0.12/0.12	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.12/0.13	% Command    : tptp2X_and_run_prover9 %d %s
0.12/0.33	% Computer   : n016.cluster.edu
0.12/0.33	% Model      : x86_64 x86_64
0.12/0.33	% CPU        : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.12/0.33	% Memory     : 8042.1875MB
0.12/0.33	% OS         : Linux 3.10.0-693.el7.x86_64
0.12/0.33	% CPULimit   : 1200
0.12/0.33	% DateTime   : Tue Jul 13 16:34:08 EDT 2021
0.12/0.34	% CPUTime    : 
7.36/7.38	============================== Prover9 ===============================
7.36/7.38	Prover9 (32) version 2009-11A, November 2009.
7.36/7.38	Process 5124 was started by sandbox on n016.cluster.edu,
7.36/7.38	Tue Jul 13 16:34:14 2021
7.36/7.38	The command was "/export/starexec/sandbox/solver/bin/prover9 -t 1200 -f /tmp/Prover9_4960_n016.cluster.edu".
7.36/7.38	============================== end of head ===========================
7.36/7.38	
7.36/7.38	============================== INPUT =================================
7.36/7.38	
7.36/7.38	% Reading from file /tmp/Prover9_4960_n016.cluster.edu
7.36/7.38	
7.36/7.38	set(prolog_style_variables).
7.36/7.38	set(auto2).
7.36/7.38	    % set(auto2) -> set(auto).
7.36/7.38	    % set(auto) -> set(auto_inference).
7.36/7.38	    % set(auto) -> set(auto_setup).
7.36/7.38	    % set(auto_setup) -> set(predicate_elim).
7.36/7.38	    % set(auto_setup) -> assign(eq_defs, unfold).
7.36/7.38	    % set(auto) -> set(auto_limits).
7.36/7.38	    % set(auto_limits) -> assign(max_weight, "100.000").
7.36/7.38	    % set(auto_limits) -> assign(sos_limit, 20000).
7.36/7.38	    % set(auto) -> set(auto_denials).
7.36/7.38	    % set(auto) -> set(auto_process).
7.36/7.38	    % set(auto2) -> assign(new_constants, 1).
7.36/7.38	    % set(auto2) -> assign(fold_denial_max, 3).
7.36/7.38	    % set(auto2) -> assign(max_weight, "200.000").
7.36/7.38	    % set(auto2) -> assign(max_hours, 1).
7.36/7.38	    % assign(max_hours, 1) -> assign(max_seconds, 3600).
7.36/7.38	    % set(auto2) -> assign(max_seconds, 0).
7.36/7.38	    % set(auto2) -> assign(max_minutes, 5).
7.36/7.38	    % assign(max_minutes, 5) -> assign(max_seconds, 300).
7.36/7.38	    % set(auto2) -> set(sort_initial_sos).
7.36/7.38	    % set(auto2) -> assign(sos_limit, -1).
7.36/7.38	    % set(auto2) -> assign(lrs_ticks, 3000).
7.36/7.38	    % set(auto2) -> assign(max_megs, 400).
7.36/7.38	    % set(auto2) -> assign(stats, some).
7.36/7.38	    % set(auto2) -> clear(echo_input).
7.36/7.38	    % set(auto2) -> set(quiet).
7.36/7.38	    % set(auto2) -> clear(print_initial_clauses).
7.36/7.38	    % set(auto2) -> clear(print_given).
7.36/7.38	assign(lrs_ticks,-1).
7.36/7.38	assign(sos_limit,10000).
7.36/7.38	assign(order,kbo).
7.36/7.38	set(lex_order_vars).
7.36/7.38	clear(print_given).
7.36/7.38	
7.36/7.38	% formulas(sos).  % not echoed (5740 formulas)
7.36/7.38	
7.36/7.38	============================== end of input ==========================
7.36/7.38	
7.36/7.38	% From the command line: assign(max_seconds, 1200).
7.36/7.38	
7.36/7.38	============================== PROCESS NON-CLAUSAL FORMULAS ==========
7.36/7.38	
7.36/7.38	% Formulas that are not ordinary clauses:
7.36/7.38	1 (all N_1 all Ma (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),N_1),Ma)) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(int,real,real_1(int),N_1)),one_one(real))),hAPP(int,real,real_1(int),Ma))))) # label(fact_3391_int__less__real__le) # label(axiom) # label(non_clause).  [assumption].
7.36/7.38	2 (all P_1 all Ma all N_1 ((hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),N_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),P_1,N_1),Ma))) -> ((N_1 = Ma -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),P_1,N_1),Ma))) -> ((hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),Ma)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),P_1,N_1),Ma))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),P_1,N_1),Ma)))))) # label(fact_520_nat__less__cases) # label(axiom) # label(non_clause).  [assumption].
7.36/7.38	3 (all X_a (field_char_0(X_a) -> (all B_1 all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_2),field_char_0_Rats(X_a))) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),B_1),field_char_0_Rats(X_a))) -> (zero_zero(X_a) != ti(X_a,B_1) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),A_2),B_1)),field_char_0_Rats(X_a))))))))) # label(fact_3689_nonzero__Rats__divide) # label(axiom) # label(non_clause).  [assumption].
7.36/7.38	4 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> (all Y_2 exists N_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),Y_2),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,real_1(nat),N_2)),X)))))) # label(fact_2409_reals__Archimedean3) # label(axiom) # label(non_clause).  [assumption].
7.36/7.38	5 (all A_1 all B hAPP(rat,rat,inverse_inverse(rat),hAPP(int,rat,hAPP(int,fun(int,rat),fract,A_1),B)) = hAPP(int,rat,hAPP(int,fun(int,rat),fract,B),A_1)) # label(fact_3750_inverse__rat) # label(axiom) # label(non_clause).  [assumption].
7.36/7.38	6 (all X_a (archim1727834104eiling(X_a) -> (all X_1 all Z (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(X_a,int,archimedean_ceiling(X_a),X_1)),Z)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),hAPP(int,X_a,ring_1_of_int(X_a),Z))))))) # label(fact_3595_ceiling__le__iff) # label(axiom) # label(non_clause).  [assumption].
7.36/7.38	7 (all X_a (real_normed_field(X_a) -> (all F all X_1 all D_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),F),X_1),D_1)) -> (zero_zero(X_a) != hAPP(X_a,X_a,F,X_1) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),hAPP(fun(X_a,X_a),fun(X_a,X_a),hAPP(fun(X_a,X_a),fun(fun(X_a,X_a),fun(X_a,X_a)),combb(X_a,X_a,X_a),inverse_inverse(X_a)),F)),X_1),hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),D_1),hAPP(X_a,X_a,inverse_inverse(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(X_a,X_a,F,X_1)),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat)))))))))))))) # label(fact_3901_DERIV__inverse__fun) # label(axiom) # label(non_clause).  [assumption].
7.36/7.38	8 (all X all Y all M (hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X),Y)),M) = one_one(nat) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),X),M) = one_one(nat))) # label(fact_3292_invertible__coprime__nat) # label(axiom) # label(non_clause).  [assumption].
7.36/7.38	9 (all X_a all A_3 all B_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),B_2)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),B_2),A_3)) -> hAPP(fun(X_a,bool),nat,finite_card(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_3),B_2)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(fun(X_a,bool),nat,finite_card(X_a),A_3)),hAPP(fun(X_a,bool),nat,finite_card(X_a),B_2))))) # label(fact_1815_card__Diff__subset) # label(axiom) # label(non_clause).  [assumption].
7.36/7.38	10 (all X_a (number(X_a) & linord1117847801e_zero(X_a) -> (all W_1 all B_1 all C_1 ((-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_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),W_1)),C_1)))) & (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(int,X_a,number_number_of(X_a),W_1)),zero_zero(X_a))))) & (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(int,X_a,number_number_of(X_a),W_1)),C_1)),B_1))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(int,X_a,number_number_of(X_a),W_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),B_1),C_1))))))) # label(fact_1753_le__divide__eq__number__of) # label(axiom) # label(non_clause).  [assumption].
7.36/7.38	11 (all X_a (real_vector(X_a) -> (all X all Xa_1 hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),hAPP(real,real,uminus_uminus(real),X)),Xa_1) = hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),X),Xa_1))))) # label(fact_4687_scaleR__left_Ominus) # label(axiom) # label(non_clause).  [assumption].
7.36/7.38	12 (all X_a all A_3 hBOOL(hAPP(fun(fun(X_a,bool),bool),bool,hAPP(fun(X_a,bool),fun(fun(fun(X_a,bool),bool),bool),member(fun(X_a,bool)),A_3),hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),pow(X_a),A_3)))) # label(fact_2776_Pow__top) # label(axiom) # label(non_clause).  [assumption].
7.36/7.38	13 (all X_b all X_a (comm_monoid_add(X_a) -> (all A_3 zero_zero(X_a) = hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co1399186613setsum(X_b,X_a),hAPP(X_a,fun(X_b,X_a),combk(X_a,X_b),zero_zero(X_a))),A_3)))) # label(fact_4217_setsum__0) # label(axiom) # label(non_clause).  [assumption].
7.36/7.39	14 (all B all Bq all Br all A_1 all C all Aq all Ar (hBOOL(hAPP(product_prod(int,int),bool,hAPP(int,fun(product_prod(int,int),bool),hAPP(int,fun(int,fun(product_prod(int,int),bool)),divmod_int_rel,A_1),C),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),Aq),Ar))) -> (hBOOL(hAPP(product_prod(int,int),bool,hAPP(int,fun(product_prod(int,int),bool),hAPP(int,fun(int,fun(product_prod(int,int),bool)),divmod_int_rel,B),C),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),Bq),Br))) -> (zero_zero(int) != ti(int,C) -> hBOOL(hAPP(product_prod(int,int),bool,hAPP(int,fun(product_prod(int,int),bool),hAPP(int,fun(int,fun(product_prod(int,int),bool)),divmod_int_rel,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A_1),B)),C),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Aq),Bq)),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Ar),Br)),C))),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Ar),Br)),C)))))))) # label(fact_1196_zadd1__lemma) # label(axiom) # label(non_clause).  [assumption].
7.36/7.39	15 (all X_a all X_b (comm_monoid_add(X_b) -> (all F all A_3 ((all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_3)) -> hAPP(X_a,X_b,F,X_2) = zero_zero(X_b))) -> zero_zero(X_b) = hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),F),A_3))))) # label(fact_4775_setsum__0_H) # label(axiom) # label(non_clause).  [assumption].
7.36/7.39	16 (all X_a (linord1117847801e_zero(X_a) -> (all A_1 all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),hAPP(X_a,X_a,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),inverse_divide(X_a),A_1),B))))) # label(fact_1848_abs__divide) # label(axiom) # label(non_clause).  [assumption].
7.36/7.39	17 (all P_4 hAPP(product_prod(int,int),product_prod(int,int),hAPP(fun(int,fun(int,product_prod(int,int))),fun(product_prod(int,int),product_prod(int,int)),product_prod_case(int,int,product_prod(int,int)),hAPP(fun(int,int),fun(int,fun(int,product_prod(int,int))),hAPP(fun(int,fun(int,product_prod(int,int))),fun(fun(int,int),fun(int,fun(int,product_prod(int,int)))),combb(int,fun(int,product_prod(int,int)),int),product_Pair(int,int)),abs_abs(int))),hAPP(rat,product_prod(int,int),quotient_of,P_4)) = hAPP(rat,product_prod(int,int),quotient_of,hAPP(rat,rat,abs_abs(rat),P_4))) # label(fact_4030_rat__abs__code) # label(axiom) # label(non_clause).  [assumption].
7.36/7.39	18 (all X_1 all P_4 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),P_4)) -> (hBOOL(hAPP(int,bool,zprime,P_4)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),hAPP(int,fun(int,bool),sRStar,P_4))) -> hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),hAPP(int,int,hAPP(int,fun(int,int),standardRes,P_4),hAPP(int,int,hAPP(int,fun(int,int),multInv,P_4),X_1))),hAPP(int,fun(int,bool),sRStar,P_4))))))) # label(fact_1165_StandardRes__SRStar__prop2) # label(axiom) # label(non_clause).  [assumption].
7.36/7.39	19 (all M all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,suc,hAPP(nat,nat,suc,hAPP(nat,nat,suc,M)))),N) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,hAPP(int,int,bit1,pls)))),M)),N)) # label(fact_1440_Suc__mod__eq__add3__mod) # label(axiom) # label(non_clause).  [assumption].
7.36/7.39	20 (all X_a (archim1727834104eiling(X_a) -> (all X_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(X_a,int,archim2085082626_floor(X_a),X_1)),one_one(int))))))) # label(fact_2847_floor__le__one) # label(axiom) # label(non_clause).  [assumption].
7.36/7.39	21 (all X_a (real_n1866405975lgebra(X_a) & divisi14063676e_zero(X_a) -> (all A_1 hAPP(real,real,inverse_inverse(real),hAPP(X_a,real,norm_norm(X_a),A_1)) = hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,inverse_inverse(X_a),A_1))))) # label(fact_2510_norm__inverse) # label(axiom) # label(non_clause).  [assumption].
7.36/7.39	22 (all P_1 all A0 all A1 (hBOOL(hAPP(product_prod(int,int),bool,hAPP(fun(product_prod(int,int),fun(product_prod(int,int),bool)),fun(product_prod(int,int),bool),accp(product_prod(int,int)),norm_frac_rel),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),A0),A1))) -> ((all A_4 all B_4 (hBOOL(hAPP(product_prod(int,int),bool,hAPP(fun(product_prod(int,int),fun(product_prod(int,int),bool)),fun(product_prod(int,int),bool),accp(product_prod(int,int)),norm_frac_rel),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),A_4),B_4))) -> ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B_4),zero_zero(int))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),P_1,hAPP(int,int,uminus_uminus(int),A_4)),hAPP(int,int,uminus_uminus(int),B_4)))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),P_1,A_4),B_4))))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),P_1,A0),A1))))) # label(fact_3553_norm__frac_Opinduct) # label(axiom) # label(non_clause).  [assumption].
7.36/7.39	23 (all P_1 ((all X_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X_2)) -> hBOOL(hAPP(nat,bool,P_1,hAPP(int,nat,nat_1,X_2))))) <-> (all X1 hBOOL(hAPP(nat,bool,P_1,X1))))) # label(fact_1106_all__nat) # label(axiom) # label(non_clause).  [assumption].
7.36/7.39	24 (all X_c all X_b all X_a (real_normed_vector(X_a) & topological_space(X_b) & topological_space(X_c) -> (all G all L all F all A_2 (hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,X_b),fun(X_a,bool),isCont(X_a,X_b),F),A_2)) -> (hBOOL(hAPP(filter(X_b),bool,hAPP(X_c,fun(filter(X_b),bool),hAPP(fun(X_b,X_c),fun(X_c,fun(filter(X_b),bool)),tendsto(X_b,X_c),G),L),hAPP(X_b,filter(X_b),at(X_b),hAPP(X_a,X_b,F,A_2)))) -> ((exists D_3 ((all X_2 (ti(X_a,A_2) != ti(X_a,X_2) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),X_2),A_2))),D_3)) -> hAPP(X_a,X_b,F,X_2) != hAPP(X_a,X_b,F,A_2))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),D_3)))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_c,fun(filter(X_a),bool),hAPP(fun(X_a,X_c),fun(X_c,fun(filter(X_a),bool)),tendsto(X_a,X_c),hAPP(fun(X_a,X_b),fun(X_a,X_c),hAPP(fun(X_b,X_c),fun(fun(X_a,X_b),fun(X_a,X_c)),combb(X_b,X_c,X_a),G),F)),L),hAPP(X_a,filter(X_a),at(X_a),A_2))))))))) # label(fact_4879_isCont__LIM__compose2) # label(axiom) # label(non_clause).  [assumption].
7.36/7.39	25 (all X_a (number_ring(X_a) & field_inverse_zero(X_a) -> (all X hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),hAPP(int,X_a,number_number_of(X_a),min_1)),X) = hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),one_one(X_a)),X))))) # label(fact_2114_minus1__divide) # label(axiom) # label(non_clause).  [assumption].
7.36/7.39	26 (all A_1 all B hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,hAPP(int,int,bit1,pls))))),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit1,hAPP(int,int,bit1,pls)))),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),B))),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit1,hAPP(int,int,bit1,pls)))),A_1)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,hAPP(int,int,bit1,pls))))) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A_1),B)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,hAPP(int,int,bit1,pls))))) # label(fact_183_zadd__power3) # label(axiom) # label(non_clause).  [assumption].
7.36/7.39	27 (all X_a (linordered_field(X_a) -> (all X all Y ((all E (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),E)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Y),E))))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y)))))) # label(fact_1540_field__le__epsilon) # label(axiom) # label(non_clause).  [assumption].
7.36/7.39	28 (all X_a all F all A_3 hAPP(int,real,real_1(int),hAPP(fun(X_a,bool),int,hAPP(fun(X_a,int),fun(fun(X_a,bool),int),big_co1399186613setsum(X_a,int),F),A_3)) = hAPP(fun(X_a,bool),real,hAPP(fun(X_a,real),fun(fun(X_a,bool),real),big_co1399186613setsum(X_a,real),hAPP(fun(X_a,int),fun(X_a,real),hAPP(fun(int,real),fun(fun(X_a,int),fun(X_a,real)),combb(int,real,X_a),real_1(int)),F)),A_3)) # label(fact_4251_real__of__int__setsum) # label(axiom) # label(non_clause).  [assumption].
7.36/7.39	29 (all T_1 ord(filter(T_1))) # label(arity_Limits_Ofilter___Orderings_Oord) # label(axiom) # label(non_clause).  [assumption].
7.36/7.39	30 (all X_a (monoid_mult(X_a) -> (all A_1 all N hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N)),A_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N))))) # label(fact_331_power__commutes) # label(axiom) # label(non_clause).  [assumption].
7.36/7.39	31 (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_757_add__pos__nonneg) # label(axiom) # label(non_clause).  [assumption].
7.36/7.39	32 (all X hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),hAPP(real,nat,natceiling,X)))) # label(fact_1887_zero__le__natceiling) # label(axiom) # label(non_clause).  [assumption].
7.36/7.39	33 (all X_a (sgn_div_norm(X_a) -> ti(fun(X_a,X_a),sgn_sgn(X_a)) = sgn_sgn(X_a))) # label(tsy_c_Groups_Osgn__class_Osgn_0_res) # label(axiom) # label(non_clause).  [assumption].
7.36/7.39	34 (all V_1 all N_1 (-hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),hAPP(int,int,pred,V_1)))) & (-hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),hAPP(int,int,pred,V_1)))) -> N_1 = hAPP(int,nat,nat_1,hAPP(int,int,number_number_of(int),hAPP(int,int,pred,V_1)))) <-> hAPP(nat,nat,suc,N_1) = hAPP(int,nat,number_number_of(nat),V_1))) # label(fact_3885_eq__number__of__Suc) # label(axiom) # label(non_clause).  [assumption].
7.36/7.39	35 (all A_2 (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),zero_zero(nat)),A_2)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_2),zero_zero(nat))) <-> zero_zero(nat) != A_2)) # label(fact_890_gcd__lcm__complete__lattice__nat_Oless__top) # label(axiom) # label(non_clause).  [assumption].
7.36/7.39	36 (all N all I_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,zero_zero(nat))),I_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,zero_zero(nat))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),I_1),N))))) # label(fact_1394_nat__one__le__power) # label(axiom) # label(non_clause).  [assumption].
7.36/7.39	37 (all Z_1 hAPP(complex,real,norm_norm(complex),Z_1) = hAPP(real,real,sqrt,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(complex,real,re,Z_1)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(complex,real,im,Z_1)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))) # label(fact_3018_cmod__def) # label(axiom) # label(non_clause).  [assumption].
7.36/7.39	38 (all X_a all X_b (comm_monoid_mult(X_b) & dvd(X_b) -> (all F all G all A_3 ((all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_3)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),dvd_dvd(X_b),hAPP(X_a,X_b,F,X_2)),hAPP(X_a,X_b,G,X_2))))) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),dvd_dvd(X_b),hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co302546470etprod(X_a,X_b),F),A_3)),hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co302546470etprod(X_a,X_b),G),A_3))))))) # label(fact_4427_setprod__dvd__setprod) # label(axiom) # label(non_clause).  [assumption].
7.36/7.39	39 (all A_2 all B_1 (hBOOL(hAPP(product_prod(int,int),bool,hAPP(fun(product_prod(int,int),fun(product_prod(int,int),bool)),fun(product_prod(int,int),bool),accp(product_prod(int,int)),posDivAlg_rel),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),A_2),B_1))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_2),B_1)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B_1),zero_zero(int))) -> hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),zero_zero(int)),A_2) = hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),posDivAlg,A_2),B_1)) & (-(hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B_1),zero_zero(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_2),B_1))) -> hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),posDivAlg,A_2),B_1) = hAPP(product_prod(int,int),product_prod(int,int),hAPP(int,fun(product_prod(int,int),product_prod(int,int)),adjust,B_1),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),posDivAlg,A_2),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),B_1)))))) # label(fact_1180_posDivAlg_Opsimps) # label(axiom) # label(non_clause).  [assumption].
7.36/7.39	40 (all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,number_number_of(real),min_1)),Y)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),Y),one_one(real))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(real,real,arccos,Y)))))) # label(fact_2262_arccos__lbound) # label(axiom) # label(non_clause).  [assumption].
7.36/7.39	41 (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_377_mult__nonneg__nonpos) # label(axiom) # label(non_clause).  [assumption].
7.36/7.39	42 (all X_a (real_normed_vector(X_a) -> (all X exists K_2 all X_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),X_2),X))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,norm_norm(real),X_2)),K_2)))))) # label(fact_4758_scaleR__left_Obounded) # label(axiom) # label(non_clause).  [assumption].
7.36/7.39	43 (all Z_1 hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(real,complex,of_real(complex),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),hAPP(complex,real,im,Z_1)))),ii) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),Z_1),hAPP(complex,complex,cnj,Z_1))) # label(fact_2970_complex__diff__cnj) # label(axiom) # label(non_clause).  [assumption].
7.36/7.39	44 (all X_a (comm_monoid_add(X_a) & topological_space(X_a) -> (all F all Sa (hBOOL(hAPP(X_a,bool,hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),F),Sa)) <-> hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),hAPP(fun(nat,fun(nat,bool)),fun(nat,X_a),hAPP(fun(fun(nat,bool),X_a),fun(fun(nat,fun(nat,bool)),fun(nat,X_a)),combb(fun(nat,bool),X_a,nat),hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F)),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)))),Sa),sequentially)))))) # label(fact_4496_sums__def) # label(axiom) # label(non_clause).  [assumption].
7.36/7.39	45 (all X_a (division_ring(X_a) -> (all A_1 (zero_zero(X_a) != ti(X_a,A_1) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),one_one(X_a)),A_1) = hAPP(X_a,X_a,inverse_inverse(X_a),A_1))))) # label(fact_2584_nonzero__inverse__eq__divide) # label(axiom) # label(non_clause).  [assumption].
7.36/7.39	46 (all A_1 all B all C all D hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(int,rat,hAPP(int,fun(int,rat),fract,A_1),B)),hAPP(int,rat,hAPP(int,fun(int,rat),fract,C),D)) = hAPP(int,rat,hAPP(int,fun(int,rat),fract,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),C)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),D))) # label(fact_3756_mult__rat) # label(axiom) # label(non_clause).  [assumption].
7.36/7.39	47 (all X hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,cos,X)),one_one(real)))) # label(fact_2208_cos__le__one) # label(axiom) # label(non_clause).  [assumption].
7.36/7.39	48 (all X_a (real_normed_vector(X_a) -> bseq(X_a) = ti(fun(fun(nat,X_a),bool),bseq(X_a)))) # label(tsy_c_SEQ_OBseq_res) # label(axiom) # label(non_clause).  [assumption].
7.36/7.39	49 (all X all Y (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y),X)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),Y)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),Y)))) # label(fact_640_dvd_Oless__imp__le) # label(axiom) # label(non_clause).  [assumption].
7.36/7.39	50 (all X_a (linordered_idom(X_a) -> (all X_1 all Y_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),Y_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),zero_zero(X_a))) <-> zero_zero(X_a) = ti(X_a,Y_1) & zero_zero(X_a) = ti(X_a,X_1))))) # label(fact_106_sum__power2__le__zero__iff) # label(axiom) # label(non_clause).  [assumption].
7.36/7.39	51 (all F all K all A_2 all B_1 (B_1 != A_2 -> ((all X_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),F),X_2),K))) -> hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),B_1),A_2)),K) = hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,F,B_1)),hAPP(real,real,F,A_2))))) # label(fact_2667_DERIV__const__ratio__const) # label(axiom) # label(non_clause).  [assumption].
7.36/7.39	52 (all X_b all X_c all X_a all F all P_4 hAPP(product_prod(X_b,X_c),X_a,hAPP(fun(X_b,fun(X_c,X_a)),fun(product_prod(X_b,X_c),X_a),product_prod_case(X_b,X_c,X_a),F),P_4) = hAPP(X_c,X_a,hAPP(X_b,fun(X_c,X_a),F,hAPP(product_prod(X_b,X_c),X_b,product_fst(X_b,X_c),P_4)),hAPP(product_prod(X_b,X_c),X_c,product_snd(X_b,X_c),P_4))) # label(fact_3991_prod__case__beta) # label(axiom) # label(non_clause).  [assumption].
7.36/7.39	53 (all X_a (linorder(X_a) -> (all X all Y hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),Y) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),Y))))) # label(fact_4813_min__max_Oinf__left__idem) # label(axiom) # label(non_clause).  [assumption].
7.36/7.39	54 (all A_2 all B_1 all C_1 all D_1 all X_1 (hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),D_1),hAPP(int,nat,nat_1,X_1)) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_2),B_1)),C_1) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),one_one(nat)),hAPP(int,nat,nat_1,X_1))) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),zOdd)) -> (one_one(int) = hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,A_2),B_1) -> (hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,B_1),C_1) = one_one(int) -> (one_one(int) = hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,C_1),A_2) -> (exists K_1 exists L_3 exists M_2 (ti(int,A_2) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),K_1),hAPP(int,nat,nat_1,X_1)) & hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),L_3),hAPP(int,nat,nat_1,X_1)) = ti(int,B_1) & hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),M_2),hAPP(int,nat,nat_1,X_1)) = ti(int,C_1)))))))))) # label(fact_3481_int__triple__relprime__odd__power__divisors) # label(axiom) # label(non_clause).  [assumption].
7.36/7.39	55 (all X_a (ring_1(X_a) -> (all A_1 all N hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),A_1)),N) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),one_one(X_a))),N)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N))))) # label(fact_2097_power__minus) # label(axiom) # label(non_clause).  [assumption].
7.36/7.39	56 (all C all A_1 all B all M (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_1),B),M)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A_1),C)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),B),C)),M)))) # label(fact_362_zcong__shift) # label(axiom) # label(non_clause).  [assumption].
7.36/7.39	57 (all X_a (linorder(X_a) -> (all Z_1 all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Z_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),Y),Z_1)))))))) # label(fact_4820_min__max_Oinf__greatest) # label(axiom) # label(non_clause).  [assumption].
7.36/7.39	58 (all F (hBOOL(hAPP(fun(nat,real),bool,summable(real),F)) -> ((all N_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(nat,real,F,N_2)))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(fun(nat,real),real,suminf(real),F)))))) # label(fact_4072_suminf__ge__zero) # label(axiom) # label(non_clause).  [assumption].
7.36/7.39	59 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,sin,X)))))) # label(fact_2384_sin__gt__zero2) # label(axiom) # label(non_clause).  [assumption].
7.36/7.39	60 (all X_a (dense_linorder(X_a) -> (all A_2 all B_1 all C_1 all D_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastLessThan(X_a),A_2),B_1)),hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastAtMost(X_a),C_1),D_1))) <-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),B_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_1),D_1)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C_1),A_2))))))) # label(fact_4528_atLeastLessThan__subseteq__atLeastAtMost__iff) # label(axiom) # label(non_clause).  [assumption].
7.36/7.39	61 (all N_1 all V_1 ((-hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),hAPP(int,int,pred,V_1)))) -> N_1 = hAPP(int,nat,nat_1,hAPP(int,int,number_number_of(int),hAPP(int,int,pred,V_1)))) & -hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),hAPP(int,int,pred,V_1)))) <-> hAPP(nat,nat,suc,N_1) = hAPP(int,nat,number_number_of(nat),V_1))) # label(fact_3884_Suc__eq__number__of) # label(axiom) # label(non_clause).  [assumption].
7.36/7.39	62 (all P_5 (hBOOL(hAPP(nat,bool,prime,P_5)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),P_5)))) # label(fact_3051_prime__g__zero) # label(axiom) # label(non_clause).  [assumption].
7.36/7.39	63 (all X_a (real_normed_field(X_a) -> (all X_3 (hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),X_3)) -> hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(X_a,X_a),fun(fun(nat,X_a),fun(nat,X_a)),combb(X_a,X_a,nat),uminus_uminus(X_a)),X_3))))))) # label(fact_4002_summable__minus) # label(axiom) # label(non_clause).  [assumption].
7.36/7.39	64 (all X_a (real_normed_field(X_a) -> (all G all E_3 all F all X_1 all D_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),F),X_1),D_2)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),G),X_1),E_3)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),hAPP(fun(X_a,X_a),fun(X_a,X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,X_a),fun(X_a,X_a)),combs(X_a,X_a,X_a),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,X_a),fun(X_a,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),X_a),plus_plus(X_a)),F)),G)),X_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),D_2),E_3)))))))) # label(fact_3823_DERIV__add) # label(axiom) # label(non_clause).  [assumption].
7.36/7.39	65 (all X_a (linord1117847801e_zero(X_a) -> (all A_2 all B_1 all C_1 ((-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),C_1)))) & (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),zero_zero(X_a))))) & (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),C_1)),B_1))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),B_1),C_1))))))) # label(fact_1735_le__divide__eq) # label(axiom) # label(non_clause).  [assumption].
7.36/7.39	66 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) -> X = hAPP(real,real,arctan,hAPP(real,real,tan,X))))) # label(fact_2279_arctan__tan) # label(axiom) # label(non_clause).  [assumption].
7.36/7.39	67 (all X_a (division_ring(X_a) -> (all A_1 all B all C (zero_zero(X_a) != ti(X_a,C) -> (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),C) = ti(X_a,B) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),B),C) = ti(X_a,A_1)))))) # label(fact_1693_eq__divide__imp) # label(axiom) # label(non_clause).  [assumption].
7.36/7.39	68 (all N all M (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),M)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,fact_fact(nat),M)),hAPP(nat,nat,fact_fact(nat),N)))))) # label(fact_2490_fact__less__mono__nat) # label(axiom) # label(non_clause).  [assumption].
7.36/7.39	69 (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_1568_order__less__imp__not__less) # label(axiom) # label(non_clause).  [assumption].
7.36/7.39	70 (all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,exp(real),X_1)),one_one(real))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_1),zero_zero(real))))) # label(fact_2594_exp__le__one__iff) # label(axiom) # label(non_clause).  [assumption].
7.36/7.39	71 (all X_a all F all F_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),F_1)) -> ((all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),F_1)) -> hAPP(X_a,nat,F,X_2) = zero_zero(nat))) <-> zero_zero(nat) = hAPP(fun(X_a,bool),nat,hAPP(fun(X_a,nat),fun(fun(X_a,bool),nat),big_co1399186613setsum(X_a,nat),F),F_1)))) # label(fact_4254_setsum__eq__0__iff) # label(axiom) # label(non_clause).  [assumption].
7.36/7.39	72 (all N hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N),N))) # label(fact_530_le__refl) # label(axiom) # label(non_clause).  [assumption].
7.36/7.39	73 (all X_a (comple44059174attice(X_a) -> (all A_3 all B_1 ((all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_3)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_2),B_1)))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(fun(X_a,bool),X_a,complete_Sup_Sup(X_a),A_3)),B_1)))))) # label(fact_1762_Sup__le__iff) # label(axiom) # label(non_clause).  [assumption].
7.36/7.39	74 (all K all L (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),K),L)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit0,K)),hAPP(int,int,bit1,L))))) # label(fact_78_rel__simps_I15_J) # label(axiom) # label(non_clause).  [assumption].
7.36/7.39	75 (all X_a (linordered_field(X_a) -> (all Z_1 all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),Y)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Z_1),Y)),X)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Z_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),X),Y)))))))) # label(fact_1740_mult__imp__le__div__pos) # label(axiom) # label(non_clause).  [assumption].
7.36/7.39	76 (all M hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),zero_zero(nat)) = M) # label(fact_660_minus__nat_Odiff__0) # label(axiom) # label(non_clause).  [assumption].
7.36/7.39	77 (all X_a (archim1727834104eiling(X_a) -> (all Z all X_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Z),hAPP(X_a,int,archim2085082626_floor(X_a),X_1))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(int,X_a,ring_1_of_int(X_a),Z)),X_1)))))) # label(fact_3593_le__floor__iff) # label(axiom) # label(non_clause).  [assumption].
7.36/7.39	78 (all N hAPP(nat,real,real_1(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),N)) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,real_1(nat),N)),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) # label(fact_2381_fact__lemma) # label(axiom) # label(non_clause).  [assumption].
7.36/7.39	79 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,ln,X)),X)))) # label(fact_1933_ln__less__self) # label(axiom) # label(non_clause).  [assumption].
7.36/7.39	80 (all X (zero_zero(real) != X -> hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,inverse_inverse(real),X)),X) = one_one(real))) # label(fact_2592_real__mult__inverse__left) # label(axiom) # label(non_clause).  [assumption].
7.36/7.39	81 (all X_a (real_normed_field(X_a) & banach(X_a) -> (all Z all F all X_1 (hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),times_times(X_a)),F)),hAPP(X_a,fun(nat,X_a),power_power(X_a),X_1)))) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,norm_norm(X_a),Z)),hAPP(X_a,real,norm_norm(X_a),X_1))) -> hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),times_times(X_a)),F)),hAPP(X_a,fun(nat,X_a),power_power(X_a),Z))))))))) # label(fact_4024_powser__inside) # label(axiom) # label(non_clause).  [assumption].
7.36/7.39	82 (all X_a (real_vector(X_a) -> (all X all Y all Xa_1 hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),Y)),Xa_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),X),Xa_1)),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),Y),Xa_1))))) # label(fact_4713_scaleR__left_Oadd) # label(axiom) # label(non_clause).  [assumption].
7.36/7.39	83 (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_259_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J) # label(axiom) # label(non_clause).  [assumption].
7.36/7.39	84 (all X_a (real_normed_field(X_a) -> (all X all Y all Ya hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),X),Y)),Ya) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),X),Ya)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),Y),Ya))))) # label(fact_1664_divide_Odiff) # label(axiom) # label(non_clause).  [assumption].
7.36/7.39	85 (all N_1 (hBOOL(hAPP(nat,bool,even_odd_even(nat),N_1)) <-> (exists M_2 N_1 = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),M_2)))) # label(fact_2467_even__mult__two__ex) # label(axiom) # label(non_clause).  [assumption].
7.36/7.39	86 (all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,number_number_of(real),min_1)),Y)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),Y),one_one(real))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,arccos,Y)),pi)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(real,real,arccos,Y)))))) # label(fact_2271_arccos__bounded) # label(axiom) # label(non_clause).  [assumption].
7.36/7.39	87 (all A_1 all B (ti(int,B) != zero_zero(int) -> hBOOL(hAPP(product_prod(int,int),bool,hAPP(int,fun(product_prod(int,int),bool),hAPP(int,fun(int,fun(product_prod(int,int),bool)),divmod_int_rel,A_1),B),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),divmod_int,A_1),B))))) # label(fact_3075_divmod__int__correct) # label(axiom) # label(non_clause).  [assumption].
7.36/7.39	88 (all Z all W_1 (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)),W_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),W_1),Z)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(int,nat,nat_1,W_1)),hAPP(int,nat,nat_1,Z)))))) # label(fact_1138_nat__le__eq__zle) # label(axiom) # label(non_clause).  [assumption].
7.36/7.39	89 (all X_b all X_a (topological_space(X_a) & real_normed_algebra(X_b) -> (all G all F all A_2 (hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,X_b),fun(X_a,bool),isCont(X_a,X_b),F),A_2)) -> (hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,X_b),fun(X_a,bool),isCont(X_a,X_b),G),A_2)) -> hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,X_b),fun(X_a,bool),isCont(X_a,X_b),hAPP(fun(X_a,X_b),fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,X_b)),combs(X_a,X_b,X_b),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,fun(X_b,X_b))),combb(X_b,fun(X_b,X_b),X_a),times_times(X_b)),F)),G)),A_2))))))) # label(fact_4910_mult_OisCont) # label(axiom) # label(non_clause).  [assumption].
7.36/7.39	90 (all X_3 all Ma (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),Ma)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),resSet,Ma),X_3)) -> hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),X_3))))) # label(fact_2915_ResSet__finite) # label(axiom) # label(non_clause).  [assumption].
7.36/7.39	91 (all X all N all M (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),M)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> hAPP(real,real,hAPP(nat,fun(real,real),root,hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),N)),X) = hAPP(real,real,hAPP(nat,fun(real,real),root,M),hAPP(real,real,hAPP(nat,fun(real,real),root,N),X))))) # label(fact_2683_real__root__mult__exp) # label(axiom) # label(non_clause).  [assumption].
7.36/7.39	92 (all N (N != zero_zero(nat) -> (exists M_2 hAPP(nat,nat,suc,M_2) = N))) # label(fact_1653_not0__implies__Suc) # label(axiom) # label(non_clause).  [assumption].
7.36/7.39	93 (all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),X_1)) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,ln,X_1)))))) # label(fact_1947_ln__gt__zero__iff) # label(axiom) # label(non_clause).  [assumption].
7.36/7.39	94 (all X_b all X_a (ab_group_add(X_a) -> (all F all A_3 hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co1399186613setsum(X_b,X_a),hAPP(fun(X_b,X_a),fun(X_b,X_a),hAPP(fun(X_a,X_a),fun(fun(X_b,X_a),fun(X_b,X_a)),combb(X_a,X_a,X_b),uminus_uminus(X_a)),F)),A_3) = hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co1399186613setsum(X_b,X_a),F),A_3))))) # label(fact_4213_setsum__negf) # label(axiom) # label(non_clause).  [assumption].
7.36/7.39	95 (all N_1 all Ma (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(quickcheck_code_int,int,quickcheck_int_of,N_1)),hAPP(quickcheck_code_int,int,quickcheck_int_of,Ma))) <-> hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),N_1),Ma)))) # label(fact_3159_less__eq__code__int__def) # label(axiom) # label(non_clause).  [assumption].
7.36/7.39	96 (all X_a all X_b bijR(X_a,X_b) = ti(fun(fun(X_a,fun(X_b,bool)),fun(product_prod(fun(X_a,bool),fun(X_b,bool)),bool)),bijR(X_a,X_b))) # label(tsy_c_BijectionRel_ObijR_res) # label(axiom) # label(non_clause).  [assumption].
7.36/7.39	97 (all X_a all X_b (ordere779506340up_add(X_b) & comm_monoid_add(X_b) -> (all F all A_3 all B_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),B_2)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_3),B_2)) -> ((all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),B_2),A_3))) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),zero_zero(X_b)),hAPP(X_a,X_b,F,X_2))))) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),F),A_3)),hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),F),B_2))))))))) # label(fact_4292_setsum__mono3) # label(axiom) # label(non_clause).  [assumption].
7.36/7.39	98 (all X_b all X_a (real_normed_vector(X_b) & metric_space(X_a) -> (all G all F all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(real,fun(filter(X_a),bool),hAPP(fun(X_a,real),fun(real,fun(filter(X_a),bool)),tendsto(X_a,real),F),zero_zero(real)),hAPP(X_a,filter(X_a),at(X_a),A_2))) -> (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),G),zero_zero(X_b)),hAPP(X_a,filter(X_a),at(X_a),A_2))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(fun(X_a,X_b),fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,X_b)),combs(X_a,X_b,X_b),hAPP(fun(X_a,real),fun(X_a,fun(X_b,X_b)),hAPP(fun(real,fun(X_b,X_b)),fun(fun(X_a,real),fun(X_a,fun(X_b,X_b))),combb(real,fun(X_b,X_b),X_a),scaleR_scaleR(X_b)),F)),G)),zero_zero(X_b)),hAPP(X_a,filter(X_a),at(X_a),A_2)))))))) # label(fact_4745_scaleR_OLIM__prod__zero) # label(axiom) # label(non_clause).  [assumption].
7.36/7.39	99 (all K hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),hAPP(nat,fun(nat,bool),ord_atMost(nat),K)))) # label(fact_4936_finite__atMost) # label(axiom) # label(non_clause).  [assumption].
7.36/7.39	100 (all X_a (linordered_idom(X_a) -> (all L_4 all K_4 (hAPP(X_a,X_a,abs_abs(X_a),K_4) = hAPP(X_a,X_a,abs_abs(X_a),L_4) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),L_4),K_4)))))) # label(fact_1847_dvd__if__abs__eq) # label(axiom) # label(non_clause).  [assumption].
7.36/7.39	101 (all X_a (archim1727834104eiling(X_a) -> (all N hAPP(X_a,int,archimedean_ceiling(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),N)) = hAPP(nat,int,semiring_1_of_nat(int),N)))) # label(fact_3285_ceiling__of__nat) # label(axiom) # label(non_clause).  [assumption].
7.36/7.39	102 (all X_a (semiring_div(X_a) -> (all A_1 zero_zero(X_a) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),zero_zero(X_a)),A_1)))) # label(fact_965_div__0) # label(axiom) # label(non_clause).  [assumption].
7.36/7.39	103 (all X_1 all Ma (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),Ma)) -> (hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,X_1),Ma) = one_one(int) -> hBOOL(hAPP(int,bool,hAPP(fun(int,bool),fun(int,bool),is_RRset,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),noXRRset,Ma),X_1)),Ma))))) # label(fact_3618_noX__is__RRset) # label(axiom) # label(non_clause).  [assumption].
7.36/7.39	104 (all A_2 all B_1 ((all D_3 (D_3 = hAPP(nat,nat,suc,zero_zero(nat)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),D_3),B_1)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),D_3),A_2)))) <-> hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),A_2),B_1) = one_one(nat))) # label(fact_3296_coprime__Suc__0__nat) # label(axiom) # label(non_clause).  [assumption].
7.36/7.39	105 (all K all F all N_1 all Ma ((all I_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Ma),I_2)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),N_1)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(nat,int,F,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_2),one_one(nat)))),hAPP(nat,int,F,I_2)))),one_one(int))))) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),N_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,F,Ma)),K)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),K),hAPP(nat,int,F,N_1))) -> (exists I_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Ma),I_2)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_2),N_1)) & ti(int,K) = hAPP(nat,int,F,I_2)))))))) # label(fact_2128_nat__intermed__int__val) # label(axiom) # label(non_clause).  [assumption].
7.36/7.39	106 (all X hAPP(real,real,inverse_inverse(real),hAPP(real,real,sqrt,X)) = hAPP(real,real,sqrt,hAPP(real,real,inverse_inverse(real),X))) # label(fact_2533_real__sqrt__inverse) # label(axiom) # label(non_clause).  [assumption].
7.36/7.39	107 (all X_b all X_a all B_2 all A_3 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_3)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),B_2)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(fun(X_a,bool),nat,finite_card(X_a),A_3)),hAPP(fun(X_b,bool),nat,finite_card(X_b),B_2)) = hAPP(fun(sum_sum(X_a,X_b),bool),nat,finite_card(sum_sum(X_a,X_b)),hAPP(fun(X_b,bool),fun(sum_sum(X_a,X_b),bool),hAPP(fun(X_a,bool),fun(fun(X_b,bool),fun(sum_sum(X_a,X_b),bool)),sum_Plus(X_a,X_b),A_3),B_2))))) # label(fact_3198_card__Plus) # label(axiom) # label(non_clause).  [assumption].
7.36/7.39	108 (all X_2 hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X_2)) = hAPP(nat,fun(nat,bool),ord_less(nat),X_2)) # label(fact_3815_less__eq__Suc__le__raw) # label(axiom) # label(non_clause).  [assumption].
7.36/7.39	109 (all X_a (real_normed_algebra(X_a) -> (all X exists K_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),K_2)) & (all X_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),X_2))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(X_a,real,norm_norm(X_a),X_2)),K_2)))))))) # label(fact_1808_mult__right_Ononneg__bounded) # label(axiom) # label(non_clause).  [assumption].
7.36/7.39	110 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X)) -> hAPP(real,nat,natceiling,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),one_one(real))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(real,nat,natceiling,X)),one_one(nat)))) # label(fact_1911_natceiling__add__one) # label(axiom) # label(non_clause).  [assumption].
7.36/7.39	111 (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_171_number__of__Bit1) # label(axiom) # label(non_clause).  [assumption].
7.36/7.39	112 (all K_4 hAPP(int,int,succ,K_4) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),K_4),min_1)) # label(fact_1530_diff__bin__simps_I2_J) # label(axiom) # label(non_clause).  [assumption].
7.36/7.39	113 (all P (ti(bool,P) = fTrue | fFalse = ti(bool,P))) # label(help_fTrue_1_1_T) # label(axiom) # label(non_clause).  [assumption].
7.36/7.39	114 (all X_a (linorder(X_a) -> (all X all Y hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),Y)),X))))) # label(fact_4829_min__max_Oinf__le1) # label(axiom) # label(non_clause).  [assumption].
7.36/7.39	115 (all N all D all A_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,D),A_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,D),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A_1),N))))) # label(fact_2858_coprime__exp) # label(axiom) # label(non_clause).  [assumption].
7.36/7.39	116 (all N hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,zero_zero(nat))),hAPP(nat,nat,fact_fact(nat),N)))) # label(fact_2496_fact__ge__Suc__0__nat) # label(axiom) # label(non_clause).  [assumption].
7.36/7.39	117 (all X_a all A_2 all R_1 all B_1 (hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,fun(X_a,bool)),fun(X_a,bool),accp(X_a),R_1),B_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),R_1,A_2),B_1)) -> hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,fun(X_a,bool)),fun(X_a,bool),accp(X_a),R_1),A_2))))) # label(fact_2919_accp__downward) # label(axiom) # label(non_clause).  [assumption].
7.36/7.39	118 (all X all A_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A_1)) -> (one_one(real) != A_1 -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> hAPP(real,real,hAPP(real,fun(real,real),log,A_1),hAPP(real,real,inverse_inverse(real),X)) = hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),log,A_1),X)))))) # label(fact_2650_log__inverse) # label(axiom) # label(non_clause).  [assumption].
7.36/7.39	119 (all X_a all X_b (comm_monoid_mult(X_b) -> (all B_1 all C_1 all A_2 all S (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),S)) -> (-hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_2),S)) -> hAPP(nat,X_b,hAPP(X_b,fun(nat,X_b),power_power(X_b),C_1),hAPP(fun(X_a,bool),nat,finite_card(X_a),S)) = hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co302546470etprod(X_a,X_b),hAPP(X_b,fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(X_b,fun(X_a,X_b)),combc(X_a,X_b,X_b),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,X_b)),hAPP(fun(X_a,fun(X_b,fun(X_b,X_b))),fun(fun(X_a,X_b),fun(X_a,fun(X_b,X_b))),combs(X_a,X_b,fun(X_b,X_b)),hAPP(fun(X_a,bool),fun(X_a,fun(X_b,fun(X_b,X_b))),hAPP(fun(bool,fun(X_b,fun(X_b,X_b))),fun(fun(X_a,bool),fun(X_a,fun(X_b,fun(X_b,X_b)))),combb(bool,fun(X_b,fun(X_b,X_b)),X_a),if(X_b)),hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,fun(X_a,bool)),fun(X_a,fun(X_a,bool)),combc(X_a,X_a,bool),fequal(X_a)),A_2))),B_1)),C_1)),S)) & (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_2),S)) -> hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(X_a,X_b,B_1,A_2)),hAPP(nat,X_b,hAPP(X_b,fun(nat,X_b),power_power(X_b),C_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(fun(X_a,bool),nat,finite_card(X_a),S)),one_one(nat)))) = hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co302546470etprod(X_a,X_b),hAPP(X_b,fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(X_b,fun(X_a,X_b)),combc(X_a,X_b,X_b),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,X_b)),hAPP(fun(X_a,fun(X_b,fun(X_b,X_b))),fun(fun(X_a,X_b),fun(X_a,fun(X_b,X_b))),combs(X_a,X_b,fun(X_b,X_b)),hAPP(fun(X_a,bool),fun(X_a,fun(X_b,fun(X_b,X_b))),hAPP(fun(bool,fun(X_b,fun(X_b,X_b))),fun(fun(X_a,bool),fun(X_a,fun(X_b,fun(X_b,X_b)))),combb(bool,fun(X_b,fun(X_b,X_b)),X_a),if(X_b)),hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,fun(X_a,bool)),fun(X_a,fun(X_a,bool)),combc(X_a,X_a,bool),fequal(X_a)),A_2))),B_1)),C_1)),S)))))) # label(fact_3936_setprod__gen__delta) # label(axiom) # label(non_clause).  [assumption].
7.36/7.39	120 (all X_b all X_a (real_normed_algebra(X_a) -> (all G all A_3 all Y_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co1399186613setsum(X_b,X_a),G),A_3)),Y_1) = hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co1399186613setsum(X_b,X_a),hAPP(X_a,fun(X_b,X_a),hAPP(fun(X_b,fun(X_a,X_a)),fun(X_a,fun(X_b,X_a)),combc(X_b,X_a,X_a),hAPP(fun(X_b,X_a),fun(X_b,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_b,X_a),fun(X_b,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),X_b),times_times(X_a)),G)),Y_1)),A_3)))) # label(fact_4190_mult__left_Osetsum) # label(axiom) # label(non_clause).  [assumption].
7.36/7.39	121 (all X_a (field_inverse_zero(X_a) -> (all X all Z_1 all Y (ti(X_a,Y) != zero_zero(X_a) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Z_1),Y))),Y) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),X),Y)),Z_1))))) # label(fact_1720_add__frac__num) # label(axiom) # label(non_clause).  [assumption].
7.36/7.39	122 (all D_1 all A_2 all B_1 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),D_1),A_2) = one_one(nat) & hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),D_1),B_1) = one_one(nat) <-> one_one(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),D_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A_2),B_1)))) # label(fact_3267_coprime__mul__eq__nat) # label(axiom) # label(non_clause).  [assumption].
7.36/7.39	123 (all K_4 hAPP(int,int,succ,hAPP(int,int,bit1,K_4)) = hAPP(int,int,bit0,hAPP(int,int,succ,K_4))) # label(fact_1526_succ__Bit1) # label(axiom) # label(non_clause).  [assumption].
7.36/7.39	124 (all X_a (ring_n68954251visors(X_a) -> (all A_2 all B_1 (ti(X_a,B_1) = zero_zero(X_a) | ti(X_a,A_2) = zero_zero(X_a) <-> zero_zero(X_a) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),B_1))))) # label(fact_321_mult__eq__0__iff) # label(axiom) # label(non_clause).  [assumption].
7.36/7.39	125 (all X_a (boolean_algebra(X_a) -> (all X ti(X_a,X) = hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),X))))) # label(fact_2953_double__compl) # label(axiom) # label(non_clause).  [assumption].
7.36/7.39	126 (all X_b all X_a (topological_space(X_a) & topological_space(X_b) -> ti(fun(fun(X_a,X_b),fun(X_a,bool)),isCont(X_a,X_b)) = isCont(X_a,X_b))) # label(tsy_c_Lim_OisCont_res) # label(axiom) # label(non_clause).  [assumption].
7.36/7.39	127 (all M all X hAPP(int,int,hAPP(int,fun(int,int),standardRes,M),X) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),X),M)) # label(fact_911_StandardRes__def) # label(axiom) # label(non_clause).  [assumption].
7.36/7.39	128 (all X_a (field_char_0(X_a) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),zero_zero(X_a)),field_char_0_Rats(X_a))))) # label(fact_3691_Rats__0) # label(axiom) # label(non_clause).  [assumption].
7.36/7.39	129 (all A_1 all P_5 (hBOOL(hAPP(int,bool,zprime,P_5)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),A_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_1),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),P_5),one_one(int)))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),inv,P_5),A_1)),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),P_5),one_one(int)))))))) # label(fact_803_inv__less__p__minus__1) # label(axiom) # label(non_clause).  [assumption].
7.36/7.39	130 (all B all A_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A_1),zero_zero(int))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),A_1)) -> ti(int,A_1) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_1),B)))) # label(fact_1029_mod__neg__neg__trivial) # label(axiom) # label(non_clause).  [assumption].
7.36/7.39	131 (all N_1 all F (hBOOL(hAPP(fun(nat,real),bool,summable(real),F)) -> ((all M_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_1),M_2)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(nat,real,F,M_2))))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),N_1))),hAPP(fun(nat,real),real,suminf(real),F)))))) # label(fact_4275_series__pos__le) # label(axiom) # label(non_clause).  [assumption].
7.36/7.39	132 (all B all A_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B)) -> hBOOL(hAPP(product_prod(int,int),bool,hAPP(int,fun(product_prod(int,int),bool),hAPP(int,fun(int,fun(product_prod(int,int),bool)),divmod_int_rel,A_1),B),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),posDivAlg,A_1),B)))))) # label(fact_1195_posDivAlg__correct) # label(axiom) # label(non_clause).  [assumption].
7.36/7.39	133 (all X_a all F1 all F2 hAPP(code_code_numeral,X_a,hAPP(fun(code_code_numeral,X_a),fun(code_code_numeral,X_a),hAPP(X_a,fun(fun(code_code_numeral,X_a),fun(code_code_numeral,X_a)),code_c600343653l_case(X_a),F1),F2),zero_zero(code_code_numeral)) = ti(X_a,F1)) # label(fact_3549_code__numeral_Osimps_I4_J) # label(axiom) # label(non_clause).  [assumption].
7.36/7.39	134 (all A_1 all B hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_1),B) = hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,uminus_uminus(int),A_1)),hAPP(int,int,uminus_uminus(int),B))) # label(fact_2148_zdiv__zminus__zminus) # label(axiom) # label(non_clause).  [assumption].
7.36/7.39	135 (all Ma all N_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),Ma),hAPP(nat,nat,suc,N_1)) = hAPP(nat,nat,hAPP(fun(nat,nat),fun(nat,nat),hAPP(nat,fun(fun(nat,nat),fun(nat,nat)),nat_case(nat),hAPP(nat,nat,suc,N_1)),hAPP(fun(nat,nat),fun(nat,nat),hAPP(fun(nat,nat),fun(fun(nat,nat),fun(nat,nat)),combb(nat,nat,nat),suc),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),ord_max(nat)),N_1))),Ma)) # label(fact_4955_max__Suc2) # label(axiom) # label(non_clause).  [assumption].
7.36/7.39	136 (all X_a (number_ring(X_a) -> (all W hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),one_one(X_a)),one_one(X_a))),hAPP(int,X_a,number_number_of(X_a),W)) = hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,bit0,W))))) # label(fact_137_double__number__of__Bit0) # label(axiom) # label(non_clause).  [assumption].
7.36/7.39	137 (all X_a (comm_semiring_1(X_a) -> (all A_1 all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),M)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N))))))) # label(fact_346_le__imp__power__dvd) # label(axiom) # label(non_clause).  [assumption].
7.36/7.39	138 (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_1556_order__eq__refl) # label(axiom) # label(non_clause).  [assumption].
7.36/7.39	139 (all F all L all C_1 (hBOOL(hAPP(filter(real),bool,hAPP(real,fun(filter(real),bool),hAPP(fun(real,real),fun(real,fun(filter(real),bool)),tendsto(real,real),F),L),hAPP(real,filter(real),at(real),C_1))) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),L)) -> (exists R_2 ((all X_2 (X_2 != C_1 & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),C_1),X_2))),R_2)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,F,X_2))))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),R_2))))))) # label(fact_4628_LIM__fun__gt__zero) # label(axiom) # label(non_clause).  [assumption].
7.36/7.39	140 (all X_a (real_normed_field(X_a) -> (all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,norm_norm(X_a),X_1)),one_one(real))) -> hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),hAPP(X_a,fun(nat,X_a),power_power(X_a),X_1))))))) # label(fact_4026_summable__geometric) # label(axiom) # label(non_clause).  [assumption].
7.36/7.39	141 (all X_a (real_normed_vector(X_a) -> (all Y_3 all B_1 all X_3 all A_2 (hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),X_3),A_2),sequentially)) -> (hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),Y_3),B_1),sequentially)) -> hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,real),fun(nat,fun(X_a,X_a)),hAPP(fun(real,fun(X_a,X_a)),fun(fun(nat,real),fun(nat,fun(X_a,X_a))),combb(real,fun(X_a,X_a),nat),scaleR_scaleR(X_a)),X_3)),Y_3)),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_2),B_1)),sequentially))))))) # label(fact_4739_scaleR_OLIMSEQ) # label(axiom) # label(non_clause).  [assumption].
7.36/7.39	142 (all X_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_1),zero_zero(real))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(nat,fun(real,real),root,N_1),X_1)),zero_zero(real)))))) # label(fact_2695_real__root__lt__0__iff) # label(axiom) # label(non_clause).  [assumption].
7.36/7.39	143 (all Ma all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),N_1)) | Ma = N_1 <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Ma),N_1)))) # label(fact_564_le__eq__less__or__eq) # label(axiom) # label(non_clause).  [assumption].
7.36/7.39	144 (all Ma all X_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,X_1),zero_zero(int)),Ma)) <-> zero_zero(int) = hAPP(int,int,hAPP(int,fun(int,int),standardRes,Ma),X_1))) # label(fact_1011_StandardRes__eq__zcong) # label(axiom) # label(non_clause).  [assumption].
7.36/7.39	145 (all M ((zero_zero(nat) != M -> hAPP(nat,nat,fact_fact(nat),M) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),hAPP(nat,nat,fact_fact(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),one_one(nat))))) & (zero_zero(nat) = M -> hAPP(nat,nat,fact_fact(nat),M) = one_one(nat)))) # label(fact_2500_fact__num__eq__if__nat) # label(axiom) # label(non_clause).  [assumption].
7.36/7.39	146 (all X_b all X_a all Q_1 all P_1 ((all X_2 all Y_2 (hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),P_1,X_2),Y_2)) -> hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),Q_1,X_2),Y_2)))) -> hBOOL(hAPP(fun(X_a,fun(X_b,bool)),bool,hAPP(fun(X_a,fun(X_b,bool)),fun(fun(X_a,fun(X_b,bool)),bool),ord_less_eq(fun(X_a,fun(X_b,bool))),P_1),Q_1)))) # label(fact_4342_predicate2I) # label(axiom) # label(non_clause).  [assumption].
7.36/7.39	147 (all R_4 all A_1 hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),R_4),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),R_4),hAPP(real,real,cos,A_1))),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),R_4),hAPP(real,real,sin,A_1))),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) # label(fact_2385_sin__cos__squared__add2__mult) # label(axiom) # label(non_clause).  [assumption].
7.36/7.39	148 (exists K_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),K_2)) & (all X_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,norm_norm(real),hAPP(complex,real,re,X_2))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(complex,real,norm_norm(complex),X_2)),K_2)))))) # label(fact_3020_Re_Opos__bounded) # label(axiom) # label(non_clause).  [assumption].
7.36/7.39	149 (all X_a (comm_semiring_1(X_a) -> (all X hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),zero_zero(nat)) = one_one(X_a)))) # label(fact_249_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J) # label(axiom) # label(non_clause).  [assumption].
7.36/7.39	150 (all Y_3 all X_3 ((exists A_4 (hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A_4)) & (all N_2 hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,abs_abs(rat),hAPP(nat,rat,X_3,N_2))),A_4))))) -> (hBOOL(hAPP(fun(nat,rat),bool,vanishes,Y_3)) -> hBOOL(hAPP(fun(nat,rat),bool,vanishes,hAPP(fun(nat,rat),fun(nat,rat),hAPP(fun(nat,fun(rat,rat)),fun(fun(nat,rat),fun(nat,rat)),combs(nat,rat,rat),hAPP(fun(nat,rat),fun(nat,fun(rat,rat)),hAPP(fun(rat,fun(rat,rat)),fun(fun(nat,rat),fun(nat,fun(rat,rat))),combb(rat,fun(rat,rat),nat),times_times(rat)),X_3)),Y_3)))))) # label(fact_4838_vanishes__mult__bounded) # label(axiom) # label(non_clause).  [assumption].
7.36/7.39	151 (all X_a (field(X_a) -> (all B all A_1 (zero_zero(X_a) != ti(X_a,A_1) -> (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),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)),hAPP(X_a,X_a,inverse_inverse(X_a),A_1))),hAPP(X_a,X_a,inverse_inverse(X_a),B)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,inverse_inverse(X_a),A_1)),hAPP(X_a,X_a,inverse_inverse(X_a),B))))))) # label(fact_2578_inverse__add) # label(axiom) # label(non_clause).  [assumption].
7.36/7.39	152 (all M all N all I_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),I_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),I_1),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),I_1),N))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N))))) # label(fact_347_nat__power__less__imp__less) # label(axiom) # label(non_clause).  [assumption].
7.36/7.39	153 (all N_1 all N_7 all F ((all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,F,N_2)),hAPP(nat,nat,F,hAPP(nat,nat,suc,N_2)))) & -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,F,hAPP(nat,nat,suc,N_2))),hAPP(nat,nat,F,N_2))))) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),N_7)) -> -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,F,N_7)),hAPP(nat,nat,F,N_1))) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,F,N_1)),hAPP(nat,nat,F,N_7)))))) # label(fact_1492_dvd_Olift__Suc__mono__less) # label(axiom) # label(non_clause).  [assumption].
7.36/7.39	154 (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_780_add__le__imp__le__right) # label(axiom) # label(non_clause).  [assumption].
7.36/7.39	155 (all W (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),W)),zero_zero(int))) -> hAPP(int,int,hAPP(int,fun(int,int),div_div(int),one_one(int)),hAPP(int,int,number_number_of(int),W)) = hAPP(product_prod(int,int),int,product_fst(int,int),hAPP(product_prod(int,int),product_prod(int,int),negateSnd,hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),negDivAlg,hAPP(int,int,uminus_uminus(int),one_one(int))),hAPP(int,int,uminus_uminus(int),hAPP(int,int,number_number_of(int),W))))))) # label(fact_3106_div__pos__neg__1__number__of) # label(axiom) # label(non_clause).  [assumption].
7.36/7.39	156 (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_428_mult__left__less__imp__less) # label(axiom) # label(non_clause).  [assumption].
7.36/7.39	157 (all N all M (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),one_one(nat)),M)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),M),hAPP(nat,nat,fact_fact(nat),N)))))) # label(fact_2497_dvd__fact__nat) # label(axiom) # label(non_clause).  [assumption].
7.36/7.39	158 (all N_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),N_1)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(int,nat,nat_1,N_1)),one_one(nat)) = hAPP(fun(int,bool),nat,finite_card(int),hAPP(fun(int,bool),fun(int,bool),collect(int),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),combs(int,bool,bool),hAPP(fun(int,bool),fun(int,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj),hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)))),hAPP(int,fun(int,bool),hAPP(fun(int,fun(int,bool)),fun(int,fun(int,bool)),combc(int,int,bool),ord_less(int)),N_1)))))) # label(fact_3882_card__bdd__int__set__l__l) # label(axiom) # label(non_clause).  [assumption].
7.36/7.39	159 (all X_a (archim1727834104eiling(X_a) -> (all Z all X_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(int,X_a,ring_1_of_int(X_a),Z)),X_1)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Z),hAPP(X_a,int,archimedean_ceiling(X_a),X_1))))))) # label(fact_3594_less__ceiling__iff) # label(axiom) # label(non_clause).  [assumption].
7.36/7.39	160 (all C all A_1 all B all Q_3 all R_4 (hBOOL(hAPP(product_prod(int,int),bool,hAPP(int,fun(product_prod(int,int),bool),hAPP(int,fun(int,fun(product_prod(int,int),bool)),divmod_int_rel,A_1),B),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),Q_3),R_4))) -> (ti(int,B) != zero_zero(int) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),C)) -> hBOOL(hAPP(product_prod(int,int),bool,hAPP(int,fun(product_prod(int,int),bool),hAPP(int,fun(int,fun(product_prod(int,int),bool)),divmod_int_rel,A_1),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),C)),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),Q_3),C)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),Q_3),C))),R_4)))))))) # label(fact_1185_zmult2__lemma) # label(axiom) # label(non_clause).  [assumption].
7.36/7.40	161 (all K_4 all I_1 all J_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_1),J_2)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_4),I_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_4),J_2))))) # label(fact_585_mult__le__mono2) # label(axiom) # label(non_clause).  [assumption].
7.36/7.40	162 (all X hAPP(complex,complex,inverse_inverse(complex),hAPP(complex,complex,cnj,X)) = hAPP(complex,complex,cnj,hAPP(complex,complex,inverse_inverse(complex),X))) # label(fact_2929_complex__cnj__inverse) # label(axiom) # label(non_clause).  [assumption].
7.36/7.40	163 (all X_a all C_1 all A_3 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),hAPP(fun(X_a,bool),fun(X_a,bool),uminus_uminus(fun(X_a,bool)),A_3))) <-> -hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),A_3)))) # label(fact_2194_Compl__iff) # label(axiom) # label(non_clause).  [assumption].
7.36/7.40	164 (all X_a (field(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,inverse_inverse(X_a),B)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),A_1),B)))) # label(fact_2558_field__divide__inverse) # label(axiom) # label(non_clause).  [assumption].
7.36/7.40	165 (all B all A_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),B)) -> hAPP(product_prod(int,int),int,product_snd(int,int),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),posDivAlg,A_1),B)) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_1),B)))) # label(fact_3118_mod__pos__pos) # label(axiom) # label(non_clause).  [assumption].
7.36/7.40	166 (all X_a (linordered_semidom(X_a) -> (all A_1 all N all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),B),N))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),B)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B))))))) # label(fact_440_power__less__imp__less__base) # label(axiom) # label(non_clause).  [assumption].
7.36/7.40	167 (all C all A_1 all B (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),B)) -> (C = B -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),C))))) # label(fact_631_dvd_Oord__le__eq__trans) # label(axiom) # label(non_clause).  [assumption].
7.36/7.40	168 (all N all X hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,real_1(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),N),X))),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(int,real,real_1(int),N)),hAPP(int,real,real_1(int),X))))) # label(fact_3360_real__of__int__div4) # label(axiom) # label(non_clause).  [assumption].
7.36/7.40	169 (all X hAPP(real,real,sin,hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),X)) = hAPP(real,real,cos,X)) # label(fact_2391_cos__sin__eq) # label(axiom) # label(non_clause).  [assumption].
7.36/7.40	170 (all Y_1 all X_1 (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),zEven)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Y_1),zOdd)) -> hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X_1),Y_1)),zOdd))))) # label(fact_1368_even__minus__odd) # label(axiom) # label(non_clause).  [assumption].
7.36/7.40	171 (all Ma all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),hAPP(nat,nat,suc,N_1))) <-> zero_zero(nat) = Ma | (exists J_1 (Ma = hAPP(nat,nat,suc,J_1) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),J_1),N_1)))))) # label(fact_1320_less__Suc__eq__0__disj) # label(axiom) # label(non_clause).  [assumption].
7.36/7.40	172 (all X_1 (X_1 = zero_zero(real) <-> zero_zero(real) = hAPP(real,real,sqrt,X_1))) # label(fact_1613_real__sqrt__eq__0__iff) # label(axiom) # label(non_clause).  [assumption].
7.36/7.40	173 (all X_a (linord1117847801e_zero(X_a) -> (all A_2 all B_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),A_2)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_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_1)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),zero_zero(X_a))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),A_2),B_1)),zero_zero(X_a))))))) # label(fact_1674_divide__le__0__iff) # label(axiom) # label(non_clause).  [assumption].
7.36/7.40	174 (all X_a all X_b all X_c ti(fun(fun(X_a,fun(X_b,X_c)),fun(fun(X_a,X_b),fun(X_a,X_c))),combs(X_a,X_b,X_c)) = combs(X_a,X_b,X_c)) # label(tsy_c_COMBS_res) # label(axiom) # label(non_clause).  [assumption].
7.36/7.40	175 (all X_a (order(X_a) -> ti(fun(fun(nat,X_a),bool),monoseq(X_a)) = monoseq(X_a))) # label(tsy_c_SEQ_Omonoseq_res) # label(axiom) # label(non_clause).  [assumption].
7.36/7.40	176 (all X_a (linord219039673up_add(X_a) -> (all A_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),A_2)) <-> 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_2),A_2))))))) # label(fact_818_zero__le__double__add__iff__zero__le__single__add) # label(axiom) # label(non_clause).  [assumption].
7.36/7.40	177 (all X_a (real_normed_vector(X_a) -> (all Ra all R_4 all X hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),R_4),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),Ra),X)) = hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),Ra),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),R_4),X))))) # label(fact_4696_scaleR__right_OscaleR) # label(axiom) # label(non_clause).  [assumption].
7.36/7.40	178 (all X_b all X_a (topological_space(X_a) & topological_space(X_b) -> (all K all A_2 hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,X_b),fun(X_a,bool),isCont(X_a,X_b),hAPP(X_b,fun(X_a,X_b),combk(X_b,X_a),K)),A_2))))) # label(fact_4898_isCont__const) # label(axiom) # label(non_clause).  [assumption].
7.36/7.40	179 (all X_a (linordered_idom(X_a) -> (all A_1 all N hAPP(X_a,X_a,abs_abs(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N)) = hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(X_a,X_a,abs_abs(X_a),A_1)),N)))) # label(fact_1844_power__abs) # label(axiom) # label(non_clause).  [assumption].
7.36/7.40	180 (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_376_mult__nonneg__nonpos2) # label(axiom) # label(non_clause).  [assumption].
7.36/7.40	181 (all X_a all F all A_3 all N_1 (hAPP(nat,nat,suc,N_1) = hAPP(fun(X_a,bool),nat,hAPP(fun(X_a,nat),fun(fun(X_a,bool),nat),big_co1399186613setsum(X_a,nat),F),A_3) -> (exists X_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(X_a,nat,F,X_2))) & hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_3)))))) # label(fact_4301_setsum__SucD) # label(axiom) # label(non_clause).  [assumption].
7.36/7.40	182 (all X_a (ring_div(X_a) -> (all A_1 all B all C hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_1),B)),C) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),B),C))),C)))) # label(fact_946_mod__diff__right__eq) # label(axiom) # label(non_clause).  [assumption].
7.36/7.40	183 (all X all Y all Z_1 hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),X),Y)),Z_1) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),X),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),Y),Z_1))) # label(fact_203_zpower__zpower) # label(axiom) # label(non_clause).  [assumption].
7.36/7.40	184 (all X_1 (hAPP(real,real,sqrt,X_1) = one_one(real) <-> one_one(real) = X_1)) # label(fact_1619_real__sqrt__eq__1__iff) # label(axiom) # label(non_clause).  [assumption].
7.36/7.40	185 (all M all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),one_one(nat))),N) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),hAPP(nat,nat,suc,N))) # label(fact_1347_diff__Suc__eq__diff__pred) # label(axiom) # label(non_clause).  [assumption].
7.36/7.40	186 (all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,number_number_of(real),min_1)),Y)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),Y),one_one(real))) -> hAPP(real,real,sin,hAPP(real,real,arcsin,Y)) = Y & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,arcsin,Y)),pi)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),hAPP(real,real,arcsin,Y)))))) # label(fact_2402_arcsin__pi) # label(axiom) # label(non_clause).  [assumption].
7.36/7.40	187 (all N_1 zero_zero(real) = hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(real,fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(real,fun(nat,real)),combc(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(nat,fun(real,fun(real,real))),fun(fun(nat,real),fun(nat,fun(real,real))),combs(nat,real,fun(real,real)),hAPP(fun(nat,bool),fun(nat,fun(real,fun(real,real))),hAPP(fun(bool,fun(real,fun(real,real))),fun(fun(nat,bool),fun(nat,fun(real,fun(real,real)))),combb(bool,fun(real,fun(real,real)),nat),if(real)),even_odd_even(nat))),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),inverse_divide(real)),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),min_1))),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),div_div(nat)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),fact_fact(nat))))),hAPP(real,fun(nat,real),power_power(real),zero_zero(real))))),zero_zero(real))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),one_one(nat)),N_1))) # label(fact_4239_lemma__STAR__cos2) # label(axiom) # label(non_clause).  [assumption].
7.36/7.40	188 (all X_a (real_n1866405975lgebra(X_a) -> (all X_3 all A_2 (hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),X_3),A_2),sequentially)) -> (ti(X_a,A_2) != zero_zero(X_a) -> hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(X_a,X_a),fun(fun(nat,X_a),fun(nat,X_a)),combb(X_a,X_a,nat),inverse_inverse(X_a)),X_3)),hAPP(X_a,X_a,inverse_inverse(X_a),A_2)),sequentially))))))) # label(fact_4483_LIMSEQ__inverse) # label(axiom) # label(non_clause).  [assumption].
