 148.12/147.98 6140 -linordered_idom(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),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),zero_zero(A))) # label(fact_1850_power2__less__0) # label(axiom). [clausify(1901)].
% 148.12/147.98 6141 -linordered_idom(A) | -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),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) | zero_zero(A) != ti(A,B) # label(fact_1851_zero__less__power2) # label(axiom). [clausify(1902)].
% 148.12/147.98 6142 -linordered_idom(A) | 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),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) | zero_zero(A) = ti(A,B) # label(fact_1851_zero__less__power2) # label(axiom). [clausify(1902)].
% 148.12/147.98 6143 -linordered_idom(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),C),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) != zero_zero(A) | zero_zero(A) = ti(A,B) # label(fact_1852_sum__power2__eq__zero__iff) # label(axiom). [clausify(1903)].
% 148.12/147.98 6144 -linordered_idom(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),C),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) != zero_zero(A) | zero_zero(A) = ti(A,C) # label(fact_1852_sum__power2__eq__zero__iff) # label(axiom). [clausify(1903)].
% 148.12/147.98 6145 -linordered_idom(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),C),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) = zero_zero(A) | zero_zero(A) != ti(A,B) | zero_zero(A) != ti(A,C) # label(fact_1852_sum__power2__eq__zero__iff) # label(axiom). [clausify(1903)].
% 148.12/147.98 6146 -linordered_idom(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(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),C),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),zero_zero(A))) | zero_zero(A) = ti(A,B) # label(fact_1883_sum__power2__le__zero__iff) # label(axiom). [clausify(1928)].
% 148.12/147.98 6147 -linordered_idom(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(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),C),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),zero_zero(A))) | zero_zero(A) = ti(A,C) # label(fact_1883_sum__power2__le__zero__iff) # label(axiom). [clausify(1928)].
% 148.12/147.98 6148 -linordered_idom(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(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),C),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),zero_zero(A))) | zero_zero(A) != ti(A,B) | zero_zero(A) != ti(A,C) # label(fact_1883_sum__power2__le__zero__iff) # label(axiom). [clausify(1928)].
% 148.12/147.98 6149 -linordered_idom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),C),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))) # label(fact_1884_sum__power2__ge__zero) # label(axiom). [clausify(1929)].
% 148.12/147.98 6150 -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),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),C),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),zero_zero(A))) # label(fact_1885_not__sum__power2__lt__zero) # label(axiom). [clausify(1930)].
% 148.12/147.98 6151 -linordered_idom(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),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),C),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))) | zero_zero(A) != ti(A,B) | zero_zero(A) != ti(A,C) # label(fact_1886_sum__power2__gt__zero__iff) # label(axiom). [clausify(1931)].
% 148.12/147.98 6152 -linordered_idom(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),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),C),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))) | zero_zero(A) = ti(A,B) # label(fact_1886_sum__power2__gt__zero__iff) # label(axiom). [clausify(1931)].
% 148.12/147.98 6153 -linordered_idom(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),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),C),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))) | zero_zero(A) = ti(A,C) # label(fact_1886_sum__power2__gt__zero__iff) # label(axiom). [clausify(1931)].
% 148.12/147.98 6154 -linordered_idom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),C)))) # label(fact_1888_zero__le__even__power_H) # label(axiom). [clausify(1933)].
% 148.12/147.98 6155 -linordered_idom(A) | -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),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),C))),zero_zero(A))) | zero_zero(A) = ti(A,B) # label(fact_1889_even__power__le__0__imp__0) # label(axiom). [clausify(1934)].
% 148.12/147.98 6156 -linordered_idom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),C))))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) # label(fact_1920_odd__0__le__power__imp__0__le) # label(axiom). [clausify(1957)].
% 148.12/147.98 6157 -linordered_idom(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(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),C)))),zero_zero(A))) # label(fact_1921_odd__power__less__zero) # label(axiom). [clausify(1958)].
% 148.12/147.98 6158 -linordered_idom(A) | hBOOL(hAPP(nat,bool,even_odd_even(nat),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),C),B)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),D),B))) # label(fact_1993_power__mono__odd) # label(axiom). [clausify(2025)].
% 148.12/147.98 6159 -linordered_idom(A) | -hBOOL(hAPP(nat,bool,even_odd_even(nat),B)) | hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),hAPP(A,A,abs_abs(A),C)),B) = hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),C),B) # label(fact_1998_power__even__abs) # label(axiom). [clausify(2030)].
% 148.12/147.98 6160 -linordered_idom(A) | hBOOL(hAPP(nat,bool,even_odd_even(nat),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),C),B))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),C)) # label(fact_2000_zero__le__odd__power) # label(axiom). [clausify(2032)].
% 148.12/147.98 6161 -linordered_idom(A) | hBOOL(hAPP(nat,bool,even_odd_even(nat),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),C),B))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),C)) # label(fact_2000_zero__le__odd__power) # label(axiom). [clausify(2032)].
% 148.12/147.98 6162 -linordered_idom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) | hBOOL(hAPP(nat,bool,even_odd_even(nat),C)) # label(fact_2002_zero__le__power__iff) # label(axiom). [clausify(2034)].
% 148.12/147.98 6163 -linordered_idom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) # label(fact_2002_zero__le__power__iff) # label(axiom). [clausify(2034)].
% 148.12/147.98 6164 -linordered_idom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C))) | -hBOOL(hAPP(nat,bool,even_odd_even(nat),C)) # label(fact_2002_zero__le__power__iff) # label(axiom). [clausify(2034)].
% 148.12/147.98 6165 -linordered_idom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C))) | hBOOL(hAPP(nat,bool,even_odd_even(nat),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) # label(fact_2003_zero__le__power__eq) # label(axiom). [clausify(2035)].
% 148.12/147.98 6166 -linordered_idom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C))) | -hBOOL(hAPP(nat,bool,even_odd_even(nat),C)) # label(fact_2003_zero__le__power__eq) # label(axiom). [clausify(2035)].
% 148.12/147.98 6167 -linordered_idom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C))) | hBOOL(hAPP(nat,bool,even_odd_even(nat),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) # label(fact_2003_zero__le__power__eq) # label(axiom). [clausify(2035)].
% 148.12/147.98 6168 -linordered_idom(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)),zero_zero(A))) | -hBOOL(hAPP(nat,bool,even_odd_even(nat),C)) # label(fact_2004_power__less__zero__eq) # label(axiom). [clausify(2036)].
% 148.12/147.98 6169 -linordered_idom(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)),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) # label(fact_2004_power__less__zero__eq) # label(axiom). [clausify(2036)].
% 148.12/147.98 6170 -linordered_idom(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)),zero_zero(A))) | hBOOL(hAPP(nat,bool,even_odd_even(nat),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) # label(fact_2004_power__less__zero__eq) # label(axiom). [clausify(2036)].
% 148.12/147.98 6171 -linordered_idom(A) | -hBOOL(hAPP(nat,bool,even_odd_even(nat),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,abs_abs(A),C)),hAPP(A,A,abs_abs(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),C),B)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),D),B))) # label(fact_2008_power__mono__even) # label(axiom). [clausify(2040)].
% 148.12/147.98 6172 -linordered_idom(A) | -hBOOL(hAPP(nat,bool,even_odd_even(nat),hAPP(int,nat,number_number_of(nat),B))) | hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),hAPP(A,A,abs_abs(A),C)),hAPP(int,nat,number_number_of(nat),B)) = hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),C),hAPP(int,nat,number_number_of(nat),B)) # label(fact_2012_power__even__abs__number__of) # label(axiom). [clausify(2044)].
% 148.12/147.98 6173 -linordered_idom(A) | -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)),zero_zero(A))) | zero_zero(nat) != C # label(fact_2020_power__le__zero__eq) # label(axiom). [clausify(2052)].
% 148.12/147.98 6174 -linordered_idom(A) | -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)),zero_zero(A))) | -hBOOL(hAPP(nat,bool,even_odd_even(nat),C)) | zero_zero(A) = ti(A,B) # label(fact_2020_power__le__zero__eq) # label(axiom). [clausify(2052)].
% 148.12/147.98 6175 -linordered_idom(A) | -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)),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),zero_zero(A))) | hBOOL(hAPP(nat,bool,even_odd_even(nat),C)) # label(fact_2020_power__le__zero__eq) # label(axiom). [clausify(2052)].
% 148.12/147.98 6176 -linordered_idom(A) | -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)),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),zero_zero(A))) | zero_zero(A) = ti(A,B) # label(fact_2020_power__le__zero__eq) # label(axiom). [clausify(2052)].
% 148.12/147.98 6177 -linordered_idom(A) | 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)),zero_zero(A))) | zero_zero(nat) = C | hBOOL(hAPP(nat,bool,even_odd_even(nat),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),zero_zero(A))) # label(fact_2020_power__le__zero__eq) # label(axiom). [clausify(2052)].
% 148.12/147.98 6178 -linordered_idom(A) | 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)),zero_zero(A))) | zero_zero(nat) = C | -hBOOL(hAPP(nat,bool,even_odd_even(nat),C)) | zero_zero(A) != ti(A,B) # label(fact_2020_power__le__zero__eq) # label(axiom). [clausify(2052)].
% 148.12/147.98 6179 -linordered_idom(A) | -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))) | zero_zero(nat) = C | hBOOL(hAPP(nat,bool,even_odd_even(nat),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) # label(fact_2021_zero__less__power__eq) # label(axiom). [clausify(2053)].
% 148.12/147.98 6180 -linordered_idom(A) | -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))) | zero_zero(nat) = C | zero_zero(A) != ti(A,B) | -hBOOL(hAPP(nat,bool,even_odd_even(nat),C)) # label(fact_2021_zero__less__power__eq) # label(axiom). [clausify(2053)].
% 148.12/147.98 6181 -linordered_idom(A) | -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))) | zero_zero(nat) = C | zero_zero(A) != ti(A,B) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) # label(fact_2021_zero__less__power__eq) # label(axiom). [clausify(2053)].
% 148.12/147.98 6182 -linordered_idom(A) | 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))) | zero_zero(nat) != C # label(fact_2021_zero__less__power__eq) # label(axiom). [clausify(2053)].
% 148.12/147.98 6183 -linordered_idom(A) | 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))) | -hBOOL(hAPP(nat,bool,even_odd_even(nat),C)) | zero_zero(A) = ti(A,B) # label(fact_2021_zero__less__power__eq) # label(axiom). [clausify(2053)].
% 148.12/147.98 6184 -linordered_idom(A) | 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))) | hBOOL(hAPP(nat,bool,even_odd_even(nat),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) # label(fact_2021_zero__less__power__eq) # label(axiom). [clausify(2053)].
% 148.12/147.98 6185 -linordered_idom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(int,nat,number_number_of(nat),C)))) | hBOOL(hAPP(nat,bool,even_odd_even(nat),hAPP(int,nat,number_number_of(nat),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) # label(fact_2022_zero__le__power__eq__number__of) # label(axiom). [clausify(2054)].
% 148.12/147.98 6186 -linordered_idom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(int,nat,number_number_of(nat),C)))) | -hBOOL(hAPP(nat,bool,even_odd_even(nat),hAPP(int,nat,number_number_of(nat),C))) # label(fact_2022_zero__le__power__eq__number__of) # label(axiom). [clausify(2054)].
% 148.12/147.98 6187 -linordered_idom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(int,nat,number_number_of(nat),C)))) | hBOOL(hAPP(nat,bool,even_odd_even(nat),hAPP(int,nat,number_number_of(nat),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) # label(fact_2022_zero__le__power__eq__number__of) # label(axiom). [clausify(2054)].
% 148.12/147.98 6188 -linordered_idom(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),hAPP(int,nat,number_number_of(nat),C))),zero_zero(A))) | -hBOOL(hAPP(nat,bool,even_odd_even(nat),hAPP(int,nat,number_number_of(nat),C))) # label(fact_2023_power__less__zero__eq__number__of) # label(axiom). [clausify(2055)].
% 148.12/147.98 6189 -linordered_idom(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),hAPP(int,nat,number_number_of(nat),C))),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) # label(fact_2023_power__less__zero__eq__number__of) # label(axiom). [clausify(2055)].
% 148.12/147.98 6190 -linordered_idom(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),hAPP(int,nat,number_number_of(nat),C))),zero_zero(A))) | hBOOL(hAPP(nat,bool,even_odd_even(nat),hAPP(int,nat,number_number_of(nat),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) # label(fact_2023_power__less__zero__eq__number__of) # label(axiom). [clausify(2055)].
% 148.12/147.98 6191 -linordered_idom(A) | -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),hAPP(int,nat,number_number_of(nat),C))),zero_zero(A))) | hAPP(int,nat,number_number_of(nat),C) != zero_zero(nat) # label(fact_2029_power__le__zero__eq__number__of) # label(axiom). [clausify(2061)].
% 148.12/147.98 6192 -linordered_idom(A) | -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),hAPP(int,nat,number_number_of(nat),C))),zero_zero(A))) | -hBOOL(hAPP(nat,bool,even_odd_even(nat),hAPP(int,nat,number_number_of(nat),C))) | zero_zero(A) = ti(A,B) # label(fact_2029_power__le__zero__eq__number__of) # label(axiom). [clausify(2061)].
% 148.12/147.98 6193 -linordered_idom(A) | -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),hAPP(int,nat,number_number_of(nat),C))),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),zero_zero(A))) | hBOOL(hAPP(nat,bool,even_odd_even(nat),hAPP(int,nat,number_number_of(nat),C))) # label(fact_2029_power__le__zero__eq__number__of) # label(axiom). [clausify(2061)].
% 148.12/147.98 6194 -linordered_idom(A) | -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),hAPP(int,nat,number_number_of(nat),C))),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),zero_zero(A))) | zero_zero(A) = ti(A,B) # label(fact_2029_power__le__zero__eq__number__of) # label(axiom). [clausify(2061)].
% 148.12/147.98 6195 -linordered_idom(A) | 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),hAPP(int,nat,number_number_of(nat),C))),zero_zero(A))) | hAPP(int,nat,number_number_of(nat),C) = zero_zero(nat) | hBOOL(hAPP(nat,bool,even_odd_even(nat),hAPP(int,nat,number_number_of(nat),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),zero_zero(A))) # label(fact_2029_power__le__zero__eq__number__of) # label(axiom). [clausify(2061)].
% 148.12/147.98 6196 -linordered_idom(A) | 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),hAPP(int,nat,number_number_of(nat),C))),zero_zero(A))) | hAPP(int,nat,number_number_of(nat),C) = zero_zero(nat) | -hBOOL(hAPP(nat,bool,even_odd_even(nat),hAPP(int,nat,number_number_of(nat),C))) | zero_zero(A) != ti(A,B) # label(fact_2029_power__le__zero__eq__number__of) # label(axiom). [clausify(2061)].
% 148.12/147.98 6197 -linordered_idom(A) | -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),hAPP(int,nat,number_number_of(nat),C)))) | hAPP(int,nat,number_number_of(nat),C) = zero_zero(nat) | hBOOL(hAPP(nat,bool,even_odd_even(nat),hAPP(int,nat,number_number_of(nat),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) # label(fact_2030_zero__less__power__eq__number__of) # label(axiom). [clausify(2062)].
% 148.12/147.98 6198 -linordered_idom(A) | -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),hAPP(int,nat,number_number_of(nat),C)))) | hAPP(int,nat,number_number_of(nat),C) = zero_zero(nat) | zero_zero(A) != ti(A,B) | -hBOOL(hAPP(nat,bool,even_odd_even(nat),hAPP(int,nat,number_number_of(nat),C))) # label(fact_2030_zero__less__power__eq__number__of) # label(axiom). [clausify(2062)].
% 148.12/147.98 6199 -linordered_idom(A) | -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),hAPP(int,nat,number_number_of(nat),C)))) | hAPP(int,nat,number_number_of(nat),C) = zero_zero(nat) | zero_zero(A) != ti(A,B) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) # label(fact_2030_zero__less__power__eq__number__of) # label(axiom). [clausify(2062)].
% 148.12/147.98 6200 -linordered_idom(A) | 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),hAPP(int,nat,number_number_of(nat),C)))) | hAPP(int,nat,number_number_of(nat),C) != zero_zero(nat) # label(fact_2030_zero__less__power__eq__number__of) # label(axiom). [clausify(2062)].
% 148.12/147.98 6201 -linordered_idom(A) | 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),hAPP(int,nat,number_number_of(nat),C)))) | -hBOOL(hAPP(nat,bool,even_odd_even(nat),hAPP(int,nat,number_number_of(nat),C))) | zero_zero(A) = ti(A,B) # label(fact_2030_zero__less__power__eq__number__of) # label(axiom). [clausify(2062)].
% 148.12/147.98 6202 -linordered_idom(A) | 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),hAPP(int,nat,number_number_of(nat),C)))) | hBOOL(hAPP(nat,bool,even_odd_even(nat),hAPP(int,nat,number_number_of(nat),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) # label(fact_2030_zero__less__power__eq__number__of) # label(axiom). [clausify(2062)].
% 148.12/147.98 6203 -linordered_idom(A) | hAPP(A,A,sgn_sgn(A),hAPP(A,A,sgn_sgn(A),B)) = hAPP(A,A,sgn_sgn(A),B) # label(fact_2062_sgn__sgn) # label(axiom). [clausify(2090)].
% 148.12/147.98 6204 -linordered_idom(A) | hAPP(A,A,sgn_sgn(A),B) != zero_zero(A) | zero_zero(A) = ti(A,B) # label(fact_2065_sgn__0__0) # label(axiom). [clausify(2093)].
% 148.12/147.98 6205 -linordered_idom(A) | hAPP(A,A,sgn_sgn(A),B) = zero_zero(A) | zero_zero(A) != ti(A,B) # label(fact_2065_sgn__0__0) # label(axiom). [clausify(2093)].
% 148.12/147.98 6206 -linordered_idom(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,sgn_sgn(A),B)),hAPP(A,A,sgn_sgn(A),C)) = hAPP(A,A,sgn_sgn(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)) # label(fact_2069_sgn__times) # label(axiom). [clausify(2097)].
% 148.12/147.98 6207 -linordered_idom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,sgn_sgn(A),B)),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) # label(fact_2078_sgn__less) # label(axiom). [clausify(2104)].
% 148.12/147.98 6208 -linordered_idom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,sgn_sgn(A),B)),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) # label(fact_2078_sgn__less) # label(axiom). [clausify(2104)].
% 148.12/147.98 6209 -linordered_idom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,sgn_sgn(A),B))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) # label(fact_2079_sgn__greater) # label(axiom). [clausify(2105)].
% 148.12/147.98 6210 -linordered_idom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,sgn_sgn(A),B))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) # label(fact_2079_sgn__greater) # label(axiom). [clausify(2105)].
% 148.12/147.98 6211 -linordered_idom(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,sgn_sgn(A),B)),hAPP(A,A,abs_abs(A),B)) = ti(A,B) # label(fact_2081_mult__sgn__abs) # label(axiom). [clausify(2107)].
% 148.12/147.98 6212 -linordered_idom(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(A,A,sgn_sgn(A),B)) = hAPP(A,A,abs_abs(A),B) # label(fact_2082_abs__sgn) # label(axiom). [clausify(2108)].
% 148.12/147.98 6213 -linordered_idom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | hAPP(A,A,sgn_sgn(A),B) = one_one(A) # label(fact_2104_sgn__pos) # label(axiom). [clausify(2130)].
% 148.12/147.98 6214 -linordered_idom(A) | hAPP(A,A,sgn_sgn(A),B) != one_one(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) # label(fact_2105_sgn__1__pos) # label(axiom). [clausify(2131)].
% 148.12/147.98 6215 -linordered_idom(A) | hAPP(A,A,sgn_sgn(A),B) = one_one(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) # label(fact_2105_sgn__1__pos) # label(axiom). [clausify(2131)].
% 148.12/147.98 6216 -linordered_idom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | hAPP(A,A,uminus_uminus(A),one_one(A)) = hAPP(A,A,sgn_sgn(A),B) # label(fact_2125_sgn__neg) # label(axiom). [clausify(2151)].
% 148.12/147.98 6217 -linordered_idom(A) | hAPP(A,A,uminus_uminus(A),one_one(A)) != hAPP(A,A,sgn_sgn(A),B) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) # label(fact_2126_sgn__1__neg) # label(axiom). [clausify(2152)].
% 148.12/147.98 6218 -linordered_idom(A) | hAPP(A,A,uminus_uminus(A),one_one(A)) = hAPP(A,A,sgn_sgn(A),B) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) # label(fact_2126_sgn__1__neg) # label(axiom). [clausify(2152)].
% 148.12/147.98 6219 -linordered_idom(A) | hAPP(nat,A,semiring_1_of_nat(A),B) = hAPP(A,A,abs_abs(A),hAPP(nat,A,semiring_1_of_nat(A),B)) # label(fact_2572_abs__of__nat) # label(axiom). [clausify(2572)].
% 148.12/147.98 6220 -number_ring(A) | -linordered_idom(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,hAPP(A,fun(nat,A),power_power(A),hAPP(int,A,number_number_of(A),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),B))) # label(fact_2680_of__nat__less__two__power) # label(axiom). [clausify(2672)].
% 148.12/147.98 6221 -linordered_idom(A) | hAPP(A,A,abs_abs(A),B) != hAPP(A,A,abs_abs(A),C) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),C)) # label(fact_3116_dvd__if__abs__eq) # label(axiom). [clausify(3083)].
% 148.12/147.98 6222 -linordered_idom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),hAPP(A,A,abs_abs(A),B)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),C)) # label(fact_3117_abs__dvd__iff) # label(axiom). [clausify(3084)].
% 148.12/147.98 6223 -linordered_idom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),hAPP(A,A,abs_abs(A),B)),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),C)) # label(fact_3117_abs__dvd__iff) # label(axiom). [clausify(3084)].
% 148.12/147.98 6224 -linordered_idom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),hAPP(A,A,abs_abs(A),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),C)) # label(fact_3118_dvd__abs__iff) # label(axiom). [clausify(3085)].
% 148.12/147.98 6225 -linordered_idom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),hAPP(A,A,abs_abs(A),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),C)) # label(fact_3118_dvd__abs__iff) # label(axiom). [clausify(3085)].
% 148.12/147.98 6226 -linordered_idom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,ring_1_of_int(A),B)),hAPP(int,A,ring_1_of_int(A),C))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),C)) # label(fact_3571_of__int__less__iff) # label(axiom). [clausify(3526)].
% 148.12/147.98 6227 -linordered_idom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,ring_1_of_int(A),B)),hAPP(int,A,ring_1_of_int(A),C))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),C)) # label(fact_3571_of__int__less__iff) # label(axiom). [clausify(3526)].
% 148.12/147.98 6228 -linordered_idom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(int,A,ring_1_of_int(A),B)),hAPP(int,A,ring_1_of_int(A),C))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),C)) # label(fact_3572_of__int__le__iff) # label(axiom). [clausify(3527)].
% 148.12/147.98 6229 -linordered_idom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(int,A,ring_1_of_int(A),B)),hAPP(int,A,ring_1_of_int(A),C))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),C)) # label(fact_3572_of__int__le__iff) # label(axiom). [clausify(3527)].
% 148.12/147.98 6230 -linordered_idom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,ring_1_of_int(A),B)),zero_zero(A))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),zero_zero(int))) # label(fact_3607_of__int__less__0__iff) # label(axiom). [clausify(3560)].
% 148.12/147.98 6231 -linordered_idom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,ring_1_of_int(A),B)),zero_zero(A))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),zero_zero(int))) # label(fact_3607_of__int__less__0__iff) # label(axiom). [clausify(3560)].
% 148.12/147.98 6232 -linordered_idom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(int,A,ring_1_of_int(A),B))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B)) # label(fact_3608_of__int__0__less__iff) # label(axiom). [clausify(3561)].
% 148.12/147.98 6233 -linordered_idom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(int,A,ring_1_of_int(A),B))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B)) # label(fact_3608_of__int__0__less__iff) # label(axiom). [clausify(3561)].
% 148.12/147.98 6234 -linordered_idom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(int,A,ring_1_of_int(A),B)),zero_zero(A))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),zero_zero(int))) # label(fact_3609_of__int__le__0__iff) # label(axiom). [clausify(3562)].
% 148.12/147.98 6235 -linordered_idom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(int,A,ring_1_of_int(A),B)),zero_zero(A))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),zero_zero(int))) # label(fact_3609_of__int__le__0__iff) # label(axiom). [clausify(3562)].
% 148.12/147.98 6236 -linordered_idom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(int,A,ring_1_of_int(A),B))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),B)) # label(fact_3610_of__int__0__le__iff) # label(axiom). [clausify(3563)].
% 148.12/147.98 6237 -linordered_idom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(int,A,ring_1_of_int(A),B))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),B)) # label(fact_3610_of__int__0__le__iff) # label(axiom). [clausify(3563)].
% 148.12/147.98 Derived: -number_ring(int) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),A)),hAPP(int,int,number_number_of(int),B))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)). [resolve(6089,a,6090,b)].
% 148.12/147.98 Derived: -number_ring(int) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),A)),hAPP(int,int,number_number_of(int),B))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)). [resolve(6089,a,6091,b)].
% 148.12/147.98 Derived: -number_ring(int) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),A)),hAPP(int,int,number_number_of(int),B))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)). [resolve(6089,a,6092,b)].
% 148.12/147.98 Derived: -number_ring(int) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),A)),hAPP(int,int,number_number_of(int),B))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)). [resolve(6089,a,6093,b)].
% 148.12/147.98 Derived: ti(int,A) = ti(int,B) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),A)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)). [resolve(6089,a,6094,a)].
% 148.12/147.98 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(6089,a,6095,a)].
% 148.12/147.99 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(6089,a,6096,a)].
% 148.12/147.99 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(6089,a,6097,a)].
% 148.12/147.99 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(6089,a,6098,a)].
% 148.12/147.99 Derived: -hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),A),ring_1_Ints(int))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),A)),A)),zero_zero(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),zero_zero(int))). [resolve(6089,a,6099,a)].
% 148.12/147.99 Derived: -hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),A),ring_1_Ints(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),A)),A)),zero_zero(int))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),zero_zero(int))). [resolve(6089,a,6100,a)].
% 148.12/147.99 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,abs_abs(int),A)),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)). [resolve(6089,a,6101,a)].
% 148.12/147.99 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,abs_abs(int),A)),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,uminus_uminus(int),A)),B)). [resolve(6089,a,6102,a)].
% 148.12/147.99 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,abs_abs(int),A)),B)) | -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,uminus_uminus(int),A)),B)). [resolve(6089,a,6103,a)].
% 148.12/147.99 Derived: -number_ring(int) | hAPP(int,int,abs_abs(int),hAPP(int,int,number_number_of(int),min)) = one_one(int). [resolve(6089,a,6104,b)].
% 148.12/147.99 Derived: hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,abs_abs(int),A)),hAPP(int,int,abs_abs(int),A)) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),A). [resolve(6089,a,6105,a)].
% 148.12/147.99 Derived: hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,abs_abs(int),A)),hAPP(int,int,abs_abs(int),B)) = hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)). [resolve(6089,a,6106,a)].
% 148.12/147.99 Derived: hAPP(int,int,abs_abs(int),one_one(int)) = one_one(int). [resolve(6089,a,6107,a)].
% 148.12/147.99 Derived: -number_ring(int) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),A)),zero_zero(int))) | hAPP(int,int,number_number_of(int),A) = hAPP(int,int,abs_abs(int),hAPP(int,int,number_number_of(int),A)). [resolve(6089,a,6109,b)].
% 148.12/147.99 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,abs_abs(int),A)),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,abs_abs(int),C)),D)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,abs_abs(int),A)),hAPP(int,int,abs_abs(int),C))),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),D))). [resolve(6089,a,6110,a)].
% 148.12/147.99 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),B))),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),B),C)),A)). [resolve(6089,a,6111,a)].
% 148.12/148.00 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),B))),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),B),C))). [resolve(6089,a,6112,a)].
% 148.12/148.00 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),B))),C)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),B),C)),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),B),C))). [resolve(6089,a,6113,a)].
% 148.12/148.00 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),hAPP(int,int,uminus_uminus(int),A))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),zero_zero(int))). [resolve(6089,a,6114,a)].
% 148.12/148.00 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),hAPP(int,int,uminus_uminus(int),A))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),zero_zero(int))). [resolve(6089,a,6115,a)].
% 148.12/148.00 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A)) | hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,abs_abs(int),B)),A) = hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),A)). [resolve(6089,a,6116,a)].
% 148.12/148.00 Derived: -number_ring(int) | hAPP(int,int,abs_abs(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,number_number_of(int),min)),A)) = one_one(int). [resolve(6089,a,6117,b)].
% 148.12/148.00 Derived: hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,abs_abs(int),A)),B) = hAPP(int,int,abs_abs(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),B)). [resolve(6089,a,6118,a)].
% 148.12/148.00 Derived: hAPP(int,int,abs_abs(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,uminus_uminus(int),A)),B)) = hAPP(int,int,abs_abs(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),B)). [resolve(6089,a,6119,a)].
% 148.12/148.00 Derived: 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),hAPP(int,int,abs_abs(int),A)),B))). [resolve(6089,a,6120,a)].
% 148.12/148.00 Derived: -number_ring(int) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,number_number_of(int),A))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),A)). [resolve(6089,a,6121,b)].
% 148.12/148.00 Derived: -number_ring(int) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,number_number_of(int),A))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),A)). [resolve(6089,a,6122,b)].
% 148.12/148.00 Derived: -number_ring(int) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),A)),zero_zero(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),pls)). [resolve(6089,a,6123,b)].
% 148.12/148.00 Derived: -number_ring(int) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),A)),zero_zero(int))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),pls)). [resolve(6089,a,6124,b)].
% 148.12/148.00 Derived: -number_ring(int) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),A))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),A)). [resolve(6089,a,6125,b)].
% 148.12/148.00 Derived: -number_ring(int) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),A))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),A)). [resolve(6089,a,6126,b)].
% 148.12/148.00 Derived: -number_ring(int) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),A)),zero_zero(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),pls)). [resolve(6089,a,6127,b)].
% 148.12/148.01 Derived: -number_ring(int) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),A)),zero_zero(int))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),pls)). [resolve(6089,a,6128,b)].
% 148.12/148.01 Derived: -number_ring(int) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),A)),one_one(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),hAPP(int,int,bit1,pls))). [resolve(6089,a,6129,b)].
% 148.12/148.01 Derived: -number_ring(int) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),A)),one_one(int))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),hAPP(int,int,bit1,pls))). [resolve(6089,a,6130,b)].
% 148.12/148.01 Derived: -number_ring(int) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),hAPP(int,int,number_number_of(int),A))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,pls)),A)). [resolve(6089,a,6131,b)].
% 148.12/148.01 Derived: -number_ring(int) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),hAPP(int,int,number_number_of(int),A))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,pls)),A)). [resolve(6089,a,6132,b)].
% 148.12/148.01 Derived: -number_ring(int) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),A)),one_one(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),hAPP(int,int,bit1,pls))). [resolve(6089,a,6133,b)].
% 148.12/148.01 Derived: -number_ring(int) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),A)),one_one(int))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),hAPP(int,int,bit1,pls))). [resolve(6089,a,6134,b)].
% 148.12/148.01 Derived: -number_ring(int) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),hAPP(int,int,number_number_of(int),A))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,pls)),A)). [resolve(6089,a,6135,b)].
% 148.12/148.01 Derived: -number_ring(int) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),hAPP(int,int,number_number_of(int),A))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,pls)),A)). [resolve(6089,a,6136,b)].
% 148.12/148.01 Derived: hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,abs_abs(int),A)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))). [resolve(6089,a,6137,a)].
% 148.12/148.01 Derived: hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(int,int,abs_abs(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))). [resolve(6089,a,6138,a)].
% 148.12/148.01 Derived: 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),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))). [resolve(6089,a,6139,a)].
% 148.12/148.01 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),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),zero_zero(int))). [resolve(6089,a,6140,a)].
% 148.12/148.01 Derived: -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),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) | zero_zero(int) != ti(int,A). [resolve(6089,a,6141,a)].
% 148.12/148.01 Derived: 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),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) | zero_zero(int) = ti(int,A). [resolve(6089,a,6142,a)].
% 148.12/148.02 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) != zero_zero(int) | zero_zero(int) = ti(int,A). [resolve(6089,a,6143,a)].
% 148.12/148.02 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) != zero_zero(int) | zero_zero(int) = ti(int,B). [resolve(6089,a,6144,a)].
% 148.12/148.02 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) = zero_zero(int) | zero_zero(int) != ti(int,A) | zero_zero(int) != ti(int,B). [resolve(6089,a,6145,a)].
% 148.12/148.02 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(nat,int,hAPP(int,fun(nat,int),power_power(int),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),zero_zero(int))) | zero_zero(int) = ti(int,A). [resolve(6089,a,6146,a)].
% 148.12/148.02 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(nat,int,hAPP(int,fun(nat,int),power_power(int),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),zero_zero(int))) | zero_zero(int) = ti(int,B). [resolve(6089,a,6147,a)].
% 148.12/148.02 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(nat,int,hAPP(int,fun(nat,int),power_power(int),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),zero_zero(int))) | zero_zero(int) != ti(int,A) | zero_zero(int) != ti(int,B). [resolve(6089,a,6148,a)].
% 148.12/148.02 Derived: 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),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))). [resolve(6089,a,6149,a)].
% 148.12/148.02 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(nat,int,hAPP(int,fun(nat,int),power_power(int),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),zero_zero(int))). [resolve(6089,a,6150,a)].
% 148.12/148.02 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))) | zero_zero(int) != ti(int,A) | zero_zero(int) != ti(int,B). [resolve(6089,a,6151,a)].
% 148.12/148.02 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))) | zero_zero(int) = ti(int,A). [resolve(6089,a,6152,a)].
% 148.22/148.03 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),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))) | zero_zero(int) = ti(int,B). [resolve(6089,a,6153,a)].
% 148.22/148.03 Derived: 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),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),B)))). [resolve(6089,a,6154,a)].
% 148.22/148.03 Derived: -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),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),B))),zero_zero(int))) | zero_zero(int) = ti(int,A). [resolve(6089,a,6155,a)].
% 148.22/148.03 Derived: -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),A),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),B))))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A)). [resolve(6089,a,6156,a)].
% 148.22/148.03 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(nat,int,hAPP(int,fun(nat,int),power_power(int),A),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),B)))),zero_zero(int))). [resolve(6089,a,6157,a)].
% 148.22/148.03 Derived: hBOOL(hAPP(nat,bool,even_odd_even(nat),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_eq(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),B),A)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),C),A))). [resolve(6089,a,6158,a)].
% 148.22/148.03 Derived: -hBOOL(hAPP(nat,bool,even_odd_even(nat),A)) | hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,abs_abs(int),B)),A) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),B),A). [resolve(6089,a,6159,a)].
% 148.22/148.03 Derived: hBOOL(hAPP(nat,bool,even_odd_even(nat),A)) | -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),B),A))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),B)). [resolve(6089,a,6160,a)].
% 148.22/148.03 Derived: hBOOL(hAPP(nat,bool,even_odd_even(nat),A)) | 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),B),A))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),B)). [resolve(6089,a,6161,a)].
% 148.22/148.03 Derived: 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),A),B))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A)). [resolve(6089,a,6163,a)].
% 148.22/148.03 Derived: 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),A),B))) | -hBOOL(hAPP(nat,bool,even_odd_even(nat),B)). [resolve(6089,a,6164,a)].
% 148.22/148.03 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)),zero_zero(int))) | -hBOOL(hAPP(nat,bool,even_odd_even(nat),B)). [resolve(6089,a,6168,a)].
% 148.22/148.04 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)),zero_zero(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),zero_zero(int))). [resolve(6089,a,6169,a)].
% 148.22/148.04 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)),zero_zero(int))) | hBOOL(hAPP(nat,bool,even_odd_even(nat),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),zero_zero(int))). [resolve(6089,a,6170,a)].
% 148.22/148.04 Derived: -hBOOL(hAPP(nat,bool,even_odd_even(nat),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,abs_abs(int),B)),hAPP(int,int,abs_abs(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),B),A)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),C),A))). [resolve(6089,a,6171,a)].
% 148.22/148.04 Derived: -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)),zero_zero(int))) | zero_zero(nat) != B. [resolve(6089,a,6173,a)].
% 148.22/148.04 Derived: -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)),zero_zero(int))) | -hBOOL(hAPP(nat,bool,even_odd_even(nat),B)) | zero_zero(int) = ti(int,A). [resolve(6089,a,6174,a)].
% 148.22/148.04 Derived: -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)),zero_zero(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),zero_zero(int))) | hBOOL(hAPP(nat,bool,even_odd_even(nat),B)). [resolve(6089,a,6175,a)].
% 148.22/148.04 Derived: -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)),zero_zero(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),zero_zero(int))) | zero_zero(int) = ti(int,A). [resolve(6089,a,6176,a)].
% 148.22/148.04 Derived: 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)),zero_zero(int))) | zero_zero(nat) = B | hBOOL(hAPP(nat,bool,even_odd_even(nat),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),zero_zero(int))). [resolve(6089,a,6177,a)].
% 148.22/148.04 Derived: 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)),zero_zero(int))) | zero_zero(nat) = B | -hBOOL(hAPP(nat,bool,even_odd_even(nat),B)) | zero_zero(int) != ti(int,A). [resolve(6089,a,6178,a)].
% 148.22/148.04 Derived: -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))) | zero_zero(nat) = B | hBOOL(hAPP(nat,bool,even_odd_even(nat),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A)). [resolve(6089,a,6179,a)].
% 148.22/148.04 Derived: -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))) | zero_zero(nat) = B | zero_zero(int) != ti(int,A) | -hBOOL(hAPP(nat,bool,even_odd_even(nat),B)). [resolve(6089,a,6180,a)].
% 148.22/148.04 Derived: -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))) | zero_zero(nat) = B | zero_zero(int) != ti(int,A) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A)). [resolve(6089,a,6181,a)].
% 148.22/148.04 Derived: 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))) | zero_zero(nat) != B. [resolve(6089,a,6182,a)].
% 148.22/148.04 Derived: 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))) | -hBOOL(hAPP(nat,bool,even_odd_even(nat),B)) | zero_zero(int) = ti(int,A). [resolve(6089,a,6183,a)].
% 148.22/148.04 Derived: 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))) | hBOOL(hAPP(nat,bool,even_odd_even(nat),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A)). [resolve(6089,a,6184,a)].
% 148.22/148.05 Derived: -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),hAPP(int,nat,number_number_of(nat),B))),zero_zero(int))) | hAPP(int,nat,number_number_of(nat),B) != zero_zero(nat). [resolve(6089,a,6191,a)].
% 148.22/148.05 Derived: 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),hAPP(int,nat,number_number_of(nat),B))),zero_zero(int))) | hAPP(int,nat,number_number_of(nat),B) = zero_zero(nat) | hBOOL(hAPP(nat,bool,even_odd_even(nat),hAPP(int,nat,number_number_of(nat),B))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),zero_zero(int))). [resolve(6089,a,6195,a)].
% 148.22/148.05 Derived: 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),hAPP(int,nat,number_number_of(nat),B))),zero_zero(int))) | hAPP(int,nat,number_number_of(nat),B) = zero_zero(nat) | -hBOOL(hAPP(nat,bool,even_odd_even(nat),hAPP(int,nat,number_number_of(nat),B))) | zero_zero(int) != ti(int,A). [resolve(6089,a,6196,a)].
% 148.22/148.05 Derived: -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),hAPP(int,nat,number_number_of(nat),B)))) | hAPP(int,nat,number_number_of(nat),B) = zero_zero(nat) | hBOOL(hAPP(nat,bool,even_odd_even(nat),hAPP(int,nat,number_number_of(nat),B))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A)). [resolve(6089,a,6197,a)].
% 148.22/148.05 Derived: -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),hAPP(int,nat,number_number_of(nat),B)))) | hAPP(int,nat,number_number_of(nat),B) = zero_zero(nat) | zero_zero(int) != ti(int,A) | -hBOOL(hAPP(nat,bool,even_odd_even(nat),hAPP(int,nat,number_number_of(nat),B))). [resolve(6089,a,6198,a)].
% 148.22/148.05 Derived: -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),hAPP(int,nat,number_number_of(nat),B)))) | hAPP(int,nat,number_number_of(nat),B) = zero_zero(nat) | zero_zero(int) != ti(int,A) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A)). [resolve(6089,a,6199,a)].
% 148.22/148.05 Derived: 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),hAPP(int,nat,number_number_of(nat),B)))) | hAPP(int,nat,number_number_of(nat),B) != zero_zero(nat). [resolve(6089,a,6200,a)].
% 148.22/148.05 Derived: hAPP(int,int,sgn_sgn(int),hAPP(int,int,sgn_sgn(int),A)) = hAPP(int,int,sgn_sgn(int),A). [resolve(6089,a,6203,a)].
% 148.22/148.05 Derived: hAPP(int,int,sgn_sgn(int),A) != zero_zero(int) | zero_zero(int) = ti(int,A). [resolve(6089,a,6204,a)].
% 148.22/148.05 Derived: hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,sgn_sgn(int),A)),hAPP(int,int,sgn_sgn(int),B)) = hAPP(int,int,sgn_sgn(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)). [resolve(6089,a,6206,a)].
% 148.22/148.05 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,sgn_sgn(int),A)),zero_zero(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),zero_zero(int))). [resolve(6089,a,6207,a)].
% 148.22/148.05 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,sgn_sgn(int),A)),zero_zero(int))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),zero_zero(int))). [resolve(6089,a,6208,a)].
% 148.22/148.05 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,sgn_sgn(int),A))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A)). [resolve(6089,a,6209,a)].
% 148.22/148.05 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,sgn_sgn(int),A))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A)). [resolve(6089,a,6210,a)].
% 148.22/148.05 Derived: hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,sgn_sgn(int),A)),hAPP(int,int,abs_abs(int),A)) = ti(int,A). [resolve(6089,a,6211,a)].
% 148.22/148.07 Derived: hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),hAPP(int,int,sgn_sgn(int),A)) = hAPP(int,int,abs_abs(int),A). [resolve(6089,a,6212,a)].
% 148.22/148.07 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A)) | hAPP(int,int,sgn_sgn(int),A) = one_one(int). [resolve(6089,a,6213,a)].
% 148.22/148.07 Derived: hAPP(int,int,sgn_sgn(int),A) != one_one(int) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A)). [resolve(6089,a,6214,a)].
% 148.22/148.07 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),zero_zero(int))) | hAPP(int,int,uminus_uminus(int),one_one(int)) = hAPP(int,int,sgn_sgn(int),A). [resolve(6089,a,6216,a)].
% 148.22/148.07 Derived: hAPP(int,int,uminus_uminus(int),one_one(int)) != hAPP(int,int,sgn_sgn(int),A) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),zero_zero(int))). [resolve(6089,a,6217,a)].
% 148.22/148.07 Derived: hAPP(nat,int,semiring_1_of_nat(int),A) = hAPP(int,int,abs_abs(int),hAPP(nat,int,semiring_1_of_nat(int),A)). [resolve(6089,a,6219,a)].
% 148.22/148.07 Derived: -number_ring(int) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,semiring_1_of_nat(int),A)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),A))). [resolve(6089,a,6220,b)].
% 148.22/148.07 Derived: hAPP(int,int,abs_abs(int),A) != hAPP(int,int,abs_abs(int),B) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),B)). [resolve(6089,a,6221,a)].
% 148.22/148.07 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(int,int,abs_abs(int),A)),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),B)). [resolve(6089,a,6222,a)].
% 148.22/148.07 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(int,int,abs_abs(int),A)),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),B)). [resolve(6089,a,6223,a)].
% 148.22/148.07 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),hAPP(int,int,abs_abs(int),B))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),B)). [resolve(6089,a,6224,a)].
% 148.22/148.07 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),hAPP(int,int,abs_abs(int),B))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),B)). [resolve(6089,a,6225,a)].
% 148.22/148.07 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,ring_1_of_int(int),A)),hAPP(int,int,ring_1_of_int(int),B))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)). [resolve(6089,a,6226,a)].
% 148.22/148.07 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,ring_1_of_int(int),A)),hAPP(int,int,ring_1_of_int(int),B))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)). [resolve(6089,a,6227,a)].
% 148.22/148.07 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,ring_1_of_int(int),A)),hAPP(int,int,ring_1_of_int(int),B))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)). [resolve(6089,a,6228,a)].
% 148.22/148.07 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,ring_1_of_int(int),A)),hAPP(int,int,ring_1_of_int(int),B))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)). [resolve(6089,a,6229,a)].
% 148.22/148.07 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,ring_1_of_int(int),A)),zero_zero(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),zero_zero(int))). [resolve(6089,a,6230,a)].
% 148.22/148.07 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,ring_1_of_int(int),A)),zero_zero(int))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),zero_zero(int))). [resolve(6089,a,6231,a)].
% 148.22/148.07 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,ring_1_of_int(int),A))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A)). [resolve(6089,a,6232,a)].
% 148.22/148.07 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,ring_1_of_int(int),A))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A)). [resolve(6089,a,6233,a)].
% 148.30/148.10 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,ring_1_of_int(int),A)),zero_zero(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),zero_zero(int))). [resolve(6089,a,6234,a)].
% 148.30/148.10 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,ring_1_of_int(int),A)),zero_zero(int))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),zero_zero(int))). [resolve(6089,a,6235,a)].
% 148.30/148.10 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,ring_1_of_int(int),A))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A)). [resolve(6089,a,6236,a)].
% 148.30/148.10 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,ring_1_of_int(int),A))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A)). [resolve(6089,a,6237,a)].
% 148.30/148.10 6238 linordered_idom(rat) # label(arity_Rat_Orat___Rings_Olinordered__idom) # label(axiom). [assumption].
% 148.30/148.10 Derived: -number_ring(rat) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(int,rat,number_number_of(rat),A)),hAPP(int,rat,number_number_of(rat),B))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)). [resolve(6238,a,6090,b)].
% 148.30/148.10 Derived: -number_ring(rat) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(int,rat,number_number_of(rat),A)),hAPP(int,rat,number_number_of(rat),B))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)). [resolve(6238,a,6091,b)].
% 148.30/148.10 Derived: -number_ring(rat) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(int,rat,number_number_of(rat),A)),hAPP(int,rat,number_number_of(rat),B))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)). [resolve(6238,a,6092,b)].
% 148.30/148.10 Derived: -number_ring(rat) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(int,rat,number_number_of(rat),A)),hAPP(int,rat,number_number_of(rat),B))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)). [resolve(6238,a,6093,b)].
% 148.30/148.10 Derived: ti(rat,A) = ti(rat,B) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),A)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),B)). [resolve(6238,a,6094,a)].
% 148.30/148.10 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),A)),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),zero_zero(rat))). [resolve(6238,a,6095,a)].
% 148.30/148.10 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),A)),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),zero_zero(rat))). [resolve(6238,a,6096,a)].
% 148.30/148.10 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),B),one_one(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),B),A)),A)). [resolve(6238,a,6097,a)].
% 148.30/148.10 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),B),one_one(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B)),A)). [resolve(6238,a,6098,a)].
% 148.30/148.10 Derived: -hBOOL(hAPP(fun(rat,bool),bool,hAPP(rat,fun(fun(rat,bool),bool),member(rat),A),ring_1_Ints(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),one_one(rat)),A)),A)),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),zero_zero(rat))). [resolve(6238,a,6099,a)].
% 148.30/148.11 Derived: -hBOOL(hAPP(fun(rat,bool),bool,hAPP(rat,fun(fun(rat,bool),bool),member(rat),A),ring_1_Ints(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),one_one(rat)),A)),A)),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),zero_zero(rat))). [resolve(6238,a,6100,a)].
% 148.30/148.11 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,abs_abs(rat),A)),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),B)). [resolve(6238,a,6101,a)].
% 148.30/148.11 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,abs_abs(rat),A)),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,uminus_uminus(rat),A)),B)). [resolve(6238,a,6102,a)].
% 148.30/148.11 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,abs_abs(rat),A)),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,uminus_uminus(rat),A)),B)). [resolve(6238,a,6103,a)].
% 148.30/148.11 Derived: -number_ring(rat) | hAPP(rat,rat,abs_abs(rat),hAPP(int,rat,number_number_of(rat),min)) = one_one(rat). [resolve(6238,a,6104,b)].
% 148.30/148.11 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(rat,rat,abs_abs(rat),A)),hAPP(rat,rat,abs_abs(rat),A)) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),A). [resolve(6238,a,6105,a)].
% 148.30/148.11 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(rat,rat,abs_abs(rat),A)),hAPP(rat,rat,abs_abs(rat),B)) = hAPP(rat,rat,abs_abs(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B)). [resolve(6238,a,6106,a)].
% 148.30/148.11 Derived: hAPP(rat,rat,abs_abs(rat),one_one(rat)) = one_one(rat). [resolve(6238,a,6107,a)].
% 148.30/148.11 Derived: -number_ring(rat) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(int,rat,number_number_of(rat),A)),zero_zero(rat))) | hAPP(int,rat,number_number_of(rat),A) = hAPP(rat,rat,abs_abs(rat),hAPP(int,rat,number_number_of(rat),A)). [resolve(6238,a,6109,b)].
% 148.30/148.11 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,abs_abs(rat),A)),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,abs_abs(rat),C)),D)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(rat,rat,abs_abs(rat),A)),hAPP(rat,rat,abs_abs(rat),C))),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),B),D))). [resolve(6238,a,6110,a)].
% 148.30/148.11 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,abs_abs(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),A),B))),C)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),B),C)),A)). [resolve(6238,a,6111,a)].
% 148.30/148.11 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,abs_abs(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),A),B))),C)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),B),C))). [resolve(6238,a,6112,a)].
% 148.30/148.11 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,abs_abs(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),A),B))),C)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),B),C)),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),B),C))). [resolve(6238,a,6113,a)].
% 148.30/148.11 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),hAPP(rat,rat,uminus_uminus(rat),A))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),zero_zero(rat))). [resolve(6238,a,6114,a)].
% 148.30/148.11 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),hAPP(rat,rat,uminus_uminus(rat),A))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),zero_zero(rat))). [resolve(6238,a,6115,a)].
% 148.30/148.11 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),A)) | hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(rat,rat,abs_abs(rat),B)),A) = hAPP(rat,rat,abs_abs(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),B),A)). [resolve(6238,a,6116,a)].
% 148.30/148.12 Derived: -number_ring(rat) | hAPP(rat,rat,abs_abs(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),hAPP(int,rat,number_number_of(rat),min)),A)) = one_one(rat). [resolve(6238,a,6117,b)].
% 148.30/148.12 Derived: hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),hAPP(rat,rat,abs_abs(rat),A)),B) = hAPP(rat,rat,abs_abs(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),B)). [resolve(6238,a,6118,a)].
% 148.30/148.12 Derived: hAPP(rat,rat,abs_abs(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),hAPP(rat,rat,uminus_uminus(rat),A)),B)) = hAPP(rat,rat,abs_abs(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),B)). [resolve(6238,a,6119,a)].
% 148.30/148.12 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),hAPP(rat,rat,abs_abs(rat),A)),B))). [resolve(6238,a,6120,a)].
% 148.30/148.12 Derived: -number_ring(rat) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(int,rat,number_number_of(rat),A))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),A)). [resolve(6238,a,6121,b)].
% 148.30/148.12 Derived: -number_ring(rat) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(int,rat,number_number_of(rat),A))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),A)). [resolve(6238,a,6122,b)].
% 148.30/148.12 Derived: -number_ring(rat) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(int,rat,number_number_of(rat),A)),zero_zero(rat))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),pls)). [resolve(6238,a,6123,b)].
% 148.30/148.12 Derived: -number_ring(rat) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(int,rat,number_number_of(rat),A)),zero_zero(rat))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),pls)). [resolve(6238,a,6124,b)].
% 148.30/148.12 Derived: -number_ring(rat) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),hAPP(int,rat,number_number_of(rat),A))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),A)). [resolve(6238,a,6125,b)].
% 148.30/148.12 Derived: -number_ring(rat) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),hAPP(int,rat,number_number_of(rat),A))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),A)). [resolve(6238,a,6126,b)].
% 148.30/148.12 Derived: -number_ring(rat) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(int,rat,number_number_of(rat),A)),zero_zero(rat))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),pls)). [resolve(6238,a,6127,b)].
% 148.30/148.12 Derived: -number_ring(rat) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(int,rat,number_number_of(rat),A)),zero_zero(rat))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),pls)). [resolve(6238,a,6128,b)].
% 148.30/148.12 Derived: -number_ring(rat) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(int,rat,number_number_of(rat),A)),one_one(rat))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),hAPP(int,int,bit1,pls))). [resolve(6238,a,6129,b)].
% 148.30/148.12 Derived: -number_ring(rat) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(int,rat,number_number_of(rat),A)),one_one(rat))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),hAPP(int,int,bit1,pls))). [resolve(6238,a,6130,b)].
% 148.30/148.12 Derived: -number_ring(rat) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),one_one(rat)),hAPP(int,rat,number_number_of(rat),A))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,pls)),A)). [resolve(6238,a,6131,b)].
% 148.30/148.12 Derived: -number_ring(rat) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),one_one(rat)),hAPP(int,rat,number_number_of(rat),A))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,pls)),A)). [resolve(6238,a,6132,b)].
% 148.30/148.12 Derived: -number_ring(rat) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(int,rat,number_number_of(rat),A)),one_one(rat))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),hAPP(int,int,bit1,pls))). [resolve(6238,a,6133,b)].
% 148.30/148.13 Derived: -number_ring(rat) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(int,rat,number_number_of(rat),A)),one_one(rat))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),hAPP(int,int,bit1,pls))). [resolve(6238,a,6134,b)].
% 148.30/148.13 Derived: -number_ring(rat) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),one_one(rat)),hAPP(int,rat,number_number_of(rat),A))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,pls)),A)). [resolve(6238,a,6135,b)].
% 148.30/148.13 Derived: -number_ring(rat) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),one_one(rat)),hAPP(int,rat,number_number_of(rat),A))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,pls)),A)). [resolve(6238,a,6136,b)].
% 148.30/148.13 Derived: hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),hAPP(rat,rat,abs_abs(rat),A)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))). [resolve(6238,a,6137,a)].
% 148.30/148.13 Derived: hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(rat,rat,abs_abs(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))). [resolve(6238,a,6138,a)].
% 148.30/148.13 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))). [resolve(6238,a,6139,a)].
% 148.30/148.13 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),zero_zero(rat))). [resolve(6238,a,6140,a)].
% 148.30/148.13 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) | zero_zero(rat) != ti(rat,A). [resolve(6238,a,6141,a)].
% 148.30/148.13 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) | zero_zero(rat) = ti(rat,A). [resolve(6238,a,6142,a)].
% 148.30/148.13 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) != zero_zero(rat) | zero_zero(rat) = ti(rat,A). [resolve(6238,a,6143,a)].
% 148.30/148.13 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) != zero_zero(rat) | zero_zero(rat) = ti(rat,B). [resolve(6238,a,6144,a)].
% 148.30/148.13 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) = zero_zero(rat) | zero_zero(rat) != ti(rat,A) | zero_zero(rat) != ti(rat,B). [resolve(6238,a,6145,a)].
% 148.30/148.13 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),zero_zero(rat))) | zero_zero(rat) = ti(rat,A). [resolve(6238,a,6146,a)].
% 148.30/148.14 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),zero_zero(rat))) | zero_zero(rat) = ti(rat,B). [resolve(6238,a,6147,a)].
% 148.30/148.14 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),zero_zero(rat))) | zero_zero(rat) != ti(rat,A) | zero_zero(rat) != ti(rat,B). [resolve(6238,a,6148,a)].
% 148.30/148.14 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))). [resolve(6238,a,6149,a)].
% 148.30/148.14 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),zero_zero(rat))). [resolve(6238,a,6150,a)].
% 148.30/148.14 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))) | zero_zero(rat) != ti(rat,A) | zero_zero(rat) != ti(rat,B). [resolve(6238,a,6151,a)].
% 148.30/148.14 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))) | zero_zero(rat) = ti(rat,A). [resolve(6238,a,6152,a)].
% 148.30/148.14 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))) | zero_zero(rat) = ti(rat,B). [resolve(6238,a,6153,a)].
% 148.30/148.14 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),B)))). [resolve(6238,a,6154,a)].
% 148.30/148.14 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),B))),zero_zero(rat))) | zero_zero(rat) = ti(rat,A). [resolve(6238,a,6155,a)].
% 148.30/148.15 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),B))))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),A)). [resolve(6238,a,6156,a)].
% 148.30/148.15 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),B)))),zero_zero(rat))). [resolve(6238,a,6157,a)].
% 148.30/148.15 Derived: hBOOL(hAPP(nat,bool,even_odd_even(nat),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),B),C)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),B),A)),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),C),A))). [resolve(6238,a,6158,a)].
% 148.30/148.15 Derived: -hBOOL(hAPP(nat,bool,even_odd_even(nat),A)) | hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),hAPP(rat,rat,abs_abs(rat),B)),A) = hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),B),A). [resolve(6238,a,6159,a)].
% 148.30/148.15 Derived: hBOOL(hAPP(nat,bool,even_odd_even(nat),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),B),A))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),B)). [resolve(6238,a,6160,a)].
% 148.30/148.15 Derived: hBOOL(hAPP(nat,bool,even_odd_even(nat),A)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),B),A))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),B)). [resolve(6238,a,6161,a)].
% 148.30/148.15 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),B))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),A)). [resolve(6238,a,6163,a)].
% 148.30/148.15 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),B))) | -hBOOL(hAPP(nat,bool,even_odd_even(nat),B)). [resolve(6238,a,6164,a)].
% 148.30/148.15 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),B)),zero_zero(rat))) | -hBOOL(hAPP(nat,bool,even_odd_even(nat),B)). [resolve(6238,a,6168,a)].
% 148.30/148.15 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),B)),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),zero_zero(rat))). [resolve(6238,a,6169,a)].
% 148.30/148.15 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),B)),zero_zero(rat))) | hBOOL(hAPP(nat,bool,even_odd_even(nat),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),zero_zero(rat))). [resolve(6238,a,6170,a)].
% 148.30/148.15 Derived: -hBOOL(hAPP(nat,bool,even_odd_even(nat),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,abs_abs(rat),B)),hAPP(rat,rat,abs_abs(rat),C))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),B),A)),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),C),A))). [resolve(6238,a,6171,a)].
% 148.30/148.15 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),B)),zero_zero(rat))) | zero_zero(nat) != B. [resolve(6238,a,6173,a)].
% 148.30/148.15 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),B)),zero_zero(rat))) | -hBOOL(hAPP(nat,bool,even_odd_even(nat),B)) | zero_zero(rat) = ti(rat,A). [resolve(6238,a,6174,a)].
% 148.30/148.16 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),B)),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),zero_zero(rat))) | hBOOL(hAPP(nat,bool,even_odd_even(nat),B)). [resolve(6238,a,6175,a)].
% 148.30/148.16 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),B)),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),zero_zero(rat))) | zero_zero(rat) = ti(rat,A). [resolve(6238,a,6176,a)].
% 148.30/148.16 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),B)),zero_zero(rat))) | zero_zero(nat) = B | hBOOL(hAPP(nat,bool,even_odd_even(nat),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),zero_zero(rat))). [resolve(6238,a,6177,a)].
% 148.30/148.16 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),B)),zero_zero(rat))) | zero_zero(nat) = B | -hBOOL(hAPP(nat,bool,even_odd_even(nat),B)) | zero_zero(rat) != ti(rat,A). [resolve(6238,a,6178,a)].
% 148.30/148.16 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),B))) | zero_zero(nat) = B | hBOOL(hAPP(nat,bool,even_odd_even(nat),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)). [resolve(6238,a,6179,a)].
% 148.30/148.16 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),B))) | zero_zero(nat) = B | zero_zero(rat) != ti(rat,A) | -hBOOL(hAPP(nat,bool,even_odd_even(nat),B)). [resolve(6238,a,6180,a)].
% 148.30/148.16 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),B))) | zero_zero(nat) = B | zero_zero(rat) != ti(rat,A) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)). [resolve(6238,a,6181,a)].
% 148.30/148.16 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),B))) | zero_zero(nat) != B. [resolve(6238,a,6182,a)].
% 148.30/148.16 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),B))) | -hBOOL(hAPP(nat,bool,even_odd_even(nat),B)) | zero_zero(rat) = ti(rat,A). [resolve(6238,a,6183,a)].
% 148.30/148.16 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),B))) | hBOOL(hAPP(nat,bool,even_odd_even(nat),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)). [resolve(6238,a,6184,a)].
% 148.30/148.16 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),hAPP(int,nat,number_number_of(nat),B))),zero_zero(rat))) | hAPP(int,nat,number_number_of(nat),B) != zero_zero(nat). [resolve(6238,a,6191,a)].
% 148.30/148.16 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),hAPP(int,nat,number_number_of(nat),B))),zero_zero(rat))) | hAPP(int,nat,number_number_of(nat),B) = zero_zero(nat) | hBOOL(hAPP(nat,bool,even_odd_even(nat),hAPP(int,nat,number_number_of(nat),B))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),zero_zero(rat))). [resolve(6238,a,6195,a)].
% 148.30/148.16 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),hAPP(int,nat,number_number_of(nat),B))),zero_zero(rat))) | hAPP(int,nat,number_number_of(nat),B) = zero_zero(nat) | -hBOOL(hAPP(nat,bool,even_odd_even(nat),hAPP(int,nat,number_number_of(nat),B))) | zero_zero(rat) != ti(rat,A). [resolve(6238,a,6196,a)].
% 148.30/148.16 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),hAPP(int,nat,number_number_of(nat),B)))) | hAPP(int,nat,number_number_of(nat),B) = zero_zero(nat) | hBOOL(hAPP(nat,bool,even_odd_even(nat),hAPP(int,nat,number_number_of(nat),B))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)). [resolve(6238,a,6197,a)].
% 148.37/148.18 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),hAPP(int,nat,number_number_of(nat),B)))) | hAPP(int,nat,number_number_of(nat),B) = zero_zero(nat) | zero_zero(rat) != ti(rat,A) | -hBOOL(hAPP(nat,bool,even_odd_even(nat),hAPP(int,nat,number_number_of(nat),B))). [resolve(6238,a,6198,a)].
% 148.37/148.18 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),hAPP(int,nat,number_number_of(nat),B)))) | hAPP(int,nat,number_number_of(nat),B) = zero_zero(nat) | zero_zero(rat) != ti(rat,A) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)). [resolve(6238,a,6199,a)].
% 148.37/148.18 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),hAPP(int,nat,number_number_of(nat),B)))) | hAPP(int,nat,number_number_of(nat),B) != zero_zero(nat). [resolve(6238,a,6200,a)].
% 148.37/148.18 Derived: hAPP(rat,rat,sgn_sgn(rat),hAPP(rat,rat,sgn_sgn(rat),A)) = hAPP(rat,rat,sgn_sgn(rat),A). [resolve(6238,a,6203,a)].
% 148.37/148.18 Derived: hAPP(rat,rat,sgn_sgn(rat),A) != zero_zero(rat) | zero_zero(rat) = ti(rat,A). [resolve(6238,a,6204,a)].
% 148.37/148.18 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(rat,rat,sgn_sgn(rat),A)),hAPP(rat,rat,sgn_sgn(rat),B)) = hAPP(rat,rat,sgn_sgn(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B)). [resolve(6238,a,6206,a)].
% 148.37/148.18 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,sgn_sgn(rat),A)),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),zero_zero(rat))). [resolve(6238,a,6207,a)].
% 148.37/148.18 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,sgn_sgn(rat),A)),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),zero_zero(rat))). [resolve(6238,a,6208,a)].
% 148.37/148.18 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(rat,rat,sgn_sgn(rat),A))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)). [resolve(6238,a,6209,a)].
% 148.37/148.18 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(rat,rat,sgn_sgn(rat),A))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)). [resolve(6238,a,6210,a)].
% 148.37/148.18 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(rat,rat,sgn_sgn(rat),A)),hAPP(rat,rat,abs_abs(rat),A)) = ti(rat,A). [resolve(6238,a,6211,a)].
% 148.37/148.18 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),hAPP(rat,rat,sgn_sgn(rat),A)) = hAPP(rat,rat,abs_abs(rat),A). [resolve(6238,a,6212,a)].
% 148.37/148.18 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)) | hAPP(rat,rat,sgn_sgn(rat),A) = one_one(rat). [resolve(6238,a,6213,a)].
% 148.37/148.18 Derived: hAPP(rat,rat,sgn_sgn(rat),A) != one_one(rat) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)). [resolve(6238,a,6214,a)].
% 148.37/148.18 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),zero_zero(rat))) | hAPP(rat,rat,uminus_uminus(rat),one_one(rat)) = hAPP(rat,rat,sgn_sgn(rat),A). [resolve(6238,a,6216,a)].
% 148.37/148.18 Derived: hAPP(rat,rat,uminus_uminus(rat),one_one(rat)) != hAPP(rat,rat,sgn_sgn(rat),A) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),zero_zero(rat))). [resolve(6238,a,6217,a)].
% 148.37/148.18 Derived: hAPP(nat,rat,semiring_1_of_nat(rat),A) = hAPP(rat,rat,abs_abs(rat),hAPP(nat,rat,semiring_1_of_nat(rat),A)). [resolve(6238,a,6219,a)].
% 148.37/148.18 Derived: -number_ring(rat) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(nat,rat,semiring_1_of_nat(rat),A)),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),hAPP(int,rat,number_number_of(rat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),A))). [resolve(6238,a,6220,b)].
% 148.37/148.18 Derived: hAPP(rat,rat,abs_abs(rat),A) != hAPP(rat,rat,abs_abs(rat),B) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),dvd_dvd(rat),A),B)). [resolve(6238,a,6221,a)].
% 148.40/148.21 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),dvd_dvd(rat),hAPP(rat,rat,abs_abs(rat),A)),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),dvd_dvd(rat),A),B)). [resolve(6238,a,6222,a)].
% 148.40/148.21 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),dvd_dvd(rat),hAPP(rat,rat,abs_abs(rat),A)),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),dvd_dvd(rat),A),B)). [resolve(6238,a,6223,a)].
% 148.40/148.21 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),dvd_dvd(rat),A),hAPP(rat,rat,abs_abs(rat),B))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),dvd_dvd(rat),A),B)). [resolve(6238,a,6224,a)].
% 148.40/148.21 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),dvd_dvd(rat),A),hAPP(rat,rat,abs_abs(rat),B))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),dvd_dvd(rat),A),B)). [resolve(6238,a,6225,a)].
% 148.40/148.21 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(int,rat,ring_1_of_int(rat),A)),hAPP(int,rat,ring_1_of_int(rat),B))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)). [resolve(6238,a,6226,a)].
% 148.40/148.21 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(int,rat,ring_1_of_int(rat),A)),hAPP(int,rat,ring_1_of_int(rat),B))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)). [resolve(6238,a,6227,a)].
% 148.40/148.21 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(int,rat,ring_1_of_int(rat),A)),hAPP(int,rat,ring_1_of_int(rat),B))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)). [resolve(6238,a,6228,a)].
% 148.40/148.21 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(int,rat,ring_1_of_int(rat),A)),hAPP(int,rat,ring_1_of_int(rat),B))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)). [resolve(6238,a,6229,a)].
% 148.40/148.21 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(int,rat,ring_1_of_int(rat),A)),zero_zero(rat))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),zero_zero(int))). [resolve(6238,a,6230,a)].
% 148.40/148.21 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(int,rat,ring_1_of_int(rat),A)),zero_zero(rat))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),zero_zero(int))). [resolve(6238,a,6231,a)].
% 148.40/148.21 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(int,rat,ring_1_of_int(rat),A))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A)). [resolve(6238,a,6232,a)].
