TSTP Solution File: SWW473+7 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SWW473+7 : TPTP v8.1.0. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n024.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Thu Jul 21 01:17:10 EDT 2022
% Result : Unknown 144.89s 145.15s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SWW473+7 : TPTP v8.1.0. Released v5.3.0.
% 0.12/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.14/0.34 % Computer : n024.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Mon Jun 6 02:30:20 EDT 2022
% 0.14/0.35 % CPUTime :
% 1.75/2.04 ============================== Prover9 ===============================
% 1.75/2.04 Prover9 (32) version 2009-11A, November 2009.
% 1.75/2.04 Process 30116 was started by sandbox2 on n024.cluster.edu,
% 1.75/2.04 Mon Jun 6 02:30:21 2022
% 1.75/2.04 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_29937_n024.cluster.edu".
% 1.75/2.04 ============================== end of head ===========================
% 1.75/2.04
% 1.75/2.04 ============================== INPUT =================================
% 1.75/2.04
% 1.75/2.04 % Reading from file /tmp/Prover9_29937_n024.cluster.edu
% 1.75/2.04
% 1.75/2.04 set(prolog_style_variables).
% 1.75/2.04 set(auto2).
% 1.75/2.04 % set(auto2) -> set(auto).
% 1.75/2.04 % set(auto) -> set(auto_inference).
% 1.75/2.04 % set(auto) -> set(auto_setup).
% 1.75/2.04 % set(auto_setup) -> set(predicate_elim).
% 1.75/2.04 % set(auto_setup) -> assign(eq_defs, unfold).
% 1.75/2.04 % set(auto) -> set(auto_limits).
% 1.75/2.04 % set(auto_limits) -> assign(max_weight, "100.000").
% 1.75/2.04 % set(auto_limits) -> assign(sos_limit, 20000).
% 1.75/2.04 % set(auto) -> set(auto_denials).
% 1.75/2.04 % set(auto) -> set(auto_process).
% 1.75/2.04 % set(auto2) -> assign(new_constants, 1).
% 1.75/2.04 % set(auto2) -> assign(fold_denial_max, 3).
% 1.75/2.04 % set(auto2) -> assign(max_weight, "200.000").
% 1.75/2.04 % set(auto2) -> assign(max_hours, 1).
% 1.75/2.04 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 1.75/2.04 % set(auto2) -> assign(max_seconds, 0).
% 1.75/2.04 % set(auto2) -> assign(max_minutes, 5).
% 1.75/2.04 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 1.75/2.04 % set(auto2) -> set(sort_initial_sos).
% 1.75/2.04 % set(auto2) -> assign(sos_limit, -1).
% 1.75/2.04 % set(auto2) -> assign(lrs_ticks, 3000).
% 1.75/2.04 % set(auto2) -> assign(max_megs, 400).
% 1.75/2.04 % set(auto2) -> assign(stats, some).
% 1.75/2.04 % set(auto2) -> clear(echo_input).
% 1.75/2.04 % set(auto2) -> set(quiet).
% 1.75/2.04 % set(auto2) -> clear(print_initial_clauses).
% 1.75/2.04 % set(auto2) -> clear(print_given).
% 1.75/2.04 assign(lrs_ticks,-1).
% 1.75/2.04 assign(sos_limit,10000).
% 1.75/2.04 assign(order,kbo).
% 1.75/2.04 set(lex_order_vars).
% 1.75/2.04 clear(print_given).
% 1.75/2.04
% 1.75/2.04 % formulas(sos). % not echoed (1201 formulas)
% 1.75/2.04
% 1.75/2.04 ============================== end of input ==========================
% 1.75/2.04
% 1.75/2.04 % From the command line: assign(max_seconds, 300).
% 1.75/2.04
% 1.75/2.04 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 1.75/2.04
% 1.75/2.04 % Formulas that are not ordinary clauses:
% 1.75/2.04 1 (all X_b all X_c all X_a ti(fun(fun(X_b,X_c),fun(fun(X_a,X_b),fun(X_a,X_c))),combb(X_b,X_c,X_a)) = combb(X_b,X_c,X_a)) # label(tsy_c_COMBB_res) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.04 2 (all X_a all X_b all X_c ti(fun(fun(X_a,fun(X_b,X_c)),fun(X_b,fun(X_a,X_c))),combc(X_a,X_b,X_c)) = combc(X_a,X_b,X_c)) # label(tsy_c_COMBC_res) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.04 3 (all X_a ti(fun(X_a,X_a),combi(X_a)) = combi(X_a)) # label(tsy_c_COMBI_res) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.04 4 (all X_a all X_b ti(fun(X_a,fun(X_b,X_a)),combk(X_a,X_b)) = combk(X_a,X_b)) # label(tsy_c_COMBK_res) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.04 5 (all X_a all X_b all X_c ti(fun(fun(X_a,fun(X_b,X_c)),fun(fun(X_a,X_b),fun(X_a,X_c))),combs(X_a,X_b,X_c)) = combs(X_a,X_b,X_c)) # label(tsy_c_COMBS_res) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.04 6 (all X_c ti(fun(fun(X_c,bool),nat),finite_card(X_c)) = finite_card(X_c)) # label(tsy_c_Finite__Set_Ocard_res) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.04 7 (all X_b all X_c ti(fun(fun(X_b,fun(X_c,X_c)),bool),finite_comp_fun_idem(X_b,X_c)) = finite_comp_fun_idem(X_b,X_c)) # label(tsy_c_Finite__Set_Ocomp__fun__idem_res) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.04 8 (all X_b ti(fun(fun(X_b,bool),bool),finite_finite(X_b)) = finite_finite(X_b)) # label(tsy_c_Finite__Set_Ofinite_res) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.04 9 (all X_b all X_c ti(fun(fun(X_b,fun(X_b,X_b)),fun(fun(X_c,X_b),fun(X_b,fun(fun(X_c,bool),X_b)))),finite_fold_image(X_b,X_c)) = finite_fold_image(X_b,X_c)) # label(tsy_c_Finite__Set_Ofold__image_res) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.04 10 (all X_b all X_c ti(fun(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool)))),finite1357897459simple(X_b,X_c)) = finite1357897459simple(X_b,X_c)) # label(tsy_c_Finite__Set_Ofolding__image__simple_res) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.04 11 (all X_b all X_c ti(fun(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool)))),finite908156982e_idem(X_b,X_c)) = finite908156982e_idem(X_b,X_c)) # label(tsy_c_Finite__Set_Ofolding__image__simple__idem_res) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.04 12 (all X_b ti(fun(fun(X_b,fun(X_b,X_b)),fun(fun(fun(X_b,bool),X_b),bool)),finite_folding_one(X_b)) = finite_folding_one(X_b)) # label(tsy_c_Finite__Set_Ofolding__one_res) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.04 13 (all X_b ti(fun(fun(X_b,fun(X_b,X_b)),fun(fun(fun(X_b,bool),X_b),bool)),finite2073411215e_idem(X_b)) = finite2073411215e_idem(X_b)) # label(tsy_c_Finite__Set_Ofolding__one__idem_res) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.04 14 (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_res) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.04 15 (all X_c (minus(X_c) -> ti(fun(X_c,fun(X_c,X_c)),minus_minus(X_c)) = minus_minus(X_c))) # label(tsy_c_Groups_Ominus__class_Ominus_res) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.04 16 (all X_b (one(X_b) -> ti(X_b,one_one(X_b)) = one_one(X_b))) # label(tsy_c_Groups_Oone__class_Oone_res) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.04 17 (all X_a (monoid_add(X_a) -> ti(fun(X_a,fun(X_a,X_a)),plus_plus(X_a)) = plus_plus(X_a))) # label(tsy_c_Groups_Oplus__class_Oplus_0_res) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.04 18 (all X_b (cancel_semigroup_add(X_b) -> ti(fun(X_b,fun(X_b,X_b)),plus_plus(X_b)) = plus_plus(X_b))) # label(tsy_c_Groups_Oplus__class_Oplus_1_res) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.04 19 (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].
% 1.75/2.04 20 (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_0_res) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.04 21 (all X_a (monoid_mult(X_a) -> ti(fun(X_a,fun(X_a,X_a)),times_times(X_a)) = times_times(X_a))) # label(tsy_c_Groups_Otimes__class_Otimes_1_res) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.04 22 (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_2_res) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.04 23 (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].
% 1.75/2.04 24 (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_4_res) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.04 25 (all X_b (zero(X_b) -> ti(X_b,zero_zero(X_b)) = zero_zero(X_b))) # label(tsy_c_Groups_Ozero__class_Ozero_res) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.04 26 (all X_b ti(fun(fun(X_b,bool),X_b),the(X_b)) = the(X_b)) # label(tsy_c_HOL_OThe_res) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.04 27 (all X_a ti(X_a,undefined(X_a)) = undefined(X_a)) # label(tsy_c_HOL_Oundefined_res) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.04 28 (all X_a ti(fun(bool,fun(X_a,fun(X_a,X_a))),if(X_a)) = if(X_a)) # label(tsy_c_If_res) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.04 29 (all X_b (number(X_b) -> ti(fun(int,X_b),number_number_of(X_b)) = number_number_of(X_b))) # label(tsy_c_Int_Onumber__class_Onumber__of_res) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.04 30 (all X_b (ring_1(X_b) -> ti(fun(X_b,bool),ring_1_Ints(X_b)) = ring_1_Ints(X_b))) # label(tsy_c_Int_Oring__1__class_OInts_res) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.04 31 (all X_b ti(fun(X_b,fun(fun(nat,X_b),fun(nat,X_b))),nat_case(X_b)) = nat_case(X_b)) # label(tsy_c_Nat_Onat_Onat__case_res) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.04 32 (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].
% 1.75/2.04 33 (all X_b (semiring_1(X_b) -> ti(fun(fun(X_b,X_b),fun(nat,fun(X_b,X_b))),semiri532925092at_aux(X_b)) = semiri532925092at_aux(X_b))) # label(tsy_c_Nat_Osemiring__1__class_Oof__nat__aux_res) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.04 34 (all X_b (bot(X_b) -> ti(X_b,bot_bot(X_b)) = bot_bot(X_b))) # label(tsy_c_Orderings_Obot__class_Obot_res) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.04 35 (all X_a (ord(X_a) -> ti(fun(X_a,fun(X_a,bool)),ord_less(X_a)) = ord_less(X_a))) # label(tsy_c_Orderings_Oord__class_Oless_res) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.04 36 (all X_a (ord(X_a) -> ti(fun(X_a,fun(X_a,bool)),ord_less_eq(X_a)) = ord_less_eq(X_a))) # label(tsy_c_Orderings_Oord__class_Oless__eq_res) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.04 37 (all X_b ti(fun(X_b,fun(fun(X_b,bool),X_b)),partial_flat_lub(X_b)) = partial_flat_lub(X_b)) # label(tsy_c_Partial__Function_Oflat__lub_res) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.04 38 (all X_b ti(fun(fun(X_b,bool),fun(X_b,bool)),collect(X_b)) = collect(X_b)) # label(tsy_c_Set_OCollect_res) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.04 39 (all X_b all X_c ti(fun(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool))),image(X_b,X_c)) = image(X_b,X_c)) # label(tsy_c_Set_Oimage_res) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.04 40 (all X_b ti(fun(X_b,fun(fun(X_b,bool),fun(X_b,bool))),insert(X_b)) = insert(X_b)) # label(tsy_c_Set_Oinsert_res) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.04 41 (all X_b ti(fun(fun(X_b,bool),X_b),the_elem(X_b)) = the_elem(X_b)) # label(tsy_c_Set_Othe__elem_res) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.04 42 (all X_b all X_c ti(fun(fun(X_b,bool),fun(fun(X_c,bool),fun(sum_sum(X_b,X_c),bool))),sum_Plus(X_b,X_c)) = sum_Plus(X_b,X_c)) # label(tsy_c_Sum__Type_OPlus_res) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.04 43 (all X_a ti(fun(X_a,fun(X_a,bool)),fequal(X_a)) = fequal(X_a)) # label(tsy_c_fequal_res) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.04 44 (all X_a all X_c all B_1_1 all B_2_1 hAPP(X_a,X_c,ti(fun(X_a,X_c),B_1_1),B_2_1) = hAPP(X_a,X_c,B_1_1,B_2_1)) # label(tsy_c_hAPP_arg1) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.04 45 (all X_a all X_c all B_1_1 all B_2_1 hAPP(X_a,X_c,B_1_1,ti(X_a,B_2_1)) = hAPP(X_a,X_c,B_1_1,B_2_1)) # label(tsy_c_hAPP_arg2) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.04 46 (all X_c all X_a all B_1_1 all B_2_1 ti(X_c,hAPP(X_a,X_c,B_1_1,B_2_1)) = hAPP(X_a,X_c,B_1_1,B_2_1)) # label(tsy_c_hAPP_res) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.04 47 (all B_1_1 (hBOOL(ti(bool,B_1_1)) <-> hBOOL(B_1_1))) # label(tsy_c_hBOOL_arg1) # label(hypothesis) # label(non_clause). [assumption].
% 1.75/2.04 48 (all X_b ti(fun(X_b,fun(fun(X_b,bool),bool)),member(X_b)) = member(X_b)) # label(tsy_c_member_res) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.04 49 (all Ts all G_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)),Ts),G_1)) -> hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),p,G_1),Ts)))) # label(fact_0_assms_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.04 50 (all X_b all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3)) -> hBOOL(hAPP(fun(fun(X_b,bool),bool),bool,finite_finite(fun(X_b,bool)),hAPP(fun(fun(X_b,bool),bool),fun(fun(X_b,bool),bool),collect(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),hAPP(fun(fun(X_b,bool),fun(fun(X_b,bool),bool)),fun(fun(X_b,bool),fun(fun(X_b,bool),bool)),combc(fun(X_b,bool),fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool))),A_3)))))) # label(fact_1_finite__Collect__subsets) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.04 51 (all X_c all X_b all H all F_1 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),F_1)) -> hBOOL(hAPP(fun(X_c,bool),bool,finite_finite(X_c),hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),H),F_1))))) # label(fact_2_finite__imageI) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.04 52 (all X_b all A_2 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3)) -> hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),A_3))))) # label(fact_3_finite_OinsertI) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.04 53 (all X_c all X_b all F all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X_c,bool),nat,finite_card(X_c),hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),F),A_3))),hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3))))) # label(fact_4_card__image__le) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.04 54 (all X_b all A_3 all B_1 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),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)),A_3),B_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3)),hAPP(fun(X_b,bool),nat,finite_card(X_b),B_1)))))) # label(fact_5_card__mono) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.04 55 (all X_b all A_3 all B_1 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),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)),A_3),B_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X_b,bool),nat,finite_card(X_b),B_1)),hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3))) -> ti(fun(X_b,bool),A_3) = ti(fun(X_b,bool),B_1))))) # label(fact_6_card__seteq) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.04 56 (all X_b all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3)),hAPP(fun(X_b,bool),nat,finite_card(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_3)))))) # label(fact_7_card__insert__le) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.04 57 (all X_b all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> hAPP(fun(X_b,bool),nat,finite_card(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_3)) = hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3)) & (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> hAPP(fun(X_b,bool),nat,finite_card(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_3)) = hAPP(nat,nat,suc,hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3))))) # label(fact_8_card__insert__if) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.04 58 (all X_b all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3)) -> (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> hAPP(fun(X_b,bool),nat,finite_card(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_3)) = hAPP(nat,nat,suc,hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3))))) # label(fact_9_card__insert__disjoint) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.04 59 (all X_b all Q_3 all Pa (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),Pa))) | hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),Q_3))) -> hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),combs(X_b,bool,bool),hAPP(fun(X_b,bool),fun(X_b,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fconj),Pa)),Q_3)))))) # label(fact_10_finite__Collect__conjI) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.04 60 (all N all M_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N),M_1)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,M_1)),N) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),N)))) # label(fact_11_Suc__diff__le) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.04 61 (all K hBOOL(hAPP(fun(nat,bool),bool,finite_finite(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_12_finite__Collect__le__nat) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.04 62 (all Na 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)),Na))) = hAPP(nat,nat,suc,Na)) # label(fact_13_card__Collect__le__nat) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.04 63 (all X_b (finite_finite_1(X_b) -> (all A_3 hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3))))) # label(fact_14_finite__code) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.04 64 (all X_b (finite_finite_1(X_b) -> (all A_3 hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3))))) # label(fact_15_finite) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.04 65 (all X all Y (hAPP(nat,nat,suc,X) = hAPP(nat,nat,suc,Y) -> X = Y)) # label(fact_16_Suc__inject) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.04 66 (all Nat_3 all Nat_4 (hAPP(nat,nat,suc,Nat_3) = hAPP(nat,nat,suc,Nat_4) <-> Nat_3 = Nat_4)) # label(fact_17_nat_Oinject) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.04 67 (all N hAPP(nat,nat,suc,N) != N) # label(fact_18_Suc__n__not__n) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.04 68 (all N N != hAPP(nat,nat,suc,N)) # label(fact_19_n__not__Suc__n) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.04 69 (all M_1 all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),N)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N),M_1)) -> M_1 = N))) # label(fact_20_le__antisym) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.04 70 (all K_1 all I_2 all J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_2),J)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),J),K_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_2),K_1))))) # label(fact_21_le__trans) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.04 71 (all M_1 all N (M_1 = N -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),N)))) # label(fact_22_eq__imp__le) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.04 72 (all M_1 all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),N)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N),M_1)))) # label(fact_23_nat__le__linear) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.04 73 (all N hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N),N))) # label(fact_24_le__refl) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.04 74 (all I_2 all J all K_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I_2),J)),K_1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I_2),K_1)),J)) # label(fact_25_diff__commute) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.04 75 (all X_b all Pa all Q_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),combs(X_b,bool,bool),hAPP(fun(X_b,bool),fun(X_b,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fdisj),Pa)),Q_3)))) <-> hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),Pa))) & hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),Q_3))))) # label(fact_26_finite__Collect__disjI) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.04 76 (all X_b all A_2 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),A_3))) <-> hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3)))) # label(fact_27_finite__insert) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.04 77 (all X_b all A_3 all 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)),A_3),B_1)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),B_1)) -> hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3))))) # label(fact_28_finite__subset) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.04 78 (all X_b all A_3 all B_1 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),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)),A_3),B_1)) -> hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3))))) # label(fact_29_rev__finite__subset) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.04 79 (all M_1 all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,M_1)),N)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),N)))) # label(fact_30_Suc__leD) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.04 80 (all M_1 all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),hAPP(nat,nat,suc,N))) -> (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),N)) -> M_1 = hAPP(nat,nat,suc,N)))) # label(fact_31_le__SucE) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.04 81 (all M_1 all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),N)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),hAPP(nat,nat,suc,N))))) # label(fact_32_le__SucI) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.04 82 (all Na all M (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,Na)),hAPP(nat,nat,suc,M))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Na),M)))) # label(fact_33_Suc__le__mono) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.04 83 (all M all Na (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),hAPP(nat,nat,suc,Na))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),Na)) | M = hAPP(nat,nat,suc,Na))) # label(fact_34_le__Suc__eq) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.04 84 (all M all Na (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),Na)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,Na)),M)))) # label(fact_35_not__less__eq__eq) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.04 85 (all N -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,N)),N))) # label(fact_36_Suc__n__not__le__n) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.04 86 (all M_1 all N all K_1 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)),hAPP(nat,nat,suc,K_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),N)),K_1)) # label(fact_37_Suc__diff__diff) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.04 87 (all M_1 all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,M_1)),hAPP(nat,nat,suc,N)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),N)) # label(fact_38_diff__Suc__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.04 88 (all Na 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),Na)) -> (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),Na),K))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),Na)))))) # label(fact_39_le__diff__iff) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.04 89 (all N all K_1 all M_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_1),M_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_1),N)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),K_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),K_1)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),N)))) # label(fact_40_Nat_Odiff__diff__eq) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.04 90 (all Na 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),Na)) -> (hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),K) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),Na),K) <-> M = Na)))) # label(fact_41_eq__diff__iff) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.04 91 (all I_2 all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_2),N)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),I_2)) = I_2)) # label(fact_42_diff__diff__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.04 92 (all L_1 all M_1 all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),N)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),L_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),L_1))))) # label(fact_43_diff__le__mono) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.04 93 (all L_1 all M_1 all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),N)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),L_1),N)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),L_1),M_1))))) # label(fact_44_diff__le__mono2) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.04 94 (all M_1 all N hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),N)),M_1))) # label(fact_45_diff__le__self) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.04 95 (all X_c all X_b all B_1 all F all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3)) -> (hBOOL(hAPP(fun(X_c,bool),bool,hAPP(fun(X_c,bool),fun(fun(X_c,bool),bool),ord_less_eq(fun(X_c,bool)),B_1),hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),F),A_3))) -> hBOOL(hAPP(fun(X_c,bool),bool,finite_finite(X_c),B_1))))) # label(fact_46_finite__surj) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.04 96 (all X_c all X_b all F all A_3 all B_1 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),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)),B_1),hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),A_3))) -> (exists C_3 (hBOOL(hAPP(fun(X_c,bool),bool,hAPP(fun(X_c,bool),fun(fun(X_c,bool),bool),ord_less_eq(fun(X_c,bool)),C_3),A_3)) & hBOOL(hAPP(fun(X_c,bool),bool,finite_finite(X_c),C_3)) & ti(fun(X_b,bool),B_1) = hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),C_3)))))) # label(fact_47_finite__subset__image) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.04 97 (all X_b (order(X_b) -> (all Na all N_3 all F ((all N_1 hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(nat,X_b,F,N_1)),hAPP(nat,X_b,F,hAPP(nat,nat,suc,N_1))))) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Na),N_3)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(nat,X_b,F,Na)),hAPP(nat,X_b,F,N_3)))))))) # label(fact_48_lift__Suc__mono__le) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.04 98 (all X_c all X_b all F all A_3 (-hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3)) -> (hBOOL(hAPP(fun(X_c,bool),bool,finite_finite(X_c),hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),F),A_3))) -> (exists X_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_3)) & -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),combs(X_b,bool,bool),hAPP(fun(X_b,bool),fun(X_b,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fconj),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(fun(X_b,bool),bool)),fun(fun(X_b,bool),fun(X_b,bool)),combc(X_b,fun(X_b,bool),bool),member(X_b)),A_3))),hAPP(X_c,fun(X_b,bool),hAPP(fun(X_b,fun(X_c,bool)),fun(X_c,fun(X_b,bool)),combc(X_b,X_c,bool),hAPP(fun(X_b,X_c),fun(X_b,fun(X_c,bool)),hAPP(fun(X_c,fun(X_c,bool)),fun(fun(X_b,X_c),fun(X_b,fun(X_c,bool))),combb(X_c,fun(X_c,bool),X_b),fequal(X_c)),F)),hAPP(X_b,X_c,F,X_2))))))))))) # label(fact_49_pigeonhole__infinite) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.05 99 (all X_b all X_c all A_3 all B_3 all F all X_1 (ti(X_b,B_3) = hAPP(X_c,X_b,F,X_1) -> (hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),X_1),A_3)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),B_3),hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),A_3)))))) # label(fact_50_image__eqI) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.05 100 (all X_b all A_3 all 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)),A_3),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)),B_1),A_3)) -> ti(fun(X_b,bool),A_3) = ti(fun(X_b,bool),B_1)))) # label(fact_51_equalityI) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.05 101 (all X_b all C_1 all A_3 all 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)),A_3),B_1)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C_1),A_3)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C_1),B_1))))) # label(fact_52_subsetD) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.05 102 (all X_b all B_3 all A_2 all B_1 ((-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),B_1)) -> ti(X_b,A_2) = ti(X_b,B_3)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),B_3),B_1))))) # label(fact_53_insertCI) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.05 103 (all X_b all A_2 all B_3 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),B_3),A_3))) -> (ti(X_b,A_2) != ti(X_b,B_3) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),A_3))))) # label(fact_54_insertE) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.05 104 (all I_1 all Pa all K (hBOOL(hAPP(nat,bool,Pa,K)) -> ((all N_1 (hBOOL(hAPP(nat,bool,Pa,hAPP(nat,nat,suc,N_1))) -> hBOOL(hAPP(nat,bool,Pa,N_1)))) -> hBOOL(hAPP(nat,bool,Pa,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),K),I_1)))))) # label(fact_55_zero__induct__lemma) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.05 105 (all N all M_4 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,N)),M_4)) -> (exists M_2 M_4 = hAPP(nat,nat,suc,M_2)))) # label(fact_56_Suc__le__D) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.05 106 (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_57_order__refl) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.05 107 (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_58_linorder__linear) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.05 108 (all X_b (order(X_b) -> (all X_1 all Y_2 (ti(X_b,X_1) = ti(X_b,Y_2) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),X_1),Y_2)) & hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),Y_2),X_1)))))) # label(fact_59_order__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.05 109 (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_60_order__eq__refl) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.05 110 (all X_b (order(X_b) -> (all Y_2 all X_1 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),Y_2),X_1)) -> (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),X_1),Y_2)) <-> ti(X_b,X_1) = ti(X_b,Y_2)))))) # label(fact_61_order__antisym__conv) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.05 111 (all X_a (ord(X_a) -> (all C all A_1 all B (A_1 = 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_62_ord__eq__le__trans) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.05 112 (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_63_xt1_I3_J) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.05 113 (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)) -> (B = C -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),C))))))) # label(fact_64_ord__le__eq__trans) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.05 114 (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_65_xt1_I4_J) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.05 115 (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_66_order__antisym) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.05 116 (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_67_order__trans) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.05 117 (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_68_xt1_I5_J) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.05 118 (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_69_xt1_I6_J) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.05 119 (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_70_linorder__le__cases) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.05 120 (all X_b all A_2 all B_1 hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),B_1)))) # label(fact_71_insertI1) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.05 121 (all X_b all A_2 all B_1 hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),B_1) = hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),combs(X_b,bool,bool),hAPP(fun(X_b,bool),fun(X_b,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fdisj),hAPP(X_b,fun(X_b,bool),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,bool)),combc(X_b,X_b,bool),fequal(X_b)),A_2))),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(fun(X_b,bool),bool)),fun(fun(X_b,bool),fun(X_b,bool)),combc(X_b,fun(X_b,bool),bool),member(X_b)),B_1)))) # label(fact_72_insert__compr) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.05 122 (all X_b all A_2 all Pa hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),Pa)) = hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),combs(X_b,bool,bool),hAPP(fun(X_b,bool),fun(X_b,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fimplies),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(bool,bool),fun(fun(X_b,bool),fun(X_b,bool)),combb(bool,bool,X_b),fNot),hAPP(X_b,fun(X_b,bool),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,bool)),combc(X_b,X_b,bool),fequal(X_b)),A_2)))),Pa))) # label(fact_73_insert__Collect) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.05 123 (all X_b all X_c all F all G ((all X_2 hAPP(X_b,X_c,F,X_2) = hAPP(X_b,X_c,G,X_2)) -> ti(fun(X_b,X_c),F) = ti(fun(X_b,X_c),G))) # label(fact_74_ext) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.05 124 (all X_b all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) <-> hBOOL(hAPP(X_b,bool,A_3,X_1)))) # label(fact_75_mem__def) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.05 125 (all X_b all Pa hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),Pa) = ti(fun(X_b,bool),Pa)) # label(fact_76_Collect__def) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.05 126 (all X_b all X_1 all A_3 hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_3)) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_3)) # label(fact_77_insert__absorb2) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.05 127 (all X_b all X_1 all Y_2 all A_3 hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),Y_2),A_3)) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),Y_2),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_3))) # label(fact_78_insert__commute) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.05 128 (all X_b all A_2 all B_3 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),B_3),A_3))) <-> ti(X_b,A_2) = ti(X_b,B_3) | hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),A_3)))) # label(fact_79_insert__iff) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.05 129 (all X_b all Y_2 all A_3 all X_1 (hBOOL(hAPP(X_b,bool,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),Y_2),A_3),X_1)) <-> ti(X_b,Y_2) = ti(X_b,X_1) | hBOOL(hAPP(X_b,bool,A_3,X_1)))) # label(fact_80_insert__code) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.05 130 (all X_b all B_1 all X_1 all A_3 (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),B_1)) -> (hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_3) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),B_1) <-> ti(fun(X_b,bool),A_3) = ti(fun(X_b,bool),B_1))))) # label(fact_81_insert__ident) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.05 131 (all X_b all B_3 all A_2 all B_1 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),B_1)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),B_3),B_1))))) # label(fact_82_insertI2) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.05 132 (all X_b all A_2 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),A_3)) -> hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),A_3) = ti(fun(X_b,bool),A_3))) # label(fact_83_insert__absorb) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.05 133 (all X_b all A_3 hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),A_3))) # label(fact_84_subset__refl) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.05 134 (all X_b all A_3 all B_1 (ti(fun(X_b,bool),A_3) = ti(fun(X_b,bool),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)),A_3),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)),B_1),A_3)))) # label(fact_85_set__eq__subset) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.05 135 (all X_b all A_3 all B_1 (ti(fun(X_b,bool),A_3) = ti(fun(X_b,bool),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)),A_3),B_1)))) # label(fact_86_equalityD1) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.05 136 (all X_b all A_3 all B_1 (ti(fun(X_b,bool),A_3) = ti(fun(X_b,bool),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)),B_1),A_3)))) # label(fact_87_equalityD2) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.05 137 (all X_b all X_1 all A_3 all 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)),A_3),B_1)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),B_1))))) # label(fact_88_in__mono) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.05 138 (all X_b all B_1 all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),B_1)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),B_1))))) # label(fact_89_set__rev__mp) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.05 139 (all X_b all X_1 all A_3 all 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)),A_3),B_1)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),B_1))))) # label(fact_90_set__mp) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.05 140 (all X_b all C_2 all A_3 all 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)),A_3),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)),B_1),C_2)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),C_2))))) # label(fact_91_subset__trans) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.05 141 (all X_b all A_3 all B_1 (ti(fun(X_b,bool),A_3) = ti(fun(X_b,bool),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)),A_3),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)),B_1),A_3))))) # label(fact_92_equalityE) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.05 142 (all X_b all X_c all Z_2 all F all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Z_2),hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),A_3))) <-> (exists X_2 (hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),X_2),A_3)) & ti(X_b,Z_2) = hAPP(X_c,X_b,F,X_2))))) # label(fact_93_image__iff) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.05 143 (all X_c all X_b all F all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),hAPP(X_b,X_c,F,X_1)),hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),F),A_3))))) # label(fact_94_imageI) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.05 144 (all X_c all X_b all B_3 all F all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> (ti(X_c,B_3) = hAPP(X_b,X_c,F,X_1) -> hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),B_3),hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),F),A_3)))))) # label(fact_95_rev__image__eqI) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.05 145 (all X_b all X_2 all Xa hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_2),Xa) = hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),combs(X_b,bool,bool),hAPP(fun(X_b,bool),fun(X_b,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fdisj),hAPP(X_b,fun(X_b,bool),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,bool)),combc(X_b,X_b,bool),fequal(X_b)),X_2))),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(fun(X_b,bool),bool)),fun(fun(X_b,bool),fun(X_b,bool)),combc(X_b,fun(X_b,bool),bool),member(X_b)),Xa)))) # label(fact_96_insert__compr__raw) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.05 146 (all X_c all X_b all X_d all F all G all A_3 hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),hAPP(fun(X_d,bool),fun(X_c,bool),hAPP(fun(X_d,X_c),fun(fun(X_d,bool),fun(X_c,bool)),image(X_d,X_c),G),A_3)) = hAPP(fun(X_d,bool),fun(X_b,bool),hAPP(fun(X_d,X_b),fun(fun(X_d,bool),fun(X_b,bool)),image(X_d,X_b),hAPP(fun(X_d,X_c),fun(X_d,X_b),hAPP(fun(X_c,X_b),fun(fun(X_d,X_c),fun(X_d,X_b)),combb(X_c,X_b,X_d),F),G)),A_3)) # label(fact_97_image__image) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.05 147 (all X_b all Y_3 hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,X_b),fun(fun(X_b,bool),fun(X_b,bool)),image(X_b,X_b),combi(X_b)),Y_3) = ti(fun(X_b,bool),Y_3)) # label(fact_98_image__ident) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.05 148 (all X_b all X_c (ord(X_c) -> (all F all G (hBOOL(hAPP(fun(X_b,X_c),bool,hAPP(fun(X_b,X_c),fun(fun(X_b,X_c),bool),ord_less_eq(fun(X_b,X_c)),F),G)) <-> (all X_2 hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less_eq(X_c),hAPP(X_b,X_c,F,X_2)),hAPP(X_b,X_c,G,X_2)))))))) # label(fact_99_le__fun__def) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.05 149 (all X_b all X_c (ord(X_c) -> (all X_1 all F all G (hBOOL(hAPP(fun(X_b,X_c),bool,hAPP(fun(X_b,X_c),fun(fun(X_b,X_c),bool),ord_less_eq(fun(X_b,X_c)),F),G)) -> hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less_eq(X_c),hAPP(X_b,X_c,F,X_1)),hAPP(X_b,X_c,G,X_1))))))) # label(fact_100_le__funD) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.05 150 (all X_b all X_c (ord(X_c) -> (all X_1 all F all G (hBOOL(hAPP(fun(X_b,X_c),bool,hAPP(fun(X_b,X_c),fun(fun(X_b,X_c),bool),ord_less_eq(fun(X_b,X_c)),F),G)) -> hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less_eq(X_c),hAPP(X_b,X_c,F,X_1)),hAPP(X_b,X_c,G,X_1))))))) # label(fact_101_le__funE) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.05 151 (all X_b all B_1 all A_2 hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),B_1),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),B_1)))) # label(fact_102_subset__insertI) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.05 152 (all X_b all X_1 all A_3 all 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_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_3)),B_1)) <-> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),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)),A_3),B_1)))) # label(fact_103_insert__subset) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.05 153 (all X_b all B_1 all X_1 all A_3 (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),B_1))) <-> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),B_1))))) # label(fact_104_subset__insert) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.05 154 (all X_b all B_3 all A_3 all 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)),A_3),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)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),B_3),B_1))))) # label(fact_105_subset__insertI2) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.05 155 (all X_b all A_2 all C_2 all D_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_2),D_3)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),C_2)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),D_3))))) # label(fact_106_insert__mono) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.05 156 (all X_c all X_b all F all A_2 all B_1 hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),hAPP(fun(X_c,bool),fun(X_c,bool),hAPP(X_c,fun(fun(X_c,bool),fun(X_c,bool)),insert(X_c),A_2),B_1)) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),hAPP(X_c,X_b,F,A_2)),hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),B_1))) # label(fact_107_image__insert) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.05 157 (all X_c all X_b all F all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> hAPP(fun(X_c,bool),fun(X_c,bool),hAPP(X_c,fun(fun(X_c,bool),fun(X_c,bool)),insert(X_c),hAPP(X_b,X_c,F,X_1)),hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),F),A_3)) = hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),F),A_3))) # label(fact_108_insert__image) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.05 158 (all X_b all X_c all B_1 all F all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),B_1),hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),A_3))) <-> (exists AA (hBOOL(hAPP(fun(X_c,bool),bool,hAPP(fun(X_c,bool),fun(fun(X_c,bool),bool),ord_less_eq(fun(X_c,bool)),AA),A_3)) & ti(fun(X_b,bool),B_1) = hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),AA))))) # label(fact_109_subset__image__iff) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.05 159 (all X_c all X_b all F all A_3 all 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)),A_3),B_1)) -> hBOOL(hAPP(fun(X_c,bool),bool,hAPP(fun(X_c,bool),fun(fun(X_c,bool),bool),ord_less_eq(fun(X_c,bool)),hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),F),A_3)),hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),F),B_1))))) # label(fact_110_image__mono) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.05 160 (all X_b all X_c all B_3 all F all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),B_3),hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),A_3))) -> -(all X_2 (ti(X_b,B_3) = hAPP(X_c,X_b,F,X_2) -> -hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),X_2),A_3)))))) # label(fact_111_imageE) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.05 161 (all X_b all B_1 all A_3 ((all X_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_3)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),B_1)))) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),B_1)))) # label(fact_112_subsetI) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.05 162 (all X_c all X_b all F all B_1 all A_3 ((all X_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_3)) -> hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),hAPP(X_b,X_c,F,X_2)),B_1)))) -> hBOOL(hAPP(fun(X_c,bool),bool,hAPP(fun(X_c,bool),fun(fun(X_c,bool),bool),ord_less_eq(fun(X_c,bool)),hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),F),A_3)),B_1)))) # label(fact_113_image__subsetI) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.05 163 (all X_b all X_c (ord(X_c) -> (all F all G ((all X_2 hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less_eq(X_c),hAPP(X_b,X_c,F,X_2)),hAPP(X_b,X_c,G,X_2)))) -> hBOOL(hAPP(fun(X_b,X_c),bool,hAPP(fun(X_b,X_c),fun(fun(X_b,X_c),bool),ord_less_eq(fun(X_b,X_c)),F),G)))))) # label(fact_114_le__funI) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.05 164 (all N_2 (hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),N_2)) <-> (exists M_2 all X_2 (hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X_2),N_2)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X_2),M_2)))))) # label(fact_115_finite__nat__set__iff__bounded__le) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.05 165 (all G_1 all C_1 (hBOOL(hAPP(com,bool,wt,C_1)) -> ((all X_2 (hBOOL(hAPP(fun(pname,bool),bool,hAPP(pname,fun(fun(pname,bool),bool),member(pname),X_2),u)) -> hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),p,G_1),hAPP(fun(x_a,bool),fun(x_a,bool),hAPP(x_a,fun(fun(x_a,bool),fun(x_a,bool)),insert(x_a),hAPP(pname,x_a,mgt_call,X_2)),bot_bot(fun(x_a,bool))))))) -> hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),p,G_1),hAPP(fun(x_a,bool),fun(x_a,bool),hAPP(x_a,fun(fun(x_a,bool),fun(x_a,bool)),insert(x_a),hAPP(com,x_a,mgt,C_1)),bot_bot(fun(x_a,bool)))))))) # label(fact_116_assms_I3_J) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.05 166 (all X_b (ordered_ab_group_add(X_b) -> (all A_2 all B_3 all C_1 all D_1 (hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),A_2),B_3) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),C_1),D_1) -> (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),A_2),B_3)) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),C_1),D_1))))))) # label(fact_117_diff__eq__diff__less__eq) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.05 167 (all M all Na (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,M)),Na)) <-> 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)),Na)))) # label(fact_118_less__eq__nat_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.05 168 (all X_c all X_b all B_1 all A_3 all F all Z_2 all G all F_1 (hBOOL(hAPP(fun(fun(X_c,bool),X_b),bool,hAPP(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool),hAPP(X_b,fun(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool)),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool))),finite908156982e_idem(X_b,X_c),F),Z_2),G),F_1)) -> (hBOOL(hAPP(fun(X_c,bool),bool,finite_finite(X_c),A_3)) -> (hBOOL(hAPP(fun(X_c,bool),bool,hAPP(fun(X_c,bool),fun(fun(X_c,bool),bool),ord_less_eq(fun(X_c,bool)),B_1),A_3)) -> hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,hAPP(fun(X_c,bool),X_b,F_1,B_1)),hAPP(fun(X_c,bool),X_b,F_1,A_3)) = hAPP(fun(X_c,bool),X_b,F_1,A_3))))) # label(fact_119_folding__image__simple__idem_Osubset__idem) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.05 169 (all X_c all X_b all X_1 all A_3 all F all Z_2 all G all F_1 (hBOOL(hAPP(fun(fun(X_c,bool),X_b),bool,hAPP(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool),hAPP(X_b,fun(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool)),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool))),finite908156982e_idem(X_b,X_c),F),Z_2),G),F_1)) -> (hBOOL(hAPP(fun(X_c,bool),bool,finite_finite(X_c),A_3)) -> hAPP(fun(X_c,bool),X_b,F_1,hAPP(fun(X_c,bool),fun(X_c,bool),hAPP(X_c,fun(fun(X_c,bool),fun(X_c,bool)),insert(X_c),X_1),A_3)) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,hAPP(X_c,X_b,G,X_1)),hAPP(fun(X_c,bool),X_b,F_1,A_3))))) # label(fact_120_folding__image__simple__idem_Oinsert__idem) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.05 170 (all X_b all A_2 -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),bot_bot(fun(X_b,bool))))) # label(fact_121_emptyE) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.05 171 (all X_b all B_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3)) -> hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_1))))) # label(fact_122_finite__Diff) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.05 172 (all X_b hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),bot_bot(fun(X_b,bool))))) # label(fact_123_finite_OemptyI) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.05 173 (all X_b all A_3 hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),bot_bot(fun(X_b,bool))),A_3))) # label(fact_124_empty__subsetI) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.05 174 (all X_b all A_2 all A_3 (ti(fun(X_b,bool),A_3) = bot_bot(fun(X_b,bool)) -> -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),A_3)))) # label(fact_125_equals0D) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.05 175 (all X_b all Pa (hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),Pa) = bot_bot(fun(X_b,bool)) <-> (all X_2 -hBOOL(hAPP(X_b,bool,Pa,X_2))))) # label(fact_126_Collect__empty__eq) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.05 176 (all X_b all A_3 hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),A_3) = bot_bot(fun(X_b,bool))) # label(fact_127_Diff__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.05 177 (all X_b all A_3 hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),bot_bot(fun(X_b,bool))) = ti(fun(X_b,bool),A_3)) # label(fact_128_Diff__empty) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.05 178 (all X_b all C_1 -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C_1),bot_bot(fun(X_b,bool))))) # label(fact_129_empty__iff) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.05 179 (all X_b all Pa (bot_bot(fun(X_b,bool)) = hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),Pa) <-> (all X_2 -hBOOL(hAPP(X_b,bool,Pa,X_2))))) # label(fact_130_empty__Collect__eq) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.05 180 (all X_b all A_3 hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),bot_bot(fun(X_b,bool))),A_3) = bot_bot(fun(X_b,bool))) # label(fact_131_empty__Diff) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.05 181 (all X_b all A_3 ((exists X_2 hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_3))) <-> ti(fun(X_b,bool),A_3) != bot_bot(fun(X_b,bool)))) # label(fact_132_ex__in__conv) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.05 182 (all X_b all A_3 ((all X_2 -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_3))) <-> ti(fun(X_b,bool),A_3) = bot_bot(fun(X_b,bool)))) # label(fact_133_all__not__in__conv) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.05 183 (all X_c all X_b (bot(X_b) -> (all X_1 hAPP(X_c,X_b,bot_bot(fun(X_c,X_b)),X_1) = bot_bot(X_b)))) # label(fact_134_bot__apply) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.05 184 (all X_b bot_bot(fun(X_b,bool)) = hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(bool,fun(X_b,bool),combk(bool,X_b),fFalse))) # label(fact_135_empty__def) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.05 185 (all X_b all X_c (bot(X_c) -> (all X_2 hAPP(X_b,X_c,bot_bot(fun(X_b,X_c)),X_2) = bot_bot(X_c)))) # label(fact_136_bot__fun__def) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.05 186 (all X_b all A_2 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),A_3)) -> hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),bot_bot(fun(X_b,bool))))) = ti(fun(X_b,bool),A_3))) # label(fact_137_insert__Diff) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.05 187 (all X_b all X_1 all A_3 (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_3)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool)))) = ti(fun(X_b,bool),A_3))) # label(fact_138_Diff__insert__absorb) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.05 188 (all X_b all A_2 all A_3 hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),bot_bot(fun(X_b,bool))))) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),A_3)) # label(fact_139_insert__Diff__single) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.05 189 (all X_b all A_3 all A_2 all B_1 hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),B_1)) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),bot_bot(fun(X_b,bool))))),B_1)) # label(fact_140_Diff__insert2) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.05 190 (all X_b all A_3 all A_2 all B_1 hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),B_1)) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_1)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),bot_bot(fun(X_b,bool))))) # label(fact_141_Diff__insert) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.05 191 (all X_c all X_b all X_1 all F all Z_2 all G all F_1 (hBOOL(hAPP(fun(fun(X_c,bool),X_b),bool,hAPP(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool),hAPP(X_b,fun(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool)),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool))),finite908156982e_idem(X_b,X_c),F),Z_2),G),F_1)) -> hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,X_1),X_1) = ti(X_b,X_1))) # label(fact_142_folding__image__simple__idem_Oidem) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.05 192 (all X_b all A_3 all X_1 all 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_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool))))),B_1)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),B_1)))))) # label(fact_143_diff__single__insert) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.05 193 (all X_b all A_3 all X_1 all 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)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),B_1))) <-> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool))))),B_1))) & (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),B_1))))) # label(fact_144_subset__insert__iff) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.05 194 (all X_b all A_3 all B_1 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),B_1)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_1))) <-> hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3))))) # label(fact_145_finite__Diff2) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.05 195 (all X_b all A_3 all X_1 all B_1 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),B_1)) -> hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_3)),B_1) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_1))) # label(fact_146_insert__Diff1) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.05 196 (all X_b all A_3 all X_1 all B_1 ((hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),B_1)) -> hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_3)),B_1) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_1)) & (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),B_1)) -> hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_3)),B_1) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_1))))) # label(fact_147_insert__Diff__if) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.05 197 (all X_b all C_2 all A_3 all 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)),A_3),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)),B_1),C_2)) -> hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),B_1),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),C_2),A_3)) = ti(fun(X_b,bool),A_3)))) # label(fact_148_double__diff) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.05 198 (all X_b all D_3 all B_1 all A_3 all C_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),C_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)),D_3),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_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_1)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),C_2),D_3)))))) # label(fact_149_Diff__mono) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.05 199 (all X_b all A_3 all 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_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_1)),A_3))) # label(fact_150_Diff__subset) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.05 200 (all X_b all A_2 all B_3 (hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),bot_bot(fun(X_b,bool))) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),B_3),bot_bot(fun(X_b,bool))) -> ti(X_b,A_2) = ti(X_b,B_3))) # label(fact_151_singleton__inject) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.05 201 (all X_b all B_3 all A_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),B_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),bot_bot(fun(X_b,bool))))) -> ti(X_b,B_3) = ti(X_b,A_2))) # label(fact_152_singletonE) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.05 202 (all X_b all A_2 all B_3 all C_1 all D_1 (hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),B_3),bot_bot(fun(X_b,bool)))) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),C_1),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),D_1),bot_bot(fun(X_b,bool)))) <-> ti(X_b,A_2) = ti(X_b,C_1) & ti(X_b,B_3) = ti(X_b,D_1) | ti(X_b,A_2) = ti(X_b,D_1) & ti(X_b,B_3) = ti(X_b,C_1))) # label(fact_153_doubleton__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.05 203 (all X_b all B_3 all A_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),B_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),bot_bot(fun(X_b,bool))))) <-> ti(X_b,B_3) = ti(X_b,A_2))) # label(fact_154_singleton__iff) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.05 204 (all X_b all A_2 all A_3 hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),A_3) != bot_bot(fun(X_b,bool))) # label(fact_155_insert__not__empty) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.05 205 (all X_b all A_2 all A_3 bot_bot(fun(X_b,bool)) != hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),A_3)) # label(fact_156_empty__not__insert) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.05 206 (all X_b all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),bot_bot(fun(X_b,bool)))) <-> ti(fun(X_b,bool),A_3) = bot_bot(fun(X_b,bool)))) # label(fact_157_subset__empty) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.05 207 (all X_c all X_b all F all A_3 (hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),A_3) = bot_bot(fun(X_b,bool)) <-> ti(fun(X_c,bool),A_3) = bot_bot(fun(X_c,bool)))) # label(fact_158_image__is__empty) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.05 208 (all X_c all X_b all F hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),bot_bot(fun(X_c,bool))) = bot_bot(fun(X_b,bool))) # label(fact_159_image__empty) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.05 209 (all X_b all X_c all F all A_3 (bot_bot(fun(X_b,bool)) = hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),A_3) <-> ti(fun(X_c,bool),A_3) = bot_bot(fun(X_c,bool)))) # label(fact_160_empty__is__image) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.05 210 (all X_a (bot(X_a) -> (all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),bot_bot(X_a))) -> ti(X_a,A_1) = bot_bot(X_a))))) # label(fact_161_le__bot) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.05 211 (all X_b (bot(X_b) -> (all A_2 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),A_2),bot_bot(X_b))) <-> ti(X_b,A_2) = bot_bot(X_b))))) # label(fact_162_bot__unique) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.05 212 (all X_a (bot(X_a) -> (all A_1 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),bot_bot(X_a)),A_1))))) # label(fact_163_bot__least) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.05 213 (all X_b all Pa all A_2 ((hBOOL(hAPP(X_b,bool,Pa,A_2)) -> hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),combs(X_b,bool,bool),hAPP(fun(X_b,bool),fun(X_b,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fconj),hAPP(X_b,fun(X_b,bool),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,bool)),combc(X_b,X_b,bool),fequal(X_b)),A_2))),Pa)) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),bot_bot(fun(X_b,bool)))) & (-hBOOL(hAPP(X_b,bool,Pa,A_2)) -> hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),combs(X_b,bool,bool),hAPP(fun(X_b,bool),fun(X_b,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fconj),hAPP(X_b,fun(X_b,bool),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,bool)),combc(X_b,X_b,bool),fequal(X_b)),A_2))),Pa)) = bot_bot(fun(X_b,bool))))) # label(fact_164_Collect__conv__if) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.05 