7.36/7.40	189 (all F all G ((all N_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),hAPP(nat,real,F,N_2))),hAPP(nat,real,G,N_2)))) -> (hBOOL(hAPP(fun(nat,real),bool,summable(real),G)) -> hBOOL(hAPP(fun(nat,real),bool,summable(real),F)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(fun(nat,real),real,suminf(real),F)),hAPP(fun(nat,real),real,suminf(real),G)))))) # label(fact_4070_summable__le2) # label(axiom) # label(non_clause).  [assumption].
7.36/7.40	190 (all X_a (comple44059174attice(X_a) -> (all Z all A_3 ((all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_3)) -> 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),hAPP(fun(X_a,bool),X_a,complete_Sup_Sup(X_a),A_3)),Z)))))) # label(fact_2734_complete__lattice__class_OSup__least) # label(axiom) # label(non_clause).  [assumption].
7.36/7.40	191 (all X_c all X_a all X_b all Z all C_1 all P_4 ((all A_4 all B_4 (hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),A_4),B_4) = ti(product_prod(X_a,X_b),P_4) -> hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),Z),hAPP(X_b,fun(X_c,bool),hAPP(X_a,fun(X_b,fun(X_c,bool)),C_1,A_4),B_4))))) -> hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),Z),hAPP(product_prod(X_a,X_b),fun(X_c,bool),hAPP(fun(X_a,fun(X_b,fun(X_c,bool))),fun(product_prod(X_a,X_b),fun(X_c,bool)),product_prod_case(X_a,X_b,fun(X_c,bool)),C_1),P_4))))) # label(fact_4057_mem__splitI2) # label(axiom) # label(non_clause).  [assumption].
7.36/7.40	192 (all X_a (dvd(X_a) -> ti(fun(X_a,fun(X_a,X_a)),times_times(X_a)) = times_times(X_a))) # label(tsy_c_Groups_Otimes__class_Otimes_2_res) # label(axiom) # label(non_clause).  [assumption].
7.36/7.40	193 (all X_3 (hBOOL(hAPP(fun(nat,complex),bool,summable(complex),X_3)) -> hAPP(complex,real,im,hAPP(fun(nat,complex),complex,suminf(complex),X_3)) = hAPP(fun(nat,real),real,suminf(real),hAPP(fun(nat,complex),fun(nat,real),hAPP(fun(complex,real),fun(fun(nat,complex),fun(nat,real)),combb(complex,real,nat),im),X_3)))) # label(fact_4049_Im_Osuminf) # label(axiom) # label(non_clause).  [assumption].
7.36/7.40	194 (all N all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(nat,real,real_1(nat),N)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,real_1(nat),N)),one_one(real)))) -> hAPP(real,nat,natceiling,X) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),one_one(nat))))) # label(fact_2383_natceiling__eq) # label(axiom) # label(non_clause).  [assumption].
7.36/7.40	195 (all X_a (real_normed_algebra(X_a) -> (all C_1 all F all A_2 (hBOOL(hAPP(X_a,bool,hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),F),A_2)) -> hBOOL(hAPP(X_a,bool,hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),hAPP(X_a,fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(X_a,fun(nat,X_a)),combc(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),times_times(X_a)),F)),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),C_1))))))) # label(fact_4080_sums__mult2) # label(axiom) # label(non_clause).  [assumption].
7.36/7.40	196 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N),M)),N) = M)) # label(fact_1120_div__mult__self1__is__m) # label(axiom) # label(non_clause).  [assumption].
7.36/7.40	197 (all X_a (division_ring(X_a) -> (all A_1 (zero_zero(X_a) != ti(X_a,A_1) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),hAPP(X_a,X_a,inverse_inverse(X_a),A_1)) = one_one(X_a))))) # label(fact_2579_right__inverse) # label(axiom) # label(non_clause).  [assumption].
7.36/7.40	198 (all X_a all X_b (order(X_a) & order(X_b) -> (all C_1 all A_2 all F all B_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),hAPP(X_b,X_a,F,B_1))) -> (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),B_1),C_1)) -> ((all X_2 all Y_2 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),X_2),Y_2)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_b,X_a,F,X_2)),hAPP(X_b,X_a,F,Y_2))))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),hAPP(X_b,X_a,F,C_1))))))))) # label(fact_2837_order__less__le__subst1) # label(axiom) # label(non_clause).  [assumption].
7.36/7.40	199 (all N all M (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),M)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N)) -> -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),N),M))))) # label(fact_486_nat__dvd__not__less) # label(axiom) # label(non_clause).  [assumption].
7.36/7.40	200 (all N all M all R_4 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,real_1(int),M)),R_4)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),R_4),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(int,real,real_1(int),N)),one_one(real)))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),M),N))))) # label(fact_3408_lemma__floor) # label(axiom) # label(non_clause).  [assumption].
7.36/7.40	201 (all X_a all F1 all Real1 all Real2 hAPP(real,X_a,hAPP(real,fun(real,X_a),F1,Real1),Real2) = hAPP(complex,X_a,hAPP(fun(real,fun(real,X_a)),fun(complex,X_a),complex_case(X_a),F1),hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,Real1),Real2))) # label(fact_2759_complex_Osimps_I2_J) # label(axiom) # label(non_clause).  [assumption].
7.36/7.40	202 (all X_a all X all Y ti(X_a,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)) # label(help_If_2_1_T) # label(axiom) # label(non_clause).  [assumption].
7.36/7.40	203 (all X hAPP(complex,complex,cnj,hAPP(real,complex,of_real(complex),X)) = hAPP(real,complex,of_real(complex),X)) # label(fact_2945_complex__cnj__complex__of__real) # label(axiom) # label(non_clause).  [assumption].
7.36/7.40	204 (all X_a all X_b all X all Y all A_1 (hAPP(product_prod(X_a,X_b),X_a,product_fst(X_a,X_b),hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),X),Y)) = ti(X_a,A_1) -> ti(X_a,A_1) = ti(X_a,X))) # label(fact_3141_fst__eqD) # label(axiom) # label(non_clause).  [assumption].
7.36/7.40	205 (all K_4 hAPP(int,real,number_number_of(real),K_4) = hAPP(rat,real,ratreal,hAPP(int,rat,number_number_of(rat),K_4))) # label(fact_3762_number__of__real__code) # label(axiom) # label(non_clause).  [assumption].
7.36/7.40	206 (all X_a (linordered_semidom(X_a) -> (all N all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),A_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N)))))))) # label(fact_444_power__less__power__Suc) # label(axiom) # label(non_clause).  [assumption].
7.36/7.40	207 (all Ma all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Ma),N_1)) -> (Ma = N_1 <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),hAPP(nat,nat,suc,Ma)))))) # label(fact_1332_le__less__Suc__eq) # label(axiom) # label(non_clause).  [assumption].
7.36/7.40	208 (all R_4 all P_5 all Q_3 (hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),P_5),Q_3) = hAPP(rat,product_prod(int,int),quotient_of,R_4) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),Q_3)))) # label(fact_3724_quotient__of__denom__pos) # label(axiom) # label(non_clause).  [assumption].
7.36/7.40	209 (all A_1 all N all B (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A_1),N)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),B),N))) -> (zero_zero(nat) != N -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),B))))) # label(fact_727_divides__rev) # label(axiom) # label(non_clause).  [assumption].
7.36/7.40	210 (all X_a (comm_monoid_add(X_a) & topological_space(X_a) -> sums(X_a) = ti(fun(fun(nat,X_a),fun(X_a,bool)),sums(X_a)))) # label(tsy_c_Series_Osums_res) # label(axiom) # label(non_clause).  [assumption].
7.36/7.40	211 (all W hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,W)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),W)),hAPP(int,nat,number_number_of(nat),W))) # label(fact_3830_nat__number__of__Bit0) # label(axiom) # label(non_clause).  [assumption].
7.36/7.40	212 (all X all A_1 all B (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),powr,X),A_1)),hAPP(real,real,hAPP(real,fun(real,real),powr,X),B))) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),X)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A_1),B))))) # label(fact_3354_powr__less__cancel) # label(axiom) # label(non_clause).  [assumption].
7.36/7.40	213 (all A_1 all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,real_1(int),A_1)),X)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A_1),hAPP(real,int,archim2085082626_floor(real),X))))) # label(fact_3362_le__floor) # label(axiom) # label(non_clause).  [assumption].
7.36/7.40	214 (all X_a (ring_div(X_a) -> (all A_1 all B all C hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),B),C))),C) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_1),B)),C)))) # label(fact_944_mod__diff__eq) # label(axiom) # label(non_clause).  [assumption].
7.36/7.40	215 (all X_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(nat,fun(real,real),root,N_1),X_1)),one_one(real))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_1),one_one(real)))))) # label(fact_2701_real__root__lt__1__iff) # label(axiom) # label(non_clause).  [assumption].
7.36/7.40	216 (all X_a (ord(X_a) -> (all X all Least ((all X_2 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Least),X_2))) -> ti(X_a,Least) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),Least),X))))) # label(fact_4836_min__leastL) # label(axiom) # label(non_clause).  [assumption].
7.36/7.40	217 (all N_1 all Ma (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),N_1),Ma)) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,real_1(int),N_1)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(int,real,real_1(int),Ma)),one_one(real)))))) # label(fact_3393_int__le__real__less) # label(axiom) # label(non_clause).  [assumption].
7.36/7.40	218 (all X_a (real_algebra_1(X_a) -> (all X_1 (X_1 = zero_zero(real) <-> zero_zero(X_a) = hAPP(real,X_a,of_real(X_a),X_1))))) # label(fact_2781_of__real__eq__0__iff) # label(axiom) # label(non_clause).  [assumption].
7.36/7.40	219 (all F all J all N_1 all H (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),H)) -> (exists B_6 hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),inverse_divide(real)),J)),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),fact_fact(nat))))),hAPP(real,fun(nat,real),power_power(real),H))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),N_1))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B_6),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),H),N_1)),hAPP(nat,real,real_1(nat),hAPP(nat,nat,fact_fact(nat),N_1))))) = hAPP(real,real,F,H)))) # label(fact_4272_Maclaurin__lemma) # label(axiom) # label(non_clause).  [assumption].
7.36/7.40	220 (all X_a (number_ring(X_a) -> (all X ((hBOOL(hAPP(nat,bool,even_odd_even(nat),X)) -> one_one(X_a) = hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(int,X_a,number_number_of(X_a),min_1)),X)) & (-hBOOL(hAPP(nat,bool,even_odd_even(nat),X)) -> hAPP(int,X_a,number_number_of(X_a),min_1) = hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(int,X_a,number_number_of(X_a),min_1)),X)))))) # label(fact_2458_neg__one__even__odd__power) # label(axiom) # label(non_clause).  [assumption].
7.36/7.40	221 (all N_1 all N_7 all F ((all N_2 hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,F,N_2)),hAPP(nat,nat,F,hAPP(nat,nat,suc,N_2))))) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_1),N_7)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,F,N_1)),hAPP(nat,nat,F,N_7)))))) # label(fact_1482_dvd_Olift__Suc__mono__le) # label(axiom) # label(non_clause).  [assumption].
7.36/7.40	222 (all A_1 all B (ti(int,B) != zero_zero(int) -> hBOOL(hAPP(product_prod(int,int),bool,hAPP(int,fun(product_prod(int,int),bool),hAPP(int,fun(int,fun(product_prod(int,int),bool)),divmod_int_rel,A_1),B),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_1),B)),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_1),B)))))) # label(fact_1194_divmod__int__rel__div__mod) # label(axiom) # label(non_clause).  [assumption].
7.36/7.40	223 (all X_1 all A_3 all Ma (hBOOL(hAPP(fun(fun(int,bool),bool),bool,hAPP(fun(int,bool),fun(fun(fun(int,bool),bool),bool),member(fun(int,bool)),A_3),hAPP(int,fun(fun(int,bool),bool),rsetR,Ma))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),Ma)) -> (one_one(int) = hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,X_1),Ma) -> hBOOL(hAPP(fun(fun(int,bool),bool),bool,hAPP(fun(int,bool),fun(fun(fun(int,bool),bool),bool),member(fun(int,bool)),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,int),fun(fun(int,bool),fun(int,bool)),image(int,int),hAPP(int,fun(int,int),hAPP(fun(int,fun(int,int)),fun(int,fun(int,int)),combc(int,int,int),times_times(int)),X_1)),A_3)),hAPP(int,fun(fun(int,bool),bool),rsetR,Ma))))))) # label(fact_3900_RsetR__zmult__mono) # label(axiom) # label(non_clause).  [assumption].
7.36/7.40	224 (all X_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(nat,fun(real,real),root,N_1),X_1)),zero_zero(real))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_1),zero_zero(real)))))) # label(fact_2692_real__root__le__0__iff) # label(axiom) # label(non_clause).  [assumption].
7.36/7.40	225 (all X_a ti(fun(product_prod(fun(X_a,bool),fun(X_a,bool)),bool),finite_psubset(X_a)) = finite_psubset(X_a)) # label(tsy_c_Wellfounded_Ofinite__psubset_res) # label(axiom) # label(non_clause).  [assumption].
7.36/7.40	226 (all B all A_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),zero_zero(int))) -> hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_1),B) = hAPP(product_prod(int,int),int,product_snd(int,int),hAPP(product_prod(int,int),product_prod(int,int),negateSnd,hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),negDivAlg,hAPP(int,int,uminus_uminus(int),A_1)),hAPP(int,int,uminus_uminus(int),B))))))) # label(fact_3120_mod__pos__neg) # label(axiom) # label(non_clause).  [assumption].
7.36/7.40	227 (all X_a (ab_group_add(X_a) -> (all F all Ma all N_1 ((hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Ma),N_1)) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(nat,X_a,F,Ma)),hAPP(nat,X_a,F,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_1),one_one(nat)))) = hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),minus_minus(X_a)),F)),hAPP(fun(nat,nat),fun(nat,X_a),hAPP(fun(nat,X_a),fun(fun(nat,nat),fun(nat,X_a)),combb(nat,X_a,nat),F),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),one_one(nat))))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),Ma),N_1))) & (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Ma),N_1)) -> zero_zero(X_a) = hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),minus_minus(X_a)),F)),hAPP(fun(nat,nat),fun(nat,X_a),hAPP(fun(nat,X_a),fun(fun(nat,nat),fun(nat,X_a)),combb(nat,X_a,nat),F),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),one_one(nat))))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),Ma),N_1))))))) # label(fact_4618_setsum__natinterval__difff) # label(axiom) # label(non_clause).  [assumption].
7.36/7.40	228 (all K all Ma all N_1 (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)),Ma)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,K)),N_1))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),N_1)))) # label(fact_1338_Suc__mult__less__cancel1) # label(axiom) # label(non_clause).  [assumption].
7.36/7.40	229 (all N all F_4 all M (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),F_4),M)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),F_4),N)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),F_4),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),M),N)))))) # label(fact_961_zdvd__zmod) # label(axiom) # label(non_clause).  [assumption].
7.36/7.40	230 (all Y_1 all X_1 (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),zEven)) -> hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X_1),Y_1)),zEven)))) # label(fact_1269_even__times__either) # label(axiom) # label(non_clause).  [assumption].
7.36/7.40	231 (all Ma all N_1 (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),N_1)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),hAPP(nat,nat,suc,Ma))))) # label(fact_1239_not__less__eq) # label(axiom) # label(non_clause).  [assumption].
7.36/7.40	232 (all A_2 all Ma all X_1 (ti(int,X_1) != zero_zero(int) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_2),Ma)) -> hAPP(fun(int,bool),int,hAPP(fun(int,int),fun(fun(int,bool),int),big_co302546470etprod(int,int),combi(int)),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,int),fun(fun(int,bool),fun(int,bool)),image(int,int),hAPP(int,fun(int,int),hAPP(fun(int,fun(int,int)),fun(int,fun(int,int)),combc(int,int,int),times_times(int)),X_1)),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),bnorRset,A_2),Ma))) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(fun(int,bool),int,hAPP(fun(int,int),fun(fun(int,bool),int),big_co302546470etprod(int,int),combi(int)),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),bnorRset,A_2),Ma))),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),X_1),hAPP(fun(int,bool),nat,finite_card(int),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),bnorRset,A_2),Ma))))))) # label(fact_3932_Bnor__prod__power) # label(axiom) # label(non_clause).  [assumption].
7.36/7.40	233 (all X hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),X)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) # label(fact_450_four__x__squared) # label(axiom) # label(non_clause).  [assumption].
7.36/7.40	234 (all Z_1 exists A_4 exists R_2 hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(real,complex,of_real(complex),R_2)),hAPP(complex,complex,expi,A_4)) = Z_1) # label(fact_2914_complex__expi__Ex) # label(axiom) # label(non_clause).  [assumption].
7.36/7.40	235 (all X_a (linord219039673up_add(X_a) -> (all A_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),hAPP(X_a,X_a,uminus_uminus(X_a),A_2))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),zero_zero(X_a))))))) # label(fact_2058_le__minus__self__iff) # label(axiom) # label(non_clause).  [assumption].
7.36/7.40	236 (all Y_1 all X_1 all A_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),A_2)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Y_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),log,A_2),X_1)),hAPP(real,real,hAPP(real,fun(real,real),log,A_2),Y_1))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_1),Y_1))))))) # label(fact_2646_log__le__cancel__iff) # label(axiom) # label(non_clause).  [assumption].
7.36/7.40	237 (all X_a (ordered_ab_group_add(X_a) -> (all A_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),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,uminus_uminus(X_a),A_2))))))) # label(fact_2061_neg__0__less__iff__less) # label(axiom) # label(non_clause).  [assumption].
7.36/7.40	238 (all X_a (field_inverse_zero(X_a) -> (all A_1 all B hAPP(X_a,X_a,inverse_inverse(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),A_1),B)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),B),A_1)))) # label(fact_2519_inverse__divide) # label(axiom) # label(non_clause).  [assumption].
7.36/7.40	239 (all X_a (semiring_div(X_a) -> (all A_1 all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),A_1),B)),B)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),A_1),B)) = ti(X_a,A_1)))) # label(fact_915_mod__div__equality) # label(axiom) # label(non_clause).  [assumption].
7.36/7.40	240 (all K_4 hAPP(int,rat,hAPP(int,fun(int,rat),fract,zero_zero(int)),K_4) = zero_zero(rat)) # label(fact_3739_rat__number__collapse_I1_J) # label(axiom) # label(non_clause).  [assumption].
7.36/7.40	241 (all N_1 (zero_zero(nat) = N_1 <-> zero_zero(real) = hAPP(nat,real,real_1(nat),N_1))) # label(fact_2301_real__of__nat__zero__iff) # label(axiom) # label(non_clause).  [assumption].
7.36/7.40	242 (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_97_zadd__assoc) # label(axiom) # label(non_clause).  [assumption].
7.36/7.40	243 (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_224_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) # label(axiom) # label(non_clause).  [assumption].
7.36/7.40	244 (all X_a all P_1 ((exists X1 hBOOL(hAPP(X_a,bool,P_1,X1))) -> hBOOL(hAPP(X_a,bool,P_1,hAPP(fun(X_a,bool),X_a,hilbert_Eps(X_a),P_1))))) # label(fact_4785_someI__ex) # label(axiom) # label(non_clause).  [assumption].
7.36/7.40	245 (all I_1 all K_4 all J_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_4),J_2)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_2),K_4)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_1),J_2)),K_4))) # label(fact_691_diff__add__assoc) # label(axiom) # label(non_clause).  [assumption].
7.36/7.40	246 (all R_4 all P_5 all Q_3 (hAPP(product_prod(int,int),product_prod(int,int),normalize,R_4) = hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),P_5),Q_3) -> hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),P_5),Q_3) = one_one(int))) # label(fact_4404_normalize__coprime) # label(axiom) # label(non_clause).  [assumption].
7.36/7.40	247 (all X_a (topological_space(X_a) -> (all F all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(real,fun(filter(X_a),bool),hAPP(fun(X_a,real),fun(real,fun(filter(X_a),bool)),tendsto(X_a,real),F),zero_zero(real)),hAPP(X_a,filter(X_a),at(X_a),A_2))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(real,fun(filter(X_a),bool),hAPP(fun(X_a,real),fun(real,fun(filter(X_a),bool)),tendsto(X_a,real),hAPP(fun(X_a,real),fun(X_a,real),hAPP(fun(real,real),fun(fun(X_a,real),fun(X_a,real)),combb(real,real,X_a),abs_abs(real)),F)),zero_zero(real)),hAPP(X_a,filter(X_a),at(X_a),A_2))))))) # label(fact_4593_LIM__rabs__zero) # label(axiom) # label(non_clause).  [assumption].
7.36/7.40	248 (all A_1 zero_zero(int) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_1),hAPP(int,int,number_number_of(int),min_1))) # label(fact_1037_zmod__minus1__right) # label(axiom) # label(non_clause).  [assumption].
7.36/7.40	249 (all X_a (linordered_field(X_a) -> (all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,inverse_inverse(X_a),B)),hAPP(X_a,X_a,inverse_inverse(X_a),A_1)))))))) # label(fact_2571_le__imp__inverse__le__neg) # label(axiom) # label(non_clause).  [assumption].
7.36/7.40	250 (all N_1 all Ma (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_1),Ma)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,N_1)),hAPP(nat,nat,suc,Ma))))) # label(fact_1246_Suc__le__mono) # label(axiom) # label(non_clause).  [assumption].
7.36/7.40	251 (all X exists N_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),hAPP(nat,real,real_1(nat),N_2)))) # label(fact_2732_reals__Archimedean2) # label(axiom) # label(non_clause).  [assumption].
7.36/7.40	252 (all X_a (group_add(X_a) -> (all A_1 zero_zero(X_a) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),hAPP(X_a,X_a,uminus_uminus(X_a),A_1))))) # label(fact_2065_right__minus) # label(axiom) # label(non_clause).  [assumption].
7.36/7.40	253 (all X_a (linordered_field(X_a) -> (all C all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),B),C)))))))) # label(fact_1683_divide__strict__right__mono) # label(axiom) # label(non_clause).  [assumption].
7.36/7.40	254 (all X_a (semiring_1(X_a) -> hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),zero_zero(X_a)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = zero_zero(X_a))) # label(fact_13_zero__power2) # label(axiom) # label(non_clause).  [assumption].
7.36/7.40	255 (all M all N hAPP(product_prod(nat,nat),nat,product_fst(nat,nat),hAPP(nat,product_prod(nat,nat),hAPP(nat,fun(nat,product_prod(nat,nat)),divmod_nat,M),N)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),M),N)) # label(fact_3125_div__nat__def) # label(axiom) # label(non_clause).  [assumption].
7.36/7.40	256 (all X_a (real_div_algebra(X_a) -> (all X (X != zero_zero(real) -> hAPP(real,X_a,of_real(X_a),hAPP(real,real,inverse_inverse(real),X)) = hAPP(X_a,X_a,inverse_inverse(X_a),hAPP(real,X_a,of_real(X_a),X)))))) # label(fact_2807_nonzero__of__real__inverse) # label(axiom) # label(non_clause).  [assumption].
7.36/7.40	257 (all A_2 all B_1 all K all Ma (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Ma)) -> (one_one(int) = hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,K),Ma) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_2),B_1),Ma)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_2),K)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B_1),K)),Ma)))))) # label(fact_3470_zcong__cancel) # label(axiom) # label(non_clause).  [assumption].
7.36/7.40	258 (all X_a (linordered_idom(X_a) -> (all A_1 all N (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),N))))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),A_1)))))) # label(fact_1470_odd__0__le__power__imp__0__le) # label(axiom) # label(non_clause).  [assumption].
7.36/7.40	259 (all X_a (semiring_div(X_a) -> (all A_1 all B all C hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),A_1),C)),B)),C) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)),C)))) # label(fact_929_mod__mult__left__eq) # label(axiom) # label(non_clause).  [assumption].
7.36/7.40	260 (all X ti(int,X) = hAPP(int,int,succ,hAPP(int,int,pred,X))) # label(fact_2899_succ__pred) # label(axiom) # label(non_clause).  [assumption].
7.36/7.40	261 (all X_a (field_char_0(X_a) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),one_one(X_a)),field_char_0_Rats(X_a))))) # label(fact_3695_Rats__1) # label(axiom) # label(non_clause).  [assumption].
7.36/7.40	262 (all X all Y hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),X),Y)),Y))) # label(fact_3245_gcd__semilattice__nat_Oinf__le2) # label(axiom) # label(non_clause).  [assumption].
7.36/7.40	263 (all Y all X all Z_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X),Z_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Y),Z_1))))) # label(fact_3040_termination__basic__simps_I2_J) # label(axiom) # label(non_clause).  [assumption].
7.36/7.40	264 (all X_a all C_1 all X_3 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),X_3)) -> hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C_1),hAPP(nat,int,semiring_1_of_nat(int),hAPP(fun(X_a,bool),nat,finite_card(X_a),X_3))) = hAPP(fun(X_a,bool),int,hAPP(fun(X_a,int),fun(fun(X_a,bool),int),big_co1399186613setsum(X_a,int),hAPP(int,fun(X_a,int),combk(int,X_a),C_1)),X_3))) # label(fact_4262_setsum__const) # label(axiom) # label(non_clause).  [assumption].
7.36/7.40	265 (all K1 all K2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit0,K1)),hAPP(int,int,bit0,K2))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),K1),K2)))) # label(fact_35_less__eq__int__code_I13_J) # label(axiom) # label(non_clause).  [assumption].
7.36/7.40	266 (all X_a (field_inverse_zero(X_a) & number_ring(X_a) -> (all X hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),X),hAPP(int,X_a,number_number_of(X_a),pls)) = zero_zero(X_a)))) # label(fact_1732_divide__Numeral0) # label(axiom) # label(non_clause).  [assumption].
7.36/7.40	267 (all A_2 all B_1 all N_1 (zero_zero(nat) != N_1 -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A_2),B_1)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A_2),N_1)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),B_1),N_1)))))) # label(fact_869_pow__divides__eq__int) # label(axiom) # label(non_clause).  [assumption].
7.36/7.40	268 (all X_a all X_b all B_2 all F all A_3 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),B_2),hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),A_3))) <-> (exists AA (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),AA),A_3)) & ti(fun(X_a,bool),B_2) = hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),AA))))) # label(fact_3634_subset__image__iff) # label(axiom) # label(non_clause).  [assumption].
7.36/7.40	269 (all X_a (real_normed_algebra(X_a) -> (all Y all S_3 all X all R_4 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,norm_norm(X_a),X)),R_4)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,norm_norm(X_a),Y)),S_3)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),Y))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),R_4),S_3)))))))) # label(fact_1789_norm__mult__less) # label(axiom) # label(non_clause).  [assumption].
7.36/7.40	270 (all Ma all X_3 ((all Y1 all Y2 (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Y2),X_3)) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,Y1),Y2),Ma)) & hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Y1),X_3)) -> ti(int,Y2) = ti(int,Y1))) <-> hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),resSet,Ma),X_3)))) # label(fact_2916_ResSet__def) # label(axiom) # label(non_clause).  [assumption].
7.36/7.40	271 (all X_a all F all F_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),F_1)) -> ((all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),F_1)) -> hAPP(X_a,nat,F,X_2) = one_one(nat))) <-> hAPP(fun(X_a,bool),nat,hAPP(fun(X_a,nat),fun(fun(X_a,bool),nat),big_co302546470etprod(X_a,nat),F),F_1) = one_one(nat)))) # label(fact_3938_setprod__eq__1__iff) # label(axiom) # label(non_clause).  [assumption].
7.36/7.40	272 (all X all N hAPP(real,real,tan,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,real_1(nat),N)),pi))) = hAPP(real,real,tan,X)) # label(fact_2347_tan__periodic__nat) # label(axiom) # label(non_clause).  [assumption].
7.36/7.40	273 (all K (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),min_1),hAPP(int,int,bit1,K))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),min_1),K)))) # label(fact_300_rel__simps_I26_J) # label(axiom) # label(non_clause).  [assumption].
7.36/7.40	274 (all N (one_one(nat) != N -> (exists P_6 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),P_6),N)) & hBOOL(hAPP(nat,bool,prime,P_6)))))) # label(fact_3088_prime__factor) # label(axiom) # label(non_clause).  [assumption].
7.36/7.40	275 (all X_a (real_algebra_1(X_a) -> (all Z_1 hAPP(int,X_a,ring_1_of_int(X_a),Z_1) = hAPP(real,X_a,of_real(X_a),hAPP(int,real,ring_1_of_int(real),Z_1))))) # label(fact_3573_of__real__of__int__eq) # label(axiom) # label(non_clause).  [assumption].
7.36/7.40	276 (all X_a all A_3 hAPP(nat,real,real_1(nat),hAPP(fun(X_a,bool),nat,finite_card(X_a),A_3)) = hAPP(fun(X_a,bool),real,hAPP(fun(X_a,real),fun(fun(X_a,bool),real),big_co1399186613setsum(X_a,real),hAPP(real,fun(X_a,real),combk(real,X_a),one_one(real))),A_3)) # label(fact_4229_real__of__card) # label(axiom) # label(non_clause).  [assumption].
7.36/7.40	277 (all K all L (hAPP(quickcheck_code_int,int,quickcheck_int_of,L) = hAPP(quickcheck_code_int,int,quickcheck_int_of,K) <-> K = L)) # label(fact_3162_Quickcheck__Narrowing_Oint__of__inject) # label(axiom) # label(non_clause).  [assumption].
7.36/7.40	278 (all X all Y all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),Y)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(nat,fun(real,real),root,N),X)),hAPP(real,real,hAPP(nat,fun(real,real),root,N),Y)))))) # label(fact_2681_real__root__less__mono) # label(axiom) # label(non_clause).  [assumption].
7.36/7.40	279 (all K (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),pls)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit0,K)),pls)))) # label(fact_158_rel__simps_I10_J) # label(axiom) # label(non_clause).  [assumption].
7.36/7.40	280 (all D all C all A_1 all B all M (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_1),B),M)) -> (ti(int,B) = ti(int,C) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,C),D),M)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_1),D),M)))))) # label(fact_315_zcong__eq__trans) # label(axiom) # label(non_clause).  [assumption].
7.36/7.40	281 (all X_a (order(X_a) -> (all Z_1 all Y all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z_1),Y)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z_1),X))))))) # label(fact_1579_xt1_I10_J) # label(axiom) # label(non_clause).  [assumption].
7.36/7.40	282 (all Z_1 all Z_4 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Z_4)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Z_4),Z_1)) -> hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),Z_1),Z_4)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(int,nat,nat_1,Z_1)),hAPP(int,nat,nat_1,Z_4))))) # label(fact_1144_nat__diff__distrib) # label(axiom) # label(non_clause).  [assumption].
7.36/7.40	283 (all M all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),M),N)),N) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),M),N))) # label(fact_1084_div__mod__equality_H) # label(axiom) # label(non_clause).  [assumption].
7.36/7.40	284 (all K_4 all I_1 all J_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_1),J_2)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_1),K_4)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J_2),K_4))))) # label(fact_575_add__le__mono1) # label(axiom) # label(non_clause).  [assumption].
7.36/7.40	285 (all X_b all X_a (real_normed_algebra(X_a) -> (all X_1 all G all A_3 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X_1),hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co1399186613setsum(X_b,X_a),G),A_3)) = hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co1399186613setsum(X_b,X_a),hAPP(fun(X_b,X_a),fun(X_b,X_a),hAPP(fun(X_a,X_a),fun(fun(X_b,X_a),fun(X_b,X_a)),combb(X_a,X_a,X_b),hAPP(X_a,fun(X_a,X_a),times_times(X_a),X_1)),G)),A_3)))) # label(fact_4191_mult__right_Osetsum) # label(axiom) # label(non_clause).  [assumption].
7.36/7.40	286 (all R_4 all X all Y hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,hAPP(real,real,hAPP(real,fun(real,real),times_times(real),R_4),X)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),R_4),Y)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(real,complex,of_real(complex),R_4)),hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,X),Y))) # label(fact_2809_complex__of__real__mult__Complex) # label(axiom) # label(non_clause).  [assumption].
7.36/7.40	287 (all A_2 all A_3 all Ma (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),Ma)) -> (hBOOL(hAPP(int,bool,hAPP(fun(int,bool),fun(int,bool),is_RRset,A_3),Ma)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),A_2),A_3)) -> hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),hAPP(int,int,hAPP(int,fun(int,int),hAPP(fun(int,bool),fun(int,fun(int,int)),rRset2norRR,A_3),Ma),A_2)),hAPP(int,fun(int,bool),norRRset,Ma))))))) # label(fact_3622_RRset2norRR__correct2) # label(axiom) # label(non_clause).  [assumption].
7.36/7.40	288 (all N_1 all Ma (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,real_1(nat),N_1)),hAPP(nat,real,real_1(nat),Ma))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_1),Ma)))) # label(fact_2306_real__of__nat__le__iff) # label(axiom) # label(non_clause).  [assumption].
7.36/7.40	289 (all M all N all Qr_1 (hBOOL(hAPP(product_prod(nat,nat),bool,hAPP(nat,fun(product_prod(nat,nat),bool),hAPP(nat,fun(nat,fun(product_prod(nat,nat),bool)),divmod_nat_rel,M),N),Qr_1)) -> Qr_1 = hAPP(nat,product_prod(nat,nat),hAPP(nat,fun(nat,product_prod(nat,nat)),divmod_nat,M),N))) # label(fact_3099_divmod__nat__eq) # label(axiom) # label(non_clause).  [assumption].
7.36/7.40	290 (all X all Y hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),nat_gcd,hAPP(int,nat,nat_1,hAPP(int,int,abs_abs(int),X))),hAPP(int,nat,nat_1,hAPP(int,int,abs_abs(int),Y)))) = hAPP(int,int,hAPP(int,fun(int,int),int_gcd,X),Y)) # label(fact_3671_Nitpick_Oint__gcd__def) # label(axiom) # label(non_clause).  [assumption].
7.36/7.40	291 (all N all A_1 hAPP(complex,real,im,hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),hAPP(real,complex,cis,A_1)),N)) = hAPP(real,real,sin,hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,real_1(nat),N)),A_1))) # label(fact_3024_sin__n__Im__cis__pow__n) # label(axiom) # label(non_clause).  [assumption].
7.36/7.40	292 (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_385_mult__strict__left__mono) # label(axiom) # label(non_clause).  [assumption].
7.36/7.40	293 (all X_a (ring(X_a) -> (all A_1 all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),hAPP(X_a,X_a,uminus_uminus(X_a),B)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),A_1)),B)))) # label(fact_2032_minus__mult__commute) # label(axiom) # label(non_clause).  [assumption].
7.36/7.40	294 (all X_a all A_3 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(fun(X_a,bool),nat,finite_card(X_a),A_3))) -> hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_3)))) # label(fact_1826_card__ge__0__finite) # label(axiom) # label(non_clause).  [assumption].
7.36/7.40	295 (all X_a (linorder(X_a) -> (all X all Y all Z_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),Y),Z_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),Y)),Z_1)))) # label(fact_4809_min__max_Oinf__assoc) # label(axiom) # label(non_clause).  [assumption].
7.36/7.40	296 (all A_2 all C_1 all D_1 all B_1 (zero_zero(int) != ti(int,B_1) -> (zero_zero(int) != ti(int,D_1) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_2),D_1)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B_1),D_1))),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C_1),B_1)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B_1),D_1)))) <-> hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(int,rat,hAPP(int,fun(int,rat),fract,A_2),B_1)),hAPP(int,rat,hAPP(int,fun(int,rat),fract,C_1),D_1))))))) # label(fact_3779_less__rat) # label(axiom) # label(non_clause).  [assumption].
7.36/7.40	297 (all X_a (linordered_idom(X_a) -> (all A_2 all N_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_2),N_1))) <-> hBOOL(hAPP(nat,bool,even_odd_even(nat),N_1)) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),A_2)))))) # label(fact_2434_zero__le__power__iff) # label(axiom) # label(non_clause).  [assumption].
7.36/7.40	298 (all X_a all R_1 (hBOOL(hAPP(fun(product_prod(X_a,X_a),bool),bool,refl(X_a),R_1)) <-> (all X_2 hBOOL(hAPP(fun(product_prod(X_a,X_a),bool),bool,hAPP(product_prod(X_a,X_a),fun(fun(product_prod(X_a,X_a),bool),bool),member(product_prod(X_a,X_a)),hAPP(X_a,product_prod(X_a,X_a),hAPP(X_a,fun(X_a,product_prod(X_a,X_a)),product_Pair(X_a,X_a),X_2),X_2)),R_1))))) # label(fact_3554_Nitpick_Orefl_H__def) # label(axiom) # label(non_clause).  [assumption].
7.36/7.40	299 (all X_a (semiring_div(X_a) -> (all A_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),A_1),A_1) = zero_zero(X_a)))) # label(fact_924_mod__self) # label(axiom) # label(non_clause).  [assumption].
7.36/7.40	300 (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),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),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),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))))) # label(fact_326_combine__common__factor) # label(axiom) # label(non_clause).  [assumption].
7.36/7.40	301 (all K hAPP(nat,fun(nat,bool),ord_lessThan(nat),hAPP(nat,nat,suc,K)) = hAPP(nat,fun(nat,bool),ord_atMost(nat),K)) # label(fact_4953_lessThan__Suc__atMost) # label(axiom) # label(non_clause).  [assumption].
7.36/7.40	302 (all X_1 all Y_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,real_1(int),X_1)),hAPP(int,real,real_1(int),Y_1))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X_1),Y_1)))) # label(fact_3321_real__of__int__less__iff) # label(axiom) # label(non_clause).  [assumption].
7.36/7.40	303 (all X_a (semiri456707255roduct(X_a) -> (all W_1 all Y_1 all X_1 all Z (ti(X_a,Z) = ti(X_a,Y_1) | ti(X_a,W_1) = ti(X_a,X_1) <-> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),W_1),Z)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X_1),Y_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),W_1),Y_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X_1),Z)))))) # label(fact_244_crossproduct__eq) # label(axiom) # label(non_clause).  [assumption].
7.36/7.40	304 (all A_2 all N_1 all B_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A_2),hAPP(nat,nat,suc,N_1))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),B_1),hAPP(nat,nat,suc,N_1)))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,A_2),B_1)))) # label(fact_2874_coprime__exp2) # label(axiom) # label(non_clause).  [assumption].
7.36/7.40	305 (all X_a (real_normed_vector(X_a) -> (all X_3 ((exists N_3 all N_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),hAPP(nat,X_a,X_3,N_2))),hAPP(nat,real,real_1(nat),hAPP(nat,nat,suc,N_3))))) <-> hBOOL(hAPP(fun(nat,X_a),bool,bseq(X_a),X_3)))))) # label(fact_3495_Bseq__iff) # label(axiom) # label(non_clause).  [assumption].
7.36/7.40	306 (all X_b all X_a (ab_group_add(X_a) -> (all F all G all A_3 hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co1399186613setsum(X_b,X_a),hAPP(fun(X_b,X_a),fun(X_b,X_a),hAPP(fun(X_b,fun(X_a,X_a)),fun(fun(X_b,X_a),fun(X_b,X_a)),combs(X_b,X_a,X_a),hAPP(fun(X_b,X_a),fun(X_b,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_b,X_a),fun(X_b,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),X_b),minus_minus(X_a)),F)),G)),A_3) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co1399186613setsum(X_b,X_a),F),A_3)),hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co1399186613setsum(X_b,X_a),G),A_3))))) # label(fact_4221_setsum__subtractf) # label(axiom) # label(non_clause).  [assumption].
7.36/7.40	307 (all X hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,number_number_of(real),min_1)),hAPP(real,real,cos,X)))) # label(fact_2217_cos__ge__minus__one) # label(axiom) # label(non_clause).  [assumption].
7.36/7.40	308 (all X_a (semiring_div(X_a) -> (all A_1 all B all C hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),A_1),C)),B)),C) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)),C)))) # label(fact_939_mod__add__left__eq) # label(axiom) # label(non_clause).  [assumption].
7.36/7.40	309 (all A_1 (hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_1),zero_zero(int)) = ti(int,A_1) & zero_zero(int) = hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_1),zero_zero(int)))) # label(fact_908_DIVISION__BY__ZERO) # label(axiom) # label(non_clause).  [assumption].
7.36/7.40	310 (all N all M hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),M)),N) = M) # label(fact_667_diff__add__inverse) # label(axiom) # label(non_clause).  [assumption].
7.36/7.40	311 (all A_1 all P_5 (hBOOL(hAPP(int,bool,zprime,P_5)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),A_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_1),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),P_5),one_one(int)))) -> hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),P_5),one_one(int)) != hAPP(int,int,hAPP(int,fun(int,int),inv,P_5),A_1))))) # label(fact_805_inv__not__p__minus__1) # label(axiom) # label(non_clause).  [assumption].
7.36/7.40	312 (all A_1 all B hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(nat,int,semiring_1_of_nat(int),A_1)),hAPP(nat,int,semiring_1_of_nat(int),B)) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),A_1),B))) # label(fact_1348_zdiv__int) # label(axiom) # label(non_clause).  [assumption].
7.36/7.40	313 (all A_2 all P_4 hAPP(fun(int,bool),fun(fun(int,bool),bool),hAPP(fun(int,fun(int,bool)),fun(fun(int,bool),fun(fun(int,bool),bool)),image(int,fun(int,bool)),hAPP(int,fun(int,fun(int,bool)),hAPP(int,fun(int,fun(int,fun(int,bool))),multInvPair,A_2),P_4)),hAPP(int,fun(int,bool),sRStar,P_4)) = hAPP(int,fun(fun(int,bool),bool),hAPP(int,fun(int,fun(fun(int,bool),bool)),setS,A_2),P_4)) # label(fact_3653_SetS__def) # label(axiom) # label(non_clause).  [assumption].
7.36/7.40	314 (all Y all X (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Y)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,nat_1,X)),hAPP(int,nat,nat_1,Y)) = hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X),Y))))) # label(fact_1141_Nat__Transfer_Otransfer__nat__int__functions_I1_J) # label(axiom) # label(non_clause).  [assumption].
7.36/7.40	315 (all B all A_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A_1),B)),zero_zero(int))) -> hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A_1),B) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_1),B)))) # label(fact_1048_mod__pos__neg__trivial) # label(axiom) # label(non_clause).  [assumption].
7.36/7.40	316 (all X_1 all Y_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y_1),X_1)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_1),Y_1)) <-> Y_1 = X_1)) # label(fact_620_dvd_Oeq__iff) # label(axiom) # label(non_clause).  [assumption].
7.36/7.40	317 (all X hAPP(real,real,cos,X) = hAPP(real,real,cos,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),pi)))) # label(fact_2239_cos__periodic) # label(axiom) # label(non_clause).  [assumption].
7.36/7.40	318 (all N hAPP(nat,nat,suc,N) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),one_one(nat))) # label(fact_1343_Suc__eq__plus1) # label(axiom) # label(non_clause).  [assumption].
7.36/7.40	319 (all A_1 all P_5 (hBOOL(hAPP(int,bool,zprime,P_5)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),A_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_1),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),P_5),one_one(int)))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),hAPP(int,int,hAPP(int,fun(int,int),inv,P_5),A_1))))))) # label(fact_804_inv__g__1) # label(axiom) # label(non_clause).  [assumption].
7.36/7.40	320 (all X all I_1 hAPP(real,real,tan,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,real_1(int),I_1)),pi))) = hAPP(real,real,tan,X)) # label(fact_3399_tan__periodic__int) # label(axiom) # label(non_clause).  [assumption].
7.36/7.40	321 (all N hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),N))) # label(fact_547_less__eq__nat_Osimps_I1_J) # label(axiom) # label(non_clause).  [assumption].
7.36/7.40	322 (all X_b all X_a all P_1 all Y_1 all X_1 (hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),P_1,Y_1),X_1)) -> hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),P_1,hAPP(product_prod(X_b,X_a),X_a,product_snd(X_b,X_a),hAPP(X_a,product_prod(X_b,X_a),hAPP(X_b,fun(X_a,product_prod(X_b,X_a)),product_Pair(X_b,X_a),X_1),Y_1))),hAPP(product_prod(X_b,X_a),X_b,product_fst(X_b,X_a),hAPP(X_a,product_prod(X_b,X_a),hAPP(X_b,fun(X_a,product_prod(X_b,X_a)),product_Pair(X_b,X_a),X_1),Y_1)))))) # label(fact_3123_exI__realizer) # label(axiom) # label(non_clause).  [assumption].
7.36/7.40	323 (all X_a (linorder(X_a) -> (all X all Y hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),Y)))))) # label(fact_4986_le__maxI1) # label(axiom) # label(non_clause).  [assumption].
7.36/7.40	324 (all X_b all X_a all F all A_3 all B_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_3),B_2)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),A_3)),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),B_2))))) # label(fact_3635_image__mono) # label(axiom) # label(non_clause).  [assumption].
7.36/7.40	325 (all X all Y (zero_zero(nat) != Y -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),Y),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),X),Y)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),X),Y))) # label(fact_3276_gcd__non__0__nat) # label(axiom) # label(non_clause).  [assumption].
7.36/7.40	326 (all M all N hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),M),N)),M))) # label(fact_1091_mod__less__eq__dividend) # label(axiom) # label(non_clause).  [assumption].
7.36/7.40	327 (all Code_numeral_2 hAPP(code_code_numeral,nat,size_size(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,code_S1047413653umeral,Code_numeral_2)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(code_code_numeral,nat,size_size(code_code_numeral),Code_numeral_2)),hAPP(nat,nat,suc,zero_zero(nat)))) # label(fact_2969_code__numeral_Osize_I4_J) # label(axiom) # label(non_clause).  [assumption].
7.36/7.40	328 (all Sa all Ta all A_2 all B_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A_2),B_1)) -> hBOOL(hAPP(fun(product_prod(product_prod(nat,nat),product_prod(nat,nat)),bool),bool,hAPP(product_prod(product_prod(nat,nat),product_prod(nat,nat)),fun(fun(product_prod(product_prod(nat,nat),product_prod(nat,nat)),bool),bool),member(product_prod(product_prod(nat,nat),product_prod(nat,nat))),hAPP(product_prod(nat,nat),product_prod(product_prod(nat,nat),product_prod(nat,nat)),hAPP(product_prod(nat,nat),fun(product_prod(nat,nat),product_prod(product_prod(nat,nat),product_prod(nat,nat))),product_Pair(product_prod(nat,nat),product_prod(nat,nat)),hAPP(nat,product_prod(nat,nat),hAPP(nat,fun(nat,product_prod(nat,nat)),product_Pair(nat,nat),A_2),Sa)),hAPP(nat,product_prod(nat,nat),hAPP(nat,fun(nat,product_prod(nat,nat)),product_Pair(nat,nat),B_1),Ta))),pair_leq)))) # label(fact_3489_pair__leqI1) # label(axiom) # label(non_clause).  [assumption].
7.36/7.40	329 (all X_a all X_b all B_2 all F all A_3 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),B_2),hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),A_3))) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),B_2))))) # label(fact_3654_finite__surjI) # label(axiom) # label(non_clause).  [assumption].
7.36/7.41	330 (all X_b all X_a (metric_space(X_a) & real_normed_vector(X_b) -> (all F all L all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),L),hAPP(X_a,filter(X_a),at(X_a),A_2))) <-> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(X_b,fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(X_b,fun(X_a,X_b)),combc(X_a,X_b,X_b),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,fun(X_b,X_b))),combb(X_b,fun(X_b,X_b),X_a),minus_minus(X_b)),F)),L)),zero_zero(X_b)),hAPP(X_a,filter(X_a),at(X_a),A_2))))))) # label(fact_4584_LIM__zero__iff) # label(axiom) # label(non_clause).  [assumption].
7.36/7.41	331 (all B_1 all A_2 (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),B_1),hAPP(int,fun(int,bool),d22set,A_2))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),B_1)))) # label(fact_866_d22set__g__1) # label(axiom) # label(non_clause).  [assumption].
7.36/7.41	332 (all X_a (semiring_div(X_a) -> (all B all B_5 all A_1 all C all A_6 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),A_1),C) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),A_6),C) -> (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),B_5),C) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),B),C) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)),C) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_6),B_5)),C)))))) # label(fact_934_mod__mult__cong) # label(axiom) # label(non_clause).  [assumption].
7.36/7.41	333 (all X_a (real_normed_vector(X_a) -> (all X_3 (hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),hAPP(fun(nat,X_a),fun(nat,real),hAPP(fun(X_a,real),fun(fun(nat,X_a),fun(nat,real)),combb(X_a,real,nat),norm_norm(X_a)),X_3)),zero_zero(real)),sequentially)) <-> hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),X_3),zero_zero(X_a)),sequentially)))))) # label(fact_4450_LIMSEQ__norm__zero) # label(axiom) # label(non_clause).  [assumption].
7.36/7.41	334 (all X_a (ordere142940540dd_abs(X_a) -> (all A_2 (zero_zero(X_a) = ti(X_a,A_2) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,abs_abs(X_a),A_2)),zero_zero(X_a))))))) # label(fact_1861_abs__le__zero__iff) # label(axiom) # label(non_clause).  [assumption].
7.36/7.41	335 (all L all F ((all N_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,F,N_2)),hAPP(nat,real,F,hAPP(nat,nat,suc,N_2))))) -> ((all N_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,F,N_2)),L))) -> ((all E (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),E)) -> (exists N_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),L),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,F,N_2)),E)))))) -> hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),F),L),sequentially)))))) # label(fact_4878_increasing__LIMSEQ) # label(axiom) # label(non_clause).  [assumption].
7.36/7.41	336 (all X_b all X_a (real_normed_vector(X_a) -> (all F all A_3 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co1399186613setsum(X_b,X_a),F),A_3))),hAPP(fun(X_b,bool),real,hAPP(fun(X_b,real),fun(fun(X_b,bool),real),big_co1399186613setsum(X_b,real),hAPP(fun(X_b,X_a),fun(X_b,real),hAPP(fun(X_a,real),fun(fun(X_b,X_a),fun(X_b,real)),combb(X_a,real,X_b),norm_norm(X_a)),F)),A_3)))))) # label(fact_4177_norm__setsum) # label(axiom) # label(non_clause).  [assumption].
7.36/7.41	337 (all X_a (finite_finite(X_a) -> (all A_3 hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_3))))) # label(fact_1819_finite) # label(axiom) # label(non_clause).  [assumption].
7.36/7.41	338 (all A_2 (hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),A_2),zero_zero(real)),sequentially)) -> (hBOOL(hAPP(fun(nat,real),bool,monoseq(real),A_2)) -> hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),hAPP(fun(nat,fun(nat,bool)),fun(nat,real),hAPP(fun(fun(nat,bool),real),fun(fun(nat,fun(nat,bool)),fun(nat,real)),combb(fun(nat,bool),real,nat),hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),min_1)))),A_2))),hAPP(fun(nat,nat),fun(nat,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(nat,nat),fun(nat,fun(nat,bool))),combb(nat,fun(nat,bool),nat),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat))),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),hAPP(fun(nat,nat),fun(nat,fun(nat,nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,nat),fun(nat,fun(nat,nat))),combb(nat,fun(nat,nat),nat),plus_plus(nat)),hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),one_one(nat))))),hAPP(fun(nat,real),real,suminf(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),min_1)))),A_2))),sequentially))))) # label(fact_4426_summable__Leibniz_I5_J) # label(axiom) # label(non_clause).  [assumption].
7.36/7.41	339 (all X_a (semiring_div(X_a) -> (all A_1 all B all C ((zero_zero(X_a) = ti(X_a,C) -> zero_zero(X_a) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),B))) & (ti(X_a,C) != zero_zero(X_a) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),B)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),A_1),B)))))) # label(fact_998_div__mult__mult1__if) # label(axiom) # label(non_clause).  [assumption].
7.36/7.41	340 (all K all L (ti(int,L) = ti(int,K) <-> hAPP(int,int,bit1,L) = hAPP(int,int,bit1,K))) # label(fact_91_rel__simps_I51_J) # label(axiom) # label(non_clause).  [assumption].
7.36/7.41	341 (all X_a all X_b (comm_monoid_add(X_b) -> (all F all S all T_3 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),T_3)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),S),T_3)) -> ((all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),T_3),S))) -> hAPP(X_a,X_b,F,X_2) = zero_zero(X_b))) -> hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),F),T_3) = hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),F),S))))))) # label(fact_4294_setsum__mono__zero__right) # label(axiom) # label(non_clause).  [assumption].
7.36/7.41	342 (all K1 all K2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit0,K1)),hAPP(int,int,bit0,K2))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K1),K2)))) # label(fact_127_less__int__code_I13_J) # label(axiom) # label(non_clause).  [assumption].
7.36/7.41	343 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N)) -> (N != M -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N))))) # label(fact_566_le__neq__implies__less) # label(axiom) # label(non_clause).  [assumption].
7.36/7.41	344 (all X_a (linorder(X_a) -> (all Z all X_1 all Y_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z),Y_1)) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z),X_1)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X_1),Y_1))))))) # label(fact_4950_less__max__iff__disj) # label(axiom) # label(non_clause).  [assumption].
7.36/7.41	345 (all Y all X (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Y)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),X),Y)))))) # label(fact_4397_transfer__nat__int__gcd__closures_I1_J) # label(axiom) # label(non_clause).  [assumption].
7.36/7.41	346 (all X_a (archim1727834104eiling(X_a) -> (all X hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(X_a,int,archimedean_ceiling(X_a),X)),one_one(int)) = hAPP(X_a,int,archimedean_ceiling(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),X),one_one(X_a)))))) # label(fact_3307_ceiling__diff__one) # label(axiom) # label(non_clause).  [assumption].
7.36/7.41	347 (all A_1 all B hAPP(int,int,uminus_uminus(int),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_1),B)) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,uminus_uminus(int),A_1)),hAPP(int,int,uminus_uminus(int),B))) # label(fact_2150_zmod__zminus__zminus) # label(axiom) # label(non_clause).  [assumption].
7.36/7.41	348 (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_1866_abs__mult__less) # label(axiom) # label(non_clause).  [assumption].
7.36/7.41	349 (all X_a (monoid_add(X_a) -> plus_plus(X_a) = ti(fun(X_a,fun(X_a,X_a)),plus_plus(X_a)))) # label(tsy_c_Groups_Oplus__class_Oplus_1_res) # label(axiom) # label(non_clause).  [assumption].
7.36/7.41	350 (all X_a (linord219039673up_add(X_a) -> (all X all Y hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),X)),hAPP(X_a,X_a,uminus_uminus(X_a),Y)) = hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),Y))))) # label(fact_4944_minus__min__eq__max) # label(axiom) # label(non_clause).  [assumption].
7.36/7.41	351 (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_226_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) # label(axiom) # label(non_clause).  [assumption].
7.36/7.41	352 (all X hAPP(nat,real,real_1(nat),X) = hAPP(real,real,abs_abs(real),hAPP(nat,real,real_1(nat),X))) # label(fact_2291_abs__real__of__nat__cancel) # label(axiom) # label(non_clause).  [assumption].
7.36/7.41	353 (all A_1 all P_5 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),P_5)) -> (hBOOL(hAPP(int,bool,zprime,P_5)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_1),zero_zero(int)),P_5)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,zero_zero(int)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A_1),hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),P_5),one_one(int))),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))),P_5)))))) # label(fact_1164_Euler__part2) # label(axiom) # label(non_clause).  [assumption].
7.36/7.41	354 (all X_a (idom(X_a) -> (all C_1 all A_2 all B_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1),A_2)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1),B_1))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_2),B_1)) | ti(X_a,C_1) = zero_zero(X_a))))) # label(fact_409_dvd__mult__cancel__left) # label(axiom) # label(non_clause).  [assumption].
7.36/7.41	355 (all X (hAPP(real,real,sin,X) = zero_zero(real) -> hAPP(real,real,abs_abs(real),hAPP(real,real,cos,X)) = one_one(real))) # label(fact_2337_sin__zero__abs__cos__one) # label(axiom) # label(non_clause).  [assumption].
7.36/7.41	356 (all N hAPP(int,int,uminus_uminus(int),hAPP(nat,int,semiring_1_of_nat(int),N)) = hAPP(real,int,archim2085082626_floor(real),hAPP(real,real,uminus_uminus(real),hAPP(nat,real,real_1(nat),N)))) # label(fact_2878_floor__minus__real__of__nat) # label(axiom) # label(non_clause).  [assumption].
7.36/7.41	357 (all X all Y ((Y != zero_zero(nat) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),Y),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),X),Y)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),X),Y)) & (zero_zero(nat) = Y -> X = hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),X),Y)))) # label(fact_3275_gcd__nat_Osimps) # label(axiom) # label(non_clause).  [assumption].
7.36/7.41	358 (all X_a (real_algebra_1(X_a) -> (all R_4 hAPP(real,X_a,of_real(X_a),R_4) = hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),R_4),one_one(X_a))))) # label(fact_4699_of__real__def) # label(axiom) # label(non_clause).  [assumption].
7.36/7.41	359 (all Code_numeral_4 zero_zero(code_code_numeral) != hAPP(code_code_numeral,code_code_numeral,code_S1047413653umeral,Code_numeral_4)) # label(fact_2946_code__numeral_Osimps_I3_J) # label(axiom) # label(non_clause).  [assumption].
7.36/7.41	360 (all A_1 all B (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A_1),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),B),one_one(int)))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_1),B)))) # label(fact_737_norR__mem__unique__aux) # label(axiom) # label(non_clause).  [assumption].
7.36/7.41	361 (all X_a all X_b all A_3 all B_2 (hBOOL(hAPP(fun(sum_sum(X_a,X_b),bool),bool,finite_finite_1(sum_sum(X_a,X_b)),hAPP(fun(X_b,bool),fun(sum_sum(X_a,X_b),bool),hAPP(fun(X_a,bool),fun(fun(X_b,bool),fun(sum_sum(X_a,X_b),bool)),sum_Plus(X_a,X_b),A_3),B_2))) -> hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_3)))) # label(fact_3183_finite__PlusD_I1_J) # label(axiom) # label(non_clause).  [assumption].
7.36/7.41	362 (all X_b all X_c all X_a all F all A_2 all B_1 hAPP(X_c,X_a,hAPP(X_b,fun(X_c,X_a),F,A_2),B_1) = hAPP(product_prod(X_b,X_c),X_a,hAPP(fun(X_b,fun(X_c,X_a)),fun(product_prod(X_b,X_c),X_a),product_prod_case(X_b,X_c,X_a),F),hAPP(X_c,product_prod(X_b,X_c),hAPP(X_b,fun(X_c,product_prod(X_b,X_c)),product_Pair(X_b,X_c),A_2),B_1))) # label(fact_3993_split__conv) # label(axiom) # label(non_clause).  [assumption].
7.36/7.41	363 (all M all N hAPP(nat,real,real_1(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N)) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,real_1(nat),M)),hAPP(nat,real,real_1(nat),N))) # label(fact_2308_real__of__nat__add) # label(axiom) # label(non_clause).  [assumption].
7.36/7.41	364 (all X_c all X_a all B_1_1 all B_2_1 hAPP(X_a,X_c,B_1_1,B_2_1) = ti(X_c,hAPP(X_a,X_c,B_1_1,B_2_1))) # label(tsy_c_hAPP_res) # label(axiom) # label(non_clause).  [assumption].
7.36/7.41	365 (all X all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Y)) -> (exists R_2 exists A_4 (Y = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),R_2),hAPP(real,real,sin,A_4)) & hAPP(real,real,hAPP(real,fun(real,real),times_times(real),R_2),hAPP(real,real,cos,A_4)) = X)))) # label(fact_2726_polar__ex1) # label(axiom) # label(non_clause).  [assumption].
7.36/7.41	366 (all K all N_2 all F_3 hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),F_3),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_2),K))) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),F_3),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),K))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),N_2))),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),F_3),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),K)))) # label(fact_4183_sumr__offset4) # label(axiom) # label(non_clause).  [assumption].
7.36/7.41	367 (all R_4 all P_5 all Q_3 (hAPP(product_prod(int,int),product_prod(int,int),normalize,R_4) = hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),P_5),Q_3) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),Q_3)))) # label(fact_3726_normalize__denom__pos) # label(axiom) # label(non_clause).  [assumption].
7.36/7.41	368 (all A_1 ((-hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A_1),zero_zero(real))) -> hAPP(real,real,abs_abs(real),A_1) = A_1) & (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A_1),zero_zero(real))) -> hAPP(real,real,abs_abs(real),A_1) = hAPP(real,real,uminus_uminus(real),A_1)))) # label(fact_2110_abs__real__def) # label(axiom) # label(non_clause).  [assumption].
7.36/7.41	369 (all X_a (real_algebra_1(X_a) & real_normed_vector(X_a) -> (exists K_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),K_2)) & (all X_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),hAPP(real,X_a,of_real(X_a),X_2))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,norm_norm(real),X_2)),K_2)))))))) # label(fact_2818_of__real_Ononneg__bounded) # label(axiom) # label(non_clause).  [assumption].
7.36/7.41	370 (all X_a (real_normed_algebra(X_a) -> (all X_1 all X_3 (hBOOL(hAPP(fun(nat,X_a),bool,cauchy(X_a),X_3)) -> hBOOL(hAPP(fun(nat,X_a),bool,cauchy(X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(X_a,X_a),fun(fun(nat,X_a),fun(nat,X_a)),combb(X_a,X_a,nat),hAPP(X_a,fun(X_a,X_a),times_times(X_a),X_1)),X_3))))))) # label(fact_4100_mult__right_OCauchy) # label(axiom) # label(non_clause).  [assumption].
7.36/7.41	371 (all B all A_1 all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A_1),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),B)) -> (exists D_3 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),D_3)) & (all Y_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),X),Y_2))),D_3)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A_1),Y_2)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),Y_2),B))))))))) # label(fact_1914_lemma__interval) # label(axiom) # label(non_clause).  [assumption].
7.36/7.41	372 (all N_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),N_1)) -> hAPP(int,nat,nat_1,N_1) = hAPP(fun(int,bool),nat,finite_card(int),hAPP(fun(int,bool),fun(int,bool),collect(int),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),combs(int,bool,bool),hAPP(fun(int,bool),fun(int,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj),hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)))),hAPP(int,fun(int,bool),hAPP(fun(int,fun(int,bool)),fun(int,fun(int,bool)),combc(int,int,bool),ord_less_eq(int)),N_1)))))) # label(fact_3810_card__bdd__int__set__l__le) # label(axiom) # label(non_clause).  [assumption].
7.36/7.41	373 (all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),one_one(nat)),N)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),N),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))) # label(fact_1152_div__2__gt__zero) # label(axiom) # label(non_clause).  [assumption].
7.36/7.41	374 (all X (-hBOOL(hAPP(nat,bool,even_odd_even(nat),X)) -> hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),X),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat))))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,suc,X)),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat)))))) # label(fact_2445_odd__nat__plus__one__div__two) # label(axiom) # label(non_clause).  [assumption].
7.36/7.41	375 (all X_1 all N_1 all Y_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),X_1),hAPP(nat,nat,suc,N_1))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),Y_1),hAPP(nat,nat,suc,N_1)))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X_1),Y_1)))) # label(fact_1362_exp__mono__le) # label(axiom) # label(non_clause).  [assumption].
7.36/7.41	376 (all X_a (topological_space(X_a) -> (all F all L all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(real,fun(filter(X_a),bool),hAPP(fun(X_a,real),fun(real,fun(filter(X_a),bool)),tendsto(X_a,real),F),L),hAPP(X_a,filter(X_a),at(X_a),A_2))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(real,fun(filter(X_a),bool),hAPP(fun(X_a,real),fun(real,fun(filter(X_a),bool)),tendsto(X_a,real),hAPP(fun(X_a,real),fun(X_a,real),hAPP(fun(real,real),fun(fun(X_a,real),fun(X_a,real)),combb(real,real,X_a),abs_abs(real)),F)),hAPP(real,real,abs_abs(real),L)),hAPP(X_a,filter(X_a),at(X_a),A_2))))))) # label(fact_4553_LIM__rabs) # label(axiom) # label(non_clause).  [assumption].
7.36/7.41	377 (all X_a (linord581940658strict(X_a) -> (all A_2 all B_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),B_1)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),zero_zero(X_a))) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_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)),A_2)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),B_1)),zero_zero(X_a))))))) # label(fact_379_mult__le__0__iff) # label(axiom) # label(non_clause).  [assumption].
7.36/7.41	378 (all X_a (linorder(X_a) -> (all Ma all N_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Ma),N_1)) <-> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less(fun(X_a,bool)),hAPP(X_a,fun(X_a,bool),ord_lessThan(X_a),Ma)),hAPP(X_a,fun(X_a,bool),ord_lessThan(X_a),N_1))))))) # label(fact_4320_lessThan__strict__subset__iff) # label(axiom) # label(non_clause).  [assumption].
7.36/7.41	379 (all M all N hBOOL(hAPP(product_prod(nat,nat),bool,hAPP(nat,fun(product_prod(nat,nat),bool),hAPP(nat,fun(nat,fun(product_prod(nat,nat),bool)),divmod_nat_rel,M),N),hAPP(nat,product_prod(nat,nat),hAPP(nat,fun(nat,product_prod(nat,nat)),divmod_nat,M),N)))) # label(fact_3100_divmod__nat__rel__divmod__nat) # label(axiom) # label(non_clause).  [assumption].
7.36/7.41	380 (all N all P_5 all M (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),M)) -> (hBOOL(hAPP(int,bool,zprime,P_5)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),P_5),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),M),N))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),P_5),M)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),P_5),N)))))) # label(fact_279_zprime__zdvd__zmult) # label(axiom) # label(non_clause).  [assumption].
7.36/7.41	381 (all G all F all X_1 all D_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),D_1)) -> ((all Z_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),Z_2),X_1))),D_1)) -> hAPP(real,real,G,hAPP(real,real,F,Z_2)) = Z_2)) -> ((all Z_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),Z_2),X_1))),D_1)) -> hBOOL(hAPP(real,bool,hAPP(fun(real,real),fun(real,bool),isCont(real,real),F),Z_2)))) -> (exists Z_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,F,X_1)),hAPP(real,real,F,Z_2))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),Z_2),X_1))),D_1)))))))) # label(fact_4933_lemma__isCont__inj) # label(axiom) # label(non_clause).  [assumption].
7.36/7.41	382 (all N_1 all V_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),hAPP(bool,fun(nat,fun(nat,nat)),if(nat),hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),hAPP(int,int,pred,V_1)))),zero_zero(nat)),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),N_1),hAPP(int,nat,nat_1,hAPP(int,int,number_number_of(int),hAPP(int,int,pred,V_1)))))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),hAPP(nat,nat,suc,N_1)),hAPP(int,nat,number_number_of(nat),V_1))) # label(fact_4796_min__number__of__Suc) # label(axiom) # label(non_clause).  [assumption].
7.36/7.41	383 (all P_4 hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),resSet,P_4),hAPP(int,fun(int,bool),sRStar,P_4)))) # label(fact_2917_ResSet__SRStar__prop) # label(axiom) # label(non_clause).  [assumption].
7.36/7.41	384 (all X_a (linorder(X_a) -> (all X_1 all Y_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y_1),X_1)) <-> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y_1)))))) # label(fact_1582_linorder__not__less) # label(axiom) # label(non_clause).  [assumption].
7.36/7.41	385 (all B all Y all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),Y)) -> hAPP(real,real,hAPP(real,fun(real,real),log,B),hAPP(real,real,hAPP(real,fun(real,real),powr,X),Y)) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),Y),hAPP(real,real,hAPP(real,fun(real,real),log,B),X))))) # label(fact_3418_log__powr) # label(axiom) # label(non_clause).  [assumption].
7.36/7.41	386 (all P_1 all A_2 all B_1 (-((exists D_3 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B_1),D_3) = A_2 & -hBOOL(hAPP(nat,bool,P_1,D_3)))) | -hBOOL(hAPP(nat,bool,P_1,zero_zero(nat))) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A_2),B_1))) <-> hBOOL(hAPP(nat,bool,P_1,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),A_2),B_1))))) # label(fact_701_nat__diff__split__asm) # label(axiom) # label(non_clause).  [assumption].
7.36/7.41	387 (all X_a (banach(X_a) & real_normed_algebra(X_a) -> (all B_1 all A_2 (hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,X_a),fun(nat,real),hAPP(fun(X_a,real),fun(fun(nat,X_a),fun(nat,real)),combb(X_a,real,nat),norm_norm(X_a)),A_2))) -> (hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,X_a),fun(nat,real),hAPP(fun(X_a,real),fun(fun(nat,X_a),fun(nat,real)),combb(X_a,real,nat),norm_norm(X_a)),B_1))) -> hBOOL(hAPP(X_a,bool,hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),hAPP(fun(nat,fun(nat,bool)),fun(nat,X_a),hAPP(fun(nat,fun(fun(nat,bool),X_a)),fun(fun(nat,fun(nat,bool)),fun(nat,X_a)),combs(nat,fun(nat,bool),X_a),hAPP(fun(nat,fun(nat,X_a)),fun(nat,fun(fun(nat,bool),X_a)),hAPP(fun(fun(nat,X_a),fun(fun(nat,bool),X_a)),fun(fun(nat,fun(nat,X_a)),fun(nat,fun(fun(nat,bool),X_a))),combb(fun(nat,X_a),fun(fun(nat,bool),X_a),nat),big_co1399186613setsum(nat,X_a)),hAPP(fun(nat,fun(nat,X_a)),fun(nat,fun(nat,X_a)),hAPP(fun(fun(nat,X_a),fun(nat,X_a)),fun(fun(nat,fun(nat,X_a)),fun(nat,fun(nat,X_a))),combb(fun(nat,X_a),fun(nat,X_a),nat),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),times_times(X_a)),A_2))),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,X_a)),hAPP(fun(fun(nat,nat),fun(nat,X_a)),fun(fun(nat,fun(nat,nat)),fun(nat,fun(nat,X_a))),combb(fun(nat,nat),fun(nat,X_a),nat),hAPP(fun(nat,X_a),fun(fun(nat,nat),fun(nat,X_a)),combb(nat,X_a,nat),B_1)),minus_minus(nat))))),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),zero_zero(nat)))),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(fun(nat,X_a),X_a,suminf(X_a),A_2)),hAPP(fun(nat,X_a),X_a,suminf(X_a),B_1))))))))) # label(fact_4623_Cauchy__product__sums) # label(axiom) # label(non_clause).  [assumption].
7.36/7.41	388 (all X_b all X_a (real_normed_vector(X_b) & topological_space(X_a) -> (all F all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),zero_zero(X_b)),hAPP(X_a,filter(X_a),at(X_a),A_2))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(real,fun(filter(X_a),bool),hAPP(fun(X_a,real),fun(real,fun(filter(X_a),bool)),tendsto(X_a,real),hAPP(fun(X_a,X_b),fun(X_a,real),hAPP(fun(X_b,real),fun(fun(X_a,X_b),fun(X_a,real)),combb(X_b,real,X_a),norm_norm(X_b)),F)),zero_zero(real)),hAPP(X_a,filter(X_a),at(X_a),A_2))))))) # label(fact_4610_LIM__norm__zero) # label(axiom) # label(non_clause).  [assumption].
7.36/7.41	389 (all X_a (order(X_a) -> ti(fun(fun(nat,fun(nat,bool)),fun(fun(nat,X_a),bool)),mono(nat,X_a)) = mono(nat,X_a))) # label(tsy_c_Orderings_Oorder_Omono_res) # label(axiom) # label(non_clause).  [assumption].
7.36/7.41	390 (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_394_mult__pos__pos) # label(axiom) # label(non_clause).  [assumption].
7.36/7.41	391 (all Y all X (hBOOL(hAPP(int,bool,even_odd_even(int),X)) -> hBOOL(hAPP(int,bool,even_odd_even(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X),Y))))) # label(fact_1258_even__times__anything) # label(axiom) # label(non_clause).  [assumption].
7.36/7.41	392 (all X_1 ((exists N_2 (X_1 = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,real_1(nat),N_2)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) & -hBOOL(hAPP(nat,bool,even_odd_even(nat),N_2)))) | (exists N_2 (hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,real_1(nat),N_2)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) = X_1 & -hBOOL(hAPP(nat,bool,even_odd_even(nat),N_2)))) <-> hAPP(real,real,cos,X_1) = zero_zero(real))) # label(fact_2412_cos__zero__iff) # label(axiom) # label(non_clause).  [assumption].
7.36/7.41	393 (all X hAPP(real,real,hAPP(real,fun(real,real),powr,X),zero_zero(real)) = one_one(real)) # label(fact_3351_powr__zero__eq__one) # label(axiom) # label(non_clause).  [assumption].
7.36/7.41	394 (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_431_mult__le__less__imp__less) # label(axiom) # label(non_clause).  [assumption].