% 148.40/148.21 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(int,rat,ring_1_of_int(rat),A))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A)). [resolve(6238,a,6233,a)].
% 148.40/148.21 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(int,rat,ring_1_of_int(rat),A)),zero_zero(rat))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),zero_zero(int))). [resolve(6238,a,6234,a)].
% 148.40/148.21 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(int,rat,ring_1_of_int(rat),A)),zero_zero(rat))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),zero_zero(int))). [resolve(6238,a,6235,a)].
% 148.40/148.21 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),hAPP(int,rat,ring_1_of_int(rat),A))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A)). [resolve(6238,a,6236,a)].
% 148.40/148.21 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),hAPP(int,rat,ring_1_of_int(rat),A))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A)). [resolve(6238,a,6237,a)].
% 148.40/148.21 6239 linordered_idom(real) # label(arity_RealDef_Oreal___Rings_Olinordered__idom) # label(axiom). [assumption].
% 148.40/148.21 Derived: -number_ring(real) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,number_number_of(real),A)),hAPP(int,real,number_number_of(real),B))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)). [resolve(6239,a,6090,b)].
% 148.40/148.21 Derived: -number_ring(real) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,number_number_of(real),A)),hAPP(int,real,number_number_of(real),B))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)). [resolve(6239,a,6091,b)].
% 148.41/148.22 Derived: -number_ring(real) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,number_number_of(real),A)),hAPP(int,real,number_number_of(real),B))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)). [resolve(6239,a,6092,b)].
% 148.41/148.22 Derived: -number_ring(real) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,number_number_of(real),A)),hAPP(int,real,number_number_of(real),B))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)). [resolve(6239,a,6093,b)].
% 148.41/148.22 Derived: ti(real,A) = ti(real,B) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),A)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)). [resolve(6239,a,6094,a)].
% 148.41/148.22 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),A)),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))). [resolve(6239,a,6095,a)].
% 148.41/148.22 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),A)),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))). [resolve(6239,a,6096,a)].
% 148.41/148.22 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),one_one(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),A)),A)). [resolve(6239,a,6097,a)].
% 148.41/148.22 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),one_one(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),A)). [resolve(6239,a,6098,a)].
% 148.41/148.22 Derived: -hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),A),ring_1_Ints(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),one_one(real)),A)),A)),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))). [resolve(6239,a,6099,a)].
% 148.41/148.22 Derived: -hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),A),ring_1_Ints(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),one_one(real)),A)),A)),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))). [resolve(6239,a,6100,a)].
% 148.41/148.22 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,abs_abs(real),A)),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)). [resolve(6239,a,6101,a)].
% 148.41/148.22 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,abs_abs(real),A)),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,uminus_uminus(real),A)),B)). [resolve(6239,a,6102,a)].
% 148.41/148.22 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,abs_abs(real),A)),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,uminus_uminus(real),A)),B)). [resolve(6239,a,6103,a)].
% 148.41/148.22 Derived: -number_ring(real) | hAPP(real,real,abs_abs(real),hAPP(int,real,number_number_of(real),min)) = one_one(real). [resolve(6239,a,6104,b)].
% 148.41/148.23 Derived: hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,abs_abs(real),A)),hAPP(real,real,abs_abs(real),A)) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),A). [resolve(6239,a,6105,a)].
% 148.41/148.23 Derived: hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,abs_abs(real),A)),hAPP(real,real,abs_abs(real),B)) = hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)). [resolve(6239,a,6106,a)].
% 148.41/148.23 Derived: hAPP(real,real,abs_abs(real),one_one(real)) = one_one(real). [resolve(6239,a,6107,a)].
% 148.41/148.23 Derived: -number_ring(real) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,number_number_of(real),A)),zero_zero(real))) | hAPP(int,real,number_number_of(real),A) = hAPP(real,real,abs_abs(real),hAPP(int,real,number_number_of(real),A)). [resolve(6239,a,6109,b)].
% 148.41/148.23 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,abs_abs(real),A)),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,abs_abs(real),C)),D)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,abs_abs(real),A)),hAPP(real,real,abs_abs(real),C))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),D))). [resolve(6239,a,6110,a)].
% 148.41/148.23 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),B))),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),B),C)),A)). [resolve(6239,a,6111,a)].
% 148.41/148.23 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),B))),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),B),C))). [resolve(6239,a,6112,a)].
% 148.41/148.23 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),B))),C)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),B),C)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),B),C))). [resolve(6239,a,6113,a)].
% 148.41/148.23 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),hAPP(real,real,uminus_uminus(real),A))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))). [resolve(6239,a,6114,a)].
% 148.41/148.23 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),hAPP(real,real,uminus_uminus(real),A))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))). [resolve(6239,a,6115,a)].
% 148.41/148.23 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A)) | hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,abs_abs(real),B)),A) = hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),A)). [resolve(6239,a,6116,a)].
% 148.41/148.23 Derived: -number_ring(real) | hAPP(real,real,abs_abs(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),min)),A)) = one_one(real). [resolve(6239,a,6117,b)].
% 148.41/148.23 Derived: hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,abs_abs(real),A)),B) = hAPP(real,real,abs_abs(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),B)). [resolve(6239,a,6118,a)].
% 148.41/148.23 Derived: hAPP(real,real,abs_abs(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,uminus_uminus(real),A)),B)) = hAPP(real,real,abs_abs(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),B)). [resolve(6239,a,6119,a)].
% 148.41/148.23 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,abs_abs(real),A)),B))). [resolve(6239,a,6120,a)].
% 148.41/148.24 Derived: -number_ring(real) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(int,real,number_number_of(real),A))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),A)). [resolve(6239,a,6121,b)].
% 148.41/148.24 Derived: -number_ring(real) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(int,real,number_number_of(real),A))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),A)). [resolve(6239,a,6122,b)].
% 148.41/148.24 Derived: -number_ring(real) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,number_number_of(real),A)),zero_zero(real))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),pls)). [resolve(6239,a,6123,b)].
% 148.41/148.24 Derived: -number_ring(real) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,number_number_of(real),A)),zero_zero(real))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),pls)). [resolve(6239,a,6124,b)].
% 148.41/148.24 Derived: -number_ring(real) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(int,real,number_number_of(real),A))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),A)). [resolve(6239,a,6125,b)].
% 148.41/148.24 Derived: -number_ring(real) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(int,real,number_number_of(real),A))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),A)). [resolve(6239,a,6126,b)].
% 148.41/148.24 Derived: -number_ring(real) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,number_number_of(real),A)),zero_zero(real))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),pls)). [resolve(6239,a,6127,b)].
% 148.41/148.24 Derived: -number_ring(real) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,number_number_of(real),A)),zero_zero(real))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),pls)). [resolve(6239,a,6128,b)].
% 148.41/148.24 Derived: -number_ring(real) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,number_number_of(real),A)),one_one(real))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),hAPP(int,int,bit1,pls))). [resolve(6239,a,6129,b)].
% 148.41/148.24 Derived: -number_ring(real) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,number_number_of(real),A)),one_one(real))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),hAPP(int,int,bit1,pls))). [resolve(6239,a,6130,b)].
% 148.41/148.24 Derived: -number_ring(real) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),hAPP(int,real,number_number_of(real),A))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,pls)),A)). [resolve(6239,a,6131,b)].
% 148.41/148.24 Derived: -number_ring(real) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),hAPP(int,real,number_number_of(real),A))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,pls)),A)). [resolve(6239,a,6132,b)].
% 148.41/148.24 Derived: -number_ring(real) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,number_number_of(real),A)),one_one(real))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),hAPP(int,int,bit1,pls))). [resolve(6239,a,6133,b)].
% 148.41/148.24 Derived: -number_ring(real) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,number_number_of(real),A)),one_one(real))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),hAPP(int,int,bit1,pls))). [resolve(6239,a,6134,b)].
% 148.41/148.24 Derived: -number_ring(real) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),one_one(real)),hAPP(int,real,number_number_of(real),A))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,pls)),A)). [resolve(6239,a,6135,b)].
% 148.41/148.24 Derived: -number_ring(real) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),one_one(real)),hAPP(int,real,number_number_of(real),A))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,pls)),A)). [resolve(6239,a,6136,b)].
% 148.41/148.25 Derived: hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,abs_abs(real),A)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))). [resolve(6239,a,6137,a)].
% 148.41/148.25 Derived: hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(real,real,abs_abs(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))). [resolve(6239,a,6138,a)].
% 148.41/148.25 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))). [resolve(6239,a,6139,a)].
% 148.41/148.25 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),zero_zero(real))). [resolve(6239,a,6140,a)].
% 148.41/148.25 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) | zero_zero(real) != ti(real,A). [resolve(6239,a,6141,a)].
% 148.41/148.25 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) | zero_zero(real) = ti(real,A). [resolve(6239,a,6142,a)].
% 148.41/148.25 Derived: hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) != zero_zero(real) | zero_zero(real) = ti(real,A). [resolve(6239,a,6143,a)].
% 148.41/148.25 Derived: hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) != zero_zero(real) | zero_zero(real) = ti(real,B). [resolve(6239,a,6144,a)].
% 148.41/148.25 Derived: hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) = zero_zero(real) | zero_zero(real) != ti(real,A) | zero_zero(real) != ti(real,B). [resolve(6239,a,6145,a)].
% 148.41/148.25 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),zero_zero(real))) | zero_zero(real) = ti(real,A). [resolve(6239,a,6146,a)].
% 148.41/148.25 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),zero_zero(real))) | zero_zero(real) = ti(real,B). [resolve(6239,a,6147,a)].
% 148.41/148.25 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),zero_zero(real))) | zero_zero(real) != ti(real,A) | zero_zero(real) != ti(real,B). [resolve(6239,a,6148,a)].
% 148.41/148.25 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))). [resolve(6239,a,6149,a)].
% 148.41/148.25 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),zero_zero(real))). [resolve(6239,a,6150,a)].
% 148.41/148.25 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))) | zero_zero(real) != ti(real,A) | zero_zero(real) != ti(real,B). [resolve(6239,a,6151,a)].
% 148.41/148.25 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))) | zero_zero(real) = ti(real,A). [resolve(6239,a,6152,a)].
% 148.41/148.25 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))) | zero_zero(real) = ti(real,B). [resolve(6239,a,6153,a)].
% 148.41/148.25 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),B)))). [resolve(6239,a,6154,a)].
% 148.41/148.25 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),B))),zero_zero(real))) | zero_zero(real) = ti(real,A). [resolve(6239,a,6155,a)].
% 148.41/148.25 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),B))))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A)). [resolve(6239,a,6156,a)].
% 148.41/148.26 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),B)))),zero_zero(real))). [resolve(6239,a,6157,a)].
% 148.41/148.26 Derived: hBOOL(hAPP(nat,bool,even_odd_even(nat),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),B),A)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),C),A))). [resolve(6239,a,6158,a)].
% 148.41/148.26 Derived: -hBOOL(hAPP(nat,bool,even_odd_even(nat),A)) | hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,abs_abs(real),B)),A) = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),B),A). [resolve(6239,a,6159,a)].
% 148.41/148.26 Derived: hBOOL(hAPP(nat,bool,even_odd_even(nat),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),B),A))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),B)). [resolve(6239,a,6160,a)].
% 148.41/148.26 Derived: hBOOL(hAPP(nat,bool,even_odd_even(nat),A)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),B),A))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),B)). [resolve(6239,a,6161,a)].
% 148.41/148.26 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),B))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A)). [resolve(6239,a,6163,a)].
% 148.41/148.26 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),B))) | -hBOOL(hAPP(nat,bool,even_odd_even(nat),B)). [resolve(6239,a,6164,a)].
% 148.41/148.26 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),B)),zero_zero(real))) | -hBOOL(hAPP(nat,bool,even_odd_even(nat),B)). [resolve(6239,a,6168,a)].
% 148.41/148.26 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),B)),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))). [resolve(6239,a,6169,a)].
% 148.41/148.26 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),B)),zero_zero(real))) | hBOOL(hAPP(nat,bool,even_odd_even(nat),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))). [resolve(6239,a,6170,a)].
% 148.41/148.26 Derived: -hBOOL(hAPP(nat,bool,even_odd_even(nat),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),B)),hAPP(real,real,abs_abs(real),C))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),B),A)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),C),A))). [resolve(6239,a,6171,a)].
% 148.41/148.26 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),B)),zero_zero(real))) | zero_zero(nat) != B. [resolve(6239,a,6173,a)].
% 148.41/148.26 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),B)),zero_zero(real))) | -hBOOL(hAPP(nat,bool,even_odd_even(nat),B)) | zero_zero(real) = ti(real,A). [resolve(6239,a,6174,a)].
% 148.41/148.26 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),B)),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),zero_zero(real))) | hBOOL(hAPP(nat,bool,even_odd_even(nat),B)). [resolve(6239,a,6175,a)].
% 148.41/148.28 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),B)),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),zero_zero(real))) | zero_zero(real) = ti(real,A). [resolve(6239,a,6176,a)].
% 148.41/148.28 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),B)),zero_zero(real))) | zero_zero(nat) = B | hBOOL(hAPP(nat,bool,even_odd_even(nat),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),zero_zero(real))). [resolve(6239,a,6177,a)].
% 148.41/148.28 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),B)),zero_zero(real))) | zero_zero(nat) = B | -hBOOL(hAPP(nat,bool,even_odd_even(nat),B)) | zero_zero(real) != ti(real,A). [resolve(6239,a,6178,a)].
% 148.41/148.28 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),B))) | zero_zero(nat) = B | hBOOL(hAPP(nat,bool,even_odd_even(nat),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)). [resolve(6239,a,6179,a)].
% 148.41/148.28 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),B))) | zero_zero(nat) = B | zero_zero(real) != ti(real,A) | -hBOOL(hAPP(nat,bool,even_odd_even(nat),B)). [resolve(6239,a,6180,a)].
% 148.41/148.28 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),B))) | zero_zero(nat) = B | zero_zero(real) != ti(real,A) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)). [resolve(6239,a,6181,a)].
% 148.41/148.28 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),B))) | zero_zero(nat) != B. [resolve(6239,a,6182,a)].
% 148.41/148.28 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),B))) | -hBOOL(hAPP(nat,bool,even_odd_even(nat),B)) | zero_zero(real) = ti(real,A). [resolve(6239,a,6183,a)].
% 148.41/148.28 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),B))) | hBOOL(hAPP(nat,bool,even_odd_even(nat),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)). [resolve(6239,a,6184,a)].
% 148.41/148.28 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),hAPP(int,nat,number_number_of(nat),B))),zero_zero(real))) | hAPP(int,nat,number_number_of(nat),B) != zero_zero(nat). [resolve(6239,a,6191,a)].
% 148.41/148.28 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),hAPP(int,nat,number_number_of(nat),B))),zero_zero(real))) | hAPP(int,nat,number_number_of(nat),B) = zero_zero(nat) | hBOOL(hAPP(nat,bool,even_odd_even(nat),hAPP(int,nat,number_number_of(nat),B))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),zero_zero(real))). [resolve(6239,a,6195,a)].
% 148.41/148.28 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),hAPP(int,nat,number_number_of(nat),B))),zero_zero(real))) | hAPP(int,nat,number_number_of(nat),B) = zero_zero(nat) | -hBOOL(hAPP(nat,bool,even_odd_even(nat),hAPP(int,nat,number_number_of(nat),B))) | zero_zero(real) != ti(real,A). [resolve(6239,a,6196,a)].
% 148.41/148.28 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),hAPP(int,nat,number_number_of(nat),B)))) | hAPP(int,nat,number_number_of(nat),B) = zero_zero(nat) | hBOOL(hAPP(nat,bool,even_odd_even(nat),hAPP(int,nat,number_number_of(nat),B))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)). [resolve(6239,a,6197,a)].
% 148.41/148.29 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),hAPP(int,nat,number_number_of(nat),B)))) | hAPP(int,nat,number_number_of(nat),B) = zero_zero(nat) | zero_zero(real) != ti(real,A) | -hBOOL(hAPP(nat,bool,even_odd_even(nat),hAPP(int,nat,number_number_of(nat),B))). [resolve(6239,a,6198,a)].
% 148.41/148.29 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),hAPP(int,nat,number_number_of(nat),B)))) | hAPP(int,nat,number_number_of(nat),B) = zero_zero(nat) | zero_zero(real) != ti(real,A) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)). [resolve(6239,a,6199,a)].
% 148.41/148.29 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),hAPP(int,nat,number_number_of(nat),B)))) | hAPP(int,nat,number_number_of(nat),B) != zero_zero(nat). [resolve(6239,a,6200,a)].
% 148.41/148.29 Derived: hAPP(real,real,sgn_sgn(real),hAPP(real,real,sgn_sgn(real),A)) = hAPP(real,real,sgn_sgn(real),A). [resolve(6239,a,6203,a)].
% 148.41/148.29 Derived: hAPP(real,real,sgn_sgn(real),A) != zero_zero(real) | zero_zero(real) = ti(real,A). [resolve(6239,a,6204,a)].
% 148.41/148.29 Derived: hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,sgn_sgn(real),A)),hAPP(real,real,sgn_sgn(real),B)) = hAPP(real,real,sgn_sgn(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)). [resolve(6239,a,6206,a)].
% 148.41/148.29 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,sgn_sgn(real),A)),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))). [resolve(6239,a,6207,a)].
% 148.41/148.29 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,sgn_sgn(real),A)),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))). [resolve(6239,a,6208,a)].
% 148.41/148.29 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,sgn_sgn(real),A))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)). [resolve(6239,a,6209,a)].
% 148.41/148.29 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,sgn_sgn(real),A))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)). [resolve(6239,a,6210,a)].
% 148.41/148.29 Derived: hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,sgn_sgn(real),A)),hAPP(real,real,abs_abs(real),A)) = ti(real,A). [resolve(6239,a,6211,a)].
% 148.41/148.29 Derived: hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),hAPP(real,real,sgn_sgn(real),A)) = hAPP(real,real,abs_abs(real),A). [resolve(6239,a,6212,a)].
% 148.41/148.29 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | hAPP(real,real,sgn_sgn(real),A) = one_one(real). [resolve(6239,a,6213,a)].
% 148.41/148.29 Derived: hAPP(real,real,sgn_sgn(real),A) != one_one(real) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)). [resolve(6239,a,6214,a)].
% 148.41/148.29 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))) | hAPP(real,real,uminus_uminus(real),one_one(real)) = hAPP(real,real,sgn_sgn(real),A). [resolve(6239,a,6216,a)].
% 148.41/148.29 Derived: hAPP(real,real,uminus_uminus(real),one_one(real)) != hAPP(real,real,sgn_sgn(real),A) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))). [resolve(6239,a,6217,a)].
% 148.41/148.29 Derived: hAPP(nat,real,semiring_1_of_nat(real),A) = hAPP(real,real,abs_abs(real),hAPP(nat,real,semiring_1_of_nat(real),A)). [resolve(6239,a,6219,a)].
% 148.41/148.29 Derived: -number_ring(real) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(nat,real,semiring_1_of_nat(real),A)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),A))). [resolve(6239,a,6220,b)].
% 152.60/152.43 Derived: hAPP(real,real,abs_abs(real),A) != hAPP(real,real,abs_abs(real),B) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),dvd_dvd(real),A),B)). [resolve(6239,a,6221,a)].
% 152.60/152.43 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),dvd_dvd(real),hAPP(real,real,abs_abs(real),A)),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),dvd_dvd(real),A),B)). [resolve(6239,a,6222,a)].
% 152.60/152.43 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),dvd_dvd(real),hAPP(real,real,abs_abs(real),A)),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),dvd_dvd(real),A),B)). [resolve(6239,a,6223,a)].
% 152.60/152.43 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),dvd_dvd(real),A),hAPP(real,real,abs_abs(real),B))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),dvd_dvd(real),A),B)). [resolve(6239,a,6224,a)].
% 152.60/152.43 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),dvd_dvd(real),A),hAPP(real,real,abs_abs(real),B))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),dvd_dvd(real),A),B)). [resolve(6239,a,6225,a)].
% 152.60/152.43 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,ring_1_of_int(real),A)),hAPP(int,real,ring_1_of_int(real),B))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)). [resolve(6239,a,6226,a)].
% 152.60/152.43 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,ring_1_of_int(real),A)),hAPP(int,real,ring_1_of_int(real),B))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)). [resolve(6239,a,6227,a)].
% 152.60/152.43 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,ring_1_of_int(real),A)),hAPP(int,real,ring_1_of_int(real),B))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)). [resolve(6239,a,6228,a)].
% 152.60/152.43 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,ring_1_of_int(real),A)),hAPP(int,real,ring_1_of_int(real),B))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)). [resolve(6239,a,6229,a)].
% 152.60/152.43 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,ring_1_of_int(real),A)),zero_zero(real))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),zero_zero(int))). [resolve(6239,a,6230,a)].
% 152.60/152.43 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,ring_1_of_int(real),A)),zero_zero(real))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),zero_zero(int))). [resolve(6239,a,6231,a)].
% 152.60/152.43 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(int,real,ring_1_of_int(real),A))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A)). [resolve(6239,a,6232,a)].
% 152.60/152.43 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(int,real,ring_1_of_int(real),A))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A)). [resolve(6239,a,6233,a)].
% 152.60/152.43 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,ring_1_of_int(real),A)),zero_zero(real))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),zero_zero(int))). [resolve(6239,a,6234,a)].
% 152.60/152.43 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,ring_1_of_int(real),A)),zero_zero(real))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),zero_zero(int))). [resolve(6239,a,6235,a)].
% 152.60/152.43 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(int,real,ring_1_of_int(real),A))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A)). [resolve(6239,a,6236,a)].
% 152.60/152.43 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(int,real,ring_1_of_int(real),A))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A)). [resolve(6239,a,6237,a)].
% 152.60/152.43 6240 linordered_semidom(int) # label(arity_Int_Oint___Rings_Olinordered__semidom) # label(axiom). [assumption].
% 152.60/152.43 6241 -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_103_less__1__mult) # label(axiom). [clausify(233)].
% 152.60/152.43 6242 -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_104_less__add__one) # label(axiom). [clausify(234)].
% 152.60/152.43 6243 -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_334_pos__add__strict) # label(axiom). [clausify(463)].
% 152.60/152.43 6244 -linordered_semidom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),one_one(A))) # label(fact_336_zero__le__one) # label(axiom). [clausify(465)].
% 152.60/152.43 6245 -linordered_semidom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),one_one(A)),zero_zero(A))) # label(fact_337_not__one__le__zero) # label(axiom). [clausify(466)].
% 152.60/152.43 6246 -linordered_semidom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),one_one(A))) # label(fact_338_zero__less__one) # label(axiom). [clausify(467)].
% 152.60/152.43 6247 -linordered_semidom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),zero_zero(A))) # label(fact_339_not__one__less__zero) # label(axiom). [clausify(468)].
% 152.60/152.43 6248 -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_376_zero__less__two) # label(axiom). [clausify(504)].
% 152.60/152.43 6249 -linordered_semidom(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),B),one_one(A))) | 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),hAPP(nat,nat,suc,C))),B)) # label(fact_1396_realpow__Suc__le__self) # label(axiom). [clausify(1499)].
% 152.60/152.43 6250 -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_1406_power__strict__mono) # label(axiom). [clausify(1509)].
% 152.60/152.43 6251 -linordered_semidom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C))) # label(fact_1408_one__less__power) # label(axiom). [clausify(1511)].
% 152.60/152.43 6252 -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_1409_power__increasing__iff) # label(axiom). [clausify(1512)].
% 152.60/152.43 6253 -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_1409_power__increasing__iff) # label(axiom). [clausify(1512)].
% 152.60/152.43 6254 -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_1410_power__le__imp__le__exp) # label(axiom). [clausify(1513)].
% 152.60/152.44 6255 -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),zero_zero(A)),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),D),one_one(A))) | 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),C)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),D),B))) # label(fact_1411_power__decreasing) # label(axiom). [clausify(1514)].
% 152.60/152.44 6256 -linordered_semidom(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)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C))) # label(fact_1440_zero__le__power) # label(axiom). [clausify(1543)].
% 152.60/152.44 6257 -linordered_semidom(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),zero_zero(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),D)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),C),D))) # label(fact_1441_power__mono) # label(axiom). [clausify(1544)].
% 152.60/152.44 6258 -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_1442_zero__less__power) # label(axiom). [clausify(1545)].
% 152.60/152.44 6259 -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_1443_one__le__power) # label(axiom). [clausify(1546)].
% 152.60/152.44 6260 -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_1444_power__inject__exp) # label(axiom). [clausify(1547)].
% 152.60/152.44 6261 -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_1444_power__inject__exp) # label(axiom). [clausify(1547)].
% 152.60/152.44 6262 -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_1454_power__less__imp__less__base) # label(axiom). [clausify(1557)].
% 152.60/152.44 6263 -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_1455_power__gt1__lemma) # label(axiom). [clausify(1558)].
% 152.60/152.44 6264 -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_1456_power__less__power__Suc) # label(axiom). [clausify(1559)].
% 152.60/152.44 6265 -linordered_semidom(A) | hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(nat,nat,suc,C)) != hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),D),hAPP(nat,nat,suc,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)) | ti(A,B) = ti(A,D) # label(fact_1457_power__inject__base) # label(axiom). [clausify(1560)].
% 152.60/152.44 6266 -linordered_semidom(A) | -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),hAPP(nat,nat,suc,C))),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),D),hAPP(nat,nat,suc,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),B),D)) # label(fact_1458_power__le__imp__le__base) # label(axiom). [clausify(1561)].
% 152.60/152.44 6267 -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(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(nat,nat,suc,C)))) # label(fact_1461_power__gt1) # label(axiom). [clausify(1564)].
% 152.60/152.44 6268 -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_1462_power__strict__increasing) # label(axiom). [clausify(1565)].
% 152.60/152.44 6269 -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_1463_power__less__imp__less__exp) # label(axiom). [clausify(1566)].
% 152.60/152.44 6270 -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_1464_power__strict__increasing__iff) # label(axiom). [clausify(1567)].
% 152.60/152.44 6271 -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_1464_power__strict__increasing__iff) # label(axiom). [clausify(1567)].
% 152.60/152.44 6272 -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_1466_power__increasing) # label(axiom). [clausify(1569)].
% 152.60/152.44 6273 -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),B),one_one(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),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),C))) # label(fact_1467_power__Suc__less) # label(axiom). [clausify(1570)].
% 152.60/152.44 6274 -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),B),one_one(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),hAPP(nat,nat,suc,C))),one_one(A))) # label(fact_1468_power__Suc__less__one) # label(axiom). [clausify(1571)].
% 152.60/152.44 6275 -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),zero_zero(A)),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),one_one(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),D),C)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),D),B))) # label(fact_1469_power__strict__decreasing) # label(axiom). [clausify(1572)].
% 152.60/152.44 6276 -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_1470_power__eq__imp__eq__base) # label(axiom). [clausify(1573)].
% 152.60/152.44 6277 -linordered_semidom(A) | hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) != hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),C),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) | ti(A,B) = ti(A,C) # label(fact_1847_power2__eq__imp__eq) # label(axiom). [clausify(1898)].
% 152.60/152.44 6278 -linordered_semidom(A) | -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),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),C),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) | -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),B),C)) # label(fact_1848_power2__le__imp__le) # label(axiom). [clausify(1899)].
% 152.60/152.44 6279 -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),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),C),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) | -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),B),C)) # label(fact_1881_power2__less__imp__less) # label(axiom). [clausify(1926)].
% 152.60/152.44 6280 -linordered_semidom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(nat,A,semiring_1_of_nat(A),B))) # label(fact_2586_zero__le__imp__of__nat) # label(axiom). [clausify(2586)].
% 152.60/152.44 6281 -linordered_semidom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(nat,A,semiring_1_of_nat(A),B))) # label(fact_2587_of__nat__0__le__iff) # label(axiom). [clausify(2587)].
% 152.60/152.44 6282 -linordered_semidom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(nat,A,semiring_1_of_nat(A),B)),zero_zero(A))) # label(fact_2588_of__nat__less__0__iff) # label(axiom). [clausify(2588)].
% 152.60/152.44 6283 -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_2590_of__nat__less__iff) # label(axiom). [clausify(2590)].
% 152.60/152.44 6284 -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_2590_of__nat__less__iff) # label(axiom). [clausify(2590)].
% 152.60/152.44 6285 -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_2591_less__imp__of__nat__less) # label(axiom). [clausify(2591)].
% 152.60/152.44 6286 -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_2592_of__nat__less__imp__less) # label(axiom). [clausify(2592)].
% 152.60/152.44 6287 -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_2593_of__nat__le__iff) # label(axiom). [clausify(2593)].
% 152.60/152.44 6288 -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_2593_of__nat__le__iff) # label(axiom). [clausify(2593)].
% 152.60/152.44 6289 -linordered_semidom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(nat,A,semiring_1_of_nat(A),hAPP(nat,nat,fact_fact(nat),B)))) # label(fact_2641_of__nat__fact__ge__zero) # label(axiom). [clausify(2636)].
% 152.60/152.44 6290 -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),hAPP(nat,nat,fact_fact(nat),B)))) # label(fact_2642_of__nat__fact__gt__zero) # label(axiom). [clausify(2637)].
% 152.60/152.44 6291 -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_2660_of__nat__0__less__iff) # label(axiom). [clausify(2654)].
% 152.60/152.44 6292 -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_2660_of__nat__0__less__iff) # label(axiom). [clausify(2654)].
% 152.60/152.44 6293 -linordered_semidom(A) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f527(B,A,C,D)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),C),D))) # label(fact_4149_setprod__pos) # label(axiom). [clausify(4081)].
% 152.60/152.44 6294 -linordered_semidom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(B,A,C,f527(B,A,C,D)))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),C),D))) # label(fact_4149_setprod__pos) # label(axiom). [clausify(4081)].
% 152.60/152.44 6295 -linordered_semidom(A) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f528(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_co302546470etprod(B,A),D),E)),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),C),E))) # label(fact_4150_setprod__mono) # label(axiom). [clausify(4082)].
% 152.60/152.44 6296 -linordered_semidom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(B,A,C,f528(B,A,D,C,E)))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(B,A,C,f528(B,A,D,C,E))),hAPP(B,A,D,f528(B,A,D,C,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_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_4150_setprod__mono) # label(axiom). [clausify(4082)].
% 152.60/152.44 6297 -linordered_semidom(A) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f529(B,A,C,D)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),C),D))) # label(fact_4151_setprod__nonneg) # label(axiom). [clausify(4083)].
% 152.60/152.44 6298 -linordered_semidom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(B,A,C,f529(B,A,C,D)))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),C),D))) # label(fact_4151_setprod__nonneg) # label(axiom). [clausify(4083)].
% 152.60/152.44 6299 -linordered_semidom(A) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),f549(A,B,C,D,E)),E)) | -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),hAPP(fun(nat,bool),A,hAPP(fun(nat,A),fun(fun(nat,bool),A),big_co1399186613setsum(nat,A),C),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),E),B)))),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(nat,A,semiring_1_of_nat(A),E)),D))) # label(fact_4273_real__setsum__nat__ivl__bounded2) # label(axiom). [clausify(4205)].
% 152.60/152.44 6300 -linordered_semidom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(nat,A,B,f549(A,C,B,D,E))),D)) | -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),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_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),E),C)))),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(nat,A,semiring_1_of_nat(A),E)),D))) # label(fact_4273_real__setsum__nat__ivl__bounded2) # label(axiom). [clausify(4205)].
% 152.60/152.45 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(6240,a,6241,a)].
% 152.60/152.45 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(6240,a,6242,a)].
% 152.60/152.45 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(6240,a,6243,a)].
% 152.60/152.45 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),one_one(int))). [resolve(6240,a,6244,a)].
% 152.60/152.45 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),zero_zero(int))). [resolve(6240,a,6245,a)].
% 152.60/152.45 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),one_one(int))). [resolve(6240,a,6246,a)].
% 152.60/152.45 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),zero_zero(int))). [resolve(6240,a,6247,a)].
% 152.60/152.45 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(6240,a,6248,a)].
% 152.60/152.45 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),A),one_one(int))) | 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),hAPP(nat,nat,suc,B))),A)). [resolve(6240,a,6249,a)].
% 152.60/152.45 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(6240,a,6250,a)].
% 152.60/152.45 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),B))). [resolve(6240,a,6251,a)].
% 152.60/152.45 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(6240,a,6252,a)].
% 152.60/152.45 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(6240,a,6253,a)].
% 152.60/152.45 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),zero_zero(int)),C)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),C),one_one(int))) | 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),B)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),C),A))). [resolve(6240,a,6255,a)].
% 152.60/152.46 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),zero_zero(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),C)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),B),C))). [resolve(6240,a,6257,a)].
% 152.60/152.46 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(6240,a,6258,a)].
% 152.60/152.46 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(6240,a,6259,a)].
% 152.60/152.46 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(6240,a,6260,a)].
% 152.60/152.46 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(6240,a,6261,a)].
% 152.60/152.46 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(6240,a,6262,a)].
% 152.60/152.46 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(6240,a,6263,a)].
% 152.60/152.46 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(6240,a,6264,a)].
% 152.60/152.46 Derived: hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),hAPP(nat,nat,suc,B)) != hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),C),hAPP(nat,nat,suc,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)) | ti(int,A) = ti(int,C). [resolve(6240,a,6265,a)].
% 152.60/152.46 Derived: -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),hAPP(nat,nat,suc,B))),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),C),hAPP(nat,nat,suc,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),A),C)). [resolve(6240,a,6266,a)].
% 152.60/152.46 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(nat,int,hAPP(int,fun(nat,int),power_power(int),A),hAPP(nat,nat,suc,B)))). [resolve(6240,a,6267,a)].
% 152.60/152.46 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(6240,a,6268,a)].
% 152.60/152.46 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(6240,a,6269,a)].
% 152.60/152.47 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(6240,a,6272,a)].
% 152.60/152.47 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),A),one_one(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),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),B))). [resolve(6240,a,6273,a)].
% 152.60/152.47 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),A),one_one(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),hAPP(nat,nat,suc,B))),one_one(int))). [resolve(6240,a,6274,a)].
% 152.60/152.47 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),zero_zero(int)),C)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),C),one_one(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),C),B)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),C),A))). [resolve(6240,a,6275,a)].
% 152.60/152.47 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(6240,a,6276,a)].
% 152.60/152.47 Derived: hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) != hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) | -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),zero_zero(int)),A)) | ti(int,A) = ti(int,B). [resolve(6240,a,6277,a)].
% 152.60/152.47 Derived: -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),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) | -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),A),B)). [resolve(6240,a,6278,a)].
% 152.60/152.47 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(nat,int,semiring_1_of_nat(int),A))). [resolve(6240,a,6280,a)].
% 152.60/152.47 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,semiring_1_of_nat(int),A)),zero_zero(int))). [resolve(6240,a,6282,a)].
% 152.60/152.47 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(6240,a,6283,a)].
% 152.60/152.47 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(6240,a,6284,a)].
% 152.60/152.48 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(6240,a,6287,a)].
% 152.60/152.48 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(6240,a,6288,a)].
% 152.60/152.48 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,fact_fact(nat),A)))). [resolve(6240,a,6290,a)].
% 152.60/152.48 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(6240,a,6291,a)].
% 152.60/152.48 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(6240,a,6292,a)].
% 152.60/152.48 Derived: hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f527(A,int,B,C)),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),B),C))). [resolve(6240,a,6293,a)].
% 152.60/152.48 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(A,int,B,f527(A,int,B,C)))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),B),C))). [resolve(6240,a,6294,a)].
% 152.60/152.48 Derived: hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f528(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_co302546470etprod(A,int),C),D)),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),B),D))). [resolve(6240,a,6295,a)].
% 152.60/152.48 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(A,int,B,f528(A,int,C,B,D)))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(A,int,B,f528(A,int,C,B,D))),hAPP(A,int,C,f528(A,int,C,B,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_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(6240,a,6296,a)].
% 152.60/152.48 Derived: hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f529(A,int,B,C)),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),B),C))). [resolve(6240,a,6297,a)].
% 152.60/152.48 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(A,int,B,f529(A,int,B,C)))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),B),C))). [resolve(6240,a,6298,a)].
% 152.60/152.48 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),f549(int,A,B,C,D)),D)) | -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),hAPP(fun(nat,bool),int,hAPP(fun(nat,int),fun(fun(nat,bool),int),big_co1399186613setsum(nat,int),B),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),D),A)))),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(nat,int,semiring_1_of_nat(int),D)),C))). [resolve(6240,a,6299,a)].
% 152.60/152.48 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,A,f549(int,B,A,C,D))),C)) | -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),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_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),D),B)))),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(nat,int,semiring_1_of_nat(int),D)),C))). [resolve(6240,a,6300,a)].
% 152.70/152.50 6301 linordered_semidom(nat) # label(arity_Nat_Onat___Rings_Olinordered__semidom) # label(axiom). [assumption].
% 152.70/152.50 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(6301,a,6241,a)].
% 152.70/152.50 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(6301,a,6242,a)].
% 152.70/152.50 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(6301,a,6243,a)].
% 152.70/152.50 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),one_one(nat))). [resolve(6301,a,6244,a)].
% 152.70/152.50 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),one_one(nat)),zero_zero(nat))). [resolve(6301,a,6245,a)].
% 152.70/152.50 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),one_one(nat))). [resolve(6301,a,6246,a)].
% 152.70/152.50 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),one_one(nat)),zero_zero(nat))). [resolve(6301,a,6247,a)].
% 152.70/152.50 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(6301,a,6248,a)].
% 152.70/152.50 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),one_one(nat))) | 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),hAPP(nat,nat,suc,B))),A)). [resolve(6301,a,6249,a)].
% 152.70/152.50 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(6301,a,6250,a)].
% 152.70/152.50 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),zero_zero(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),power_power(nat),A),B))). [resolve(6301,a,6251,a)].
% 152.70/152.50 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(6301,a,6252,a)].
% 152.70/152.50 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(6301,a,6253,a)].
% 152.70/152.50 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),zero_zero(nat)),C)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),C),one_one(nat))) | 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),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),C),A))). [resolve(6301,a,6255,a)].
% 152.70/152.51 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),A)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),B))). [resolve(6301,a,6256,a)].
% 152.70/152.51 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),zero_zero(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),C)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),B),C))). [resolve(6301,a,6257,a)].
% 152.70/152.51 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(6301,a,6258,a)].
% 152.70/152.51 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(6301,a,6259,a)].
% 152.70/152.51 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(6301,a,6260,a)].
% 152.70/152.51 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(6301,a,6261,a)].
% 152.70/152.51 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(6301,a,6262,a)].
% 152.70/152.51 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(6301,a,6263,a)].
% 152.70/152.51 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(6301,a,6264,a)].
% 152.70/152.51 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),hAPP(nat,nat,suc,B)) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),C),hAPP(nat,nat,suc,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)) | ti(nat,A) = ti(nat,C). [resolve(6301,a,6265,a)].
% 152.70/152.51 Derived: -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),hAPP(nat,nat,suc,B))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),C),hAPP(nat,nat,suc,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),A),C)). [resolve(6301,a,6266,a)].
% 152.70/152.51 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),power_power(nat),A),hAPP(nat,nat,suc,B)))). [resolve(6301,a,6267,a)].
% 152.70/152.51 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(6301,a,6268,a)].
% 152.70/152.52 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(6301,a,6269,a)].
% 152.70/152.52 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(6301,a,6272,a)].
% 152.70/152.52 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),A),one_one(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),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),B))). [resolve(6301,a,6273,a)].
% 152.70/152.52 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),A),one_one(nat))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),hAPP(nat,nat,suc,B))),one_one(nat))). [resolve(6301,a,6274,a)].
% 152.70/152.52 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),C),one_one(nat))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),C),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),C),A))). [resolve(6301,a,6275,a)].
% 152.70/152.52 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(6301,a,6276,a)].
% 152.70/152.52 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) | -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_eq(nat),zero_zero(nat)),A)) | ti(nat,A) = ti(nat,B). [resolve(6301,a,6277,a)].
% 152.70/152.52 Derived: -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),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) | -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_eq(nat),A),B)). [resolve(6301,a,6278,a)].
% 152.70/152.52 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),hAPP(nat,nat,semiring_1_of_nat(nat),A))). [resolve(6301,a,6280,a)].
% 152.70/152.52 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,semiring_1_of_nat(nat),A)),zero_zero(nat))). [resolve(6301,a,6282,a)].
% 152.70/152.52 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(6301,a,6283,a)].
% 152.70/152.53 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(6301,a,6284,a)].
% 152.70/152.53 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(6301,a,6287,a)].
% 152.70/152.53 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(6301,a,6288,a)].
% 152.70/152.53 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,semiring_1_of_nat(nat),hAPP(nat,nat,fact_fact(nat),A)))). [resolve(6301,a,6290,a)].
% 152.70/152.53 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(6301,a,6291,a)].
% 152.70/152.53 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(6301,a,6292,a)].
% 152.70/152.53 Derived: hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f527(A,nat,B,C)),C)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),B),C))). [resolve(6301,a,6293,a)].
% 152.70/152.53 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(A,nat,B,f527(A,nat,B,C)))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),B),C))). [resolve(6301,a,6294,a)].
% 152.70/152.53 Derived: hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f528(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_co302546470etprod(A,nat),C),D)),hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),B),D))). [resolve(6301,a,6295,a)].
% 152.70/152.53 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),hAPP(A,nat,B,f528(A,nat,C,B,D)))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(A,nat,B,f528(A,nat,C,B,D))),hAPP(A,nat,C,f528(A,nat,C,B,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_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(6301,a,6296,a)].
% 152.70/152.53 Derived: hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f529(A,nat,B,C)),C)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),B),C))). [resolve(6301,a,6297,a)].
% 152.70/152.53 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),hAPP(A,nat,B,f529(A,nat,B,C)))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),B),C))). [resolve(6301,a,6298,a)].
% 152.70/152.53 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),f549(nat,A,B,C,D)),D)) | -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),hAPP(fun(nat,bool),nat,hAPP(fun(nat,nat),fun(fun(nat,bool),nat),big_co1399186613setsum(nat,nat),B),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),D),A)))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,semiring_1_of_nat(nat),D)),C))). [resolve(6301,a,6299,a)].
% 152.70/152.55 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,A,f549(nat,B,A,C,D))),C)) | -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),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_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),D),B)))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,semiring_1_of_nat(nat),D)),C))). [resolve(6301,a,6300,a)].
% 152.70/152.55 6302 linordered_semidom(rat) # label(arity_Rat_Orat___Rings_Olinordered__semidom) # label(axiom). [assumption].
% 152.70/152.55 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),one_one(rat)),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),one_one(rat)),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),one_one(rat)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B))). [resolve(6302,a,6241,a)].
% 152.70/152.55 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),one_one(rat)))). [resolve(6302,a,6242,a)].
% 152.70/152.55 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),C)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),C))). [resolve(6302,a,6243,a)].
% 152.70/152.55 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),one_one(rat))). [resolve(6302,a,6244,a)].
% 152.70/152.55 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),one_one(rat)),zero_zero(rat))). [resolve(6302,a,6245,a)].
% 152.70/152.55 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),one_one(rat))). [resolve(6302,a,6246,a)].
% 152.70/152.55 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),one_one(rat)),zero_zero(rat))). [resolve(6302,a,6247,a)].
% 152.70/152.55 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),one_one(rat)),one_one(rat)))). [resolve(6302,a,6248,a)].
% 152.70/152.55 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),one_one(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),hAPP(nat,nat,suc,B))),A)). [resolve(6302,a,6249,a)].
% 152.70/152.55 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),C)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),C)),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),B),C))). [resolve(6302,a,6250,a)].
% 152.70/152.55 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),one_one(rat)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),one_one(rat)),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),B))). [resolve(6302,a,6251,a)].
% 152.70/152.55 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),one_one(rat)),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),B)),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),C))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),C)). [resolve(6302,a,6252,a)].
% 152.70/152.55 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),one_one(rat)),A)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),B)),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),C))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),C)). [resolve(6302,a,6253,a)].
% 152.70/152.56 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),C)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),C),one_one(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),C),B)),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),C),A))). [resolve(6302,a,6255,a)].
% 152.70/152.56 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),A)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),C)),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),B),C))). [resolve(6302,a,6257,a)].
% 152.70/152.56 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),B))). [resolve(6302,a,6258,a)].
% 152.70/152.56 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),one_one(rat)),A)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),one_one(rat)),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),B))). [resolve(6302,a,6259,a)].
% 152.70/152.56 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),one_one(rat)),A)) | hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),B) != hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),C) | B = C. [resolve(6302,a,6260,a)].
% 152.70/152.56 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),one_one(rat)),A)) | hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),B) = hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),C) | B != C. [resolve(6302,a,6261,a)].
% 152.70/152.56 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),B)),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),C),B))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),C)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),C)). [resolve(6302,a,6262,a)].
% 152.70/152.56 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),one_one(rat)),A)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),one_one(rat)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),B)))). [resolve(6302,a,6263,a)].
% 152.70/152.56 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),one_one(rat)),A)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),B)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),B)))). [resolve(6302,a,6264,a)].
% 152.70/152.56 Derived: hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),hAPP(nat,nat,suc,B)) != hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),C),hAPP(nat,nat,suc,B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),C)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),A)) | ti(rat,A) = ti(rat,C). [resolve(6302,a,6265,a)].
% 152.70/152.56 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),hAPP(nat,nat,suc,B))),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),C),hAPP(nat,nat,suc,B)))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),C)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),C)). [resolve(6302,a,6266,a)].
% 152.70/152.56 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),one_one(rat)),A)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),one_one(rat)),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),hAPP(nat,nat,suc,B)))). [resolve(6302,a,6267,a)].
% 152.70/152.56 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),one_one(rat)),C)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),C),A)),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),C),B))). [resolve(6302,a,6268,a)].
% 152.70/152.57 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),one_one(rat)),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),B)),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),C))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),C)). [resolve(6302,a,6269,a)].
% 152.70/152.57 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),one_one(rat)),C)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),C),A)),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),C),B))). [resolve(6302,a,6272,a)].
% 152.70/152.57 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),one_one(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),B))),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),B))). [resolve(6302,a,6273,a)].
% 152.70/152.57 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),one_one(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),hAPP(nat,nat,suc,B))),one_one(rat))). [resolve(6302,a,6274,a)].
% 152.70/152.57 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),C)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),C),one_one(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),C),B)),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),C),A))). [resolve(6302,a,6275,a)].
% 152.70/152.57 Derived: hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),B) != hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),C),B) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),C)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),B)) | ti(rat,A) = ti(rat,C). [resolve(6302,a,6276,a)].
% 152.70/152.57 Derived: hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) != hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),A)) | ti(rat,A) = ti(rat,B). [resolve(6302,a,6277,a)].
% 152.70/152.57 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),B)). [resolve(6302,a,6278,a)].
% 152.70/152.57 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),hAPP(nat,rat,semiring_1_of_nat(rat),A))). [resolve(6302,a,6280,a)].
% 152.70/152.57 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(nat,rat,semiring_1_of_nat(rat),A)),zero_zero(rat))). [resolve(6302,a,6282,a)].
% 152.70/152.57 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(nat,rat,semiring_1_of_nat(rat),A)),hAPP(nat,rat,semiring_1_of_nat(rat),B))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)). [resolve(6302,a,6283,a)].
% 152.70/152.57 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(nat,rat,semiring_1_of_nat(rat),A)),hAPP(nat,rat,semiring_1_of_nat(rat),B))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)). [resolve(6302,a,6284,a)].
% 152.80/152.58 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(nat,rat,semiring_1_of_nat(rat),A)),hAPP(nat,rat,semiring_1_of_nat(rat),B))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)). [resolve(6302,a,6287,a)].
% 152.80/152.58 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(nat,rat,semiring_1_of_nat(rat),A)),hAPP(nat,rat,semiring_1_of_nat(rat),B))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)). [resolve(6302,a,6288,a)].
% 152.80/152.58 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(nat,rat,semiring_1_of_nat(rat),hAPP(nat,nat,fact_fact(nat),A)))). [resolve(6302,a,6290,a)].
% 152.80/152.58 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(nat,rat,semiring_1_of_nat(rat),A))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A)). [resolve(6302,a,6291,a)].
% 152.80/152.58 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(nat,rat,semiring_1_of_nat(rat),A))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A)). [resolve(6302,a,6292,a)].
% 152.80/152.58 Derived: hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f527(A,rat,B,C)),C)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co302546470etprod(A,rat),B),C))). [resolve(6302,a,6293,a)].
% 152.80/152.58 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(A,rat,B,f527(A,rat,B,C)))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co302546470etprod(A,rat),B),C))). [resolve(6302,a,6294,a)].
% 152.80/152.58 Derived: hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f528(A,rat,B,C,D)),D)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co302546470etprod(A,rat),C),D)),hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co302546470etprod(A,rat),B),D))). [resolve(6302,a,6295,a)].
% 152.80/152.58 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),hAPP(A,rat,B,f528(A,rat,C,B,D)))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(A,rat,B,f528(A,rat,C,B,D))),hAPP(A,rat,C,f528(A,rat,C,B,D)))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co302546470etprod(A,rat),B),D)),hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co302546470etprod(A,rat),C),D))). [resolve(6302,a,6296,a)].
% 152.80/152.58 Derived: hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f529(A,rat,B,C)),C)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co302546470etprod(A,rat),B),C))). [resolve(6302,a,6297,a)].
% 152.80/152.58 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),hAPP(A,rat,B,f529(A,rat,B,C)))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co302546470etprod(A,rat),B),C))). [resolve(6302,a,6298,a)].
% 152.80/152.58 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),f549(rat,A,B,C,D)),D)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),C)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(fun(nat,bool),rat,hAPP(fun(nat,rat),fun(fun(nat,bool),rat),big_co1399186613setsum(nat,rat),B),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),D),A)))),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(nat,rat,semiring_1_of_nat(rat),D)),C))). [resolve(6302,a,6299,a)].
% 152.80/152.61 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(nat,rat,A,f549(rat,B,A,C,D))),C)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),C)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(fun(nat,bool),rat,hAPP(fun(nat,rat),fun(fun(nat,bool),rat),big_co1399186613setsum(nat,rat),A),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),D),B)))),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(nat,rat,semiring_1_of_nat(rat),D)),C))). [resolve(6302,a,6300,a)].
% 152.80/152.61 6303 linordered_semidom(real) # label(arity_RealDef_Oreal___Rings_Olinordered__semidom) # label(axiom). [assumption].
% 152.80/152.61 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B))). [resolve(6303,a,6241,a)].
% 152.80/152.61 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),one_one(real)))). [resolve(6303,a,6242,a)].
% 152.80/152.61 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),C))). [resolve(6303,a,6243,a)].
% 152.80/152.61 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),one_one(real))). [resolve(6303,a,6244,a)].
% 152.80/152.61 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),one_one(real)),zero_zero(real))). [resolve(6303,a,6245,a)].
% 152.80/152.61 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),one_one(real))). [resolve(6303,a,6246,a)].
% 152.80/152.61 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),zero_zero(real))). [resolve(6303,a,6247,a)].
% 152.80/152.61 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),one_one(real)),one_one(real)))). [resolve(6303,a,6248,a)].
% 152.80/152.61 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),one_one(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),hAPP(nat,nat,suc,B))),A)). [resolve(6303,a,6249,a)].
% 152.80/152.61 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),C)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),B),C))). [resolve(6303,a,6250,a)].
% 152.80/152.61 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),B))). [resolve(6303,a,6251,a)].
% 152.80/152.61 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),B)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),C))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),C)). [resolve(6303,a,6252,a)].
% 152.80/152.61 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),A)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),B)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),C))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),C)). [resolve(6303,a,6253,a)].
% 152.83/152.62 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),C)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),C),one_one(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),C),B)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),C),A))). [resolve(6303,a,6255,a)].
% 152.83/152.62 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),C)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),B),C))). [resolve(6303,a,6257,a)].
% 152.83/152.62 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),B))). [resolve(6303,a,6258,a)].
% 152.83/152.62 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),one_one(real)),A)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),one_one(real)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),B))). [resolve(6303,a,6259,a)].
% 152.83/152.62 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),A)) | hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),B) != hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),C) | B = C. [resolve(6303,a,6260,a)].
% 152.83/152.62 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),A)) | hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),B) = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),C) | B != C. [resolve(6303,a,6261,a)].
% 152.83/152.62 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),B)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),C),B))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),C)). [resolve(6303,a,6262,a)].
% 152.83/152.62 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),A)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),B)))). [resolve(6303,a,6263,a)].
% 152.83/152.62 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),A)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),B)))). [resolve(6303,a,6264,a)].
% 152.83/152.62 Derived: hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),hAPP(nat,nat,suc,B)) != hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),C),hAPP(nat,nat,suc,B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),C)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A)) | ti(real,A) = ti(real,C). [resolve(6303,a,6265,a)].
% 152.83/152.62 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),hAPP(nat,nat,suc,B))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),C),hAPP(nat,nat,suc,B)))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),C)). [resolve(6303,a,6266,a)].
% 152.83/152.62 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),A)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),hAPP(nat,nat,suc,B)))). [resolve(6303,a,6267,a)].
% 152.84/152.63 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),C),A)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),C),B))). [resolve(6303,a,6268,a)].
% 152.84/152.63 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),B)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),C))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),C)). [resolve(6303,a,6269,a)].
% 152.84/152.63 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),one_one(real)),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),C),A)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),C),B))). [resolve(6303,a,6272,a)].
% 152.84/152.63 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),one_one(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),B))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),B))). [resolve(6303,a,6273,a)].
% 152.84/152.63 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),one_one(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),hAPP(nat,nat,suc,B))),one_one(real))). [resolve(6303,a,6274,a)].
% 152.84/152.63 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),C)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),C),one_one(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),C),B)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),C),A))). [resolve(6303,a,6275,a)].
% 152.84/152.63 Derived: hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),B) != hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),C),B) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),C)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),B)) | ti(real,A) = ti(real,C). [resolve(6303,a,6276,a)].
% 152.84/152.63 Derived: hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) != hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A)) | ti(real,A) = ti(real,B). [resolve(6303,a,6277,a)].
% 152.84/152.63 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),B)). [resolve(6303,a,6278,a)].
% 152.84/152.63 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(nat,real,semiring_1_of_nat(real),A))). [resolve(6303,a,6280,a)].
% 152.84/152.64 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(nat,real,semiring_1_of_nat(real),A)),zero_zero(real))). [resolve(6303,a,6282,a)].
% 152.84/152.64 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(nat,real,semiring_1_of_nat(real),A)),hAPP(nat,real,semiring_1_of_nat(real),B))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)). [resolve(6303,a,6283,a)].
% 152.84/152.64 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(nat,real,semiring_1_of_nat(real),A)),hAPP(nat,real,semiring_1_of_nat(real),B))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)). [resolve(6303,a,6284,a)].
% 152.84/152.64 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,semiring_1_of_nat(real),A)),hAPP(nat,real,semiring_1_of_nat(real),B))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)). [resolve(6303,a,6287,a)].
% 152.84/152.64 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,semiring_1_of_nat(real),A)),hAPP(nat,real,semiring_1_of_nat(real),B))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)). [resolve(6303,a,6288,a)].
% 152.84/152.64 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(nat,real,semiring_1_of_nat(real),hAPP(nat,nat,fact_fact(nat),A)))). [resolve(6303,a,6290,a)].
% 152.84/152.64 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(nat,real,semiring_1_of_nat(real),A))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A)). [resolve(6303,a,6291,a)].
% 152.84/152.64 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(nat,real,semiring_1_of_nat(real),A))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A)). [resolve(6303,a,6292,a)].
% 152.84/152.64 Derived: hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f527(A,real,B,C)),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co302546470etprod(A,real),B),C))). [resolve(6303,a,6293,a)].
% 152.84/152.64 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(A,real,B,f527(A,real,B,C)))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co302546470etprod(A,real),B),C))). [resolve(6303,a,6294,a)].
% 152.84/152.64 Derived: hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f528(A,real,B,C,D)),D)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co302546470etprod(A,real),C),D)),hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co302546470etprod(A,real),B),D))). [resolve(6303,a,6295,a)].
% 152.84/152.64 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(A,real,B,f528(A,real,C,B,D)))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(A,real,B,f528(A,real,C,B,D))),hAPP(A,real,C,f528(A,real,C,B,D)))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co302546470etprod(A,real),B),D)),hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co302546470etprod(A,real),C),D))). [resolve(6303,a,6296,a)].
% 152.84/152.64 Derived: hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f529(A,real,B,C)),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co302546470etprod(A,real),B),C))). [resolve(6303,a,6297,a)].
% 152.84/152.64 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(A,real,B,f529(A,real,B,C)))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co302546470etprod(A,real),B),C))). [resolve(6303,a,6298,a)].
% 152.84/152.68 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),f549(real,A,B,C,D)),D)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),B),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),D),A)))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,semiring_1_of_nat(real),D)),C))). [resolve(6303,a,6299,a)].
% 152.84/152.68 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,A,f549(real,B,A,C,D))),C)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),A),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),D),B)))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,semiring_1_of_nat(real),D)),C))). [resolve(6303,a,6300,a)].
% 152.84/152.68 6304 linordered_semidom(code_code_numeral) # label(arity_Code__Numeral_Ocode__numeral___Rings_Olinordered__semidom) # label(axiom). [assumption].
% 152.84/152.68 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),one_one(code_code_numeral)),A)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),one_one(code_code_numeral)),B)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),one_one(code_code_numeral)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),B))). [resolve(6304,a,6241,a)].
% 152.84/152.68 Derived: hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),A),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),A),one_one(code_code_numeral)))). [resolve(6304,a,6242,a)].
% 152.84/152.68 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),zero_zero(code_code_numeral)),A)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),B),C)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),B),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),A),C))). [resolve(6304,a,6243,a)].
% 152.84/152.68 Derived: hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),zero_zero(code_code_numeral)),one_one(code_code_numeral))). [resolve(6304,a,6244,a)].
% 152.84/152.68 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),one_one(code_code_numeral)),zero_zero(code_code_numeral))). [resolve(6304,a,6245,a)].
% 152.84/152.68 Derived: hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),zero_zero(code_code_numeral)),one_one(code_code_numeral))). [resolve(6304,a,6246,a)].
% 152.84/152.68 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),one_one(code_code_numeral)),zero_zero(code_code_numeral))). [resolve(6304,a,6247,a)].
% 152.84/152.68 Derived: hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),zero_zero(code_code_numeral)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),one_one(code_code_numeral)),one_one(code_code_numeral)))). [resolve(6304,a,6248,a)].
% 152.84/152.68 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),zero_zero(code_code_numeral)),A)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),A),one_one(code_code_numeral))) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A),hAPP(nat,nat,suc,B))),A)). [resolve(6304,a,6249,a)].
% 152.84/152.68 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),A),B)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),zero_zero(code_code_numeral)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),C)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A),C)),hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),B),C))). [resolve(6304,a,6250,a)].
% 152.84/152.68 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),one_one(code_code_numeral)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),B)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),one_one(code_code_numeral)),hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A),B))). [resolve(6304,a,6251,a)].
% 152.84/152.68 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),one_one(code_code_numeral)),A)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A),B)),hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A),C))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),C)). [resolve(6304,a,6252,a)].
% 152.84/152.68 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),one_one(code_code_numeral)),A)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A),B)),hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A),C))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),C)). [resolve(6304,a,6253,a)].
% 152.84/152.68 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),zero_zero(code_code_numeral)),C)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),C),one_one(code_code_numeral))) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),C),B)),hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),C),A))). [resolve(6304,a,6255,a)].
% 152.84/152.68 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),zero_zero(code_code_numeral)),A)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),zero_zero(code_code_numeral)),hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A),B))). [resolve(6304,a,6256,a)].
% 152.84/152.69 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),A),B)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),zero_zero(code_code_numeral)),A)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A),C)),hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),B),C))). [resolve(6304,a,6257,a)].
% 152.84/152.69 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),zero_zero(code_code_numeral)),A)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),zero_zero(code_code_numeral)),hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A),B))). [resolve(6304,a,6258,a)].
% 152.84/152.69 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),one_one(code_code_numeral)),A)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),one_one(code_code_numeral)),hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A),B))). [resolve(6304,a,6259,a)].
% 152.84/152.69 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),one_one(code_code_numeral)),A)) | hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A),B) != hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A),C) | B = C. [resolve(6304,a,6260,a)].
% 152.84/152.69 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),one_one(code_code_numeral)),A)) | hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A),B) = hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A),C) | B != C. [resolve(6304,a,6261,a)].
% 152.84/152.69 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A),B)),hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),C),B))) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),zero_zero(code_code_numeral)),C)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),A),C)). [resolve(6304,a,6262,a)].
% 152.84/152.69 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),one_one(code_code_numeral)),A)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),one_one(code_code_numeral)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A),B)))). [resolve(6304,a,6263,a)].
% 152.84/152.69 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),one_one(code_code_numeral)),A)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A),B)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A),B)))). [resolve(6304,a,6264,a)].
% 152.84/152.69 Derived: hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A),hAPP(nat,nat,suc,B)) != hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),C),hAPP(nat,nat,suc,B)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),zero_zero(code_code_numeral)),C)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),zero_zero(code_code_numeral)),A)) | ti(code_code_numeral,A) = ti(code_code_numeral,C). [resolve(6304,a,6265,a)].
% 152.84/152.69 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A),hAPP(nat,nat,suc,B))),hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),C),hAPP(nat,nat,suc,B)))) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),zero_zero(code_code_numeral)),C)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),A),C)). [resolve(6304,a,6266,a)].
% 152.84/152.69 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),one_one(code_code_numeral)),A)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),one_one(code_code_numeral)),hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A),hAPP(nat,nat,suc,B)))). [resolve(6304,a,6267,a)].
% 152.84/152.69 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),one_one(code_code_numeral)),C)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),C),A)),hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),C),B))). [resolve(6304,a,6268,a)].
% 152.84/152.69 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),one_one(code_code_numeral)),A)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A),B)),hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A),C))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),C)). [resolve(6304,a,6269,a)].
% 152.84/152.69 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),one_one(code_code_numeral)),C)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),C),A)),hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),C),B))). [resolve(6304,a,6272,a)].
% 152.84/152.70 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),zero_zero(code_code_numeral)),A)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),A),one_one(code_code_numeral))) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A),B))),hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A),B))). [resolve(6304,a,6273,a)].
% 152.84/152.70 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),zero_zero(code_code_numeral)),A)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),A),one_one(code_code_numeral))) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A),hAPP(nat,nat,suc,B))),one_one(code_code_numeral))). [resolve(6304,a,6274,a)].
% 152.84/152.70 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),zero_zero(code_code_numeral)),C)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),C),one_one(code_code_numeral))) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),C),B)),hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),C),A))). [resolve(6304,a,6275,a)].
% 152.84/152.70 Derived: hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A),B) != hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),C),B) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),zero_zero(code_code_numeral)),C)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),zero_zero(code_code_numeral)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),B)) | ti(code_code_numeral,A) = ti(code_code_numeral,C). [resolve(6304,a,6276,a)].
% 152.84/152.70 Derived: hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) != hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),zero_zero(code_code_numeral)),B)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),zero_zero(code_code_numeral)),A)) | ti(code_code_numeral,A) = ti(code_code_numeral,B). [resolve(6304,a,6277,a)].
% 152.84/152.70 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),zero_zero(code_code_numeral)),B)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),A),B)). [resolve(6304,a,6278,a)].
% 152.84/152.71 Derived: hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),zero_zero(code_code_numeral)),hAPP(nat,code_code_numeral,semiring_1_of_nat(code_code_numeral),A))). [resolve(6304,a,6280,a)].
% 152.84/152.71 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),hAPP(nat,code_code_numeral,semiring_1_of_nat(code_code_numeral),A)),zero_zero(code_code_numeral))). [resolve(6304,a,6282,a)].
% 152.84/152.71 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),hAPP(nat,code_code_numeral,semiring_1_of_nat(code_code_numeral),A)),hAPP(nat,code_code_numeral,semiring_1_of_nat(code_code_numeral),B))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)). [resolve(6304,a,6283,a)].
% 152.84/152.71 Derived: hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),hAPP(nat,code_code_numeral,semiring_1_of_nat(code_code_numeral),A)),hAPP(nat,code_code_numeral,semiring_1_of_nat(code_code_numeral),B))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)). [resolve(6304,a,6284,a)].
% 152.84/152.71 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),hAPP(nat,code_code_numeral,semiring_1_of_nat(code_code_numeral),A)),hAPP(nat,code_code_numeral,semiring_1_of_nat(code_code_numeral),B))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)). [resolve(6304,a,6287,a)].
% 152.84/152.71 Derived: hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),hAPP(nat,code_code_numeral,semiring_1_of_nat(code_code_numeral),A)),hAPP(nat,code_code_numeral,semiring_1_of_nat(code_code_numeral),B))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)). [resolve(6304,a,6288,a)].
% 152.84/152.71 Derived: hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),zero_zero(code_code_numeral)),hAPP(nat,code_code_numeral,semiring_1_of_nat(code_code_numeral),hAPP(nat,nat,fact_fact(nat),A)))). [resolve(6304,a,6290,a)].
% 152.84/152.71 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),zero_zero(code_code_numeral)),hAPP(nat,code_code_numeral,semiring_1_of_nat(code_code_numeral),A))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A)). [resolve(6304,a,6291,a)].
% 152.84/152.71 Derived: hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),zero_zero(code_code_numeral)),hAPP(nat,code_code_numeral,semiring_1_of_nat(code_code_numeral),A))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A)). [resolve(6304,a,6292,a)].
% 152.84/152.71 Derived: hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f527(A,code_code_numeral,B,C)),C)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),zero_zero(code_code_numeral)),hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co302546470etprod(A,code_code_numeral),B),C))). [resolve(6304,a,6293,a)].
% 152.84/152.71 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),zero_zero(code_code_numeral)),hAPP(A,code_code_numeral,B,f527(A,code_code_numeral,B,C)))) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),zero_zero(code_code_numeral)),hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co302546470etprod(A,code_code_numeral),B),C))). [resolve(6304,a,6294,a)].
% 152.84/152.71 Derived: hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f528(A,code_code_numeral,B,C,D)),D)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co302546470etprod(A,code_code_numeral),C),D)),hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co302546470etprod(A,code_code_numeral),B),D))). [resolve(6304,a,6295,a)].
% 152.84/152.71 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),zero_zero(code_code_numeral)),hAPP(A,code_code_numeral,B,f528(A,code_code_numeral,C,B,D)))) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),hAPP(A,code_code_numeral,B,f528(A,code_code_numeral,C,B,D))),hAPP(A,code_code_numeral,C,f528(A,code_code_numeral,C,B,D)))) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co302546470etprod(A,code_code_numeral),B),D)),hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co302546470etprod(A,code_code_numeral),C),D))). [resolve(6304,a,6296,a)].
% 152.84/152.71 Derived: hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f529(A,code_code_numeral,B,C)),C)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),zero_zero(code_code_numeral)),hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co302546470etprod(A,code_code_numeral),B),C))). [resolve(6304,a,6297,a)].
% 152.84/152.71 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),zero_zero(code_code_numeral)),hAPP(A,code_code_numeral,B,f529(A,code_code_numeral,B,C)))) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),zero_zero(code_code_numeral)),hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co302546470etprod(A,code_code_numeral),B),C))). [resolve(6304,a,6298,a)].
% 152.84/152.71 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),f549(code_code_numeral,A,B,C,D)),D)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),zero_zero(code_code_numeral)),C)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),hAPP(fun(nat,bool),code_code_numeral,hAPP(fun(nat,code_code_numeral),fun(fun(nat,bool),code_code_numeral),big_co1399186613setsum(nat,code_code_numeral),B),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),D),A)))),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),hAPP(nat,code_code_numeral,semiring_1_of_nat(code_code_numeral),D)),C))). [resolve(6304,a,6299,a)].