214 (all X_b all Pa all A_2 ((hBOOL(hAPP(X_b,bool,Pa,A_2)) -> hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),combs(X_b,bool,bool),hAPP(fun(X_b,bool),fun(X_b,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fconj),hAPP(X_b,fun(X_b,bool),fequal(X_b),A_2))),Pa)) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),bot_bot(fun(X_b,bool)))) & (-hBOOL(hAPP(X_b,bool,Pa,A_2)) -> hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),combs(X_b,bool,bool),hAPP(fun(X_b,bool),fun(X_b,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fconj),hAPP(X_b,fun(X_b,bool),fequal(X_b),A_2))),Pa)) = bot_bot(fun(X_b,bool))))) # label(fact_165_Collect__conv__if2) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.05 215 (all X_b all A_2 hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(X_b,fun(X_b,bool),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,bool)),combc(X_b,X_b,bool),fequal(X_b)),A_2)) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),bot_bot(fun(X_b,bool)))) # label(fact_166_singleton__conv) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.05 216 (all X_b all A_2 hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(X_b,fun(X_b,bool),fequal(X_b),A_2)) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),bot_bot(fun(X_b,bool)))) # label(fact_167_singleton__conv2) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.05 217 (all X_b all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> hAPP(nat,nat,suc,hAPP(fun(X_b,bool),nat,finite_card(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool)))))) = hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3)))) # label(fact_168_card__Suc__Diff1) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.05 218 (all X_b all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3)) -> hAPP(fun(X_b,bool),nat,finite_card(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_3)) = hAPP(nat,nat,suc,hAPP(fun(X_b,bool),nat,finite_card(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool)))))))) # label(fact_169_card__insert) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.05 219 (all X_b all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X_b,bool),nat,finite_card(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool)))))),hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3))))) # label(fact_170_card__Diff1__le) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.05 220 (all X_b all A_3 all A_2 all B_1 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),B_1)))) <-> hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_1))))) # label(fact_171_finite__Diff__insert) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.05 221 (all X_b all X_c all F all A_3 all 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_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),A_3)),hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),B_1))),hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),hAPP(fun(X_c,bool),fun(X_c,bool),hAPP(fun(X_c,bool),fun(fun(X_c,bool),fun(X_c,bool)),minus_minus(fun(X_c,bool)),A_3),B_1))))) # label(fact_172_image__diff__subset) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.05 222 (all X_b all A_3 all X_1 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool))))) -> ti(fun(X_b,bool),A_3) = bot_bot(fun(X_b,bool)) | ti(fun(X_b,bool),A_3) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool))))) # label(fact_173_subset__singletonD) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.05 223 (all X_b all F1 all F2 all Nat_3 hAPP(nat,X_b,hAPP(fun(nat,X_b),fun(nat,X_b),hAPP(X_b,fun(fun(nat,X_b),fun(nat,X_b)),nat_case(X_b),F1),F2),hAPP(nat,nat,suc,Nat_3)) = hAPP(nat,X_b,F2,Nat_3)) # label(fact_174_nat__case__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.05 224 (all X_c all X_b all C_1 all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),hAPP(X_c,fun(X_b,X_c),combk(X_c,X_b),C_1)),A_3) = hAPP(fun(X_c,bool),fun(X_c,bool),hAPP(X_c,fun(fun(X_c,bool),fun(X_c,bool)),insert(X_c),C_1),bot_bot(fun(X_c,bool))))) # label(fact_175_image__constant) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.05 225 (all X_c all X_b all C_1 all A_3 ((ti(fun(X_b,bool),A_3) = bot_bot(fun(X_b,bool)) -> hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),hAPP(X_c,fun(X_b,X_c),combk(X_c,X_b),C_1)),A_3) = bot_bot(fun(X_c,bool))) & (ti(fun(X_b,bool),A_3) != bot_bot(fun(X_b,bool)) -> hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),hAPP(X_c,fun(X_b,X_c),combk(X_c,X_b),C_1)),A_3) = hAPP(fun(X_c,bool),fun(X_c,bool),hAPP(X_c,fun(fun(X_c,bool),fun(X_c,bool)),insert(X_c),C_1),bot_bot(fun(X_c,bool)))))) # label(fact_176_image__constant__conv) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.05 226 (all X_c all X_b all X_1 all A_3 all F all Z_2 all G all F_1 (hBOOL(hAPP(fun(fun(X_c,bool),X_b),bool,hAPP(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool),hAPP(X_b,fun(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool)),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool))),finite908156982e_idem(X_b,X_c),F),Z_2),G),F_1)) -> (hBOOL(hAPP(fun(X_c,bool),bool,finite_finite(X_c),A_3)) -> (hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),X_1),A_3)) -> hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,hAPP(X_c,X_b,G,X_1)),hAPP(fun(X_c,bool),X_b,F_1,A_3)) = hAPP(fun(X_c,bool),X_b,F_1,A_3))))) # label(fact_177_folding__image__simple__idem_Oin__idem) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.05 227 (all X_b (ab_group_add(X_b) -> (all A_2 all B_3 all C_1 all D_1 (hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),A_2),B_3) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),C_1),D_1) -> (ti(X_b,A_2) = ti(X_b,B_3) <-> ti(X_b,C_1) = ti(X_b,D_1)))))) # label(fact_178_diff__eq__diff__eq) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.05 228 (all X_b all A_3 all B_1 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),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)),B_1),A_3)) -> hAPP(fun(X_b,bool),nat,finite_card(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_1)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3)),hAPP(fun(X_b,bool),nat,finite_card(X_b),B_1))))) # label(fact_179_card__Diff__subset) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.05 229 (all X_b all A_3 all B_1 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),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_b,bool),nat,finite_card(X_b),A_3)),hAPP(fun(X_b,bool),nat,finite_card(X_b),B_1))),hAPP(fun(X_b,bool),nat,finite_card(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_1)))))) # label(fact_180_diff__card__le__card__Diff) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.05 230 (all X_b all Pa all A_3 all F_1 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),F_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)),F_1),A_3)) -> (hBOOL(hAPP(fun(X_b,bool),bool,Pa,bot_bot(fun(X_b,bool)))) -> ((all A_4 all F_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),F_3)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_4),A_3)) -> (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_4),F_3)) -> (hBOOL(hAPP(fun(X_b,bool),bool,Pa,F_3)) -> hBOOL(hAPP(fun(X_b,bool),bool,Pa,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_4),F_3)))))))) -> hBOOL(hAPP(fun(X_b,bool),bool,Pa,F_1))))))) # label(fact_181_finite__subset__induct) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.05 231 (all Pn all G_1 (hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),p,hAPP(fun(x_a,bool),fun(x_a,bool),hAPP(x_a,fun(fun(x_a,bool),fun(x_a,bool)),insert(x_a),hAPP(pname,x_a,mgt_call,Pn)),G_1)),hAPP(fun(x_a,bool),fun(x_a,bool),hAPP(x_a,fun(fun(x_a,bool),fun(x_a,bool)),insert(x_a),hAPP(com,x_a,mgt,hAPP(option(com),com,the_1(com),hAPP(pname,option(com),body,Pn)))),bot_bot(fun(x_a,bool))))) -> hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),p,G_1),hAPP(fun(x_a,bool),fun(x_a,bool),hAPP(x_a,fun(fun(x_a,bool),fun(x_a,bool)),insert(x_a),hAPP(pname,x_a,mgt_call,Pn)),bot_bot(fun(x_a,bool))))))) # label(fact_182_assms_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.05 232 (all X_b all Pa all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3)) -> (hBOOL(hAPP(fun(X_b,bool),bool,Pa,A_3)) -> ((all A_4 all A_5 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_5)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_4),A_5)) -> (hBOOL(hAPP(fun(X_b,bool),bool,Pa,A_5)) -> hBOOL(hAPP(fun(X_b,bool),bool,Pa,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_5),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_4),bot_bot(fun(X_b,bool)))))))))) -> hBOOL(hAPP(fun(X_b,bool),bool,Pa,bot_bot(fun(X_b,bool)))))))) # label(fact_183_finite__empty__induct) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.05 233 (all X_b all Pa all F_1 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),F_1)) -> (hBOOL(hAPP(fun(X_b,bool),bool,Pa,bot_bot(fun(X_b,bool)))) -> ((all X_2 all F_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),F_3)) -> (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),F_3)) -> (hBOOL(hAPP(fun(X_b,bool),bool,Pa,F_3)) -> hBOOL(hAPP(fun(X_b,bool),bool,Pa,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_2),F_3))))))) -> hBOOL(hAPP(fun(X_b,bool),bool,Pa,F_1)))))) # label(fact_184_finite__induct) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.05 234 (all X_b all A_2 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_2)) <-> ti(fun(X_b,bool),A_2) = bot_bot(fun(X_b,bool)) | (exists A_5 exists A_4 (ti(fun(X_b,bool),A_2) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_4),A_5) & hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_5)))))) # label(fact_185_finite_Osimps) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.05 235 (all U all F ((all N_1 hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_1),hAPP(nat,nat,F,N_1)))) -> hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),hAPP(fun(nat,nat),fun(nat,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(nat,nat),fun(nat,fun(nat,bool))),combb(nat,fun(nat,bool),nat),ord_less_eq(nat)),F)),U)))))) # label(fact_186_finite__less__ub) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.05 236 (all X_b all X_1 hAPP(fun(X_b,bool),X_b,the_elem(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool)))) = ti(X_b,X_1)) # label(fact_187_the__elem__eq) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.05 237 (all X_b all A_3 (ti(fun(X_b,bool),A_3) != bot_bot(fun(X_b,bool)) <-> (exists X_2 exists B_4 (ti(fun(X_b,bool),A_3) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_2),B_4) & -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),B_4)))))) # label(fact_188_nonempty__iff) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.05 238 (all Pn (hBOOL(hAPP(fun(pname,bool),bool,hAPP(pname,fun(fun(pname,bool),bool),member(pname),Pn),u)) -> hBOOL(hAPP(com,bool,wt,hAPP(option(com),com,the_1(com),hAPP(pname,option(com),body,Pn)))))) # label(fact_189_assms_I4_J) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.05 239 (all X_b all C_1 all A_3 all B_1 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C_1),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_1))) -> -(hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C_1),A_3)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C_1),B_1))))) # label(fact_190_DiffE) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.05 240 (all X_b all B_1 all C_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C_1),A_3)) -> (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C_1),B_1)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C_1),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_1)))))) # label(fact_191_DiffI) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.05 241 (all X_b all C_1 all A_3 all B_1 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C_1),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_1))) -> -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C_1),B_1)))) # label(fact_192_DiffD2) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.05 242 (all X_b all C_1 all A_3 all B_1 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C_1),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_1))) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C_1),A_3)))) # label(fact_193_DiffD1) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.05 243 (all X_b all A_3 all B_1 hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_1)),B_1) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_1)) # label(fact_194_Diff__idemp) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.05 244 (all X_b all C_1 all A_3 all B_1 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C_1),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_1))) <-> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C_1),A_3)) & -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C_1),B_1)))) # label(fact_195_Diff__iff) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.05 245 (all X_b all A_3 all B_1 hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_1) = hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),combs(X_b,bool,bool),hAPP(fun(X_b,bool),fun(X_b,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fconj),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(fun(X_b,bool),bool)),fun(fun(X_b,bool),fun(X_b,bool)),combc(X_b,fun(X_b,bool),bool),member(X_b)),A_3))),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(bool,bool),fun(fun(X_b,bool),fun(X_b,bool)),combb(bool,bool,X_b),fNot),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(fun(X_b,bool),bool)),fun(fun(X_b,bool),fun(X_b,bool)),combc(X_b,fun(X_b,bool),bool),member(X_b)),B_1))))) # label(fact_196_set__diff__eq) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.05 246 (all X_b all X_1 all A_3 all F all F_1 (hBOOL(hAPP(fun(fun(X_b,bool),X_b),bool,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(fun(X_b,bool),X_b),bool),finite_folding_one(X_b),F),F_1)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3)) -> (hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool)))) = bot_bot(fun(X_b,bool)) -> hAPP(fun(X_b,bool),X_b,F_1,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_3)) = ti(X_b,X_1)) & (hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool)))) != bot_bot(fun(X_b,bool)) -> hAPP(fun(X_b,bool),X_b,F_1,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_3)) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,X_1),hAPP(fun(X_b,bool),X_b,F_1,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool)))))))))) # label(fact_197_folding__one_Oinsert__remove) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.05 247 (all X_b all X_1 all A_3 all F all F_1 (hBOOL(hAPP(fun(fun(X_b,bool),X_b),bool,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(fun(X_b,bool),X_b),bool),finite_folding_one(X_b),F),F_1)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> (hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool)))) = bot_bot(fun(X_b,bool)) -> hAPP(fun(X_b,bool),X_b,F_1,A_3) = ti(X_b,X_1)) & (hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool)))) != bot_bot(fun(X_b,bool)) -> hAPP(fun(X_b,bool),X_b,F_1,A_3) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,X_1),hAPP(fun(X_b,bool),X_b,F_1,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool))))))))))) # label(fact_198_folding__one_Oremove) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.05 248 (all X_c all X_b all X_1 all A_3 all F all Z_2 all G all F_1 (hBOOL(hAPP(fun(fun(X_c,bool),X_b),bool,hAPP(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool),hAPP(X_b,fun(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool)),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool))),finite1357897459simple(X_b,X_c),F),Z_2),G),F_1)) -> (hBOOL(hAPP(fun(X_c,bool),bool,finite_finite(X_c),A_3)) -> hAPP(fun(X_c,bool),X_b,F_1,hAPP(fun(X_c,bool),fun(X_c,bool),hAPP(X_c,fun(fun(X_c,bool),fun(X_c,bool)),insert(X_c),X_1),A_3)) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,hAPP(X_c,X_b,G,X_1)),hAPP(fun(X_c,bool),X_b,F_1,hAPP(fun(X_c,bool),fun(X_c,bool),hAPP(fun(X_c,bool),fun(fun(X_c,bool),fun(X_c,bool)),minus_minus(fun(X_c,bool)),A_3),hAPP(fun(X_c,bool),fun(X_c,bool),hAPP(X_c,fun(fun(X_c,bool),fun(X_c,bool)),insert(X_c),X_1),bot_bot(fun(X_c,bool))))))))) # label(fact_199_folding__image__simple_Oinsert__remove) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.05 249 (all X_c all X_b all X_1 all A_3 all F all Z_2 all G all F_1 (hBOOL(hAPP(fun(fun(X_c,bool),X_b),bool,hAPP(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool),hAPP(X_b,fun(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool)),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool))),finite1357897459simple(X_b,X_c),F),Z_2),G),F_1)) -> (hBOOL(hAPP(fun(X_c,bool),bool,finite_finite(X_c),A_3)) -> (hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),X_1),A_3)) -> hAPP(fun(X_c,bool),X_b,F_1,A_3) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,hAPP(X_c,X_b,G,X_1)),hAPP(fun(X_c,bool),X_b,F_1,hAPP(fun(X_c,bool),fun(X_c,bool),hAPP(fun(X_c,bool),fun(fun(X_c,bool),fun(X_c,bool)),minus_minus(fun(X_c,bool)),A_3),hAPP(fun(X_c,bool),fun(X_c,bool),hAPP(X_c,fun(fun(X_c,bool),fun(X_c,bool)),insert(X_c),X_1),bot_bot(fun(X_c,bool)))))))))) # label(fact_200_folding__image__simple_Oremove) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 250 (all X_b all X_c (minus(X_c) -> (all A_3 all B_1 all X_2 hAPP(X_b,X_c,hAPP(fun(X_b,X_c),fun(X_b,X_c),hAPP(fun(X_b,X_c),fun(fun(X_b,X_c),fun(X_b,X_c)),minus_minus(fun(X_b,X_c)),A_3),B_1),X_2) = hAPP(X_c,X_c,hAPP(X_c,fun(X_c,X_c),minus_minus(X_c),hAPP(X_b,X_c,A_3,X_2)),hAPP(X_b,X_c,B_1,X_2))))) # label(fact_201_fun__diff__def) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 251 (all X_c all X_b (minus(X_b) -> (all A_3 all B_1 all X_1 hAPP(X_c,X_b,hAPP(fun(X_c,X_b),fun(X_c,X_b),hAPP(fun(X_c,X_b),fun(fun(X_c,X_b),fun(X_c,X_b)),minus_minus(fun(X_c,X_b)),A_3),B_1),X_1) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),hAPP(X_c,X_b,A_3,X_1)),hAPP(X_c,X_b,B_1,X_1))))) # label(fact_202_minus__apply) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 252 (all X_b all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> hAPP(fun(X_b,bool),nat,finite_card(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool))))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3)),one_one(nat))) & (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> hAPP(fun(X_b,bool),nat,finite_card(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool))))) = hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3)))) # label(fact_203_card__Diff__singleton__if) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 253 (all X_b all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> hAPP(fun(X_b,bool),nat,finite_card(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool))))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3)),one_one(nat))))) # label(fact_204_card__Diff__singleton) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 254 (all X_b (one(X_b) -> (all X_1 (one_one(X_b) = ti(X_b,X_1) <-> ti(X_b,X_1) = one_one(X_b))))) # label(fact_205_one__reorient) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 255 (all X_c all X_b all F all Z_2 all G all F_1 (hBOOL(hAPP(fun(fun(X_c,bool),X_b),bool,hAPP(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool),hAPP(X_b,fun(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool)),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool))),finite1357897459simple(X_b,X_c),F),Z_2),G),F_1)) -> hAPP(fun(X_c,bool),X_b,F_1,bot_bot(fun(X_c,bool))) = ti(X_b,Z_2))) # label(fact_206_folding__image__simple_Oempty) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 256 (all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,N)),one_one(nat)) = N) # label(fact_207_diff__Suc__1) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 257 (all M_1 all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),hAPP(nat,nat,suc,N)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),one_one(nat))),N)) # label(fact_208_diff__Suc__eq__diff__pred) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 258 (all X_b all X_1 all F all F_1 (hBOOL(hAPP(fun(fun(X_b,bool),X_b),bool,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(fun(X_b,bool),X_b),bool),finite_folding_one(X_b),F),F_1)) -> hAPP(fun(X_b,bool),X_b,F_1,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool)))) = ti(X_b,X_1))) # label(fact_209_folding__one_Osingleton) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 259 (all X_c all X_b all X_1 all A_3 all F all Z_2 all G all F_1 (hBOOL(hAPP(fun(fun(X_c,bool),X_b),bool,hAPP(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool),hAPP(X_b,fun(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool)),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool))),finite1357897459simple(X_b,X_c),F),Z_2),G),F_1)) -> (hBOOL(hAPP(fun(X_c,bool),bool,finite_finite(X_c),A_3)) -> (-hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),X_1),A_3)) -> hAPP(fun(X_c,bool),X_b,F_1,hAPP(fun(X_c,bool),fun(X_c,bool),hAPP(X_c,fun(fun(X_c,bool),fun(X_c,bool)),insert(X_c),X_1),A_3)) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,hAPP(X_c,X_b,G,X_1)),hAPP(fun(X_c,bool),X_b,F_1,A_3)))))) # label(fact_210_folding__image__simple_Oinsert) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 260 (all X_b all B_1 all A_2 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),A_3)) -> (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),B_1)) -> hAPP(fun(X_b,bool),nat,finite_card(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),B_1))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(fun(X_b,bool),nat,finite_card(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_1))),one_one(nat)))))) # label(fact_211_card__Diff__insert) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 261 (all X_b all X_1 all A_3 all F all F_1 (hBOOL(hAPP(fun(fun(X_b,bool),X_b),bool,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(fun(X_b,bool),X_b),bool),finite_folding_one(X_b),F),F_1)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3)) -> (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> (ti(fun(X_b,bool),A_3) != bot_bot(fun(X_b,bool)) -> hAPP(fun(X_b,bool),X_b,F_1,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_3)) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,X_1),hAPP(fun(X_b,bool),X_b,F_1,A_3))))))) # label(fact_212_folding__one_Oinsert) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 262 (all X_b all A_3 all F all F_1 (hBOOL(hAPP(fun(fun(X_b,bool),X_b),bool,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(fun(X_b,bool),X_b),bool),finite_folding_one(X_b),F),F_1)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3)) -> (ti(fun(X_b,bool),A_3) != bot_bot(fun(X_b,bool)) -> ((all X_2 all Y_1 hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,X_2),Y_1)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_2),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),Y_1),bot_bot(fun(X_b,bool))))))) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),hAPP(fun(X_b,bool),X_b,F_1,A_3)),A_3))))))) # label(fact_213_folding__one_Oclosed) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 263 (all X_c all X_b all A_3 all F all Z_2 all G all F_1 (hBOOL(hAPP(fun(fun(X_c,bool),X_b),bool,hAPP(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool),hAPP(X_b,fun(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool)),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool))),finite1357897459simple(X_b,X_c),F),Z_2),G),F_1)) -> (hBOOL(hAPP(fun(X_c,bool),bool,finite_finite(X_c),A_3)) -> ((all X_2 (hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),X_2),A_3)) -> hAPP(X_c,X_b,G,X_2) = ti(X_b,Z_2))) -> hAPP(fun(X_c,bool),X_b,F_1,A_3) = ti(X_b,Z_2))))) # label(fact_214_folding__image__simple_Oneutral) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 264 (all X_b all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),hAPP(fun(X_b,bool),nat,finite_card(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool))))))))) # label(fact_215_card_Oremove) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 265 (all X_b all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3)) -> hAPP(fun(X_b,bool),nat,finite_card(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_3)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),hAPP(fun(X_b,bool),nat,finite_card(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool)))))))) # label(fact_216_card_Oinsert__remove) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 266 (all X_b all B_1 all A_3 all F all F_1 (hBOOL(hAPP(fun(fun(X_b,bool),X_b),bool,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(fun(X_b,bool),X_b),bool),finite2073411215e_idem(X_b),F),F_1)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3)) -> (ti(fun(X_b,bool),B_1) != bot_bot(fun(X_b,bool)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),B_1),A_3)) -> hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,hAPP(fun(X_b,bool),X_b,F_1,B_1)),hAPP(fun(X_b,bool),X_b,F_1,A_3)) = hAPP(fun(X_b,bool),X_b,F_1,A_3)))))) # label(fact_217_folding__one__idem_Osubset__idem) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 267 (all X_b all X_1 all A_3 all F all F_1 (hBOOL(hAPP(fun(fun(X_b,bool),X_b),bool,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(fun(X_b,bool),X_b),bool),finite2073411215e_idem(X_b),F),F_1)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3)) -> (ti(fun(X_b,bool),A_3) != bot_bot(fun(X_b,bool)) -> hAPP(fun(X_b,bool),X_b,F_1,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_3)) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,X_1),hAPP(fun(X_b,bool),X_b,F_1,A_3)))))) # label(fact_218_folding__one__idem_Oinsert__idem) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 268 (all X_b all Pa all F_1 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),F_1)) -> (ti(fun(X_b,bool),F_1) != bot_bot(fun(X_b,bool)) -> ((all X_2 hBOOL(hAPP(fun(X_b,bool),bool,Pa,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_2),bot_bot(fun(X_b,bool)))))) -> ((all X_2 all F_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),F_3)) -> (ti(fun(X_b,bool),F_3) != bot_bot(fun(X_b,bool)) -> (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),F_3)) -> (hBOOL(hAPP(fun(X_b,bool),bool,Pa,F_3)) -> hBOOL(hAPP(fun(X_b,bool),bool,Pa,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_2),F_3)))))))) -> hBOOL(hAPP(fun(X_b,bool),bool,Pa,F_1))))))) # label(fact_219_finite__ne__induct) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 269 (all X_b all X_3 hAPP(fun(X_b,bool),X_b,the_elem(X_b),X_3) = hAPP(fun(X_b,bool),X_b,the(X_b),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,bool),hAPP(fun(fun(X_b,bool),bool),fun(fun(X_b,fun(X_b,bool)),fun(X_b,bool)),combb(fun(X_b,bool),bool,X_b),hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),fequal(fun(X_b,bool)),X_3)),hAPP(fun(X_b,bool),fun(X_b,fun(X_b,bool)),hAPP(fun(X_b,fun(fun(X_b,bool),fun(X_b,bool))),fun(fun(X_b,bool),fun(X_b,fun(X_b,bool))),combc(X_b,fun(X_b,bool),fun(X_b,bool)),insert(X_b)),bot_bot(fun(X_b,bool)))))) # label(fact_220_the__elem__def) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 270 (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_221_ab__semigroup__add__class_Oadd__ac_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 271 (all X_b (cancel_semigroup_add(X_b) -> (all A_2 all B_3 all C_1 (hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),A_2),B_3) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),A_2),C_1) <-> ti(X_b,B_3) = ti(X_b,C_1))))) # label(fact_222_add__left__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 272 (all X_b (cancel_semigroup_add(X_b) -> (all B_3 all A_2 all C_1 (hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),B_3),A_2) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),C_1),A_2) <-> ti(X_b,B_3) = ti(X_b,C_1))))) # label(fact_223_add__right__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 273 (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_224_add__left__imp__eq) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 274 (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_225_add__imp__eq) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 275 (all X_a (cancel_semigroup_add(X_a) -> (all B all A_1 all C (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B),A_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),A_1) -> ti(X_a,B) = ti(X_a,C))))) # label(fact_226_add__right__imp__eq) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 276 (all X_b all X_1 all F all F_1 (hBOOL(hAPP(fun(fun(X_b,bool),X_b),bool,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(fun(X_b,bool),X_b),bool),finite2073411215e_idem(X_b),F),F_1)) -> hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,X_1),X_1) = ti(X_b,X_1))) # label(fact_227_folding__one__idem_Oidem) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 277 (all M_1 all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),N) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),M_1)) # label(fact_228_nat__add__commute) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 278 (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_229_nat__add__left__commute) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 279 (all M_1 all N all K_1 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)),K_1) = 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),K_1))) # label(fact_230_nat__add__assoc) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 280 (all K all M all Na (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),Na) <-> M = Na)) # label(fact_231_nat__add__left__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 281 (all M all K all Na (hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),K) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Na),K) <-> M = Na)) # label(fact_232_nat__add__right__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 282 (all X_b (ordere236663937imp_le(X_b) -> (all A_2 all C_1 all B_3 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),A_2),C_1)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),B_3),C_1))) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),A_2),B_3)))))) # label(fact_233_add__le__cancel__right) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 283 (all X_b (ordere236663937imp_le(X_b) -> (all C_1 all A_2 all B_3 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),C_1),A_2)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),C_1),B_3))) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),A_2),B_3)))))) # label(fact_234_add__le__cancel__left) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 284 (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_235_add__right__mono) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 285 (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_236_add__left__mono) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 286 (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_237_add__mono) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 287 (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_238_add__le__imp__le__right) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 288 (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_239_add__le__imp__le__left) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 289 (all X_a (group_add(X_a) -> (all A_1 all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_1),B)),B) = ti(X_a,A_1)))) # label(fact_240_diff__add__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 290 (all X_a (group_add(X_a) -> (all A_1 all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)),B) = ti(X_a,A_1)))) # label(fact_241_add__diff__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 291 (all M_1 all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),hAPP(nat,nat,suc,N)) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),N))) # label(fact_242_add__Suc__right) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 292 (all M_1 all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,suc,M_1)),N) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),N))) # label(fact_243_add__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 293 (all M_1 all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,suc,M_1)),N) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),hAPP(nat,nat,suc,N))) # label(fact_244_add__Suc__shift) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 294 (all N all M_1 hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),N)))) # label(fact_245_le__add2) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 295 (all N all M_1 hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),M_1)))) # label(fact_246_le__add1) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 296 (all M all Na (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),Na)) <-> (exists K_2 Na = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),K_2)))) # label(fact_247_le__iff__add) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 297 (all K all M all Na (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),Na))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),Na)))) # label(fact_248_nat__add__left__cancel__le) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 298 (all M_1 all I_2 all J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_2),J)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_2),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J),M_1))))) # label(fact_249_trans__le__add1) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 299 (all M_1 all I_2 all J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_2),J)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_2),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),J))))) # label(fact_250_trans__le__add2) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 300 (all K_1 all I_2 all J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_2),J)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_2),K_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J),K_1))))) # label(fact_251_add__le__mono1) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 301 (all K_1 all L_1 all I_2 all J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_2),J)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_1),L_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_2),K_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J),L_1)))))) # label(fact_252_add__le__mono) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 302 (all M_1 all K_1 all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),K_1)),N)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_1),N)))) # label(fact_253_add__leD2) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 303 (all M_1 all K_1 all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),K_1)),N)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),N)))) # label(fact_254_add__leD1) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 304 (all M_1 all K_1 all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),K_1)),N)) -> -(hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),N)) -> -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_1),N))))) # label(fact_255_add__leE) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 305 (all M_1 all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),N)),N) = M_1) # label(fact_256_diff__add__inverse2) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 306 (all N 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),M_1)),N) = M_1) # label(fact_257_diff__add__inverse) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 307 (all I_2 all J all K_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I_2),J)),K_1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I_2),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J),K_1))) # label(fact_258_diff__diff__left) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 308 (all K_1 all M_1 all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_1),M_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_1),N)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),N)) # label(fact_259_diff__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 309 (all M_1 all K_1 all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),K_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),K_1)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),N)) # label(fact_260_diff__cancel2) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 310 (all I_2 all K_1 all J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_1),J)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I_2),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J),K_1)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_2),K_1)),J))) # label(fact_261_diff__diff__right) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 311 (all J_1 all K all I_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_1),K)),I_1)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),J_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_1),K))))) # label(fact_262_le__diff__conv) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 312 (all M_1 all K_1 all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_1),N)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),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),M_1)),K_1))))) # label(fact_263_le__add__diff) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 313 (all N all M_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N),M_1)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),N)) = M_1)) # label(fact_264_le__add__diff__inverse) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 314 (all I_2 all K_1 all J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_1),J)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_2),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J),K_1)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_2),J)),K_1))) # label(fact_265_add__diff__assoc) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 315 (all I_1 all K all J_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K),J_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_1),K))) <-> 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)),J_1))))) # label(fact_266_le__diff__conv2) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 316 (all N all M_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N),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)),N) = M_1)) # label(fact_267_le__add__diff__inverse2) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 317 (all K all I_1 all J_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_1),J_1)) -> (hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_1),I_1) = K <-> J_1 = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K),I_1)))) # label(fact_268_le__imp__diff__is__add) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 318 (all I_2 all K_1 all J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_1),J)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_2),J)),K_1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_2),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J),K_1)))) # label(fact_269_diff__add__assoc) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 319 (all I_2 all K_1 all J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_1),J)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J),K_1)),I_2) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J),I_2)),K_1))) # label(fact_270_add__diff__assoc2) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 320 (all I_2 all K_1 all J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_1),J)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J),I_2)),K_1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J),K_1)),I_2))) # label(fact_271_diff__add__assoc2) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 321 (all N hAPP(nat,nat,suc,N) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),N)) # label(fact_272_Suc__eq__plus1__left) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 322 (all N hAPP(nat,nat,suc,N) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),one_one(nat))) # label(fact_273_Suc__eq__plus1) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 323 (all X_b all X_1 all A_3 all F all F_1 (hBOOL(hAPP(fun(fun(X_b,bool),X_b),bool,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(fun(X_b,bool),X_b),bool),finite2073411215e_idem(X_b),F),F_1)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,X_1),hAPP(fun(X_b,bool),X_b,F_1,A_3)) = hAPP(fun(X_b,bool),X_b,F_1,A_3))))) # label(fact_274_folding__one__idem_Oin__idem) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 324 (all M_1 all K_1 all J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_1),J)) -> 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),K_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_1)),hAPP(nat,nat,suc,J)))) # label(fact_275_diff__Suc__diff__eq1) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 325 (all M_1 all K_1 all J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_1),J)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J),K_1))),M_1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,J)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_1),M_1)))) # label(fact_276_diff__Suc__diff__eq2) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 326 (all X_b all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3)) -> (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> hAPP(fun(X_b,bool),nat,finite_card(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_3)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3))))) # label(fact_277_card_Oinsert) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 327 (all X_b all N_2 all H all F all F_1 (hBOOL(hAPP(fun(fun(X_b,bool),X_b),bool,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(fun(X_b,bool),X_b),bool),finite2073411215e_idem(X_b),F),F_1)) -> ((all X_2 all Y_1 hAPP(X_b,X_b,H,hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,X_2),Y_1)) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,hAPP(X_b,X_b,H,X_2)),hAPP(X_b,X_b,H,Y_1))) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),N_2)) -> (ti(fun(X_b,bool),N_2) != bot_bot(fun(X_b,bool)) -> hAPP(X_b,X_b,H,hAPP(fun(X_b,bool),X_b,F_1,N_2)) = hAPP(fun(X_b,bool),X_b,F_1,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,X_b),fun(fun(X_b,bool),fun(X_b,bool)),image(X_b,X_b),H),N_2))))))) # label(fact_278_folding__one__idem_Ohom__commute) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 328 (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_279_termination__basic__simps_I4_J) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 329 (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_280_termination__basic__simps_I3_J) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 330 (all X_b all A_3 all B_3 ((hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),B_3),bot_bot(fun(X_b,bool))))) -> hAPP(fun(X_b,bool),X_b,hAPP(X_b,fun(fun(X_b,bool),X_b),partial_flat_lub(X_b),B_3),A_3) = ti(X_b,B_3)) & (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),B_3),bot_bot(fun(X_b,bool))))) -> hAPP(fun(X_b,bool),X_b,hAPP(X_b,fun(fun(X_b,bool),X_b),partial_flat_lub(X_b),B_3),A_3) = hAPP(fun(X_b,bool),X_b,the(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(fun(X_b,bool),bool)),fun(fun(X_b,bool),fun(X_b,bool)),combc(X_b,fun(X_b,bool),bool),member(X_b)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),B_3),bot_bot(fun(X_b,bool))))))))) # label(fact_281_flat__lub__def) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 331 (all X_b hBOOL(hAPP(fun(X_b,fun(fun(X_b,bool),fun(X_b,bool))),bool,finite_comp_fun_idem(X_b,fun(X_b,bool)),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(fun(X_b,bool),fun(X_b,bool))),hAPP(fun(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool))),fun(fun(X_b,fun(X_b,bool)),fun(X_b,fun(fun(X_b,bool),fun(X_b,bool)))),combb(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),X_b),hAPP(fun(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool))),fun(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool))),combc(fun(X_b,bool),fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)))),hAPP(fun(X_b,bool),fun(X_b,fun(X_b,bool)),hAPP(fun(X_b,fun(fun(X_b,bool),fun(X_b,bool))),fun(fun(X_b,bool),fun(X_b,fun(X_b,bool))),combc(X_b,fun(X_b,bool),fun(X_b,bool)),insert(X_b)),bot_bot(fun(X_b,bool))))))) # label(fact_282_comp__fun__idem__remove) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 332 (all X_b all X_1 all Y_2 all Pa ((hBOOL(Pa) -> ti(X_b,X_1) = hAPP(fun(X_b,bool),X_b,the(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),combs(X_b,bool,bool),hAPP(fun(X_b,bool),fun(X_b,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fconj),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(bool,bool),fun(fun(X_b,bool),fun(X_b,bool)),combb(bool,bool,X_b),hAPP(bool,fun(bool,bool),fimplies,Pa)),hAPP(X_b,fun(X_b,bool),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,bool)),combc(X_b,X_b,bool),fequal(X_b)),X_1)))),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(bool,bool),fun(fun(X_b,bool),fun(X_b,bool)),combb(bool,bool,X_b),hAPP(bool,fun(bool,bool),fimplies,hAPP(bool,bool,fNot,Pa))),hAPP(X_b,fun(X_b,bool),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,bool)),combc(X_b,X_b,bool),fequal(X_b)),Y_2))))) & (-hBOOL(Pa) -> ti(X_b,Y_2) = hAPP(fun(X_b,bool),X_b,the(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),combs(X_b,bool,bool),hAPP(fun(X_b,bool),fun(X_b,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fconj),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(bool,bool),fun(fun(X_b,bool),fun(X_b,bool)),combb(bool,bool,X_b),hAPP(bool,fun(bool,bool),fimplies,Pa)),hAPP(X_b,fun(X_b,bool),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,bool)),combc(X_b,X_b,bool),fequal(X_b)),X_1)))),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(bool,bool),fun(fun(X_b,bool),fun(X_b,bool)),combb(bool,bool,X_b),hAPP(bool,fun(bool,bool),fimplies,hAPP(bool,bool,fNot,Pa))),hAPP(X_b,fun(X_b,bool),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,bool)),combc(X_b,X_b,bool),fequal(X_b)),Y_2))))))) # label(fact_283_If__def) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 333 (all X_b all A_2 hAPP(fun(X_b,bool),X_b,the(X_b),hAPP(X_b,fun(X_b,bool),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,bool)),combc(X_b,X_b,bool),fequal(X_b)),A_2)) = ti(X_b,A_2)) # label(fact_284_the__eq__trivial) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 334 (all X_b all X_c all X_1 all Z_2 all F (hBOOL(hAPP(fun(X_b,fun(X_c,X_c)),bool,finite_comp_fun_idem(X_b,X_c),F)) -> hAPP(X_c,X_c,hAPP(X_b,fun(X_c,X_c),F,X_1),hAPP(X_c,X_c,hAPP(X_b,fun(X_c,X_c),F,X_1),Z_2)) = hAPP(X_c,X_c,hAPP(X_b,fun(X_c,X_c),F,X_1),Z_2))) # label(fact_285_comp__fun__idem_Ofun__left__idem) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 335 (all X_b hBOOL(hAPP(fun(X_b,fun(fun(X_b,bool),fun(X_b,bool))),bool,finite_comp_fun_idem(X_b,fun(X_b,bool)),insert(X_b)))) # label(fact_286_comp__fun__idem__insert) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 336 (all X_b all X_1 hAPP(fun(X_b,bool),X_b,the(X_b),hAPP(X_b,fun(X_b,bool),fequal(X_b),X_1)) = ti(X_b,X_1)) # label(fact_287_the__sym__eq__trivial) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 337 (all X_b all Pa all A_2 (hBOOL(hAPP(X_b,bool,Pa,A_2)) -> ((all X_2 (hBOOL(hAPP(X_b,bool,Pa,X_2)) -> ti(X_b,X_2) = ti(X_b,A_2))) -> hAPP(fun(X_b,bool),X_b,the(X_b),Pa) = ti(X_b,A_2)))) # label(fact_288_the__equality) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 338 (all X_b all Pa ((exists X_2 (hBOOL(hAPP(X_b,bool,Pa,X_2)) & (all Y_1 (hBOOL(hAPP(X_b,bool,Pa,Y_1)) -> ti(X_b,Y_1) = ti(X_b,X_2))))) -> hBOOL(hAPP(X_b,bool,Pa,hAPP(fun(X_b,bool),X_b,the(X_b),Pa))))) # label(fact_289_theI_H) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 339 (all X_b all A_2 all Pa ((exists X_2 (hBOOL(hAPP(X_b,bool,Pa,X_2)) & (all Y_1 (hBOOL(hAPP(X_b,bool,Pa,Y_1)) -> ti(X_b,Y_1) = ti(X_b,X_2))))) -> (hBOOL(hAPP(X_b,bool,Pa,A_2)) -> hAPP(fun(X_b,bool),X_b,the(X_b),Pa) = ti(X_b,A_2)))) # label(fact_290_the1__equality) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 340 (all X_b all Pa all A_2 (hBOOL(hAPP(X_b,bool,Pa,A_2)) -> ((all X_2 (hBOOL(hAPP(X_b,bool,Pa,X_2)) -> ti(X_b,X_2) = ti(X_b,A_2))) -> hBOOL(hAPP(X_b,bool,Pa,hAPP(fun(X_b,bool),X_b,the(X_b),Pa)))))) # label(fact_291_theI) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 341 (all X_b all Y_2 all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Y_2),A_3)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(X_b,bool),nat,finite_card(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool))))),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),Y_2),bot_bot(fun(X_b,bool)))))),hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3))))))) # label(fact_292_card__Diff2__less) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 342 (all X_b all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(X_b,bool),nat,finite_card(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool)))))),hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3)))))) # label(fact_293_card__Diff1__less) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 343 (all N hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),hAPP(nat,nat,suc,N)))) # label(fact_294_lessI) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 344 (all M_1 all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,M_1)),hAPP(nat,nat,suc,N))))) # label(fact_295_Suc__mono) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 345 (all K hBOOL(hAPP(fun(nat,bool),bool,finite_finite(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_296_finite__Collect__less__nat) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 346 (all N -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),N))) # label(fact_297_less__not__refl) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 347 (all M all Na (M != Na <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),Na)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Na),M)))) # label(fact_298_nat__neq__iff) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 348 (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_299_linorder__neqE__nat) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 349 (all N -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),N))) # label(fact_300_less__irrefl__nat) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 350 (all N all M_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),M_1)) -> M_1 != N)) # label(fact_301_less__not__refl2) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 351 (all S_1 all T_4 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),S_1),T_4)) -> S_1 != T_4)) # label(fact_302_less__not__refl3) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 352 (all Pa all M all Na ((hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),Na)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),Pa,Na),M))) -> ((M = Na -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),Pa,Na),M))) -> ((hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Na),M)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),Pa,Na),M))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),Pa,Na),M)))))) # label(fact_303_nat__less__cases) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 353 (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_304_order__less__irrefl) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 354 (all X_b (linorder(X_b) -> (all X_1 all Y_2 (ti(X_b,X_1) != ti(X_b,Y_2) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_1),Y_2)) | hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Y_2),X_1)))))) # label(fact_305_linorder__neq__iff) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 355 (all X_b (linorder(X_b) -> (all X_1 all Y_2 (-hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_1),Y_2)) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Y_2),X_1)) | ti(X_b,X_1) = ti(X_b,Y_2))))) # label(fact_306_not__less__iff__gr__or__eq) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 356 (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_307_linorder__less__linear) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 357 (all X_b (linorder(X_b) -> (all Y_2 all X_1 (-hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Y_2),X_1)) -> (-hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_1),Y_2)) <-> ti(X_b,X_1) = ti(X_b,Y_2)))))) # label(fact_308_linorder__antisym__conv3) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 358 (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_309_linorder__neqE) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 359 (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_310_less__imp__neq) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 360 (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_311_order__less__not__sym) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 361 (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_312_order__less__imp__not__less) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 362 (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_313_order__less__imp__not__eq) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 363 (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_314_order__less__imp__not__eq2) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 364 (all X_b (preorder(X_b) -> (all Pa all X_1 all Y_2 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_1),Y_2)) -> (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Y_2),X_1)) -> hBOOL(Pa)))))) # label(fact_315_order__less__imp__triv) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 365 (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_316_order__less__asym_H) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 366 (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_317_xt1_I9_J) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 367 (all X_a (ord(X_a) -> (all C all A_1 all B (A_1 = 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_318_ord__eq__less__trans) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 368 (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_319_xt1_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 369 (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)) -> (B = C -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),C))))))) # label(fact_320_ord__less__eq__trans) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 370 (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_321_xt1_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 371 (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_322_order__less__trans) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 372 (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_323_xt1_I10_J) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 373 (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_324_order__less__asym) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 374 (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_325_linorder__cases) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 375 (all X_b (linorder(X_b) -> (all X_1 all Y_2 (-hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_1),Y_2)) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),Y_2),X_1)))))) # label(fact_326_linorder__not__less) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 376 (all X_b (linorder(X_b) -> (all X_1 all Y_2 (-hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),X_1),Y_2)) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Y_2),X_1)))))) # label(fact_327_linorder__not__le) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 377 (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_328_linorder__le__less__linear) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 378 (all X_b (order(X_b) -> (all X_1 all Y_2 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_1),Y_2)) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),X_1),Y_2)) & ti(X_b,X_1) != ti(X_b,Y_2))))) # label(fact_329_order__less__le) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 379 (all X_b (preorder(X_b) -> (all X_1 all Y_2 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_1),Y_2)) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),X_1),Y_2)) & -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),Y_2),X_1)))))) # label(fact_330_less__le__not__le) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 380 (all X_b (order(X_b) -> (all X_1 all Y_2 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),X_1),Y_2)) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_1),Y_2)) | ti(X_b,X_1) = ti(X_b,Y_2))))) # label(fact_331_order__le__less) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 381 (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_332_leI) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 382 (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_333_not__leE) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 383 (all X_b (linorder(X_b) -> (all X_1 all Y_2 (-hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_1),Y_2)) -> (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),X_1),Y_2)) <-> ti(X_b,X_1) = ti(X_b,Y_2)))))) # label(fact_334_linorder__antisym__conv1) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 384 (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_335_order__neq__le__trans) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 385 (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_336_xt1_I12_J) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 386 (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_337_leD) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 387 (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_338_order__less__imp__le) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 388 (all X_b (linorder(X_b) -> (all X_1 all Y_2 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),X_1),Y_2)) -> (-hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_1),Y_2)) <-> ti(X_b,X_1) = ti(X_b,Y_2)))))) # label(fact_339_linorder__antisym__conv2) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 389 (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_340_order__le__imp__less__or__eq) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 390 (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_341_order__le__neq__trans) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 391 (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_342_xt1_I11_J) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 392 (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_343_order__less__le__trans) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 393 (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_344_xt1_I7_J) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 394 (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_345_order__le__less__trans) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 395 (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_346_xt1_I8_J) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 396 (all X_b (ordere236663937imp_le(X_b) -> (all A_2 all C_1 all B_3 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),A_2),C_1)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),B_3),C_1))) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),A_2),B_3)))))) # label(fact_347_add__less__cancel__right) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 397 (all X_b (ordere236663937imp_le(X_b) -> (all C_1 all A_2 all B_3 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),C_1),A_2)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),C_1),B_3))) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),A_2),B_3)))))) # label(fact_348_add__less__cancel__left) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 398 (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_349_add__strict__right__mono) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 399 (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_350_add__strict__left__mono) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 400 (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_351_add__strict__mono) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 401 (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_352_add__less__imp__less__right) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 