7.36/7.41	395 (all X_a all X_b all Sa all Ta (hAPP(product_prod(X_a,X_b),X_b,product_snd(X_a,X_b),Sa) = hAPP(product_prod(X_a,X_b),X_b,product_snd(X_a,X_b),Ta) & hAPP(product_prod(X_a,X_b),X_a,product_fst(X_a,X_b),Sa) = hAPP(product_prod(X_a,X_b),X_a,product_fst(X_a,X_b),Ta) <-> ti(product_prod(X_a,X_b),Sa) = ti(product_prod(X_a,X_b),Ta))) # label(fact_3143_prod__eq__iff) # label(axiom) # label(non_clause).  [assumption].
7.36/7.41	396 (all F all Y_1 all G all X_1 (hBOOL(hAPP(real,bool,hAPP(fun(nat,real),fun(real,bool),sums(real),G),X_1)) -> (hBOOL(hAPP(real,bool,hAPP(fun(nat,real),fun(real,bool),sums(real),F),Y_1)) -> hBOOL(hAPP(real,bool,hAPP(fun(nat,real),fun(real,bool),sums(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(nat,fun(real,fun(real,real))),fun(fun(nat,real),fun(nat,fun(real,real))),combs(nat,real,fun(real,real)),hAPP(fun(nat,bool),fun(nat,fun(real,fun(real,real))),hAPP(fun(bool,fun(real,fun(real,real))),fun(fun(nat,bool),fun(nat,fun(real,fun(real,real)))),combb(bool,fun(real,fun(real,real)),nat),if(real)),even_odd_even(nat))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),F),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),div_div(nat)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),G),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),hAPP(fun(nat,nat),fun(nat,fun(nat,nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,nat),fun(nat,fun(nat,nat))),combb(nat,fun(nat,nat),nat),div_div(nat)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),minus_minus(nat)),one_one(nat)))),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X_1),Y_1)))))) # label(fact_4105_sums__if) # label(axiom) # label(non_clause).  [assumption].
7.36/7.41	397 (all X_1 hBOOL(hAPP(real,bool,hAPP(fun(nat,real),fun(real,bool),sums(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),inverse_divide(real)),hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),min_1)))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),hAPP(fun(nat,nat),fun(nat,nat),hAPP(fun(nat,nat),fun(fun(nat,nat),fun(nat,nat)),combb(nat,nat,nat),fact_fact(nat)),hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),hAPP(real,fun(nat,real),power_power(real),X_1)),hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))),hAPP(real,real,cos,X_1)))) # label(fact_4106_cos__paired) # label(axiom) # label(non_clause).  [assumption].
7.36/7.41	398 (all R_4 ((hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),R_4),zero_zero(real))) -> hAPP(real,real,abs_abs(real),R_4) = hAPP(real,real,uminus_uminus(real),R_4)) & (-hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),R_4),zero_zero(real))) -> R_4 = hAPP(real,real,abs_abs(real),R_4)))) # label(fact_2111_real__abs__def) # label(axiom) # label(non_clause).  [assumption].
7.36/7.41	399 (all X_a (linorder(X_a) -> (all T_5 exists Z_2 all X_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_2),Z_2)) -> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),T_5),X_2)))))) # label(fact_2830_minf_I8_J) # label(axiom) # label(non_clause).  [assumption].
7.36/7.41	400 (all X_1 hAPP(fun(real,bool),real,the(real),hAPP(real,fun(real,bool),hAPP(fun(real,fun(real,bool)),fun(real,fun(real,bool)),combc(real,real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),hAPP(fun(real,fun(real,bool)),fun(fun(real,real),fun(real,fun(real,bool))),combb(real,fun(real,bool),real),fequal(real)),exp(real))),X_1)) = hAPP(real,real,ln,X_1)) # label(fact_4134_ln__def) # label(axiom) # label(non_clause).  [assumption].
7.36/7.41	401 (all N_1 all Ma (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,real_1(nat),N_1)),one_one(real))),hAPP(nat,real,real_1(nat),Ma))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),Ma)))) # label(fact_2341_nat__less__real__le) # label(axiom) # label(non_clause).  [assumption].
7.36/7.41	402 (all M hAPP(nat,nat,suc,M) != zero_zero(nat)) # label(fact_1223_Zero__neq__Suc) # label(axiom) # label(non_clause).  [assumption].
7.36/7.41	403 (all X_a (ring_1(X_a) -> (all Z_1 hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(int,X_a,ring_1_of_int(X_a),Z_1)) = hAPP(int,X_a,ring_1_of_int(X_a),hAPP(int,int,uminus_uminus(int),Z_1))))) # label(fact_3568_of__int__minus) # label(axiom) # label(non_clause).  [assumption].
7.36/7.41	404 (all N (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),N))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,N)))) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),hAPP(int,int,bit1,N)))))) # label(fact_471_number__of1) # label(axiom) # label(non_clause).  [assumption].
7.36/7.41	405 (all X_a (semiring_div(X_a) -> (all N all K_4 all M (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),K_4),M)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),K_4),N)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),K_4),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),M),N)))))))) # label(fact_949_dvd__mod) # label(axiom) # label(non_clause).  [assumption].
7.36/7.41	406 (all X_a all A_3 all F all N_1 (ti(fun(X_a,bool),A_3) = hAPP(fun(nat,bool),fun(X_a,bool),hAPP(fun(nat,X_a),fun(fun(nat,bool),fun(X_a,bool)),image(nat,X_a),F),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),N_1))) -> hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_3)))) # label(fact_3868_nat__seg__image__imp__finite) # label(axiom) # label(non_clause).  [assumption].
7.36/7.41	407 (all X all Y hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),powr,X),Y)))) # label(fact_3346_powr__ge__pzero) # label(axiom) # label(non_clause).  [assumption].
7.36/7.41	408 (all X_b all X_c all X_a all P_1 all Z hAPP(X_c,X_a,hAPP(X_b,fun(X_c,X_a),P_1,hAPP(product_prod(X_b,X_c),X_b,product_fst(X_b,X_c),Z)),hAPP(product_prod(X_b,X_c),X_c,product_snd(X_b,X_c),Z)) = hAPP(product_prod(X_b,X_c),X_a,hAPP(fun(X_b,fun(X_c,X_a)),fun(product_prod(X_b,X_c),X_a),product_prod_case(X_b,X_c,X_a),P_1),Z)) # label(fact_4016_split__beta) # label(axiom) # label(non_clause).  [assumption].
7.36/7.41	409 (all X_a nat_rec(X_a) = ti(fun(X_a,fun(fun(nat,fun(X_a,X_a)),fun(nat,X_a))),nat_rec(X_a))) # label(tsy_c_Nat_Onat_Onat__rec_res) # label(axiom) # label(non_clause).  [assumption].
7.36/7.41	410 (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_44_number__of__mult) # label(axiom) # label(non_clause).  [assumption].
7.36/7.41	411 (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),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),zero_zero(X_a)),hAPP(int,X_a,number_number_of(X_a),W))),hAPP(int,X_a,number_number_of(X_a),W)) = hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,bit0,W))))) # label(fact_170_number__of__Bit0) # label(axiom) # label(non_clause).  [assumption].
7.36/7.41	412 (all X all Y hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),X),Y) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),X),hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),X),Y))) # label(fact_3223_gcd__semilattice__nat_Oinf__left__idem) # label(axiom) # label(non_clause).  [assumption].
7.36/7.41	413 (all X_1 ((exists Y_2 X_1 = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat)))),Y_2)) <-> hBOOL(hAPP(nat,bool,even_odd_even(nat),X_1)))) # label(fact_2442_even__nat__equiv__def2) # label(axiom) # label(non_clause).  [assumption].
7.36/7.41	414 (all X_a (metric_space(X_a) -> (all X_3 all L_2 (hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),X_3),L_2),sequentially)) -> ti(X_a,L_2) = hAPP(fun(nat,X_a),X_a,lim(X_a),X_3))))) # label(fact_4494_limI) # label(axiom) # label(non_clause).  [assumption].
7.36/7.41	415 (all N 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,bit0,hAPP(int,int,bit1,pls)))),N)) # label(fact_1428_add__2__eq__Suc) # label(axiom) # label(non_clause).  [assumption].
7.36/7.41	416 (all N hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),min_1)),N) = hAPP(real,real,cos,hAPP(real,real,hAPP(real,fun(real,real),times_times(real),pi),hAPP(nat,real,real_1(nat),N)))) # label(fact_2374_cos__npi2) # label(axiom) # label(non_clause).  [assumption].
7.36/7.41	417 (all P_1 all A0 all A1 (hBOOL(hAPP(product_prod(nat,nat),bool,hAPP(fun(product_prod(nat,nat),fun(product_prod(nat,nat),bool)),fun(product_prod(nat,nat),bool),accp(product_prod(nat,nat)),nat_gcd_rel),hAPP(nat,product_prod(nat,nat),hAPP(nat,fun(nat,product_prod(nat,nat)),product_Pair(nat,nat),A0),A1))) -> ((all X_2 all Y_2 (hBOOL(hAPP(product_prod(nat,nat),bool,hAPP(fun(product_prod(nat,nat),fun(product_prod(nat,nat),bool)),fun(product_prod(nat,nat),bool),accp(product_prod(nat,nat)),nat_gcd_rel),hAPP(nat,product_prod(nat,nat),hAPP(nat,fun(nat,product_prod(nat,nat)),product_Pair(nat,nat),X_2),Y_2))) -> ((Y_2 != zero_zero(nat) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),P_1,Y_2),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),X_2),Y_2)))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),P_1,X_2),Y_2))))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),P_1,A0),A1))))) # label(fact_3672_nat__gcd_Opinduct) # label(axiom) # label(non_clause).  [assumption].
7.36/7.41	418 (all X_a all X_b (real_normed_vector(X_b) -> (all F all A_2 all A_3 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),A_2),A_3)) -> hBOOL(hAPP(filter(X_a),bool,hAPP(real,fun(filter(X_a),bool),hAPP(fun(X_a,real),fun(real,fun(filter(X_a),bool)),tendsto(X_a,real),hAPP(fun(X_a,X_b),fun(X_a,real),hAPP(fun(X_b,real),fun(fun(X_a,X_b),fun(X_a,real)),combb(X_b,real,X_a),norm_norm(X_b)),F)),hAPP(X_b,real,norm_norm(X_b),A_2)),A_3)))))) # label(fact_4459_tendsto__norm) # label(axiom) # label(non_clause).  [assumption].
7.36/7.41	419 (all X_1 hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),X_1))) = X_1) # label(fact_3867_card__bdd__nat__set__l) # label(axiom) # label(non_clause).  [assumption].
7.36/7.41	420 (all X_a (archim1727834104eiling(X_a) -> (all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(int,X_a,ring_1_of_int(X_a),hAPP(X_a,int,archim2085082626_floor(X_a),X))),X)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),hAPP(int,X_a,ring_1_of_int(X_a),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(X_a,int,archim2085082626_floor(X_a),X)),one_one(int))))))))) # label(fact_3612_floor__correct) # label(axiom) # label(non_clause).  [assumption].
7.36/7.41	421 (all X_a (order(X_a) -> (all Z_1 all Y all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),X)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Z_1),Y)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Z_1),X))))))) # label(fact_1546_xt1_I6_J) # label(axiom) # label(non_clause).  [assumption].
7.36/7.41	422 (all N exists P_6 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),P_6)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),P_6),hAPP(nat,nat,suc,hAPP(nat,nat,fact,N)))) & hBOOL(hAPP(nat,bool,prime,P_6)))) # label(fact_3551_euclid__bound) # label(axiom) # label(non_clause).  [assumption].
7.36/7.41	423 (all Nat_4 zero_zero(nat) != hAPP(nat,nat,suc,Nat_4)) # label(fact_1224_nat_Osimps_I3_J) # label(axiom) # label(non_clause).  [assumption].
7.36/7.41	424 (all X_a (semiring_1(X_a) -> semiring_1_of_nat(X_a) = ti(fun(nat,X_a),semiring_1_of_nat(X_a)))) # label(tsy_c_Nat_Osemiring__1__class_Oof__nat_res) # label(axiom) # label(non_clause).  [assumption].
7.36/7.41	425 (all Y_1 all X_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Y_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(int,nat,nat_1,X_1)),hAPP(int,nat,nat_1,Y_1))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),X_1),Y_1)))))) # label(fact_1143_transfer__nat__int__relations_I4_J) # label(axiom) # label(non_clause).  [assumption].
7.36/7.41	426 (all N hAPP(real,real,sin,hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,real_1(nat),N)),pi)) = zero_zero(real)) # label(fact_2297_sin__npi) # label(axiom) # label(non_clause).  [assumption].
7.36/7.41	427 (all A_2 all P_4 (hBOOL(hAPP(int,bool,zprime,P_4)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit1,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),P_4)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_2),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),P_4),one_one(int)))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(fun(int,bool),int,hAPP(fun(int,int),fun(fun(int,bool),int),big_co302546470etprod(int,int),combi(int)),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),wset,A_2),P_4))),one_one(int)),P_4)))))) # label(fact_3934_wset__zcong__prod__1) # label(axiom) # label(non_clause).  [assumption].
7.36/7.41	428 (all A_1 (one_one(int) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) -> hAPP(int,int,abs_abs(int),A_1) = one_one(int))) # label(fact_1985_power2__eq1__iff) # label(axiom) # label(non_clause).  [assumption].
7.36/7.41	429 (all A_1 all B hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(real,complex,cis,A_1)),hAPP(real,complex,cis,B)) = hAPP(real,complex,cis,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A_1),B))) # label(fact_3028_cis__mult) # label(axiom) # label(non_clause).  [assumption].
7.36/7.41	430 (all P_5 (hBOOL(hAPP(nat,bool,prime,P_5)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),P_5)))) # label(fact_3078_prime__ge__2) # label(axiom) # label(non_clause).  [assumption].
7.36/7.41	431 (all R_1 hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),hAPP(real,fun(real,real),plus_plus(real),R_1)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),inverse_inverse(real)),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),suc)))),R_1),sequentially))) # label(fact_4437_LIMSEQ__inverse__real__of__nat__add) # label(axiom) # label(non_clause).  [assumption].
7.36/7.41	432 (all X_a (real_normed_algebra(X_a) -> (all Y_1 all X_3 (hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),X_3)) -> hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),hAPP(X_a,fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(X_a,fun(nat,X_a)),combc(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),times_times(X_a)),X_3)),Y_1))))))) # label(fact_4000_mult__left_Osummable) # label(axiom) # label(non_clause).  [assumption].
7.36/7.41	433 (all Ma hAPP(int,nat,phi,Ma) = hAPP(fun(int,bool),nat,finite_card(int),hAPP(int,fun(int,bool),norRRset,Ma))) # label(fact_3613_phi__def) # label(axiom) # label(non_clause).  [assumption].
7.36/7.41	434 (all K_4 all I_1 all J_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_1),J_2)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),J_2),K_4)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_1),K_4))))) # label(fact_527_le__trans) # label(axiom) # label(non_clause).  [assumption].
7.36/7.41	435 (all K_4 hAPP(int,rat,hAPP(int,fun(int,rat),fract,one_one(int)),hAPP(int,int,number_number_of(int),K_4)) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),one_one(rat)),hAPP(int,rat,number_number_of(rat),K_4))) # label(fact_3733_Fract__1__number__of) # label(axiom) # label(non_clause).  [assumption].
7.36/7.41	436 (all X_a (power(X_a) -> power_power(X_a) = ti(fun(X_a,fun(nat,X_a)),power_power(X_a)))) # label(tsy_c_Power_Opower__class_Opower_res) # label(axiom) # label(non_clause).  [assumption].
7.36/7.41	437 (all X hAPP(real,real,uminus_uminus(real),hAPP(real,real,arctan,X)) = hAPP(real,real,arctan,hAPP(real,real,uminus_uminus(real),X))) # label(fact_2055_arctan__minus) # label(axiom) # label(non_clause).  [assumption].
7.36/7.41	438 (all X_a (number(X_a) & linord1117847801e_zero(X_a) -> (all A_2 all B_1 all W_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),B_1),hAPP(int,X_a,number_number_of(X_a),W_1)))) <-> (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(int,X_a,number_number_of(X_a),W_1))) -> (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(int,X_a,number_number_of(X_a),W_1)),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),zero_zero(X_a)))) & (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(int,X_a,number_number_of(X_a),W_1)),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),hAPP(int,X_a,number_number_of(X_a),W_1)))))) & (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(int,X_a,number_number_of(X_a),W_1))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),hAPP(int,X_a,number_number_of(X_a),W_1))),B_1))))))) # label(fact_1752_le__divide__eq__number__of1) # label(axiom) # label(non_clause).  [assumption].
7.36/7.41	439 (all X_a (real_normed_vector(X_a) -> (all X_3 (hBOOL(hAPP(fun(nat,X_a),bool,bseq(X_a),X_3)) -> -(all K_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),K_2)) -> -(all N_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),hAPP(nat,X_a,X_3,N_2))),K_2))))))))) # label(fact_3501_BseqE) # label(axiom) # label(non_clause).  [assumption].
7.36/7.41	440 (all Y all X (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),X)) -> (exists N_2 hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),Y),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),N_2),X))))),X))))) # label(fact_2006_best__division__abs) # label(axiom) # label(non_clause).  [assumption].
7.36/7.41	441 (all I_1 all U all J_2 all K_4 hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_1),J_2)),U)),K_4) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I_1),U)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J_2),U)),K_4))) # label(fact_745_left__add__mult__distrib) # label(axiom) # label(non_clause).  [assumption].
7.36/7.41	442 (all X hAPP(int,int,abs_abs(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,hAPP(int,int,bit1,pls))))) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,abs_abs(int),X)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,hAPP(int,int,bit1,pls))))) # label(fact_1968_abs__power3__distrib) # label(axiom) # label(non_clause).  [assumption].
7.36/7.41	443 (all X_1 all Y_1 (X_1 = Y_1 <-> hAPP(nat,int,semiring_1_of_nat(int),Y_1) = hAPP(nat,int,semiring_1_of_nat(int),X_1))) # label(fact_1485_Nat__Transfer_Otransfer__int__nat__relations_I1_J) # label(axiom) # label(non_clause).  [assumption].
7.36/7.41	444 (all X all Y hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),X),Y) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),X),hAPP(complex,complex,inverse_inverse(complex),Y))) # label(fact_2755_complex__divide__def) # label(axiom) # label(non_clause).  [assumption].
7.36/7.41	445 (all X_a (comm_semiring_1(X_a) -> (all M all A_1 all N all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N)),B)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),M)),B))))))) # label(fact_344_power__le__dvd) # label(axiom) # label(non_clause).  [assumption].
7.36/7.41	446 (all X_a (real_normed_algebra(X_a) -> (all Xa_1 all X all Y hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Xa_1),X)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Xa_1),Y)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Xa_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X),Y))))) # label(fact_881_mult__right_Oadd) # label(axiom) # label(non_clause).  [assumption].
7.36/7.41	447 (all X_a (metric_space(X_a) -> (all X hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),X),X) = zero_zero(real)))) # label(fact_3516_dist__self) # label(axiom) # label(non_clause).  [assumption].
7.36/7.41	448 (all A_1 all B hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),A_1)),B))),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A_1),B)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) # label(fact_592_zdiff__power2) # label(axiom) # label(non_clause).  [assumption].
7.36/7.41	449 (all N -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),zero_zero(nat)))) # label(fact_472_less__zeroE) # label(axiom) # label(non_clause).  [assumption].
7.36/7.41	450 (all Z_1 all X all Y (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),Y)) -> (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Z_1),Y)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y),Z_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),Z_1)) & -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Z_1),X))))) # label(fact_637_dvd_Ole__less__trans) # label(axiom) # label(non_clause).  [assumption].
7.36/7.41	451 (all X_a (archim1727834104eiling(X_a) -> (all N hAPP(nat,int,semiring_1_of_nat(int),N) = hAPP(X_a,int,archim2085082626_floor(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),N))))) # label(fact_2875_floor__of__nat) # label(axiom) # label(non_clause).  [assumption].
7.36/7.41	452 (all N exists P_6 (hBOOL(hAPP(nat,bool,prime,P_6)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),P_6)))) # label(fact_3105_euclid) # label(axiom) # label(non_clause).  [assumption].
7.36/7.41	453 (all N -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),N))) # label(fact_517_less__irrefl__nat) # label(axiom) # label(non_clause).  [assumption].
7.36/7.41	454 (all X_a (ordered_ab_group_add(X_a) -> (all X_1 all Y_1 hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_gr676655987ssThan(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),Y_1)),hAPP(X_a,X_a,uminus_uminus(X_a),X_1)) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,X_a),fun(fun(X_a,bool),fun(X_a,bool)),image(X_a,X_a),uminus_uminus(X_a)),hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_gr676655987ssThan(X_a),X_1),Y_1))))) # label(fact_3678_image__uminus__greaterThanLessThan) # label(axiom) # label(non_clause).  [assumption].
7.36/7.41	455 (all X_1 (-hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),zEven)) <-> hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),zOdd)))) # label(fact_1276_odd__iff__not__even) # label(axiom) # label(non_clause).  [assumption].
7.36/7.41	456 (all X all A_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A_1)) -> (one_one(real) != A_1 -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> hAPP(real,real,hAPP(real,fun(real,real),powr,A_1),hAPP(real,real,hAPP(real,fun(real,real),log,A_1),X)) = X)))) # label(fact_3406_powr__log__cancel) # label(axiom) # label(non_clause).  [assumption].
7.36/7.41	457 (all X all Y X = hAPP(complex,real,re,hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,X),Y))) # label(fact_2993_Re) # label(axiom) # label(non_clause).  [assumption].
7.36/7.41	458 (all A_1 all B all M hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),M),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_1),M)),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),B),M)))),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_1),M)),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),B),M))) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A_1),B)) # label(fact_969_zcong__zmod__aux) # label(axiom) # label(non_clause).  [assumption].
7.36/7.41	459 (all M all N all K_4 all L_4 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),K_4),L_4)) -> (hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_4),N) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),L_4) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N))))) # label(fact_561_less__add__eq__less) # label(axiom) # label(non_clause).  [assumption].
7.36/7.41	460 (all K all F all N_1 ((all I_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),N_1)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(nat,int,F,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_2),one_one(nat)))),hAPP(nat,int,F,I_2)))),one_one(int))))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,F,zero_zero(nat))),K)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),K),hAPP(nat,int,F,N_1))) -> (exists I_2 (hAPP(nat,int,F,I_2) = ti(int,K) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_2),N_1)))))))) # label(fact_2008_int__val__lemma) # label(axiom) # label(non_clause).  [assumption].
7.36/7.41	461 (all D all A_1 all B (one_one(int) = hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),D),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),B)) -> one_one(int) = hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),D),B))) # label(fact_4382_coprime__rmult__int) # label(axiom) # label(non_clause).  [assumption].
7.36/7.41	462 (all A_1 -(hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),one_one(nat))) & -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),one_one(nat)),A_1)))) # label(fact_893_gcd__lcm__complete__lattice__nat_Onot__less__bot) # label(axiom) # label(non_clause).  [assumption].
7.36/7.41	463 (all A_1 hAPP(real,real,cos,A_1) = hAPP(complex,real,re,hAPP(real,complex,cis,A_1))) # label(fact_3026_Re__cis) # label(axiom) # label(non_clause).  [assumption].
7.36/7.41	464 (all X_a (real_normed_vector(X_a) -> (all R_4 all A_1 all B hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),R_4),A_1)),B) = hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),R_4),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_1),B))))) # label(fact_4697_scaleR_OscaleR__left) # label(axiom) # label(non_clause).  [assumption].
7.36/7.41	465 (all M 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)) -> 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),N)))))) # label(fact_1381_one__less__mult) # label(axiom) # label(non_clause).  [assumption].
7.36/7.41	466 (all X_3 all A_2 (hBOOL(hAPP(complex,bool,hAPP(fun(nat,complex),fun(complex,bool),sums(complex),X_3),A_2)) -> hBOOL(hAPP(real,bool,hAPP(fun(nat,real),fun(real,bool),sums(real),hAPP(fun(nat,complex),fun(nat,real),hAPP(fun(complex,real),fun(fun(nat,complex),fun(nat,real)),combb(complex,real,nat),re),X_3)),hAPP(complex,real,re,A_2))))) # label(fact_4114_Re_Osums) # label(axiom) # label(non_clause).  [assumption].
7.36/7.41	467 (all P_5 all Q_3 (hBOOL(hAPP(nat,bool,prime,hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),P_5),Q_3))) -> Q_3 = one_one(nat) | P_5 = one_one(nat))) # label(fact_3055_prime__product) # label(axiom) # label(non_clause).  [assumption].
7.36/7.41	468 (all X_a (real_normed_field(X_a) & banach(X_a) -> (all Z all F all X_1 (hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),times_times(X_a)),F)),hAPP(X_a,fun(nat,X_a),power_power(X_a),X_1)))) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,norm_norm(X_a),Z)),hAPP(X_a,real,norm_norm(X_a),X_1))) -> hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,X_a),fun(nat,real),hAPP(fun(X_a,real),fun(fun(nat,X_a),fun(nat,real)),combb(X_a,real,nat),norm_norm(X_a)),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),times_times(X_a)),F)),hAPP(X_a,fun(nat,X_a),power_power(X_a),Z)))))))))) # label(fact_3996_powser__insidea) # label(axiom) # label(non_clause).  [assumption].
7.36/7.41	469 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X)) -> (zero_zero(real) = hAPP(real,real,cos,X) -> (exists N_2 (-hBOOL(hAPP(nat,bool,even_odd_even(nat),N_2)) & X = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,real_1(nat),N_2)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))))) # label(fact_2476_cos__zero__lemma) # label(axiom) # label(non_clause).  [assumption].
7.36/7.41	470 (all Z all Ma ((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),dvd_dvd(int),Z),hAPP(nat,int,semiring_1_of_nat(int),Ma)))) & (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Z)) -> zero_zero(nat) = Ma) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(int,nat,nat_1,Z)),Ma)))) # label(fact_1449_nat__dvd__iff) # label(axiom) # label(non_clause).  [assumption].
7.36/7.41	471 (all X_a (ring(X_a) -> (all X all Y all A_1 all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),Y),B))),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),X),A_1)),B)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),Y)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B))))) # label(fact_729_mult__diff__mult) # label(axiom) # label(non_clause).  [assumption].
7.36/7.41	472 (all Z_1 all X all Y (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),Y)) & -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y),X)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y),Z_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),Z_1)) & -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Z_1),X))))) # label(fact_646_dvd_Oless__le__trans) # label(axiom) # label(non_clause).  [assumption].
7.36/7.41	473 (all X_a (linorder(X_a) -> (all X_1 all Y_1 (hAPP(X_a,fun(X_a,bool),ord_atMost(X_a),Y_1) = hAPP(X_a,fun(X_a,bool),ord_atMost(X_a),X_1) <-> ti(X_a,X_1) = ti(X_a,Y_1))))) # label(fact_4962_atMost__eq__iff) # label(axiom) # label(non_clause).  [assumption].
7.36/7.41	474 (all P_1 all Ma all N_1 ((exists Q_4 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N_1),hAPP(nat,nat,suc,Q_4)))) & hBOOL(hAPP(nat,bool,P_1,Q_4)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N_1),Q_4)),Ma)))) | hBOOL(hAPP(nat,bool,P_1,zero_zero(nat))) & zero_zero(nat) = N_1 <-> hBOOL(hAPP(nat,bool,P_1,hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),Ma),N_1))))) # label(fact_1443_split__div_H) # label(axiom) # label(non_clause).  [assumption].
7.36/7.41	475 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),hAPP(nat,nat,suc,N))))) # label(fact_1234_less__SucI) # label(axiom) # label(non_clause).  [assumption].
7.36/7.41	476 (all A_1 all B all C all Q_3 all R_4 (hBOOL(hAPP(product_prod(nat,nat),bool,hAPP(nat,fun(product_prod(nat,nat),bool),hAPP(nat,fun(nat,fun(product_prod(nat,nat),bool)),divmod_nat_rel,B),C),hAPP(nat,product_prod(nat,nat),hAPP(nat,fun(nat,product_prod(nat,nat)),product_Pair(nat,nat),Q_3),R_4))) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),C)) -> hBOOL(hAPP(product_prod(nat,nat),bool,hAPP(nat,fun(product_prod(nat,nat),bool),hAPP(nat,fun(nat,fun(product_prod(nat,nat),bool)),divmod_nat_rel,hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A_1),B)),C),hAPP(nat,product_prod(nat,nat),hAPP(nat,fun(nat,product_prod(nat,nat)),product_Pair(nat,nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A_1),Q_3)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A_1),R_4)),C))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A_1),R_4)),C))))))) # label(fact_3095_divmod__nat__rel__mult1__eq) # label(axiom) # label(non_clause).  [assumption].
7.36/7.41	477 (all P_5 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),P_5)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),P_5),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))))) # label(fact_1157_Int2_Oaux__2) # label(axiom) # label(non_clause).  [assumption].
7.36/7.41	478 (all X_a (linordered_semidom(X_a) -> (all A_1 all N all N_5 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),N_5)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),A_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N_5)))))))) # label(fact_447_power__strict__increasing) # label(axiom) # label(non_clause).  [assumption].
7.36/7.41	479 (all N all K_4 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),K_4)) -> hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,K_4),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K_4),N)) = ti(int,K_4))) # label(fact_3454_zgcd__zmult__eq__self) # label(axiom) # label(non_clause).  [assumption].
7.36/7.42	480 (all X_a (linordered_semidom(X_a) -> (all K all F all K_3 all N_1 ((all P_6 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),P_6),N_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(nat,X_a,F,P_6)),K_3)))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),K_3)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),K)))),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),N_1)),K_3)))))))) # label(fact_4273_real__setsum__nat__ivl__bounded2) # label(axiom) # label(non_clause).  [assumption].
7.36/7.42	481 (all X_a (linord1117847801e_zero(X_a) -> (all X_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),hAPP(X_a,X_a,inverse_inverse(X_a),X_1))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),X_1)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),one_one(X_a))))))) # label(fact_2575_one__less__inverse__iff) # label(axiom) # label(non_clause).  [assumption].
7.36/7.42	482 (all X_a (semiring_div(X_a) -> (all C_1 all B_1 all A_2 (zero_zero(X_a) != ti(X_a,A_2) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_2),B_1)) -> (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),B_1),A_2) = ti(X_a,C_1) <-> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1),A_2) = ti(X_a,B_1))))))) # label(fact_1044_dvd__div__eq__mult) # label(axiom) # label(non_clause).  [assumption].
7.36/7.42	483 (all X_a (order(X_a) -> (all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y)) -> ti(X_a,Y) = ti(X_a,X) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)))))) # label(fact_1596_order__le__imp__less__or__eq) # label(axiom) # label(non_clause).  [assumption].
7.36/7.42	484 (all X_a (real_normed_field(X_a) -> (all Y_1 all A_2 hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,X_a),fun(X_a,bool),isCont(X_a,X_a),hAPP(X_a,fun(X_a,X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(X_a,X_a)),combc(X_a,X_a,X_a),inverse_divide(X_a)),Y_1)),A_2))))) # label(fact_4897_divide_OisCont) # label(axiom) # label(non_clause).  [assumption].
7.36/7.42	485 (all W hAPP(int,int,uminus_uminus(int),hAPP(int,int,number_number_of(int),W)) = hAPP(int,int,number_number_of(int),hAPP(int,int,uminus_uminus(int),W))) # label(fact_2141_minus__numeral__code_I5_J) # label(axiom) # label(non_clause).  [assumption].
7.36/7.42	486 (all L_4 all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),L_4)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),L_4),N)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),L_4),M)))))) # label(fact_662_diff__less__mono2) # label(axiom) # label(non_clause).  [assumption].
7.36/7.42	487 (all X_a (real_normed_vector(X_a) -> (all X_3 all L_2 ((all R_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),R_2)) -> (exists No all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),No),N_2)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(nat,X_a,X_3,N_2)),L_2))),R_2)))))) -> hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),X_3),L_2),sequentially)))))) # label(fact_4659_LIMSEQ__I) # label(axiom) # label(non_clause).  [assumption].
7.36/7.42	488 (all X_1 all Y_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(rat,real,ratreal,X_1)),hAPP(rat,real,ratreal,Y_1))) <-> hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),X_1),Y_1)))) # label(fact_3759_real__less__code) # label(axiom) # label(non_clause).  [assumption].
7.36/7.42	489 (all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,number_number_of(real),min_1)),X_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_1),one_one(real))) -> hBOOL(hAPP(real,bool,hAPP(fun(real,real),fun(real,bool),isCont(real,real),arccos),X_1))))) # label(fact_4921_isCont__arccos) # label(axiom) # label(non_clause).  [assumption].
7.36/7.42	490 (all X (-hBOOL(hAPP(int,bool,even_odd_even(int),X)) -> hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),X),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),one_one(int)) = hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X),one_one(int))),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) # label(fact_1472_odd__plus__one__div__two) # label(axiom) # label(non_clause).  [assumption].
7.36/7.42	491 (all X_a (semiring_div(X_a) -> (all A_1 all C all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),A_1),C)),B)),C) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)),C)))) # label(fact_933_zmod__simps_I4_J) # label(axiom) # label(non_clause).  [assumption].
7.36/7.42	492 (all K_4 all L_4 hAPP(int,int,bit0,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),K_4),L_4)) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,bit0,K_4)),hAPP(int,int,bit0,L_4))) # label(fact_480_diff__bin__simps_I7_J) # label(axiom) # label(non_clause).  [assumption].
7.36/7.42	493 (all X_a (linordered_idom(X_a) & number_ring(X_a) -> (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),N)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),N)))))) # label(fact_1445_of__nat__less__two__power) # label(axiom) # label(non_clause).  [assumption].
7.36/7.42	494 (all X_a (idom(X_a) -> (all A_2 all C_1 all B_1 (ti(X_a,C_1) = zero_zero(X_a) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_2),B_1)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B_1),C_1))))))) # label(fact_410_dvd__mult__cancel__right) # label(axiom) # label(non_clause).  [assumption].
7.36/7.42	495 (all Ma all D_1 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),Ma),D_1) = zero_zero(nat) <-> (exists Q_4 hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),D_1),Q_4) = Ma))) # label(fact_1104_mod__eq__0__iff) # label(axiom) # label(non_clause).  [assumption].
7.36/7.42	496 (all W hAPP(complex,complex,cnj,hAPP(int,complex,number_number_of(complex),W)) = hAPP(int,complex,number_number_of(complex),W)) # label(fact_2932_complex__cnj__number__of) # label(axiom) # label(non_clause).  [assumption].
7.36/7.42	497 (all X hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),one_one(real)),X)),hAPP(real,real,exp(real),X)))) # label(fact_2598_exp__ge__add__one__self) # label(axiom) # label(non_clause).  [assumption].
7.36/7.42	498 (all X_a all X_c all B_1_1 all B_2_1 hAPP(X_a,X_c,B_1_1,B_2_1) = hAPP(X_a,X_c,B_1_1,ti(X_a,B_2_1))) # label(tsy_c_hAPP_arg2) # label(axiom) # label(non_clause).  [assumption].
7.36/7.42	499 (all X_1 all Y_1 all P_1 ((hBOOL(P_1) -> hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),hAPP(bool,fun(int,fun(int,int)),if(int),P_1),X_1),Y_1)) = hAPP(int,nat,nat_1,X_1)) & (-hBOOL(P_1) -> hAPP(int,nat,nat_1,Y_1) = hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),hAPP(bool,fun(int,fun(int,int)),if(int),P_1),X_1),Y_1))))) # label(fact_1081_nat__if__cong) # label(axiom) # label(non_clause).  [assumption].
7.36/7.42	500 (all X all Y (X = Y -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),Y)))) # label(fact_626_dvd_Oeq__refl) # label(axiom) # label(non_clause).  [assumption].
7.36/7.42	501 (all K_4 hAPP(int,int,hAPP(int,fun(int,int),times_times(int),min_1),K_4) = hAPP(int,int,uminus_uminus(int),K_4)) # label(fact_2160_mult__Min) # label(axiom) # label(non_clause).  [assumption].
7.36/7.42	502 (all Z_1 Z_1 = hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,hAPP(complex,real,re,Z_1)),hAPP(complex,real,im,Z_1))) # label(fact_3000_complex__surj) # label(axiom) # label(non_clause).  [assumption].
7.36/7.42	503 (all C all A_1 all B (B = A_1 -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),B),C)) & -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),C),B)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),C)) & -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),C),A_1))))) # label(fact_636_dvd_Oord__eq__less__trans) # label(axiom) # label(non_clause).  [assumption].
7.36/7.42	504 (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_1550_xt1_I4_J) # label(axiom) # label(non_clause).  [assumption].
7.36/7.42	505 (all X_a all X_1 hAPP(fun(X_a,bool),X_a,hilbert_Eps(X_a),hAPP(X_a,fun(X_a,bool),fequal(X_a),X_1)) = ti(X_a,X_1)) # label(fact_4788_some__sym__eq__trivial) # label(axiom) # label(non_clause).  [assumption].
7.36/7.42	506 (all X_a (number_semiring(X_a) -> (all Z_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Z_1),Z_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Z_1),hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))) # label(fact_141_semiring__mult__2__right) # label(axiom) # label(non_clause).  [assumption].
7.36/7.42	507 (all R_4 (hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),R_4)) -> -(all S_1 (hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),S_1)) -> (all T_4 (hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),T_4)) -> hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),S_1),T_4) != R_4)))))) # label(fact_3731_obtain__pos__sum) # label(axiom) # label(non_clause).  [assumption].
7.36/7.42	508 (all N_1 (zero_zero(nat) = N_1 <-> zero_zero(int) = hAPP(nat,int,semiring_1_of_nat(int),N_1))) # label(fact_1290_int__eq__0__conv) # label(axiom) # label(non_clause).  [assumption].
7.36/7.42	509 (all B all A_1 (A_1 != zero_zero(nat) -> (exists X_2 exists Y_2 hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A_1),X_2) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),Y_2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),A_1),B))))) # label(fact_3313_bezout__nat) # label(axiom) # label(non_clause).  [assumption].
7.36/7.42	510 (all N_1 all Ma all F ((all N_2 (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,F,hAPP(nat,nat,suc,N_2))),hAPP(nat,nat,F,N_2))) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,F,N_2)),hAPP(nat,nat,F,hAPP(nat,nat,suc,N_2)))))) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),Ma)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,F,N_1)),hAPP(nat,nat,F,Ma))) & -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,F,Ma)),hAPP(nat,nat,F,N_1)))))) # label(fact_1493_dvd_Olift__Suc__mono__less__iff) # label(axiom) # label(non_clause).  [assumption].
7.36/7.42	511 (all A_2 all B_1 all P_4 (hBOOL(hAPP(nat,bool,prime,P_4)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),P_4),A_2)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),P_4),B_1)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),P_4),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A_2),B_1)))))) # label(fact_3052_prime__divprod__eq) # label(axiom) # label(non_clause).  [assumption].
7.36/7.42	512 (all N_1 all G all X_1 all Ma (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),G),X_1),Ma)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(nat,fun(real,real),hAPP(fun(real,fun(nat,real)),fun(nat,fun(real,real)),combc(real,nat,real),hAPP(fun(real,real),fun(real,fun(nat,real)),hAPP(fun(real,fun(nat,real)),fun(fun(real,real),fun(real,fun(nat,real))),combb(real,fun(nat,real),real),power_power(real)),G)),N_1)),X_1),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,real_1(nat),N_1)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,G,X_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),one_one(nat))))),Ma))))) # label(fact_3879_DERIV__fun__pow) # label(axiom) # label(non_clause).  [assumption].
7.36/7.42	513 (all X_a (real_vector(X_a) -> (all A_1 all X hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_1),X)) = hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),hAPP(real,real,uminus_uminus(real),A_1)),X)))) # label(fact_4686_scaleR__minus__left) # label(axiom) # label(non_clause).  [assumption].
7.36/7.42	514 (all X_a (real_normed_vector(X_a) -> (all G all F all L_2 (hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),F),L_2),sequentially)) -> (hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),minus_minus(X_a)),F)),G)),zero_zero(X_a)),sequentially)) -> hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),G),L_2),sequentially))))))) # label(fact_4447_LIMSEQ__diff__approach__zero2) # label(axiom) # label(non_clause).  [assumption].
7.36/7.42	515 (all X_a (field_char_0(X_a) -> (all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_2),field_char_0_Rats(X_a))) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),A_2)),field_char_0_Rats(X_a))))))) # label(fact_3698_Rats__minus) # label(axiom) # label(non_clause).  [assumption].
7.36/7.42	516 (all X_a (real_n2089651433ebra_1(X_a) -> (all X all N hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),N))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(X_a,real,norm_norm(X_a),X)),N)))))) # label(fact_1794_norm__power__ineq) # label(axiom) # label(non_clause).  [assumption].
7.36/7.42	517 (all X_a (real_field(X_a) -> (all X all Y (Y != zero_zero(real) -> hAPP(real,X_a,of_real(X_a),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),X),Y)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),hAPP(real,X_a,of_real(X_a),X)),hAPP(real,X_a,of_real(X_a),Y)))))) # label(fact_2805_nonzero__of__real__divide) # label(axiom) # label(non_clause).  [assumption].
7.36/7.42	518 (all X_a (real_normed_algebra(X_a) -> (all X all Y all Ya hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),Ya)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Y),Ya)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),X),Y)),Ya)))) # label(fact_884_mult__left_Odiff) # label(axiom) # label(non_clause).  [assumption].
7.36/7.42	519 (all W all V ((-hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V))) -> hAPP(int,nat,nat_1,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,number_number_of(int),V)),hAPP(int,nat,number_number_of(nat),W))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),hAPP(int,nat,number_number_of(nat),V)),hAPP(int,nat,number_number_of(nat),W))) & (hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V))) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),zero_zero(nat)),hAPP(int,nat,number_number_of(nat),W)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),hAPP(int,nat,number_number_of(nat),V)),hAPP(int,nat,number_number_of(nat),W))))) # label(fact_1516_power__nat__number__of__number__of) # label(axiom) # label(non_clause).  [assumption].
7.36/7.42	520 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),M),N)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),N),M)) -> M = N))) # label(fact_632_dvd__antisym) # label(axiom) # label(non_clause).  [assumption].
7.36/7.42	521 (all X_1 (-hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),zOdd)) -> hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),zEven)))) # label(fact_1274_not__odd__impl__even) # label(axiom) # label(non_clause).  [assumption].
7.36/7.42	522 (all X_a all X_b (real_n1866405975lgebra(X_b) -> (all F all A_2 all A_3 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),A_2),A_3)) -> (ti(X_b,A_2) != zero_zero(X_b) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(fun(X_a,X_b),fun(X_a,X_b),hAPP(fun(X_b,X_b),fun(fun(X_a,X_b),fun(X_a,X_b)),combb(X_b,X_b,X_a),inverse_inverse(X_b)),F)),hAPP(X_b,X_b,inverse_inverse(X_b),A_2)),A_3))))))) # label(fact_4481_tendsto__inverse) # label(axiom) # label(non_clause).  [assumption].
7.36/7.42	523 (all B all A_1 all A_6 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A_1),A_6)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),zero_zero(int))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_6),B)),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_1),B)))))) # label(fact_1014_zdiv__mono1__neg) # label(axiom) # label(non_clause).  [assumption].
7.36/7.42	524 (all X_a all X_b (ord(X_b) -> (all F all G (hBOOL(hAPP(fun(X_a,X_b),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,X_b),bool),ord_less_eq(fun(X_a,X_b)),F),G)) & -hBOOL(hAPP(fun(X_a,X_b),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,X_b),bool),ord_less_eq(fun(X_a,X_b)),G),F)) <-> hBOOL(hAPP(fun(X_a,X_b),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,X_b),bool),ord_less(fun(X_a,X_b)),F),G)))))) # label(fact_1609_less__fun__def) # label(axiom) # label(non_clause).  [assumption].
7.36/7.42	525 (all X_1 (hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),X_1),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = zero_zero(int) <-> hBOOL(hAPP(int,bool,even_odd_even(int),X_1)))) # label(fact_1453_even__def) # label(axiom) # label(non_clause).  [assumption].
7.36/7.42	526 (all X_a (linordered_field(X_a) -> (all B_1 all A_2 all C_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),zero_zero(X_a))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),B_1),C_1)),A_2)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),C_1)),B_1))))))) # label(fact_1742_neg__divide__le__eq) # label(axiom) # label(non_clause).  [assumption].
7.36/7.42	527 (all X all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),Y)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),Y),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X),pi)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,cos,X)),hAPP(real,real,cos,Y))))))) # label(fact_2216_cos__monotone__0__pi_H) # label(axiom) # label(non_clause).  [assumption].
7.36/7.42	528 (all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),Y)),one_one(real))) -> hAPP(real,real,sqrt,hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),one_one(real)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),Y),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) = hAPP(real,real,sin,hAPP(real,real,arccos,Y)))) # label(fact_2401_sin__arccos__abs) # label(axiom) # label(non_clause).  [assumption].
7.36/7.42	529 (all X_a (linordered_ring(X_a) & monoid_mult(X_a) -> (all X all N (hBOOL(hAPP(nat,bool,even_odd_even(nat),N)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),N))))))) # label(fact_2433_zero__le__even__power) # label(axiom) # label(non_clause).  [assumption].
7.36/7.42	530 (all N all M (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N),M)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),M),N) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N)),N))) # label(fact_3274_gcd__diff1__nat) # label(axiom) # label(non_clause).  [assumption].
7.36/7.42	531 (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_eq(int),hAPP(int,int,bit1,K)),hAPP(int,int,bit0,L))))) # label(fact_73_rel__simps_I33_J) # label(axiom) # label(non_clause).  [assumption].
7.36/7.42	532 (all X all Y all N (N != zero_zero(nat) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),X),N)),Y)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),Y))))) # label(fact_728_divides__exp2) # label(axiom) # label(non_clause).  [assumption].
7.36/7.42	533 (all X_a (one(X_a) -> (all X_1 (one_one(X_a) = ti(X_a,X_1) <-> ti(X_a,X_1) = one_one(X_a))))) # label(fact_772_one__reorient) # label(axiom) # label(non_clause).  [assumption].
7.36/7.42	534 (all X_b all X_a (ordere142940540dd_abs(X_a) -> (all F all A_3 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co1399186613setsum(X_b,X_a),hAPP(fun(X_b,X_a),fun(X_b,X_a),hAPP(fun(X_a,X_a),fun(fun(X_b,X_a),fun(X_b,X_a)),combb(X_a,X_a,X_b),abs_abs(X_a)),F)),A_3)))))) # label(fact_4166_setsum__abs__ge__zero) # label(axiom) # label(non_clause).  [assumption].
7.36/7.42	535 (all X_a all X_b (real_normed_vector(X_b) -> (all X_3 all L_2 all S ((all N_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),N_2),S)) -> hBOOL(hAPP(filter(nat),bool,hAPP(X_b,fun(filter(nat),bool),hAPP(fun(nat,X_b),fun(X_b,fun(filter(nat),bool)),tendsto(nat,X_b),hAPP(X_a,fun(nat,X_b),X_3,N_2)),hAPP(X_a,X_b,L_2,N_2)),sequentially)))) -> hBOOL(hAPP(filter(nat),bool,hAPP(X_b,fun(filter(nat),bool),hAPP(fun(nat,X_b),fun(X_b,fun(filter(nat),bool)),tendsto(nat,X_b),hAPP(fun(X_a,bool),fun(nat,X_b),hAPP(fun(nat,fun(fun(X_a,bool),X_b)),fun(fun(X_a,bool),fun(nat,X_b)),combc(nat,fun(X_a,bool),X_b),hAPP(fun(nat,fun(X_a,X_b)),fun(nat,fun(fun(X_a,bool),X_b)),hAPP(fun(fun(X_a,X_b),fun(fun(X_a,bool),X_b)),fun(fun(nat,fun(X_a,X_b)),fun(nat,fun(fun(X_a,bool),X_b))),combb(fun(X_a,X_b),fun(fun(X_a,bool),X_b),nat),big_co1399186613setsum(X_a,X_b)),hAPP(fun(X_a,fun(nat,X_b)),fun(nat,fun(X_a,X_b)),combc(X_a,nat,X_b),X_3))),S)),hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),L_2),S)),sequentially)))))) # label(fact_4658_LIMSEQ__setsum) # label(axiom) # label(non_clause).  [assumption].
7.36/7.42	536 (all A_2 all A_3 all Ma (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),Ma)) -> (hBOOL(hAPP(int,bool,hAPP(fun(int,bool),fun(int,bool),is_RRset,A_3),Ma)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),A_2),A_3)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_2),hAPP(int,int,hAPP(int,fun(int,int),hAPP(fun(int,bool),fun(int,fun(int,int)),rRset2norRR,A_3),Ma),A_2)),Ma)))))) # label(fact_3623_RRset2norRR__correct1) # label(axiom) # label(non_clause).  [assumption].
7.36/7.42	537 (all X_1 all Y_1 all Z (X_1 = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),Y_1),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),Z)) <-> hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),X_1) = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),Y_1),Z))) # label(fact_1772_eq__divide__2__times__iff) # label(axiom) # label(non_clause).  [assumption].
7.36/7.42	538 (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_213_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J) # label(axiom) # label(non_clause).  [assumption].
7.36/7.42	539 (all X_a (comm_semiring_1(X_a) -> (all X hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),X)))) # label(fact_193_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J) # label(axiom) # label(non_clause).  [assumption].
7.36/7.42	540 (all A_1 one_one(real) = hAPP(real,real,hAPP(real,fun(real,real),powr,one_one(real)),A_1)) # label(fact_3323_powr__one__eq__one) # label(axiom) # label(non_clause).  [assumption].
7.36/7.42	541 (all X_a all X_b (comm_semiring_1(X_b) -> (all F all G all A_3 all B_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),B_2)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_3),B_2)) -> ((all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_3)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),dvd_dvd(X_b),hAPP(X_a,X_b,F,X_2)),hAPP(X_a,X_b,G,X_2))))) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),dvd_dvd(X_b),hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co302546470etprod(X_a,X_b),F),A_3)),hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co302546470etprod(X_a,X_b),G),B_2))))))))) # label(fact_3965_setprod__dvd__setprod__subset2) # label(axiom) # label(non_clause).  [assumption].
7.36/7.42	542 (all P_1 all A_2 all B_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A_2),B_1)) -> (all N_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(product_prod(real,real),real,product_fst(real,real),hAPP(nat,product_prod(real,real),hAPP(real,fun(nat,product_prod(real,real)),hAPP(real,fun(real,fun(nat,product_prod(real,real))),hAPP(fun(product_prod(real,real),bool),fun(real,fun(real,fun(nat,product_prod(real,real)))),bolzano_bisect,P_1),A_2),B_1),N_2))),hAPP(product_prod(real,real),real,product_fst(real,real),hAPP(nat,product_prod(real,real),hAPP(real,fun(nat,product_prod(real,real)),hAPP(real,fun(real,fun(nat,product_prod(real,real))),hAPP(fun(product_prod(real,real),bool),fun(real,fun(real,fun(nat,product_prod(real,real)))),bolzano_bisect,P_1),A_2),B_1),hAPP(nat,nat,suc,N_2)))))))) # label(fact_3133_Bolzano__bisect__fst__le__Suc) # label(axiom) # label(non_clause).  [assumption].
7.36/7.42	543 (all A_1 all B hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,A_1),B)),ii) = hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,hAPP(real,real,uminus_uminus(real),B)),A_1)) # label(fact_2767_Complex__mult__i) # label(axiom) # label(non_clause).  [assumption].
7.36/7.42	544 (all J_2 all I_1 -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J_2),I_1)),I_1))) # label(fact_555_not__add__less2) # label(axiom) # label(non_clause).  [assumption].
7.36/7.42	545 (all A_2 all B_1 all Ma (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,B_1),A_2),Ma)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_2),B_1),Ma)))) # label(fact_313_zcong__sym) # label(axiom) # label(non_clause).  [assumption].
7.36/7.42	546 (all M all X (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),X)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X),M)) -> -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,X),zero_zero(int)),M))))) # label(fact_418_zcong__not__zero) # label(axiom) # label(non_clause).  [assumption].
7.36/7.42	547 (all M hAPP(int,int,abs_abs(int),hAPP(nat,int,semiring_1_of_nat(int),M)) = hAPP(nat,int,semiring_1_of_nat(int),M)) # label(fact_1923_abs__int__eq) # label(axiom) # label(non_clause).  [assumption].
7.36/7.42	548 (all X_a all X_b (real_normed_vector(X_b) -> (all F all A_2 all A_3 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(fun(X_a,X_b),fun(X_a,X_b),hAPP(fun(X_b,X_b),fun(fun(X_a,X_b),fun(X_a,X_b)),combb(X_b,X_b,X_a),uminus_uminus(X_b)),F)),hAPP(X_b,X_b,uminus_uminus(X_b),A_2)),A_3)) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),A_2),A_3)))))) # label(fact_4473_tendsto__minus__cancel) # label(axiom) # label(non_clause).  [assumption].
7.36/7.42	549 (all X_1 hAPP(real,real,sin,X_1) = hAPP(fun(nat,real),real,suminf(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),sin_coeff)),hAPP(real,fun(nat,real),power_power(real),X_1)))) # label(fact_3970_sin__def) # label(axiom) # label(non_clause).  [assumption].
7.36/7.42	550 (all X all Y (Y = hAPP(real,real,sqrt,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),Y),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) -> X = zero_zero(real))) # label(fact_1646_real__sqrt__sum__squares__eq__cancel2) # label(axiom) # label(non_clause).  [assumption].
7.36/7.42	551 (all N (hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,hAPP(int,int,bit1,pls))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),N),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) -> -hBOOL(hAPP(nat,bool,even_odd_even(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),one_one(nat))),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))) # label(fact_2473_lemma__odd__mod__4__div__2) # label(axiom) # label(non_clause).  [assumption].
7.36/7.42	552 (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),C) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B) -> ti(X_a,C) = ti(X_a,B))))) # label(fact_767_add__imp__eq) # label(axiom) # label(non_clause).  [assumption].
7.36/7.42	553 (all X_a (real_vector(X_a) -> (all A_2 all X_1 all Y_1 (hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_2),Y_1) = hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_2),X_1) <-> zero_zero(real) = A_2 | ti(X_a,Y_1) = ti(X_a,X_1))))) # label(fact_4700_scaleR__cancel__left) # label(axiom) # label(non_clause).  [assumption].
7.36/7.42	554 (all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),zero_zero(nat)),N) = zero_zero(nat)) # label(fact_549_mult__0) # label(axiom) # label(non_clause).  [assumption].
7.36/7.42	555 (all X_1 all Y_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X_1),Y_1)),zero_zero(real))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),Y_1),hAPP(real,real,uminus_uminus(real),X_1))))) # label(fact_2107_real__add__le__0__iff) # label(axiom) # label(non_clause).  [assumption].
7.36/7.42	556 (all K_4 all L_4 (hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,uminus_uminus(int),K_4)),L_4) != zero_zero(int) -> hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),K_4),L_4) != zero_zero(int))) # label(fact_2158_zmod__zminus1__not__zero) # label(axiom) # label(non_clause).  [assumption].
7.36/7.42	557 (all M all N all Q_3 all R_4 (hBOOL(hAPP(product_prod(nat,nat),bool,hAPP(nat,fun(product_prod(nat,nat),bool),hAPP(nat,fun(nat,fun(product_prod(nat,nat),bool)),divmod_nat_rel,M),N),hAPP(nat,product_prod(nat,nat),hAPP(nat,fun(nat,product_prod(nat,nat)),product_Pair(nat,nat),Q_3),R_4))) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),M),N) = Q_3)) # label(fact_3101_div__eq) # label(axiom) # label(non_clause).  [assumption].
7.36/7.42	558 (all X_1 all Y_1 (zero_zero(nat) = X_1 & Y_1 = zero_zero(nat) <-> zero_zero(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),X_1),Y_1))) # label(fact_3256_gcd__lcm__complete__lattice__nat_Oinf__eq__top__iff) # label(axiom) # label(non_clause).  [assumption].
7.36/7.42	559 (all A_1 all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A_1)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),powr,hAPP(real,real,ln,X)),A_1)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),powr,A_1),A_1)),X)))))) # label(fact_3421_ln__powr__bound2) # label(axiom) # label(non_clause).  [assumption].
7.36/7.42	560 (all N all X (hBOOL(hAPP(int,bool,nat_is_nat,X)) -> hBOOL(hAPP(int,bool,nat_is_nat,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),X),N))))) # label(fact_4846_Nat__Transfer_Otransfer__int__nat__function__closures_I4_J) # label(axiom) # label(non_clause).  [assumption].
7.36/7.42	561 (all A_2 all X_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_2),hAPP(real,int,archim2085082626_floor(real),X_1))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(int,real,real_1(int),A_2)),one_one(real))),X_1)))) # label(fact_3413_less__floor__eq) # label(axiom) # label(non_clause).  [assumption].
7.36/7.42	562 (all X_b all X_a (topological_space(X_b) & topological_space(X_a) -> (all F all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),hAPP(X_a,X_b,F,A_2)),hAPP(X_a,filter(X_a),at(X_a),A_2))) <-> hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,X_b),fun(X_a,bool),isCont(X_a,X_b),F),A_2)))))) # label(fact_4880_isCont__def) # label(axiom) # label(non_clause).  [assumption].
7.36/7.42	563 (all X_a (order(X_a) -> (all F (hBOOL(hAPP(fun(nat,X_a),bool,hAPP(fun(nat,fun(nat,bool)),fun(fun(nat,X_a),bool),strict_mono(nat,X_a),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),hAPP(fun(nat,fun(fun(nat,bool),fun(nat,bool))),fun(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool))),combs(nat,fun(nat,bool),fun(nat,bool)),hAPP(fun(nat,fun(nat,fun(bool,bool))),fun(nat,fun(fun(nat,bool),fun(nat,bool))),hAPP(fun(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool))),fun(fun(nat,fun(nat,fun(bool,bool))),fun(nat,fun(fun(nat,bool),fun(nat,bool)))),combb(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),nat),combs(nat,bool,bool)),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,fun(bool,bool))),hAPP(fun(fun(nat,bool),fun(nat,fun(bool,bool))),fun(fun(nat,fun(nat,bool)),fun(nat,fun(nat,fun(bool,bool)))),combb(fun(nat,bool),fun(nat,fun(bool,bool)),nat),hAPP(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fconj)),dvd_dvd(nat)))),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),hAPP(fun(fun(nat,bool),fun(nat,bool)),fun(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool))),combb(fun(nat,bool),fun(nat,bool),nat),hAPP(fun(bool,bool),fun(fun(nat,bool),fun(nat,bool)),combb(bool,bool,nat),fNot)),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),dvd_dvd(nat))))),F)) -> hBOOL(hAPP(fun(nat,X_a),bool,hAPP(fun(nat,fun(nat,bool)),fun(fun(nat,X_a),bool),mono(nat,X_a),dvd_dvd(nat)),F)))))) # label(fact_4792_dvd_Ostrict__mono__mono) # label(axiom) # label(non_clause).  [assumption].
7.36/7.42	564 (all Y exists X_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_2),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) & (all Y_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),Y_2),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) & Y = hAPP(real,real,tan,Y_2) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),Y_2)) -> Y_2 = X_2)) & hAPP(real,real,tan,X_2) = Y & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),X_2)))) # label(fact_2283_tan__total) # label(axiom) # label(non_clause).  [assumption].
7.36/7.42	565 (all X (zero_zero(real) != hAPP(real,real,cos,X) -> (hAPP(real,real,cos,hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),X)) != zero_zero(real) -> hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),hAPP(real,real,tan,X))),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),one_one(real)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,tan,X)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) = hAPP(real,real,tan,hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),X))))) # label(fact_2250_tan__double) # label(axiom) # label(non_clause).  [assumption].
7.36/7.42	566 (all N all M (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),hAPP(nat,nat,suc,M))) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,M)),N)),hAPP(nat,nat,fact_fact(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N))) = hAPP(nat,nat,fact_fact(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,M)),N)))) # label(fact_2452_fact__diff__Suc) # label(axiom) # label(non_clause).  [assumption].
7.36/7.42	567 (all X_1 all Y_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_1),Y_1)) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(nat,fun(real,real),root,N_1),X_1)),hAPP(real,real,hAPP(nat,fun(real,real),root,N_1),Y_1)))))) # label(fact_2680_real__root__less__iff) # label(axiom) # label(non_clause).  [assumption].
7.36/7.42	568 (all X_a (archim1727834104eiling(X_a) -> (all X_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),one_one(X_a)),X_1)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(X_a,int,archim2085082626_floor(X_a),X_1))))))) # label(fact_2881_zero__less__floor) # label(axiom) # label(non_clause).  [assumption].
7.36/7.42	569 (all X_a (real_normed_algebra(X_a) -> (all Y_1 all A_2 hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,X_a),fun(X_a,bool),isCont(X_a,X_a),hAPP(X_a,fun(X_a,X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(X_a,X_a)),combc(X_a,X_a,X_a),times_times(X_a)),Y_1)),A_2))))) # label(fact_4908_mult__left_OisCont) # label(axiom) # label(non_clause).  [assumption].
7.36/7.42	570 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),hAPP(nat,nat,suc,N))))) # label(fact_1334_le__imp__less__Suc) # label(axiom) # label(non_clause).  [assumption].
7.36/7.42	571 (all M all N hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N)),hAPP(nat,nat,suc,M)))) # label(fact_1339_diff__less__Suc) # label(axiom) # label(non_clause).  [assumption].
7.36/7.42	572 (all X_a (semiring_div(X_a) -> (all B all B_5 all A_1 all C all A_6 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),A_6),C) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),A_1),C) -> (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),B),C) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),B_5),C) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_6),B_5)),C) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)),C)))))) # label(fact_935_mod__add__cong) # label(axiom) # label(non_clause).  [assumption].
7.36/7.42	573 (all M all N (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N)),N) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),M),N))) # label(fact_1109_mod__geq) # label(axiom) # label(non_clause).  [assumption].
7.36/7.42	574 (all A_2 all B_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_2),B_1)),zero_zero(int))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_2),zero_zero(int)))))) # label(fact_983_pos__imp__zdiv__neg__iff) # label(axiom) # label(non_clause).  [assumption].
7.36/7.42	575 (all N_1 all Ma (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,number_number_of(real),N_1)),hAPP(int,real,real_1(int),Ma))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),N_1)),Ma)))) # label(fact_3390_number__of__le__real__of__int__iff) # label(axiom) # label(non_clause).  [assumption].
7.36/7.42	576 (all X_a (ab_semigroup_add(X_a) -> plus_plus(X_a) = ti(fun(X_a,fun(X_a,X_a)),plus_plus(X_a)))) # label(tsy_c_Groups_Oplus__class_Oplus_2_res) # label(axiom) # label(non_clause).  [assumption].
7.36/7.42	577 (all X_b all X_a all R_3 all K all T_3 all S (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),S)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),T_3)) -> ((all X_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),T_3)) -> K = hAPP(fun(X_a,bool),nat,finite_card(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,bool)),combs(X_a,bool,bool),hAPP(fun(X_a,bool),fun(X_a,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,fun(bool,bool))),combb(bool,fun(bool,bool),X_a),fconj),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(X_a,bool)),combc(X_a,fun(X_a,bool),bool),member(X_a)),S))),hAPP(X_b,fun(X_a,bool),hAPP(fun(X_a,fun(X_b,bool)),fun(X_b,fun(X_a,bool)),combc(X_a,X_b,bool),R_3),X_2)))))) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),hAPP(fun(X_b,bool),nat,finite_card(X_b),T_3)) = hAPP(fun(X_a,bool),nat,hAPP(fun(X_a,nat),fun(fun(X_a,bool),nat),big_co1399186613setsum(X_a,nat),hAPP(fun(X_a,fun(X_b,bool)),fun(X_a,nat),hAPP(fun(fun(X_b,bool),nat),fun(fun(X_a,fun(X_b,bool)),fun(X_a,nat)),combb(fun(X_b,bool),nat,X_a),finite_card(X_b)),hAPP(fun(X_a,fun(X_b,bool)),fun(X_a,fun(X_b,bool)),hAPP(fun(fun(X_b,bool),fun(X_b,bool)),fun(fun(X_a,fun(X_b,bool)),fun(X_a,fun(X_b,bool))),combb(fun(X_b,bool),fun(X_b,bool),X_a),collect(X_b)),hAPP(fun(X_a,fun(X_b,bool)),fun(X_a,fun(X_b,bool)),hAPP(fun(fun(X_b,bool),fun(X_b,bool)),fun(fun(X_a,fun(X_b,bool)),fun(X_a,fun(X_b,bool))),combb(fun(X_b,bool),fun(X_b,bool),X_a),hAPP(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),combs(X_b,bool,bool),hAPP(fun(X_b,bool),fun(X_b,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fconj),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(fun(X_b,bool),bool)),fun(fun(X_b,bool),fun(X_b,bool)),combc(X_b,fun(X_b,bool),bool),member(X_b)),T_3)))),R_3)))),S))))) # label(fact_4298_setsum__multicount) # label(axiom) # label(non_clause).  [assumption].
7.36/7.42	578 (all X_a (semiring_div(X_a) -> (all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_1),B)) -> zero_zero(X_a) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),B),A_1))))) # label(fact_979_dvd__imp__mod__0) # label(axiom) # label(non_clause).  [assumption].
7.36/7.42	579 (all A_1 all B all C all Q_3 all R_4 (hBOOL(hAPP(product_prod(int,int),bool,hAPP(int,fun(product_prod(int,int),bool),hAPP(int,fun(int,fun(product_prod(int,int),bool)),divmod_int_rel,B),C),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),Q_3),R_4))) -> (zero_zero(int) != ti(int,C) -> hBOOL(hAPP(product_prod(int,int),bool,hAPP(int,fun(product_prod(int,int),bool),hAPP(int,fun(int,fun(product_prod(int,int),bool)),divmod_int_rel,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),B)),C),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),Q_3)),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),R_4)),C))),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),R_4)),C))))))) # label(fact_1198_zmult1__lemma) # label(axiom) # label(non_clause).  [assumption].
7.36/7.42	580 (all X_a (number_ring(X_a) & linordered_idom(X_a) -> (all Y_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),Y_1)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),hAPP(int,X_a,number_number_of(X_a),Y_1))))))) # label(fact_48_le__special_I1_J) # label(axiom) # label(non_clause).  [assumption].
7.36/7.42	581 (all X_a (comm_monoid_add(X_a) -> (all F all P_4 all Ma all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Ma),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_1),one_one(nat)))) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),Ma),N_1))),hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_1),one_one(nat))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_1),P_4)))) = hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),Ma),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_1),P_4))))))) # label(fact_4604_setsum__ub__add__nat) # label(axiom) # label(non_clause).  [assumption].
7.36/7.42	582 (all X_a (division_ring(X_a) -> (all A_1 all B all C hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),B),C)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)),C)))) # label(fact_1659_times__divide__eq__right) # label(axiom) # label(non_clause).  [assumption].
7.36/7.42	583 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),one_one(real)),X)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),one_one(real)),hAPP(real,real,sqrt,X))))) # label(fact_1629_real__sqrt__ge__one) # label(axiom) # label(non_clause).  [assumption].
7.36/7.42	584 (all X hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),one_one(real)),hAPP(real,real,abs_abs(real),X))))) # label(fact_1897_abs__add__one__gt__zero) # label(axiom) # label(non_clause).  [assumption].
7.36/7.42	585 (all X_a (linorder(X_a) -> (all X_1 all Y_1 all Z (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X_1),Y_1)),Z)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Z)) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y_1),Z)))))) # label(fact_4798_min__less__iff__disj) # label(axiom) # label(non_clause).  [assumption].
7.36/7.42	586 (all X_a (division_ring(X_a) -> (all A_1 all B (zero_zero(X_a) != ti(X_a,B) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),A_1)),hAPP(X_a,X_a,uminus_uminus(X_a),B)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),A_1),B))))) # label(fact_2078_nonzero__minus__divide__divide) # label(axiom) # label(non_clause).  [assumption].
7.36/7.42	587 (all X_1 all Y_1 all F ((all X_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),F),X_2),zero_zero(real)))) -> hAPP(real,real,F,X_1) = hAPP(real,real,F,Y_1))) # label(fact_2731_DERIV__isconst__all) # label(axiom) # label(non_clause).  [assumption].
7.36/7.42	588 (all X_a all A_3 hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(bool,bool),fun(fun(X_a,bool),fun(X_a,bool)),combb(bool,bool,X_a),fNot),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(X_a,bool)),combc(X_a,fun(X_a,bool),bool),member(X_a)),A_3))) = hAPP(fun(X_a,bool),fun(X_a,bool),uminus_uminus(fun(X_a,bool)),A_3)) # label(fact_2192_Compl__eq) # label(axiom) # label(non_clause).  [assumption].
7.36/7.42	589 (all X_2 hAPP(fun(nat,real),real,suminf(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),sin_coeff)),hAPP(real,fun(nat,real),power_power(real),X_2))) = hAPP(real,real,sin,X_2)) # label(fact_3969_lemma__sin__ext) # label(axiom) # label(non_clause).  [assumption].
7.36/7.42	590 (all V_3 all V ((hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V))) -> zero_zero(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(int,nat,number_number_of(nat),V)),hAPP(int,nat,number_number_of(nat),V_3))) & (-hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V))) -> hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,number_number_of(int),V)),hAPP(int,int,number_number_of(int),V_3))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(int,nat,number_number_of(nat),V)),hAPP(int,nat,number_number_of(nat),V_3))))) # label(fact_1515_div__nat__number__of) # label(axiom) # label(non_clause).  [assumption].
7.36/7.42	591 (all X_a (linorder(X_a) -> (all X all Y ti(X_a,X) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),Y))))) # label(fact_4942_min__max_Osup__inf__absorb) # label(axiom) # label(non_clause).  [assumption].
7.36/7.42	592 (all X_a (linord1117847801e_zero(X_a) -> (all A_2 all B_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,inverse_inverse(X_a),A_2)),hAPP(X_a,X_a,inverse_inverse(X_a),B_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),A_2),B_1))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_1),A_2))) & (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),B_1)),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),B_1))))))) # label(fact_2606_inverse__less__iff) # label(axiom) # label(non_clause).  [assumption].
7.36/7.42	593 (all W (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),W)),zero_zero(int))) -> hAPP(product_prod(int,int),int,product_snd(int,int),hAPP(product_prod(int,int),product_prod(int,int),negateSnd,hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),negDivAlg,hAPP(int,int,uminus_uminus(int),one_one(int))),hAPP(int,int,uminus_uminus(int),hAPP(int,int,number_number_of(int),W))))) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),one_one(int)),hAPP(int,int,number_number_of(int),W)))) # label(fact_3115_mod__pos__neg__1__number__of) # label(axiom) # label(non_clause).  [assumption].
7.36/7.42	594 (all Ma all N_1 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),Ma),N_1)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),Ma)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),N_1)))))) # label(fact_740_nat__mult__le__cancel1) # label(axiom) # label(non_clause).  [assumption].
7.36/7.42	595 (all X_a all X_b (real_algebra_1(X_b) & real_normed_vector(X_b) -> (all G all A_2 all A_3 (hBOOL(hAPP(filter(X_a),bool,hAPP(real,fun(filter(X_a),bool),hAPP(fun(X_a,real),fun(real,fun(filter(X_a),bool)),tendsto(X_a,real),G),A_2),A_3)) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(fun(X_a,real),fun(X_a,X_b),hAPP(fun(real,X_b),fun(fun(X_a,real),fun(X_a,X_b)),combb(real,X_b,X_a),of_real(X_b)),G)),hAPP(real,X_b,of_real(X_b),A_2)),A_3)))))) # label(fact_4458_of__real_Otendsto) # label(axiom) # label(non_clause).  [assumption].
7.36/7.42	596 (all Z_1 ((all N_2 ti(int,Z_1) != hAPP(nat,int,semiring_1_of_nat(int),N_2)) -> -(all N_2 hAPP(int,int,uminus_uminus(int),hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,N_2))) != ti(int,Z_1)))) # label(fact_3526_int__cases) # label(axiom) # label(non_clause).  [assumption].
7.36/7.42	597 (all X_a number_of_frac(X_a) = ti(fun(int,X_a),number_of_frac(X_a))) # label(tsy_c_Nitpick_Onumber__of__frac_res) # label(axiom) # label(non_clause).  [assumption].
7.36/7.42	598 (all Ma all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),N_1)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Ma),N_1)) & N_1 != Ma)) # label(fact_563_nat__less__le) # label(axiom) # label(non_clause).  [assumption].
7.36/7.42	599 (all A_1 hAPP(int,int,uminus_uminus(int),A_1) = hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_1),hAPP(int,int,number_number_of(int),min_1))) # label(fact_2172_zdiv__minus1__right) # label(axiom) # label(non_clause).  [assumption].