% 152.84/152.71 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),hAPP(nat,code_code_numeral,A,f549(code_code_numeral,B,A,C,D))),C)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),zero_zero(code_code_numeral)),C)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),hAPP(fun(nat,bool),code_code_numeral,hAPP(fun(nat,code_code_numeral),fun(fun(nat,bool),code_code_numeral),big_co1399186613setsum(nat,code_code_numeral),A),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),D),B)))),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),hAPP(nat,code_code_numeral,semiring_1_of_nat(code_code_numeral),D)),C))). [resolve(6304,a,6300,a)].
% 152.93/152.73 6305 linordered_semidom(quickcheck_code_int) # label(arity_Quickcheck__Narrowing_Ocode__int___Rings_Olinordered__semidom) # label(axiom). [assumption].
% 152.93/152.73 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),one_one(quickcheck_code_int)),A)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),one_one(quickcheck_code_int)),B)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),one_one(quickcheck_code_int)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),B))). [resolve(6305,a,6241,a)].
% 152.93/152.73 Derived: hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),A),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),A),one_one(quickcheck_code_int)))). [resolve(6305,a,6242,a)].
% 152.93/152.73 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),zero_zero(quickcheck_code_int)),A)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),B),C)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),B),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),A),C))). [resolve(6305,a,6243,a)].
% 152.93/152.73 Derived: hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),zero_zero(quickcheck_code_int)),one_one(quickcheck_code_int))). [resolve(6305,a,6244,a)].
% 152.93/152.73 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),one_one(quickcheck_code_int)),zero_zero(quickcheck_code_int))). [resolve(6305,a,6245,a)].
% 152.93/152.73 Derived: hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),zero_zero(quickcheck_code_int)),one_one(quickcheck_code_int))). [resolve(6305,a,6246,a)].
% 152.93/152.73 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),one_one(quickcheck_code_int)),zero_zero(quickcheck_code_int))). [resolve(6305,a,6247,a)].
% 152.93/152.73 Derived: hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),zero_zero(quickcheck_code_int)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),one_one(quickcheck_code_int)),one_one(quickcheck_code_int)))). [resolve(6305,a,6248,a)].
% 152.93/152.73 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),zero_zero(quickcheck_code_int)),A)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),A),one_one(quickcheck_code_int))) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A),hAPP(nat,nat,suc,B))),A)). [resolve(6305,a,6249,a)].
% 152.93/152.73 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),A),B)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),zero_zero(quickcheck_code_int)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),C)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A),C)),hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),B),C))). [resolve(6305,a,6250,a)].
% 152.93/152.73 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),one_one(quickcheck_code_int)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),B)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),one_one(quickcheck_code_int)),hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A),B))). [resolve(6305,a,6251,a)].
% 152.93/152.73 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),one_one(quickcheck_code_int)),A)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A),B)),hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A),C))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),C)). [resolve(6305,a,6252,a)].
% 152.93/152.73 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),one_one(quickcheck_code_int)),A)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A),B)),hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A),C))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),C)). [resolve(6305,a,6253,a)].
% 152.93/152.73 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),zero_zero(quickcheck_code_int)),C)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),C),one_one(quickcheck_code_int))) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),C),B)),hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),C),A))). [resolve(6305,a,6255,a)].
% 152.93/152.73 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),zero_zero(quickcheck_code_int)),A)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),zero_zero(quickcheck_code_int)),hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A),B))). [resolve(6305,a,6256,a)].
% 152.93/152.73 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),A),B)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),zero_zero(quickcheck_code_int)),A)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A),C)),hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),B),C))). [resolve(6305,a,6257,a)].
% 152.93/152.74 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),zero_zero(quickcheck_code_int)),A)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),zero_zero(quickcheck_code_int)),hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A),B))). [resolve(6305,a,6258,a)].
% 152.93/152.74 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),one_one(quickcheck_code_int)),A)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),one_one(quickcheck_code_int)),hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A),B))). [resolve(6305,a,6259,a)].
% 152.93/152.74 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),one_one(quickcheck_code_int)),A)) | hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A),B) != hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A),C) | B = C. [resolve(6305,a,6260,a)].
% 152.93/152.74 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),one_one(quickcheck_code_int)),A)) | hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A),B) = hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A),C) | B != C. [resolve(6305,a,6261,a)].
% 152.93/152.74 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A),B)),hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),C),B))) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),zero_zero(quickcheck_code_int)),C)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),A),C)). [resolve(6305,a,6262,a)].
% 152.93/152.74 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),one_one(quickcheck_code_int)),A)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),one_one(quickcheck_code_int)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A),B)))). [resolve(6305,a,6263,a)].
% 152.93/152.74 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),one_one(quickcheck_code_int)),A)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A),B)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A),B)))). [resolve(6305,a,6264,a)].
% 152.93/152.74 Derived: hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A),hAPP(nat,nat,suc,B)) != hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),C),hAPP(nat,nat,suc,B)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),zero_zero(quickcheck_code_int)),C)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),zero_zero(quickcheck_code_int)),A)) | ti(quickcheck_code_int,A) = ti(quickcheck_code_int,C). [resolve(6305,a,6265,a)].
% 152.93/152.74 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A),hAPP(nat,nat,suc,B))),hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),C),hAPP(nat,nat,suc,B)))) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),zero_zero(quickcheck_code_int)),C)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),A),C)). [resolve(6305,a,6266,a)].
% 152.93/152.74 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),one_one(quickcheck_code_int)),A)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),one_one(quickcheck_code_int)),hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A),hAPP(nat,nat,suc,B)))). [resolve(6305,a,6267,a)].
% 152.93/152.74 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),one_one(quickcheck_code_int)),C)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),C),A)),hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),C),B))). [resolve(6305,a,6268,a)].
% 152.93/152.74 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),one_one(quickcheck_code_int)),A)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A),B)),hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A),C))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),C)). [resolve(6305,a,6269,a)].
% 152.93/152.74 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),one_one(quickcheck_code_int)),C)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),C),A)),hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),C),B))). [resolve(6305,a,6272,a)].
% 152.93/152.75 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),zero_zero(quickcheck_code_int)),A)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),A),one_one(quickcheck_code_int))) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A),B))),hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A),B))). [resolve(6305,a,6273,a)].
% 152.93/152.75 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),zero_zero(quickcheck_code_int)),A)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),A),one_one(quickcheck_code_int))) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A),hAPP(nat,nat,suc,B))),one_one(quickcheck_code_int))). [resolve(6305,a,6274,a)].
% 152.93/152.75 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),zero_zero(quickcheck_code_int)),C)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),C),one_one(quickcheck_code_int))) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),C),B)),hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),C),A))). [resolve(6305,a,6275,a)].
% 152.93/152.75 Derived: hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A),B) != hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),C),B) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),zero_zero(quickcheck_code_int)),C)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),zero_zero(quickcheck_code_int)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),B)) | ti(quickcheck_code_int,A) = ti(quickcheck_code_int,C). [resolve(6305,a,6276,a)].
% 152.93/152.75 Derived: hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) != hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),zero_zero(quickcheck_code_int)),B)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),zero_zero(quickcheck_code_int)),A)) | ti(quickcheck_code_int,A) = ti(quickcheck_code_int,B). [resolve(6305,a,6277,a)].
% 152.93/152.75 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),zero_zero(quickcheck_code_int)),B)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),A),B)). [resolve(6305,a,6278,a)].
% 152.93/152.76 Derived: hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),zero_zero(quickcheck_code_int)),hAPP(nat,quickcheck_code_int,semiring_1_of_nat(quickcheck_code_int),A))). [resolve(6305,a,6280,a)].
% 152.93/152.76 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),hAPP(nat,quickcheck_code_int,semiring_1_of_nat(quickcheck_code_int),A)),zero_zero(quickcheck_code_int))). [resolve(6305,a,6282,a)].
% 152.93/152.76 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),hAPP(nat,quickcheck_code_int,semiring_1_of_nat(quickcheck_code_int),A)),hAPP(nat,quickcheck_code_int,semiring_1_of_nat(quickcheck_code_int),B))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)). [resolve(6305,a,6283,a)].
% 152.93/152.76 Derived: hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),hAPP(nat,quickcheck_code_int,semiring_1_of_nat(quickcheck_code_int),A)),hAPP(nat,quickcheck_code_int,semiring_1_of_nat(quickcheck_code_int),B))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)). [resolve(6305,a,6284,a)].
% 152.93/152.76 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),hAPP(nat,quickcheck_code_int,semiring_1_of_nat(quickcheck_code_int),A)),hAPP(nat,quickcheck_code_int,semiring_1_of_nat(quickcheck_code_int),B))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)). [resolve(6305,a,6287,a)].
% 152.93/152.76 Derived: hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),hAPP(nat,quickcheck_code_int,semiring_1_of_nat(quickcheck_code_int),A)),hAPP(nat,quickcheck_code_int,semiring_1_of_nat(quickcheck_code_int),B))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)). [resolve(6305,a,6288,a)].
% 152.93/152.76 Derived: hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),zero_zero(quickcheck_code_int)),hAPP(nat,quickcheck_code_int,semiring_1_of_nat(quickcheck_code_int),hAPP(nat,nat,fact_fact(nat),A)))). [resolve(6305,a,6290,a)].
% 152.93/152.76 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),zero_zero(quickcheck_code_int)),hAPP(nat,quickcheck_code_int,semiring_1_of_nat(quickcheck_code_int),A))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A)). [resolve(6305,a,6291,a)].
% 152.93/152.76 Derived: hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),zero_zero(quickcheck_code_int)),hAPP(nat,quickcheck_code_int,semiring_1_of_nat(quickcheck_code_int),A))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A)). [resolve(6305,a,6292,a)].
% 152.93/152.76 Derived: hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f527(A,quickcheck_code_int,B,C)),C)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),zero_zero(quickcheck_code_int)),hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co302546470etprod(A,quickcheck_code_int),B),C))). [resolve(6305,a,6293,a)].
% 152.93/152.76 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),zero_zero(quickcheck_code_int)),hAPP(A,quickcheck_code_int,B,f527(A,quickcheck_code_int,B,C)))) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),zero_zero(quickcheck_code_int)),hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co302546470etprod(A,quickcheck_code_int),B),C))). [resolve(6305,a,6294,a)].
% 152.93/152.76 Derived: hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f528(A,quickcheck_code_int,B,C,D)),D)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co302546470etprod(A,quickcheck_code_int),C),D)),hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co302546470etprod(A,quickcheck_code_int),B),D))). [resolve(6305,a,6295,a)].
% 152.93/152.76 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),zero_zero(quickcheck_code_int)),hAPP(A,quickcheck_code_int,B,f528(A,quickcheck_code_int,C,B,D)))) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),hAPP(A,quickcheck_code_int,B,f528(A,quickcheck_code_int,C,B,D))),hAPP(A,quickcheck_code_int,C,f528(A,quickcheck_code_int,C,B,D)))) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co302546470etprod(A,quickcheck_code_int),B),D)),hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co302546470etprod(A,quickcheck_code_int),C),D))). [resolve(6305,a,6296,a)].
% 152.93/152.76 Derived: hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f529(A,quickcheck_code_int,B,C)),C)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),zero_zero(quickcheck_code_int)),hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co302546470etprod(A,quickcheck_code_int),B),C))). [resolve(6305,a,6297,a)].
% 152.93/152.76 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),zero_zero(quickcheck_code_int)),hAPP(A,quickcheck_code_int,B,f529(A,quickcheck_code_int,B,C)))) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),zero_zero(quickcheck_code_int)),hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co302546470etprod(A,quickcheck_code_int),B),C))). [resolve(6305,a,6298,a)].
% 152.93/152.76 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),f549(quickcheck_code_int,A,B,C,D)),D)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),zero_zero(quickcheck_code_int)),C)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),hAPP(fun(nat,bool),quickcheck_code_int,hAPP(fun(nat,quickcheck_code_int),fun(fun(nat,bool),quickcheck_code_int),big_co1399186613setsum(nat,quickcheck_code_int),B),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),D),A)))),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),hAPP(nat,quickcheck_code_int,semiring_1_of_nat(quickcheck_code_int),D)),C))). [resolve(6305,a,6299,a)].
% 157.15/157.02 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),hAPP(nat,quickcheck_code_int,A,f549(quickcheck_code_int,B,A,C,D))),C)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),zero_zero(quickcheck_code_int)),C)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),hAPP(fun(nat,bool),quickcheck_code_int,hAPP(fun(nat,quickcheck_code_int),fun(fun(nat,bool),quickcheck_code_int),big_co1399186613setsum(nat,quickcheck_code_int),A),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),D),B)))),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),hAPP(nat,quickcheck_code_int,semiring_1_of_nat(quickcheck_code_int),D)),C))). [resolve(6305,a,6300,a)].
% 157.15/157.02 6306 ordere223160158up_add(int) # label(arity_Int_Oint___Groups_Oordered__cancel__ab__semigroup__add) # label(axiom). [assumption].
% 157.15/157.02 6307 -ordere223160158up_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),E)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),D)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),E))) # label(fact_105_add__le__less__mono) # label(axiom). [clausify(235)].
% 157.15/157.02 6308 -ordere223160158up_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),D),E)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),D)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),E))) # label(fact_106_add__less__le__mono) # label(axiom). [clausify(236)].
% 157.15/157.02 6309 -ordere223160158up_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),D)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),D))) # label(fact_111_add__strict__right__mono) # label(axiom). [clausify(241)].
% 157.15/157.02 6310 -ordere223160158up_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),D),B)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),D),C))) # label(fact_112_add__strict__left__mono) # label(axiom). [clausify(242)].
% 157.15/157.02 6311 -ordere223160158up_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),E)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),D)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),E))) # label(fact_113_add__strict__mono) # label(axiom). [clausify(243)].
% 157.15/157.02 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(int),C),D)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),C)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),B),D))). [resolve(6306,a,6307,a)].
% 157.15/157.02 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),C),D)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),C)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),B),D))). [resolve(6306,a,6308,a)].
% 157.15/157.02 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),plus_plus(int),A),C)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),B),C))). [resolve(6306,a,6309,a)].
% 157.15/157.02 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),plus_plus(int),C),A)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),C),B))). [resolve(6306,a,6310,a)].
% 157.23/157.07 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),C),D)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),C)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),B),D))). [resolve(6306,a,6311,a)].
% 157.23/157.07 6312 ordere223160158up_add(nat) # label(arity_Nat_Onat___Groups_Oordered__cancel__ab__semigroup__add) # label(axiom). [assumption].
% 157.23/157.07 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),C),D)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),C)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),D))). [resolve(6312,a,6307,a)].
% 157.23/157.07 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),C),D)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),C)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),D))). [resolve(6312,a,6308,a)].
% 157.23/157.07 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),C)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),C))). [resolve(6312,a,6309,a)].
% 157.23/157.07 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),C),A)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),C),B))). [resolve(6312,a,6310,a)].
% 157.23/157.07 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),C),D)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),C)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),D))). [resolve(6312,a,6311,a)].
% 157.23/157.07 6313 ordere223160158up_add(rat) # label(arity_Rat_Orat___Groups_Oordered__cancel__ab__semigroup__add) # label(axiom). [assumption].
% 157.23/157.07 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),C),D)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),C)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),B),D))). [resolve(6313,a,6307,a)].
% 157.23/157.07 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),C),D)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),C)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),B),D))). [resolve(6313,a,6308,a)].
% 157.23/157.07 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),C)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),B),C))). [resolve(6313,a,6309,a)].
% 157.23/157.07 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),C),A)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),C),B))). [resolve(6313,a,6310,a)].
% 157.23/157.07 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),C),D)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),C)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),B),D))). [resolve(6313,a,6311,a)].
% 157.23/157.07 6314 ordere223160158up_add(real) # label(arity_RealDef_Oreal___Groups_Oordered__cancel__ab__semigroup__add) # label(axiom). [assumption].
% 157.29/157.11 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),C),D)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),C)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),B),D))). [resolve(6314,a,6307,a)].
% 157.29/157.11 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),C),D)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),C)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),B),D))). [resolve(6314,a,6308,a)].
% 157.29/157.11 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),C)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),B),C))). [resolve(6314,a,6309,a)].
% 157.29/157.11 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),C),A)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),C),B))). [resolve(6314,a,6310,a)].
% 157.29/157.11 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),C),D)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),C)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),B),D))). [resolve(6314,a,6311,a)].
% 157.29/157.11 6315 ordere223160158up_add(code_code_numeral) # label(arity_Code__Numeral_Ocode__numeral___Groups_Oordered__cancel__ab__semigroup__add) # label(axiom). [assumption].
% 157.29/157.11 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),A),B)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),C),D)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),A),C)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),B),D))). [resolve(6315,a,6307,a)].
% 157.29/157.11 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),A),B)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),C),D)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),A),C)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),B),D))). [resolve(6315,a,6308,a)].
% 157.29/157.11 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),A),B)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),A),C)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),B),C))). [resolve(6315,a,6309,a)].
% 157.29/157.11 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),A),B)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),C),A)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),C),B))). [resolve(6315,a,6310,a)].
% 157.29/157.12 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),A),B)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),C),D)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),A),C)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),B),D))). [resolve(6315,a,6311,a)].
% 157.29/157.12 6316 ordere223160158up_add(quickcheck_code_int) # label(arity_Quickcheck__Narrowing_Ocode__int___Groups_Oordered__cancel__ab__semigroup_) # label(axiom). [assumption].
% 157.29/157.12 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),A),B)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),C),D)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),A),C)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),B),D))). [resolve(6316,a,6307,a)].
% 157.29/157.12 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),A),B)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),C),D)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),A),C)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),B),D))). [resolve(6316,a,6308,a)].
% 157.29/157.12 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),A),B)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),A),C)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),B),C))). [resolve(6316,a,6309,a)].
% 157.29/157.12 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),A),B)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),C),A)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),C),B))). [resolve(6316,a,6310,a)].
% 157.29/157.12 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),A),B)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),C),D)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),A),C)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),B),D))). [resolve(6316,a,6311,a)].
% 161.57/161.37 6317 ordere236663937imp_le(int) # label(arity_Int_Oint___Groups_Oordered__ab__semigroup__add__imp__le) # label(axiom). [assumption].
% 161.57/161.37 6318 -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_109_add__less__cancel__right) # label(axiom). [clausify(239)].
% 161.57/161.37 6319 -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_109_add__less__cancel__right) # label(axiom). [clausify(239)].
% 161.57/161.37 6320 -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_110_add__less__cancel__left) # label(axiom). [clausify(240)].
% 161.57/161.37 6321 -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_110_add__less__cancel__left) # label(axiom). [clausify(240)].
% 161.57/161.37 6322 -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_114_add__less__imp__less__right) # label(axiom). [clausify(244)].
% 161.57/161.37 6323 -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_115_add__less__imp__less__left) # label(axiom). [clausify(245)].
% 161.57/161.37 6324 -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_123_add__le__cancel__right) # label(axiom). [clausify(253)].
% 161.57/161.37 6325 -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_123_add__le__cancel__right) # label(axiom). [clausify(253)].
% 161.57/161.37 6326 -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_124_add__le__cancel__left) # label(axiom). [clausify(254)].
% 161.57/161.37 6327 -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_124_add__le__cancel__left) # label(axiom). [clausify(254)].
% 161.57/161.37 6328 -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_128_add__le__imp__le__right) # label(axiom). [clausify(258)].
% 161.57/161.37 6329 -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_129_add__le__imp__le__left) # label(axiom). [clausify(259)].
% 161.57/161.40 6330 -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_4823_min__add__distrib__left) # label(axiom). [clausify(4747)].
% 161.57/161.40 6331 -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_4977_max__add__distrib__left) # label(axiom). [clausify(4897)].
% 161.57/161.40 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(6317,a,6318,a)].
% 161.57/161.40 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(6317,a,6320,a)].
% 161.57/161.40 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(6317,a,6324,a)].
% 161.57/161.40 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(6317,a,6325,a)].
% 161.57/161.40 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(6317,a,6326,a)].
% 161.57/161.40 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(6317,a,6327,a)].
% 161.57/161.40 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(6317,a,6330,a)].
% 161.57/161.40 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(6317,a,6331,a)].
% 161.57/161.40 6332 ordere236663937imp_le(nat) # label(arity_Nat_Onat___Groups_Oordered__ab__semigroup__add__imp__le) # label(axiom). [assumption].
% 161.57/161.40 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(6332,a,6318,a)].
% 161.57/161.40 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(6332,a,6320,a)].
% 161.57/161.40 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(6332,a,6324,a)].
% 161.57/161.40 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(6332,a,6325,a)].
% 161.57/161.44 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(6332,a,6326,a)].
% 161.57/161.44 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(6332,a,6327,a)].
% 161.57/161.44 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(6332,a,6330,a)].
% 161.57/161.44 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(6332,a,6331,a)].
% 161.57/161.44 6333 ordere236663937imp_le(rat) # label(arity_Rat_Orat___Groups_Oordered__ab__semigroup__add__imp__le) # label(axiom). [assumption].
% 161.57/161.44 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),B)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),C),B))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),C)). [resolve(6333,a,6318,a)].
% 161.57/161.44 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),B)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),C))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),C)). [resolve(6333,a,6320,a)].
% 161.57/161.44 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),B)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),C),B))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),C)). [resolve(6333,a,6324,a)].
% 161.57/161.44 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),B)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),C),B))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),C)). [resolve(6333,a,6325,a)].
% 161.57/161.44 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),B)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),C))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),B),C)). [resolve(6333,a,6326,a)].
% 161.57/161.44 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),B)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),C))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),B),C)). [resolve(6333,a,6327,a)].
% 161.57/161.44 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_min(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),B)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),C),B)) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_min(rat),A),C)),B). [resolve(6333,a,6330,a)].
% 161.57/161.44 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_max(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),B)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),C),B)) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_max(rat),A),C)),B). [resolve(6333,a,6331,a)].
% 161.57/161.44 6334 ordere236663937imp_le(real) # label(arity_RealDef_Oreal___Groups_Oordered__ab__semigroup__add__imp__le) # label(axiom). [assumption].
% 161.57/161.44 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),C),B))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),C)). [resolve(6334,a,6318,a)].
% 161.67/161.48 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),C))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),C)). [resolve(6334,a,6320,a)].
% 161.67/161.48 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),C),B))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),C)). [resolve(6334,a,6324,a)].
% 161.67/161.48 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),C),B))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),C)). [resolve(6334,a,6325,a)].
% 161.67/161.48 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),C))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),C)). [resolve(6334,a,6326,a)].
% 161.67/161.48 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),C))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),C)). [resolve(6334,a,6327,a)].
% 161.67/161.48 Derived: hAPP(real,real,hAPP(real,fun(real,real),ord_min(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),C),B)) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),ord_min(real),A),C)),B). [resolve(6334,a,6330,a)].
% 161.67/161.48 Derived: hAPP(real,real,hAPP(real,fun(real,real),ord_max(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),C),B)) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),ord_max(real),A),C)),B). [resolve(6334,a,6331,a)].
% 161.67/161.48 6335 ordere236663937imp_le(code_code_numeral) # label(arity_Code__Numeral_Ocode__numeral___Groups_Oordered__ab__semigroup__add__imp__l) # label(axiom). [assumption].
% 161.67/161.48 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),A),B)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),C),B))) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),A),C)). [resolve(6335,a,6318,a)].
% 161.67/161.48 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),A),B)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),A),C))) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),B),C)). [resolve(6335,a,6320,a)].
% 161.67/161.48 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),A),B)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),C),B))) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),A),C)). [resolve(6335,a,6324,a)].
% 161.71/161.50 Derived: hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),A),B)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),C),B))) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),A),C)). [resolve(6335,a,6325,a)].
% 161.71/161.50 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),A),B)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),A),C))) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),B),C)). [resolve(6335,a,6326,a)].
% 161.71/161.50 Derived: hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),A),B)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),A),C))) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),B),C)). [resolve(6335,a,6327,a)].
% 161.71/161.50 Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),ord_min(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),A),B)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),C),B)) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),ord_min(code_code_numeral),A),C)),B). [resolve(6335,a,6330,a)].
% 161.71/161.50 Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),ord_max(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),A),B)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),C),B)) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),ord_max(code_code_numeral),A),C)),B). [resolve(6335,a,6331,a)].
% 161.71/161.50 6336 ordere236663937imp_le(quickcheck_code_int) # label(arity_Quickcheck__Narrowing_Ocode__int___Groups_Oordered__ab__semigroup__add__im) # label(axiom). [assumption].
% 161.71/161.50 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),A),B)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),C),B))) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),A),C)). [resolve(6336,a,6318,a)].
% 161.71/161.50 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),A),B)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),A),C))) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),B),C)). [resolve(6336,a,6320,a)].
% 161.71/161.51 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),A),B)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),C),B))) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),A),C)). [resolve(6336,a,6324,a)].
% 161.71/161.51 Derived: hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),A),B)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),C),B))) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),A),C)). [resolve(6336,a,6325,a)].
% 161.71/161.51 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),A),B)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),A),C))) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),B),C)). [resolve(6336,a,6326,a)].
% 161.71/161.51 Derived: hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),A),B)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),A),C))) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),B),C)). [resolve(6336,a,6327,a)].
% 161.71/161.51 Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),ord_min(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),A),B)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),C),B)) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),ord_min(quickcheck_code_int),A),C)),B). [resolve(6336,a,6330,a)].
% 161.71/161.51 Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),ord_max(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),A),B)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),C),B)) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),ord_max(quickcheck_code_int),A),C)),B). [resolve(6336,a,6331,a)].
% 166.02/165.86 6337 monoid_mult(int) # label(arity_Int_Oint___Groups_Omonoid__mult) # label(axiom). [assumption].
% 166.02/165.86 6338 -monoid_mult(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),one_one(A)),B) = ti(A,B) # label(fact_118_mult__1__left) # label(axiom). [clausify(248)].
% 166.02/165.86 6339 -monoid_mult(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),one_one(A)) = ti(A,B) # label(fact_120_mult__1__right) # label(axiom). [clausify(250)].
% 166.02/165.86 6340 -monoid_mult(A) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),C)) | hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),D),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,C)),B)) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),D),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),C),B))),D) # label(fact_1398_lemma__realpow__diff) # label(axiom). [clausify(1501)].
% 166.02/165.86 6341 -monoid_mult(A) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),B)) | hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),C),B) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),C),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),B),one_one(nat)))),C) # label(fact_1403_realpow__minus__mult) # label(axiom). [clausify(1506)].
% 166.02/165.86 6342 -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_1433_power__commutes) # label(axiom). [clausify(1536)].
% 166.02/165.86 6343 -monoid_mult(A) | hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),one_one(A)),B) = one_one(A) # label(fact_1435_power__one) # label(axiom). [clausify(1538)].
% 166.02/165.86 6344 -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_1437_power__mult) # label(axiom). [clausify(1540)].
% 166.02/165.86 6345 -monoid_mult(A) | hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),one_one(nat)) = ti(A,B) # label(fact_1439_power__one__right) # label(axiom). [clausify(1542)].
% 166.02/165.86 6346 -monoid_mult(A) | hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(nat,nat,suc,C)) = 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) # label(fact_1450_power__Suc2) # label(axiom). [clausify(1553)].
% 166.02/165.86 6347 -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_1451_power__add) # label(axiom). [clausify(1554)].
% 166.02/165.86 6348 -monoid_mult(A) | hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,hAPP(int,int,bit1,pls)))) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),B)),B) # label(fact_1719_power3__eq__cube) # label(axiom). [clausify(1786)].
% 166.02/165.86 6349 -monoid_mult(A) | hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),B) # label(fact_1814_power2__eq__square) # label(axiom). [clausify(1875)].
% 166.02/165.86 6350 -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)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),C)) # label(fact_1820_power__even__eq) # label(axiom). [clausify(1878)].
% 166.02/165.86 6351 -monoid_mult(A) | -number(A) | hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),hAPP(int,A,number_number_of(A),B)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),B)),hAPP(int,A,number_number_of(A),B)) # label(fact_1853_power2__eq__square__number__of) # label(axiom). [clausify(1904)].
% 166.02/165.86 6352 -monoid_mult(A) | hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),C))) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) # label(fact_1891_power__odd__eq) # label(axiom). [clausify(1936)].
% 166.02/165.86 6353 -monoid_mult(A) | -linordered_ring(A) | -hBOOL(hAPP(nat,bool,even_odd_even(nat),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),C),B))) # label(fact_2001_zero__le__even__power) # label(axiom). [clausify(2033)].
% 166.02/165.86 6354 -monoid_mult(A) | hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,C))) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(int,nat,number_number_of(nat),C))),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(int,nat,number_number_of(nat),C))) # label(fact_3871_power__number__of__even) # label(axiom). [clausify(3812)].
% 166.02/165.86 6355 -monoid_mult(A) | -number(A) | hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),hAPP(int,A,number_number_of(A),B)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,C))) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),hAPP(int,A,number_number_of(A),B)),hAPP(int,nat,number_number_of(nat),C))),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),hAPP(int,A,number_number_of(A),B)),hAPP(int,nat,number_number_of(nat),C))) # label(fact_3872_power__number__of__even__number__of) # label(axiom). [clausify(3813)].
% 166.02/165.86 6356 -monoid_mult(A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),B))) | hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),C),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,B))) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),C),hAPP(int,nat,number_number_of(nat),B)))),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),C),hAPP(int,nat,number_number_of(nat),B))) # label(fact_3898_power__number__of__odd) # label(axiom). [clausify(3839)].
% 166.02/165.86 6357 -monoid_mult(A) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),B))) | hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),C),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,B))) = one_one(A) # label(fact_3898_power__number__of__odd) # label(axiom). [clausify(3839)].
% 166.02/165.86 6358 -monoid_mult(A) | -number(A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),B))) | hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),hAPP(int,A,number_number_of(A),C)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,B))) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),C)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),hAPP(int,A,number_number_of(A),C)),hAPP(int,nat,number_number_of(nat),B)))),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),hAPP(int,A,number_number_of(A),C)),hAPP(int,nat,number_number_of(nat),B))) # label(fact_3904_power__number__of__odd__number__of) # label(axiom). [clausify(3845)].
% 166.02/165.86 6359 -monoid_mult(A) | -number(A) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),B))) | hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),hAPP(int,A,number_number_of(A),C)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,B))) = one_one(A) # label(fact_3904_power__number__of__odd__number__of) # label(axiom). [clausify(3845)].
% 166.02/165.86 6360 -monoid_mult(A) | -comm_semiring_0(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(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),times_times(A)),hAPP(A,fun(nat,A),power_power(A),B))),hAPP(fun(nat,nat),fun(nat,A),hAPP(fun(nat,A),fun(fun(nat,nat),fun(nat,A)),combb(nat,A,nat),hAPP(A,fun(nat,A),power_power(A),C)),hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,D))))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,suc,D))) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),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),times_times(A)),hAPP(A,fun(nat,A),power_power(A),B))),hAPP(fun(nat,nat),fun(nat,A),hAPP(fun(nat,A),fun(fun(nat,nat),fun(nat,A)),combb(nat,A,nat),hAPP(A,fun(nat,A),power_power(A),C)),hAPP(nat,fun(nat,nat),minus_minus(nat),D)))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,suc,D)))) # label(fact_4173_lemma__realpow__diff__sumr) # label(axiom). [clausify(4105)].
% 166.02/165.86 6361 -monoid_mult(A) | -comm_ring(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(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),times_times(A)),hAPP(A,fun(nat,A),power_power(A),B))),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)),hAPP(fun(nat,nat),fun(nat,A),hAPP(fun(nat,A),fun(fun(nat,nat),fun(nat,A)),combb(nat,A,nat),hAPP(A,fun(nat,A),power_power(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C))),hAPP(nat,fun(nat,nat),minus_minus(nat),D)))),hAPP(fun(nat,nat),fun(nat,A),hAPP(fun(nat,A),fun(fun(nat,nat),fun(nat,A)),combb(nat,A,nat),hAPP(A,fun(nat,A),power_power(A),B)),hAPP(nat,fun(nat,nat),minus_minus(nat),D))))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),D)) = hAPP(fun(nat,bool),A,hAPP(fun(nat,A),fun(fun(nat,bool),A),big_co1399186613setsum(nat,A),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),minus_minus(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),times_times(A)),hAPP(fun(nat,nat),fun(nat,A),hAPP(fun(nat,A),fun(fun(nat,nat),fun(nat,A)),combb(nat,A,nat),hAPP(A,fun(nat,A),power_power(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C))),hAPP(nat,fun(nat,nat),minus_minus(nat),D)))),hAPP(A,fun(nat,A),power_power(A),B)))),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),D))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),D)) # label(fact_4226_lemma__termdiff1) # label(axiom). [clausify(4158)].
% 166.02/165.86 6362 -monoid_mult(A) | -comm_ring(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),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),times_times(A)),hAPP(A,fun(nat,A),power_power(A),B))),hAPP(fun(nat,nat),fun(nat,A),hAPP(fun(nat,A),fun(fun(nat,nat),fun(nat,A)),combb(nat,A,nat),hAPP(A,fun(nat,A),power_power(A),C)),hAPP(nat,fun(nat,nat),minus_minus(nat),D)))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,suc,D)))) = hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(nat,nat,suc,D))),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),C),hAPP(nat,nat,suc,D))) # label(fact_4227_lemma__realpow__diff__sumr2) # label(axiom). [clausify(4159)].
% 166.02/165.88 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),C),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,B)),A)) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),C),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),B),A))),C). [resolve(6337,a,6340,a)].
% 166.02/165.88 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A)) | hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),B),A) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),A),one_one(nat)))),B). [resolve(6337,a,6341,a)].
% 166.02/165.88 Derived: hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),one_one(int)),A) = one_one(int). [resolve(6337,a,6343,a)].
% 166.02/165.88 Derived: hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,hAPP(int,int,bit1,pls)))) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),A)),A). [resolve(6337,a,6348,a)].
% 166.02/165.88 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)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),B)). [resolve(6337,a,6350,a)].
% 166.02/165.88 Derived: hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),B))) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),B)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))). [resolve(6337,a,6352,a)].
% 166.02/165.88 Derived: hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,B))) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),hAPP(int,nat,number_number_of(nat),B))),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),hAPP(int,nat,number_number_of(nat),B))). [resolve(6337,a,6354,a)].
% 166.02/165.88 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),A))) | hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,A))) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),B),hAPP(int,nat,number_number_of(nat),A)))),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),B),hAPP(int,nat,number_number_of(nat),A))). [resolve(6337,a,6356,a)].
% 166.02/165.88 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),A))) | hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,A))) = one_one(int). [resolve(6337,a,6357,a)].
% 166.02/165.88 Derived: -comm_semiring_0(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(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),times_times(int)),hAPP(int,fun(nat,int),power_power(int),A))),hAPP(fun(nat,nat),fun(nat,int),hAPP(fun(nat,int),fun(fun(nat,nat),fun(nat,int)),combb(nat,int,nat),hAPP(int,fun(nat,int),power_power(int),B)),hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,C))))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,suc,C))) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),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),times_times(int)),hAPP(int,fun(nat,int),power_power(int),A))),hAPP(fun(nat,nat),fun(nat,int),hAPP(fun(nat,int),fun(fun(nat,nat),fun(nat,int)),combb(nat,int,nat),hAPP(int,fun(nat,int),power_power(int),B)),hAPP(nat,fun(nat,nat),minus_minus(nat),C)))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,suc,C)))). [resolve(6337,a,6360,a)].
% 166.02/165.88 Derived: -comm_ring(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(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),times_times(int)),hAPP(int,fun(nat,int),power_power(int),A))),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)),hAPP(fun(nat,nat),fun(nat,int),hAPP(fun(nat,int),fun(fun(nat,nat),fun(nat,int)),combb(nat,int,nat),hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B))),hAPP(nat,fun(nat,nat),minus_minus(nat),C)))),hAPP(fun(nat,nat),fun(nat,int),hAPP(fun(nat,int),fun(fun(nat,nat),fun(nat,int)),combb(nat,int,nat),hAPP(int,fun(nat,int),power_power(int),A)),hAPP(nat,fun(nat,nat),minus_minus(nat),C))))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),C)) = hAPP(fun(nat,bool),int,hAPP(fun(nat,int),fun(fun(nat,bool),int),big_co1399186613setsum(nat,int),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),minus_minus(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),times_times(int)),hAPP(fun(nat,nat),fun(nat,int),hAPP(fun(nat,int),fun(fun(nat,nat),fun(nat,int)),combb(nat,int,nat),hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B))),hAPP(nat,fun(nat,nat),minus_minus(nat),C)))),hAPP(int,fun(nat,int),power_power(int),A)))),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),C))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),C)). [resolve(6337,a,6361,a)].
% 166.02/165.88 Derived: -comm_ring(int) | hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),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),times_times(int)),hAPP(int,fun(nat,int),power_power(int),A))),hAPP(fun(nat,nat),fun(nat,int),hAPP(fun(nat,int),fun(fun(nat,nat),fun(nat,int)),combb(nat,int,nat),hAPP(int,fun(nat,int),power_power(int),B)),hAPP(nat,fun(nat,nat),minus_minus(nat),C)))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,suc,C)))) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),hAPP(nat,nat,suc,C))),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),B),hAPP(nat,nat,suc,C))). [resolve(6337,a,6362,a)].
% 166.11/165.90 6363 monoid_mult(nat) # label(arity_Nat_Onat___Groups_Omonoid__mult) # label(axiom). [assumption].
% 166.11/165.90 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),C),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,B)),A)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),C),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),B),A))),C). [resolve(6363,a,6340,a)].
% 166.11/165.90 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A)) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),B),A) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),A),one_one(nat)))),B). [resolve(6363,a,6341,a)].
% 166.11/165.90 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),one_one(nat)),A) = one_one(nat). [resolve(6363,a,6343,a)].
% 166.11/165.90 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,hAPP(int,int,bit1,pls)))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),A)),A). [resolve(6363,a,6348,a)].
% 166.11/165.90 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)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),B)). [resolve(6363,a,6350,a)].
% 166.11/165.90 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),B))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),B)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))). [resolve(6363,a,6352,a)].
% 166.11/165.90 Derived: -linordered_ring(nat) | -hBOOL(hAPP(nat,bool,even_odd_even(nat),A)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),B),A))). [resolve(6363,a,6353,a)].
% 166.11/165.90 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,B))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),hAPP(int,nat,number_number_of(nat),B))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),hAPP(int,nat,number_number_of(nat),B))). [resolve(6363,a,6354,a)].
% 166.11/165.90 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),A))) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,A))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),B),hAPP(int,nat,number_number_of(nat),A)))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),B),hAPP(int,nat,number_number_of(nat),A))). [resolve(6363,a,6356,a)].
% 166.11/165.90 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),A))) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,A))) = one_one(nat). [resolve(6363,a,6357,a)].
% 166.11/165.90 Derived: -comm_semiring_0(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,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),times_times(nat)),hAPP(nat,fun(nat,nat),power_power(nat),A))),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),power_power(nat),B)),hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,C))))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,suc,C))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),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),times_times(nat)),hAPP(nat,fun(nat,nat),power_power(nat),A))),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),power_power(nat),B)),hAPP(nat,fun(nat,nat),minus_minus(nat),C)))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,suc,C)))). [resolve(6363,a,6360,a)].
% 166.11/165.90 Derived: -comm_ring(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,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),times_times(nat)),hAPP(nat,fun(nat,nat),power_power(nat),A))),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)),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),power_power(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B))),hAPP(nat,fun(nat,nat),minus_minus(nat),C)))),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),power_power(nat),A)),hAPP(nat,fun(nat,nat),minus_minus(nat),C))))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),C)) = hAPP(fun(nat,bool),nat,hAPP(fun(nat,nat),fun(fun(nat,bool),nat),big_co1399186613setsum(nat,nat),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),minus_minus(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),times_times(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),power_power(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B))),hAPP(nat,fun(nat,nat),minus_minus(nat),C)))),hAPP(nat,fun(nat,nat),power_power(nat),A)))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),C))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),C)). [resolve(6363,a,6361,a)].
% 166.11/165.93 Derived: -comm_ring(nat) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),A),B)),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),times_times(nat)),hAPP(nat,fun(nat,nat),power_power(nat),A))),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),power_power(nat),B)),hAPP(nat,fun(nat,nat),minus_minus(nat),C)))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,suc,C)))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),hAPP(nat,nat,suc,C))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),B),hAPP(nat,nat,suc,C))). [resolve(6363,a,6362,a)].
% 166.11/165.93 6364 monoid_mult(rat) # label(arity_Rat_Orat___Groups_Omonoid__mult) # label(axiom). [assumption].
% 166.11/165.93 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),C),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,B)),A)) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),C),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),B),A))),C). [resolve(6364,a,6340,a)].
% 166.11/165.93 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A)) | hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),B),A) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),A),one_one(nat)))),B). [resolve(6364,a,6341,a)].
% 166.11/165.93 Derived: hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),one_one(rat)),A) = one_one(rat). [resolve(6364,a,6343,a)].
% 166.11/165.93 Derived: hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,hAPP(int,int,bit1,pls)))) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),A)),A). [resolve(6364,a,6348,a)].
% 166.11/165.93 Derived: hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),B)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),B)). [resolve(6364,a,6350,a)].
% 166.11/165.93 Derived: hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),B))) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),B)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))). [resolve(6364,a,6352,a)].
% 166.11/165.93 Derived: hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,B))) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),hAPP(int,nat,number_number_of(nat),B))),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),hAPP(int,nat,number_number_of(nat),B))). [resolve(6364,a,6354,a)].
% 166.11/165.93 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),A))) | hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,A))) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),B),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),B),hAPP(int,nat,number_number_of(nat),A)))),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),B),hAPP(int,nat,number_number_of(nat),A))). [resolve(6364,a,6356,a)].
% 166.11/165.93 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),A))) | hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,A))) = one_one(rat). [resolve(6364,a,6357,a)].
% 166.11/165.93 Derived: -comm_semiring_0(rat) | hAPP(fun(nat,bool),rat,hAPP(fun(nat,rat),fun(fun(nat,bool),rat),big_co1399186613setsum(nat,rat),hAPP(fun(nat,rat),fun(nat,rat),hAPP(fun(nat,fun(rat,rat)),fun(fun(nat,rat),fun(nat,rat)),combs(nat,rat,rat),hAPP(fun(nat,rat),fun(nat,fun(rat,rat)),hAPP(fun(rat,fun(rat,rat)),fun(fun(nat,rat),fun(nat,fun(rat,rat))),combb(rat,fun(rat,rat),nat),times_times(rat)),hAPP(rat,fun(nat,rat),power_power(rat),A))),hAPP(fun(nat,nat),fun(nat,rat),hAPP(fun(nat,rat),fun(fun(nat,nat),fun(nat,rat)),combb(nat,rat,nat),hAPP(rat,fun(nat,rat),power_power(rat),B)),hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,C))))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,suc,C))) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),B),hAPP(fun(nat,bool),rat,hAPP(fun(nat,rat),fun(fun(nat,bool),rat),big_co1399186613setsum(nat,rat),hAPP(fun(nat,rat),fun(nat,rat),hAPP(fun(nat,fun(rat,rat)),fun(fun(nat,rat),fun(nat,rat)),combs(nat,rat,rat),hAPP(fun(nat,rat),fun(nat,fun(rat,rat)),hAPP(fun(rat,fun(rat,rat)),fun(fun(nat,rat),fun(nat,fun(rat,rat))),combb(rat,fun(rat,rat),nat),times_times(rat)),hAPP(rat,fun(nat,rat),power_power(rat),A))),hAPP(fun(nat,nat),fun(nat,rat),hAPP(fun(nat,rat),fun(fun(nat,nat),fun(nat,rat)),combb(nat,rat,nat),hAPP(rat,fun(nat,rat),power_power(rat),B)),hAPP(nat,fun(nat,nat),minus_minus(nat),C)))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,suc,C)))). [resolve(6364,a,6360,a)].
% 166.11/165.93 Derived: -comm_ring(rat) | hAPP(fun(nat,bool),rat,hAPP(fun(nat,rat),fun(fun(nat,bool),rat),big_co1399186613setsum(nat,rat),hAPP(fun(nat,rat),fun(nat,rat),hAPP(fun(nat,fun(rat,rat)),fun(fun(nat,rat),fun(nat,rat)),combs(nat,rat,rat),hAPP(fun(nat,rat),fun(nat,fun(rat,rat)),hAPP(fun(rat,fun(rat,rat)),fun(fun(nat,rat),fun(nat,fun(rat,rat))),combb(rat,fun(rat,rat),nat),times_times(rat)),hAPP(rat,fun(nat,rat),power_power(rat),A))),hAPP(fun(nat,rat),fun(nat,rat),hAPP(fun(nat,fun(rat,rat)),fun(fun(nat,rat),fun(nat,rat)),combs(nat,rat,rat),hAPP(fun(nat,rat),fun(nat,fun(rat,rat)),hAPP(fun(rat,fun(rat,rat)),fun(fun(nat,rat),fun(nat,fun(rat,rat))),combb(rat,fun(rat,rat),nat),minus_minus(rat)),hAPP(fun(nat,nat),fun(nat,rat),hAPP(fun(nat,rat),fun(fun(nat,nat),fun(nat,rat)),combb(nat,rat,nat),hAPP(rat,fun(nat,rat),power_power(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),B))),hAPP(nat,fun(nat,nat),minus_minus(nat),C)))),hAPP(fun(nat,nat),fun(nat,rat),hAPP(fun(nat,rat),fun(fun(nat,nat),fun(nat,rat)),combb(nat,rat,nat),hAPP(rat,fun(nat,rat),power_power(rat),A)),hAPP(nat,fun(nat,nat),minus_minus(nat),C))))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),C)) = hAPP(fun(nat,bool),rat,hAPP(fun(nat,rat),fun(fun(nat,bool),rat),big_co1399186613setsum(nat,rat),hAPP(rat,fun(nat,rat),hAPP(fun(nat,fun(rat,rat)),fun(rat,fun(nat,rat)),combc(nat,rat,rat),hAPP(fun(nat,rat),fun(nat,fun(rat,rat)),hAPP(fun(rat,fun(rat,rat)),fun(fun(nat,rat),fun(nat,fun(rat,rat))),combb(rat,fun(rat,rat),nat),minus_minus(rat)),hAPP(fun(nat,rat),fun(nat,rat),hAPP(fun(nat,fun(rat,rat)),fun(fun(nat,rat),fun(nat,rat)),combs(nat,rat,rat),hAPP(fun(nat,rat),fun(nat,fun(rat,rat)),hAPP(fun(rat,fun(rat,rat)),fun(fun(nat,rat),fun(nat,fun(rat,rat))),combb(rat,fun(rat,rat),nat),times_times(rat)),hAPP(fun(nat,nat),fun(nat,rat),hAPP(fun(nat,rat),fun(fun(nat,nat),fun(nat,rat)),combb(nat,rat,nat),hAPP(rat,fun(nat,rat),power_power(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),B))),hAPP(nat,fun(nat,nat),minus_minus(nat),C)))),hAPP(rat,fun(nat,rat),power_power(rat),A)))),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),C))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),C)). [resolve(6364,a,6361,a)].
% 166.11/165.96 Derived: -comm_ring(rat) | hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),A),B)),hAPP(fun(nat,bool),rat,hAPP(fun(nat,rat),fun(fun(nat,bool),rat),big_co1399186613setsum(nat,rat),hAPP(fun(nat,rat),fun(nat,rat),hAPP(fun(nat,fun(rat,rat)),fun(fun(nat,rat),fun(nat,rat)),combs(nat,rat,rat),hAPP(fun(nat,rat),fun(nat,fun(rat,rat)),hAPP(fun(rat,fun(rat,rat)),fun(fun(nat,rat),fun(nat,fun(rat,rat))),combb(rat,fun(rat,rat),nat),times_times(rat)),hAPP(rat,fun(nat,rat),power_power(rat),A))),hAPP(fun(nat,nat),fun(nat,rat),hAPP(fun(nat,rat),fun(fun(nat,nat),fun(nat,rat)),combb(nat,rat,nat),hAPP(rat,fun(nat,rat),power_power(rat),B)),hAPP(nat,fun(nat,nat),minus_minus(nat),C)))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,suc,C)))) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),hAPP(nat,nat,suc,C))),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),B),hAPP(nat,nat,suc,C))). [resolve(6364,a,6362,a)].
% 166.11/165.96 6365 monoid_mult(real) # label(arity_RealDef_Oreal___Groups_Omonoid__mult) # label(axiom). [assumption].
% 166.11/165.96 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),C),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,B)),A)) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),C),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),B),A))),C). [resolve(6365,a,6340,a)].
% 166.11/165.96 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A)) | hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),B),A) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),A),one_one(nat)))),B). [resolve(6365,a,6341,a)].
% 166.11/165.96 Derived: hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),one_one(real)),A) = one_one(real). [resolve(6365,a,6343,a)].
% 166.11/165.96 Derived: hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,hAPP(int,int,bit1,pls)))) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),A)),A). [resolve(6365,a,6348,a)].
% 166.11/165.96 Derived: hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),B)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),B)). [resolve(6365,a,6350,a)].
% 166.11/165.96 Derived: hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),B))) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),B)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))). [resolve(6365,a,6352,a)].
% 166.11/165.96 Derived: hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,B))) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),hAPP(int,nat,number_number_of(nat),B))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),hAPP(int,nat,number_number_of(nat),B))). [resolve(6365,a,6354,a)].
% 166.11/165.96 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),A))) | hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,A))) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),B),hAPP(int,nat,number_number_of(nat),A)))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),B),hAPP(int,nat,number_number_of(nat),A))). [resolve(6365,a,6356,a)].
% 166.11/165.96 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),A))) | hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,A))) = one_one(real). [resolve(6365,a,6357,a)].
% 166.11/165.96 Derived: -comm_semiring_0(real) | hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(real,fun(nat,real),power_power(real),A))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),hAPP(real,fun(nat,real),power_power(real),B)),hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,C))))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,suc,C))) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(real,fun(nat,real),power_power(real),A))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),hAPP(real,fun(nat,real),power_power(real),B)),hAPP(nat,fun(nat,nat),minus_minus(nat),C)))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,suc,C)))). [resolve(6365,a,6360,a)].
% 166.11/165.96 Derived: -comm_ring(real) | hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(real,fun(nat,real),power_power(real),A))),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),minus_minus(real)),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),B))),hAPP(nat,fun(nat,nat),minus_minus(nat),C)))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),hAPP(real,fun(nat,real),power_power(real),A)),hAPP(nat,fun(nat,nat),minus_minus(nat),C))))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),C)) = hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(real,fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(real,fun(nat,real)),combc(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),minus_minus(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),B))),hAPP(nat,fun(nat,nat),minus_minus(nat),C)))),hAPP(real,fun(nat,real),power_power(real),A)))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),C))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),C)). [resolve(6365,a,6361,a)].
% 166.21/165.98 Derived: -comm_ring(real) | hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),B)),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(real,fun(nat,real),power_power(real),A))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),hAPP(real,fun(nat,real),power_power(real),B)),hAPP(nat,fun(nat,nat),minus_minus(nat),C)))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,suc,C)))) = hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),hAPP(nat,nat,suc,C))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),B),hAPP(nat,nat,suc,C))). [resolve(6365,a,6362,a)].
% 166.21/165.98 6366 monoid_mult(complex) # label(arity_Complex_Ocomplex___Groups_Omonoid__mult) # label(axiom). [assumption].
% 166.21/165.98 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),C),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,B)),A)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),C),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),B),A))),C). [resolve(6366,a,6340,a)].
% 166.21/165.98 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A)) | hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),B),A) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),A),one_one(nat)))),B). [resolve(6366,a,6341,a)].
% 166.21/165.98 Derived: hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),one_one(complex)),A) = one_one(complex). [resolve(6366,a,6343,a)].
% 166.21/165.98 Derived: hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,hAPP(int,int,bit1,pls)))) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),A)),A). [resolve(6366,a,6348,a)].
% 166.21/165.98 Derived: hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),A),B)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),B)). [resolve(6366,a,6350,a)].
% 166.21/165.98 Derived: hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),A),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),B))) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),A),B)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))). [resolve(6366,a,6352,a)].
% 166.21/165.99 Derived: -linordered_ring(complex) | -hBOOL(hAPP(nat,bool,even_odd_even(nat),A)) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less_eq(complex),zero_zero(complex)),hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),B),A))). [resolve(6366,a,6353,a)].
% 166.21/165.99 Derived: hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,B))) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),A),hAPP(int,nat,number_number_of(nat),B))),hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),A),hAPP(int,nat,number_number_of(nat),B))). [resolve(6366,a,6354,a)].
% 166.21/165.99 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),A))) | hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,A))) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),B),hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),B),hAPP(int,nat,number_number_of(nat),A)))),hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),B),hAPP(int,nat,number_number_of(nat),A))). [resolve(6366,a,6356,a)].
% 166.21/165.99 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),A))) | hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,A))) = one_one(complex). [resolve(6366,a,6357,a)].
% 166.21/165.99 Derived: -comm_semiring_0(complex) | hAPP(fun(nat,bool),complex,hAPP(fun(nat,complex),fun(fun(nat,bool),complex),big_co1399186613setsum(nat,complex),hAPP(fun(nat,complex),fun(nat,complex),hAPP(fun(nat,fun(complex,complex)),fun(fun(nat,complex),fun(nat,complex)),combs(nat,complex,complex),hAPP(fun(nat,complex),fun(nat,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(nat,complex),fun(nat,fun(complex,complex))),combb(complex,fun(complex,complex),nat),times_times(complex)),hAPP(complex,fun(nat,complex),power_power(complex),A))),hAPP(fun(nat,nat),fun(nat,complex),hAPP(fun(nat,complex),fun(fun(nat,nat),fun(nat,complex)),combb(nat,complex,nat),hAPP(complex,fun(nat,complex),power_power(complex),B)),hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,C))))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,suc,C))) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),B),hAPP(fun(nat,bool),complex,hAPP(fun(nat,complex),fun(fun(nat,bool),complex),big_co1399186613setsum(nat,complex),hAPP(fun(nat,complex),fun(nat,complex),hAPP(fun(nat,fun(complex,complex)),fun(fun(nat,complex),fun(nat,complex)),combs(nat,complex,complex),hAPP(fun(nat,complex),fun(nat,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(nat,complex),fun(nat,fun(complex,complex))),combb(complex,fun(complex,complex),nat),times_times(complex)),hAPP(complex,fun(nat,complex),power_power(complex),A))),hAPP(fun(nat,nat),fun(nat,complex),hAPP(fun(nat,complex),fun(fun(nat,nat),fun(nat,complex)),combb(nat,complex,nat),hAPP(complex,fun(nat,complex),power_power(complex),B)),hAPP(nat,fun(nat,nat),minus_minus(nat),C)))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,suc,C)))). [resolve(6366,a,6360,a)].
% 166.21/165.99 Derived: -comm_ring(complex) | hAPP(fun(nat,bool),complex,hAPP(fun(nat,complex),fun(fun(nat,bool),complex),big_co1399186613setsum(nat,complex),hAPP(fun(nat,complex),fun(nat,complex),hAPP(fun(nat,fun(complex,complex)),fun(fun(nat,complex),fun(nat,complex)),combs(nat,complex,complex),hAPP(fun(nat,complex),fun(nat,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(nat,complex),fun(nat,fun(complex,complex))),combb(complex,fun(complex,complex),nat),times_times(complex)),hAPP(complex,fun(nat,complex),power_power(complex),A))),hAPP(fun(nat,complex),fun(nat,complex),hAPP(fun(nat,fun(complex,complex)),fun(fun(nat,complex),fun(nat,complex)),combs(nat,complex,complex),hAPP(fun(nat,complex),fun(nat,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(nat,complex),fun(nat,fun(complex,complex))),combb(complex,fun(complex,complex),nat),minus_minus(complex)),hAPP(fun(nat,nat),fun(nat,complex),hAPP(fun(nat,complex),fun(fun(nat,nat),fun(nat,complex)),combb(nat,complex,nat),hAPP(complex,fun(nat,complex),power_power(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),A),B))),hAPP(nat,fun(nat,nat),minus_minus(nat),C)))),hAPP(fun(nat,nat),fun(nat,complex),hAPP(fun(nat,complex),fun(fun(nat,nat),fun(nat,complex)),combb(nat,complex,nat),hAPP(complex,fun(nat,complex),power_power(complex),A)),hAPP(nat,fun(nat,nat),minus_minus(nat),C))))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),C)) = hAPP(fun(nat,bool),complex,hAPP(fun(nat,complex),fun(fun(nat,bool),complex),big_co1399186613setsum(nat,complex),hAPP(complex,fun(nat,complex),hAPP(fun(nat,fun(complex,complex)),fun(complex,fun(nat,complex)),combc(nat,complex,complex),hAPP(fun(nat,complex),fun(nat,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(nat,complex),fun(nat,fun(complex,complex))),combb(complex,fun(complex,complex),nat),minus_minus(complex)),hAPP(fun(nat,complex),fun(nat,complex),hAPP(fun(nat,fun(complex,complex)),fun(fun(nat,complex),fun(nat,complex)),combs(nat,complex,complex),hAPP(fun(nat,complex),fun(nat,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(nat,complex),fun(nat,fun(complex,complex))),combb(complex,fun(complex,complex),nat),times_times(complex)),hAPP(fun(nat,nat),fun(nat,complex),hAPP(fun(nat,complex),fun(fun(nat,nat),fun(nat,complex)),combb(nat,complex,nat),hAPP(complex,fun(nat,complex),power_power(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),A),B))),hAPP(nat,fun(nat,nat),minus_minus(nat),C)))),hAPP(complex,fun(nat,complex),power_power(complex),A)))),hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),A),C))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),C)). [resolve(6366,a,6361,a)].
% 166.21/166.00 Derived: -comm_ring(complex) | hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),A),B)),hAPP(fun(nat,bool),complex,hAPP(fun(nat,complex),fun(fun(nat,bool),complex),big_co1399186613setsum(nat,complex),hAPP(fun(nat,complex),fun(nat,complex),hAPP(fun(nat,fun(complex,complex)),fun(fun(nat,complex),fun(nat,complex)),combs(nat,complex,complex),hAPP(fun(nat,complex),fun(nat,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(nat,complex),fun(nat,fun(complex,complex))),combb(complex,fun(complex,complex),nat),times_times(complex)),hAPP(complex,fun(nat,complex),power_power(complex),A))),hAPP(fun(nat,nat),fun(nat,complex),hAPP(fun(nat,complex),fun(fun(nat,nat),fun(nat,complex)),combb(nat,complex,nat),hAPP(complex,fun(nat,complex),power_power(complex),B)),hAPP(nat,fun(nat,nat),minus_minus(nat),C)))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,suc,C)))) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),A),hAPP(nat,nat,suc,C))),hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),B),hAPP(nat,nat,suc,C))). [resolve(6366,a,6362,a)].
% 166.21/166.00 6367 monoid_mult(code_code_numeral) # label(arity_Code__Numeral_Ocode__numeral___Groups_Omonoid__mult) # label(axiom). [assumption].
% 166.21/166.01 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),C),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,B)),A)) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),C),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),B),A))),C). [resolve(6367,a,6340,a)].
% 166.21/166.01 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A)) | hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),B),A) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),A),one_one(nat)))),B). [resolve(6367,a,6341,a)].
% 166.21/166.01 Derived: hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),one_one(code_code_numeral)),A) = one_one(code_code_numeral). [resolve(6367,a,6343,a)].
% 166.21/166.01 Derived: hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,hAPP(int,int,bit1,pls)))) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),A)),A). [resolve(6367,a,6348,a)].
% 166.21/166.01 Derived: hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A),B)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),B)). [resolve(6367,a,6350,a)].
% 166.21/166.01 Derived: hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),B))) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A),B)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))). [resolve(6367,a,6352,a)].
% 166.21/166.01 Derived: -linordered_ring(code_code_numeral) | -hBOOL(hAPP(nat,bool,even_odd_even(nat),A)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),zero_zero(code_code_numeral)),hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),B),A))). [resolve(6367,a,6353,a)].
% 166.21/166.01 Derived: hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,B))) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A),hAPP(int,nat,number_number_of(nat),B))),hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A),hAPP(int,nat,number_number_of(nat),B))). [resolve(6367,a,6354,a)].
% 166.24/166.02 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),A))) | hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,A))) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),B),hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),B),hAPP(int,nat,number_number_of(nat),A)))),hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),B),hAPP(int,nat,number_number_of(nat),A))). [resolve(6367,a,6356,a)].
% 166.24/166.02 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),A))) | hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,A))) = one_one(code_code_numeral). [resolve(6367,a,6357,a)].
% 166.24/166.02 Derived: -comm_semiring_0(code_code_numeral) | hAPP(fun(nat,bool),code_code_numeral,hAPP(fun(nat,code_code_numeral),fun(fun(nat,bool),code_code_numeral),big_co1399186613setsum(nat,code_code_numeral),hAPP(fun(nat,code_code_numeral),fun(nat,code_code_numeral),hAPP(fun(nat,fun(code_code_numeral,code_code_numeral)),fun(fun(nat,code_code_numeral),fun(nat,code_code_numeral)),combs(nat,code_code_numeral,code_code_numeral),hAPP(fun(nat,code_code_numeral),fun(nat,fun(code_code_numeral,code_code_numeral)),hAPP(fun(code_code_numeral,fun(code_code_numeral,code_code_numeral)),fun(fun(nat,code_code_numeral),fun(nat,fun(code_code_numeral,code_code_numeral))),combb(code_code_numeral,fun(code_code_numeral,code_code_numeral),nat),times_times(code_code_numeral)),hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A))),hAPP(fun(nat,nat),fun(nat,code_code_numeral),hAPP(fun(nat,code_code_numeral),fun(fun(nat,nat),fun(nat,code_code_numeral)),combb(nat,code_code_numeral,nat),hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),B)),hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,C))))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,suc,C))) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),B),hAPP(fun(nat,bool),code_code_numeral,hAPP(fun(nat,code_code_numeral),fun(fun(nat,bool),code_code_numeral),big_co1399186613setsum(nat,code_code_numeral),hAPP(fun(nat,code_code_numeral),fun(nat,code_code_numeral),hAPP(fun(nat,fun(code_code_numeral,code_code_numeral)),fun(fun(nat,code_code_numeral),fun(nat,code_code_numeral)),combs(nat,code_code_numeral,code_code_numeral),hAPP(fun(nat,code_code_numeral),fun(nat,fun(code_code_numeral,code_code_numeral)),hAPP(fun(code_code_numeral,fun(code_code_numeral,code_code_numeral)),fun(fun(nat,code_code_numeral),fun(nat,fun(code_code_numeral,code_code_numeral))),combb(code_code_numeral,fun(code_code_numeral,code_code_numeral),nat),times_times(code_code_numeral)),hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A))),hAPP(fun(nat,nat),fun(nat,code_code_numeral),hAPP(fun(nat,code_code_numeral),fun(fun(nat,nat),fun(nat,code_code_numeral)),combb(nat,code_code_numeral,nat),hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),B)),hAPP(nat,fun(nat,nat),minus_minus(nat),C)))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,suc,C)))). [resolve(6367,a,6360,a)].
% 166.24/166.02 Derived: -comm_ring(code_code_numeral) | hAPP(fun(nat,bool),code_code_numeral,hAPP(fun(nat,code_code_numeral),fun(fun(nat,bool),code_code_numeral),big_co1399186613setsum(nat,code_code_numeral),hAPP(fun(nat,code_code_numeral),fun(nat,code_code_numeral),hAPP(fun(nat,fun(code_code_numeral,code_code_numeral)),fun(fun(nat,code_code_numeral),fun(nat,code_code_numeral)),combs(nat,code_code_numeral,code_code_numeral),hAPP(fun(nat,code_code_numeral),fun(nat,fun(code_code_numeral,code_code_numeral)),hAPP(fun(code_code_numeral,fun(code_code_numeral,code_code_numeral)),fun(fun(nat,code_code_numeral),fun(nat,fun(code_code_numeral,code_code_numeral))),combb(code_code_numeral,fun(code_code_numeral,code_code_numeral),nat),times_times(code_code_numeral)),hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A))),hAPP(fun(nat,code_code_numeral),fun(nat,code_code_numeral),hAPP(fun(nat,fun(code_code_numeral,code_code_numeral)),fun(fun(nat,code_code_numeral),fun(nat,code_code_numeral)),combs(nat,code_code_numeral,code_code_numeral),hAPP(fun(nat,code_code_numeral),fun(nat,fun(code_code_numeral,code_code_numeral)),hAPP(fun(code_code_numeral,fun(code_code_numeral,code_code_numeral)),fun(fun(nat,code_code_numeral),fun(nat,fun(code_code_numeral,code_code_numeral))),combb(code_code_numeral,fun(code_code_numeral,code_code_numeral),nat),minus_minus(code_code_numeral)),hAPP(fun(nat,nat),fun(nat,code_code_numeral),hAPP(fun(nat,code_code_numeral),fun(fun(nat,nat),fun(nat,code_code_numeral)),combb(nat,code_code_numeral,nat),hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),A),B))),hAPP(nat,fun(nat,nat),minus_minus(nat),C)))),hAPP(fun(nat,nat),fun(nat,code_code_numeral),hAPP(fun(nat,code_code_numeral),fun(fun(nat,nat),fun(nat,code_code_numeral)),combb(nat,code_code_numeral,nat),hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A)),hAPP(nat,fun(nat,nat),minus_minus(nat),C))))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),C)) = hAPP(fun(nat,bool),code_code_numeral,hAPP(fun(nat,code_code_numeral),fun(fun(nat,bool),code_code_numeral),big_co1399186613setsum(nat,code_code_numeral),hAPP(code_code_numeral,fun(nat,code_code_numeral),hAPP(fun(nat,fun(code_code_numeral,code_code_numeral)),fun(code_code_numeral,fun(nat,code_code_numeral)),combc(nat,code_code_numeral,code_code_numeral),hAPP(fun(nat,code_code_numeral),fun(nat,fun(code_code_numeral,code_code_numeral)),hAPP(fun(code_code_numeral,fun(code_code_numeral,code_code_numeral)),fun(fun(nat,code_code_numeral),fun(nat,fun(code_code_numeral,code_code_numeral))),combb(code_code_numeral,fun(code_code_numeral,code_code_numeral),nat),minus_minus(code_code_numeral)),hAPP(fun(nat,code_code_numeral),fun(nat,code_code_numeral),hAPP(fun(nat,fun(code_code_numeral,code_code_numeral)),fun(fun(nat,code_code_numeral),fun(nat,code_code_numeral)),combs(nat,code_code_numeral,code_code_numeral),hAPP(fun(nat,code_code_numeral),fun(nat,fun(code_code_numeral,code_code_numeral)),hAPP(fun(code_code_numeral,fun(code_code_numeral,code_code_numeral)),fun(fun(nat,code_code_numeral),fun(nat,fun(code_code_numeral,code_code_numeral))),combb(code_code_numeral,fun(code_code_numeral,code_code_numeral),nat),times_times(code_code_numeral)),hAPP(fun(nat,nat),fun(nat,code_code_numeral),hAPP(fun(nat,code_code_numeral),fun(fun(nat,nat),fun(nat,code_code_numeral)),combb(nat,code_code_numeral,nat),hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),A),B))),hAPP(nat,fun(nat,nat),minus_minus(nat),C)))),hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A)))),hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A),C))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),C)). [resolve(6367,a,6361,a)].