402 (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_353_add__less__imp__less__left) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 403 (all X_a (bot(X_a) -> (all A_1 -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),bot_bot(X_a)))))) # label(fact_354_not__less__bot) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 404 (all X_b (bot(X_b) -> (all A_2 (ti(X_b,A_2) != bot_bot(X_b) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),bot_bot(X_b)),A_2)))))) # label(fact_355_bot__less) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 405 (all X_b (ordered_ab_group_add(X_b) -> (all A_2 all B_3 all C_1 all D_1 (hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),A_2),B_3) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),C_1),D_1) -> (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),A_2),B_3)) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),C_1),D_1))))))) # label(fact_356_diff__eq__diff__less) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 406 (all M all Na (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),Na)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Na),hAPP(nat,nat,suc,M))))) # label(fact_357_not__less__eq) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 407 (all M all Na (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),hAPP(nat,nat,suc,Na))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),Na)) | M = Na)) # label(fact_358_less__Suc__eq) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 408 (all M all Na (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,M)),hAPP(nat,nat,suc,Na))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),Na)))) # label(fact_359_Suc__less__eq) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 409 (all Na all M (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Na),M)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Na),hAPP(nat,nat,suc,M))) <-> Na = M))) # label(fact_360_not__less__less__Suc__eq) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 410 (all N all M_1 (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),M_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),hAPP(nat,nat,suc,M_1))) -> M_1 = N))) # label(fact_361_less__antisym) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 411 (all M_1 all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),hAPP(nat,nat,suc,N))))) # label(fact_362_less__SucI) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 412 (all M_1 all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N)) -> (hAPP(nat,nat,suc,M_1) != N -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,M_1)),N))))) # label(fact_363_Suc__lessI) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 413 (all K_1 all I_2 all J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),J)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),J),K_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,I_2)),K_1))))) # label(fact_364_less__trans__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 414 (all M_1 all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),hAPP(nat,nat,suc,N))) -> (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N)) -> M_1 = N))) # label(fact_365_less__SucE) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 415 (all M_1 all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,M_1)),N)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N)))) # label(fact_366_Suc__lessD) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 416 (all M_1 all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,M_1)),hAPP(nat,nat,suc,N))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N)))) # label(fact_367_Suc__less__SucD) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 417 (all I_2 all J -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_2),J)),I_2))) # label(fact_368_not__add__less1) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 418 (all J all I_2 -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J),I_2)),I_2))) # label(fact_369_not__add__less2) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 419 (all K all M all Na (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),Na))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),Na)))) # label(fact_370_nat__add__left__cancel__less) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 420 (all M_1 all I_2 all J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),J)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J),M_1))))) # label(fact_371_trans__less__add1) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 421 (all M_1 all I_2 all J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),J)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),J))))) # label(fact_372_trans__less__add2) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 422 (all K_1 all I_2 all J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),J)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_2),K_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J),K_1))))) # label(fact_373_add__less__mono1) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 423 (all K_1 all L_1 all I_2 all J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),J)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),K_1),L_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_2),K_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J),L_1)))))) # label(fact_374_add__less__mono) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 424 (all M_1 all N all K_1 all L_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),K_1),L_1)) -> (hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),L_1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_1),N) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N))))) # label(fact_375_less__add__eq__less) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 425 (all I_2 all J all K_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_2),J)),K_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),K_1)))) # label(fact_376_add__lessD1) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 426 (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_377_termination__basic__simps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 427 (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_378_termination__basic__simps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 428 (all M all Na (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),Na)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),Na)) & M != Na)) # label(fact_379_nat__less__le) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 429 (all M all Na (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),Na)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),Na)) | M = Na)) # label(fact_380_le__eq__less__or__eq) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 430 (all M_1 all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),N)))) # label(fact_381_less__imp__le__nat) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 431 (all M_1 all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),N)) -> (M_1 != N -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N))))) # label(fact_382_le__neq__implies__less) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 432 (all M_1 all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N)) | M_1 = N -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),N)))) # label(fact_383_less__or__eq__imp__le) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 433 (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_384_termination__basic__simps_I5_J) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 434 (all N all J all K_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),J),K_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J),N)),K_1)))) # label(fact_385_less__imp__diff__less) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 435 (all L_1 all M_1 all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),L_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),L_1),N)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),L_1),M_1)))))) # label(fact_386_diff__less__mono2) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 436 (all N_2 (hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),N_2)) <-> (exists M_2 all X_2 (hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X_2),N_2)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X_2),M_2)))))) # label(fact_387_finite__nat__set__iff__bounded) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 437 (all X_b all A_3 all F all Na (ti(fun(X_b,bool),A_3) = hAPP(fun(nat,bool),fun(X_b,bool),hAPP(fun(nat,X_b),fun(fun(nat,bool),fun(X_b,bool)),image(nat,X_b),F),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),Na))) -> hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3)))) # label(fact_388_nat__seg__image__imp__finite) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 438 (all Na 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)),Na))) = Na) # label(fact_389_card__Collect__less__nat) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 439 (all Pa all I_1 hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),combs(nat,bool,bool),hAPP(fun(nat,bool),fun(nat,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fconj),Pa)),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),I_1)))))) # label(fact_390_finite__M__bounded__by__nat) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 440 (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_391_add__less__le__mono) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 441 (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_392_add__le__less__mono) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 442 (all I_2 all M_1 hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_2),M_1))))) # label(fact_393_less__add__Suc1) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 443 (all I_2 all M_1 hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),I_2))))) # label(fact_394_less__add__Suc2) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 444 (all M all Na (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),Na)) <-> (exists K_2 Na = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),K_2))))) # label(fact_395_less__iff__Suc__add) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 445 (all Na all M (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Na),M)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,Na)),M)))) # label(fact_396_less__eq__Suc__le) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 446 (all M all Na (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),hAPP(nat,nat,suc,Na))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),Na)))) # label(fact_397_less__Suc__eq__le) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 447 (all M all Na (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,M)),Na)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),Na)))) # label(fact_398_Suc__le__eq) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 448 (all M_1 all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),N)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),hAPP(nat,nat,suc,N))))) # label(fact_399_le__imp__less__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.06 449 (all M_1 all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,M_1)),N)))) # label(fact_400_Suc__leI) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.07 450 (all M all Na (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),Na)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Na),hAPP(nat,nat,suc,M))) <-> Na = M))) # label(fact_401_le__less__Suc__eq) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.07 451 (all M_1 all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,M_1)),N)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N)))) # label(fact_402_Suc__le__lessD) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.07 452 (all M_1 all N hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),N)),hAPP(nat,nat,suc,M_1)))) # label(fact_403_diff__less__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.07 453 (all I_1 all J_1 all K (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_1),K))) <-> 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)),J_1)))) # label(fact_404_less__diff__conv) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.07 454 (all M_1 all N (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),N)) = M_1)) # label(fact_405_add__diff__inverse) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.07 455 (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_406_diff__less__mono) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.07 456 (all Na 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),Na)) -> (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),Na),K))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),Na)))))) # label(fact_407_less__diff__iff) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.07 457 (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_408_less__eq__Suc__le__raw) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.07 458 (all M all K all F ((all M_2 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_2),N_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,F,M_2)),hAPP(nat,nat,F,N_1))))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,F,M)),K)),hAPP(nat,nat,F,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),K)))))) # label(fact_409_mono__nat__linear__lb) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.07 459 (all Pa all I_1 all J_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_1),J_1)) -> (hBOOL(hAPP(nat,bool,Pa,J_1)) -> ((all I (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),J_1)) -> (hBOOL(hAPP(nat,bool,Pa,hAPP(nat,nat,suc,I))) -> hBOOL(hAPP(nat,bool,Pa,I))))) -> hBOOL(hAPP(nat,bool,Pa,I_1)))))) # label(fact_410_inc__induct) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.07 460 (all M_1 all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N)) -> (exists K_2 N = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),K_2))))) # label(fact_411_less__imp__Suc__add) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.07 461 (all X_b (order(X_b) -> (all Na all M all F ((all N_1 hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(nat,X_b,F,N_1)),hAPP(nat,X_b,F,hAPP(nat,nat,suc,N_1))))) -> (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(nat,X_b,F,Na)),hAPP(nat,X_b,F,M))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Na),M))))))) # label(fact_412_lift__Suc__mono__less__iff) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.07 462 (all X_b (order(X_b) -> (all Na all N_3 all F ((all N_1 hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(nat,X_b,F,N_1)),hAPP(nat,X_b,F,hAPP(nat,nat,suc,N_1))))) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Na),N_3)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(nat,X_b,F,Na)),hAPP(nat,X_b,F,N_3)))))))) # label(fact_413_lift__Suc__mono__less) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.07 463 (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_414_less__add__one) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.07 464 (all X_b all X_c (ord(X_c) -> (all F all G (hBOOL(hAPP(fun(X_b,X_c),bool,hAPP(fun(X_b,X_c),fun(fun(X_b,X_c),bool),ord_less(fun(X_b,X_c)),F),G)) <-> hBOOL(hAPP(fun(X_b,X_c),bool,hAPP(fun(X_b,X_c),fun(fun(X_b,X_c),bool),ord_less_eq(fun(X_b,X_c)),F),G)) & -hBOOL(hAPP(fun(X_b,X_c),bool,hAPP(fun(X_b,X_c),fun(fun(X_b,X_c),bool),ord_less_eq(fun(X_b,X_c)),G),F)))))) # label(fact_415_less__fun__def) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.07 465 (all X_b all A_3 -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less(fun(X_b,bool)),A_3),bot_bot(fun(X_b,bool))))) # label(fact_416_not__psubset__empty) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.07 466 (all X_b all C_2 all A_3 all 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)),A_3),B_1)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less(fun(X_b,bool)),B_1),C_2)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less(fun(X_b,bool)),A_3),C_2))))) # label(fact_417_subset__psubset__trans) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.07 467 (all X_b all C_2 all A_3 all B_1 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less(fun(X_b,bool)),A_3),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)),B_1),C_2)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less(fun(X_b,bool)),A_3),C_2))))) # label(fact_418_psubset__subset__trans) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.07 468 (all X_b all A_3 all B_1 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less(fun(X_b,bool)),A_3),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)),A_3),B_1)))) # label(fact_419_psubset__imp__subset) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.07 469 (all X_b all A_3 all 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)),A_3),B_1)) <-> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less(fun(X_b,bool)),A_3),B_1)) | ti(fun(X_b,bool),A_3) = ti(fun(X_b,bool),B_1))) # label(fact_420_subset__iff__psubset__eq) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.07 470 (all X_b all A_3 all B_1 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less(fun(X_b,bool)),A_3),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)),A_3),B_1)) & ti(fun(X_b,bool),A_3) != ti(fun(X_b,bool),B_1))) # label(fact_421_psubset__eq) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.07 471 (all X_b all A_3 all B_1 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),B_1)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less(fun(X_b,bool)),A_3),B_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3)),hAPP(fun(X_b,bool),nat,finite_card(X_b),B_1)))))) # label(fact_422_psubset__card__mono) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.07 472 (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_423_linorder__neqE__linordered__idom) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.07 473 (all X_b all A_3 all X_1 all B_1 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),B_1))) <-> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),B_1)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less(fun(X_b,bool)),A_3),B_1))) & (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),B_1)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool))))),B_1))) & (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),B_1)))))) # label(fact_424_psubset__insert__iff) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.07 474 (all X_b all A_3 all B_1 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),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)),A_3),B_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3)),hAPP(fun(X_b,bool),nat,finite_card(X_b),B_1))) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less(fun(X_b,bool)),A_3),B_1)))))) # label(fact_425_card__psubset) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.07 475 (all X_b all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3)) <-> (exists N_1 exists F_2 ti(fun(X_b,bool),A_3) = hAPP(fun(nat,bool),fun(X_b,bool),hAPP(fun(nat,X_b),fun(fun(nat,bool),fun(X_b,bool)),image(nat,X_b),F_2),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_1)))))) # label(fact_426_finite__conv__nat__seg__image) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.07 476 (all Na all N_2 ((all X_2 (hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X_2),N_2)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X_2),Na)))) -> hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),N_2)))) # label(fact_427_bounded__nat__set__is__finite) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.07 477 (all I_1 all J_1 all F ((all I all J_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),J_2)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,F,I)),hAPP(nat,nat,F,J_2))))) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_1),J_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,F,I_1)),hAPP(nat,nat,F,J_1)))))) # label(fact_428_less__mono__imp__le__mono) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.07 478 (all I_2 all K_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),K_1)) -> (K_1 != hAPP(nat,nat,suc,I_2) -> -(all J_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),J_2)) -> K_1 != hAPP(nat,nat,suc,J_2)))))) # label(fact_429_lessE) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.07 479 (all I_2 all K_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,I_2)),K_1)) -> -(all J_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),J_2)) -> K_1 != hAPP(nat,nat,suc,J_2))))) # label(fact_430_Suc__lessE) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.07 480 (all X_b all C_1 all A_3 all B_1 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less(fun(X_b,bool)),A_3),B_1)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C_1),A_3)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C_1),B_1))))) # label(fact_431_psubsetD) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.07 481 (all X_b all C_2 all A_3 all B_1 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less(fun(X_b,bool)),A_3),B_1)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less(fun(X_b,bool)),B_1),C_2)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less(fun(X_b,bool)),A_3),C_2))))) # label(fact_432_psubset__trans) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.07 482 (all X_b all A_3 all B_1 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less(fun(X_b,bool)),A_3),B_1)) -> (exists B_5 hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),B_5),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),B_1),A_3)))))) # label(fact_433_psubset__imp__ex__mem) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.07 483 (all X_c all X_b (order(X_b) & ord(X_c) -> (all C_1 all F all B_3 all A_2 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_c,X_b,F,B_3)),A_2)) -> (hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less(X_c),C_1),B_3)) -> ((all X_2 all Y_1 (hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less(X_c),Y_1),X_2)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_c,X_b,F,Y_1)),hAPP(X_c,X_b,F,X_2))))) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_c,X_b,F,C_1)),A_2)))))))) # label(fact_434_xt6) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.07 484 (all X_c all X_b (order(X_b) & order(X_c) -> (all C_1 all F all B_3 all A_2 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_c,X_b,F,B_3)),A_2)) -> (hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less_eq(X_c),C_1),B_3)) -> ((all X_2 all Y_1 (hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less_eq(X_c),Y_1),X_2)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_c,X_b,F,Y_1)),hAPP(X_c,X_b,F,X_2))))) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_c,X_b,F,C_1)),A_2)))))))) # label(fact_435_xt4) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.07 485 (all X_b all X_c (order(X_c) & order(X_b) -> (all C_1 all A_2 all F all B_3 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),A_2),hAPP(X_c,X_b,F,B_3))) -> (hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less(X_c),B_3),C_1)) -> ((all X_2 all Y_1 (hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less(X_c),X_2),Y_1)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_c,X_b,F,X_2)),hAPP(X_c,X_b,F,Y_1))))) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),A_2),hAPP(X_c,X_b,F,C_1))))))))) # label(fact_436_order__le__less__subst1) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.07 486 (all X_b all X_c (order(X_c) & order(X_b) -> (all C_1 all A_2 all F all B_3 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),A_2),hAPP(X_c,X_b,F,B_3))) -> (hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less_eq(X_c),B_3),C_1)) -> ((all X_2 all Y_1 (hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less_eq(X_c),X_2),Y_1)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_c,X_b,F,X_2)),hAPP(X_c,X_b,F,Y_1))))) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),A_2),hAPP(X_c,X_b,F,C_1))))))))) # label(fact_437_order__less__le__subst1) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.07 487 (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_438_dense__le) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.07 488 (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_3 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),W_3)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),W_3),Y)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),W_3),Z))))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),Z))))))) # label(fact_439_dense__le__bounded) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.07 489 (all X_c all X_b (order(X_b) & order(X_c) -> (all C_1 all F all B_3 all A_2 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),B_3),A_2)) -> (hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less_eq(X_c),C_1),hAPP(X_b,X_c,F,B_3))) -> ((all X_2 all Y_1 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Y_1),X_2)) -> hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less(X_c),hAPP(X_b,X_c,F,Y_1)),hAPP(X_b,X_c,F,X_2))))) -> hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less(X_c),C_1),hAPP(X_b,X_c,F,A_2))))))))) # label(fact_440_xt5) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.07 490 (all X_c all X_b (order(X_b) & order(X_c) -> (all C_1 all F all B_3 all A_2 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),B_3),A_2)) -> (hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less(X_c),C_1),hAPP(X_b,X_c,F,B_3))) -> ((all X_2 all Y_1 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),Y_1),X_2)) -> hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less_eq(X_c),hAPP(X_b,X_c,F,Y_1)),hAPP(X_b,X_c,F,X_2))))) -> hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less(X_c),C_1),hAPP(X_b,X_c,F,A_2))))))))) # label(fact_441_xt7) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.07 491 (all X_b all X_c (order(X_c) & order(X_b) -> (all F all C_1 all A_2 all B_3 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),A_2),B_3)) -> (hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less(X_c),hAPP(X_b,X_c,F,B_3)),C_1)) -> ((all X_2 all Y_1 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),X_2),Y_1)) -> hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less_eq(X_c),hAPP(X_b,X_c,F,X_2)),hAPP(X_b,X_c,F,Y_1))))) -> hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less(X_c),hAPP(X_b,X_c,F,A_2)),C_1)))))))) # label(fact_442_order__le__less__subst2) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.07 492 (all X_b all X_c (order(X_c) & order(X_b) -> (all F all C_1 all A_2 all B_3 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),A_2),B_3)) -> (hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less_eq(X_c),hAPP(X_b,X_c,F,B_3)),C_1)) -> ((all X_2 all Y_1 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_2),Y_1)) -> hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less(X_c),hAPP(X_b,X_c,F,X_2)),hAPP(X_b,X_c,F,Y_1))))) -> hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less(X_c),hAPP(X_b,X_c,F,A_2)),C_1)))))))) # label(fact_443_order__less__le__subst2) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.07 493 (all X_c all X_b all B_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3)) -> (hBOOL(hAPP(fun(X_c,bool),bool,finite_finite(X_c),B_1)) -> hAPP(fun(sum_sum(X_b,X_c),bool),nat,finite_card(sum_sum(X_b,X_c)),hAPP(fun(X_c,bool),fun(sum_sum(X_b,X_c),bool),hAPP(fun(X_b,bool),fun(fun(X_c,bool),fun(sum_sum(X_b,X_c),bool)),sum_Plus(X_b,X_c),A_3),B_1)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3)),hAPP(fun(X_c,bool),nat,finite_card(X_c),B_1))))) # label(fact_444_card__Plus) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.07 494 (all X_c all X_b all F all G all M_3 all N_2 (ti(fun(X_b,bool),M_3) = ti(fun(X_b,bool),N_2) -> ((all X_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),N_2)) -> hAPP(X_b,X_c,F,X_2) = hAPP(X_b,X_c,G,X_2))) -> hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),F),M_3) = hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),G),N_2)))) # label(fact_445_image__cong) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.07 495 (all X_b all X_c all A_3 all B_1 (hBOOL(hAPP(fun(sum_sum(X_b,X_c),bool),bool,finite_finite(sum_sum(X_b,X_c)),hAPP(fun(X_c,bool),fun(sum_sum(X_b,X_c),bool),hAPP(fun(X_b,bool),fun(fun(X_c,bool),fun(sum_sum(X_b,X_c),bool)),sum_Plus(X_b,X_c),A_3),B_1))) -> hBOOL(hAPP(fun(X_c,bool),bool,finite_finite(X_c),B_1)))) # label(fact_446_finite__PlusD_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.07 496 (all X_b all X_c all A_3 all B_1 (hBOOL(hAPP(fun(sum_sum(X_b,X_c),bool),bool,finite_finite(sum_sum(X_b,X_c)),hAPP(fun(X_c,bool),fun(sum_sum(X_b,X_c),bool),hAPP(fun(X_b,bool),fun(fun(X_c,bool),fun(sum_sum(X_b,X_c),bool)),sum_Plus(X_b,X_c),A_3),B_1))) -> hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3)))) # label(fact_447_finite__PlusD_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.07 497 (all X_c all X_b all B_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3)) -> (hBOOL(hAPP(fun(X_c,bool),bool,finite_finite(X_c),B_1)) -> hBOOL(hAPP(fun(sum_sum(X_b,X_c),bool),bool,finite_finite(sum_sum(X_b,X_c)),hAPP(fun(X_c,bool),fun(sum_sum(X_b,X_c),bool),hAPP(fun(X_b,bool),fun(fun(X_c,bool),fun(sum_sum(X_b,X_c),bool)),sum_Plus(X_b,X_c),A_3),B_1)))))) # label(fact_448_finite__Plus) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.07 498 (all X_b all X_c all A_3 all B_1 (hBOOL(hAPP(fun(sum_sum(X_b,X_c),bool),bool,finite_finite(sum_sum(X_b,X_c)),hAPP(fun(X_c,bool),fun(sum_sum(X_b,X_c),bool),hAPP(fun(X_b,bool),fun(fun(X_c,bool),fun(sum_sum(X_b,X_c),bool)),sum_Plus(X_b,X_c),A_3),B_1))) <-> hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3)) & hBOOL(hAPP(fun(X_c,bool),bool,finite_finite(X_c),B_1)))) # label(fact_449_finite__Plus__iff) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.07 499 (all X_c all X_b all A_3 all B_1 (hAPP(fun(X_c,bool),fun(sum_sum(X_b,X_c),bool),hAPP(fun(X_b,bool),fun(fun(X_c,bool),fun(sum_sum(X_b,X_c),bool)),sum_Plus(X_b,X_c),A_3),B_1) = bot_bot(fun(sum_sum(X_b,X_c),bool)) <-> ti(fun(X_b,bool),A_3) = bot_bot(fun(X_b,bool)) & ti(fun(X_c,bool),B_1) = bot_bot(fun(X_c,bool)))) # label(fact_450_Plus__eq__empty__conv) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.07 500 (all X_c all X_b all B_1 all A_3 ((hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3)) & hBOOL(hAPP(fun(X_c,bool),bool,finite_finite(X_c),B_1)) -> hAPP(fun(sum_sum(X_b,X_c),bool),nat,finite_card(sum_sum(X_b,X_c)),hAPP(fun(X_c,bool),fun(sum_sum(X_b,X_c),bool),hAPP(fun(X_b,bool),fun(fun(X_c,bool),fun(sum_sum(X_b,X_c),bool)),sum_Plus(X_b,X_c),A_3),B_1)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3)),hAPP(fun(X_c,bool),nat,finite_card(X_c),B_1))) & (-(hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3)) & hBOOL(hAPP(fun(X_c,bool),bool,finite_finite(X_c),B_1))) -> hAPP(fun(sum_sum(X_b,X_c),bool),nat,finite_card(sum_sum(X_b,X_c)),hAPP(fun(X_c,bool),fun(sum_sum(X_b,X_c),bool),hAPP(fun(X_b,bool),fun(fun(X_c,bool),fun(sum_sum(X_b,X_c),bool)),sum_Plus(X_b,X_c),A_3),B_1)) = zero_zero(nat)))) # label(fact_451_card__Plus__conv__if) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.07 501 (all X_b all R_1 all S (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(fun(X_b,bool),bool)),fun(fun(X_b,bool),fun(X_b,bool)),combc(X_b,fun(X_b,bool),bool),member(X_b)),R_1)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(fun(X_b,bool),bool)),fun(fun(X_b,bool),fun(X_b,bool)),combc(X_b,fun(X_b,bool),bool),member(X_b)),S))) <-> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),R_1),S)))) # label(fact_452_pred__subset__eq) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.07 502 (all X_b all Q_3 all Pa ((all X_2 (hBOOL(hAPP(X_b,bool,Pa,X_2)) -> hBOOL(hAPP(X_b,bool,Q_3,X_2)))) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),Pa)),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),Q_3))))) # label(fact_453_Collect__mono) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.07 503 (all N -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),zero_zero(nat)))) # label(fact_454_less__zeroE) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.07 504 (all N hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),N))) # label(fact_455_le0) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.07 505 (all N hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,suc,N)))) # label(fact_456_zero__less__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.07 506 (all Na (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Na),zero_zero(nat))) <-> Na = zero_zero(nat))) # label(fact_457_le__0__eq) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.07 507 (all N hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),N))) # label(fact_458_less__eq__nat_Osimps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.07 508 (all M_1 all N (hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),N) = zero_zero(nat) -> (hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),M_1) = zero_zero(nat) -> M_1 = N))) # label(fact_459_diffs0__imp__equal) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.07 509 (all M_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),M_1) = zero_zero(nat)) # label(fact_460_diff__self__eq__0) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.07 510 (all M_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),zero_zero(nat)) = M_1) # label(fact_461_minus__nat_Odiff__0) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.07 511 (all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),zero_zero(nat)),N) = zero_zero(nat)) # label(fact_462_diff__0__eq__0) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.07 512 (all X_a (zero_neq_one(X_a) -> one_one(X_a) != zero_zero(X_a))) # label(fact_463_one__neq__zero) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.07 513 (all X_a (zero_neq_one(X_a) -> zero_zero(X_a) != one_one(X_a))) # label(fact_464_zero__neq__one) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.07 514 (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_465_add_Ocomm__neutral) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.07 515 (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_466_add__0__right) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.07 516 (all X_b (linord219039673up_add(X_b) -> (all A_2 (zero_zero(X_b) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),A_2),A_2) <-> ti(X_b,A_2) = zero_zero(X_b))))) # label(fact_467_double__zero__sym) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.07 517 (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_468_add__0) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.07 518 (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_469_add__0__left) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.07 519 (all X_b (group_add(X_b) -> (all A_2 all B_3 (hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),A_2),B_3) = zero_zero(X_b) <-> ti(X_b,A_2) = ti(X_b,B_3))))) # label(fact_470_right__minus__eq) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.07 520 (all X_b (ab_group_add(X_b) -> (all A_2 all B_3 (ti(X_b,A_2) = ti(X_b,B_3) <-> hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),A_2),B_3) = zero_zero(X_b))))) # label(fact_471_eq__iff__diff__eq__0) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.07 521 (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_472_diff__self) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.07 522 (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_473_diff__0__right) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.07 523 (all X_b (zero(X_b) -> (all X_1 (zero_zero(X_b) = ti(X_b,X_1) <-> ti(X_b,X_1) = zero_zero(X_b))))) # label(fact_474_zero__reorient) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.07 524 (all M_1 all N (hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),N) = M_1 -> N = zero_zero(nat))) # label(fact_476_add__eq__self__zero) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.07 525 (all M all Na (hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),Na) = zero_zero(nat) <-> M = zero_zero(nat) & Na = zero_zero(nat))) # label(fact_477_add__is__0) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.07 526 (all M_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),zero_zero(nat)) = M_1) # label(fact_478_Nat_Oadd__0__right) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.07 527 (all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),zero_zero(nat)),N) = N) # label(fact_479_plus__nat_Oadd__0) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.07 528 (all N (N != zero_zero(nat) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)))) # label(fact_480_gr0I) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.07 529 (all M_1 all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N)) -> N != zero_zero(nat))) # label(fact_481_gr__implies__not0) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.07 530 (all N -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),zero_zero(nat)))) # label(fact_482_less__nat__zero__code) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.07 531 (all Na (Na != zero_zero(nat) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Na)))) # label(fact_483_neq0__conv) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.07 532 (all N -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),zero_zero(nat)))) # label(fact_484_not__less0) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.07 533 (all M_1 hAPP(nat,nat,suc,M_1) != zero_zero(nat)) # label(fact_485_Suc__neq__Zero) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.07 534 (all M_1 zero_zero(nat) != hAPP(nat,nat,suc,M_1)) # label(fact_486_Zero__neq__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.07 535 (all Nat_2 hAPP(nat,nat,suc,Nat_2) != zero_zero(nat)) # label(fact_487_nat_Osimps_I3_J) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.07 536 (all M_1 hAPP(nat,nat,suc,M_1) != zero_zero(nat)) # label(fact_488_Suc__not__Zero) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.07 537 (all Nat_1 zero_zero(nat) != hAPP(nat,nat,suc,Nat_1)) # label(fact_489_nat_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.07 538 (all M_1 zero_zero(nat) != hAPP(nat,nat,suc,M_1)) # label(fact_490_Zero__not__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.07 539 (all X_b all F1 all F2 hAPP(nat,X_b,hAPP(fun(nat,X_b),fun(nat,X_b),hAPP(X_b,fun(fun(nat,X_b),fun(nat,X_b)),nat_case(X_b),F1),F2),zero_zero(nat)) = ti(X_b,F1)) # label(fact_491_nat__case__0) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.07 540 (all X_b (linord219039673up_add(X_b) -> (all 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_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),A_2),A_2))) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),zero_zero(X_b)),A_2)))))) # label(fact_492_zero__le__double__add__iff__zero__le__single__add) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.07 541 (all X_b (linord219039673up_add(X_b) -> (all A_2 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),A_2),A_2)),zero_zero(X_b))) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),A_2),zero_zero(X_b))))))) # label(fact_493_double__add__le__zero__iff__single__add__le__zero) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.07 542 (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_494_add__nonneg__nonneg) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.07 543 (all X_b (ordere216010020id_add(X_b) -> (all Y_2 all X_1 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),zero_zero(X_b)),X_1)) -> (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),zero_zero(X_b)),Y_2)) -> (hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),X_1),Y_2) = zero_zero(X_b) <-> ti(X_b,X_1) = zero_zero(X_b) & ti(X_b,Y_2) = zero_zero(X_b))))))) # label(fact_495_add__nonneg__eq__0__iff) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.07 544 (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_496_add__increasing) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.07 545 (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_497_add__increasing2) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.07 546 (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_498_add__nonpos__nonpos) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.07 547 (all X_b (linord219039673up_add(X_b) -> (all A_2 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),zero_zero(X_b)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),A_2),A_2))) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),zero_zero(X_b)),A_2)))))) # label(fact_499_zero__less__double__add__iff__zero__less__single__add) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.07 548 (all X_b (linord219039673up_add(X_b) -> (all A_2 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),A_2),A_2)),zero_zero(X_b))) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),A_2),zero_zero(X_b))))))) # label(fact_500_double__add__less__zero__iff__single__add__less__zero) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.07 549 (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_501_add__pos__pos) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.07 550 (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_502_add__neg__neg) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.07 551 (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_503_pos__add__strict) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.07 552 (all X_b (ordered_ab_group_add(X_b) -> (all A_2 all B_3 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),A_2),B_3)) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),A_2),B_3)),zero_zero(X_b))))))) # label(fact_504_le__iff__diff__le__0) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.07 553 (all X_b (ordered_ab_group_add(X_b) -> (all A_2 all B_3 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),A_2),B_3)) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),A_2),B_3)),zero_zero(X_b))))))) # label(fact_505_less__iff__diff__less__0) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.07 554 (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_506_not__one__le__zero) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.07 555 (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_507_zero__le__one) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.07 556 (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_508_zero__less__one) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.07 557 (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_509_not__one__less__zero) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.07 558 (all Na (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Na)) <-> (exists M_2 Na = hAPP(nat,nat,suc,M_2)))) # label(fact_510_gr0__conv__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.07 559 (all Na (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Na),hAPP(nat,nat,suc,zero_zero(nat)))) <-> Na = zero_zero(nat))) # label(fact_511_less__Suc0) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.07 560 (all M all Na (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),hAPP(nat,nat,suc,Na))) <-> M = zero_zero(nat) | (exists J_2 (M = hAPP(nat,nat,suc,J_2) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),J_2),Na)))))) # label(fact_512_less__Suc__eq__0__disj) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.07 561 (all M all Na (hAPP(nat,nat,suc,zero_zero(nat)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),Na) <-> M = hAPP(nat,nat,suc,zero_zero(nat)) & Na = zero_zero(nat) | M = zero_zero(nat) & Na = hAPP(nat,nat,suc,zero_zero(nat)))) # label(fact_513_one__is__add) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.07 562 (all M all Na (hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),Na) = hAPP(nat,nat,suc,zero_zero(nat)) <-> M = hAPP(nat,nat,suc,zero_zero(nat)) & Na = zero_zero(nat) | M = zero_zero(nat) & Na = hAPP(nat,nat,suc,zero_zero(nat)))) # label(fact_514_add__is__1) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.07 563 (all M all Na (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),Na))) <-> 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)),Na)))) # label(fact_515_add__gr__0) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.07 564 (all X_b hAPP(fun(X_b,bool),nat,finite_card(X_b),bot_bot(fun(X_b,bool))) = zero_zero(nat)) # label(fact_516_card_Oempty) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.07 565 (all X_b all A_3 (-hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3)) -> hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3) = zero_zero(nat))) # label(fact_517_card__infinite) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.07 566 (all Na 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),Na),M))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),Na)))) # label(fact_518_zero__less__diff) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.07 567 (all M_1 all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),M_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)),M_1))))) # label(fact_519_diff__less) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.07 568 (all N all M_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),M_1)) = zero_zero(nat)) # label(fact_520_diff__add__0) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.07 569 (all M all Na (hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),Na) = zero_zero(nat) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),Na)))) # label(fact_521_diff__is__0__eq) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.07 570 (all M_1 all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),N)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),N) = zero_zero(nat))) # label(fact_522_diff__is__0__eq_H) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.07 571 (all M all Na hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),hAPP(nat,nat,suc,Na)) = 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),Na))) # label(fact_524_diff__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.07 572 (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_525_add__pos__nonneg) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.07 573 (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_526_add__nonneg__pos) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.07 574 (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_527_add__strict__increasing) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.07 575 (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_528_add__strict__increasing2) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.07 576 (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_529_add__neg__nonpos) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.07 577 (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_530_add__nonpos__neg) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.07 578 (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_531_zero__less__two) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.07 579 (all X_b all X_2 (hBOOL(hAPP(X_b,bool,bot_bot(fun(X_b,bool)),X_2)) <-> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),bot_bot(fun(X_b,bool)))))) # label(fact_532_bot__empty__eq) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.07 580 (all X_b all A_3 (hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3) = zero_zero(nat) <-> ti(fun(X_b,bool),A_3) = bot_bot(fun(X_b,bool)) | -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3)))) # label(fact_533_card__eq__0__iff) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.07 581 (all X_b all A_3 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3))) -> hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3)))) # label(fact_534_card__ge__0__finite) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.07 582 (all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),hAPP(nat,nat,suc,zero_zero(nat)))) = N)) # label(fact_535_Suc__pred) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.07 583 (all I_2 all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),hAPP(nat,nat,suc,I_2))),N)))) # label(fact_536_diff__Suc__less) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.07 584 (all X_b all Q_3 all Pa all X_1 (hBOOL(hAPP(X_b,bool,Pa,X_1)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),Pa),Q_3)) -> hBOOL(hAPP(X_b,bool,Q_3,X_1))))) # label(fact_537_rev__predicate1D) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.07 585 (all X_b all X_1 all Pa all Q_3 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),Pa),Q_3)) -> (hBOOL(hAPP(X_b,bool,Pa,X_1)) -> hBOOL(hAPP(X_b,bool,Q_3,X_1))))) # label(fact_538_predicate1D) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.07 586 (all Pa all A_2 all B_3 (hBOOL(hAPP(nat,bool,Pa,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),A_2),B_3))) <-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A_2),B_3)) -> hBOOL(hAPP(nat,bool,Pa,zero_zero(nat)))) & (all D_2 (A_2 = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B_3),D_2) -> hBOOL(hAPP(nat,bool,Pa,D_2)))))) # label(fact_539_nat__diff__split) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.07 587 (all Pa all A_2 all B_3 (hBOOL(hAPP(nat,bool,Pa,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),A_2),B_3))) <-> -(hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A_2),B_3)) & -hBOOL(hAPP(nat,bool,Pa,zero_zero(nat))) | (exists D_2 (A_2 = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B_3),D_2) & -hBOOL(hAPP(nat,bool,Pa,D_2))))))) # label(fact_540_nat__diff__split__asm) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.07 588 (all I_1 all M_3 (hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),zero_zero(nat)),M_3)) -> 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_3))),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),I_1))))) = 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_3))),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_1))))))) # label(fact_541_card__less__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.07 589 (all I_1 all M_3 (hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),zero_zero(nat)),M_3)) -> 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_3))),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_1))))) != zero_zero(nat))) # label(fact_542_card__less) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.07 590 (all I_1 all M_3 (-hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),zero_zero(nat)),M_3)) -> 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_3))),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),I_1)))) = 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_3))),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_1))))))) # label(fact_543_card__less__Suc2) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.07 591 (all X_b all A_3 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3))) <-> ti(fun(X_b,bool),A_3) != bot_bot(fun(X_b,bool)) & hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3)))) # label(fact_544_card__gt__0__iff) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.07 592 (all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),one_one(nat))) = N)) # label(fact_545_Suc__diff__1) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.07 593 (all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> N = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),one_one(nat))))) # label(fact_546_Suc__pred_H) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.07 594 (all N all M_1 ((M_1 = zero_zero(nat) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),N) = N) & (M_1 != zero_zero(nat) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),N) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),one_one(nat))),N))))) # label(fact_547_add__eq__if) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.07 595 (all Na all Pa (-hBOOL(hAPP(nat,bool,Pa,zero_zero(nat))) -> (hBOOL(hAPP(nat,bool,Pa,Na)) -> (exists K_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),K_2),Na)) & (all I (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I),K_2)) -> -hBOOL(hAPP(nat,bool,Pa,I)))) & hBOOL(hAPP(nat,bool,Pa,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_2),one_one(nat))))))))) # label(fact_548_ex__least__nat__less) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.07 596 (all X_b all A_3 all K (hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3) = hAPP(nat,nat,suc,K) <-> (exists B_5 exists B_4 (ti(fun(X_b,bool),A_3) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),B_5),B_4) & -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),B_5),B_4)) & hAPP(fun(X_b,bool),nat,finite_card(X_b),B_4) = K & (K = zero_zero(nat) -> ti(fun(X_b,bool),B_4) = bot_bot(fun(X_b,bool))))))) # label(fact_549_card__Suc__eq) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.07 597 (all X_b all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3)) -> (((exists X_2 hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_3))) -> one_one(nat) = zero_zero(nat)) -> hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3) = zero_zero(nat)))) # label(fact_550_card_Oneutral) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.07 598 (all Na all Pa (-hBOOL(hAPP(nat,bool,Pa,zero_zero(nat))) -> (hBOOL(hAPP(nat,bool,Pa,Na)) -> (exists K_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_2),Na)) & (all I (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),K_2)) -> -hBOOL(hAPP(nat,bool,Pa,I)))) & hBOOL(hAPP(nat,bool,Pa,K_2))))))) # label(fact_551_ex__least__nat__le) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.07 599 (all I_2 all J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),J)) -> (exists K_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K_2)) & hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_2),K_2) = J)))) # label(fact_552_less__imp__add__positive) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.07 600 (all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> (exists M_2 N = hAPP(nat,nat,suc,M_2)))) # label(fact_553_gr0__implies__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.07 601 (all X_b (linordered_idom(X_b) -> (all A_2 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),A_2),A_2)),zero_zero(X_b))) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),A_2),zero_zero(X_b))))))) # label(fact_554_even__less__0__iff) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.07 602 (all X_b (linord219039673up_add(X_b) -> (all A_2 (hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),A_2),A_2) = zero_zero(X_b) <-> ti(X_b,A_2) = zero_zero(X_b))))) # label(fact_555_double__eq__0__iff) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.07 603 (all X_b all A_3 all K (hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3) = hAPP(nat,nat,suc,K) -> (exists B_5 exists B_4 (ti(fun(X_b,bool),A_3) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),B_5),B_4) & -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),B_5),B_4)) & hAPP(fun(X_b,bool),nat,finite_card(X_b),B_4) = K & (K = zero_zero(nat) -> ti(fun(X_b,bool),B_4) = bot_bot(fun(X_b,bool))))))) # label(fact_556_card__eq__SucD) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.07 604 (all Y (Y != zero_zero(nat) -> -(all Nat Y != hAPP(nat,nat,suc,Nat)))) # label(fact_557_nat_Oexhaust) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.07 605 (all Pa all K (hBOOL(hAPP(nat,bool,Pa,K)) -> ((all N_1 (hBOOL(hAPP(nat,bool,Pa,hAPP(nat,nat,suc,N_1))) -> hBOOL(hAPP(nat,bool,Pa,N_1)))) -> hBOOL(hAPP(nat,bool,Pa,zero_zero(nat)))))) # label(fact_558_zero__induct) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.07 606 (all N (N != zero_zero(nat) -> (exists M_2 N = hAPP(nat,nat,suc,M_2)))) # label(fact_559_not0__implies__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.07 607 (all Na all Pa (hBOOL(hAPP(nat,bool,Pa,zero_zero(nat))) -> ((all N_1 (hBOOL(hAPP(nat,bool,Pa,N_1)) -> hBOOL(hAPP(nat,bool,Pa,hAPP(nat,nat,suc,N_1))))) -> hBOOL(hAPP(nat,bool,Pa,Na))))) # label(fact_560_nat__induct) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.07 608 (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_561_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.07 609 (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_562_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.07 610 (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_563_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.07 611 (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_564_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.07 612 (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_565_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.07 613 (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_566_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.07 614 (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_567_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.07 615 (all X_b (semiri456707255roduct(X_b) -> (all B_3 all A_2 (ti(X_b,B_3) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),B_3),A_2) <-> ti(X_b,A_2) = zero_zero(X_b))))) # label(fact_568_add__0__iff) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.07 616 (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_569_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.07 617 (all X_a (linordered_field(X_a) -> (all X all Y ((all E_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),E_2)) -> 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_2))))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y)))))) # label(fact_570_field__le__epsilon) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.07 618 (all X_b all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3)) -> hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3) = hAPP(fun(X_b,bool),nat,hAPP(nat,fun(fun(X_b,bool),nat),hAPP(fun(X_b,nat),fun(nat,fun(fun(X_b,bool),nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(X_b,nat),fun(nat,fun(fun(X_b,bool),nat))),finite_fold_image(nat,X_b),plus_plus(nat)),hAPP(nat,fun(X_b,nat),combk(nat,X_b),one_one(nat))),zero_zero(nat)),A_3))) # label(fact_571_card_Oeq__fold__g) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.07 619 (all X_b all A_3 ((hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3)) -> hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3) = hAPP(fun(X_b,bool),nat,hAPP(nat,fun(fun(X_b,bool),nat),hAPP(fun(X_b,nat),fun(nat,fun(fun(X_b,bool),nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(X_b,nat),fun(nat,fun(fun(X_b,bool),nat))),finite_fold_image(nat,X_b),plus_plus(nat)),hAPP(nat,fun(X_b,nat),combk(nat,X_b),one_one(nat))),zero_zero(nat)),A_3)) & (-hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3)) -> hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3) = zero_zero(nat)))) # label(fact_572_card__def) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.07 620 (all X_c all X_b all F all G all Z_2 hAPP(fun(X_c,bool),X_b,hAPP(X_b,fun(fun(X_c,bool),X_b),hAPP(fun(X_c,X_b),fun(X_b,fun(fun(X_c,bool),X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_c,X_b),fun(X_b,fun(fun(X_c,bool),X_b))),finite_fold_image(X_b,X_c),F),G),Z_2),bot_bot(fun(X_c,bool))) = ti(X_b,Z_2)) # label(fact_573_fold__image__empty) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.07 621 (all X_c all X_b all A_3 all F all Z_2 all G all F_1 (hBOOL(hAPP(fun(fun(X_c,bool),X_b),bool,hAPP(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool),hAPP(X_b,fun(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool)),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool))),finite1357897459simple(X_b,X_c),F),Z_2),G),F_1)) -> (hBOOL(hAPP(fun(X_c,bool),bool,finite_finite(X_c),A_3)) -> hAPP(fun(X_c,bool),X_b,F_1,A_3) = hAPP(fun(X_c,bool),X_b,hAPP(X_b,fun(fun(X_c,bool),X_b),hAPP(fun(X_c,X_b),fun(X_b,fun(fun(X_c,bool),X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_c,X_b),fun(X_b,fun(fun(X_c,bool),X_b))),finite_fold_image(X_b,X_c),F),G),Z_2),A_3)))) # label(fact_574_folding__image__simple_Oeq__fold__g) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.07 622 (all X_b (linordered_idom(X_b) -> (all A_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),ring_1_Ints(X_b))) -> (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),one_one(X_b)),A_2)),A_2)),zero_zero(X_b))) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),A_2),zero_zero(X_b)))))))) # label(fact_575_Ints__odd__less__0) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.07 623 (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_576_expand__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.07 624 (all X_a (linord626643107strict(X_a) -> (all V all U_1 