7.36/7.42	600 (all X_a ti(fun(fun(X_a,bool),bool),fEx(X_a)) = fEx(X_a)) # label(tsy_c_fEx_res) # label(axiom) # label(non_clause).  [assumption].
7.36/7.42	601 (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_1422_tsub__eq) # label(axiom) # label(non_clause).  [assumption].
7.36/7.42	602 (all X_a (linord1278240602ring_1(X_a) -> (all V all U all Y all X all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),U)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),V)) -> (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),U),V) = one_one(X_a) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),U),X)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),V),Y))),A_1)))))))))) # label(fact_457_convex__bound__le) # label(axiom) # label(non_clause).  [assumption].
7.36/7.42	603 (all Z_1 exists R_2 exists A_4 Z_1 = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(real,complex,of_real(complex),R_2)),hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,hAPP(real,real,cos,A_4)),hAPP(real,real,sin,A_4)))) # label(fact_2823_complex__split__polar) # label(axiom) # label(non_clause).  [assumption].
7.36/7.42	604 (all X_a (sgn_div_norm(X_a) -> ti(fun(X_a,real),norm_norm(X_a)) = norm_norm(X_a))) # label(tsy_c_RealVector_Onorm__class_Onorm_0_res) # label(axiom) # label(non_clause).  [assumption].
7.36/7.42	605 (all X_a (linordered_semidom(X_a) -> (all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),Y),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),Y)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y))))))) # label(fact_103_power2__le__imp__le) # label(axiom) # label(non_clause).  [assumption].
7.36/7.42	606 (all Y_3 all X_3 (hBOOL(hAPP(fun(nat,rat),bool,vanishes,X_3)) -> (hBOOL(hAPP(fun(nat,rat),bool,vanishes,Y_3)) -> hBOOL(hAPP(fun(nat,rat),bool,vanishes,hAPP(fun(nat,rat),fun(nat,rat),hAPP(fun(nat,fun(rat,rat)),fun(fun(nat,rat),fun(nat,rat)),combs(nat,rat,rat),hAPP(fun(nat,rat),fun(nat,fun(rat,rat)),hAPP(fun(rat,fun(rat,rat)),fun(fun(nat,rat),fun(nat,fun(rat,rat))),combb(rat,fun(rat,rat),nat),minus_minus(rat)),X_3)),Y_3)))))) # label(fact_4841_vanishes__diff) # label(axiom) # label(non_clause).  [assumption].
7.36/7.42	607 (all R_4 all X hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,hAPP(real,real,hAPP(real,fun(real,real),times_times(real),R_4),hAPP(complex,real,re,X))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),R_4),hAPP(complex,real,im,X))) = hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),R_4),X)) # label(fact_4744_complex__scaleR__def) # label(axiom) # label(non_clause).  [assumption].
7.36/7.42	608 (all N zero_zero(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),N),zero_zero(nat))) # label(fact_4806_min__0R) # label(axiom) # label(non_clause).  [assumption].
7.36/7.42	609 (all X hAPP(complex,real,re,X) = hAPP(complex,real,re,hAPP(complex,complex,cnj,X))) # label(fact_2995_complex__Re__cnj) # label(axiom) # label(non_clause).  [assumption].
7.36/7.42	610 (all A_2 all X_1 (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),zEven)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X_1)) -> hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,uminus_uminus(int),A_2)),hAPP(int,nat,nat_1,X_1)) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A_2),hAPP(int,nat,nat_1,X_1))))) # label(fact_2181_neg__even__power) # label(axiom) # label(non_clause).  [assumption].
7.36/7.42	611 (all X_a (linord1117847801e_zero(X_a) -> (all A_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,inverse_inverse(X_a),A_2))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_2)))))) # label(fact_2541_inverse__positive__iff__positive) # label(axiom) # label(non_clause).  [assumption].
7.36/7.42	612 (all X_a (number_ring(X_a) -> (all Z_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),min_1)),Z_1) = hAPP(X_a,X_a,uminus_uminus(X_a),Z_1)))) # label(fact_2101_mult__minus1) # label(axiom) # label(non_clause).  [assumption].
7.36/7.42	613 (all X_a (linordered_field(X_a) -> (all Y all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),zero_zero(X_a))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),Y)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),X),Y)),zero_zero(X_a)))))))) # label(fact_1706_divide__nonpos__pos) # label(axiom) # label(non_clause).  [assumption].
7.36/7.42	614 (all X all Y hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(nat,int,semiring_1_of_nat(int),X)),hAPP(nat,int,semiring_1_of_nat(int),Y)) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),X),Y))) # label(fact_1349_Divides_Otransfer__int__nat__functions_I1_J) # label(axiom) # label(non_clause).  [assumption].
7.36/7.42	615 (all N hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(nat,real,real_1(nat),N)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),N)))) # label(fact_2369_two__realpow__gt) # label(axiom) # label(non_clause).  [assumption].
7.36/7.42	616 (all Z_1 all W ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),W))) -> hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Z_1),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),Z_1),hAPP(int,nat,number_number_of(nat),W)))),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),Z_1),hAPP(int,nat,number_number_of(nat),W))) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),Z_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,W)))) & (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),W))) -> hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),Z_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,W))) = one_one(int)))) # label(fact_3902_zpower__number__of__odd) # label(axiom) # label(non_clause).  [assumption].
7.36/7.42	617 (all X_a (linordered_field(X_a) -> (all B_1 all A_2 all C_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),C_1))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),B_1),C_1)),A_2))))))) # label(fact_1711_pos__divide__less__eq) # label(axiom) # label(non_clause).  [assumption].
7.36/7.42	618 (all X_a (comm_monoid_add(X_a) -> (all F all Ma all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Ma),N_1)) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(nat,X_a,F,Ma)),hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,suc,Ma)),N_1))) = hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),Ma),N_1)))))) # label(fact_4598_setsum__head__Suc) # label(axiom) # label(non_clause).  [assumption].
7.36/7.42	619 (all X_1 all Y_1 (hBOOL(hAPP(fun(product_prod(product_prod(int,int),product_prod(int,int)),bool),bool,hAPP(product_prod(product_prod(int,int),product_prod(int,int)),fun(fun(product_prod(product_prod(int,int),product_prod(int,int)),bool),bool),member(product_prod(product_prod(int,int),product_prod(int,int))),hAPP(product_prod(int,int),product_prod(product_prod(int,int),product_prod(int,int)),hAPP(product_prod(int,int),fun(product_prod(int,int),product_prod(product_prod(int,int),product_prod(int,int))),product_Pair(product_prod(int,int),product_prod(int,int)),X_1),Y_1)),ratrel)) <-> hAPP(product_prod(int,int),int,product_snd(int,int),Y_1) != zero_zero(int) & hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(product_prod(int,int),int,product_fst(int,int),Y_1)),hAPP(product_prod(int,int),int,product_snd(int,int),X_1)) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(product_prod(int,int),int,product_fst(int,int),X_1)),hAPP(product_prod(int,int),int,product_snd(int,int),Y_1)) & zero_zero(int) != hAPP(product_prod(int,int),int,product_snd(int,int),X_1))) # label(fact_3732_ratrel__iff) # label(axiom) # label(non_clause).  [assumption].
7.36/7.42	620 (all K all Ma all N_1 ((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),Ma),N_1))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),Ma)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),N_1))))) # label(fact_604_mult__le__cancel1) # label(axiom) # label(non_clause).  [assumption].
7.36/7.42	621 (all X_a (linordered_field(X_a) -> (all Z_1 all W all Y all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),X)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),W)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),W),Z_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),X),Z_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),Y),W)))))))))) # label(fact_1704_frac__less) # label(axiom) # label(non_clause).  [assumption].
7.36/7.42	622 (all X_a (comm_ring_1(X_a) -> (all X all Y hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),X),Y)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X),Y)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat))))),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),Y),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat)))))))) # label(fact_1424_realpow__two__diff) # label(axiom) # label(non_clause).  [assumption].
7.36/7.42	623 (all X_a (real_normed_algebra(X_a) -> (all C_1 all F (hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),F)) -> hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),hAPP(X_a,fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(X_a,fun(nat,X_a)),combc(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),times_times(X_a)),F)),C_1))))))) # label(fact_3998_summable__mult2) # label(axiom) # label(non_clause).  [assumption].
7.36/7.42	624 (all X_1 all Y_1 all Z (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),Y_1),Z))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_1),Y_1)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_1),Z)))) # label(fact_3242_gcd__semilattice__nat_Ole__inf__iff) # label(axiom) # label(non_clause).  [assumption].
7.36/7.42	625 (all I all P_1 all P_4 ((all I_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),P_4)) -> (hBOOL(hAPP(nat,bool,P_1,I_2)) -> hBOOL(hAPP(nat,bool,P_1,hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,suc,I_2)),P_4)))))) -> (hBOOL(hAPP(nat,bool,P_1,I)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),P_4)) -> hBOOL(hAPP(nat,bool,P_1,zero_zero(nat))))))) # label(fact_1478_mod__induct__0) # label(axiom) # label(non_clause).  [assumption].
7.36/7.42	626 (all X_a all X_b lex_prod(X_a,X_b) = ti(fun(fun(product_prod(X_a,X_a),bool),fun(fun(product_prod(X_b,X_b),bool),fun(product_prod(product_prod(X_a,X_b),product_prod(X_a,X_b)),bool))),lex_prod(X_a,X_b))) # label(tsy_c_Wellfounded_Olex__prod_res) # label(axiom) # label(non_clause).  [assumption].
7.36/7.42	627 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),M)),N) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),M),N))) # label(fact_3273_gcd__diff2__nat) # label(axiom) # label(non_clause).  [assumption].
7.36/7.42	628 (all A_2 all A_3 all Ma (hBOOL(hAPP(int,bool,hAPP(fun(int,bool),fun(int,bool),is_RRset,A_3),Ma)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),A_2),A_3)) -> one_one(int) = hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,A_2),Ma)))) # label(fact_3619_RRset__gcd) # label(axiom) # label(non_clause).  [assumption].
7.36/7.42	629 (all X_1 all F ((all N_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(nat,real,F,N_2)))) -> ((all N_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),N_2))),X_1))) -> hBOOL(hAPP(fun(nat,real),bool,summable(real),F))))) # label(fact_4306_pos__summable) # label(axiom) # label(non_clause).  [assumption].
7.36/7.42	630 (all X_a (archim1727834104eiling(X_a) -> (all Z_1 all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(int,X_a,ring_1_of_int(X_a),Z_1)),X)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(int,X_a,ring_1_of_int(X_a),Z_1)),one_one(X_a)))) -> hAPP(X_a,int,archim2085082626_floor(X_a),X) = ti(int,Z_1)))))) # label(fact_3605_floor__unique) # label(axiom) # label(non_clause).  [assumption].
7.36/7.42	631 (all X_a (real_vector(X_a) -> (all A_2 all X_1 all B_1 (hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),B_1),X_1) = hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_2),X_1) <-> B_1 = A_2 | zero_zero(X_a) = ti(X_a,X_1))))) # label(fact_4704_scaleR__cancel__right) # label(axiom) # label(non_clause).  [assumption].
7.36/7.43	632 (all X_a (division_ring(X_a) -> (all A_2 all B_1 (zero_zero(X_a) != ti(X_a,B_1) -> (ti(X_a,A_2) = ti(X_a,B_1) <-> one_one(X_a) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),A_2),B_1)))))) # label(fact_1696_right__inverse__eq) # label(axiom) # label(non_clause).  [assumption].
7.36/7.43	633 (all N N = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),one_one(nat)),N)) # label(fact_587_nat__mult__1) # label(axiom) # label(non_clause).  [assumption].
7.36/7.43	634 (all Ta all A_3 all D_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D_2)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Ta),one_one(int))),A_3)) -> (all X_2 ((all Xa (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xa),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastAtMost(int),one_one(int)),D_2))) -> (all Xb (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xb),A_3)) -> hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),Xb),Xa) != ti(int,X_2))))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X_2),Ta)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X_2),D_2)),Ta)))))))) # label(fact_4630_aset_I6_J) # label(axiom) # label(non_clause).  [assumption].
7.36/7.43	635 (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_71_rel__simps_I5_J) # label(axiom) # label(non_clause).  [assumption].
7.36/7.43	636 (all B all A_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_1),zero_zero(int))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B)) -> hBOOL(hAPP(product_prod(int,int),bool,hAPP(int,fun(product_prod(int,int),bool),hAPP(int,fun(int,fun(product_prod(int,int),bool)),divmod_int_rel,A_1),B),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),negDivAlg,A_1),B)))))) # label(fact_1193_negDivAlg__correct) # label(axiom) # label(non_clause).  [assumption].
7.36/7.43	637 (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_1584_linorder__le__less__linear) # label(axiom) # label(non_clause).  [assumption].
7.36/7.43	638 (all X_b all X_a (comm_monoid_add(X_a) -> (all H all G all S all R_3 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),R_3,zero_zero(X_a)),zero_zero(X_a))) -> ((all X1 all Y1 all X2 all Y2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),R_3,X1),X2)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),R_3,Y1),Y2)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),R_3,hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X1),Y1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X2),Y2))))) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),S)) -> ((all X_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),S)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),R_3,hAPP(X_b,X_a,H,X_2)),hAPP(X_b,X_a,G,X_2))))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),R_3,hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co1399186613setsum(X_b,X_a),H),S)),hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co1399186613setsum(X_b,X_a),G),S)))))))))) # label(fact_4795_setsum_Orelated) # label(axiom) # label(non_clause).  [assumption].
7.36/7.43	639 (all I_1 all K_4 all J_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_4),J_2)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_1),K_4)),J_2) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_2),K_4)))) # label(fact_699_diff__diff__right) # label(axiom) # label(non_clause).  [assumption].
7.36/7.43	640 (all X_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,real)),combs(real,real,real),hAPP(fun(real,real),fun(real,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,fun(real,real))),combb(real,fun(real,real),real),plus_plus(real)),hAPP(nat,fun(real,real),hAPP(fun(real,fun(nat,real)),fun(nat,fun(real,real)),combc(real,nat,real),hAPP(fun(real,real),fun(real,fun(nat,real)),hAPP(fun(real,fun(nat,real)),fun(fun(real,real),fun(real,fun(nat,real))),combb(real,fun(nat,real),real),power_power(real)),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,real)),combs(real,real,real),hAPP(fun(real,real),fun(real,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,fun(real,real))),combb(real,fun(real,real),real),plus_plus(real)),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,real),fun(fun(real,real),fun(real,real)),combb(real,real,real),sin),uminus_uminus(real)))),sin))),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),hAPP(nat,fun(real,real),hAPP(fun(real,fun(nat,real)),fun(nat,fun(real,real)),combc(real,nat,real),hAPP(fun(real,real),fun(real,fun(nat,real)),hAPP(fun(real,fun(nat,real)),fun(fun(real,real),fun(real,fun(nat,real))),combb(real,fun(nat,real),real),power_power(real)),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,real)),combs(real,real,real),hAPP(fun(real,real),fun(real,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,fun(real,real))),combb(real,fun(real,real),real),minus_minus(real)),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,real),fun(fun(real,real),fun(real,real)),combb(real,real,real),cos),uminus_uminus(real)))),cos))),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),X_2),zero_zero(real)))) # label(fact_3918_lemma__DERIV__sin__cos__minus) # label(axiom) # label(non_clause).  [assumption].
7.36/7.43	641 (all X_a (real_vector(X_a) -> (all X ti(X_a,X) = hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),one_one(real)),X)))) # label(fact_4706_real__vector_Oscale__one) # label(axiom) # label(non_clause).  [assumption].
7.36/7.43	642 (all X_1 hBOOL(hAPP(real,bool,hAPP(fun(real,real),fun(real,bool),isCont(real,real),cos),X_1))) # label(fact_4887_isCont__cos) # label(axiom) # label(non_clause).  [assumption].
7.36/7.43	643 (all L all U_1 hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),L),hAPP(nat,nat,suc,U_1)) = hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),L),U_1)) # label(fact_4542_atLeastLessThanSuc__atLeastAtMost) # label(axiom) # label(non_clause).  [assumption].
7.36/7.43	644 (all A_1 all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X)) -> hAPP(real,nat,natfloor,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),hAPP(nat,real,real_1(nat),A_1))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(real,nat,natfloor,X)),A_1))) # label(fact_2360_natfloor__add) # label(axiom) # label(non_clause).  [assumption].
7.36/7.43	645 (all X all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),Y)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,arctan,X)),hAPP(real,real,arctan,Y))))) # label(fact_1836_arctan__monotone) # label(axiom) # label(non_clause).  [assumption].
7.36/7.43	646 (all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X_1)) -> (one_one(real) = X_1 <-> zero_zero(real) = hAPP(real,real,ln,X_1)))) # label(fact_1948_ln__eq__zero__iff) # label(axiom) # label(non_clause).  [assumption].
7.36/7.43	647 (all A_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),zero_zero(nat)),A_1)) -> A_1 = zero_zero(nat))) # label(fact_892_gcd__lcm__complete__lattice__nat_Otop__le) # label(axiom) # label(non_clause).  [assumption].
7.36/7.43	648 (all W_1 all Ma ((-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),W_1)) -> zero_zero(nat) = Ma) & (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),W_1)) -> ti(int,W_1) = hAPP(nat,int,semiring_1_of_nat(int),Ma)) <-> Ma = hAPP(int,nat,nat_1,W_1))) # label(fact_1407_nat__eq__iff) # label(axiom) # label(non_clause).  [assumption].
7.36/7.43	649 (all X_1 all Y_1 (-hBOOL(hAPP(int,bool,even_odd_even(int),Y_1)) & -hBOOL(hAPP(int,bool,even_odd_even(int),X_1)) | hBOOL(hAPP(int,bool,even_odd_even(int),X_1)) & hBOOL(hAPP(int,bool,even_odd_even(int),Y_1)) <-> hBOOL(hAPP(int,bool,even_odd_even(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X_1),Y_1))))) # label(fact_1265_even__sum) # label(axiom) # label(non_clause).  [assumption].
7.36/7.43	650 (all X_a (order(X_a) -> (all C all A_1 all B (ti(X_a,B) = ti(X_a,A_1) -> (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_1552_xt1_I3_J) # label(axiom) # label(non_clause).  [assumption].
7.36/7.43	651 (all Y_1 all X_1 (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),zEven)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Y_1),zEven)) -> hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),X_1),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),Y_1),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) = hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X_1),Y_1)),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))) # label(fact_1466_even__sum__div__2) # label(axiom) # label(non_clause).  [assumption].
7.36/7.43	652 (all X_a (division_ring(X_a) -> (all A_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),A_1),one_one(X_a)) = ti(X_a,A_1)))) # label(fact_1663_divide__1) # label(axiom) # label(non_clause).  [assumption].
7.36/7.43	653 (all M all N (hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),M),N)) = one_one(int) -> hAPP(int,int,abs_abs(int),M) = one_one(int))) # label(fact_1927_abs__zmult__eq__1) # label(axiom) # label(non_clause).  [assumption].
7.36/7.43	654 (all B_1 all P_4 all A_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),A_2)) -> (-hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),B_1),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),wset,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A_2),one_one(int))),P_4))) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),B_1),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),wset,A_2),P_4))) -> ti(int,B_1) = hAPP(int,int,hAPP(int,fun(int,int),inv,P_4),A_2) | ti(int,B_1) = ti(int,A_2))))) # label(fact_841_wset__mem__imp__or) # label(axiom) # label(non_clause).  [assumption].
7.36/7.43	655 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N)) -> hAPP(nat,product_prod(nat,nat),hAPP(nat,fun(nat,product_prod(nat,nat)),product_Pair(nat,nat),zero_zero(nat)),M) = hAPP(nat,product_prod(nat,nat),hAPP(nat,fun(nat,product_prod(nat,nat)),divmod_nat,M),N))) # label(fact_3093_divmod__nat__base) # label(axiom) # label(non_clause).  [assumption].
7.36/7.43	656 (all U_1 all Ma all N_1 all J all I (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),J),I)) -> (hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I),J)),U_1)),Ma) = N_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_1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I),U_1)),Ma)))) # label(fact_752_nat__eq__add__iff1) # label(axiom) # label(non_clause).  [assumption].
7.36/7.43	657 (all N N != hAPP(nat,nat,suc,N)) # label(fact_1216_Suc__n__not__n) # label(axiom) # label(non_clause).  [assumption].
7.36/7.43	658 (all X hAPP(real,int,archim2085082626_floor(real),hAPP(rat,real,ratreal,X)) = hAPP(rat,int,archim2085082626_floor(rat),X)) # label(fact_3748_real__floor__code) # label(axiom) # label(non_clause).  [assumption].
7.36/7.43	659 (all X all P_5 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),P_5)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),standardRes,P_5),X)),P_5)))) # label(fact_1010_StandardRes__ubound) # label(axiom) # label(non_clause).  [assumption].
7.36/7.43	660 (all M all X (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X),M)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,X),zero_zero(int)),M)) -> ti(int,X) = zero_zero(int))))) # label(fact_451_Int2_Ozcong__zero) # label(axiom) # label(non_clause).  [assumption].
7.36/7.43	661 (all X_a (comm_semiring_1(X_a) -> (all A_1 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_1),zero_zero(X_a)))))) # label(fact_282_dvd__0__right) # label(axiom) # label(non_clause).  [assumption].
7.36/7.43	662 (all X_b all X_c all X_a (metric_space(X_b) & metric_space(X_c) & topological_space(X_a) -> (all G all Ma all F all L all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),L),hAPP(X_a,filter(X_a),at(X_a),A_2))) -> ((all X_2 (ti(X_a,A_2) != ti(X_a,X_2) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_c,real,hAPP(X_c,fun(X_c,real),dist_dist(X_c),hAPP(X_a,X_c,G,X_2)),Ma)),hAPP(X_b,real,hAPP(X_b,fun(X_b,real),dist_dist(X_b),hAPP(X_a,X_b,F,X_2)),L))))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_c,fun(filter(X_a),bool),hAPP(fun(X_a,X_c),fun(X_c,fun(filter(X_a),bool)),tendsto(X_a,X_c),G),Ma),hAPP(X_a,filter(X_a),at(X_a),A_2)))))))) # label(fact_4656_metric__LIM__imp__LIM) # label(axiom) # label(non_clause).  [assumption].
7.36/7.43	663 (all A_2 all Ma (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_2),zero_zero(int)),Ma)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),Ma),A_2)))) # label(fact_423_zcong__zero__equiv__div) # label(axiom) # label(non_clause).  [assumption].
7.36/7.43	664 (all X hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,sin,X)),hAPP(real,real,cos,X)) = hAPP(real,real,tan,X)) # label(fact_2329_tan__def) # label(axiom) # label(non_clause).  [assumption].
7.36/7.43	665 (all X_a (metric_space(X_a) -> (all X all Z_1 all Y hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),X),Z_1)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),X),Y)),hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),Y),Z_1))))))) # label(fact_3506_dist__triangle) # label(axiom) # label(non_clause).  [assumption].
7.36/7.43	666 (all A_2 all B_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_2),B_1)) -> -hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),B_1),hAPP(int,fun(int,bool),d22set,A_2))))) # label(fact_864_d22set__le__swap) # label(axiom) # label(non_clause).  [assumption].
7.36/7.43	667 (all X zero_zero(real) != hAPP(real,real,cos,hAPP(real,real,arctan,X))) # label(fact_2210_cos__arctan__not__zero) # label(axiom) # label(non_clause).  [assumption].
7.36/7.43	668 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,cos,X)))))) # label(fact_2244_cos__gt__zero) # label(axiom) # label(non_clause).  [assumption].
7.36/7.43	669 (all Z hAPP(complex,real,arg,Z) = hAPP(fun(real,bool),real,hilbert_Eps(real),hAPP(fun(real,bool),fun(real,bool),hAPP(fun(real,fun(bool,bool)),fun(fun(real,bool),fun(real,bool)),combs(real,bool,bool),hAPP(fun(real,bool),fun(real,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(real,bool),fun(real,fun(bool,bool))),combb(bool,fun(bool,bool),real),fconj),hAPP(fun(real,real),fun(real,bool),hAPP(fun(real,bool),fun(fun(real,real),fun(real,bool)),combb(real,bool,real),hAPP(real,fun(real,bool),fequal(real),hAPP(complex,real,re,hAPP(complex,complex,sgn_sgn(complex),Z)))),cos))),hAPP(fun(real,bool),fun(real,bool),hAPP(fun(real,fun(bool,bool)),fun(fun(real,bool),fun(real,bool)),combs(real,bool,bool),hAPP(fun(real,bool),fun(real,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(real,bool),fun(real,fun(bool,bool))),combb(bool,fun(bool,bool),real),fconj),hAPP(fun(real,real),fun(real,bool),hAPP(fun(real,bool),fun(fun(real,real),fun(real,bool)),combb(real,bool,real),hAPP(real,fun(real,bool),fequal(real),hAPP(complex,real,im,hAPP(complex,complex,sgn_sgn(complex),Z)))),sin))),hAPP(fun(real,bool),fun(real,bool),hAPP(fun(real,fun(bool,bool)),fun(fun(real,bool),fun(real,bool)),combs(real,bool,bool),hAPP(fun(real,bool),fun(real,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(real,bool),fun(real,fun(bool,bool))),combb(bool,fun(bool,bool),real),fconj),hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,uminus_uminus(real),pi)))),hAPP(real,fun(real,bool),hAPP(fun(real,fun(real,bool)),fun(real,fun(real,bool)),combc(real,real,bool),ord_less_eq(real)),pi)))))) # label(fact_3926_arg__def) # label(axiom) # label(non_clause).  [assumption].
7.36/7.43	670 (all X_a all A_3 hAPP(fun(X_a,bool),nat,finite_card(X_a),A_3) = hAPP(fun(X_a,bool),nat,hAPP(fun(X_a,nat),fun(fun(X_a,bool),nat),big_co1399186613setsum(X_a,nat),hAPP(nat,fun(X_a,nat),combk(nat,X_a),one_one(nat))),A_3)) # label(fact_4255_card__eq__setsum) # label(axiom) # label(non_clause).  [assumption].
7.36/7.43	671 (all X_a (ordered_ab_group_add(X_a) -> (all A_2 (hBOOL(hAPP(fun(nat,X_a),bool,monoseq(X_a),A_2)) -> hBOOL(hAPP(fun(nat,X_a),bool,monoseq(X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(X_a,X_a),fun(fun(nat,X_a),fun(nat,X_a)),combb(X_a,X_a,nat),uminus_uminus(X_a)),A_2))))))) # label(fact_3921_monoseq__minus) # label(axiom) # label(non_clause).  [assumption].
7.36/7.43	672 (all M all N M = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N)),N)) # label(fact_668_diff__add__inverse2) # label(axiom) # label(non_clause).  [assumption].
7.36/7.43	673 (all X_a (linorder(X_a) -> (all B all A_1 all C hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),B),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),A_1),C)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),B),C))))) # label(fact_4967_min__max_Osup_Oleft__commute) # label(axiom) # label(non_clause).  [assumption].
7.36/7.43	674 (all X_a (order(X_a) -> (all X_1 all Y_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(X_a,fun(X_a,bool),ord_atMost(X_a),X_1)),hAPP(X_a,fun(X_a,bool),ord_atMost(X_a),Y_1))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),Y_1)))))) # label(fact_4990_atMost__subset__iff) # label(axiom) # label(non_clause).  [assumption].
7.36/7.43	675 (all X_1 (hBOOL(hAPP(nat,bool,even_odd_even(nat),hAPP(nat,nat,suc,X_1))) <-> -hBOOL(hAPP(nat,bool,even_odd_even(nat),X_1)))) # label(fact_2417_even__Suc) # label(axiom) # label(non_clause).  [assumption].
7.36/7.43	676 (all M all N all Q_3 all R_4 (hBOOL(hAPP(product_prod(nat,nat),bool,hAPP(nat,fun(product_prod(nat,nat),bool),hAPP(nat,fun(nat,fun(product_prod(nat,nat),bool)),divmod_nat_rel,M),N),hAPP(nat,product_prod(nat,nat),hAPP(nat,fun(nat,product_prod(nat,nat)),product_Pair(nat,nat),Q_3),R_4))) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),M),N) = R_4)) # label(fact_3102_mod__eq) # label(axiom) # label(non_clause).  [assumption].
7.36/7.43	677 (all X_a (real_normed_algebra(X_a) -> (all X_1 all X_3 all A_2 (hBOOL(hAPP(X_a,bool,hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),X_3),A_2)) -> hBOOL(hAPP(X_a,bool,hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(X_a,X_a),fun(fun(nat,X_a),fun(nat,X_a)),combb(X_a,X_a,nat),hAPP(X_a,fun(X_a,X_a),times_times(X_a),X_1)),X_3)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X_1),A_2))))))) # label(fact_4081_mult__right_Osums) # label(axiom) # label(non_clause).  [assumption].
7.36/7.43	678 (all X_a (ring_1(X_a) -> (all A_1 hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),A_1)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))) # label(fact_2115_power2__minus) # label(axiom) # label(non_clause).  [assumption].
7.36/7.43	679 (all X_a (t2_space(X_a) & comm_monoid_add(X_a) -> zero_zero(X_a) = hAPP(fun(nat,X_a),X_a,suminf(X_a),hAPP(X_a,fun(nat,X_a),combk(X_a,nat),zero_zero(X_a))))) # label(fact_3968_suminf__zero) # label(axiom) # label(non_clause).  [assumption].
7.36/7.43	680 (all X_a (linordered_field(X_a) -> (all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,inverse_inverse(X_a),B)),hAPP(X_a,X_a,inverse_inverse(X_a),A_1)))))))) # label(fact_2570_le__imp__inverse__le) # label(axiom) # label(non_clause).  [assumption].
7.36/7.43	681 (all X_a (dist_norm(X_a) -> ti(fun(X_a,fun(X_a,real)),dist_dist(X_a)) = dist_dist(X_a))) # label(tsy_c_RealVector_Odist__class_Odist_0_res) # label(axiom) # label(non_clause).  [assumption].
7.36/7.43	682 (all X_a (real_normed_field(X_a) -> (all K all F (hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),F)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K)) -> hBOOL(hAPP(X_a,bool,hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),hAPP(fun(nat,fun(nat,bool)),fun(nat,X_a),hAPP(fun(fun(nat,bool),X_a),fun(fun(nat,fun(nat,bool)),fun(nat,X_a)),combb(fun(nat,bool),X_a,nat),hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F)),hAPP(fun(nat,nat),fun(nat,fun(nat,bool)),hAPP(fun(nat,fun(nat,fun(nat,bool))),fun(fun(nat,nat),fun(nat,fun(nat,bool))),combs(nat,nat,fun(nat,bool)),hAPP(fun(nat,nat),fun(nat,fun(nat,fun(nat,bool))),hAPP(fun(nat,fun(nat,fun(nat,bool))),fun(fun(nat,nat),fun(nat,fun(nat,fun(nat,bool)))),combb(nat,fun(nat,fun(nat,bool)),nat),ord_atLeastLessThan(nat)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),times_times(nat)),K))),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),hAPP(fun(nat,nat),fun(nat,fun(nat,nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,nat),fun(nat,fun(nat,nat))),combb(nat,fun(nat,nat),nat),plus_plus(nat)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),times_times(nat)),K))),K)))),hAPP(fun(nat,X_a),X_a,suminf(X_a),F)))))))) # label(fact_4231_sums__group) # label(axiom) # label(non_clause).  [assumption].
7.36/7.43	683 (all X_1 all P_4 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),P_4)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),hAPP(int,int,hAPP(int,fun(int,int),standardRes,P_4),X_1)),hAPP(int,fun(int,bool),sRStar,P_4))) <-> -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,X_1),zero_zero(int)),P_4))))) # label(fact_1162_StandardRes__SRStar__prop1) # label(axiom) # label(non_clause).  [assumption].
7.36/7.43	684 (all X_a (real_normed_algebra(X_a) -> (all X exists K_2 ((all X_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),X_2))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(X_a,real,norm_norm(X_a),X_2)),K_2)))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),K_2)))))) # label(fact_1804_mult__right_Opos__bounded) # label(axiom) # label(non_clause).  [assumption].
7.36/7.43	685 (all Z_3 all Z (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Z)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Z_3)) -> (ti(int,Z_3) = ti(int,Z) <-> hAPP(int,nat,nat_1,Z_3) = hAPP(int,nat,nat_1,Z))))) # label(fact_1108_eq__nat__nat__iff) # label(axiom) # label(non_clause).  [assumption].
7.36/7.43	686 (all X_b all X_a all X_c (real_normed_vector(X_c) -> (all F all A_2 all A_3 all S ((all I_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),I_2),S)) -> hBOOL(hAPP(filter(X_b),bool,hAPP(X_c,fun(filter(X_b),bool),hAPP(fun(X_b,X_c),fun(X_c,fun(filter(X_b),bool)),tendsto(X_b,X_c),hAPP(X_a,fun(X_b,X_c),F,I_2)),hAPP(X_a,X_c,A_2,I_2)),A_3)))) -> hBOOL(hAPP(filter(X_b),bool,hAPP(X_c,fun(filter(X_b),bool),hAPP(fun(X_b,X_c),fun(X_c,fun(filter(X_b),bool)),tendsto(X_b,X_c),hAPP(fun(X_a,bool),fun(X_b,X_c),hAPP(fun(X_b,fun(fun(X_a,bool),X_c)),fun(fun(X_a,bool),fun(X_b,X_c)),combc(X_b,fun(X_a,bool),X_c),hAPP(fun(X_b,fun(X_a,X_c)),fun(X_b,fun(fun(X_a,bool),X_c)),hAPP(fun(fun(X_a,X_c),fun(fun(X_a,bool),X_c)),fun(fun(X_b,fun(X_a,X_c)),fun(X_b,fun(fun(X_a,bool),X_c))),combb(fun(X_a,X_c),fun(fun(X_a,bool),X_c),X_b),big_co1399186613setsum(X_a,X_c)),hAPP(fun(X_a,fun(X_b,X_c)),fun(X_b,fun(X_a,X_c)),combc(X_a,X_b,X_c),F))),S)),hAPP(fun(X_a,bool),X_c,hAPP(fun(X_a,X_c),fun(fun(X_a,bool),X_c),big_co1399186613setsum(X_a,X_c),A_2),S)),A_3)))))) # label(fact_4763_tendsto__setsum) # label(axiom) # label(non_clause).  [assumption].
7.36/7.43	687 (all N all P_5 (hBOOL(hAPP(int,bool,zprime,P_5)) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),P_5),N)) -> one_one(int) = hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,N),P_5)))) # label(fact_3466_zprime__imp__zrelprime) # label(axiom) # label(non_clause).  [assumption].
7.36/7.43	688 (all X_a (real_div_algebra(X_a) -> (all X all A_1 (zero_zero(real) != A_1 -> (zero_zero(X_a) != ti(X_a,X) -> hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),hAPP(real,real,inverse_inverse(real),A_1)),hAPP(X_a,X_a,inverse_inverse(X_a),X)) = hAPP(X_a,X_a,inverse_inverse(X_a),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_1),X))))))) # label(fact_4743_nonzero__inverse__scaleR__distrib) # label(axiom) # label(non_clause).  [assumption].
7.36/7.43	689 (all X_a all A_3 all B_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),B_2)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_3),B_2)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X_a,bool),nat,finite_card(X_a),B_2)),hAPP(fun(X_a,bool),nat,finite_card(X_a),A_3))) -> ti(fun(X_a,bool),B_2) = ti(fun(X_a,bool),A_3))))) # label(fact_1828_card__seteq) # label(axiom) # label(non_clause).  [assumption].
7.36/7.43	690 (all X all Y hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X),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))) # label(fact_1314_Nat__Transfer_Otransfer__int__nat__functions_I1_J) # label(axiom) # label(non_clause).  [assumption].
7.36/7.43	691 (all M all N ((-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),M),N) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N)),N)) & (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N)) -> M = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),M),N)))) # label(fact_1110_mod__if) # label(axiom) # label(non_clause).  [assumption].
7.36/7.43	692 (all X_a (ring_1(X_a) -> (all N_1 hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),N_1)),ring_1_Ints(X_a)))))) # label(fact_3805_Ints__of__nat) # label(axiom) # label(non_clause).  [assumption].
7.36/7.43	693 (all X_a (semiring_div(X_a) -> (all A_1 all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),A_1),B)),B) = zero_zero(X_a)))) # label(fact_909_mod__div__trivial) # label(axiom) # label(non_clause).  [assumption].
7.36/7.43	694 (all N_1 hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less_eq(nat)),N_1))) = hAPP(nat,nat,suc,N_1)) # label(fact_3828_card__Collect__le__nat) # label(axiom) # label(non_clause).  [assumption].
7.36/7.43	695 (all X all Y zero_zero(real) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,sin,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),Y))),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,sin,X)),hAPP(real,real,cos,Y))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,cos,X)),hAPP(real,real,sin,Y))))),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,cos,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),Y))),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,cos,X)),hAPP(real,real,cos,Y))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,sin,X)),hAPP(real,real,sin,Y))))),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) # label(fact_2399_sin__cos__add) # label(axiom) # label(non_clause).  [assumption].
7.36/7.43	696 (all X all Y hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),Y),X) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),X),Y)) # label(fact_3221_gcd__semilattice__nat_Oinf__commute) # label(axiom) # label(non_clause).  [assumption].
7.36/7.43	697 (all X all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(real,real,hAPP(nat,fun(real,real),root,N),X)))))) # label(fact_2693_real__root__ge__zero) # label(axiom) # label(non_clause).  [assumption].
7.36/7.43	698 (all X_a (order(X_a) -> (all A_2 all B_1 all C_1 all D_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C_1),D_1)) & (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),B_1)) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_1),D_1)) & (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),A_2)) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_1),D_1))) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C_1),A_2))) <-> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less(fun(X_a,bool)),hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastAtMost(X_a),A_2),B_1)),hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastAtMost(X_a),C_1),D_1))))))) # label(fact_4527_atLeastatMost__psubset__iff) # label(axiom) # label(non_clause).  [assumption].
7.36/7.43	699 (all X_a (linordered_idom(X_a) & number_ring(X_a) -> (all X_1 all Y_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(int,X_a,number_number_of(X_a),X_1)),hAPP(int,X_a,number_number_of(X_a),Y_1))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X_1),Y_1)))))) # label(fact_27_le__number__of) # label(axiom) # label(non_clause).  [assumption].
7.36/7.43	700 (all A_1 all B (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),zero_zero(int))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_1),B)),zero_zero(int))) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_1),B))))) # label(fact_1030_neg__mod__conj) # label(axiom) # label(non_clause).  [assumption].
7.36/7.43	701 (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)) = hAPP(int,nat,number_number_of(nat),hAPP(int,int,succ,V))) & (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V),pls)) -> one_one(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),hAPP(int,nat,number_number_of(nat),V))))) # label(fact_1536_nat__1__add__number__of) # label(axiom) # label(non_clause).  [assumption].
7.36/7.43	702 (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_152_add__number__of__eq) # label(axiom) # label(non_clause).  [assumption].
7.36/7.43	703 (all X_a (archim1727834104eiling(X_a) -> (all X_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(X_a,int,archim2085082626_floor(X_a),X_1))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),X_1)))))) # label(fact_2880_zero__le__floor) # label(axiom) # label(non_clause).  [assumption].
7.36/7.43	704 (all X_a (topological_space(X_a) -> (all F all L (hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),F),L),sequentially)) <-> hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),hAPP(fun(nat,nat),fun(nat,X_a),hAPP(fun(nat,X_a),fun(fun(nat,nat),fun(nat,X_a)),combb(nat,X_a,nat),F),suc)),L),sequentially)))))) # label(fact_4461_LIMSEQ__Suc__iff) # label(axiom) # label(non_clause).  [assumption].
7.36/7.43	705 -(all S1 -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),S1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(int,int,number_number_of(int),min_1)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))))) # label(fact_283__096_B_Bthesis_O_A_I_B_Bs1_O_A_091s1_A_094_A2_A_061_A_N1_093_A_Imod_A4_) # label(axiom) # label(non_clause).  [assumption].
7.36/7.43	706 (all X_a (ring_1(X_a) & real_normed_vector(X_a) -> (all C_1 all X_1 (hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),times_times(X_a)),hAPP(fun(nat,X_a),fun(nat,X_a),diffs(X_a),C_1))),hAPP(X_a,fun(nat,X_a),power_power(X_a),X_1)))) -> hBOOL(hAPP(X_a,bool,hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),times_times(X_a)),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),times_times(X_a)),semiring_1_of_nat(X_a))),C_1))),hAPP(fun(nat,nat),fun(nat,X_a),hAPP(fun(nat,X_a),fun(fun(nat,nat),fun(nat,X_a)),combb(nat,X_a,nat),hAPP(X_a,fun(nat,X_a),power_power(X_a),X_1)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),minus_minus(nat)),hAPP(nat,nat,suc,zero_zero(nat)))))),hAPP(fun(nat,X_a),X_a,suminf(X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),times_times(X_a)),hAPP(fun(nat,X_a),fun(nat,X_a),diffs(X_a),C_1))),hAPP(X_a,fun(nat,X_a),power_power(X_a),X_1))))))))) # label(fact_4107_diffs__equiv) # label(axiom) # label(non_clause).  [assumption].
7.36/7.43	707 (all V_1 all N_1 ((-hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),hAPP(int,int,pred,V_1)))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(int,nat,nat_1,hAPP(int,int,number_number_of(int),hAPP(int,int,pred,V_1)))),N_1))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(int,nat,number_number_of(nat),V_1)),hAPP(nat,nat,suc,N_1))))) # label(fact_3896_le__number__of__Suc) # label(axiom) # label(non_clause).  [assumption].
7.36/7.43	708 (all K_4 pls != hAPP(int,int,bit1,K_4)) # label(fact_116_rel__simps_I46_J) # label(axiom) # label(non_clause).  [assumption].
7.36/7.43	709 (all N_1 all A_2 (hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),A_2),zero_zero(real)),sequentially)) -> ((all N_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(nat,real,A_2,N_2)))) -> ((all N_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,A_2,hAPP(nat,nat,suc,N_2))),hAPP(nat,real,A_2,N_2)))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(fun(nat,real),real,suminf(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),min_1)))),A_2))),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),min_1)))),A_2)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),N_1)),one_one(nat)))))))))) # label(fact_4504_summable__Leibniz_H_I4_J) # label(axiom) # label(non_clause).  [assumption].
7.36/7.43	710 (all R1 all A_1 all R2 all B hAPP(real,complex,hAPP(real,fun(real,complex),rcis,hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),R1),R2)),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A_1),B)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),hAPP(real,complex,hAPP(real,fun(real,complex),rcis,R1),A_1)),hAPP(real,complex,hAPP(real,fun(real,complex),rcis,R2),B))) # label(fact_3172_rcis__divide) # label(axiom) # label(non_clause).  [assumption].
7.36/7.43	711 (all X_a all X_b ti(fun(X_a,fun(X_b,X_a)),combk(X_a,X_b)) = combk(X_a,X_b)) # label(tsy_c_COMBK_res) # label(axiom) # label(non_clause).  [assumption].
7.36/7.43	712 (all A_2 all Ma (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),Ma)) -> (hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,A_2),Ma) = one_one(int) -> (exists X_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_2),X_2),Ma)) & hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_2),hAPP(int,fun(int,bool),norRRset,Ma))) & (all Y_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_2),Y_2),Ma)) & hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Y_2),hAPP(int,fun(int,bool),norRRset,Ma))) -> ti(int,X_2) = ti(int,Y_2)))))))) # label(fact_3614_norR__mem__unique) # label(axiom) # label(non_clause).  [assumption].
7.36/7.43	713 (all A_2 all A_3 all Ma (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),Ma)) -> (hBOOL(hAPP(int,bool,hAPP(fun(int,bool),fun(int,bool),is_RRset,A_3),Ma)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),A_2),A_3)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_2),hAPP(int,int,hAPP(int,fun(int,int),hAPP(fun(int,bool),fun(int,fun(int,int)),rRset2norRR,A_3),Ma),A_2)),Ma)) & hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),hAPP(int,int,hAPP(int,fun(int,int),hAPP(fun(int,bool),fun(int,fun(int,int)),rRset2norRR,A_3),Ma),A_2)),hAPP(int,fun(int,bool),norRRset,Ma))))))) # label(fact_3621_RRset2norRR__correct) # label(axiom) # label(non_clause).  [assumption].
7.36/7.43	714 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> (exists N_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,inverse_inverse(real),hAPP(nat,real,real_1(nat),hAPP(nat,nat,suc,N_2)))),X))))) # label(fact_2629_reals__Archimedean) # label(axiom) # label(non_clause).  [assumption].
7.36/7.43	715 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X)) -> hAPP(real,real,inverse_inverse(real),hAPP(real,real,sqrt,X)) = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,sqrt,X)),X))) # label(fact_2615_sqrt__divide__self__eq) # label(axiom) # label(non_clause).  [assumption].
7.36/7.43	716 (all X_a (ring_1(X_a) -> (all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_2),ring_1_Ints(X_a))) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),A_2)),ring_1_Ints(X_a))))))) # label(fact_3858_Ints__minus) # label(axiom) # label(non_clause).  [assumption].
7.36/7.43	717 (all X all Y hAPP(rat,real,ratreal,hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),X),Y)) = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(rat,real,ratreal,X)),hAPP(rat,real,ratreal,Y))) # label(fact_3770_real__divide__code) # label(axiom) # label(non_clause).  [assumption].
7.36/7.43	718 (all X_a (division_ring(X_a) -> (all A_1 (zero_zero(X_a) = hAPP(X_a,X_a,inverse_inverse(X_a),A_1) -> ti(X_a,A_1) = zero_zero(X_a))))) # label(fact_2530_inverse__zero__imp__zero) # label(axiom) # label(non_clause).  [assumption].
7.36/7.43	719 (all Y_1 all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Y_1)) -> (X_1 = Y_1 <-> hAPP(real,real,ln,Y_1) = hAPP(real,real,ln,X_1))))) # label(fact_1934_ln__inj__iff) # label(axiom) # label(non_clause).  [assumption].
7.36/7.43	720 (all X_a (comm_ring_1(X_a) -> (all X all N (-hBOOL(hAPP(nat,bool,even_odd_even(nat),N)) -> hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),N)) = hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),X)),N))))) # label(fact_2425_power__minus__odd) # label(axiom) # label(non_clause).  [assumption].
7.36/7.43	721 (all X_a (group_add(X_a) -> (all A_2 all B_1 (hAPP(X_a,X_a,uminus_uminus(X_a),B_1) = ti(X_a,A_2) <-> hAPP(X_a,X_a,uminus_uminus(X_a),A_2) = ti(X_a,B_1))))) # label(fact_2042_equation__minus__iff) # label(axiom) # label(non_clause).  [assumption].
7.36/7.43	722 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),one_one(real)),X)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(real,real,ln,X))))) # label(fact_1945_ln__ge__zero) # label(axiom) # label(non_clause).  [assumption].
7.36/7.43	723 (all X_a (division_ring(X_a) -> (all A_1 all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),A_1),B) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),hAPP(X_a,X_a,inverse_inverse(X_a),B))))) # label(fact_2557_divide__inverse) # label(axiom) # label(non_clause).  [assumption].
7.36/7.43	724 (all S_3 all T_5 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),S_3),T_5)) -> S_3 != T_5)) # label(fact_519_less__not__refl3) # label(axiom) # label(non_clause).  [assumption].
7.36/7.43	725 (all X_a (real_normed_field(X_a) -> (all F (hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),F)) -> hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),F),zero_zero(X_a)),sequentially)))))) # label(fact_4435_summable__LIMSEQ__zero) # label(axiom) # label(non_clause).  [assumption].
7.36/7.43	726 (all M all N (hAPP(int,int,hAPP(int,fun(int,int),times_times(int),M),N) = one_one(int) -> one_one(int) = ti(int,M) | hAPP(int,int,number_number_of(int),min_1) = ti(int,M))) # label(fact_309_pos__zmult__eq__1__iff__lemma) # label(axiom) # label(non_clause).  [assumption].
7.36/7.43	727 (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_823_add__le__less__mono) # label(axiom) # label(non_clause).  [assumption].
7.36/7.43	728 (all X_a (real_algebra_1(X_a) -> (all R_4 all X hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),R_4),X) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(real,X_a,of_real(X_a),R_4)),X)))) # label(fact_4680_scaleR__conv__of__real) # label(axiom) # label(non_clause).  [assumption].
7.36/7.43	729 (all X_1 hAPP(fun(nat,real),real,suminf(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),cos_coeff)),hAPP(real,fun(nat,real),power_power(real),X_1))) = hAPP(real,real,cos,X_1)) # label(fact_3972_cos__def) # label(axiom) # label(non_clause).  [assumption].
7.36/7.43	730 (all A_2 all B_1 all K all Ma (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Ma)) -> (one_one(int) = hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,K),Ma) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_2),B_1),Ma)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K),A_2)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K),B_1)),Ma)))))) # label(fact_3471_zcong__cancel2) # label(axiom) # label(non_clause).  [assumption].
7.36/7.43	731 (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_439_zero__less__two) # label(axiom) # label(non_clause).  [assumption].
7.36/7.43	732 (all X all Y hAPP(real,real,sqrt,hAPP(real,real,hAPP(real,fun(real,real),times_times(real),X),Y)) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,sqrt,X)),hAPP(real,real,sqrt,Y))) # label(fact_1617_real__sqrt__mult) # label(axiom) # label(non_clause).  [assumption].
7.36/7.43	733 (all X_3 all A_2 (hBOOL(hAPP(filter(nat),bool,hAPP(complex,fun(filter(nat),bool),hAPP(fun(nat,complex),fun(complex,fun(filter(nat),bool)),tendsto(nat,complex),X_3),A_2),sequentially)) -> hBOOL(hAPP(filter(nat),bool,hAPP(complex,fun(filter(nat),bool),hAPP(fun(nat,complex),fun(complex,fun(filter(nat),bool)),tendsto(nat,complex),hAPP(fun(nat,complex),fun(nat,complex),hAPP(fun(complex,complex),fun(fun(nat,complex),fun(nat,complex)),combb(complex,complex,nat),cnj),X_3)),hAPP(complex,complex,cnj,A_2)),sequentially)))) # label(fact_4506_cnj_OLIMSEQ) # label(axiom) # label(non_clause).  [assumption].
7.36/7.43	734 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,fact_fact(nat),M)),hAPP(nat,nat,fact_fact(nat),N))))) # label(fact_2484_fact__mono__nat) # label(axiom) # label(non_clause).  [assumption].
7.36/7.43	735 (all M all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),M),hAPP(nat,nat,suc,hAPP(nat,nat,suc,hAPP(nat,nat,suc,N)))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),M),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_1441_mod__Suc__eq__mod__add3) # label(axiom) # label(non_clause).  [assumption].
7.36/7.43	736 (all X_a (real_normed_vector(X_a) -> (all X all Y all A_1 all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),X),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),Y),B))),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),X),A_1)),B))),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),Y),B))) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),X),Y)),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_1),B))))) # label(fact_4722_scaleR_Oprod__diff__prod) # label(axiom) # label(non_clause).  [assumption].
7.36/7.43	737 (all K_4 all I_1 all J_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),I_1),J_2)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),K_4)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K_4),I_1)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K_4),J_2)))))) # label(fact_101_zmult__zless__mono2) # label(axiom) # label(non_clause).  [assumption].
7.36/7.43	738 (all X_b all X_a (metric_space(X_a) & topological_space(X_b) -> (all L all F all G all A_2 all R_3 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),R_3)) -> ((all X_2 (ti(X_a,A_2) != ti(X_a,X_2) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),X_2),A_2)),R_3)) -> hAPP(X_a,X_b,G,X_2) = hAPP(X_a,X_b,F,X_2)))) -> (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),G),L),hAPP(X_a,filter(X_a),at(X_a),A_2))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),L),hAPP(X_a,filter(X_a),at(X_a),A_2))))))))) # label(fact_4652_metric__LIM__equal2) # label(axiom) # label(non_clause).  [assumption].
7.36/7.43	739 (all X_1 ((exists Y_2 ti(int,X_1) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),Y_2)) <-> hBOOL(hAPP(int,bool,even_odd_even(int),X_1)))) # label(fact_1447_even__equiv__def) # label(axiom) # label(non_clause).  [assumption].
7.36/7.43	740 (all K hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less_eq(nat)),K))))) # label(fact_3802_finite__Collect__le__nat) # label(axiom) # label(non_clause).  [assumption].
7.36/7.43	741 (all K_4 all A_1 all B all M (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_1),B),M)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),K_4)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),K_4)),M)))) # label(fact_358_zcong__scalar) # label(axiom) # label(non_clause).  [assumption].
7.36/7.43	742 (all X hAPP(real,real,sqrt,hAPP(real,real,hAPP(real,fun(real,real),times_times(real),X),X)) = hAPP(real,real,abs_abs(real),X)) # label(fact_1872_real__sqrt__abs2) # label(axiom) # label(non_clause).  [assumption].
7.36/7.43	743 (all X all Y (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),Y)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y),X)) -> Y = X))) # label(fact_633_dvd_Oantisym) # label(axiom) # label(non_clause).  [assumption].
7.36/7.43	744 (all X_a all X_b all X_c (topological_space(X_b) & topological_space(X_a) & topological_space(X_c) -> (all F all A_2 all G all L (hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,X_b),fun(X_a,bool),isCont(X_a,X_b),G),L)) -> (hBOOL(hAPP(filter(X_c),bool,hAPP(X_a,fun(filter(X_c),bool),hAPP(fun(X_c,X_a),fun(X_a,fun(filter(X_c),bool)),tendsto(X_c,X_a),F),L),hAPP(X_c,filter(X_c),at(X_c),A_2))) -> hBOOL(hAPP(filter(X_c),bool,hAPP(X_b,fun(filter(X_c),bool),hAPP(fun(X_c,X_b),fun(X_b,fun(filter(X_c),bool)),tendsto(X_c,X_b),hAPP(fun(X_c,X_a),fun(X_c,X_b),hAPP(fun(X_a,X_b),fun(fun(X_c,X_a),fun(X_c,X_b)),combb(X_a,X_b,X_c),G),F)),hAPP(X_a,X_b,G,L)),hAPP(X_c,filter(X_c),at(X_c),A_2)))))))) # label(fact_4881_isCont__LIM__compose) # label(axiom) # label(non_clause).  [assumption].
7.36/7.43	745 (all X_a (metric_space(X_a) -> (all X all Y all A_1 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),X),Y)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),A_1),X)),hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),A_1),Y))))))) # label(fact_3504_dist__triangle3) # label(axiom) # label(non_clause).  [assumption].
7.36/7.43	746 (all X_a (linorder(X_a) -> (all X all Y all Z_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),Y),Z_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),Y),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),Z_1))))) # label(fact_4966_min__max_Osup__left__commute) # label(axiom) # label(non_clause).  [assumption].
7.36/7.43	747 (all Z_4 all Z_1 all W_3 all W (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_3),W)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Z_4),Z_1)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),W_3),Z_4)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),W),Z_1)))))) # label(fact_56_zadd__zless__mono) # label(axiom) # label(non_clause).  [assumption].
7.36/7.43	748 (all A_2 all P_4 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),P_4)) -> hBOOL(hAPP(fun(fun(int,bool),bool),bool,finite_finite_1(fun(int,bool)),hAPP(int,fun(fun(int,bool),bool),hAPP(int,fun(int,fun(fun(int,bool),bool)),setS,A_2),P_4))))) # label(fact_1798_SetS__finite) # label(axiom) # label(non_clause).  [assumption].
7.36/7.43	749 (all X_a all One all Times all A_2 all N_1 hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(nat,X_a)),hAPP(X_a,fun(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(nat,X_a))),power_1(X_a),One),Times),A_2),hAPP(nat,nat,suc,N_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),Times,A_2),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(nat,X_a)),hAPP(X_a,fun(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(nat,X_a))),power_1(X_a),One),Times),A_2),N_1))) # label(fact_2841_power_Opower_Opower__Suc) # label(axiom) # label(non_clause).  [assumption].
7.36/7.43	750 (all X_a all C_1 all A_3 all B_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_3),B_2))) -> -(hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),A_3)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),B_2))))) # label(fact_1918_DiffE) # label(axiom) # label(non_clause).  [assumption].
7.36/7.43	751 (all Y_1 all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Y_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_1),Y_1)) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,ln,X_1)),hAPP(real,real,ln,Y_1))))))) # label(fact_1944_ln__le__cancel__iff) # label(axiom) # label(non_clause).  [assumption].
7.36/7.43	752 (all X_a all A_3 all B_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less(fun(X_a,bool)),A_3),B_2)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_3),B_2)))) # label(fact_2001_psubset__imp__subset) # label(axiom) # label(non_clause).  [assumption].
7.36/7.43	753 (all X_a all A_3 all B_2 (hBOOL(hAPP(fun(fun(X_a,bool),bool),bool,hAPP(fun(fun(X_a,bool),bool),fun(fun(fun(X_a,bool),bool),bool),ord_less_eq(fun(fun(X_a,bool),bool)),A_3),B_2)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(fun(fun(X_a,bool),bool),fun(X_a,bool),complete_Sup_Sup(fun(X_a,bool)),A_3)),hAPP(fun(fun(X_a,bool),bool),fun(X_a,bool),complete_Sup_Sup(fun(X_a,bool)),B_2))))) # label(fact_1749_Union__mono) # label(axiom) # label(non_clause).  [assumption].
7.36/7.43	754 (all T all A ti(T,A) = ti(T,ti(T,A))) # label(help_ti_idem) # label(axiom) # label(non_clause).  [assumption].
7.36/7.43	755 (all X_b all X_a (topological_space(X_b) & topological_space(X_a) -> (all K_3 all F all L_2 all X_1 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),L_2),hAPP(X_a,filter(X_a),at(X_a),X_1))) -> (ti(X_b,L_2) = ti(X_b,K_3) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),K_3),hAPP(X_a,filter(X_a),at(X_a),X_1)))))))) # label(fact_4545_LIM__cong__limit) # label(axiom) # label(non_clause).  [assumption].
7.36/7.43	756 (all X all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),Y)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),Y)),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))) # label(fact_1758_real__less__half__sum) # label(axiom) # label(non_clause).  [assumption].
7.36/7.43	757 (all X_a (real_normed_algebra(X_a) -> (all C_1 all F (hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),F)) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1),hAPP(fun(nat,X_a),X_a,suminf(X_a),F)) = hAPP(fun(nat,X_a),X_a,suminf(X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(X_a,X_a),fun(fun(nat,X_a),fun(nat,X_a)),combb(X_a,X_a,nat),hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1)),F)))))) # label(fact_3990_suminf__mult) # label(axiom) # label(non_clause).  [assumption].
7.36/7.43	758 (all X_a (linordered_semidom(X_a) -> (all Ma all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),N_1)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),Ma)),hAPP(nat,X_a,semiring_1_of_nat(X_a),N_1))))))) # label(fact_1284_of__nat__less__iff) # label(axiom) # label(non_clause).  [assumption].
7.36/7.43	759 (all X_b all X_a (topological_space(X_b) & real_normed_vector(X_a) -> (all F all X_1 (hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,X_b),fun(X_a,bool),isCont(X_a,X_b),F),X_1)) <-> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(fun(X_a,X_a),fun(X_a,X_b),hAPP(fun(X_a,X_b),fun(fun(X_a,X_a),fun(X_a,X_b)),combb(X_a,X_b,X_a),F),hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X_1))),hAPP(X_a,X_b,F,X_1)),hAPP(X_a,filter(X_a),at(X_a),zero_zero(X_a)))))))) # label(fact_4920_isCont__iff) # label(axiom) # label(non_clause).  [assumption].
7.36/7.43	760 (all X_a (archim1727834104eiling(X_a) -> (all Y all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),X)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(X_a,int,archimedean_ceiling(X_a),Y)),hAPP(X_a,int,archimedean_ceiling(X_a),X))))))) # label(fact_3281_ceiling__mono) # label(axiom) # label(non_clause).  [assumption].
7.36/7.43	761 (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,prime,N)) -> (exists M_2 exists K_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_2),N)) & hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_2),K_1) = N & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),K_1),N)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),K_1)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),M_2)))))) # label(fact_3091_not__prime__ex__mk) # label(axiom) # label(non_clause).  [assumption].
7.36/7.43	762 (all M (hBOOL(hAPP(int,bool,zprime,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),M)),one_one(int)))) -> hAPP(int,int,hAPP(int,fun(int,int),legendre,hAPP(int,int,number_number_of(int),min_1)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),M)),one_one(int))) = one_one(int))) # label(fact_469_Legendre__1mod4) # label(axiom) # label(non_clause).  [assumption].
7.36/7.43	763 (all B all A_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_1),zero_zero(int))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),zero_zero(int))) -> hAPP(product_prod(int,int),int,product_snd(int,int),hAPP(product_prod(int,int),product_prod(int,int),negateSnd,hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),posDivAlg,hAPP(int,int,uminus_uminus(int),A_1)),hAPP(int,int,uminus_uminus(int),B)))) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_1),B)))) # label(fact_3121_mod__neg__neg) # label(axiom) # label(non_clause).  [assumption].
7.36/7.43	764 (all A_1 all B hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A_1),B)),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A_1),B)) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) # label(fact_568_zspecial__product) # label(axiom) # label(non_clause).  [assumption].
7.36/7.43	765 (all K_4 all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),K_4),N)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_4),N))))) # label(fact_497_dvd__imp__le) # label(axiom) # label(non_clause).  [assumption].
7.36/7.43	766 (all I all M_1 (hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),zero_zero(nat)),M_1)) -> 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_1))),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),I))))) = 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_1))),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),hAPP(nat,nat,suc,I))))))) # label(fact_3875_card__less__Suc) # label(axiom) # label(non_clause).  [assumption].
7.36/7.43	767 (all X_a (comm_monoid_add(X_a) & topological_space(X_a) -> (all Sa all F (zero_zero(X_a) = hAPP(nat,X_a,F,zero_zero(nat)) -> (hBOOL(hAPP(X_a,bool,hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),hAPP(fun(nat,nat),fun(nat,X_a),hAPP(fun(nat,X_a),fun(fun(nat,nat),fun(nat,X_a)),combb(nat,X_a,nat),F),suc)),Sa)) -> hBOOL(hAPP(X_a,bool,hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),F),Sa))))))) # label(fact_4094_sums__Suc__imp) # label(axiom) # label(non_clause).  [assumption].
7.36/7.44	768 (all I all K (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),K)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),I),K))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),K),I))))) # label(fact_1024_pos__imp__zdiv__pos__iff) # label(axiom) # label(non_clause).  [assumption].
7.36/7.44	769 (all X all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(nat,fun(real,real),root,N),X)) = hAPP(real,real,hAPP(nat,fun(real,real),root,N),hAPP(real,real,abs_abs(real),X)))) # label(fact_2689_real__root__abs) # label(axiom) # label(non_clause).  [assumption].
7.36/7.44	770 (all P_1 all D_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D_1)) -> ((all X_2 all K_1 (hBOOL(hAPP(int,bool,P_1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X_2),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K_1),D_1)))) <-> hBOOL(hAPP(int,bool,P_1,X_2)))) -> ((exists X1 hBOOL(hAPP(int,bool,P_1,X1))) <-> (exists X_2 (hBOOL(hAPP(int,bool,P_1,X_2)) & hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_2),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastAtMost(int),one_one(int)),D_1))))))))) # label(fact_4643_periodic__finite__ex) # label(axiom) # label(non_clause).  [assumption].
7.36/7.44	771 (all X_a (semiring_div(X_a) -> (all A_1 all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)),B) = zero_zero(X_a)))) # label(fact_974_mod__mult__self2__is__0) # label(axiom) # label(non_clause).  [assumption].
7.36/7.44	772 (all X all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,hAPP(nat,fun(real,real),root,N),X)))))) # label(fact_2696_real__root__gt__zero) # label(axiom) # label(non_clause).  [assumption].
7.36/7.44	773 (all Z_1 -(all M_2 all N_2 ti(int,Z_1) != hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(nat,int,semiring_1_of_nat(int),M_2)),hAPP(nat,int,semiring_1_of_nat(int),N_2)))) # label(fact_1521_int__diff__cases) # label(axiom) # label(non_clause).  [assumption].
7.36/7.44	774 (all V_3 all V ((hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V))) -> zero_zero(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(int,nat,number_number_of(nat),V)),hAPP(int,nat,number_number_of(nat),V_3))) & (-hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V))) -> (-hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V_3))) -> hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,number_number_of(int),V)),hAPP(int,int,number_number_of(int),V_3))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(int,nat,number_number_of(nat),V)),hAPP(int,nat,number_number_of(nat),V_3))) & (hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V_3))) -> hAPP(int,nat,number_number_of(nat),V) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(int,nat,number_number_of(nat),V)),hAPP(int,nat,number_number_of(nat),V_3)))))) # label(fact_1518_mod__nat__number__of) # label(axiom) # label(non_clause).  [assumption].
7.36/7.44	775 (all X_c all X_a all X_b all R_3 all A_2 all B_1 all C_1 (hBOOL(hAPP(X_c,bool,hAPP(product_prod(X_a,X_b),fun(X_c,bool),hAPP(fun(X_a,fun(X_b,fun(X_c,bool))),fun(product_prod(X_a,X_b),fun(X_c,bool)),product_prod_case(X_a,X_b,fun(X_c,bool)),R_3),hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),A_2),B_1)),C_1)) -> hBOOL(hAPP(X_c,bool,hAPP(X_b,fun(X_c,bool),hAPP(X_a,fun(X_b,fun(X_c,bool)),R_3,A_2),B_1),C_1)))) # label(fact_4042_splitD_H) # label(axiom) # label(non_clause).  [assumption].
7.36/7.44	776 (all X_a (real_normed_vector(X_a) -> (all X exists K_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),K_2)) & (all X_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),X_2),X))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,norm_norm(real),X_2)),K_2)))))))) # label(fact_4756_scaleR__left_Ononneg__bounded) # label(axiom) # label(non_clause).  [assumption].
7.36/7.44	777 (all X_a (number_ring(X_a) -> (all A_1 ti(X_a,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)))) # label(fact_110_mult__numeral__1) # label(axiom) # label(non_clause).  [assumption].
7.36/7.44	778 (all Real1_1 all Real2_1 hAPP(complex,nat,complex_size,hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,Real1_1),Real2_1)) = zero_zero(nat)) # label(fact_2751_complex_Osize_I1_J) # label(axiom) # label(non_clause).  [assumption].
7.36/7.44	779 (all X_a (ring_char_0(X_a) -> (all Z (zero_zero(X_a) = hAPP(int,X_a,ring_1_of_int(X_a),Z) <-> zero_zero(int) = ti(int,Z))))) # label(fact_3579_of__int__0__eq__iff) # label(axiom) # label(non_clause).  [assumption].
7.36/7.44	780 (all X_a (comm_semiring_1(X_a) -> (all C all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_1),B)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),C))))))) # label(fact_334_dvd__mult2) # label(axiom) # label(non_clause).  [assumption].
7.36/7.44	781 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),X)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,ln,X))))) # label(fact_1946_ln__gt__zero) # label(axiom) # label(non_clause).  [assumption].
7.36/7.44	782 (all K all N_1 all F_3 hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),F_3),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),K))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),N_1)) = hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),F_3),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_1),K)))),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),F_3),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),K)))) # label(fact_4181_sumr__offset2) # label(axiom) # label(non_clause).  [assumption].
7.36/7.44	783 (all N all M all R_4 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),M),R_4)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),N),R_4)) -> (one_one(int) = hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),M),N) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),M),N)),R_4)))))) # label(fact_4393_divides__mult__int) # label(axiom) # label(non_clause).  [assumption].
7.36/7.44	784 (all A_1 hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,one_one(nat)),A_1))) # label(fact_2854_coprime__1_H) # label(axiom) # label(non_clause).  [assumption].
7.36/7.44	785 (all X_a (monoid_mult(X_a) -> (all A_1 all M all N hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),M)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N)) = hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N))))) # label(fact_416_power__add) # label(axiom) # label(non_clause).  [assumption].
7.36/7.44	786 (all X_a (banach(X_a) -> (all F all N_4 all C_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),C_1),one_one(real))) -> ((all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_4),N_2)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),hAPP(nat,X_a,F,hAPP(nat,nat,suc,N_2)))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C_1),hAPP(X_a,real,norm_norm(X_a),hAPP(nat,X_a,F,N_2))))))) -> hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),F))))))) # label(fact_4054_ratio__test) # label(axiom) # label(non_clause).  [assumption].
7.36/7.44	787 (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_109_not__sum__squares__lt__zero) # label(axiom) # label(non_clause).  [assumption].
7.36/7.44	788 (all X_a all X_b ti(fun(fun(X_a,nat),fun(fun(X_b,nat),fun(product_prod(X_a,X_b),nat))),product_prod_size(X_a,X_b)) = product_prod_size(X_a,X_b)) # label(tsy_c_Product__Type_Oprod_Oprod__size_res) # label(axiom) # label(non_clause).  [assumption].
7.36/7.44	789 (all K_4 all I_1 all J_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),J_2)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),J_2),K_4)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,I_1)),K_4))))) # label(fact_1232_less__trans__Suc) # label(axiom) # label(non_clause).  [assumption].
7.36/7.44	790 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),hAPP(nat,nat,suc,N))))) # label(fact_1247_le__SucI) # label(axiom) # label(non_clause).  [assumption].
7.36/7.44	791 (all M hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,M)) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),M))) # label(fact_1221_int__Suc) # label(axiom) # label(non_clause).  [assumption].
7.36/7.44	792 (all X_a (comm_semiring_1(X_a) -> (all B all A_1 all C (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_1),C)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),C))))))) # label(fact_335_dvd__mult) # label(axiom) # label(non_clause).  [assumption].
7.36/7.44	793 (all X_a (field_inverse_zero(X_a) -> (all A_1 all B all N hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),A_1),B)),N) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),B),N))))) # label(fact_1666_power__divide) # label(axiom) # label(non_clause).  [assumption].
7.36/7.44	794 (all M all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,M)),hAPP(nat,nat,suc,N))) # label(fact_1251_diff__Suc__Suc) # label(axiom) # label(non_clause).  [assumption].
7.36/7.44	795 (all X_1 (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),zEven)) | hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),zOdd)))) # label(fact_1275_even__odd__disj) # label(axiom) # label(non_clause).  [assumption].
7.36/7.44	796 (all Ma all N_1 (one_one(nat) = N_1 & one_one(nat) = Ma <-> hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),Ma),N_1) = one_one(nat))) # label(fact_588_nat__1__eq__mult__iff) # label(axiom) # label(non_clause).  [assumption].
7.36/7.44	797 (all A_2 all B_1 ((all D_3 (ti(int,D_3) = one_one(int) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),D_3)) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),D_3),A_2)) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),D_3),B_1)))) <-> one_one(int) = hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),A_2),B_1))) # label(fact_4405_coprime__int) # label(axiom) # label(non_clause).  [assumption].
7.36/7.44	798 (all P_5 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),P_5)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(int,nat,nat_1,P_5)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),P_5),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))) # label(fact_1158_Int2_Oaux__1) # label(axiom) # label(non_clause).  [assumption].
7.36/7.44	799 (all X_a (semiring_char_0(X_a) -> (all Ma all N_1 (N_1 = Ma <-> hAPP(nat,X_a,semiring_1_of_nat(X_a),N_1) = hAPP(nat,X_a,semiring_1_of_nat(X_a),Ma))))) # label(fact_1214_of__nat__eq__iff) # label(axiom) # label(non_clause).  [assumption].
7.36/7.44	800 (all X_a (linordered_idom(X_a) -> (all X all Y all N (-hBOOL(hAPP(nat,bool,even_odd_even(nat),N)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),N)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),Y),N)))))))) # label(fact_2421_power__mono__odd) # label(axiom) # label(non_clause).  [assumption].
7.36/7.44	801 (all Ma all N_1 (zero_zero(int) != ti(int,N_1) | zero_zero(int) != ti(int,Ma) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),Ma),N_1))))) # label(fact_4381_gcd__pos__int) # label(axiom) # label(non_clause).  [assumption].
7.36/7.44	802 (all X_a (real_normed_vector(X_a) -> (all A_1 all B hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_1),B))),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(X_a,real,norm_norm(X_a),A_1)),hAPP(X_a,real,norm_norm(X_a),B))))))) # label(fact_1793_norm__triangle__ineq4) # label(axiom) # label(non_clause).  [assumption].
7.36/7.44	803 (all X_a (real_algebra_1(X_a) -> ti(fun(real,X_a),of_real(X_a)) = of_real(X_a))) # label(tsy_c_RealVector_Oof__real_res) # label(axiom) # label(non_clause).  [assumption].
7.36/7.44	804 (all M all N hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),M),N)),N) = hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),M),N)) # label(fact_4354_gcd__add1__int) # label(axiom) # label(non_clause).  [assumption].