% 166.25/166.03 Derived: -comm_ring(code_code_numeral) | hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),minus_minus(code_code_numeral),A),B)),hAPP(fun(nat,bool),code_code_numeral,hAPP(fun(nat,code_code_numeral),fun(fun(nat,bool),code_code_numeral),big_co1399186613setsum(nat,code_code_numeral),hAPP(fun(nat,code_code_numeral),fun(nat,code_code_numeral),hAPP(fun(nat,fun(code_code_numeral,code_code_numeral)),fun(fun(nat,code_code_numeral),fun(nat,code_code_numeral)),combs(nat,code_code_numeral,code_code_numeral),hAPP(fun(nat,code_code_numeral),fun(nat,fun(code_code_numeral,code_code_numeral)),hAPP(fun(code_code_numeral,fun(code_code_numeral,code_code_numeral)),fun(fun(nat,code_code_numeral),fun(nat,fun(code_code_numeral,code_code_numeral))),combb(code_code_numeral,fun(code_code_numeral,code_code_numeral),nat),times_times(code_code_numeral)),hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A))),hAPP(fun(nat,nat),fun(nat,code_code_numeral),hAPP(fun(nat,code_code_numeral),fun(fun(nat,nat),fun(nat,code_code_numeral)),combb(nat,code_code_numeral,nat),hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),B)),hAPP(nat,fun(nat,nat),minus_minus(nat),C)))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,suc,C)))) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),minus_minus(code_code_numeral),hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A),hAPP(nat,nat,suc,C))),hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),B),hAPP(nat,nat,suc,C))). [resolve(6367,a,6362,a)].
% 166.25/166.03 6368 monoid_mult(quickcheck_code_int) # label(arity_Quickcheck__Narrowing_Ocode__int___Groups_Omonoid__mult) # label(axiom). [assumption].
% 166.25/166.03 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),C),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,B)),A)) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),C),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),B),A))),C). [resolve(6368,a,6340,a)].
% 166.25/166.03 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A)) | hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),B),A) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),A),one_one(nat)))),B). [resolve(6368,a,6341,a)].
% 166.25/166.03 Derived: hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),one_one(quickcheck_code_int)),A) = one_one(quickcheck_code_int). [resolve(6368,a,6343,a)].
% 166.25/166.03 Derived: hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,hAPP(int,int,bit1,pls)))) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),A)),A). [resolve(6368,a,6348,a)].
% 166.25/166.04 Derived: hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A),B)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),B)). [resolve(6368,a,6350,a)].
% 166.25/166.04 Derived: hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),B))) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A),B)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))). [resolve(6368,a,6352,a)].
% 166.25/166.04 Derived: -linordered_ring(quickcheck_code_int) | -hBOOL(hAPP(nat,bool,even_odd_even(nat),A)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),zero_zero(quickcheck_code_int)),hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),B),A))). [resolve(6368,a,6353,a)].
% 166.25/166.04 Derived: hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,B))) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A),hAPP(int,nat,number_number_of(nat),B))),hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A),hAPP(int,nat,number_number_of(nat),B))). [resolve(6368,a,6354,a)].
% 166.25/166.04 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),A))) | hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,A))) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),B),hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),B),hAPP(int,nat,number_number_of(nat),A)))),hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),B),hAPP(int,nat,number_number_of(nat),A))). [resolve(6368,a,6356,a)].
% 166.25/166.04 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),A))) | hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,A))) = one_one(quickcheck_code_int). [resolve(6368,a,6357,a)].
% 166.25/166.04 Derived: -comm_semiring_0(quickcheck_code_int) | hAPP(fun(nat,bool),quickcheck_code_int,hAPP(fun(nat,quickcheck_code_int),fun(fun(nat,bool),quickcheck_code_int),big_co1399186613setsum(nat,quickcheck_code_int),hAPP(fun(nat,quickcheck_code_int),fun(nat,quickcheck_code_int),hAPP(fun(nat,fun(quickcheck_code_int,quickcheck_code_int)),fun(fun(nat,quickcheck_code_int),fun(nat,quickcheck_code_int)),combs(nat,quickcheck_code_int,quickcheck_code_int),hAPP(fun(nat,quickcheck_code_int),fun(nat,fun(quickcheck_code_int,quickcheck_code_int)),hAPP(fun(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int)),fun(fun(nat,quickcheck_code_int),fun(nat,fun(quickcheck_code_int,quickcheck_code_int))),combb(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),nat),times_times(quickcheck_code_int)),hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A))),hAPP(fun(nat,nat),fun(nat,quickcheck_code_int),hAPP(fun(nat,quickcheck_code_int),fun(fun(nat,nat),fun(nat,quickcheck_code_int)),combb(nat,quickcheck_code_int,nat),hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),B)),hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,C))))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,suc,C))) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),B),hAPP(fun(nat,bool),quickcheck_code_int,hAPP(fun(nat,quickcheck_code_int),fun(fun(nat,bool),quickcheck_code_int),big_co1399186613setsum(nat,quickcheck_code_int),hAPP(fun(nat,quickcheck_code_int),fun(nat,quickcheck_code_int),hAPP(fun(nat,fun(quickcheck_code_int,quickcheck_code_int)),fun(fun(nat,quickcheck_code_int),fun(nat,quickcheck_code_int)),combs(nat,quickcheck_code_int,quickcheck_code_int),hAPP(fun(nat,quickcheck_code_int),fun(nat,fun(quickcheck_code_int,quickcheck_code_int)),hAPP(fun(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int)),fun(fun(nat,quickcheck_code_int),fun(nat,fun(quickcheck_code_int,quickcheck_code_int))),combb(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),nat),times_times(quickcheck_code_int)),hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A))),hAPP(fun(nat,nat),fun(nat,quickcheck_code_int),hAPP(fun(nat,quickcheck_code_int),fun(fun(nat,nat),fun(nat,quickcheck_code_int)),combb(nat,quickcheck_code_int,nat),hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),B)),hAPP(nat,fun(nat,nat),minus_minus(nat),C)))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,suc,C)))). [resolve(6368,a,6360,a)].
% 166.25/166.04 Derived: -comm_ring(quickcheck_code_int) | hAPP(fun(nat,bool),quickcheck_code_int,hAPP(fun(nat,quickcheck_code_int),fun(fun(nat,bool),quickcheck_code_int),big_co1399186613setsum(nat,quickcheck_code_int),hAPP(fun(nat,quickcheck_code_int),fun(nat,quickcheck_code_int),hAPP(fun(nat,fun(quickcheck_code_int,quickcheck_code_int)),fun(fun(nat,quickcheck_code_int),fun(nat,quickcheck_code_int)),combs(nat,quickcheck_code_int,quickcheck_code_int),hAPP(fun(nat,quickcheck_code_int),fun(nat,fun(quickcheck_code_int,quickcheck_code_int)),hAPP(fun(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int)),fun(fun(nat,quickcheck_code_int),fun(nat,fun(quickcheck_code_int,quickcheck_code_int))),combb(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),nat),times_times(quickcheck_code_int)),hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A))),hAPP(fun(nat,quickcheck_code_int),fun(nat,quickcheck_code_int),hAPP(fun(nat,fun(quickcheck_code_int,quickcheck_code_int)),fun(fun(nat,quickcheck_code_int),fun(nat,quickcheck_code_int)),combs(nat,quickcheck_code_int,quickcheck_code_int),hAPP(fun(nat,quickcheck_code_int),fun(nat,fun(quickcheck_code_int,quickcheck_code_int)),hAPP(fun(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int)),fun(fun(nat,quickcheck_code_int),fun(nat,fun(quickcheck_code_int,quickcheck_code_int))),combb(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),nat),minus_minus(quickcheck_code_int)),hAPP(fun(nat,nat),fun(nat,quickcheck_code_int),hAPP(fun(nat,quickcheck_code_int),fun(fun(nat,nat),fun(nat,quickcheck_code_int)),combb(nat,quickcheck_code_int,nat),hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),A),B))),hAPP(nat,fun(nat,nat),minus_minus(nat),C)))),hAPP(fun(nat,nat),fun(nat,quickcheck_code_int),hAPP(fun(nat,quickcheck_code_int),fun(fun(nat,nat),fun(nat,quickcheck_code_int)),combb(nat,quickcheck_code_int,nat),hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A)),hAPP(nat,fun(nat,nat),minus_minus(nat),C))))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),C)) = hAPP(fun(nat,bool),quickcheck_code_int,hAPP(fun(nat,quickcheck_code_int),fun(fun(nat,bool),quickcheck_code_int),big_co1399186613setsum(nat,quickcheck_code_int),hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),hAPP(fun(nat,fun(quickcheck_code_int,quickcheck_code_int)),fun(quickcheck_code_int,fun(nat,quickcheck_code_int)),combc(nat,quickcheck_code_int,quickcheck_code_int),hAPP(fun(nat,quickcheck_code_int),fun(nat,fun(quickcheck_code_int,quickcheck_code_int)),hAPP(fun(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int)),fun(fun(nat,quickcheck_code_int),fun(nat,fun(quickcheck_code_int,quickcheck_code_int))),combb(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),nat),minus_minus(quickcheck_code_int)),hAPP(fun(nat,quickcheck_code_int),fun(nat,quickcheck_code_int),hAPP(fun(nat,fun(quickcheck_code_int,quickcheck_code_int)),fun(fun(nat,quickcheck_code_int),fun(nat,quickcheck_code_int)),combs(nat,quickcheck_code_int,quickcheck_code_int),hAPP(fun(nat,quickcheck_code_int),fun(nat,fun(quickcheck_code_int,quickcheck_code_int)),hAPP(fun(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int)),fun(fun(nat,quickcheck_code_int),fun(nat,fun(quickcheck_code_int,quickcheck_code_int))),combb(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),nat),times_times(quickcheck_code_int)),hAPP(fun(nat,nat),fun(nat,quickcheck_code_int),hAPP(fun(nat,quickcheck_code_int),fun(fun(nat,nat),fun(nat,quickcheck_code_int)),combb(nat,quickcheck_code_int,nat),hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),A),B))),hAPP(nat,fun(nat,nat),minus_minus(nat),C)))),hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A)))),hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A),C))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),C)). [resolve(6368,a,6361,a)].
% 166.25/166.04 Derived: -comm_ring(quickcheck_code_int) | hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),minus_minus(quickcheck_code_int),A),B)),hAPP(fun(nat,bool),quickcheck_code_int,hAPP(fun(nat,quickcheck_code_int),fun(fun(nat,bool),quickcheck_code_int),big_co1399186613setsum(nat,quickcheck_code_int),hAPP(fun(nat,quickcheck_code_int),fun(nat,quickcheck_code_int),hAPP(fun(nat,fun(quickcheck_code_int,quickcheck_code_int)),fun(fun(nat,quickcheck_code_int),fun(nat,quickcheck_code_int)),combs(nat,quickcheck_code_int,quickcheck_code_int),hAPP(fun(nat,quickcheck_code_int),fun(nat,fun(quickcheck_code_int,quickcheck_code_int)),hAPP(fun(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int)),fun(fun(nat,quickcheck_code_int),fun(nat,fun(quickcheck_code_int,quickcheck_code_int))),combb(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),nat),times_times(quickcheck_code_int)),hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A))),hAPP(fun(nat,nat),fun(nat,quickcheck_code_int),hAPP(fun(nat,quickcheck_code_int),fun(fun(nat,nat),fun(nat,quickcheck_code_int)),combb(nat,quickcheck_code_int,nat),hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),B)),hAPP(nat,fun(nat,nat),minus_minus(nat),C)))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,suc,C)))) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),minus_minus(quickcheck_code_int),hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A),hAPP(nat,nat,suc,C))),hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),B),hAPP(nat,nat,suc,C))). [resolve(6368,a,6362,a)].
% 175.03/174.85 6369 linord626643107strict(int) # label(arity_Int_Oint___Rings_Olinordered__semiring__1__strict) # label(axiom). [assumption].
% 175.03/174.85 6370 -linord626643107strict(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),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),E)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),F)) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),E),F) != one_one(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),E),B)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),F),D))),C)) # label(fact_245_convex__bound__lt) # label(axiom). [clausify(375)].
% 175.03/174.85 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),C),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),D)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),E)) | hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),D),E) != one_one(int) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),D),A)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),E),C))),B)). [resolve(6369,a,6370,a)].
% 175.03/174.85 6371 linord626643107strict(rat) # label(arity_Rat_Orat___Rings_Olinordered__semiring__1__strict) # label(axiom). [assumption].
% 175.03/174.85 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),C),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),D)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),E)) | hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),D),E) != one_one(rat) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),D),A)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),E),C))),B)). [resolve(6371,a,6370,a)].
% 175.03/174.85 6372 linord626643107strict(real) # label(arity_RealDef_Oreal___Rings_Olinordered__semiring__1__strict) # label(axiom). [assumption].
% 175.03/174.85 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),C),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),D)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),E)) | hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),D),E) != one_one(real) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),D),A)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),E),C))),B)). [resolve(6372,a,6370,a)].
% 175.03/174.85 6373 ring_n68954251visors(int) # label(arity_Int_Oint___Rings_Oring__no__zero__divisors) # label(axiom). [assumption].
% 175.03/174.85 6374 -ring_n68954251visors(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C) != zero_zero(A) | zero_zero(A) = ti(A,B) | zero_zero(A) = ti(A,C) # label(fact_256_mult__eq__0__iff) # label(axiom). [clausify(386)].
% 179.55/179.33 6375 -ring_n68954251visors(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C) = zero_zero(A) | zero_zero(A) != ti(A,B) # label(fact_256_mult__eq__0__iff) # label(axiom). [clausify(386)].
% 179.55/179.33 6376 -ring_n68954251visors(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C) = zero_zero(A) | zero_zero(A) != ti(A,C) # label(fact_256_mult__eq__0__iff) # label(axiom). [clausify(386)].
% 179.55/179.33 Derived: hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B) != zero_zero(int) | zero_zero(int) = ti(int,A) | zero_zero(int) = ti(int,B). [resolve(6373,a,6374,a)].
% 179.55/179.33 Derived: hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B) = zero_zero(int) | zero_zero(int) != ti(int,A). [resolve(6373,a,6375,a)].
% 179.55/179.33 Derived: hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B) = zero_zero(int) | zero_zero(int) != ti(int,B). [resolve(6373,a,6376,a)].
% 179.55/179.33 6377 ring_n68954251visors(rat) # label(arity_Rat_Orat___Rings_Oring__no__zero__divisors) # label(axiom). [assumption].
% 179.55/179.33 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B) != zero_zero(rat) | zero_zero(rat) = ti(rat,A) | zero_zero(rat) = ti(rat,B). [resolve(6377,a,6374,a)].
% 179.55/179.33 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B) = zero_zero(rat) | zero_zero(rat) != ti(rat,A). [resolve(6377,a,6375,a)].
% 179.55/179.33 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B) = zero_zero(rat) | zero_zero(rat) != ti(rat,B). [resolve(6377,a,6376,a)].
% 179.55/179.33 6378 ring_n68954251visors(real) # label(arity_RealDef_Oreal___Rings_Oring__no__zero__divisors) # label(axiom). [assumption].
% 179.55/179.33 Derived: hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B) != zero_zero(real) | zero_zero(real) = ti(real,A) | zero_zero(real) = ti(real,B). [resolve(6378,a,6374,a)].
% 179.55/179.33 Derived: hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B) = zero_zero(real) | zero_zero(real) != ti(real,A). [resolve(6378,a,6375,a)].
% 179.55/179.33 Derived: hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B) = zero_zero(real) | zero_zero(real) != ti(real,B). [resolve(6378,a,6376,a)].
% 179.55/179.33 6379 ring_n68954251visors(complex) # label(arity_Complex_Ocomplex___Rings_Oring__no__zero__divisors) # label(axiom). [assumption].
% 179.55/179.33 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),B) != zero_zero(complex) | zero_zero(complex) = ti(complex,A) | zero_zero(complex) = ti(complex,B). [resolve(6379,a,6374,a)].
% 179.55/179.33 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),B) = zero_zero(complex) | zero_zero(complex) != ti(complex,A). [resolve(6379,a,6375,a)].
% 179.55/179.33 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),B) = zero_zero(complex) | zero_zero(complex) != ti(complex,B). [resolve(6379,a,6376,a)].
% 179.55/179.33 6380 linord219039673up_add(int) # label(arity_Int_Oint___Groups_Olinordered__ab__group__add) # label(axiom). [assumption].
% 179.55/179.33 6381 -linord219039673up_add(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),B) != zero_zero(A) | zero_zero(A) = ti(A,B) # label(fact_265_double__eq__0__iff) # label(axiom). [clausify(395)].
% 179.55/179.33 6382 -linord219039673up_add(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),B) = zero_zero(A) | zero_zero(A) != ti(A,B) # label(fact_265_double__eq__0__iff) # label(axiom). [clausify(395)].
% 179.55/179.33 6383 -linord219039673up_add(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),B) != zero_zero(A) | zero_zero(A) = ti(A,B) # label(fact_268_double__zero__sym) # label(axiom). [clausify(398)].
% 179.55/179.33 6384 -linord219039673up_add(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),B) = zero_zero(A) | zero_zero(A) != ti(A,B) # label(fact_268_double__zero__sym) # label(axiom). [clausify(398)].
% 179.55/179.33 6385 -linord219039673up_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),B))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) # label(fact_323_zero__le__double__add__iff__zero__le__single__add) # label(axiom). [clausify(452)].
% 179.55/179.33 6386 -linord219039673up_add(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),B))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) # label(fact_323_zero__le__double__add__iff__zero__le__single__add) # label(axiom). [clausify(452)].
% 179.55/179.33 6387 -linord219039673up_add(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),B)),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),zero_zero(A))) # label(fact_324_double__add__le__zero__iff__single__add__le__zero) # label(axiom). [clausify(453)].
% 179.55/179.33 6388 -linord219039673up_add(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),B)),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),zero_zero(A))) # label(fact_324_double__add__le__zero__iff__single__add__le__zero) # label(axiom). [clausify(453)].
% 179.55/179.33 6389 -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_330_zero__less__double__add__iff__zero__less__single__add) # label(axiom). [clausify(459)].
% 179.55/179.33 6390 -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_330_zero__less__double__add__iff__zero__less__single__add) # label(axiom). [clausify(459)].
% 179.55/179.33 6391 -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_332_double__add__less__zero__iff__single__add__less__zero) # label(axiom). [clausify(461)].
% 179.55/179.33 6392 -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_332_double__add__less__zero__iff__single__add__less__zero) # label(axiom). [clausify(461)].
% 179.55/179.33 6393 -linord219039673up_add(A) | hAPP(A,A,uminus_uminus(A),B) != ti(A,B) | zero_zero(A) = ti(A,B) # label(fact_553_neg__equal__zero) # label(axiom). [clausify(677)].
% 179.55/179.33 6394 -linord219039673up_add(A) | hAPP(A,A,uminus_uminus(A),B) = ti(A,B) | zero_zero(A) != ti(A,B) # label(fact_553_neg__equal__zero) # label(axiom). [clausify(677)].
% 179.55/179.33 6395 -linord219039673up_add(A) | hAPP(A,A,uminus_uminus(A),B) != ti(A,B) | zero_zero(A) = ti(A,B) # label(fact_555_equal__neg__zero) # label(axiom). [clausify(679)].
% 179.55/179.33 6396 -linord219039673up_add(A) | hAPP(A,A,uminus_uminus(A),B) = ti(A,B) | zero_zero(A) != ti(A,B) # label(fact_555_equal__neg__zero) # label(axiom). [clausify(679)].
% 179.55/179.33 6397 -linord219039673up_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,uminus_uminus(A),B)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) # label(fact_626_minus__le__self__iff) # label(axiom). [clausify(747)].
% 179.55/179.33 6398 -linord219039673up_add(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,uminus_uminus(A),B)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) # label(fact_626_minus__le__self__iff) # label(axiom). [clausify(747)].
% 179.55/179.33 6399 -linord219039673up_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,uminus_uminus(A),B))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),zero_zero(A))) # label(fact_628_le__minus__self__iff) # label(axiom). [clausify(749)].
% 179.55/179.33 6400 -linord219039673up_add(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,uminus_uminus(A),B))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),zero_zero(A))) # label(fact_628_le__minus__self__iff) # label(axiom). [clausify(749)].
% 179.55/179.33 6401 -linord219039673up_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,uminus_uminus(A),B)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) # label(fact_631_neg__less__nonneg) # label(axiom). [clausify(752)].
% 179.55/179.33 6402 -linord219039673up_add(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,uminus_uminus(A),B)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) # label(fact_631_neg__less__nonneg) # label(axiom). [clausify(752)].
% 179.55/179.35 6403 -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_4945_minus__min__eq__max) # label(axiom). [clausify(4865)].
% 179.55/179.35 6404 -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_4946_minus__max__eq__min) # label(axiom). [clausify(4866)].
% 179.55/179.35 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),A) != zero_zero(int) | zero_zero(int) = ti(int,A). [resolve(6380,a,6381,a)].
% 179.55/179.35 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),A) = zero_zero(int) | zero_zero(int) != ti(int,A). [resolve(6380,a,6382,a)].
% 179.55/179.35 Derived: -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),A),A))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A)). [resolve(6380,a,6385,a)].
% 179.55/179.35 Derived: 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),A),A))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A)). [resolve(6380,a,6386,a)].
% 179.55/179.35 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),A)),zero_zero(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),zero_zero(int))). [resolve(6380,a,6387,a)].
% 179.55/179.35 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),A)),zero_zero(int))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),zero_zero(int))). [resolve(6380,a,6388,a)].
% 179.55/179.35 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(6380,a,6389,a)].
% 179.55/179.35 Derived: hAPP(int,int,uminus_uminus(int),A) != ti(int,A) | zero_zero(int) = ti(int,A). [resolve(6380,a,6393,a)].
% 179.55/179.35 Derived: hAPP(int,int,uminus_uminus(int),A) = ti(int,A) | zero_zero(int) != ti(int,A). [resolve(6380,a,6394,a)].
% 179.55/179.35 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,uminus_uminus(int),A)),A)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A)). [resolve(6380,a,6397,a)].
% 179.55/179.35 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,uminus_uminus(int),A)),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A)). [resolve(6380,a,6398,a)].
% 179.55/179.35 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),hAPP(int,int,uminus_uminus(int),A))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),zero_zero(int))). [resolve(6380,a,6399,a)].
% 179.55/179.35 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),hAPP(int,int,uminus_uminus(int),A))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),zero_zero(int))). [resolve(6380,a,6400,a)].
% 179.55/179.35 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,uminus_uminus(int),A)),A)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A)). [resolve(6380,a,6401,a)].
% 179.55/179.35 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,uminus_uminus(int),A)),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A)). [resolve(6380,a,6402,a)].
% 179.55/179.35 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(6380,a,6403,a)].
% 179.61/179.40 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(6380,a,6404,a)].
% 179.61/179.40 6405 linord219039673up_add(rat) # label(arity_Rat_Orat___Groups_Olinordered__ab__group__add) # label(axiom). [assumption].
% 179.61/179.40 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),A) != zero_zero(rat) | zero_zero(rat) = ti(rat,A). [resolve(6405,a,6381,a)].
% 179.61/179.40 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),A) = zero_zero(rat) | zero_zero(rat) != ti(rat,A). [resolve(6405,a,6382,a)].
% 179.61/179.40 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),A))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),A)). [resolve(6405,a,6385,a)].
% 179.61/179.40 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),A))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),A)). [resolve(6405,a,6386,a)].
% 179.61/179.40 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),A)),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),zero_zero(rat))). [resolve(6405,a,6387,a)].
% 179.61/179.40 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),A)),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),zero_zero(rat))). [resolve(6405,a,6388,a)].
% 179.61/179.40 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),A))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)). [resolve(6405,a,6389,a)].
% 179.61/179.40 Derived: hAPP(rat,rat,uminus_uminus(rat),A) != ti(rat,A) | zero_zero(rat) = ti(rat,A). [resolve(6405,a,6393,a)].
% 179.61/179.40 Derived: hAPP(rat,rat,uminus_uminus(rat),A) = ti(rat,A) | zero_zero(rat) != ti(rat,A). [resolve(6405,a,6394,a)].
% 179.61/179.40 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,uminus_uminus(rat),A)),A)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),A)). [resolve(6405,a,6397,a)].
% 179.61/179.40 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,uminus_uminus(rat),A)),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),A)). [resolve(6405,a,6398,a)].
% 179.61/179.40 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),hAPP(rat,rat,uminus_uminus(rat),A))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),zero_zero(rat))). [resolve(6405,a,6399,a)].
% 179.61/179.40 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),hAPP(rat,rat,uminus_uminus(rat),A))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),zero_zero(rat))). [resolve(6405,a,6400,a)].
% 179.61/179.40 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,uminus_uminus(rat),A)),A)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)). [resolve(6405,a,6401,a)].
% 179.61/179.40 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,uminus_uminus(rat),A)),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)). [resolve(6405,a,6402,a)].
% 179.61/179.40 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_max(rat),hAPP(rat,rat,uminus_uminus(rat),A)),hAPP(rat,rat,uminus_uminus(rat),B)) = hAPP(rat,rat,uminus_uminus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_min(rat),A),B)). [resolve(6405,a,6403,a)].
% 179.61/179.40 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_min(rat),hAPP(rat,rat,uminus_uminus(rat),A)),hAPP(rat,rat,uminus_uminus(rat),B)) = hAPP(rat,rat,uminus_uminus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_max(rat),A),B)). [resolve(6405,a,6404,a)].
% 179.61/179.40 6406 linord219039673up_add(real) # label(arity_RealDef_Oreal___Groups_Olinordered__ab__group__add) # label(axiom). [assumption].
% 184.44/184.27 Derived: hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),A) != zero_zero(real) | zero_zero(real) = ti(real,A). [resolve(6406,a,6381,a)].
% 184.44/184.27 Derived: hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),A) = zero_zero(real) | zero_zero(real) != ti(real,A). [resolve(6406,a,6382,a)].
% 184.44/184.27 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),A))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A)). [resolve(6406,a,6385,a)].
% 184.44/184.27 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),A))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A)). [resolve(6406,a,6386,a)].
% 184.44/184.27 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),A)),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),zero_zero(real))). [resolve(6406,a,6387,a)].
% 184.44/184.27 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),A)),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),zero_zero(real))). [resolve(6406,a,6388,a)].
% 184.44/184.27 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),A))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)). [resolve(6406,a,6389,a)].
% 184.44/184.27 Derived: hAPP(real,real,uminus_uminus(real),A) != ti(real,A) | zero_zero(real) = ti(real,A). [resolve(6406,a,6393,a)].
% 184.44/184.27 Derived: hAPP(real,real,uminus_uminus(real),A) = ti(real,A) | zero_zero(real) != ti(real,A). [resolve(6406,a,6394,a)].
% 184.44/184.27 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,uminus_uminus(real),A)),A)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A)). [resolve(6406,a,6397,a)].
% 184.44/184.27 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,uminus_uminus(real),A)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A)). [resolve(6406,a,6398,a)].
% 184.44/184.27 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),hAPP(real,real,uminus_uminus(real),A))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),zero_zero(real))). [resolve(6406,a,6399,a)].
% 184.44/184.27 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),hAPP(real,real,uminus_uminus(real),A))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),zero_zero(real))). [resolve(6406,a,6400,a)].
% 184.44/184.27 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,uminus_uminus(real),A)),A)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)). [resolve(6406,a,6401,a)].
% 184.44/184.27 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,uminus_uminus(real),A)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)). [resolve(6406,a,6402,a)].
% 184.44/184.27 Derived: hAPP(real,real,hAPP(real,fun(real,real),ord_max(real),hAPP(real,real,uminus_uminus(real),A)),hAPP(real,real,uminus_uminus(real),B)) = hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),ord_min(real),A),B)). [resolve(6406,a,6403,a)].
% 184.44/184.27 Derived: hAPP(real,real,hAPP(real,fun(real,real),ord_min(real),hAPP(real,real,uminus_uminus(real),A)),hAPP(real,real,uminus_uminus(real),B)) = hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),ord_max(real),A),B)). [resolve(6406,a,6404,a)].
% 184.44/184.27 6407 linord581940658strict(int) # label(arity_Int_Oint___Rings_Olinordered__ring__strict) # label(axiom). [assumption].
% 184.44/184.27 6408 -linord581940658strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(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_eq(A),zero_zero(A)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),zero_zero(A))) # label(fact_290_zero__le__mult__iff) # label(axiom). [clausify(419)].
% 184.44/184.27 6409 -linord581940658strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(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_eq(A),zero_zero(A)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),zero_zero(A))) # label(fact_290_zero__le__mult__iff) # label(axiom). [clausify(419)].
% 184.44/184.27 6410 -linord581940658strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(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_eq(A),zero_zero(A)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),zero_zero(A))) # label(fact_290_zero__le__mult__iff) # label(axiom). [clausify(419)].
% 184.44/184.27 6411 -linord581940658strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(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_eq(A),zero_zero(A)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),zero_zero(A))) # label(fact_290_zero__le__mult__iff) # label(axiom). [clausify(419)].
% 184.44/184.27 6412 -linord581940658strict(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(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_eq(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),C)) # label(fact_290_zero__le__mult__iff) # label(axiom). [clausify(419)].
% 184.44/184.27 6413 -linord581940658strict(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(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_eq(A),B),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),zero_zero(A))) # label(fact_290_zero__le__mult__iff) # label(axiom). [clausify(419)].
% 184.44/184.27 6414 -linord581940658strict(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)),zero_zero(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),B),zero_zero(A))) # label(fact_291_mult__le__0__iff) # label(axiom). [clausify(420)].
% 184.44/184.27 6415 -linord581940658strict(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)),zero_zero(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)) # label(fact_291_mult__le__0__iff) # label(axiom). [clausify(420)].
% 184.44/184.27 6416 -linord581940658strict(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)),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),zero_zero(A))) # label(fact_291_mult__le__0__iff) # label(axiom). [clausify(420)].
% 184.44/184.27 6417 -linord581940658strict(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)),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),C)) # label(fact_291_mult__le__0__iff) # label(axiom). [clausify(420)].
% 184.44/184.27 6418 -linord581940658strict(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)),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),zero_zero(A))) # label(fact_291_mult__le__0__iff) # label(axiom). [clausify(420)].
% 184.44/184.27 6419 -linord581940658strict(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)),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),C)) # label(fact_291_mult__le__0__iff) # label(axiom). [clausify(420)].
% 184.44/184.27 6420 -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_307_mult__less__cancel__right__disj) # label(axiom). [clausify(436)].
% 184.44/184.27 6421 -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_307_mult__less__cancel__right__disj) # label(axiom). [clausify(436)].
% 184.44/184.27 6422 -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_307_mult__less__cancel__right__disj) # label(axiom). [clausify(436)].
% 184.44/184.27 6423 -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_307_mult__less__cancel__right__disj) # label(axiom). [clausify(436)].
% 184.44/184.27 6424 -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_307_mult__less__cancel__right__disj) # label(axiom). [clausify(436)].
% 184.44/184.27 6425 -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_307_mult__less__cancel__right__disj) # label(axiom). [clausify(436)].
% 184.44/184.27 6426 -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_308_mult__less__cancel__left__disj) # label(axiom). [clausify(437)].
% 184.44/184.27 6427 -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_308_mult__less__cancel__left__disj) # label(axiom). [clausify(437)].
% 184.44/184.27 6428 -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_308_mult__less__cancel__left__disj) # label(axiom). [clausify(437)].
% 184.44/184.27 6429 -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_308_mult__less__cancel__left__disj) # label(axiom). [clausify(437)].
% 184.44/184.27 6430 -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_308_mult__less__cancel__left__disj) # label(axiom). [clausify(437)].
% 184.44/184.27 6431 -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_308_mult__less__cancel__left__disj) # label(axiom). [clausify(437)].
% 184.44/184.27 6432 -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_309_mult__less__cancel__left__pos) # label(axiom). [clausify(438)].
% 184.44/184.27 6433 -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_309_mult__less__cancel__left__pos) # label(axiom). [clausify(438)].
% 184.44/184.27 6434 -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_315_mult__less__cancel__left__neg) # label(axiom). [clausify(444)].
% 184.44/184.27 6435 -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_315_mult__less__cancel__left__neg) # label(axiom). [clausify(444)].
% 184.44/184.27 6436 -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_317_mult__neg__neg) # label(axiom). [clausify(446)].
% 184.44/184.27 6437 -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_321_mult__strict__right__mono__neg) # label(axiom). [clausify(450)].
% 184.44/184.27 6438 -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_322_mult__strict__left__mono__neg) # label(axiom). [clausify(451)].
% 184.44/184.27 6439 -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_eq(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_eq(A),D),C)) # label(fact_366_mult__le__cancel__left__neg) # label(axiom). [clausify(494)].
% 184.44/184.27 6440 -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_eq(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_eq(A),D),C)) # label(fact_366_mult__le__cancel__left__neg) # label(axiom). [clausify(494)].
% 184.44/184.27 6441 -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_eq(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_eq(A),C),D)) # label(fact_367_mult__le__cancel__left__pos) # label(axiom). [clausify(495)].
% 184.44/184.27 6442 -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_eq(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_eq(A),C),D)) # label(fact_367_mult__le__cancel__left__pos) # label(axiom). [clausify(495)].
% 184.44/184.27 6443 -linord581940658strict(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),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)))) | zero_zero(A) != ti(A,B) | zero_zero(A) != ti(A,C) # label(fact_390_sum__squares__gt__zero__iff) # label(axiom). [clausify(518)].
% 184.44/184.27 6444 -linord581940658strict(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),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)))) | zero_zero(A) = ti(A,B) # label(fact_390_sum__squares__gt__zero__iff) # label(axiom). [clausify(518)].
% 184.44/184.27 6445 -linord581940658strict(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),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)))) | zero_zero(A) = ti(A,C) # label(fact_390_sum__squares__gt__zero__iff) # label(axiom). [clausify(518)].
% 184.44/184.27 6446 -linord581940658strict(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),B)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),C))),zero_zero(A))) | zero_zero(A) = ti(A,B) # label(fact_392_sum__squares__le__zero__iff) # label(axiom). [clausify(520)].
% 184.44/184.27 6447 -linord581940658strict(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),B)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),C))),zero_zero(A))) | zero_zero(A) = ti(A,C) # label(fact_392_sum__squares__le__zero__iff) # label(axiom). [clausify(520)].
% 184.44/184.27 6448 -linord581940658strict(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),B)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),C))),zero_zero(A))) | zero_zero(A) != ti(A,B) | zero_zero(A) != ti(A,C) # label(fact_392_sum__squares__le__zero__iff) # label(axiom). [clausify(520)].
% 184.44/184.27 6449 -linord581940658strict(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(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)) != zero_zero(A) | zero_zero(A) = ti(A,B) # label(fact_393_sum__squares__eq__zero__iff) # label(axiom). [clausify(521)].
% 184.44/184.27 6450 -linord581940658strict(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(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)) != zero_zero(A) | zero_zero(A) = ti(A,C) # label(fact_393_sum__squares__eq__zero__iff) # label(axiom). [clausify(521)].
% 184.44/184.27 6451 -linord581940658strict(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(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)) = zero_zero(A) | zero_zero(A) != ti(A,B) | zero_zero(A) != ti(A,C) # label(fact_393_sum__squares__eq__zero__iff) # label(axiom). [clausify(521)].
% 184.44/184.27 Derived: -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),A),B))) | 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),A),zero_zero(int))). [resolve(6407,a,6408,a)].
% 184.50/184.28 Derived: -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),A),B))) | 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),B),zero_zero(int))). [resolve(6407,a,6409,a)].
% 184.50/184.28 Derived: -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),A),B))) | 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),A),zero_zero(int))). [resolve(6407,a,6410,a)].
% 184.50/184.28 Derived: -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),A),B))) | 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),zero_zero(int))). [resolve(6407,a,6411,a)].
% 184.50/184.28 Derived: -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)),zero_zero(int))) | 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),A),zero_zero(int))). [resolve(6407,a,6414,a)].
% 184.50/184.28 Derived: -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)),zero_zero(int))) | 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)). [resolve(6407,a,6415,a)].
% 184.50/184.28 Derived: -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)),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_eq(int),A),zero_zero(int))). [resolve(6407,a,6416,a)].
% 184.50/184.28 Derived: -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)),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_eq(int),zero_zero(int)),B)). [resolve(6407,a,6417,a)].
% 184.50/184.28 Derived: 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)),zero_zero(int))) | -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),B),zero_zero(int))). [resolve(6407,a,6418,a)].
% 184.50/184.28 Derived: 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)),zero_zero(int))) | -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_eq(int),zero_zero(int)),B)). [resolve(6407,a,6419,a)].
% 184.50/184.28 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(6407,a,6420,a)].
% 184.50/184.28 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(6407,a,6421,a)].
% 184.50/184.28 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(6407,a,6422,a)].
% 184.50/184.29 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(6407,a,6423,a)].
% 184.50/184.29 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(6407,a,6424,a)].
% 184.50/184.29 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(6407,a,6425,a)].
% 184.50/184.29 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(6407,a,6426,a)].
% 184.50/184.29 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(6407,a,6427,a)].
% 184.50/184.29 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(6407,a,6428,a)].
% 184.50/184.29 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(6407,a,6429,a)].
% 184.50/184.29 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(6407,a,6430,a)].
% 184.50/184.29 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(6407,a,6431,a)].
% 184.50/184.29 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(6407,a,6432,a)].
% 184.50/184.29 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(6407,a,6434,a)].
% 184.50/184.29 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(6407,a,6436,a)].
% 184.50/184.30 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),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_eq(int),C),B)). [resolve(6407,a,6439,a)].
% 184.50/184.30 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),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_eq(int),C),B)). [resolve(6407,a,6440,a)].
% 184.50/184.30 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),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_eq(int),B),C)). [resolve(6407,a,6441,a)].
% 184.50/184.30 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),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_eq(int),B),C)). [resolve(6407,a,6442,a)].
% 184.50/184.30 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),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)))) | zero_zero(int) != ti(int,A) | zero_zero(int) != ti(int,B). [resolve(6407,a,6443,a)].
% 184.50/184.30 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),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)))) | zero_zero(int) = ti(int,A). [resolve(6407,a,6444,a)].
% 184.50/184.30 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),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)))) | zero_zero(int) = ti(int,B). [resolve(6407,a,6445,a)].
% 184.50/184.30 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),A)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),B))),zero_zero(int))) | zero_zero(int) = ti(int,A). [resolve(6407,a,6446,a)].
% 184.50/184.30 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),A)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),B))),zero_zero(int))) | zero_zero(int) = ti(int,B). [resolve(6407,a,6447,a)].
% 184.50/184.30 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),A)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),B))),zero_zero(int))) | zero_zero(int) != ti(int,A) | zero_zero(int) != ti(int,B). [resolve(6407,a,6448,a)].
% 184.50/184.30 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),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)) != zero_zero(int) | zero_zero(int) = ti(int,A). [resolve(6407,a,6449,a)].
% 184.50/184.30 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),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)) != zero_zero(int) | zero_zero(int) = ti(int,B). [resolve(6407,a,6450,a)].
% 184.50/184.33 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),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)) = zero_zero(int) | zero_zero(int) != ti(int,A) | zero_zero(int) != ti(int,B). [resolve(6407,a,6451,a)].
% 184.50/184.33 6452 linord581940658strict(rat) # label(arity_Rat_Orat___Rings_Olinordered__ring__strict) # label(axiom). [assumption].
% 184.50/184.33 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),A)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),zero_zero(rat))). [resolve(6452,a,6408,a)].
% 184.50/184.33 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),A)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),B),zero_zero(rat))). [resolve(6452,a,6409,a)].
% 184.50/184.33 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),zero_zero(rat))). [resolve(6452,a,6410,a)].
% 184.50/184.33 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),B),zero_zero(rat))). [resolve(6452,a,6411,a)].
% 184.50/184.33 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B)),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),A)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),zero_zero(rat))). [resolve(6452,a,6414,a)].
% 184.50/184.33 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B)),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),A)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),B)). [resolve(6452,a,6415,a)].
% 184.50/184.33 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B)),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),B),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),zero_zero(rat))). [resolve(6452,a,6416,a)].
% 184.50/184.33 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B)),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),B),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),B)). [resolve(6452,a,6417,a)].
% 184.50/184.33 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B)),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),B),zero_zero(rat))). [resolve(6452,a,6418,a)].
% 184.50/184.33 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B)),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),B)). [resolve(6452,a,6419,a)].
% 184.50/184.33 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),C),B))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),zero_zero(rat))). [resolve(6452,a,6420,a)].
% 184.50/184.34 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),C),B))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),C),A)). [resolve(6452,a,6421,a)].
% 184.50/184.34 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),C),B))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),C)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),zero_zero(rat))). [resolve(6452,a,6422,a)].
% 184.50/184.34 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),C),B))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),C)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),C),A)). [resolve(6452,a,6423,a)].
% 184.50/184.34 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),C),B))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),C)). [resolve(6452,a,6424,a)].
% 184.50/184.34 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),C),B))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),C),A)). [resolve(6452,a,6425,a)].
% 184.50/184.34 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),C))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),zero_zero(rat))). [resolve(6452,a,6426,a)].
% 184.50/184.34 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),C))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),C),B)). [resolve(6452,a,6427,a)].
% 184.50/184.34 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),C))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),C)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),zero_zero(rat))). [resolve(6452,a,6428,a)].
% 184.50/184.34 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),C))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),C)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),C),B)). [resolve(6452,a,6429,a)].
% 184.50/184.34 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),C))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),C)). [resolve(6452,a,6430,a)].
% 184.50/184.34 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),C))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),C),B)). [resolve(6452,a,6431,a)].
% 184.50/184.34 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),C))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),C)). [resolve(6452,a,6432,a)].
% 184.50/184.35 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),C))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),C),B)). [resolve(6452,a,6434,a)].
% 184.50/184.35 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B))). [resolve(6452,a,6436,a)].
% 184.50/184.35 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),C))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),C),B)). [resolve(6452,a,6439,a)].
% 184.50/184.35 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),C))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),C),B)). [resolve(6452,a,6440,a)].
% 184.50/184.35 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),C))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),B),C)). [resolve(6452,a,6441,a)].
% 184.50/184.35 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),C))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),B),C)). [resolve(6452,a,6442,a)].
% 184.50/184.35 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),A)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),B),B)))) | zero_zero(rat) != ti(rat,A) | zero_zero(rat) != ti(rat,B). [resolve(6452,a,6443,a)].
% 184.50/184.35 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),A)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),B),B)))) | zero_zero(rat) = ti(rat,A). [resolve(6452,a,6444,a)].
% 184.50/184.35 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),A)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),B),B)))) | zero_zero(rat) = ti(rat,B). [resolve(6452,a,6445,a)].
% 184.50/184.35 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),A)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),B),B))),zero_zero(rat))) | zero_zero(rat) = ti(rat,A). [resolve(6452,a,6446,a)].
% 184.50/184.35 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),A)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),B),B))),zero_zero(rat))) | zero_zero(rat) = ti(rat,B). [resolve(6452,a,6447,a)].
% 184.50/184.35 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),A)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),B),B))),zero_zero(rat))) | zero_zero(rat) != ti(rat,A) | zero_zero(rat) != ti(rat,B). [resolve(6452,a,6448,a)].
% 184.60/184.38 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),A)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),B),B)) != zero_zero(rat) | zero_zero(rat) = ti(rat,A). [resolve(6452,a,6449,a)].
% 184.60/184.38 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),A)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),B),B)) != zero_zero(rat) | zero_zero(rat) = ti(rat,B). [resolve(6452,a,6450,a)].
% 184.60/184.38 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),A)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),B),B)) = zero_zero(rat) | zero_zero(rat) != ti(rat,A) | zero_zero(rat) != ti(rat,B). [resolve(6452,a,6451,a)].
% 184.60/184.38 6453 linord581940658strict(real) # label(arity_RealDef_Oreal___Rings_Olinordered__ring__strict) # label(axiom). [assumption].
% 184.60/184.38 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),zero_zero(real))). [resolve(6453,a,6408,a)].
% 184.60/184.38 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),zero_zero(real))). [resolve(6453,a,6409,a)].
% 184.60/184.38 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),zero_zero(real))). [resolve(6453,a,6410,a)].
% 184.60/184.38 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),zero_zero(real))). [resolve(6453,a,6411,a)].
% 184.60/184.38 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),zero_zero(real))). [resolve(6453,a,6414,a)].
% 184.60/184.38 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),B)). [resolve(6453,a,6415,a)].
% 184.60/184.38 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),zero_zero(real))). [resolve(6453,a,6416,a)].
% 184.60/184.38 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),B)). [resolve(6453,a,6417,a)].
% 184.60/184.38 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),zero_zero(real))). [resolve(6453,a,6418,a)].
% 184.60/184.39 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),B)). [resolve(6453,a,6419,a)].
% 184.60/184.39 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),B))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),zero_zero(real))). [resolve(6453,a,6420,a)].
% 184.60/184.39 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),B))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),C),A)). [resolve(6453,a,6421,a)].
% 184.60/184.39 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),B))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),zero_zero(real))). [resolve(6453,a,6422,a)].
% 184.60/184.39 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),B))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),C),A)). [resolve(6453,a,6423,a)].
% 184.60/184.39 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),B))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),C)). [resolve(6453,a,6424,a)].
% 184.60/184.39 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),B))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),C),A)). [resolve(6453,a,6425,a)].
% 184.60/184.39 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),C))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))). [resolve(6453,a,6426,a)].
% 184.60/184.39 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),C))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),C),B)). [resolve(6453,a,6427,a)].
% 184.60/184.39 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),C))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))). [resolve(6453,a,6428,a)].
% 184.63/184.40 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),C))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),C),B)). [resolve(6453,a,6429,a)].
% 184.63/184.40 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),C))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),C)). [resolve(6453,a,6430,a)].
% 184.63/184.40 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),C))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),C),B)). [resolve(6453,a,6431,a)].
% 184.63/184.40 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),C))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),C)). [resolve(6453,a,6432,a)].
% 184.63/184.40 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),C))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),C),B)). [resolve(6453,a,6434,a)].
% 184.63/184.40 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B))). [resolve(6453,a,6436,a)].
% 184.63/184.40 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),C))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),C),B)). [resolve(6453,a,6439,a)].
% 184.63/184.40 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),C))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),C),B)). [resolve(6453,a,6440,a)].
% 184.63/184.40 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),C))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),C)). [resolve(6453,a,6441,a)].
% 184.63/184.40 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),C))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),C)). [resolve(6453,a,6442,a)].
% 184.63/184.40 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),A)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),B)))) | zero_zero(real) != ti(real,A) | zero_zero(real) != ti(real,B). [resolve(6453,a,6443,a)].
% 189.01/188.85 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),A)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),B)))) | zero_zero(real) = ti(real,A). [resolve(6453,a,6444,a)].
% 189.01/188.85 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),A)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),B)))) | zero_zero(real) = ti(real,B). [resolve(6453,a,6445,a)].
% 189.01/188.85 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),A)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),B))),zero_zero(real))) | zero_zero(real) = ti(real,A). [resolve(6453,a,6446,a)].
% 189.01/188.85 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),A)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),B))),zero_zero(real))) | zero_zero(real) = ti(real,B). [resolve(6453,a,6447,a)].
% 189.01/188.85 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),A)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),B))),zero_zero(real))) | zero_zero(real) != ti(real,A) | zero_zero(real) != ti(real,B). [resolve(6453,a,6448,a)].
% 189.01/188.85 Derived: hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),A)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),B)) != zero_zero(real) | zero_zero(real) = ti(real,A). [resolve(6453,a,6449,a)].
% 189.01/188.85 Derived: hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),A)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),B)) != zero_zero(real) | zero_zero(real) = ti(real,B). [resolve(6453,a,6450,a)].
% 189.01/188.85 Derived: hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),A)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),B)) = zero_zero(real) | zero_zero(real) != ti(real,A) | zero_zero(real) != ti(real,B). [resolve(6453,a,6451,a)].
% 189.01/188.85 6454 ordere453448008miring(int) # label(arity_Int_Oint___Rings_Oordered__cancel__semiring) # label(axiom). [assumption].
% 189.01/188.85 6455 -ordere453448008miring(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C))) # label(fact_292_mult__nonneg__nonneg) # label(axiom). [clausify(421)].
% 189.01/188.85 6456 -ordere453448008miring(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),zero_zero(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)),zero_zero(A))) # label(fact_293_mult__nonneg__nonpos) # label(axiom). [clausify(422)].
% 189.01/188.85 6457 -ordere453448008miring(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),zero_zero(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)),zero_zero(A))) # label(fact_294_mult__nonneg__nonpos2) # label(axiom). [clausify(423)].
% 189.01/188.85 6458 -ordere453448008miring(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),C)) | 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)),zero_zero(A))) # label(fact_295_mult__nonpos__nonneg) # label(axiom). [clausify(424)].
% 189.15/188.93 6459 -ordere453448008miring(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),zero_zero(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)),zero_zero(A))) # label(fact_305_split__mult__neg__le) # label(axiom). [clausify(434)].
% 189.15/188.93 6460 -ordere453448008miring(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),C)) | 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)),zero_zero(A))) # label(fact_305_split__mult__neg__le) # label(axiom). [clausify(434)].
% 189.15/188.93 6461 ordere453448008miring(nat) # label(arity_Nat_Onat___Rings_Oordered__cancel__semiring) # label(axiom). [assumption].
% 189.15/188.93 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),B))). [resolve(6461,a,6455,a)].
% 189.15/188.93 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),zero_zero(nat))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),B)),zero_zero(nat))). [resolve(6461,a,6456,a)].
% 189.15/188.93 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),zero_zero(nat))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),A)),zero_zero(nat))). [resolve(6461,a,6457,a)].
% 189.15/188.93 6462 ordere453448008miring(rat) # label(arity_Rat_Orat___Rings_Oordered__cancel__semiring) # label(axiom). [assumption].
% 189.15/188.93 6463 ordere453448008miring(real) # label(arity_RealDef_Oreal___Rings_Oordered__cancel__semiring) # label(axiom). [assumption].
% 189.15/188.93 6464 ordere453448008miring(code_code_numeral) # label(arity_Code__Numeral_Ocode__numeral___Rings_Oordered__cancel__semiring) # label(axiom). [assumption].
% 189.15/188.93 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),zero_zero(code_code_numeral)),A)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),zero_zero(code_code_numeral)),B)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),zero_zero(code_code_numeral)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),B))). [resolve(6464,a,6455,a)].
% 189.15/188.93 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),zero_zero(code_code_numeral)),A)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),B),zero_zero(code_code_numeral))) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),B)),zero_zero(code_code_numeral))). [resolve(6464,a,6456,a)].
% 189.15/188.93 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),zero_zero(code_code_numeral)),A)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),B),zero_zero(code_code_numeral))) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),B),A)),zero_zero(code_code_numeral))). [resolve(6464,a,6457,a)].
% 193.56/193.35 6465 ordere453448008miring(quickcheck_code_int) # label(arity_Quickcheck__Narrowing_Ocode__int___Rings_Oordered__cancel__semiring) # label(axiom). [assumption].
% 193.56/193.35 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),zero_zero(quickcheck_code_int)),A)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),zero_zero(quickcheck_code_int)),B)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),zero_zero(quickcheck_code_int)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),B))). [resolve(6465,a,6455,a)].
% 193.56/193.36 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),zero_zero(quickcheck_code_int)),A)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),B),zero_zero(quickcheck_code_int))) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),B)),zero_zero(quickcheck_code_int))). [resolve(6465,a,6456,a)].
% 193.56/193.36 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),zero_zero(quickcheck_code_int)),A)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),B),zero_zero(quickcheck_code_int))) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),B),A)),zero_zero(quickcheck_code_int))). [resolve(6465,a,6457,a)].
% 193.56/193.36 6466 ordered_semiring(int) # label(arity_Int_Oint___Rings_Oordered__semiring) # label(axiom). [assumption].
% 193.56/193.36 6467 -ordered_semiring(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),zero_zero(A)),D)) | 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),D)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),D))) # label(fact_297_mult__right__mono) # label(axiom). [clausify(426)].
% 193.56/193.36 6468 -ordered_semiring(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),zero_zero(A)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(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_298_mult__left__mono) # label(axiom). [clausify(427)].
% 193.56/193.36 6469 -ordered_semiring(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),zero_zero(A)),B)) | -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),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_302_mult__mono_H) # label(axiom). [clausify(431)].
% 193.56/193.36 6470 -ordered_semiring(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),zero_zero(A)),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),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_303_mult__mono) # label(axiom). [clausify(432)].
% 193.56/193.38 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),zero_zero(int)),C)) | 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),C)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),C))). [resolve(6466,a,6467,a)].
% 193.56/193.38 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),zero_zero(int)),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),A)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),B))). [resolve(6466,a,6468,a)].
% 193.56/193.38 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),zero_zero(int)),A)) | -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),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(6466,a,6469,a)].
% 193.56/193.38 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),zero_zero(int)),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),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(6466,a,6470,a)].
% 193.56/193.38 6471 ordered_semiring(nat) # label(arity_Nat_Onat___Rings_Oordered__semiring) # label(axiom). [assumption].
% 193.56/193.38 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),zero_zero(nat)),C)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(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(6471,a,6467,a)].
% 193.56/193.38 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),zero_zero(nat)),C)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(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(6471,a,6468,a)].
% 193.56/193.38 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),zero_zero(nat)),A)) | -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),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(6471,a,6469,a)].
% 193.56/193.38 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),zero_zero(nat)),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),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(6471,a,6470,a)].
% 193.56/193.38 6472 ordered_semiring(rat) # label(arity_Rat_Orat___Rings_Oordered__semiring) # label(axiom). [assumption].
% 193.56/193.38 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),C)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),C)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),B),C))). [resolve(6472,a,6467,a)].
% 193.63/193.43 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),C)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),C),A)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),C),B))). [resolve(6472,a,6468,a)].
% 193.63/193.43 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),C),D)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),C)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),C)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),B),D))). [resolve(6472,a,6469,a)].
% 193.63/193.43 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),C),D)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),C)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),C)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),B),D))). [resolve(6472,a,6470,a)].
% 193.63/193.43 6473 ordered_semiring(real) # label(arity_RealDef_Oreal___Rings_Oordered__semiring) # label(axiom). [assumption].
% 193.63/193.43 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),C)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),C))). [resolve(6473,a,6467,a)].
% 193.63/193.43 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),A)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),B))). [resolve(6473,a,6468,a)].
% 193.63/193.43 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),C),D)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),C)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),D))). [resolve(6473,a,6469,a)].
% 193.63/193.43 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),C),D)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),C)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),D))). [resolve(6473,a,6470,a)].
% 193.63/193.43 6474 ordered_semiring(code_code_numeral) # label(arity_Code__Numeral_Ocode__numeral___Rings_Oordered__semiring) # label(axiom). [assumption].
% 193.63/193.43 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),A),B)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),zero_zero(code_code_numeral)),C)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),C)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),B),C))). [resolve(6474,a,6467,a)].
% 193.63/193.44 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),A),B)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),zero_zero(code_code_numeral)),C)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),C),A)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),C),B))). [resolve(6474,a,6468,a)].
% 193.63/193.44 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),A),B)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),C),D)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),zero_zero(code_code_numeral)),A)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),zero_zero(code_code_numeral)),C)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),C)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),B),D))). [resolve(6474,a,6469,a)].
% 193.63/193.44 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),A),B)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),C),D)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),zero_zero(code_code_numeral)),B)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),zero_zero(code_code_numeral)),C)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),C)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),B),D))). [resolve(6474,a,6470,a)].
% 193.63/193.44 6475 ordered_semiring(quickcheck_code_int) # label(arity_Quickcheck__Narrowing_Ocode__int___Rings_Oordered__semiring) # label(axiom). [assumption].
% 193.63/193.44 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),A),B)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),zero_zero(quickcheck_code_int)),C)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),C)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),B),C))). [resolve(6475,a,6467,a)].
% 198.21/197.98 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),A),B)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),zero_zero(quickcheck_code_int)),C)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),C),A)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),C),B))). [resolve(6475,a,6468,a)].
% 198.21/197.98 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),A),B)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),C),D)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),zero_zero(quickcheck_code_int)),A)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),zero_zero(quickcheck_code_int)),C)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),C)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),B),D))). [resolve(6475,a,6469,a)].
% 198.21/197.98 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),A),B)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),C),D)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),zero_zero(quickcheck_code_int)),B)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),zero_zero(quickcheck_code_int)),C)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),C)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),B),D))). [resolve(6475,a,6470,a)].
% 198.21/197.98 6476 ordere1490568538miring(int) # label(arity_Int_Oint___Rings_Oordered__comm__semiring) # label(axiom). [assumption].
% 198.21/197.98 6477 -ordere1490568538miring(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),zero_zero(A)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(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_299_comm__mult__left__mono) # label(axiom). [clausify(428)].
% 198.21/197.98 6478 ordere1490568538miring(nat) # label(arity_Nat_Onat___Rings_Oordered__comm__semiring) # label(axiom). [assumption].
% 198.21/197.98 6479 ordere1490568538miring(rat) # label(arity_Rat_Orat___Rings_Oordered__comm__semiring) # label(axiom). [assumption].
% 198.21/197.98 6480 ordere1490568538miring(real) # label(arity_RealDef_Oreal___Rings_Oordered__comm__semiring) # label(axiom). [assumption].
% 198.21/197.98 6481 ordere1490568538miring(code_code_numeral) # label(arity_Code__Numeral_Ocode__numeral___Rings_Oordered__comm__semiring) # label(axiom). [assumption].
% 198.21/197.98 6482 ordere1490568538miring(quickcheck_code_int) # label(arity_Quickcheck__Narrowing_Ocode__int___Rings_Oordered__comm__semiring) # label(axiom). [assumption].
% 202.64/202.42 6483 linord20386208strict(int) # label(arity_Int_Oint___Rings_Olinordered__semiring__strict) # label(axiom). [assumption].
% 202.64/202.42 6484 -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_310_mult__pos__pos) # label(axiom). [clausify(439)].
% 202.64/202.42 6485 -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_311_mult__pos__neg) # label(axiom). [clausify(440)].
% 202.64/202.42 6486 -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_312_mult__pos__neg2) # label(axiom). [clausify(441)].
% 202.64/202.42 6487 -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_313_zero__less__mult__pos) # label(axiom). [clausify(442)].
% 202.64/202.42 6488 -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_314_zero__less__mult__pos2) # label(axiom). [clausify(443)].
% 202.64/202.42 6489 -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_316_mult__neg__pos) # label(axiom). [clausify(445)].
% 202.64/202.42 6490 -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_318_mult__strict__right__mono) # label(axiom). [clausify(447)].
% 202.64/202.42 6491 -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_319_mult__strict__left__mono) # label(axiom). [clausify(448)].
% 202.64/202.42 6492 -linord20386208strict(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)),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_eq(A),C),D)) # label(fact_356_mult__left__le__imp__le) # label(axiom). [clausify(484)].
% 202.64/202.42 6493 -linord20386208strict(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)),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_eq(A),B),D)) # label(fact_357_mult__right__le__imp__le) # label(axiom). [clausify(485)].
% 202.64/202.42 6494 -linord20386208strict(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_eq(A),zero_zero(A)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),D)) # label(fact_358_mult__less__imp__less__left) # label(axiom). [clausify(486)].
% 202.64/202.43 6495 -linord20386208strict(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_eq(A),zero_zero(A)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),D)) # label(fact_360_mult__less__imp__less__right) # label(axiom). [clausify(488)].
% 202.64/202.43 6496 -linord20386208strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),E)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | -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),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_362_mult__le__less__imp__less) # label(axiom). [clausify(490)].
% 202.64/202.43 6497 -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_eq(A),D),E)) | -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)),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),E))) # label(fact_363_mult__less__le__imp__less) # label(axiom). [clausify(491)].
% 202.64/202.43 6498 -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),D),E)) | -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)),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),E))) # label(fact_364_mult__strict__mono_H) # label(axiom). [clausify(492)].
% 202.64/202.43 6499 -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),D),E)) | -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_eq(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),E))) # label(fact_365_mult__strict__mono) # label(axiom). [clausify(493)].
% 202.64/202.43 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(6483,a,6484,a)].
% 202.64/202.43 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(6483,a,6485,a)].
% 202.64/202.43 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(6483,a,6486,a)].
% 202.64/202.43 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(6483,a,6487,a)].
% 202.64/202.43 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(6483,a,6488,a)].
% 202.64/202.45 Derived: -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)),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_eq(int),A),C)). [resolve(6483,a,6493,a)].
% 202.64/202.45 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_eq(int),zero_zero(int)),A)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),C)). [resolve(6483,a,6494,a)].
% 202.64/202.45 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_eq(int),zero_zero(int)),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),C)). [resolve(6483,a,6495,a)].
% 202.64/202.45 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),C),D)) | -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)),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(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(6483,a,6496,a)].
% 202.64/202.45 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),C),D)) | -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)),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(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(6483,a,6497,a)].
% 202.64/202.45 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),C),D)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A)) | -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),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(6483,a,6498,a)].
% 202.64/202.45 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),C),D)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),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),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(6483,a,6499,a)].
% 202.64/202.45 6500 linord20386208strict(nat) # label(arity_Nat_Onat___Rings_Olinordered__semiring__strict) # label(axiom). [assumption].
% 202.64/202.45 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(6500,a,6484,a)].
% 202.64/202.45 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(6500,a,6485,a)].
% 202.64/202.45 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(6500,a,6486,a)].
% 202.64/202.46 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(6500,a,6487,a)].
% 202.64/202.46 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(6500,a,6488,a)].
% 202.64/202.46 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(6500,a,6490,a)].
% 202.64/202.46 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(6500,a,6491,a)].
% 202.64/202.46 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(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))) | -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)). [resolve(6500,a,6492,a)].
% 202.64/202.46 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(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),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_eq(nat),A),C)). [resolve(6500,a,6493,a)].
% 202.64/202.46 Derived: -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)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),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),B),C)). [resolve(6500,a,6494,a)].
% 202.64/202.46 Derived: -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)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),C),B))) | -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),A),C)). [resolve(6500,a,6495,a)].
% 202.64/202.46 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),C),D)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A)) | -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),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(6500,a,6496,a)].
% 202.64/202.46 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),C),D)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_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),times_times(nat),A),C)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),D))). [resolve(6500,a,6497,a)].
% 202.73/202.48 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),C),D)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),A)) | -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),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(6500,a,6498,a)].
% 202.73/202.48 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),C),D)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),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),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(6500,a,6499,a)].
% 202.73/202.48 6501 linord20386208strict(rat) # label(arity_Rat_Orat___Rings_Olinordered__semiring__strict) # label(axiom). [assumption].
% 202.73/202.48 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B))). [resolve(6501,a,6484,a)].
% 202.73/202.48 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B)),zero_zero(rat))). [resolve(6501,a,6485,a)].
% 202.73/202.48 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),B),A)),zero_zero(rat))). [resolve(6501,a,6486,a)].
% 202.73/202.48 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),B)). [resolve(6501,a,6487,a)].
% 202.73/202.48 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)). [resolve(6501,a,6488,a)].
% 202.73/202.48 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),C),B))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),C)). [resolve(6501,a,6493,a)].
% 202.73/202.48 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),C))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),A)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),C)). [resolve(6501,a,6494,a)].
% 202.73/202.48 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),C),B))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),C)). [resolve(6501,a,6495,a)].
% 202.73/202.48 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),C),D)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),C)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),C)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),B),D))). [resolve(6501,a,6496,a)].
% 202.76/202.51 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),C),D)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),C)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),C)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),B),D))). [resolve(6501,a,6497,a)].
% 202.76/202.51 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),C),D)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),C)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),C)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),B),D))). [resolve(6501,a,6498,a)].
% 202.76/202.51 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),C),D)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),C)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),C)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),B),D))). [resolve(6501,a,6499,a)].
% 202.76/202.51 6502 linord20386208strict(real) # label(arity_RealDef_Oreal___Rings_Olinordered__semiring__strict) # label(axiom). [assumption].
% 202.76/202.51 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B))). [resolve(6502,a,6484,a)].
% 202.76/202.51 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),zero_zero(real))). [resolve(6502,a,6485,a)].
% 202.76/202.51 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),A)),zero_zero(real))). [resolve(6502,a,6486,a)].
% 202.76/202.51 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B)). [resolve(6502,a,6487,a)].
% 202.76/202.51 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)). [resolve(6502,a,6488,a)].
% 202.76/202.51 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),B))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),C)). [resolve(6502,a,6493,a)].
% 202.76/202.55 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),C))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),C)). [resolve(6502,a,6494,a)].
% 202.76/202.55 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),B))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),C)). [resolve(6502,a,6495,a)].
% 202.76/202.55 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),C),D)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),C)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),D))). [resolve(6502,a,6496,a)].
% 202.76/202.55 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),C),D)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),C)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),D))). [resolve(6502,a,6497,a)].
% 202.76/202.55 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),C),D)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),C)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),D))). [resolve(6502,a,6498,a)].
% 202.76/202.55 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),C),D)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),C)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),D))). [resolve(6502,a,6499,a)].
% 202.76/202.55 6503 linord20386208strict(code_code_numeral) # label(arity_Code__Numeral_Ocode__numeral___Rings_Olinordered__semiring__strict) # label(axiom). [assumption].
% 202.76/202.55 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),zero_zero(code_code_numeral)),A)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),zero_zero(code_code_numeral)),B)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),zero_zero(code_code_numeral)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),B))). [resolve(6503,a,6484,a)].
% 202.76/202.55 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),zero_zero(code_code_numeral)),A)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),B),zero_zero(code_code_numeral))) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),B)),zero_zero(code_code_numeral))). [resolve(6503,a,6485,a)].
% 202.76/202.55 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),zero_zero(code_code_numeral)),A)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),B),zero_zero(code_code_numeral))) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),B),A)),zero_zero(code_code_numeral))). [resolve(6503,a,6486,a)].
% 202.76/202.55 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),zero_zero(code_code_numeral)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),B))) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),zero_zero(code_code_numeral)),A)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),zero_zero(code_code_numeral)),B)). [resolve(6503,a,6487,a)].
% 202.76/202.55 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),zero_zero(code_code_numeral)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),B))) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),zero_zero(code_code_numeral)),B)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),zero_zero(code_code_numeral)),A)). [resolve(6503,a,6488,a)].
% 202.76/202.55 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),A),B)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),zero_zero(code_code_numeral)),C)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),C)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),B),C))). [resolve(6503,a,6490,a)].
% 202.76/202.55 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),A),B)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),zero_zero(code_code_numeral)),C)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),C),A)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),C),B))). [resolve(6503,a,6491,a)].
% 202.76/202.55 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),B)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),C))) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),zero_zero(code_code_numeral)),A)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),B),C)). [resolve(6503,a,6492,a)].
% 202.76/202.56 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),B)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),C),B))) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),zero_zero(code_code_numeral)),B)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),A),C)). [resolve(6503,a,6493,a)].
% 202.76/202.56 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),B)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),C))) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),zero_zero(code_code_numeral)),A)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),B),C)). [resolve(6503,a,6494,a)].
% 202.76/202.56 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),B)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),C),B))) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),zero_zero(code_code_numeral)),B)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),A),C)). [resolve(6503,a,6495,a)].
% 202.76/202.56 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),A),B)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),C),D)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),zero_zero(code_code_numeral)),A)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),zero_zero(code_code_numeral)),C)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),C)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),B),D))). [resolve(6503,a,6496,a)].
% 202.76/202.56 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),A),B)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),C),D)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),zero_zero(code_code_numeral)),A)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),zero_zero(code_code_numeral)),C)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),C)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),B),D))). [resolve(6503,a,6497,a)].
% 202.76/202.57 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),A),B)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),C),D)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),zero_zero(code_code_numeral)),A)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),zero_zero(code_code_numeral)),C)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),C)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),B),D))). [resolve(6503,a,6498,a)].
% 202.76/202.57 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),A),B)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),C),D)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),zero_zero(code_code_numeral)),B)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),zero_zero(code_code_numeral)),C)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),C)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),B),D))). [resolve(6503,a,6499,a)].