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_1)) -> (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_1),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_1),X)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),V),Y))),A_1)))))))))) # label(fact_577_convex__bound__lt) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.07 625 (all X_b (ring_1(X_b) -> (all B_3 all A_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),ring_1_Ints(X_b))) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),B_3),ring_1_Ints(X_b))) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),A_2),B_3)),ring_1_Ints(X_b)))))))) # label(fact_578_Ints__diff) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.07 626 (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_579_mult__zero__left) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.07 627 (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_580_mult__zero__right) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.07 628 (all X_b (ring_n68954251visors(X_b) -> (all A_2 all B_3 (hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),A_2),B_3) = zero_zero(X_b) <-> ti(X_b,A_2) = zero_zero(X_b) | ti(X_b,B_3) = zero_zero(X_b))))) # label(fact_581_mult__eq__0__iff) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.07 629 (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_582_no__zero__divisors) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.07 630 (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_583_divisors__zero) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.07 631 (all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),zero_zero(nat)),N) = zero_zero(nat)) # label(fact_584_mult__0) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.07 632 (all M_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),zero_zero(nat)) = zero_zero(nat)) # label(fact_585_mult__0__right) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.07 633 (all M all Na (hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),Na) = zero_zero(nat) <-> M = zero_zero(nat) | Na = zero_zero(nat))) # label(fact_586_mult__is__0) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.07 634 (all K all M all Na (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),Na) <-> M = Na | K = zero_zero(nat))) # label(fact_587_mult__cancel1) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.07 635 (all M all K all Na (hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),K) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),Na),K) <-> M = Na | K = zero_zero(nat))) # label(fact_588_mult__cancel2) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.07 636 (all X_b (ab_sem1668676832m_mult(X_b) -> hBOOL(hAPP(fun(X_b,fun(X_b,X_b)),bool,finite_comp_fun_idem(X_b,X_b),times_times(X_b))))) # label(fact_589_comp__fun__idem) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.07 637 (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_590_comm__semiring__class_Odistrib) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.07 638 (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_591_combine__common__factor) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.07 639 (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_592_mult_Ocomm__neutral) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.07 640 (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_593_mult__1__right) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.07 641 (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_594_mult__1) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.08 642 (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_595_mult__1__left) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.08 643 (all K all M all Na (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)),Na) <-> M = Na)) # label(fact_596_Suc__mult__cancel1) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.08 644 (all M_1 all N all K_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)),K_1) = 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_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N),K_1))) # label(fact_597_add__mult__distrib) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.08 645 (all K_1 all M_1 all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),N)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_1),M_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_1),N))) # label(fact_598_add__mult__distrib2) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.08 646 (all K_1 all L_1 all I_2 all J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_2),J)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_1),L_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I_2),K_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J),L_1)))))) # label(fact_599_mult__le__mono) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.08 647 (all K_1 all I_2 all J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_2),J)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_1),I_2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_1),J))))) # label(fact_600_mult__le__mono2) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.08 648 (all K_1 all I_2 all J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_2),J)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I_2),K_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J),K_1))))) # label(fact_601_mult__le__mono1) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.08 649 (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_602_le__cube) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.08 650 (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_603_le__square) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.08 651 (all M_1 all N all K_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),N)),K_1) = 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_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N),K_1))) # label(fact_604_diff__mult__distrib) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.08 652 (all K_1 all M_1 all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),N)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_1),M_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_1),N))) # label(fact_605_diff__mult__distrib2) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.08 653 (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_606_times_Oidem) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.08 654 (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_607_mult__idem) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.08 655 (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_608_mult__left__idem) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.08 656 (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_609_ab__semigroup__mult__class_Omult__ac_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.08 657 (all M all Na (hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),Na) = one_one(nat) <-> M = one_one(nat) & Na = one_one(nat))) # label(fact_610_nat__mult__eq__1__iff) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.08 658 (all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N),one_one(nat)) = N) # label(fact_611_nat__mult__1__right) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.08 659 (all M all Na (one_one(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),Na) <-> M = one_one(nat) & Na = one_one(nat))) # label(fact_612_nat__1__eq__mult__iff) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.08 660 (all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),one_one(nat)),N) = N) # label(fact_613_nat__mult__1) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.08 661 (all X_b (number_ring(X_b) & linordered_idom(X_b) -> (all X_1 all Y_2 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(int,X_b,number_number_of(X_b),X_1)),hAPP(int,X_b,number_number_of(X_b),Y_2))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X_1),Y_2)))))) # label(fact_614_less__number__of) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.08 662 (all X_b (number_ring(X_b) -> (all W_1 hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),hAPP(int,X_b,number_number_of(X_b),W_1)),ring_1_Ints(X_b)))))) # label(fact_615_Ints__number__of) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.08 663 (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_616_number__of__mult) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.08 664 (all X_b (number(X_b) -> (all W_1 all X_1 (hAPP(int,X_b,number_number_of(X_b),W_1) = ti(X_b,X_1) <-> ti(X_b,X_1) = hAPP(int,X_b,number_number_of(X_b),W_1))))) # label(fact_617_number__of__reorient) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.08 665 (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_618_arith__simps_I32_J) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.08 666 (all X_b (number_ring(X_b) & ring_char_0(X_b) -> (all X_1 all Y_2 (hAPP(int,X_b,number_number_of(X_b),X_1) = hAPP(int,X_b,number_number_of(X_b),Y_2) <-> X_1 = Y_2)))) # label(fact_619_eq__number__of) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.08 667 (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_620_mult__number__of__left) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.08 668 (all X_b (ring_1(X_b) -> (all B_3 all A_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),ring_1_Ints(X_b))) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),B_3),ring_1_Ints(X_b))) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),A_2),B_3)),ring_1_Ints(X_b)))))))) # label(fact_621_Ints__mult) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.08 669 (all X_b (number_ring(X_b) & linordered_idom(X_b) -> (all X_1 all Y_2 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(int,X_b,number_number_of(X_b),X_1)),hAPP(int,X_b,number_number_of(X_b),Y_2))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X_1),Y_2)))))) # label(fact_622_le__number__of) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.08 670 (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_623_number__of__diff) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.08 671 (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_624_left__diff__distrib__number__of) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.08 672 (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_625_right__diff__distrib__number__of) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.08 673 (all X_b (ring_1(X_b) -> (all B_3 all A_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),ring_1_Ints(X_b))) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),B_3),ring_1_Ints(X_b))) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),A_2),B_3)),ring_1_Ints(X_b)))))))) # label(fact_626_Ints__add) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.08 674 (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_627_number__of__add) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.08 675 (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_628_add__number__of__eq) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.08 676 (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_629_right__distrib__number__of) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.08 677 (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_630_add__number__of__left) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.08 678 (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_631_left__distrib__number__of) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.08 679 (all X_b (ring_1(X_b) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),zero_zero(X_b)),ring_1_Ints(X_b))))) # label(fact_632_Ints__0) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.08 680 (all X_b (ring_1(X_b) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),one_one(X_b)),ring_1_Ints(X_b))))) # label(fact_633_Ints__1) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.08 681 (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_634_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.08 682 (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_635_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.08 683 (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_636_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.08 684 (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_637_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.08 685 (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_638_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.08 686 (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_639_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.08 687 (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_640_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.08 688 (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_641_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.08 689 (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_642_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.08 690 (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_643_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.08 691 (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_644_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.08 692 (all X_b (semiri456707255roduct(X_b) -> (all C_1 all D_1 all A_2 all B_3 (ti(X_b,A_2) != ti(X_b,B_3) & ti(X_b,C_1) != ti(X_b,D_1) <-> hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),A_2),C_1)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),B_3),D_1)) != hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),A_2),D_1)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),B_3),C_1)))))) # label(fact_645_crossproduct__noteq) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.08 693 (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_646_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.08 694 (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_647_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.08 695 (all X_b (semiri456707255roduct(X_b) -> (all W_1 all Y_2 all X_1 all Z_2 (hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),W_1),Y_2)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),X_1),Z_2)) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),W_1),Z_2)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),X_1),Y_2)) <-> ti(X_b,W_1) = ti(X_b,X_1) | ti(X_b,Y_2) = ti(X_b,Z_2))))) # label(fact_648_crossproduct__eq) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.08 696 (all X_a (comm_semiring_1(X_a) -> (all A_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),zero_zero(X_a)),A_1) = zero_zero(X_a)))) # label(fact_649_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.08 697 (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_650_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.08 698 (all X_b (number(X_b) & linorder(X_b) -> (all V_3 all W_1 (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),V_3)),hAPP(int,X_b,number_number_of(X_b),W_1))) <-> -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(int,X_b,number_number_of(X_b),W_1)),hAPP(int,X_b,number_number_of(X_b),V_3))))))) # label(fact_651_le__number__of__eq__not__less) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.08 699 (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_652_add__number__of__diff1) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.08 700 (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_653_split__mult__neg__le) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.08 701 (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_654_split__mult__pos__le) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.08 702 (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_655_mult__mono) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.08 703 (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_656_mult__mono_H) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.08 704 (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_657_mult__left__mono__neg) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.08 705 (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_658_mult__right__mono__neg) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.08 706 (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_659_comm__mult__left__mono) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.08 707 (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_660_mult__left__mono) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.08 708 (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_661_mult__right__mono) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.08 709 (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_662_mult__nonpos__nonpos) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.08 710 (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_663_mult__nonpos__nonneg) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.08 711 (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_664_mult__nonneg__nonpos2) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.08 712 (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_665_mult__nonneg__nonpos) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.08 713 (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_666_mult__nonneg__nonneg) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.08 714 (all X_b (linord581940658strict(X_b) -> (all A_2 all B_3 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),A_2),B_3)),zero_zero(X_b))) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),zero_zero(X_b)),A_2)) & hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),B_3),zero_zero(X_b))) | hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),A_2),zero_zero(X_b))) & hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),zero_zero(X_b)),B_3)))))) # label(fact_667_mult__le__0__iff) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.08 715 (all X_b (linord581940658strict(X_b) -> (all A_2 all B_3 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),zero_zero(X_b)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),A_2),B_3))) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),zero_zero(X_b)),A_2)) & hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),zero_zero(X_b)),B_3)) | hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),A_2),zero_zero(X_b))) & hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),B_3),zero_zero(X_b))))))) # label(fact_668_zero__le__mult__iff) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.08 716 (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_669_zero__le__square) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.08 717 (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_670_not__square__less__zero) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.08 718 (all X_b (linord581940658strict(X_b) -> (all A_2 all C_1 all B_3 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),A_2),C_1)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),B_3),C_1))) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),zero_zero(X_b)),C_1)) & hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),A_2),B_3)) | hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),C_1),zero_zero(X_b))) & hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),B_3),A_2)))))) # label(fact_671_mult__less__cancel__right__disj) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.08 719 (all X_b (linord581940658strict(X_b) -> (all C_1 all A_2 all B_3 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),C_1),A_2)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),C_1),B_3))) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),zero_zero(X_b)),C_1)) & hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),A_2),B_3)) | hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),C_1),zero_zero(X_b))) & hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),B_3),A_2)))))) # label(fact_672_mult__less__cancel__left__disj) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.08 720 (all X_b (linord581940658strict(X_b) -> (all A_2 all B_3 all C_1 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),zero_zero(X_b)),C_1)) -> (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),C_1),A_2)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),C_1),B_3))) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),A_2),B_3))))))) # label(fact_673_mult__less__cancel__left__pos) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.08 721 (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_674_mult__pos__pos) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.08 722 (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_675_mult__pos__neg) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.08 723 (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_676_mult__pos__neg2) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.08 724 (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_677_zero__less__mult__pos) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.08 725 (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_678_zero__less__mult__pos2) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.08 726 (all X_b (linord581940658strict(X_b) -> (all A_2 all B_3 all C_1 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),C_1),zero_zero(X_b))) -> (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),C_1),A_2)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),C_1),B_3))) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),B_3),A_2))))))) # label(fact_679_mult__less__cancel__left__neg) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.08 727 (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_680_mult__neg__pos) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.08 728 (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_681_mult__neg__neg) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.08 729 (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_682_mult__strict__right__mono) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.08 730 (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_683_mult__strict__left__mono) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.08 731 (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_684_comm__mult__strict__left__mono) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.08 732 (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_685_mult__strict__right__mono__neg) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.08 733 (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_686_mult__strict__left__mono__neg) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.08 734 (all X_a (semiri456707255roduct(X_a) -> (all C all D all A_1 all B all R_3 (ti(X_a,R_3) != 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_3),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_3),D))))))) # label(fact_687_add__scale__eq__noteq) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.08 735 (all X_b (linord581940658strict(X_b) -> (all X_1 all Y_2 (hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),X_1),X_1)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),Y_2),Y_2)) = zero_zero(X_b) <-> ti(X_b,X_1) = zero_zero(X_b) & ti(X_b,Y_2) = zero_zero(X_b))))) # label(fact_688_sum__squares__eq__zero__iff) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.08 736 (all X_a (linordered_semidom(X_a) -> (all N 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)) -> 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)))))))) # label(fact_689_less__1__mult) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.08 737 (all X_b (ring(X_b) -> (all A_2 all E all C_1 all B_3 all D_1 (hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),A_2),E)),C_1) = 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),B_3),E)),D_1) <-> ti(X_b,C_1) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),B_3),A_2)),E)),D_1))))) # label(fact_690_eq__add__iff2) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.08 738 (all X_b (ring(X_b) -> (all A_2 all E all C_1 all B_3 all D_1 (hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),A_2),E)),C_1) = 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),B_3),E)),D_1) <-> hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),A_2),B_3)),E)),C_1) = ti(X_b,D_1))))) # label(fact_691_eq__add__iff1) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.08 739 (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_692_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.08 740 (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_693_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.08 741 (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_694_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.08 742 (all M all Na (hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),Na) = hAPP(nat,nat,suc,zero_zero(nat)) <-> M = hAPP(nat,nat,suc,zero_zero(nat)) & Na = hAPP(nat,nat,suc,zero_zero(nat)))) # label(fact_695_mult__eq__1__iff) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.08 743 (all K_1 all I_2 all J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),J)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_1),I_2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_1),J)))))) # label(fact_696_mult__less__mono2) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.08 744 (all K_1 all I_2 all J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),J)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I_2),K_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J),K_1)))))) # label(fact_697_mult__less__mono1) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.08 745 (all M all K all Na (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),Na),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),Na)))) # label(fact_698_mult__less__cancel2) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.08 746 (all K all M all Na (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),Na))) <-> 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),Na)))) # label(fact_699_mult__less__cancel1) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.08 747 (all M all Na (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),Na))) <-> 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)),Na)))) # label(fact_700_nat__0__less__mult__iff) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.08 748 (all K all M all Na (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)),Na))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),Na)))) # label(fact_701_Suc__mult__less__cancel1) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.08 749 (all M_1 all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),hAPP(nat,nat,suc,N)) = 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))) # label(fact_702_mult__Suc__right) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.08 750 (all M_1 all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,M_1)),N) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),N))) # label(fact_703_mult__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.08 751 (all K all M all Na (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)),Na))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),Na)))) # label(fact_704_Suc__mult__le__cancel1) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.08 752 (all M_1 all N (M_1 = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),N) -> N = one_one(nat) | M_1 = zero_zero(nat))) # label(fact_705_mult__eq__self__implies__10) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.08 753 (all X_b (ring_char_0(X_b) -> (all A_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),ring_1_Ints(X_b))) -> (hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),A_2),A_2) = zero_zero(X_b) <-> ti(X_b,A_2) = zero_zero(X_b)))))) # label(fact_706_Ints__double__eq__0__iff) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.08 754 (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_707_mult__left__le__imp__le) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.08 755 (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_708_mult__right__le__imp__le) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.08 756 (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_709_mult__less__imp__less__left) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.08 757 (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_710_mult__left__less__imp__less) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.08 758 (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_711_mult__less__imp__less__right) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.08 759 (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_712_mult__right__less__imp__less) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.08 760 (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_713_mult__le__less__imp__less) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.08 761 (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_714_mult__less__le__imp__less) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.08 762 (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_715_mult__strict__mono_H) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.08 763 (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_716_mult__strict__mono) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.08 764 (all X_b (linord581940658strict(X_b) -> (all A_2 all B_3 all C_1 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),C_1),zero_zero(X_b))) -> (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),C_1),A_2)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),C_1),B_3))) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),B_3),A_2))))))) # label(fact_717_mult__le__cancel__left__neg) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.08 765 (all X_b (linord581940658strict(X_b) -> (all A_2 all B_3 all C_1 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),zero_zero(X_b)),C_1)) -> (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),C_1),A_2)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),C_1),B_3))) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),A_2),B_3))))))) # label(fact_718_mult__le__cancel__left__pos) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.08 766 (all X_b (linord581940658strict(X_b) -> (all X_1 all Y_2 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_b,X_b,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),X_1),X_1)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),Y_2),Y_2))),zero_zero(X_b))) <-> ti(X_b,X_1) = zero_zero(X_b) & ti(X_b,Y_2) = zero_zero(X_b))))) # label(fact_719_sum__squares__le__zero__iff) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.08 767 (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_720_sum__squares__ge__zero) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.08 768 (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_721_not__sum__squares__lt__zero) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.08 769 (all X_b (linord581940658strict(X_b) -> (all X_1 all Y_2 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),zero_zero(X_b)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),X_1),X_1)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),Y_2),Y_2)))) <-> ti(X_b,X_1) != zero_zero(X_b) | ti(X_b,Y_2) != zero_zero(X_b))))) # label(fact_722_sum__squares__gt__zero__iff) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.08 770 (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_723_mult__left__le__one__le) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.08 771 (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_724_mult__right__le__one__le) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.08 772 (all X_b (ordered_ring(X_b) -> (all A_2 all E all C_1 all B_3 all D_1 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),A_2),E)),C_1)),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),B_3),E)),D_1))) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),C_1),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),B_3),A_2)),E)),D_1))))))) # label(fact_725_le__add__iff2) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.08 773 (all X_b (ordered_ring(X_b) -> (all A_2 all E all C_1 all B_3 all D_1 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),A_2),E)),C_1)),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),B_3),E)),D_1))) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),A_2),B_3)),E)),C_1)),D_1)))))) # label(fact_726_le__add__iff1) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.08 774 (all X_b (ordered_ring(X_b) -> (all A_2 all E all C_1 all B_3 all D_1 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),A_2),E)),C_1)),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),B_3),E)),D_1))) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),C_1),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),B_3),A_2)),E)),D_1))))))) # label(fact_727_less__add__iff2) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.08 775 (all X_b (ordered_ring(X_b) -> (all A_2 all E all C_1 all B_3 all D_1 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),A_2),E)),C_1)),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),B_3),E)),D_1))) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),A_2),B_3)),E)),C_1)),D_1)))))) # label(fact_728_less__add__iff1) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.08 776 (all M_1 all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),N)) -> (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),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),N)))))) # label(fact_729_n__less__m__mult__n) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.08 777 (all M_1 all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),N)) -> (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),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N),M_1)))))) # label(fact_730_n__less__n__mult__m) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.08 778 (all M_1 all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),N)) -> (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)))))) # label(fact_731_one__less__mult) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.08 779 (all M all Na (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),Na))) <-> 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))),Na)))) # label(fact_732_one__le__mult__iff) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.08 780 (all K all M all Na (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),Na))) <-> (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),Na))))) # label(fact_733_mult__le__cancel1) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.08 781 (all M all K all Na (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),Na),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),Na))))) # label(fact_734_mult__le__cancel2) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.08 782 (all X_b all X_c (ab_semigroup_mult(X_c) -> (all G all Z_2 all A_2 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3)) -> (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),A_3)) -> hAPP(fun(X_b,bool),X_c,hAPP(X_c,fun(fun(X_b,bool),X_c),hAPP(fun(X_b,X_c),fun(X_c,fun(fun(X_b,bool),X_c)),hAPP(fun(X_c,fun(X_c,X_c)),fun(fun(X_b,X_c),fun(X_c,fun(fun(X_b,bool),X_c))),finite_fold_image(X_c,X_b),times_times(X_c)),G),Z_2),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),A_3)) = hAPP(X_c,X_c,hAPP(X_c,fun(X_c,X_c),times_times(X_c),hAPP(X_b,X_c,G,A_2)),hAPP(fun(X_b,bool),X_c,hAPP(X_c,fun(fun(X_b,bool),X_c),hAPP(fun(X_b,X_c),fun(X_c,fun(fun(X_b,bool),X_c)),hAPP(fun(X_c,fun(X_c,X_c)),fun(fun(X_b,X_c),fun(X_c,fun(fun(X_b,bool),X_c))),finite_fold_image(X_c,X_b),times_times(X_c)),G),Z_2),A_3))))))) # label(fact_735_fold__image__insert) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.08 783 (all X_b all X_c (comm_monoid_mult(X_c) -> (all G all H all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3)) -> hAPP(fun(X_b,bool),X_c,hAPP(X_c,fun(fun(X_b,bool),X_c),hAPP(fun(X_b,X_c),fun(X_c,fun(fun(X_b,bool),X_c)),hAPP(fun(X_c,fun(X_c,X_c)),fun(fun(X_b,X_c),fun(X_c,fun(fun(X_b,bool),X_c))),finite_fold_image(X_c,X_b),times_times(X_c)),hAPP(fun(X_b,X_c),fun(X_b,X_c),hAPP(fun(X_b,fun(X_c,X_c)),fun(fun(X_b,X_c),fun(X_b,X_c)),combs(X_b,X_c,X_c),hAPP(fun(X_b,X_c),fun(X_b,fun(X_c,X_c)),hAPP(fun(X_c,fun(X_c,X_c)),fun(fun(X_b,X_c),fun(X_b,fun(X_c,X_c))),combb(X_c,fun(X_c,X_c),X_b),times_times(X_c)),G)),H)),one_one(X_c)),A_3) = hAPP(X_c,X_c,hAPP(X_c,fun(X_c,X_c),times_times(X_c),hAPP(fun(X_b,bool),X_c,hAPP(X_c,fun(fun(X_b,bool),X_c),hAPP(fun(X_b,X_c),fun(X_c,fun(fun(X_b,bool),X_c)),hAPP(fun(X_c,fun(X_c,X_c)),fun(fun(X_b,X_c),fun(X_c,fun(fun(X_b,bool),X_c))),finite_fold_image(X_c,X_b),times_times(X_c)),G),one_one(X_c)),A_3)),hAPP(fun(X_b,bool),X_c,hAPP(X_c,fun(fun(X_b,bool),X_c),hAPP(fun(X_b,X_c),fun(X_c,fun(fun(X_b,bool),X_c)),hAPP(fun(X_c,fun(X_c,X_c)),fun(fun(X_b,X_c),fun(X_c,fun(fun(X_b,bool),X_c))),finite_fold_image(X_c,X_b),times_times(X_c)),H),one_one(X_c)),A_3)))))) # label(fact_736_fold__image__distrib) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.08 784 (all X_a (linord1278240602ring_1(X_a) -> (all V all U_1 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_1)) -> (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_1),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_1),X)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),V),Y))),A_1)))))))))) # label(fact_737_convex__bound__le) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.08 785 (all N all M_1 ((M_1 = zero_zero(nat) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),N) = zero_zero(nat)) & (M_1 != zero_zero(nat) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),N) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),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))))) # label(fact_738_mult__eq__if) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.08 786 (all X_b (ring_char_0(X_b) -> (all A_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),ring_1_Ints(X_b))) -> hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),one_one(X_b)),A_2)),A_2) != zero_zero(X_b))))) # label(fact_739_Ints__odd__nonzero) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.08 787 (all X_a (linord1117847801e_zero(X_a) -> (all X all Y ((all Z_3 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),Z_3)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z_3),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_3),X)),Y))))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y)))))) # label(fact_740_field__le__mult__one__interval) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.08 788 (all X_b all X_c (comm_monoid_mult(X_c) -> (all F all S (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(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)) -> hAPP(X_b,X_c,F,X_2) = one_one(X_c))) -> hAPP(fun(X_b,bool),X_c,hAPP(X_c,fun(fun(X_b,bool),X_c),hAPP(fun(X_b,X_c),fun(X_c,fun(fun(X_b,bool),X_c)),hAPP(fun(X_c,fun(X_c,X_c)),fun(fun(X_b,X_c),fun(X_c,fun(fun(X_b,bool),X_c))),finite_fold_image(X_c,X_b),times_times(X_c)),F),one_one(X_c)),S) = one_one(X_c)))))) # label(fact_741_fold__image__1) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.08 789 (all U all M all Na all I_1 all J_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_1),J_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I_1),U)),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J_1),U)),Na))) <-> 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_1),I_1)),U)),Na)))))) # label(fact_742_nat__less__add__iff2) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.08 790 (all M_1 all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),N) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N),M_1)) # label(fact_743_nat__mult__commute) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.08 791 (all M_1 all N all K_1 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)),K_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),N),K_1))) # label(fact_744_nat__mult__assoc) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.08 792 (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_745_less__number__of__int__code) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.08 793 (all Z hAPP(int,int,hAPP(int,fun(int,int),times_times(int),one_one(int)),Z) = Z) # label(fact_746_zmult__1) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.08 794 (all Z hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Z),one_one(int)) = Z) # label(fact_747_zmult__1__right) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.08 795 (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_748_zmult__commute) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.08 796 (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_749_times__numeral__code_I5_J) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.08 797 (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_750_zmult__assoc) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.08 798 (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_751_less__eq__number__of__int__code) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.08 799 (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_752_zdiff__zmult__distrib) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.08 800 (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_753_zdiff__zmult__distrib2) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.08 801 (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_754_zadd__zmult__distrib2) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.08 802 (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_755_plus__numeral__code_I9_J) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.08 803 (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_756_zadd__zmult__distrib) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.08 804 (all K_1 all I_2 all J (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),I_2),J)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),K_1)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K_1),I_2)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K_1),J)))))) # label(fact_757_zmult__zless__mono2) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.08 805 (all Na 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),Na) = one_one(int) <-> M = one_one(int) & Na = one_one(int)))) # label(fact_758_pos__zmult__eq__1__iff) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.08 806 (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_759_odd__nonzero) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.08 807 (all Z hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Z),zero_zero(int)) = Z) # label(fact_760_zadd__0__right) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.08 808 (all Z hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),zero_zero(int)),Z) = Z) # label(fact_761_zadd__0) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.08 809 (all Z_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),Z_2)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),Z_2)))) # label(fact_763_int__one__le__iff__zero__less) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.08 810 (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_764_less__bin__lemma) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.08 811 (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_765_le__imp__0__less) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.08 812 (all Z_2 (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_2)),Z_2)),zero_zero(int))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Z_2),zero_zero(int))))) # label(fact_766_odd__less__0) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.08 813 (all K_1 all I_2 all J (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),I_2),J)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),K_1),I_2)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),K_1),J))))) # label(fact_767_zadd__left__mono) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.08 814 (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_768_zadd__assoc) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.08 815 (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_769_zadd__left__commute) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.08 816 (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_770_zadd__commute) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.08 817 (all W hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),W),W))) # label(fact_771_zle__refl) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.08 818 (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_772_zle__linear) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.09 819 (all K_1 all I_2 all J (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),I_2),J)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),J),K_1)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),I_2),K_1))))) # label(fact_773_zle__trans) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.09 820 (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_774_zle__antisym) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.09 821 (all W_1 all Z_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),W_1),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),Z_2),one_one(int)))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_1),Z_2)))) # label(fact_775_zle__diff1__eq) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.09 822 (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_776_zless__linear) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.09 823 (all Z_2 all W_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Z_2),W_1)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Z_2),W_1)) & Z_2 != W_1)) # label(fact_777_zless__le) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.09 824 (all K_1 all I_2 all J (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),I_2),J)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),I_2),K_1)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),J),K_1))))) # label(fact_778_zadd__strict__right__mono) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.09 825 (all Z_4 all Z all W_2 all W (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_2),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_2),Z_4)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),W),Z)))))) # label(fact_779_zadd__zless__mono) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.09 826 (all W_1 all Z_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_1),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Z_2),one_one(int)))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),W_1),Z_2)))) # label(fact_780_zle__add1__eq__le) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.09 827 (all W_1 all Z_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),W_1),one_one(int))),Z_2)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_1),Z_2)))) # label(fact_781_add1__zle__eq) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.09 828 (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_782_zless__imp__add1__zle) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.09 829 (all W_1 all Z_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_1),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Z_2),one_one(int)))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_1),Z_2)) | W_1 = Z_2)) # label(fact_783_zless__add1__eq) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.09 830 (all K all M all Na (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),Na) <-> K = zero_zero(nat) | M = Na)) # label(fact_784_nat__mult__eq__cancel__disj) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.09 831 (all I_2 all U_1 all J all K_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I_2),U_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J),U_1)),K_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),plus_plus(nat),I_2),J)),U_1)),K_1)) # label(fact_785_left__add__mult__distrib) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.09 832 (all M all Na 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),Na) <-> M = Na))) # label(fact_786_nat__mult__eq__cancel1) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.09 833 (all M all Na 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),Na))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),Na))))) # label(fact_787_nat__mult__less__cancel1) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.09 834 (all M all Na 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),Na))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),Na))))) # label(fact_788_nat__mult__le__cancel1) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.09 835 (all U all M all Na all J_1 all I_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),J_1),I_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I_1),U)),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J_1),U)),Na))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I_1),J_1)),U)),M)),Na))))) # label(fact_789_nat__le__add__iff1) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.09 836 (all U_1 all M_1 all N all J all I_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),J),I_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_2),U_1)),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),U_1)),N)) = 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_2),J)),U_1)),M_1)),N))) # label(fact_790_nat__diff__add__eq1) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.09 837 (all U all M all Na all J_1 all I_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),J_1),I_1)) -> (hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I_1),U)),M) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J_1),U)),Na) <-> hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I_1),J_1)),U)),M) = Na))) # label(fact_791_nat__eq__add__iff1) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.09 838 (all U all M all Na all I_1 all J_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_1),J_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I_1),U)),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J_1),U)),Na))) <-> 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_1),I_1)),U)),Na)))))) # label(fact_792_nat__le__add__iff2) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.09 839 (all U_1 all M_1 all N all I_2 all J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_2),J)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I_2),U_1)),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),U_1)),N)) = 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),I_2)),U_1)),N)))) # label(fact_793_nat__diff__add__eq2) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.09 840 (all U all M all Na all I_1 all J_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_1),J_1)) -> (hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I_1),U)),M) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J_1),U)),Na) <-> 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_1),I_1)),U)),Na)))) # label(fact_794_nat__eq__add__iff2) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.09 841 (all U all M all Na all J_1 all I_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),J_1),I_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I_1),U)),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J_1),U)),Na))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I_1),J_1)),U)),M)),Na))))) # label(fact_795_nat__less__add__iff1) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.09 842 (all B all Q_2 all R_3 all B_2 all Q_1 all R_2 (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_3) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B_2),Q_1)),R_2) -> (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_2),Q_1)),R_2)),zero_zero(int))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),R_3),B)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),R_2)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B_2)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B_2),B)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Q_1),Q_2))))))))) # label(fact_796_zdiv__mono2__neg__lemma) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.09 843 (all B all Q_1 all R_2 all Q_2 all R_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),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),Q_1)),R_2)),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_3))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),R_3),zero_zero(int))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),R_3)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),R_2)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Q_2),Q_1))))))) # label(fact_797_unique__quotient__lemma__neg) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.09 844 (all K_1 hAPP(int,int,number_number_of(int),K_1) = K_1) # label(fact_798_number__of__is__id) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.09 845 (all R_3 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_3),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_3),A_1)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),Q_2)))))) # label(fact_800_self__quotient__aux1) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.09 846 (all R_3 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_3),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_3)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Q_2),one_one(int))))))) # label(fact_801_self__quotient__aux2) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.09 847 (all B_2 all Q_1 all R_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),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B_2),Q_1)),R_2))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),R_2),B_2)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B_2)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Q_1)))))) # label(fact_802_q__pos__lemma) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.09 848 (all B_2 all Q_1 all R_2 (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_2),Q_1)),R_2)),zero_zero(int))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),R_2)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B_2)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Q_1),zero_zero(int))))))) # label(fact_803_q__neg__lemma) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.09 849 (all B all Q_1 all R_2 all Q_2 all R_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),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),Q_1)),R_2)),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_3))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),R_2)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),R_2),B)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),R_3),B)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Q_1),Q_2))))))) # label(fact_804_unique__quotient__lemma) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.09 850 (all B all Q_2 all R_3 all B_2 all Q_1 all R_2 (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_3) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B_2),Q_1)),R_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),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B_2),Q_1)),R_2))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),R_2),B_2)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),R_3)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B_2)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B_2),B)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Q_2),Q_1))))))))) # label(fact_805_zdiv__mono2__lemma) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.09 851 (all Pa all I_1 all K (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),I_1),K)) -> (hBOOL(hAPP(int,bool,Pa,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),K),one_one(int)))) -> ((all I (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),I),K)) -> (hBOOL(hAPP(int,bool,Pa,I)) -> hBOOL(hAPP(int,bool,Pa,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),I),one_one(int))))))) -> hBOOL(hAPP(int,bool,Pa,I_1)))))) # label(fact_806_int__less__induct) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.09 852 (all Pa all I_1 all K (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),I_1),K)) -> (hBOOL(hAPP(int,bool,Pa,K)) -> ((all I (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),I),K)) -> (hBOOL(hAPP(int,bool,Pa,I)) -> hBOOL(hAPP(int,bool,Pa,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),I),one_one(int))))))) -> hBOOL(hAPP(int,bool,Pa,I_1)))))) # label(fact_807_int__le__induct) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.09 853 (all X_b all X_c (ab_semigroup_mult(X_c) -> (all Z_2 all G all H all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3)) -> ((all X_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_3)) -> hAPP(X_b,X_c,G,X_2) = hAPP(X_b,X_c,H,X_2))) -> hAPP(fun(X_b,bool),X_c,hAPP(X_c,fun(fun(X_b,bool),X_c),hAPP(fun(X_b,X_c),fun(X_c,fun(fun(X_b,bool),X_c)),hAPP(fun(X_c,fun(X_c,X_c)),fun(fun(X_b,X_c),fun(X_c,fun(fun(X_b,bool),X_c))),finite_fold_image(X_c,X_b),times_times(X_c)),G),Z_2),A_3) = hAPP(fun(X_b,bool),X_c,hAPP(X_c,fun(fun(X_b,bool),X_c),hAPP(fun(X_b,X_c),fun(X_c,fun(fun(X_b,bool),X_c)),hAPP(fun(X_c,fun(X_c,X_c)),fun(fun(X_b,X_c),fun(X_c,fun(fun(X_b,bool),X_c))),finite_fold_image(X_c,X_b),times_times(X_c)),H),Z_2),A_3)))))) # label(fact_808_fold__image__cong) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.09 854 (all Pa all K all I_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),I_1)) -> (hBOOL(hAPP(int,bool,Pa,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),K),one_one(int)))) -> ((all I (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),I)) -> (hBOOL(hAPP(int,bool,Pa,I)) -> hBOOL(hAPP(int,bool,Pa,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),I),one_one(int))))))) -> hBOOL(hAPP(int,bool,Pa,I_1)))))) # label(fact_809_int__gr__induct) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.09 855 (all Pa all K all I_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),K),I_1)) -> (hBOOL(hAPP(int,bool,Pa,K)) -> ((all I (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),K),I)) -> (hBOOL(hAPP(int,bool,Pa,I)) -> hBOOL(hAPP(int,bool,Pa,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),I),one_one(int))))))) -> hBOOL(hAPP(int,bool,Pa,I_1)))))) # label(fact_810_int__ge__induct) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.09 856 (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_811_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.09 857 (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_813_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.09 858 (all P_1 all Pa ((all X_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X_2)) -> (hBOOL(hAPP(int,bool,Pa,X_2)) <-> hBOOL(hAPP(int,bool,P_1,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)))),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)))),P_1)))) # label(fact_815_transfer__nat__int__set__cong) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.09 859 (all K all Pa 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,Pa,X_2)) -> hBOOL(hAPP(int,bool,Pa,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,Pa,X_2)) -> hBOOL(hAPP(int,bool,Pa,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_816_decr__mult__lemma) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.09 860 (all P_1 all Pa all X_1 ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X_1)) -> (hBOOL(Pa) <-> hBOOL(P_1))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X_1)) & hBOOL(Pa) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X_1)) & hBOOL(P_1)))) # label(fact_817_conj__le__cong) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.09 861 (all P_1 all Pa all X_1 ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X_1)) -> (hBOOL(Pa) <-> hBOOL(P_1))) -> ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X_1)) -> hBOOL(Pa)) <-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X_1)) -> hBOOL(P_1))))) # label(fact_818_imp__le__cong) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.09 862 (all K all Pa 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,Pa,X_2)) -> hBOOL(hAPP(int,bool,Pa,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,Pa,X_2)) -> hBOOL(hAPP(int,bool,Pa,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_819_incr__mult__lemma) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.09 863 (all X_a (linorder(X_a) -> (all T_4 exists Z_3 all X_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_2),Z_3)) -> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),T_4),X_2)))))) # label(fact_820_minf_I8_J) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.09 864 (all X_a (linorder(X_a) -> (all T_4 exists Z_3 all