7.36/7.44	805 (all X_a all P_1 all X_1 (hBOOL(hAPP(X_a,bool,P_1,X_1)) -> hBOOL(hAPP(X_a,bool,P_1,hAPP(fun(X_a,bool),X_a,hilbert_Eps(X_a),P_1))))) # label(fact_4784_someI) # label(axiom) # label(non_clause).  [assumption].
7.36/7.44	806 (all Y_1 all X_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Y_1)) -> (hAPP(int,nat,nat_1,Y_1) = hAPP(int,nat,nat_1,X_1) <-> ti(int,X_1) = ti(int,Y_1))))) # label(fact_1105_transfer__nat__int__relations_I1_J) # label(axiom) # label(non_clause).  [assumption].
7.36/7.44	807 (all P_4 (hBOOL(hAPP(nat,bool,prime,P_4)) <-> (all M_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),M_2),P_4)) -> one_one(nat) = M_2 | P_4 = M_2)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),one_one(nat)),P_4)))) # label(fact_3067_prime__def) # label(axiom) # label(non_clause).  [assumption].
7.36/7.44	808 (all B all A_1 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),B),A_1))),hAPP(complex,real,norm_norm(complex),B))),hAPP(complex,real,norm_norm(complex),A_1)))) # label(fact_1784_complex__mod__triangle__ineq2) # label(axiom) # label(non_clause).  [assumption].
7.36/7.44	809 (all X_a (number_ring(X_a) -> (all X (-hBOOL(hAPP(nat,bool,even_odd_even(nat),X)) -> hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(int,X_a,number_number_of(X_a),min_1)),X) = hAPP(int,X_a,number_number_of(X_a),min_1))))) # label(fact_2443_Parity_Oneg__one__odd__power) # label(axiom) # label(non_clause).  [assumption].
7.36/7.44	810 (all X_a (field(X_a) -> (all X all Y all Z_1 (zero_zero(X_a) != ti(X_a,Z_1) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),X),Z_1)),Y) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Z_1),Y))),Z_1))))) # label(fact_1728_divide__diff__eq__iff) # label(axiom) # label(non_clause).  [assumption].
7.36/7.44	811 (all X_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),zOdd)) <-> hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),X_1),N_1)),zOdd))))) # label(fact_1046_power__preserves__odd) # label(axiom) # label(non_clause).  [assumption].
7.36/7.44	812 (all Ma all N_1 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Ma),N_1) = hAPP(nat,nat,suc,zero_zero(nat)) <-> zero_zero(nat) = N_1 & Ma = hAPP(nat,nat,suc,zero_zero(nat)) | N_1 = hAPP(nat,nat,suc,zero_zero(nat)) & Ma = zero_zero(nat))) # label(fact_1325_one__is__add) # label(axiom) # label(non_clause).  [assumption].
7.36/7.44	813 (all W_1 all Z ((exists N_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_2))) = ti(int,Z)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_1),Z)))) # label(fact_1220_zless__iff__Suc__zadd) # label(axiom) # label(non_clause).  [assumption].
7.36/7.44	814 (all X_1 all A_2 all P_4 (hBOOL(hAPP(int,bool,zprime,P_4)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),P_4)) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_2),zero_zero(int)),P_4)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),hAPP(int,fun(int,bool),sRStar,P_4))) -> hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),hAPP(int,int,hAPP(int,fun(int,int),standardRes,P_4),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_2),hAPP(int,int,hAPP(int,fun(int,int),multInv,P_4),X_1)))),hAPP(int,fun(int,bool),sRStar,P_4)))))))) # label(fact_1073_SRStar__mult__prop2) # label(axiom) # label(non_clause).  [assumption].
7.36/7.44	815 (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_1547_xt1_I5_J) # label(axiom) # label(non_clause).  [assumption].
7.36/7.44	816 (all X_a (linord219039673up_add(X_a) -> (all A_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),A_2)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),A_2)),A_2)))))) # label(fact_2056_minus__le__self__iff) # label(axiom) # label(non_clause).  [assumption].
7.36/7.44	817 (all N all D all A_1 (one_one(int) = hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),D),A_1) -> one_one(int) = hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),D),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A_1),N)))) # label(fact_4359_coprime__exp__int) # label(axiom) # label(non_clause).  [assumption].
7.36/7.44	818 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> hAPP(real,real,sqrt,X) != zero_zero(real))) # label(fact_1626_real__sqrt__not__eq__zero) # label(axiom) # label(non_clause).  [assumption].
7.36/7.44	819 (all T_2 all T_1 (finite_finite(T_2) & finite_finite(T_1) -> finite_finite(sum_sum(T_2,T_1)))) # label(arity_sum___Finite__Set_Ofinite) # label(axiom) # label(non_clause).  [assumption].
7.36/7.44	820 (all M all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),M),N) = hAPP(product_prod(nat,nat),nat,product_snd(nat,nat),hAPP(nat,product_prod(nat,nat),hAPP(nat,fun(nat,product_prod(nat,nat)),divmod_nat,M),N))) # label(fact_3126_mod__nat__def) # label(axiom) # label(non_clause).  [assumption].
7.36/7.44	821 (all N_1 all Ma (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_1),Ma)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,fact_fact(nat),Ma)),hAPP(nat,nat,fact_fact(nat),N_1)) = hAPP(fun(nat,bool),nat,hAPP(fun(nat,nat),fun(fun(nat,bool),nat),big_co302546470etprod(nat,nat),combi(nat)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_1),one_one(nat))),Ma)))) # label(fact_4612_fact__div__fact) # label(axiom) # label(non_clause).  [assumption].
7.36/7.44	822 (all M_5 all D_4 (zero_zero(int) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),M_5),D_4) -> (exists Q_4 hAPP(int,int,hAPP(int,fun(int,int),times_times(int),D_4),Q_4) = ti(int,M_5)))) # label(fact_1171_zmod__eq__0D) # label(axiom) # label(non_clause).  [assumption].
7.36/7.44	823 (all X_a (linordered_idom(X_a) -> (all Z (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Z),zero_zero(int))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(int,X_a,ring_1_of_int(X_a),Z)),zero_zero(X_a))))))) # label(fact_3603_of__int__le__0__iff) # label(axiom) # label(non_clause).  [assumption].
7.36/7.44	824 (all X_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X_1)) -> (hBOOL(hAPP(int,bool,even_odd_even(int),X_1)) <-> hBOOL(hAPP(nat,bool,even_odd_even(nat),hAPP(int,nat,nat_1,X_1)))))) # label(fact_2462_pos__int__even__equiv__nat__even) # label(axiom) # label(non_clause).  [assumption].
7.36/7.44	825 (all X_1 hBOOL(hAPP(real,bool,hAPP(fun(nat,real),fun(real,bool),sums(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),cos_coeff)),hAPP(real,fun(nat,real),power_power(real),X_1))),hAPP(real,real,cos,X_1)))) # label(fact_4097_cos__converges) # label(axiom) # label(non_clause).  [assumption].
7.36/7.44	826 (all I_1 all J_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),J_2)) -> (exists K_1 (J_2 = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_1),K_1) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K_1)))))) # label(fact_860_less__imp__add__positive) # label(axiom) # label(non_clause).  [assumption].
7.36/7.44	827 (all N_1 (N_1 = one_one(nat) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,N_1),N_1)))) # label(fact_2852_coprime__refl) # label(axiom) # label(non_clause).  [assumption].
7.36/7.44	828 (all X_a (linordered_field(X_a) -> (all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,inverse_inverse(X_a),B)),hAPP(X_a,X_a,inverse_inverse(X_a),A_1)))))))) # label(fact_2547_less__imp__inverse__less__neg) # label(axiom) # label(non_clause).  [assumption].
7.36/7.44	829 (all Y all X (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),Y),X)) -> hAPP(int,int,abs_abs(int),Y) = hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),X),Y))) # label(fact_4379_gcd__proj2__if__dvd__int) # label(axiom) # label(non_clause).  [assumption].
7.36/7.44	830 (all P_1 ((exists X1 hBOOL(hAPP(nat,bool,P_1,X1))) <-> (exists X_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X_2)) & hBOOL(hAPP(nat,bool,P_1,hAPP(int,nat,nat_1,X_2))))))) # label(fact_1107_ex__nat) # label(axiom) # label(non_clause).  [assumption].
7.36/7.44	831 (all X_1 all Y_1 (-hBOOL(hAPP(int,bool,even_odd_even(int),X_1)) & -hBOOL(hAPP(int,bool,even_odd_even(int),Y_1)) | hBOOL(hAPP(int,bool,even_odd_even(int),Y_1)) & hBOOL(hAPP(int,bool,even_odd_even(int),X_1)) <-> hBOOL(hAPP(int,bool,even_odd_even(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X_1),Y_1))))) # label(fact_1266_even__difference) # label(axiom) # label(non_clause).  [assumption].
7.36/7.44	832 (all X_a (linorder(X_a) -> (all B all X all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),A_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),A_1),B))))))) # label(fact_4982_min__max_Ole__supI1) # label(axiom) # label(non_clause).  [assumption].
7.36/7.44	833 (all N_1 all P_1 (hBOOL(hAPP(nat,bool,P_1,zero_zero(nat))) -> ((all N_2 (hBOOL(hAPP(nat,bool,P_1,N_2)) -> hBOOL(hAPP(nat,bool,P_1,hAPP(nat,nat,suc,N_2))))) -> hBOOL(hAPP(nat,bool,P_1,N_1))))) # label(fact_1654_nat__induct) # label(axiom) # label(non_clause).  [assumption].
7.36/7.44	834 (all L all U_1 hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),L),U_1)))) # label(fact_4533_finite__atLeastAtMost) # label(axiom) # label(non_clause).  [assumption].
7.36/7.44	835 (all X_a (real_n2089651433ebra_1(X_a) -> (all Z_1 hAPP(real,real,abs_abs(real),hAPP(int,real,ring_1_of_int(real),Z_1)) = hAPP(X_a,real,norm_norm(X_a),hAPP(int,X_a,ring_1_of_int(X_a),Z_1))))) # label(fact_3575_norm__of__int) # label(axiom) # label(non_clause).  [assumption].
7.36/7.44	836 (all X_a (ordere142940540dd_abs(X_a) -> (all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),zero_zero(X_a))) -> hAPP(X_a,X_a,abs_abs(X_a),A_1) = hAPP(X_a,X_a,uminus_uminus(X_a),A_1))))) # label(fact_2099_abs__of__neg) # label(axiom) # label(non_clause).  [assumption].
7.36/7.44	837 (all Y_1 all X_1 all P_4 (hBOOL(hAPP(int,bool,zprime,P_4)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),P_4)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),hAPP(int,fun(int,bool),sRStar,P_4))) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Y_1),hAPP(int,fun(int,bool),sRStar,P_4))) -> hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),hAPP(int,int,hAPP(int,fun(int,int),standardRes,P_4),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X_1),Y_1))),hAPP(int,fun(int,bool),sRStar,P_4)))))))) # label(fact_1163_SRStar__mult__prop1) # label(axiom) # label(non_clause).  [assumption].
7.36/7.44	838 (all Z_1 all X all Y all M (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,X),Y),M)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),X),Z_1)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),Y),Z_1)),M)))) # label(fact_363_zcong__zpower) # label(axiom) # label(non_clause).  [assumption].
7.36/7.44	839 (all V_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(int,nat,number_number_of(nat),V_1)),hAPP(nat,nat,suc,N_1))) <-> (-hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),hAPP(int,int,pred,V_1)))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(int,nat,nat_1,hAPP(int,int,number_number_of(int),hAPP(int,int,pred,V_1)))),N_1))))) # label(fact_3893_less__number__of__Suc) # label(axiom) # label(non_clause).  [assumption].
7.36/7.44	840 (all X_a (archim1727834104eiling(X_a) -> (all Z_1 all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(int,X_a,ring_1_of_int(X_a),Z_1)),one_one(X_a))),X)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),hAPP(int,X_a,ring_1_of_int(X_a),Z_1))) -> hAPP(X_a,int,archimedean_ceiling(X_a),X) = ti(int,Z_1)))))) # label(fact_3606_ceiling__unique) # label(axiom) # label(non_clause).  [assumption].
7.36/7.44	841 (all F (hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),abs_abs(real)),F))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),hAPP(fun(nat,real),real,suminf(real),F))),hAPP(fun(nat,real),real,suminf(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),abs_abs(real)),F)))))) # label(fact_4019_summable__rabs) # label(axiom) # label(non_clause).  [assumption].
7.36/7.44	842 (all X_a all A_3 all B_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),B_2)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_3),B_2)) -> hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_3))))) # label(fact_1821_rev__finite__subset) # label(axiom) # label(non_clause).  [assumption].
7.36/7.44	843 (all X_a (real_normed_field(X_a) & banach(X_a) -> one_one(X_a) = hAPP(X_a,X_a,exp(X_a),zero_zero(X_a)))) # label(fact_2583_exp__zero) # label(axiom) # label(non_clause).  [assumption].
7.36/7.44	844 (all X_a (comm_semiring_1(X_a) -> (all X all N hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),N))) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),N)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),N)))))) # label(fact_1457_comm__semiring__1__class_Onormalizing__semiring__rules_I37_J) # label(axiom) # label(non_clause).  [assumption].
7.36/7.44	845 (all X_a (real_normed_vector(X_a) & real_algebra_1(X_a) -> (exists K_2 all X_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),hAPP(real,X_a,of_real(X_a),X_2))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,norm_norm(real),X_2)),K_2)))))) # label(fact_2822_of__real_Obounded) # label(axiom) # label(non_clause).  [assumption].
7.36/7.44	846 (all X_a (comm_semiring_1(X_a) -> (all C all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_1),B)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),B),C)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_1),C))))))) # label(fact_312_dvd__trans) # label(axiom) # label(non_clause).  [assumption].
7.36/7.44	847 (all X_a (linordered_idom(X_a) -> (all X all Y -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),Y),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),zero_zero(X_a)))))) # label(fact_7_not__sum__power2__lt__zero) # label(axiom) # label(non_clause).  [assumption].
7.36/7.44	848 (all P_4 hAPP(fun(int,bool),fun(int,bool),collect(int),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),combs(int,bool,bool),hAPP(fun(int,bool),fun(int,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj),hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)))),hAPP(int,fun(int,bool),hAPP(fun(int,fun(int,bool)),fun(int,fun(int,bool)),combc(int,int,bool),ord_less(int)),P_4))) = hAPP(int,fun(int,bool),sr,P_4)) # label(fact_898_SR__def) # label(axiom) # label(non_clause).  [assumption].
7.36/7.44	849 (all N_1 all Ma hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),hAPP(nat,nat,suc,N_1)),Ma) = hAPP(nat,nat,hAPP(fun(nat,nat),fun(nat,nat),hAPP(nat,fun(fun(nat,nat),fun(nat,nat)),nat_case(nat),zero_zero(nat)),hAPP(fun(nat,nat),fun(nat,nat),hAPP(fun(nat,nat),fun(fun(nat,nat),fun(nat,nat)),combb(nat,nat,nat),suc),hAPP(nat,fun(nat,nat),ord_min(nat),N_1))),Ma)) # label(fact_4833_min__Suc1) # label(axiom) # label(non_clause).  [assumption].
7.36/7.44	850 (all N all K_4 all M (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_4),M)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_4),N)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),K_4)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),K_4))))) # label(fact_674_Nat_Odiff__diff__eq) # label(axiom) # label(non_clause).  [assumption].
7.36/7.44	851 (all A_1 all P_5 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),P_5)) -> (hBOOL(hAPP(int,bool,zprime,P_5)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(int,int,hAPP(int,fun(int,int),legendre,A_1),P_5)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A_1),hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),P_5),one_one(int))),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))),P_5))))) # label(fact_1166_Euler__Criterion) # label(axiom) # label(non_clause).  [assumption].
7.36/7.44	852 (all X_a all X_b all F all G all P_4 hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(X_a,nat,F,hAPP(product_prod(X_a,X_b),X_a,product_fst(X_a,X_b),P_4))),hAPP(X_b,nat,G,hAPP(product_prod(X_a,X_b),X_b,product_snd(X_a,X_b),P_4)))),hAPP(nat,nat,suc,zero_zero(nat))) = hAPP(product_prod(X_a,X_b),nat,hAPP(fun(X_b,nat),fun(product_prod(X_a,X_b),nat),hAPP(fun(X_a,nat),fun(fun(X_b,nat),fun(product_prod(X_a,X_b),nat)),product_prod_size(X_a,X_b),F),G),P_4)) # label(fact_3122_prod__size__simp) # label(axiom) # label(non_clause).  [assumption].
7.36/7.44	853 (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),C)),B) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)),C)))) # label(fact_225_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) # label(axiom) # label(non_clause).  [assumption].
7.36/7.44	854 (all B all Q_3 all R_4 all B_5 all Q_5 all R_5 (hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),Q_3)),R_4) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B_5),Q_5)),R_5) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B_5),Q_5)),R_5))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),R_5),B_5)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),R_4)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B_5)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B_5),B)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Q_3),Q_5))))))))) # label(fact_267_zdiv__mono2__lemma) # label(axiom) # label(non_clause).  [assumption].
7.36/7.44	855 (all X_a (comm_monoid_mult(X_a) -> (all A_1 all B all N hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)),N) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),B),N))))) # label(fact_330_power__mult__distrib) # label(axiom) # label(non_clause).  [assumption].
7.36/7.44	856 (all X_a (comm_monoid_add(X_a) & topological_space(X_a) -> the(X_a) = ti(fun(fun(X_a,bool),X_a),the(X_a)))) # label(tsy_c_HOL_OThe_3_res) # label(axiom) # label(non_clause).  [assumption].
7.36/7.44	857 (all X_a (linorder(X_a) -> (all A_2 all B_1 all C_1 all D_1 (hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastLessThan(X_a),A_2),B_1) = hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastLessThan(X_a),C_1),D_1) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),B_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),D_1)) -> ti(X_a,C_1) = ti(X_a,A_2))))))) # label(fact_4196_atLeastLessThan__inj_I1_J) # label(axiom) # label(non_clause).  [assumption].
7.36/7.44	858 (all X_a (metric_space(X_a) -> (all X all Z_1 all Y all E_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),X),Z_1)),hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),Y),Z_1))),E_1)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),X),Y)),E_1)))))) # label(fact_3508_dist__triangle__le) # label(axiom) # label(non_clause).  [assumption].
7.36/7.44	859 (all X_a (number_ring(X_a) -> (all W hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(int,X_a,number_number_of(X_a),W)) = hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,uminus_uminus(int),W))))) # label(fact_2039_arith__simps_I30_J) # label(axiom) # label(non_clause).  [assumption].
7.36/7.44	860 (all X_a (real_normed_algebra(X_a) -> (all B zero_zero(X_a) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),zero_zero(X_a)),B)))) # label(fact_876_mult_Ozero__left) # label(axiom) # label(non_clause).  [assumption].
7.36/7.44	861 (all N all M hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),N),M) = hAPP(int,quickcheck_code_int,quickcheck_of_int,hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(quickcheck_code_int,int,quickcheck_int_of,N)),hAPP(quickcheck_code_int,int,quickcheck_int_of,M)))) # label(fact_3550_div__code__int__def) # label(axiom) # label(non_clause).  [assumption].
7.36/7.44	862 (all X_a (linordered_semidom(X_a) -> (all A_1 all N all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),hAPP(nat,nat,suc,N))),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),B),hAPP(nat,nat,suc,N)))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),B)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B))))))) # label(fact_1374_power__le__imp__le__base) # label(axiom) # label(non_clause).  [assumption].
7.36/7.44	863 (all Z_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)),Z_1)),Z_1) != zero_zero(int)) # label(fact_166_odd__nonzero) # label(axiom) # label(non_clause).  [assumption].
7.36/7.44	864 (all A_2 all B_1 (hBOOL(hAPP(product_prod(int,int),bool,hAPP(fun(product_prod(int,int),fun(product_prod(int,int),bool)),fun(product_prod(int,int),bool),accp(product_prod(int,int)),negDivAlg_rel),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),A_2),B_1))) -> (-(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_2),B_1))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B_1),zero_zero(int)))) -> hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),negDivAlg,A_2),B_1) = hAPP(product_prod(int,int),product_prod(int,int),hAPP(int,fun(product_prod(int,int),product_prod(int,int)),adjust,B_1),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),negDivAlg,A_2),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),B_1)))) & (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_2),B_1))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B_1),zero_zero(int))) -> hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),hAPP(int,int,number_number_of(int),min_1)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A_2),B_1)) = hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),negDivAlg,A_2),B_1)))) # label(fact_1174_negDivAlg_Opsimps) # label(axiom) # label(non_clause).  [assumption].
7.36/7.44	865 (all A_2 all C_1 all D_1 all B_1 (zero_zero(int) != ti(int,B_1) -> (zero_zero(int) != ti(int,D_1) -> (hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(int,rat,hAPP(int,fun(int,rat),fract,A_2),B_1)),hAPP(int,rat,hAPP(int,fun(int,rat),fract,C_1),D_1))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_2),D_1)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B_1),D_1))),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C_1),B_1)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B_1),D_1)))))))) # label(fact_3784_le__rat) # label(axiom) # label(non_clause).  [assumption].
7.36/7.44	866 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X),one_one(real))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),X),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),hAPP(real,real,ln,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),one_one(real)),X))))))) # label(fact_1998_ln__one__plus__pos__lower__bound) # label(axiom) # label(non_clause).  [assumption].
7.36/7.44	867 (all K_4 all M all N (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),K_4),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),M),N))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),K_4),N)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),K_4),M))))) # label(fact_962_zdvd__zmod__imp__zdvd) # label(axiom) # label(non_clause).  [assumption].
7.36/7.44	868 (all X_a all X_b (comm_monoid_mult(X_b) -> (all F all A_3 (-hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_3)) -> hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co302546470etprod(X_a,X_b),F),A_3) = one_one(X_b))))) # label(fact_3951_setprod__infinite) # label(axiom) # label(non_clause).  [assumption].
7.36/7.44	869 (all X_a (real_normed_field(X_a) -> (all Y exists K_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),K_2)) & (all X_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),X_2),Y))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(X_a,real,norm_norm(X_a),X_2)),K_2)))))))) # label(fact_1802_divide_Opos__bounded) # label(axiom) # label(non_clause).  [assumption].
7.36/7.44	870 (all X_a (group_add(X_a) -> (all A_2 (zero_zero(X_a) = hAPP(X_a,X_a,uminus_uminus(X_a),A_2) <-> ti(X_a,A_2) = zero_zero(X_a))))) # label(fact_2024_neg__0__equal__iff__equal) # label(axiom) # label(non_clause).  [assumption].
7.36/7.44	871 (all X all N all M (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),M)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> hAPP(real,real,hAPP(nat,fun(real,real),root,hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),N)),X) = hAPP(real,real,hAPP(nat,fun(real,real),root,M),hAPP(real,real,hAPP(nat,fun(real,real),root,N),X)))))) # label(fact_2707_real__root__pos__mult__exp) # label(axiom) # label(non_clause).  [assumption].
7.36/7.44	872 (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),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)),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_1878_abs__eq__mult) # label(axiom) # label(non_clause).  [assumption].
7.36/7.44	873 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X),zero_zero(real))) -> hAPP(real,nat,natfloor,X) = zero_zero(nat))) # label(fact_1895_natfloor__neg) # label(axiom) # label(non_clause).  [assumption].
7.36/7.44	874 (all D all A_1 all B (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),D),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A_1),B))) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,D),A_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),D),B))))) # label(fact_2869_coprime__divprod) # label(axiom) # label(non_clause).  [assumption].
7.36/7.44	875 (all X_a (real_algebra(X_a) -> (all X all A_1 all Y hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_1),Y)) = hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),Y))))) # label(fact_4675_mult__scaleR__right) # label(axiom) # label(non_clause).  [assumption].
7.36/7.44	876 (all X_1 all P_1 ((all A_4 ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),A_4)) -> hBOOL(hAPP(int,bool,P_1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A_4),one_one(int))))) -> hBOOL(hAPP(int,bool,P_1,A_4)))) -> hBOOL(hAPP(int,bool,P_1,X_1)))) # label(fact_832_d22set__induct__old) # label(axiom) # label(non_clause).  [assumption].
7.36/7.44	877 (all X_a (comm_ring_1(X_a) -> (all X all Y hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),X),Y) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X),hAPP(X_a,X_a,uminus_uminus(X_a),Y))))) # label(fact_2073_comm__ring__1__class_Onormalizing__ring__rules_I2_J) # label(axiom) # label(non_clause).  [assumption].
7.36/7.44	878 (all X_1 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,real)),combs(real,real,real),hAPP(fun(real,real),fun(real,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,fun(real,real))),combb(real,fun(real,real),real),times_times(real)),sin)),sin)),X_1),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,cos,X_1)),hAPP(real,real,sin,X_1))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,cos,X_1)),hAPP(real,real,sin,X_1)))))) # label(fact_3819_DERIV__sin__sin__mult) # label(axiom) # label(non_clause).  [assumption].
7.36/7.44	879 (all L all U_1 hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_gr676655987ssThan(nat),L),U_1)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1),hAPP(nat,nat,suc,L))) # label(fact_3683_card__greaterThanLessThan) # label(axiom) # label(non_clause).  [assumption].
7.36/7.44	880 (all X all Y hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,real_1(int),X)),hAPP(int,real,real_1(int),Y)) = hAPP(int,real,real_1(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X),Y))) # label(fact_3339_real__of__int__mult) # label(axiom) # label(non_clause).  [assumption].
7.36/7.44	881 (all X_a (topological_space(X_a) -> (all A_2 hBOOL(hAPP(filter(X_a),bool,hAPP(X_a,fun(filter(X_a),bool),hAPP(fun(X_a,X_a),fun(X_a,fun(filter(X_a),bool)),tendsto(X_a,X_a),combi(X_a)),A_2),hAPP(X_a,filter(X_a),at(X_a),A_2)))))) # label(fact_4560_LIM__ident) # label(axiom) # label(non_clause).  [assumption].
7.36/7.44	882 (all N (N != zero_zero(nat) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),one_one(nat))),N)))) # label(fact_2876_coprime__minus1) # label(axiom) # label(non_clause).  [assumption].
7.36/7.44	883 (all A_9 all B_8 all Q_6 all Y (ti(int,A_9) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B_8),Q_6)),Y) -> ((-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B_8)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B_8),Y)) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Y),zero_zero(int)))) & (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B_8)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Y)) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Y),B_8))) -> (ti(int,B_8) != zero_zero(int) -> ti(int,Y) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_9),B_8))))) # label(fact_1056_divmod__int__rel__mod__eq) # label(axiom) # label(non_clause).  [assumption].
7.36/7.44	884 (all X_a (cancel_semigroup_add(X_a) -> (all A_2 all B_1 all C_1 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),B_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),C_1) <-> ti(X_a,B_1) = ti(X_a,C_1))))) # label(fact_770_add__left__cancel) # label(axiom) # label(non_clause).  [assumption].
7.36/7.44	885 (all X_a (linordered_field(X_a) -> (all N hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,inverse_inverse(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),hAPP(nat,nat,fact_fact(nat),N)))))))) # label(fact_2613_inv__of__nat__fact__gt__zero) # label(axiom) # label(non_clause).  [assumption].
7.36/7.44	886 (all X_a (semiring_div(X_a) -> (all A_1 all B (ti(X_a,B) != zero_zero(X_a) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),A_1)),B) = ti(X_a,A_1))))) # label(fact_996_div__mult__self1__is__id) # label(axiom) # label(non_clause).  [assumption].
7.36/7.44	887 (all X all P_5 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),P_5)) -> (hBOOL(hAPP(int,bool,zprime,P_5)) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,X),zero_zero(int)),P_5)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(int,int,hAPP(int,fun(int,int),multInv,P_5),hAPP(int,int,hAPP(int,fun(int,int),multInv,P_5),X))),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X),hAPP(int,int,hAPP(int,fun(int,int),multInv,P_5),X))),hAPP(int,int,hAPP(int,fun(int,int),multInv,P_5),hAPP(int,int,hAPP(int,fun(int,int),multInv,P_5),X)))),P_5)))))) # label(fact_848_Int2_Oaux____1) # label(axiom) # label(non_clause).  [assumption].
7.36/7.44	888 (all Ma all N_1 (ti(int,Ma) = one_one(int) & one_one(int) = ti(int,N_1) | ti(int,Ma) = hAPP(int,int,number_number_of(int),min_1) & ti(int,N_1) = hAPP(int,int,number_number_of(int),min_1) <-> hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Ma),N_1) = one_one(int))) # label(fact_308_zmult__eq__1__iff) # label(axiom) # label(non_clause).  [assumption].
7.36/7.44	889 (all B_1 all A_2 all P_4 (hBOOL(hAPP(int,bool,zprime,P_4)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_2),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),P_4),one_one(int)))) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),B_1),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),wset,A_2),P_4))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B_1),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),P_4),one_one(int)))))))) # label(fact_840_wset__less) # label(axiom) # label(non_clause).  [assumption].
7.36/7.44	890 (all X all Y hAPP(real,real,sin,hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),X),Y)) = hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,sin,X)),hAPP(real,real,cos,Y))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,cos,X)),hAPP(real,real,sin,Y)))) # label(fact_2323_sin__diff) # label(axiom) # label(non_clause).  [assumption].
7.36/7.44	891 (all X_1 all Y_1 (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X_1),Y_1)),zEven)) -> hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),zEven)) | hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Y_1),zEven)))) # label(fact_1270_EvenOdd_Oeven__product) # label(axiom) # label(non_clause).  [assumption].
7.36/7.44	892 (all X_a all X_b (topological_space(X_b) -> (all K all A_3 hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(X_b,fun(X_a,X_b),combk(X_b,X_a),K)),K),A_3))))) # label(fact_4460_tendsto__const) # label(axiom) # label(non_clause).  [assumption].
7.36/7.44	893 (all X_a all X_b all A_3 all B_2 all P_1 (hBOOL(hAPP(fun(product_prod(fun(X_a,bool),fun(X_b,bool)),bool),bool,hAPP(product_prod(fun(X_a,bool),fun(X_b,bool)),fun(fun(product_prod(fun(X_a,bool),fun(X_b,bool)),bool),bool),member(product_prod(fun(X_a,bool),fun(X_b,bool))),hAPP(fun(X_b,bool),product_prod(fun(X_a,bool),fun(X_b,bool)),hAPP(fun(X_a,bool),fun(fun(X_b,bool),product_prod(fun(X_a,bool),fun(X_b,bool))),product_Pair(fun(X_a,bool),fun(X_b,bool)),A_3),B_2)),hAPP(fun(X_a,fun(X_b,bool)),fun(product_prod(fun(X_a,bool),fun(X_b,bool)),bool),bijR(X_a,X_b),P_1))) -> hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),B_2)))) # label(fact_4877_fin__bijRr) # label(axiom) # label(non_clause).  [assumption].
7.36/7.44	894 (all Y_1 all X_1 (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),zEven)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Y_1),zEven)) -> hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X_1),Y_1)),zEven))))) # label(fact_1273_even__minus__even) # label(axiom) # label(non_clause).  [assumption].
7.36/7.44	895 (all X_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X_1)) -> hBOOL(hAPP(real,bool,hAPP(fun(real,real),fun(real,bool),isCont(real,real),hAPP(nat,fun(real,real),root,N_1)),X_1))))) # label(fact_4919_isCont__root__pos) # label(axiom) # label(non_clause).  [assumption].
7.36/7.44	896 (all A_1 all C all D all B (zero_zero(int) != ti(int,B) -> (zero_zero(int) != ti(int,D) -> hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(int,rat,hAPP(int,fun(int,rat),fract,A_1),B)),hAPP(int,rat,hAPP(int,fun(int,rat),fract,C),D)) = hAPP(int,rat,hAPP(int,fun(int,rat),fract,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),D)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),B))),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),D))))) # label(fact_3785_add__rat) # label(axiom) # label(non_clause).  [assumption].
7.36/7.44	897 (all N all M (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),M)) -> M != N)) # label(fact_518_less__not__refl2) # label(axiom) # label(non_clause).  [assumption].
7.36/7.44	898 (all X_a (divisi14063676e_zero(X_a) -> (all A_1 hAPP(X_a,X_a,inverse_inverse(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),A_1)) = hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(X_a,X_a,inverse_inverse(X_a),A_1))))) # label(fact_2536_inverse__minus__eq) # label(axiom) # label(non_clause).  [assumption].
7.36/7.44	899 (all X_1 all Y_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_1),Y_1)) | Y_1 = X_1 <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_1),Y_1)))) # label(fact_654_less__eq__real__def) # label(axiom) # label(non_clause).  [assumption].
7.36/7.44	900 (all X_a (number(X_a) -> number_number_of(X_a) = ti(fun(int,X_a),number_number_of(X_a)))) # label(tsy_c_Int_Onumber__class_Onumber__of_res) # label(axiom) # label(non_clause).  [assumption].
7.36/7.44	901 (all V_3 all K_4 all V ((-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V),pls)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),V),V_3))),K_4) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),V)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),V_3)),K_4))) & (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V),pls)) -> zero_zero(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),V)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),V_3)),K_4))))) # label(fact_232_nat__number__of__mult__left) # label(axiom) # label(non_clause).  [assumption].
7.36/7.44	902 (all N all Z_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Z_1)) -> hAPP(int,nat,nat_1,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),Z_1),N)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),hAPP(int,nat,nat_1,Z_1)),N))) # label(fact_1146_nat__power__eq) # label(axiom) # label(non_clause).  [assumption].
7.36/7.44	903 (all X_a (linordered_field(X_a) -> (all Y all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),X)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),X),Y)),zero_zero(X_a)))))))) # label(fact_1680_divide__pos__neg) # label(axiom) # label(non_clause).  [assumption].
7.36/7.44	904 (all X_a (group_add(X_a) -> (all A_1 ti(X_a,A_1) = hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),A_1))))) # label(fact_2041_minus__minus) # label(axiom) # label(non_clause).  [assumption].
7.36/7.44	905 (all X_a (linordered_idom(X_a) -> one_one(X_a) = hAPP(X_a,X_a,abs_abs(X_a),one_one(X_a)))) # label(fact_1853_abs__one) # label(axiom) # label(non_clause).  [assumption].
7.36/7.44	906 (all X_1 all Y_1 (hBOOL(hAPP(nat,bool,even_odd_even(nat),Y_1)) | hBOOL(hAPP(nat,bool,even_odd_even(nat),X_1)) <-> hBOOL(hAPP(nat,bool,even_odd_even(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X_1),Y_1))))) # label(fact_2419_even__product__nat) # label(axiom) # label(non_clause).  [assumption].
7.36/7.44	907 (all X_a (number_ring(X_a) -> (all X all Y hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),Y),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),X)),Y)) = hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),X),Y)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))) # label(fact_591_power2__diff) # label(axiom) # label(non_clause).  [assumption].
7.36/7.44	908 (all X_a (real_n2089651433ebra_1(X_a) -> one_one(real) = hAPP(X_a,real,norm_norm(X_a),one_one(X_a)))) # label(fact_1781_norm__one) # label(axiom) # label(non_clause).  [assumption].
7.36/7.44	909 (all I_1 all J_2 all K_4 hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I_1),J_2)),K_4) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J_2),K_4))) # label(fact_666_diff__diff__left) # label(axiom) # label(non_clause).  [assumption].
7.36/7.44	910 (all X_a all X_b all R_3 all S (hBOOL(hAPP(fun(product_prod(X_a,X_b),bool),bool,hAPP(fun(product_prod(X_a,X_b),bool),fun(fun(product_prod(X_a,X_b),bool),bool),ord_less_eq(fun(product_prod(X_a,X_b),bool)),R_3),S)) <-> hBOOL(hAPP(fun(X_a,fun(X_b,bool)),bool,hAPP(fun(X_a,fun(X_b,bool)),fun(fun(X_a,fun(X_b,bool)),bool),ord_less_eq(fun(X_a,fun(X_b,bool))),hAPP(fun(product_prod(X_a,X_b),bool),fun(X_a,fun(X_b,bool)),hAPP(fun(X_a,fun(fun(product_prod(X_a,X_b),bool),fun(X_b,bool))),fun(fun(product_prod(X_a,X_b),bool),fun(X_a,fun(X_b,bool))),combc(X_a,fun(product_prod(X_a,X_b),bool),fun(X_b,bool)),hAPP(fun(X_a,fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool))),fun(X_a,fun(fun(product_prod(X_a,X_b),bool),fun(X_b,bool))),hAPP(fun(fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool)),fun(fun(product_prod(X_a,X_b),bool),fun(X_b,bool))),fun(fun(X_a,fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool))),fun(X_a,fun(fun(product_prod(X_a,X_b),bool),fun(X_b,bool)))),combb(fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool)),fun(fun(product_prod(X_a,X_b),bool),fun(X_b,bool)),X_a),combc(X_b,fun(product_prod(X_a,X_b),bool),bool)),hAPP(fun(X_a,fun(X_b,product_prod(X_a,X_b))),fun(X_a,fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool))),hAPP(fun(fun(X_b,product_prod(X_a,X_b)),fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool))),fun(fun(X_a,fun(X_b,product_prod(X_a,X_b))),fun(X_a,fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool)))),combb(fun(X_b,product_prod(X_a,X_b)),fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool)),X_a),hAPP(fun(product_prod(X_a,X_b),fun(fun(product_prod(X_a,X_b),bool),bool)),fun(fun(X_b,product_prod(X_a,X_b)),fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool))),combb(product_prod(X_a,X_b),fun(fun(product_prod(X_a,X_b),bool),bool),X_b),member(product_prod(X_a,X_b)))),product_Pair(X_a,X_b)))),R_3)),hAPP(fun(product_prod(X_a,X_b),bool),fun(X_a,fun(X_b,bool)),hAPP(fun(X_a,fun(fun(product_prod(X_a,X_b),bool),fun(X_b,bool))),fun(fun(product_prod(X_a,X_b),bool),fun(X_a,fun(X_b,bool))),combc(X_a,fun(product_prod(X_a,X_b),bool),fun(X_b,bool)),hAPP(fun(X_a,fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool))),fun(X_a,fun(fun(product_prod(X_a,X_b),bool),fun(X_b,bool))),hAPP(fun(fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool)),fun(fun(product_prod(X_a,X_b),bool),fun(X_b,bool))),fun(fun(X_a,fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool))),fun(X_a,fun(fun(product_prod(X_a,X_b),bool),fun(X_b,bool)))),combb(fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool)),fun(fun(product_prod(X_a,X_b),bool),fun(X_b,bool)),X_a),combc(X_b,fun(product_prod(X_a,X_b),bool),bool)),hAPP(fun(X_a,fun(X_b,product_prod(X_a,X_b))),fun(X_a,fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool))),hAPP(fun(fun(X_b,product_prod(X_a,X_b)),fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool))),fun(fun(X_a,fun(X_b,product_prod(X_a,X_b))),fun(X_a,fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool)))),combb(fun(X_b,product_prod(X_a,X_b)),fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool)),X_a),hAPP(fun(product_prod(X_a,X_b),fun(fun(product_prod(X_a,X_b),bool),bool)),fun(fun(X_b,product_prod(X_a,X_b)),fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool))),combb(product_prod(X_a,X_b),fun(fun(product_prod(X_a,X_b),bool),bool),X_b),member(product_prod(X_a,X_b)))),product_Pair(X_a,X_b)))),S))))) # label(fact_4335_pred__subset__eq2) # label(axiom) # label(non_clause).  [assumption].
7.36/7.44	911 (all X_a (number_semiring(X_a) -> (all V (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),V)) -> hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,succ,V)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),one_one(X_a)),hAPP(int,X_a,number_number_of(X_a),V)))))) # label(fact_1534_semiring__1__add__number__of) # label(axiom) # label(non_clause).  [assumption].
7.36/7.44	912 (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_786_add__less__imp__less__left) # label(axiom) # label(non_clause).  [assumption].
7.36/7.44	913 (all M hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),zero_zero(nat)) = M) # label(fact_542_Nat_Oadd__0__right) # label(axiom) # label(non_clause).  [assumption].
7.36/7.44	914 (all W_1 all Z (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),one_one(int)))) <-> ti(int,W_1) = ti(int,Z) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_1),Z)))) # label(fact_167_zless__add1__eq) # label(axiom) # label(non_clause).  [assumption].
7.36/7.44	915 (all Z_1 hAPP(real,real,hAPP(real,fun(real,real),times_times(real),one_one(real)),Z_1) = Z_1) # label(fact_703_real__mult__1) # label(axiom) # label(non_clause).  [assumption].
7.36/7.44	916 (all X_a all X_b (real_normed_vector(X_b) -> (all F all A_3 (hBOOL(hAPP(filter(X_a),bool,hAPP(real,fun(filter(X_a),bool),hAPP(fun(X_a,real),fun(real,fun(filter(X_a),bool)),tendsto(X_a,real),hAPP(fun(X_a,X_b),fun(X_a,real),hAPP(fun(X_b,real),fun(fun(X_a,X_b),fun(X_a,real)),combb(X_b,real,X_a),norm_norm(X_b)),F)),zero_zero(real)),A_3)) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),zero_zero(X_b)),A_3)))))) # label(fact_4453_tendsto__norm__zero__cancel) # label(axiom) # label(non_clause).  [assumption].
7.36/7.44	917 (all X all Y hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),nat_lcm,hAPP(int,nat,nat_1,hAPP(int,int,abs_abs(int),X))),hAPP(int,nat,nat_1,hAPP(int,int,abs_abs(int),Y)))) = hAPP(int,int,hAPP(int,fun(int,int),int_lcm,X),Y)) # label(fact_3631_Nitpick_Oint__lcm__def) # label(axiom) # label(non_clause).  [assumption].
7.36/7.44	918 (all M all N hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),M),N) = hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),M),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),M),N))) # label(fact_4355_gcd__add2__int) # label(axiom) # label(non_clause).  [assumption].
7.36/7.44	919 (all L all U_1 hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_gr676655987ssThan(nat),L),U_1)))) # label(fact_3681_finite__greaterThanLessThan) # label(axiom) # label(non_clause).  [assumption].
7.36/7.44	920 (all Ma all X_2 all Xa (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,X_2),Xa),Ma)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcongm,Ma),X_2),Xa)))) # label(fact_4872_zcongm__def) # label(axiom) # label(non_clause).  [assumption].
7.36/7.44	921 (all X_a all X_b (ordere779506340up_add(X_b) & comm_monoid_add(X_b) -> (all F all A_3 ((all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_3)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_a,X_b,F,X_2)),zero_zero(X_b))))) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),F),A_3)),zero_zero(X_b))))))) # label(fact_4308_setsum__nonpos) # label(axiom) # label(non_clause).  [assumption].
7.36/7.44	922 (all X_a (linordered_semidom(X_a) -> (all M all N (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),M)),hAPP(nat,X_a,semiring_1_of_nat(X_a),N))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N)))))) # label(fact_1282_of__nat__less__imp__less) # label(axiom) # label(non_clause).  [assumption].
7.36/7.44	923 (all P_4 hAPP(int,fun(int,bool),sRStar,P_4) = hAPP(fun(int,bool),fun(int,bool),collect(int),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),combs(int,bool,bool),hAPP(fun(int,bool),fun(int,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj),hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)))),hAPP(int,fun(int,bool),hAPP(fun(int,fun(int,bool)),fun(int,fun(int,bool)),combc(int,int,bool),ord_less(int)),P_4)))) # label(fact_1129_SRStar__def) # label(axiom) # label(non_clause).  [assumption].
7.36/7.44	924 (all X_a all X_c all B_1_1 all B_2_1 hAPP(X_a,X_c,ti(fun(X_a,X_c),B_1_1),B_2_1) = hAPP(X_a,X_c,B_1_1,B_2_1)) # label(tsy_c_hAPP_arg1) # label(axiom) # label(non_clause).  [assumption].
7.36/7.44	925 (all X_a (real_normed_algebra(X_a) -> (all A_1 all B all B_5 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B_5)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),B),B_5))))) # label(fact_887_mult_Odiff__right) # label(axiom) # label(non_clause).  [assumption].
7.36/7.44	926 (all X all Y hAPP(complex,real,norm_norm(complex),hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,X),Y)) = hAPP(real,real,sqrt,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),Y),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))) # label(fact_2735_complex__norm) # label(axiom) # label(non_clause).  [assumption].
7.36/7.44	927 (all F all Y_1 all X_1 all A_2 all B_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A_2),B_1)) -> (hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),X_1),hAPP(real,fun(real,bool),hAPP(real,fun(real,fun(real,bool)),ord_gr676655987ssThan(real),A_2),B_1))) -> (hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),Y_1),hAPP(real,fun(real,bool),hAPP(real,fun(real,fun(real,bool)),ord_gr676655987ssThan(real),A_2),B_1))) -> ((all X_2 (hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),X_2),hAPP(real,fun(real,bool),hAPP(real,fun(real,fun(real,bool)),ord_gr676655987ssThan(real),A_2),B_1))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),F),X_2),zero_zero(real))))) -> hAPP(real,real,F,X_1) = hAPP(real,real,F,Y_1)))))) # label(fact_3687_DERIV__isconst3) # label(axiom) # label(non_clause).  [assumption].
7.36/7.45	928 (all B all A_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A_1),zero_zero(int))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_1),B)),zero_zero(int)))))) # label(fact_1018_div__nonpos__pos__le0) # label(axiom) # label(non_clause).  [assumption].
7.36/7.45	929 (all K_4 ((zero_zero(quickcheck_code_int) = K_4 -> hAPP(quickcheck_code_int,int,quickcheck_int_of,K_4) = zero_zero(int)) & (zero_zero(quickcheck_code_int) != K_4 -> (hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),K_4),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = zero_zero(quickcheck_code_int) -> hAPP(quickcheck_code_int,int,quickcheck_int_of,K_4) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),hAPP(quickcheck_code_int,int,quickcheck_int_of,hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),K_4),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))) & (zero_zero(quickcheck_code_int) != hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),K_4),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) -> hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),hAPP(quickcheck_code_int,int,quickcheck_int_of,hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),K_4),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))),one_one(int)) = hAPP(quickcheck_code_int,int,quickcheck_int_of,K_4))))) # label(fact_3157_Quickcheck__Narrowing_Oint__of__code) # label(axiom) # label(non_clause).  [assumption].
7.36/7.45	930 (all M all K_4 all N (one_one(int) = hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,K_4),N) -> hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K_4),M)),N) = hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,M),N))) # label(fact_3430_zgcd__zmult__cancel) # label(axiom) # label(non_clause).  [assumption].
7.36/7.45	931 (all X_a (semiring_div(X_a) -> (all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_1),B)) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),B),A_1)),A_1) = ti(X_a,B))))) # label(fact_1002_dvd__div__mult__self) # label(axiom) # label(non_clause).  [assumption].
7.36/7.45	932 (all Z all Y_1 all X_1 all X_3 (hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),X_1),X_3)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),Y_1),X_1)) -> ((all X_2 (hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),X_2),X_3)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_2),Z)))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),Y_1),hAPP(fun(real,bool),real,complete_Sup_Sup(real),X_3))))))) # label(fact_3714_SupInf_OSup__upper2) # label(axiom) # label(non_clause).  [assumption].
7.36/7.45	933 (all X hAPP(real,real,sqrt,hAPP(real,real,uminus_uminus(real),X)) = hAPP(real,real,uminus_uminus(real),hAPP(real,real,sqrt,X))) # label(fact_2054_real__sqrt__minus) # label(axiom) # label(non_clause).  [assumption].
7.36/7.45	934 (all X_a (real_n2089651433ebra_1(X_a) & banach(X_a) -> (all X_1 hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,X_a),fun(nat,real),hAPP(fun(X_a,real),fun(fun(nat,X_a),fun(nat,real)),combb(X_a,real,nat),norm_norm(X_a)),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,real),fun(nat,fun(X_a,X_a)),hAPP(fun(real,fun(X_a,X_a)),fun(fun(nat,real),fun(nat,fun(X_a,X_a))),combb(real,fun(X_a,X_a),nat),scaleR_scaleR(X_a)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),inverse_inverse(real)),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),fact_fact(nat))))),hAPP(X_a,fun(nat,X_a),power_power(X_a),X_1)))))))) # label(fact_4749_summable__norm__exp) # label(axiom) # label(non_clause).  [assumption].
7.45/7.45	935 (all X_a all X_1 all A_3 all B_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_3),B_2)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_3)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),B_2))))) # label(fact_1956_in__mono) # label(axiom) # label(non_clause).  [assumption].
7.45/7.45	936 (all X_a (semiri456707255roduct(X_a) -> (all C all D all A_1 all B all R_4 (zero_zero(X_a) != ti(X_a,R_4) -> (ti(X_a,A_1) = ti(X_a,B) & ti(X_a,D) != ti(X_a,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),times_times(X_a),R_4),C)) != hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),R_4),D))))))) # label(fact_252_add__scale__eq__noteq) # label(axiom) # label(non_clause).  [assumption].
7.45/7.45	937 (all A_2 all B_1 (hBOOL(hAPP(product_prod(int,int),bool,hAPP(fun(product_prod(int,int),fun(product_prod(int,int),bool)),fun(product_prod(int,int),bool),accp(product_prod(int,int)),norm_frac_rel),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),A_2),B_1))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B_1),zero_zero(int))) -> hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),norm_frac,A_2),B_1) = hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),norm_frac,hAPP(int,int,uminus_uminus(int),A_2)),hAPP(int,int,uminus_uminus(int),B_1))) & (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B_1),zero_zero(int))) -> (-(ti(int,A_2) = zero_zero(int) | zero_zero(int) = ti(int,B_1)) -> hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_2),hAPP(int,int,hAPP(int,fun(int,int),int_gcd,A_2),B_1))),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),B_1),hAPP(int,int,hAPP(int,fun(int,int),int_gcd,A_2),B_1))) = hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),norm_frac,A_2),B_1)) & (zero_zero(int) = ti(int,B_1) | zero_zero(int) = ti(int,A_2) -> hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),zero_zero(int)),one_one(int)) = hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),norm_frac,A_2),B_1))))) # label(fact_3919_norm__frac_Opsimps) # label(axiom) # label(non_clause).  [assumption].
7.45/7.45	938 (all Ma all N_1 all K (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),Ma)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),N_1))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Ma),N_1))))) # label(fact_741_nat__mult__dvd__cancel1) # label(axiom) # label(non_clause).  [assumption].
7.45/7.45	939 (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_173_numeral__1__eq__1) # label(axiom) # label(non_clause).  [assumption].
7.45/7.45	940 (all X_a (ordere236663937imp_le(X_a) -> (all C_1 all A_2 all B_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),B_1)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C_1),A_2)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C_1),B_1))))))) # label(fact_791_add__less__cancel__left) # label(axiom) # label(non_clause).  [assumption].
7.45/7.45	941 (all X_a (archim1804426504_field(X_a) -> (all Y all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),X)) -> (exists N_2 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),N_2)),X)))))))) # label(fact_2724_ex__less__of__nat__mult) # label(axiom) # label(non_clause).  [assumption].
7.45/7.45	942 (all Z all W_1 (ti(int,Z) != ti(int,W_1) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Z),W_1)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Z),W_1)))) # label(fact_37_zless__le) # label(axiom) # label(non_clause).  [assumption].
7.45/7.45	943 (all Z all X_1 all X_3 (hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),X_1),X_3)) -> ((all X_2 (hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),X_2),X_3)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_2),Z)))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_1),hAPP(fun(real,bool),real,complete_Sup_Sup(real),X_3)))))) # label(fact_3706_SupInf_OSup__upper) # label(axiom) # label(non_clause).  [assumption].
7.45/7.45	944 (all A_1 all C all D all B (ti(int,B) != zero_zero(int) -> (zero_zero(int) != ti(int,D) -> hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),hAPP(int,rat,hAPP(int,fun(int,rat),fract,A_1),B)),hAPP(int,rat,hAPP(int,fun(int,rat),fract,C),D)) = hAPP(int,rat,hAPP(int,fun(int,rat),fract,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),D)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),B))),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),D))))) # label(fact_3786_diff__rat) # label(axiom) # label(non_clause).  [assumption].
7.45/7.45	945 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X),pi)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(real,real,sin,X)))))) # label(fact_2313_sin__ge__zero) # label(axiom) # label(non_clause).  [assumption].
7.45/7.45	946 (all X_a combi(X_a) = ti(fun(X_a,X_a),combi(X_a))) # label(tsy_c_COMBI_res) # label(axiom) # label(non_clause).  [assumption].
7.45/7.45	947 (all V all W hAPP(int,int,number_number_of(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),V),hAPP(int,int,uminus_uminus(int),W))) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,number_number_of(int),V)),hAPP(int,int,number_number_of(int),W))) # label(fact_2169_minus__numeral__code_I6_J) # label(axiom) # label(non_clause).  [assumption].
7.45/7.45	948 (all X_a (real_normed_algebra(X_a) -> (all X all Y hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),Y)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),X)),Y)))) # label(fact_2035_mult__left_Ominus) # label(axiom) # label(non_clause).  [assumption].
7.45/7.45	949 (all X (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) -> ti(int,X) = zero_zero(int) | ti(int,X) = one_one(int)))) # label(fact_185_int__pos__lt__two__imp__zero__or__one) # label(axiom) # label(non_clause).  [assumption].
7.45/7.45	950 (all X_a (ring_div(X_a) -> (all A_1 all B all C hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),A_1),C)),B)),C) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_1),B)),C)))) # label(fact_945_mod__diff__left__eq) # label(axiom) # label(non_clause).  [assumption].
7.45/7.45	951 (all A_2 all Ma hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),bnorRset,A_2),Ma)))) # label(fact_3208_Bnor__fin) # label(axiom) # label(non_clause).  [assumption].
7.45/7.45	952 (all X_a all X_b (comm_semiring_1(X_b) & no_zero_divisors(X_b) -> (all F all A_3 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_3)) -> ((exists X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_3)) & hAPP(X_a,X_b,F,X_2) = zero_zero(X_b))) <-> zero_zero(X_b) = hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co302546470etprod(X_a,X_b),F),A_3)))))) # label(fact_3949_setprod__zero__iff) # label(axiom) # label(non_clause).  [assumption].
7.45/7.45	953 (all A_1 all B (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B)) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_1),B)) -> hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),posDivAlg,A_1),B) = hAPP(product_prod(int,int),product_prod(int,int),hAPP(int,fun(product_prod(int,int),product_prod(int,int)),adjust,B),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),posDivAlg,A_1),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),B)))) & (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_1),B)) -> hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),zero_zero(int)),A_1) = hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),posDivAlg,A_1),B)))) # label(fact_1167_posDivAlg__eqn) # label(axiom) # label(non_clause).  [assumption].
7.45/7.45	954 (all X_a (t2_space(X_a) & comm_monoid_add(X_a) -> (all F (hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),F)) -> hBOOL(hAPP(X_a,bool,hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),F),hAPP(fun(nat,X_a),X_a,suminf(X_a),F))))))) # label(fact_4092_summable__sums) # label(axiom) # label(non_clause).  [assumption].
7.45/7.45	955 (all X all Y all Z_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),Z_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Y),Z_1))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),X),Z_1)),Y))))) # label(fact_1027_div__prop1) # label(axiom) # label(non_clause).  [assumption].
7.45/7.45	956 (all Z_1 hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,cnj,Z_1)) = hAPP(complex,real,norm_norm(complex),Z_1)) # label(fact_2941_complex__mod__cnj) # label(axiom) # label(non_clause).  [assumption].
7.45/7.45	957 (all X_a (topological_space(X_a) -> (all F all A_2 (hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,real),fun(X_a,bool),isCont(X_a,real),F),A_2)) -> hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,real),fun(X_a,bool),isCont(X_a,real),hAPP(fun(X_a,real),fun(X_a,real),hAPP(fun(real,real),fun(fun(X_a,real),fun(X_a,real)),combb(real,real,X_a),abs_abs(real)),F)),A_2)))))) # label(fact_4906_isCont__rabs) # label(axiom) # label(non_clause).  [assumption].
7.45/7.45	958 (all Ma all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Ma),hAPP(nat,nat,suc,N_1))) <-> hAPP(nat,nat,suc,N_1) = Ma | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Ma),N_1)))) # label(fact_1245_le__Suc__eq) # label(axiom) # label(non_clause).  [assumption].
7.45/7.45	959 (all N_1 all A_2 all B_1 all P_1 ((all A_4 all B_4 all C_4 (hBOOL(hAPP(product_prod(real,real),bool,P_1,hAPP(real,product_prod(real,real),hAPP(real,fun(real,product_prod(real,real)),product_Pair(real,real),A_4),B_4))) -> (hBOOL(hAPP(product_prod(real,real),bool,P_1,hAPP(real,product_prod(real,real),hAPP(real,fun(real,product_prod(real,real)),product_Pair(real,real),B_4),C_4))) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A_4),B_4)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B_4),C_4)) -> hBOOL(hAPP(product_prod(real,real),bool,P_1,hAPP(real,product_prod(real,real),hAPP(real,fun(real,product_prod(real,real)),product_Pair(real,real),A_4),C_4)))))))) -> (-hBOOL(hAPP(product_prod(real,real),bool,P_1,hAPP(real,product_prod(real,real),hAPP(real,fun(real,product_prod(real,real)),product_Pair(real,real),A_2),B_1))) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A_2),B_1)) -> -hBOOL(hAPP(product_prod(real,real),bool,P_1,hAPP(real,product_prod(real,real),hAPP(real,fun(real,product_prod(real,real)),product_Pair(real,real),hAPP(product_prod(real,real),real,product_fst(real,real),hAPP(nat,product_prod(real,real),hAPP(real,fun(nat,product_prod(real,real)),hAPP(real,fun(real,fun(nat,product_prod(real,real))),hAPP(fun(product_prod(real,real),bool),fun(real,fun(real,fun(nat,product_prod(real,real)))),bolzano_bisect,P_1),A_2),B_1),N_1))),hAPP(product_prod(real,real),real,product_snd(real,real),hAPP(nat,product_prod(real,real),hAPP(real,fun(nat,product_prod(real,real)),hAPP(real,fun(real,fun(nat,product_prod(real,real))),hAPP(fun(product_prod(real,real),bool),fun(real,fun(real,fun(nat,product_prod(real,real)))),bolzano_bisect,P_1),A_2),B_1),N_1))))))))) # label(fact_3144_not__P__Bolzano__bisect) # label(axiom) # label(non_clause).  [assumption].
7.45/7.45	960 (all X_a (linordered_idom(X_a) -> (all Z (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(int,X_a,ring_1_of_int(X_a),Z)),zero_zero(X_a))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Z),zero_zero(int))))))) # label(fact_3601_of__int__less__0__iff) # label(axiom) # label(non_clause).  [assumption].
7.45/7.45	961 (all X_1 (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),zOdd)) -> hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X_1),one_one(int))),zEven)))) # label(fact_1400_odd__minus__one__even) # label(axiom) # label(non_clause).  [assumption].
7.45/7.45	962 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X),zero_zero(real))) -> hAPP(real,nat,natceiling,X) = zero_zero(nat))) # label(fact_1899_natceiling__neg) # label(axiom) # label(non_clause).  [assumption].
7.45/7.45	963 (all D_1 hAPP(fun(product_prod(int,int),bool),fun(product_prod(int,int),bool),collect(product_prod(int,int)),hAPP(fun(int,fun(int,bool)),fun(product_prod(int,int),bool),product_prod_case(int,int,bool),hAPP(fun(int,fun(int,bool)),fun(int,fun(int,bool)),hAPP(fun(int,fun(fun(int,bool),fun(int,bool))),fun(fun(int,fun(int,bool)),fun(int,fun(int,bool))),combs(int,fun(int,bool),fun(int,bool)),hAPP(fun(int,fun(bool,bool)),fun(int,fun(fun(int,bool),fun(int,bool))),hAPP(fun(fun(bool,bool),fun(fun(int,bool),fun(int,bool))),fun(fun(int,fun(bool,bool)),fun(int,fun(fun(int,bool),fun(int,bool)))),combb(fun(bool,bool),fun(fun(int,bool),fun(int,bool)),int),combb(bool,bool,int)),hAPP(fun(int,bool),fun(int,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj),hAPP(int,fun(int,bool),ord_less_eq(int),D_1)))),ord_less(int)))) = hAPP(int,fun(product_prod(int,int),bool),int_ge_less_than,D_1)) # label(fact_4074_int__ge__less__than__def) # label(axiom) # label(non_clause).  [assumption].
7.45/7.45	964 (all X_a all A_3 hBOOL(hAPP(fun(fun(X_a,bool),bool),bool,hAPP(fun(fun(X_a,bool),bool),fun(fun(fun(X_a,bool),bool),bool),ord_less_eq(fun(fun(X_a,bool),bool)),A_3),hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),pow(X_a),hAPP(fun(fun(X_a,bool),bool),fun(X_a,bool),complete_Sup_Sup(fun(X_a,bool)),A_3))))) # label(fact_2806_subset__Pow__Union) # label(axiom) # label(non_clause).  [assumption].
7.45/7.45	965 (all V_3 hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),div_div(int),one_one(int)),hAPP(int,int,number_number_of(int),V_3))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,suc,zero_zero(nat))),hAPP(int,nat,number_number_of(nat),V_3))) # label(fact_1467_one__div__nat__number__of) # label(axiom) # label(non_clause).  [assumption].
7.45/7.45	966 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(real,real,sqrt,X))))) # label(fact_1622_real__sqrt__ge__zero) # label(axiom) # label(non_clause).  [assumption].
7.45/7.45	967 (all X_a (semiring_div(X_a) -> ti(fun(X_a,fun(X_a,X_a)),div_mod(X_a)) = div_mod(X_a))) # label(tsy_c_Divides_Odiv__class_Omod_res) # label(axiom) # label(non_clause).  [assumption].
7.45/7.45	968 (all Q_3 all P_5 (hBOOL(hAPP(nat,bool,prime,P_5)) -> (hBOOL(hAPP(nat,bool,prime,Q_3)) -> (P_5 != Q_3 -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,P_5),Q_3)))))) # label(fact_3049_distinct__prime__coprime) # label(axiom) # label(non_clause).  [assumption].
7.45/7.45	969 (all K_4 all M hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,K_4),K_4),M))) # label(fact_314_zcong__refl) # label(axiom) # label(non_clause).  [assumption].
7.45/7.45	970 (all X_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,real)),combs(real,real,real),hAPP(fun(real,real),fun(real,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,fun(real,real))),combb(real,fun(real,real),real),plus_plus(real)),hAPP(nat,fun(real,real),hAPP(fun(real,fun(nat,real)),fun(nat,fun(real,real)),combc(real,nat,real),hAPP(fun(real,real),fun(real,fun(nat,real)),hAPP(fun(real,fun(nat,real)),fun(fun(real,real),fun(real,fun(nat,real))),combb(real,fun(nat,real),real),power_power(real)),sin)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),hAPP(nat,fun(real,real),hAPP(fun(real,fun(nat,real)),fun(nat,fun(real,real)),combc(real,nat,real),hAPP(fun(real,real),fun(real,fun(nat,real)),hAPP(fun(real,fun(nat,real)),fun(fun(real,real),fun(real,fun(nat,real))),combb(real,fun(nat,real),real),power_power(real)),cos)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),X_2),zero_zero(real)))) # label(fact_3908_DERIV__sin__circle__all__zero) # label(axiom) # label(non_clause).  [assumption].
7.45/7.45	971 (all N all X (-hBOOL(hAPP(int,bool,even_odd_even(int),X)) -> -hBOOL(hAPP(int,bool,even_odd_even(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),X),N))))) # label(fact_1267_odd__pow) # label(axiom) # label(non_clause).  [assumption].
7.45/7.45	972 (all N hAPP(nat,int,semiring_1_of_nat(int),N) = hAPP(real,int,archimedean_ceiling(real),hAPP(nat,real,real_1(nat),N))) # label(fact_3278_ceiling__real__of__nat) # label(axiom) # label(non_clause).  [assumption].
7.45/7.45	973 (all P_4 (hBOOL(hAPP(int,bool,zprime,P_4)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),P_4)) <-> hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),P_4),zOdd))))) # label(fact_1068_zprime__zOdd__eq__grt__2) # label(axiom) # label(non_clause).  [assumption].
7.45/7.45	974 (all M all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N),M) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),N)) # label(fact_531_nat__mult__commute) # label(axiom) # label(non_clause).  [assumption].
7.45/7.45	975 (all Ta all B_2 all D_1 all D_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),D_1),D_2)) -> (all X_2 ((all Xa (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xa),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastAtMost(int),one_one(int)),D_2))) -> (all Xb (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xb),B_2)) -> hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Xb),Xa) != ti(int,X_2))))) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),D_1),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X_2),Ta))) -> -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),D_1),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X_2),D_2)),Ta)))))))) # label(fact_4648_bset_I10_J) # label(axiom) # label(non_clause).  [assumption].
7.45/7.45	976 (all X_a (archim1727834104eiling(X_a) -> (all X hAPP(int,int,uminus_uminus(int),hAPP(X_a,int,archim2085082626_floor(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),X))) = hAPP(X_a,int,archimedean_ceiling(X_a),X)))) # label(fact_3295_ceiling__def) # label(axiom) # label(non_clause).  [assumption].
7.45/7.45	977 (all K_4 all M all N hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,K_4),M)),N) = hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,K_4),hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,M),N))) # label(fact_3438_zgcd__assoc) # label(axiom) # label(non_clause).  [assumption].
7.45/7.45	978 (all X_a (ring_1(X_a) -> hAPP(int,X_a,ring_1_of_int(X_a),zero_zero(int)) = zero_zero(X_a))) # label(fact_3580_of__int__0) # label(axiom) # label(non_clause).  [assumption].
7.45/7.45	979 (all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,number_number_of(real),min_1)),X_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_1),one_one(real))) -> hBOOL(hAPP(real,bool,hAPP(fun(real,real),fun(real,bool),isCont(real,real),arcsin),X_1))))) # label(fact_4922_isCont__arcsin) # label(axiom) # label(non_clause).  [assumption].
7.45/7.45	980 (all X all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X),Y)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,arctan,X)),hAPP(real,real,arctan,Y))))) # label(fact_1834_arctan__monotone_H) # label(axiom) # label(non_clause).  [assumption].
7.45/7.45	981 (all X_a all A_3 all B_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),B_2)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_3),B_2)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X_a,bool),nat,finite_card(X_a),A_3)),hAPP(fun(X_a,bool),nat,finite_card(X_a),B_2)))))) # label(fact_1816_card__mono) # label(axiom) # label(non_clause).  [assumption].
7.45/7.45	982 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,M)),hAPP(nat,nat,suc,N))))) # label(fact_1206_Suc__mono) # label(axiom) # label(non_clause).  [assumption].
7.45/7.45	983 (all X_a all X_b (comm_monoid_mult(X_b) -> ti(fun(fun(X_a,X_b),fun(fun(X_a,bool),X_b)),big_co302546470etprod(X_a,X_b)) = big_co302546470etprod(X_a,X_b))) # label(tsy_c_Big__Operators_Ocomm__monoid__mult__class_Osetprod_res) # label(axiom) # label(non_clause).  [assumption].
7.45/7.45	984 (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_1414_Suc__diff__1) # label(axiom) # label(non_clause).  [assumption].
7.45/7.45	985 (all P_5 hAPP(product_prod(int,int),rat,frct,P_5) = hAPP(int,rat,hAPP(int,fun(int,rat),fract,hAPP(product_prod(int,int),int,product_fst(int,int),P_5)),hAPP(product_prod(int,int),int,product_snd(int,int),P_5))) # label(fact_3778_Frct__def) # label(axiom) # label(non_clause).  [assumption].
7.45/7.45	986 (all M all N hAPP(nat,product_prod(nat,nat),hAPP(nat,fun(nat,product_prod(nat,nat)),divmod_nat,M),N) = hAPP(nat,product_prod(nat,nat),hAPP(nat,fun(nat,product_prod(nat,nat)),product_Pair(nat,nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),M),N)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),M),N))) # label(fact_3094_divmod__nat__div__mod) # label(axiom) # label(non_clause).  [assumption].
7.45/7.45	987 (all X_a all A_3 all B_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_3),B_2)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),uminus_uminus(fun(X_a,bool)),B_2)),hAPP(fun(X_a,bool),fun(X_a,bool),uminus_uminus(fun(X_a,bool)),A_3))))) # label(fact_2136_Compl__anti__mono) # label(axiom) # label(non_clause).  [assumption].
7.45/7.45	988 (all N hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,uminus_uminus(int),hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,N)))),zero_zero(int)))) # label(fact_2175_negative__zless__0) # label(axiom) # label(non_clause).  [assumption].
7.45/7.45	989 (all X_3 all A_2 (hBOOL(hAPP(filter(nat),bool,hAPP(complex,fun(filter(nat),bool),hAPP(fun(nat,complex),fun(complex,fun(filter(nat),bool)),tendsto(nat,complex),X_3),A_2),sequentially)) -> hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),hAPP(fun(nat,complex),fun(nat,real),hAPP(fun(complex,real),fun(fun(nat,complex),fun(nat,real)),combb(complex,real,nat),im),X_3)),hAPP(complex,real,im,A_2)),sequentially)))) # label(fact_4512_Im_OLIMSEQ) # label(axiom) # label(non_clause).  [assumption].
7.45/7.45	990 (all X_a all X_b all C_1 all P_4 (hBOOL(hAPP(product_prod(X_a,X_b),bool,hAPP(fun(X_a,fun(X_b,bool)),fun(product_prod(X_a,X_b),bool),product_prod_case(X_a,X_b,bool),C_1),P_4)) -> -(all X_2 all Y_2 (hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),X_2),Y_2) = ti(product_prod(X_a,X_b),P_4) -> -hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),C_1,X_2),Y_2)))))) # label(fact_4062_splitE) # label(axiom) # label(non_clause).  [assumption].
7.45/7.45	991 (all X_a (ordered_ab_group_add(X_a) -> (all A_2 all B_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),hAPP(X_a,X_a,uminus_uminus(X_a),B_1))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_1),hAPP(X_a,X_a,uminus_uminus(X_a),A_2))))))) # label(fact_2026_le__minus__iff) # label(axiom) # label(non_clause).  [assumption].
7.45/7.45	992 (all U_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),U_1)) -> hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastLessThan(int),zero_zero(int)),U_1) = hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),hAPP(nat,fun(nat,bool),ord_lessThan(nat),hAPP(int,nat,nat_1,U_1))))) # label(fact_4323_image__atLeastZeroLessThan__int) # label(axiom) # label(non_clause).  [assumption].
7.45/7.45	993 (all Ta all B_2 all D_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D_2)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),Ta),one_one(int))),B_2)) -> (all X_2 ((all Xa (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xa),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastAtMost(int),one_one(int)),D_2))) -> (all Xb (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xb),B_2)) -> ti(int,X_2) != hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Xb),Xa))))) -> (ti(int,X_2) = ti(int,Ta) -> ti(int,Ta) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X_2),D_2))))))) # label(fact_4637_bset_I3_J) # label(axiom) # label(non_clause).  [assumption].
7.45/7.45	994 (all N all A_1 all B all M (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_1),B),M)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_1),B),N)) -> (hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,M),N) = one_one(int) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_1),B),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),M),N))))))) # label(fact_3460_zcong__zgcd__zmult__zmod) # label(axiom) # label(non_clause).  [assumption].
7.45/7.45	995 (all K all Ma all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),K),N_1)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),K),Ma)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),K),hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),Ma),N_1))))) # label(fact_3243_gcd__greatest__iff__nat) # label(axiom) # label(non_clause).  [assumption].
7.45/7.45	996 (all R_4 all Q_3 all A_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A_1)) -> (ti(int,A_1) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),R_4),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),Q_3)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),R_4)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Q_3),one_one(int))))))) # label(fact_190_self__quotient__aux2) # label(axiom) # label(non_clause).  [assumption].
7.45/7.45	997 (all X_a all X_b all X_c all X_d all X_e all X_f all X_1 all P_1 ((all A_4 all B_4 all C_4 all D_3 all E all F_3 hBOOL(hAPP(product_prod(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f))))),bool,P_1,hAPP(product_prod(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f)))),product_prod(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f))))),hAPP(X_a,fun(product_prod(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f)))),product_prod(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f)))))),product_Pair(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f))))),A_4),hAPP(product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f))),product_prod(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f)))),hAPP(X_b,fun(product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f))),product_prod(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f))))),product_Pair(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f)))),B_4),hAPP(product_prod(X_d,product_prod(X_e,X_f)),product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f))),hAPP(X_c,fun(product_prod(X_d,product_prod(X_e,X_f)),product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f)))),product_Pair(X_c,product_prod(X_d,product_prod(X_e,X_f))),C_4),hAPP(product_prod(X_e,X_f),product_prod(X_d,product_prod(X_e,X_f)),hAPP(X_d,fun(product_prod(X_e,X_f),product_prod(X_d,product_prod(X_e,X_f))),product_Pair(X_d,product_prod(X_e,X_f)),D_3),hAPP(X_f,product_prod(X_e,X_f),hAPP(X_e,fun(X_f,product_prod(X_e,X_f)),product_Pair(X_e,X_f),E),F_3)))))))) -> hBOOL(hAPP(product_prod(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f))))),bool,P_1,X_1)))) # label(fact_3150_prod__induct6) # label(axiom) # label(non_clause).  [assumption].