% 202.76/202.57 6504 linord20386208strict(quickcheck_code_int) # label(arity_Quickcheck__Narrowing_Ocode__int___Rings_Olinordered__semiring__strict) # label(axiom). [assumption].
% 202.76/202.57 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),zero_zero(quickcheck_code_int)),A)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),zero_zero(quickcheck_code_int)),B)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),zero_zero(quickcheck_code_int)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),B))). [resolve(6504,a,6484,a)].
% 202.76/202.57 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),zero_zero(quickcheck_code_int)),A)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),B),zero_zero(quickcheck_code_int))) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),B)),zero_zero(quickcheck_code_int))). [resolve(6504,a,6485,a)].
% 202.76/202.57 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),zero_zero(quickcheck_code_int)),A)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),B),zero_zero(quickcheck_code_int))) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),B),A)),zero_zero(quickcheck_code_int))). [resolve(6504,a,6486,a)].
% 202.76/202.57 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),zero_zero(quickcheck_code_int)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),B))) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),zero_zero(quickcheck_code_int)),A)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),zero_zero(quickcheck_code_int)),B)). [resolve(6504,a,6487,a)].
% 202.76/202.57 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),zero_zero(quickcheck_code_int)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),B))) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),zero_zero(quickcheck_code_int)),B)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),zero_zero(quickcheck_code_int)),A)). [resolve(6504,a,6488,a)].
% 202.76/202.57 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),A),B)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),zero_zero(quickcheck_code_int)),C)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),C)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),B),C))). [resolve(6504,a,6490,a)].
% 202.76/202.57 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),A),B)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),zero_zero(quickcheck_code_int)),C)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),C),A)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),C),B))). [resolve(6504,a,6491,a)].
% 202.76/202.57 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),B)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),C))) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),zero_zero(quickcheck_code_int)),A)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),B),C)). [resolve(6504,a,6492,a)].
% 202.76/202.57 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),B)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),C),B))) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),zero_zero(quickcheck_code_int)),B)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),A),C)). [resolve(6504,a,6493,a)].
% 202.76/202.58 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),B)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),C))) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),zero_zero(quickcheck_code_int)),A)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),B),C)). [resolve(6504,a,6494,a)].
% 202.76/202.58 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),B)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),C),B))) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),zero_zero(quickcheck_code_int)),B)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),A),C)). [resolve(6504,a,6495,a)].
% 202.76/202.58 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),A),B)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),C),D)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),zero_zero(quickcheck_code_int)),A)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),zero_zero(quickcheck_code_int)),C)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),C)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),B),D))). [resolve(6504,a,6496,a)].
% 202.76/202.58 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),A),B)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),C),D)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),zero_zero(quickcheck_code_int)),A)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),zero_zero(quickcheck_code_int)),C)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),C)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),B),D))). [resolve(6504,a,6497,a)].
% 211.71/211.52 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),A),B)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),C),D)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),zero_zero(quickcheck_code_int)),A)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),zero_zero(quickcheck_code_int)),C)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),C)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),B),D))). [resolve(6504,a,6498,a)].
% 211.71/211.52 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),A),B)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),C),D)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),zero_zero(quickcheck_code_int)),B)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),zero_zero(quickcheck_code_int)),C)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),C)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),B),D))). [resolve(6504,a,6499,a)].
% 211.71/211.52 6505 linord893533164strict(int) # label(arity_Int_Oint___Rings_Olinordered__comm__semiring__strict) # label(axiom). [assumption].
% 211.71/211.52 6506 -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_320_comm__mult__strict__left__mono) # label(axiom). [clausify(449)].
% 211.71/211.52 6507 linord893533164strict(nat) # label(arity_Nat_Onat___Rings_Olinordered__comm__semiring__strict) # label(axiom). [assumption].
% 211.71/211.52 6508 linord893533164strict(rat) # label(arity_Rat_Orat___Rings_Olinordered__comm__semiring__strict) # label(axiom). [assumption].
% 211.71/211.52 6509 linord893533164strict(real) # label(arity_RealDef_Oreal___Rings_Olinordered__comm__semiring__strict) # label(axiom). [assumption].
% 211.71/211.52 6510 linord893533164strict(code_code_numeral) # label(arity_Code__Numeral_Ocode__numeral___Rings_Olinordered__comm__semiring__strict) # label(axiom). [assumption].
% 211.71/211.52 6511 linord893533164strict(quickcheck_code_int) # label(arity_Quickcheck__Narrowing_Ocode__int___Rings_Olinordered__comm__semiring__stri) # label(axiom). [assumption].
% 211.71/211.52 6512 ordere216010020id_add(int) # label(arity_Int_Oint___Groups_Oordered__comm__monoid__add) # label(axiom). [assumption].
% 211.71/211.52 6513 -ordere216010020id_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C))) # label(fact_325_add__nonneg__nonneg) # label(axiom). [clausify(454)].
% 211.71/211.52 6514 -ordere216010020id_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),C)) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C) != zero_zero(A) | zero_zero(A) = ti(A,B) # label(fact_326_add__nonneg__eq__0__iff) # label(axiom). [clausify(455)].
% 211.71/211.52 6515 -ordere216010020id_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),C)) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C) != zero_zero(A) | zero_zero(A) = ti(A,C) # label(fact_326_add__nonneg__eq__0__iff) # label(axiom). [clausify(455)].
% 211.71/211.52 6516 -ordere216010020id_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),C)) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C) = zero_zero(A) | zero_zero(A) != ti(A,B) | zero_zero(A) != ti(A,C) # label(fact_326_add__nonneg__eq__0__iff) # label(axiom). [clausify(455)].
% 211.71/211.52 6517 -ordere216010020id_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),D))) # label(fact_327_add__increasing) # label(axiom). [clausify(456)].
% 211.71/211.52 6518 -ordere216010020id_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),D),B))) # label(fact_328_add__increasing2) # label(axiom). [clausify(457)].
% 211.71/211.52 6519 -ordere216010020id_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),zero_zero(A))) # label(fact_329_add__nonpos__nonpos) # label(axiom). [clausify(458)].
% 211.71/211.52 6520 -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_333_add__pos__pos) # label(axiom). [clausify(462)].
% 211.71/211.52 6521 -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_335_add__neg__neg) # label(axiom). [clausify(464)].
% 211.71/211.52 6522 -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_368_add__nonpos__neg) # label(axiom). [clausify(496)].
% 211.71/211.52 6523 -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_369_add__neg__nonpos) # label(axiom). [clausify(497)].
% 211.71/211.52 6524 -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_370_add__strict__increasing2) # label(axiom). [clausify(498)].
% 211.71/211.52 6525 -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_371_add__strict__increasing) # label(axiom). [clausify(499)].
% 211.71/211.52 6526 -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_372_add__nonneg__pos) # label(axiom). [clausify(500)].
% 211.71/211.53 6527 -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_373_add__pos__nonneg) # label(axiom). [clausify(501)].
% 211.71/211.53 6528 -ordere216010020id_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)) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f594(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))) | 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),E),D)),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),E),C))) # label(fact_4293_setsum__mono2) # label(axiom). [clausify(4225)].
% 211.71/211.53 6529 -ordere216010020id_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)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(B,A,E,f594(B,A,E,D,C)))) | 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),E),D)),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),E),C))) # label(fact_4293_setsum__mono2) # label(axiom). [clausify(4225)].
% 211.71/211.53 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),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B))). [resolve(6512,a,6513,a)].
% 211.71/211.53 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)) | hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B) != zero_zero(int) | zero_zero(int) = ti(int,A). [resolve(6512,a,6514,a)].
% 211.71/211.53 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)) | hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B) != zero_zero(int) | zero_zero(int) = ti(int,B). [resolve(6512,a,6515,a)].
% 211.71/211.53 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)) | hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B) = zero_zero(int) | zero_zero(int) != ti(int,A) | zero_zero(int) != ti(int,B). [resolve(6512,a,6516,a)].
% 211.71/211.53 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),B),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),C))). [resolve(6512,a,6517,a)].
% 211.71/211.53 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),B),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),C),A))). [resolve(6512,a,6518,a)].
% 211.71/211.53 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_eq(int),B),zero_zero(int))) | 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)),zero_zero(int))). [resolve(6512,a,6519,a)].
% 211.71/211.55 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(6512,a,6521,a)].
% 211.71/211.55 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(6512,a,6522,a)].
% 211.71/211.55 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(6512,a,6523,a)].
% 211.71/211.55 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(6512,a,6524,a)].
% 211.71/211.55 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(6512,a,6525,a)].
% 211.71/211.55 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),f594(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))) | 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),D),C)),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),D),B))). [resolve(6512,a,6528,a)].
% 211.71/211.55 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(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(A,int,D,f594(A,int,D,C,B)))) | 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),D),C)),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),D),B))). [resolve(6512,a,6529,a)].
% 211.71/211.55 6530 ordere216010020id_add(nat) # label(arity_Nat_Onat___Groups_Oordered__comm__monoid__add) # label(axiom). [assumption].
% 211.71/211.55 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B))). [resolve(6530,a,6513,a)].
% 211.71/211.55 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),B)) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B) != zero_zero(nat) | zero_zero(nat) = ti(nat,A). [resolve(6530,a,6514,a)].
% 211.71/211.55 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),B)) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B) != zero_zero(nat) | zero_zero(nat) = ti(nat,B). [resolve(6530,a,6515,a)].
% 211.71/211.55 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),B)) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B) = zero_zero(nat) | zero_zero(nat) != ti(nat,A) | zero_zero(nat) != ti(nat,B). [resolve(6530,a,6516,a)].
% 211.81/211.57 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),C)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),C))). [resolve(6530,a,6517,a)].
% 211.81/211.57 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),C)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),C),A))). [resolve(6530,a,6518,a)].
% 211.81/211.57 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),zero_zero(nat))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),zero_zero(nat))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B)),zero_zero(nat))). [resolve(6530,a,6519,a)].
% 211.81/211.57 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(6530,a,6521,a)].
% 211.81/211.57 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(6530,a,6522,a)].
% 211.81/211.57 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(6530,a,6523,a)].
% 211.81/211.57 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(6530,a,6524,a)].
% 211.81/211.57 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(6530,a,6525,a)].
% 211.81/211.57 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),f594(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))) | 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),D),C)),hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),D),B))). [resolve(6530,a,6528,a)].
% 211.81/211.57 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(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),hAPP(A,nat,D,f594(A,nat,D,C,B)))) | 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),D),C)),hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),D),B))). [resolve(6530,a,6529,a)].
% 211.81/211.57 6531 ordere216010020id_add(rat) # label(arity_Rat_Orat___Groups_Oordered__comm__monoid__add) # label(axiom). [assumption].
% 211.81/211.57 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),B))). [resolve(6531,a,6513,a)].
% 211.81/211.58 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),B)) | hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),B) != zero_zero(rat) | zero_zero(rat) = ti(rat,A). [resolve(6531,a,6514,a)].
% 211.81/211.58 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),B)) | hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),B) != zero_zero(rat) | zero_zero(rat) = ti(rat,B). [resolve(6531,a,6515,a)].
% 211.81/211.58 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),B)) | hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),B) = zero_zero(rat) | zero_zero(rat) != ti(rat,A) | zero_zero(rat) != ti(rat,B). [resolve(6531,a,6516,a)].
% 211.81/211.58 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),B),C)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),B),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),C))). [resolve(6531,a,6517,a)].
% 211.81/211.58 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),B),C)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),B),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),C),A))). [resolve(6531,a,6518,a)].
% 211.81/211.58 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),B),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),B)),zero_zero(rat))). [resolve(6531,a,6519,a)].
% 211.81/211.58 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),B)),zero_zero(rat))). [resolve(6531,a,6521,a)].
% 211.81/211.58 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),B)),zero_zero(rat))). [resolve(6531,a,6522,a)].
% 211.81/211.58 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),B),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),B)),zero_zero(rat))). [resolve(6531,a,6523,a)].
% 211.81/211.58 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),C)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),C))). [resolve(6531,a,6524,a)].
% 211.81/211.58 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),B),C)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),C))). [resolve(6531,a,6525,a)].
% 211.81/211.58 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),f594(A,rat,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))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),D),C)),hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),D),B))). [resolve(6531,a,6528,a)].
% 211.84/211.61 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(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),hAPP(A,rat,D,f594(A,rat,D,C,B)))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),D),C)),hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),D),B))). [resolve(6531,a,6529,a)].
% 211.84/211.61 6532 ordere216010020id_add(real) # label(arity_RealDef_Oreal___Groups_Oordered__comm__monoid__add) # label(axiom). [assumption].
% 211.84/211.61 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),B))). [resolve(6532,a,6513,a)].
% 211.84/211.61 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),B)) | hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),B) != zero_zero(real) | zero_zero(real) = ti(real,A). [resolve(6532,a,6514,a)].
% 211.84/211.61 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),B)) | hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),B) != zero_zero(real) | zero_zero(real) = ti(real,B). [resolve(6532,a,6515,a)].
% 211.84/211.61 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),B)) | hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),B) = zero_zero(real) | zero_zero(real) != ti(real,A) | zero_zero(real) != ti(real,B). [resolve(6532,a,6516,a)].
% 211.84/211.61 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),C))). [resolve(6532,a,6517,a)].
% 211.84/211.61 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),C),A))). [resolve(6532,a,6518,a)].
% 211.84/211.61 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),B)),zero_zero(real))). [resolve(6532,a,6519,a)].
% 211.84/211.61 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),B)),zero_zero(real))). [resolve(6532,a,6521,a)].
% 211.84/211.61 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),B)),zero_zero(real))). [resolve(6532,a,6522,a)].
% 211.87/211.64 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),B)),zero_zero(real))). [resolve(6532,a,6523,a)].
% 211.87/211.64 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),C))). [resolve(6532,a,6524,a)].
% 211.87/211.64 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),C))). [resolve(6532,a,6525,a)].
% 211.87/211.64 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),f594(A,real,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))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),D),C)),hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),D),B))). [resolve(6532,a,6528,a)].
% 211.87/211.64 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(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(A,real,D,f594(A,real,D,C,B)))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),D),C)),hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),D),B))). [resolve(6532,a,6529,a)].
% 211.87/211.64 6533 ordere216010020id_add(code_code_numeral) # label(arity_Code__Numeral_Ocode__numeral___Groups_Oordered__comm__monoid__add) # label(axiom). [assumption].
% 211.87/211.64 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),zero_zero(code_code_numeral)),A)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),zero_zero(code_code_numeral)),B)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),zero_zero(code_code_numeral)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),A),B))). [resolve(6533,a,6513,a)].
% 211.87/211.64 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),zero_zero(code_code_numeral)),A)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),zero_zero(code_code_numeral)),B)) | hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),A),B) != zero_zero(code_code_numeral) | zero_zero(code_code_numeral) = ti(code_code_numeral,A). [resolve(6533,a,6514,a)].
% 211.87/211.64 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),zero_zero(code_code_numeral)),A)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),zero_zero(code_code_numeral)),B)) | hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),A),B) != zero_zero(code_code_numeral) | zero_zero(code_code_numeral) = ti(code_code_numeral,B). [resolve(6533,a,6515,a)].
% 211.87/211.65 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),zero_zero(code_code_numeral)),A)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),zero_zero(code_code_numeral)),B)) | hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),A),B) = zero_zero(code_code_numeral) | zero_zero(code_code_numeral) != ti(code_code_numeral,A) | zero_zero(code_code_numeral) != ti(code_code_numeral,B). [resolve(6533,a,6516,a)].
% 211.87/211.65 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),zero_zero(code_code_numeral)),A)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),B),C)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),B),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),A),C))). [resolve(6533,a,6517,a)].
% 211.87/211.65 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),zero_zero(code_code_numeral)),A)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),B),C)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),B),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),C),A))). [resolve(6533,a,6518,a)].
% 211.87/211.65 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),A),zero_zero(code_code_numeral))) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),B),zero_zero(code_code_numeral))) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),A),B)),zero_zero(code_code_numeral))). [resolve(6533,a,6519,a)].
% 211.87/211.65 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),A),zero_zero(code_code_numeral))) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),B),zero_zero(code_code_numeral))) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),A),B)),zero_zero(code_code_numeral))). [resolve(6533,a,6521,a)].
% 211.87/211.65 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),A),zero_zero(code_code_numeral))) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),B),zero_zero(code_code_numeral))) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),A),B)),zero_zero(code_code_numeral))). [resolve(6533,a,6522,a)].
% 211.87/211.65 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),A),zero_zero(code_code_numeral))) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),B),zero_zero(code_code_numeral))) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),A),B)),zero_zero(code_code_numeral))). [resolve(6533,a,6523,a)].
% 211.87/211.66 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),zero_zero(code_code_numeral)),A)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),B),C)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),B),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),A),C))). [resolve(6533,a,6524,a)].
% 211.87/211.66 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),zero_zero(code_code_numeral)),A)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),B),C)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),B),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),A),C))). [resolve(6533,a,6525,a)].
% 211.87/211.66 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),f594(A,code_code_numeral,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))) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),D),C)),hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),D),B))). [resolve(6533,a,6528,a)].
% 211.87/211.66 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(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),zero_zero(code_code_numeral)),hAPP(A,code_code_numeral,D,f594(A,code_code_numeral,D,C,B)))) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),D),C)),hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),D),B))). [resolve(6533,a,6529,a)].
% 211.87/211.66 6534 ordere216010020id_add(quickcheck_code_int) # label(arity_Quickcheck__Narrowing_Ocode__int___Groups_Oordered__comm__monoid__add) # label(axiom). [assumption].
% 211.87/211.66 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),zero_zero(quickcheck_code_int)),A)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),zero_zero(quickcheck_code_int)),B)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),zero_zero(quickcheck_code_int)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),A),B))). [resolve(6534,a,6513,a)].
% 211.87/211.66 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),zero_zero(quickcheck_code_int)),A)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),zero_zero(quickcheck_code_int)),B)) | hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),A),B) != zero_zero(quickcheck_code_int) | zero_zero(quickcheck_code_int) = ti(quickcheck_code_int,A). [resolve(6534,a,6514,a)].
% 211.87/211.67 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),zero_zero(quickcheck_code_int)),A)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),zero_zero(quickcheck_code_int)),B)) | hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),A),B) != zero_zero(quickcheck_code_int) | zero_zero(quickcheck_code_int) = ti(quickcheck_code_int,B). [resolve(6534,a,6515,a)].
% 211.87/211.67 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),zero_zero(quickcheck_code_int)),A)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),zero_zero(quickcheck_code_int)),B)) | hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),A),B) = zero_zero(quickcheck_code_int) | zero_zero(quickcheck_code_int) != ti(quickcheck_code_int,A) | zero_zero(quickcheck_code_int) != ti(quickcheck_code_int,B). [resolve(6534,a,6516,a)].
% 211.87/211.67 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),zero_zero(quickcheck_code_int)),A)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),B),C)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),B),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),A),C))). [resolve(6534,a,6517,a)].
% 211.87/211.67 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),zero_zero(quickcheck_code_int)),A)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),B),C)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),B),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),C),A))). [resolve(6534,a,6518,a)].
% 211.87/211.67 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),A),zero_zero(quickcheck_code_int))) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),B),zero_zero(quickcheck_code_int))) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),A),B)),zero_zero(quickcheck_code_int))). [resolve(6534,a,6519,a)].
% 211.87/211.67 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),A),zero_zero(quickcheck_code_int))) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),B),zero_zero(quickcheck_code_int))) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),A),B)),zero_zero(quickcheck_code_int))). [resolve(6534,a,6521,a)].
% 211.87/211.67 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),A),zero_zero(quickcheck_code_int))) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),B),zero_zero(quickcheck_code_int))) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),A),B)),zero_zero(quickcheck_code_int))). [resolve(6534,a,6522,a)].
% 211.87/211.67 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),A),zero_zero(quickcheck_code_int))) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),B),zero_zero(quickcheck_code_int))) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),A),B)),zero_zero(quickcheck_code_int))). [resolve(6534,a,6523,a)].
% 211.87/211.67 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),zero_zero(quickcheck_code_int)),A)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),B),C)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),B),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),A),C))). [resolve(6534,a,6524,a)].
% 211.87/211.67 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),zero_zero(quickcheck_code_int)),A)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),B),C)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),B),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),A),C))). [resolve(6534,a,6525,a)].
% 211.87/211.67 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),f594(A,quickcheck_code_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))) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),D),C)),hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),D),B))). [resolve(6534,a,6528,a)].
% 211.87/211.67 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(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),zero_zero(quickcheck_code_int)),hAPP(A,quickcheck_code_int,D,f594(A,quickcheck_code_int,D,C,B)))) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),D),C)),hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),D),B))). [resolve(6534,a,6529,a)].
% 221.01/220.85 6535 linordered_semiring(int) # label(arity_Int_Oint___Rings_Olinordered__semiring) # label(axiom). [assumption].
% 221.01/220.85 6536 -linordered_semiring(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_eq(A),zero_zero(A)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),D)) # label(fact_359_mult__left__less__imp__less) # label(axiom). [clausify(487)].
% 221.01/220.85 6537 -linordered_semiring(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_eq(A),zero_zero(A)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),D)) # label(fact_361_mult__right__less__imp__less) # label(axiom). [clausify(489)].
% 221.01/220.85 6538 linordered_semiring(nat) # label(arity_Nat_Onat___Rings_Olinordered__semiring) # label(axiom). [assumption].
% 221.01/220.85 6539 linordered_semiring(rat) # label(arity_Rat_Orat___Rings_Olinordered__semiring) # label(axiom). [assumption].
% 221.01/220.85 6540 linordered_semiring(real) # label(arity_RealDef_Oreal___Rings_Olinordered__semiring) # label(axiom). [assumption].
% 221.01/220.85 6541 linordered_semiring(code_code_numeral) # label(arity_Code__Numeral_Ocode__numeral___Rings_Olinordered__semiring) # label(axiom). [assumption].
% 221.01/220.85 6542 linordered_semiring(quickcheck_code_int) # label(arity_Quickcheck__Narrowing_Ocode__int___Rings_Olinordered__semiring) # label(axiom). [assumption].
% 221.01/220.85 6543 linord1278240602ring_1(int) # label(arity_Int_Oint___Rings_Olinordered__semiring__1) # label(axiom). [assumption].
% 221.01/220.85 6544 -linord1278240602ring_1(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),zero_zero(A)),E)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),F)) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),E),F) != one_one(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),E),B)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),F),D))),C)) # label(fact_380_convex__bound__le) # label(axiom). [clausify(508)].
% 221.01/220.85 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),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),D)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),E)) | hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),D),E) != one_one(int) | 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),D),A)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),E),C))),B)). [resolve(6543,a,6544,a)].
% 221.01/220.85 6545 linord1278240602ring_1(rat) # label(arity_Rat_Orat___Rings_Olinordered__semiring__1) # label(axiom). [assumption].
% 221.01/220.85 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),C),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),D)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),E)) | hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),D),E) != one_one(rat) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),D),A)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),E),C))),B)). [resolve(6545,a,6544,a)].
% 221.01/220.85 6546 linord1278240602ring_1(real) # label(arity_RealDef_Oreal___Rings_Olinordered__semiring__1) # label(axiom). [assumption].
% 225.57/225.40 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),C),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),D)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),E)) | hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),D),E) != one_one(real) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),D),A)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),E),C))),B)). [resolve(6546,a,6544,a)].
% 225.57/225.40 6547 linord1117847801e_zero(rat) # label(arity_Rat_Orat___Fields_Olinordered__field__inverse__zero) # label(axiom). [assumption].
% 225.57/225.40 6548 -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),f79(A,B,C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) # label(fact_403_field__le__mult__one__interval) # label(axiom). [clausify(530)].
% 225.57/225.40 6549 -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),f79(A,B,C)),one_one(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) # label(fact_403_field__le__mult__one__interval) # label(axiom). [clausify(530)].
% 225.57/225.40 6550 -linord1117847801e_zero(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),f79(A,B,C)),B)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) # label(fact_403_field__le__mult__one__interval) # label(axiom). [clausify(530)].
% 225.57/225.40 6551 -linord1117847801e_zero(A) | hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),hAPP(A,A,abs_abs(A),B)),hAPP(A,A,abs_abs(A),C)) = hAPP(A,A,abs_abs(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)) # label(fact_1085_abs__divide) # label(axiom). [clausify(1196)].
% 225.57/225.40 6552 -linord1117847801e_zero(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),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),D)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),D))) # label(fact_1091_divide__right__mono__neg) # label(axiom). [clausify(1202)].
% 225.57/225.40 6553 -linord1117847801e_zero(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),zero_zero(A)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),D)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),D))) # label(fact_1092_divide__right__mono) # label(axiom). [clausify(1203)].
% 225.57/225.40 6554 -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)),zero_zero(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),B),zero_zero(A))) # label(fact_1093_divide__le__0__iff) # label(axiom). [clausify(1204)].
% 225.57/225.40 6555 -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)),zero_zero(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)) # label(fact_1093_divide__le__0__iff) # label(axiom). [clausify(1204)].
% 225.57/225.40 6556 -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),zero_zero(A))) # label(fact_1093_divide__le__0__iff) # label(axiom). [clausify(1204)].
% 225.57/225.40 6557 -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),C)) # label(fact_1093_divide__le__0__iff) # label(axiom). [clausify(1204)].
% 225.57/225.40 6558 -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),zero_zero(A))) # label(fact_1093_divide__le__0__iff) # label(axiom). [clausify(1204)].
% 225.57/225.40 6559 -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),C)) # label(fact_1093_divide__le__0__iff) # label(axiom). [clausify(1204)].
% 225.57/225.40 6560 -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C))) | 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),B),zero_zero(A))) # label(fact_1094_zero__le__divide__iff) # label(axiom). [clausify(1205)].
% 225.57/225.40 6561 -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),zero_zero(A))) # label(fact_1094_zero__le__divide__iff) # label(axiom). [clausify(1205)].
% 225.57/225.40 6562 -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C))) | 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),B),zero_zero(A))) # label(fact_1094_zero__le__divide__iff) # label(axiom). [clausify(1205)].
% 225.57/225.40 6563 -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C))) | 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),zero_zero(A))) # label(fact_1094_zero__le__divide__iff) # label(axiom). [clausify(1205)].
% 225.57/225.40 6564 -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C))) | -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)) # label(fact_1094_zero__le__divide__iff) # label(axiom). [clausify(1205)].
% 225.57/225.40 6565 -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),zero_zero(A))) # label(fact_1094_zero__le__divide__iff) # label(axiom). [clausify(1205)].
% 225.57/225.40 6566 -linord1117847801e_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),inverse_divide(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),B),zero_zero(A))) # label(fact_1095_zero__less__divide__iff) # label(axiom). [clausify(1206)].
% 225.57/225.40 6567 -linord1117847801e_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),inverse_divide(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),C),zero_zero(A))) # label(fact_1095_zero__less__divide__iff) # label(axiom). [clausify(1206)].
% 225.57/225.40 6568 -linord1117847801e_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),inverse_divide(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),B),zero_zero(A))) # label(fact_1095_zero__less__divide__iff) # label(axiom). [clausify(1206)].
% 225.57/225.40 6569 -linord1117847801e_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),inverse_divide(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),C),zero_zero(A))) # label(fact_1095_zero__less__divide__iff) # label(axiom). [clausify(1206)].
% 225.57/225.40 6570 -linord1117847801e_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),inverse_divide(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_1095_zero__less__divide__iff) # label(axiom). [clausify(1206)].
% 225.57/225.40 6571 -linord1117847801e_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),inverse_divide(A),B),C))) | -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))) # label(fact_1095_zero__less__divide__iff) # label(axiom). [clausify(1206)].
% 225.57/225.40 6572 -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)),zero_zero(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),B),zero_zero(A))) # label(fact_1096_divide__less__0__iff) # label(axiom). [clausify(1207)].
% 225.57/225.40 6573 -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)),zero_zero(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)) # label(fact_1096_divide__less__0__iff) # label(axiom). [clausify(1207)].
% 225.57/225.40 6574 -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)),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),B),zero_zero(A))) # label(fact_1096_divide__less__0__iff) # label(axiom). [clausify(1207)].
% 225.57/225.40 6575 -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)),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)),C)) # label(fact_1096_divide__less__0__iff) # label(axiom). [clausify(1207)].
% 225.57/225.40 6576 -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)),zero_zero(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))) # label(fact_1096_divide__less__0__iff) # label(axiom). [clausify(1207)].
% 225.57/225.40 6577 -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)),zero_zero(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)) # label(fact_1096_divide__less__0__iff) # label(axiom). [clausify(1207)].
% 225.57/225.40 6578 -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(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_1097_divide__less__cancel) # label(axiom). [clausify(1208)].
% 225.57/225.40 6579 -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(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_1097_divide__less__cancel) # label(axiom). [clausify(1208)].
% 225.57/225.40 6580 -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),C))) | zero_zero(A) != ti(A,C) # label(fact_1097_divide__less__cancel) # label(axiom). [clausify(1208)].
% 225.57/225.40 6581 -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(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))) | zero_zero(A) = ti(A,C) # label(fact_1097_divide__less__cancel) # label(axiom). [clausify(1208)].
% 225.57/225.40 6582 -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(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)) | zero_zero(A) = ti(A,C) # label(fact_1097_divide__less__cancel) # label(axiom). [clausify(1208)].
% 225.57/225.40 6583 -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(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))) | zero_zero(A) = ti(A,C) # label(fact_1097_divide__less__cancel) # label(axiom). [clausify(1208)].
% 225.57/225.40 6584 -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(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)) | zero_zero(A) = ti(A,C) # label(fact_1097_divide__less__cancel) # label(axiom). [clausify(1208)].
% 225.57/225.40 6585 -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(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_eq(A),B),D)) # label(fact_1123_divide__le__cancel) # label(axiom). [clausify(1234)].
% 225.57/225.40 6586 -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(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_eq(A),D),B)) # label(fact_1123_divide__le__cancel) # label(axiom). [clausify(1234)].
% 225.57/225.40 6587 -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(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_1123_divide__le__cancel) # label(axiom). [clausify(1234)].
% 225.57/225.40 6588 -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(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_eq(A),D),B)) # label(fact_1123_divide__le__cancel) # label(axiom). [clausify(1234)].
% 225.57/225.40 6589 -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),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(A),C),zero_zero(A))) # label(fact_1123_divide__le__cancel) # label(axiom). [clausify(1234)].
% 225.57/225.40 6590 -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),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),D),B)) # label(fact_1123_divide__le__cancel) # label(axiom). [clausify(1234)].
% 225.57/225.40 6591 -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)),D)) | -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),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),C))) # label(fact_1139_divide__less__eq) # label(axiom). [clausify(1250)].
% 225.57/225.40 6592 -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)),D)) | 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))) | 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)),B)) # label(fact_1139_divide__less__eq) # label(axiom). [clausify(1250)].
% 225.57/225.40 6593 -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)),D)) | 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))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),D)) # label(fact_1139_divide__less__eq) # label(axiom). [clausify(1250)].
% 225.57/225.40 6594 -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)),D)) | 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))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),D)) # label(fact_1139_divide__less__eq) # label(axiom). [clausify(1250)].
% 225.57/225.40 6595 -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)),D)) | 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),D),C)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),zero_zero(A))) # label(fact_1139_divide__less__eq) # label(axiom). [clausify(1250)].
% 225.57/225.40 6596 -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)),D)) | 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),D),C)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),D)) # label(fact_1139_divide__less__eq) # label(axiom). [clausify(1250)].
% 225.57/225.40 6597 -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),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)) # label(fact_1139_divide__less__eq) # label(axiom). [clausify(1250)].
% 225.57/225.40 6598 -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),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),zero_zero(A)),D)) # label(fact_1139_divide__less__eq) # label(axiom). [clausify(1250)].
% 225.57/225.40 6599 -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),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),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),C)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),zero_zero(A))) # label(fact_1139_divide__less__eq) # label(axiom). [clausify(1250)].
% 225.57/225.40 6600 -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),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),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),C)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),D)) # label(fact_1139_divide__less__eq) # label(axiom). [clausify(1250)].
% 225.57/225.40 6601 -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),D))) | -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)),C)) # label(fact_1140_less__divide__eq) # label(axiom). [clausify(1251)].
% 225.57/225.40 6602 -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),D))) | 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),D),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D))) # label(fact_1140_less__divide__eq) # label(axiom). [clausify(1251)].
% 225.57/225.40 6603 -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),D))) | 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),D),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) # label(fact_1140_less__divide__eq) # label(axiom). [clausify(1251)].
% 225.57/225.40 6604 -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),D))) | 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),D),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) # label(fact_1140_less__divide__eq) # label(axiom). [clausify(1251)].
% 225.57/225.40 6605 -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),D))) | 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),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),zero_zero(A))) # label(fact_1140_less__divide__eq) # label(axiom). [clausify(1251)].
% 225.57/225.40 6606 -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),D))) | 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),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))) # label(fact_1140_less__divide__eq) # label(axiom). [clausify(1251)].
% 225.57/225.40 6607 -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),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)),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),D)) # label(fact_1140_less__divide__eq) # label(axiom). [clausify(1251)].
% 225.57/225.40 6608 -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),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)),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),B),zero_zero(A))) # label(fact_1140_less__divide__eq) # label(axiom). [clausify(1251)].
% 225.57/225.40 6609 -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),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)),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),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),zero_zero(A))) # label(fact_1140_less__divide__eq) # label(axiom). [clausify(1251)].
% 225.57/225.40 6610 -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),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)),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),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))) # label(fact_1140_less__divide__eq) # label(axiom). [clausify(1251)].
% 225.57/225.40 6611 -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),hAPP(A,A,abs_abs(A),C)),B) = hAPP(A,A,abs_abs(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),B)) # label(fact_1156_abs__div__pos) # label(axiom). [clausify(1267)].
% 225.57/225.40 6612 -linord1117847801e_zero(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),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))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),B)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),C))) # label(fact_1159_divide__left__mono__neg) # label(axiom). [clausify(1270)].
% 225.57/225.40 6613 -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)),D)) | -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_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),C))) # label(fact_1167_divide__le__eq) # label(axiom). [clausify(1278)].
% 225.57/225.40 6614 -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)),D)) | 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))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),C)),B)) # label(fact_1167_divide__le__eq) # label(axiom). [clausify(1278)].
% 225.57/225.40 6615 -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)),D)) | 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))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),D)) # label(fact_1167_divide__le__eq) # label(axiom). [clausify(1278)].
% 225.57/225.40 6616 -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)),D)) | 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))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),D)) # label(fact_1167_divide__le__eq) # label(axiom). [clausify(1278)].
% 225.57/225.40 6617 -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)),D)) | 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_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),C)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),zero_zero(A))) # label(fact_1167_divide__le__eq) # label(axiom). [clausify(1278)].
% 225.57/225.40 6618 -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)),D)) | 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_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),C)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),D)) # label(fact_1167_divide__le__eq) # label(axiom). [clausify(1278)].
% 225.57/225.40 6619 -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),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)) # label(fact_1167_divide__le__eq) # label(axiom). [clausify(1278)].
% 225.57/225.40 6620 -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),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_eq(A),zero_zero(A)),D)) # label(fact_1167_divide__le__eq) # label(axiom). [clausify(1278)].
% 225.57/225.40 6621 -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),C)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),zero_zero(A))) # label(fact_1167_divide__le__eq) # label(axiom). [clausify(1278)].
% 225.57/225.40 6622 -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),C)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),D)) # label(fact_1167_divide__le__eq) # label(axiom). [clausify(1278)].
% 225.57/225.40 6623 -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),D))) | -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_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D)),C)) # label(fact_1168_le__divide__eq) # label(axiom). [clausify(1279)].
% 225.57/225.40 6624 -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),D))) | 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),D),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D))) # label(fact_1168_le__divide__eq) # label(axiom). [clausify(1279)].
% 225.57/225.40 6625 -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),D))) | 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),D),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),zero_zero(A))) # label(fact_1168_le__divide__eq) # label(axiom). [clausify(1279)].
% 225.57/225.40 6626 -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),D))) | 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),D),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),zero_zero(A))) # label(fact_1168_le__divide__eq) # label(axiom). [clausify(1279)].
% 225.57/225.40 6627 -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),D))) | 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_eq(A),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),zero_zero(A))) # label(fact_1168_le__divide__eq) # label(axiom). [clausify(1279)].
% 225.57/225.40 6628 -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),D))) | 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_eq(A),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_eq(A),B),zero_zero(A))) # label(fact_1168_le__divide__eq) # label(axiom). [clausify(1279)].
% 225.57/225.40 6629 -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),D))) | -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),D)),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),D)) # label(fact_1168_le__divide__eq) # label(axiom). [clausify(1279)].
% 225.57/225.40 6630 -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),D))) | -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),D)),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_eq(A),B),zero_zero(A))) # label(fact_1168_le__divide__eq) # label(axiom). [clausify(1279)].
% 225.57/225.40 6631 -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),D))) | -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),D)),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),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),zero_zero(A))) # label(fact_1168_le__divide__eq) # label(axiom). [clausify(1279)].
% 225.57/225.40 6632 -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),D))) | -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),D)),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),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_eq(A),B),zero_zero(A))) # label(fact_1168_le__divide__eq) # label(axiom). [clausify(1279)].
% 225.57/225.40 6633 -linord1117847801e_zero(A) | -number(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),hAPP(int,A,number_number_of(A),C))),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(int,A,number_number_of(A),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),hAPP(int,A,number_number_of(A),C)))) # label(fact_1169_divide__less__eq__number__of1) # label(axiom). [clausify(1280)].
% 225.57/225.40 6634 -linord1117847801e_zero(A) | -number(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),hAPP(int,A,number_number_of(A),C))),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(int,A,number_number_of(A),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(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),D),hAPP(int,A,number_number_of(A),C))),B)) # label(fact_1169_divide__less__eq__number__of1) # label(axiom). [clausify(1280)].
% 225.57/225.40 6635 -linord1117847801e_zero(A) | -number(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),hAPP(int,A,number_number_of(A),C))),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(int,A,number_number_of(A),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),C)),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),D)) # label(fact_1169_divide__less__eq__number__of1) # label(axiom). [clausify(1280)].
% 225.57/225.40 6636 -linord1117847801e_zero(A) | -number(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),hAPP(int,A,number_number_of(A),C))),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(int,A,number_number_of(A),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),C)),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),D)) # label(fact_1169_divide__less__eq__number__of1) # label(axiom). [clausify(1280)].
% 225.57/225.40 6637 -linord1117847801e_zero(A) | -number(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),hAPP(int,A,number_number_of(A),C))),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(int,A,number_number_of(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),D),hAPP(int,A,number_number_of(A),C))),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),C)),zero_zero(A))) # label(fact_1169_divide__less__eq__number__of1) # label(axiom). [clausify(1280)].
% 225.57/225.40 6638 -linord1117847801e_zero(A) | -number(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),hAPP(int,A,number_number_of(A),C))),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(int,A,number_number_of(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),D),hAPP(int,A,number_number_of(A),C))),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),D)) # label(fact_1169_divide__less__eq__number__of1) # label(axiom). [clausify(1280)].
% 225.57/225.40 6639 -linord1117847801e_zero(A) | -number(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),hAPP(int,A,number_number_of(A),C))),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),hAPP(int,A,number_number_of(A),C)))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(int,A,number_number_of(A),C))) # label(fact_1169_divide__less__eq__number__of1) # label(axiom). [clausify(1280)].
% 225.57/225.40 6640 -linord1117847801e_zero(A) | -number(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),hAPP(int,A,number_number_of(A),C))),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),hAPP(int,A,number_number_of(A),C)))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),C)),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),D)) # label(fact_1169_divide__less__eq__number__of1) # label(axiom). [clausify(1280)].
% 225.57/225.40 6641 -linord1117847801e_zero(A) | -number(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),hAPP(int,A,number_number_of(A),C))),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),hAPP(int,A,number_number_of(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),D),hAPP(int,A,number_number_of(A),C))),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),C)),zero_zero(A))) # label(fact_1169_divide__less__eq__number__of1) # label(axiom). [clausify(1280)].
% 225.57/225.40 6642 -linord1117847801e_zero(A) | -number(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),hAPP(int,A,number_number_of(A),C))),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),hAPP(int,A,number_number_of(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),D),hAPP(int,A,number_number_of(A),C))),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),D)) # label(fact_1169_divide__less__eq__number__of1) # label(axiom). [clausify(1280)].
% 225.57/225.40 6643 -linord1117847801e_zero(A) | -number(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)),hAPP(int,A,number_number_of(A),D))) | -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),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),D)),C))) # label(fact_1170_divide__less__eq__number__of) # label(axiom). [clausify(1281)].
% 225.57/225.40 6644 -linord1117847801e_zero(A) | -number(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)),hAPP(int,A,number_number_of(A),D))) | 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))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),D)),C)),B)) # label(fact_1170_divide__less__eq__number__of) # label(axiom). [clausify(1281)].
% 225.57/225.40 6645 -linord1117847801e_zero(A) | -number(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)),hAPP(int,A,number_number_of(A),D))) | 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))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(int,A,number_number_of(A),D))) # label(fact_1170_divide__less__eq__number__of) # label(axiom). [clausify(1281)].
% 225.57/225.40 6646 -linord1117847801e_zero(A) | -number(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)),hAPP(int,A,number_number_of(A),D))) | 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))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(int,A,number_number_of(A),D))) # label(fact_1170_divide__less__eq__number__of) # label(axiom). [clausify(1281)].
% 225.57/225.40 6647 -linord1117847801e_zero(A) | -number(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)),hAPP(int,A,number_number_of(A),D))) | 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),hAPP(int,A,number_number_of(A),D)),C)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),zero_zero(A))) # label(fact_1170_divide__less__eq__number__of) # label(axiom). [clausify(1281)].
% 225.57/225.40 6648 -linord1117847801e_zero(A) | -number(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)),hAPP(int,A,number_number_of(A),D))) | 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),hAPP(int,A,number_number_of(A),D)),C)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(int,A,number_number_of(A),D))) # label(fact_1170_divide__less__eq__number__of) # label(axiom). [clausify(1281)].
% 225.57/225.40 6649 -linord1117847801e_zero(A) | -number(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)),hAPP(int,A,number_number_of(A),D))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),D)),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),C)) # label(fact_1170_divide__less__eq__number__of) # label(axiom). [clausify(1281)].
% 225.57/225.40 6650 -linord1117847801e_zero(A) | -number(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)),hAPP(int,A,number_number_of(A),D))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(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),zero_zero(A)),hAPP(int,A,number_number_of(A),D))) # label(fact_1170_divide__less__eq__number__of) # label(axiom). [clausify(1281)].
% 225.57/225.40 6651 -linord1117847801e_zero(A) | -number(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)),hAPP(int,A,number_number_of(A),D))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),D)),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),D)),C)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),zero_zero(A))) # label(fact_1170_divide__less__eq__number__of) # label(axiom). [clausify(1281)].
% 225.57/225.40 6652 -linord1117847801e_zero(A) | -number(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)),hAPP(int,A,number_number_of(A),D))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),D)),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),D)),C)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(int,A,number_number_of(A),D))) # label(fact_1170_divide__less__eq__number__of) # label(axiom). [clausify(1281)].
% 225.57/225.40 6653 -linord1117847801e_zero(A) | -number(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),B)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),D))) | -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),hAPP(int,A,number_number_of(A),B)),D)),C)) # label(fact_1171_less__divide__eq__number__of) # label(axiom). [clausify(1282)].
% 225.57/225.40 6654 -linord1117847801e_zero(A) | -number(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),B)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),D))) | 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),D),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),B)),D))) # label(fact_1171_less__divide__eq__number__of) # label(axiom). [clausify(1282)].
% 225.57/225.40 6655 -linord1117847801e_zero(A) | -number(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),B)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),D))) | 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),D),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),B)),zero_zero(A))) # label(fact_1171_less__divide__eq__number__of) # label(axiom). [clausify(1282)].
% 225.57/225.40 6656 -linord1117847801e_zero(A) | -number(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),B)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),D))) | 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),D),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),B)),zero_zero(A))) # label(fact_1171_less__divide__eq__number__of) # label(axiom). [clausify(1282)].
% 225.57/225.40 6657 -linord1117847801e_zero(A) | -number(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),B)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),D))) | 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),C),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),B)),D))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),zero_zero(A))) # label(fact_1171_less__divide__eq__number__of) # label(axiom). [clausify(1282)].
% 225.57/225.40 6658 -linord1117847801e_zero(A) | -number(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),B)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),D))) | 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),C),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),B)),D))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),B)),zero_zero(A))) # label(fact_1171_less__divide__eq__number__of) # label(axiom). [clausify(1282)].
% 225.57/225.40 6659 -linord1117847801e_zero(A) | -number(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),B)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),D))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),B)),D)),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),D)) # label(fact_1171_less__divide__eq__number__of) # label(axiom). [clausify(1282)].
% 225.57/225.40 6660 -linord1117847801e_zero(A) | -number(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),B)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),D))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),B)),D)),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(int,A,number_number_of(A),B)),zero_zero(A))) # label(fact_1171_less__divide__eq__number__of) # label(axiom). [clausify(1282)].
% 225.57/225.40 6661 -linord1117847801e_zero(A) | -number(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),B)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),D))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),B)),D)),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),B)),D))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),zero_zero(A))) # label(fact_1171_less__divide__eq__number__of) # label(axiom). [clausify(1282)].
% 225.57/225.40 6662 -linord1117847801e_zero(A) | -number(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),B)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),D))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),B)),D)),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),B)),D))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),B)),zero_zero(A))) # label(fact_1171_less__divide__eq__number__of) # label(axiom). [clausify(1282)].
% 225.57/225.40 6663 -linord1117847801e_zero(A) | -number(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),hAPP(int,A,number_number_of(A),D)))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(int,A,number_number_of(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),hAPP(int,A,number_number_of(A),D))),C)) # label(fact_1172_less__divide__eq__number__of1) # label(axiom). [clausify(1283)].
% 225.57/225.40 6664 -linord1117847801e_zero(A) | -number(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),hAPP(int,A,number_number_of(A),D)))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(int,A,number_number_of(A),D))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),D)),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(int,A,number_number_of(A),D)))) # label(fact_1172_less__divide__eq__number__of1) # label(axiom). [clausify(1283)].
% 225.57/225.40 6665 -linord1117847801e_zero(A) | -number(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),hAPP(int,A,number_number_of(A),D)))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(int,A,number_number_of(A),D))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),D)),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) # label(fact_1172_less__divide__eq__number__of1) # label(axiom). [clausify(1283)].
% 225.57/225.40 6666 -linord1117847801e_zero(A) | -number(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),hAPP(int,A,number_number_of(A),D)))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(int,A,number_number_of(A),D))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),D)),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) # label(fact_1172_less__divide__eq__number__of1) # label(axiom). [clausify(1283)].
% 225.57/225.40 6667 -linord1117847801e_zero(A) | -number(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),hAPP(int,A,number_number_of(A),D)))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(int,A,number_number_of(A),D))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(int,A,number_number_of(A),D)))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),D)),zero_zero(A))) # label(fact_1172_less__divide__eq__number__of1) # label(axiom). [clausify(1283)].
% 225.57/225.40 6668 -linord1117847801e_zero(A) | -number(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),hAPP(int,A,number_number_of(A),D)))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(int,A,number_number_of(A),D))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(int,A,number_number_of(A),D)))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) # label(fact_1172_less__divide__eq__number__of1) # label(axiom). [clausify(1283)].
% 225.57/225.40 6669 -linord1117847801e_zero(A) | -number(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),hAPP(int,A,number_number_of(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),hAPP(int,A,number_number_of(A),D))),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(int,A,number_number_of(A),D))) # label(fact_1172_less__divide__eq__number__of1) # label(axiom). [clausify(1283)].
% 225.57/225.40 6670 -linord1117847801e_zero(A) | -number(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),hAPP(int,A,number_number_of(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),hAPP(int,A,number_number_of(A),D))),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),D)),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) # label(fact_1172_less__divide__eq__number__of1) # label(axiom). [clausify(1283)].
% 225.57/225.40 6671 -linord1117847801e_zero(A) | -number(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),hAPP(int,A,number_number_of(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),hAPP(int,A,number_number_of(A),D))),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(int,A,number_number_of(A),D)))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),D)),zero_zero(A))) # label(fact_1172_less__divide__eq__number__of1) # label(axiom). [clausify(1283)].
% 225.57/225.40 6672 -linord1117847801e_zero(A) | -number(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),hAPP(int,A,number_number_of(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),hAPP(int,A,number_number_of(A),D))),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(int,A,number_number_of(A),D)))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) # label(fact_1172_less__divide__eq__number__of1) # label(axiom). [clausify(1283)].
% 225.57/225.40 6673 -linord1117847801e_zero(A) | -number(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),hAPP(int,A,number_number_of(A),C))),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(int,A,number_number_of(A),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),hAPP(int,A,number_number_of(A),C)))) # label(fact_1176_divide__le__eq__number__of1) # label(axiom). [clausify(1287)].
% 225.57/225.40 6674 -linord1117847801e_zero(A) | -number(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),hAPP(int,A,number_number_of(A),C))),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(int,A,number_number_of(A),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),C)),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),hAPP(int,A,number_number_of(A),C))),B)) # label(fact_1176_divide__le__eq__number__of1) # label(axiom). [clausify(1287)].
% 225.57/225.40 6675 -linord1117847801e_zero(A) | -number(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),hAPP(int,A,number_number_of(A),C))),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(int,A,number_number_of(A),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),C)),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),D)) # label(fact_1176_divide__le__eq__number__of1) # label(axiom). [clausify(1287)].
% 225.57/225.40 6676 -linord1117847801e_zero(A) | -number(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),hAPP(int,A,number_number_of(A),C))),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(int,A,number_number_of(A),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),C)),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),D)) # label(fact_1176_divide__le__eq__number__of1) # label(axiom). [clausify(1287)].
% 225.57/225.40 6677 -linord1117847801e_zero(A) | -number(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),hAPP(int,A,number_number_of(A),C))),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(int,A,number_number_of(A),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),hAPP(int,A,number_number_of(A),C))),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),C)),zero_zero(A))) # label(fact_1176_divide__le__eq__number__of1) # label(axiom). [clausify(1287)].
% 225.57/225.40 6678 -linord1117847801e_zero(A) | -number(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),hAPP(int,A,number_number_of(A),C))),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(int,A,number_number_of(A),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),hAPP(int,A,number_number_of(A),C))),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),D)) # label(fact_1176_divide__le__eq__number__of1) # label(axiom). [clausify(1287)].
% 225.57/225.40 6679 -linord1117847801e_zero(A) | -number(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),hAPP(int,A,number_number_of(A),C))),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),hAPP(int,A,number_number_of(A),C)))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(int,A,number_number_of(A),C))) # label(fact_1176_divide__le__eq__number__of1) # label(axiom). [clausify(1287)].
% 225.57/225.40 6680 -linord1117847801e_zero(A) | -number(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),hAPP(int,A,number_number_of(A),C))),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),hAPP(int,A,number_number_of(A),C)))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),C)),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),D)) # label(fact_1176_divide__le__eq__number__of1) # label(axiom). [clausify(1287)].
% 225.57/225.40 6681 -linord1117847801e_zero(A) | -number(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),hAPP(int,A,number_number_of(A),C))),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),hAPP(int,A,number_number_of(A),C)))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),hAPP(int,A,number_number_of(A),C))),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),C)),zero_zero(A))) # label(fact_1176_divide__le__eq__number__of1) # label(axiom). [clausify(1287)].
% 225.57/225.40 6682 -linord1117847801e_zero(A) | -number(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),hAPP(int,A,number_number_of(A),C))),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),hAPP(int,A,number_number_of(A),C)))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),hAPP(int,A,number_number_of(A),C))),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),D)) # label(fact_1176_divide__le__eq__number__of1) # label(axiom). [clausify(1287)].
% 225.57/225.40 6683 -linord1117847801e_zero(A) | -number(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)),hAPP(int,A,number_number_of(A),D))) | -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_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),D)),C))) # label(fact_1177_divide__le__eq__number__of) # label(axiom). [clausify(1288)].
% 225.57/225.40 6684 -linord1117847801e_zero(A) | -number(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)),hAPP(int,A,number_number_of(A),D))) | 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))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),D)),C)),B)) # label(fact_1177_divide__le__eq__number__of) # label(axiom). [clausify(1288)].
% 225.57/225.40 6685 -linord1117847801e_zero(A) | -number(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)),hAPP(int,A,number_number_of(A),D))) | 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))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(int,A,number_number_of(A),D))) # label(fact_1177_divide__le__eq__number__of) # label(axiom). [clausify(1288)].
% 225.57/225.40 6686 -linord1117847801e_zero(A) | -number(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)),hAPP(int,A,number_number_of(A),D))) | 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))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(int,A,number_number_of(A),D))) # label(fact_1177_divide__le__eq__number__of) # label(axiom). [clausify(1288)].
% 225.57/225.40 6687 -linord1117847801e_zero(A) | -number(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)),hAPP(int,A,number_number_of(A),D))) | 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_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),D)),C)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),zero_zero(A))) # label(fact_1177_divide__le__eq__number__of) # label(axiom). [clausify(1288)].
% 225.57/225.40 6688 -linord1117847801e_zero(A) | -number(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)),hAPP(int,A,number_number_of(A),D))) | 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_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),D)),C)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(int,A,number_number_of(A),D))) # label(fact_1177_divide__le__eq__number__of) # label(axiom). [clausify(1288)].
% 225.57/225.40 6689 -linord1117847801e_zero(A) | -number(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)),hAPP(int,A,number_number_of(A),D))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),D)),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),C)) # label(fact_1177_divide__le__eq__number__of) # label(axiom). [clausify(1288)].
% 225.57/225.40 6690 -linord1117847801e_zero(A) | -number(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)),hAPP(int,A,number_number_of(A),D))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(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_eq(A),zero_zero(A)),hAPP(int,A,number_number_of(A),D))) # label(fact_1177_divide__le__eq__number__of) # label(axiom). [clausify(1288)].
% 225.57/225.40 6691 -linord1117847801e_zero(A) | -number(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)),hAPP(int,A,number_number_of(A),D))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),D)),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),D)),C)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),zero_zero(A))) # label(fact_1177_divide__le__eq__number__of) # label(axiom). [clausify(1288)].
% 225.57/225.40 6692 -linord1117847801e_zero(A) | -number(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)),hAPP(int,A,number_number_of(A),D))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),D)),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),D)),C)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(int,A,number_number_of(A),D))) # label(fact_1177_divide__le__eq__number__of) # label(axiom). [clausify(1288)].
% 225.57/225.40 6693 -linord1117847801e_zero(A) | -number(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(int,A,number_number_of(A),B)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),D))) | -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_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),B)),D)),C)) # label(fact_1178_le__divide__eq__number__of) # label(axiom). [clausify(1289)].
% 225.57/225.40 6694 -linord1117847801e_zero(A) | -number(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(int,A,number_number_of(A),B)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),D))) | 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),D),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),B)),D))) # label(fact_1178_le__divide__eq__number__of) # label(axiom). [clausify(1289)].
% 225.57/225.40 6695 -linord1117847801e_zero(A) | -number(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(int,A,number_number_of(A),B)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),D))) | 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),D),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(int,A,number_number_of(A),B)),zero_zero(A))) # label(fact_1178_le__divide__eq__number__of) # label(axiom). [clausify(1289)].
% 225.57/225.40 6696 -linord1117847801e_zero(A) | -number(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(int,A,number_number_of(A),B)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),D))) | 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),D),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(int,A,number_number_of(A),B)),zero_zero(A))) # label(fact_1178_le__divide__eq__number__of) # label(axiom). [clausify(1289)].
% 225.57/225.40 6697 -linord1117847801e_zero(A) | -number(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(int,A,number_number_of(A),B)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),D))) | 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_eq(A),C),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),B)),D))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),zero_zero(A))) # label(fact_1178_le__divide__eq__number__of) # label(axiom). [clausify(1289)].
% 225.57/225.40 6698 -linord1117847801e_zero(A) | -number(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(int,A,number_number_of(A),B)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),D))) | 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_eq(A),C),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),B)),D))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(int,A,number_number_of(A),B)),zero_zero(A))) # label(fact_1178_le__divide__eq__number__of) # label(axiom). [clausify(1289)].
% 225.57/225.40 6699 -linord1117847801e_zero(A) | -number(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(int,A,number_number_of(A),B)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),D))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),B)),D)),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),D)) # label(fact_1178_le__divide__eq__number__of) # label(axiom). [clausify(1289)].
% 225.57/225.40 6700 -linord1117847801e_zero(A) | -number(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(int,A,number_number_of(A),B)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),D))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),B)),D)),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_eq(A),hAPP(int,A,number_number_of(A),B)),zero_zero(A))) # label(fact_1178_le__divide__eq__number__of) # label(axiom). [clausify(1289)].
% 225.57/225.40 6701 -linord1117847801e_zero(A) | -number(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(int,A,number_number_of(A),B)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),D))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),B)),D)),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),B)),D))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),zero_zero(A))) # label(fact_1178_le__divide__eq__number__of) # label(axiom). [clausify(1289)].
% 225.57/225.40 6702 -linord1117847801e_zero(A) | -number(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(int,A,number_number_of(A),B)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),D))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),B)),D)),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),B)),D))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(int,A,number_number_of(A),B)),zero_zero(A))) # label(fact_1178_le__divide__eq__number__of) # label(axiom). [clausify(1289)].
% 225.57/225.40 6703 -linord1117847801e_zero(A) | -number(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),hAPP(int,A,number_number_of(A),D)))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(int,A,number_number_of(A),D))) | 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),hAPP(int,A,number_number_of(A),D))),C)) # label(fact_1179_le__divide__eq__number__of1) # label(axiom). [clausify(1290)].
% 225.57/225.40 6704 -linord1117847801e_zero(A) | -number(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),hAPP(int,A,number_number_of(A),D)))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(int,A,number_number_of(A),D))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),D)),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(int,A,number_number_of(A),D)))) # label(fact_1179_le__divide__eq__number__of1) # label(axiom). [clausify(1290)].
% 225.57/225.40 6705 -linord1117847801e_zero(A) | -number(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),hAPP(int,A,number_number_of(A),D)))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(int,A,number_number_of(A),D))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),D)),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),zero_zero(A))) # label(fact_1179_le__divide__eq__number__of1) # label(axiom). [clausify(1290)].
% 225.57/225.40 6706 -linord1117847801e_zero(A) | -number(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),hAPP(int,A,number_number_of(A),D)))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(int,A,number_number_of(A),D))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),D)),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),zero_zero(A))) # label(fact_1179_le__divide__eq__number__of1) # label(axiom). [clausify(1290)].
% 225.57/225.40 6707 -linord1117847801e_zero(A) | -number(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),hAPP(int,A,number_number_of(A),D)))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(int,A,number_number_of(A),D))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(int,A,number_number_of(A),D)))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),D)),zero_zero(A))) # label(fact_1179_le__divide__eq__number__of1) # label(axiom). [clausify(1290)].
% 225.57/225.40 6708 -linord1117847801e_zero(A) | -number(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),hAPP(int,A,number_number_of(A),D)))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(int,A,number_number_of(A),D))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(int,A,number_number_of(A),D)))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),zero_zero(A))) # label(fact_1179_le__divide__eq__number__of1) # label(axiom). [clausify(1290)].
% 225.57/225.40 6709 -linord1117847801e_zero(A) | -number(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),hAPP(int,A,number_number_of(A),D)))) | -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),hAPP(int,A,number_number_of(A),D))),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(int,A,number_number_of(A),D))) # label(fact_1179_le__divide__eq__number__of1) # label(axiom). [clausify(1290)].
% 225.57/225.40 6710 -linord1117847801e_zero(A) | -number(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),hAPP(int,A,number_number_of(A),D)))) | -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),hAPP(int,A,number_number_of(A),D))),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),D)),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),zero_zero(A))) # label(fact_1179_le__divide__eq__number__of1) # label(axiom). [clausify(1290)].
% 225.57/225.40 6711 -linord1117847801e_zero(A) | -number(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),hAPP(int,A,number_number_of(A),D)))) | -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),hAPP(int,A,number_number_of(A),D))),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(int,A,number_number_of(A),D)))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),D)),zero_zero(A))) # label(fact_1179_le__divide__eq__number__of1) # label(axiom). [clausify(1290)].
% 225.57/225.40 6712 -linord1117847801e_zero(A) | -number(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),hAPP(int,A,number_number_of(A),D)))) | -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),hAPP(int,A,number_number_of(A),D))),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(int,A,number_number_of(A),D)))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),zero_zero(A))) # label(fact_1179_le__divide__eq__number__of1) # label(axiom). [clausify(1290)].
% 225.57/225.40 6713 -linord1117847801e_zero(A) | -number_ring(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),hAPP(int,A,number_number_of(A),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) # label(fact_1845_half__gt__zero__iff) # label(axiom). [clausify(1896)].
% 225.57/225.40 6714 -linord1117847801e_zero(A) | -number_ring(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),hAPP(int,A,number_number_of(A),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) # label(fact_1845_half__gt__zero__iff) # label(axiom). [clausify(1896)].
% 225.57/225.40 6715 -linord1117847801e_zero(A) | -number_ring(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(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),hAPP(int,A,number_number_of(A),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) # label(fact_1846_half__gt__zero) # label(axiom). [clausify(1897)].
% 225.57/225.40 6716 -linord1117847801e_zero(A) | -number_ring(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),one_one(A)),hAPP(int,A,number_number_of(A),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) # label(fact_1882_half) # label(axiom). [clausify(1927)].
% 225.57/225.40 6717 -linord1117847801e_zero(A) | hAPP(A,A,abs_abs(A),hAPP(A,A,inverse_inverse(A),B)) = hAPP(A,A,inverse_inverse(A),hAPP(A,A,abs_abs(A),B)) # label(fact_2168_abs__inverse) # label(axiom). [clausify(2190)].
% 225.57/225.40 6718 -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(A,A,inverse_inverse(A),B))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) # label(fact_2201_inverse__nonnegative__iff__nonnegative) # label(axiom). [clausify(2220)].
% 225.57/225.40 6719 -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(A,A,inverse_inverse(A),B))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) # label(fact_2201_inverse__nonnegative__iff__nonnegative) # label(axiom). [clausify(2220)].
% 225.57/225.40 6720 -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,inverse_inverse(A),B)),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),zero_zero(A))) # label(fact_2202_inverse__nonpositive__iff__nonpositive) # label(axiom). [clausify(2221)].
% 225.57/225.40 6721 -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,inverse_inverse(A),B)),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),zero_zero(A))) # label(fact_2202_inverse__nonpositive__iff__nonpositive) # label(axiom). [clausify(2221)].
% 225.57/225.40 6722 -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,inverse_inverse(A),B)),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) # label(fact_2211_inverse__negative__iff__negative) # label(axiom). [clausify(2230)].
% 225.57/225.40 6723 -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,inverse_inverse(A),B)),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) # label(fact_2211_inverse__negative__iff__negative) # label(axiom). [clausify(2230)].
% 225.57/225.40 6724 -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,inverse_inverse(A),B))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) # label(fact_2212_inverse__positive__iff__positive) # label(axiom). [clausify(2231)].
% 225.57/225.40 6725 -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,inverse_inverse(A),B))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) # label(fact_2212_inverse__positive__iff__positive) # label(axiom). [clausify(2231)].
% 225.57/225.40 6726 -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,inverse_inverse(A),B)),one_one(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),one_one(A)),B)) # label(fact_2242_inverse__le__1__iff) # label(axiom). [clausify(2261)].
% 225.57/225.40 6727 -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,inverse_inverse(A),B)),one_one(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),zero_zero(A))) # label(fact_2242_inverse__le__1__iff) # label(axiom). [clausify(2261)].
% 225.57/225.40 6728 -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,inverse_inverse(A),B)),one_one(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),one_one(A)),B)) # label(fact_2242_inverse__le__1__iff) # label(axiom). [clausify(2261)].
% 225.57/225.40 6729 -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),hAPP(A,A,inverse_inverse(A),B))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) # label(fact_2244_one__less__inverse__iff) # label(axiom). [clausify(2263)].
% 225.57/225.40 6730 -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),hAPP(A,A,inverse_inverse(A),B))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),one_one(A))) # label(fact_2244_one__less__inverse__iff) # label(axiom). [clausify(2263)].
% 225.57/225.40 6731 -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),hAPP(A,A,inverse_inverse(A),B))) | -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),one_one(A))) # label(fact_2244_one__less__inverse__iff) # label(axiom). [clausify(2263)].
% 225.57/225.40 6732 -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,inverse_inverse(A),B)),hAPP(A,A,inverse_inverse(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))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B)) # label(fact_2259_inverse__less__iff) # label(axiom). [clausify(2278)].
% 225.57/225.40 6733 -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,inverse_inverse(A),B)),hAPP(A,A,inverse_inverse(A),C))) | -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)),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) # label(fact_2259_inverse__less__iff) # label(axiom). [clausify(2278)].
% 225.57/225.40 6734 -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,inverse_inverse(A),B)),hAPP(A,A,inverse_inverse(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))) | 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)),zero_zero(A))) # label(fact_2259_inverse__less__iff) # label(axiom). [clausify(2278)].
% 225.57/225.40 6735 -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,inverse_inverse(A),B)),hAPP(A,A,inverse_inverse(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))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) # label(fact_2259_inverse__less__iff) # label(axiom). [clausify(2278)].
% 225.57/225.40 6736 -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,inverse_inverse(A),B)),hAPP(A,A,inverse_inverse(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_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),zero_zero(A))) # label(fact_2259_inverse__less__iff) # label(axiom). [clausify(2278)].
% 225.57/225.40 6737 -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,inverse_inverse(A),B)),hAPP(A,A,inverse_inverse(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_2259_inverse__less__iff) # label(axiom). [clausify(2278)].
% 225.57/225.40 6738 -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,inverse_inverse(A),B)),hAPP(A,A,inverse_inverse(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))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),B)) # label(fact_2260_inverse__le__iff) # label(axiom). [clausify(2279)].
% 225.57/225.40 6739 -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,inverse_inverse(A),B)),hAPP(A,A,inverse_inverse(A),C))) | -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)),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) # label(fact_2260_inverse__le__iff) # label(axiom). [clausify(2279)].
% 225.57/225.40 6740 -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,inverse_inverse(A),B)),hAPP(A,A,inverse_inverse(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))) | 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)),zero_zero(A))) # label(fact_2260_inverse__le__iff) # label(axiom). [clausify(2279)].
% 225.57/225.40 6741 -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,inverse_inverse(A),B)),hAPP(A,A,inverse_inverse(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))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) # label(fact_2260_inverse__le__iff) # label(axiom). [clausify(2279)].
% 225.57/225.40 6742 -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,inverse_inverse(A),B)),hAPP(A,A,inverse_inverse(A),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),B)) | 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)),zero_zero(A))) # label(fact_2260_inverse__le__iff) # label(axiom). [clausify(2279)].
% 225.57/225.40 6743 -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,inverse_inverse(A),B)),hAPP(A,A,inverse_inverse(A),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) # label(fact_2260_inverse__le__iff) # label(axiom). [clausify(2279)].
% 225.57/225.41 6744 -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,inverse_inverse(A),B)),one_one(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),one_one(A)),B)) # label(fact_2262_inverse__less__1__iff) # label(axiom). [clausify(2281)].
% 225.57/225.41 6745 -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,inverse_inverse(A),B)),one_one(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),zero_zero(A))) # label(fact_2262_inverse__less__1__iff) # label(axiom). [clausify(2281)].
% 225.57/225.41 6746 -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,inverse_inverse(A),B)),one_one(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),B)) # label(fact_2262_inverse__less__1__iff) # label(axiom). [clausify(2281)].
% 225.57/225.41 6747 -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),one_one(A)),hAPP(A,A,inverse_inverse(A),B))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) # label(fact_2263_one__le__inverse__iff) # label(axiom). [clausify(2282)].