X_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z_3),X_2)) -> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_2),T_4)))))) # label(fact_821_pinf_I6_J) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.09 865 (all X_a (linorder(X_a) -> (all T_4 exists Z_3 all X_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_2),Z_3)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_2),T_4)))))) # label(fact_822_minf_I6_J) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.09 866 (all X_a (linorder(X_a) -> (all T_4 exists Z_3 all X_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z_3),X_2)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),T_4),X_2)))))) # label(fact_823_pinf_I8_J) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.09 867 (all I_1 all Pa all K (hBOOL(hAPP(int,bool,Pa,K)) -> ((all I (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),K),I)) -> (hBOOL(hAPP(int,bool,Pa,I)) -> hBOOL(hAPP(int,bool,Pa,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),I),one_one(int))))))) -> ((all I (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),I),K)) -> (hBOOL(hAPP(int,bool,Pa,I)) -> hBOOL(hAPP(int,bool,Pa,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),I),one_one(int))))))) -> hBOOL(hAPP(int,bool,Pa,I_1)))))) # label(fact_824_int__induct) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.09 868 (all Pa 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_2 (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_2),D_1)))))) -> ((exists Z_3 all X_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X_2),Z_3)) -> (hBOOL(hAPP(int,bool,Pa,X_2)) <-> hBOOL(hAPP(int,bool,P1,X_2))))) -> ((exists X1 hBOOL(hAPP(int,bool,P1,X1))) -> (exists X1 hBOOL(hAPP(int,bool,Pa,X1)))))))) # label(fact_825_minusinfinity) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.09 869 (all Pa 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_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_2),D_1)))))) -> ((exists Z_3 all X_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Z_3),X_2)) -> (hBOOL(hAPP(int,bool,Pa,X_2)) <-> hBOOL(hAPP(int,bool,P_1,X_2))))) -> ((exists X1 hBOOL(hAPP(int,bool,P_1,X1))) -> (exists X1 hBOOL(hAPP(int,bool,Pa,X1)))))))) # label(fact_826_plusinfinity) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.09 870 (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_827_tsub__def) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.09 871 (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_828_of__nat__number__of__lemma) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.09 872 (all X_a (number_semiring(X_a) -> (all N hAPP(int,X_a,number_number_of(X_a),hAPP(nat,int,semiring_1_of_nat(int),N)) = hAPP(nat,X_a,semiring_1_of_nat(X_a),N)))) # label(fact_829_number__of__int) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.09 873 (all N 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)))) # label(fact_830_zero__zle__int) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.09 874 (all K_1 -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,semiring_1_of_nat(int),K_1)),zero_zero(int)))) # label(fact_831_int__less__0__conv) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.09 875 (all X_a (linordered_semidom(X_a) -> (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,semiring_1_of_nat(X_a),N)))))) # label(fact_832_of__nat__0__le__iff) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.09 876 (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_833_zero__le__imp__of__nat) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.09 877 (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_834_of__nat__less__0__iff) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.09 878 (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_835_of__nat__0) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.09 879 (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_836_of__nat__1) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.09 880 (all Na (hAPP(nat,int,semiring_1_of_nat(int),Na) = zero_zero(int) <-> Na = zero_zero(nat))) # label(fact_839_int__eq__0__conv) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.09 881 (all X_b (ring_1(X_b) -> (all Na hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),hAPP(nat,X_b,semiring_1_of_nat(X_b),Na)),ring_1_Ints(X_b)))))) # label(fact_840_Ints__of__nat) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.09 882 (all X_b (semiring_char_0(X_b) -> (all M all Na (hAPP(nat,X_b,semiring_1_of_nat(X_b),M) = hAPP(nat,X_b,semiring_1_of_nat(X_b),Na) <-> M = Na)))) # label(fact_841_of__nat__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.09 883 (all X_a (semiring_1(X_a) -> (all M_1 all N hAPP(nat,X_a,semiring_1_of_nat(X_a),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),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),M_1)),hAPP(nat,X_a,semiring_1_of_nat(X_a),N))))) # label(fact_842_of__nat__add) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.09 884 (all X_b (linordered_semidom(X_b) -> (all M all Na (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(nat,X_b,semiring_1_of_nat(X_b),M)),hAPP(nat,X_b,semiring_1_of_nat(X_b),Na))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),Na)))))) # label(fact_843_of__nat__le__iff) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.09 885 (all X_b (linordered_semidom(X_b) -> (all M all Na (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(nat,X_b,semiring_1_of_nat(X_b),M)),hAPP(nat,X_b,semiring_1_of_nat(X_b),Na))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),Na)))))) # label(fact_844_of__nat__less__iff) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.09 886 (all X_a (linordered_semidom(X_a) -> (all M_1 all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),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_1)),hAPP(nat,X_a,semiring_1_of_nat(X_a),N))))))) # label(fact_845_less__imp__of__nat__less) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.09 887 (all X_a (linordered_semidom(X_a) -> (all M_1 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_1)),hAPP(nat,X_a,semiring_1_of_nat(X_a),N))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N)))))) # label(fact_846_of__nat__less__imp__less) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.09 888 (all M all Na (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),Na))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),Na)))) # label(fact_847_zless__int) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.09 889 (all M all Na (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),Na))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),Na)))) # label(fact_848_zle__int) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.09 890 (all M_1 all N 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)) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),N))) # label(fact_849_zadd__int) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.09 891 (all M_1 all N 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)),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))),Z)) # label(fact_850_zadd__int__left) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.09 892 (all W_1 all Z_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),W_1),Z_2)) <-> (exists N_1 Z_2 = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),W_1),hAPP(nat,int,semiring_1_of_nat(int),N_1))))) # label(fact_851_zle__iff__zadd) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.09 893 (all M_1 all N 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)) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),N))) # label(fact_852_zmult__int) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.09 894 (all M_1 all N hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),N)) = 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))) # label(fact_853_int__mult) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.09 895 (all X_a (semiring_1(X_a) -> (all M_1 all N hAPP(nat,X_a,semiring_1_of_nat(X_a),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),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),M_1)),hAPP(nat,X_a,semiring_1_of_nat(X_a),N))))) # label(fact_854_of__nat__mult) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.09 896 (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_855_Nat__Transfer_Otransfer__int__nat__functions_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.09 897 (all X_1 all Y_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,semiring_1_of_nat(int),X_1)),hAPP(nat,int,semiring_1_of_nat(int),Y_2))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X_1),Y_2)))) # label(fact_856_transfer__int__nat__relations_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.09 898 (all X_1 all Y_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,semiring_1_of_nat(int),X_1)),hAPP(nat,int,semiring_1_of_nat(int),Y_2))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X_1),Y_2)))) # label(fact_857_transfer__int__nat__relations_I3_J) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.09 899 (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_858_Nat__Transfer_Otransfer__int__nat__functions_I3_J) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.09 900 (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_859_Nat__Transfer_Otransfer__int__nat__functions_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.09 901 (all A_3 hAPP(fun(nat,bool),nat,finite_card(nat),A_3) = hAPP(fun(int,bool),nat,finite_card(int),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),A_3))) # label(fact_860_Nat__Transfer_Otransfer__nat__int__set__functions_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.09 902 (all A_3 (hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),A_3)) <-> hBOOL(hAPP(fun(int,bool),bool,finite_finite(int),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),A_3))))) # label(fact_861_transfer__nat__int__set__relations_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.09 903 (all 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)))),Pa)) = 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),Pa),semiring_1_of_nat(int))))) # label(fact_864_Nat__Transfer_Otransfer__int__nat__set__functions_I5_J) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.09 904 (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_865_Nat__Transfer_Otransfer__nat__int__function__closures_I9_J) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.09 905 (all Pa ((exists X_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X_2)) & hBOOL(hAPP(int,bool,Pa,X_2)))) <-> (exists X_2 hBOOL(hAPP(int,bool,Pa,hAPP(nat,int,semiring_1_of_nat(int),X_2)))))) # label(fact_866_transfer__int__nat__quantifiers_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.09 906 (all Pa ((all X_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X_2)) -> hBOOL(hAPP(int,bool,Pa,X_2)))) <-> (all X_2 hBOOL(hAPP(int,bool,Pa,hAPP(nat,int,semiring_1_of_nat(int),X_2)))))) # label(fact_867_transfer__int__nat__quantifiers_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.09 907 (all Na (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,semiring_1_of_nat(int),Na)),zero_zero(int))) <-> Na = zero_zero(nat))) # label(fact_868_int__le__0__conv) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.09 908 (all W_1 all Z_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_1),Z_2)) <-> (exists N_1 Z_2 = 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_1)))))) # label(fact_870_zless__iff__Suc__zadd) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.09 909 (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_871_int__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.09 910 (all N all M_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N),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)) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),N)))) # label(fact_872_zdiff__int) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.09 911 (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_873_of__nat__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.09 912 (all X_a (ring_1(X_a) -> (all N all M_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N),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)) = 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)))))) # label(fact_874_of__nat__diff) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.09 913 (all Na (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(nat,int,semiring_1_of_nat(int),Na))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Na)))) # label(fact_875_zero__less__int__conv) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.09 914 (all K_1 all I_2 all J (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),I_2),J)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K_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(nat,int,semiring_1_of_nat(int),K_1)),I_2)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(nat,int,semiring_1_of_nat(int),K_1)),J)))))) # label(fact_876_zmult__zless__mono2__lemma) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.09 915 (all X_b (linordered_semidom(X_b) -> (all Na (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),zero_zero(X_b)),hAPP(nat,X_b,semiring_1_of_nat(X_b),Na))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Na)))))) # label(fact_877_of__nat__0__less__iff) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.09 916 (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_878_Nat__Transfer_Otransfer__nat__int__function__closures_I3_J) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.09 917 (all Pa all X_1 all Y_2 (hBOOL(hAPP(int,bool,Pa,hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X_1),Y_2)))) <-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Y_2),X_1)) -> hBOOL(hAPP(int,bool,Pa,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_2))))) & (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X_1),Y_2)) -> hBOOL(hAPP(int,bool,Pa,zero_zero(int)))))) # label(fact_879_zdiff__int__split) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.09 918 (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_880_tsub__eq) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.09 919 (all K_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),K_1)) -> (exists N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)) & K_1 = hAPP(nat,int,semiring_1_of_nat(int),N_1))))) # label(fact_881_zero__less__imp__eq__int) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.09 920 (all X_b (semiring_1(X_b) -> (all Na hAPP(nat,X_b,semiring_1_of_nat(X_b),Na) = hAPP(X_b,X_b,hAPP(nat,fun(X_b,X_b),hAPP(fun(X_b,X_b),fun(nat,fun(X_b,X_b)),semiri532925092at_aux(X_b),hAPP(X_b,fun(X_b,X_b),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(X_b,X_b)),combc(X_b,X_b,X_b),plus_plus(X_b)),one_one(X_b))),Na),zero_zero(X_b))))) # label(fact_882_semiring__1__class_Oof__nat__code) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.09 921 (all M all Na (hAPP(nat,int,semiring_1_of_nat(int),M) = hAPP(nat,int,semiring_1_of_nat(int),Na) <-> M = Na)) # label(fact_883_int__int__eq) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.09 922 (all A_3 all B_1 (hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,bool),fun(fun(nat,bool),bool),ord_less(fun(nat,bool)),A_3),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_3)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),B_1))))) # label(fact_884_transfer__nat__int__set__relations_I4_J) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.09 923 (all A_3 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_3),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_3)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),B_1))))) # label(fact_885_transfer__nat__int__set__relations_I5_J) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.09 924 (all A_3 all B_1 (A_3 = 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_3) = hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),B_1))) # label(fact_887_transfer__nat__int__set__relations_I3_J) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.09 925 (all X_1 all A_3 (hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X_1),A_3)) <-> hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),hAPP(nat,int,semiring_1_of_nat(int),X_1)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),A_3))))) # label(fact_888_transfer__nat__int__set__relations_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.09 926 (all X_1 all Y_2 all Pa ((hBOOL(Pa) -> hAPP(nat,int,semiring_1_of_nat(int),X_1) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),hAPP(bool,fun(nat,fun(nat,nat)),if(nat),Pa),X_1),Y_2))) & (-hBOOL(Pa) -> hAPP(nat,int,semiring_1_of_nat(int),Y_2) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),hAPP(bool,fun(nat,fun(nat,nat)),if(nat),Pa),X_1),Y_2))))) # label(fact_889_int__if__cong) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.09 927 (all X_1 all Y_2 (hAPP(nat,int,semiring_1_of_nat(int),X_1) = hAPP(nat,int,semiring_1_of_nat(int),Y_2) <-> X_1 = Y_2)) # label(fact_890_transfer__int__nat__relations_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.09 928 (all X_b (semiring_1(X_b) -> (all Inc all I_1 hAPP(X_b,X_b,hAPP(nat,fun(X_b,X_b),hAPP(fun(X_b,X_b),fun(nat,fun(X_b,X_b)),semiri532925092at_aux(X_b),Inc),zero_zero(nat)),I_1) = ti(X_b,I_1)))) # label(fact_891_of__nat__aux_Osimps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.09 929 (all X_b (semiring_1(X_b) -> (all Inc all Na all I_1 hAPP(X_b,X_b,hAPP(nat,fun(X_b,X_b),hAPP(fun(X_b,X_b),fun(nat,fun(X_b,X_b)),semiri532925092at_aux(X_b),Inc),hAPP(nat,nat,suc,Na)),I_1) = hAPP(X_b,X_b,hAPP(nat,fun(X_b,X_b),hAPP(fun(X_b,X_b),fun(nat,fun(X_b,X_b)),semiri532925092at_aux(X_b),Inc),Na),hAPP(X_b,X_b,Inc,I_1))))) # label(fact_892_of__nat__aux_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.09 930 (all K_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),K_1)) -> -(all N_1 K_1 != hAPP(nat,int,semiring_1_of_nat(int),N_1)))) # label(fact_893_nonneg__int__cases) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.09 931 (all Z (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Z)) -> -(all M_2 Z != hAPP(nat,int,semiring_1_of_nat(int),M_2)))) # label(fact_894_nonneg__eq__int) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.09 932 (all K_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),K_1)) -> (exists N_1 K_1 = hAPP(nat,int,semiring_1_of_nat(int),N_1)))) # label(fact_895_zero__le__imp__eq__int) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.09 933 (all Z -(all M_2 all N_1 Z != hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(nat,int,semiring_1_of_nat(int),M_2)),hAPP(nat,int,semiring_1_of_nat(int),N_1)))) # label(fact_896_int__diff__cases) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.09 934 (all X_c all X_b (comm_monoid_mult(X_b) -> (all H all G all S all R_1 all E (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),R_1,E),E)) -> ((all X1 all Y1 all X2 all Y2 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),R_1,X1),X2)) & hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),R_1,Y1),Y2)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),R_1,hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),X1),Y1)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),X2),Y2))))) -> (hBOOL(hAPP(fun(X_c,bool),bool,finite_finite(X_c),S)) -> ((all X_2 (hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),X_2),S)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),R_1,hAPP(X_c,X_b,H,X_2)),hAPP(X_c,X_b,G,X_2))))) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),R_1,hAPP(fun(X_c,bool),X_b,hAPP(X_b,fun(fun(X_c,bool),X_b),hAPP(fun(X_c,X_b),fun(X_b,fun(fun(X_c,bool),X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_c,X_b),fun(X_b,fun(fun(X_c,bool),X_b))),finite_fold_image(X_b,X_c),times_times(X_b)),H),E),S)),hAPP(fun(X_c,bool),X_b,hAPP(X_b,fun(fun(X_c,bool),X_b),hAPP(fun(X_c,X_b),fun(X_b,fun(fun(X_c,bool),X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_c,X_b),fun(X_b,fun(fun(X_c,bool),X_b))),finite_fold_image(X_b,X_c),times_times(X_b)),G),E),S)))))))))) # label(fact_897_fold__image__related) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.09 935 (all X_c all X_b all X_d (comm_monoid_mult(X_d) -> (all E all G all F all H all K all T_3 all S (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),S)) -> ((all Y_1 (hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),Y_1),T_3)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),hAPP(X_c,X_b,K,Y_1)),S)) & hAPP(X_b,X_c,H,hAPP(X_c,X_b,K,Y_1)) = ti(X_c,Y_1))) -> ((all X_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),S)) -> hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),hAPP(X_b,X_c,H,X_2)),T_3)) & hAPP(X_c,X_b,K,hAPP(X_b,X_c,H,X_2)) = ti(X_b,X_2) & hAPP(X_c,X_d,G,hAPP(X_b,X_c,H,X_2)) = hAPP(X_b,X_d,F,X_2))) -> hAPP(fun(X_b,bool),X_d,hAPP(X_d,fun(fun(X_b,bool),X_d),hAPP(fun(X_b,X_d),fun(X_d,fun(fun(X_b,bool),X_d)),hAPP(fun(X_d,fun(X_d,X_d)),fun(fun(X_b,X_d),fun(X_d,fun(fun(X_b,bool),X_d))),finite_fold_image(X_d,X_b),times_times(X_d)),F),E),S) = hAPP(fun(X_c,bool),X_d,hAPP(X_d,fun(fun(X_c,bool),X_d),hAPP(fun(X_c,X_d),fun(X_d,fun(fun(X_c,bool),X_d)),hAPP(fun(X_d,fun(X_d,X_d)),fun(fun(X_c,X_d),fun(X_d,fun(fun(X_c,bool),X_d))),finite_fold_image(X_d,X_c),times_times(X_d)),G),E),T_3))))))) # label(fact_898_fold__image__eq__general__inverses) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.09 936 (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_899_of__nat__number__of__eq) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.09 937 (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_900_decr__lemma) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.09 938 (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_901_abs__triangle__ineq4) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.09 939 (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_902_abs__diff__triangle__ineq) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.09 940 (all Z_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,abs_abs(int),Z_2)),one_one(int))) <-> Z_2 = zero_zero(int))) # label(fact_903_zabs__less__one__iff) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.09 941 (all Z_1 (hBOOL(hAPP(int,bool,nat_neg,Z_1)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Z_1),zero_zero(int))))) # label(fact_904_neg__def) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.09 942 (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_905_not__neg__eq__ge__0) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.09 943 (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_906_abs__of__nonneg) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.09 944 (all X_b (ordere142940540dd_abs(X_b) -> (all A_2 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_b,X_b,abs_abs(X_b),A_2)),zero_zero(X_b))) <-> ti(X_b,A_2) = zero_zero(X_b))))) # label(fact_907_abs__le__zero__iff) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.09 945 (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_908_abs__ge__zero) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.09 946 (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_909_abs__not__less__zero) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.09 947 (all X_b (ordere142940540dd_abs(X_b) -> (all A_2 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),zero_zero(X_b)),hAPP(X_b,X_b,abs_abs(X_b),A_2))) <-> ti(X_b,A_2) != zero_zero(X_b))))) # label(fact_910_zero__less__abs__iff) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.09 948 (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_911_abs__of__pos) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.09 949 (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_912_abs__triangle__ineq3) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.09 950 (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_913_abs__triangle__ineq2) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.09 951 (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_914_abs__triangle__ineq2__sym) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.09 952 (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_915_abs__mult__less) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.09 953 (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_916_abs__triangle__ineq) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.09 954 (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_917_abs__le__D1) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.09 955 (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_918_abs__ge__self) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.09 956 (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_919_abs__eq__mult) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.09 957 (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_920_abs__mult__pos) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.09 958 (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_921_abs__mult) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.09 959 (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_922_abs__mult__self) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.09 960 (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_923_abs__minus__commute) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.09 961 (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_924_abs__add__abs) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.09 962 (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_925_abs__idempotent) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.09 963 (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_927_abs__one) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.09 964 (all X_b (ordere142940540dd_abs(X_b) -> (all A_2 (hAPP(X_b,X_b,abs_abs(X_b),A_2) = zero_zero(X_b) <-> ti(X_b,A_2) = zero_zero(X_b))))) # label(fact_929_abs__eq__0) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.09 965 (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_930_abs__zero) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.09 966 (all M_1 all N (hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),M_1),N)) = one_one(int) -> hAPP(int,int,abs_abs(int),M_1) = one_one(int))) # label(fact_931_abs__zmult__eq__1) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.09 967 (all X_a (linordered_idom(X_a) -> (all N hAPP(X_a,X_a,abs_abs(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),N)) = hAPP(nat,X_a,semiring_1_of_nat(X_a),N)))) # label(fact_932_abs__of__nat) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.09 968 (all N -hBOOL(hAPP(int,bool,nat_neg,hAPP(nat,int,semiring_1_of_nat(int),N)))) # label(fact_933_not__neg__int) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.09 969 (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_934_abs__int__eq) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.09 970 (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_935_neg__imp__number__of__eq__0) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.09 971 (all V_3 all V_2 (hAPP(int,nat,number_number_of(nat),V_3) = hAPP(int,nat,number_number_of(nat),V_2) <-> (hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V_3))) -> 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_3))) -> (hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V_2))) -> hAPP(int,int,number_number_of(int),V_3) = zero_zero(int)) & (-hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V_2))) -> V_3 = V_2)))) # label(fact_936_eq__nat__number__of) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.09 972 (all V_1 all K_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),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_1)),K_1)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),V_1)),K_1)) & (-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_1))) -> 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_1)),K_1)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),V)),K_1)) & (-hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V_1))) -> 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_1)),K_1)) = 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_1))),K_1))))) # label(fact_937_nat__number__of__add__left) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.09 973 (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_938_int__nat__number__of) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.09 974 (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_939_incr__lemma) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.09 975 (all K all F all Na ((all I (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),Na)) -> 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),one_one(nat)))),hAPP(nat,int,F,I)))),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,Na))) -> (exists I (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I),Na)) & hAPP(nat,int,F,I) = K)))))) # label(fact_940_int__val__lemma) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.09 976 (all K all F all Na ((all I (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),Na)) -> 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),one_one(nat)))),hAPP(nat,int,F,I)))),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,Na))) -> (exists I (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I),Na)) & hAPP(nat,int,F,I) = K)))))) # label(fact_941_nat0__intermed__int__val) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.09 977 (all K all F all Na all M ((all I (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),I)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),Na)) -> 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),one_one(nat)))),hAPP(nat,int,F,I)))),one_one(int))))) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),Na)) -> (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,Na))) -> (exists I (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),I)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I),Na)) & hAPP(nat,int,F,I) = K))))))) # label(fact_942_nat__intermed__int__val) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.09 978 (all N 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)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),N)) & (-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)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,succ,V))),N)))) # label(fact_943_Suc__nat__number__of__add) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.09 979 (all K_1 hAPP(int,int,succ,K_1) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),K_1),one_one(int))) # label(fact_944_succ__def) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.09 980 (all X_a (number_ring(X_a) -> (all K_1 hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,succ,K_1)) = 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_1))))) # label(fact_945_number__of__succ) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.09 981 (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_946_Suc__nat__number__of) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.09 982 (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_947_nat__number__of__Bit1) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.10 983 (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_948_nat__1__add__number__of) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.10 984 (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_950_neg__number__of__Bit1) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.10 985 (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_953_number__of__Bit1) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.10 986 (all N hAPP(nat,nat,suc,hAPP(nat,nat,suc,hAPP(nat,nat,suc,N))) = 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)) # label(fact_956_Suc3__eq__add__3) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.10 987 (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_957_semiring__norm_I110_J) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.10 988 (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_961_numeral__1__eq__1) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.10 989 (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_962_semiring__numeral__1__eq__1) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.10 990 (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_963_mult__numeral__1__right) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.10 991 (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_964_mult__numeral__1) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.10 992 (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_965_add__special_I3_J) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.10 993 (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_966_add__special_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.10 994 (all K_1 hAPP(int,int,bit1,K_1) = 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_1)),K_1)) # label(fact_968_Bit1__def) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.10 995 (all X_a (number_semiring(X_a) -> hAPP(int,X_a,number_number_of(X_a),pls) = zero_zero(X_a))) # label(fact_969_semiring__numeral__0__eq__0) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.10 996 (all X_a (number_ring(X_a) -> hAPP(int,X_a,number_number_of(X_a),pls) = zero_zero(X_a))) # label(fact_970_number__of__Pls) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.10 997 (all X_a (number_ring(X_a) -> zero_zero(X_a) = hAPP(int,X_a,number_number_of(X_a),pls))) # label(fact_971_semiring__norm_I112_J) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.10 998 (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_972_add__numeral__0) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.10 999 (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_973_add__numeral__0__right) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.10 1000 (all K all L (hAPP(int,int,bit1,K) = hAPP(int,int,bit1,L) <-> K = L)) # label(fact_977_rel__simps_I51_J) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.10 1001 (all K_1 hAPP(int,int,bit1,K_1) != pls) # label(fact_978_rel__simps_I46_J) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.10 1002 (all L_1 pls != hAPP(int,int,bit1,L_1)) # label(fact_979_rel__simps_I39_J) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.10 1003 (all K_1 hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),K_1),pls) = K_1) # label(fact_980_diff__bin__simps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.10 1004 (all K_1 hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),pls),K_1) = K_1) # label(fact_981_add__Pls) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.10 1005 (all K_1 hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),K_1),pls) = K_1) # label(fact_982_add__Pls__right) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.10 1006 (all W hAPP(int,int,hAPP(int,fun(int,int),times_times(int),pls),W) = pls) # label(fact_983_mult__Pls) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.10 1007 (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_986_rel__simps_I22_J) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.10 1008 (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_987_rel__simps_I34_J) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.10 1009 (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_988_less__eq__int__code_I16_J) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.10 1010 (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_990_rel__simps_I12_J) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.10 1011 (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_991_rel__simps_I17_J) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.10 1012 (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_992_less__int__code_I16_J) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.10 1013 (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_993_rel__simps_I29_J) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.10 1014 (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_994_rel__simps_I5_J) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.10 1015 (all T_2 all T_1 (preorder(T_1) -> preorder(fun(T_2,T_1)))) # label(arity_fun___Orderings_Opreorder) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.10 1016 (all T_2 all T_1 (finite_finite_1(T_1) & finite_finite_1(T_2) -> finite_finite_1(fun(T_2,T_1)))) # label(arity_fun___Finite__Set_Ofinite) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.10 1017 (all T_2 all T_1 (order(T_1) -> order(fun(T_2,T_1)))) # label(arity_fun___Orderings_Oorder) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.10 1018 (all T_2 all T_1 (ord(T_1) -> ord(fun(T_2,T_1)))) # label(arity_fun___Orderings_Oord) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.10 1019 (all T_2 all T_1 (bot(T_1) -> bot(fun(T_2,T_1)))) # label(arity_fun___Orderings_Obot) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.10 1020 (all T_2 all T_1 (minus(T_1) -> minus(fun(T_2,T_1)))) # label(arity_fun___Groups_Ominus) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.10 1021 (all T_2 all T_1 (finite_finite_1(T_1) & finite_finite_1(T_2) -> finite_finite_1(sum_sum(T_2,T_1)))) # label(arity_sum___Finite__Set_Ofinite) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.10 1022 (all T all A ti(T,ti(T,A)) = ti(T,A)) # label(help_ti_idem) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.10 1023 (all X_a all X all Y hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),hAPP(bool,fun(X_a,fun(X_a,X_a)),if(X_a),fTrue),X),Y) = ti(X_a,X)) # label(help_If_1_1_T) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.10 1024 (all X_a all X all Y hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),hAPP(bool,fun(X_a,fun(X_a,X_a)),if(X_a),fFalse),X),Y) = ti(X_a,Y)) # label(help_If_2_1_T) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.10 1025 (all P (ti(bool,P) = fTrue | ti(bool,P) = fFalse)) # label(help_If_3_1_T) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.10 1026 (all P (-hBOOL(hAPP(bool,bool,fNot,P)) | -hBOOL(P))) # label(help_fNot_1_1_U) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.10 1027 (all P (hBOOL(P) | hBOOL(hAPP(bool,bool,fNot,P)))) # label(help_fNot_2_1_U) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.10 1028 (all X_a all X_c all X_b all P all Q all R hAPP(X_a,X_c,hAPP(fun(X_a,X_b),fun(X_a,X_c),hAPP(fun(X_b,X_c),fun(fun(X_a,X_b),fun(X_a,X_c)),combb(X_b,X_c,X_a),P),Q),R) = hAPP(X_b,X_c,P,hAPP(X_a,X_b,Q,R))) # label(help_COMBB_1_1_U) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.10 1029 (all X_a all X_c all X_b all P all Q all R hAPP(X_a,X_c,hAPP(X_b,fun(X_a,X_c),hAPP(fun(X_a,fun(X_b,X_c)),fun(X_b,fun(X_a,X_c)),combc(X_a,X_b,X_c),P),Q),R) = hAPP(X_b,X_c,hAPP(X_a,fun(X_b,X_c),P,R),Q)) # label(help_COMBC_1_1_U) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.10 1030 (all X_a all P hAPP(X_a,X_a,combi(X_a),P) = ti(X_a,P)) # label(help_COMBI_1_1_U) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.10 1031 (all X_b all X_a all P all Q hAPP(X_b,X_a,hAPP(X_a,fun(X_b,X_a),combk(X_a,X_b),P),Q) = ti(X_a,P)) # label(help_COMBK_1_1_U) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.10 1032 (all X_a all X_c all X_b all P all Q all R hAPP(X_a,X_c,hAPP(fun(X_a,X_b),fun(X_a,X_c),hAPP(fun(X_a,fun(X_b,X_c)),fun(fun(X_a,X_b),fun(X_a,X_c)),combs(X_a,X_b,X_c),P),Q),R) = hAPP(X_b,X_c,hAPP(X_a,fun(X_b,X_c),P,R),hAPP(X_a,X_b,Q,R))) # label(help_COMBS_1_1_U) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.10 1033 (all Q all P (-hBOOL(P) | -hBOOL(Q) | hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,P),Q)))) # label(help_fconj_1_1_U) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.10 1034 (all P all Q (-hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,P),Q)) | hBOOL(P))) # label(help_fconj_2_1_U) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.10 1035 (all P all Q (-hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,P),Q)) | hBOOL(Q))) # label(help_fconj_3_1_U) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.10 1036 (all Q all P (-hBOOL(P) | hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,P),Q)))) # label(help_fdisj_1_1_U) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.10 1037 (all P all Q (-hBOOL(Q) | hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,P),Q)))) # label(help_fdisj_2_1_U) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.19 1038 (all P all Q (-hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,P),Q)) | hBOOL(P) | hBOOL(Q))) # label(help_fdisj_3_1_U) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.19 1039 (all P (ti(bool,P) = fTrue | ti(bool,P) = fFalse)) # label(help_fFalse_1_1_T) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.19 1040 (all X_a all X all Y (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),fequal(X_a),X),Y)) | ti(X_a,X) = ti(X_a,Y))) # label(help_fequal_1_1_T) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.19 1041 (all X_a all X all Y (ti(X_a,X) != ti(X_a,Y) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),fequal(X_a),X),Y)))) # label(help_fequal_2_1_T) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.19 1042 (all Q all P (hBOOL(P) | hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fimplies,P),Q)))) # label(help_fimplies_1_1_U) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.19 1043 (all P all Q (-hBOOL(Q) | hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fimplies,P),Q)))) # label(help_fimplies_2_1_U) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.19 1044 (all P all Q (-hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fimplies,P),Q)) | -hBOOL(P) | hBOOL(Q))) # label(help_fimplies_3_1_U) # label(axiom) # label(non_clause). [assumption].
% 1.75/2.19
% 1.75/2.19 ============================== end of process non-clausal formulas ===
% 1.75/2.19
% 1.75/2.19 ============================== PROCESS INITIAL CLAUSES ===============
% 1.75/2.19
% 1.75/2.19 ============================== PREDICATE ELIMINATION =================
% 1.75/2.19 1045 ordere142940540dd_abs(int) # label(arity_Int_Oint___Groups_Oordered__ab__group__add__abs) # label(axiom). [assumption].
% 1.75/2.19 1046 -ordere142940540dd_abs(A) | abs_abs(A) = ti(fun(A,A),abs_abs(A)) # label(tsy_c_Groups_Oabs__class_Oabs_res) # label(axiom). [clausify(14)].
% 1.75/2.19 1047 -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_901_abs__triangle__ineq4) # label(axiom). [clausify(938)].
% 1.75/2.19 1048 -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_902_abs__diff__triangle__ineq) # label(axiom). [clausify(939)].
% 1.75/2.19 1049 -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_906_abs__of__nonneg) # label(axiom). [clausify(943)].
% 1.75/2.19 1050 -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_907_abs__le__zero__iff) # label(axiom). [clausify(944)].
% 1.75/2.19 1051 -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_907_abs__le__zero__iff) # label(axiom). [clausify(944)].
% 1.75/2.19 1052 -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_908_abs__ge__zero) # label(axiom). [clausify(945)].
% 1.75/2.19 1053 -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_909_abs__not__less__zero) # label(axiom). [clausify(946)].
% 1.75/2.19 1054 -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_910_zero__less__abs__iff) # label(axiom). [clausify(947)].
% 1.75/2.19 1055 -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_910_zero__less__abs__iff) # label(axiom). [clausify(947)].
% 1.75/2.19 1056 -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_911_abs__of__pos) # label(axiom). [clausify(948)].
% 1.75/2.19 1057 -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_912_abs__triangle__ineq3) # label(axiom). [clausify(949)].
% 1.75/2.19 1058 -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_913_abs__triangle__ineq2) # label(axiom). [clausify(950)].
% 1.75/2.19 1059 -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_914_abs__triangle__ineq2__sym) # label(axiom). [clausify(951)].
% 1.75/2.19 1060 -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_916_abs__triangle__ineq) # label(axiom). [clausify(953)].
% 1.75/2.19 1061 -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_917_abs__le__D1) # label(axiom). [clausify(954)].
% 1.75/2.19 1062 -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_918_abs__ge__self) # label(axiom). [clausify(955)].
% 1.75/2.19 1063 -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_923_abs__minus__commute) # label(axiom). [clausify(960)].
% 1.75/2.19 1064 -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_924_abs__add__abs) # label(axiom). [clausify(961)].
% 1.75/2.19 1065 -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_925_abs__idempotent) # label(axiom). [clausify(962)].
% 1.75/2.19 1066 -ordere142940540dd_abs(A) | hAPP(A,A,abs_abs(A),B) != zero_zero(A) | zero_zero(A) = ti(A,B) # label(fact_929_abs__eq__0) # label(axiom). [clausify(964)].
% 1.75/2.19 1067 -ordere142940540dd_abs(A) | hAPP(A,A,abs_abs(A),B) = zero_zero(A) | zero_zero(A) != ti(A,B) # label(fact_929_abs__eq__0) # label(axiom). [clausify(964)].
% 1.75/2.19 1068 -ordere142940540dd_abs(A) | hAPP(A,A,abs_abs(A),zero_zero(A)) = zero_zero(A) # label(fact_930_abs__zero) # label(axiom). [clausify(965)].
% 1.75/2.19 Derived: abs_abs(int) = ti(fun(int,int),abs_abs(int)). [resolve(1045,a,1046,a)].
% 1.75/2.19 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(1045,a,1047,a)].
% 1.75/2.19 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(1045,a,1048,a)].
% 1.75/2.19 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(1045,a,1049,a)].
% 2.20/2.41 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(1045,a,1050,a)].
% 2.20/2.41 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(1045,a,1051,a)].
% 2.20/2.41 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(1045,a,1052,a)].
% 2.20/2.41 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,abs_abs(int),A)),zero_zero(int))). [resolve(1045,a,1053,a)].
% 2.20/2.41 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(1045,a,1054,a)].
% 2.20/2.41 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(1045,a,1055,a)].
% 2.20/2.41 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(1045,a,1056,a)].
% 2.20/2.41 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(1045,a,1057,a)].
% 2.20/2.41 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(1045,a,1058,a)].
% 2.20/2.41 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(1045,a,1059,a)].
% 2.20/2.41 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(1045,a,1060,a)].
% 2.20/2.41 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(1045,a,1061,a)].
% 2.20/2.41 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),hAPP(int,int,abs_abs(int),A))). [resolve(1045,a,1062,a)].
% 2.20/2.41 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(1045,a,1063,a)].
% 2.20/2.41 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(1045,a,1064,a)].
% 2.20/2.41 Derived: hAPP(int,int,abs_abs(int),hAPP(int,int,abs_abs(int),A)) = hAPP(int,int,abs_abs(int),A). [resolve(1045,a,1065,a)].
% 2.20/2.41 Derived: hAPP(int,int,abs_abs(int),A) != zero_zero(int) | zero_zero(int) = ti(int,A). [resolve(1045,a,1066,a)].
% 2.20/2.41 Derived: hAPP(int,int,abs_abs(int),A) = zero_zero(int) | zero_zero(int) != ti(int,A). [resolve(1045,a,1067,a)].
% 2.20/2.41 Derived: hAPP(int,int,abs_abs(int),zero_zero(int)) = zero_zero(int). [resolve(1045,a,1068,a)].
% 2.20/2.41 1069 one(int) # label(arity_Int_Oint___Groups_Oone) # label(axiom). [assumption].
% 2.20/2.41 1070 -one(A) | one_one(A) = ti(A,one_one(A)) # label(tsy_c_Groups_Oone__class_Oone_res) # label(axiom). [clausify(16)].
% 2.20/2.41 Derived: one_one(int) = ti(int,one_one(int)). [resolve(1069,a,1070,a)].
% 2.20/2.41 1071 one(nat) # label(arity_Nat_Onat___Groups_Oone) # label(axiom). [assumption].
% 2.20/2.41 Derived: one_one(nat) = ti(nat,one_one(nat)). [resolve(1071,a,1070,a)].
% 2.20/2.41 1072 monoid_add(int) # label(arity_Int_Oint___Groups_Omonoid__add) # label(axiom). [assumption].
% 2.30/2.52 1073 -monoid_add(A) | plus_plus(A) = ti(fun(A,fun(A,A)),plus_plus(A)) # label(tsy_c_Groups_Oplus__class_Oplus_0_res) # label(axiom). [clausify(17)].
% 2.30/2.52 1074 -monoid_add(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),zero_zero(A)) = ti(A,B) # label(fact_466_add__0__right) # label(axiom). [clausify(515)].
% 2.30/2.52 1075 -monoid_add(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),zero_zero(A)),B) = ti(A,B) # label(fact_469_add__0__left) # label(axiom). [clausify(518)].
% 2.30/2.52 Derived: plus_plus(int) = ti(fun(int,fun(int,int)),plus_plus(int)). [resolve(1072,a,1073,a)].
% 2.30/2.52 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),zero_zero(int)) = ti(int,A). [resolve(1072,a,1074,a)].
% 2.30/2.52 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),zero_zero(int)),A) = ti(int,A). [resolve(1072,a,1075,a)].
% 2.30/2.52 1076 monoid_add(nat) # label(arity_Nat_Onat___Groups_Omonoid__add) # label(axiom). [assumption].
% 2.30/2.52 Derived: plus_plus(nat) = ti(fun(nat,fun(nat,nat)),plus_plus(nat)). [resolve(1076,a,1073,a)].
% 2.30/2.52 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),zero_zero(nat)) = ti(nat,A). [resolve(1076,a,1074,a)].
% 2.30/2.52 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),zero_zero(nat)),A) = ti(nat,A). [resolve(1076,a,1075,a)].
% 2.30/2.52 1077 cancel_semigroup_add(int) # label(arity_Int_Oint___Groups_Ocancel__semigroup__add) # label(axiom). [assumption].
% 2.30/2.52 1078 -cancel_semigroup_add(A) | plus_plus(A) = ti(fun(A,fun(A,A)),plus_plus(A)) # label(tsy_c_Groups_Oplus__class_Oplus_1_res) # label(axiom). [clausify(18)].
% 2.30/2.52 1079 -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_222_add__left__cancel) # label(axiom). [clausify(271)].
% 2.30/2.52 1080 -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_222_add__left__cancel) # label(axiom). [clausify(271)].
% 2.30/2.52 1081 -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_223_add__right__cancel) # label(axiom). [clausify(272)].
% 2.30/2.52 1082 -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_223_add__right__cancel) # label(axiom). [clausify(272)].
% 2.30/2.52 1083 -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_224_add__left__imp__eq) # label(axiom). [clausify(273)].
% 2.30/2.52 1084 -cancel_semigroup_add(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C) != hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),D),C) | ti(A,B) = ti(A,D) # label(fact_226_add__right__imp__eq) # label(axiom). [clausify(275)].
% 2.30/2.52 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(1077,a,1079,a)].
% 2.30/2.52 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(1077,a,1080,a)].
% 2.30/2.52 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(1077,a,1081,a)].
% 2.30/2.52 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(1077,a,1082,a)].
% 2.30/2.52 1085 cancel_semigroup_add(nat) # label(arity_Nat_Onat___Groups_Ocancel__semigroup__add) # label(axiom). [assumption].
% 2.30/2.52 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(1085,a,1079,a)].
% 2.30/2.52 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(1085,a,1080,a)].
% 2.30/2.52 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(1085,a,1081,a)].
% 2.52/2.73 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(1085,a,1082,a)].
% 2.52/2.73 1086 ab_semigroup_add(int) # label(arity_Int_Oint___Groups_Oab__semigroup__add) # label(axiom). [assumption].
% 2.52/2.73 1087 -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(19)].
% 2.52/2.73 1088 -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_221_ab__semigroup__add__class_Oadd__ac_I1_J) # label(axiom). [clausify(270)].
% 2.52/2.73 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(1086,a,1088,a)].
% 2.52/2.73 1089 ab_semigroup_add(nat) # label(arity_Nat_Onat___Groups_Oab__semigroup__add) # label(axiom). [assumption].
% 2.52/2.73 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(1089,a,1088,a)].
% 2.52/2.73 1090 ab_semigroup_mult(int) # label(arity_Int_Oint___Groups_Oab__semigroup__mult) # label(axiom). [assumption].
% 2.52/2.73 1091 -ab_semigroup_mult(A) | times_times(A) = ti(fun(A,fun(A,A)),times_times(A)) # label(tsy_c_Groups_Otimes__class_Otimes_0_res) # label(axiom). [clausify(20)].
% 2.52/2.73 1092 -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_609_ab__semigroup__mult__class_Omult__ac_I1_J) # label(axiom). [clausify(656)].
% 2.52/2.73 1093 -ab_semigroup_mult(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite(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(A,fun(fun(B,bool),A),hAPP(fun(B,A),fun(A,fun(fun(B,bool),A)),hAPP(fun(A,fun(A,A)),fun(fun(B,A),fun(A,fun(fun(B,bool),A))),finite_fold_image(A,B),times_times(A)),E),F),hAPP(fun(B,bool),fun(B,bool),hAPP(B,fun(fun(B,bool),fun(B,bool)),insert(B),D),C)) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(B,A,E,D)),hAPP(fun(B,bool),A,hAPP(A,fun(fun(B,bool),A),hAPP(fun(B,A),fun(A,fun(fun(B,bool),A)),hAPP(fun(A,fun(A,A)),fun(fun(B,A),fun(A,fun(fun(B,bool),A))),finite_fold_image(A,B),times_times(A)),E),F),C)) # label(fact_735_fold__image__insert) # label(axiom). [clausify(782)].
% 2.52/2.73 1094 -ab_semigroup_mult(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite(B),C)) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f104(B,A,D,E,F,C)),C)) | hAPP(fun(B,bool),A,hAPP(A,fun(fun(B,bool),A),hAPP(fun(B,A),fun(A,fun(fun(B,bool),A)),hAPP(fun(A,fun(A,A)),fun(fun(B,A),fun(A,fun(fun(B,bool),A))),finite_fold_image(A,B),times_times(A)),E),D),C) = hAPP(fun(B,bool),A,hAPP(A,fun(fun(B,bool),A),hAPP(fun(B,A),fun(A,fun(fun(B,bool),A)),hAPP(fun(A,fun(A,A)),fun(fun(B,A),fun(A,fun(fun(B,bool),A))),finite_fold_image(A,B),times_times(A)),F),D),C) # label(fact_808_fold__image__cong) # label(axiom). [clausify(853)].
% 2.52/2.73 1095 -ab_semigroup_mult(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite(B),C)) | hAPP(B,A,D,f104(B,A,E,D,F,C)) != hAPP(B,A,F,f104(B,A,E,D,F,C)) | hAPP(fun(B,bool),A,hAPP(A,fun(fun(B,bool),A),hAPP(fun(B,A),fun(A,fun(fun(B,bool),A)),hAPP(fun(A,fun(A,A)),fun(fun(B,A),fun(A,fun(fun(B,bool),A))),finite_fold_image(A,B),times_times(A)),D),E),C) = hAPP(fun(B,bool),A,hAPP(A,fun(fun(B,bool),A),hAPP(fun(B,A),fun(A,fun(fun(B,bool),A)),hAPP(fun(A,fun(A,A)),fun(fun(B,A),fun(A,fun(fun(B,bool),A))),finite_fold_image(A,B),times_times(A)),F),E),C) # label(fact_808_fold__image__cong) # label(axiom). [clausify(853)].
% 2.52/2.73 Derived: times_times(int) = ti(fun(int,fun(int,int)),times_times(int)). [resolve(1090,a,1091,a)].
% 2.52/2.73 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(1090,a,1092,a)].
% 2.52/2.73 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite(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(int,fun(fun(A,bool),int),hAPP(fun(A,int),fun(int,fun(fun(A,bool),int)),hAPP(fun(int,fun(int,int)),fun(fun(A,int),fun(int,fun(fun(A,bool),int))),finite_fold_image(int,A),times_times(int)),D),E),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),C),B)) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(A,int,D,C)),hAPP(fun(A,bool),int,hAPP(int,fun(fun(A,bool),int),hAPP(fun(A,int),fun(int,fun(fun(A,bool),int)),hAPP(fun(int,fun(int,int)),fun(fun(A,int),fun(int,fun(fun(A,bool),int))),finite_fold_image(int,A),times_times(int)),D),E),B)). [resolve(1090,a,1093,a)].
% 2.52/2.73 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f104(A,int,C,D,E,B)),B)) | hAPP(fun(A,bool),int,hAPP(int,fun(fun(A,bool),int),hAPP(fun(A,int),fun(int,fun(fun(A,bool),int)),hAPP(fun(int,fun(int,int)),fun(fun(A,int),fun(int,fun(fun(A,bool),int))),finite_fold_image(int,A),times_times(int)),D),C),B) = hAPP(fun(A,bool),int,hAPP(int,fun(fun(A,bool),int),hAPP(fun(A,int),fun(int,fun(fun(A,bool),int)),hAPP(fun(int,fun(int,int)),fun(fun(A,int),fun(int,fun(fun(A,bool),int))),finite_fold_image(int,A),times_times(int)),E),C),B). [resolve(1090,a,1094,a)].
% 2.52/2.73 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite(A),B)) | hAPP(A,int,C,f104(A,int,D,C,E,B)) != hAPP(A,int,E,f104(A,int,D,C,E,B)) | hAPP(fun(A,bool),int,hAPP(int,fun(fun(A,bool),int),hAPP(fun(A,int),fun(int,fun(fun(A,bool),int)),hAPP(fun(int,fun(int,int)),fun(fun(A,int),fun(int,fun(fun(A,bool),int))),finite_fold_image(int,A),times_times(int)),C),D),B) = hAPP(fun(A,bool),int,hAPP(int,fun(fun(A,bool),int),hAPP(fun(A,int),fun(int,fun(fun(A,bool),int)),hAPP(fun(int,fun(int,int)),fun(fun(A,int),fun(int,fun(fun(A,bool),int))),finite_fold_image(int,A),times_times(int)),E),D),B). [resolve(1090,a,1095,a)].
% 2.52/2.73 1096 ab_semigroup_mult(nat) # label(arity_Nat_Onat___Groups_Oab__semigroup__mult) # label(axiom). [assumption].
% 2.52/2.73 Derived: times_times(nat) = ti(fun(nat,fun(nat,nat)),times_times(nat)). [resolve(1096,a,1091,a)].
% 2.52/2.73 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(1096,a,1092,a)].
% 2.52/2.73 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite(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(nat,fun(fun(A,bool),nat),hAPP(fun(A,nat),fun(nat,fun(fun(A,bool),nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(A,nat),fun(nat,fun(fun(A,bool),nat))),finite_fold_image(nat,A),times_times(nat)),D),E),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),C),B)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(A,nat,D,C)),hAPP(fun(A,bool),nat,hAPP(nat,fun(fun(A,bool),nat),hAPP(fun(A,nat),fun(nat,fun(fun(A,bool),nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(A,nat),fun(nat,fun(fun(A,bool),nat))),finite_fold_image(nat,A),times_times(nat)),D),E),B)). [resolve(1096,a,1093,a)].
% 2.52/2.73 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f104(A,nat,C,D,E,B)),B)) | hAPP(fun(A,bool),nat,hAPP(nat,fun(fun(A,bool),nat),hAPP(fun(A,nat),fun(nat,fun(fun(A,bool),nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(A,nat),fun(nat,fun(fun(A,bool),nat))),finite_fold_image(nat,A),times_times(nat)),D),C),B) = hAPP(fun(A,bool),nat,hAPP(nat,fun(fun(A,bool),nat),hAPP(fun(A,nat),fun(nat,fun(fun(A,bool),nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(A,nat),fun(nat,fun(fun(A,bool),nat))),finite_fold_image(nat,A),times_times(nat)),E),C),B). [resolve(1096,a,1094,a)].
% 2.70/2.96 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite(A),B)) | hAPP(A,nat,C,f104(A,nat,D,C,E,B)) != hAPP(A,nat,E,f104(A,nat,D,C,E,B)) | hAPP(fun(A,bool),nat,hAPP(nat,fun(fun(A,bool),nat),hAPP(fun(A,nat),fun(nat,fun(fun(A,bool),nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(A,nat),fun(nat,fun(fun(A,bool),nat))),finite_fold_image(nat,A),times_times(nat)),C),D),B) = hAPP(fun(A,bool),nat,hAPP(nat,fun(fun(A,bool),nat),hAPP(fun(A,nat),fun(nat,fun(fun(A,bool),nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(A,nat),fun(nat,fun(fun(A,bool),nat))),finite_fold_image(nat,A),times_times(nat)),E),D),B). [resolve(1096,a,1095,a)].
% 2.70/2.96 1097 monoid_mult(int) # label(arity_Int_Oint___Groups_Omonoid__mult) # label(axiom). [assumption].
% 2.70/2.96 1098 -monoid_mult(A) | times_times(A) = ti(fun(A,fun(A,A)),times_times(A)) # label(tsy_c_Groups_Otimes__class_Otimes_1_res) # label(axiom). [clausify(21)].
% 2.70/2.96 1099 -monoid_mult(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),one_one(A)) = ti(A,B) # label(fact_593_mult__1__right) # label(axiom). [clausify(640)].
% 2.70/2.96 1100 -monoid_mult(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),one_one(A)),B) = ti(A,B) # label(fact_595_mult__1__left) # label(axiom). [clausify(642)].
% 2.70/2.96 Derived: hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),one_one(int)) = ti(int,A). [resolve(1097,a,1099,a)].
% 2.70/2.96 Derived: hAPP(int,int,hAPP(int,fun(int,int),times_times(int),one_one(int)),A) = ti(int,A). [resolve(1097,a,1100,a)].
% 2.70/2.96 1101 monoid_mult(nat) # label(arity_Nat_Onat___Groups_Omonoid__mult) # label(axiom). [assumption].
% 2.70/2.96 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),one_one(nat)) = ti(nat,A). [resolve(1101,a,1099,a)].
% 2.70/2.96 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),one_one(nat)),A) = ti(nat,A). [resolve(1101,a,1100,a)].
% 2.70/2.96 1102 semiring(int) # label(arity_Int_Oint___Rings_Osemiring) # label(axiom). [assumption].
% 2.70/2.96 1103 -semiring(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(22)].
% 2.70/2.96 1104 -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_591_combine__common__factor) # label(axiom). [clausify(638)].
% 2.70/2.96 1105 -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_629_right__distrib__number__of) # label(axiom). [clausify(676)].
% 2.70/2.96 1106 -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_631_left__distrib__number__of) # label(axiom). [clausify(678)].
% 2.70/2.96 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(1102,a,1104,a)].
% 2.70/2.96 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(1102,a,1105,b)].