7.45/7.45	998 (all X_a (division_ring(X_a) -> (all B all A_1 (zero_zero(X_a) != ti(X_a,A_1) -> (ti(X_a,B) != zero_zero(X_a) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_a,X_a,inverse_inverse(X_a),A_1)),hAPP(X_a,X_a,inverse_inverse(X_a),B)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,inverse_inverse(X_a),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),B),A_1))),hAPP(X_a,X_a,inverse_inverse(X_a),B))))))) # label(fact_2582_division__ring__inverse__diff) # label(axiom) # label(non_clause).  [assumption].
7.45/7.45	999 (all X_a (real_normed_field(X_a) -> (all Y_3 all B_1 all X_3 all A_2 (hBOOL(hAPP(X_a,bool,hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),X_3),A_2)) -> (hBOOL(hAPP(X_a,bool,hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),Y_3),B_1)) -> hBOOL(hAPP(X_a,bool,hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),plus_plus(X_a)),X_3)),Y_3)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),B_1)))))))) # label(fact_4087_sums__add) # label(axiom) # label(non_clause).  [assumption].
7.45/7.45	1000 (all X_a all Y_3 hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,X_a),fun(fun(X_a,bool),fun(X_a,bool)),image(X_a,X_a),combi(X_a)),Y_3) = ti(fun(X_a,bool),Y_3)) # label(fact_3845_image__ident) # label(axiom) # label(non_clause).  [assumption].
7.45/7.45	1001 (all X_1 (hAPP(real,real,cos,X_1) != zero_zero(real) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),tan),X_1),hAPP(real,real,inverse_inverse(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,cos,X_1)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))))) # label(fact_2653_DERIV__tan) # label(axiom) # label(non_clause).  [assumption].
7.45/7.45	1002 (all X_1 hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),hAPP(int,real,real_1(int),X_1)),ring_1_Ints(real)))) # label(fact_3853_Ints__real__of__int) # label(axiom) # label(non_clause).  [assumption].
7.45/7.45	1003 (all Y_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(real,real,sqrt,Y_1))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),Y_1)))) # label(fact_1624_real__sqrt__ge__0__iff) # label(axiom) # label(non_clause).  [assumption].
7.45/7.45	1004 (all M all N all K_4 hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N),K_4)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),N)),K_4)) # label(fact_532_nat__mult__assoc) # label(axiom) # label(non_clause).  [assumption].
7.45/7.45	1005 (all X_a (metric_space(X_a) -> (all X_3 all L_2 ((all R_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),R_2)) -> (exists No (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),No)) & (all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),No),N_2)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),hAPP(nat,X_a,X_3,N_2)),L_2)),R_2)))))))) <-> hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),X_3),L_2),sequentially)))))) # label(fact_4517_LIMSEQ__iff__nz) # label(axiom) # label(non_clause).  [assumption].
7.45/7.45	1006 (all X hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),hAPP(real,real,cos,X))),one_one(real)))) # label(fact_2218_abs__cos__le__one) # label(axiom) # label(non_clause).  [assumption].
7.45/7.45	1007 (all X_1 (one_one(real) = hAPP(real,real,exp(real),X_1) <-> zero_zero(real) = X_1)) # label(fact_2569_exp__eq__one__iff) # label(axiom) # label(non_clause).  [assumption].
7.45/7.45	1008 (all I all J hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,nat),fun(fun(nat,bool),fun(nat,bool)),image(nat,nat),suc),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),I),J)) = hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,suc,I)),hAPP(nat,nat,suc,J))) # label(fact_4539_image__Suc__atLeastAtMost) # label(axiom) # label(non_clause).  [assumption].
7.45/7.45	1009 (all X_1 all K (ti(int,X_1) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),K) -> hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),zEven)))) # label(fact_1450_zEvenI) # label(axiom) # label(non_clause).  [assumption].
7.45/7.45	1010 (all X_a all B_2 all X_1 all A_3 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_3)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_3),B_2)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),B_2))))) # label(fact_1955_set__rev__mp) # label(axiom) # label(non_clause).  [assumption].
7.45/7.45	1011 (all J all A_2 all P_4 (hBOOL(hAPP(int,bool,zprime,P_4)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),P_4)) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_2),zero_zero(int)),P_4)) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),quadRes,P_4),A_2)) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,J),zero_zero(int)),P_4)) -> hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))) = hAPP(fun(int,bool),nat,finite_card(int),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),hAPP(int,fun(int,fun(int,fun(int,bool))),multInvPair,A_2),P_4),J)))))))) # label(fact_1538_MultInvPair__card__two) # label(axiom) # label(non_clause).  [assumption].
7.45/7.45	1012 (all A_1 all X (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A_1),hAPP(real,int,archim2085082626_floor(real),X))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,real_1(int),A_1)),X)))) # label(fact_3363_real__le__floor) # label(axiom) # label(non_clause).  [assumption].
7.45/7.45	1013 (all X_b all X_a (topological_space(X_a) & real_normed_vector(X_b) -> (all F all A_2 (hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,X_b),fun(X_a,bool),isCont(X_a,X_b),F),A_2)) -> hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,X_b),fun(X_a,bool),isCont(X_a,X_b),hAPP(fun(X_a,X_b),fun(X_a,X_b),hAPP(fun(X_b,X_b),fun(fun(X_a,X_b),fun(X_a,X_b)),combb(X_b,X_b,X_a),uminus_uminus(X_b)),F)),A_2)))))) # label(fact_4905_isCont__minus) # label(axiom) # label(non_clause).  [assumption].
7.45/7.45	1014 (all P_1 all I all K (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),I),K)) -> (hBOOL(hAPP(int,bool,P_1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),K),one_one(int)))) -> ((all I_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),I_2),K)) -> (hBOOL(hAPP(int,bool,P_1,I_2)) -> hBOOL(hAPP(int,bool,P_1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),I_2),one_one(int))))))) -> hBOOL(hAPP(int,bool,P_1,I)))))) # label(fact_833_int__less__induct) # label(axiom) # label(non_clause).  [assumption].
7.45/7.45	1015 (all X all Y hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),X),Y)))) # label(fact_4396_gcd__ge__0__int) # label(axiom) # label(non_clause).  [assumption].
7.45/7.45	1016 (all X_a (real_normed_vector(X_a) -> (all X_3 all K (hBOOL(hAPP(fun(nat,X_a),bool,bseq(X_a),hAPP(fun(nat,nat),fun(nat,X_a),hAPP(fun(nat,X_a),fun(fun(nat,nat),fun(nat,X_a)),combb(nat,X_a,nat),X_3),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),K)))) -> hBOOL(hAPP(fun(nat,X_a),bool,bseq(X_a),X_3)))))) # label(fact_3826_Bseq__offset) # label(axiom) # label(non_clause).  [assumption].
7.45/7.45	1017 (all X_a (comm_ring_1(X_a) -> (all X_1 all Y_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),X_1),Y_1)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),X_1)),Y_1)))))) # label(fact_2047_minus__dvd__iff) # label(axiom) # label(non_clause).  [assumption].
7.45/7.45	1018 (all X_a (semiring_div(X_a) -> (all A_1 all B (ti(X_a,B) != zero_zero(X_a) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)),B) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),A_1),B)),one_one(X_a)))))) # label(fact_1042_div__add__self2) # label(axiom) # label(non_clause).  [assumption].
7.45/7.45	1019 (all X_a (order(X_a) -> (all N_1 all N_7 all F ((all N_2 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,F,N_2)),hAPP(nat,X_a,F,hAPP(nat,nat,suc,N_2))))) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),N_7)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,F,N_1)),hAPP(nat,X_a,F,N_7)))))))) # label(fact_1496_lift__Suc__mono__less) # label(axiom) # label(non_clause).  [assumption].
7.45/7.45	1020 (all X_1 all Y_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(nat,fun(real,real),root,N_1),X_1)),hAPP(real,real,hAPP(nat,fun(real,real),root,N_1),Y_1))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_1),Y_1))))) # label(fact_2677_real__root__le__iff) # label(axiom) # label(non_clause).  [assumption].
7.45/7.45	1021 (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_1842_abs__le__D1) # label(axiom) # label(non_clause).  [assumption].
7.45/7.45	1022 (all W hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),W),W))) # label(fact_21_zle__refl) # label(axiom) # label(non_clause).  [assumption].
7.45/7.45	1023 (all A_1 all B all C hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),B)),C) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),B),C))),C)) # label(fact_955_zmod__simps_I3_J) # label(axiom) # label(non_clause).  [assumption].
7.45/7.45	1024 (all X_a (real_normed_vector(X_a) -> (all K all F all Sa (hBOOL(hAPP(X_a,bool,hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),F),Sa)) -> hBOOL(hAPP(X_a,bool,hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),hAPP(fun(nat,nat),fun(nat,X_a),hAPP(fun(nat,X_a),fun(fun(nat,nat),fun(nat,X_a)),combb(nat,X_a,nat),F),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),K))),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),Sa),hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),K))))))))) # label(fact_4167_sums__split__initial__segment) # label(axiom) # label(non_clause).  [assumption].
7.45/7.45	1025 (all X_a (real_normed_algebra(X_a) -> (all X all Y hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),Y))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(X_a,real,norm_norm(X_a),X)),hAPP(X_a,real,norm_norm(X_a),Y))))))) # label(fact_1788_norm__mult__ineq) # label(axiom) # label(non_clause).  [assumption].
7.45/7.45	1026 (all X_a all X_b (ordered_ab_group_add(X_b) -> (all I all B_2 all F all Sa (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),Sa)) -> ((all I_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),I_2),Sa)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),zero_zero(X_b)),hAPP(X_a,X_b,F,I_2))))) -> (hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),F),Sa) = B_2 -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),I),Sa)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_a,X_b,F,I)),B_2))))))))) # label(fact_4299_setsum__nonneg__leq__bound) # label(axiom) # label(non_clause).  [assumption].
7.45/7.45	1027 (all X_a (ring_1(X_a) -> (all B_1 all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_2),ring_1_Ints(X_a))) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),B_1),ring_1_Ints(X_a))) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),B_1)),ring_1_Ints(X_a)))))))) # label(fact_3824_Ints__add) # label(axiom) # label(non_clause).  [assumption].
7.45/7.45	1028 (all A_1 all B all C (ti(int,C) != zero_zero(int) -> hAPP(int,rat,hAPP(int,fun(int,rat),fract,A_1),B) = hAPP(int,rat,hAPP(int,fun(int,rat),fract,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),A_1)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),B)))) # label(fact_3752_mult__rat__cancel) # label(axiom) # label(non_clause).  [assumption].
7.45/7.45	1029 (all L_4 hAPP(int,int,bit0,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),pls),L_4)) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),pls),hAPP(int,int,bit0,L_4))) # label(fact_495_diff__bin__simps_I3_J) # label(axiom) # label(non_clause).  [assumption].
7.45/7.45	1030 (all X_a (linorder(X_a) -> (all B all A_1 all C hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),B),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),A_1),C)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),B),C))))) # label(fact_4812_min__max_Oinf_Oleft__commute) # label(axiom) # label(non_clause).  [assumption].
7.45/7.45	1031 (all N (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),N)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,fact_fact(int),N))))) # label(fact_3194_fact__gt__zero__int) # label(axiom) # label(non_clause).  [assumption].
7.45/7.45	1032 (all X_a all A_3 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_3)) -> hBOOL(hAPP(fun(fun(X_a,bool),bool),bool,finite_finite_1(fun(X_a,bool)),hAPP(fun(fun(X_a,bool),bool),fun(fun(X_a,bool),bool),collect(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),hAPP(fun(fun(X_a,bool),fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(fun(X_a,bool),bool)),combc(fun(X_a,bool),fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool))),A_3)))))) # label(fact_3803_finite__Collect__subsets) # label(axiom) # label(non_clause).  [assumption].
7.45/7.45	1033 (all X_a (boolean_algebra(X_a) -> (all Y all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),Y)),X)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),X)),Y)))))) # label(fact_2959_compl__le__swap2) # label(axiom) # label(non_clause).  [assumption].
7.45/7.45	1034 (all X_b (ring(X_b) & number(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_491_right__diff__distrib__number__of) # label(axiom) # label(non_clause).  [assumption].
7.45/7.45	1035 (all X_a (banach(X_a) & real_n2089651433ebra_1(X_a) -> (all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,norm_norm(X_a),X_1)),one_one(real))) -> hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),hAPP(X_a,fun(nat,X_a),power_power(X_a),X_1))))))) # label(fact_4025_complete__algebra__summable__geometric) # label(axiom) # label(non_clause).  [assumption].
7.45/7.45	1036 (all Q_3 ((-hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),Q_3),zero_zero(rat))) -> hAPP(rat,rat,abs_abs(rat),Q_3) = Q_3) & (hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),Q_3),zero_zero(rat))) -> hAPP(rat,rat,abs_abs(rat),Q_3) = hAPP(rat,rat,uminus_uminus(rat),Q_3)))) # label(fact_3715_abs__rat__def) # label(axiom) # label(non_clause).  [assumption].
7.45/7.45	1037 (all A_1 all C hAPP(int,rat,hAPP(int,fun(int,rat),fract,zero_zero(int)),A_1) = hAPP(int,rat,hAPP(int,fun(int,rat),fract,zero_zero(int)),C)) # label(fact_3741_eq__rat_I3_J) # label(axiom) # label(non_clause).  [assumption].
7.45/7.45	1038 (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_1567_order__less__not__sym) # label(axiom) # label(non_clause).  [assumption].
7.45/7.45	1039 (all S (-hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),S)) <-> (all M_2 exists N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_2),N_2)) & hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),N_2),S)))))) # label(fact_3657_infinite__nat__iff__unbounded) # label(axiom) # label(non_clause).  [assumption].
7.45/7.45	1040 (all B all Bq all Br all A_1 all C all Aq all Ar (hBOOL(hAPP(product_prod(nat,nat),bool,hAPP(nat,fun(product_prod(nat,nat),bool),hAPP(nat,fun(nat,fun(product_prod(nat,nat),bool)),divmod_nat_rel,A_1),C),hAPP(nat,product_prod(nat,nat),hAPP(nat,fun(nat,product_prod(nat,nat)),product_Pair(nat,nat),Aq),Ar))) -> (hBOOL(hAPP(product_prod(nat,nat),bool,hAPP(nat,fun(product_prod(nat,nat),bool),hAPP(nat,fun(nat,fun(product_prod(nat,nat),bool)),divmod_nat_rel,B),C),hAPP(nat,product_prod(nat,nat),hAPP(nat,fun(nat,product_prod(nat,nat)),product_Pair(nat,nat),Bq),Br))) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),C)) -> hBOOL(hAPP(product_prod(nat,nat),bool,hAPP(nat,fun(product_prod(nat,nat),bool),hAPP(nat,fun(nat,fun(product_prod(nat,nat),bool)),divmod_nat_rel,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A_1),B)),C),hAPP(nat,product_prod(nat,nat),hAPP(nat,fun(nat,product_prod(nat,nat)),product_Pair(nat,nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Aq),Bq)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Ar),Br)),C))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Ar),Br)),C)))))))) # label(fact_3097_divmod__nat__rel__add1__eq) # label(axiom) # label(non_clause).  [assumption].
7.45/7.45	1041 (all X_b all X_a (real_vector(X_a) -> (all G all A_3 all X_1 hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),hAPP(fun(X_b,bool),real,hAPP(fun(X_b,real),fun(fun(X_b,bool),real),big_co1399186613setsum(X_b,real),G),A_3)),X_1) = hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co1399186613setsum(X_b,X_a),hAPP(X_a,fun(X_b,X_a),hAPP(fun(X_b,fun(X_a,X_a)),fun(X_a,fun(X_b,X_a)),combc(X_b,X_a,X_a),hAPP(fun(X_b,real),fun(X_b,fun(X_a,X_a)),hAPP(fun(real,fun(X_a,X_a)),fun(fun(X_b,real),fun(X_b,fun(X_a,X_a))),combb(real,fun(X_a,X_a),X_b),scaleR_scaleR(X_a)),G)),X_1)),A_3)))) # label(fact_4731_scaleR__left_Osetsum) # label(axiom) # label(non_clause).  [assumption].
7.45/7.45	1042 (all X_a (banach(X_a) -> (all F (hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,X_a),fun(nat,real),hAPP(fun(X_a,real),fun(fun(nat,X_a),fun(nat,real)),combb(X_a,real,nat),norm_norm(X_a)),F))) -> hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),F)))))) # label(fact_4007_summable__norm__cancel) # label(axiom) # label(non_clause).  [assumption].
7.45/7.45	1043 (all X_a ti(fun(X_a,fun(X_a,bool)),fequal(X_a)) = fequal(X_a)) # label(tsy_c_fequal_res) # label(axiom) # label(non_clause).  [assumption].
7.45/7.45	1044 (all A_1 hAPP(int,rat,hAPP(int,fun(int,rat),fract,A_1),zero_zero(int)) = hAPP(int,rat,hAPP(int,fun(int,rat),fract,zero_zero(int)),one_one(int))) # label(fact_3736_eq__rat_I2_J) # label(axiom) # label(non_clause).  [assumption].
7.45/7.45	1045 (all X_a (ab_semigroup_mult(X_a) -> times_times(X_a) = ti(fun(X_a,fun(X_a,X_a)),times_times(X_a)))) # label(tsy_c_Groups_Otimes__class_Otimes_0_res) # label(axiom) # label(non_clause).  [assumption].
7.45/7.45	1046 (all N_1 hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),hAPP(fun(int,bool),fun(int,bool),collect(int),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),combs(int,bool,bool),hAPP(fun(int,bool),fun(int,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj),hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)))),hAPP(int,fun(int,bool),hAPP(fun(int,fun(int,bool)),fun(int,fun(int,bool)),combc(int,int,bool),ord_less_eq(int)),N_1)))))) # label(fact_3812_bdd__int__set__l__le__finite) # label(axiom) # label(non_clause).  [assumption].
7.45/7.45	1047 (all Z_1 all W hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),Z_1),W) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Z_1),hAPP(int,int,uminus_uminus(int),W))) # label(fact_2161_diff__int__def) # label(axiom) # label(non_clause).  [assumption].
7.45/7.45	1048 (all X_a (banach(X_a) & real_normed_algebra(X_a) -> (all B_1 all A_2 (hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,X_a),fun(nat,real),hAPP(fun(X_a,real),fun(fun(nat,X_a),fun(nat,real)),combb(X_a,real,nat),norm_norm(X_a)),A_2))) -> (hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,X_a),fun(nat,real),hAPP(fun(X_a,real),fun(fun(nat,X_a),fun(nat,real)),combb(X_a,real,nat),norm_norm(X_a)),B_1))) -> hAPP(fun(nat,X_a),X_a,suminf(X_a),hAPP(fun(nat,fun(nat,bool)),fun(nat,X_a),hAPP(fun(nat,fun(fun(nat,bool),X_a)),fun(fun(nat,fun(nat,bool)),fun(nat,X_a)),combs(nat,fun(nat,bool),X_a),hAPP(fun(nat,fun(nat,X_a)),fun(nat,fun(fun(nat,bool),X_a)),hAPP(fun(fun(nat,X_a),fun(fun(nat,bool),X_a)),fun(fun(nat,fun(nat,X_a)),fun(nat,fun(fun(nat,bool),X_a))),combb(fun(nat,X_a),fun(fun(nat,bool),X_a),nat),big_co1399186613setsum(nat,X_a)),hAPP(fun(nat,fun(nat,X_a)),fun(nat,fun(nat,X_a)),hAPP(fun(fun(nat,X_a),fun(nat,X_a)),fun(fun(nat,fun(nat,X_a)),fun(nat,fun(nat,X_a))),combb(fun(nat,X_a),fun(nat,X_a),nat),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),times_times(X_a)),A_2))),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,X_a)),hAPP(fun(fun(nat,nat),fun(nat,X_a)),fun(fun(nat,fun(nat,nat)),fun(nat,fun(nat,X_a))),combb(fun(nat,nat),fun(nat,X_a),nat),hAPP(fun(nat,X_a),fun(fun(nat,nat),fun(nat,X_a)),combb(nat,X_a,nat),B_1)),minus_minus(nat))))),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),zero_zero(nat)))) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(fun(nat,X_a),X_a,suminf(X_a),A_2)),hAPP(fun(nat,X_a),X_a,suminf(X_a),B_1))))))) # label(fact_4621_Cauchy__product) # label(axiom) # label(non_clause).  [assumption].
7.45/7.45	1049 (all A_1 all B (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),zero_zero(int))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_1),B)),zero_zero(int))))) # label(fact_1031_neg__mod__sign) # label(axiom) # label(non_clause).  [assumption].
7.45/7.45	1050 (all N all X (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X)) -> hAPP(int,nat,nat_1,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),X),N)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),hAPP(int,nat,nat_1,X)),N))) # label(fact_1145_Nat__Transfer_Otransfer__nat__int__functions_I4_J) # label(axiom) # label(non_clause).  [assumption].
7.45/7.45	1051 (all X X = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),X),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),X),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) # label(fact_1771_real__sum__of__halves) # label(axiom) # label(non_clause).  [assumption].
7.45/7.45	1052 (all N all M hAPP(int,int,hAPP(int,fun(int,int),times_times(int),N),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),M),N)) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),M),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),M),N))) # label(fact_923_zmult__div__cancel) # label(axiom) # label(non_clause).  [assumption].
7.45/7.45	1053 (all W_1 all Z (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),W_1),Z)) <-> (exists N_2 hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),W_1),hAPP(nat,int,semiring_1_of_nat(int),N_2)) = ti(int,Z)))) # label(fact_1306_zle__iff__zadd) # label(axiom) # label(non_clause).  [assumption].
7.45/7.45	1054 (all K_4 all I_1 all J_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),I_1),J_2)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),J_2),K_4)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),I_1),K_4))))) # label(fact_652_real__le__trans) # label(axiom) # label(non_clause).  [assumption].
7.45/7.45	1055 (all N_1 all Ma (hBOOL(hAPP(int,bool,nat_is_nat,Ma)) -> (hBOOL(hAPP(int,bool,nat_is_nat,N_1)) -> hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastAtMost(int),Ma),N_1) = hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(int,nat,nat_1,Ma)),hAPP(int,nat,nat_1,N_1)))))) # label(fact_4839_SetInterval_Otransfer__int__nat__set__functions) # label(axiom) # label(non_clause).  [assumption].
7.45/7.45	1056 (all X_a (archim1727834104eiling(X_a) -> (all V_1 all X_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),V_1)),hAPP(X_a,int,archim2085082626_floor(X_a),X_1))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(int,X_a,number_number_of(X_a),V_1)),X_1)))))) # label(fact_2886_number__of__le__floor) # label(axiom) # label(non_clause).  [assumption].
7.45/7.45	1057 (all K_4 hAPP(rat,product_prod(int,int),quotient_of,hAPP(int,rat,number_number_of(rat),K_4)) = hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),hAPP(int,int,number_number_of(int),K_4)),one_one(int))) # label(fact_3730_quotient__of__number_I3_J) # label(axiom) # label(non_clause).  [assumption].
7.45/7.45	1058 (all X_a (topological_space(X_a) -> (all G all L all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(complex,fun(filter(X_a),bool),hAPP(fun(X_a,complex),fun(complex,fun(filter(X_a),bool)),tendsto(X_a,complex),G),L),hAPP(X_a,filter(X_a),at(X_a),A_2))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(complex,fun(filter(X_a),bool),hAPP(fun(X_a,complex),fun(complex,fun(filter(X_a),bool)),tendsto(X_a,complex),hAPP(fun(X_a,complex),fun(X_a,complex),hAPP(fun(complex,complex),fun(fun(X_a,complex),fun(X_a,complex)),combb(complex,complex,X_a),cnj),G)),hAPP(complex,complex,cnj,L)),hAPP(X_a,filter(X_a),at(X_a),A_2))))))) # label(fact_4567_cnj_OLIM) # label(axiom) # label(non_clause).  [assumption].
7.45/7.45	1059 (all X all M (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),M)) -> (one_one(int) = hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,X),M) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),X),hAPP(int,nat,phi,M))),one_one(int)),M))))) # label(fact_3427_Euler__Fermat) # label(axiom) # label(non_clause).  [assumption].
7.45/7.45	1060 (all X_a all X_b (minus(X_b) -> (all A_3 all B_2 all X_2 hAPP(X_a,X_b,hAPP(fun(X_a,X_b),fun(X_a,X_b),hAPP(fun(X_a,X_b),fun(fun(X_a,X_b),fun(X_a,X_b)),minus_minus(fun(X_a,X_b)),A_3),B_2),X_2) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),hAPP(X_a,X_b,A_3,X_2)),hAPP(X_a,X_b,B_2,X_2))))) # label(fact_2963_fun__diff__def) # label(axiom) # label(non_clause).  [assumption].
7.45/7.45	1061 (all X_b (ord(X_b) & number(X_b) -> (all U all V ((hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(int,X_b,number_number_of(X_b),U)),hAPP(int,X_b,number_number_of(X_b),V))) -> hAPP(int,X_b,number_number_of(X_b),V) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),ord_max(X_b),hAPP(int,X_b,number_number_of(X_b),U)),hAPP(int,X_b,number_number_of(X_b),V))) & (-hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(int,X_b,number_number_of(X_b),U)),hAPP(int,X_b,number_number_of(X_b),V))) -> hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),ord_max(X_b),hAPP(int,X_b,number_number_of(X_b),U)),hAPP(int,X_b,number_number_of(X_b),V)) = hAPP(int,X_b,number_number_of(X_b),U)))))) # label(fact_4989_max__number__of) # label(axiom) # label(non_clause).  [assumption].
7.45/7.45	1062 (all M all K_4 all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),M),N) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),M),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_4),M)),N))) # label(fact_3263_gcd__add__mult__nat) # label(axiom) # label(non_clause).  [assumption].
7.45/7.45	1063 (all X all Y hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(complex,real,re,X)),hAPP(complex,real,re,Y)) = hAPP(complex,real,re,hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),X),Y))) # label(fact_3006_Re_Odiff) # label(axiom) # label(non_clause).  [assumption].
7.45/7.45	1064 (all N_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,semiring_1_of_nat(int),N_1)),zero_zero(int))) <-> zero_zero(nat) = N_1)) # label(fact_1372_int__le__0__conv) # label(axiom) # label(non_clause).  [assumption].
7.45/7.45	1065 (all A_1 all B hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,expi,A_1)),hAPP(complex,complex,expi,B)) = hAPP(complex,complex,expi,hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),A_1),B))) # label(fact_2820_expi__add) # label(axiom) # label(non_clause).  [assumption].
7.45/7.45	1066 (all X_b all X_a (metric_space(X_a) & real_normed_algebra(X_b) -> (all G all F all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),zero_zero(X_b)),hAPP(X_a,filter(X_a),at(X_a),A_2))) -> (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),G),zero_zero(X_b)),hAPP(X_a,filter(X_a),at(X_a),A_2))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(fun(X_a,X_b),fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,X_b)),combs(X_a,X_b,X_b),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,fun(X_b,X_b))),combb(X_b,fun(X_b,X_b),X_a),times_times(X_b)),F)),G)),zero_zero(X_b)),hAPP(X_a,filter(X_a),at(X_a),A_2)))))))) # label(fact_4577_LIM__mult__zero) # label(axiom) # label(non_clause).  [assumption].
7.45/7.45	1067 (all V hAPP(int,real,number_number_of(real),V) = hAPP(int,real,real_1(int),hAPP(int,int,number_number_of(int),V))) # label(fact_3337_real__number__of) # label(axiom) # label(non_clause).  [assumption].
7.45/7.45	1068 (all X_a (division_ring(X_a) -> inverse_divide(X_a) = ti(fun(X_a,fun(X_a,X_a)),inverse_divide(X_a)))) # label(tsy_c_Fields_Oinverse__class_Odivide_1_res) # label(axiom) # label(non_clause).  [assumption].
7.45/7.45	1069 (all X_a (banach(X_a) -> (all F (hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,X_a),fun(nat,real),hAPP(fun(X_a,real),fun(fun(nat,X_a),fun(nat,real)),combb(X_a,real,nat),norm_norm(X_a)),F))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),hAPP(fun(nat,X_a),X_a,suminf(X_a),F))),hAPP(fun(nat,real),real,suminf(real),hAPP(fun(nat,X_a),fun(nat,real),hAPP(fun(X_a,real),fun(fun(nat,X_a),fun(nat,real)),combb(X_a,real,nat),norm_norm(X_a)),F)))))))) # label(fact_4023_summable__norm) # label(axiom) # label(non_clause).  [assumption].
7.45/7.45	1070 (all V hAPP(int,nat,number_number_of(nat),V) = hAPP(int,nat,nat_1,hAPP(int,int,number_number_of(int),V))) # label(fact_1112_nat__number__of__def) # label(axiom) # label(non_clause).  [assumption].
7.45/7.45	1071 (all Y_1 all X_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Y_1)) -> ((hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Y_1),zEven)) <-> hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),zEven))) -> hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,number_number_of(int),min_1)),hAPP(int,nat,nat_1,Y_1)) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,number_number_of(int),min_1)),hAPP(int,nat,nat_1,X_1)))))) # label(fact_1468_neg__one__power__parity) # label(axiom) # label(non_clause).  [assumption].
7.45/7.45	1072 (all W_1 all 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_1),one_one(int))),Z)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_1),Z)))) # label(fact_84_add1__zle__eq) # label(axiom) # label(non_clause).  [assumption].
7.45/7.45	1073 (all X_a (field(X_a) & number_ring(X_a) -> hAPP(X_a,X_a,inverse_inverse(X_a),hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,bit1,pls))) = hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,bit1,pls)))) # label(fact_2587_inverse__numeral__1) # label(axiom) # label(non_clause).  [assumption].
7.45/7.45	1074 (all A_2 all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,real_1(nat),A_2)),X_1)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A_2),hAPP(real,nat,natfloor,X_1)))))) # label(fact_2343_le__natfloor__eq) # label(axiom) # label(non_clause).  [assumption].
7.45/7.45	1075 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X),pi)) -> X = hAPP(real,real,arccos,hAPP(real,real,cos,X))))) # label(fact_2259_arccos__cos) # label(axiom) # label(non_clause).  [assumption].
7.45/7.45	1076 (all X_a (linorder(X_a) -> (all X all Y all Z_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),Y),Z_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),Y)),Z_1)))) # label(fact_4964_min__max_Osup__assoc) # label(axiom) # label(non_clause).  [assumption].
7.45/7.45	1077 (all X_a (dense_linorder(X_a) -> (all Z_1 all Y ((all X_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_2),Y)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_2),Z_1)))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),Z_1)))))) # label(fact_2825_dense__le) # label(axiom) # label(non_clause).  [assumption].
7.45/7.46	1078 (all B_1 all A_2 all Ma (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),B_1),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),bnorRset,A_2),Ma))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B_1),A_2)))) # label(fact_3207_Bnor__mem__zle) # label(axiom) # label(non_clause).  [assumption].
7.45/7.46	1079 -(all T_4 hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),one_one(int)) != hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))),T_4)) # label(fact_18__096_B_Bthesis_O_A_I_B_Bt_O_As_A_094_A2_A_L_A1_A_061_A_I4_A_K_Am_A_L_A1_) # label(axiom) # label(non_clause).  [assumption].
7.45/7.46	1080 (all X_a (real_normed_algebra(X_a) & power(X_a) -> (all Ma all X_3 all A_2 (hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),X_3),A_2),sequentially)) -> hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),hAPP(nat,fun(nat,X_a),hAPP(fun(nat,fun(nat,X_a)),fun(nat,fun(nat,X_a)),combc(nat,nat,X_a),hAPP(fun(nat,X_a),fun(nat,fun(nat,X_a)),hAPP(fun(X_a,fun(nat,X_a)),fun(fun(nat,X_a),fun(nat,fun(nat,X_a))),combb(X_a,fun(nat,X_a),nat),power_power(X_a)),X_3)),Ma)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_2),Ma)),sequentially)))))) # label(fact_4467_LIMSEQ__pow) # label(axiom) # label(non_clause).  [assumption].
7.45/7.46	1081 (all X_1 hBOOL(hAPP(real,bool,hAPP(fun(nat,real),fun(real,bool),sums(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),inverse_divide(real)),hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),min_1)))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),hAPP(fun(nat,nat),fun(nat,nat),hAPP(fun(nat,nat),fun(fun(nat,nat),fun(nat,nat)),combb(nat,nat,nat),fact_fact(nat)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),hAPP(fun(nat,nat),fun(nat,fun(nat,nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,nat),fun(nat,fun(nat,nat))),combb(nat,fun(nat,nat),nat),plus_plus(nat)),hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),one_one(nat))))))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),hAPP(real,fun(nat,real),power_power(real),X_1)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),hAPP(fun(nat,nat),fun(nat,fun(nat,nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,nat),fun(nat,fun(nat,nat))),combb(nat,fun(nat,nat),nat),plus_plus(nat)),hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),one_one(nat))))),hAPP(real,real,sin,X_1)))) # label(fact_4076_sin__paired) # label(axiom) # label(non_clause).  [assumption].
7.45/7.46	1082 (all D hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(int,int,abs_abs(int),D)),D))) # label(fact_1925_zdvd__self__abs2) # label(axiom) # label(non_clause).  [assumption].
7.45/7.46	1083 (all A_3 all B_2 (hBOOL(hAPP(fun(int,bool),bool,hAPP(fun(int,bool),fun(fun(int,bool),bool),ord_less_eq(fun(int,bool)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),A_3)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),B_2))) <-> hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,bool),fun(fun(nat,bool),bool),ord_less_eq(fun(nat,bool)),A_3),B_2)))) # label(fact_3646_transfer__nat__int__set__relations_I5_J) # label(axiom) # label(non_clause).  [assumption].
7.45/7.46	1084 (all P_5 all A_1 all B (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,A_1),B)) -> -(hBOOL(hAPP(nat,bool,prime,P_5)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),P_5),A_1)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),P_5),B))))) # label(fact_3060_coprime__prime) # label(axiom) # label(non_clause).  [assumption].
7.45/7.46	1085 (all X_b all X_a all F1 all A_2 all B_1 (hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),F1,A_2),B_1)) -> hBOOL(hAPP(product_prod(X_a,X_b),bool,hAPP(fun(X_a,fun(X_b,bool)),fun(product_prod(X_a,X_b),bool),product_prod_case(X_a,X_b,bool),F1),hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),A_2),B_1))))) # label(fact_4039_prod__caseI) # label(axiom) # label(non_clause).  [assumption].
7.45/7.46	1086 (all X_a (power(X_a) -> hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(nat,X_a)),hAPP(X_a,fun(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(nat,X_a))),power_1(X_a),one_one(X_a)),times_times(X_a)) = power_power(X_a))) # label(fact_2838_power__power__power) # label(axiom) # label(non_clause).  [assumption].
7.45/7.46	1087 (all N_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),N_1)) -> hAPP(fun(int,bool),nat,finite_card(int),hAPP(fun(int,bool),fun(int,bool),collect(int),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),combs(int,bool,bool),hAPP(fun(int,bool),fun(int,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj),hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)))),hAPP(int,fun(int,bool),hAPP(fun(int,fun(int,bool)),fun(int,fun(int,bool)),combc(int,int,bool),ord_less(int)),N_1)))) = hAPP(int,nat,nat_1,N_1))) # label(fact_3809_card__bdd__int__set__l) # label(axiom) # label(non_clause).  [assumption].
7.45/7.46	1088 (all X_a (banach(X_a) & real_normed_field(X_a) -> (all X_1 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),exp(X_a)),X_1),hAPP(X_a,X_a,exp(X_a),X_1)))))) # label(fact_2632_DERIV__exp) # label(axiom) # label(non_clause).  [assumption].
7.45/7.46	1089 (all X_a all A_3 all C_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_3),hAPP(fun(fun(X_a,bool),bool),fun(X_a,bool),complete_Sup_Sup(fun(X_a,bool)),C_2))) -> -(all X_4 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_3),X_4)) -> -hBOOL(hAPP(fun(fun(X_a,bool),bool),bool,hAPP(fun(X_a,bool),fun(fun(fun(X_a,bool),bool),bool),member(fun(X_a,bool)),X_4),C_2)))))) # label(fact_1832_UnionE) # label(axiom) # label(non_clause).  [assumption].
7.45/7.46	1090 (all A_1 all B (ti(int,B) != zero_zero(int) -> (hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_1),B) = zero_zero(int) -> hAPP(int,int,uminus_uminus(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_1),B)) = hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_1),hAPP(int,int,uminus_uminus(int),B))) & (hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_1),B) != zero_zero(int) -> hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_1),hAPP(int,int,uminus_uminus(int),B)) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,uminus_uminus(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_1),B))),one_one(int))))) # label(fact_2179_zdiv__zminus2__eq__if) # label(axiom) # label(non_clause).  [assumption].
7.45/7.46	1091 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),one_one(real)),X)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,ln,X)),X)))) # label(fact_2190_ln__bound) # label(axiom) # label(non_clause).  [assumption].
7.45/7.46	1092 (all X_a (number_ring(X_a) -> (all V all C all W hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),V),hAPP(int,int,uminus_uminus(int),W)))),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),C),hAPP(int,X_a,number_number_of(X_a),W)))))) # label(fact_2174_add__number__of__diff2) # label(axiom) # label(non_clause).  [assumption].
7.45/7.46	1093 (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_378_mult__nonneg__nonneg) # label(axiom) # label(non_clause).  [assumption].
7.45/7.46	1094 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,cos,X)))))) # label(fact_2247_cos__gt__zero__pi) # label(axiom) # label(non_clause).  [assumption].
7.45/7.46	1095 (all A_3 all B_2 (A_3 = B_2 <-> hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),B_2) = hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),A_3))) # label(fact_3648_transfer__nat__int__set__relations_I3_J) # label(axiom) # label(non_clause).  [assumption].
7.45/7.46	1096 (all X_a (real_vector(X_a) -> (all A_1 all B all X hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_1),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),B),X)) = hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),B),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_1),X))))) # label(fact_4694_scaleR__left__commute) # label(axiom) # label(non_clause).  [assumption].
7.45/7.46	1097 (all D_1 all F all X_1 all L (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),F),X_1),L)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),D_1)) -> ((all Y_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),X_1),Y_2))),D_1)) -> hAPP(real,real,F,Y_2) = hAPP(real,real,F,X_1))) -> L = zero_zero(real))))) # label(fact_2661_DERIV__local__const) # label(axiom) # label(non_clause).  [assumption].
7.45/7.46	1098 (all N_1 all Ma hAPP(nat,nat,hAPP(fun(nat,nat),fun(nat,nat),hAPP(nat,fun(fun(nat,nat),fun(nat,nat)),nat_case(nat),hAPP(nat,nat,suc,N_1)),hAPP(fun(nat,nat),fun(nat,nat),hAPP(fun(nat,nat),fun(fun(nat,nat),fun(nat,nat)),combb(nat,nat,nat),suc),hAPP(nat,fun(nat,nat),ord_max(nat),N_1))),Ma) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),hAPP(nat,nat,suc,N_1)),Ma)) # label(fact_4954_max__Suc1) # label(axiom) # label(non_clause).  [assumption].
7.45/7.46	1099 (all V all W hAPP(int,int,number_number_of(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),V),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))) # label(fact_25_times__numeral__code_I5_J) # label(axiom) # label(non_clause).  [assumption].
7.45/7.46	1100 (all X_a (comm_monoid_add(X_a) -> (all A_1 ti(X_a,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)))) # label(fact_777_add__0) # label(axiom) # label(non_clause).  [assumption].
7.45/7.46	1101 (all X_1 all Y_1 (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X_1),Y_1)),zOdd)) -> hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),zOdd)))) # label(fact_971_odd__mult__odd__prop) # label(axiom) # label(non_clause).  [assumption].
7.45/7.46	1102 (all X_1 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),arctan),X_1),hAPP(real,real,inverse_inverse(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),one_one(real)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))))) # label(fact_2654_DERIV__arctan) # label(axiom) # label(non_clause).  [assumption].
7.45/7.46	1103 (all X_a (comm_semiring_1(X_a) -> (all A_2 all D_1 all N_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))),hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(X_a,X_a),fun(fun(nat,X_a),fun(nat,X_a)),combb(X_a,X_a,nat),hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2)),hAPP(X_a,fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(X_a,fun(nat,X_a)),combc(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),times_times(X_a)),semiring_1_of_nat(X_a))),D_1))),hAPP(nat,fun(nat,bool),ord_lessThan(nat),N_1))) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),N_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),one_one(nat)))),D_1))))))) # label(fact_4324_arith__series__general) # label(axiom) # label(non_clause).  [assumption].
7.45/7.46	1104 (all A_1 all B (A_1 != B -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),B)) -> -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),B),A_1)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),B))))) # label(fact_625_dvd_Oneq__le__trans) # label(axiom) # label(non_clause).  [assumption].
7.45/7.46	1105 (all X hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) # label(fact_270_quartic__square__square) # label(axiom) # label(non_clause).  [assumption].
7.45/7.46	1106 (all M all K_4 all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),K_4)),N)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_4),N)))) # label(fact_577_add__leD2) # label(axiom) # label(non_clause).  [assumption].
7.45/7.46	1107 (all X_a (linordered_semidom(X_a) -> (all X all Y (hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),Y),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),X)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),Y)) -> ti(X_a,X) = ti(X_a,Y))))))) # label(fact_102_power2__eq__imp__eq) # label(axiom) # label(non_clause).  [assumption].
7.45/7.46	1108 (all N_1 all Diff all F all H (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),H)) -> (hAPP(nat,fun(real,real),Diff,zero_zero(nat)) = F -> ((all M_2 all T_4 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_2),N_1)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),T_4),H)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),T_4)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(nat,fun(real,real),Diff,M_2)),T_4),hAPP(real,real,hAPP(nat,fun(real,real),Diff,hAPP(nat,nat,suc,M_2)),T_4))))) -> (exists T_4 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),T_4)) & hAPP(real,real,F,H) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),inverse_divide(real)),hAPP(real,fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(real,fun(nat,real)),combc(nat,real,real),Diff),zero_zero(real)))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),fact_fact(nat))))),hAPP(real,fun(nat,real),power_power(real),H))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),N_1))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(nat,fun(real,real),Diff,N_1),T_4)),hAPP(nat,real,real_1(nat),hAPP(nat,nat,fact_fact(nat),N_1)))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),H),N_1))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),T_4),H)))))))) # label(fact_4282_Maclaurin2) # label(axiom) # label(non_clause).  [assumption].
7.45/7.46	1109 (all X_a (linordered_semidom(X_a) -> (all A_1 all N all N_5 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),N_5)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),one_one(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N_5)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N))))))))) # label(fact_459_power__strict__decreasing) # label(axiom) # label(non_clause).  [assumption].
7.45/7.46	1110 (all X_a (ord(X_a) -> ti(fun(X_a,fun(X_a,bool)),ord_less(X_a)) = ord_less(X_a))) # label(tsy_c_Orderings_Oord__class_Oless_res) # label(axiom) # label(non_clause).  [assumption].
7.45/7.46	1111 (all X_b all X_a (real_normed_algebra(X_b) & topological_space(X_a) -> (all Y_1 all G all L all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),G),L),hAPP(X_a,filter(X_a),at(X_a),A_2))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(X_b,fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(X_b,fun(X_a,X_b)),combc(X_a,X_b,X_b),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,fun(X_b,X_b))),combb(X_b,fun(X_b,X_b),X_a),times_times(X_b)),G)),Y_1)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),L),Y_1)),hAPP(X_a,filter(X_a),at(X_a),A_2))))))) # label(fact_4549_mult__left_OLIM) # label(axiom) # label(non_clause).  [assumption].
7.45/7.46	1112 (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_1577_xt1_I2_J) # label(axiom) # label(non_clause).  [assumption].
7.45/7.46	1113 (all A_1 all B all X (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),B),X)) & -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),B)) -> -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),A_1),B))) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),A_1),B)),X)))) # label(fact_3228_gcd__semilattice__nat_Oless__infI2) # label(axiom) # label(non_clause).  [assumption].
7.45/7.46	1114 (all X all Y hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(complex,real,re,X)),hAPP(complex,real,re,Y))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(complex,real,im,X)),hAPP(complex,real,im,Y))) = hAPP(complex,real,re,hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),X),Y))) # label(fact_3011_complex__Re__mult) # label(axiom) # label(non_clause).  [assumption].
7.45/7.46	1115 (all Ma all N_1 ((-(hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),N_1)) | zero_zero(nat) = N_1) -> hAPP(nat,product_prod(nat,nat),hAPP(nat,fun(nat,product_prod(nat,nat)),divmod_nat,Ma),N_1) = hAPP(product_prod(nat,nat),product_prod(nat,nat),hAPP(fun(nat,fun(nat,product_prod(nat,nat))),fun(product_prod(nat,nat),product_prod(nat,nat)),product_prod_case(nat,nat,product_prod(nat,nat)),hAPP(fun(nat,nat),fun(nat,fun(nat,product_prod(nat,nat))),hAPP(fun(nat,fun(nat,product_prod(nat,nat))),fun(fun(nat,nat),fun(nat,fun(nat,product_prod(nat,nat)))),combb(nat,fun(nat,product_prod(nat,nat)),nat),product_Pair(nat,nat)),suc)),hAPP(nat,product_prod(nat,nat),hAPP(nat,fun(nat,product_prod(nat,nat)),divmod_nat,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),Ma),N_1)),N_1))) & (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),N_1)) | zero_zero(nat) = N_1 -> hAPP(nat,product_prod(nat,nat),hAPP(nat,fun(nat,product_prod(nat,nat)),product_Pair(nat,nat),zero_zero(nat)),Ma) = hAPP(nat,product_prod(nat,nat),hAPP(nat,fun(nat,product_prod(nat,nat)),divmod_nat,Ma),N_1)))) # label(fact_4052_divmod__nat__if) # label(axiom) # label(non_clause).  [assumption].
7.45/7.46	1116 (all X_b all X_c all X_a all F all G ((all X_2 all Y_2 hAPP(product_prod(X_a,X_b),X_c,G,hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),X_2),Y_2)) = hAPP(X_b,X_c,hAPP(X_a,fun(X_b,X_c),F,X_2),Y_2)) -> hAPP(fun(X_a,fun(X_b,X_c)),fun(product_prod(X_a,X_b),X_c),product_prod_case(X_a,X_b,X_c),F) = ti(fun(product_prod(X_a,X_b),X_c),G))) # label(fact_4329_cond__split__eta) # label(axiom) # label(non_clause).  [assumption].
7.45/7.46	1117 (all I_1 all K_4 all J_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_4),J_2)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_2),K_4)),I_1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J_2),I_1)),K_4))) # label(fact_689_diff__add__assoc2) # label(axiom) # label(non_clause).  [assumption].
7.45/7.46	1118 (all X all Y hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),hAPP(nat,int,semiring_1_of_nat(int),X)),hAPP(nat,int,semiring_1_of_nat(int),Y)) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),X),Y))) # label(fact_4352_transfer__int__nat__gcd_I1_J) # label(axiom) # label(non_clause).  [assumption].
7.45/7.46	1119 (all M all N all K_4 (hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,N),K_4) = one_one(int) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),K_4),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),M),N))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),K_4),M))))) # label(fact_3462_zrelprime__zdvd__zmult) # label(axiom) # label(non_clause).  [assumption].
7.45/7.46	1120 (all X all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),Y)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,sqrt,X)),hAPP(real,real,sqrt,Y))))) # label(fact_1615_real__sqrt__less__mono) # label(axiom) # label(non_clause).  [assumption].
7.45/7.46	1121 (all M all N all K_4 hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),K_4)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N)),K_4)) # label(fact_523_nat__add__assoc) # label(axiom) # label(non_clause).  [assumption].
7.45/7.46	1122 (all X_a (zero(X_a) -> ti(X_a,zero_zero(X_a)) = zero_zero(X_a))) # label(tsy_c_Groups_Ozero__class_Ozero_res) # label(axiom) # label(non_clause).  [assumption].
7.45/7.46	1123 (all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),X_1)),one_one(real))) -> hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),hAPP(real,fun(real,real),inverse_divide(real),one_one(real))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),hAPP(fun(nat,nat),fun(nat,fun(nat,nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,nat),fun(nat,fun(nat,nat))),combb(nat,fun(nat,nat),nat),plus_plus(nat)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),times_times(nat)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),one_one(nat)))))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),hAPP(real,fun(nat,real),power_power(real),X_1)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),hAPP(fun(nat,nat),fun(nat,fun(nat,nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,nat),fun(nat,fun(nat,nat))),combb(nat,fun(nat,nat),nat),plus_plus(nat)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),times_times(nat)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),one_one(nat))))),zero_zero(real)),sequentially)))) # label(fact_4500_zeroseq__arctan__series) # label(axiom) # label(non_clause).  [assumption].
7.45/7.46	1124 (all B all M all A_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_1),M)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),A_1)) -> -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_1),B),M))))))) # label(fact_417_zcong__not) # label(axiom) # label(non_clause).  [assumption].
7.45/7.46	1125 (all A_2 all A_3 all Ma ((hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),A_2),A_3)) & hBOOL(hAPP(int,bool,hAPP(fun(int,bool),fun(int,bool),is_RRset,A_3),Ma)) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),Ma)) -> hAPP(int,int,hAPP(int,fun(int,int),hAPP(fun(int,bool),fun(int,fun(int,int)),rRset2norRR,A_3),Ma),A_2) = hAPP(fun(int,bool),int,hilbert_Eps(int),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),combs(int,bool,bool),hAPP(fun(int,bool),fun(int,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj),hAPP(int,fun(int,bool),hAPP(fun(int,fun(int,bool)),fun(int,fun(int,bool)),combc(int,int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_2)),Ma))),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,fun(fun(int,bool),bool)),fun(fun(int,bool),fun(int,bool)),combc(int,fun(int,bool),bool),member(int)),hAPP(int,fun(int,bool),norRRset,Ma))))) & (-(hBOOL(hAPP(int,bool,hAPP(fun(int,bool),fun(int,bool),is_RRset,A_3),Ma)) & hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),A_2),A_3)) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),Ma))) -> hAPP(int,int,hAPP(int,fun(int,int),hAPP(fun(int,bool),fun(int,fun(int,int)),rRset2norRR,A_3),Ma),A_2) = zero_zero(int)))) # label(fact_4153_RRset2norRR__def) # label(axiom) # label(non_clause).  [assumption].
7.45/7.46	1126 (all X_a (semiring_div(X_a) -> (all C_1 all A_2 all B_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_2),B_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_2),C_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),B_1),A_2)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),C_1),A_2))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),B_1),C_1)))))))) # label(fact_967_div__dvd__div) # label(axiom) # label(non_clause).  [assumption].
7.45/7.46	1127 (all X_a (real_n2089651433ebra_1(X_a) -> one_one(X_a) = hAPP(X_a,X_a,sgn_sgn(X_a),one_one(X_a)))) # label(fact_2206_sgn__one) # label(axiom) # label(non_clause).  [assumption].
7.45/7.46	1128 (all J_2 all A_1 all K_4 all P_5 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),P_5)) -> (hBOOL(hAPP(int,bool,zprime,P_5)) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,K_4),zero_zero(int)),P_5)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),J_2),K_4)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),hAPP(int,int,hAPP(int,fun(int,int),multInv,P_5),K_4))),K_4)),P_5)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),J_2),K_4)),A_1),P_5))))))) # label(fact_852_aux______2) # label(axiom) # label(non_clause).  [assumption].
7.45/7.46	1129 (all P_1 all A_2 all B_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A_2),B_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A_2),B_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A_2),B_1)) -> (hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),minus_minus(real)),hAPP(fun(nat,product_prod(real,real)),fun(nat,real),hAPP(fun(product_prod(real,real),real),fun(fun(nat,product_prod(real,real)),fun(nat,real)),combb(product_prod(real,real),real,nat),product_fst(real,real)),hAPP(real,fun(nat,product_prod(real,real)),hAPP(real,fun(real,fun(nat,product_prod(real,real))),hAPP(fun(product_prod(real,real),bool),fun(real,fun(real,fun(nat,product_prod(real,real)))),bolzano_bisect,P_1),A_2),B_1)))),hAPP(fun(nat,product_prod(real,real)),fun(nat,real),hAPP(fun(product_prod(real,real),real),fun(fun(nat,product_prod(real,real)),fun(nat,real)),combb(product_prod(real,real),real,nat),product_snd(real,real)),hAPP(real,fun(nat,product_prod(real,real)),hAPP(real,fun(real,fun(nat,product_prod(real,real))),hAPP(fun(product_prod(real,real),bool),fun(real,fun(real,fun(nat,product_prod(real,real)))),bolzano_bisect,P_1),A_2),B_1)))),zero_zero(real)),sequentially)) -> (exists L_3 ((all N_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(product_prod(real,real),real,product_fst(real,real),hAPP(nat,product_prod(real,real),hAPP(real,fun(nat,product_prod(real,real)),hAPP(real,fun(real,fun(nat,product_prod(real,real))),hAPP(fun(product_prod(real,real),bool),fun(real,fun(real,fun(nat,product_prod(real,real)))),bolzano_bisect,P_1),A_2),B_1),N_2))),L_3))) & hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),hAPP(fun(nat,product_prod(real,real)),fun(nat,real),hAPP(fun(product_prod(real,real),real),fun(fun(nat,product_prod(real,real)),fun(nat,real)),combb(product_prod(real,real),real,nat),product_fst(real,real)),hAPP(real,fun(nat,product_prod(real,real)),hAPP(real,fun(real,fun(nat,product_prod(real,real))),hAPP(fun(product_prod(real,real),bool),fun(real,fun(real,fun(nat,product_prod(real,real)))),bolzano_bisect,P_1),A_2),B_1))),L_3),sequentially)) & (all N_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),L_3),hAPP(product_prod(real,real),real,product_snd(real,real),hAPP(nat,product_prod(real,real),hAPP(real,fun(nat,product_prod(real,real)),hAPP(real,fun(real,fun(nat,product_prod(real,real))),hAPP(fun(product_prod(real,real),bool),fun(real,fun(real,fun(nat,product_prod(real,real)))),bolzano_bisect,P_1),A_2),B_1),N_2))))) & hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),hAPP(fun(nat,product_prod(real,real)),fun(nat,real),hAPP(fun(product_prod(real,real),real),fun(fun(nat,product_prod(real,real)),fun(nat,real)),combb(product_prod(real,real),real,nat),product_snd(real,real)),hAPP(real,fun(nat,product_prod(real,real)),hAPP(real,fun(real,fun(nat,product_prod(real,real))),hAPP(fun(product_prod(real,real),bool),fun(real,fun(real,fun(nat,product_prod(real,real)))),bolzano_bisect,P_1),A_2),B_1))),L_3),sequentially))))))))) # label(fact_4514_Bolzano__nest__unique) # label(axiom) # label(non_clause).  [assumption].
7.45/7.46	1130 (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),A_1) = hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))) # label(fact_143_power2__eq__square) # label(axiom) # label(non_clause).  [assumption].
7.45/7.46	1131 (all I_1 ((ti(int,I_1) = zero_zero(int) -> hAPP(int,int,sgn_sgn(int),I_1) = zero_zero(int)) & (zero_zero(int) != ti(int,I_1) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),I_1)) -> hAPP(int,int,uminus_uminus(int),one_one(int)) = hAPP(int,int,sgn_sgn(int),I_1)) & (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),I_1)) -> one_one(int) = hAPP(int,int,sgn_sgn(int),I_1))))) # label(fact_2258_zsgn__def) # label(axiom) # label(non_clause).  [assumption].
7.45/7.46	1132 (all X_a (comple44059174attice(X_a) -> (all A_3 all B_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_3),B_2)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(fun(X_a,bool),X_a,complete_Sup_Sup(X_a),A_3)),hAPP(fun(X_a,bool),X_a,complete_Sup_Sup(X_a),B_2))))))) # label(fact_1764_Sup__subset__mono) # label(axiom) # label(non_clause).  [assumption].
7.45/7.46	1133 (all M all N hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),M),N)),N))) # label(fact_3213_gcd__dvd2__nat) # label(axiom) # label(non_clause).  [assumption].
7.45/7.46	1134 (all X_c all X_b all X_a (real_normed_vector(X_a) & topological_space(X_b) & topological_space(X_c) -> (all G all C_1 all F all B_1 all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),B_1),hAPP(X_a,filter(X_a),at(X_a),A_2))) -> (hBOOL(hAPP(filter(X_b),bool,hAPP(X_c,fun(filter(X_b),bool),hAPP(fun(X_b,X_c),fun(X_c,fun(filter(X_b),bool)),tendsto(X_b,X_c),G),C_1),hAPP(X_b,filter(X_b),at(X_b),B_1))) -> ((exists D_3 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),D_3)) & (all X_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),X_2),A_2))),D_3)) & ti(X_a,A_2) != ti(X_a,X_2) -> ti(X_b,B_1) != hAPP(X_a,X_b,F,X_2))))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_c,fun(filter(X_a),bool),hAPP(fun(X_a,X_c),fun(X_c,fun(filter(X_a),bool)),tendsto(X_a,X_c),hAPP(fun(X_a,X_b),fun(X_a,X_c),hAPP(fun(X_b,X_c),fun(fun(X_a,X_b),fun(X_a,X_c)),combb(X_b,X_c,X_a),G),F)),C_1),hAPP(X_a,filter(X_a),at(X_a),A_2))))))))) # label(fact_4608_LIM__compose2) # label(axiom) # label(non_clause).  [assumption].
7.45/7.46	1135 (all X hAPP(real,real,sin,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),pi),X)) = hAPP(real,real,uminus_uminus(real),hAPP(real,real,sin,X))) # label(fact_2325_sin__periodic__pi2) # label(axiom) # label(non_clause).  [assumption].
7.45/7.46	1136 (all X all Y (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y),X)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),Y)) -> -(hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y),X)) & -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),Y))))) # label(fact_649_dvd_Oless__asym) # label(axiom) # label(non_clause).  [assumption].
7.45/7.46	1137 (all X_a (order(X_a) -> (all X_3 ((all M_2 all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_2),N_2)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(nat,X_a,X_3,M_2)),hAPP(nat,X_a,X_3,N_2))))) -> hBOOL(hAPP(fun(nat,X_a),bool,monoseq(X_a),X_3)))))) # label(fact_4131_monoI1) # label(axiom) # label(non_clause).  [assumption].
7.45/7.46	1138 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> X = hAPP(real,real,exp(real),hAPP(real,real,ln,X)))) # label(fact_2601_exp__ln) # label(axiom) # label(non_clause).  [assumption].
7.45/7.46	1139 (all N all A_1 hAPP(real,complex,cis,hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,real_1(nat),hAPP(nat,nat,suc,N))),A_1)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(real,complex,cis,A_1)),hAPP(real,complex,cis,hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,real_1(nat),N)),A_1)))) # label(fact_3034_cis__real__of__nat__Suc__mult) # label(axiom) # label(non_clause).  [assumption].
7.45/7.46	1140 (all I_1 ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),I_1),zero_zero(int))) -> hAPP(int,int,abs_abs(int),I_1) = hAPP(int,int,uminus_uminus(int),I_1)) & (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),I_1),zero_zero(int))) -> hAPP(int,int,abs_abs(int),I_1) = ti(int,I_1)))) # label(fact_2168_zabs__def) # label(axiom) # label(non_clause).  [assumption].
7.45/7.46	1141 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N)) -> (exists K_1 N = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),K_1))))) # label(fact_1491_less__imp__Suc__add) # label(axiom) # label(non_clause).  [assumption].
7.45/7.46	1142 (all Y_1 all X_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y_1),X_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_1),Y_1)) <-> Y_1 = X_1))) # label(fact_627_dvd_Oantisym__conv) # label(axiom) # label(non_clause).  [assumption].
7.45/7.46	1143 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N)) -> zero_zero(nat) != N)) # label(fact_539_gr__implies__not0) # label(axiom) # label(non_clause).  [assumption].
7.45/7.46	1144 (all X_a (real_normed_vector(X_a) -> (all K all F (hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),F)) -> hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),hAPP(fun(nat,nat),fun(nat,X_a),hAPP(fun(nat,X_a),fun(fun(nat,nat),fun(nat,X_a)),combb(nat,X_a,nat),F),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),K)))))))) # label(fact_4010_summable__ignore__initial__segment) # label(axiom) # label(non_clause).  [assumption].
7.45/7.46	1145 (all I_1 all J_2 all K_4 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_1),J_2)),K_4)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),K_4)))) # label(fact_562_add__lessD1) # label(axiom) # label(non_clause).  [assumption].
7.45/7.46	1146 (all P_5 hAPP(rat,product_prod(int,int),quotient_of,hAPP(rat,rat,sgn_sgn(rat),P_5)) = hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),hAPP(int,int,sgn_sgn(int),hAPP(product_prod(int,int),int,product_fst(int,int),hAPP(rat,product_prod(int,int),quotient_of,P_5)))),one_one(int))) # label(fact_3719_rat__sgn__code) # label(axiom) # label(non_clause).  [assumption].
7.45/7.46	1147 (all N all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,real_1(nat),N)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,real_1(nat),N)),one_one(real)))) -> hAPP(real,nat,natfloor,X) = N))) # label(fact_2363_natfloor__eq) # label(axiom) # label(non_clause).  [assumption].
7.45/7.46	1148 (all X_a all C_2 all A_3 all B_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_3),B_2)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less(fun(X_a,bool)),B_2),C_2)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less(fun(X_a,bool)),A_3),C_2))))) # label(fact_2003_subset__psubset__trans) # label(axiom) # label(non_clause).  [assumption].
7.45/7.46	1149 (all D_1 all Ta (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),D_1),Ta)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(int,int,uminus_uminus(int),D_1)),Ta)))) # label(fact_2145_uminus__dvd__conv_I1_J) # label(axiom) # label(non_clause).  [assumption].
7.45/7.46	1150 (all A_2 (hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),A_2),zero_zero(real)),sequentially)) -> (hBOOL(hAPP(fun(nat,real),bool,monoseq(real),A_2)) -> hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),hAPP(fun(nat,fun(nat,bool)),fun(nat,real),hAPP(fun(fun(nat,bool),real),fun(fun(nat,fun(nat,bool)),fun(nat,real)),combb(fun(nat,bool),real,nat),hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),min_1)))),A_2))),hAPP(fun(nat,nat),fun(nat,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(nat,nat),fun(nat,fun(nat,bool))),combb(nat,fun(nat,bool),nat),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat))),hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))),hAPP(fun(nat,real),real,suminf(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),min_1)))),A_2))),sequentially))))) # label(fact_4502_summable__Leibniz_I4_J) # label(axiom) # label(non_clause).  [assumption].
7.45/7.46	1151 (all X_a (field(X_a) -> (all X all Y all Z_1 (zero_zero(X_a) != ti(X_a,Z_1) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Z_1),X)),Y)),Z_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),Y),Z_1)))))) # label(fact_1719_add__divide__eq__iff) # label(axiom) # label(non_clause).  [assumption].
7.45/7.46	1152 (all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)) -> hBOOL(hAPP(real,bool,hAPP(fun(real,real),fun(real,bool),isCont(real,real),hAPP(nat,fun(real,real),root,N_1)),zero_zero(real))))) # label(fact_4917_isCont__root__zero) # label(axiom) # label(non_clause).  [assumption].
7.45/7.46	1153 (all K all L (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,K)),hAPP(int,int,bit0,L))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),L)))) # label(fact_156_rel__simps_I16_J) # label(axiom) # label(non_clause).  [assumption].
7.45/7.46	1154 (all B all A_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A_1),zero_zero(int))) -> hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),B))),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),A_1)) = hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),B),one_one(int))),A_1))) # label(fact_1071_neg__zdiv__mult__2) # label(axiom) # label(non_clause).  [assumption].
7.45/7.46	1155 (all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Y)) -> (exists X_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X_2)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_2),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),Y),hAPP(real,real,tan,X_2))))))) # label(fact_2285_lemma__tan__total) # label(axiom) # label(non_clause).  [assumption].
7.45/7.46	1156 (all R_4 all A_1 hAPP(complex,real,norm_norm(complex),hAPP(real,complex,hAPP(real,fun(real,complex),rcis,R_4),A_1)) = hAPP(real,real,abs_abs(real),R_4)) # label(fact_3166_complex__mod__rcis) # label(axiom) # label(non_clause).  [assumption].
7.45/7.46	1157 (all X_a (real_normed_field(X_a) -> (all F all X_1 all D_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),F),X_1),D_2)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),hAPP(fun(X_a,X_a),fun(X_a,X_a),hAPP(fun(X_a,X_a),fun(fun(X_a,X_a),fun(X_a,X_a)),combb(X_a,X_a,X_a),uminus_uminus(X_a)),F)),X_1),hAPP(X_a,X_a,uminus_uminus(X_a),D_2))))))) # label(fact_3856_DERIV__minus) # label(axiom) # label(non_clause).  [assumption].
7.45/7.46	1158 (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_1210_Nat__Transfer_Otransfer__int__nat__functions_I3_J) # label(axiom) # label(non_clause).  [assumption].
7.45/7.46	1159 (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_775_add__0__right) # label(axiom) # label(non_clause).  [assumption].
7.45/7.46	1160 (all X_a (linordered_idom(X_a) -> (all A_1 -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),zero_zero(X_a)))))) # label(fact_10_power2__less__0) # label(axiom) # label(non_clause).  [assumption].
7.45/7.46	1161 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,number_number_of(real),min_1)),X)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,ln,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),one_one(real)),X))),X)))) # label(fact_1979_ln__add__one__self__le__self2) # label(axiom) # label(non_clause).  [assumption].
7.45/7.46	1162 (all X_a (real_normed_field(X_a) -> (all E_3 all F all X_1 all D_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),F),X_1),D_2)) -> (ti(X_a,D_2) = ti(X_a,E_3) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),F),X_1),E_3))))))) # label(fact_2635_Deriv_Olemma__DERIV__subst) # label(axiom) # label(non_clause).  [assumption].
7.45/7.46	1163 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),M),N)),N)))) # label(fact_1101_mod__less__divisor) # label(axiom) # label(non_clause).  [assumption].
7.45/7.46	1164 (all X_a (number_ring(X_a) -> (all N hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(int,X_a,number_number_of(X_a),min_1)),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),N))) = hAPP(int,X_a,number_number_of(X_a),min_1)))) # label(fact_1474_power__m1__odd) # label(axiom) # label(non_clause).  [assumption].
7.45/7.46	1165 (all X_a all X_b ti(fun(product_prod(X_a,X_b),X_b),product_snd(X_a,X_b)) = product_snd(X_a,X_b)) # label(tsy_c_Product__Type_Osnd_res) # label(axiom) # label(non_clause).  [assumption].
7.45/7.46	1166 (all X_a (real_normed_algebra(X_a) -> (all Xa_1 all R_4 all X hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Xa_1),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),R_4),X)) = hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),R_4),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Xa_1),X))))) # label(fact_4676_mult__right_OscaleR) # label(axiom) # label(non_clause).  [assumption].
7.45/7.46	1167 (all Ma all N_1 all P_1 ((all M_2 hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),P_1,M_2),zero_zero(nat)))) -> ((all M_2 all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_2)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),P_1,N_2),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),M_2),N_2))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),P_1,M_2),N_2))))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),P_1,Ma),N_1))))) # label(fact_3530_gcd__nat__induct) # label(axiom) # label(non_clause).  [assumption].
7.45/7.46	1168 (all X all Y all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X),Y)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(nat,fun(real,real),root,N),X)),hAPP(real,real,hAPP(nat,fun(real,real),root,N),Y)))))) # label(fact_2678_real__root__le__mono) # label(axiom) # label(non_clause).  [assumption].
7.45/7.46	1169 (all A_2 all X_3 all X_1 (hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),X_3),X_1),sequentially)) -> ((exists N_3 all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_3),N_2)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A_2),hAPP(nat,real,X_3,N_2))))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A_2),X_1))))) # label(fact_4433_LIMSEQ__le__const) # label(axiom) # label(non_clause).  [assumption].
7.45/7.46	1170 (all X_a (metric_space(X_a) -> ti(fun(fun(nat,X_a),bool),cauchy(X_a)) = cauchy(X_a))) # label(tsy_c_SEQ_OCauchy_res) # label(axiom) # label(non_clause).  [assumption].
7.45/7.46	1171 (all X_a (division_ring(X_a) -> (all B all A_1 (zero_zero(X_a) != ti(X_a,A_1) -> (ti(X_a,B) != zero_zero(X_a) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_a,X_a,inverse_inverse(X_a),A_1)),hAPP(X_a,X_a,inverse_inverse(X_a),B)) = hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,inverse_inverse(X_a),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_1),B))),hAPP(X_a,X_a,inverse_inverse(X_a),B)))))))) # label(fact_2611_inverse__diff__inverse) # label(axiom) # label(non_clause).  [assumption].