% 225.57/225.41 6748 -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),one_one(A)),hAPP(A,A,inverse_inverse(A),B))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),one_one(A))) # label(fact_2263_one__le__inverse__iff) # label(axiom). [clausify(2282)].
% 225.57/225.41 6749 -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),one_one(A)),hAPP(A,A,inverse_inverse(A),B))) | -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),B),one_one(A))) # label(fact_2263_one__le__inverse__iff) # label(axiom). [clausify(2282)].
% 225.57/225.41 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),f79(rat,A,B))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),B)). [resolve(6547,a,6548,a)].
% 225.57/225.41 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),f79(rat,A,B)),one_one(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),B)). [resolve(6547,a,6549,a)].
% 225.57/225.41 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),f79(rat,A,B)),A)),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),B)). [resolve(6547,a,6550,a)].
% 225.57/225.41 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),hAPP(rat,rat,abs_abs(rat),A)),hAPP(rat,rat,abs_abs(rat),B)) = hAPP(rat,rat,abs_abs(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),B)). [resolve(6547,a,6551,a)].
% 225.57/225.41 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),C),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),B),C)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),C))). [resolve(6547,a,6552,a)].
% 225.57/225.41 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),C)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),C)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),B),C))). [resolve(6547,a,6553,a)].
% 225.57/225.41 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),B)),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),A)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),zero_zero(rat))). [resolve(6547,a,6554,a)].
% 225.57/225.41 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),B)),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),A)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),B)). [resolve(6547,a,6555,a)].
% 225.57/225.42 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),B)),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),B),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),zero_zero(rat))). [resolve(6547,a,6556,a)].
% 225.57/225.42 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),B)),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),B),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),B)). [resolve(6547,a,6557,a)].
% 225.57/225.42 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),B)),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),B),zero_zero(rat))). [resolve(6547,a,6558,a)].
% 225.57/225.42 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),B)),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),B)). [resolve(6547,a,6559,a)].
% 225.57/225.42 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),B))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),A)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),zero_zero(rat))). [resolve(6547,a,6560,a)].
% 225.57/225.42 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),B))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),A)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),B),zero_zero(rat))). [resolve(6547,a,6561,a)].
% 225.57/225.42 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),B))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),zero_zero(rat))). [resolve(6547,a,6562,a)].
% 225.57/225.42 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),B))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),B),zero_zero(rat))). [resolve(6547,a,6563,a)].
% 225.57/225.42 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),B))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),B)). [resolve(6547,a,6564,a)].
% 225.57/225.42 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),B))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),B),zero_zero(rat))). [resolve(6547,a,6565,a)].
% 225.57/225.42 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),B))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),zero_zero(rat))). [resolve(6547,a,6566,a)].
% 225.57/225.42 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),B))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),zero_zero(rat))). [resolve(6547,a,6567,a)].
% 225.57/225.43 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),B))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),zero_zero(rat))). [resolve(6547,a,6568,a)].
% 225.57/225.43 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),B))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),zero_zero(rat))). [resolve(6547,a,6569,a)].
% 225.57/225.43 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),B))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),B)). [resolve(6547,a,6570,a)].
% 225.57/225.43 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),B))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),zero_zero(rat))). [resolve(6547,a,6571,a)].
% 225.57/225.43 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),B)),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),zero_zero(rat))). [resolve(6547,a,6572,a)].
% 225.57/225.43 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),B)),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),B)). [resolve(6547,a,6573,a)].
% 225.57/225.43 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),B)),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),zero_zero(rat))). [resolve(6547,a,6574,a)].
% 225.57/225.43 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),B)),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),B)). [resolve(6547,a,6575,a)].
% 225.57/225.43 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),B)),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),zero_zero(rat))). [resolve(6547,a,6576,a)].
% 225.57/225.43 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),B)),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),B)). [resolve(6547,a,6577,a)].
% 225.57/225.43 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),B)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),C),B))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),C)). [resolve(6547,a,6578,a)].
% 225.57/225.43 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),B)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),C),B))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),C),A)). [resolve(6547,a,6579,a)].
% 225.68/225.44 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),B)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),C),B))) | zero_zero(rat) != ti(rat,B). [resolve(6547,a,6580,a)].
% 225.68/225.44 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),B)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),C),B))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),zero_zero(rat))) | zero_zero(rat) = ti(rat,B). [resolve(6547,a,6581,a)].
% 225.68/225.44 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),B)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),C),B))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),C),A)) | zero_zero(rat) = ti(rat,B). [resolve(6547,a,6582,a)].
% 225.68/225.44 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),B)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),C),B))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),C)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),zero_zero(rat))) | zero_zero(rat) = ti(rat,B). [resolve(6547,a,6583,a)].
% 225.68/225.44 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),B)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),C),B))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),C)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),C),A)) | zero_zero(rat) = ti(rat,B). [resolve(6547,a,6584,a)].
% 225.68/225.44 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),B)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),C),B))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),C)). [resolve(6547,a,6585,a)].
% 225.68/225.44 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),B)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),C),B))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),C),A)). [resolve(6547,a,6586,a)].
% 225.68/225.44 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),B)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),C),B))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),zero_zero(rat))). [resolve(6547,a,6587,a)].
% 225.68/225.44 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),B)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),C),B))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),C),A)). [resolve(6547,a,6588,a)].
% 225.68/225.44 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),B)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),C),B))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),C)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),zero_zero(rat))). [resolve(6547,a,6589,a)].
% 225.68/225.44 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),B)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),C),B))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),C)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),C),A)). [resolve(6547,a,6590,a)].
% 225.68/225.44 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),B)),C)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),C),B))). [resolve(6547,a,6591,a)].
% 225.68/225.45 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),B)),C)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),C),B)),A)). [resolve(6547,a,6592,a)].
% 225.68/225.45 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),B)),C)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),C)). [resolve(6547,a,6593,a)].
% 225.68/225.45 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),B)),C)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),C)). [resolve(6547,a,6594,a)].
% 225.68/225.45 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),B)),C)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),C),B)),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),zero_zero(rat))). [resolve(6547,a,6595,a)].
% 225.68/225.45 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),B)),C)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),C),B)),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),C)). [resolve(6547,a,6596,a)].
% 225.68/225.45 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),B)),C)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),C),B))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),B)). [resolve(6547,a,6597,a)].
% 225.68/225.45 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),B)),C)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),C),B))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),C)). [resolve(6547,a,6598,a)].
% 225.68/225.45 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),B)),C)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),C),B))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),C),B)),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),zero_zero(rat))). [resolve(6547,a,6599,a)].
% 225.68/225.45 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),B)),C)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),C),B))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),C),B)),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),C)). [resolve(6547,a,6600,a)].
% 225.68/225.46 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),B),C))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),C)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),C)),B)). [resolve(6547,a,6601,a)].
% 225.68/225.46 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),B),C))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),C)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),C),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),C))). [resolve(6547,a,6602,a)].
% 225.68/225.46 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),B),C))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),C)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),C),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),zero_zero(rat))). [resolve(6547,a,6603,a)].
% 225.68/225.46 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),B),C))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),C)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),C),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),zero_zero(rat))). [resolve(6547,a,6604,a)].
% 225.68/225.46 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),B),C))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),C)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),C))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),C),zero_zero(rat))). [resolve(6547,a,6605,a)].
% 225.68/225.46 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),B),C))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),C)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),C))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),zero_zero(rat))). [resolve(6547,a,6606,a)].
% 225.68/225.46 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),B),C))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),C)),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),C)). [resolve(6547,a,6607,a)].
% 225.68/225.46 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),B),C))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),C)),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),C),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),zero_zero(rat))). [resolve(6547,a,6608,a)].
% 225.68/225.46 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),B),C))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),C)),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),C))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),C),zero_zero(rat))). [resolve(6547,a,6609,a)].
% 225.68/225.46 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),B),C))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),C)),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),C))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),zero_zero(rat))). [resolve(6547,a,6610,a)].
% 225.68/225.47 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)) | hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),hAPP(rat,rat,abs_abs(rat),B)),A) = hAPP(rat,rat,abs_abs(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),B),A)). [resolve(6547,a,6611,a)].
% 225.68/225.47 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),C),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),C),A)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),C),B))). [resolve(6547,a,6612,a)].
% 225.68/225.47 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),B)),C)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),C),B))). [resolve(6547,a,6613,a)].
% 225.68/225.47 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),B)),C)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),C),B)),A)). [resolve(6547,a,6614,a)].
% 225.68/225.47 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),B)),C)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),C)). [resolve(6547,a,6615,a)].
% 225.68/225.47 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),B)),C)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),C)). [resolve(6547,a,6616,a)].
% 225.68/225.47 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),B)),C)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),C),B)),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),zero_zero(rat))). [resolve(6547,a,6617,a)].
% 225.68/225.47 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),B)),C)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),C),B)),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),C)). [resolve(6547,a,6618,a)].
% 225.68/225.47 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),B)),C)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),C),B))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),B)). [resolve(6547,a,6619,a)].
% 225.68/225.47 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),B)),C)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),C),B))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),C)). [resolve(6547,a,6620,a)].
% 225.68/225.48 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),B)),C)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),C),B))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),C),B)),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),zero_zero(rat))). [resolve(6547,a,6621,a)].
% 225.68/225.48 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),B)),C)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),C),B))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),C),B)),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),C)). [resolve(6547,a,6622,a)].
% 225.68/225.48 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),B),C))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),C)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),C)),B)). [resolve(6547,a,6623,a)].
% 225.68/225.48 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),B),C))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),C)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),C),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),B),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),C))). [resolve(6547,a,6624,a)].
% 225.68/225.48 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),B),C))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),C)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),C),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),zero_zero(rat))). [resolve(6547,a,6625,a)].
% 225.68/225.48 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),B),C))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),C)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),C),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),zero_zero(rat))). [resolve(6547,a,6626,a)].
% 225.68/225.48 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),B),C))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),C)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),B),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),C))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),C),zero_zero(rat))). [resolve(6547,a,6627,a)].
% 225.68/225.48 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),B),C))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),C)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),B),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),C))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),zero_zero(rat))). [resolve(6547,a,6628,a)].
% 225.68/225.48 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),B),C))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),C)),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),C)). [resolve(6547,a,6629,a)].
% 225.77/225.55 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),B),C))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),C)),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),C),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),zero_zero(rat))). [resolve(6547,a,6630,a)].
% 225.77/225.55 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),B),C))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),C)),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),B),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),C))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),C),zero_zero(rat))). [resolve(6547,a,6631,a)].
% 225.77/225.55 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),B),C))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),C)),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),B),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),C))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),zero_zero(rat))). [resolve(6547,a,6632,a)].
% 225.77/225.55 Derived: -number_ring(rat) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),hAPP(int,rat,number_number_of(rat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)). [resolve(6547,a,6713,a)].
% 225.77/225.55 Derived: -number_ring(rat) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),hAPP(int,rat,number_number_of(rat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)). [resolve(6547,a,6714,a)].
% 225.77/225.55 Derived: -number_ring(rat) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),one_one(rat)),hAPP(int,rat,number_number_of(rat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))). [resolve(6547,a,6716,a)].
% 225.77/225.55 Derived: hAPP(rat,rat,abs_abs(rat),hAPP(rat,rat,inverse_inverse(rat),A)) = hAPP(rat,rat,inverse_inverse(rat),hAPP(rat,rat,abs_abs(rat),A)). [resolve(6547,a,6717,a)].
% 225.77/225.55 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),hAPP(rat,rat,inverse_inverse(rat),A))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),A)). [resolve(6547,a,6718,a)].
% 225.77/225.55 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),hAPP(rat,rat,inverse_inverse(rat),A))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),A)). [resolve(6547,a,6719,a)].
% 225.77/225.55 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,inverse_inverse(rat),A)),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),zero_zero(rat))). [resolve(6547,a,6720,a)].
% 225.77/225.55 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,inverse_inverse(rat),A)),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),zero_zero(rat))). [resolve(6547,a,6721,a)].
% 225.77/225.55 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,inverse_inverse(rat),A)),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),zero_zero(rat))). [resolve(6547,a,6722,a)].
% 225.77/225.55 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,inverse_inverse(rat),A)),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),zero_zero(rat))). [resolve(6547,a,6723,a)].
% 225.77/225.56 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(rat,rat,inverse_inverse(rat),A))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)). [resolve(6547,a,6724,a)].
% 225.77/225.56 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(rat,rat,inverse_inverse(rat),A))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)). [resolve(6547,a,6725,a)].
% 225.77/225.56 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,inverse_inverse(rat),A)),one_one(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),one_one(rat)),A)). [resolve(6547,a,6726,a)].
% 225.77/225.56 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,inverse_inverse(rat),A)),one_one(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),zero_zero(rat))). [resolve(6547,a,6727,a)].
% 225.77/225.56 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,inverse_inverse(rat),A)),one_one(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),one_one(rat)),A)). [resolve(6547,a,6728,a)].
% 225.77/225.56 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),one_one(rat)),hAPP(rat,rat,inverse_inverse(rat),A))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)). [resolve(6547,a,6729,a)].
% 225.77/225.56 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),one_one(rat)),hAPP(rat,rat,inverse_inverse(rat),A))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),one_one(rat))). [resolve(6547,a,6730,a)].
% 225.77/225.56 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),one_one(rat)),hAPP(rat,rat,inverse_inverse(rat),A))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),one_one(rat))). [resolve(6547,a,6731,a)].
% 225.77/225.56 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,inverse_inverse(rat),A)),hAPP(rat,rat,inverse_inverse(rat),B))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),A)). [resolve(6547,a,6732,a)].
% 225.77/225.56 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,inverse_inverse(rat),A)),hAPP(rat,rat,inverse_inverse(rat),B))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B)),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),B)). [resolve(6547,a,6733,a)].
% 225.77/225.56 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,inverse_inverse(rat),A)),hAPP(rat,rat,inverse_inverse(rat),B))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B)),zero_zero(rat))). [resolve(6547,a,6734,a)].
% 225.77/225.56 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,inverse_inverse(rat),A)),hAPP(rat,rat,inverse_inverse(rat),B))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),B)). [resolve(6547,a,6735,a)].
% 225.77/225.56 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,inverse_inverse(rat),A)),hAPP(rat,rat,inverse_inverse(rat),B))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),A)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B)),zero_zero(rat))). [resolve(6547,a,6736,a)].
% 225.77/225.56 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,inverse_inverse(rat),A)),hAPP(rat,rat,inverse_inverse(rat),B))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),B)). [resolve(6547,a,6737,a)].
% 225.77/225.59 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,inverse_inverse(rat),A)),hAPP(rat,rat,inverse_inverse(rat),B))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),B),A)). [resolve(6547,a,6738,a)].
% 225.77/225.59 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,inverse_inverse(rat),A)),hAPP(rat,rat,inverse_inverse(rat),B))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B)),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),B)). [resolve(6547,a,6739,a)].
% 225.77/225.59 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,inverse_inverse(rat),A)),hAPP(rat,rat,inverse_inverse(rat),B))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B)),zero_zero(rat))). [resolve(6547,a,6740,a)].
% 225.77/225.59 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,inverse_inverse(rat),A)),hAPP(rat,rat,inverse_inverse(rat),B))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),B)). [resolve(6547,a,6741,a)].
% 225.77/225.59 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,inverse_inverse(rat),A)),hAPP(rat,rat,inverse_inverse(rat),B))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),B),A)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B)),zero_zero(rat))). [resolve(6547,a,6742,a)].
% 225.77/225.59 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,inverse_inverse(rat),A)),hAPP(rat,rat,inverse_inverse(rat),B))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),B),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),B)). [resolve(6547,a,6743,a)].
% 225.77/225.59 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,inverse_inverse(rat),A)),one_one(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),one_one(rat)),A)). [resolve(6547,a,6744,a)].
% 225.77/225.59 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,inverse_inverse(rat),A)),one_one(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),zero_zero(rat))). [resolve(6547,a,6745,a)].
% 225.77/225.59 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,inverse_inverse(rat),A)),one_one(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),one_one(rat)),A)). [resolve(6547,a,6746,a)].
% 225.77/225.59 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),one_one(rat)),hAPP(rat,rat,inverse_inverse(rat),A))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)). [resolve(6547,a,6747,a)].
% 225.77/225.59 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),one_one(rat)),hAPP(rat,rat,inverse_inverse(rat),A))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),one_one(rat))). [resolve(6547,a,6748,a)].
% 225.77/225.59 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),one_one(rat)),hAPP(rat,rat,inverse_inverse(rat),A))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),one_one(rat))). [resolve(6547,a,6749,a)].
% 225.77/225.59 6750 linord1117847801e_zero(real) # label(arity_RealDef_Oreal___Fields_Olinordered__field__inverse__zero) # label(axiom). [assumption].
% 225.84/225.60 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),f79(real,A,B))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),B)). [resolve(6750,a,6548,a)].
% 225.84/225.60 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),f79(real,A,B)),one_one(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),B)). [resolve(6750,a,6549,a)].
% 225.84/225.60 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),f79(real,A,B)),A)),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),B)). [resolve(6750,a,6550,a)].
% 225.84/225.60 Derived: hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,abs_abs(real),A)),hAPP(real,real,abs_abs(real),B)) = hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B)). [resolve(6750,a,6551,a)].
% 225.84/225.60 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),C),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),B),C)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),C))). [resolve(6750,a,6552,a)].
% 225.84/225.60 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),C)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),B),C))). [resolve(6750,a,6553,a)].
% 225.84/225.60 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B)),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),zero_zero(real))). [resolve(6750,a,6554,a)].
% 225.84/225.60 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B)),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),B)). [resolve(6750,a,6555,a)].
% 225.84/225.60 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B)),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),zero_zero(real))). [resolve(6750,a,6556,a)].
% 225.84/225.60 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B)),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),B)). [resolve(6750,a,6557,a)].
% 225.84/225.60 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B)),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),zero_zero(real))). [resolve(6750,a,6558,a)].
% 225.84/225.60 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B)),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),B)). [resolve(6750,a,6559,a)].
% 225.84/225.60 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),zero_zero(real))). [resolve(6750,a,6560,a)].
% 225.84/225.61 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),zero_zero(real))). [resolve(6750,a,6561,a)].
% 225.84/225.61 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),zero_zero(real))). [resolve(6750,a,6562,a)].
% 225.84/225.61 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),zero_zero(real))). [resolve(6750,a,6563,a)].
% 225.84/225.61 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),B)). [resolve(6750,a,6564,a)].
% 225.84/225.61 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),zero_zero(real))). [resolve(6750,a,6565,a)].
% 225.84/225.61 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))). [resolve(6750,a,6566,a)].
% 225.84/225.61 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),zero_zero(real))). [resolve(6750,a,6567,a)].
% 225.84/225.61 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))). [resolve(6750,a,6568,a)].
% 225.84/225.61 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),zero_zero(real))). [resolve(6750,a,6569,a)].
% 225.84/225.61 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B)). [resolve(6750,a,6570,a)].
% 225.84/225.61 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),zero_zero(real))). [resolve(6750,a,6571,a)].
% 225.84/225.62 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B)),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))). [resolve(6750,a,6572,a)].
% 225.84/225.62 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B)),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B)). [resolve(6750,a,6573,a)].
% 225.84/225.62 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B)),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))). [resolve(6750,a,6574,a)].
% 225.84/225.62 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B)),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B)). [resolve(6750,a,6575,a)].
% 225.84/225.62 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B)),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),zero_zero(real))). [resolve(6750,a,6576,a)].
% 225.84/225.62 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B)),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B)). [resolve(6750,a,6577,a)].
% 225.84/225.62 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),C),B))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),C)). [resolve(6750,a,6578,a)].
% 225.84/225.62 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),C),B))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),C),A)). [resolve(6750,a,6579,a)].
% 225.84/225.62 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),C),B))) | zero_zero(real) != ti(real,B). [resolve(6750,a,6580,a)].
% 225.84/225.62 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),C),B))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),zero_zero(real))) | zero_zero(real) = ti(real,B). [resolve(6750,a,6581,a)].
% 225.84/225.62 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),C),B))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),C),A)) | zero_zero(real) = ti(real,B). [resolve(6750,a,6582,a)].
% 225.84/225.62 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),C),B))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),zero_zero(real))) | zero_zero(real) = ti(real,B). [resolve(6750,a,6583,a)].
% 225.84/225.63 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),C),B))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),C)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),C),A)) | zero_zero(real) = ti(real,B). [resolve(6750,a,6584,a)].
% 225.84/225.63 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),C),B))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),C)). [resolve(6750,a,6585,a)].
% 225.84/225.63 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),C),B))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),C),A)). [resolve(6750,a,6586,a)].
% 225.84/225.63 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),C),B))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),zero_zero(real))). [resolve(6750,a,6587,a)].
% 225.84/225.63 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),C),B))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),C),A)). [resolve(6750,a,6588,a)].
% 225.84/225.63 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),C),B))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),zero_zero(real))). [resolve(6750,a,6589,a)].
% 225.84/225.63 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),C),B))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),C)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),C),A)). [resolve(6750,a,6590,a)].
% 225.84/225.63 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B)),C)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),B))). [resolve(6750,a,6591,a)].
% 225.84/225.63 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B)),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),B)),A)). [resolve(6750,a,6592,a)].
% 225.84/225.63 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B)),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),C)). [resolve(6750,a,6593,a)].
% 225.84/225.64 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B)),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),C)). [resolve(6750,a,6594,a)].
% 225.84/225.64 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B)),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),B)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),zero_zero(real))). [resolve(6750,a,6595,a)].
% 225.84/225.64 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B)),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),B)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),C)). [resolve(6750,a,6596,a)].
% 225.84/225.64 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B)),C)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),B))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B)). [resolve(6750,a,6597,a)].
% 225.84/225.64 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B)),C)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),B))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),C)). [resolve(6750,a,6598,a)].
% 225.84/225.64 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B)),C)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),B))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),B)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),zero_zero(real))). [resolve(6750,a,6599,a)].
% 225.84/225.64 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B)),C)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),B))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),B)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),C)). [resolve(6750,a,6600,a)].
% 225.84/225.64 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),B),C))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),C)),B)). [resolve(6750,a,6601,a)].
% 225.84/225.64 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),B),C))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),C)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),C),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),C))). [resolve(6750,a,6602,a)].
% 225.84/225.64 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),B),C))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),C),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))). [resolve(6750,a,6603,a)].
% 225.84/225.64 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),B),C))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),C),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))). [resolve(6750,a,6604,a)].
% 225.84/225.64 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),B),C))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),C)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),C))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),C),zero_zero(real))). [resolve(6750,a,6605,a)].
% 225.84/225.64 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),B),C))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),C)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),C))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))). [resolve(6750,a,6606,a)].
% 225.84/225.64 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),B),C))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),C)),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),C)). [resolve(6750,a,6607,a)].
% 225.84/225.64 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),B),C))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),C)),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),C),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))). [resolve(6750,a,6608,a)].
% 225.84/225.64 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),B),C))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),C)),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),C))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),C),zero_zero(real))). [resolve(6750,a,6609,a)].
% 225.84/225.64 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),B),C))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),C)),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),C))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))). [resolve(6750,a,6610,a)].
% 225.84/225.65 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,abs_abs(real),B)),A) = hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),B),A)). [resolve(6750,a,6611,a)].
% 225.84/225.65 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),C),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),C),A)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),C),B))). [resolve(6750,a,6612,a)].
% 225.84/225.65 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B)),C)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),B))). [resolve(6750,a,6613,a)].
% 225.84/225.65 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B)),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),B)),A)). [resolve(6750,a,6614,a)].
% 225.84/225.65 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B)),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),C)). [resolve(6750,a,6615,a)].
% 225.84/225.65 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B)),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),C)). [resolve(6750,a,6616,a)].
% 225.84/225.65 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B)),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),B)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),zero_zero(real))). [resolve(6750,a,6617,a)].
% 225.84/225.65 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B)),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),B)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),C)). [resolve(6750,a,6618,a)].
% 225.84/225.65 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B)),C)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),B))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B)). [resolve(6750,a,6619,a)].
% 225.84/225.65 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B)),C)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),B))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),C)). [resolve(6750,a,6620,a)].
% 225.84/225.66 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B)),C)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),B))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),B)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),zero_zero(real))). [resolve(6750,a,6621,a)].
% 225.84/225.66 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B)),C)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),B))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),B)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),C)). [resolve(6750,a,6622,a)].
% 225.84/225.66 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),B),C))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),C)),B)). [resolve(6750,a,6623,a)].
% 225.84/225.66 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),B),C))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),C)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),C),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),C))). [resolve(6750,a,6624,a)].
% 225.84/225.66 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),B),C))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),C),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),zero_zero(real))). [resolve(6750,a,6625,a)].
% 225.84/225.66 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),B),C))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),C),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),zero_zero(real))). [resolve(6750,a,6626,a)].
% 225.84/225.66 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),B),C))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),C)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),C))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),C),zero_zero(real))). [resolve(6750,a,6627,a)].
% 225.84/225.66 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),B),C))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),C)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),C))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),zero_zero(real))). [resolve(6750,a,6628,a)].
% 225.84/225.66 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),B),C))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),C)),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),C)). [resolve(6750,a,6629,a)].
% 225.98/225.74 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),B),C))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),C)),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),C),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),zero_zero(real))). [resolve(6750,a,6630,a)].
% 225.98/225.74 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),B),C))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),C)),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),C))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),C),zero_zero(real))). [resolve(6750,a,6631,a)].
% 225.98/225.74 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),B),C))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),C)),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),C))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),zero_zero(real))). [resolve(6750,a,6632,a)].
% 225.98/225.74 Derived: -number_ring(real) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)). [resolve(6750,a,6713,a)].
% 225.98/225.74 Derived: -number_ring(real) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)). [resolve(6750,a,6714,a)].
% 225.98/225.74 Derived: -number_ring(real) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),one_one(real)),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))). [resolve(6750,a,6716,a)].
% 225.98/225.74 Derived: hAPP(real,real,abs_abs(real),hAPP(real,real,inverse_inverse(real),A)) = hAPP(real,real,inverse_inverse(real),hAPP(real,real,abs_abs(real),A)). [resolve(6750,a,6717,a)].
% 225.98/225.74 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(real,real,inverse_inverse(real),A))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A)). [resolve(6750,a,6718,a)].
% 225.98/225.74 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(real,real,inverse_inverse(real),A))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A)). [resolve(6750,a,6719,a)].
% 225.98/225.74 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,inverse_inverse(real),A)),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),zero_zero(real))). [resolve(6750,a,6720,a)].
% 225.98/225.74 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,inverse_inverse(real),A)),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),zero_zero(real))). [resolve(6750,a,6721,a)].
% 225.98/225.75 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,inverse_inverse(real),A)),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))). [resolve(6750,a,6722,a)].
% 225.98/225.75 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,inverse_inverse(real),A)),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))). [resolve(6750,a,6723,a)].
% 225.98/225.75 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,inverse_inverse(real),A))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)). [resolve(6750,a,6724,a)].
% 225.98/225.75 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,inverse_inverse(real),A))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)). [resolve(6750,a,6725,a)].
% 225.98/225.75 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,inverse_inverse(real),A)),one_one(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),one_one(real)),A)). [resolve(6750,a,6726,a)].
% 225.98/225.75 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,inverse_inverse(real),A)),one_one(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),zero_zero(real))). [resolve(6750,a,6727,a)].
% 225.98/225.75 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,inverse_inverse(real),A)),one_one(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),one_one(real)),A)). [resolve(6750,a,6728,a)].
% 225.98/225.75 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),hAPP(real,real,inverse_inverse(real),A))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)). [resolve(6750,a,6729,a)].
% 225.98/225.75 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),hAPP(real,real,inverse_inverse(real),A))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),one_one(real))). [resolve(6750,a,6730,a)].
% 225.98/225.75 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),hAPP(real,real,inverse_inverse(real),A))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),one_one(real))). [resolve(6750,a,6731,a)].
% 225.98/225.75 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,inverse_inverse(real),A)),hAPP(real,real,inverse_inverse(real),B))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),A)). [resolve(6750,a,6732,a)].
% 225.98/225.75 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,inverse_inverse(real),A)),hAPP(real,real,inverse_inverse(real),B))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)). [resolve(6750,a,6733,a)].
% 225.98/225.75 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,inverse_inverse(real),A)),hAPP(real,real,inverse_inverse(real),B))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),zero_zero(real))). [resolve(6750,a,6734,a)].
% 225.98/225.75 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,inverse_inverse(real),A)),hAPP(real,real,inverse_inverse(real),B))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)). [resolve(6750,a,6735,a)].
% 225.98/225.76 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,inverse_inverse(real),A)),hAPP(real,real,inverse_inverse(real),B))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),A)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),zero_zero(real))). [resolve(6750,a,6736,a)].
% 225.98/225.76 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,inverse_inverse(real),A)),hAPP(real,real,inverse_inverse(real),B))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)). [resolve(6750,a,6737,a)].
% 225.98/225.76 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,inverse_inverse(real),A)),hAPP(real,real,inverse_inverse(real),B))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),A)). [resolve(6750,a,6738,a)].
% 225.98/225.76 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,inverse_inverse(real),A)),hAPP(real,real,inverse_inverse(real),B))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),B)). [resolve(6750,a,6739,a)].
% 225.98/225.76 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,inverse_inverse(real),A)),hAPP(real,real,inverse_inverse(real),B))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),zero_zero(real))). [resolve(6750,a,6740,a)].
% 225.98/225.76 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,inverse_inverse(real),A)),hAPP(real,real,inverse_inverse(real),B))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),B)). [resolve(6750,a,6741,a)].
% 225.98/225.76 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,inverse_inverse(real),A)),hAPP(real,real,inverse_inverse(real),B))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),A)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),zero_zero(real))). [resolve(6750,a,6742,a)].
% 225.98/225.76 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,inverse_inverse(real),A)),hAPP(real,real,inverse_inverse(real),B))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),B)). [resolve(6750,a,6743,a)].
% 225.98/225.76 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,inverse_inverse(real),A)),one_one(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),A)). [resolve(6750,a,6744,a)].
% 225.98/225.76 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,inverse_inverse(real),A)),one_one(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),zero_zero(real))). [resolve(6750,a,6745,a)].
% 225.98/225.76 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,inverse_inverse(real),A)),one_one(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),A)). [resolve(6750,a,6746,a)].
% 230.64/230.41 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),one_one(real)),hAPP(real,real,inverse_inverse(real),A))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)). [resolve(6750,a,6747,a)].
% 230.64/230.41 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),one_one(real)),hAPP(real,real,inverse_inverse(real),A))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),one_one(real))). [resolve(6750,a,6748,a)].
% 230.64/230.41 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),one_one(real)),hAPP(real,real,inverse_inverse(real),A))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),one_one(real))). [resolve(6750,a,6749,a)].
% 230.64/230.41 6751 linordered_field(rat) # label(arity_Rat_Orat___Fields_Olinordered__field) # label(axiom). [assumption].
% 230.64/230.41 6752 -linordered_field(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),f80(A,B,C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) # label(fact_414_field__le__epsilon) # label(axiom). [clausify(540)].
% 230.64/230.41 6753 -linordered_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),f80(A,B,C)))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) # label(fact_414_field__le__epsilon) # label(axiom). [clausify(540)].
% 230.64/230.41 6754 -linordered_field(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),inverse_divide(A),B),C))) # label(fact_1098_divide__pos__pos) # label(axiom). [clausify(1209)].
% 230.64/230.41 6755 -linordered_field(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),inverse_divide(A),B),C)),zero_zero(A))) # label(fact_1099_divide__pos__neg) # label(axiom). [clausify(1210)].
% 230.64/230.41 6756 -linordered_field(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),inverse_divide(A),B),C)),zero_zero(A))) # label(fact_1100_divide__neg__pos) # label(axiom). [clausify(1211)].
% 230.64/230.41 6757 -linordered_field(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),inverse_divide(A),B),C))) # label(fact_1101_divide__neg__neg) # label(axiom). [clausify(1212)].
% 230.64/230.41 6758 -linordered_field(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),inverse_divide(A),B),D)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),D))) # label(fact_1102_divide__strict__right__mono) # label(axiom). [clausify(1213)].
% 230.64/230.41 6759 -linordered_field(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),inverse_divide(A),C),D)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),D))) # label(fact_1103_divide__strict__right__mono__neg) # label(axiom). [clausify(1214)].
% 230.64/230.41 6760 -linordered_field(A) | zero_zero(A) = ti(A,B) | hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),hAPP(A,A,abs_abs(A),C)),hAPP(A,A,abs_abs(A),B)) = hAPP(A,A,abs_abs(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),B)) # label(fact_1118_nonzero__abs__divide) # label(axiom). [clausify(1229)].
% 230.64/230.41 6761 -linordered_field(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_eq(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C))) # label(fact_1124_divide__nonneg__pos) # label(axiom). [clausify(1235)].
% 230.64/230.41 6762 -linordered_field(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),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)),zero_zero(A))) # label(fact_1125_divide__nonneg__neg) # label(axiom). [clausify(1236)].
% 230.64/230.41 6763 -linordered_field(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),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),D),E)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),E)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),D))) # label(fact_1126_frac__less2) # label(axiom). [clausify(1237)].
% 230.64/230.41 6764 -linordered_field(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),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_eq(A),D),E)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),E)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),D))) # label(fact_1127_frac__less) # label(axiom). [clausify(1238)].
% 230.64/230.41 6765 -linordered_field(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),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_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),inverse_divide(A),B),E)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),D))) # label(fact_1128_frac__le) # label(axiom). [clausify(1239)].
% 230.64/230.41 6766 -linordered_field(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),zero_zero(A)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)),zero_zero(A))) # label(fact_1129_divide__nonpos__pos) # label(axiom). [clausify(1240)].
% 230.64/230.41 6767 -linordered_field(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_eq(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C))) # label(fact_1130_divide__nonpos__neg) # label(axiom). [clausify(1241)].
% 230.64/230.41 6768 -linordered_field(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),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),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),B)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),C))) # label(fact_1131_divide__strict__left__mono__neg) # label(axiom). [clausify(1242)].
% 230.64/230.41 6769 -linordered_field(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),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),B))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),C)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),B))) # label(fact_1132_divide__strict__left__mono) # label(axiom). [clausify(1243)].
% 230.64/230.41 6770 -linordered_field(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),inverse_divide(A),C),B)),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)),C)) # label(fact_1133_neg__divide__less__eq) # label(axiom). [clausify(1244)].
% 230.64/230.41 6771 -linordered_field(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),inverse_divide(A),C),B)),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)),C)) # label(fact_1133_neg__divide__less__eq) # label(axiom). [clausify(1244)].
% 230.64/230.41 6772 -linordered_field(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),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),B))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),B))) # label(fact_1134_neg__less__divide__eq) # label(axiom). [clausify(1245)].
% 230.64/230.41 6773 -linordered_field(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),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),B))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),B))) # label(fact_1134_neg__less__divide__eq) # label(axiom). [clausify(1245)].
% 230.64/230.41 6774 -linordered_field(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),C),B)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),B))) # label(fact_1135_mult__imp__less__div__pos) # label(axiom). [clausify(1246)].
% 230.64/230.41 6775 -linordered_field(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),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),B))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),B)),D)) # label(fact_1136_mult__imp__div__pos__less) # label(axiom). [clausify(1247)].
% 230.64/230.41 6776 -linordered_field(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),inverse_divide(A),C),B)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),B))) # label(fact_1137_pos__divide__less__eq) # label(axiom). [clausify(1248)].
% 230.64/230.41 6777 -linordered_field(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),inverse_divide(A),C),B)),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),B))) # label(fact_1137_pos__divide__less__eq) # label(axiom). [clausify(1248)].
% 230.64/230.41 6778 -linordered_field(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),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),B))) | 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)),D)) # label(fact_1138_pos__less__divide__eq) # label(axiom). [clausify(1249)].
% 230.64/230.41 6779 -linordered_field(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),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),B))) | -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)),D)) # label(fact_1138_pos__less__divide__eq) # label(axiom). [clausify(1249)].
% 230.64/230.41 6780 -linordered_field(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),inverse_divide(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),one_one(A)),one_one(A)))),C)) # label(fact_1153_gt__half__sum) # label(axiom). [clausify(1264)].
% 230.64/230.41 6781 -linordered_field(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),inverse_divide(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),one_one(A)),one_one(A))))) # label(fact_1154_less__half__sum) # label(axiom). [clausify(1265)].
% 230.64/230.41 6782 -linordered_field(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),zero_zero(A)),D)) | -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),C),B))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),C)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),B))) # label(fact_1160_divide__left__mono) # label(axiom). [clausify(1271)].
% 230.64/230.41 6783 -linordered_field(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),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),B)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),B)),C)) # label(fact_1161_neg__divide__le__eq) # label(axiom). [clausify(1272)].
% 230.64/230.41 6784 -linordered_field(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),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),B)),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),B)),C)) # label(fact_1161_neg__divide__le__eq) # label(axiom). [clausify(1272)].
% 230.64/230.41 6785 -linordered_field(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),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),B))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),D),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),B))) # label(fact_1162_neg__le__divide__eq) # label(axiom). [clausify(1273)].
% 230.64/230.41 6786 -linordered_field(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),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),B))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),D),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),B))) # label(fact_1162_neg__le__divide__eq) # label(axiom). [clausify(1273)].
% 230.64/230.41 6787 -linordered_field(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),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),B)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),B))) # label(fact_1163_mult__imp__le__div__pos) # label(axiom). [clausify(1274)].
% 230.64/230.41 6788 -linordered_field(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),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),B))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),B)),D)) # label(fact_1164_mult__imp__div__pos__le) # label(axiom). [clausify(1275)].
% 230.64/230.41 6789 -linordered_field(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),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),B)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),B))) # label(fact_1165_pos__divide__le__eq) # label(axiom). [clausify(1276)].
% 230.64/230.41 6790 -linordered_field(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),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),B)),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),B))) # label(fact_1165_pos__divide__le__eq) # label(axiom). [clausify(1276)].
% 230.64/230.41 6791 -linordered_field(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),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),B))) | 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)),D)) # label(fact_1166_pos__le__divide__eq) # label(axiom). [clausify(1277)].
% 230.64/230.41 6792 -linordered_field(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),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),B))) | -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)),D)) # label(fact_1166_pos__le__divide__eq) # label(axiom). [clausify(1277)].
% 230.64/230.41 6793 -linordered_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,inverse_inverse(A),B)),hAPP(A,A,inverse_inverse(A),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),C),B)) # label(fact_2203_inverse__less__imp__less__neg) # label(axiom). [clausify(2222)].
% 230.64/230.41 6794 -linordered_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,inverse_inverse(A),B)),hAPP(A,A,inverse_inverse(A),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),C),B)) # label(fact_2204_inverse__less__imp__less) # label(axiom). [clausify(2223)].
% 230.64/230.41 6795 -linordered_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,inverse_inverse(A),B)),zero_zero(A))) | zero_zero(A) = ti(A,B) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) # label(fact_2205_inverse__negative__imp__negative) # label(axiom). [clausify(2224)].
% 230.64/230.41 6796 -linordered_field(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),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,inverse_inverse(A),C)),hAPP(A,A,inverse_inverse(A),B))) # label(fact_2206_less__imp__inverse__less__neg) # label(axiom). [clausify(2225)].
% 230.64/230.41 6797 -linordered_field(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)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,inverse_inverse(A),C)),hAPP(A,A,inverse_inverse(A),B))) # label(fact_2207_less__imp__inverse__less) # label(axiom). [clausify(2226)].
% 230.64/230.41 6798 -linordered_field(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,inverse_inverse(A),B)),zero_zero(A))) # label(fact_2208_negative__imp__inverse__negative) # label(axiom). [clausify(2227)].
% 230.64/230.41 6799 -linordered_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,inverse_inverse(A),B))) | zero_zero(A) = ti(A,B) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) # label(fact_2209_inverse__positive__imp__positive) # label(axiom). [clausify(2228)].
% 230.64/230.41 6800 -linordered_field(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(A,A,inverse_inverse(A),B))) # label(fact_2210_positive__imp__inverse__positive) # label(axiom). [clausify(2229)].
% 230.64/230.41 6801 -linordered_field(A) | zero_zero(A) = ti(A,B) | hAPP(A,A,abs_abs(A),hAPP(A,A,inverse_inverse(A),B)) = hAPP(A,A,inverse_inverse(A),hAPP(A,A,abs_abs(A),B)) # label(fact_2227_nonzero__abs__inverse) # label(axiom). [clausify(2246)].
% 230.64/230.41 6802 -linordered_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,inverse_inverse(A),B)),hAPP(A,A,inverse_inverse(A),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_eq(A),C),B)) # label(fact_2238_inverse__le__imp__le__neg) # label(axiom). [clausify(2257)].
% 230.64/230.41 6803 -linordered_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,inverse_inverse(A),B)),hAPP(A,A,inverse_inverse(A),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_eq(A),C),B)) # label(fact_2239_inverse__le__imp__le) # label(axiom). [clausify(2258)].
% 230.64/230.41 6804 -linordered_field(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),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,inverse_inverse(A),C)),hAPP(A,A,inverse_inverse(A),B))) # label(fact_2240_le__imp__inverse__le__neg) # label(axiom). [clausify(2259)].
% 230.64/230.42 6805 -linordered_field(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),zero_zero(A)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,inverse_inverse(A),C)),hAPP(A,A,inverse_inverse(A),B))) # label(fact_2241_le__imp__inverse__le) # label(axiom). [clausify(2260)].
% 230.64/230.42 6806 -linordered_field(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),B),one_one(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),hAPP(A,A,inverse_inverse(A),B))) # label(fact_2243_one__less__inverse) # label(axiom). [clausify(2262)].
% 230.64/230.42 6807 -linordered_field(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),B),one_one(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),one_one(A)),hAPP(A,A,inverse_inverse(A),B))) # label(fact_2261_one__le__inverse) # label(axiom). [clausify(2280)].
% 230.64/230.42 6808 -linordered_field(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(A,A,inverse_inverse(A),hAPP(nat,A,semiring_1_of_nat(A),hAPP(nat,nat,fact_fact(nat),B))))) # label(fact_2661_inv__of__nat__fact__ge__zero) # label(axiom). [clausify(2655)].
% 230.64/230.42 6809 -linordered_field(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,inverse_inverse(A),hAPP(nat,A,semiring_1_of_nat(A),hAPP(nat,nat,fact_fact(nat),B))))) # label(fact_2662_inv__of__nat__fact__gt__zero) # label(axiom). [clausify(2656)].
% 230.64/230.42 6810 -linordered_field(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(A,A),fun(fun(B,A),fun(B,A)),combb(A,A,B),abs_abs(A)),C)),D) = hAPP(A,A,abs_abs(A),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),C),D)) # label(fact_3945_abs__setprod) # label(axiom). [clausify(3886)].
% 230.64/230.42 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),f80(rat,A,B))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),B)). [resolve(6751,a,6752,a)].
% 230.64/230.42 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),B),f80(rat,A,B)))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),B)). [resolve(6751,a,6753,a)].
% 230.64/230.42 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),C)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),C)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),B),C))). [resolve(6751,a,6758,a)].
% 230.64/230.42 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),C),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),B),C)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),C))). [resolve(6751,a,6759,a)].
% 230.64/230.42 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),B))). [resolve(6751,a,6761,a)].
% 230.64/230.42 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),B)),zero_zero(rat))). [resolve(6751,a,6762,a)].
% 230.64/230.42 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),C)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),C),D)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),D)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),B),C))). [resolve(6751,a,6763,a)].
% 230.64/230.43 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),C)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),C),D)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),D)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),B),C))). [resolve(6751,a,6764,a)].
% 230.64/230.43 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),C)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),C),D)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),D)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),B),C))). [resolve(6751,a,6765,a)].
% 230.64/230.43 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),B)),zero_zero(rat))). [resolve(6751,a,6766,a)].
% 230.64/230.43 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),B))). [resolve(6751,a,6767,a)].
% 230.64/230.43 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),C),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),C),A)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),C),B))). [resolve(6751,a,6768,a)].
% 230.64/230.43 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),C)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),B),A))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),C),B)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),C),A))). [resolve(6751,a,6769,a)].
% 230.64/230.43 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),B),A)),C)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),C),A)),B)). [resolve(6751,a,6770,a)].
% 230.64/230.43 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),B),A)),C)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),C),A)),B)). [resolve(6751,a,6771,a)].
% 230.64/230.43 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),C),A))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),C),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),B),A))). [resolve(6751,a,6772,a)].
% 230.71/230.45 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),C),A))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),C),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),B),A))). [resolve(6751,a,6773,a)].
% 230.71/230.45 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),B)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),one_one(rat)),one_one(rat)))),B)). [resolve(6751,a,6780,a)].
% 230.71/230.45 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),B)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),one_one(rat)),one_one(rat))))). [resolve(6751,a,6781,a)].
% 230.71/230.45 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),C)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),B),A))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),C),B)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),C),A))). [resolve(6751,a,6782,a)].
% 230.71/230.45 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),B),A)),C)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),C),A)),B)). [resolve(6751,a,6783,a)].
% 230.71/230.45 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),B),A)),C)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),C),A)),B)). [resolve(6751,a,6784,a)].
% 230.71/230.45 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),B),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),C),A))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),C),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),B),A))). [resolve(6751,a,6785,a)].
% 230.71/230.45 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),B),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),C),A))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),C),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),B),A))). [resolve(6751,a,6786,a)].
% 230.71/230.45 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,inverse_inverse(rat),A)),hAPP(rat,rat,inverse_inverse(rat),B))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),A)). [resolve(6751,a,6793,a)].
% 230.71/230.45 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,inverse_inverse(rat),A)),hAPP(rat,rat,inverse_inverse(rat),B))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),A)). [resolve(6751,a,6794,a)].
% 230.71/230.45 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,inverse_inverse(rat),B)),hAPP(rat,rat,inverse_inverse(rat),A))). [resolve(6751,a,6796,a)].
% 230.73/230.49 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,inverse_inverse(rat),B)),hAPP(rat,rat,inverse_inverse(rat),A))). [resolve(6751,a,6797,a)].
% 230.73/230.49 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,inverse_inverse(rat),A)),hAPP(rat,rat,inverse_inverse(rat),B))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),B),A)). [resolve(6751,a,6802,a)].
% 230.73/230.49 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,inverse_inverse(rat),A)),hAPP(rat,rat,inverse_inverse(rat),B))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),B),A)). [resolve(6751,a,6803,a)].
% 230.73/230.49 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,inverse_inverse(rat),B)),hAPP(rat,rat,inverse_inverse(rat),A))). [resolve(6751,a,6804,a)].
% 230.73/230.49 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,inverse_inverse(rat),B)),hAPP(rat,rat,inverse_inverse(rat),A))). [resolve(6751,a,6805,a)].
% 230.73/230.49 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),hAPP(rat,rat,inverse_inverse(rat),hAPP(nat,rat,semiring_1_of_nat(rat),hAPP(nat,nat,fact_fact(nat),A))))). [resolve(6751,a,6808,a)].
% 230.73/230.49 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(rat,rat,inverse_inverse(rat),hAPP(nat,rat,semiring_1_of_nat(rat),hAPP(nat,nat,fact_fact(nat),A))))). [resolve(6751,a,6809,a)].
% 230.73/230.49 Derived: hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co302546470etprod(A,rat),hAPP(fun(A,rat),fun(A,rat),hAPP(fun(rat,rat),fun(fun(A,rat),fun(A,rat)),combb(rat,rat,A),abs_abs(rat)),B)),C) = hAPP(rat,rat,abs_abs(rat),hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co302546470etprod(A,rat),B),C)). [resolve(6751,a,6810,a)].
% 230.73/230.49 6811 linordered_field(real) # label(arity_RealDef_Oreal___Fields_Olinordered__field) # label(axiom). [assumption].
% 230.73/230.49 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),f80(real,A,B))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),B)). [resolve(6811,a,6752,a)].
% 230.73/230.49 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),B),f80(real,A,B)))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),B)). [resolve(6811,a,6753,a)].
% 230.73/230.49 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),C)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),B),C))). [resolve(6811,a,6758,a)].
% 230.73/230.49 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),C),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),B),C)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),C))). [resolve(6811,a,6759,a)].
% 230.73/230.49 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B))). [resolve(6811,a,6761,a)].
% 230.73/230.50 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B)),zero_zero(real))). [resolve(6811,a,6762,a)].
% 230.73/230.50 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),C)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),C),D)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),D)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),B),C))). [resolve(6811,a,6763,a)].
% 230.73/230.50 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),C)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),C),D)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),D)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),B),C))). [resolve(6811,a,6764,a)].
% 230.73/230.50 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),C)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),C),D)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),D)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),B),C))). [resolve(6811,a,6765,a)].
% 230.73/230.50 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B)),zero_zero(real))). [resolve(6811,a,6766,a)].
% 230.73/230.50 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B))). [resolve(6811,a,6767,a)].
% 230.73/230.50 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),C),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),C),A)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),C),B))). [resolve(6811,a,6768,a)].
% 230.73/230.50 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),C)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),A))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),C),B)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),C),A))). [resolve(6811,a,6769,a)].
% 230.73/230.50 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),B),A)),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),A)),B)). [resolve(6811,a,6770,a)].
% 230.73/230.51 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),B),A)),C)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),A)),B)). [resolve(6811,a,6771,a)].
% 230.73/230.51 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),C),A))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),C),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),A))). [resolve(6811,a,6772,a)].
% 230.73/230.51 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),C),A))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),C),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),A))). [resolve(6811,a,6773,a)].
% 230.73/230.51 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),one_one(real)),one_one(real)))),B)). [resolve(6811,a,6780,a)].
% 230.73/230.51 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),one_one(real)),one_one(real))))). [resolve(6811,a,6781,a)].
% 230.73/230.51 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),C)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),A))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),C),B)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),C),A))). [resolve(6811,a,6782,a)].
% 230.73/230.51 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),B),A)),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),A)),B)). [resolve(6811,a,6783,a)].
% 230.73/230.51 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),B),A)),C)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),A)),B)). [resolve(6811,a,6784,a)].
% 230.73/230.51 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),C),A))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),C),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),A))). [resolve(6811,a,6785,a)].
% 230.73/230.51 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),C),A))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),C),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),A))). [resolve(6811,a,6786,a)].
% 235.32/235.08 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,inverse_inverse(real),A)),hAPP(real,real,inverse_inverse(real),B))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),A)). [resolve(6811,a,6793,a)].
% 235.32/235.08 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,inverse_inverse(real),A)),hAPP(real,real,inverse_inverse(real),B))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),A)). [resolve(6811,a,6794,a)].
% 235.32/235.08 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,inverse_inverse(real),B)),hAPP(real,real,inverse_inverse(real),A))). [resolve(6811,a,6796,a)].
% 235.32/235.08 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,inverse_inverse(real),B)),hAPP(real,real,inverse_inverse(real),A))). [resolve(6811,a,6797,a)].
% 235.32/235.08 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,inverse_inverse(real),A)),hAPP(real,real,inverse_inverse(real),B))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),A)). [resolve(6811,a,6802,a)].
% 235.32/235.08 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,inverse_inverse(real),A)),hAPP(real,real,inverse_inverse(real),B))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),A)). [resolve(6811,a,6803,a)].
% 235.32/235.08 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,inverse_inverse(real),B)),hAPP(real,real,inverse_inverse(real),A))). [resolve(6811,a,6804,a)].
% 235.32/235.08 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,inverse_inverse(real),B)),hAPP(real,real,inverse_inverse(real),A))). [resolve(6811,a,6805,a)].
% 235.32/235.08 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(real,real,inverse_inverse(real),hAPP(nat,real,semiring_1_of_nat(real),hAPP(nat,nat,fact_fact(nat),A))))). [resolve(6811,a,6808,a)].
% 235.32/235.08 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,inverse_inverse(real),hAPP(nat,real,semiring_1_of_nat(real),hAPP(nat,nat,fact_fact(nat),A))))). [resolve(6811,a,6809,a)].
% 235.32/235.08 Derived: hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co302546470etprod(A,real),hAPP(fun(A,real),fun(A,real),hAPP(fun(real,real),fun(fun(A,real),fun(A,real)),combb(real,real,A),abs_abs(real)),B)),C) = hAPP(real,real,abs_abs(real),hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co302546470etprod(A,real),B),C)). [resolve(6811,a,6810,a)].
% 235.32/235.08 6812 ring_div(int) # label(arity_Int_Oint___Divides_Oring__div) # label(axiom). [assumption].
% 235.32/235.08 6813 -ring_div(A) | hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),B),C) != hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),D),C) | hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),hAPP(A,A,uminus_uminus(A),B)),C) = hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),hAPP(A,A,uminus_uminus(A),D)),C) # label(fact_466_mod__minus__cong) # label(axiom). [clausify(591)].
% 235.32/235.09 6814 -ring_div(A) | hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),hAPP(A,A,uminus_uminus(A),hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),B),C))),C) = hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),hAPP(A,A,uminus_uminus(A),B)),C) # label(fact_470_mod__minus__eq) # label(axiom). [clausify(595)].
% 235.32/235.09 6815 -ring_div(A) | hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),B),C) != hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),D),C) | hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),E),C) != hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),F),C) | hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),E)),C) = hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),D),F)),C) # label(fact_544_mod__diff__cong) # label(axiom). [clausify(668)].
% 235.32/235.09 6816 -ring_div(A) | hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),D),C))),C) = hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),D)),C) # label(fact_545_mod__diff__eq) # label(axiom). [clausify(669)].
% 235.32/235.09 6817 -ring_div(A) | hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),B),C)),D)),C) = hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),D)),C) # label(fact_546_mod__diff__left__eq) # label(axiom). [clausify(670)].
% 235.32/235.09 6818 -ring_div(A) | hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),C),D))),D) = hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C)),D) # label(fact_547_mod__diff__right__eq) # label(axiom). [clausify(671)].
% 235.32/235.09 6819 -ring_div(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),C)) | hAPP(A,A,hAPP(A,fun(A,A),div_div(A),hAPP(A,A,uminus_uminus(A),C)),B) = hAPP(A,A,uminus_uminus(A),hAPP(A,A,hAPP(A,fun(A,A),div_div(A),C),B)) # label(fact_3137_dvd__neg__div) # label(axiom). [clausify(3104)].
% 235.32/235.09 6820 -ring_div(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),C)) | hAPP(A,A,hAPP(A,fun(A,A),div_div(A),C),hAPP(A,A,uminus_uminus(A),B)) = hAPP(A,A,uminus_uminus(A),hAPP(A,A,hAPP(A,fun(A,A),div_div(A),C),B)) # label(fact_3138_dvd__div__neg) # label(axiom). [clausify(3105)].
% 235.32/235.09 Derived: hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A),B) != hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),C),B) | hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,uminus_uminus(int),A)),B) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,uminus_uminus(int),C)),B). [resolve(6812,a,6813,a)].
% 235.32/235.09 Derived: hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,uminus_uminus(int),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A),B))),B) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,uminus_uminus(int),A)),B). [resolve(6812,a,6814,a)].
% 235.32/235.09 Derived: hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A),B) != hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),C),B) | hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),D),B) != hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),E),B) | hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),D)),B) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),C),E)),B). [resolve(6812,a,6815,a)].
% 235.32/235.09 Derived: hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),C),B))),B) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),C)),B). [resolve(6812,a,6816,a)].
% 235.32/235.09 Derived: hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A),B)),C)),B) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),C)),B). [resolve(6812,a,6817,a)].
% 235.32/235.09 Derived: hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),B),C))),C) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),B)),C). [resolve(6812,a,6818,a)].
% 239.80/239.56 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),B)) | hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,uminus_uminus(int),B)),A) = hAPP(int,int,uminus_uminus(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),B),A)). [resolve(6812,a,6819,a)].
% 239.80/239.56 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),B)) | hAPP(int,int,hAPP(int,fun(int,int),div_div(int),B),hAPP(int,int,uminus_uminus(int),A)) = hAPP(int,int,uminus_uminus(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),B),A)). [resolve(6812,a,6820,a)].
% 239.80/239.56 6821 idom(int) # label(arity_Int_Oint___Rings_Oidom) # label(axiom). [assumption].
% 239.80/239.56 6822 -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_572_square__eq__iff) # label(axiom). [clausify(696)].
% 239.80/239.56 6823 -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_572_square__eq__iff) # label(axiom). [clausify(696)].
% 239.80/239.56 6824 -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_572_square__eq__iff) # label(axiom). [clausify(696)].
% 239.80/239.56 6825 -idom(A) | hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat)))) != hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),C),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat)))) | ti(A,B) = ti(A,C) | hAPP(A,A,uminus_uminus(A),B) = ti(A,C) # label(fact_1394_realpow__two__disj) # label(axiom). [clausify(1497)].
% 239.80/239.56 6826 -idom(A) | hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat)))) = hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),C),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat)))) | ti(A,B) != ti(A,C) # label(fact_1394_realpow__two__disj) # label(axiom). [clausify(1497)].
% 239.80/239.56 6827 -idom(A) | hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat)))) = hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),C),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat)))) | hAPP(A,A,uminus_uminus(A),B) != ti(A,C) # label(fact_1394_realpow__two__disj) # label(axiom). [clausify(1497)].
% 239.80/239.56 6828 -idom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(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))) | zero_zero(A) = ti(A,B) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),C),D)) # label(fact_3123_dvd__mult__cancel__left) # label(axiom). [clausify(3090)].
% 239.80/239.56 6829 -idom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(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))) | zero_zero(A) != ti(A,B) # label(fact_3123_dvd__mult__cancel__left) # label(axiom). [clausify(3090)].
% 239.80/239.56 6830 -idom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(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),dvd_dvd(A),C),D)) # label(fact_3123_dvd__mult__cancel__left) # label(axiom). [clausify(3090)].
% 239.80/239.56 6831 -idom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(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))) | zero_zero(A) = ti(A,C) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),D)) # label(fact_3124_dvd__mult__cancel__right) # label(axiom). [clausify(3091)].
% 239.80/239.56 6832 -idom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(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))) | zero_zero(A) != ti(A,C) # label(fact_3124_dvd__mult__cancel__right) # label(axiom). [clausify(3091)].
% 239.80/239.56 6833 -idom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(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),dvd_dvd(A),B),D)) # label(fact_3124_dvd__mult__cancel__right) # label(axiom). [clausify(3091)].
% 239.80/239.59 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(6821,a,6822,a)].
% 239.80/239.59 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(6821,a,6823,a)].
% 239.80/239.59 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(6821,a,6824,a)].
% 239.80/239.59 Derived: hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat)))) != hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),B),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat)))) | ti(int,A) = ti(int,B) | hAPP(int,int,uminus_uminus(int),A) = ti(int,B). [resolve(6821,a,6825,a)].
% 239.80/239.59 Derived: hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat)))) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),B),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat)))) | ti(int,A) != ti(int,B). [resolve(6821,a,6826,a)].
% 239.80/239.59 Derived: hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat)))) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),B),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat)))) | hAPP(int,int,uminus_uminus(int),A) != ti(int,B). [resolve(6821,a,6827,a)].
% 239.80/239.59 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(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))) | zero_zero(int) = ti(int,A) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),B),C)). [resolve(6821,a,6828,a)].
% 239.80/239.59 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(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))) | zero_zero(int) != ti(int,A). [resolve(6821,a,6829,a)].
% 239.80/239.59 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(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),dvd_dvd(int),B),C)). [resolve(6821,a,6830,a)].
% 239.80/239.59 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(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))) | zero_zero(int) = ti(int,B) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),C)). [resolve(6821,a,6831,a)].
% 239.80/239.59 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(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))) | zero_zero(int) != ti(int,B). [resolve(6821,a,6832,a)].
% 239.80/239.59 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(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),dvd_dvd(int),A),C)). [resolve(6821,a,6833,a)].
% 239.80/239.59 6834 idom(rat) # label(arity_Rat_Orat___Rings_Oidom) # label(axiom). [assumption].
% 239.80/239.59 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),A) != hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),B),B) | ti(rat,A) = ti(rat,B) | hAPP(rat,rat,uminus_uminus(rat),A) = ti(rat,B). [resolve(6834,a,6822,a)].
% 239.80/239.59 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),A) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),B),B) | ti(rat,A) != ti(rat,B). [resolve(6834,a,6823,a)].
% 239.80/239.59 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),A) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),B),B) | hAPP(rat,rat,uminus_uminus(rat),A) != ti(rat,B). [resolve(6834,a,6824,a)].
% 239.80/239.59 Derived: hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat)))) != hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),B),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat)))) | ti(rat,A) = ti(rat,B) | hAPP(rat,rat,uminus_uminus(rat),A) = ti(rat,B). [resolve(6834,a,6825,a)].
% 239.87/239.62 Derived: hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat)))) = hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),B),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat)))) | ti(rat,A) != ti(rat,B). [resolve(6834,a,6826,a)].
% 239.87/239.62 Derived: hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat)))) = hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),B),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat)))) | hAPP(rat,rat,uminus_uminus(rat),A) != ti(rat,B). [resolve(6834,a,6827,a)].
% 239.87/239.62 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),dvd_dvd(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),C))) | zero_zero(rat) = ti(rat,A) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),dvd_dvd(rat),B),C)). [resolve(6834,a,6828,a)].
% 239.87/239.62 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),dvd_dvd(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),C))) | zero_zero(rat) != ti(rat,A). [resolve(6834,a,6829,a)].
% 239.87/239.62 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),dvd_dvd(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),C))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),dvd_dvd(rat),B),C)). [resolve(6834,a,6830,a)].
% 239.87/239.62 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),dvd_dvd(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),C),B))) | zero_zero(rat) = ti(rat,B) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),dvd_dvd(rat),A),C)). [resolve(6834,a,6831,a)].
% 239.87/239.62 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),dvd_dvd(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),C),B))) | zero_zero(rat) != ti(rat,B). [resolve(6834,a,6832,a)].
% 239.87/239.62 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),dvd_dvd(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),C),B))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),dvd_dvd(rat),A),C)). [resolve(6834,a,6833,a)].
% 239.87/239.62 6835 idom(real) # label(arity_RealDef_Oreal___Rings_Oidom) # label(axiom). [assumption].
% 239.87/239.62 Derived: hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),A) != hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),B) | ti(real,A) = ti(real,B) | hAPP(real,real,uminus_uminus(real),A) = ti(real,B). [resolve(6835,a,6822,a)].
% 239.87/239.62 Derived: hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),A) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),B) | ti(real,A) != ti(real,B). [resolve(6835,a,6823,a)].
% 239.87/239.62 Derived: hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),A) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),B) | hAPP(real,real,uminus_uminus(real),A) != ti(real,B). [resolve(6835,a,6824,a)].
% 239.87/239.62 Derived: hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat)))) != hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),B),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat)))) | ti(real,A) = ti(real,B) | hAPP(real,real,uminus_uminus(real),A) = ti(real,B). [resolve(6835,a,6825,a)].
% 239.87/239.62 Derived: hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat)))) = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),B),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat)))) | ti(real,A) != ti(real,B). [resolve(6835,a,6826,a)].
% 239.87/239.62 Derived: hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat)))) = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),B),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat)))) | hAPP(real,real,uminus_uminus(real),A) != ti(real,B). [resolve(6835,a,6827,a)].
% 239.87/239.64 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),dvd_dvd(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),C))) | zero_zero(real) = ti(real,A) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),dvd_dvd(real),B),C)). [resolve(6835,a,6828,a)].
% 239.87/239.64 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),dvd_dvd(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),C))) | zero_zero(real) != ti(real,A). [resolve(6835,a,6829,a)].
% 239.87/239.64 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),dvd_dvd(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),C))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),dvd_dvd(real),B),C)). [resolve(6835,a,6830,a)].
% 239.87/239.64 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),dvd_dvd(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),B))) | zero_zero(real) = ti(real,B) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),dvd_dvd(real),A),C)). [resolve(6835,a,6831,a)].
% 239.87/239.64 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),dvd_dvd(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),B))) | zero_zero(real) != ti(real,B). [resolve(6835,a,6832,a)].
% 239.87/239.64 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),dvd_dvd(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),B))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),dvd_dvd(real),A),C)). [resolve(6835,a,6833,a)].
% 239.87/239.64 6836 idom(complex) # label(arity_Complex_Ocomplex___Rings_Oidom) # label(axiom). [assumption].
% 239.87/239.64 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),A) != hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),B),B) | ti(complex,A) = ti(complex,B) | hAPP(complex,complex,uminus_uminus(complex),A) = ti(complex,B). [resolve(6836,a,6822,a)].
% 239.87/239.64 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),A) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),B),B) | ti(complex,A) != ti(complex,B). [resolve(6836,a,6823,a)].
% 239.87/239.64 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),A) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),B),B) | hAPP(complex,complex,uminus_uminus(complex),A) != ti(complex,B). [resolve(6836,a,6824,a)].
% 239.87/239.64 Derived: hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),A),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat)))) != hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),B),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat)))) | ti(complex,A) = ti(complex,B) | hAPP(complex,complex,uminus_uminus(complex),A) = ti(complex,B). [resolve(6836,a,6825,a)].
% 239.87/239.64 Derived: hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),A),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat)))) = hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),B),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat)))) | ti(complex,A) != ti(complex,B). [resolve(6836,a,6826,a)].
% 239.87/239.64 Derived: hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),A),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat)))) = hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),B),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat)))) | hAPP(complex,complex,uminus_uminus(complex),A) != ti(complex,B). [resolve(6836,a,6827,a)].
% 239.87/239.64 Derived: -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),dvd_dvd(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),B)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),C))) | zero_zero(complex) = ti(complex,A) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),dvd_dvd(complex),B),C)). [resolve(6836,a,6828,a)].
% 244.42/244.16 Derived: hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),dvd_dvd(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),B)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),C))) | zero_zero(complex) != ti(complex,A). [resolve(6836,a,6829,a)].
% 244.42/244.16 Derived: hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),dvd_dvd(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),B)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),C))) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),dvd_dvd(complex),B),C)). [resolve(6836,a,6830,a)].
% 244.42/244.16 Derived: -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),dvd_dvd(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),B)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),C),B))) | zero_zero(complex) = ti(complex,B) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),dvd_dvd(complex),A),C)). [resolve(6836,a,6831,a)].
% 244.42/244.16 Derived: hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),dvd_dvd(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),B)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),C),B))) | zero_zero(complex) != ti(complex,B). [resolve(6836,a,6832,a)].
% 244.42/244.16 Derived: hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),dvd_dvd(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),B)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),C),B))) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),dvd_dvd(complex),A),C)). [resolve(6836,a,6833,a)].
% 244.42/244.16 6837 ring_11004092258visors(int) # label(arity_Int_Oint___Rings_Oring__1__no__zero__divisors) # label(axiom). [assumption].
% 244.42/244.16 6838 -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_642_square__eq__1__iff) # label(axiom). [clausify(763)].
% 244.42/244.16 6839 -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_642_square__eq__1__iff) # label(axiom). [clausify(763)].
% 244.42/244.16 6840 -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_642_square__eq__1__iff) # label(axiom). [clausify(763)].
% 244.42/244.16 6841 -ring_11004092258visors(A) | zero_zero(A) = ti(A,B) | hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C) != zero_zero(A) # label(fact_1432_field__power__not__zero) # label(axiom). [clausify(1535)].
% 244.42/244.16 6842 -ring_11004092258visors(A) | hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) != zero_zero(A) | zero_zero(A) = ti(A,B) # label(fact_1811_zero__eq__power2) # label(axiom). [clausify(1872)].
% 244.42/244.16 6843 -ring_11004092258visors(A) | hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = zero_zero(A) | zero_zero(A) != ti(A,B) # label(fact_1811_zero__eq__power2) # label(axiom). [clausify(1872)].