% 2.91/3.17 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(1102,a,1106,b)].
% 2.91/3.17 1107 semiring(nat) # label(arity_Nat_Onat___Rings_Osemiring) # label(axiom). [assumption].
% 2.91/3.17 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),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(1107,a,1104,a)].
% 2.91/3.17 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(1107,a,1105,b)].
% 2.91/3.17 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(1107,a,1106,b)].
% 2.91/3.17 1108 no_zero_divisors(int) # label(arity_Int_Oint___Rings_Ono__zero__divisors) # label(axiom). [assumption].
% 2.91/3.17 1109 -no_zero_divisors(A) | times_times(A) = ti(fun(A,fun(A,A)),times_times(A)) # label(tsy_c_Groups_Otimes__class_Otimes_3_res) # label(axiom). [clausify(23)].
% 2.91/3.17 1110 -no_zero_divisors(A) | zero_zero(A) = ti(A,B) | zero_zero(A) = ti(A,C) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C) != zero_zero(A) # label(fact_582_no__zero__divisors) # label(axiom). [clausify(629)].
% 2.91/3.17 1111 -no_zero_divisors(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_583_divisors__zero) # label(axiom). [clausify(630)].
% 2.91/3.17 Derived: zero_zero(int) = ti(int,A) | zero_zero(int) = ti(int,B) | hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B) != zero_zero(int). [resolve(1108,a,1110,a)].
% 2.91/3.17 1112 no_zero_divisors(nat) # label(arity_Nat_Onat___Rings_Ono__zero__divisors) # label(axiom). [assumption].
% 2.91/3.17 Derived: zero_zero(nat) = ti(nat,A) | zero_zero(nat) = ti(nat,B) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),B) != zero_zero(nat). [resolve(1112,a,1110,a)].
% 2.91/3.17 1113 mult_zero(int) # label(arity_Int_Oint___Rings_Omult__zero) # label(axiom). [assumption].
% 2.91/3.17 1114 -mult_zero(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(24)].
% 2.91/3.17 1115 -mult_zero(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),zero_zero(A)),B) = zero_zero(A) # label(fact_579_mult__zero__left) # label(axiom). [clausify(626)].
% 2.91/3.17 1116 -mult_zero(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),zero_zero(A)) = zero_zero(A) # label(fact_580_mult__zero__right) # label(axiom). [clausify(627)].
% 2.91/3.17 Derived: hAPP(int,int,hAPP(int,fun(int,int),times_times(int),zero_zero(int)),A) = zero_zero(int). [resolve(1113,a,1115,a)].
% 2.91/3.17 Derived: hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),zero_zero(int)) = zero_zero(int). [resolve(1113,a,1116,a)].
% 2.91/3.17 1117 mult_zero(nat) # label(arity_Nat_Onat___Rings_Omult__zero) # label(axiom). [assumption].
% 2.91/3.17 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),zero_zero(nat)),A) = zero_zero(nat). [resolve(1117,a,1115,a)].
% 3.17/3.39 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),zero_zero(nat)) = zero_zero(nat). [resolve(1117,a,1116,a)].
% 3.17/3.39 1118 zero(int) # label(arity_Int_Oint___Groups_Ozero) # label(axiom). [assumption].
% 3.17/3.39 1119 -zero(A) | zero_zero(A) = ti(A,zero_zero(A)) # label(tsy_c_Groups_Ozero__class_Ozero_res) # label(axiom). [clausify(25)].
% 3.17/3.39 Derived: zero_zero(int) = ti(int,zero_zero(int)). [resolve(1118,a,1119,a)].
% 3.17/3.39 1120 zero(nat) # label(arity_Nat_Onat___Groups_Ozero) # label(axiom). [assumption].
% 3.17/3.39 Derived: zero_zero(nat) = ti(nat,zero_zero(nat)). [resolve(1120,a,1119,a)].
% 3.17/3.39 1121 ring_1(int) # label(arity_Int_Oint___Rings_Oring__1) # label(axiom). [assumption].
% 3.17/3.39 1122 -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(30)].
% 3.17/3.39 1123 -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_578_Ints__diff) # label(axiom). [clausify(625)].
% 3.17/3.39 1124 -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_621_Ints__mult) # label(axiom). [clausify(668)].
% 3.17/3.39 1125 -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_626_Ints__add) # label(axiom). [clausify(673)].
% 3.17/3.39 1126 -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_632_Ints__0) # label(axiom). [clausify(679)].
% 3.17/3.39 1127 -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_633_Ints__1) # label(axiom). [clausify(680)].
% 3.17/3.39 1128 -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_840_Ints__of__nat) # label(axiom). [clausify(881)].
% 3.17/3.39 1129 -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_874_of__nat__diff) # label(axiom). [clausify(912)].
% 3.17/3.39 Derived: ring_1_Ints(int) = ti(fun(int,bool),ring_1_Ints(int)). [resolve(1121,a,1122,a)].
% 3.17/3.39 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(1121,a,1123,a)].
% 3.17/3.39 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(1121,a,1124,a)].
% 3.17/3.39 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(1121,a,1125,a)].
% 3.24/3.50 Derived: hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),zero_zero(int)),ring_1_Ints(int))). [resolve(1121,a,1126,a)].
% 3.24/3.50 Derived: hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),one_one(int)),ring_1_Ints(int))). [resolve(1121,a,1127,a)].
% 3.24/3.50 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(1121,a,1128,a)].
% 3.24/3.50 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(1121,a,1129,a)].
% 3.24/3.50 1130 semiring_1(int) # label(arity_Int_Oint___Rings_Osemiring__1) # label(axiom). [assumption].
% 3.24/3.50 1131 -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(32)].
% 3.24/3.50 1132 -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(33)].
% 3.24/3.50 1133 -semiring_1(A) | hAPP(nat,A,semiring_1_of_nat(A),zero_zero(nat)) = zero_zero(A) # label(fact_835_of__nat__0) # label(axiom). [clausify(878)].
% 3.24/3.50 1134 -semiring_1(A) | hAPP(nat,A,semiring_1_of_nat(A),one_one(nat)) = one_one(A) # label(fact_836_of__nat__1) # label(axiom). [clausify(879)].
% 3.24/3.50 1135 -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_842_of__nat__add) # label(axiom). [clausify(883)].
% 3.24/3.50 1136 -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_854_of__nat__mult) # label(axiom). [clausify(895)].
% 3.24/3.50 1137 -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_873_of__nat__Suc) # label(axiom). [clausify(911)].
% 3.24/3.50 1138 -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_882_semiring__1__class_Oof__nat__code) # label(axiom). [clausify(920)].
% 3.24/3.50 1139 -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_891_of__nat__aux_Osimps_I1_J) # label(axiom). [clausify(928)].
% 3.24/3.50 1140 -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_892_of__nat__aux_Osimps_I2_J) # label(axiom). [clausify(929)].
% 3.24/3.50 Derived: semiring_1_of_nat(int) = ti(fun(nat,int),semiring_1_of_nat(int)). [resolve(1130,a,1131,a)].
% 3.24/3.50 Derived: semiri532925092at_aux(int) = ti(fun(fun(int,int),fun(nat,fun(int,int))),semiri532925092at_aux(int)). [resolve(1130,a,1132,a)].
% 3.24/3.50 Derived: hAPP(nat,int,semiring_1_of_nat(int),zero_zero(nat)) = zero_zero(int). [resolve(1130,a,1133,a)].
% 3.24/3.50 Derived: hAPP(nat,int,semiring_1_of_nat(int),one_one(nat)) = one_one(int). [resolve(1130,a,1134,a)].
% 3.24/3.50 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(1130,a,1135,a)].
% 3.24/3.50 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(1130,a,1136,a)].
% 3.36/3.60 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(1130,a,1137,a)].
% 3.36/3.60 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(1130,a,1138,a)].
% 3.36/3.60 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(1130,a,1139,a)].
% 3.36/3.60 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(1130,a,1140,a)].
% 3.36/3.60 1141 semiring_1(nat) # label(arity_Nat_Onat___Rings_Osemiring__1) # label(axiom). [assumption].
% 3.36/3.60 Derived: semiring_1_of_nat(nat) = ti(fun(nat,nat),semiring_1_of_nat(nat)). [resolve(1141,a,1131,a)].
% 3.36/3.60 Derived: semiri532925092at_aux(nat) = ti(fun(fun(nat,nat),fun(nat,fun(nat,nat))),semiri532925092at_aux(nat)). [resolve(1141,a,1132,a)].
% 3.36/3.60 Derived: hAPP(nat,nat,semiring_1_of_nat(nat),zero_zero(nat)) = zero_zero(nat). [resolve(1141,a,1133,a)].
% 3.36/3.60 Derived: hAPP(nat,nat,semiring_1_of_nat(nat),one_one(nat)) = one_one(nat). [resolve(1141,a,1134,a)].
% 3.36/3.60 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(1141,a,1135,a)].
% 3.36/3.60 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(1141,a,1136,a)].
% 3.36/3.60 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(1141,a,1137,a)].
% 3.36/3.60 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(1141,a,1138,a)].
% 3.36/3.60 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(1141,a,1139,a)].
% 3.36/3.60 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(1141,a,1140,a)].
% 3.36/3.60 1142 linorder(int) # label(arity_Int_Oint___Orderings_Olinorder) # label(axiom). [assumption].
% 3.36/3.60 1143 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),B)) # label(fact_58_linorder__linear) # label(axiom). [clausify(107)].
% 3.36/3.60 1144 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),B)) # label(fact_70_linorder__le__cases) # label(axiom). [clausify(119)].
% 3.36/3.60 1145 -linorder(A) | ti(A,B) = ti(A,C) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) # label(fact_305_linorder__neq__iff) # label(axiom). [clausify(354)].
% 3.36/3.60 1146 -linorder(A) | ti(A,B) != ti(A,C) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B)) # label(fact_305_linorder__neq__iff) # label(axiom). [clausify(354)].
% 3.36/3.60 1147 -linorder(A) | ti(A,B) != ti(A,C) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) # label(fact_305_linorder__neq__iff) # label(axiom). [clausify(354)].
% 3.36/3.60 1148 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B)) | ti(A,C) = ti(A,B) # label(fact_306_not__less__iff__gr__or__eq) # label(axiom). [clausify(355)].
% 3.36/3.60 1149 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B)) # label(fact_306_not__less__iff__gr__or__eq) # label(axiom). [clausify(355)].
% 3.36/3.60 1150 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | ti(A,C) != ti(A,B) # label(fact_306_not__less__iff__gr__or__eq) # label(axiom). [clausify(355)].
% 3.36/3.60 1151 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | ti(A,C) = ti(A,B) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B)) # label(fact_307_linorder__less__linear) # label(axiom). [clausify(356)].
% 3.36/3.60 1152 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B)) | ti(A,B) = ti(A,C) # label(fact_308_linorder__antisym__conv3) # label(axiom). [clausify(357)].
% 3.36/3.60 1153 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B)) | ti(A,B) != ti(A,C) # label(fact_308_linorder__antisym__conv3) # label(axiom). [clausify(357)].
% 3.36/3.60 1154 -linorder(A) | ti(A,B) = ti(A,C) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) # label(fact_309_linorder__neqE) # label(axiom). [clausify(358)].
% 3.36/3.60 1155 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | ti(A,C) = ti(A,B) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B)) # label(fact_325_linorder__cases) # label(axiom). [clausify(374)].
% 3.36/3.60 1156 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),B)) # label(fact_326_linorder__not__less) # label(axiom). [clausify(375)].
% 3.36/3.60 1157 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),B)) # label(fact_326_linorder__not__less) # label(axiom). [clausify(375)].
% 3.36/3.60 1158 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B)) # label(fact_327_linorder__not__le) # label(axiom). [clausify(376)].
% 3.36/3.60 1159 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B)) # label(fact_327_linorder__not__le) # label(axiom). [clausify(376)].
% 3.36/3.60 1160 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B)) # label(fact_328_linorder__le__less__linear) # label(axiom). [clausify(377)].
% 3.36/3.60 1161 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),B)) # label(fact_332_leI) # label(axiom). [clausify(381)].
% 3.36/3.60 1162 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B)) # label(fact_333_not__leE) # label(axiom). [clausify(382)].
% 3.36/3.60 1163 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | ti(A,C) = ti(A,B) # label(fact_334_linorder__antisym__conv1) # label(axiom). [clausify(383)].
% 3.36/3.60 1164 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | ti(A,C) != ti(A,B) # label(fact_334_linorder__antisym__conv1) # label(axiom). [clausify(383)].
% 3.36/3.60 1165 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B)) # label(fact_337_leD) # label(axiom). [clausify(386)].
% 3.36/3.61 1166 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | ti(A,C) = ti(A,B) # label(fact_339_linorder__antisym__conv2) # label(axiom). [clausify(388)].
% 3.36/3.61 1167 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | ti(A,C) != ti(A,B) # label(fact_339_linorder__antisym__conv2) # label(axiom). [clausify(388)].
% 3.36/3.61 1168 -number(A) | -linorder(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(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),C)),hAPP(int,A,number_number_of(A),B))) # label(fact_651_le__number__of__eq__not__less) # label(axiom). [clausify(698)].
% 3.36/3.61 1169 -number(A) | -linorder(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(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),C)),hAPP(int,A,number_number_of(A),B))) # label(fact_651_le__number__of__eq__not__less) # label(axiom). [clausify(698)].
% 3.36/3.61 1170 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),f110(A,C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),B)) # label(fact_820_minf_I8_J) # label(axiom). [clausify(863)].
% 3.36/3.61 1171 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),f111(A,B)),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),B)) # label(fact_821_pinf_I6_J) # label(axiom). [clausify(864)].
% 3.36/3.61 1172 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),f112(A,C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) # label(fact_822_minf_I6_J) # label(axiom). [clausify(865)].
% 3.36/3.61 1173 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),f113(A,B)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) # label(fact_823_pinf_I8_J) # label(axiom). [clausify(866)].
% 3.36/3.61 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),A)). [resolve(1142,a,1143,a)].
% 3.36/3.61 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(1142,a,1145,a)].
% 3.36/3.61 Derived: ti(int,A) != ti(int,B) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),A)). [resolve(1142,a,1146,a)].
% 3.36/3.61 Derived: ti(int,A) != ti(int,B) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)). [resolve(1142,a,1147,a)].
% 3.36/3.61 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),A)). [resolve(1142,a,1149,a)].
% 3.36/3.61 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),A)). [resolve(1142,a,1156,a)].
% 3.36/3.61 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),A)). [resolve(1142,a,1157,a)].
% 3.36/3.61 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)) | ti(int,B) = ti(int,A). [resolve(1142,a,1163,a)].
% 3.36/3.61 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)) | ti(int,B) != ti(int,A). [resolve(1142,a,1164,a)].
% 3.36/3.61 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),f110(int,B))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),A)). [resolve(1142,a,1170,a)].
% 3.36/3.61 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),f111(int,A)),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),A)). [resolve(1142,a,1171,a)].
% 3.36/3.61 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),f112(int,B))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)). [resolve(1142,a,1172,a)].
% 3.48/3.72 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),f113(int,A)),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)). [resolve(1142,a,1173,a)].
% 3.48/3.72 1174 linorder(nat) # label(arity_Nat_Onat___Orderings_Olinorder) # label(axiom). [assumption].
% 3.48/3.72 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),A)). [resolve(1174,a,1143,a)].
% 3.48/3.72 Derived: ti(nat,A) = ti(nat,B) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),A)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)). [resolve(1174,a,1145,a)].
% 3.48/3.72 Derived: ti(nat,A) != ti(nat,B) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),A)). [resolve(1174,a,1146,a)].
% 3.48/3.72 Derived: ti(nat,A) != ti(nat,B) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)). [resolve(1174,a,1147,a)].
% 3.48/3.72 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),A)). [resolve(1174,a,1149,a)].
% 3.48/3.72 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),A)). [resolve(1174,a,1156,a)].
% 3.48/3.72 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),A)). [resolve(1174,a,1157,a)].
% 3.48/3.72 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | ti(nat,B) = ti(nat,A). [resolve(1174,a,1163,a)].
% 3.48/3.72 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | ti(nat,B) != ti(nat,A). [resolve(1174,a,1164,a)].
% 3.48/3.72 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),f110(nat,B))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),A)). [resolve(1174,a,1170,a)].
% 3.48/3.72 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),f111(nat,A)),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),A)). [resolve(1174,a,1171,a)].
% 3.48/3.72 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),f112(nat,B))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)). [resolve(1174,a,1172,a)].
% 3.48/3.72 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),f113(nat,A)),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)). [resolve(1174,a,1173,a)].
% 3.48/3.72 1175 ordered_ab_group_add(int) # label(arity_Int_Oint___Groups_Oordered__ab__group__add) # label(axiom). [assumption].
% 3.48/3.72 1176 -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_117_diff__eq__diff__less__eq) # label(axiom). [clausify(166)].
% 3.48/3.72 1177 -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_117_diff__eq__diff__less__eq) # label(axiom). [clausify(166)].
% 3.48/3.72 1178 -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_356_diff__eq__diff__less) # label(axiom). [clausify(405)].
% 3.48/3.72 1179 -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_356_diff__eq__diff__less) # label(axiom). [clausify(405)].
% 3.48/3.72 1180 -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_504_le__iff__diff__le__0) # label(axiom). [clausify(552)].
% 3.60/3.82 1181 -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_504_le__iff__diff__le__0) # label(axiom). [clausify(552)].
% 3.60/3.82 1182 -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_505_less__iff__diff__less__0) # label(axiom). [clausify(553)].
% 3.60/3.82 1183 -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_505_less__iff__diff__less__0) # label(axiom). [clausify(553)].
% 3.60/3.82 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(1175,a,1176,a)].
% 3.60/3.82 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(1175,a,1177,a)].
% 3.60/3.82 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(1175,a,1178,a)].
% 3.60/3.82 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(1175,a,1179,a)].
% 3.60/3.82 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),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),B)),zero_zero(int))). [resolve(1175,a,1180,a)].
% 3.60/3.82 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),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),B)),zero_zero(int))). [resolve(1175,a,1181,a)].
% 3.60/3.82 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(1175,a,1182,a)].
% 3.60/3.82 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(1175,a,1183,a)].
% 3.60/3.82 1184 ab_group_add(int) # label(arity_Int_Oint___Groups_Oab__group__add) # label(axiom). [assumption].
% 3.60/3.82 1185 -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_178_diff__eq__diff__eq) # label(axiom). [clausify(227)].
% 3.60/3.82 1186 -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_178_diff__eq__diff__eq) # label(axiom). [clausify(227)].
% 3.60/3.82 1187 -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_471_eq__iff__diff__eq__0) # label(axiom). [clausify(520)].
% 3.60/3.82 1188 -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_471_eq__iff__diff__eq__0) # label(axiom). [clausify(520)].
% 3.60/3.82 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(1184,a,1185,a)].
% 3.80/4.03 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(1184,a,1186,a)].
% 3.80/4.03 Derived: ti(int,A) != ti(int,B) | hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),B),A) = zero_zero(int). [resolve(1184,a,1187,a)].
% 3.80/4.03 Derived: ti(int,A) = ti(int,B) | hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),B),A) != zero_zero(int). [resolve(1184,a,1188,a)].
% 3.80/4.03 1189 cancel146912293up_add(int) # label(arity_Int_Oint___Groups_Ocancel__ab__semigroup__add) # label(axiom). [assumption].
% 3.80/4.03 1190 -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_225_add__imp__eq) # label(axiom). [clausify(274)].
% 3.80/4.03 1191 cancel146912293up_add(nat) # label(arity_Nat_Onat___Groups_Ocancel__ab__semigroup__add) # label(axiom). [assumption].
% 3.80/4.03 1192 ordere236663937imp_le(int) # label(arity_Int_Oint___Groups_Oordered__ab__semigroup__add__imp__le) # label(axiom). [assumption].
% 3.80/4.03 1193 -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_233_add__le__cancel__right) # label(axiom). [clausify(282)].
% 3.80/4.03 1194 -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_233_add__le__cancel__right) # label(axiom). [clausify(282)].
% 3.80/4.03 1195 -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_234_add__le__cancel__left) # label(axiom). [clausify(283)].
% 3.80/4.03 1196 -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_234_add__le__cancel__left) # label(axiom). [clausify(283)].
% 3.80/4.03 1197 -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_238_add__le__imp__le__right) # label(axiom). [clausify(287)].
% 3.80/4.03 1198 -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_239_add__le__imp__le__left) # label(axiom). [clausify(288)].
% 3.80/4.03 1199 -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_347_add__less__cancel__right) # label(axiom). [clausify(396)].
% 3.80/4.03 1200 -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_347_add__less__cancel__right) # label(axiom). [clausify(396)].
% 3.80/4.03 1201 -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_348_add__less__cancel__left) # label(axiom). [clausify(397)].
% 3.80/4.03 1202 -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_348_add__less__cancel__left) # label(axiom). [clausify(397)].
% 3.80/4.03 1203 -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_352_add__less__imp__less__right) # label(axiom). [clausify(401)].
% 3.80/4.03 1204 -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_353_add__less__imp__less__left) # label(axiom). [clausify(402)].
% 3.80/4.03 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(1192,a,1193,a)].
% 3.80/4.03 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(1192,a,1194,a)].
% 3.80/4.03 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(1192,a,1195,a)].
% 3.80/4.03 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(1192,a,1196,a)].
% 3.80/4.03 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(1192,a,1199,a)].
% 3.80/4.03 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(1192,a,1200,a)].
% 3.80/4.03 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(1192,a,1201,a)].
% 3.80/4.03 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(1192,a,1202,a)].
% 3.80/4.03 1205 ordere236663937imp_le(nat) # label(arity_Nat_Onat___Groups_Oordered__ab__semigroup__add__imp__le) # label(axiom). [assumption].
% 3.80/4.03 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(1205,a,1193,a)].
% 3.80/4.03 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(1205,a,1194,a)].
% 3.80/4.03 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(1205,a,1195,a)].
% 3.80/4.03 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(1205,a,1196,a)].
% 4.04/4.24 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(1205,a,1199,a)].
% 4.04/4.24 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(1205,a,1200,a)].
% 4.04/4.24 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(1205,a,1201,a)].
% 4.04/4.24 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(1205,a,1202,a)].
% 4.04/4.24 1206 ordere779506340up_add(int) # label(arity_Int_Oint___Groups_Oordered__ab__semigroup__add) # label(axiom). [assumption].
% 4.04/4.24 1207 -ordere779506340up_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),D)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),D))) # label(fact_235_add__right__mono) # label(axiom). [clausify(284)].
% 4.04/4.24 1208 -ordere779506340up_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),D),B)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),D),C))) # label(fact_236_add__left__mono) # label(axiom). [clausify(285)].
% 4.04/4.24 1209 -ordere779506340up_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),D),E)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),D)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),E))) # label(fact_237_add__mono) # label(axiom). [clausify(286)].
% 4.04/4.24 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),C),D)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),C)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),B),D))). [resolve(1206,a,1209,a)].
% 4.04/4.24 1210 ordere779506340up_add(nat) # label(arity_Nat_Onat___Groups_Oordered__ab__semigroup__add) # label(axiom). [assumption].
% 4.04/4.24 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),C),D)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),C)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),D))). [resolve(1210,a,1209,a)].
% 4.04/4.24 1211 group_add(int) # label(arity_Int_Oint___Groups_Ogroup__add) # label(axiom). [assumption].
% 4.04/4.24 1212 -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_240_diff__add__cancel) # label(axiom). [clausify(289)].
% 4.04/4.24 1213 -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_241_add__diff__cancel) # label(axiom). [clausify(290)].
% 4.04/4.24 1214 -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_470_right__minus__eq) # label(axiom). [clausify(519)].
% 4.04/4.24 1215 -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_470_right__minus__eq) # label(axiom). [clausify(519)].
% 4.04/4.24 1216 -group_add(A) | hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),B) = zero_zero(A) # label(fact_472_diff__self) # label(axiom). [clausify(521)].
% 4.10/4.35 1217 -group_add(A) | hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),zero_zero(A)) = ti(A,B) # label(fact_473_diff__0__right) # label(axiom). [clausify(522)].
% 4.10/4.35 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(1211,a,1212,a)].
% 4.10/4.35 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(1211,a,1213,a)].
% 4.10/4.35 Derived: hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),A) = zero_zero(int). [resolve(1211,a,1216,a)].
% 4.10/4.35 Derived: hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),zero_zero(int)) = ti(int,A). [resolve(1211,a,1217,a)].
% 4.10/4.35 1218 ordere223160158up_add(int) # label(arity_Int_Oint___Groups_Oordered__cancel__ab__semigroup__add) # label(axiom). [assumption].
% 4.10/4.35 1219 -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_349_add__strict__right__mono) # label(axiom). [clausify(398)].
% 4.10/4.35 1220 -ordere223160158up_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(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_350_add__strict__left__mono) # label(axiom). [clausify(399)].
% 4.10/4.35 1221 -ordere223160158up_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),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_351_add__strict__mono) # label(axiom). [clausify(400)].
% 4.10/4.35 1222 -ordere223160158up_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_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_391_add__less__le__mono) # label(axiom). [clausify(440)].
% 4.10/4.35 1223 -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_392_add__le__less__mono) # label(axiom). [clausify(441)].
% 4.10/4.35 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(1218,a,1221,a)].
% 4.10/4.35 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(1218,a,1222,a)].
% 4.10/4.35 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(1218,a,1223,a)].
% 4.10/4.35 1224 ordere223160158up_add(nat) # label(arity_Nat_Onat___Groups_Oordered__cancel__ab__semigroup__add) # label(axiom). [assumption].
% 4.10/4.35 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(1224,a,1221,a)].
% 4.24/4.45 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(1224,a,1222,a)].
% 4.24/4.45 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(1224,a,1223,a)].
% 4.24/4.45 1225 linordered_semidom(int) # label(arity_Int_Oint___Rings_Olinordered__semidom) # label(axiom). [assumption].
% 4.24/4.45 1226 -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_414_less__add__one) # label(axiom). [clausify(463)].
% 4.24/4.45 1227 -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_503_pos__add__strict) # label(axiom). [clausify(551)].
% 4.24/4.45 1228 -linordered_semidom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),one_one(A)),zero_zero(A))) # label(fact_506_not__one__le__zero) # label(axiom). [clausify(554)].
% 4.24/4.45 1229 -linordered_semidom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),one_one(A))) # label(fact_507_zero__le__one) # label(axiom). [clausify(555)].
% 4.24/4.45 1230 -linordered_semidom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),one_one(A))) # label(fact_508_zero__less__one) # label(axiom). [clausify(556)].
% 4.24/4.45 1231 -linordered_semidom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),zero_zero(A))) # label(fact_509_not__one__less__zero) # label(axiom). [clausify(557)].
% 4.24/4.45 1232 -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_531_zero__less__two) # label(axiom). [clausify(578)].
% 4.24/4.45 1233 -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_689_less__1__mult) # label(axiom). [clausify(736)].
% 4.24/4.45 1234 -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_832_of__nat__0__le__iff) # label(axiom). [clausify(875)].
% 4.24/4.45 1235 -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_833_zero__le__imp__of__nat) # label(axiom). [clausify(876)].
% 4.24/4.45 1236 -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_834_of__nat__less__0__iff) # label(axiom). [clausify(877)].
% 4.24/4.45 1237 -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_843_of__nat__le__iff) # label(axiom). [clausify(884)].
% 4.24/4.45 1238 -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_843_of__nat__le__iff) # label(axiom). [clausify(884)].
% 4.24/4.45 1239 -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_844_of__nat__less__iff) # label(axiom). [clausify(885)].
% 4.24/4.45 1240 -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_844_of__nat__less__iff) # label(axiom). [clausify(885)].
% 4.24/4.45 1241 -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_845_less__imp__of__nat__less) # label(axiom). [clausify(886)].
% 4.24/4.45 1242 -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_846_of__nat__less__imp__less) # label(axiom). [clausify(887)].
% 4.24/4.45 1243 -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_877_of__nat__0__less__iff) # label(axiom). [clausify(915)].
% 4.24/4.45 1244 -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_877_of__nat__0__less__iff) # label(axiom). [clausify(915)].
% 4.24/4.45 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(1225,a,1226,a)].
% 4.24/4.45 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(1225,a,1227,a)].
% 4.24/4.45 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),zero_zero(int))). [resolve(1225,a,1228,a)].
% 4.24/4.45 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),one_one(int))). [resolve(1225,a,1229,a)].
% 4.24/4.45 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),one_one(int))). [resolve(1225,a,1230,a)].
% 4.24/4.45 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),zero_zero(int))). [resolve(1225,a,1231,a)].
% 4.24/4.45 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(1225,a,1232,a)].
% 4.24/4.45 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(1225,a,1233,a)].
% 4.24/4.45 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(1225,a,1234,a)].
% 4.24/4.45 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(1225,a,1236,a)].
% 4.24/4.45 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(1225,a,1237,a)].
% 4.24/4.45 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(1225,a,1238,a)].
% 4.24/4.45 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(1225,a,1239,a)].
% 4.24/4.45 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(1225,a,1240,a)].
% 4.35/4.56 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(1225,a,1243,a)].
% 4.35/4.56 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(1225,a,1244,a)].
% 4.35/4.56 1245 linordered_semidom(nat) # label(arity_Nat_Onat___Rings_Olinordered__semidom) # label(axiom). [assumption].
% 4.35/4.56 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(1245,a,1226,a)].
% 4.35/4.56 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(1245,a,1227,a)].
% 4.35/4.56 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),one_one(nat)),zero_zero(nat))). [resolve(1245,a,1228,a)].
% 4.35/4.56 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),one_one(nat))). [resolve(1245,a,1229,a)].
% 4.35/4.56 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),one_one(nat))). [resolve(1245,a,1230,a)].
% 4.35/4.56 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),one_one(nat)),zero_zero(nat))). [resolve(1245,a,1231,a)].
% 4.35/4.56 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(1245,a,1232,a)].
% 4.35/4.56 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(1245,a,1233,a)].
% 4.35/4.56 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(1245,a,1234,a)].
% 4.35/4.56 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(1245,a,1236,a)].
% 4.35/4.56 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(1245,a,1237,a)].
% 4.35/4.56 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(1245,a,1238,a)].
% 4.35/4.56 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(1245,a,1239,a)].
% 4.35/4.56 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(1245,a,1240,a)].
% 4.35/4.56 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(1245,a,1243,a)].
% 4.35/4.56 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(1245,a,1244,a)].
% 4.35/4.56 1246 linordered_idom(int) # label(arity_Int_Oint___Rings_Olinordered__idom) # label(axiom). [assumption].
% 4.35/4.56 1247 -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_423_linorder__neqE__linordered__idom) # label(axiom). [clausify(472)].
% 4.35/4.56 1248 -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_554_even__less__0__iff) # label(axiom). [clausify(601)].
% 4.35/4.56 1249 -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_554_even__less__0__iff) # label(axiom). [clausify(601)].
% 4.35/4.56 1250 -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_575_Ints__odd__less__0) # label(axiom). [clausify(622)].
% 4.35/4.56 1251 -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_575_Ints__odd__less__0) # label(axiom). [clausify(622)].
% 4.35/4.56 1252 -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_614_less__number__of) # label(axiom). [clausify(661)].
% 4.35/4.56 1253 -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_614_less__number__of) # label(axiom). [clausify(661)].
% 4.35/4.56 1254 -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_622_le__number__of) # label(axiom). [clausify(669)].
% 4.35/4.56 1255 -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_622_le__number__of) # label(axiom). [clausify(669)].
% 4.35/4.56 1256 -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_723_mult__left__le__one__le) # label(axiom). [clausify(770)].
% 4.35/4.56 1257 -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_724_mult__right__le__one__le) # label(axiom). [clausify(771)].
% 4.35/4.56 1258 -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_915_abs__mult__less) # label(axiom). [clausify(952)].
% 4.35/4.56 1259 -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_920_abs__mult__pos) # label(axiom). [clausify(957)].
% 4.35/4.56 1260 -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_921_abs__mult) # label(axiom). [clausify(958)].
% 4.35/4.56 1261 -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_922_abs__mult__self) # label(axiom). [clausify(959)].
% 4.35/4.56 1262 -linordered_idom(A) | hAPP(A,A,abs_abs(A),one_one(A)) = one_one(A) # label(fact_927_abs__one) # label(axiom). [clausify(963)].
% 4.35/4.56 1263 -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_932_abs__of__nat) # label(axiom). [clausify(967)].
% 4.35/4.56 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(1246,a,1248,a)].
% 4.35/4.56 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(1246,a,1249,a)].
% 4.35/4.56 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(1246,a,1250,a)].
% 4.35/4.56 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(1246,a,1251,a)].
% 4.35/4.56 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(1246,a,1252,b)].
% 4.35/4.56 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(1246,a,1253,b)].
% 4.35/4.56 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(1246,a,1254,b)].
% 4.35/4.56 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(1246,a,1255,b)].
% 4.35/4.56 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(1246,a,1256,a)].
% 4.35/4.56 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(1246,a,1257,a)].
% 4.75/4.96 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(1246,a,1258,a)].
% 4.75/4.96 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(1246,a,1259,a)].
% 4.75/4.96 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(1246,a,1260,a)].
% 4.75/4.96 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(1246,a,1261,a)].
% 4.75/4.96 Derived: hAPP(int,int,abs_abs(int),one_one(int)) = one_one(int). [resolve(1246,a,1262,a)].
% 4.75/4.96 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(1246,a,1263,a)].
% 4.75/4.96 1264 zero_neq_one(int) # label(arity_Int_Oint___Rings_Ozero__neq__one) # label(axiom). [assumption].
% 4.75/4.96 1265 -zero_neq_one(A) | zero_zero(A) != one_one(A) # label(fact_463_one__neq__zero) # label(axiom). [clausify(512)].
% 4.75/4.96 1266 -zero_neq_one(A) | zero_zero(A) != one_one(A) # label(fact_464_zero__neq__one) # label(axiom). [clausify(513)].
% 4.75/4.96 Derived: zero_zero(int) != one_one(int). [resolve(1264,a,1265,a)].
% 4.75/4.96 1267 zero_neq_one(nat) # label(arity_Nat_Onat___Rings_Ozero__neq__one) # label(axiom). [assumption].
% 4.75/4.96 Derived: zero_zero(nat) != one_one(nat). [resolve(1267,a,1265,a)].
% 4.75/4.96 1268 comm_monoid_add(int) # label(arity_Int_Oint___Groups_Ocomm__monoid__add) # label(axiom). [assumption].
% 4.75/4.96 1269 -comm_monoid_add(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),zero_zero(A)) = ti(A,B) # label(fact_465_add_Ocomm__neutral) # label(axiom). [clausify(514)].
% 4.75/4.96 1270 -comm_monoid_add(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),zero_zero(A)),B) = ti(A,B) # label(fact_468_add__0) # label(axiom). [clausify(517)].
% 4.75/4.96 1271 comm_monoid_add(nat) # label(arity_Nat_Onat___Groups_Ocomm__monoid__add) # label(axiom). [assumption].
% 4.75/4.96 1272 linord219039673up_add(int) # label(arity_Int_Oint___Groups_Olinordered__ab__group__add) # label(axiom). [assumption].
% 4.75/4.96 1273 -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_467_double__zero__sym) # label(axiom). [clausify(516)].
% 4.75/4.96 1274 -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_467_double__zero__sym) # label(axiom). [clausify(516)].
% 4.75/4.96 1275 -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_492_zero__le__double__add__iff__zero__le__single__add) # label(axiom). [clausify(540)].
% 4.75/4.96 1276 -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_492_zero__le__double__add__iff__zero__le__single__add) # label(axiom). [clausify(540)].
% 4.75/4.96 1277 -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_493_double__add__le__zero__iff__single__add__le__zero) # label(axiom). [clausify(541)].
% 4.82/5.06 1278 -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_493_double__add__le__zero__iff__single__add__le__zero) # label(axiom). [clausify(541)].
% 4.82/5.06 1279 -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_499_zero__less__double__add__iff__zero__less__single__add) # label(axiom). [clausify(547)].
% 4.82/5.06 1280 -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_499_zero__less__double__add__iff__zero__less__single__add) # label(axiom). [clausify(547)].
% 4.82/5.06 1281 -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_500_double__add__less__zero__iff__single__add__less__zero) # label(axiom). [clausify(548)].
% 4.82/5.06 1282 -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_500_double__add__less__zero__iff__single__add__less__zero) # label(axiom). [clausify(548)].
% 4.82/5.06 1283 -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_555_double__eq__0__iff) # label(axiom). [clausify(602)].
% 4.82/5.06 1284 -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_555_double__eq__0__iff) # label(axiom). [clausify(602)].
% 4.82/5.06 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),A) != zero_zero(int) | zero_zero(int) = ti(int,A). [resolve(1272,a,1273,a)].
% 4.82/5.06 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),A) = zero_zero(int) | zero_zero(int) != ti(int,A). [resolve(1272,a,1274,a)].
% 4.82/5.06 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(1272,a,1275,a)].
% 4.82/5.06 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(1272,a,1276,a)].
% 4.82/5.06 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(1272,a,1277,a)].
% 4.82/5.06 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(1272,a,1278,a)].
% 4.82/5.06 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(1272,a,1279,a)].
% 4.82/5.06 1285 ordere216010020id_add(int) # label(arity_Int_Oint___Groups_Oordered__comm__monoid__add) # label(axiom). [assumption].
% 4.82/5.06 1286 -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_494_add__nonneg__nonneg) # label(axiom). [clausify(542)].
% 4.82/5.06 1287 -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_495_add__nonneg__eq__0__iff) # label(axiom). [clausify(543)].
% 4.82/5.06 1288 -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_495_add__nonneg__eq__0__iff) # label(axiom). [clausify(543)].
% 4.82/5.06 1289 -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_495_add__nonneg__eq__0__iff) # label(axiom). [clausify(543)].
% 4.82/5.06 1290 -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_496_add__increasing) # label(axiom). [clausify(544)].
% 4.82/5.06 1291 -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_497_add__increasing2) # label(axiom). [clausify(545)].
% 4.82/5.06 1292 -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_498_add__nonpos__nonpos) # label(axiom). [clausify(546)].
% 4.82/5.06 1293 -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_501_add__pos__pos) # label(axiom). [clausify(549)].
% 4.82/5.06 1294 -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_502_add__neg__neg) # label(axiom). [clausify(550)].
% 4.82/5.06 1295 -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_525_add__pos__nonneg) # label(axiom). [clausify(572)].
% 4.82/5.06 1296 -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_526_add__nonneg__pos) # label(axiom). [clausify(573)].
% 4.82/5.06 1297 -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_527_add__strict__increasing) # label(axiom). [clausify(574)].
% 4.82/5.06 1298 -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_528_add__strict__increasing2) # label(axiom). [clausify(575)].
% 4.82/5.06 1299 -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_529_add__neg__nonpos) # label(axiom). [clausify(576)].
% 4.82/5.06 1300 -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_530_add__nonpos__neg) # label(axiom). [clausify(577)].
% 4.82/5.06 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(1285,a,1286,a)].
% 4.82/5.06 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(1285,a,1287,a)].
% 4.82/5.06 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(1285,a,1288,a)].
% 4.82/5.06 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(1285,a,1289,a)].
% 4.82/5.06 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(1285,a,1290,a)].
% 4.82/5.06 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(1285,a,1291,a)].
% 4.82/5.06 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(1285,a,1292,a)].
% 4.82/5.06 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(1285,a,1294,a)].
% 4.82/5.06 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B))). [resolve(1285,a,1295,a)].
% 4.82/5.06 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B))). [resolve(1285,a,1296,a)].
% 4.82/5.06 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(1285,a,1297,a)].
% 4.82/5.06 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(1285,a,1298,a)].
% 4.82/5.06 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(1285,a,1299,a)].
% 4.82/5.06 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(1285,a,1300,a)].
% 4.82/5.06 1301 ordere216010020id_add(nat) # label(arity_Nat_Onat___Groups_Oordered__comm__monoid__add) # label(axiom). [assumption].
% 4.82/5.06 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(1301,a,1286,a)].
% 4.82/5.06 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(1301,a,1287,a)].
% 4.82/5.06 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(1301,a,1288,a)].
% 4.82/5.06 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(1301,a,1289,a)].
% 4.82/5.06 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(1301,a,1290,a)].
% 4.82/5.06 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(1301,a,1291,a)].
% 4.82/5.06 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(1301,a,1292,a)].
% 4.82/5.06 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(1301,a,1294,a)].
% 4.82/5.06 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B))). [resolve(1301,a,1295,a)].
% 4.95/5.17 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B))). [resolve(1301,a,1296,a)].
% 4.95/5.17 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(1301,a,1297,a)].
% 4.95/5.17 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(1301,a,1298,a)].
% 4.95/5.17 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(1301,a,1299,a)].
% 4.95/5.17 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(1301,a,1300,a)].
% 4.95/5.17 1302 comm_semiring_1(int) # label(arity_Int_Oint___Rings_Ocomm__semiring__1) # label(axiom). [assumption].
% 4.95/5.17 1303 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),zero_zero(A)),B) = ti(A,B) # label(fact_561_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) # label(axiom). [clausify(608)].
% 4.95/5.17 1304 -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_562_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) # label(axiom). [clausify(609)].
% 4.95/5.17 1305 -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_563_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) # label(axiom). [clausify(610)].
% 4.95/5.17 1306 -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_564_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) # label(axiom). [clausify(611)].
% 4.95/5.17 1307 -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_565_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) # label(axiom). [clausify(612)].
% 4.95/5.17 1308 -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_566_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) # label(axiom). [clausify(613)].
% 4.95/5.17 1309 -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_567_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) # label(axiom). [clausify(614)].
% 4.95/5.17 1310 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),zero_zero(A)) = ti(A,B) # label(fact_569_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) # label(axiom). [clausify(616)].
% 4.95/5.17 1311 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),one_one(A)),B) = ti(A,B) # label(fact_634_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J) # label(axiom). [clausify(681)].
% 4.95/5.17 1312 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),one_one(A)) = ti(A,B) # label(fact_635_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J) # label(axiom). [clausify(682)].
% 4.95/5.17 1313 -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_636_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) # label(axiom). [clausify(683)].
% 4.95/5.17 1314 -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_637_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J) # label(axiom). [clausify(684)].
% 4.95/5.17 1315 -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_638_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J) # label(axiom). [clausify(685)].
% 4.95/5.17 1316 -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_639_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J) # label(axiom). [clausify(686)].
% 4.95/5.17 1317 -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_640_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J) # label(axiom). [clausify(687)].
% 4.95/5.17 1318 -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_641_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J) # label(axiom). [clausify(688)].
% 4.95/5.17 1319 -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_642_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J) # label(axiom). [clausify(689)].
% 4.95/5.17 1320 -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_643_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J) # label(axiom). [clausify(690)].
% 4.95/5.17 1321 -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_644_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J) # label(axiom). [clausify(691)].
% 4.95/5.17 1322 -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_646_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J) # label(axiom). [clausify(693)].
% 4.95/5.17 1323 -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_647_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J) # label(axiom). [clausify(694)].
% 4.95/5.17 1324 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),zero_zero(A)),B) = zero_zero(A) # label(fact_649_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J) # label(axiom). [clausify(696)].
% 4.95/5.17 1325 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),zero_zero(A)) = zero_zero(A) # label(fact_650_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J) # label(axiom). [clausify(697)].
% 4.95/5.17 1326 -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_692_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J) # label(axiom). [clausify(739)].
% 4.95/5.17 1327 -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_693_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J) # label(axiom). [clausify(740)].
% 4.95/5.17 1328 -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_694_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J) # label(axiom). [clausify(741)].
% 4.95/5.17 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(1302,a,1304,a)].
% 4.95/5.17 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(1302,a,1305,a)].
% 4.95/5.17 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(1302,a,1308,a)].
% 4.95/5.17 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(1302,a,1309,a)].
% 4.95/5.17 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(1302,a,1313,a)].
% 4.95/5.17 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(1302,a,1314,a)].
% 4.95/5.17 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(1302,a,1317,a)].
% 4.95/5.17 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(1302,a,1320,a)].
% 4.95/5.17 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(1302,a,1321,a)].
% 4.95/5.17 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(1302,a,1322,a)].
% 4.95/5.17 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(1302,a,1326,a)].
% 4.95/5.17 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(1302,a,1327,a)].
% 4.95/5.17 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(1302,a,1328,a)].
% 4.95/5.17 1329 comm_semiring_1(nat) # label(arity_Nat_Onat___Rings_Ocomm__semiring__1) # label(axiom). [assumption].
% 4.95/5.17 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(1329,a,1304,a)].
% 4.95/5.17 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(1329,a,1305,a)].
% 4.95/5.17 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(1329,a,1308,a)].
% 4.95/5.17 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(1329,a,1309,a)].
% 4.95/5.17 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(1329,a,1313,a)].
% 4.95/5.17 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(1329,a,1314,a)].
% 4.95/5.17 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(1329,a,1317,a)].
% 4.95/5.17 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(1329,a,1320,a)].
% 4.95/5.17 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(1329,a,1321,a)].
% 4.95/5.17 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(1329,a,1322,a)].
% 4.95/5.17 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(1329,a,1326,a)].
% 5.03/5.27 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(1329,a,1327,a)].
% 5.03/5.27 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(1329,a,1328,a)].
% 5.03/5.27 1330 semiri456707255roduct(int) # label(arity_Int_Oint___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduc) # label(axiom). [assumption].
% 5.03/5.27 1331 -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_568_add__0__iff) # label(axiom). [clausify(615)].
% 5.03/5.27 1332 -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_568_add__0__iff) # label(axiom). [clausify(615)].
% 5.03/5.27 1333 -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_645_crossproduct__noteq) # label(axiom). [clausify(692)].
% 5.03/5.27 1334 -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_645_crossproduct__noteq) # label(axiom). [clausify(692)].