7.45/7.46	1172 (all P_1 all A_2 all B_1 all N_1 hAPP(nat,product_prod(real,real),hAPP(real,fun(nat,product_prod(real,real)),hAPP(real,fun(real,fun(nat,product_prod(real,real))),hAPP(fun(product_prod(real,real),bool),fun(real,fun(real,fun(nat,product_prod(real,real)))),bolzano_bisect,P_1),A_2),B_1),hAPP(nat,nat,suc,N_1)) = hAPP(product_prod(real,real),product_prod(real,real),hAPP(fun(real,fun(real,product_prod(real,real))),fun(product_prod(real,real),product_prod(real,real)),product_prod_case(real,real,product_prod(real,real)),hAPP(fun(real,fun(real,product_prod(real,real))),fun(real,fun(real,product_prod(real,real))),hAPP(fun(real,fun(fun(real,product_prod(real,real)),fun(real,product_prod(real,real)))),fun(fun(real,fun(real,product_prod(real,real))),fun(real,fun(real,product_prod(real,real)))),combs(real,fun(real,product_prod(real,real)),fun(real,product_prod(real,real))),hAPP(fun(real,fun(real,fun(product_prod(real,real),product_prod(real,real)))),fun(real,fun(fun(real,product_prod(real,real)),fun(real,product_prod(real,real)))),hAPP(fun(fun(real,fun(product_prod(real,real),product_prod(real,real))),fun(fun(real,product_prod(real,real)),fun(real,product_prod(real,real)))),fun(fun(real,fun(real,fun(product_prod(real,real),product_prod(real,real)))),fun(real,fun(fun(real,product_prod(real,real)),fun(real,product_prod(real,real))))),combb(fun(real,fun(product_prod(real,real),product_prod(real,real))),fun(fun(real,product_prod(real,real)),fun(real,product_prod(real,real))),real),combs(real,product_prod(real,real),product_prod(real,real))),hAPP(fun(real,fun(real,product_prod(real,real))),fun(real,fun(real,fun(product_prod(real,real),product_prod(real,real)))),hAPP(fun(real,fun(fun(real,product_prod(real,real)),fun(real,fun(product_prod(real,real),product_prod(real,real))))),fun(fun(real,fun(real,product_prod(real,real))),fun(real,fun(real,fun(product_prod(real,real),product_prod(real,real))))),combs(real,fun(real,product_prod(real,real)),fun(real,fun(product_prod(real,real),product_prod(real,real)))),hAPP(fun(real,fun(real,fun(product_prod(real,real),fun(product_prod(real,real),product_prod(real,real))))),fun(real,fun(fun(real,product_prod(real,real)),fun(real,fun(product_prod(real,real),product_prod(real,real))))),hAPP(fun(fun(real,fun(product_prod(real,real),fun(product_prod(real,real),product_prod(real,real)))),fun(fun(real,product_prod(real,real)),fun(real,fun(product_prod(real,real),product_prod(real,real))))),fun(fun(real,fun(real,fun(product_prod(real,real),fun(product_prod(real,real),product_prod(real,real))))),fun(real,fun(fun(real,product_prod(real,real)),fun(real,fun(product_prod(real,real),product_prod(real,real)))))),combb(fun(real,fun(product_prod(real,real),fun(product_prod(real,real),product_prod(real,real)))),fun(fun(real,product_prod(real,real)),fun(real,fun(product_prod(real,real),product_prod(real,real)))),real),combs(real,product_prod(real,real),fun(product_prod(real,real),product_prod(real,real)))),hAPP(fun(real,fun(real,bool)),fun(real,fun(real,fun(product_prod(real,real),fun(product_prod(real,real),product_prod(real,real))))),hAPP(fun(fun(real,bool),fun(real,fun(product_prod(real,real),fun(product_prod(real,real),product_prod(real,real))))),fun(fun(real,fun(real,bool)),fun(real,fun(real,fun(product_prod(real,real),fun(product_prod(real,real),product_prod(real,real)))))),combb(fun(real,bool),fun(real,fun(product_prod(real,real),fun(product_prod(real,real),product_prod(real,real)))),real),hAPP(fun(bool,fun(product_prod(real,real),fun(product_prod(real,real),product_prod(real,real)))),fun(fun(real,bool),fun(real,fun(product_prod(real,real),fun(product_prod(real,real),product_prod(real,real))))),combb(bool,fun(product_prod(real,real),fun(product_prod(real,real),product_prod(real,real))),real),if(product_prod(real,real)))),hAPP(fun(real,fun(real,product_prod(real,real))),fun(real,fun(real,bool)),hAPP(fun(fun(real,product_prod(real,real)),fun(real,bool)),fun(fun(real,fun(real,product_prod(real,real))),fun(real,fun(real,bool))),combb(fun(real,product_prod(real,real)),fun(real,bool),real),hAPP(fun(product_prod(real,real),bool),fun(fun(real,product_prod(real,real)),fun(real,bool)),combb(product_prod(real,real),bool,real),P_1)),hAPP(fun(real,fun(real,real)),fun(real,fun(real,product_prod(real,real))),hAPP(fun(real,fun(fun(real,real),fun(real,product_prod(real,real)))),fun(fun(real,fun(real,real)),fun(real,fun(real,product_prod(real,real)))),combs(real,fun(real,real),fun(real,product_prod(real,real))),hAPP(fun(real,fun(real,product_prod(real,real))),fun(real,fun(fun(real,real),fun(real,product_prod(real,real)))),hAPP(fun(fun(real,product_prod(real,real)),fun(fun(real,real),fun(real,product_prod(real,real)))),fun(fun(real,fun(real,product_prod(real,real))),fun(real,fun(fun(real,real),fun(real,product_prod(real,real))))),combb(fun(real,product_prod(real,real)),fun(fun(real,real),fun(real,product_prod(real,real))),real),combb(real,product_prod(real,real),real)),product_Pair(real,real))),hAPP(real,fun(real,fun(real,real)),hAPP(fun(real,fun(real,fun(real,real))),fun(real,fun(real,fun(real,real))),combc(real,real,fun(real,real)),hAPP(fun(real,fun(real,fun(real,real))),fun(real,fun(real,fun(real,real))),hAPP(fun(fun(real,fun(real,real)),fun(real,fun(real,real))),fun(fun(real,fun(real,fun(real,real))),fun(real,fun(real,fun(real,real)))),combb(fun(real,fun(real,real)),fun(real,fun(real,real)),real),combc(real,real,real)),hAPP(fun(real,fun(real,real)),fun(real,fun(real,fun(real,real))),hAPP(fun(fun(real,real),fun(real,fun(real,real))),fun(fun(real,fun(real,real)),fun(real,fun(real,fun(real,real)))),combb(fun(real,real),fun(real,fun(real,real)),real),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,fun(real,real))),combb(real,fun(real,real),real),inverse_divide(real))),plus_plus(real)))),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))))),hAPP(fun(real,real),fun(real,fun(real,product_prod(real,real))),hAPP(fun(real,fun(fun(real,real),fun(real,product_prod(real,real)))),fun(fun(real,real),fun(real,fun(real,product_prod(real,real)))),combc(real,fun(real,real),fun(real,product_prod(real,real))),hAPP(fun(real,fun(real,fun(real,product_prod(real,real)))),fun(real,fun(fun(real,real),fun(real,product_prod(real,real)))),hAPP(fun(fun(real,fun(real,product_prod(real,real))),fun(fun(real,real),fun(real,product_prod(real,real)))),fun(fun(real,fun(real,fun(real,product_prod(real,real)))),fun(real,fun(fun(real,real),fun(real,product_prod(real,real))))),combb(fun(real,fun(real,product_prod(real,real))),fun(fun(real,real),fun(real,product_prod(real,real))),real),combs(real,real,product_prod(real,real))),hAPP(fun(real,fun(real,real)),fun(real,fun(real,fun(real,product_prod(real,real)))),hAPP(fun(fun(real,real),fun(real,fun(real,product_prod(real,real)))),fun(fun(real,fun(real,real)),fun(real,fun(real,fun(real,product_prod(real,real))))),combb(fun(real,real),fun(real,fun(real,product_prod(real,real))),real),hAPP(fun(real,fun(real,product_prod(real,real))),fun(fun(real,real),fun(real,fun(real,product_prod(real,real)))),combb(real,fun(real,product_prod(real,real)),real),product_Pair(real,real))),hAPP(real,fun(real,fun(real,real)),hAPP(fun(real,fun(real,fun(real,real))),fun(real,fun(real,fun(real,real))),combc(real,real,fun(real,real)),hAPP(fun(real,fun(real,fun(real,real))),fun(real,fun(real,fun(real,real))),hAPP(fun(fun(real,fun(real,real)),fun(real,fun(real,real))),fun(fun(real,fun(real,fun(real,real))),fun(real,fun(real,fun(real,real)))),combb(fun(real,fun(real,real)),fun(real,fun(real,real)),real),combc(real,real,real)),hAPP(fun(real,fun(real,real)),fun(real,fun(real,fun(real,real))),hAPP(fun(fun(real,real),fun(real,fun(real,real))),fun(fun(real,fun(real,real)),fun(real,fun(real,fun(real,real)))),combb(fun(real,real),fun(real,fun(real,real)),real),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,fun(real,real))),combb(real,fun(real,real),real),inverse_divide(real))),plus_plus(real)))),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))),combi(real))))),hAPP(fun(real,fun(real,real)),fun(real,fun(real,product_prod(real,real))),hAPP(fun(real,fun(fun(real,real),fun(real,product_prod(real,real)))),fun(fun(real,fun(real,real)),fun(real,fun(real,product_prod(real,real)))),combs(real,fun(real,real),fun(real,product_prod(real,real))),hAPP(fun(real,fun(real,product_prod(real,real))),fun(real,fun(fun(real,real),fun(real,product_prod(real,real)))),hAPP(fun(fun(real,product_prod(real,real)),fun(fun(real,real),fun(real,product_prod(real,real)))),fun(fun(real,fun(real,product_prod(real,real))),fun(real,fun(fun(real,real),fun(real,product_prod(real,real))))),combb(fun(real,product_prod(real,real)),fun(fun(real,real),fun(real,product_prod(real,real))),real),combb(real,product_prod(real,real),real)),product_Pair(real,real))),hAPP(real,fun(real,fun(real,real)),hAPP(fun(real,fun(real,fun(real,real))),fun(real,fun(real,fun(real,real))),combc(real,real,fun(real,real)),hAPP(fun(real,fun(real,fun(real,real))),fun(real,fun(real,fun(real,real))),hAPP(fun(fun(real,fun(real,real)),fun(real,fun(real,real))),fun(fun(real,fun(real,fun(real,real))),fun(real,fun(real,fun(real,real)))),combb(fun(real,fun(real,real)),fun(real,fun(real,real)),real),combc(real,real,real)),hAPP(fun(real,fun(real,real)),fun(real,fun(real,fun(real,real))),hAPP(fun(fun(real,real),fun(real,fun(real,real))),fun(fun(real,fun(real,real)),fun(real,fun(real,fun(real,real)))),combb(fun(real,real),fun(real,fun(real,real)),real),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,fun(real,real))),combb(real,fun(real,real),real),inverse_divide(real))),plus_plus(real)))),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))),hAPP(nat,product_prod(real,real),hAPP(real,fun(nat,product_prod(real,real)),hAPP(real,fun(real,fun(nat,product_prod(real,real))),hAPP(fun(product_prod(real,real),bool),fun(real,fun(real,fun(nat,product_prod(real,real)))),bolzano_bisect,P_1),A_2),B_1),N_1))) # label(fact_4053_Bolzano__bisect_Osimps_I2_J) # label(axiom) # label(non_clause).  [assumption].
7.45/7.46	1173 (all X_a (real_normed_algebra(X_a) -> (all Y zero_zero(X_a) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),zero_zero(X_a)),Y)))) # label(fact_877_mult__left_Ozero) # label(axiom) # label(non_clause).  [assumption].
7.45/7.47	1174 (all X_a ti(fun(fun(real,fun(real,X_a)),fun(complex,X_a)),complex_rec(X_a)) = complex_rec(X_a)) # label(tsy_c_Complex_Ocomplex_Ocomplex__rec_res) # label(axiom) # label(non_clause).  [assumption].
7.45/7.47	1175 (all X_a (linord219039673up_add(X_a) -> (all X all Y hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),Y)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),X)),hAPP(X_a,X_a,uminus_uminus(X_a),Y))))) # label(fact_4943_minus__max__eq__min) # label(axiom) # label(non_clause).  [assumption].
7.45/7.47	1176 (all A_2 all X_3 all X_1 (hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),X_3),X_1),sequentially)) -> ((exists N_3 all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_3),N_2)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,X_3,N_2)),A_2)))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_1),A_2))))) # label(fact_4432_LIMSEQ__le__const2) # label(axiom) # label(non_clause).  [assumption].
7.45/7.47	1177 (all B all A_1 (zero_zero(int) != ti(int,A_1) | zero_zero(int) != ti(int,B) -> (exists C_4 exists D_3 (hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,A_1),B)),C_4) = ti(int,A_1) & hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,C_4),D_3) = one_one(int) & hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,A_1),B)),D_3) = ti(int,B))))) # label(fact_3484_make__zrelprime) # label(axiom) # label(non_clause).  [assumption].
7.45/7.47	1178 (all X_a all X_b (real_n2089651433ebra_1(X_b) & metric_space(X_a) & zero(X_a) -> (all A_2 all K (ti(X_a,K) != zero_zero(X_a) -> -hBOOL(hAPP(filter(X_b),bool,hAPP(X_a,fun(filter(X_b),bool),hAPP(fun(X_b,X_a),fun(X_a,fun(filter(X_b),bool)),tendsto(X_b,X_a),hAPP(X_a,fun(X_b,X_a),combk(X_a,X_b),K)),zero_zero(X_a)),hAPP(X_b,filter(X_b),at(X_b),A_2))))))) # label(fact_4562_LIM__not__zero) # label(axiom) # label(non_clause).  [assumption].
7.45/7.47	1179 (all X hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),X),one_one(nat)) = one_one(nat)) # label(fact_3252_gcd__lcm__complete__lattice__nat_Oinf__bot__right) # label(axiom) # label(non_clause).  [assumption].
7.45/7.47	1180 (all X_1 all Y_1 all Z (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Z)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_1),Y_1)) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),X_1),Z)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),Y_1),Z)))))) # label(fact_714_real__mult__le__cancel__iff1) # label(axiom) # label(non_clause).  [assumption].
7.45/7.47	1181 (all X_b all X_a (topological_space(X_b) & topological_space(X_a) -> (all L all Ma all F all G all A_2 all B_1 (ti(X_a,B_1) = ti(X_a,A_2) -> ((all X_2 (ti(X_a,X_2) != ti(X_a,B_1) -> hAPP(X_a,X_b,F,X_2) = hAPP(X_a,X_b,G,X_2))) -> (ti(X_b,Ma) = ti(X_b,L) -> (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),G),Ma),hAPP(X_a,filter(X_a),at(X_a),B_1))) <-> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),L),hAPP(X_a,filter(X_a),at(X_a),A_2)))))))))) # label(fact_4762_LIM__cong) # label(axiom) # label(non_clause).  [assumption].
7.45/7.47	1182 (all X_a (ring(X_a) -> (all A_1 all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),hAPP(X_a,X_a,uminus_uminus(X_a),B)) = hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B))))) # label(fact_2030_minus__mult__right) # label(axiom) # label(non_clause).  [assumption].
7.45/7.47	1183 (all X all N all P_5 (hBOOL(hAPP(nat,bool,prime,P_5)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),P_5),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),X),N))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),P_5),N)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),X),N)))))) # label(fact_3056_prime__divexp__n) # label(axiom) # label(non_clause).  [assumption].
7.45/7.47	1184 (all Y_1 hAPP(fun(real,bool),real,the(real),hAPP(fun(real,bool),fun(real,bool),hAPP(fun(real,fun(bool,bool)),fun(fun(real,bool),fun(real,bool)),combs(real,bool,bool),hAPP(fun(real,bool),fun(real,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(real,bool),fun(real,fun(bool,bool))),combb(bool,fun(bool,bool),real),fconj),hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)))),hAPP(fun(real,bool),fun(real,bool),hAPP(fun(real,fun(bool,bool)),fun(fun(real,bool),fun(real,bool)),combs(real,bool,bool),hAPP(fun(real,bool),fun(real,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(real,bool),fun(real,fun(bool,bool))),combb(bool,fun(bool,bool),real),fconj),hAPP(real,fun(real,bool),hAPP(fun(real,fun(real,bool)),fun(real,fun(real,bool)),combc(real,real,bool),ord_less_eq(real)),pi))),hAPP(real,fun(real,bool),hAPP(fun(real,fun(real,bool)),fun(real,fun(real,bool)),combc(real,real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),hAPP(fun(real,fun(real,bool)),fun(fun(real,real),fun(real,fun(real,bool))),combb(real,fun(real,bool),real),fequal(real)),cos)),Y_1)))) = hAPP(real,real,arccos,Y_1)) # label(fact_4137_arccos__def) # label(axiom) # label(non_clause).  [assumption].
7.45/7.47	1185 (all X all N (-hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),N))) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(real,nat,natfloor,X)),hAPP(int,nat,number_number_of(nat),N)) = hAPP(real,nat,natfloor,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),hAPP(int,real,number_number_of(real),N)))))) # label(fact_1841_natfloor__add__number__of) # label(axiom) # label(non_clause).  [assumption].
7.45/7.47	1186 (all X_a (linorder(X_a) -> (all X all Y hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),Y),X) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),Y)))) # label(fact_4970_min__max_Osup__commute) # label(axiom) # label(non_clause).  [assumption].
7.45/7.47	1187 (all X all K_4 hAPP(real,real,sqrt,hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),K_4)) = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,sqrt,X)),K_4)) # label(fact_1618_real__sqrt__power) # label(axiom) # label(non_clause).  [assumption].
7.45/7.47	1188 (all X_a (real_normed_field(X_a) -> (all Y_3 all X_3 (hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),X_3)) -> (hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),Y_3)) -> hAPP(fun(nat,X_a),X_a,suminf(X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),plus_plus(X_a)),X_3)),Y_3)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(fun(nat,X_a),X_a,suminf(X_a),X_3)),hAPP(fun(nat,X_a),X_a,suminf(X_a),Y_3))))))) # label(fact_3983_suminf__add) # label(axiom) # label(non_clause).  [assumption].
7.45/7.47	1189 (all X_b all X_a (topological_space(X_b) & real_normed_vector(X_a) -> (all F all A_2 all L_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(fun(X_a,X_a),fun(X_a,X_b),hAPP(fun(X_a,X_b),fun(fun(X_a,X_a),fun(X_a,X_b)),combb(X_a,X_b,X_a),F),hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2))),L_2),hAPP(X_a,filter(X_a),at(X_a),zero_zero(X_a)))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),L_2),hAPP(X_a,filter(X_a),at(X_a),A_2))))))) # label(fact_4581_LIM__offset__zero__cancel) # label(axiom) # label(non_clause).  [assumption].
7.45/7.47	1190 (all B all B_5 all A_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B_5)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B_5),B)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_1),B)),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_1),B_5))))))) # label(fact_1022_zdiv__mono2) # label(axiom) # label(non_clause).  [assumption].
7.45/7.47	1191 (all X_a (real_algebra_1(X_a) & real_normed_vector(X_a) -> (all X_3 (hBOOL(hAPP(fun(nat,real),bool,summable(real),X_3)) -> hAPP(real,X_a,of_real(X_a),hAPP(fun(nat,real),real,suminf(real),X_3)) = hAPP(fun(nat,X_a),X_a,suminf(X_a),hAPP(fun(nat,real),fun(nat,X_a),hAPP(fun(real,X_a),fun(fun(nat,real),fun(nat,X_a)),combb(real,X_a,nat),of_real(X_a)),X_3)))))) # label(fact_4020_of__real_Osuminf) # label(axiom) # label(non_clause).  [assumption].
7.45/7.47	1192 (all X_a (topological_space(X_a) -> (all A_2 hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,X_a),fun(X_a,bool),isCont(X_a,X_a),combi(X_a)),A_2))))) # label(fact_4899_isCont__ident) # label(axiom) # label(non_clause).  [assumption].
7.45/7.47	1193 (all K_4 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),K_4)) -> (exists N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_2)) & hAPP(nat,int,semiring_1_of_nat(int),N_2) = ti(int,K_4))))) # label(fact_1480_zero__less__imp__eq__int) # label(axiom) # label(non_clause).  [assumption].
7.45/7.47	1194 (all Y all X (hBOOL(hAPP(int,bool,nat_is_nat,X)) -> (hBOOL(hAPP(int,bool,nat_is_nat,Y)) -> hBOOL(hAPP(int,bool,nat_is_nat,hAPP(int,int,hAPP(int,fun(int,int),div_div(int),X),Y)))))) # label(fact_4848_Divides_Otransfer__int__nat__function__closures_I1_J) # label(axiom) # label(non_clause).  [assumption].
7.45/7.47	1195 (all X one_one(real) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,sin,X)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,cos,X)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) # label(fact_2386_sin__cos__squared__add) # label(axiom) # label(non_clause).  [assumption].
7.45/7.47	1196 (all K (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),min_1),hAPP(int,int,bit0,K))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),min_1),K)))) # label(fact_298_rel__simps_I8_J) # label(axiom) # label(non_clause).  [assumption].
7.45/7.47	1197 (all N hAPP(nat,nat,suc,hAPP(nat,nat,suc,N)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) # label(fact_1429_add__2__eq__Suc_H) # label(axiom) # label(non_clause).  [assumption].
7.45/7.47	1198 (all I_1 all M all N (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),I_1),hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),M),N))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),I_1),M)))) # label(fact_4367_dvd__gcd__D1__int) # label(axiom) # label(non_clause).  [assumption].
7.45/7.47	1199 (all N all X hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,real_1(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),N),X))),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(nat,real,real_1(nat),N)),hAPP(nat,real,real_1(nat),X))))) # label(fact_2328_real__of__nat__div4) # label(axiom) # label(non_clause).  [assumption].
7.45/7.47	1200 (all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),Y)),one_one(real))) -> hAPP(real,real,cos,hAPP(real,real,arccos,Y)) = Y)) # label(fact_2260_cos__arccos__abs) # label(axiom) # label(non_clause).  [assumption].
7.45/7.47	1201 (all N all M hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),M),N)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),M),N))) # label(fact_1085_mult__div__cancel) # label(axiom) # label(non_clause).  [assumption].
7.45/7.47	1202 (all X_a (real_vector(X_a) -> (all A_2 all X_1 (zero_zero(X_a) = hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_2),X_1) <-> A_2 = zero_zero(real) | zero_zero(X_a) = ti(X_a,X_1))))) # label(fact_4708_scaleR__eq__0__iff) # label(axiom) # label(non_clause).  [assumption].
7.45/7.47	1203 (all Ma all N_1 (zero_zero(nat) = Ma & N_1 = zero_zero(nat) <-> zero_zero(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Ma),N_1))) # label(fact_543_add__is__0) # label(axiom) # label(non_clause).  [assumption].
7.45/7.47	1204 (all N all M (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N),M)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N)),N) = M)) # label(fact_693_le__add__diff__inverse2) # label(axiom) # label(non_clause).  [assumption].
7.45/7.47	1205 (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_219_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J) # label(axiom) # label(non_clause).  [assumption].
7.45/7.47	1206 (all X_a all X_b all X_c all Y -(all A_4 all B_4 all C_4 ti(product_prod(X_a,product_prod(X_b,X_c)),Y) != hAPP(product_prod(X_b,X_c),product_prod(X_a,product_prod(X_b,X_c)),hAPP(X_a,fun(product_prod(X_b,X_c),product_prod(X_a,product_prod(X_b,X_c))),product_Pair(X_a,product_prod(X_b,X_c)),A_4),hAPP(X_c,product_prod(X_b,X_c),hAPP(X_b,fun(X_c,product_prod(X_b,X_c)),product_Pair(X_b,X_c),B_4),C_4)))) # label(fact_3147_prod__cases3) # label(axiom) # label(non_clause).  [assumption].
7.45/7.47	1207 (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_68_zadd__zmult__distrib) # label(axiom) # label(non_clause).  [assumption].
7.45/7.47	1208 (all X_a (linorder(X_a) -> (all X_1 all Y_1 all Z (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X_1),Y_1)),Z)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),Z)) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y_1),Z)))))) # label(fact_4830_min__le__iff__disj) # label(axiom) # label(non_clause).  [assumption].
7.45/7.47	1209 (all B all Q_5 all R_5 all Q_3 all R_4 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),Q_5)),R_5)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),Q_3)),R_4))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),R_5)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),R_5),B)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),R_4),B)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Q_5),Q_3))))))) # label(fact_266_unique__quotient__lemma) # label(axiom) # label(non_clause).  [assumption].
7.45/7.47	1210 (all X_a (semiring_div(X_a) -> (all A_1 all C all B (ti(X_a,B) != zero_zero(X_a) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),B))),B) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),A_1),B)))))) # label(fact_1039_div__mult__self1) # label(axiom) # label(non_clause).  [assumption].
7.45/7.47	1211 (all Y_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,hAPP(nat,fun(real,real),root,N_1),Y_1))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Y_1))))) # label(fact_2694_real__root__gt__0__iff) # label(axiom) # label(non_clause).  [assumption].
7.45/7.47	1212 (all A_1 all B (zero_zero(int) != ti(int,B) -> (zero_zero(int) != hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_1),B) -> hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,uminus_uminus(int),A_1)),B) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,uminus_uminus(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_1),B))),one_one(int))) & (zero_zero(int) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_1),B) -> hAPP(int,int,uminus_uminus(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_1),B)) = hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,uminus_uminus(int),A_1)),B)))) # label(fact_2180_zdiv__zminus1__eq__if) # label(axiom) # label(non_clause).  [assumption].
7.45/7.47	1213 (all X_a (field_inverse_zero(X_a) -> (all A_1 all B all C (zero_zero(X_a) != ti(X_a,C) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),A_1),B) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),hAPP(X_a,X_a,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_1690_mult__divide__mult__cancel__left) # label(axiom) # label(non_clause).  [assumption].
7.45/7.47	1214 (all W hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),W),W))) # label(fact_657_real__le__refl) # label(axiom) # label(non_clause).  [assumption].
7.45/7.47	1215 (all A_1 all B (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_1),B)),B)))) # label(fact_988_pos__mod__bound) # label(axiom) # label(non_clause).  [assumption].
7.45/7.47	1216 (all R_4 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),R_4),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(int,real,real_1(int),hAPP(real,int,archim2085082626_floor(real),R_4))),one_one(real))))) # label(fact_3397_real__of__int__floor__add__one__gt) # label(axiom) # label(non_clause).  [assumption].
7.45/7.47	1217 (all J_2 all A_1 all P_5 (hBOOL(hAPP(int,bool,zprime,P_5)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),P_5)) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_1),zero_zero(int)),P_5)) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,J_2),zero_zero(int)),P_5)) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),quadRes,P_5),A_1)) -> -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,J_2),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),hAPP(int,int,hAPP(int,fun(int,int),multInv,P_5),J_2))),P_5)))))))) # label(fact_830_MultInvPair__distinct) # label(axiom) # label(non_clause).  [assumption].
7.45/7.47	1218 (all X_a all C_1 all A_3 all B_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_3),B_2)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),A_3)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),B_2))))) # label(fact_1920_subsetD) # label(axiom) # label(non_clause).  [assumption].
7.45/7.47	1219 (all X_a (real_normed_field(X_a) -> ti(fun(fun(X_a,X_a),fun(X_a,fun(X_a,bool))),deriv(X_a)) = deriv(X_a))) # label(tsy_c_Deriv_Oderiv_res) # label(axiom) # label(non_clause).  [assumption].
7.45/7.47	1220 (all X_b all X_a (real_normed_vector(X_b) & topological_space(X_a) -> (all R_1 all G all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),G),zero_zero(X_b)),hAPP(X_a,filter(X_a),at(X_a),A_2))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(fun(X_a,X_b),fun(X_a,X_b),hAPP(fun(X_b,X_b),fun(fun(X_a,X_b),fun(X_a,X_b)),combb(X_b,X_b,X_a),hAPP(real,fun(X_b,X_b),scaleR_scaleR(X_b),R_1)),G)),zero_zero(X_b)),hAPP(X_a,filter(X_a),at(X_a),A_2))))))) # label(fact_4735_scaleR__right_OLIM__zero) # label(axiom) # label(non_clause).  [assumption].
7.45/7.47	1221 (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_1867_abs__triangle__ineq) # label(axiom) # label(non_clause).  [assumption].
7.45/7.47	1222 (all U_1 U_1 = hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(nat,fun(nat,bool),ord_lessThan(nat),U_1))) # label(fact_4315_card__lessThan) # label(axiom) # label(non_clause).  [assumption].
7.45/7.47	1223 (all X_a (linorder(X_a) -> (all X_1 all Y_1 (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y_1)) <-> ti(X_a,X_1) = ti(X_a,Y_1) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y_1),X_1)))))) # label(fact_1562_not__less__iff__gr__or__eq) # label(axiom) # label(non_clause).  [assumption].
7.45/7.47	1224 (all X_a (metric_space(X_a) -> ti(fun(fun(nat,X_a),X_a),lim(X_a)) = lim(X_a))) # label(tsy_c_SEQ_Olim_res) # label(axiom) # label(non_clause).  [assumption].
7.45/7.47	1225 (all D all A_1 all B (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,D),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A_1),B))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,D),A_1)))) # label(fact_2849_coprime__rmul2) # label(axiom) # label(non_clause).  [assumption].
7.45/7.47	1226 (all X_a (divisi14063676e_zero(X_a) -> (all A_2 all B_1 (ti(X_a,B_1) = ti(X_a,A_2) <-> hAPP(X_a,X_a,inverse_inverse(X_a),B_1) = hAPP(X_a,X_a,inverse_inverse(X_a),A_2))))) # label(fact_2522_inverse__eq__iff__eq) # label(axiom) # label(non_clause).  [assumption].
7.45/7.47	1227 (all X_1 all Y_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X_1),Y_1)),zero_zero(real))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),Y_1),hAPP(real,real,uminus_uminus(real),X_1))))) # label(fact_2108_real__add__less__0__iff) # label(axiom) # label(non_clause).  [assumption].
7.45/7.47	1228 (all X_c all X_a all X_b all F all A_2 all B_1 all A_3 (hBOOL(hAPP(fun(product_prod(X_a,X_b),bool),bool,hAPP(product_prod(X_a,X_b),fun(fun(product_prod(X_a,X_b),bool),bool),member(product_prod(X_a,X_b)),hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),A_2),B_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,hAPP(X_a,fun(X_b,X_c),F,A_2),B_1)),hAPP(fun(product_prod(X_a,X_b),bool),fun(X_c,bool),hAPP(fun(product_prod(X_a,X_b),X_c),fun(fun(product_prod(X_a,X_b),bool),fun(X_c,bool)),image(product_prod(X_a,X_b),X_c),hAPP(fun(X_a,fun(X_b,X_c)),fun(product_prod(X_a,X_b),X_c),product_prod_case(X_a,X_b,X_c),F)),A_3))))) # label(fact_3981_pair__imageI) # label(axiom) # label(non_clause).  [assumption].
7.45/7.47	1229 (all X_b all X_a all Q_1 all Q_2 all P_1 all P_4 (hBOOL(hAPP(X_a,bool,P_1,P_4)) -> (hBOOL(hAPP(X_b,bool,Q_1,Q_2)) -> hBOOL(hAPP(X_b,bool,Q_1,hAPP(product_prod(X_a,X_b),X_b,product_snd(X_a,X_b),hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),P_4),Q_2)))) & hBOOL(hAPP(X_a,bool,P_1,hAPP(product_prod(X_a,X_b),X_a,product_fst(X_a,X_b),hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),P_4),Q_2))))))) # label(fact_3124_conjI__realizer) # label(axiom) # label(non_clause).  [assumption].
7.45/7.47	1230 (all X_b all X_a (semiring_0(X_a) -> (all R_1 all F all A_3 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),R_1),hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co1399186613setsum(X_b,X_a),F),A_3)) = hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co1399186613setsum(X_b,X_a),hAPP(fun(X_b,X_a),fun(X_b,X_a),hAPP(fun(X_a,X_a),fun(fun(X_b,X_a),fun(X_b,X_a)),combb(X_a,X_a,X_b),hAPP(X_a,fun(X_a,X_a),times_times(X_a),R_1)),F)),A_3)))) # label(fact_4211_setsum__right__distrib) # label(axiom) # label(non_clause).  [assumption].
7.45/7.47	1231 (all N all M (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),M)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),N)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),M),N)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),N),M)) -> ti(int,M) = ti(int,N)))))) # label(fact_205_zdvd__antisym__nonneg) # label(axiom) # label(non_clause).  [assumption].
7.45/7.47	1232 (all X_a (semiring_1(X_a) -> (all M 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)) = hAPP(nat,X_a,semiring_1_of_nat(X_a),hAPP(nat,nat,suc,M))))) # label(fact_1218_of__nat__Suc) # label(axiom) # label(non_clause).  [assumption].
7.45/7.47	1233 (all B all A_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),B))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B))))) # label(fact_257_pos__zmult__pos) # label(axiom) # label(non_clause).  [assumption].
7.45/7.47	1234 (all X_1 hBOOL(hAPP(real,bool,hAPP(fun(real,real),fun(real,bool),isCont(real,real),sqrt),X_1))) # label(fact_4889_isCont__real__sqrt) # label(axiom) # label(non_clause).  [assumption].
7.45/7.47	1235 (all X_a (semiring_div(X_a) -> (all A_1 all B all C hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),B),C))),C) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)),C)))) # label(fact_938_mod__add__eq) # label(axiom) # label(non_clause).  [assumption].
7.45/7.47	1236 (all C all A_1 all B all M (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_1),B),M)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,B),C),M)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_1),C),M))))) # label(fact_316_zcong__trans) # label(axiom) # label(non_clause).  [assumption].
7.45/7.47	1237 (all I_1 all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),I_1),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),I_1),N))) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),one_one(nat)),I_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N))))) # label(fact_533_power__dvd__imp__le) # label(axiom) # label(non_clause).  [assumption].
7.45/7.47	1238 (all X_a (number_ring(X_a) -> hAPP(X_a,X_a,uminus_uminus(X_a),one_one(X_a)) = hAPP(int,X_a,number_number_of(X_a),min_1))) # label(fact_2104_number__of__Min) # label(axiom) # label(non_clause).  [assumption].
7.45/7.47	1239 (all Z_1 hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(complex,real,re,Z_1)),hAPP(complex,real,norm_norm(complex),Z_1)) = hAPP(complex,real,re,hAPP(complex,complex,sgn_sgn(complex),Z_1))) # label(fact_3009_Re__sgn) # label(axiom) # label(non_clause).  [assumption].
7.45/7.47	1240 (all X_a (real_normed_field(X_a) -> (all Y exists K_2 ((all X_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),X_2),Y))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(X_a,real,norm_norm(X_a),X_2)),K_2)))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),K_2)))))) # label(fact_1806_divide_Ononneg__bounded) # label(axiom) # label(non_clause).  [assumption].
7.45/7.47	1241 (all X_a (linorder(X_a) -> (all Z all X_1 all Y_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z),Y_1)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z),X_1)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X_1),Y_1))))))) # label(fact_4799_min__less__iff__conj) # label(axiom) # label(non_clause).  [assumption].
7.45/7.47	1242 (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_437_mult__left__le__one__le) # label(axiom) # label(non_clause).  [assumption].
7.45/7.47	1243 (all X hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(complex,real,re,X)),hAPP(complex,real,norm_norm(complex),X)))) # label(fact_2998_complex__Re__le__cmod) # label(axiom) # label(non_clause).  [assumption].
7.45/7.47	1244 (all P_1 all X_1 all Y_1 ((hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X_1),Y_1)) -> hBOOL(hAPP(int,bool,P_1,zero_zero(int)))) & (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Y_1),X_1)) -> hBOOL(hAPP(int,bool,P_1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(nat,int,semiring_1_of_nat(int),X_1)),hAPP(nat,int,semiring_1_of_nat(int),Y_1))))) <-> hBOOL(hAPP(int,bool,P_1,hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X_1),Y_1)))))) # label(fact_1425_zdiff__int__split) # label(axiom) # label(non_clause).  [assumption].
7.45/7.47	1245 (all A_1 all B all C all D hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,A_1),B)),hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,C),D)) = hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A_1),C)),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),B),D))) # label(fact_2747_complex__diff) # label(axiom) # label(non_clause).  [assumption].
7.45/7.47	1246 (all R_4 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),R_4),one_one(real))),hAPP(int,real,real_1(int),hAPP(real,int,archim2085082626_floor(real),R_4))))) # label(fact_3400_real__of__int__floor__ge__diff__one) # label(axiom) # label(non_clause).  [assumption].
7.45/7.47	1247 (all X_a (comm_semiring_1(X_a) -> (all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),zero_zero(X_a)),A_1)) -> ti(X_a,A_1) = zero_zero(X_a))))) # label(fact_329_dvd__0__left) # label(axiom) # label(non_clause).  [assumption].
7.45/7.47	1248 (all Y all X (zero_zero(real) != hAPP(real,real,cos,X) -> (hAPP(real,real,cos,Y) != zero_zero(real) -> hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,tan,X)),hAPP(real,real,tan,Y)) = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,sin,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),Y))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,cos,X)),hAPP(real,real,cos,Y)))))) # label(fact_2371_add__tan__eq) # label(axiom) # label(non_clause).  [assumption].
7.45/7.47	1249 (all X_a all A_3 all B_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_3),B_2)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),B_2),A_3)) -> ti(fun(X_a,bool),A_3) = ti(fun(X_a,bool),B_2)))) # label(fact_1919_equalityI) # label(axiom) # label(non_clause).  [assumption].
7.45/7.47	1250 (all X_a all A_3 all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),powp(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(X_a,bool)),combc(X_a,fun(X_a,bool),bool),member(X_a)),A_3)),X_2)) <-> hBOOL(hAPP(fun(fun(X_a,bool),bool),bool,hAPP(fun(X_a,bool),fun(fun(fun(X_a,bool),bool),bool),member(fun(X_a,bool)),X_2),hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),pow(X_a),A_3))))) # label(fact_4871_Powp__Pow__eq) # label(axiom) # label(non_clause).  [assumption].
7.45/7.47	1251 (all X_a (metric_space(X_a) -> (all X_3 ((all E (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),E)) -> (exists M_3 all M_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_3),M_2)) -> (all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_3),N_2)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),hAPP(nat,X_a,X_3,M_2)),hAPP(nat,X_a,X_3,N_2))),E)))))))) -> hBOOL(hAPP(fun(nat,X_a),bool,cauchy(X_a),X_3)))))) # label(fact_3525_metric__CauchyI) # label(axiom) # label(non_clause).  [assumption].
7.45/7.47	1252 (all X_1 all P_4 (hBOOL(hAPP(int,bool,zprime,P_4)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),P_4)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),hAPP(int,fun(int,bool),sRStar,P_4))) -> hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),hAPP(int,int,hAPP(int,fun(int,int),standardRes,P_4),X_1)),hAPP(int,fun(int,bool),sRStar,P_4))))))) # label(fact_1161_StandardRes__SRStar__prop4) # label(axiom) # label(non_clause).  [assumption].
7.45/7.47	1253 (all X_a (semiring_0(X_a) & power(X_a) -> (all W ((hAPP(int,nat,number_number_of(nat),W) != zero_zero(nat) -> zero_zero(X_a) = hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),zero_zero(X_a)),hAPP(int,nat,number_number_of(nat),W))) & (zero_zero(nat) = hAPP(int,nat,number_number_of(nat),W) -> hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),zero_zero(X_a)),hAPP(int,nat,number_number_of(nat),W)) = one_one(X_a)))))) # label(fact_262_power__0__left__number__of) # label(axiom) # label(non_clause).  [assumption].
7.45/7.47	1254 (all X_a (number_ring(X_a) -> (all Z_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Z_1),hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Z_1),Z_1)))) # label(fact_142_mult__2__right) # label(axiom) # label(non_clause).  [assumption].
7.45/7.47	1255 (all M hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),M)))) # label(fact_582_le__square) # label(axiom) # label(non_clause).  [assumption].
7.45/7.47	1256 (all C all D all A_1 all B all M (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_1),B),M)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,C),D),M)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),C)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),D)),M))))) # label(fact_360_zcong__zmult) # label(axiom) # label(non_clause).  [assumption].
7.45/7.47	1257 (all W_1 all Z (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),one_one(int)))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_1),Z)))) # label(fact_509_zle__diff1__eq) # label(axiom) # label(non_clause).  [assumption].
7.45/7.47	1258 (all X_1 hAPP(real,real,exp(real),X_1) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),one_one(real)),X_1)),hAPP(fun(nat,real),real,suminf(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),inverse_inverse(real)),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),hAPP(fun(nat,nat),fun(nat,nat),hAPP(fun(nat,nat),fun(fun(nat,nat),fun(nat,nat)),combb(nat,nat,nat),fact_fact(nat)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),hAPP(real,fun(nat,real),power_power(real),X_1)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))))) # label(fact_3975_exp__first__two__terms) # label(axiom) # label(non_clause).  [assumption].
7.45/7.47	1259 (all X_a (archim1804426504_field(X_a) -> (all X exists Z_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),hAPP(int,X_a,ring_1_of_int(X_a),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Z_2),one_one(int))))) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(int,X_a,ring_1_of_int(X_a),Z_2)),X)))))) # label(fact_3616_floor__exists) # label(axiom) # label(non_clause).  [assumption].
7.45/7.47	1260 (all M all N all K_4 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K_4)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_4),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_4),N)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),M),N))) # label(fact_1118_nat__mult__div__cancel1) # label(axiom) # label(non_clause).  [assumption].
7.45/7.47	1261 (all X_a (ord(X_a) -> ord_lessThan(X_a) = ti(fun(X_a,fun(X_a,bool)),ord_lessThan(X_a)))) # label(tsy_c_SetInterval_Oord__class_OlessThan_res) # label(axiom) # label(non_clause).  [assumption].
7.45/7.47	1262 (all A_2 hBOOL(hAPP(complex,bool,hAPP(fun(complex,real),fun(complex,bool),isCont(complex,real),im),A_2))) # label(fact_4893_Im_OisCont) # label(axiom) # label(non_clause).  [assumption].
7.45/7.47	1263 (all X_a (comm_ring_1(X_a) -> (all X (-hBOOL(hAPP(nat,bool,even_odd_even(nat),X)) -> hAPP(X_a,X_a,uminus_uminus(X_a),one_one(X_a)) = hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),one_one(X_a))),X))))) # label(fact_2439_minus__one__odd__power) # label(axiom) # label(non_clause).  [assumption].
7.45/7.47	1264 (all X_a (ring(X_a) -> (all A_2 all E_2 all C_1 all B_1 all D_1 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),E_2)),C_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B_1),E_2)),D_1) <-> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),B_1),A_2)),E_2)),D_1) = ti(X_a,C_1))))) # label(fact_489_eq__add__iff2) # label(axiom) # label(non_clause).  [assumption].
7.45/7.47	1265 (all N_1 all Q_1 all P_1 ((all X_2 hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,Q_1,X_2)),hAPP(nat,nat,P_1,X_2)))) -> hAPP(fun(nat,bool),nat,hAPP(fun(nat,nat),fun(fun(nat,bool),nat),big_co1399186613setsum(nat,nat),hAPP(fun(nat,nat),fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,nat),fun(nat,nat)),combs(nat,nat,nat),hAPP(fun(nat,nat),fun(nat,fun(nat,nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,nat),fun(nat,fun(nat,nat))),combb(nat,fun(nat,nat),nat),minus_minus(nat)),P_1)),Q_1)),hAPP(nat,fun(nat,bool),ord_lessThan(nat),N_1)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(fun(nat,bool),nat,hAPP(fun(nat,nat),fun(fun(nat,bool),nat),big_co1399186613setsum(nat,nat),P_1),hAPP(nat,fun(nat,bool),ord_lessThan(nat),N_1))),hAPP(fun(nat,bool),nat,hAPP(fun(nat,nat),fun(fun(nat,bool),nat),big_co1399186613setsum(nat,nat),Q_1),hAPP(nat,fun(nat,bool),ord_lessThan(nat),N_1))))) # label(fact_4326_sum__diff__distrib) # label(axiom) # label(non_clause).  [assumption].
7.45/7.47	1266 (all X_a (comm_monoid_add(X_a) & topological_space(X_a) -> hBOOL(hAPP(X_a,bool,hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),hAPP(X_a,fun(nat,X_a),combk(X_a,nat),zero_zero(X_a))),zero_zero(X_a))))) # label(fact_4078_sums__zero) # label(axiom) # label(non_clause).  [assumption].
7.45/7.47	1267 (all N all A_1 all B all P_5 (hBOOL(hAPP(nat,bool,prime,P_5)) -> (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),P_5),B)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),P_5),N)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A_1),B))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),P_5),N)),A_1)))))) # label(fact_3069_prime__power__dvd__cancel__right) # label(axiom) # label(non_clause).  [assumption].
7.45/7.47	1268 (all X_a (real_normed_vector(X_a) -> (exists K_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),K_2)) & (all A_4 all B_4 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_4),B_4))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,norm_norm(real),A_4)),hAPP(X_a,real,norm_norm(X_a),B_4))),K_2)))))))) # label(fact_4755_scaleR_Ononneg__bounded) # label(axiom) # label(non_clause).  [assumption].
7.45/7.47	1269 (all Ma all N_1 all Qr ((zero_zero(nat) != N_1 -> (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),hAPP(product_prod(nat,nat),nat,product_snd(nat,nat),Qr))) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(product_prod(nat,nat),nat,product_snd(nat,nat),Qr)),zero_zero(nat)))) & (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),hAPP(product_prod(nat,nat),nat,product_snd(nat,nat),Qr))) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(product_prod(nat,nat),nat,product_snd(nat,nat),Qr)),N_1)))) & (zero_zero(nat) = N_1 -> hAPP(product_prod(nat,nat),nat,product_fst(nat,nat),Qr) = zero_zero(nat)) & Ma = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(product_prod(nat,nat),nat,product_fst(nat,nat),Qr)),N_1)),hAPP(product_prod(nat,nat),nat,product_snd(nat,nat),Qr)) <-> hBOOL(hAPP(product_prod(nat,nat),bool,hAPP(nat,fun(product_prod(nat,nat),bool),hAPP(nat,fun(nat,fun(product_prod(nat,nat),bool)),divmod_nat_rel,Ma),N_1),Qr)))) # label(fact_3127_divmod__nat__rel__def) # label(axiom) # label(non_clause).  [assumption].
7.45/7.47	1270 (all X hAPP(real,nat,natfloor,X) = hAPP(int,nat,nat_1,hAPP(real,int,archim2085082626_floor(real),X))) # label(fact_2860_natfloor__def) # label(axiom) # label(non_clause).  [assumption].
7.45/7.47	1271 (all K_4 hAPP(product_prod(int,int),rat,frct,hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),K_4),zero_zero(int))) = zero_zero(rat)) # label(fact_3708_Frct__code__post_I2_J) # label(axiom) # label(non_clause).  [assumption].
7.45/7.47	1272 (all X_a all X_b ti(fun(fun(X_a,bool),fun(fun(X_b,bool),fun(sum_sum(X_a,X_b),bool))),sum_Plus(X_a,X_b)) = sum_Plus(X_a,X_b)) # label(tsy_c_Sum__Type_OPlus_res) # label(axiom) # label(non_clause).  [assumption].
7.45/7.47	1273 (all X_a (group_add(X_a) -> (all A_2 (zero_zero(X_a) = ti(X_a,A_2) <-> zero_zero(X_a) = hAPP(X_a,X_a,uminus_uminus(X_a),A_2))))) # label(fact_2022_neg__equal__0__iff__equal) # label(axiom) # label(non_clause).  [assumption].
7.45/7.47	1274 (all X_a (linordered_idom(X_a) -> (all X_1 all W_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X_1),hAPP(int,nat,number_number_of(nat),W_1)))) <-> hAPP(int,nat,number_number_of(nat),W_1) = zero_zero(nat) | zero_zero(X_a) != ti(X_a,X_1) & hBOOL(hAPP(nat,bool,even_odd_even(nat),hAPP(int,nat,number_number_of(nat),W_1))) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),X_1)) & -hBOOL(hAPP(nat,bool,even_odd_even(nat),hAPP(int,nat,number_number_of(nat),W_1))))))) # label(fact_2464_zero__less__power__eq__number__of) # label(axiom) # label(non_clause).  [assumption].
7.45/7.47	1275 (all X_a (division_ring(X_a) -> (all A_1 (zero_zero(X_a) != ti(X_a,A_1) -> hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(X_a,X_a,inverse_inverse(X_a),A_1)) = hAPP(X_a,X_a,inverse_inverse(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),A_1)))))) # label(fact_2556_nonzero__inverse__minus__eq) # label(axiom) # label(non_clause).  [assumption].
7.45/7.47	1276 (all X_2 hAPP(nat,real,hAPP(fun(nat,real),fun(nat,real),diffs(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),inverse_inverse(real)),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),fact_fact(nat)))),X_2) = hAPP(real,real,inverse_inverse(real),hAPP(nat,real,real_1(nat),hAPP(nat,nat,fact_fact(nat),X_2)))) # label(fact_4119_exp__fdiffs) # label(axiom) # label(non_clause).  [assumption].
7.45/7.47	1277 (all X_a (division_ring(X_a) -> (all A_1 all B all C hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),B),C)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)),C)))) # label(fact_1662_add__divide__distrib) # label(axiom) # label(non_clause).  [assumption].
7.45/7.47	1278 (all X_1 all Y_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_1),Y_1)) & -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y_1),X_1)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_1),Y_1)) & -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y_1),X_1)))) # label(fact_623_dvd_Oless__le__not__le) # label(axiom) # label(non_clause).  [assumption].
7.45/7.47	1279 (all Ma all K all N_1 (hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),K),N_1) = one_one(int) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),K),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Ma),N_1))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),K),Ma))))) # label(fact_4392_coprime__dvd__mult__iff__int) # label(axiom) # label(non_clause).  [assumption].
7.45/7.47	1280 (all X_a all R_1 all A_2 ((exists X_2 (ti(X_a,X_2) = ti(X_a,A_2) & (all Xa (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),R_1,Xa),X_2)) -> hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,fun(X_a,bool)),fun(X_a,bool),accp(X_a),R_1),Xa)))))) <-> hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,fun(X_a,bool)),fun(X_a,bool),accp(X_a),R_1),A_2)))) # label(fact_2918_accp_Osimps) # label(axiom) # label(non_clause).  [assumption].
7.45/7.47	1281 (all N all M hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),N),M) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),M)),M)) # label(fact_4957_nat__minus__add__max) # label(axiom) # label(non_clause).  [assumption].
7.45/7.47	1282 (all X_a (real_normed_field(X_a) -> (all C_1 all F all X_1 all D_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),F),X_1),D_2)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),hAPP(fun(X_a,X_a),fun(X_a,X_a),hAPP(fun(X_a,X_a),fun(fun(X_a,X_a),fun(X_a,X_a)),combb(X_a,X_a,X_a),hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1)),F)),X_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1),D_2))))))) # label(fact_3863_DERIV__cmult) # label(axiom) # label(non_clause).  [assumption].
7.45/7.47	1283 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X),one_one(real))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,exp(real),X)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),one_one(real)),X)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))))) # label(fact_2626_exp__bound) # label(axiom) # label(non_clause).  [assumption].
7.45/7.47	1284 (all X_a (division_ring(X_a) -> (all B all A_1 (ti(X_a,A_1) != zero_zero(X_a) -> (ti(X_a,B) != zero_zero(X_a) -> hAPP(X_a,X_a,inverse_inverse(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,inverse_inverse(X_a),B)),hAPP(X_a,X_a,inverse_inverse(X_a),A_1))))))) # label(fact_2551_nonzero__inverse__mult__distrib) # label(axiom) # label(non_clause).  [assumption].
7.45/7.47	1285 (all R_4 all X hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),R_4),hAPP(complex,real,im,X)) = hAPP(complex,real,im,hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),R_4),X))) # label(fact_4691_Im_OscaleR) # label(axiom) # label(non_clause).  [assumption].
7.45/7.47	1286 (all X_a (real_normed_field(X_a) -> (all N_1 all F all X_1 all D_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),F),X_1),D_2)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),hAPP(nat,fun(X_a,X_a),hAPP(fun(X_a,fun(nat,X_a)),fun(nat,fun(X_a,X_a)),combc(X_a,nat,X_a),hAPP(fun(X_a,X_a),fun(X_a,fun(nat,X_a)),hAPP(fun(X_a,fun(nat,X_a)),fun(fun(X_a,X_a),fun(X_a,fun(nat,X_a))),combb(X_a,fun(nat,X_a),X_a),power_power(X_a)),F)),N_1)),X_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),N_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),D_2),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(X_a,X_a,F,X_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),hAPP(nat,nat,suc,zero_zero(nat)))))))))))) # label(fact_3889_DERIV__power) # label(axiom) # label(non_clause).  [assumption].
7.45/7.47	1287 (all X_a ti(fun(fun(X_a,nat),fun(fun(product_prod(X_a,X_a),bool),fun(product_prod(X_a,X_a),bool))),mlex_prod(X_a)) = mlex_prod(X_a)) # label(tsy_c_Wellfounded_Omlex__prod_res) # label(axiom) # label(non_clause).  [assumption].
7.45/7.47	1288 (all X_a (linord581940658strict(X_a) -> (all A_2 all C_1 all B_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_2),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B_1),C_1))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),B_1)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C_1)) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),zero_zero(X_a))) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_1),A_2)))))) # label(fact_397_mult__less__cancel__right__disj) # label(axiom) # label(non_clause).  [assumption].
7.45/7.47	1289 (all A_1 all B (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),zero_zero(int))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_1),B))))) # label(fact_987_neg__mod__bound) # label(axiom) # label(non_clause).  [assumption].
7.45/7.47	1290 (all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,number_number_of(real),min_1)),Y)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),Y),one_one(real))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,arcsin,Y)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))))) # label(fact_2132_arcsin__ubound) # label(axiom) # label(non_clause).  [assumption].
7.45/7.47	1291 (all X_a (linorder(X_a) -> (all X_1 all Y_1 (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y_1)) -> (ti(X_a,Y_1) = ti(X_a,X_1) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),Y_1))))))) # label(fact_1590_linorder__antisym__conv1) # label(axiom) # label(non_clause).  [assumption].
7.45/7.47	1292 (all N hAPP(int,nat,nat_1,hAPP(nat,int,semiring_1_of_nat(int),N)) = N) # label(fact_1228_nat__int) # label(axiom) # label(non_clause).  [assumption].
7.45/7.47	1293 (all X_a all D_2 all B_2 all A_3 all C_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_3),C_2)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),D_2),B_2)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_3),B_2)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),C_2),D_2)))))) # label(fact_1996_Diff__mono) # label(axiom) # label(non_clause).  [assumption].
7.45/7.47	1294 (all X_a (field_inverse_zero(X_a) & real_field(X_a) -> (all X all Y hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),hAPP(real,X_a,of_real(X_a),X)),hAPP(real,X_a,of_real(X_a),Y)) = hAPP(real,X_a,of_real(X_a),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),X),Y))))) # label(fact_2792_of__real__divide) # label(axiom) # label(non_clause).  [assumption].
7.45/7.47	1295 (all X_a (number(X_a) -> (all W_1 all X_1 (ti(X_a,X_1) = hAPP(int,X_a,number_number_of(X_a),W_1) <-> ti(X_a,X_1) = hAPP(int,X_a,number_number_of(X_a),W_1))))) # label(fact_90_number__of__reorient) # label(axiom) # label(non_clause).  [assumption].
7.45/7.47	1296 (all Ma all W_1 ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),W_1)) -> ti(int,W_1) = hAPP(nat,int,semiring_1_of_nat(int),Ma)) & (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),W_1)) -> zero_zero(nat) = Ma) <-> Ma = hAPP(int,nat,nat_1,W_1))) # label(fact_1406_nat__eq__iff2) # label(axiom) # label(non_clause).  [assumption].
7.45/7.47	1297 (all X_a (sgn_if(X_a) -> zero_zero(X_a) = hAPP(X_a,X_a,sgn_sgn(X_a),zero_zero(X_a)))) # label(fact_2203_sgn0) # label(axiom) # label(non_clause).  [assumption].
7.45/7.47	1298 (all G all X_1 (hBOOL(hAPP(real,bool,hAPP(fun(nat,real),fun(real,bool),sums(real),G),X_1)) -> hBOOL(hAPP(real,bool,hAPP(fun(nat,real),fun(real,bool),sums(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(real,fun(nat,fun(real,real)),hAPP(fun(nat,fun(real,fun(real,real))),fun(real,fun(nat,fun(real,real))),combc(nat,real,fun(real,real)),hAPP(fun(nat,bool),fun(nat,fun(real,fun(real,real))),hAPP(fun(bool,fun(real,fun(real,real))),fun(fun(nat,bool),fun(nat,fun(real,fun(real,real)))),combb(bool,fun(real,fun(real,real)),nat),if(real)),even_odd_even(nat))),zero_zero(real))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),G),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),hAPP(fun(nat,nat),fun(nat,fun(nat,nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,nat),fun(nat,fun(nat,nat))),combb(nat,fun(nat,nat),nat),div_div(nat)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),minus_minus(nat)),one_one(nat)))),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))),X_1)))) # label(fact_4104_sums__if_H) # label(axiom) # label(non_clause).  [assumption].
7.45/7.47	1299 (all M all V hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,hAPP(int,int,bit1,pls)))),M)),hAPP(int,nat,number_number_of(nat),V)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,suc,hAPP(nat,nat,suc,hAPP(nat,nat,suc,M)))),hAPP(int,nat,number_number_of(nat),V))) # label(fact_1436_Suc__div__eq__add3__div__number__of) # label(axiom) # label(non_clause).  [assumption].
7.45/7.47	1300 (all N all M (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),M)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),M),N)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,fact_fact(int),M)),hAPP(int,int,fact_fact(int),N)))))) # label(fact_3187_fact__less__mono__int) # label(axiom) # label(non_clause).  [assumption].
7.45/7.47	1301 (all X_a (real_n1866405975lgebra(X_a) -> (all X all Y hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),Y)) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(X_a,real,norm_norm(X_a),X)),hAPP(X_a,real,norm_norm(X_a),Y))))) # label(fact_1778_norm__mult) # label(axiom) # label(non_clause).  [assumption].
7.45/7.47	1302 (all X_a (dvd(X_a) -> dvd_dvd(X_a) = ti(fun(X_a,fun(X_a,bool)),dvd_dvd(X_a)))) # label(tsy_c_Rings_Odvd__class_Odvd_res) # label(axiom) # label(non_clause).  [assumption].
7.45/7.47	1303 (all N all M (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),N),M)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),N)),M)) | M = N | M = zero_zero(nat))) # label(fact_610_divides__cases) # label(axiom) # label(non_clause).  [assumption].
7.45/7.47	1304 (all X (-hBOOL(hAPP(int,bool,even_odd_even(int),X)) -> ti(int,X) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),X),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),one_one(int)))) # label(fact_1201_two__times__odd__div__two__plus__one) # label(axiom) # label(non_clause).  [assumption].
7.45/7.47	1305 (all A_1 all B hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A_1),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,uminus_uminus(real),B)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))) = hAPP(complex,complex,inverse_inverse(complex),hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,A_1),B))) # label(fact_2750_complex__inverse) # label(axiom) # label(non_clause).  [assumption].
7.45/7.47	1306 (all X_a (plus(X_a) & linorder(X_a) & dvd(X_a) -> (all D_1 all Sa exists Z_2 all X_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_2),Z_2)) -> (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),D_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X_2),Sa))) <-> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),D_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X_2),Sa)))))))) # label(fact_861_minf_I10_J) # label(axiom) # label(non_clause).  [assumption].
7.45/7.47	1307 (all X_a (order(X_a) -> (all F ((all X_2 all Y_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_2),Y_2)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(nat,X_a,F,X_2)),hAPP(nat,X_a,F,Y_2))))) -> hBOOL(hAPP(fun(nat,X_a),bool,hAPP(fun(nat,fun(nat,bool)),fun(fun(nat,X_a),bool),mono(nat,X_a),dvd_dvd(nat)),F)))))) # label(fact_4794_dvd_OmonoI) # label(axiom) # label(non_clause).  [assumption].
7.45/7.47	1308 (all V_1 all K all A_2 all B_1 (A_2 != B_1 -> ((all X_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),V_1),X_2),K))) -> hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,V_1,A_2)),hAPP(real,real,V_1,B_1))),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(real,real,V_1,hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A_2),B_1)),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))) # label(fact_2658_DERIV__const__average) # label(axiom) # label(non_clause).  [assumption].
7.45/7.47	1309 (all X_a (real_n1866405975lgebra(X_a) -> (all X all N hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(X_a,real,norm_norm(X_a),X)),N) = hAPP(X_a,real,norm_norm(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),N))))) # label(fact_1782_norm__power) # label(axiom) # label(non_clause).  [assumption].
7.45/7.47	1310 (all Z_1 all W hAPP(real,real,hAPP(real,fun(real,real),times_times(real),Z_1),W) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),W),Z_1)) # label(fact_704_real__mult__commute) # label(axiom) # label(non_clause).  [assumption].
7.45/7.47	1311 (all X_b all X_a all Q_1 all P_1 all X_1 all Y_1 (hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),P_1,X_1),Y_1)) -> (hBOOL(hAPP(fun(X_a,fun(X_b,bool)),bool,hAPP(fun(X_a,fun(X_b,bool)),fun(fun(X_a,fun(X_b,bool)),bool),ord_less_eq(fun(X_a,fun(X_b,bool))),P_1),Q_1)) -> hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),Q_1,X_1),Y_1))))) # label(fact_4341_rev__predicate2D) # label(axiom) # label(non_clause).  [assumption].
7.45/7.47	1312 (all M all N hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),M),N) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),M),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),M),N)),N))) # label(fact_922_zmod__zdiv__equality_H) # label(axiom) # label(non_clause).  [assumption].
7.45/7.47	1313 (all X_a (linordered_idom(X_a) -> (all X_1 all W_1 (hBOOL(hAPP(nat,bool,even_odd_even(nat),hAPP(int,nat,number_number_of(nat),W_1))) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),X_1)) & -hBOOL(hAPP(nat,bool,even_odd_even(nat),hAPP(int,nat,number_number_of(nat),W_1))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X_1),hAPP(int,nat,number_number_of(nat),W_1)))))))) # label(fact_2455_zero__le__power__eq__number__of) # label(axiom) # label(non_clause).  [assumption].
7.45/7.47	1314 (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_1411_Suc3__eq__add__3) # label(axiom) # label(non_clause).  [assumption].
7.45/7.47	1315 (all X_1 ((exists Y_2 hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat)))),Y_2)) = X_1) <-> -hBOOL(hAPP(nat,bool,even_odd_even(nat),X_1)))) # label(fact_2441_odd__nat__equiv__def2) # label(axiom) # label(non_clause).  [assumption].
7.45/7.47	1316 (all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),X_1)) -> hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),inverse_inverse(real)),hAPP(real,fun(nat,real),power_power(real),X_1))),zero_zero(real)),sequentially)))) # label(fact_4436_LIMSEQ__inverse__realpow__zero) # label(axiom) # label(non_clause).  [assumption].
7.45/7.47	1317 (all X_a (linorder(X_a) -> (all A_1 all B all C hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),B),C)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),A_1),B)),C)))) # label(fact_4810_min__max_Oinf_Oassoc) # label(axiom) # label(non_clause).  [assumption].
7.45/7.47	1318 (all Diff all N_1 all X_1 (X_1 = zero_zero(real) -> (zero_zero(nat) != N_1 -> hAPP(real,real,hAPP(nat,fun(real,real),Diff,zero_zero(nat)),zero_zero(real)) = hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),inverse_divide(real)),hAPP(real,fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(real,fun(nat,real)),combc(nat,real,real),Diff),zero_zero(real)))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),fact_fact(nat))))),hAPP(real,fun(nat,real),power_power(real),X_1))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),N_1))))) # label(fact_4230_Maclaurin__zero) # label(axiom) # label(non_clause).  [assumption].
7.45/7.48	1319 (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),C),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),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))))) # label(fact_222_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) # label(axiom) # label(non_clause).  [assumption].
7.45/7.48	1320 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,sin,X)))))) # label(fact_2366_sin__gt__zero) # label(axiom) # label(non_clause).  [assumption].
7.45/7.48	1321 (all X_a ti(fun(X_a,fun(fun(code_code_numeral,X_a),fun(code_code_numeral,X_a))),code_c600343653l_case(X_a)) = code_c600343653l_case(X_a)) # label(tsy_c_Code__Numeral_Ocode__numeral_Ocode__numeral__case_res) # label(axiom) # label(non_clause).  [assumption].
7.45/7.48	1322 (all X all Y hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X),hAPP(real,real,sqrt,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),Y),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))))) # label(fact_1645_real__sqrt__sum__squares__ge1) # label(axiom) # label(non_clause).  [assumption].
7.45/7.48	1323 (all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,number_number_of(real),min_1)),Y)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),Y),one_one(real))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,arccos,Y)),pi))))) # label(fact_2264_arccos__ubound) # label(axiom) # label(non_clause).  [assumption].
7.45/7.48	1324 (all X_a (real_normed_vector(X_a) -> (all R_4 all X all Xa_1 hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),R_4),X)),Xa_1) = hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),R_4),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),X),Xa_1))))) # label(fact_4698_scaleR__left_OscaleR) # label(axiom) # label(non_clause).  [assumption].
7.45/7.48	1325 (all Z_1 all X all Y all P_5 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),X),Y)),one_one(int)),P_5)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),X),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),Y),Z_1))),one_one(int)),P_5)))) # label(fact_455_zcong__zpower__zmult) # label(axiom) # label(non_clause).  [assumption].
7.45/7.48	1326 (all N_1 all Ma (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),Ma))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),N_1)))) # label(fact_681_zero__less__diff) # label(axiom) # label(non_clause).  [assumption].
7.45/7.48	1327 (all X_a (semiring_1(X_a) -> (all M all N hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),M)),N) = hAPP(nat,X_a,semiring_1_of_nat(X_a),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),M),N))))) # label(fact_1292_of__nat__power) # label(axiom) # label(non_clause).  [assumption].
7.45/7.48	1328 (all X_a (field_inverse_zero(X_a) -> (all B_1 all C_1 all A_2 ((ti(X_a,C_1) != zero_zero(X_a) -> ti(X_a,B_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),C_1)) & (zero_zero(X_a) = ti(X_a,C_1) -> ti(X_a,A_2) = zero_zero(X_a)) <-> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),B_1),C_1) = ti(X_a,A_2))))) # label(fact_1686_divide__eq__eq) # label(axiom) # label(non_clause).  [assumption].
7.45/7.48	1329 (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_766_add__right__imp__eq) # label(axiom) # label(non_clause).  [assumption].
7.45/7.48	1330 (all F all A_2 all B_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A_2),B_1)) -> ((all X_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A_2),X_2)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_2),B_1)) -> (exists Y_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),Y_2),zero_zero(real))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),F),X_2),Y_2)))))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,F,B_1)),hAPP(real,real,F,A_2)))))) # label(fact_2842_DERIV__neg__imp__decreasing) # label(axiom) # label(non_clause).  [assumption].
7.45/7.48	1331 (all N hAPP(real,nat,natfloor,hAPP(nat,real,real_1(nat),N)) = N) # label(fact_2294_natfloor__real__of__nat) # label(axiom) # label(non_clause).  [assumption].
7.45/7.48	1332 (all X_a (linorder(X_a) -> (all X_1 all Y_1 all Z (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),Z)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y_1),Z)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X_1),Y_1)),Z)))))) # label(fact_4983_min__max_Ole__sup__iff) # label(axiom) # label(non_clause).  [assumption].
7.45/7.48	1333 (all Z all W_1 (hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),Z),W_1)) <-> Z != W_1 & hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),Z),W_1)))) # label(fact_3723_less__rat__def) # label(axiom) # label(non_clause).  [assumption].
7.45/7.48	1334 (all P_5 all M ((M = zero_zero(nat) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),P_5),M) = one_one(nat)) & (zero_zero(nat) != M -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),P_5),M) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),P_5),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),P_5),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),one_one(nat))))))) # label(fact_720_power__eq__if) # label(axiom) # label(non_clause).  [assumption].
7.45/7.48	1335 (all N_1 all Diff all F all H ((all M_2 all T_4 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),T_4),H)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),T_4)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_2),N_1)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(nat,fun(real,real),Diff,M_2)),T_4),hAPP(real,real,hAPP(nat,fun(real,real),Diff,hAPP(nat,nat,suc,M_2)),T_4))))) & hAPP(nat,fun(real,real),Diff,zero_zero(nat)) = F & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),H)) -> (exists T_4 (hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),inverse_divide(real)),hAPP(real,fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(real,fun(nat,real)),combc(nat,real,real),Diff),zero_zero(real)))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),fact_fact(nat))))),hAPP(real,fun(nat,real),power_power(real),H))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),N_1))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(nat,fun(real,real),Diff,N_1),T_4)),hAPP(nat,real,real_1(nat),hAPP(nat,nat,fact_fact(nat),N_1)))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),H),N_1))) = hAPP(real,real,F,H) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),T_4),H)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),T_4)))))) # label(fact_4280_Maclaurin2__objl) # label(axiom) # label(non_clause).  [assumption].
7.45/7.48	1336 (all N (-hBOOL(hAPP(nat,bool,even_odd_even(nat),N)) -> (exists X_2 hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),N),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),X_2)),one_one(nat))))) # label(fact_2477_odd__square) # label(axiom) # label(non_clause).  [assumption].
7.45/7.48	1337 (all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),hAPP(real,real,exp(real),X_1))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X_1)))) # label(fact_2597_one__less__exp__iff) # label(axiom) # label(non_clause).  [assumption].
7.45/7.48	1338 (all X_a (linorder(X_a) -> (all X all Y hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),Y) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),Y))))) # label(fact_4968_min__max_Osup__left__idem) # label(axiom) # label(non_clause).  [assumption].
7.45/7.48	1339 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,M)),N)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N)))) # label(fact_1331_Suc__le__lessD) # label(axiom) # label(non_clause).  [assumption].
7.45/7.48	1340 (all X_a (linordered_idom(X_a) -> (all A_2 all B_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_2)),B_1)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),B_1)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),A_2)),B_1)))))) # label(fact_2083_abs__less__iff) # label(axiom) # label(non_clause).  [assumption].
7.45/7.48	1341 (all X_a (comm_semiring_1(X_a) -> (all A_1 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_1),A_1))))) # label(fact_311_dvd__refl) # label(axiom) # label(non_clause).  [assumption].
7.45/7.48	1342 (all B all A_1 all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A_1),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),B)) -> (exists D_3 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),D_3)) & (all Y_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),X),Y_2))),D_3)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A_1),Y_2)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),Y_2),B))))))))) # label(fact_1915_lemma__interval__lt) # label(axiom) # label(non_clause).  [assumption].
7.45/7.48	1343 (all N -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),zero_zero(nat)))) # label(fact_536_not__less0) # label(axiom) # label(non_clause).  [assumption].
7.45/7.48	1344 (all M all K_4 all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),K_4)),N)) -> -(hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N)) -> -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_4),N))))) # label(fact_579_add__leE) # label(axiom) # label(non_clause).  [assumption].
7.45/7.48	1345 (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_812_add__nonpos__nonpos) # label(axiom) # label(non_clause).  [assumption].
7.45/7.48	1346 (all X_a (metric_space(X_a) -> (all E_2 all X_3 (hBOOL(hAPP(fun(nat,X_a),bool,cauchy(X_a),X_3)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),E_2)) -> (exists M_3 all M_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_3),M_2)) -> (all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_3),N_2)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),hAPP(nat,X_a,X_3,M_2)),hAPP(nat,X_a,X_3,N_2))),E_2))))))))))) # label(fact_3523_metric__CauchyD) # label(axiom) # label(non_clause).  [assumption].
7.45/7.48	1347 (all X all N hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,abs_abs(int),X)),N)))) # label(fact_1941_zero__le__zpower__abs) # label(axiom) # label(non_clause).  [assumption].
7.45/7.48	1348 (all N all M hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),N),M) = hAPP(int,quickcheck_code_int,quickcheck_of_int,hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(quickcheck_code_int,int,quickcheck_int_of,N)),hAPP(quickcheck_code_int,int,quickcheck_int_of,M)))) # label(fact_3533_mod__code__int__def) # label(axiom) # label(non_clause).  [assumption].
7.45/7.48	1349 (all Y hAPP(real,real,tan,hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),Y)) = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),one_one(real)),hAPP(real,real,tan,Y))) # label(fact_2275_tan__inverse) # label(axiom) # label(non_clause).  [assumption].
7.45/7.48	1350 (all X_a (real_normed_field(X_a) -> (all R_4 all X all Y hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),R_4),X)),Y) = hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),R_4),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),X),Y))))) # label(fact_4707_divide_OscaleR) # label(axiom) # label(non_clause).  [assumption].
7.45/7.48	1351 (all X_a all X_b all X_c all Z all C_1 all P_4 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Z),hAPP(product_prod(X_b,X_c),fun(X_a,bool),hAPP(fun(X_b,fun(X_c,fun(X_a,bool))),fun(product_prod(X_b,X_c),fun(X_a,bool)),product_prod_case(X_b,X_c,fun(X_a,bool)),C_1),P_4))) -> -(all X_2 all Y_2 (hAPP(X_c,product_prod(X_b,X_c),hAPP(X_b,fun(X_c,product_prod(X_b,X_c)),product_Pair(X_b,X_c),X_2),Y_2) = ti(product_prod(X_b,X_c),P_4) -> -hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Z),hAPP(X_c,fun(X_a,bool),hAPP(X_b,fun(X_c,fun(X_a,bool)),C_1,X_2),Y_2))))))) # label(fact_4059_mem__splitE) # label(axiom) # label(non_clause).  [assumption].
7.45/7.48	1352 (all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),hAPP(nat,nat,suc,zero_zero(nat)))) <-> N_1 = zero_zero(nat))) # label(fact_1321_less__Suc0) # label(axiom) # label(non_clause).  [assumption].
7.45/7.48	1353 (all X_a (archim1727834104eiling(X_a) -> (all X hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),hAPP(int,X_a,ring_1_of_int(X_a),hAPP(X_a,int,archimedean_ceiling(X_a),X))))))) # label(fact_3586_le__of__int__ceiling) # label(axiom) # label(non_clause).  [assumption].
7.45/7.48	1354 (all X_a (monoid_mult(X_a) & comm_ring(X_a) -> (all Z all H all Ma hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),hAPP(X_a,fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(X_a,fun(nat,X_a)),combc(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),minus_minus(X_a)),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),times_times(X_a)),hAPP(fun(nat,nat),fun(nat,X_a),hAPP(fun(nat,X_a),fun(fun(nat,nat),fun(nat,X_a)),combb(nat,X_a,nat),hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Z),H))),hAPP(nat,fun(nat,nat),minus_minus(nat),Ma)))),hAPP(X_a,fun(nat,X_a),power_power(X_a),Z)))),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),Z),Ma))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),Ma)) = hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),times_times(X_a)),hAPP(X_a,fun(nat,X_a),power_power(X_a),Z))),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),minus_minus(X_a)),hAPP(fun(nat,nat),fun(nat,X_a),hAPP(fun(nat,X_a),fun(fun(nat,nat),fun(nat,X_a)),combb(nat,X_a,nat),hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Z),H))),hAPP(nat,fun(nat,nat),minus_minus(nat),Ma)))),hAPP(fun(nat,nat),fun(nat,X_a),hAPP(fun(nat,X_a),fun(fun(nat,nat),fun(nat,X_a)),combb(nat,X_a,nat),hAPP(X_a,fun(nat,X_a),power_power(X_a),Z)),hAPP(nat,fun(nat,nat),minus_minus(nat),Ma))))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),Ma))))) # label(fact_4226_lemma__termdiff1) # label(axiom) # label(non_clause).  [assumption].
7.45/7.48	1355 (all X_b all X_a all P_5 ti(product_prod(X_a,X_b),P_5) = hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),hAPP(product_prod(X_a,X_b),X_a,product_fst(X_a,X_b),P_5)),hAPP(product_prod(X_a,X_b),X_b,product_snd(X_a,X_b),P_5))) # label(fact_3130_pair__collapse) # label(axiom) # label(non_clause).  [assumption].
7.45/7.48	1356 (all K_4 all L_4 all I_1 all J_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_1),J_2)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_4),L_4)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I_1),K_4)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J_2),L_4)))))) # label(fact_586_mult__le__mono) # label(axiom) # label(non_clause).  [assumption].