% 244.42/244.16 6844 -ring_11004092258visors(A) | hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) != one_one(A) | one_one(A) = ti(A,B) | hAPP(A,A,uminus_uminus(A),one_one(A)) = ti(A,B) # label(fact_1854_power2__eq__1__iff) # label(axiom). [clausify(1905)].
% 244.42/244.16 6845 -ring_11004092258visors(A) | hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = one_one(A) | one_one(A) != ti(A,B) # label(fact_1854_power2__eq__1__iff) # label(axiom). [clausify(1905)].
% 244.42/244.16 6846 -ring_11004092258visors(A) | hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = one_one(A) | hAPP(A,A,uminus_uminus(A),one_one(A)) != ti(A,B) # label(fact_1854_power2__eq__1__iff) # label(axiom). [clausify(1905)].
% 244.42/244.21 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(6837,a,6838,a)].
% 244.42/244.21 Derived: hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),A) = one_one(int) | one_one(int) != ti(int,A). [resolve(6837,a,6839,a)].
% 244.42/244.21 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(6837,a,6840,a)].
% 244.42/244.21 Derived: zero_zero(int) = ti(int,A) | hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),B) != zero_zero(int). [resolve(6837,a,6841,a)].
% 244.42/244.21 Derived: hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = zero_zero(int) | zero_zero(int) != ti(int,A). [resolve(6837,a,6843,a)].
% 244.42/244.21 Derived: hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) != one_one(int) | one_one(int) = ti(int,A) | hAPP(int,int,uminus_uminus(int),one_one(int)) = ti(int,A). [resolve(6837,a,6844,a)].
% 244.42/244.21 Derived: hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = one_one(int) | one_one(int) != ti(int,A). [resolve(6837,a,6845,a)].
% 244.42/244.21 Derived: hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = one_one(int) | hAPP(int,int,uminus_uminus(int),one_one(int)) != ti(int,A). [resolve(6837,a,6846,a)].
% 244.42/244.21 6847 ring_11004092258visors(rat) # label(arity_Rat_Orat___Rings_Oring__1__no__zero__divisors) # label(axiom). [assumption].
% 244.42/244.21 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),A) != one_one(rat) | one_one(rat) = ti(rat,A) | hAPP(rat,rat,uminus_uminus(rat),one_one(rat)) = ti(rat,A). [resolve(6847,a,6838,a)].
% 244.42/244.21 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),A) = one_one(rat) | one_one(rat) != ti(rat,A). [resolve(6847,a,6839,a)].
% 244.42/244.21 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),A) = one_one(rat) | hAPP(rat,rat,uminus_uminus(rat),one_one(rat)) != ti(rat,A). [resolve(6847,a,6840,a)].
% 244.42/244.21 Derived: zero_zero(rat) = ti(rat,A) | hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),B) != zero_zero(rat). [resolve(6847,a,6841,a)].
% 244.42/244.21 Derived: hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = zero_zero(rat) | zero_zero(rat) != ti(rat,A). [resolve(6847,a,6843,a)].
% 244.42/244.21 Derived: hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) != one_one(rat) | one_one(rat) = ti(rat,A) | hAPP(rat,rat,uminus_uminus(rat),one_one(rat)) = ti(rat,A). [resolve(6847,a,6844,a)].
% 244.42/244.21 Derived: hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = one_one(rat) | one_one(rat) != ti(rat,A). [resolve(6847,a,6845,a)].
% 244.42/244.21 Derived: hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = one_one(rat) | hAPP(rat,rat,uminus_uminus(rat),one_one(rat)) != ti(rat,A). [resolve(6847,a,6846,a)].
% 244.42/244.21 6848 ring_11004092258visors(real) # label(arity_RealDef_Oreal___Rings_Oring__1__no__zero__divisors) # label(axiom). [assumption].
% 244.42/244.21 Derived: hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),A) != one_one(real) | one_one(real) = ti(real,A) | hAPP(real,real,uminus_uminus(real),one_one(real)) = ti(real,A). [resolve(6848,a,6838,a)].
% 244.42/244.21 Derived: hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),A) = one_one(real) | one_one(real) != ti(real,A). [resolve(6848,a,6839,a)].
% 244.42/244.21 Derived: hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),A) = one_one(real) | hAPP(real,real,uminus_uminus(real),one_one(real)) != ti(real,A). [resolve(6848,a,6840,a)].
% 249.01/248.80 Derived: zero_zero(real) = ti(real,A) | hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),B) != zero_zero(real). [resolve(6848,a,6841,a)].
% 249.01/248.80 Derived: hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = zero_zero(real) | zero_zero(real) != ti(real,A). [resolve(6848,a,6843,a)].
% 249.01/248.80 Derived: hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) != one_one(real) | one_one(real) = ti(real,A) | hAPP(real,real,uminus_uminus(real),one_one(real)) = ti(real,A). [resolve(6848,a,6844,a)].
% 249.01/248.80 Derived: hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = one_one(real) | one_one(real) != ti(real,A). [resolve(6848,a,6845,a)].
% 249.01/248.80 Derived: hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = one_one(real) | hAPP(real,real,uminus_uminus(real),one_one(real)) != ti(real,A). [resolve(6848,a,6846,a)].
% 249.01/248.80 6849 ring_11004092258visors(complex) # label(arity_Complex_Ocomplex___Rings_Oring__1__no__zero__divisors) # label(axiom). [assumption].
% 249.01/248.80 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),A) != one_one(complex) | one_one(complex) = ti(complex,A) | hAPP(complex,complex,uminus_uminus(complex),one_one(complex)) = ti(complex,A). [resolve(6849,a,6838,a)].
% 249.01/248.80 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),A) = one_one(complex) | one_one(complex) != ti(complex,A). [resolve(6849,a,6839,a)].
% 249.01/248.80 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),A) = one_one(complex) | hAPP(complex,complex,uminus_uminus(complex),one_one(complex)) != ti(complex,A). [resolve(6849,a,6840,a)].
% 249.01/248.80 Derived: zero_zero(complex) = ti(complex,A) | hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),A),B) != zero_zero(complex). [resolve(6849,a,6841,a)].
% 249.01/248.80 Derived: hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = zero_zero(complex) | zero_zero(complex) != ti(complex,A). [resolve(6849,a,6843,a)].
% 249.01/248.80 Derived: hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) != one_one(complex) | one_one(complex) = ti(complex,A) | hAPP(complex,complex,uminus_uminus(complex),one_one(complex)) = ti(complex,A). [resolve(6849,a,6844,a)].
% 249.01/248.80 Derived: hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = one_one(complex) | one_one(complex) != ti(complex,A). [resolve(6849,a,6845,a)].
% 249.01/248.80 Derived: hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = one_one(complex) | hAPP(complex,complex,uminus_uminus(complex),one_one(complex)) != ti(complex,A). [resolve(6849,a,6846,a)].
% 249.01/248.80 6850 ordered_ring_abs(int) # label(arity_Int_Oint___Rings_Oordered__ring__abs) # label(axiom). [assumption].
% 249.01/248.80 6851 -ordered_ring_abs(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),C)) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,abs_abs(A),B)),hAPP(A,A,abs_abs(A),C)) = hAPP(A,A,abs_abs(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)) # label(fact_659_abs__eq__mult) # label(axiom). [clausify(779)].
% 249.01/248.80 6852 -ordered_ring_abs(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),zero_zero(A))) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,abs_abs(A),B)),hAPP(A,A,abs_abs(A),C)) = hAPP(A,A,abs_abs(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)) # label(fact_659_abs__eq__mult) # label(axiom). [clausify(779)].
% 253.65/253.40 6853 -ordered_ring_abs(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),C)) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,abs_abs(A),B)),hAPP(A,A,abs_abs(A),C)) = hAPP(A,A,abs_abs(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)) # label(fact_659_abs__eq__mult) # label(axiom). [clausify(779)].
% 253.65/253.40 6854 -ordered_ring_abs(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),zero_zero(A))) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,abs_abs(A),B)),hAPP(A,A,abs_abs(A),C)) = hAPP(A,A,abs_abs(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)) # label(fact_659_abs__eq__mult) # label(axiom). [clausify(779)].
% 253.65/253.40 6855 ordered_ring_abs(rat) # label(arity_Rat_Orat___Rings_Oordered__ring__abs) # label(axiom). [assumption].
% 253.65/253.40 6856 ordered_ring_abs(real) # label(arity_RealDef_Oreal___Rings_Oordered__ring__abs) # label(axiom). [assumption].
% 253.65/253.40 6857 divisi14063676e_zero(rat) # label(arity_Rat_Orat___Fields_Odivision__ring__inverse__zero) # label(axiom). [assumption].
% 253.65/253.40 6858 -divisi14063676e_zero(A) | hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),zero_zero(A)) = zero_zero(A) # label(fact_1072_divide__zero) # label(axiom). [clausify(1183)].
% 253.65/253.40 6859 -divisi14063676e_zero(A) | zero_zero(A) != ti(A,B) | hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),B) = zero_zero(A) # label(fact_1113_divide__self__if) # label(axiom). [clausify(1224)].
% 253.65/253.40 6860 -divisi14063676e_zero(A) | zero_zero(A) = ti(A,B) | hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),B) = one_one(A) # label(fact_1113_divide__self__if) # label(axiom). [clausify(1224)].
% 253.65/253.40 6861 -divisi14063676e_zero(A) | hAPP(A,A,inverse_inverse(A),B) != zero_zero(A) | zero_zero(A) = ti(A,B) # label(fact_2175_inverse__nonzero__iff__nonzero) # label(axiom). [clausify(2196)].
% 253.65/253.40 6862 -divisi14063676e_zero(A) | hAPP(A,A,inverse_inverse(A),B) = zero_zero(A) | zero_zero(A) != ti(A,B) # label(fact_2175_inverse__nonzero__iff__nonzero) # label(axiom). [clausify(2196)].
% 253.65/253.40 6863 -divisi14063676e_zero(A) | hAPP(A,A,inverse_inverse(A),zero_zero(A)) = zero_zero(A) # label(fact_2176_inverse__zero) # label(axiom). [clausify(2197)].
% 253.65/253.40 6864 -divisi14063676e_zero(A) | hAPP(A,A,inverse_inverse(A),hAPP(A,A,inverse_inverse(A),B)) = ti(A,B) # label(fact_2183_inverse__inverse__eq) # label(axiom). [clausify(2203)].
% 253.65/253.40 6865 -divisi14063676e_zero(A) | hAPP(A,A,inverse_inverse(A),B) != hAPP(A,A,inverse_inverse(A),C) | ti(A,B) = ti(A,C) # label(fact_2184_inverse__eq__iff__eq) # label(axiom). [clausify(2204)].
% 253.65/253.40 6866 -divisi14063676e_zero(A) | hAPP(A,A,inverse_inverse(A),B) = hAPP(A,A,inverse_inverse(A),C) | ti(A,B) != ti(A,C) # label(fact_2184_inverse__eq__iff__eq) # label(axiom). [clausify(2204)].
% 253.65/253.40 6867 -divisi14063676e_zero(A) | hAPP(A,A,inverse_inverse(A),B) != hAPP(A,A,inverse_inverse(A),C) | ti(A,B) = ti(A,C) # label(fact_2185_inverse__eq__imp__eq) # label(axiom). [clausify(2205)].
% 253.65/253.40 6868 -divisi14063676e_zero(A) | hAPP(A,A,uminus_uminus(A),hAPP(A,A,inverse_inverse(A),B)) = hAPP(A,A,inverse_inverse(A),hAPP(A,A,uminus_uminus(A),B)) # label(fact_2193_inverse__minus__eq) # label(axiom). [clausify(2212)].
% 253.65/253.40 6869 -divisi14063676e_zero(A) | hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),hAPP(A,A,inverse_inverse(A),B)),C) = hAPP(A,A,inverse_inverse(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C)) # label(fact_2194_power__inverse) # label(axiom). [clausify(2213)].
% 253.65/253.40 6870 -divisi14063676e_zero(A) | -real_n1866405975lgebra(A) | hAPP(real,real,inverse_inverse(real),hAPP(A,real,norm_norm(A),B)) = hAPP(A,real,norm_norm(A),hAPP(A,A,inverse_inverse(A),B)) # label(fact_2706_norm__inverse) # label(axiom). [clausify(2698)].
% 253.65/253.40 6871 -divisi14063676e_zero(A) | -real_div_algebra(A) | hAPP(real,A,of_real(A),hAPP(real,real,inverse_inverse(real),B)) = hAPP(A,A,inverse_inverse(A),hAPP(real,A,of_real(A),B)) # label(fact_2804_of__real__inverse) # label(axiom). [clausify(2789)].
% 253.69/253.43 6872 -divisi14063676e_zero(A) | -real_div_algebra(A) | hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),hAPP(real,real,inverse_inverse(real),B)),hAPP(A,A,inverse_inverse(A),C)) = hAPP(A,A,inverse_inverse(A),hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),B),C)) # label(fact_4724_inverse__scaleR__distrib) # label(axiom). [clausify(4650)].
% 253.69/253.43 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),zero_zero(rat)) = zero_zero(rat). [resolve(6857,a,6858,a)].
% 253.69/253.43 Derived: zero_zero(rat) != ti(rat,A) | hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),A) = zero_zero(rat). [resolve(6857,a,6859,a)].
% 253.69/253.43 Derived: hAPP(rat,rat,inverse_inverse(rat),A) = zero_zero(rat) | zero_zero(rat) != ti(rat,A). [resolve(6857,a,6862,a)].
% 253.69/253.43 Derived: hAPP(rat,rat,inverse_inverse(rat),zero_zero(rat)) = zero_zero(rat). [resolve(6857,a,6863,a)].
% 253.69/253.43 Derived: hAPP(rat,rat,inverse_inverse(rat),hAPP(rat,rat,inverse_inverse(rat),A)) = ti(rat,A). [resolve(6857,a,6864,a)].
% 253.69/253.43 Derived: hAPP(rat,rat,inverse_inverse(rat),A) != hAPP(rat,rat,inverse_inverse(rat),B) | ti(rat,A) = ti(rat,B). [resolve(6857,a,6865,a)].
% 253.69/253.43 Derived: hAPP(rat,rat,inverse_inverse(rat),A) = hAPP(rat,rat,inverse_inverse(rat),B) | ti(rat,A) != ti(rat,B). [resolve(6857,a,6866,a)].
% 253.69/253.43 Derived: hAPP(rat,rat,uminus_uminus(rat),hAPP(rat,rat,inverse_inverse(rat),A)) = hAPP(rat,rat,inverse_inverse(rat),hAPP(rat,rat,uminus_uminus(rat),A)). [resolve(6857,a,6868,a)].
% 253.69/253.43 Derived: hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),hAPP(rat,rat,inverse_inverse(rat),A)),B) = hAPP(rat,rat,inverse_inverse(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),B)). [resolve(6857,a,6869,a)].
% 253.69/253.43 Derived: -real_n1866405975lgebra(rat) | hAPP(real,real,inverse_inverse(real),hAPP(rat,real,norm_norm(rat),A)) = hAPP(rat,real,norm_norm(rat),hAPP(rat,rat,inverse_inverse(rat),A)). [resolve(6857,a,6870,a)].
% 253.69/253.43 Derived: -real_div_algebra(rat) | hAPP(real,rat,of_real(rat),hAPP(real,real,inverse_inverse(real),A)) = hAPP(rat,rat,inverse_inverse(rat),hAPP(real,rat,of_real(rat),A)). [resolve(6857,a,6871,a)].
% 253.69/253.43 Derived: -real_div_algebra(rat) | hAPP(rat,rat,hAPP(real,fun(rat,rat),scaleR_scaleR(rat),hAPP(real,real,inverse_inverse(real),A)),hAPP(rat,rat,inverse_inverse(rat),B)) = hAPP(rat,rat,inverse_inverse(rat),hAPP(rat,rat,hAPP(real,fun(rat,rat),scaleR_scaleR(rat),A),B)). [resolve(6857,a,6872,a)].
% 253.69/253.43 6873 divisi14063676e_zero(real) # label(arity_RealDef_Oreal___Fields_Odivision__ring__inverse__zero) # label(axiom). [assumption].
% 253.69/253.43 Derived: hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),zero_zero(real)) = zero_zero(real). [resolve(6873,a,6858,a)].
% 253.69/253.43 Derived: zero_zero(real) != ti(real,A) | hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),A) = zero_zero(real). [resolve(6873,a,6859,a)].
% 253.69/253.43 Derived: hAPP(real,real,inverse_inverse(real),A) = zero_zero(real) | zero_zero(real) != ti(real,A). [resolve(6873,a,6862,a)].
% 253.69/253.43 Derived: hAPP(real,real,inverse_inverse(real),zero_zero(real)) = zero_zero(real). [resolve(6873,a,6863,a)].
% 253.69/253.43 Derived: hAPP(real,real,inverse_inverse(real),hAPP(real,real,inverse_inverse(real),A)) = ti(real,A). [resolve(6873,a,6864,a)].
% 253.69/253.43 Derived: hAPP(real,real,inverse_inverse(real),A) != hAPP(real,real,inverse_inverse(real),B) | ti(real,A) = ti(real,B). [resolve(6873,a,6865,a)].
% 253.69/253.43 Derived: hAPP(real,real,inverse_inverse(real),A) = hAPP(real,real,inverse_inverse(real),B) | ti(real,A) != ti(real,B). [resolve(6873,a,6866,a)].
% 253.69/253.43 Derived: hAPP(real,real,uminus_uminus(real),hAPP(real,real,inverse_inverse(real),A)) = hAPP(real,real,inverse_inverse(real),hAPP(real,real,uminus_uminus(real),A)). [resolve(6873,a,6868,a)].
% 253.69/253.43 Derived: hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,inverse_inverse(real),A)),B) = hAPP(real,real,inverse_inverse(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),B)). [resolve(6873,a,6869,a)].
% 253.69/253.43 Derived: -real_n1866405975lgebra(real) | hAPP(real,real,inverse_inverse(real),hAPP(real,real,norm_norm(real),A)) = hAPP(real,real,norm_norm(real),hAPP(real,real,inverse_inverse(real),A)). [resolve(6873,a,6870,a)].
% 253.69/253.43 Derived: -real_div_algebra(real) | hAPP(real,real,of_real(real),hAPP(real,real,inverse_inverse(real),A)) = hAPP(real,real,inverse_inverse(real),hAPP(real,real,of_real(real),A)). [resolve(6873,a,6871,a)].
% 258.33/258.08 Derived: -real_div_algebra(real) | hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),hAPP(real,real,inverse_inverse(real),A)),hAPP(real,real,inverse_inverse(real),B)) = hAPP(real,real,inverse_inverse(real),hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),A),B)). [resolve(6873,a,6872,a)].
% 258.33/258.08 6874 divisi14063676e_zero(complex) # label(arity_Complex_Ocomplex___Fields_Odivision__ring__inverse__zero) # label(axiom). [assumption].
% 258.33/258.08 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),A),zero_zero(complex)) = zero_zero(complex). [resolve(6874,a,6858,a)].
% 258.33/258.08 Derived: zero_zero(complex) != ti(complex,A) | hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),A),A) = zero_zero(complex). [resolve(6874,a,6859,a)].
% 258.33/258.08 Derived: hAPP(complex,complex,inverse_inverse(complex),A) = zero_zero(complex) | zero_zero(complex) != ti(complex,A). [resolve(6874,a,6862,a)].
% 258.33/258.08 Derived: hAPP(complex,complex,inverse_inverse(complex),zero_zero(complex)) = zero_zero(complex). [resolve(6874,a,6863,a)].
% 258.33/258.08 Derived: hAPP(complex,complex,inverse_inverse(complex),hAPP(complex,complex,inverse_inverse(complex),A)) = ti(complex,A). [resolve(6874,a,6864,a)].
% 258.33/258.08 Derived: hAPP(complex,complex,inverse_inverse(complex),A) != hAPP(complex,complex,inverse_inverse(complex),B) | ti(complex,A) = ti(complex,B). [resolve(6874,a,6865,a)].
% 258.33/258.08 Derived: hAPP(complex,complex,inverse_inverse(complex),A) = hAPP(complex,complex,inverse_inverse(complex),B) | ti(complex,A) != ti(complex,B). [resolve(6874,a,6866,a)].
% 258.33/258.08 Derived: hAPP(complex,complex,uminus_uminus(complex),hAPP(complex,complex,inverse_inverse(complex),A)) = hAPP(complex,complex,inverse_inverse(complex),hAPP(complex,complex,uminus_uminus(complex),A)). [resolve(6874,a,6868,a)].
% 258.33/258.08 Derived: hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),hAPP(complex,complex,inverse_inverse(complex),A)),B) = hAPP(complex,complex,inverse_inverse(complex),hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),A),B)). [resolve(6874,a,6869,a)].
% 258.33/258.08 Derived: -real_n1866405975lgebra(complex) | hAPP(real,real,inverse_inverse(real),hAPP(complex,real,norm_norm(complex),A)) = hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,inverse_inverse(complex),A)). [resolve(6874,a,6870,a)].
% 258.33/258.08 Derived: -real_div_algebra(complex) | hAPP(real,complex,of_real(complex),hAPP(real,real,inverse_inverse(real),A)) = hAPP(complex,complex,inverse_inverse(complex),hAPP(real,complex,of_real(complex),A)). [resolve(6874,a,6871,a)].
% 258.33/258.08 Derived: -real_div_algebra(complex) | hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),hAPP(real,real,inverse_inverse(real),A)),hAPP(complex,complex,inverse_inverse(complex),B)) = hAPP(complex,complex,inverse_inverse(complex),hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),A),B)). [resolve(6874,a,6872,a)].
% 258.33/258.08 6875 field(rat) # label(arity_Rat_Orat___Fields_Ofield) # label(axiom). [assumption].
% 258.33/258.08 6876 -field(A) | zero_zero(A) = ti(A,B) | zero_zero(A) = ti(A,C) | hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),C) != hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),E),B) | 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) # label(fact_1106_frac__eq__eq) # label(axiom). [clausify(1217)].
% 258.33/258.08 6877 -field(A) | zero_zero(A) = ti(A,B) | zero_zero(A) = ti(A,C) | hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),C) = hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),E),B) | 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) # label(fact_1106_frac__eq__eq) # label(axiom). [clausify(1217)].
% 258.33/258.08 6878 -field(A) | zero_zero(A) = ti(A,B) | zero_zero(A) = ti(A,C) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),B)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),E),C)) = hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),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))),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)) # label(fact_1141_add__frac__eq) # label(axiom). [clausify(1252)].
% 258.33/258.08 6879 -field(A) | zero_zero(A) = ti(A,B) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),B)),D) = hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D))),B) # label(fact_1142_divide__add__eq__iff) # label(axiom). [clausify(1253)].
% 258.33/258.08 6880 -field(A) | zero_zero(A) = ti(A,B) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),B)) = hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(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)),B) # label(fact_1144_add__divide__eq__iff) # label(axiom). [clausify(1255)].
% 258.33/258.08 6881 -field(A) | zero_zero(A) = ti(A,B) | zero_zero(A) = ti(A,C) | hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),B)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),E),C)) = hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(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))),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)) # label(fact_1150_diff__frac__eq) # label(axiom). [clausify(1261)].
% 258.33/258.08 6882 -field(A) | zero_zero(A) = ti(A,B) | hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),B)),D) = hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),C),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D))),B) # label(fact_1151_divide__diff__eq__iff) # label(axiom). [clausify(1262)].
% 258.33/258.08 6883 -field(A) | zero_zero(A) = ti(A,B) | hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),C),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),B)) = hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),D)),B) # label(fact_1152_diff__divide__eq__iff) # label(axiom). [clausify(1263)].
% 258.33/258.08 6884 -field(A) | zero_zero(A) = ti(A,B) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),C),D)) | hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),D),C)) = hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(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),B),C)) # label(fact_1407_power__diff) # label(axiom). [clausify(1510)].
% 258.33/258.08 6885 -field(A) | zero_zero(A) = ti(A,B) | hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),B)),D) = hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),C),D)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),D)) # label(fact_1447_nonzero__power__divide) # label(axiom). [clausify(1550)].
% 258.33/258.08 6886 -field(A) | -number_ring(A) | hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),hAPP(int,A,number_number_of(A),hAPP(int,int,bit1,pls))) = ti(A,B) # label(fact_1708_divide__numeral__1) # label(axiom). [clausify(1779)].
% 258.33/258.08 6887 -field(A) | -number_ring(A) | hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),hAPP(int,A,number_number_of(A),hAPP(int,int,bit1,pls))) = ti(A,B) # label(fact_1709_divide__Numeral1) # label(axiom). [clausify(1780)].
% 258.33/258.08 6888 -field(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(A,A,inverse_inverse(A),C)) = hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C) # label(fact_2226_field__divide__inverse) # label(axiom). [clausify(2245)].
% 258.33/258.08 6889 -field(A) | hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),one_one(A)),B) = hAPP(A,A,inverse_inverse(A),B) # label(fact_2233_field__class_Onormalizing__field__rules_I2_J) # label(axiom). [clausify(2252)].
% 258.33/258.08 6890 -field(A) | zero_zero(A) = ti(A,B) | zero_zero(A) = ti(A,C) | hAPP(A,A,hAPP(A,fun(A,A),times_times(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)),hAPP(A,A,inverse_inverse(A),B))),hAPP(A,A,inverse_inverse(A),C)) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,inverse_inverse(A),B)),hAPP(A,A,inverse_inverse(A),C)) # label(fact_2246_inverse__add) # label(axiom). [clausify(2265)].
% 258.33/258.08 6891 -field(A) | zero_zero(A) = ti(A,B) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,inverse_inverse(A),B)),B) = one_one(A) # label(fact_2248_field__inverse) # label(axiom). [clausify(2267)].
% 258.33/258.08 6892 -field(A) | -number_ring(A) | hAPP(int,A,number_number_of(A),hAPP(int,int,bit1,pls)) = hAPP(A,A,inverse_inverse(A),hAPP(int,A,number_number_of(A),hAPP(int,int,bit1,pls))) # label(fact_2252_inverse__numeral__1) # label(axiom). [clausify(2271)].
% 258.33/258.08 6893 -field(A) | one_one(A) = ti(A,B) | hAPP(fun(nat,bool),A,hAPP(fun(nat,A),fun(fun(nat,bool),A),big_co1399186613setsum(nat,A),hAPP(A,fun(nat,A),power_power(A),B)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),C)) = hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C)),one_one(A))),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),one_one(A))) # label(fact_4179_geometric__sum) # label(axiom). [clausify(4111)].
% 258.33/258.08 6894 -field(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),inverse_divide(A)),C)),D)),E) = hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),C),E)),D) # label(fact_4217_setsum__divide__distrib) # label(axiom). [clausify(4149)].
% 258.33/258.08 6895 -field(A) | zero_zero(A) = ti(A,B) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(fun(nat,bool),A,hAPP(fun(nat,A),fun(fun(nat,bool),A),big_co1399186613setsum(nat,A),hAPP(fun(nat,fun(nat,bool)),fun(nat,A),hAPP(fun(fun(nat,bool),A),fun(fun(nat,fun(nat,bool)),fun(nat,A)),combb(fun(nat,bool),A,nat),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),times_times(A)),hAPP(A,fun(nat,A),power_power(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),B)))),hAPP(fun(nat,nat),fun(nat,A),hAPP(fun(nat,A),fun(fun(nat,nat),fun(nat,A)),combb(nat,A,nat),hAPP(A,fun(nat,A),power_power(A),C)),hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),D),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))))),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),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat))),hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),D),hAPP(nat,nat,suc,zero_zero(nat))))))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),D),hAPP(nat,nat,suc,zero_zero(nat)))))) = hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),B)),D)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),C),D))),B)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(nat,A,semiring_1_of_nat(A),D)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),C),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),D),hAPP(nat,nat,suc,zero_zero(nat)))))) # label(fact_4238_lemma__termdiff2) # label(axiom). [clausify(4170)].
% 258.33/258.08 Derived: zero_zero(rat) = ti(rat,A) | zero_zero(rat) = ti(rat,B) | hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),C),B) != hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),D),A) | hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),C),A) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),D),B). [resolve(6875,a,6876,a)].
% 258.33/258.08 Derived: zero_zero(rat) = ti(rat,A) | zero_zero(rat) = ti(rat,B) | hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),C),B) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),D),A) | hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),C),A) != hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),D),B). [resolve(6875,a,6877,a)].
% 258.33/258.09 Derived: zero_zero(rat) = ti(rat,A) | zero_zero(rat) = ti(rat,B) | hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),C),A)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),D),B)) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),C),B)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),D),A))),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B)). [resolve(6875,a,6878,a)].
% 258.33/258.09 Derived: zero_zero(rat) = ti(rat,A) | hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),B),A)),C) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),B),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),C))),A). [resolve(6875,a,6879,a)].
% 258.33/258.09 Derived: zero_zero(rat) = ti(rat,A) | hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),B),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),C),A)) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B)),C)),A). [resolve(6875,a,6880,a)].
% 258.33/258.09 Derived: zero_zero(rat) = ti(rat,A) | zero_zero(rat) = ti(rat,B) | hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),C),A)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),D),B)) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),C),B)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),D),A))),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B)). [resolve(6875,a,6881,a)].
% 258.33/258.09 Derived: zero_zero(rat) = ti(rat,A) | hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),B),A)),C) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),B),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),C))),A). [resolve(6875,a,6882,a)].
% 258.33/258.09 Derived: zero_zero(rat) = ti(rat,A) | hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),B),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),C),A)) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B)),C)),A). [resolve(6875,a,6883,a)].
% 258.33/258.09 Derived: zero_zero(rat) = ti(rat,A) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),C)) | hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),C),B)) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),C)),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),B)). [resolve(6875,a,6884,a)].
% 258.33/258.09 Derived: zero_zero(rat) = ti(rat,A) | hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),B),A)),C) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),B),C)),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),C)). [resolve(6875,a,6885,a)].
% 258.33/258.09 Derived: -number_ring(rat) | hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),hAPP(int,rat,number_number_of(rat),hAPP(int,int,bit1,pls))) = ti(rat,A). [resolve(6875,a,6886,a)].
% 258.33/258.09 Derived: zero_zero(rat) = ti(rat,A) | zero_zero(rat) = ti(rat,B) | hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),B)),hAPP(rat,rat,inverse_inverse(rat),A))),hAPP(rat,rat,inverse_inverse(rat),B)) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(rat,rat,inverse_inverse(rat),A)),hAPP(rat,rat,inverse_inverse(rat),B)). [resolve(6875,a,6890,a)].
% 258.33/258.11 Derived: -number_ring(rat) | hAPP(int,rat,number_number_of(rat),hAPP(int,int,bit1,pls)) = hAPP(rat,rat,inverse_inverse(rat),hAPP(int,rat,number_number_of(rat),hAPP(int,int,bit1,pls))). [resolve(6875,a,6892,a)].
% 258.33/258.11 Derived: one_one(rat) = ti(rat,A) | hAPP(fun(nat,bool),rat,hAPP(fun(nat,rat),fun(fun(nat,bool),rat),big_co1399186613setsum(nat,rat),hAPP(rat,fun(nat,rat),power_power(rat),A)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),B)) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),B)),one_one(rat))),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),A),one_one(rat))). [resolve(6875,a,6893,a)].
% 258.33/258.11 Derived: hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),hAPP(rat,fun(A,rat),hAPP(fun(A,fun(rat,rat)),fun(rat,fun(A,rat)),combc(A,rat,rat),hAPP(fun(A,rat),fun(A,fun(rat,rat)),hAPP(fun(rat,fun(rat,rat)),fun(fun(A,rat),fun(A,fun(rat,rat))),combb(rat,fun(rat,rat),A),inverse_divide(rat)),B)),C)),D) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),B),D)),C). [resolve(6875,a,6894,a)].
% 258.33/258.11 Derived: zero_zero(rat) = ti(rat,A) | hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),hAPP(fun(nat,bool),rat,hAPP(fun(nat,rat),fun(fun(nat,bool),rat),big_co1399186613setsum(nat,rat),hAPP(fun(nat,fun(nat,bool)),fun(nat,rat),hAPP(fun(fun(nat,bool),rat),fun(fun(nat,fun(nat,bool)),fun(nat,rat)),combb(fun(nat,bool),rat,nat),hAPP(fun(nat,rat),fun(fun(nat,bool),rat),big_co1399186613setsum(nat,rat),hAPP(fun(nat,rat),fun(nat,rat),hAPP(fun(nat,fun(rat,rat)),fun(fun(nat,rat),fun(nat,rat)),combs(nat,rat,rat),hAPP(fun(nat,rat),fun(nat,fun(rat,rat)),hAPP(fun(rat,fun(rat,rat)),fun(fun(nat,rat),fun(nat,fun(rat,rat))),combb(rat,fun(rat,rat),nat),times_times(rat)),hAPP(rat,fun(nat,rat),power_power(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),B),A)))),hAPP(fun(nat,nat),fun(nat,rat),hAPP(fun(nat,rat),fun(fun(nat,nat),fun(nat,rat)),combb(nat,rat,nat),hAPP(rat,fun(nat,rat),power_power(rat),B)),hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),C),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))))),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),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat))),hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),C),hAPP(nat,nat,suc,zero_zero(nat))))))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),C),hAPP(nat,nat,suc,zero_zero(nat)))))) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),B),A)),C)),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),B),C))),A)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(nat,rat,semiring_1_of_nat(rat),C)),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),C),hAPP(nat,nat,suc,zero_zero(nat)))))). [resolve(6875,a,6895,a)].
% 258.33/258.11 6896 field(real) # label(arity_RealDef_Oreal___Fields_Ofield) # label(axiom). [assumption].
% 258.33/258.11 Derived: zero_zero(real) = ti(real,A) | zero_zero(real) = ti(real,B) | hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),C),B) != hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),D),A) | hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),A) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),D),B). [resolve(6896,a,6876,a)].
% 258.33/258.11 Derived: zero_zero(real) = ti(real,A) | zero_zero(real) = ti(real,B) | hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),C),B) = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),D),A) | hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),A) != hAPP(real,real,hAPP(real,fun(real,real),times_times(real),D),B). [resolve(6896,a,6877,a)].
% 258.33/258.12 Derived: zero_zero(real) = ti(real,A) | zero_zero(real) = ti(real,B) | hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),C),A)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),D),B)) = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),B)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),D),A))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)). [resolve(6896,a,6878,a)].
% 258.33/258.12 Derived: zero_zero(real) = ti(real,A) | hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),B),A)),C) = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),B),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),C))),A). [resolve(6896,a,6879,a)].
% 258.33/258.12 Derived: zero_zero(real) = ti(real,A) | hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),B),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),C),A)) = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),C)),A). [resolve(6896,a,6880,a)].
% 258.33/258.12 Derived: zero_zero(real) = ti(real,A) | zero_zero(real) = ti(real,B) | hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),C),A)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),D),B)) = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),B)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),D),A))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)). [resolve(6896,a,6881,a)].
% 258.33/258.12 Derived: zero_zero(real) = ti(real,A) | hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),B),A)),C) = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),B),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),C))),A). [resolve(6896,a,6882,a)].
% 258.33/258.12 Derived: zero_zero(real) = ti(real,A) | hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),B),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),C),A)) = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),C)),A). [resolve(6896,a,6883,a)].
% 258.33/258.12 Derived: zero_zero(real) = ti(real,A) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),C)) | hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),C),B)) = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),C)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),B)). [resolve(6896,a,6884,a)].
% 258.33/258.12 Derived: zero_zero(real) = ti(real,A) | hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),B),A)),C) = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),B),C)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),C)). [resolve(6896,a,6885,a)].
% 258.33/258.12 Derived: -number_ring(real) | hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),hAPP(int,real,number_number_of(real),hAPP(int,int,bit1,pls))) = ti(real,A). [resolve(6896,a,6886,a)].
% 258.40/258.14 Derived: zero_zero(real) = ti(real,A) | zero_zero(real) = ti(real,B) | hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),B)),hAPP(real,real,inverse_inverse(real),A))),hAPP(real,real,inverse_inverse(real),B)) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,inverse_inverse(real),A)),hAPP(real,real,inverse_inverse(real),B)). [resolve(6896,a,6890,a)].
% 258.40/258.14 Derived: -number_ring(real) | hAPP(int,real,number_number_of(real),hAPP(int,int,bit1,pls)) = hAPP(real,real,inverse_inverse(real),hAPP(int,real,number_number_of(real),hAPP(int,int,bit1,pls))). [resolve(6896,a,6892,a)].
% 258.40/258.14 Derived: one_one(real) = ti(real,A) | hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(real,fun(nat,real),power_power(real),A)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),B)) = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),B)),one_one(real))),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),one_one(real))). [resolve(6896,a,6893,a)].
% 258.40/258.14 Derived: zero_zero(real) = ti(real,A) | hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,fun(nat,bool)),fun(nat,real),hAPP(fun(fun(nat,bool),real),fun(fun(nat,fun(nat,bool)),fun(nat,real)),combb(fun(nat,bool),real,nat),hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),B),A)))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),hAPP(real,fun(nat,real),power_power(real),B)),hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),C),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))))),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),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat))),hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),C),hAPP(nat,nat,suc,zero_zero(nat))))))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),C),hAPP(nat,nat,suc,zero_zero(nat)))))) = hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),B),A)),C)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),B),C))),A)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,semiring_1_of_nat(real),C)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),C),hAPP(nat,nat,suc,zero_zero(nat)))))). [resolve(6896,a,6895,a)].
% 258.40/258.14 6897 field(complex) # label(arity_Complex_Ocomplex___Fields_Ofield) # label(axiom). [assumption].
% 258.40/258.14 Derived: zero_zero(complex) = ti(complex,A) | zero_zero(complex) = ti(complex,B) | hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),C),B) != hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),D),A) | hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),C),A) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),D),B). [resolve(6897,a,6876,a)].
% 258.40/258.14 Derived: zero_zero(complex) = ti(complex,A) | zero_zero(complex) = ti(complex,B) | hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),C),B) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),D),A) | hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),C),A) != hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),D),B). [resolve(6897,a,6877,a)].
% 258.40/258.14 Derived: zero_zero(complex) = ti(complex,A) | zero_zero(complex) = ti(complex,B) | hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),C),A)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),D),B)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),C),B)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),D),A))),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),B)). [resolve(6897,a,6878,a)].
% 258.40/258.14 Derived: zero_zero(complex) = ti(complex,A) | hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),B),A)),C) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),B),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),C))),A). [resolve(6897,a,6879,a)].
% 258.40/258.14 Derived: zero_zero(complex) = ti(complex,A) | hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),B),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),C),A)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),B)),C)),A). [resolve(6897,a,6880,a)].
% 258.40/258.14 Derived: zero_zero(complex) = ti(complex,A) | zero_zero(complex) = ti(complex,B) | hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),C),A)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),D),B)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),C),B)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),D),A))),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),B)). [resolve(6897,a,6881,a)].
% 258.40/258.14 Derived: zero_zero(complex) = ti(complex,A) | hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),B),A)),C) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),B),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),C))),A). [resolve(6897,a,6882,a)].
% 258.40/258.14 Derived: zero_zero(complex) = ti(complex,A) | hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),B),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),C),A)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),B)),C)),A). [resolve(6897,a,6883,a)].
% 258.40/258.14 Derived: zero_zero(complex) = ti(complex,A) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),C)) | hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),C),B)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),A),C)),hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),A),B)). [resolve(6897,a,6884,a)].
% 258.40/258.15 Derived: zero_zero(complex) = ti(complex,A) | hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),B),A)),C) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),B),C)),hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),A),C)). [resolve(6897,a,6885,a)].
% 258.40/258.15 Derived: -number_ring(complex) | hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),A),hAPP(int,complex,number_number_of(complex),hAPP(int,int,bit1,pls))) = ti(complex,A). [resolve(6897,a,6886,a)].
% 258.40/258.15 Derived: zero_zero(complex) = ti(complex,A) | zero_zero(complex) = ti(complex,B) | hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),A),B)),hAPP(complex,complex,inverse_inverse(complex),A))),hAPP(complex,complex,inverse_inverse(complex),B)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(complex,complex,inverse_inverse(complex),A)),hAPP(complex,complex,inverse_inverse(complex),B)). [resolve(6897,a,6890,a)].
% 258.40/258.15 Derived: -number_ring(complex) | hAPP(int,complex,number_number_of(complex),hAPP(int,int,bit1,pls)) = hAPP(complex,complex,inverse_inverse(complex),hAPP(int,complex,number_number_of(complex),hAPP(int,int,bit1,pls))). [resolve(6897,a,6892,a)].
% 258.40/258.15 Derived: one_one(complex) = ti(complex,A) | hAPP(fun(nat,bool),complex,hAPP(fun(nat,complex),fun(fun(nat,bool),complex),big_co1399186613setsum(nat,complex),hAPP(complex,fun(nat,complex),power_power(complex),A)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),B)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),A),B)),one_one(complex))),hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),A),one_one(complex))). [resolve(6897,a,6893,a)].
% 258.40/258.15 Derived: zero_zero(complex) = ti(complex,A) | hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),hAPP(fun(nat,bool),complex,hAPP(fun(nat,complex),fun(fun(nat,bool),complex),big_co1399186613setsum(nat,complex),hAPP(fun(nat,fun(nat,bool)),fun(nat,complex),hAPP(fun(fun(nat,bool),complex),fun(fun(nat,fun(nat,bool)),fun(nat,complex)),combb(fun(nat,bool),complex,nat),hAPP(fun(nat,complex),fun(fun(nat,bool),complex),big_co1399186613setsum(nat,complex),hAPP(fun(nat,complex),fun(nat,complex),hAPP(fun(nat,fun(complex,complex)),fun(fun(nat,complex),fun(nat,complex)),combs(nat,complex,complex),hAPP(fun(nat,complex),fun(nat,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(nat,complex),fun(nat,fun(complex,complex))),combb(complex,fun(complex,complex),nat),times_times(complex)),hAPP(complex,fun(nat,complex),power_power(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),B),A)))),hAPP(fun(nat,nat),fun(nat,complex),hAPP(fun(nat,complex),fun(fun(nat,nat),fun(nat,complex)),combb(nat,complex,nat),hAPP(complex,fun(nat,complex),power_power(complex),B)),hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),C),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))))),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),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat))),hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),C),hAPP(nat,nat,suc,zero_zero(nat))))))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),C),hAPP(nat,nat,suc,zero_zero(nat)))))) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),B),A)),C)),hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),B),C))),A)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(nat,complex,semiring_1_of_nat(complex),C)),hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),C),hAPP(nat,nat,suc,zero_zero(nat)))))). [resolve(6897,a,6895,a)].
% 262.92/262.73 6898 real_field(real) # label(arity_RealDef_Oreal___RealVector_Oreal__field) # label(axiom). [assumption].
% 262.92/262.73 6899 -real_field(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),C),D)),E))),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),F)),E)),D)) = hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(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),F),D))),E) # label(fact_1155_DERIV__mult__lemma) # label(axiom). [clausify(1266)].
% 262.92/262.73 6900 -field_inverse_zero(A) | -real_field(A) | hAPP(real,A,of_real(A),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),B),C)) = hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),hAPP(real,A,of_real(A),B)),hAPP(real,A,of_real(A),C)) # label(fact_2798_of__real__divide) # label(axiom). [clausify(2783)].
% 262.92/262.73 6901 -real_field(A) | zero_zero(real) = B | hAPP(real,A,of_real(A),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),C),B)) = hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),hAPP(real,A,of_real(A),C)),hAPP(real,A,of_real(A),B)) # label(fact_2809_nonzero__of__real__divide) # label(axiom). [clausify(2794)].
% 262.92/262.73 6902 -real_field(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(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),times_times(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,real),fun(nat,fun(A,A)),hAPP(fun(real,fun(A,A)),fun(fun(nat,real),fun(nat,fun(A,A))),combb(real,fun(A,A),nat),scaleR_scaleR(A)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),inverse_inverse(real)),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),fact_fact(nat))))),hAPP(A,fun(nat,A),power_power(A),B)))),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,real),fun(nat,fun(A,A)),hAPP(fun(real,fun(A,A)),fun(fun(nat,real),fun(nat,fun(A,A))),combb(real,fun(A,A),nat),scaleR_scaleR(A)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),inverse_inverse(real)),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),hAPP(fun(nat,nat),fun(nat,nat),hAPP(fun(nat,nat),fun(fun(nat,nat),fun(nat,nat)),combb(nat,nat,nat),fact_fact(nat)),hAPP(nat,fun(nat,nat),minus_minus(nat),C)))))),hAPP(fun(nat,nat),fun(nat,A),hAPP(fun(nat,A),fun(fun(nat,nat),fun(nat,A)),combb(nat,A,nat),hAPP(A,fun(nat,A),power_power(A),D)),hAPP(nat,fun(nat,nat),minus_minus(nat),C))))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),zero_zero(nat)),C)) = hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),hAPP(real,real,inverse_inverse(real),hAPP(nat,real,real_1(nat),hAPP(nat,nat,fact_fact(nat),C)))),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),D)),C)) # label(fact_4668_exp__series__add) # label(axiom). [clausify(4594)].
% 262.92/262.74 Derived: hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),B),C)),D))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),E)),D)),C)) = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),E),C))),D). [resolve(6898,a,6899,a)].
% 262.92/262.74 Derived: -field_inverse_zero(real) | hAPP(real,real,of_real(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B)) = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,of_real(real),A)),hAPP(real,real,of_real(real),B)). [resolve(6898,a,6900,b)].
% 262.92/262.74 Derived: zero_zero(real) = A | hAPP(real,real,of_real(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),B),A)) = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,of_real(real),B)),hAPP(real,real,of_real(real),A)). [resolve(6898,a,6901,a)].
% 262.92/262.74 Derived: hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),scaleR_scaleR(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),inverse_inverse(real)),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),fact_fact(nat))))),hAPP(real,fun(nat,real),power_power(real),A)))),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),scaleR_scaleR(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),inverse_inverse(real)),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),hAPP(fun(nat,nat),fun(nat,nat),hAPP(fun(nat,nat),fun(fun(nat,nat),fun(nat,nat)),combb(nat,nat,nat),fact_fact(nat)),hAPP(nat,fun(nat,nat),minus_minus(nat),B)))))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),hAPP(real,fun(nat,real),power_power(real),C)),hAPP(nat,fun(nat,nat),minus_minus(nat),B))))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),zero_zero(nat)),B)) = hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),hAPP(real,real,inverse_inverse(real),hAPP(nat,real,real_1(nat),hAPP(nat,nat,fact_fact(nat),B)))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),C)),B)). [resolve(6898,a,6902,a)].
% 263.02/262.75 6903 real_field(complex) # label(arity_Complex_Ocomplex___RealVector_Oreal__field) # label(axiom). [assumption].
% 263.02/262.75 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),B),C)),D))),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),A),E)),D)),C)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),B)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),E),C))),D). [resolve(6903,a,6899,a)].
% 263.02/262.75 Derived: -field_inverse_zero(complex) | hAPP(real,complex,of_real(complex),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),hAPP(real,complex,of_real(complex),A)),hAPP(real,complex,of_real(complex),B)). [resolve(6903,a,6900,b)].
% 263.02/262.75 Derived: zero_zero(real) = A | hAPP(real,complex,of_real(complex),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),B),A)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),hAPP(real,complex,of_real(complex),B)),hAPP(real,complex,of_real(complex),A)). [resolve(6903,a,6901,a)].
% 263.02/262.75 Derived: hAPP(fun(nat,bool),complex,hAPP(fun(nat,complex),fun(fun(nat,bool),complex),big_co1399186613setsum(nat,complex),hAPP(fun(nat,complex),fun(nat,complex),hAPP(fun(nat,fun(complex,complex)),fun(fun(nat,complex),fun(nat,complex)),combs(nat,complex,complex),hAPP(fun(nat,complex),fun(nat,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(nat,complex),fun(nat,fun(complex,complex))),combb(complex,fun(complex,complex),nat),times_times(complex)),hAPP(fun(nat,complex),fun(nat,complex),hAPP(fun(nat,fun(complex,complex)),fun(fun(nat,complex),fun(nat,complex)),combs(nat,complex,complex),hAPP(fun(nat,real),fun(nat,fun(complex,complex)),hAPP(fun(real,fun(complex,complex)),fun(fun(nat,real),fun(nat,fun(complex,complex))),combb(real,fun(complex,complex),nat),scaleR_scaleR(complex)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),inverse_inverse(real)),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),fact_fact(nat))))),hAPP(complex,fun(nat,complex),power_power(complex),A)))),hAPP(fun(nat,complex),fun(nat,complex),hAPP(fun(nat,fun(complex,complex)),fun(fun(nat,complex),fun(nat,complex)),combs(nat,complex,complex),hAPP(fun(nat,real),fun(nat,fun(complex,complex)),hAPP(fun(real,fun(complex,complex)),fun(fun(nat,real),fun(nat,fun(complex,complex))),combb(real,fun(complex,complex),nat),scaleR_scaleR(complex)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),inverse_inverse(real)),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),hAPP(fun(nat,nat),fun(nat,nat),hAPP(fun(nat,nat),fun(fun(nat,nat),fun(nat,nat)),combb(nat,nat,nat),fact_fact(nat)),hAPP(nat,fun(nat,nat),minus_minus(nat),B)))))),hAPP(fun(nat,nat),fun(nat,complex),hAPP(fun(nat,complex),fun(fun(nat,nat),fun(nat,complex)),combb(nat,complex,nat),hAPP(complex,fun(nat,complex),power_power(complex),C)),hAPP(nat,fun(nat,nat),minus_minus(nat),B))))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),zero_zero(nat)),B)) = hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),hAPP(real,real,inverse_inverse(real),hAPP(nat,real,real_1(nat),hAPP(nat,nat,fact_fact(nat),B)))),hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),A),C)),B)). [resolve(6903,a,6902,a)].
% 267.61/267.33 6904 semiring_0(int) # label(arity_Int_Oint___Rings_Osemiring__0) # label(axiom). [assumption].
% 267.61/267.33 6905 -power(A) | -semiring_0(A) | hAPP(int,nat,number_number_of(nat),B) != zero_zero(nat) | hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),zero_zero(A)),hAPP(int,nat,number_number_of(nat),B)) = one_one(A) # label(fact_1397_power__0__left__number__of) # label(axiom). [clausify(1500)].
% 267.61/267.33 6906 -power(A) | -semiring_0(A) | hAPP(int,nat,number_number_of(nat),B) = zero_zero(nat) | hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),zero_zero(A)),hAPP(int,nat,number_number_of(nat),B)) = zero_zero(A) # label(fact_1397_power__0__left__number__of) # label(axiom). [clausify(1500)].
% 267.61/267.33 6907 -power(A) | -semiring_0(A) | hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),zero_zero(A)),hAPP(nat,nat,suc,B)) = zero_zero(A) # label(fact_1446_power__0__Suc) # label(axiom). [clausify(1549)].
% 267.61/267.33 6908 -power(A) | -semiring_0(A) | zero_zero(nat) != B | hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),zero_zero(A)),B) = one_one(A) # label(fact_1459_power__0__left) # label(axiom). [clausify(1562)].
% 267.61/267.33 6909 -power(A) | -semiring_0(A) | zero_zero(nat) = B | hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),zero_zero(A)),B) = zero_zero(A) # label(fact_1459_power__0__left) # label(axiom). [clausify(1562)].
% 267.61/267.33 6910 -dvd(A) | -semiring_0(A) | -hBOOL(hAPP(A,bool,B,hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),D))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),C),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),f310(A,B,C)),zero_zero(A)))) # label(fact_3156_unity__coeff__ex) # label(axiom). [clausify(3123)].
% 267.61/267.33 6911 -dvd(A) | -semiring_0(A) | -hBOOL(hAPP(A,bool,B,hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),D))) | hBOOL(hAPP(A,bool,B,f310(A,B,C))) # label(fact_3156_unity__coeff__ex) # label(axiom). [clausify(3123)].
% 267.61/267.33 6912 -dvd(A) | -semiring_0(A) | hBOOL(hAPP(A,bool,B,hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),f311(A,B,C)))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),C),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),D),zero_zero(A)))) | -hBOOL(hAPP(A,bool,B,D)) # label(fact_3156_unity__coeff__ex) # label(axiom). [clausify(3123)].
% 267.61/267.33 6913 -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_4211_setsum__right__distrib) # label(axiom). [clausify(4143)].
% 267.61/267.33 6914 -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_4212_setsum__left__distrib) # label(axiom). [clausify(4144)].
% 267.61/267.33 6915 -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_4213_setsum__product) # label(axiom). [clausify(4145)].
% 267.62/267.35 Derived: -power(int) | hAPP(int,nat,number_number_of(nat),A) != zero_zero(nat) | hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),zero_zero(int)),hAPP(int,nat,number_number_of(nat),A)) = one_one(int). [resolve(6904,a,6905,b)].
% 267.62/267.35 Derived: -power(int) | hAPP(int,nat,number_number_of(nat),A) = zero_zero(nat) | hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),zero_zero(int)),hAPP(int,nat,number_number_of(nat),A)) = zero_zero(int). [resolve(6904,a,6906,b)].
% 267.62/267.35 Derived: -power(int) | hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),zero_zero(int)),hAPP(nat,nat,suc,A)) = zero_zero(int). [resolve(6904,a,6907,b)].
% 267.62/267.35 Derived: -power(int) | zero_zero(nat) != A | hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),zero_zero(int)),A) = one_one(int). [resolve(6904,a,6908,b)].
% 267.62/267.35 Derived: -power(int) | zero_zero(nat) = A | hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),zero_zero(int)),A) = zero_zero(int). [resolve(6904,a,6909,b)].
% 267.62/267.35 Derived: -dvd(int) | -hBOOL(hAPP(int,bool,A,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),C))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),B),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),f310(int,A,B)),zero_zero(int)))). [resolve(6904,a,6910,b)].
% 267.62/267.35 Derived: -dvd(int) | -hBOOL(hAPP(int,bool,A,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),C))) | hBOOL(hAPP(int,bool,A,f310(int,A,B))). [resolve(6904,a,6911,b)].
% 267.62/267.35 Derived: -dvd(int) | hBOOL(hAPP(int,bool,A,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),f311(int,A,B)))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),B),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),C),zero_zero(int)))) | -hBOOL(hAPP(int,bool,A,C)). [resolve(6904,a,6912,b)].
% 267.62/267.35 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(6904,a,6913,a)].
% 267.62/267.35 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(6904,a,6914,a)].
% 267.62/267.35 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(6904,a,6915,a)].
% 267.62/267.35 6916 semiring_0(nat) # label(arity_Nat_Onat___Rings_Osemiring__0) # label(axiom). [assumption].
% 267.62/267.37 Derived: -power(nat) | hAPP(int,nat,number_number_of(nat),A) != zero_zero(nat) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),zero_zero(nat)),hAPP(int,nat,number_number_of(nat),A)) = one_one(nat). [resolve(6916,a,6905,b)].
% 267.62/267.37 Derived: -power(nat) | hAPP(int,nat,number_number_of(nat),A) = zero_zero(nat) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),zero_zero(nat)),hAPP(int,nat,number_number_of(nat),A)) = zero_zero(nat). [resolve(6916,a,6906,b)].
% 267.62/267.37 Derived: -power(nat) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),zero_zero(nat)),hAPP(nat,nat,suc,A)) = zero_zero(nat). [resolve(6916,a,6907,b)].
% 267.62/267.37 Derived: -power(nat) | zero_zero(nat) != A | hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),zero_zero(nat)),A) = one_one(nat). [resolve(6916,a,6908,b)].
% 267.62/267.37 Derived: -power(nat) | zero_zero(nat) = A | hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),zero_zero(nat)),A) = zero_zero(nat). [resolve(6916,a,6909,b)].
% 267.62/267.37 Derived: -dvd(nat) | -hBOOL(hAPP(nat,bool,A,hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),C))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),f310(nat,A,B)),zero_zero(nat)))). [resolve(6916,a,6910,b)].
% 267.62/267.37 Derived: -dvd(nat) | -hBOOL(hAPP(nat,bool,A,hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),C))) | hBOOL(hAPP(nat,bool,A,f310(nat,A,B))). [resolve(6916,a,6911,b)].
% 267.62/267.37 Derived: -dvd(nat) | hBOOL(hAPP(nat,bool,A,hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),f311(nat,A,B)))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),C),zero_zero(nat)))) | -hBOOL(hAPP(nat,bool,A,C)). [resolve(6916,a,6912,b)].
% 267.62/267.37 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(6916,a,6913,a)].
% 267.62/267.37 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(6916,a,6914,a)].
% 267.62/267.37 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(6916,a,6915,a)].
% 267.62/267.37 6917 semiring_0(rat) # label(arity_Rat_Orat___Rings_Osemiring__0) # label(axiom). [assumption].
% 267.62/267.37 Derived: -power(rat) | hAPP(int,nat,number_number_of(nat),A) != zero_zero(nat) | hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),zero_zero(rat)),hAPP(int,nat,number_number_of(nat),A)) = one_one(rat). [resolve(6917,a,6905,b)].
% 267.62/267.39 Derived: -power(rat) | hAPP(int,nat,number_number_of(nat),A) = zero_zero(nat) | hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),zero_zero(rat)),hAPP(int,nat,number_number_of(nat),A)) = zero_zero(rat). [resolve(6917,a,6906,b)].
% 267.62/267.39 Derived: -power(rat) | hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),zero_zero(rat)),hAPP(nat,nat,suc,A)) = zero_zero(rat). [resolve(6917,a,6907,b)].
% 267.62/267.39 Derived: -power(rat) | zero_zero(nat) != A | hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),zero_zero(rat)),A) = one_one(rat). [resolve(6917,a,6908,b)].
% 267.62/267.39 Derived: -power(rat) | zero_zero(nat) = A | hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),zero_zero(rat)),A) = zero_zero(rat). [resolve(6917,a,6909,b)].
% 267.62/267.39 Derived: -dvd(rat) | -hBOOL(hAPP(rat,bool,A,hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),B),C))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),dvd_dvd(rat),B),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),f310(rat,A,B)),zero_zero(rat)))). [resolve(6917,a,6910,b)].
% 267.62/267.39 Derived: -dvd(rat) | -hBOOL(hAPP(rat,bool,A,hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),B),C))) | hBOOL(hAPP(rat,bool,A,f310(rat,A,B))). [resolve(6917,a,6911,b)].
% 267.62/267.39 Derived: -dvd(rat) | hBOOL(hAPP(rat,bool,A,hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),B),f311(rat,A,B)))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),dvd_dvd(rat),B),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),C),zero_zero(rat)))) | -hBOOL(hAPP(rat,bool,A,C)). [resolve(6917,a,6912,b)].
% 267.62/267.39 Derived: hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),hAPP(fun(A,rat),fun(A,rat),hAPP(fun(rat,rat),fun(fun(A,rat),fun(A,rat)),combb(rat,rat,A),hAPP(rat,fun(rat,rat),times_times(rat),B)),C)),D) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),B),hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),C),D)). [resolve(6917,a,6913,a)].
% 267.62/267.39 Derived: hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),hAPP(rat,fun(A,rat),hAPP(fun(A,fun(rat,rat)),fun(rat,fun(A,rat)),combc(A,rat,rat),hAPP(fun(A,rat),fun(A,fun(rat,rat)),hAPP(fun(rat,fun(rat,rat)),fun(fun(A,rat),fun(A,fun(rat,rat))),combb(rat,fun(rat,rat),A),times_times(rat)),B)),C)),D) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),B),D)),C). [resolve(6917,a,6914,a)].
% 267.62/267.39 Derived: hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),hAPP(fun(B,bool),fun(A,rat),hAPP(fun(A,fun(fun(B,bool),rat)),fun(fun(B,bool),fun(A,rat)),combc(A,fun(B,bool),rat),hAPP(fun(A,fun(B,rat)),fun(A,fun(fun(B,bool),rat)),hAPP(fun(fun(B,rat),fun(fun(B,bool),rat)),fun(fun(A,fun(B,rat)),fun(A,fun(fun(B,bool),rat))),combb(fun(B,rat),fun(fun(B,bool),rat),A),big_co1399186613setsum(B,rat)),hAPP(fun(B,rat),fun(A,fun(B,rat)),hAPP(fun(A,fun(fun(B,rat),fun(B,rat))),fun(fun(B,rat),fun(A,fun(B,rat))),combc(A,fun(B,rat),fun(B,rat)),hAPP(fun(A,fun(rat,rat)),fun(A,fun(fun(B,rat),fun(B,rat))),hAPP(fun(fun(rat,rat),fun(fun(B,rat),fun(B,rat))),fun(fun(A,fun(rat,rat)),fun(A,fun(fun(B,rat),fun(B,rat)))),combb(fun(rat,rat),fun(fun(B,rat),fun(B,rat)),A),combb(rat,rat,B)),hAPP(fun(A,rat),fun(A,fun(rat,rat)),hAPP(fun(rat,fun(rat,rat)),fun(fun(A,rat),fun(A,fun(rat,rat))),combb(rat,fun(rat,rat),A),times_times(rat)),C))),D))),E)),F) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),C),F)),hAPP(fun(B,bool),rat,hAPP(fun(B,rat),fun(fun(B,bool),rat),big_co1399186613setsum(B,rat),D),E)). [resolve(6917,a,6915,a)].
% 267.62/267.39 6918 semiring_0(real) # label(arity_RealDef_Oreal___Rings_Osemiring__0) # label(axiom). [assumption].
% 267.62/267.39 Derived: -power(real) | hAPP(int,nat,number_number_of(nat),A) != zero_zero(nat) | hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),zero_zero(real)),hAPP(int,nat,number_number_of(nat),A)) = one_one(real). [resolve(6918,a,6905,b)].
% 267.62/267.42 Derived: -power(real) | hAPP(int,nat,number_number_of(nat),A) = zero_zero(nat) | hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),zero_zero(real)),hAPP(int,nat,number_number_of(nat),A)) = zero_zero(real). [resolve(6918,a,6906,b)].
% 267.62/267.42 Derived: -power(real) | hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),zero_zero(real)),hAPP(nat,nat,suc,A)) = zero_zero(real). [resolve(6918,a,6907,b)].
% 267.62/267.42 Derived: -power(real) | zero_zero(nat) != A | hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),zero_zero(real)),A) = one_one(real). [resolve(6918,a,6908,b)].
% 267.62/267.42 Derived: -power(real) | zero_zero(nat) = A | hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),zero_zero(real)),A) = zero_zero(real). [resolve(6918,a,6909,b)].
% 267.62/267.42 Derived: -dvd(real) | -hBOOL(hAPP(real,bool,A,hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),C))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),dvd_dvd(real),B),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),f310(real,A,B)),zero_zero(real)))). [resolve(6918,a,6910,b)].
% 267.62/267.42 Derived: -dvd(real) | -hBOOL(hAPP(real,bool,A,hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),C))) | hBOOL(hAPP(real,bool,A,f310(real,A,B))). [resolve(6918,a,6911,b)].
% 267.62/267.42 Derived: -dvd(real) | hBOOL(hAPP(real,bool,A,hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),f311(real,A,B)))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),dvd_dvd(real),B),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),C),zero_zero(real)))) | -hBOOL(hAPP(real,bool,A,C)). [resolve(6918,a,6912,b)].
% 267.62/267.42 Derived: hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),hAPP(fun(B,bool),fun(A,real),hAPP(fun(A,fun(fun(B,bool),real)),fun(fun(B,bool),fun(A,real)),combc(A,fun(B,bool),real),hAPP(fun(A,fun(B,real)),fun(A,fun(fun(B,bool),real)),hAPP(fun(fun(B,real),fun(fun(B,bool),real)),fun(fun(A,fun(B,real)),fun(A,fun(fun(B,bool),real))),combb(fun(B,real),fun(fun(B,bool),real),A),big_co1399186613setsum(B,real)),hAPP(fun(B,real),fun(A,fun(B,real)),hAPP(fun(A,fun(fun(B,real),fun(B,real))),fun(fun(B,real),fun(A,fun(B,real))),combc(A,fun(B,real),fun(B,real)),hAPP(fun(A,fun(real,real)),fun(A,fun(fun(B,real),fun(B,real))),hAPP(fun(fun(real,real),fun(fun(B,real),fun(B,real))),fun(fun(A,fun(real,real)),fun(A,fun(fun(B,real),fun(B,real)))),combb(fun(real,real),fun(fun(B,real),fun(B,real)),A),combb(real,real,B)),hAPP(fun(A,real),fun(A,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(A,real),fun(A,fun(real,real))),combb(real,fun(real,real),A),times_times(real)),C))),D))),E)),F) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),C),F)),hAPP(fun(B,bool),real,hAPP(fun(B,real),fun(fun(B,bool),real),big_co1399186613setsum(B,real),D),E)). [resolve(6918,a,6915,a)].
% 267.62/267.42 6919 semiring_0(complex) # label(arity_Complex_Ocomplex___Rings_Osemiring__0) # label(axiom). [assumption].
% 267.62/267.42 Derived: -power(complex) | hAPP(int,nat,number_number_of(nat),A) != zero_zero(nat) | hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),zero_zero(complex)),hAPP(int,nat,number_number_of(nat),A)) = one_one(complex). [resolve(6919,a,6905,b)].
% 267.62/267.42 Derived: -power(complex) | hAPP(int,nat,number_number_of(nat),A) = zero_zero(nat) | hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),zero_zero(complex)),hAPP(int,nat,number_number_of(nat),A)) = zero_zero(complex). [resolve(6919,a,6906,b)].
% 267.62/267.42 Derived: -power(complex) | hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),zero_zero(complex)),hAPP(nat,nat,suc,A)) = zero_zero(complex). [resolve(6919,a,6907,b)].
% 267.62/267.42 Derived: -power(complex) | zero_zero(nat) != A | hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),zero_zero(complex)),A) = one_one(complex). [resolve(6919,a,6908,b)].
% 267.62/267.42 Derived: -power(complex) | zero_zero(nat) = A | hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),zero_zero(complex)),A) = zero_zero(complex). [resolve(6919,a,6909,b)].
% 267.62/267.42 Derived: -dvd(complex) | -hBOOL(hAPP(complex,bool,A,hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),B),C))) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),dvd_dvd(complex),B),hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),f310(complex,A,B)),zero_zero(complex)))). [resolve(6919,a,6910,b)].
% 267.70/267.43 Derived: -dvd(complex) | -hBOOL(hAPP(complex,bool,A,hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),B),C))) | hBOOL(hAPP(complex,bool,A,f310(complex,A,B))). [resolve(6919,a,6911,b)].
% 267.70/267.43 Derived: -dvd(complex) | hBOOL(hAPP(complex,bool,A,hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),B),f311(complex,A,B)))) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),dvd_dvd(complex),B),hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),C),zero_zero(complex)))) | -hBOOL(hAPP(complex,bool,A,C)). [resolve(6919,a,6912,b)].
% 267.70/267.43 Derived: hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),hAPP(fun(B,bool),fun(A,complex),hAPP(fun(A,fun(fun(B,bool),complex)),fun(fun(B,bool),fun(A,complex)),combc(A,fun(B,bool),complex),hAPP(fun(A,fun(B,complex)),fun(A,fun(fun(B,bool),complex)),hAPP(fun(fun(B,complex),fun(fun(B,bool),complex)),fun(fun(A,fun(B,complex)),fun(A,fun(fun(B,bool),complex))),combb(fun(B,complex),fun(fun(B,bool),complex),A),big_co1399186613setsum(B,complex)),hAPP(fun(B,complex),fun(A,fun(B,complex)),hAPP(fun(A,fun(fun(B,complex),fun(B,complex))),fun(fun(B,complex),fun(A,fun(B,complex))),combc(A,fun(B,complex),fun(B,complex)),hAPP(fun(A,fun(complex,complex)),fun(A,fun(fun(B,complex),fun(B,complex))),hAPP(fun(fun(complex,complex),fun(fun(B,complex),fun(B,complex))),fun(fun(A,fun(complex,complex)),fun(A,fun(fun(B,complex),fun(B,complex)))),combb(fun(complex,complex),fun(fun(B,complex),fun(B,complex)),A),combb(complex,complex,B)),hAPP(fun(A,complex),fun(A,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(A,complex),fun(A,fun(complex,complex))),combb(complex,fun(complex,complex),A),times_times(complex)),C))),D))),E)),F) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),C),F)),hAPP(fun(B,bool),complex,hAPP(fun(B,complex),fun(fun(B,bool),complex),big_co1399186613setsum(B,complex),D),E)). [resolve(6919,a,6915,a)].