% 5.03/5.27 1335 -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_645_crossproduct__noteq) # label(axiom). [clausify(692)].
% 5.03/5.27 1336 -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_648_crossproduct__eq) # label(axiom). [clausify(695)].
% 5.03/5.27 1337 -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_648_crossproduct__eq) # label(axiom). [clausify(695)].
% 5.03/5.27 1338 -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_648_crossproduct__eq) # label(axiom). [clausify(695)].
% 5.03/5.27 1339 -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_687_add__scale__eq__noteq) # label(axiom). [clausify(734)].
% 5.03/5.27 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B) != ti(int,A) | zero_zero(int) = ti(int,B). [resolve(1330,a,1331,a)].
% 5.03/5.27 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B) = ti(int,A) | zero_zero(int) != ti(int,B). [resolve(1330,a,1332,a)].
% 5.03/5.27 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(1330,a,1333,a)].
% 5.03/5.27 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(1330,a,1334,a)].
% 5.03/5.27 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),C),A)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),D),B)) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(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),D),A)). [resolve(1330,a,1335,a)].
% 5.03/5.27 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(1330,a,1336,a)].
% 5.03/5.27 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(1330,a,1337,a)].
% 5.03/5.27 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(1330,a,1339,a)].
% 5.03/5.27 1340 semiri456707255roduct(nat) # label(arity_Nat_Onat___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduc) # label(axiom). [assumption].
% 5.03/5.27 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B) != ti(nat,A) | zero_zero(nat) = ti(nat,B). [resolve(1340,a,1331,a)].
% 5.03/5.27 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B) = ti(nat,A) | zero_zero(nat) != ti(nat,B). [resolve(1340,a,1332,a)].
% 5.03/5.27 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(1340,a,1333,a)].
% 5.03/5.27 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(1340,a,1334,a)].
% 5.03/5.27 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),C),A)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),D),B)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),C),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),D),A)). [resolve(1340,a,1335,a)].
% 5.03/5.27 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(1340,a,1336,a)].
% 5.63/5.86 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(1340,a,1337,a)].
% 5.63/5.86 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(1340,a,1339,a)].
% 5.63/5.86 1341 linord626643107strict(int) # label(arity_Int_Oint___Rings_Olinordered__semiring__1__strict) # label(axiom). [assumption].
% 5.63/5.86 1342 -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_577_convex__bound__lt) # label(axiom). [clausify(624)].
% 5.63/5.86 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(1341,a,1342,a)].
% 5.63/5.86 1343 ring_n68954251visors(int) # label(arity_Int_Oint___Rings_Oring__no__zero__divisors) # label(axiom). [assumption].
% 5.63/5.86 1344 -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_581_mult__eq__0__iff) # label(axiom). [clausify(628)].
% 5.63/5.86 1345 -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_581_mult__eq__0__iff) # label(axiom). [clausify(628)].
% 5.63/5.86 1346 -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_581_mult__eq__0__iff) # label(axiom). [clausify(628)].
% 5.63/5.86 Derived: hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B) = zero_zero(int) | zero_zero(int) != ti(int,A). [resolve(1343,a,1345,a)].
% 5.63/5.86 Derived: hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B) = zero_zero(int) | zero_zero(int) != ti(int,B). [resolve(1343,a,1346,a)].
% 5.63/5.86 1347 comm_semiring(int) # label(arity_Int_Oint___Rings_Ocomm__semiring) # label(axiom). [assumption].
% 5.63/5.86 1348 -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_590_comm__semiring__class_Odistrib) # label(axiom). [clausify(637)].
% 5.63/5.86 1349 comm_semiring(nat) # label(arity_Nat_Onat___Rings_Ocomm__semiring) # label(axiom). [assumption].
% 5.63/5.86 1350 comm_monoid_mult(int) # label(arity_Int_Oint___Groups_Ocomm__monoid__mult) # label(axiom). [assumption].
% 5.63/5.86 1351 -comm_monoid_mult(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),one_one(A)) = ti(A,B) # label(fact_592_mult_Ocomm__neutral) # label(axiom). [clausify(639)].
% 5.63/5.86 1352 -comm_monoid_mult(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),one_one(A)),B) = ti(A,B) # label(fact_594_mult__1) # label(axiom). [clausify(641)].
% 5.63/5.86 1353 -comm_monoid_mult(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite(B),C)) | hAPP(fun(B,bool),A,hAPP(A,fun(fun(B,bool),A),hAPP(fun(B,A),fun(A,fun(fun(B,bool),A)),hAPP(fun(A,fun(A,A)),fun(fun(B,A),fun(A,fun(fun(B,bool),A))),finite_fold_image(A,B),times_times(A)),hAPP(fun(B,A),fun(B,A),hAPP(fun(B,fun(A,A)),fun(fun(B,A),fun(B,A)),combs(B,A,A),hAPP(fun(B,A),fun(B,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(B,A),fun(B,fun(A,A))),combb(A,fun(A,A),B),times_times(A)),D)),E)),one_one(A)),C) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(fun(B,bool),A,hAPP(A,fun(fun(B,bool),A),hAPP(fun(B,A),fun(A,fun(fun(B,bool),A)),hAPP(fun(A,fun(A,A)),fun(fun(B,A),fun(A,fun(fun(B,bool),A))),finite_fold_image(A,B),times_times(A)),D),one_one(A)),C)),hAPP(fun(B,bool),A,hAPP(A,fun(fun(B,bool),A),hAPP(fun(B,A),fun(A,fun(fun(B,bool),A)),hAPP(fun(A,fun(A,A)),fun(fun(B,A),fun(A,fun(fun(B,bool),A))),finite_fold_image(A,B),times_times(A)),E),one_one(A)),C)) # label(fact_736_fold__image__distrib) # label(axiom). [clausify(783)].
% 5.63/5.86 1354 -comm_monoid_mult(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite(B),C)) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f101(B,A,D,C)),C)) | hAPP(fun(B,bool),A,hAPP(A,fun(fun(B,bool),A),hAPP(fun(B,A),fun(A,fun(fun(B,bool),A)),hAPP(fun(A,fun(A,A)),fun(fun(B,A),fun(A,fun(fun(B,bool),A))),finite_fold_image(A,B),times_times(A)),D),one_one(A)),C) = one_one(A) # label(fact_741_fold__image__1) # label(axiom). [clausify(788)].
% 5.63/5.86 1355 -comm_monoid_mult(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite(B),C)) | hAPP(B,A,D,f101(B,A,D,C)) != one_one(A) | hAPP(fun(B,bool),A,hAPP(A,fun(fun(B,bool),A),hAPP(fun(B,A),fun(A,fun(fun(B,bool),A)),hAPP(fun(A,fun(A,A)),fun(fun(B,A),fun(A,fun(fun(B,bool),A))),finite_fold_image(A,B),times_times(A)),D),one_one(A)),C) = one_one(A) # label(fact_741_fold__image__1) # label(axiom). [clausify(788)].
% 5.63/5.86 1356 -comm_monoid_mult(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),B,C),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),B,f136(D,A,E,F,V6,B,C)),f138(D,A,E,F,V6,B,C))) | -hBOOL(hAPP(fun(D,bool),bool,finite_finite(D),V6)) | hBOOL(hAPP(fun(D,bool),bool,hAPP(D,fun(fun(D,bool),bool),member(D),f140(D,A,E,F,V6,B,C)),V6)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),B,hAPP(fun(D,bool),A,hAPP(A,fun(fun(D,bool),A),hAPP(fun(D,A),fun(A,fun(fun(D,bool),A)),hAPP(fun(A,fun(A,A)),fun(fun(D,A),fun(A,fun(fun(D,bool),A))),finite_fold_image(A,D),times_times(A)),E),C),V6)),hAPP(fun(D,bool),A,hAPP(A,fun(fun(D,bool),A),hAPP(fun(D,A),fun(A,fun(fun(D,bool),A)),hAPP(fun(A,fun(A,A)),fun(fun(D,A),fun(A,fun(fun(D,bool),A))),finite_fold_image(A,D),times_times(A)),F),C),V6))) # label(fact_897_fold__image__related) # label(axiom). [clausify(934)].
% 5.63/5.86 1357 -comm_monoid_mult(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),B,C),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),B,f136(D,A,E,F,V6,B,C)),f138(D,A,E,F,V6,B,C))) | -hBOOL(hAPP(fun(D,bool),bool,finite_finite(D),V6)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),B,hAPP(D,A,E,f140(D,A,E,F,V6,B,C))),hAPP(D,A,F,f140(D,A,E,F,V6,B,C)))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),B,hAPP(fun(D,bool),A,hAPP(A,fun(fun(D,bool),A),hAPP(fun(D,A),fun(A,fun(fun(D,bool),A)),hAPP(fun(A,fun(A,A)),fun(fun(D,A),fun(A,fun(fun(D,bool),A))),finite_fold_image(A,D),times_times(A)),E),C),V6)),hAPP(fun(D,bool),A,hAPP(A,fun(fun(D,bool),A),hAPP(fun(D,A),fun(A,fun(fun(D,bool),A)),hAPP(fun(A,fun(A,A)),fun(fun(D,A),fun(A,fun(fun(D,bool),A))),finite_fold_image(A,D),times_times(A)),F),C),V6))) # label(fact_897_fold__image__related) # label(axiom). [clausify(934)].
% 5.63/5.86 1358 -comm_monoid_mult(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),B,C),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),B,f137(D,A,E,F,V6,B,C)),f139(D,A,E,F,V6,B,C))) | -hBOOL(hAPP(fun(D,bool),bool,finite_finite(D),V6)) | hBOOL(hAPP(fun(D,bool),bool,hAPP(D,fun(fun(D,bool),bool),member(D),f140(D,A,E,F,V6,B,C)),V6)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),B,hAPP(fun(D,bool),A,hAPP(A,fun(fun(D,bool),A),hAPP(fun(D,A),fun(A,fun(fun(D,bool),A)),hAPP(fun(A,fun(A,A)),fun(fun(D,A),fun(A,fun(fun(D,bool),A))),finite_fold_image(A,D),times_times(A)),E),C),V6)),hAPP(fun(D,bool),A,hAPP(A,fun(fun(D,bool),A),hAPP(fun(D,A),fun(A,fun(fun(D,bool),A)),hAPP(fun(A,fun(A,A)),fun(fun(D,A),fun(A,fun(fun(D,bool),A))),finite_fold_image(A,D),times_times(A)),F),C),V6))) # label(fact_897_fold__image__related) # label(axiom). [clausify(934)].
% 5.63/5.86 1359 -comm_monoid_mult(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),B,C),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),B,f137(D,A,E,F,V6,B,C)),f139(D,A,E,F,V6,B,C))) | -hBOOL(hAPP(fun(D,bool),bool,finite_finite(D),V6)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),B,hAPP(D,A,E,f140(D,A,E,F,V6,B,C))),hAPP(D,A,F,f140(D,A,E,F,V6,B,C)))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),B,hAPP(fun(D,bool),A,hAPP(A,fun(fun(D,bool),A),hAPP(fun(D,A),fun(A,fun(fun(D,bool),A)),hAPP(fun(A,fun(A,A)),fun(fun(D,A),fun(A,fun(fun(D,bool),A))),finite_fold_image(A,D),times_times(A)),E),C),V6)),hAPP(fun(D,bool),A,hAPP(A,fun(fun(D,bool),A),hAPP(fun(D,A),fun(A,fun(fun(D,bool),A)),hAPP(fun(A,fun(A,A)),fun(fun(D,A),fun(A,fun(fun(D,bool),A))),finite_fold_image(A,D),times_times(A)),F),C),V6))) # label(fact_897_fold__image__related) # label(axiom). [clausify(934)].
% 5.63/5.86 1360 -comm_monoid_mult(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),B,C),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),B,hAPP(A,A,hAPP(A,fun(A,A),times_times(A),f136(D,A,E,F,V6,B,C)),f137(D,A,E,F,V6,B,C))),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),f138(D,A,E,F,V6,B,C)),f139(D,A,E,F,V6,B,C)))) | -hBOOL(hAPP(fun(D,bool),bool,finite_finite(D),V6)) | hBOOL(hAPP(fun(D,bool),bool,hAPP(D,fun(fun(D,bool),bool),member(D),f140(D,A,E,F,V6,B,C)),V6)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),B,hAPP(fun(D,bool),A,hAPP(A,fun(fun(D,bool),A),hAPP(fun(D,A),fun(A,fun(fun(D,bool),A)),hAPP(fun(A,fun(A,A)),fun(fun(D,A),fun(A,fun(fun(D,bool),A))),finite_fold_image(A,D),times_times(A)),E),C),V6)),hAPP(fun(D,bool),A,hAPP(A,fun(fun(D,bool),A),hAPP(fun(D,A),fun(A,fun(fun(D,bool),A)),hAPP(fun(A,fun(A,A)),fun(fun(D,A),fun(A,fun(fun(D,bool),A))),finite_fold_image(A,D),times_times(A)),F),C),V6))) # label(fact_897_fold__image__related) # label(axiom). [clausify(934)].
% 5.63/5.86 1361 -comm_monoid_mult(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),B,C),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),B,hAPP(A,A,hAPP(A,fun(A,A),times_times(A),f136(D,A,E,F,V6,B,C)),f137(D,A,E,F,V6,B,C))),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),f138(D,A,E,F,V6,B,C)),f139(D,A,E,F,V6,B,C)))) | -hBOOL(hAPP(fun(D,bool),bool,finite_finite(D),V6)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),B,hAPP(D,A,E,f140(D,A,E,F,V6,B,C))),hAPP(D,A,F,f140(D,A,E,F,V6,B,C)))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),B,hAPP(fun(D,bool),A,hAPP(A,fun(fun(D,bool),A),hAPP(fun(D,A),fun(A,fun(fun(D,bool),A)),hAPP(fun(A,fun(A,A)),fun(fun(D,A),fun(A,fun(fun(D,bool),A))),finite_fold_image(A,D),times_times(A)),E),C),V6)),hAPP(fun(D,bool),A,hAPP(A,fun(fun(D,bool),A),hAPP(fun(D,A),fun(A,fun(fun(D,bool),A)),hAPP(fun(A,fun(A,A)),fun(fun(D,A),fun(A,fun(fun(D,bool),A))),finite_fold_image(A,D),times_times(A)),F),C),V6))) # label(fact_897_fold__image__related) # label(axiom). [clausify(934)].
% 5.63/5.86 1362 -comm_monoid_mult(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite(B),C)) | hBOOL(hAPP(fun(D,bool),bool,hAPP(D,fun(fun(D,bool),bool),member(D),f141(D,B,A,E,F,V6,V7,V8,V9,C)),V9)) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f142(D,B,A,E,F,V6,V7,V8,V9,C)),C)) | hAPP(fun(D,bool),A,hAPP(A,fun(fun(D,bool),A),hAPP(fun(D,A),fun(A,fun(fun(D,bool),A)),hAPP(fun(A,fun(A,A)),fun(fun(D,A),fun(A,fun(fun(D,bool),A))),finite_fold_image(A,D),times_times(A)),F),E),V9) = hAPP(fun(B,bool),A,hAPP(A,fun(fun(B,bool),A),hAPP(fun(B,A),fun(A,fun(fun(B,bool),A)),hAPP(fun(A,fun(A,A)),fun(fun(B,A),fun(A,fun(fun(B,bool),A))),finite_fold_image(A,B),times_times(A)),V6),E),C) # label(fact_898_fold__image__eq__general__inverses) # label(axiom). [clausify(935)].
% 5.63/5.86 1363 -comm_monoid_mult(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite(B),C)) | hBOOL(hAPP(fun(D,bool),bool,hAPP(D,fun(fun(D,bool),bool),member(D),f141(D,B,A,E,F,V6,V7,V8,V9,C)),V9)) | -hBOOL(hAPP(fun(D,bool),bool,hAPP(D,fun(fun(D,bool),bool),member(D),hAPP(B,D,V7,f142(D,B,A,E,F,V6,V7,V8,V9,C))),V9)) | hAPP(D,B,V8,hAPP(B,D,V7,f142(D,B,A,E,F,V6,V7,V8,V9,C))) != ti(B,f142(D,B,A,E,F,V6,V7,V8,V9,C)) | hAPP(D,A,F,hAPP(B,D,V7,f142(D,B,A,E,F,V6,V7,V8,V9,C))) != hAPP(B,A,V6,f142(D,B,A,E,F,V6,V7,V8,V9,C)) | hAPP(fun(D,bool),A,hAPP(A,fun(fun(D,bool),A),hAPP(fun(D,A),fun(A,fun(fun(D,bool),A)),hAPP(fun(A,fun(A,A)),fun(fun(D,A),fun(A,fun(fun(D,bool),A))),finite_fold_image(A,D),times_times(A)),F),E),V9) = hAPP(fun(B,bool),A,hAPP(A,fun(fun(B,bool),A),hAPP(fun(B,A),fun(A,fun(fun(B,bool),A)),hAPP(fun(A,fun(A,A)),fun(fun(B,A),fun(A,fun(fun(B,bool),A))),finite_fold_image(A,B),times_times(A)),V6),E),C) # label(fact_898_fold__image__eq__general__inverses) # label(axiom). [clausify(935)].
% 5.63/5.87 1364 -comm_monoid_mult(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite(B),C)) | -hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),hAPP(D,B,E,f141(D,B,A,F,V6,V7,V8,E,V9,C))),C)) | hAPP(B,D,V8,hAPP(D,B,E,f141(D,B,A,F,V6,V7,V8,E,V9,C))) != ti(D,f141(D,B,A,F,V6,V7,V8,E,V9,C)) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f142(D,B,A,F,V6,V7,V8,E,V9,C)),C)) | hAPP(fun(D,bool),A,hAPP(A,fun(fun(D,bool),A),hAPP(fun(D,A),fun(A,fun(fun(D,bool),A)),hAPP(fun(A,fun(A,A)),fun(fun(D,A),fun(A,fun(fun(D,bool),A))),finite_fold_image(A,D),times_times(A)),V6),F),V9) = hAPP(fun(B,bool),A,hAPP(A,fun(fun(B,bool),A),hAPP(fun(B,A),fun(A,fun(fun(B,bool),A)),hAPP(fun(A,fun(A,A)),fun(fun(B,A),fun(A,fun(fun(B,bool),A))),finite_fold_image(A,B),times_times(A)),V7),F),C) # label(fact_898_fold__image__eq__general__inverses) # label(axiom). [clausify(935)].
% 5.63/5.87 1365 -comm_monoid_mult(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite(B),C)) | -hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),hAPP(D,B,E,f141(D,B,A,F,V6,V7,V8,E,V9,C))),C)) | hAPP(B,D,V8,hAPP(D,B,E,f141(D,B,A,F,V6,V7,V8,E,V9,C))) != ti(D,f141(D,B,A,F,V6,V7,V8,E,V9,C)) | -hBOOL(hAPP(fun(D,bool),bool,hAPP(D,fun(fun(D,bool),bool),member(D),hAPP(B,D,V8,f142(D,B,A,F,V6,V7,V8,E,V9,C))),V9)) | hAPP(D,B,E,hAPP(B,D,V8,f142(D,B,A,F,V6,V7,V8,E,V9,C))) != ti(B,f142(D,B,A,F,V6,V7,V8,E,V9,C)) | hAPP(D,A,V6,hAPP(B,D,V8,f142(D,B,A,F,V6,V7,V8,E,V9,C))) != hAPP(B,A,V7,f142(D,B,A,F,V6,V7,V8,E,V9,C)) | hAPP(fun(D,bool),A,hAPP(A,fun(fun(D,bool),A),hAPP(fun(D,A),fun(A,fun(fun(D,bool),A)),hAPP(fun(A,fun(A,A)),fun(fun(D,A),fun(A,fun(fun(D,bool),A))),finite_fold_image(A,D),times_times(A)),V6),F),V9) = hAPP(fun(B,bool),A,hAPP(A,fun(fun(B,bool),A),hAPP(fun(B,A),fun(A,fun(fun(B,bool),A)),hAPP(fun(A,fun(A,A)),fun(fun(B,A),fun(A,fun(fun(B,bool),A))),finite_fold_image(A,B),times_times(A)),V7),F),C) # label(fact_898_fold__image__eq__general__inverses) # label(axiom). [clausify(935)].
% 5.63/5.87 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite(A),B)) | hAPP(fun(A,bool),int,hAPP(int,fun(fun(A,bool),int),hAPP(fun(A,int),fun(int,fun(fun(A,bool),int)),hAPP(fun(int,fun(int,int)),fun(fun(A,int),fun(int,fun(fun(A,bool),int))),finite_fold_image(int,A),times_times(int)),hAPP(fun(A,int),fun(A,int),hAPP(fun(A,fun(int,int)),fun(fun(A,int),fun(A,int)),combs(A,int,int),hAPP(fun(A,int),fun(A,fun(int,int)),hAPP(fun(int,fun(int,int)),fun(fun(A,int),fun(A,fun(int,int))),combb(int,fun(int,int),A),times_times(int)),C)),D)),one_one(int)),B) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(fun(A,bool),int,hAPP(int,fun(fun(A,bool),int),hAPP(fun(A,int),fun(int,fun(fun(A,bool),int)),hAPP(fun(int,fun(int,int)),fun(fun(A,int),fun(int,fun(fun(A,bool),int))),finite_fold_image(int,A),times_times(int)),C),one_one(int)),B)),hAPP(fun(A,bool),int,hAPP(int,fun(fun(A,bool),int),hAPP(fun(A,int),fun(int,fun(fun(A,bool),int)),hAPP(fun(int,fun(int,int)),fun(fun(A,int),fun(int,fun(fun(A,bool),int))),finite_fold_image(int,A),times_times(int)),D),one_one(int)),B)). [resolve(1350,a,1353,a)].
% 5.63/5.87 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f101(A,int,C,B)),B)) | hAPP(fun(A,bool),int,hAPP(int,fun(fun(A,bool),int),hAPP(fun(A,int),fun(int,fun(fun(A,bool),int)),hAPP(fun(int,fun(int,int)),fun(fun(A,int),fun(int,fun(fun(A,bool),int))),finite_fold_image(int,A),times_times(int)),C),one_one(int)),B) = one_one(int). [resolve(1350,a,1354,a)].
% 5.63/5.87 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite(A),B)) | hAPP(A,int,C,f101(A,int,C,B)) != one_one(int) | hAPP(fun(A,bool),int,hAPP(int,fun(fun(A,bool),int),hAPP(fun(A,int),fun(int,fun(fun(A,bool),int)),hAPP(fun(int,fun(int,int)),fun(fun(A,int),fun(int,fun(fun(A,bool),int))),finite_fold_image(int,A),times_times(int)),C),one_one(int)),B) = one_one(int). [resolve(1350,a,1355,a)].
% 5.63/5.87 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),A,B),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),A,f136(C,int,D,E,F,A,B)),f138(C,int,D,E,F,A,B))) | -hBOOL(hAPP(fun(C,bool),bool,finite_finite(C),F)) | hBOOL(hAPP(fun(C,bool),bool,hAPP(C,fun(fun(C,bool),bool),member(C),f140(C,int,D,E,F,A,B)),F)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),A,hAPP(fun(C,bool),int,hAPP(int,fun(fun(C,bool),int),hAPP(fun(C,int),fun(int,fun(fun(C,bool),int)),hAPP(fun(int,fun(int,int)),fun(fun(C,int),fun(int,fun(fun(C,bool),int))),finite_fold_image(int,C),times_times(int)),D),B),F)),hAPP(fun(C,bool),int,hAPP(int,fun(fun(C,bool),int),hAPP(fun(C,int),fun(int,fun(fun(C,bool),int)),hAPP(fun(int,fun(int,int)),fun(fun(C,int),fun(int,fun(fun(C,bool),int))),finite_fold_image(int,C),times_times(int)),E),B),F))). [resolve(1350,a,1356,a)].
% 5.63/5.87 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),A,B),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),A,f136(C,int,D,E,F,A,B)),f138(C,int,D,E,F,A,B))) | -hBOOL(hAPP(fun(C,bool),bool,finite_finite(C),F)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),A,hAPP(C,int,D,f140(C,int,D,E,F,A,B))),hAPP(C,int,E,f140(C,int,D,E,F,A,B)))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),A,hAPP(fun(C,bool),int,hAPP(int,fun(fun(C,bool),int),hAPP(fun(C,int),fun(int,fun(fun(C,bool),int)),hAPP(fun(int,fun(int,int)),fun(fun(C,int),fun(int,fun(fun(C,bool),int))),finite_fold_image(int,C),times_times(int)),D),B),F)),hAPP(fun(C,bool),int,hAPP(int,fun(fun(C,bool),int),hAPP(fun(C,int),fun(int,fun(fun(C,bool),int)),hAPP(fun(int,fun(int,int)),fun(fun(C,int),fun(int,fun(fun(C,bool),int))),finite_fold_image(int,C),times_times(int)),E),B),F))). [resolve(1350,a,1357,a)].
% 5.63/5.87 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),A,B),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),A,f137(C,int,D,E,F,A,B)),f139(C,int,D,E,F,A,B))) | -hBOOL(hAPP(fun(C,bool),bool,finite_finite(C),F)) | hBOOL(hAPP(fun(C,bool),bool,hAPP(C,fun(fun(C,bool),bool),member(C),f140(C,int,D,E,F,A,B)),F)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),A,hAPP(fun(C,bool),int,hAPP(int,fun(fun(C,bool),int),hAPP(fun(C,int),fun(int,fun(fun(C,bool),int)),hAPP(fun(int,fun(int,int)),fun(fun(C,int),fun(int,fun(fun(C,bool),int))),finite_fold_image(int,C),times_times(int)),D),B),F)),hAPP(fun(C,bool),int,hAPP(int,fun(fun(C,bool),int),hAPP(fun(C,int),fun(int,fun(fun(C,bool),int)),hAPP(fun(int,fun(int,int)),fun(fun(C,int),fun(int,fun(fun(C,bool),int))),finite_fold_image(int,C),times_times(int)),E),B),F))). [resolve(1350,a,1358,a)].
% 5.63/5.87 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),A,B),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),A,f137(C,int,D,E,F,A,B)),f139(C,int,D,E,F,A,B))) | -hBOOL(hAPP(fun(C,bool),bool,finite_finite(C),F)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),A,hAPP(C,int,D,f140(C,int,D,E,F,A,B))),hAPP(C,int,E,f140(C,int,D,E,F,A,B)))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),A,hAPP(fun(C,bool),int,hAPP(int,fun(fun(C,bool),int),hAPP(fun(C,int),fun(int,fun(fun(C,bool),int)),hAPP(fun(int,fun(int,int)),fun(fun(C,int),fun(int,fun(fun(C,bool),int))),finite_fold_image(int,C),times_times(int)),D),B),F)),hAPP(fun(C,bool),int,hAPP(int,fun(fun(C,bool),int),hAPP(fun(C,int),fun(int,fun(fun(C,bool),int)),hAPP(fun(int,fun(int,int)),fun(fun(C,int),fun(int,fun(fun(C,bool),int))),finite_fold_image(int,C),times_times(int)),E),B),F))). [resolve(1350,a,1359,a)].
% 5.63/5.87 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),A,B),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),A,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),f136(C,int,D,E,F,A,B)),f137(C,int,D,E,F,A,B))),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),f138(C,int,D,E,F,A,B)),f139(C,int,D,E,F,A,B)))) | -hBOOL(hAPP(fun(C,bool),bool,finite_finite(C),F)) | hBOOL(hAPP(fun(C,bool),bool,hAPP(C,fun(fun(C,bool),bool),member(C),f140(C,int,D,E,F,A,B)),F)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),A,hAPP(fun(C,bool),int,hAPP(int,fun(fun(C,bool),int),hAPP(fun(C,int),fun(int,fun(fun(C,bool),int)),hAPP(fun(int,fun(int,int)),fun(fun(C,int),fun(int,fun(fun(C,bool),int))),finite_fold_image(int,C),times_times(int)),D),B),F)),hAPP(fun(C,bool),int,hAPP(int,fun(fun(C,bool),int),hAPP(fun(C,int),fun(int,fun(fun(C,bool),int)),hAPP(fun(int,fun(int,int)),fun(fun(C,int),fun(int,fun(fun(C,bool),int))),finite_fold_image(int,C),times_times(int)),E),B),F))). [resolve(1350,a,1360,a)].
% 5.63/5.87 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),A,B),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),A,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),f136(C,int,D,E,F,A,B)),f137(C,int,D,E,F,A,B))),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),f138(C,int,D,E,F,A,B)),f139(C,int,D,E,F,A,B)))) | -hBOOL(hAPP(fun(C,bool),bool,finite_finite(C),F)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),A,hAPP(C,int,D,f140(C,int,D,E,F,A,B))),hAPP(C,int,E,f140(C,int,D,E,F,A,B)))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),A,hAPP(fun(C,bool),int,hAPP(int,fun(fun(C,bool),int),hAPP(fun(C,int),fun(int,fun(fun(C,bool),int)),hAPP(fun(int,fun(int,int)),fun(fun(C,int),fun(int,fun(fun(C,bool),int))),finite_fold_image(int,C),times_times(int)),D),B),F)),hAPP(fun(C,bool),int,hAPP(int,fun(fun(C,bool),int),hAPP(fun(C,int),fun(int,fun(fun(C,bool),int)),hAPP(fun(int,fun(int,int)),fun(fun(C,int),fun(int,fun(fun(C,bool),int))),finite_fold_image(int,C),times_times(int)),E),B),F))). [resolve(1350,a,1361,a)].
% 5.63/5.87 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite(A),B)) | hBOOL(hAPP(fun(C,bool),bool,hAPP(C,fun(fun(C,bool),bool),member(C),f141(C,A,int,D,E,F,V6,V7,V8,B)),V8)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f142(C,A,int,D,E,F,V6,V7,V8,B)),B)) | hAPP(fun(C,bool),int,hAPP(int,fun(fun(C,bool),int),hAPP(fun(C,int),fun(int,fun(fun(C,bool),int)),hAPP(fun(int,fun(int,int)),fun(fun(C,int),fun(int,fun(fun(C,bool),int))),finite_fold_image(int,C),times_times(int)),E),D),V8) = hAPP(fun(A,bool),int,hAPP(int,fun(fun(A,bool),int),hAPP(fun(A,int),fun(int,fun(fun(A,bool),int)),hAPP(fun(int,fun(int,int)),fun(fun(A,int),fun(int,fun(fun(A,bool),int))),finite_fold_image(int,A),times_times(int)),F),D),B). [resolve(1350,a,1362,a)].
% 5.63/5.87 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite(A),B)) | hBOOL(hAPP(fun(C,bool),bool,hAPP(C,fun(fun(C,bool),bool),member(C),f141(C,A,int,D,E,F,V6,V7,V8,B)),V8)) | -hBOOL(hAPP(fun(C,bool),bool,hAPP(C,fun(fun(C,bool),bool),member(C),hAPP(A,C,V6,f142(C,A,int,D,E,F,V6,V7,V8,B))),V8)) | hAPP(C,A,V7,hAPP(A,C,V6,f142(C,A,int,D,E,F,V6,V7,V8,B))) != ti(A,f142(C,A,int,D,E,F,V6,V7,V8,B)) | hAPP(C,int,E,hAPP(A,C,V6,f142(C,A,int,D,E,F,V6,V7,V8,B))) != hAPP(A,int,F,f142(C,A,int,D,E,F,V6,V7,V8,B)) | hAPP(fun(C,bool),int,hAPP(int,fun(fun(C,bool),int),hAPP(fun(C,int),fun(int,fun(fun(C,bool),int)),hAPP(fun(int,fun(int,int)),fun(fun(C,int),fun(int,fun(fun(C,bool),int))),finite_fold_image(int,C),times_times(int)),E),D),V8) = hAPP(fun(A,bool),int,hAPP(int,fun(fun(A,bool),int),hAPP(fun(A,int),fun(int,fun(fun(A,bool),int)),hAPP(fun(int,fun(int,int)),fun(fun(A,int),fun(int,fun(fun(A,bool),int))),finite_fold_image(int,A),times_times(int)),F),D),B). [resolve(1350,a,1363,a)].
% 5.63/5.87 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),hAPP(C,A,D,f141(C,A,int,E,F,V6,V7,D,V8,B))),B)) | hAPP(A,C,V7,hAPP(C,A,D,f141(C,A,int,E,F,V6,V7,D,V8,B))) != ti(C,f141(C,A,int,E,F,V6,V7,D,V8,B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f142(C,A,int,E,F,V6,V7,D,V8,B)),B)) | hAPP(fun(C,bool),int,hAPP(int,fun(fun(C,bool),int),hAPP(fun(C,int),fun(int,fun(fun(C,bool),int)),hAPP(fun(int,fun(int,int)),fun(fun(C,int),fun(int,fun(fun(C,bool),int))),finite_fold_image(int,C),times_times(int)),F),E),V8) = hAPP(fun(A,bool),int,hAPP(int,fun(fun(A,bool),int),hAPP(fun(A,int),fun(int,fun(fun(A,bool),int)),hAPP(fun(int,fun(int,int)),fun(fun(A,int),fun(int,fun(fun(A,bool),int))),finite_fold_image(int,A),times_times(int)),V6),E),B). [resolve(1350,a,1364,a)].
% 5.63/5.87 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),hAPP(C,A,D,f141(C,A,int,E,F,V6,V7,D,V8,B))),B)) | hAPP(A,C,V7,hAPP(C,A,D,f141(C,A,int,E,F,V6,V7,D,V8,B))) != ti(C,f141(C,A,int,E,F,V6,V7,D,V8,B)) | -hBOOL(hAPP(fun(C,bool),bool,hAPP(C,fun(fun(C,bool),bool),member(C),hAPP(A,C,V7,f142(C,A,int,E,F,V6,V7,D,V8,B))),V8)) | hAPP(C,A,D,hAPP(A,C,V7,f142(C,A,int,E,F,V6,V7,D,V8,B))) != ti(A,f142(C,A,int,E,F,V6,V7,D,V8,B)) | hAPP(C,int,F,hAPP(A,C,V7,f142(C,A,int,E,F,V6,V7,D,V8,B))) != hAPP(A,int,V6,f142(C,A,int,E,F,V6,V7,D,V8,B)) | hAPP(fun(C,bool),int,hAPP(int,fun(fun(C,bool),int),hAPP(fun(C,int),fun(int,fun(fun(C,bool),int)),hAPP(fun(int,fun(int,int)),fun(fun(C,int),fun(int,fun(fun(C,bool),int))),finite_fold_image(int,C),times_times(int)),F),E),V8) = hAPP(fun(A,bool),int,hAPP(int,fun(fun(A,bool),int),hAPP(fun(A,int),fun(int,fun(fun(A,bool),int)),hAPP(fun(int,fun(int,int)),fun(fun(A,int),fun(int,fun(fun(A,bool),int))),finite_fold_image(int,A),times_times(int)),V6),E),B). [resolve(1350,a,1365,a)].
% 5.63/5.87 1366 comm_monoid_mult(nat) # label(arity_Nat_Onat___Groups_Ocomm__monoid__mult) # label(axiom). [assumption].
% 5.63/5.87 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite(A),B)) | hAPP(fun(A,bool),nat,hAPP(nat,fun(fun(A,bool),nat),hAPP(fun(A,nat),fun(nat,fun(fun(A,bool),nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(A,nat),fun(nat,fun(fun(A,bool),nat))),finite_fold_image(nat,A),times_times(nat)),hAPP(fun(A,nat),fun(A,nat),hAPP(fun(A,fun(nat,nat)),fun(fun(A,nat),fun(A,nat)),combs(A,nat,nat),hAPP(fun(A,nat),fun(A,fun(nat,nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(A,nat),fun(A,fun(nat,nat))),combb(nat,fun(nat,nat),A),times_times(nat)),C)),D)),one_one(nat)),B) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(fun(A,bool),nat,hAPP(nat,fun(fun(A,bool),nat),hAPP(fun(A,nat),fun(nat,fun(fun(A,bool),nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(A,nat),fun(nat,fun(fun(A,bool),nat))),finite_fold_image(nat,A),times_times(nat)),C),one_one(nat)),B)),hAPP(fun(A,bool),nat,hAPP(nat,fun(fun(A,bool),nat),hAPP(fun(A,nat),fun(nat,fun(fun(A,bool),nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(A,nat),fun(nat,fun(fun(A,bool),nat))),finite_fold_image(nat,A),times_times(nat)),D),one_one(nat)),B)). [resolve(1366,a,1353,a)].
% 5.63/5.87 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f101(A,nat,C,B)),B)) | hAPP(fun(A,bool),nat,hAPP(nat,fun(fun(A,bool),nat),hAPP(fun(A,nat),fun(nat,fun(fun(A,bool),nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(A,nat),fun(nat,fun(fun(A,bool),nat))),finite_fold_image(nat,A),times_times(nat)),C),one_one(nat)),B) = one_one(nat). [resolve(1366,a,1354,a)].
% 5.63/5.87 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite(A),B)) | hAPP(A,nat,C,f101(A,nat,C,B)) != one_one(nat) | hAPP(fun(A,bool),nat,hAPP(nat,fun(fun(A,bool),nat),hAPP(fun(A,nat),fun(nat,fun(fun(A,bool),nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(A,nat),fun(nat,fun(fun(A,bool),nat))),finite_fold_image(nat,A),times_times(nat)),C),one_one(nat)),B) = one_one(nat). [resolve(1366,a,1355,a)].
% 5.63/5.87 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),A,B),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),A,f136(C,nat,D,E,F,A,B)),f138(C,nat,D,E,F,A,B))) | -hBOOL(hAPP(fun(C,bool),bool,finite_finite(C),F)) | hBOOL(hAPP(fun(C,bool),bool,hAPP(C,fun(fun(C,bool),bool),member(C),f140(C,nat,D,E,F,A,B)),F)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),A,hAPP(fun(C,bool),nat,hAPP(nat,fun(fun(C,bool),nat),hAPP(fun(C,nat),fun(nat,fun(fun(C,bool),nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(C,nat),fun(nat,fun(fun(C,bool),nat))),finite_fold_image(nat,C),times_times(nat)),D),B),F)),hAPP(fun(C,bool),nat,hAPP(nat,fun(fun(C,bool),nat),hAPP(fun(C,nat),fun(nat,fun(fun(C,bool),nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(C,nat),fun(nat,fun(fun(C,bool),nat))),finite_fold_image(nat,C),times_times(nat)),E),B),F))). [resolve(1366,a,1356,a)].
% 5.63/5.87 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),A,B),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),A,f136(C,nat,D,E,F,A,B)),f138(C,nat,D,E,F,A,B))) | -hBOOL(hAPP(fun(C,bool),bool,finite_finite(C),F)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),A,hAPP(C,nat,D,f140(C,nat,D,E,F,A,B))),hAPP(C,nat,E,f140(C,nat,D,E,F,A,B)))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),A,hAPP(fun(C,bool),nat,hAPP(nat,fun(fun(C,bool),nat),hAPP(fun(C,nat),fun(nat,fun(fun(C,bool),nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(C,nat),fun(nat,fun(fun(C,bool),nat))),finite_fold_image(nat,C),times_times(nat)),D),B),F)),hAPP(fun(C,bool),nat,hAPP(nat,fun(fun(C,bool),nat),hAPP(fun(C,nat),fun(nat,fun(fun(C,bool),nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(C,nat),fun(nat,fun(fun(C,bool),nat))),finite_fold_image(nat,C),times_times(nat)),E),B),F))). [resolve(1366,a,1357,a)].
% 5.63/5.87 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),A,B),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),A,f137(C,nat,D,E,F,A,B)),f139(C,nat,D,E,F,A,B))) | -hBOOL(hAPP(fun(C,bool),bool,finite_finite(C),F)) | hBOOL(hAPP(fun(C,bool),bool,hAPP(C,fun(fun(C,bool),bool),member(C),f140(C,nat,D,E,F,A,B)),F)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),A,hAPP(fun(C,bool),nat,hAPP(nat,fun(fun(C,bool),nat),hAPP(fun(C,nat),fun(nat,fun(fun(C,bool),nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(C,nat),fun(nat,fun(fun(C,bool),nat))),finite_fold_image(nat,C),times_times(nat)),D),B),F)),hAPP(fun(C,bool),nat,hAPP(nat,fun(fun(C,bool),nat),hAPP(fun(C,nat),fun(nat,fun(fun(C,bool),nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(C,nat),fun(nat,fun(fun(C,bool),nat))),finite_fold_image(nat,C),times_times(nat)),E),B),F))). [resolve(1366,a,1358,a)].
% 5.63/5.87 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),A,B),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),A,f137(C,nat,D,E,F,A,B)),f139(C,nat,D,E,F,A,B))) | -hBOOL(hAPP(fun(C,bool),bool,finite_finite(C),F)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),A,hAPP(C,nat,D,f140(C,nat,D,E,F,A,B))),hAPP(C,nat,E,f140(C,nat,D,E,F,A,B)))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),A,hAPP(fun(C,bool),nat,hAPP(nat,fun(fun(C,bool),nat),hAPP(fun(C,nat),fun(nat,fun(fun(C,bool),nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(C,nat),fun(nat,fun(fun(C,bool),nat))),finite_fold_image(nat,C),times_times(nat)),D),B),F)),hAPP(fun(C,bool),nat,hAPP(nat,fun(fun(C,bool),nat),hAPP(fun(C,nat),fun(nat,fun(fun(C,bool),nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(C,nat),fun(nat,fun(fun(C,bool),nat))),finite_fold_image(nat,C),times_times(nat)),E),B),F))). [resolve(1366,a,1359,a)].
% 5.63/5.87 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),A,B),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),A,hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),f136(C,nat,D,E,F,A,B)),f137(C,nat,D,E,F,A,B))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),f138(C,nat,D,E,F,A,B)),f139(C,nat,D,E,F,A,B)))) | -hBOOL(hAPP(fun(C,bool),bool,finite_finite(C),F)) | hBOOL(hAPP(fun(C,bool),bool,hAPP(C,fun(fun(C,bool),bool),member(C),f140(C,nat,D,E,F,A,B)),F)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),A,hAPP(fun(C,bool),nat,hAPP(nat,fun(fun(C,bool),nat),hAPP(fun(C,nat),fun(nat,fun(fun(C,bool),nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(C,nat),fun(nat,fun(fun(C,bool),nat))),finite_fold_image(nat,C),times_times(nat)),D),B),F)),hAPP(fun(C,bool),nat,hAPP(nat,fun(fun(C,bool),nat),hAPP(fun(C,nat),fun(nat,fun(fun(C,bool),nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(C,nat),fun(nat,fun(fun(C,bool),nat))),finite_fold_image(nat,C),times_times(nat)),E),B),F))). [resolve(1366,a,1360,a)].
% 5.63/5.87 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),A,B),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),A,hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),f136(C,nat,D,E,F,A,B)),f137(C,nat,D,E,F,A,B))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),f138(C,nat,D,E,F,A,B)),f139(C,nat,D,E,F,A,B)))) | -hBOOL(hAPP(fun(C,bool),bool,finite_finite(C),F)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),A,hAPP(C,nat,D,f140(C,nat,D,E,F,A,B))),hAPP(C,nat,E,f140(C,nat,D,E,F,A,B)))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),A,hAPP(fun(C,bool),nat,hAPP(nat,fun(fun(C,bool),nat),hAPP(fun(C,nat),fun(nat,fun(fun(C,bool),nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(C,nat),fun(nat,fun(fun(C,bool),nat))),finite_fold_image(nat,C),times_times(nat)),D),B),F)),hAPP(fun(C,bool),nat,hAPP(nat,fun(fun(C,bool),nat),hAPP(fun(C,nat),fun(nat,fun(fun(C,bool),nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(C,nat),fun(nat,fun(fun(C,bool),nat))),finite_fold_image(nat,C),times_times(nat)),E),B),F))). [resolve(1366,a,1361,a)].
% 5.63/5.87 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite(A),B)) | hBOOL(hAPP(fun(C,bool),bool,hAPP(C,fun(fun(C,bool),bool),member(C),f141(C,A,nat,D,E,F,V6,V7,V8,B)),V8)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f142(C,A,nat,D,E,F,V6,V7,V8,B)),B)) | hAPP(fun(C,bool),nat,hAPP(nat,fun(fun(C,bool),nat),hAPP(fun(C,nat),fun(nat,fun(fun(C,bool),nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(C,nat),fun(nat,fun(fun(C,bool),nat))),finite_fold_image(nat,C),times_times(nat)),E),D),V8) = hAPP(fun(A,bool),nat,hAPP(nat,fun(fun(A,bool),nat),hAPP(fun(A,nat),fun(nat,fun(fun(A,bool),nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(A,nat),fun(nat,fun(fun(A,bool),nat))),finite_fold_image(nat,A),times_times(nat)),F),D),B). [resolve(1366,a,1362,a)].
% 5.63/5.87 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite(A),B)) | hBOOL(hAPP(fun(C,bool),bool,hAPP(C,fun(fun(C,bool),bool),member(C),f141(C,A,nat,D,E,F,V6,V7,V8,B)),V8)) | -hBOOL(hAPP(fun(C,bool),bool,hAPP(C,fun(fun(C,bool),bool),member(C),hAPP(A,C,V6,f142(C,A,nat,D,E,F,V6,V7,V8,B))),V8)) | hAPP(C,A,V7,hAPP(A,C,V6,f142(C,A,nat,D,E,F,V6,V7,V8,B))) != ti(A,f142(C,A,nat,D,E,F,V6,V7,V8,B)) | hAPP(C,nat,E,hAPP(A,C,V6,f142(C,A,nat,D,E,F,V6,V7,V8,B))) != hAPP(A,nat,F,f142(C,A,nat,D,E,F,V6,V7,V8,B)) | hAPP(fun(C,bool),nat,hAPP(nat,fun(fun(C,bool),nat),hAPP(fun(C,nat),fun(nat,fun(fun(C,bool),nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(C,nat),fun(nat,fun(fun(C,bool),nat))),finite_fold_image(nat,C),times_times(nat)),E),D),V8) = hAPP(fun(A,bool),nat,hAPP(nat,fun(fun(A,bool),nat),hAPP(fun(A,nat),fun(nat,fun(fun(A,bool),nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(A,nat),fun(nat,fun(fun(A,bool),nat))),finite_fold_image(nat,A),times_times(nat)),F),D),B). [resolve(1366,a,1363,a)].