% 267.70/267.43 6920 semiring_0(code_code_numeral) # label(arity_Code__Numeral_Ocode__numeral___Rings_Osemiring__0) # label(axiom). [assumption].
% 267.70/267.43 Derived: -power(code_code_numeral) | hAPP(int,nat,number_number_of(nat),A) != zero_zero(nat) | hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),zero_zero(code_code_numeral)),hAPP(int,nat,number_number_of(nat),A)) = one_one(code_code_numeral). [resolve(6920,a,6905,b)].
% 267.70/267.43 Derived: -power(code_code_numeral) | hAPP(int,nat,number_number_of(nat),A) = zero_zero(nat) | hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),zero_zero(code_code_numeral)),hAPP(int,nat,number_number_of(nat),A)) = zero_zero(code_code_numeral). [resolve(6920,a,6906,b)].
% 267.70/267.43 Derived: -power(code_code_numeral) | hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),zero_zero(code_code_numeral)),hAPP(nat,nat,suc,A)) = zero_zero(code_code_numeral). [resolve(6920,a,6907,b)].
% 267.70/267.43 Derived: -power(code_code_numeral) | zero_zero(nat) != A | hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),zero_zero(code_code_numeral)),A) = one_one(code_code_numeral). [resolve(6920,a,6908,b)].
% 267.70/267.43 Derived: -power(code_code_numeral) | zero_zero(nat) = A | hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),zero_zero(code_code_numeral)),A) = zero_zero(code_code_numeral). [resolve(6920,a,6909,b)].
% 267.70/267.43 Derived: -dvd(code_code_numeral) | -hBOOL(hAPP(code_code_numeral,bool,A,hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),B),C))) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),B),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),f310(code_code_numeral,A,B)),zero_zero(code_code_numeral)))). [resolve(6920,a,6910,b)].
% 267.70/267.44 Derived: -dvd(code_code_numeral) | -hBOOL(hAPP(code_code_numeral,bool,A,hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),B),C))) | hBOOL(hAPP(code_code_numeral,bool,A,f310(code_code_numeral,A,B))). [resolve(6920,a,6911,b)].
% 267.70/267.44 Derived: -dvd(code_code_numeral) | hBOOL(hAPP(code_code_numeral,bool,A,hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),B),f311(code_code_numeral,A,B)))) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),B),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),C),zero_zero(code_code_numeral)))) | -hBOOL(hAPP(code_code_numeral,bool,A,C)). [resolve(6920,a,6912,b)].
% 267.70/267.44 Derived: hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),hAPP(fun(A,code_code_numeral),fun(A,code_code_numeral),hAPP(fun(code_code_numeral,code_code_numeral),fun(fun(A,code_code_numeral),fun(A,code_code_numeral)),combb(code_code_numeral,code_code_numeral,A),hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),B)),C)),D) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),B),hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),C),D)). [resolve(6920,a,6913,a)].
% 267.70/267.44 Derived: hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),hAPP(code_code_numeral,fun(A,code_code_numeral),hAPP(fun(A,fun(code_code_numeral,code_code_numeral)),fun(code_code_numeral,fun(A,code_code_numeral)),combc(A,code_code_numeral,code_code_numeral),hAPP(fun(A,code_code_numeral),fun(A,fun(code_code_numeral,code_code_numeral)),hAPP(fun(code_code_numeral,fun(code_code_numeral,code_code_numeral)),fun(fun(A,code_code_numeral),fun(A,fun(code_code_numeral,code_code_numeral))),combb(code_code_numeral,fun(code_code_numeral,code_code_numeral),A),times_times(code_code_numeral)),B)),C)),D) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),B),D)),C). [resolve(6920,a,6914,a)].
% 267.70/267.44 Derived: hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),hAPP(fun(B,bool),fun(A,code_code_numeral),hAPP(fun(A,fun(fun(B,bool),code_code_numeral)),fun(fun(B,bool),fun(A,code_code_numeral)),combc(A,fun(B,bool),code_code_numeral),hAPP(fun(A,fun(B,code_code_numeral)),fun(A,fun(fun(B,bool),code_code_numeral)),hAPP(fun(fun(B,code_code_numeral),fun(fun(B,bool),code_code_numeral)),fun(fun(A,fun(B,code_code_numeral)),fun(A,fun(fun(B,bool),code_code_numeral))),combb(fun(B,code_code_numeral),fun(fun(B,bool),code_code_numeral),A),big_co1399186613setsum(B,code_code_numeral)),hAPP(fun(B,code_code_numeral),fun(A,fun(B,code_code_numeral)),hAPP(fun(A,fun(fun(B,code_code_numeral),fun(B,code_code_numeral))),fun(fun(B,code_code_numeral),fun(A,fun(B,code_code_numeral))),combc(A,fun(B,code_code_numeral),fun(B,code_code_numeral)),hAPP(fun(A,fun(code_code_numeral,code_code_numeral)),fun(A,fun(fun(B,code_code_numeral),fun(B,code_code_numeral))),hAPP(fun(fun(code_code_numeral,code_code_numeral),fun(fun(B,code_code_numeral),fun(B,code_code_numeral))),fun(fun(A,fun(code_code_numeral,code_code_numeral)),fun(A,fun(fun(B,code_code_numeral),fun(B,code_code_numeral)))),combb(fun(code_code_numeral,code_code_numeral),fun(fun(B,code_code_numeral),fun(B,code_code_numeral)),A),combb(code_code_numeral,code_code_numeral,B)),hAPP(fun(A,code_code_numeral),fun(A,fun(code_code_numeral,code_code_numeral)),hAPP(fun(code_code_numeral,fun(code_code_numeral,code_code_numeral)),fun(fun(A,code_code_numeral),fun(A,fun(code_code_numeral,code_code_numeral))),combb(code_code_numeral,fun(code_code_numeral,code_code_numeral),A),times_times(code_code_numeral)),C))),D))),E)),F) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),C),F)),hAPP(fun(B,bool),code_code_numeral,hAPP(fun(B,code_code_numeral),fun(fun(B,bool),code_code_numeral),big_co1399186613setsum(B,code_code_numeral),D),E)). [resolve(6920,a,6915,a)].
% 267.70/267.45 6921 semiring_0(quickcheck_code_int) # label(arity_Quickcheck__Narrowing_Ocode__int___Rings_Osemiring__0) # label(axiom). [assumption].
% 267.70/267.45 Derived: -power(quickcheck_code_int) | hAPP(int,nat,number_number_of(nat),A) != zero_zero(nat) | hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),zero_zero(quickcheck_code_int)),hAPP(int,nat,number_number_of(nat),A)) = one_one(quickcheck_code_int). [resolve(6921,a,6905,b)].
% 267.70/267.45 Derived: -power(quickcheck_code_int) | hAPP(int,nat,number_number_of(nat),A) = zero_zero(nat) | hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),zero_zero(quickcheck_code_int)),hAPP(int,nat,number_number_of(nat),A)) = zero_zero(quickcheck_code_int). [resolve(6921,a,6906,b)].
% 267.70/267.45 Derived: -power(quickcheck_code_int) | hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),zero_zero(quickcheck_code_int)),hAPP(nat,nat,suc,A)) = zero_zero(quickcheck_code_int). [resolve(6921,a,6907,b)].
% 267.70/267.45 Derived: -power(quickcheck_code_int) | zero_zero(nat) != A | hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),zero_zero(quickcheck_code_int)),A) = one_one(quickcheck_code_int). [resolve(6921,a,6908,b)].
% 267.70/267.45 Derived: -power(quickcheck_code_int) | zero_zero(nat) = A | hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),zero_zero(quickcheck_code_int)),A) = zero_zero(quickcheck_code_int). [resolve(6921,a,6909,b)].
% 267.70/267.45 Derived: -dvd(quickcheck_code_int) | -hBOOL(hAPP(quickcheck_code_int,bool,A,hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),B),C))) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),B),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),f310(quickcheck_code_int,A,B)),zero_zero(quickcheck_code_int)))). [resolve(6921,a,6910,b)].
% 267.70/267.45 Derived: -dvd(quickcheck_code_int) | -hBOOL(hAPP(quickcheck_code_int,bool,A,hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),B),C))) | hBOOL(hAPP(quickcheck_code_int,bool,A,f310(quickcheck_code_int,A,B))). [resolve(6921,a,6911,b)].
% 267.70/267.45 Derived: -dvd(quickcheck_code_int) | hBOOL(hAPP(quickcheck_code_int,bool,A,hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),B),f311(quickcheck_code_int,A,B)))) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),B),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),C),zero_zero(quickcheck_code_int)))) | -hBOOL(hAPP(quickcheck_code_int,bool,A,C)). [resolve(6921,a,6912,b)].
% 267.70/267.45 Derived: hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),hAPP(fun(A,quickcheck_code_int),fun(A,quickcheck_code_int),hAPP(fun(quickcheck_code_int,quickcheck_code_int),fun(fun(A,quickcheck_code_int),fun(A,quickcheck_code_int)),combb(quickcheck_code_int,quickcheck_code_int,A),hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),B)),C)),D) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),B),hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),C),D)). [resolve(6921,a,6913,a)].
% 267.70/267.45 Derived: hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),hAPP(quickcheck_code_int,fun(A,quickcheck_code_int),hAPP(fun(A,fun(quickcheck_code_int,quickcheck_code_int)),fun(quickcheck_code_int,fun(A,quickcheck_code_int)),combc(A,quickcheck_code_int,quickcheck_code_int),hAPP(fun(A,quickcheck_code_int),fun(A,fun(quickcheck_code_int,quickcheck_code_int)),hAPP(fun(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int)),fun(fun(A,quickcheck_code_int),fun(A,fun(quickcheck_code_int,quickcheck_code_int))),combb(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),A),times_times(quickcheck_code_int)),B)),C)),D) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),B),D)),C). [resolve(6921,a,6914,a)].
% 267.70/267.45 Derived: hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),hAPP(fun(B,bool),fun(A,quickcheck_code_int),hAPP(fun(A,fun(fun(B,bool),quickcheck_code_int)),fun(fun(B,bool),fun(A,quickcheck_code_int)),combc(A,fun(B,bool),quickcheck_code_int),hAPP(fun(A,fun(B,quickcheck_code_int)),fun(A,fun(fun(B,bool),quickcheck_code_int)),hAPP(fun(fun(B,quickcheck_code_int),fun(fun(B,bool),quickcheck_code_int)),fun(fun(A,fun(B,quickcheck_code_int)),fun(A,fun(fun(B,bool),quickcheck_code_int))),combb(fun(B,quickcheck_code_int),fun(fun(B,bool),quickcheck_code_int),A),big_co1399186613setsum(B,quickcheck_code_int)),hAPP(fun(B,quickcheck_code_int),fun(A,fun(B,quickcheck_code_int)),hAPP(fun(A,fun(fun(B,quickcheck_code_int),fun(B,quickcheck_code_int))),fun(fun(B,quickcheck_code_int),fun(A,fun(B,quickcheck_code_int))),combc(A,fun(B,quickcheck_code_int),fun(B,quickcheck_code_int)),hAPP(fun(A,fun(quickcheck_code_int,quickcheck_code_int)),fun(A,fun(fun(B,quickcheck_code_int),fun(B,quickcheck_code_int))),hAPP(fun(fun(quickcheck_code_int,quickcheck_code_int),fun(fun(B,quickcheck_code_int),fun(B,quickcheck_code_int))),fun(fun(A,fun(quickcheck_code_int,quickcheck_code_int)),fun(A,fun(fun(B,quickcheck_code_int),fun(B,quickcheck_code_int)))),combb(fun(quickcheck_code_int,quickcheck_code_int),fun(fun(B,quickcheck_code_int),fun(B,quickcheck_code_int)),A),combb(quickcheck_code_int,quickcheck_code_int,B)),hAPP(fun(A,quickcheck_code_int),fun(A,fun(quickcheck_code_int,quickcheck_code_int)),hAPP(fun(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int)),fun(fun(A,quickcheck_code_int),fun(A,fun(quickcheck_code_int,quickcheck_code_int))),combb(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),A),times_times(quickcheck_code_int)),C))),D))),E)),F) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),C),F)),hAPP(fun(B,bool),quickcheck_code_int,hAPP(fun(B,quickcheck_code_int),fun(fun(B,bool),quickcheck_code_int),big_co1399186613setsum(B,quickcheck_code_int),D),E)). [resolve(6921,a,6915,a)].
% 272.32/272.06 6922 number_semiring(int) # label(arity_Int_Oint___Int_Onumber__semiring) # label(axiom). [assumption].
% 272.32/272.06 6923 -number_semiring(A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),B)) | hAPP(int,A,number_number_of(A),hAPP(int,int,succ,B)) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(int,A,number_number_of(A),B)),one_one(A)) # label(fact_1609_semiring__number__of__add__1) # label(axiom). [clausify(1703)].
% 272.32/272.06 6924 -number_semiring(A) | hAPP(int,A,number_number_of(A),pls) = zero_zero(A) # label(fact_1625_semiring__numeral__0__eq__0) # label(axiom). [clausify(1712)].
% 272.32/272.06 6925 -number_semiring(A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),C)) | hAPP(int,A,number_number_of(A),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),C)) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),B)),hAPP(int,A,number_number_of(A),C)) # label(fact_1651_semiring__mult__number__of) # label(axiom). [clausify(1725)].
% 272.32/272.06 6926 -number_semiring(A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),C)) | hAPP(int,A,number_number_of(A),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),B),C)) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(int,A,number_number_of(A),B)),hAPP(int,A,number_number_of(A),C)) # label(fact_1652_semiring__add__number__of) # label(axiom). [clausify(1726)].
% 272.32/272.06 6927 -number_semiring(A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),B)) | hAPP(int,A,number_number_of(A),hAPP(int,int,succ,B)) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),one_one(A)),hAPP(int,A,number_number_of(A),B)) # label(fact_1661_semiring__1__add__number__of) # label(axiom). [clausify(1735)].
% 272.32/272.06 6928 -number_semiring(A) | hAPP(int,A,number_number_of(A),hAPP(int,int,bit1,pls)) = one_one(A) # label(fact_1705_semiring__numeral__1__eq__1) # label(axiom). [clausify(1776)].
% 272.32/272.06 6929 -number_semiring(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),B) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),B) # label(fact_1805_semiring__mult__2) # label(axiom). [clausify(1866)].
% 272.32/272.06 6930 -number_semiring(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(int,A,number_number_of(A),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),B) # label(fact_1807_semiring__mult__2__right) # label(axiom). [clausify(1868)].
% 272.32/272.06 6931 -number_semiring(A) | hAPP(int,A,number_number_of(A),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),one_one(A)),one_one(A)) # label(fact_1809_semiring__one__add__one__is__two) # label(axiom). [clausify(1870)].
% 272.32/272.06 6932 -number_semiring(A) | hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),C),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),B)),C)) # label(fact_1887_power2__sum) # label(axiom). [clausify(1932)].
% 272.32/272.06 6933 -number_semiring(A) | hAPP(nat,A,semiring_1_of_nat(A),B) = hAPP(int,A,number_number_of(A),hAPP(nat,int,semiring_1_of_nat(int),B)) # label(fact_2567_number__of__int) # label(axiom). [clausify(2569)].
% 272.32/272.08 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),A)) | hAPP(int,int,number_number_of(int),hAPP(int,int,succ,A)) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,number_number_of(int),A)),one_one(int)). [resolve(6922,a,6923,a)].
% 272.32/272.08 Derived: hAPP(int,int,number_number_of(int),pls) = zero_zero(int). [resolve(6922,a,6924,a)].
% 272.32/272.08 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),B)) | hAPP(int,int,number_number_of(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),hAPP(int,int,number_number_of(int),A)),hAPP(int,int,number_number_of(int),B)). [resolve(6922,a,6925,a)].
% 272.32/272.08 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),B)) | hAPP(int,int,number_number_of(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),hAPP(int,int,number_number_of(int),A)),hAPP(int,int,number_number_of(int),B)). [resolve(6922,a,6926,a)].
% 272.32/272.08 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),A)) | hAPP(int,int,number_number_of(int),hAPP(int,int,succ,A)) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),hAPP(int,int,number_number_of(int),A)). [resolve(6922,a,6927,a)].
% 272.32/272.08 Derived: hAPP(int,int,number_number_of(int),hAPP(int,int,bit1,pls)) = one_one(int). [resolve(6922,a,6928,a)].
% 272.32/272.08 Derived: hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),A) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),A). [resolve(6922,a,6929,a)].
% 272.32/272.08 Derived: hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),A). [resolve(6922,a,6930,a)].
% 272.32/272.08 Derived: hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),one_one(int)). [resolve(6922,a,6931,a)].
% 272.32/272.08 Derived: hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),A)),B)). [resolve(6922,a,6932,a)].
% 272.32/272.08 Derived: hAPP(nat,int,semiring_1_of_nat(int),A) = hAPP(int,int,number_number_of(int),hAPP(nat,int,semiring_1_of_nat(int),A)). [resolve(6922,a,6933,a)].
% 272.32/272.08 6934 number_semiring(nat) # label(arity_Nat_Onat___Int_Onumber__semiring) # label(axiom). [assumption].
% 272.32/272.08 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),A)) | hAPP(int,nat,number_number_of(nat),hAPP(int,int,succ,A)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),A)),one_one(nat)). [resolve(6934,a,6923,a)].
% 272.32/272.08 Derived: hAPP(int,nat,number_number_of(nat),pls) = zero_zero(nat). [resolve(6934,a,6924,a)].
% 272.32/272.08 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),B)) | hAPP(int,nat,number_number_of(nat),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),A)),hAPP(int,nat,number_number_of(nat),B)). [resolve(6934,a,6925,a)].
% 272.32/272.10 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),B)) | hAPP(int,nat,number_number_of(nat),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),A)),hAPP(int,nat,number_number_of(nat),B)). [resolve(6934,a,6926,a)].
% 272.32/272.10 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),A)) | hAPP(int,nat,number_number_of(nat),hAPP(int,int,succ,A)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),hAPP(int,nat,number_number_of(nat),A)). [resolve(6934,a,6927,a)].
% 272.32/272.10 Derived: hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,pls)) = one_one(nat). [resolve(6934,a,6928,a)].
% 272.32/272.10 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),A) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),A). [resolve(6934,a,6929,a)].
% 272.32/272.10 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),A). [resolve(6934,a,6930,a)].
% 272.32/272.10 Derived: hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),one_one(nat)). [resolve(6934,a,6931,a)].
% 272.32/272.10 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),A)),B)). [resolve(6934,a,6932,a)].
% 272.32/272.10 Derived: hAPP(nat,nat,semiring_1_of_nat(nat),A) = hAPP(int,nat,number_number_of(nat),hAPP(nat,int,semiring_1_of_nat(int),A)). [resolve(6934,a,6933,a)].
% 272.32/272.10 6935 number_semiring(rat) # label(arity_Rat_Orat___Int_Onumber__semiring) # label(axiom). [assumption].
% 272.32/272.10 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),A)) | hAPP(int,rat,number_number_of(rat),hAPP(int,int,succ,A)) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(int,rat,number_number_of(rat),A)),one_one(rat)). [resolve(6935,a,6923,a)].
% 272.32/272.10 Derived: hAPP(int,rat,number_number_of(rat),pls) = zero_zero(rat). [resolve(6935,a,6924,a)].
% 272.32/272.10 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),B)) | hAPP(int,rat,number_number_of(rat),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(int,rat,number_number_of(rat),A)),hAPP(int,rat,number_number_of(rat),B)). [resolve(6935,a,6925,a)].
% 272.32/272.10 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),B)) | hAPP(int,rat,number_number_of(rat),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B)) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(int,rat,number_number_of(rat),A)),hAPP(int,rat,number_number_of(rat),B)). [resolve(6935,a,6926,a)].
% 272.32/272.10 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),A)) | hAPP(int,rat,number_number_of(rat),hAPP(int,int,succ,A)) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),one_one(rat)),hAPP(int,rat,number_number_of(rat),A)). [resolve(6935,a,6927,a)].
% 272.32/272.10 Derived: hAPP(int,rat,number_number_of(rat),hAPP(int,int,bit1,pls)) = one_one(rat). [resolve(6935,a,6928,a)].
% 272.32/272.12 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(int,rat,number_number_of(rat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),A) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),A). [resolve(6935,a,6929,a)].
% 272.32/272.12 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),hAPP(int,rat,number_number_of(rat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),A). [resolve(6935,a,6930,a)].
% 272.32/272.12 Derived: hAPP(int,rat,number_number_of(rat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),one_one(rat)),one_one(rat)). [resolve(6935,a,6931,a)].
% 272.32/272.12 Derived: hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),B)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(int,rat,number_number_of(rat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),A)),B)). [resolve(6935,a,6932,a)].
% 272.32/272.12 Derived: hAPP(nat,rat,semiring_1_of_nat(rat),A) = hAPP(int,rat,number_number_of(rat),hAPP(nat,int,semiring_1_of_nat(int),A)). [resolve(6935,a,6933,a)].
% 272.32/272.12 6936 number_semiring(real) # label(arity_RealDef_Oreal___Int_Onumber__semiring) # label(axiom). [assumption].
% 272.32/272.12 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),A)) | hAPP(int,real,number_number_of(real),hAPP(int,int,succ,A)) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(int,real,number_number_of(real),A)),one_one(real)). [resolve(6936,a,6923,a)].
% 272.32/272.12 Derived: hAPP(int,real,number_number_of(real),pls) = zero_zero(real). [resolve(6936,a,6924,a)].
% 272.32/272.12 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),B)) | hAPP(int,real,number_number_of(real),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),A)),hAPP(int,real,number_number_of(real),B)). [resolve(6936,a,6925,a)].
% 272.32/272.12 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),B)) | hAPP(int,real,number_number_of(real),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B)) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(int,real,number_number_of(real),A)),hAPP(int,real,number_number_of(real),B)). [resolve(6936,a,6926,a)].
% 272.32/272.12 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),A)) | hAPP(int,real,number_number_of(real),hAPP(int,int,succ,A)) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),one_one(real)),hAPP(int,real,number_number_of(real),A)). [resolve(6936,a,6927,a)].
% 272.32/272.12 Derived: hAPP(int,real,number_number_of(real),hAPP(int,int,bit1,pls)) = one_one(real). [resolve(6936,a,6928,a)].
% 272.32/272.12 Derived: hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),A) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),A). [resolve(6936,a,6929,a)].
% 272.32/272.12 Derived: hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),A). [resolve(6936,a,6930,a)].
% 272.32/272.12 Derived: hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),one_one(real)),one_one(real)). [resolve(6936,a,6931,a)].
% 272.32/272.12 Derived: hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),B)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),A)),B)). [resolve(6936,a,6932,a)].
% 272.41/272.14 Derived: hAPP(nat,real,semiring_1_of_nat(real),A) = hAPP(int,real,number_number_of(real),hAPP(nat,int,semiring_1_of_nat(int),A)). [resolve(6936,a,6933,a)].
% 272.41/272.14 6937 number_semiring(complex) # label(arity_Complex_Ocomplex___Int_Onumber__semiring) # label(axiom). [assumption].
% 272.41/272.14 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),A)) | hAPP(int,complex,number_number_of(complex),hAPP(int,int,succ,A)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(int,complex,number_number_of(complex),A)),one_one(complex)). [resolve(6937,a,6923,a)].
% 272.41/272.14 Derived: hAPP(int,complex,number_number_of(complex),pls) = zero_zero(complex). [resolve(6937,a,6924,a)].
% 272.41/272.14 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),B)) | hAPP(int,complex,number_number_of(complex),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(int,complex,number_number_of(complex),A)),hAPP(int,complex,number_number_of(complex),B)). [resolve(6937,a,6925,a)].
% 272.41/272.14 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),B)) | hAPP(int,complex,number_number_of(complex),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(int,complex,number_number_of(complex),A)),hAPP(int,complex,number_number_of(complex),B)). [resolve(6937,a,6926,a)].
% 272.41/272.14 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),A)) | hAPP(int,complex,number_number_of(complex),hAPP(int,int,succ,A)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),one_one(complex)),hAPP(int,complex,number_number_of(complex),A)). [resolve(6937,a,6927,a)].
% 272.41/272.14 Derived: hAPP(int,complex,number_number_of(complex),hAPP(int,int,bit1,pls)) = one_one(complex). [resolve(6937,a,6928,a)].
% 272.41/272.14 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(int,complex,number_number_of(complex),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),A) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),A),A). [resolve(6937,a,6929,a)].
% 272.41/272.14 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),hAPP(int,complex,number_number_of(complex),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),A),A). [resolve(6937,a,6930,a)].
% 272.41/272.14 Derived: hAPP(int,complex,number_number_of(complex),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),one_one(complex)),one_one(complex)). [resolve(6937,a,6931,a)].
% 272.41/272.14 Derived: hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),A),B)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(int,complex,number_number_of(complex),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),A)),B)). [resolve(6937,a,6932,a)].
% 276.97/276.72 Derived: hAPP(nat,complex,semiring_1_of_nat(complex),A) = hAPP(int,complex,number_number_of(complex),hAPP(nat,int,semiring_1_of_nat(int),A)). [resolve(6937,a,6933,a)].
% 276.97/276.72 6938 real_n2089651433ebra_1(real) # label(arity_RealDef_Oreal___RealVector_Oreal__normed__algebra__1) # label(axiom). [assumption].
% 276.97/276.72 6939 -real_n2089651433ebra_1(A) | hAPP(A,A,sgn_sgn(A),one_one(A)) = one_one(A) # label(fact_2070_sgn__one) # label(axiom). [clausify(2098)].
% 276.97/276.72 6940 -real_n2089651433ebra_1(A) | hAPP(nat,real,semiring_1_of_nat(real),B) = hAPP(A,real,norm_norm(A),hAPP(nat,A,semiring_1_of_nat(A),B)) # label(fact_2688_norm__of__nat) # label(axiom). [clausify(2680)].
% 276.97/276.72 6941 -real_n2089651433ebra_1(A) | hAPP(A,real,norm_norm(A),one_one(A)) = one_one(real) # label(fact_2701_norm__one) # label(axiom). [clausify(2693)].
% 276.97/276.72 6942 -real_n2089651433ebra_1(A) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(A,real,norm_norm(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(A,real,norm_norm(A),B)),C))) # label(fact_2716_norm__power__ineq) # label(axiom). [clausify(2708)].
% 276.97/276.72 6943 -number_ring(A) | -real_n2089651433ebra_1(A) | hAPP(real,real,abs_abs(real),hAPP(int,real,number_number_of(real),B)) = hAPP(A,real,norm_norm(A),hAPP(int,A,number_number_of(A),B)) # label(fact_2720_norm__number__of) # label(axiom). [clausify(2712)].
% 276.97/276.72 6944 -real_n2089651433ebra_1(A) | hAPP(real,real,abs_abs(real),B) = hAPP(A,real,norm_norm(A),hAPP(real,A,of_real(A),B)) # label(fact_2803_norm__of__real) # label(axiom). [clausify(2788)].
% 276.97/276.72 6945 -real_n2089651433ebra_1(A) | hAPP(real,A,of_real(A),hAPP(real,real,sgn_sgn(real),B)) = hAPP(A,A,sgn_sgn(A),hAPP(real,A,of_real(A),B)) # label(fact_2807_sgn__of__real) # label(axiom). [clausify(2792)].
% 276.97/276.72 6946 -real_n2089651433ebra_1(A) | hAPP(real,real,abs_abs(real),hAPP(int,real,ring_1_of_int(real),B)) = hAPP(A,real,norm_norm(A),hAPP(int,A,ring_1_of_int(A),B)) # label(fact_3581_norm__of__int) # label(axiom). [clausify(3534)].
% 276.97/276.72 6947 -real_n2089651433ebra_1(A) | hAPP(fun(nat,A),A,suminf(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),times_times(A)),B)),hAPP(A,fun(nat,A),power_power(A),zero_zero(A)))) = hAPP(nat,A,B,zero_zero(nat)) # label(fact_3970_powser__zero) # label(axiom). [clausify(3911)].
% 276.97/276.72 6948 -real_n2089651433ebra_1(A) | -banach(A) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(A,real,norm_norm(A),B)),one_one(real))) | hBOOL(hAPP(fun(nat,A),bool,summable(A),hAPP(A,fun(nat,A),power_power(A),B))) # label(fact_4025_complete__algebra__summable__geometric) # label(axiom). [clausify(3965)].
% 276.97/276.72 6949 -real_n2089651433ebra_1(A) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(A,real,norm_norm(A),B)),one_one(real))) | hBOOL(hAPP(filter(nat),bool,hAPP(A,fun(filter(nat),bool),hAPP(fun(nat,A),fun(A,fun(filter(nat),bool)),tendsto(nat,A),hAPP(A,fun(nat,A),power_power(A),B)),zero_zero(A)),sequentially)) # label(fact_4434_LIMSEQ__power__zero) # label(axiom). [clausify(4363)].
% 276.97/276.72 6950 -metric_space(A) | -real_n2089651433ebra_1(B) | -hBOOL(hAPP(filter(B),bool,hAPP(A,fun(filter(B),bool),hAPP(fun(B,A),fun(A,fun(filter(B),bool)),tendsto(B,A),hAPP(A,fun(B,A),combk(A,B),C)),D),hAPP(B,filter(B),at(B),E))) | ti(A,D) = ti(A,C) # label(fact_4556_LIM__const__eq) # label(axiom). [clausify(4483)].
% 276.97/276.72 6951 -real_n2089651433ebra_1(A) | -metric_space(B) | ti(B,C) = ti(B,D) | -hBOOL(hAPP(filter(A),bool,hAPP(B,fun(filter(A),bool),hAPP(fun(A,B),fun(B,fun(filter(A),bool)),tendsto(A,B),hAPP(B,fun(A,B),combk(B,A),D)),C),hAPP(A,filter(A),at(A),E))) # label(fact_4558_LIM__const__not__eq) # label(axiom). [clausify(4485)].
% 276.97/276.73 6952 -metric_space(A) | -real_n2089651433ebra_1(B) | -hBOOL(hAPP(filter(B),bool,hAPP(A,fun(filter(B),bool),hAPP(fun(B,A),fun(A,fun(filter(B),bool)),tendsto(B,A),C),D),hAPP(B,filter(B),at(B),E))) | -hBOOL(hAPP(filter(B),bool,hAPP(A,fun(filter(B),bool),hAPP(fun(B,A),fun(A,fun(filter(B),bool)),tendsto(B,A),C),F),hAPP(B,filter(B),at(B),E))) | ti(A,D) = ti(A,F) # label(fact_4571_LIM__unique) # label(axiom). [clausify(4498)].
% 276.97/276.73 6953 -real_n2089651433ebra_1(A) | -banach(A) | hBOOL(hAPP(fun(nat,A),bool,summable(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,real),fun(nat,fun(A,A)),hAPP(fun(real,fun(A,A)),fun(fun(nat,real),fun(nat,fun(A,A))),combb(real,fun(A,A),nat),scaleR_scaleR(A)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),inverse_inverse(real)),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),fact_fact(nat))))),hAPP(A,fun(nat,A),power_power(A),B)))) # label(fact_4755_summable__exp__generic) # label(axiom). [clausify(4681)].
% 276.97/276.73 6954 -real_n2089651433ebra_1(A) | -banach(A) | hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,A),fun(nat,real),hAPP(fun(A,real),fun(fun(nat,A),fun(nat,real)),combb(A,real,nat),norm_norm(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,real),fun(nat,fun(A,A)),hAPP(fun(real,fun(A,A)),fun(fun(nat,real),fun(nat,fun(A,A))),combb(real,fun(A,A),nat),scaleR_scaleR(A)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),inverse_inverse(real)),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),fact_fact(nat))))),hAPP(A,fun(nat,A),power_power(A),B))))) # label(fact_4756_summable__norm__exp) # label(axiom). [clausify(4682)].
% 276.97/276.73 6955 -topological_space(A) | -real_n2089651433ebra_1(B) | -hBOOL(hAPP(A,bool,hAPP(fun(A,real),fun(A,bool),isCont(A,real),C),D)) | hBOOL(hAPP(A,bool,hAPP(fun(A,B),fun(A,bool),isCont(A,B),hAPP(fun(A,real),fun(A,B),hAPP(fun(real,B),fun(fun(A,real),fun(A,B)),combb(real,B,A),of_real(B)),C)),D)) # label(fact_4907_isCont__of__real) # label(axiom). [clausify(4827)].
% 276.97/276.73 Derived: hAPP(real,real,sgn_sgn(real),one_one(real)) = one_one(real). [resolve(6938,a,6939,a)].
% 276.97/276.73 Derived: hAPP(nat,real,semiring_1_of_nat(real),A) = hAPP(real,real,norm_norm(real),hAPP(nat,real,semiring_1_of_nat(real),A)). [resolve(6938,a,6940,a)].
% 276.97/276.73 Derived: hAPP(real,real,norm_norm(real),one_one(real)) = one_one(real). [resolve(6938,a,6941,a)].
% 276.97/276.73 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,norm_norm(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),B))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,norm_norm(real),A)),B))). [resolve(6938,a,6942,a)].
% 276.97/276.73 Derived: -number_ring(real) | hAPP(real,real,abs_abs(real),hAPP(int,real,number_number_of(real),A)) = hAPP(real,real,norm_norm(real),hAPP(int,real,number_number_of(real),A)). [resolve(6938,a,6943,b)].
% 276.97/276.73 Derived: hAPP(real,real,abs_abs(real),A) = hAPP(real,real,norm_norm(real),hAPP(real,real,of_real(real),A)). [resolve(6938,a,6944,a)].
% 276.97/276.73 Derived: hAPP(real,real,of_real(real),hAPP(real,real,sgn_sgn(real),A)) = hAPP(real,real,sgn_sgn(real),hAPP(real,real,of_real(real),A)). [resolve(6938,a,6945,a)].
% 276.97/276.73 Derived: hAPP(real,real,abs_abs(real),hAPP(int,real,ring_1_of_int(real),A)) = hAPP(real,real,norm_norm(real),hAPP(int,real,ring_1_of_int(real),A)). [resolve(6938,a,6946,a)].
% 276.97/276.73 Derived: hAPP(fun(nat,real),real,suminf(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),A)),hAPP(real,fun(nat,real),power_power(real),zero_zero(real)))) = hAPP(nat,real,A,zero_zero(nat)). [resolve(6938,a,6947,a)].
% 276.97/276.75 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,norm_norm(real),A)),one_one(real))) | hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),hAPP(real,fun(nat,real),power_power(real),A)),zero_zero(real)),sequentially)). [resolve(6938,a,6949,a)].
% 276.97/276.75 Derived: -metric_space(A) | -hBOOL(hAPP(filter(real),bool,hAPP(A,fun(filter(real),bool),hAPP(fun(real,A),fun(A,fun(filter(real),bool)),tendsto(real,A),hAPP(A,fun(real,A),combk(A,real),B)),C),hAPP(real,filter(real),at(real),D))) | ti(A,C) = ti(A,B). [resolve(6938,a,6950,b)].
% 276.97/276.75 Derived: -metric_space(A) | -hBOOL(hAPP(filter(real),bool,hAPP(A,fun(filter(real),bool),hAPP(fun(real,A),fun(A,fun(filter(real),bool)),tendsto(real,A),B),C),hAPP(real,filter(real),at(real),D))) | -hBOOL(hAPP(filter(real),bool,hAPP(A,fun(filter(real),bool),hAPP(fun(real,A),fun(A,fun(filter(real),bool)),tendsto(real,A),B),E),hAPP(real,filter(real),at(real),D))) | ti(A,C) = ti(A,E). [resolve(6938,a,6952,b)].
% 276.97/276.75 Derived: -banach(real) | hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),scaleR_scaleR(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),inverse_inverse(real)),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),fact_fact(nat))))),hAPP(real,fun(nat,real),power_power(real),A)))). [resolve(6938,a,6953,a)].
% 276.97/276.75 Derived: -banach(real) | hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),norm_norm(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),scaleR_scaleR(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),inverse_inverse(real)),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),fact_fact(nat))))),hAPP(real,fun(nat,real),power_power(real),A))))). [resolve(6938,a,6954,a)].
% 276.97/276.75 Derived: -topological_space(A) | -hBOOL(hAPP(A,bool,hAPP(fun(A,real),fun(A,bool),isCont(A,real),B),C)) | hBOOL(hAPP(A,bool,hAPP(fun(A,real),fun(A,bool),isCont(A,real),hAPP(fun(A,real),fun(A,real),hAPP(fun(real,real),fun(fun(A,real),fun(A,real)),combb(real,real,A),of_real(real)),B)),C)). [resolve(6938,a,6955,b)].
% 276.97/276.75 6956 real_n2089651433ebra_1(complex) # label(arity_Complex_Ocomplex___RealVector_Oreal__normed__algebra__1) # label(axiom). [assumption].
% 276.97/276.75 Derived: hAPP(complex,complex,sgn_sgn(complex),one_one(complex)) = one_one(complex). [resolve(6956,a,6939,a)].
% 276.97/276.75 Derived: hAPP(nat,real,semiring_1_of_nat(real),A) = hAPP(complex,real,norm_norm(complex),hAPP(nat,complex,semiring_1_of_nat(complex),A)). [resolve(6956,a,6940,a)].
% 276.97/276.75 Derived: hAPP(complex,real,norm_norm(complex),one_one(complex)) = one_one(real). [resolve(6956,a,6941,a)].
% 276.97/276.75 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(complex,real,norm_norm(complex),hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),A),B))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(complex,real,norm_norm(complex),A)),B))). [resolve(6956,a,6942,a)].
% 276.97/276.75 Derived: -number_ring(complex) | hAPP(real,real,abs_abs(real),hAPP(int,real,number_number_of(real),A)) = hAPP(complex,real,norm_norm(complex),hAPP(int,complex,number_number_of(complex),A)). [resolve(6956,a,6943,b)].
% 276.97/276.76 Derived: hAPP(real,real,abs_abs(real),A) = hAPP(complex,real,norm_norm(complex),hAPP(real,complex,of_real(complex),A)). [resolve(6956,a,6944,a)].
% 276.97/276.76 Derived: hAPP(real,complex,of_real(complex),hAPP(real,real,sgn_sgn(real),A)) = hAPP(complex,complex,sgn_sgn(complex),hAPP(real,complex,of_real(complex),A)). [resolve(6956,a,6945,a)].
% 276.97/276.76 Derived: hAPP(real,real,abs_abs(real),hAPP(int,real,ring_1_of_int(real),A)) = hAPP(complex,real,norm_norm(complex),hAPP(int,complex,ring_1_of_int(complex),A)). [resolve(6956,a,6946,a)].
% 276.97/276.76 Derived: hAPP(fun(nat,complex),complex,suminf(complex),hAPP(fun(nat,complex),fun(nat,complex),hAPP(fun(nat,fun(complex,complex)),fun(fun(nat,complex),fun(nat,complex)),combs(nat,complex,complex),hAPP(fun(nat,complex),fun(nat,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(nat,complex),fun(nat,fun(complex,complex))),combb(complex,fun(complex,complex),nat),times_times(complex)),A)),hAPP(complex,fun(nat,complex),power_power(complex),zero_zero(complex)))) = hAPP(nat,complex,A,zero_zero(nat)). [resolve(6956,a,6947,a)].
% 276.97/276.76 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(complex,real,norm_norm(complex),A)),one_one(real))) | hBOOL(hAPP(filter(nat),bool,hAPP(complex,fun(filter(nat),bool),hAPP(fun(nat,complex),fun(complex,fun(filter(nat),bool)),tendsto(nat,complex),hAPP(complex,fun(nat,complex),power_power(complex),A)),zero_zero(complex)),sequentially)). [resolve(6956,a,6949,a)].
% 276.97/276.76 Derived: -metric_space(A) | -hBOOL(hAPP(filter(complex),bool,hAPP(A,fun(filter(complex),bool),hAPP(fun(complex,A),fun(A,fun(filter(complex),bool)),tendsto(complex,A),hAPP(A,fun(complex,A),combk(A,complex),B)),C),hAPP(complex,filter(complex),at(complex),D))) | ti(A,C) = ti(A,B). [resolve(6956,a,6950,b)].
% 276.97/276.76 Derived: -metric_space(A) | -hBOOL(hAPP(filter(complex),bool,hAPP(A,fun(filter(complex),bool),hAPP(fun(complex,A),fun(A,fun(filter(complex),bool)),tendsto(complex,A),B),C),hAPP(complex,filter(complex),at(complex),D))) | -hBOOL(hAPP(filter(complex),bool,hAPP(A,fun(filter(complex),bool),hAPP(fun(complex,A),fun(A,fun(filter(complex),bool)),tendsto(complex,A),B),E),hAPP(complex,filter(complex),at(complex),D))) | ti(A,C) = ti(A,E). [resolve(6956,a,6952,b)].
% 276.97/276.76 Derived: -banach(complex) | hBOOL(hAPP(fun(nat,complex),bool,summable(complex),hAPP(fun(nat,complex),fun(nat,complex),hAPP(fun(nat,fun(complex,complex)),fun(fun(nat,complex),fun(nat,complex)),combs(nat,complex,complex),hAPP(fun(nat,real),fun(nat,fun(complex,complex)),hAPP(fun(real,fun(complex,complex)),fun(fun(nat,real),fun(nat,fun(complex,complex))),combb(real,fun(complex,complex),nat),scaleR_scaleR(complex)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),inverse_inverse(real)),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),fact_fact(nat))))),hAPP(complex,fun(nat,complex),power_power(complex),A)))). [resolve(6956,a,6953,a)].
% 276.97/276.76 Derived: -banach(complex) | hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,complex),fun(nat,real),hAPP(fun(complex,real),fun(fun(nat,complex),fun(nat,real)),combb(complex,real,nat),norm_norm(complex)),hAPP(fun(nat,complex),fun(nat,complex),hAPP(fun(nat,fun(complex,complex)),fun(fun(nat,complex),fun(nat,complex)),combs(nat,complex,complex),hAPP(fun(nat,real),fun(nat,fun(complex,complex)),hAPP(fun(real,fun(complex,complex)),fun(fun(nat,real),fun(nat,fun(complex,complex))),combb(real,fun(complex,complex),nat),scaleR_scaleR(complex)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),inverse_inverse(real)),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),fact_fact(nat))))),hAPP(complex,fun(nat,complex),power_power(complex),A))))). [resolve(6956,a,6954,a)].
% 276.97/276.76 Derived: -topological_space(A) | -hBOOL(hAPP(A,bool,hAPP(fun(A,real),fun(A,bool),isCont(A,real),B),C)) | hBOOL(hAPP(A,bool,hAPP(fun(A,complex),fun(A,bool),isCont(A,complex),hAPP(fun(A,real),fun(A,complex),hAPP(fun(real,complex),fun(fun(A,real),fun(A,complex)),combb(real,complex,A),of_real(complex)),B)),C)). [resolve(6956,a,6955,b)].
% 277.90/277.63 6957 -real_n2089651433ebra_1(A) | -metric_space(int) | zero_zero(int) = ti(int,B) | -hBOOL(hAPP(filter(A),bool,hAPP(int,fun(filter(A),bool),hAPP(fun(A,int),fun(int,fun(filter(A),bool)),tendsto(A,int),hAPP(int,fun(A,int),combk(int,A),B)),zero_zero(int)),hAPP(A,filter(A),at(A),C))). [resolve(5549,a,5552,b)].
% 277.90/277.63 Derived: -metric_space(int) | zero_zero(int) = ti(int,A) | -hBOOL(hAPP(filter(real),bool,hAPP(int,fun(filter(real),bool),hAPP(fun(real,int),fun(int,fun(filter(real),bool)),tendsto(real,int),hAPP(int,fun(real,int),combk(int,real),A)),zero_zero(int)),hAPP(real,filter(real),at(real),B))). [resolve(6957,a,6938,a)].
% 277.90/277.63 Derived: -metric_space(int) | zero_zero(int) = ti(int,A) | -hBOOL(hAPP(filter(complex),bool,hAPP(int,fun(filter(complex),bool),hAPP(fun(complex,int),fun(int,fun(filter(complex),bool)),tendsto(complex,int),hAPP(int,fun(complex,int),combk(int,complex),A)),zero_zero(int)),hAPP(complex,filter(complex),at(complex),B))). [resolve(6957,a,6956,a)].
% 277.90/277.63 6958 -real_n2089651433ebra_1(A) | -metric_space(nat) | zero_zero(nat) = ti(nat,B) | -hBOOL(hAPP(filter(A),bool,hAPP(nat,fun(filter(A),bool),hAPP(fun(A,nat),fun(nat,fun(filter(A),bool)),tendsto(A,nat),hAPP(nat,fun(A,nat),combk(nat,A),B)),zero_zero(nat)),hAPP(A,filter(A),at(A),C))). [resolve(5553,a,5552,b)].
% 277.90/277.63 Derived: -metric_space(nat) | zero_zero(nat) = ti(nat,A) | -hBOOL(hAPP(filter(real),bool,hAPP(nat,fun(filter(real),bool),hAPP(fun(real,nat),fun(nat,fun(filter(real),bool)),tendsto(real,nat),hAPP(nat,fun(real,nat),combk(nat,real),A)),zero_zero(nat)),hAPP(real,filter(real),at(real),B))). [resolve(6958,a,6938,a)].
% 277.90/277.63 Derived: -metric_space(nat) | zero_zero(nat) = ti(nat,A) | -hBOOL(hAPP(filter(complex),bool,hAPP(nat,fun(filter(complex),bool),hAPP(fun(complex,nat),fun(nat,fun(filter(complex),bool)),tendsto(complex,nat),hAPP(nat,fun(complex,nat),combk(nat,complex),A)),zero_zero(nat)),hAPP(complex,filter(complex),at(complex),B))). [resolve(6958,a,6956,a)].
% 277.90/277.63 6959 -real_n2089651433ebra_1(A) | -metric_space(rat) | zero_zero(rat) = ti(rat,B) | -hBOOL(hAPP(filter(A),bool,hAPP(rat,fun(filter(A),bool),hAPP(fun(A,rat),fun(rat,fun(filter(A),bool)),tendsto(A,rat),hAPP(rat,fun(A,rat),combk(rat,A),B)),zero_zero(rat)),hAPP(A,filter(A),at(A),C))). [resolve(5554,a,5552,b)].
% 277.90/277.63 Derived: -metric_space(rat) | zero_zero(rat) = ti(rat,A) | -hBOOL(hAPP(filter(real),bool,hAPP(rat,fun(filter(real),bool),hAPP(fun(real,rat),fun(rat,fun(filter(real),bool)),tendsto(real,rat),hAPP(rat,fun(real,rat),combk(rat,real),A)),zero_zero(rat)),hAPP(real,filter(real),at(real),B))). [resolve(6959,a,6938,a)].
% 277.90/277.63 Derived: -metric_space(rat) | zero_zero(rat) = ti(rat,A) | -hBOOL(hAPP(filter(complex),bool,hAPP(rat,fun(filter(complex),bool),hAPP(fun(complex,rat),fun(rat,fun(filter(complex),bool)),tendsto(complex,rat),hAPP(rat,fun(complex,rat),combk(rat,complex),A)),zero_zero(rat)),hAPP(complex,filter(complex),at(complex),B))). [resolve(6959,a,6956,a)].
% 277.90/277.63 6960 -real_n2089651433ebra_1(A) | -metric_space(real) | zero_zero(real) = ti(real,B) | -hBOOL(hAPP(filter(A),bool,hAPP(real,fun(filter(A),bool),hAPP(fun(A,real),fun(real,fun(filter(A),bool)),tendsto(A,real),hAPP(real,fun(A,real),combk(real,A),B)),zero_zero(real)),hAPP(A,filter(A),at(A),C))). [resolve(5555,a,5552,b)].
% 277.90/277.63 Derived: -metric_space(real) | zero_zero(real) = ti(real,A) | -hBOOL(hAPP(filter(real),bool,hAPP(real,fun(filter(real),bool),hAPP(fun(real,real),fun(real,fun(filter(real),bool)),tendsto(real,real),hAPP(real,fun(real,real),combk(real,real),A)),zero_zero(real)),hAPP(real,filter(real),at(real),B))). [resolve(6960,a,6938,a)].
% 277.90/277.63 Derived: -metric_space(real) | zero_zero(real) = ti(real,A) | -hBOOL(hAPP(filter(complex),bool,hAPP(real,fun(filter(complex),bool),hAPP(fun(complex,real),fun(real,fun(filter(complex),bool)),tendsto(complex,real),hAPP(real,fun(complex,real),combk(real,complex),A)),zero_zero(real)),hAPP(complex,filter(complex),at(complex),B))). [resolve(6960,a,6956,a)].
% 277.90/277.63 6961 -real_n2089651433ebra_1(A) | -metric_space(complex) | zero_zero(complex) = ti(complex,B) | -hBOOL(hAPP(filter(A),bool,hAPP(complex,fun(filter(A),bool),hAPP(fun(A,complex),fun(complex,fun(filter(A),bool)),tendsto(A,complex),hAPP(complex,fun(A,complex),combk(complex,A),B)),zero_zero(complex)),hAPP(A,filter(A),at(A),C))). [resolve(5556,a,5552,b)].
% 281.65/281.42 Derived: -metric_space(complex) | zero_zero(complex) = ti(complex,A) | -hBOOL(hAPP(filter(real),bool,hAPP(complex,fun(filter(real),bool),hAPP(fun(real,complex),fun(complex,fun(filter(real),bool)),tendsto(real,complex),hAPP(complex,fun(real,complex),combk(complex,real),A)),zero_zero(complex)),hAPP(real,filter(real),at(real),B))). [resolve(6961,a,6938,a)].
% 281.65/281.42 Derived: -metric_space(complex) | zero_zero(complex) = ti(complex,A) | -hBOOL(hAPP(filter(complex),bool,hAPP(complex,fun(filter(complex),bool),hAPP(fun(complex,complex),fun(complex,fun(filter(complex),bool)),tendsto(complex,complex),hAPP(complex,fun(complex,complex),combk(complex,complex),A)),zero_zero(complex)),hAPP(complex,filter(complex),at(complex),B))). [resolve(6961,a,6956,a)].
% 281.65/281.42 6962 -real_n2089651433ebra_1(A) | -metric_space(code_code_numeral) | zero_zero(code_code_numeral) = ti(code_code_numeral,B) | -hBOOL(hAPP(filter(A),bool,hAPP(code_code_numeral,fun(filter(A),bool),hAPP(fun(A,code_code_numeral),fun(code_code_numeral,fun(filter(A),bool)),tendsto(A,code_code_numeral),hAPP(code_code_numeral,fun(A,code_code_numeral),combk(code_code_numeral,A),B)),zero_zero(code_code_numeral)),hAPP(A,filter(A),at(A),C))). [resolve(5557,a,5552,b)].
% 281.65/281.42 Derived: -metric_space(code_code_numeral) | zero_zero(code_code_numeral) = ti(code_code_numeral,A) | -hBOOL(hAPP(filter(real),bool,hAPP(code_code_numeral,fun(filter(real),bool),hAPP(fun(real,code_code_numeral),fun(code_code_numeral,fun(filter(real),bool)),tendsto(real,code_code_numeral),hAPP(code_code_numeral,fun(real,code_code_numeral),combk(code_code_numeral,real),A)),zero_zero(code_code_numeral)),hAPP(real,filter(real),at(real),B))). [resolve(6962,a,6938,a)].
% 281.65/281.42 Derived: -metric_space(code_code_numeral) | zero_zero(code_code_numeral) = ti(code_code_numeral,A) | -hBOOL(hAPP(filter(complex),bool,hAPP(code_code_numeral,fun(filter(complex),bool),hAPP(fun(complex,code_code_numeral),fun(code_code_numeral,fun(filter(complex),bool)),tendsto(complex,code_code_numeral),hAPP(code_code_numeral,fun(complex,code_code_numeral),combk(code_code_numeral,complex),A)),zero_zero(code_code_numeral)),hAPP(complex,filter(complex),at(complex),B))). [resolve(6962,a,6956,a)].
% 281.65/281.42 6963 -real_n2089651433ebra_1(A) | -metric_space(quickcheck_code_int) | zero_zero(quickcheck_code_int) = ti(quickcheck_code_int,B) | -hBOOL(hAPP(filter(A),bool,hAPP(quickcheck_code_int,fun(filter(A),bool),hAPP(fun(A,quickcheck_code_int),fun(quickcheck_code_int,fun(filter(A),bool)),tendsto(A,quickcheck_code_int),hAPP(quickcheck_code_int,fun(A,quickcheck_code_int),combk(quickcheck_code_int,A),B)),zero_zero(quickcheck_code_int)),hAPP(A,filter(A),at(A),C))). [resolve(5558,a,5552,b)].
% 281.65/281.42 Derived: -metric_space(quickcheck_code_int) | zero_zero(quickcheck_code_int) = ti(quickcheck_code_int,A) | -hBOOL(hAPP(filter(real),bool,hAPP(quickcheck_code_int,fun(filter(real),bool),hAPP(fun(real,quickcheck_code_int),fun(quickcheck_code_int,fun(filter(real),bool)),tendsto(real,quickcheck_code_int),hAPP(quickcheck_code_int,fun(real,quickcheck_code_int),combk(quickcheck_code_int,real),A)),zero_zero(quickcheck_code_int)),hAPP(real,filter(real),at(real),B))). [resolve(6963,a,6938,a)].
% 281.65/281.42 Derived: -metric_space(quickcheck_code_int) | zero_zero(quickcheck_code_int) = ti(quickcheck_code_int,A) | -hBOOL(hAPP(filter(complex),bool,hAPP(quickcheck_code_int,fun(filter(complex),bool),hAPP(fun(complex,quickcheck_code_int),fun(quickcheck_code_int,fun(filter(complex),bool)),tendsto(complex,quickcheck_code_int),hAPP(quickcheck_code_int,fun(complex,quickcheck_code_int),combk(quickcheck_code_int,complex),A)),zero_zero(quickcheck_code_int)),hAPP(complex,filter(complex),at(complex),B))). [resolve(6963,a,6956,a)].
% 281.65/281.42 6964 semiring_char_0(int) # label(arity_Int_Oint___Nat_Osemiring__char__0) # label(axiom). [assumption].
% 281.65/281.42 6965 -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_2575_of__nat__eq__iff) # label(axiom). [clausify(2575)].
% 281.73/281.48 6966 -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_2575_of__nat__eq__iff) # label(axiom). [clausify(2575)].
% 281.73/281.48 6967 -semiring_char_0(A) | hAPP(nat,A,semiring_1_of_nat(A),hAPP(nat,nat,fact_fact(nat),B)) != zero_zero(A) # label(fact_2597_of__nat__fact__not__zero) # label(axiom). [clausify(2597)].
% 281.73/281.48 Derived: hAPP(nat,int,semiring_1_of_nat(int),A) != hAPP(nat,int,semiring_1_of_nat(int),B) | A = B. [resolve(6964,a,6965,a)].
% 281.73/281.48 Derived: hAPP(nat,int,semiring_1_of_nat(int),A) = hAPP(nat,int,semiring_1_of_nat(int),B) | A != B. [resolve(6964,a,6966,a)].
% 281.73/281.48 Derived: hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,fact_fact(nat),A)) != zero_zero(int). [resolve(6964,a,6967,a)].
% 281.73/281.48 6968 semiring_char_0(nat) # label(arity_Nat_Onat___Nat_Osemiring__char__0) # label(axiom). [assumption].
% 281.73/281.48 Derived: hAPP(nat,nat,semiring_1_of_nat(nat),A) != hAPP(nat,nat,semiring_1_of_nat(nat),B) | A = B. [resolve(6968,a,6965,a)].
% 281.73/281.48 Derived: hAPP(nat,nat,semiring_1_of_nat(nat),A) = hAPP(nat,nat,semiring_1_of_nat(nat),B) | A != B. [resolve(6968,a,6966,a)].
% 281.73/281.48 Derived: hAPP(nat,nat,semiring_1_of_nat(nat),hAPP(nat,nat,fact_fact(nat),A)) != zero_zero(nat). [resolve(6968,a,6967,a)].
% 281.73/281.48 6969 semiring_char_0(rat) # label(arity_Rat_Orat___Nat_Osemiring__char__0) # label(axiom). [assumption].
% 281.73/281.48 Derived: hAPP(nat,rat,semiring_1_of_nat(rat),A) != hAPP(nat,rat,semiring_1_of_nat(rat),B) | A = B. [resolve(6969,a,6965,a)].
% 281.73/281.48 Derived: hAPP(nat,rat,semiring_1_of_nat(rat),A) = hAPP(nat,rat,semiring_1_of_nat(rat),B) | A != B. [resolve(6969,a,6966,a)].
% 281.73/281.48 Derived: hAPP(nat,rat,semiring_1_of_nat(rat),hAPP(nat,nat,fact_fact(nat),A)) != zero_zero(rat). [resolve(6969,a,6967,a)].
% 281.73/281.48 6970 semiring_char_0(real) # label(arity_RealDef_Oreal___Nat_Osemiring__char__0) # label(axiom). [assumption].
% 281.73/281.48 Derived: hAPP(nat,real,semiring_1_of_nat(real),A) != hAPP(nat,real,semiring_1_of_nat(real),B) | A = B. [resolve(6970,a,6965,a)].
% 281.73/281.48 Derived: hAPP(nat,real,semiring_1_of_nat(real),A) = hAPP(nat,real,semiring_1_of_nat(real),B) | A != B. [resolve(6970,a,6966,a)].
% 281.73/281.48 Derived: hAPP(nat,real,semiring_1_of_nat(real),hAPP(nat,nat,fact_fact(nat),A)) != zero_zero(real). [resolve(6970,a,6967,a)].
% 281.73/281.48 6971 semiring_char_0(complex) # label(arity_Complex_Ocomplex___Nat_Osemiring__char__0) # label(axiom). [assumption].
% 281.73/281.48 Derived: hAPP(nat,complex,semiring_1_of_nat(complex),A) != hAPP(nat,complex,semiring_1_of_nat(complex),B) | A = B. [resolve(6971,a,6965,a)].
% 281.73/281.48 Derived: hAPP(nat,complex,semiring_1_of_nat(complex),A) = hAPP(nat,complex,semiring_1_of_nat(complex),B) | A != B. [resolve(6971,a,6966,a)].
% 281.73/281.48 Derived: hAPP(nat,complex,semiring_1_of_nat(complex),hAPP(nat,nat,fact_fact(nat),A)) != zero_zero(complex). [resolve(6971,a,6967,a)].
% 281.73/281.48 6972 semiring_char_0(code_code_numeral) # label(arity_Code__Numeral_Ocode__numeral___Nat_Osemiring__char__0) # label(axiom). [assumption].
% 281.73/281.48 Derived: hAPP(nat,code_code_numeral,semiring_1_of_nat(code_code_numeral),A) != hAPP(nat,code_code_numeral,semiring_1_of_nat(code_code_numeral),B) | A = B. [resolve(6972,a,6965,a)].
% 281.73/281.48 Derived: hAPP(nat,code_code_numeral,semiring_1_of_nat(code_code_numeral),A) = hAPP(nat,code_code_numeral,semiring_1_of_nat(code_code_numeral),B) | A != B. [resolve(6972,a,6966,a)].
% 281.73/281.48 Derived: hAPP(nat,code_code_numeral,semiring_1_of_nat(code_code_numeral),hAPP(nat,nat,fact_fact(nat),A)) != zero_zero(code_code_numeral). [resolve(6972,a,6967,a)].
% 281.73/281.48 6973 semiring_char_0(quickcheck_code_int) # label(arity_Quickcheck__Narrowing_Ocode__int___Nat_Osemiring__char__0) # label(axiom). [assumption].
% 281.73/281.48 Derived: hAPP(nat,quickcheck_code_int,semiring_1_of_nat(quickcheck_code_int),A) != hAPP(nat,quickcheck_code_int,semiring_1_of_nat(quickcheck_code_int),B) | A = B. [resolve(6973,a,6965,a)].
% 281.73/281.48 Derived: hAPP(nat,quickcheck_code_int,semiring_1_of_nat(quickcheck_code_int),A) = hAPP(nat,quickcheck_code_int,semiring_1_of_nat(quickcheck_code_int),B) | A != B. [resolve(6973,a,6966,a)].
% 281.73/281.48 Derived: hAPP(nat,quickcheck_code_int,semiring_1_of_nat(quickcheck_code_int),hAPP(nat,nat,fact_fact(nat),A)) != zero_zero(quickcheck_code_int). [resolve(6973,a,6967,a)].
% 286.53/286.27 6974 archim1804426504_field(rat) # label(arity_Rat_Orat___Archimedean__Field_Oarchimedean__field) # label(axiom). [assumption].
% 286.53/286.27 6975 -archim1804426504_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),f246(A,B))) # label(fact_2682_ex__inverse__of__nat__less) # label(axiom). [clausify(2674)].
% 286.53/286.27 6976 -archim1804426504_field(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,inverse_inverse(A),hAPP(nat,A,semiring_1_of_nat(A),f246(A,B)))),B)) # label(fact_2682_ex__inverse__of__nat__less) # label(axiom). [clausify(2674)].
% 286.53/286.27 6977 -archim1804426504_field(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,inverse_inverse(A),hAPP(nat,A,semiring_1_of_nat(A),hAPP(nat,nat,suc,f247(A,B))))),B)) # label(fact_2683_ex__inverse__of__nat__Suc__less) # label(axiom). [clausify(2675)].
% 286.53/286.27 6978 -archim1804426504_field(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),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(nat,A,semiring_1_of_nat(A),f274(A,C,B))),B))) # label(fact_2754_ex__less__of__nat__mult) # label(axiom). [clausify(2746)].
% 286.53/286.27 6979 -archim1804426504_field(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(nat,A,semiring_1_of_nat(A),f294(A,B)))) # label(fact_2903_ex__less__of__nat) # label(axiom). [clausify(2884)].
% 286.53/286.27 6980 -archim1804426504_field(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(nat,A,semiring_1_of_nat(A),f295(A,B)))) # label(fact_2904_ex__le__of__nat) # label(axiom). [clausify(2885)].
% 286.53/286.27 6981 -archim1804426504_field(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(int,A,ring_1_of_int(A),f436(A,B))),B)) # label(fact_3623_floor__exists) # label(axiom). [clausify(3576)].
% 286.53/286.27 6982 -archim1804426504_field(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(int,A,ring_1_of_int(A),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),f436(A,B)),one_one(int))))) # label(fact_3623_floor__exists) # label(axiom). [clausify(3576)].
% 286.53/286.27 6983 -archim1804426504_field(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(int,A,ring_1_of_int(A),f437(A,B))),B)) # label(fact_3624_floor__exists1) # label(axiom). [clausify(3577)].
% 286.53/286.27 6984 -archim1804426504_field(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(int,A,ring_1_of_int(A),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),f437(A,B)),one_one(int))))) # label(fact_3624_floor__exists1) # label(axiom). [clausify(3577)].
% 286.53/286.27 6985 -archim1804426504_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(int,A,ring_1_of_int(A),B)),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),hAPP(int,A,ring_1_of_int(A),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),B),one_one(int))))) | B = f437(A,C) # label(fact_3624_floor__exists1) # label(axiom). [clausify(3577)].
% 286.53/286.27 6986 -archim1804426504_field(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(int,A,ring_1_of_int(A),f440(A,B)))) # label(fact_3633_ex__less__of__int) # label(axiom). [clausify(3586)].
% 286.53/286.27 6987 -archim1804426504_field(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,ring_1_of_int(A),f441(A,B))),B)) # label(fact_3634_ex__of__int__less) # label(axiom). [clausify(3587)].
% 286.53/286.27 6988 -archim1804426504_field(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(int,A,ring_1_of_int(A),f442(A,B)))) # label(fact_3635_ex__le__of__int) # label(axiom). [clausify(3588)].
% 286.53/286.27 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),f246(rat,A))). [resolve(6974,a,6975,a)].
% 286.53/286.27 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,inverse_inverse(rat),hAPP(nat,rat,semiring_1_of_nat(rat),f246(rat,A)))),A)). [resolve(6974,a,6976,a)].
% 286.58/286.30 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,inverse_inverse(rat),hAPP(nat,rat,semiring_1_of_nat(rat),hAPP(nat,nat,suc,f247(rat,A))))),A)). [resolve(6974,a,6977,a)].
% 286.58/286.30 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(nat,rat,semiring_1_of_nat(rat),f274(rat,B,A))),A))). [resolve(6974,a,6978,a)].
% 286.58/286.30 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),hAPP(nat,rat,semiring_1_of_nat(rat),f294(rat,A)))). [resolve(6974,a,6979,a)].
% 286.58/286.30 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),hAPP(nat,rat,semiring_1_of_nat(rat),f295(rat,A)))). [resolve(6974,a,6980,a)].
% 286.58/286.30 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(int,rat,ring_1_of_int(rat),f436(rat,A))),A)). [resolve(6974,a,6981,a)].
% 286.58/286.30 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),hAPP(int,rat,ring_1_of_int(rat),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),f436(rat,A)),one_one(int))))). [resolve(6974,a,6982,a)].
% 286.58/286.30 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(int,rat,ring_1_of_int(rat),f437(rat,A))),A)). [resolve(6974,a,6983,a)].
% 286.58/286.30 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),hAPP(int,rat,ring_1_of_int(rat),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),f437(rat,A)),one_one(int))))). [resolve(6974,a,6984,a)].
% 286.58/286.30 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(int,rat,ring_1_of_int(rat),A)),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),hAPP(int,rat,ring_1_of_int(rat),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),one_one(int))))) | A = f437(rat,B). [resolve(6974,a,6985,a)].
% 286.58/286.30 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),hAPP(int,rat,ring_1_of_int(rat),f440(rat,A)))). [resolve(6974,a,6986,a)].
% 286.58/286.30 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(int,rat,ring_1_of_int(rat),f441(rat,A))),A)). [resolve(6974,a,6987,a)].
% 286.58/286.30 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),hAPP(int,rat,ring_1_of_int(rat),f442(rat,A)))). [resolve(6974,a,6988,a)].
% 286.58/286.30 6989 archim1804426504_field(real) # label(arity_RealDef_Oreal___Archimedean__Field_Oarchimedean__field) # label(axiom). [assumption].
% 286.58/286.30 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),f246(real,A))). [resolve(6989,a,6975,a)].
% 286.58/286.30 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,inverse_inverse(real),hAPP(nat,real,semiring_1_of_nat(real),f246(real,A)))),A)). [resolve(6989,a,6976,a)].
% 286.58/286.30 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,inverse_inverse(real),hAPP(nat,real,semiring_1_of_nat(real),hAPP(nat,nat,suc,f247(real,A))))),A)). [resolve(6989,a,6977,a)].
% 286.58/286.30 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,semiring_1_of_nat(real),f274(real,B,A))),A))). [resolve(6989,a,6978,a)].
% 286.58/286.30 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),hAPP(nat,real,semiring_1_of_nat(real),f294(real,A)))). [resolve(6989,a,6979,a)].
% 286.58/286.30 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),hAPP(nat,real,semiring_1_of_nat(real),f295(real,A)))). [resolve(6989,a,6980,a)].
% 286.58/286.30 Derived: hBOOL(hAPP(real,bool,hAPPCputime limit exceeded (core dumped)
%------------------------------------------------------------------------------