% 5.63/5.87 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),hAPP(C,A,D,f141(C,A,nat,E,F,V6,V7,D,V8,B))),B)) | hAPP(A,C,V7,hAPP(C,A,D,f141(C,A,nat,E,F,V6,V7,D,V8,B))) != ti(C,f141(C,A,nat,E,F,V6,V7,D,V8,B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f142(C,A,nat,E,F,V6,V7,D,V8,B)),B)) | hAPP(fun(C,bool),nat,hAPP(nat,fun(fun(C,bool),nat),hAPP(fun(C,nat),fun(nat,fun(fun(C,bool),nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(C,nat),fun(nat,fun(fun(C,bool),nat))),finite_fold_image(nat,C),times_times(nat)),F),E),V8) = hAPP(fun(A,bool),nat,hAPP(nat,fun(fun(A,bool),nat),hAPP(fun(A,nat),fun(nat,fun(fun(A,bool),nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(A,nat),fun(nat,fun(fun(A,bool),nat))),finite_fold_image(nat,A),times_times(nat)),V6),E),B). [resolve(1366,a,1364,a)].
% 5.63/5.87 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),hAPP(C,A,D,f141(C,A,nat,E,F,V6,V7,D,V8,B))),B)) | hAPP(A,C,V7,hAPP(C,A,D,f141(C,A,nat,E,F,V6,V7,D,V8,B))) != ti(C,f141(C,A,nat,E,F,V6,V7,D,V8,B)) | -hBOOL(hAPP(fun(C,bool),bool,hAPP(C,fun(fun(C,bool),bool),member(C),hAPP(A,C,V7,f142(C,A,nat,E,F,V6,V7,D,V8,B))),V8)) | hAPP(C,A,D,hAPP(A,C,V7,f142(C,A,nat,E,F,V6,V7,D,V8,B))) != ti(A,f142(C,A,nat,E,F,V6,V7,D,V8,B)) | hAPP(C,nat,F,hAPP(A,C,V7,f142(C,A,nat,E,F,V6,V7,D,V8,B))) != hAPP(A,nat,V6,f142(C,A,nat,E,F,V6,V7,D,V8,B)) | hAPP(fun(C,bool),nat,hAPP(nat,fun(fun(C,bool),nat),hAPP(fun(C,nat),fun(nat,fun(fun(C,bool),nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(C,nat),fun(nat,fun(fun(C,bool),nat))),finite_fold_image(nat,C),times_times(nat)),F),E),V8) = hAPP(fun(A,bool),nat,hAPP(nat,fun(fun(A,bool),nat),hAPP(fun(A,nat),fun(nat,fun(fun(A,bool),nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(A,nat),fun(nat,fun(fun(A,bool),nat))),finite_fold_image(nat,A),times_times(nat)),V6),E),B). [resolve(1366,a,1365,a)].
% 5.80/6.07 1367 ring_char_0(int) # label(arity_Int_Oint___Int_Oring__char__0) # label(axiom). [assumption].
% 5.80/6.07 1368 -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_619_eq__number__of) # label(axiom). [clausify(666)].
% 5.80/6.07 1369 -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_619_eq__number__of) # label(axiom). [clausify(666)].
% 5.80/6.07 1370 -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_706_Ints__double__eq__0__iff) # label(axiom). [clausify(753)].
% 5.80/6.07 1371 -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_706_Ints__double__eq__0__iff) # label(axiom). [clausify(753)].
% 5.80/6.07 1372 -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_739_Ints__odd__nonzero) # label(axiom). [clausify(786)].
% 5.80/6.07 Derived: -number_ring(int) | hAPP(int,int,number_number_of(int),A) != hAPP(int,int,number_number_of(int),B) | A = B. [resolve(1367,a,1368,b)].
% 5.80/6.07 Derived: -number_ring(int) | hAPP(int,int,number_number_of(int),A) = hAPP(int,int,number_number_of(int),B) | A != B. [resolve(1367,a,1369,b)].
% 5.80/6.07 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(1367,a,1372,a)].
% 5.80/6.07 1373 ring(int) # label(arity_Int_Oint___Rings_Oring) # label(axiom). [assumption].
% 5.80/6.07 1374 -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_624_left__diff__distrib__number__of) # label(axiom). [clausify(671)].
% 5.80/6.07 1375 -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_625_right__diff__distrib__number__of) # label(axiom). [clausify(672)].
% 5.80/6.07 1376 -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_690_eq__add__iff2) # label(axiom). [clausify(737)].
% 5.80/6.07 1377 -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_690_eq__add__iff2) # label(axiom). [clausify(737)].
% 5.80/6.07 1378 -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_691_eq__add__iff1) # label(axiom). [clausify(738)].
% 5.95/6.17 1379 -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_691_eq__add__iff1) # label(axiom). [clausify(738)].
% 5.95/6.17 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(1373,a,1374,b)].
% 5.95/6.17 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(1373,a,1375,b)].
% 5.95/6.17 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(1373,a,1376,a)].
% 5.95/6.17 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(1373,a,1377,a)].
% 5.95/6.17 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(1373,a,1378,a)].
% 5.95/6.17 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(1373,a,1379,a)].
% 5.95/6.17 1380 ordere453448008miring(int) # label(arity_Int_Oint___Rings_Oordered__cancel__semiring) # label(axiom). [assumption].
% 5.95/6.17 1381 -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_653_split__mult__neg__le) # label(axiom). [clausify(700)].
% 5.95/6.17 1382 -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_653_split__mult__neg__le) # label(axiom). [clausify(700)].
% 6.04/6.27 1383 -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_663_mult__nonpos__nonneg) # label(axiom). [clausify(710)].
% 6.04/6.27 1384 -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_664_mult__nonneg__nonpos2) # label(axiom). [clausify(711)].
% 6.04/6.27 1385 -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_665_mult__nonneg__nonpos) # label(axiom). [clausify(712)].
% 6.04/6.27 1386 -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_666_mult__nonneg__nonneg) # label(axiom). [clausify(713)].
% 6.04/6.27 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),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)),zero_zero(int))). [resolve(1380,a,1381,a)].
% 6.04/6.27 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),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),times_times(int),A),B)),zero_zero(int))). [resolve(1380,a,1382,a)].
% 6.04/6.27 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(1380,a,1386,a)].
% 6.04/6.27 1387 ordere453448008miring(nat) # label(arity_Nat_Onat___Rings_Oordered__cancel__semiring) # label(axiom). [assumption].
% 6.04/6.27 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(1387,a,1381,a)].
% 6.04/6.27 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),zero_zero(nat)),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),A),B)),zero_zero(nat))). [resolve(1387,a,1382,a)].
% 6.04/6.27 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(1387,a,1386,a)].
% 6.04/6.27 1388 ordered_ring(int) # label(arity_Int_Oint___Rings_Oordered__ring) # label(axiom). [assumption].
% 6.04/6.27 1389 -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_654_split__mult__pos__le) # label(axiom). [clausify(701)].
% 6.04/6.27 1390 -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_654_split__mult__pos__le) # label(axiom). [clausify(701)].
% 6.04/6.27 1391 -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_657_mult__left__mono__neg) # label(axiom). [clausify(704)].
% 6.04/6.27 1392 -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_658_mult__right__mono__neg) # label(axiom). [clausify(705)].
% 6.04/6.27 1393 -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_662_mult__nonpos__nonpos) # label(axiom). [clausify(709)].
% 6.04/6.27 1394 -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_725_le__add__iff2) # label(axiom). [clausify(772)].
% 6.04/6.27 1395 -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_725_le__add__iff2) # label(axiom). [clausify(772)].
% 6.04/6.27 1396 -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_726_le__add__iff1) # label(axiom). [clausify(773)].
% 6.04/6.27 1397 -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_726_le__add__iff1) # label(axiom). [clausify(773)].
% 6.04/6.27 1398 -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_727_less__add__iff2) # label(axiom). [clausify(774)].
% 6.04/6.27 1399 -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_727_less__add__iff2) # label(axiom). [clausify(774)].
% 6.04/6.27 1400 -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_728_less__add__iff1) # label(axiom). [clausify(775)].
% 6.04/6.27 1401 -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_728_less__add__iff1) # label(axiom). [clausify(775)].
% 6.04/6.27 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(1388,a,1390,a)].
% 6.04/6.27 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(1388,a,1391,a)].
% 6.04/6.27 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(1388,a,1392,a)].
% 6.04/6.27 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(1388,a,1394,a)].
% 6.04/6.27 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(1388,a,1395,a)].
% 6.04/6.27 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(1388,a,1396,a)].
% 6.11/6.37 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(1388,a,1397,a)].
% 6.11/6.37 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(1388,a,1398,a)].
% 6.11/6.37 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(1388,a,1399,a)].
% 6.11/6.37 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(1388,a,1400,a)].
% 6.11/6.37 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(1388,a,1401,a)].
% 6.11/6.37 1402 ordered_semiring(int) # label(arity_Int_Oint___Rings_Oordered__semiring) # label(axiom). [assumption].
% 6.11/6.37 1403 -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_655_mult__mono) # label(axiom). [clausify(702)].
% 6.11/6.37 1404 -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_656_mult__mono_H) # label(axiom). [clausify(703)].
% 6.11/6.37 1405 -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_660_mult__left__mono) # label(axiom). [clausify(707)].
% 6.11/6.37 1406 -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_661_mult__right__mono) # label(axiom). [clausify(708)].
% 6.11/6.37 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(1402,a,1403,a)].
% 6.11/6.37 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(1402,a,1404,a)].
% 6.11/6.37 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(1402,a,1405,a)].
% 6.11/6.37 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(1402,a,1406,a)].
% 6.11/6.37 1407 ordered_semiring(nat) # label(arity_Nat_Onat___Rings_Oordered__semiring) # label(axiom). [assumption].
% 6.11/6.37 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(1407,a,1403,a)].
% 6.11/6.37 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(1407,a,1404,a)].
% 6.11/6.37 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(1407,a,1405,a)].
% 6.11/6.37 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(1407,a,1406,a)].
% 6.34/6.57 1408 ordere1490568538miring(int) # label(arity_Int_Oint___Rings_Oordered__comm__semiring) # label(axiom). [assumption].
% 6.34/6.57 1409 -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_659_comm__mult__left__mono) # label(axiom). [clausify(706)].
% 6.34/6.57 1410 ordere1490568538miring(nat) # label(arity_Nat_Onat___Rings_Oordered__comm__semiring) # label(axiom). [assumption].
% 6.34/6.57 1411 linord581940658strict(int) # label(arity_Int_Oint___Rings_Olinordered__ring__strict) # label(axiom). [assumption].
% 6.34/6.57 1412 -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_667_mult__le__0__iff) # label(axiom). [clausify(714)].
% 6.34/6.57 1413 -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_667_mult__le__0__iff) # label(axiom). [clausify(714)].
% 6.34/6.57 1414 -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_667_mult__le__0__iff) # label(axiom). [clausify(714)].
% 6.34/6.57 1415 -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_667_mult__le__0__iff) # label(axiom). [clausify(714)].
% 6.34/6.57 1416 -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_667_mult__le__0__iff) # label(axiom). [clausify(714)].
% 6.34/6.57 1417 -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_667_mult__le__0__iff) # label(axiom). [clausify(714)].
% 6.34/6.57 1418 -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_668_zero__le__mult__iff) # label(axiom). [clausify(715)].
% 6.34/6.57 1419 -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_668_zero__le__mult__iff) # label(axiom). [clausify(715)].
% 6.34/6.57 1420 -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_668_zero__le__mult__iff) # label(axiom). [clausify(715)].
% 6.34/6.57 1421 -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_668_zero__le__mult__iff) # label(axiom). [clausify(715)].
% 6.34/6.57 1422 -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_668_zero__le__mult__iff) # label(axiom). [clausify(715)].
% 6.34/6.57 1423 -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_668_zero__le__mult__iff) # label(axiom). [clausify(715)].
% 6.34/6.57 1424 -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_671_mult__less__cancel__right__disj) # label(axiom). [clausify(718)].
% 6.34/6.57 1425 -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_671_mult__less__cancel__right__disj) # label(axiom). [clausify(718)].
% 6.34/6.57 1426 -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_671_mult__less__cancel__right__disj) # label(axiom). [clausify(718)].
% 6.34/6.57 1427 -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_671_mult__less__cancel__right__disj) # label(axiom). [clausify(718)].
% 6.34/6.57 1428 -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_671_mult__less__cancel__right__disj) # label(axiom). [clausify(718)].
% 6.34/6.57 1429 -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_671_mult__less__cancel__right__disj) # label(axiom). [clausify(718)].
% 6.34/6.57 1430 -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_672_mult__less__cancel__left__disj) # label(axiom). [clausify(719)].
% 6.34/6.57 1431 -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_672_mult__less__cancel__left__disj) # label(axiom). [clausify(719)].
% 6.34/6.57 1432 -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_672_mult__less__cancel__left__disj) # label(axiom). [clausify(719)].
% 6.34/6.57 1433 -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_672_mult__less__cancel__left__disj) # label(axiom). [clausify(719)].
% 6.34/6.57 1434 -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_672_mult__less__cancel__left__disj) # label(axiom). [clausify(719)].
% 6.34/6.57 1435 -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_672_mult__less__cancel__left__disj) # label(axiom). [clausify(719)].
% 6.34/6.57 1436 -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_673_mult__less__cancel__left__pos) # label(axiom). [clausify(720)].
% 6.34/6.57 1437 -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_673_mult__less__cancel__left__pos) # label(axiom). [clausify(720)].
% 6.34/6.57 1438 -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_679_mult__less__cancel__left__neg) # label(axiom). [clausify(726)].
% 6.34/6.57 1439 -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_679_mult__less__cancel__left__neg) # label(axiom). [clausify(726)].
% 6.34/6.57 1440 -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_681_mult__neg__neg) # label(axiom). [clausify(728)].
% 6.34/6.57 1441 -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_685_mult__strict__right__mono__neg) # label(axiom). [clausify(732)].
% 6.34/6.58 1442 -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_686_mult__strict__left__mono__neg) # label(axiom). [clausify(733)].
% 6.34/6.58 1443 -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_688_sum__squares__eq__zero__iff) # label(axiom). [clausify(735)].
% 6.34/6.58 1444 -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_688_sum__squares__eq__zero__iff) # label(axiom). [clausify(735)].
% 6.34/6.58 1445 -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_688_sum__squares__eq__zero__iff) # label(axiom). [clausify(735)].
% 6.34/6.58 1446 -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_717_mult__le__cancel__left__neg) # label(axiom). [clausify(764)].
% 6.34/6.58 1447 -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_717_mult__le__cancel__left__neg) # label(axiom). [clausify(764)].
% 6.34/6.58 1448 -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_718_mult__le__cancel__left__pos) # label(axiom). [clausify(765)].
% 6.34/6.58 1449 -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_718_mult__le__cancel__left__pos) # label(axiom). [clausify(765)].
% 6.34/6.58 1450 -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_719_sum__squares__le__zero__iff) # label(axiom). [clausify(766)].
% 6.34/6.58 1451 -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_719_sum__squares__le__zero__iff) # label(axiom). [clausify(766)].
% 6.34/6.58 1452 -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_719_sum__squares__le__zero__iff) # label(axiom). [clausify(766)].
% 6.34/6.58 1453 -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_722_sum__squares__gt__zero__iff) # label(axiom). [clausify(769)].
% 6.34/6.58 1454 -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_722_sum__squares__gt__zero__iff) # label(axiom). [clausify(769)].
% 6.34/6.58 1455 -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_722_sum__squares__gt__zero__iff) # label(axiom). [clausify(769)].
% 6.34/6.58 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(1411,a,1413,a)].
% 6.34/6.58 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(1411,a,1414,a)].
% 6.34/6.58 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(1411,a,1419,a)].
% 6.34/6.58 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(1411,a,1420,a)].
% 6.34/6.58 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(1411,a,1424,a)].
% 6.34/6.58 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(1411,a,1425,a)].
% 6.34/6.58 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(1411,a,1426,a)].
% 6.34/6.58 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(1411,a,1427,a)].
% 6.34/6.58 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(1411,a,1428,a)].
% 6.34/6.58 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(1411,a,1429,a)].
% 6.34/6.58 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(1411,a,1430,a)].
% 6.34/6.58 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(1411,a,1431,a)].
% 6.34/6.58 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(1411,a,1432,a)].
% 6.34/6.58 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(1411,a,1433,a)].
% 6.34/6.58 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(1411,a,1434,a)].
% 6.34/6.58 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(1411,a,1435,a)].
% 6.34/6.58 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(1411,a,1436,a)].
% 6.34/6.58 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(1411,a,1438,a)].
% 6.34/6.58 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(1411,a,1440,a)].
% 6.34/6.58 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(1411,a,1443,a)].
% 6.34/6.58 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(1411,a,1444,a)].
% 6.34/6.58 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(1411,a,1445,a)].
% 6.48/6.68 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(1411,a,1446,a)].
% 6.48/6.68 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(1411,a,1447,a)].
% 6.48/6.68 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(1411,a,1448,a)].
% 6.48/6.68 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(1411,a,1449,a)].
% 6.48/6.68 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(1411,a,1450,a)].
% 6.48/6.68 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(1411,a,1451,a)].
% 6.48/6.68 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(1411,a,1452,a)].
% 6.48/6.68 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(1411,a,1453,a)].
% 6.48/6.68 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(1411,a,1454,a)].
% 6.48/6.68 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(1411,a,1455,a)].
% 6.48/6.68 1456 linordered_ring(int) # label(arity_Int_Oint___Rings_Olinordered__ring) # label(axiom). [assumption].
% 6.48/6.68 1457 -linordered_ring(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),B))) # label(fact_669_zero__le__square) # label(axiom). [clausify(716)].
% 6.48/6.68 1458 -linordered_ring(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),B)),zero_zero(A))) # label(fact_670_not__square__less__zero) # label(axiom). [clausify(717)].
% 6.59/6.77 1459 -linordered_ring(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(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)))) # label(fact_720_sum__squares__ge__zero) # label(axiom). [clausify(767)].
% 6.59/6.77 1460 -linordered_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),B)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),C))),zero_zero(A))) # label(fact_721_not__sum__squares__lt__zero) # label(axiom). [clausify(768)].
% 6.59/6.77 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),A))). [resolve(1456,a,1457,a)].
% 6.59/6.77 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),A)),zero_zero(int))). [resolve(1456,a,1458,a)].
% 6.59/6.77 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(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)))). [resolve(1456,a,1459,a)].
% 6.59/6.77 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),A)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),B))),zero_zero(int))). [resolve(1456,a,1460,a)].
% 6.59/6.77 1461 linord20386208strict(int) # label(arity_Int_Oint___Rings_Olinordered__semiring__strict) # label(axiom). [assumption].
% 6.59/6.77 1462 -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_674_mult__pos__pos) # label(axiom). [clausify(721)].
% 6.59/6.77 1463 -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_675_mult__pos__neg) # label(axiom). [clausify(722)].
% 6.59/6.77 1464 -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_676_mult__pos__neg2) # label(axiom). [clausify(723)].
% 6.59/6.77 1465 -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_677_zero__less__mult__pos) # label(axiom). [clausify(724)].
% 6.59/6.77 1466 -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_678_zero__less__mult__pos2) # label(axiom). [clausify(725)].
% 6.59/6.77 1467 -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_680_mult__neg__pos) # label(axiom). [clausify(727)].
% 6.59/6.77 1468 -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_682_mult__strict__right__mono) # label(axiom). [clausify(729)].
% 6.59/6.77 1469 -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_683_mult__strict__left__mono) # label(axiom). [clausify(730)].
% 6.59/6.77 1470 -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_707_mult__left__le__imp__le) # label(axiom). [clausify(754)].
% 6.59/6.77 1471 -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_708_mult__right__le__imp__le) # label(axiom). [clausify(755)].
% 6.59/6.77 1472 -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_709_mult__less__imp__less__left) # label(axiom). [clausify(756)].
% 6.59/6.77 1473 -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_711_mult__less__imp__less__right) # label(axiom). [clausify(758)].
% 6.59/6.77 1474 -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_713_mult__le__less__imp__less) # label(axiom). [clausify(760)].
% 6.59/6.77 1475 -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_714_mult__less__le__imp__less) # label(axiom). [clausify(761)].
% 6.59/6.77 1476 -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_715_mult__strict__mono_H) # label(axiom). [clausify(762)].
% 6.59/6.77 1477 -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_716_mult__strict__mono) # label(axiom). [clausify(763)].
% 6.59/6.77 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(1461,a,1462,a)].
% 6.59/6.77 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(1461,a,1463,a)].
% 6.59/6.77 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(1461,a,1464,a)].
% 6.59/6.77 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(1461,a,1465,a)].
% 6.59/6.77 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(1461,a,1466,a)].
% 6.59/6.77 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(1461,a,1471,a)].
% 6.59/6.77 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(1461,a,1472,a)].
% 6.59/6.77 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(1461,a,1473,a)].
% 6.59/6.77 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(1461,a,1474,a)].
% 6.59/6.77 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(1461,a,1475,a)].
% 6.59/6.77 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(1461,a,1476,a)].
% 6.59/6.77 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(1461,a,1477,a)].
% 6.59/6.77 1478 linord20386208strict(nat) # label(arity_Nat_Onat___Rings_Olinordered__semiring__strict) # label(axiom). [assumption].
% 6.59/6.77 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(1478,a,1462,a)].
% 6.59/6.77 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(1478,a,1463,a)].
% 6.59/6.77 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(1478,a,1464,a)].
% 6.59/6.77 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(1478,a,1465,a)].
% 6.59/6.77 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(1478,a,1466,a)].
% 6.59/6.77 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(1478,a,1468,a)].
% 6.59/6.77 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(1478,a,1469,a)].
% 6.59/6.77 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(1478,a,1470,a)].
% 6.59/6.77 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(1478,a,1471,a)].
% 6.59/6.77 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(1478,a,1472,a)].
% 6.77/6.97 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(1478,a,1473,a)].
% 6.77/6.97 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(1478,a,1474,a)].
% 6.77/6.97 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(1478,a,1475,a)].
% 6.77/6.97 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(1478,a,1476,a)].
% 6.77/6.97 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(1478,a,1477,a)].
% 6.77/6.97 1479 linord893533164strict(int) # label(arity_Int_Oint___Rings_Olinordered__comm__semiring__strict) # label(axiom). [assumption].
% 6.77/6.97 1480 -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_684_comm__mult__strict__left__mono) # label(axiom). [clausify(731)].
% 6.77/6.97 1481 linord893533164strict(nat) # label(arity_Nat_Onat___Rings_Olinordered__comm__semiring__strict) # label(axiom). [assumption].
% 6.77/6.97 1482 linordered_semiring(int) # label(arity_Int_Oint___Rings_Olinordered__semiring) # label(axiom). [assumption].
% 6.77/6.97 1483 -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_710_mult__left__less__imp__less) # label(axiom). [clausify(757)].
% 6.77/6.97 1484 -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_712_mult__right__less__imp__less) # label(axiom). [clausify(759)].
% 7.24/7.44 1485 linordered_semiring(nat) # label(arity_Nat_Onat___Rings_Olinordered__semiring) # label(axiom). [assumption].
% 7.24/7.44 1486 linord1278240602ring_1(int) # label(arity_Int_Oint___Rings_Olinordered__semiring__1) # label(axiom). [assumption].
% 7.24/7.44 1487 -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_737_convex__bound__le) # label(axiom). [clausify(784)].
% 7.24/7.44 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(1486,a,1487,a)].
% 7.24/7.44 1488 number_semiring(int) # label(arity_Int_Oint___Int_Onumber__semiring) # label(axiom). [assumption].
% 7.24/7.44 1489 -number_semiring(A) | hAPP(int,A,number_number_of(A),hAPP(nat,int,semiring_1_of_nat(int),B)) = hAPP(nat,A,semiring_1_of_nat(A),B) # label(fact_829_number__of__int) # label(axiom). [clausify(872)].
% 7.24/7.44 1490 -number_semiring(A) | hAPP(int,A,number_number_of(A),hAPP(int,int,bit1,pls)) = one_one(A) # label(fact_962_semiring__numeral__1__eq__1) # label(axiom). [clausify(989)].
% 7.24/7.44 1491 -number_semiring(A) | hAPP(int,A,number_number_of(A),pls) = zero_zero(A) # label(fact_969_semiring__numeral__0__eq__0) # label(axiom). [clausify(995)].
% 7.24/7.44 Derived: hAPP(int,int,number_number_of(int),hAPP(nat,int,semiring_1_of_nat(int),A)) = hAPP(nat,int,semiring_1_of_nat(int),A). [resolve(1488,a,1489,a)].
% 7.24/7.44 Derived: hAPP(int,int,number_number_of(int),hAPP(int,int,bit1,pls)) = one_one(int). [resolve(1488,a,1490,a)].
% 7.24/7.44 Derived: hAPP(int,int,number_number_of(int),pls) = zero_zero(int). [resolve(1488,a,1491,a)].
% 7.24/7.44 1492 number_semiring(nat) # label(arity_Nat_Onat___Int_Onumber__semiring) # label(axiom). [assumption].
% 7.24/7.44 Derived: hAPP(int,nat,number_number_of(nat),hAPP(nat,int,semiring_1_of_nat(int),A)) = hAPP(nat,nat,semiring_1_of_nat(nat),A). [resolve(1492,a,1489,a)].
% 7.24/7.44 Derived: hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,pls)) = one_one(nat). [resolve(1492,a,1490,a)].
% 7.24/7.44 Derived: hAPP(int,nat,number_number_of(nat),pls) = zero_zero(nat). [resolve(1492,a,1491,a)].
% 7.24/7.44 1493 semiring_char_0(int) # label(arity_Int_Oint___Nat_Osemiring__char__0) # label(axiom). [assumption].
% 7.24/7.44 1494 -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_841_of__nat__eq__iff) # label(axiom). [clausify(882)].
% 7.24/7.44 1495 -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_841_of__nat__eq__iff) # label(axiom). [clausify(882)].
% 7.24/7.44 Derived: hAPP(nat,int,semiring_1_of_nat(int),A) != hAPP(nat,int,semiring_1_of_nat(int),B) | A = B. [resolve(1493,a,1494,a)].
% 7.24/7.44 Derived: hAPP(nat,int,semiring_1_of_nat(int),A) = hAPP(nat,int,semiring_1_of_nat(int),B) | A != B. [resolve(1493,a,1495,a)].
% 7.24/7.44 1496 semiring_char_0(nat) # label(arity_Nat_Onat___Nat_Osemiring__char__0) # label(axiom). [assumption].
% 7.24/7.44 Derived: hAPP(nat,nat,semiring_1_of_nat(nat),A) != hAPP(nat,nat,semiring_1_of_nat(nat),B) | A = B. [resolve(1496,a,1494,a)].
% 7.24/7.44 Derived: hAPP(nat,nat,semiring_1_of_nat(nat),A) = hAPP(nat,nat,semiring_1_of_nat(nat),B) | A != B. [resolve(1496,a,1495,a)].
% 7.24/7.44 1497 ordered_ring_abs(int) # label(arity_Int_Oint___Rings_Oordered__ring__abs) # label(axiom). [assumption].
% 8.69/8.88 1498 -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_919_abs__eq__mult) # label(axiom). [clausify(956)].
% 8.69/8.88 1499 -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_919_abs__eq__mult) # label(axiom). [clausify(956)].
% 8.69/8.88 1500 -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_919_abs__eq__mult) # label(axiom). [clausify(956)].
% 8.69/8.88 1501 -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_919_abs__eq__mult) # label(axiom). [clausify(956)].
% 8.69/8.88
% 8.69/8.88 ============================== end predicate elimination =============
% 8.69/8.88
% 8.69/8.88 Auto_denials: (non-Horn, no changes).
% 8.69/8.88
% 8.69/8.88 Term ordering decisions:
% 8.69/8.88 Function symbol KB weights: nat=1. int=1. bool=1. suc=1. x_a=1. bit1=1. pls=1. nat_neg=1. pname=1. fconj=1. com=1. fdisj=1. fimplies=1. u=1. fFalse=1. mgt_call=1. p=1. succ=1. fNot=1. nat_tsub=1. fTrue=1. mgt=1. wt=1. body=1. g=1. na=1. pn=1. fun=1. ti=1. image=1. finite_fold_image=1. sum_sum=1. sum_Plus=1. combk=1. finite1357897459simple=1. finite908156982e_idem=1. finite_comp_fun_idem=1. f5=1. f15=1. f16=1. f17=1. f18=1. f19=1. f20=1. f27=1. f28=1. f29=1. f30=1. f31=1. f38=1. f46=1. f47=1. f51=1. f54=1. f55=1. f56=1. f59=1. f60=1. f83=1. f86=1. f89=1. f90=1. f91=1. f96=1. f98=1. f107=1. f110=1. f111=1. f112=1. f113=1. f124=1. f129=1. ord_less_eq=1. ord_less=1. zero_zero=1. times_times=1. plus_plus=1. minus_minus=1. number_number_of=1. finite_finite=1. member=1. semiring_1_of_nat=1. insert=1. one_one=1. bot_bot=1. finite_card=1. abs_abs=1. collect=1. fequal=1. ring_1_Ints=1. the=1. semiri532925092at_aux=1. finite_folding_one=1. finite2073411215e_idem=1. nat_case=1. if=1. option=1. combi=1. partial_flat_lub=1. the_1=1. the_elem=1. undefined=1. f14=1. f45=1. f82=1. f92=1. f95=1. f97=1. f125=1. f126=1. f127=1. f128=1. f130=1. f131=1. f132=1. f133=1. f134=1. f135=1. combc=1. combb=1. combs=1. f4=1. f11=1. f23=1. f24=1. f25=1. f26=1. f35=1. f36=1. f37=1. f41=1. f42=1. f44=1. f48=1. f49=1. f50=1. f57=1. f58=1. f61=1. f81=1. f84=1. f85=1. f87=1. f88=1. f93=1. f94=1. f102=1. f103=1. f105=1. f106=1. f108=1. f109=1. f114=1. f115=1. f116=1. f117=1. f119=1. f120=1. f121=1. f123=1. f143=1. f144=1. f145=1. f146=1. hAPP=1. f2=1. f3=1. f6=1. f8=1. f13=1. f21=1. f22=1. f32=1. f33=1. f43=1. f52=1. f53=1. f101=1. f118=1. f122=1. f147=1. f148=1. f1=1. f7=1. f9=1. f10=1. f12=1. f39=1. f40=1. f62=1. f63=1. f64=1. f65=1. f66=1. f67=1. f68=1. f69=1. f72=1. f73=1. f74=1. f75=1. f76=1. f77=1. f78=1. f79=1. f80=1. f104=1. f34=1. f136=1. f137=1. f138=1. f139=1. f140=1. f141=1. f142=1.
% 8.69/8.88
% 8.69/8.88 ============================== end of process initial clauses ========
% 8.69/8.88
% 8.69/8.88 ============================== CLAUSES FOR SEARCH ====================
% 8.69/8.88
% 8.69/8.88 ============================== end of clauses for search =============
% 8.69/8.88
% 8.69/8.88 ============================== SEARCH ================================
% 8.69/8.88
% 8.69/8.88 % Starting search at 6.04 seconds.
% 8.69/8.88
% 8.69/8.88 Low Water (keep): wt=154.000, iters=3583
% 8.69/8.88
% 8.69/8.88 Low Water (keep): wt=139.000, iters=3416
% 144.89/145.14
% 144.89/145.14 Low Water (keep): wt=124.000, iters=3425
% 144.89/145.14
% 144.89/145.14 Low Water (keep): wt=116.000, iters=3337
% 144.89/145.14
% 144.89/145.14 Low Water (keep): wt=111.000, iters=3333
% 144.89/145.14
% 144.89/145.14 Low Water (keep): wt=110.000, iters=3388
% 144.89/145.14
% 144.89/145.14 Low Water (keep): wt=106.000, iters=3360
% 144.89/145.14
% 144.89/145.14 Low Water (keep): wt=102.000, iters=3387
% 144.89/145.14
% 144.89/145.14 Low Water (keep): wt=100.000, iters=3417
% 144.89/145.14
% 144.89/145.14 Low Water (keep): wt=99.000, iters=3380
% 144.89/145.14
% 144.89/145.14 Low Water (keep): wt=97.000, iters=3352
% 144.89/145.14
% 144.89/145.14 Low Water (keep): wt=96.000, iters=3368
% 144.89/145.14
% 144.89/145.14 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 81 (0.00 of 7.27 sec).
% 144.89/145.14
% 144.89/145.14 Low Water (keep): wt=94.000, iters=3340
% 144.89/145.14
% 144.89/145.14 Low Water (keep): wt=93.000, iters=3384
% 144.89/145.14
% 144.89/145.14 Low Water (keep): wt=90.000, iters=3347
% 144.89/145.14
% 144.89/145.14 Low Water (keep): wt=89.000, iters=3360
% 144.89/145.14
% 144.89/145.14 Low Water (keep): wt=85.000, iters=3333
% 144.89/145.14
% 144.89/145.14 Low Water (keep): wt=84.000, iters=3371
% 144.89/145.14
% 144.89/145.14 Low Water (keep): wt=83.000, iters=3591
% 144.89/145.14
% 144.89/145.14 Low Water (keep): wt=81.000, iters=3489
% 144.89/145.14
% 144.89/145.14 Low Water (keep): wt=78.000, iters=3384
% 144.89/145.14
% 144.89/145.14 Low Water (keep): wt=77.000, iters=3340
% 144.89/145.14
% 144.89/145.14 Low Water (keep): wt=76.000, iters=3389
% 144.89/145.14
% 144.89/145.14 Low Water (keep): wt=75.000, iters=3377
% 144.89/145.14
% 144.89/145.14 Low Water (keep): wt=74.000, iters=3335
% 144.89/145.14
% 144.89/145.14 Low Water (keep): wt=73.000, iters=3335
% 144.89/145.14
% 144.89/145.14 Low Water (keep): wt=71.000, iters=3362
% 144.89/145.14
% 144.89/145.14 Low Water (keep): wt=70.000, iters=3407
% 144.89/145.14
% 144.89/145.14 Low Water (keep): wt=67.000, iters=3608
% 144.89/145.14
% 144.89/145.14 Low Water (keep): wt=64.000, iters=3464
% 144.89/145.14
% 144.89/145.14 Low Water (keep): wt=63.000, iters=3417
% 144.89/145.14
% 144.89/145.14 Low Water (keep): wt=62.000, iters=3394
% 144.89/145.14
% 144.89/145.14 Low Water (keep): wt=61.000, iters=3335
% 144.89/145.14
% 144.89/145.14 Low Water (keep): wt=60.000, iters=3376
% 144.89/145.14
% 144.89/145.14 Low Water (keep): wt=59.000, iters=3428
% 144.89/145.14
% 144.89/145.14 Low Water (keep): wt=57.000, iters=3341
% 144.89/145.14
% 144.89/145.14 Low Water (keep): wt=56.000, iters=3367
% 144.89/145.14
% 144.89/145.14 Low Water (keep): wt=55.000, iters=3338
% 144.89/145.14
% 144.89/145.14 Low Water (keep): wt=54.000, iters=3379
% 144.89/145.14
% 144.89/145.14 Low Water (keep): wt=53.000, iters=3334
% 144.89/145.14
% 144.89/145.14 Low Water (keep): wt=52.000, iters=3355
% 144.89/145.14
% 144.89/145.14 Low Water (keep): wt=51.000, iters=3334
% 144.89/145.14
% 144.89/145.14 Low Water (keep): wt=50.000, iters=3352
% 144.89/145.14
% 144.89/145.14 Low Water (keep): wt=49.000, iters=3337
% 144.89/145.14
% 144.89/145.14 Low Water (keep): wt=48.000, iters=3334
% 144.89/145.14
% 144.89/145.14 Low Water (keep): wt=47.000, iters=3494
% 144.89/145.14
% 144.89/145.14 Low Water (keep): wt=46.000, iters=3463
% 144.89/145.14
% 144.89/145.14 Low Water (keep): wt=45.000, iters=3333
% 144.89/145.14
% 144.89/145.14 Low Water (keep): wt=44.000, iters=3386
% 144.89/145.14
% 144.89/145.14 Low Water (keep): wt=43.000, iters=3366
% 144.89/145.14
% 144.89/145.14 Low Water (keep): wt=42.000, iters=3402
% 144.89/145.14
% 144.89/145.14 Low Water (keep): wt=41.000, iters=3433
% 144.89/145.14
% 144.89/145.14 Low Water (keep): wt=40.000, iters=3373
% 144.89/145.14
% 144.89/145.14 Low Water (keep): wt=39.000, iters=3354
% 144.89/145.14
% 144.89/145.14 Low Water (keep): wt=38.000, iters=3551
% 144.89/145.14
% 144.89/145.14 Low Water (keep): wt=37.000, iters=3459
% 144.89/145.14
% 144.89/145.14 Low Water (keep): wt=36.000, iters=3413
% 144.89/145.14
% 144.89/145.14 Low Water (keep): wt=35.000, iters=3528
% 144.89/145.14
% 144.89/145.14 Low Water (keep): wt=34.000, iters=3742
% 144.89/145.14
% 144.89/145.14 Low Water (keep): wt=30.000, iters=3646
% 144.89/145.14
% 144.89/145.14 Low Water (keep): wt=28.000, iters=3512
% 144.89/145.14
% 144.89/145.14 Low Water (keep): wt=26.000, iters=3448
% 144.89/145.14
% 144.89/145.14 Low Water (keep): wt=25.000, iters=3346
% 144.89/145.14
% 144.89/145.14 Low Water (displace): id=15767, wt=16.000
% 144.89/145.14
% 144.89/145.14 Low Water (displace): id=15790, wt=14.000
% 144.89/145.14
% 144.89/145.14 Low Water (displace): id=15800, wt=12.000
% 144.89/145.14
% 144.89/145.14 Low Water (keep): wt=23.000, iters=3492
% 144.89/145.14
% 144.89/145.14 Low Water (keep): wt=22.000, iters=3420
% 144.89/145.14
% 144.89/145.14 Low Water (keep): wt=21.000, iters=3335
% 144.89/145.14
% 144.89/145.14 Low Water (keep): wt=20.000, iters=3333
% 144.89/145.14
% 144.89/145.14 Low Water (keep): wt=19.000, iters=3340
% 144.89/145.14
% 144.89/145.14 Low Water (keep): wt=18.000, iters=3333
% 144.89/145.14
% 144.89/145.14 Low Water (keep): wt=16.000, iters=3333
% 144.89/145.14
% 144.89/145.14 ============================== STATISTICS ============================
% 144.89/145.14
% 144.89/145.14 Given=15049. Generated=2788213. Kept=218989. proofs=0.
% 144.89/145.14 Usable=14115. Sos=9999. Demods=787. Limbo=46, Disabled=196951. Hints=0.
% 144.89/145.14 Kept_by_rule=0, Deleted_by_rule=55207.
% 144.89/145.14 Forward_subsumed=262719. Back_subsumed=62.
% 144.89/145.14 Sos_limit_deleted=2251298. Sos_displaced=191075. Sos_removed=0.
% 144.89/145.14 New_demodulators=1135 (0 lex), Back_demodulated=3611. Back_unit_deleted=81.
% 144.89/145.14 Demod_attempts=128431739. Demod_rewrites=641400.
% 144.89/145.14 Res_instance_prunes=0. Para_instance_prunes=0. Basic_paramod_prunes=0.
% 144.89/145.14 Nonunit_fsub_feature_tests=810927. Nonunit_bsub_feature_tests=12638.
% 144.89/145.14 Megabytes=419.43.
% 144.89/145.14 User_CPU=141.51, System_CPU=1.68, Wall_clock=144.
% 144.89/145.14
% 144.89/145.14 Megs malloced by palloc(): 400.
% 144.89/145.14 type (bytes each) gets frees in use bytes
% 144.89/145.14 chunk ( 104) 80569 80569 0 0.0 K
% 144.89/145.14 string_buf ( 8) 71253 71253 0 0.0 K
% 144.89/145.14 token ( 20) 178563 178563 0 0.0 K
% 144.89/145.14 pterm ( 16) 123745 123745 0 0.0 K
% 144.89/145.14 hashtab ( 8) 1044 1044 0 0.0 K
% 144.89/145.15 hashnode ( 8) 4637 4637 0 0.0 K
% 144.89/145.15 term ( 20) 161664423 152012235 9652188 188519.3 K
% 144.89/145.15 term arg arrays: 43485.0 K
% 144.89/145.15 attribute ( 12) 8336 304 8032 94.1 K
% 144.89/145.15 ilist ( 8) 766395637 765280986 1114651 8708.2 K
% 144.89/145.15 plist ( 8) 10710544 10451847 258697 2021.1 K
% 144.89/145.15 i2list ( 12) 6410261 6410261 0 0.0 K
% 144.89/145.15 just ( 12) 3500938 3240052 260886 3057.3 K
% 144.89/145.15 parajust ( 16) 942589 841707 100882 1576.3 K
% 144.89/145.15 instancejust ( 8) 0 0 0 0.0 K
% 144.89/145.15 ivyjust ( 24) 0 0 0 0.0 K
% 144.89/145.15 formula ( 28) 48149 32395 15754 430.8 K
% 144.89/145.15 formula arg arrays: 53.4 K
% 144.89/145.15 topform ( 52) 2791548 2569224 222324 11289.9 K
% 144.89/145.15 clist_pos ( 20) 654413 432515 221898 4333.9 K
% 144.89/145.15 clist ( 16) 8 1 7 0.1 K
% 144.89/145.15 context ( 808) 14334528 14334526 2 1.6 K
% 144.89/145.15 trail ( 12) 11958067 11958066 1 0.0 K
% 144.89/145.15 ac_match_pos (70044) 0 0 0 0.0 K
% 144.89/145.15 ac_match_free_vars_pos (20020)
% 144.89/145.15 0 0 0 0.0 K
% 144.89/145.15 btm_state ( 60) 0 0 0 0.0 K
% 144.89/145.15 btu_state ( 60) 0 0 0 0.0 K
% 144.89/145.15 ac_position (285432) 0 0 0 0.0 K
% 144.89/145.15 fpa_trie ( 20) 4035651 3607495 428156 8362.4 K
% 144.89/145.15 fpa_state ( 28) 14786889 14786889 0 0.0 K
% 144.89/145.15 fpa_index ( 12) 10 0 10 0.1 K
% 144.89/145.15 fpa_chunk ( 20) 5310472 5161629 148843 2907.1 K
% 144.89/145.15 fpa_list ( 16) 3680358 0 3680358 57505.6 K
% 144.89/145.15 fpa_list chunks: 13724.3 K
% 144.89/145.15 discrim ( 12) 5395788 5238448 157340 1843.8 K
% 144.89/145.15 discrim_pos ( 16) 817330 817330 0 0.0 K
% 144.89/145.15 flat2 ( 32) 68798783 68798783 0 0.0 K
% 144.89/145.15 flat ( 48) 0 0 0 0.0 K
% 144.89/145.15 flatterm ( 32) 148148288 148148288 0 0.0 K
% 144.89/145.15 mindex ( 28) 13 0 13 0.4 K
% 144.89/145.15 mindex_pos ( 56) 7601311 7601311 0 0.0 K
% 144.89/145.15 lindex ( 12) 5 0 5 0.1 K
% 144.89/145.15 clash ( 40) 0 0 0 0.0 K
% 144.89/145.15 di_tree ( 12) 8393808 3300953 5092855 59681.9 K
% 144.89/145.15 avl_node ( 20) 436029 416031 19998 390.6 K
% 144.89/145.15
% 144.89/145.15 Memory report, 20 @ 20 = 400 megs (400.00 megs used).
% 144.89/145.15 List 1, length 9, 0.0 K
% 144.89/145.15 List 2, length 883, 6.9 K
% 144.89/145.15 List 8, length 178, 5.6 K
% 144.89/145.15 List 10, length 8, 0.3 K
% 144.89/145.15 List 11, length 7, 0.3 K
% 144.89/145.15 List 12, length 34, 1.6 K
% 144.89/145.15 List 14, length 2, 0.1 K
% 144.89/145.15 List 15, length 14, 0.8 K
% 144.89/145.15 List 26, length 389, 39.5 K
% 144.89/145.15 List 32, length 52, 6.5 K
% 144.89/145.15 List 128, length 189, 94.5 K
% 144.89/145.15 List 202, length 2, 1.6 K
% 144.89/145.15 List 256, length 1, 1.0 K
% 144.89/145.15
% 144.89/145.15 ============================== SELECTOR REPORT =======================
% 144.89/145.15 Sos_deleted=2251298, Sos_displaced=191075, Sos_size=9999
% 144.89/145.15 SELECTOR PART PRIORITY ORDER SIZE SELECTED
% 144.89/145.15 I 2147483647 high age 0 1347
% 144.89/145.15 H 1 high weight 0 0
% 144.89/145.15 A 1 low age 9999 1523
% 144.89/145.15 F 4 low weight 1751 6091
% 144.89/145.15 T 4 low weight 8248 6088
% 144.89/145.15 ============================== end of selector report ================
% 144.89/145.15
% 144.89/145.15 ============================== end of statistics =====================
% 144.89/145.15
% 144.89/145.15 Exiting with failure.
% 144.89/145.15
% 144.89/145.15 Process 30116 exit (max_megs) Mon Jun 6 02:32:45 2022
% 144.89/145.15 Prover9 interrupted
%------------------------------------------------------------------------------