7.45/7.48	1357 (all X_b all X_a (linordered_field(X_a) -> (all F all A_3 hAPP(X_a,X_a,abs_abs(X_a),hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co302546470etprod(X_b,X_a),F),A_3)) = hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co302546470etprod(X_b,X_a),hAPP(fun(X_b,X_a),fun(X_b,X_a),hAPP(fun(X_a,X_a),fun(fun(X_b,X_a),fun(X_b,X_a)),combb(X_a,X_a,X_b),abs_abs(X_a)),F)),A_3)))) # label(fact_3948_abs__setprod) # label(axiom) # label(non_clause).  [assumption].
7.45/7.48	1358 (all X all Y (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),Y)) & -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y),X)) -> X != Y)) # label(fact_642_dvd_Oless__imp__not__eq) # label(axiom) # label(non_clause).  [assumption].
7.45/7.48	1359 (all J all I all P_1 all P_4 ((all I_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),P_4)) -> (hBOOL(hAPP(nat,bool,P_1,I_2)) -> hBOOL(hAPP(nat,bool,P_1,hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,suc,I_2)),P_4)))))) -> (hBOOL(hAPP(nat,bool,P_1,I)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),P_4)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),J),P_4)) -> hBOOL(hAPP(nat,bool,P_1,J))))))) # label(fact_1481_mod__induct) # label(axiom) # label(non_clause).  [assumption].
7.45/7.48	1360 (all A_1 all B hAPP(int,rat,hAPP(int,fun(int,rat),fract,hAPP(int,int,uminus_uminus(int),A_1)),hAPP(int,int,uminus_uminus(int),B)) = hAPP(int,rat,hAPP(int,fun(int,rat),fract,A_1),B)) # label(fact_3751_minus__rat__cancel) # label(axiom) # label(non_clause).  [assumption].
7.45/7.48	1361 (all A_2 hBOOL(hAPP(filter(complex),bool,hAPP(real,fun(filter(complex),bool),hAPP(fun(complex,real),fun(real,fun(filter(complex),bool)),tendsto(complex,real),im),hAPP(complex,real,im,A_2)),hAPP(complex,filter(complex),at(complex),A_2)))) # label(fact_4569_Im_Ocont) # label(axiom) # label(non_clause).  [assumption].
7.45/7.48	1362 (all N_1 all Ma (ti(int,Ma) != zero_zero(int) -> (one_one(int) = hAPP(int,int,abs_abs(int),N_1) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Ma),N_1)),Ma))))) # label(fact_1969_zdvd__mult__cancel1) # label(axiom) # label(non_clause).  [assumption].
7.45/7.48	1363 (all B (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B)) -> hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),B),one_one(int)) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,number_number_of(int),min_1)),B))) # label(fact_1064_zmod__minus1) # label(axiom) # label(non_clause).  [assumption].
7.45/7.48	1364 (all N one_one(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),hAPP(nat,nat,suc,N)),N)) # label(fact_3262_coprime__Suc__nat) # label(axiom) # label(non_clause).  [assumption].
7.45/7.48	1365 (all P_5 (hBOOL(hAPP(int,bool,zprime,P_5)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(int,int,zfact,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),P_5),one_one(int)))),hAPP(int,int,number_number_of(int),min_1)),P_5)))) # label(fact_756_Wilson__Russ) # label(axiom) # label(non_clause).  [assumption].
7.45/7.48	1366 (all X_a (number_ring(X_a) -> (all V 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))) = 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))))) # label(fact_16_add__special_I3_J) # label(axiom) # label(non_clause).  [assumption].
7.45/7.48	1367 (all P_1 all A0 all A1 (hBOOL(hAPP(product_prod(int,int),bool,hAPP(fun(product_prod(int,int),fun(product_prod(int,int),bool)),fun(product_prod(int,int),bool),accp(product_prod(int,int)),upto_rel),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),A0),A1))) -> ((all I_2 all J_1 (hBOOL(hAPP(product_prod(int,int),bool,hAPP(fun(product_prod(int,int),fun(product_prod(int,int),bool)),fun(product_prod(int,int),bool),accp(product_prod(int,int)),upto_rel),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),I_2),J_1))) -> ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),I_2),J_1)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),P_1,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),I_2),one_one(int))),J_1))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),P_1,I_2),J_1))))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),P_1,A0),A1))))) # label(fact_3555_upto_Opinduct) # label(axiom) # label(non_clause).  [assumption].
7.45/7.48	1368 (all A_1 all B all C all D hAPP(int,rat,hAPP(int,fun(int,rat),fract,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),D)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),C)) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),hAPP(int,rat,hAPP(int,fun(int,rat),fract,A_1),B)),hAPP(int,rat,hAPP(int,fun(int,rat),fract,C),D))) # label(fact_3754_divide__rat) # label(axiom) # label(non_clause).  [assumption].
7.45/7.48	1369 (all Ma all K all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),Ma),K)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N_1),K))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Ma),N_1)) | zero_zero(nat) = K)) # label(fact_724_nat__mult__dvd__cancel__disj_H) # label(axiom) # label(non_clause).  [assumption].
7.45/7.48	1370 (all X_a (real_normed_vector(X_a) -> (all X_1 (zero_zero(X_a) = ti(X_a,X_1) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),X_1)),zero_zero(real))))))) # label(fact_1786_norm__le__zero__iff) # label(axiom) # label(non_clause).  [assumption].
7.45/7.48	1371 (all M all R_4 all S_3 all T_5 all N (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),N)) -> (hAPP(product_prod(int,int),product_prod(int,product_prod(int,int)),hAPP(int,fun(product_prod(int,int),product_prod(int,product_prod(int,int))),product_Pair(int,product_prod(int,int)),R_4),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),S_3),T_5)) = hAPP(int,product_prod(int,product_prod(int,int)),hAPP(int,fun(int,product_prod(int,product_prod(int,int))),xzgcd,M),N) -> hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),S_3),M)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),T_5),N)) = ti(int,R_4)))) # label(fact_3082_xzgcd__linear) # label(axiom) # label(non_clause).  [assumption].
7.45/7.48	1372 (all X_a (real_normed_vector(X_a) -> (all Y_3 all B_1 all X_3 all A_2 (hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),X_3),A_2),sequentially)) -> (hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),Y_3),B_1),sequentially)) -> hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),minus_minus(X_a)),X_3)),Y_3)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_2),B_1)),sequentially))))))) # label(fact_4442_LIMSEQ__diff) # label(axiom) # label(non_clause).  [assumption].
7.45/7.48	1373 (all X hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(real,real,exp(real),X)))) # label(fact_2566_exp__ge__zero) # label(axiom) # label(non_clause).  [assumption].
7.45/7.48	1374 (all X_a (linord581940658strict(X_a) -> (all A_2 all B_1 all C_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),zero_zero(X_a))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1),A_2)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1),B_1))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_1),A_2))))))) # label(fact_389_mult__less__cancel__left__neg) # label(axiom) # label(non_clause).  [assumption].
7.45/7.48	1375 (all A_1 all B (hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(int,rat,ring_1_of_int(rat),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_1),B))),hAPP(int,rat,hAPP(int,fun(int,rat),fract,A_1),B))) & hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(int,rat,hAPP(int,fun(int,rat),fract,A_1),B)),hAPP(int,rat,ring_1_of_int(rat),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_1),B)),one_one(int))))))) # label(fact_3792_rat__floor__lemma) # label(axiom) # label(non_clause).  [assumption].
7.45/7.48	1376 (all X_1 all Y_1 (X_1 = zero_zero(real) & zero_zero(real) = Y_1 <-> hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),X_1),X_1)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),Y_1),Y_1)) = zero_zero(real))) # label(fact_707_real__two__squares__add__zero__iff) # label(axiom) # label(non_clause).  [assumption].
7.45/7.48	1377 (all N hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,fact,N)))) # label(fact_3544_fact__lt) # label(axiom) # label(non_clause).  [assumption].
7.45/7.48	1378 (all X all B all A_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A_1)) -> (one_one(real) != A_1 -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B)) -> (one_one(real) != B -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> hAPP(real,real,hAPP(real,fun(real,real),log,A_1),X) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,ln,B)),hAPP(real,real,ln,A_1))),hAPP(real,real,hAPP(real,fun(real,real),log,B),X)))))))) # label(fact_2651_log__eq__div__ln__mult__log) # label(axiom) # label(non_clause).  [assumption].
7.45/7.48	1379 (all X_a (ordered_ab_group_add(X_a) -> (all A_2 all B_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_2),B_1)),zero_zero(X_a))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),B_1)))))) # label(fact_826_less__iff__diff__less__0) # label(axiom) # label(non_clause).  [assumption].
7.45/7.48	1380 (all X all Y hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),hAPP(int,int,uminus_uminus(int),X)),Y) = hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),X),Y)) # label(fact_4376_gcd__neg1__int) # label(axiom) # label(non_clause).  [assumption].
7.45/7.48	1381 (all X_b all X_a all R_3 all X_1 all Y_1 (hBOOL(hAPP(fun(product_prod(X_a,X_b),bool),bool,hAPP(product_prod(X_a,X_b),fun(fun(product_prod(X_a,X_b),bool),bool),member(product_prod(X_a,X_b)),hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),X_1),Y_1)),R_3)) <-> hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),hAPP(fun(product_prod(X_a,X_b),bool),fun(X_a,fun(X_b,bool)),in_rel(X_a,X_b),R_3),X_1),Y_1)))) # label(fact_3043_in__rel__def) # label(axiom) # label(non_clause).  [assumption].
7.45/7.48	1382 (all X_a (linordered_field(X_a) -> (all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),one_one(X_a)),one_one(X_a)))),B)))))) # label(fact_1731_gt__half__sum) # label(axiom) # label(non_clause).  [assumption].
7.45/7.48	1383 (all X_a (linordered_semidom(X_a) -> (all A_1 all N all N_5 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N),N_5)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),one_one(X_a)),A_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N_5)))))))) # label(fact_411_power__increasing) # label(axiom) # label(non_clause).  [assumption].
7.45/7.48	1384 (all X_a (real_normed_vector(X_a) -> (all X hAPP(X_a,X_a,sgn_sgn(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),X)) = hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(X_a,X_a,sgn_sgn(X_a),X))))) # label(fact_2207_sgn__minus) # label(axiom) # label(non_clause).  [assumption].
7.45/7.48	1385 (all X all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X),Y)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,sqrt,X)),hAPP(real,real,sqrt,Y))))) # label(fact_1611_real__sqrt__le__mono) # label(axiom) # label(non_clause).  [assumption].
7.45/7.48	1386 (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_1389_Suc__pred) # label(axiom) # label(non_clause).  [assumption].
7.45/7.48	1387 (all X_a (ab_group_add(X_a) -> (all F all P_4 all Ma all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Ma),N_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_1),P_4)) -> hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),N_1),P_4)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),Ma),P_4))),hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),Ma),N_1)))))))) # label(fact_4200_setsum__diff__nat__ivl) # label(axiom) # label(non_clause).  [assumption].
7.45/7.48	1388 (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].
7.45/7.48	1389 (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_790_add__strict__right__mono) # label(axiom) # label(non_clause).  [assumption].
7.45/7.48	1390 (all N_1 all Ma (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(nat,real,real_1(nat),N_1)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,real_1(nat),Ma)),one_one(real)))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_1),Ma)))) # label(fact_2342_nat__le__real__less) # label(axiom) # label(non_clause).  [assumption].
7.45/7.48	1391 (all R_4 hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,zero_zero(real)),R_4) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),ii),hAPP(real,complex,of_real(complex),R_4))) # label(fact_2814_i__complex__of__real) # label(axiom) # label(non_clause).  [assumption].
7.45/7.48	1392 (all N all P_5 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),one_one(nat)),P_5)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),P_5),N)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),P_5),hAPP(nat,nat,fact,N)))))) # label(fact_3532_divides__fact) # label(axiom) # label(non_clause).  [assumption].
7.45/7.48	1393 (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_1856_abs__add__abs) # label(axiom) # label(non_clause).  [assumption].
7.45/7.48	1394 (all A_1 all B all C hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),A_1),B)),C) = hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),A_1),hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),B),C))) # label(fact_4365_gcd__assoc__int) # label(axiom) # label(non_clause).  [assumption].
7.45/7.48	1395 (all Ma all X_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),quadRes,Ma),X_1)) <-> (exists Y_2 hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),Y_2),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),X_1),Ma))))) # label(fact_608_QuadRes__def) # label(axiom) # label(non_clause).  [assumption].
7.45/7.48	1396 (all X_a all X_b all X_c all X_d all X_1 all P_1 ((all A_4 all B_4 all C_4 all D_3 hBOOL(hAPP(product_prod(X_a,product_prod(X_b,product_prod(X_c,X_d))),bool,P_1,hAPP(product_prod(X_b,product_prod(X_c,X_d)),product_prod(X_a,product_prod(X_b,product_prod(X_c,X_d))),hAPP(X_a,fun(product_prod(X_b,product_prod(X_c,X_d)),product_prod(X_a,product_prod(X_b,product_prod(X_c,X_d)))),product_Pair(X_a,product_prod(X_b,product_prod(X_c,X_d))),A_4),hAPP(product_prod(X_c,X_d),product_prod(X_b,product_prod(X_c,X_d)),hAPP(X_b,fun(product_prod(X_c,X_d),product_prod(X_b,product_prod(X_c,X_d))),product_Pair(X_b,product_prod(X_c,X_d)),B_4),hAPP(X_d,product_prod(X_c,X_d),hAPP(X_c,fun(X_d,product_prod(X_c,X_d)),product_Pair(X_c,X_d),C_4),D_3)))))) -> hBOOL(hAPP(product_prod(X_a,product_prod(X_b,product_prod(X_c,X_d))),bool,P_1,X_1)))) # label(fact_3154_prod__induct4) # label(axiom) # label(non_clause).  [assumption].
7.45/7.48	1397 (all P_1 all N_1 all K (hBOOL(hAPP(int,bool,P_1,hAPP(int,int,hAPP(int,fun(int,int),div_div(int),N_1),K))) <-> (zero_zero(int) = ti(int,K) -> hBOOL(hAPP(int,bool,P_1,zero_zero(int)))) & (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),zero_zero(int))) -> (all I_2 all J_1 (ti(int,N_1) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K),I_2)),J_1) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),J_1),zero_zero(int))) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),J_1)) -> hBOOL(hAPP(int,bool,P_1,I_2))))) & (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),K)) -> (all I_2 all J_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),J_1),K)) & ti(int,N_1) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K),I_2)),J_1) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),J_1)) -> hBOOL(hAPP(int,bool,P_1,I_2))))))) # label(fact_1055_split__zdiv) # label(axiom) # label(non_clause).  [assumption].
7.45/7.48	1398 (all A_3 all K (hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,bool),fun(fun(nat,bool),bool),ord_less_eq(fun(nat,bool)),A_3),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),K),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K),hAPP(fun(nat,bool),nat,finite_card(nat),A_3))))) -> A_3 = hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),K),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K),hAPP(fun(nat,bool),nat,finite_card(nat),A_3))))) # label(fact_4232_subset__card__intvl__is__intvl) # label(axiom) # label(non_clause).  [assumption].
7.45/7.48	1399 (all X_b all X_c all X_a (topological_space(X_a) & real_normed_vector(X_b) & real_normed_vector(X_c) -> (all G all Ma all F all L all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),L),hAPP(X_a,filter(X_a),at(X_a),A_2))) -> ((all X_2 (ti(X_a,A_2) != ti(X_a,X_2) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_c,real,norm_norm(X_c),hAPP(X_c,X_c,hAPP(X_c,fun(X_c,X_c),minus_minus(X_c),hAPP(X_a,X_c,G,X_2)),Ma))),hAPP(X_b,real,norm_norm(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),hAPP(X_a,X_b,F,X_2)),L)))))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_c,fun(filter(X_a),bool),hAPP(fun(X_a,X_c),fun(X_c,fun(filter(X_a),bool)),tendsto(X_a,X_c),G),Ma),hAPP(X_a,filter(X_a),at(X_a),A_2)))))))) # label(fact_4654_LIM__imp__LIM) # label(axiom) # label(non_clause).  [assumption].
7.45/7.48	1400 (all X_a (archim1727834104eiling(X_a) -> (all Z all X_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Z),hAPP(X_a,int,archim2085082626_floor(X_a),X_1))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(int,X_a,ring_1_of_int(X_a),Z)),one_one(X_a))),X_1)))))) # label(fact_3608_less__floor__iff) # label(axiom) # label(non_clause).  [assumption].
7.45/7.48	1401 (all A_2 all B_1 all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),X_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),powr,X_1),A_2)),hAPP(real,real,hAPP(real,fun(real,real),powr,X_1),B_1))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A_2),B_1))))) # label(fact_3352_powr__less__cancel__iff) # label(axiom) # label(non_clause).  [assumption].
7.45/7.48	1402 (all X_a (ord(X_a) -> (all I all K (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),I),K)) <-> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),I),hAPP(X_a,fun(X_a,bool),ord_lessThan(X_a),K))))))) # label(fact_4314_lessThan__iff) # label(axiom) # label(non_clause).  [assumption].
7.45/7.48	1403 (all X_a all X_b all F all A_3 all B_2 hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),A_3)),hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),B_2))),hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_2))))) # label(fact_3641_image__diff__subset) # label(axiom) # label(non_clause).  [assumption].
7.45/7.48	1404 (all X_a (number_ring(X_a) -> (all V hAPP(int,X_a,number_number_of(X_a),V) = hAPP(int,X_a,ring_1_of_int(X_a),hAPP(int,int,number_number_of(int),V))))) # label(fact_3565_of__int__number__of__eq) # label(axiom) # label(non_clause).  [assumption].
7.45/7.48	1405 (all X_a (linordered_semidom(X_a) -> (all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),Y),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),Y)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y))))))) # label(fact_105_power2__less__imp__less) # label(axiom) # label(non_clause).  [assumption].
7.45/7.48	1406 (all Ta all A_3 all D_1 all D_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),D_1),D_2)) -> (all X_2 ((all Xa (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xa),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastAtMost(int),one_one(int)),D_2))) -> (all Xb (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xb),A_3)) -> hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),Xb),Xa) != ti(int,X_2))))) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),D_1),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X_2),Ta))) -> -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),D_1),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X_2),D_2)),Ta)))))))) # label(fact_4647_aset_I10_J) # label(axiom) # label(non_clause).  [assumption].
7.45/7.48	1407 (all Ma all A_2 all B_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_2),B_1)) -> -hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),B_1),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),bnorRset,A_2),Ma))))) # label(fact_3206_Bnor__mem__zle__swap) # label(axiom) # label(non_clause).  [assumption].
7.45/7.48	1408 (all X_a all X_b (uminus(X_b) -> (all A_3 all X_2 hAPP(X_a,X_b,hAPP(fun(X_a,X_b),fun(X_a,X_b),uminus_uminus(fun(X_a,X_b)),A_3),X_2) = hAPP(X_b,X_b,uminus_uminus(X_b),hAPP(X_a,X_b,A_3,X_2))))) # label(fact_2965_fun__Compl__def) # label(axiom) # label(non_clause).  [assumption].
7.45/7.48	1409 (all A_1 hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_1),A_1) = zero_zero(int)) # label(fact_952_zmod__self) # label(axiom) # label(non_clause).  [assumption].
7.45/7.48	1410 (all X_a (real_normed_field(X_a) -> (all K all X_1 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),hAPP(X_a,fun(X_a,X_a),combk(X_a,X_a),K)),X_1),zero_zero(X_a)))))) # label(fact_3840_DERIV__const) # label(axiom) # label(non_clause).  [assumption].
7.45/7.48	1411 (all X_a (linordered_idom(X_a) & number_ring(X_a) -> (all Y_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,pls)),Y_1)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),one_one(X_a)),hAPP(int,X_a,number_number_of(X_a),Y_1))))))) # label(fact_60_le__special_I2_J) # label(axiom) # label(non_clause).  [assumption].
7.45/7.48	1412 (all R_4 all X hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),R_4),hAPP(complex,complex,cnj,X)) = hAPP(complex,complex,cnj,hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),R_4),X))) # label(fact_4692_cnj_OscaleR) # label(axiom) # label(non_clause).  [assumption].
7.45/7.48	1413 (all X_b all X_a (real_normed_algebra(X_b) & power(X_b) & topological_space(X_a) -> (all N_1 all F all A_2 (hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,X_b),fun(X_a,bool),isCont(X_a,X_b),F),A_2)) -> hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,X_b),fun(X_a,bool),isCont(X_a,X_b),hAPP(nat,fun(X_a,X_b),hAPP(fun(X_a,fun(nat,X_b)),fun(nat,fun(X_a,X_b)),combc(X_a,nat,X_b),hAPP(fun(X_a,X_b),fun(X_a,fun(nat,X_b)),hAPP(fun(X_b,fun(nat,X_b)),fun(fun(X_a,X_b),fun(X_a,fun(nat,X_b))),combb(X_b,fun(nat,X_b),X_a),power_power(X_b)),F)),N_1)),A_2)))))) # label(fact_4902_isCont__power) # label(axiom) # label(non_clause).  [assumption].
7.45/7.48	1414 (all X all D (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),D)) -> hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,real_1(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),X),D))),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(nat,real,real_1(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),X),D))),hAPP(nat,real,real_1(nat),D))) = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(nat,real,real_1(nat),X)),hAPP(nat,real,real_1(nat),D)))) # label(fact_2372_real__of__nat__div__aux) # label(axiom) # label(non_clause).  [assumption].
7.45/7.48	1415 (all X_1 all Y_1 all Z (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Z)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_1),Y_1)) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),Z),X_1)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),Z),Y_1)))))) # label(fact_713_real__mult__le__cancel__iff2) # label(axiom) # label(non_clause).  [assumption].
7.45/7.48	1416 (all X all A_1 hAPP(real,real,inverse_inverse(real),hAPP(real,real,hAPP(real,fun(real,real),powr,X),A_1)) = hAPP(real,real,hAPP(real,fun(real,real),powr,X),hAPP(real,real,uminus_uminus(real),A_1))) # label(fact_3359_powr__minus) # label(axiom) # label(non_clause).  [assumption].
7.45/7.48	1417 (all X hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,sin,X)),one_one(real)))) # label(fact_2300_sin__le__one) # label(axiom) # label(non_clause).  [assumption].
7.45/7.48	1418 (all K_3 all K all F ((all N_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),K),hAPP(nat,real,F,N_2))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,F,N_2)),K_3)))) -> hBOOL(hAPP(fun(nat,real),bool,bseq(real),F)))) # label(fact_4312_BseqI2) # label(axiom) # label(non_clause).  [assumption].
7.45/7.48	1419 (all X_b all X_a all R_3 all K all Ta all Sa (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),Sa)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),Ta)) -> ((all X_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),Ta)) -> hAPP(fun(X_a,bool),nat,finite_card(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,bool)),combs(X_a,bool,bool),hAPP(fun(X_a,bool),fun(X_a,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,fun(bool,bool))),combb(bool,fun(bool,bool),X_a),fconj),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(X_a,bool)),combc(X_a,fun(X_a,bool),bool),member(X_a)),Sa))),hAPP(X_b,fun(X_a,bool),hAPP(fun(X_a,fun(X_b,bool)),fun(X_b,fun(X_a,bool)),combc(X_a,X_b,bool),R_3),X_2)))) = hAPP(X_b,nat,K,X_2))) -> hAPP(fun(X_a,bool),nat,hAPP(fun(X_a,nat),fun(fun(X_a,bool),nat),big_co1399186613setsum(X_a,nat),hAPP(fun(X_a,fun(X_b,bool)),fun(X_a,nat),hAPP(fun(fun(X_b,bool),nat),fun(fun(X_a,fun(X_b,bool)),fun(X_a,nat)),combb(fun(X_b,bool),nat,X_a),finite_card(X_b)),hAPP(fun(X_a,fun(X_b,bool)),fun(X_a,fun(X_b,bool)),hAPP(fun(fun(X_b,bool),fun(X_b,bool)),fun(fun(X_a,fun(X_b,bool)),fun(X_a,fun(X_b,bool))),combb(fun(X_b,bool),fun(X_b,bool),X_a),collect(X_b)),hAPP(fun(X_a,fun(X_b,bool)),fun(X_a,fun(X_b,bool)),hAPP(fun(fun(X_b,bool),fun(X_b,bool)),fun(fun(X_a,fun(X_b,bool)),fun(X_a,fun(X_b,bool))),combb(fun(X_b,bool),fun(X_b,bool),X_a),hAPP(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),combs(X_b,bool,bool),hAPP(fun(X_b,bool),fun(X_b,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fconj),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(fun(X_b,bool),bool)),fun(fun(X_b,bool),fun(X_b,bool)),combc(X_b,fun(X_b,bool),bool),member(X_b)),Ta)))),R_3)))),Sa) = hAPP(fun(X_b,bool),nat,hAPP(fun(X_b,nat),fun(fun(X_b,bool),nat),big_co1399186613setsum(X_b,nat),K),Ta))))) # label(fact_4303_setsum__multicount__gen) # label(axiom) # label(non_clause).  [assumption].
7.45/7.48	1420 (exists X_2 (hAPP(real,real,cos,X_2) = zero_zero(real) & (all Y_2 (hAPP(real,real,cos,Y_2) = zero_zero(real) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),Y_2),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),Y_2)) -> Y_2 = X_2)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_2),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X_2)))) # label(fact_2249_cos__is__zero) # label(axiom) # label(non_clause).  [assumption].
7.45/7.48	1421 (all X_a (ordered_ab_group_add(X_a) -> ti(fun(X_a,fun(X_a,fun(X_a,bool))),ord_gr676655987ssThan(X_a)) = ord_gr676655987ssThan(X_a))) # label(tsy_c_SetInterval_Oord__class_OgreaterThanLessThan_2_res) # label(axiom) # label(non_clause).  [assumption].
7.45/7.48	1422 (all R_4 all X hAPP(complex,real,re,hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),R_4),X)) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),R_4),hAPP(complex,real,re,X))) # label(fact_4682_complex__Re__scaleR) # label(axiom) # label(non_clause).  [assumption].
7.45/7.48	1423 (all M all K_4 all N (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),N)) -> (hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,M),N) = ti(int,K_4) -> (exists S_1 exists T_4 hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),S_1),M)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),T_4),N)) = ti(int,K_4))))) # label(fact_3482_zgcd__ex__linear) # label(axiom) # label(non_clause).  [assumption].
7.45/7.48	1424 (all A_1 hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),zero_zero(nat)))) # label(fact_889_gcd__lcm__complete__lattice__nat_Otop__greatest) # label(axiom) # label(non_clause).  [assumption].
7.45/7.48	1425 (all Ta all A_3 all D_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D_2)) -> (all X_2 ((all Xa (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xa),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastAtMost(int),one_one(int)),D_2))) -> (all Xb (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xb),A_3)) -> hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),Xb),Xa) != ti(int,X_2))))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Ta),X_2)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Ta),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X_2),D_2)))))))) # label(fact_4631_aset_I8_J) # label(axiom) # label(non_clause).  [assumption].
7.45/7.48	1426 (all K hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),hAPP(nat,fun(nat,bool),ord_lessThan(nat),K)))) # label(fact_4313_finite__lessThan) # label(axiom) # label(non_clause).  [assumption].
7.45/7.48	1427 (all K_4 hAPP(rat,real,ratreal,hAPP(int,rat,number_number_of(rat),K_4)) = hAPP(int,real,number_number_of(real),K_4)) # label(fact_3763_Ratreal__number__collapse_I3_J) # label(axiom) # label(non_clause).  [assumption].
7.45/7.48	1428 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X),one_one(real))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,ln,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),one_one(real)),X))),X))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))))) # label(fact_2004_abs__ln__one__plus__x__minus__x__bound__nonneg) # label(axiom) # label(non_clause).  [assumption].
7.45/7.48	1429 (all X all A_1 all B hAPP(real,real,hAPP(real,fun(real,real),powr,X),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A_1),B)) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),powr,X),A_1)),hAPP(real,real,hAPP(real,fun(real,real),powr,X),B))) # label(fact_3356_powr__add) # label(axiom) # label(non_clause).  [assumption].
7.45/7.48	1430 (all P_2 all P_1 ((all X_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X_2)) -> (hBOOL(hAPP(int,bool,P_1,X_2)) <-> hBOOL(hAPP(int,bool,P_2,X_2))))) -> hAPP(fun(int,bool),fun(int,bool),collect(int),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),combs(int,bool,bool),hAPP(fun(int,bool),fun(int,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj),hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)))),P_1)) = hAPP(fun(int,bool),fun(int,bool),collect(int),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),combs(int,bool,bool),hAPP(fun(int,bool),fun(int,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj),hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)))),P_2)))) # label(fact_4334_transfer__nat__int__set__cong) # label(axiom) # label(non_clause).  [assumption].
7.45/7.48	1431 (all M all N ((hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),M),N)) != N -> hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),M),N)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,suc,M)),N)) & (N = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),M),N)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,suc,M)),N) = zero_zero(nat)))) # label(fact_1352_mod__Suc) # label(axiom) # label(non_clause).  [assumption].
7.45/7.48	1432 (all X_a all A_3 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_3)) <-> hBOOL(hAPP(fun(fun(X_a,bool),bool),bool,finite_finite_1(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),pow(X_a),A_3))))) # label(fact_2804_finite__Pow__iff) # label(axiom) # label(non_clause).  [assumption].
7.45/7.48	1433 (all K_4 hAPP(int,rat,number_number_of(rat),K_4) = hAPP(product_prod(int,int),rat,frct,hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),hAPP(int,int,number_number_of(int),K_4)),one_one(int)))) # label(fact_3707_Frct__code__post_I4_J) # label(axiom) # label(non_clause).  [assumption].
7.45/7.48	1434 (all X (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat))))) -> X = hAPP(nat,nat,suc,zero_zero(nat)) | X = zero_zero(nat))) # label(fact_1319_nat__lt__two__imp__zero__or__one) # label(axiom) # label(non_clause).  [assumption].
7.45/7.48	1435 (all A_1 all C all B all D hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,sqrt,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A_1),C)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),B),D)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,sqrt,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))),hAPP(real,real,sqrt,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),C),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),D),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))))) # label(fact_1643_real__sqrt__sum__squares__triangle__ineq) # label(axiom) # label(non_clause).  [assumption].
7.45/7.48	1436 (all X hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,real_1(nat),hAPP(real,nat,natfloor,X))),one_one(real))))) # label(fact_2346_real__natfloor__add__one__gt) # label(axiom) # label(non_clause).  [assumption].
7.45/7.48	1437 (all P_1 all K all I (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),I)) -> (hBOOL(hAPP(int,bool,P_1,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),K),one_one(int)))) -> ((all I_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),I_2)) -> (hBOOL(hAPP(int,bool,P_1,I_2)) -> hBOOL(hAPP(int,bool,P_1,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),I_2),one_one(int))))))) -> hBOOL(hAPP(int,bool,P_1,I)))))) # label(fact_856_int__gr__induct) # label(axiom) # label(non_clause).  [assumption].
7.45/7.48	1438 (all A_1 all B hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_1),B),one_one(int)))) # label(fact_354_zcong__1) # label(axiom) # label(non_clause).  [assumption].
7.45/7.48	1439 (all X_a (ordered_ab_group_add(X_a) -> (all A_2 all B_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),A_2)),B_1)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),B_1)),A_2)))))) # label(fact_2015_minus__less__iff) # label(axiom) # label(non_clause).  [assumption].
7.45/7.48	1440 (all X_a (real_normed_vector(X_a) -> (all R_4 exists K_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),K_2)) & (all X_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),R_4),X_2))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(X_a,real,norm_norm(X_a),X_2)),K_2)))))))) # label(fact_4757_scaleR__right_Opos__bounded) # label(axiom) # label(non_clause).  [assumption].
7.45/7.48	1441 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X)) -> (hAPP(real,real,sin,X) = zero_zero(real) -> (exists N_2 (X = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,real_1(nat),N_2)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) & hBOOL(hAPP(nat,bool,even_odd_even(nat),N_2))))))) # label(fact_2475_sin__zero__lemma) # label(axiom) # label(non_clause).  [assumption].
7.45/7.48	1442 (all P_4 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),P_4)) -> hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),P_4),one_one(int)) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(fun(int,bool),nat,finite_card(int),hAPP(int,fun(int,bool),sRStar,P_4))))) # label(fact_1520_SRStar__card) # label(axiom) # label(non_clause).  [assumption].
7.49/7.48	1443 (all X_b all X_a (order(X_b) & order(X_a) -> (all C_1 all F all B_1 all A_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_1),A_2)) -> (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),C_1),hAPP(X_a,X_b,F,B_1))) -> ((all X_2 all Y_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y_2),X_2)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_a,X_b,F,Y_2)),hAPP(X_a,X_b,F,X_2))))) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),C_1),hAPP(X_a,X_b,F,A_2))))))))) # label(fact_2831_xt7) # label(axiom) # label(non_clause).  [assumption].
7.49/7.48	1444 (all K_4 all A_1 all J_2 all P_5 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),P_5)) -> (hBOOL(hAPP(int,bool,zprime,P_5)) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,J_2),zero_zero(int)),P_5)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),multInv,P_5),J_2)),J_2)),K_4)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),multInv,P_5),J_2)),A_1)),P_5)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,K_4),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),hAPP(int,int,hAPP(int,fun(int,int),multInv,P_5),J_2))),P_5))))))) # label(fact_853_aux______4) # label(axiom) # label(non_clause).  [assumption].
7.49/7.48	1445 (all K all Ma all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Ma),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),K),Ma)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K),N_1))))) # label(fact_572_nat__add__left__cancel__le) # label(axiom) # label(non_clause).  [assumption].
7.49/7.48	1446 (all X_a all X_b all P_5 all Q_3 (hAPP(product_prod(X_a,X_b),X_a,product_fst(X_a,X_b),P_5) = hAPP(product_prod(X_a,X_b),X_a,product_fst(X_a,X_b),Q_3) -> (hAPP(product_prod(X_a,X_b),X_b,product_snd(X_a,X_b),P_5) = hAPP(product_prod(X_a,X_b),X_b,product_snd(X_a,X_b),Q_3) -> ti(product_prod(X_a,X_b),Q_3) = ti(product_prod(X_a,X_b),P_5)))) # label(fact_3142_prod__eqI) # label(axiom) # label(non_clause).  [assumption].
7.49/7.48	1447 (all X_1 hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),inverse_inverse(real)),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),fact_fact(nat))))),hAPP(real,fun(nat,real),power_power(real),X_1))))) # label(fact_4029_summable__exp) # label(axiom) # label(non_clause).  [assumption].
7.49/7.48	1448 (all X_a (topological_space(X_a) & comm_monoid_add(X_a) -> ti(fun(fun(nat,X_a),X_a),suminf(X_a)) = suminf(X_a))) # label(tsy_c_Series_Osuminf_res) # label(axiom) # label(non_clause).  [assumption].
7.49/7.48	1449 (all X_a (linordered_idom(X_a) -> (all A_1 all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,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),times_times(X_a),A_1),B))))) # label(fact_1854_abs__mult) # label(axiom) # label(non_clause).  [assumption].
7.49/7.48	1450 (all X_a (comm_semiring_1(X_a) -> (all X all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) | ti(X_a,X) = one_one(X_a) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),X),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),N))))))) # label(fact_462_dvd__power) # label(axiom) # label(non_clause).  [assumption].
7.49/7.49	1451 (all F all G ((all N_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,F,N_2)),hAPP(nat,real,G,N_2)))) -> (hBOOL(hAPP(fun(nat,real),bool,summable(real),F)) -> (hBOOL(hAPP(fun(nat,real),bool,summable(real),G)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(fun(nat,real),real,suminf(real),F)),hAPP(fun(nat,real),real,suminf(real),G))))))) # label(fact_4129_summable__le) # label(axiom) # label(non_clause).  [assumption].
7.49/7.49	1452 (all X_a (ring_11004092258visors(X_a) -> (all N all A_1 (ti(X_a,A_1) != zero_zero(X_a) -> hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N) != zero_zero(X_a))))) # label(fact_328_field__power__not__zero) # label(axiom) # label(non_clause).  [assumption].
7.49/7.49	1453 (all X_a (ring_1(X_a) -> (all N all M (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N),M)) -> hAPP(nat,X_a,semiring_1_of_nat(X_a),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),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)),hAPP(nat,X_a,semiring_1_of_nat(X_a),N)))))) # label(fact_1371_of__nat__diff) # label(axiom) # label(non_clause).  [assumption].
7.49/7.49	1454 (all M all N -(all Q_4 all R_2 -hBOOL(hAPP(product_prod(nat,nat),bool,hAPP(nat,fun(product_prod(nat,nat),bool),hAPP(nat,fun(nat,fun(product_prod(nat,nat),bool)),divmod_nat_rel,M),N),hAPP(nat,product_prod(nat,nat),hAPP(nat,fun(nat,product_prod(nat,nat)),product_Pair(nat,nat),Q_4),R_2))))) # label(fact_3104_divmod__nat__rel__ex) # label(axiom) # label(non_clause).  [assumption].
7.49/7.49	1455 (all N all M (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N),M)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N)) = M)) # label(fact_696_le__add__diff__inverse) # label(axiom) # label(non_clause).  [assumption].
7.49/7.49	1456 (all X_a all X_b (comm_monoid_add(X_b) -> (all G all A_3 (-hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_3)) -> hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),G),A_3) = zero_zero(X_b))))) # label(fact_4207_setsum_Oinfinite) # label(axiom) # label(non_clause).  [assumption].
7.49/7.49	1457 (all X_a (number_ring(X_a) -> (all V all W all Z_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(int,X_a,number_number_of(X_a),V)),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_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),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),V),W))),Z_1)))) # label(fact_151_add__number__of__left) # label(axiom) # label(non_clause).  [assumption].
7.49/7.49	1458 (all A_1 all B hAPP(rat,int,archim2085082626_floor(rat),hAPP(int,rat,hAPP(int,fun(int,rat),fract,A_1),B)) = hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_1),B)) # label(fact_3749_floor__Fract) # label(axiom) # label(non_clause).  [assumption].
7.49/7.49	1459 (all X_a (group_add(X_a) -> (all A_1 all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_1),B) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),hAPP(X_a,X_a,uminus_uminus(X_a),B))))) # label(fact_2076_Groups_Odiff__def) # label(axiom) # label(non_clause).  [assumption].
7.49/7.49	1460 (all X_a (metric_space(X_a) -> (all B_1 all X_3 all A_2 (hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),X_3),A_2),sequentially)) -> (hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),X_3),B_1),sequentially)) -> ti(X_a,A_2) = ti(X_a,B_1)))))) # label(fact_4485_LIMSEQ__unique) # label(axiom) # label(non_clause).  [assumption].
7.49/7.49	1461 (all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> hAPP(real,real,hAPP(nat,fun(real,real),root,N),one_one(real)) = one_one(real))) # label(fact_2685_real__root__one) # label(axiom) # label(non_clause).  [assumption].
7.49/7.49	1462 (all M all K_4 all J_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_4),J_2)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),K_4)),hAPP(nat,nat,suc,J_2)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_2),K_4))))) # label(fact_1392_diff__Suc__diff__eq1) # label(axiom) # label(non_clause).  [assumption].
7.49/7.49	1463 (all A_1 all B zero_zero(int) = hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_1),B)),B)) # label(fact_907_zmod__zdiv__trivial) # label(axiom) # label(non_clause).  [assumption].
7.49/7.49	1464 (all K_4 all I_1 all J_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),I_1),J_2)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),J_2),K_4)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),I_1),K_4))))) # label(fact_29_zle__trans) # label(axiom) # label(non_clause).  [assumption].
7.49/7.49	1465 (all X all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X)) -> hAPP(real,real,hAPP(nat,fun(real,real),root,N),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),N)) = X))) # label(fact_2708_real__root__pos2) # label(axiom) # label(non_clause).  [assumption].
7.49/7.49	1466 (all X_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)) -> (X_1 = zero_zero(real) <-> zero_zero(real) = hAPP(real,real,hAPP(nat,fun(real,real),root,N_1),X_1)))) # label(fact_2679_real__root__eq__0__iff) # label(axiom) # label(non_clause).  [assumption].
7.49/7.49	1467 (all X_a (dist_norm(X_a) -> (all X all Y hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),X),Y)) = hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),X),Y)))) # label(fact_3503_dist__norm) # label(axiom) # label(non_clause).  [assumption].
7.49/7.49	1468 (all X_a ti(fun(bool,fun(X_a,fun(X_a,X_a))),if(X_a)) = if(X_a)) # label(tsy_c_If_res) # label(axiom) # label(non_clause).  [assumption].
7.49/7.49	1469 (all R1 all A_1 all R2 all B hAPP(real,complex,hAPP(real,fun(real,complex),rcis,hAPP(real,real,hAPP(real,fun(real,real),times_times(real),R1),R2)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A_1),B)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(real,complex,hAPP(real,fun(real,complex),rcis,R1),A_1)),hAPP(real,complex,hAPP(real,fun(real,complex),rcis,R2),B))) # label(fact_3171_rcis__mult) # label(axiom) # label(non_clause).  [assumption].
7.49/7.49	1470 (all N -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),zero_zero(nat)))) # label(fact_538_less__nat__zero__code) # label(axiom) # label(non_clause).  [assumption].
7.49/7.49	1471 (all X_a all X_b all X_1 all Y_1 all P_1 all Q_1 (hBOOL(hAPP(fun(X_a,fun(X_b,bool)),bool,hAPP(fun(X_a,fun(X_b,bool)),fun(fun(X_a,fun(X_b,bool)),bool),ord_less_eq(fun(X_a,fun(X_b,bool))),P_1),Q_1)) -> (hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),P_1,X_1),Y_1)) -> hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),Q_1,X_1),Y_1))))) # label(fact_4340_predicate2D) # label(axiom) # label(non_clause).  [assumption].
7.49/7.49	1472 (all X_a (real_n1866405975lgebra(X_a) -> (all R_4 all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),R_4),hAPP(X_a,real,norm_norm(X_a),X))) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),R_4)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,inverse_inverse(X_a),X))),hAPP(real,real,inverse_inverse(real),R_4)))))))) # label(fact_2538_Bseq__inverse__lemma) # label(axiom) # label(non_clause).  [assumption].
7.49/7.49	1473 (all X_b all X_a (real_normed_field(X_b) & topological_space(X_a) -> (all Y_1 all G all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),G),zero_zero(X_b)),hAPP(X_a,filter(X_a),at(X_a),A_2))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(X_b,fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(X_b,fun(X_a,X_b)),combc(X_a,X_b,X_b),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,fun(X_b,X_b))),combb(X_b,fun(X_b,X_b),X_a),inverse_divide(X_b)),G)),Y_1)),zero_zero(X_b)),hAPP(X_a,filter(X_a),at(X_a),A_2))))))) # label(fact_4586_divide_OLIM__zero) # label(axiom) # label(non_clause).  [assumption].
7.49/7.49	1474 (all X_a (number_ring(X_a) -> hAPP(int,X_a,ring_1_of_int(X_a),hAPP(int,int,number_number_of(int),min_1)) = hAPP(int,X_a,number_number_of(X_a),min_1))) # label(fact_3591_of__int__m1) # label(axiom) # label(non_clause).  [assumption].
7.49/7.49	1475 (all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),one_one(real)),hAPP(real,real,exp(real),X_1))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X_1)))) # label(fact_2593_one__le__exp__iff) # label(axiom) # label(non_clause).  [assumption].
7.49/7.49	1476 (all K all I all J hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I),K)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J),K)) = hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,nat),fun(fun(nat,bool),fun(nat,bool)),image(nat,nat),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),K)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),I),J))) # label(fact_4223_image__add__atLeastLessThan) # label(axiom) # label(non_clause).  [assumption].
7.49/7.49	1477 (all Ma all Z (hAPP(nat,int,semiring_1_of_nat(int),Ma) = ti(int,Z) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Z)) & Ma = hAPP(int,nat,nat_1,Z))) # label(fact_1377_int__eq__iff) # label(axiom) # label(non_clause).  [assumption].
7.49/7.49	1478 (all P_5 all Q_3 hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),P_5),Q_3)),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),P_5),Q_3)) = hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),divmod_int,P_5),Q_3)) # label(fact_3080_divmod__int__mod__div) # label(axiom) # label(non_clause).  [assumption].
7.49/7.49	1479 (all X_a (real_vector(X_a) -> (all A_1 all X hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_1),hAPP(X_a,X_a,uminus_uminus(X_a),X)) = hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_1),X))))) # label(fact_4688_scaleR__minus__right) # label(axiom) # label(non_clause).  [assumption].
7.49/7.49	1480 (all B all A_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_1),B)) -> hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_1),B) = ti(int,A_1)))) # label(fact_1032_mod__pos__pos__trivial) # label(axiom) # label(non_clause).  [assumption].
7.49/7.49	1481 (all B_1 all C_1 all A_2 all D_1 (one_one(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),A_2),D_1) -> (hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),B_1),C_1) = one_one(nat) -> (hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A_2),C_1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B_1),D_1) <-> C_1 = D_1 & B_1 = A_2)))) # label(fact_3270_coprime__crossproduct__nat) # label(axiom) # label(non_clause).  [assumption].
7.49/7.49	1482 (all X_a all X_b (real_normed_algebra(X_b) -> (all G all B_1 all F all A_2 all A_3 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),A_2),A_3)) -> (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),G),B_1),A_3)) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(fun(X_a,X_b),fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,X_b)),combs(X_a,X_b,X_b),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,fun(X_b,X_b))),combb(X_b,fun(X_b,X_b),X_a),times_times(X_b)),F)),G)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),A_2),B_1)),A_3))))))) # label(fact_4474_mult_Otendsto) # label(axiom) # label(non_clause).  [assumption].
7.49/7.49	1483 (all M all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),hAPP(nat,nat,suc,M)),hAPP(nat,nat,suc,N)) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),M),N))) # label(fact_4963_max__Suc__Suc) # label(axiom) # label(non_clause).  [assumption].
7.49/7.49	1484 (all Z_1 hAPP(complex,real,im,hAPP(complex,complex,sgn_sgn(complex),Z_1)) = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(complex,real,im,Z_1)),hAPP(complex,real,norm_norm(complex),Z_1))) # label(fact_2985_Im__sgn) # label(axiom) # label(non_clause).  [assumption].
7.49/7.49	1485 (all X all Y all Z_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Z_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),Y)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),Z_1),X)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),Z_1),Y)))))) # label(fact_712_real__mult__less__mono2) # label(axiom) # label(non_clause).  [assumption].
7.49/7.49	1486 (all X_a (field(X_a) -> (all X all W all Z_1 all Y (zero_zero(X_a) != ti(X_a,Y) -> (ti(X_a,Z_1) != zero_zero(X_a) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),X),Y)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),W),Z_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),Z_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),W),Y))),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Y),Z_1))))))) # label(fact_1727_diff__frac__eq) # label(axiom) # label(non_clause).  [assumption].
7.49/7.49	1487 (all N all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,real_1(nat),N)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),hAPP(nat,real,real_1(nat),hAPP(nat,nat,suc,N)))) -> N = hAPP(int,nat,nat_1,hAPP(real,int,archim2085082626_floor(real),X))))) # label(fact_2892_floor__eq4) # label(axiom) # label(non_clause).  [assumption].
7.49/7.49	1488 (all X_1 (one_one(int) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),X_1),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) <-> hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),X_1),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) != zero_zero(int))) # label(fact_1062_neq__one__mod__two) # label(axiom) # label(non_clause).  [assumption].
7.49/7.49	1489 (all X_a (linordered_field(X_a) -> (all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,inverse_inverse(X_a),A_1)),hAPP(X_a,X_a,inverse_inverse(X_a),B))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),A_1))))))) # label(fact_2550_inverse__less__imp__less__neg) # label(axiom) # label(non_clause).  [assumption].
7.49/7.49	1490 (all M hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,fact_fact(int),M)))) # label(fact_3192_fact__ge__zero__int) # label(axiom) # label(non_clause).  [assumption].
7.49/7.49	1491 (all K (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),K)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),hAPP(int,int,bit0,K))))) # label(fact_159_rel__simps_I4_J) # label(axiom) # label(non_clause).  [assumption].
7.49/7.49	1492 (all X_a (real_vector(X_a) -> (all X hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),hAPP(int,real,number_number_of(real),min_1)),X) = hAPP(X_a,X_a,uminus_uminus(X_a),X)))) # label(fact_4724_scaleR__minus1__left) # label(axiom) # label(non_clause).  [assumption].
7.49/7.49	1493 (all K_4 all M all N hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K_4),M)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K_4),N)) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,abs_abs(int),K_4)),hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,M),N))) # label(fact_3448_zgcd__zmult__distrib2__abs) # label(axiom) # label(non_clause).  [assumption].
7.49/7.49	1494 (all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,sqrt,X_1)),one_one(real))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_1),one_one(real))))) # label(fact_1632_real__sqrt__lt__1__iff) # label(axiom) # label(non_clause).  [assumption].
7.49/7.49	1495 (all Z_1 all W hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),W),Z_1) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Z_1),W)) # label(fact_99_zadd__commute) # label(axiom) # label(non_clause).  [assumption].
7.49/7.49	1496 (all X_a (power(X_a) -> times_times(X_a) = ti(fun(X_a,fun(X_a,X_a)),times_times(X_a)))) # label(tsy_c_Groups_Otimes__class_Otimes_1_res) # label(axiom) # label(non_clause).  [assumption].
7.49/7.49	1497 (all B all A_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_1),zero_zero(int))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B)) -> hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_1),B) = hAPP(product_prod(int,int),int,product_snd(int,int),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),negDivAlg,A_1),B))))) # label(fact_3117_mod__neg__pos) # label(axiom) # label(non_clause).  [assumption].
7.49/7.49	1498 (all Q_3 all B all R_4 all C (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),C)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),R_4)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),R_4),zero_zero(int))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),Q_3),C))),R_4)),zero_zero(int))))))) # label(fact_1057_zmult2__lemma__aux2) # label(axiom) # label(non_clause).  [assumption].
7.49/7.49	1499 (all U_1 all Ma all N_1 all I all J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I),J)) -> (Ma = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J),I)),U_1)),N_1) <-> hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J),U_1)),N_1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I),U_1)),Ma)))) # label(fact_749_nat__eq__add__iff2) # label(axiom) # label(non_clause).  [assumption].
7.49/7.49	1500 (all W_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_1),zero_zero(int))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,W_1)),zero_zero(int))))) # label(fact_157_bin__less__0__simps_I4_J) # label(axiom) # label(non_clause).  [assumption].
7.49/7.49	1501 (all B all A_1 hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),B),A_1)),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),A_1) = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),B),A_1)),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) # label(fact_1770_real__average__minus__second) # label(axiom) # label(non_clause).  [assumption].
7.49/7.49	1502 (all A_2 all B_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,A_2),B_1)) <-> (all P_6 -(hBOOL(hAPP(nat,bool,prime,P_6)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),P_6),A_2)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),P_6),B_1)))))) # label(fact_3062_coprime__prime__eq) # label(axiom) # label(non_clause).  [assumption].
7.49/7.49	1503 (all X all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,uminus_uminus(real),pi)),Y)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),Y),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X),zero_zero(real))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,cos,Y)),hAPP(real,real,cos,X))))))) # label(fact_2225_cos__monotone__minus__pi__0_H) # label(axiom) # label(non_clause).  [assumption].
7.49/7.49	1504 (all M all K_4 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),one_one(nat)),K_4)) -> one_one(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_4),M))),K_4))) # label(fact_1418_Suc__times__mod__eq) # label(axiom) # label(non_clause).  [assumption].
7.49/7.49	1505 (all X_a (power(X_a) -> (all M all N ((zero_zero(nat) = N -> hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),M),N) = one_one(X_a)) & (zero_zero(nat) != N -> hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),M),N) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),M),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),M),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),one_one(nat))))))))) # label(fact_735_realpow__num__eq__if) # label(axiom) # label(non_clause).  [assumption].
7.49/7.49	1506 (all X_a all X_b (linordered_semidom(X_b) -> (all F all A_3 ((all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_3)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),zero_zero(X_b)),hAPP(X_a,X_b,F,X_2))))) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),zero_zero(X_b)),hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co302546470etprod(X_a,X_b),F),A_3))))))) # label(fact_4149_setprod__pos) # label(axiom) # label(non_clause).  [assumption].
7.49/7.49	1507 (all Ma all N_1 (Ma = zero_zero(nat) & zero_zero(nat) = N_1 <-> zero_zero(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),Ma),N_1))) # label(fact_3255_gcd__zero__nat) # label(axiom) # label(non_clause).  [assumption].
7.49/7.49	1508 (all X all Y hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,X),Y)))) # label(fact_3446_zgcd__geq__zero) # label(axiom) # label(non_clause).  [assumption].
7.49/7.49	1509 (all X all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),Y)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),Y),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,tan,Y)),hAPP(real,real,tan,X))))))) # label(fact_2272_tan__monotone) # label(axiom) # label(non_clause).  [assumption].
7.49/7.49	1510 (all X_a (real_normed_vector(X_a) -> (all B_1 all F all A_2 (hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),F),A_2),sequentially)) -> hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),hAPP(X_a,fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(X_a,fun(nat,X_a)),combc(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),plus_plus(X_a)),F)),B_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),B_1)),sequentially)))))) # label(fact_4445_LIMSEQ__add__const) # label(axiom) # label(non_clause).  [assumption].
7.49/7.49	1511 (all I_1 all K_4 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,I_1)),K_4)) -> -(all J_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),J_1)) -> K_4 != hAPP(nat,nat,suc,J_1))))) # label(fact_1543_Suc__lessE) # label(axiom) # label(non_clause).  [assumption].
7.49/7.49	1512 (all N hAPP(nat,real,real_1(nat),hAPP(nat,nat,fact_fact(nat),N)) != zero_zero(real)) # label(fact_2420_real__of__nat__fact__not__zero) # label(axiom) # label(non_clause).  [assumption].
7.49/7.49	1513 (all B_1 hAPP(fun(int,fun(int,product_prod(int,int))),fun(product_prod(int,int),product_prod(int,int)),product_prod_case(int,int,product_prod(int,int)),hAPP(fun(int,fun(int,product_prod(int,int))),fun(int,fun(int,product_prod(int,int))),hAPP(fun(int,fun(fun(int,product_prod(int,int)),fun(int,product_prod(int,int)))),fun(fun(int,fun(int,product_prod(int,int))),fun(int,fun(int,product_prod(int,int)))),combs(int,fun(int,product_prod(int,int)),fun(int,product_prod(int,int))),hAPP(fun(int,fun(int,fun(product_prod(int,int),product_prod(int,int)))),fun(int,fun(fun(int,product_prod(int,int)),fun(int,product_prod(int,int)))),hAPP(fun(fun(int,fun(product_prod(int,int),product_prod(int,int))),fun(fun(int,product_prod(int,int)),fun(int,product_prod(int,int)))),fun(fun(int,fun(int,fun(product_prod(int,int),product_prod(int,int)))),fun(int,fun(fun(int,product_prod(int,int)),fun(int,product_prod(int,int))))),combb(fun(int,fun(product_prod(int,int),product_prod(int,int))),fun(fun(int,product_prod(int,int)),fun(int,product_prod(int,int))),int),combs(int,product_prod(int,int),product_prod(int,int))),hAPP(fun(int,fun(int,product_prod(int,int))),fun(int,fun(int,fun(product_prod(int,int),product_prod(int,int)))),hAPP(fun(fun(int,product_prod(int,int)),fun(int,fun(product_prod(int,int),product_prod(int,int)))),fun(fun(int,fun(int,product_prod(int,int))),fun(int,fun(int,fun(product_prod(int,int),product_prod(int,int))))),combb(fun(int,product_prod(int,int)),fun(int,fun(product_prod(int,int),product_prod(int,int))),int),hAPP(fun(int,fun(product_prod(int,int),fun(product_prod(int,int),product_prod(int,int)))),fun(fun(int,product_prod(int,int)),fun(int,fun(product_prod(int,int),product_prod(int,int)))),combs(int,product_prod(int,int),fun(product_prod(int,int),product_prod(int,int))),hAPP(fun(int,bool),fun(int,fun(product_prod(int,int),fun(product_prod(int,int),product_prod(int,int)))),hAPP(fun(bool,fun(product_prod(int,int),fun(product_prod(int,int),product_prod(int,int)))),fun(fun(int,bool),fun(int,fun(product_prod(int,int),fun(product_prod(int,int),product_prod(int,int))))),combb(bool,fun(product_prod(int,int),fun(product_prod(int,int),product_prod(int,int))),int),if(product_prod(int,int))),hAPP(fun(int,int),fun(int,bool),hAPP(fun(int,bool),fun(fun(int,int),fun(int,bool)),combb(int,bool,int),hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int))),hAPP(int,fun(int,int),hAPP(fun(int,fun(int,int)),fun(int,fun(int,int)),combc(int,int,int),minus_minus(int)),B_1))))),hAPP(fun(int,int),fun(int,fun(int,product_prod(int,int))),hAPP(fun(int,fun(fun(int,int),fun(int,product_prod(int,int)))),fun(fun(int,int),fun(int,fun(int,product_prod(int,int)))),combc(int,fun(int,int),fun(int,product_prod(int,int))),hAPP(fun(int,fun(int,product_prod(int,int))),fun(int,fun(fun(int,int),fun(int,product_prod(int,int)))),hAPP(fun(fun(int,product_prod(int,int)),fun(fun(int,int),fun(int,product_prod(int,int)))),fun(fun(int,fun(int,product_prod(int,int))),fun(int,fun(fun(int,int),fun(int,product_prod(int,int))))),combb(fun(int,product_prod(int,int)),fun(fun(int,int),fun(int,product_prod(int,int))),int),combb(int,product_prod(int,int),int)),hAPP(fun(int,int),fun(int,fun(int,product_prod(int,int))),hAPP(fun(int,fun(int,product_prod(int,int))),fun(fun(int,int),fun(int,fun(int,product_prod(int,int)))),combb(int,fun(int,product_prod(int,int)),int),product_Pair(int,int)),hAPP(int,fun(int,int),hAPP(fun(int,fun(int,int)),fun(int,fun(int,int)),combc(int,int,int),hAPP(fun(int,int),fun(int,fun(int,int)),hAPP(fun(int,fun(int,int)),fun(fun(int,int),fun(int,fun(int,int))),combb(int,fun(int,int),int),plus_plus(int)),hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),one_one(int))))),hAPP(int,fun(int,int),hAPP(fun(int,fun(int,int)),fun(int,fun(int,int)),combc(int,int,int),minus_minus(int)),B_1))))),hAPP(fun(int,int),fun(int,fun(int,product_prod(int,int))),hAPP(fun(int,fun(int,product_prod(int,int))),fun(fun(int,int),fun(int,fun(int,product_prod(int,int)))),combb(int,fun(int,product_prod(int,int)),int),product_Pair(int,int)),hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))) = hAPP(int,fun(product_prod(int,int),product_prod(int,int)),adjust,B_1)) # label(fact_4035_adjust__def) # label(axiom) # label(non_clause).  [assumption].
7.49/7.49	1514 (all X_1 all Y_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(nat,int,semiring_1_of_nat(int),X_1)),hAPP(nat,int,semiring_1_of_nat(int),Y_1))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_1),Y_1)))) # label(fact_1318_zdvd__int) # label(axiom) # label(non_clause).  [assumption].
7.49/7.49	1515 (all V ((hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V))) -> hAPP(nat,real,real_1(nat),hAPP(int,nat,number_number_of(nat),V)) = zero_zero(real)) & (-hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V))) -> hAPP(int,real,number_number_of(real),V) = hAPP(nat,real,real_1(nat),hAPP(int,nat,number_number_of(nat),V))))) # label(fact_2358_real__of__nat__number__of) # label(axiom) # label(non_clause).  [assumption].
7.49/7.49	1516 (all U_1 hAPP(int,nat,nat_1,U_1) = hAPP(fun(int,bool),nat,finite_card(int),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastLessThan(int),zero_zero(int)),U_1))) # label(fact_4258_card__atLeastZeroLessThan__int) # label(axiom) # label(non_clause).  [assumption].
7.49/7.49	1517 (all X_b all X_a all P_1 all P_4 (hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),P_1,hAPP(product_prod(X_b,X_a),X_a,product_snd(X_b,X_a),P_4)),hAPP(product_prod(X_b,X_a),X_b,product_fst(X_b,X_a),P_4))) -> -(all X_2 all Y_2 -hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),P_1,Y_2),X_2))))) # label(fact_3146_exE__realizer_H) # label(axiom) # label(non_clause).  [assumption].
7.49/7.49	1518 (all X_a (linordered_field(X_a) -> (all X all Z_1 all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),Y)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Z_1),Y))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),X),Y)),Z_1))))))) # label(fact_1712_mult__imp__div__pos__less) # label(axiom) # label(non_clause).  [assumption].
7.49/7.49	1519 (all A_2 all B_1 all Ma (one_one(int) = hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,B_1),Ma) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B_1),A_2)) -> hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),B_1),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),bnorRset,A_2),Ma))))))) # label(fact_3473_Bnor__mem__if) # label(axiom) # label(non_clause).  [assumption].
7.49/7.49	1520 (all X_a (linordered_semidom(X_a) -> (all N all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),A_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N)))))))) # label(fact_445_power__gt1__lemma) # label(axiom) # label(non_clause).  [assumption].
7.49/7.49	1521 (all N hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,uminus_uminus(int),hAPP(nat,int,semiring_1_of_nat(int),N))),zero_zero(int)))) # label(fact_2166_negative__zle__0) # label(axiom) # label(non_clause).  [assumption].
7.49/7.49	1522 (all X hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,cos,X)),hAPP(real,real,cos,X))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,sin,X)),hAPP(real,real,sin,X))) = one_one(real)) # label(fact_2336_sin__cos__squared__add3) # label(axiom) # label(non_clause).  [assumption].
7.49/7.49	1523 (all Ma all N_1 (hAPP(nat,nat,suc,zero_zero(nat)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Ma),N_1) <-> N_1 = zero_zero(nat) & Ma = hAPP(nat,nat,suc,zero_zero(nat)) | hAPP(nat,nat,suc,zero_zero(nat)) = N_1 & zero_zero(nat) = Ma)) # label(fact_1324_add__is__1) # label(axiom) # label(non_clause).  [assumption].
7.49/7.49	1524 (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_368_mult__mono_H) # label(axiom) # label(non_clause).  [assumption].
7.49/7.49	1525 (all M all N (M = N | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N)))) # label(fact_567_less__or__eq__imp__le) # label(axiom) # label(non_clause).  [assumption].
7.49/7.49	1526 (all X_a (number_ring(X_a) -> (all 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)) = 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))))) # label(fact_15_add__special_I2_J) # label(axiom) # label(non_clause).  [assumption].
7.49/7.49	1527 (all N_1 all K all Ma (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K),Ma)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K),N_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Ma),N_1)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),Ma),K)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),K))))))) # label(fact_675_le__diff__iff) # label(axiom) # label(non_clause).  [assumption].
7.49/7.49	1528 (all Z_1 Z_1 = hAPP(complex,real,re,hAPP(real,complex,of_real(complex),Z_1))) # label(fact_2994_Re__complex__of__real) # label(axiom) # label(non_clause).  [assumption].
7.49/7.49	1529 (all X_a (ring_11004092258visors(X_a) -> (all A_2 (hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_2),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = zero_zero(X_a) <-> ti(X_a,A_2) = zero_zero(X_a))))) # label(fact_14_zero__eq__power2) # label(axiom) # label(non_clause).  [assumption].
7.49/7.49	1530 (all X_a (number_ring(X_a) -> hBOOL(hAPP(X_a,bool,iszero(X_a),hAPP(int,X_a,number_number_of(X_a),pls))))) # label(fact_2603_iszero__Numeral0) # label(axiom) # label(non_clause).  [assumption].
7.49/7.49	1531 (all Q_2 all Ma all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N_1),hAPP(nat,nat,suc,Q_2)))) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N_1),Q_2)),Ma)) <-> hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),Ma),N_1) = Q_2))) # label(fact_1442_split__div__lemma) # label(axiom) # label(non_clause).  [assumption].
7.49/7.49	1532 (all B all A_1 all C hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),A_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),B),C)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),A_1),C))) # label(fact_3224_gcd__left__commute__nat) # label(axiom) # label(non_clause).  [assumption].
7.49/7.49	1533 (all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)) <-> (exists M_2 hAPP(nat,nat,suc,M_2) = N_1))) # label(fact_1322_gr0__conv__Suc) # label(axiom) # label(non_clause).  [assumption].
7.49/7.49	1534 (all P_1 all K all I (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),K),I)) -> (hBOOL(hAPP(int,bool,P_1,K)) -> ((all I_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),K),I_2)) -> (hBOOL(hAPP(int,bool,P_1,I_2)) -> hBOOL(hAPP(int,bool,P_1,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),I_2),one_one(int))))))) -> hBOOL(hAPP(int,bool,P_1,I)))))) # label(fact_834_int__ge__induct) # label(axiom) # label(non_clause).  [assumption].
7.49/7.49	1535 (all X_b all X_a all A_3 all B_2 hAPP(fun(X_b,bool),fun(product_prod(X_a,X_b),bool),hAPP(fun(X_a,bool),fun(fun(X_b,bool),fun(product_prod(X_a,X_b),bool)),prod(X_a,X_b),A_3),B_2) = hAPP(fun(product_prod(X_a,X_b),bool),fun(product_prod(X_a,X_b),bool),collect(product_prod(X_a,X_b)),hAPP(fun(X_a,fun(X_b,bool)),fun(product_prod(X_a,X_b),bool),product_prod_case(X_a,X_b,bool),hAPP(fun(X_b,bool),fun(X_a,fun(X_b,bool)),hAPP(fun(X_a,fun(fun(X_b,bool),fun(X_b,bool))),fun(fun(X_b,bool),fun(X_a,fun(X_b,bool))),combc(X_a,fun(X_b,bool),fun(X_b,bool)),hAPP(fun(X_a,fun(bool,bool)),fun(X_a,fun(fun(X_b,bool),fun(X_b,bool))),hAPP(fun(fun(bool,bool),fun(fun(X_b,bool),fun(X_b,bool))),fun(fun(X_a,fun(bool,bool)),fun(X_a,fun(fun(X_b,bool),fun(X_b,bool)))),combb(fun(bool,bool),fun(fun(X_b,bool),fun(X_b,bool)),X_a),combb(bool,bool,X_b)),hAPP(fun(X_a,bool),fun(X_a,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,fun(bool,bool))),combb(bool,fun(bool,bool),X_a),fconj),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(X_a,bool)),combc(X_a,fun(X_a,bool),bool),member(X_a)),A_3)))),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(fun(X_b,bool),bool)),fun(fun(X_b,bool),fun(X_b,bool)),combc(X_b,fun(X_b,bool),bool),member(X_b)),B_2))))) # label(fact_4159_Nitpick_Oprod__def) # label(axiom) # label(non_clause).  [assumption].
7.49/7.49	1536 (all P_1 ((all X_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X_2)) -> hBOOL(hAPP(int,bool,P_1,X_2)))) <-> (all X_2 hBOOL(hAPP(int,bool,P_1,hAPP(nat,int,semiring_1_of_nat(int),X_2)))))) # label(fact_1297_transfer__int__nat__quantifiers_I1_J) # label(axiom) # label(non_clause).  [assumption].
7.49/7.49	1537 (all N all M all R_4 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),M),R_4)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),N),R_4)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,M),N)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),N)),R_4)))))) # label(fact_2868_divides__mul) # label(axiom) # label(non_clause).  [assumption].
7.49/7.49	1538 (all X_a all B_2 all A_3 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_3)) -> hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_3),B_2))))) # label(fact_1817_finite__Diff) # label(axiom) # label(non_clause).  [assumption].
7.49/7.49	1539 (all X_a (real_normed_algebra(X_a) -> (all Y_1 all X_3 (hBOOL(hAPP(fun(nat,X_a),bool,cauchy(X_a),X_3)) -> hBOOL(hAPP(fun(nat,X_a),bool,cauchy(X_a),hAPP(X_a,fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(X_a,fun(nat,X_a)),combc(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),times_times(X_a)),X_3)),Y_1))))))) # label(fact_4101_mult__left_OCauchy) # label(axiom) # label(non_clause).  [assumption].
7.49/7.49	1540 (all X_a (real_normed_vector(X_a) -> hAPP(X_a,X_a,sgn_sgn(X_a),zero_zero(X_a)) = zero_zero(X_a))) # label(fact_2201_sgn__zero) # label(axiom) # label(non_clause).  [assumption].
7.49/7.49	1541 (all X_a (ring_char_0(X_a) -> (all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_2),ring_1_Ints(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),plus_plus(X_a),one_one(X_a)),A_2)),A_2))))) # label(fact_3907_Ints__odd__nonzero) # label(axiom) # label(non_clause).  [assumption].
7.49/7.49	1542 (all X all Y hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),X),Y) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),Y),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),X),Y))) # label(fact_3257_gcd__red__nat) # label(axiom) # label(non_clause).  [assumption].
7.49/7.49	1543 (all M all I_1 all J_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_1),J_2)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),J_2))))) # label(fact_574_trans__le__add2) # label(axiom) # label(non_clause).  [assumption].
7.49/7.49	1544 (all X_a all X_b all A_1 all B hAPP(product_prod(X_a,X_b),X_a,product_fst(X_a,X_b),hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),A_1),B)) = ti(X_a,A_1)) # label(fact_3140_fst__conv) # label(axiom) # label(non_clause).  [assumption].
7.49/7.49	1545 (all X hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,cos,X)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,sin,X)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) = one_one(real)) # label(fact_2387_sin__cos__squared__add2) # label(axiom) # label(non_clause).  [assumption].
7.49/7.49	1546 (all X all P_5 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),P_5)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,X),hAPP(int,int,number_number_of(int),min_1)),P_5)) -> -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,X),one_one(int)),P_5))))) # label(fact_317_zcong__neg__1__impl__ne__1) # label(axiom) # label(non_clause).  [assumption].
7.49/7.49	1547 (all M all N all K_4 hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),K_4)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N),K_4)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N)),K_4)) # label(fact_678_diff__mult__distrib) # label(axiom) # label(non_clause).  [assumption].
7.49/7.49	1548 (all U_1 all F ((all N_2 hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_2),hAPP(nat,nat,F,N_2)))) -> hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),hAPP(fun(nat,nat),fun(nat,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(nat,nat),fun(nat,fun(nat,bool))),combb(nat,fun(nat,bool),nat),ord_less_eq(nat)),F)),U_1)))))) # label(fact_4163_finite__less__ub) # label(axiom) # label(non_clause).  [assumption].
7.49/7.49	1549 (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),times_times(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),C)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)),C)))) # label(fact_242_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J) # label(axiom) # label(non_clause).  [assumption].
7.49/7.49	1550 (all X_a all A_3 hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),pow(X_a),A_3) = hAPP(fun(fun(X_a,bool),bool),fun(fun(X_a,bool),bool),collect(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),hAPP(fun(fun(X_a,bool),fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(fun(X_a,bool),bool)),combc(fun(X_a,bool),fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool))),A_3))) # label(fact_2778_Pow__def) # label(axiom) # label(non_clause).  [assumption].
7.49/7.49	1551 (all A_2 hBOOL(hAPP(real,bool,hAPP(fun(real,real),fun(real,bool),isCont(real,real),abs_abs(real)),A_2))) # label(fact_4913_isCont__abs) # label(axiom) # label(non_clause).  [assumption].
7.49/7.49	1552 (all X_1 all Y_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)) -> (hAPP(real,real,hAPP(nat,fun(real,real),root,N_1),X_1) = hAPP(real,real,hAPP(nat,fun(real,real),root,N_1),Y_1) <-> X_1 = Y_1))) # label(fact_2672_real__root__eq__iff) # label(axiom) # label(non_clause).  [assumption].
7.49/7.49	1553 (all X_a (linorder(X_a) -> (all X all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),A_1),B))) -> -(hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),A_1)) -> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),B))))))) # label(fact_4818_min__max_Ole__infE) # label(axiom) # label(non_clause).  [assumption].
7.49/7.49	1554 (all X_a (ring_1(X_a) -> (all C_1 all X_2 hAPP(nat,X_a,hAPP(fun(nat,X_a),fun(nat,X_a),diffs(X_a),C_1),X_2) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),hAPP(nat,nat,suc,X_2))),hAPP(nat,X_a,C_1,hAPP(nat,nat,suc,X_2)))))) # label(fact_4118_diffs__def) # label(axiom) # label(non_clause).  [assumption].
7.49/7.49	1555 (all X_a (linord581940658strict(X_a) -> (all A_2 all B_1 all C_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),zero_zero(X_a))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1),A_2)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1),B_1))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_1),A_2))))))) # label(fact_435_mult__le__cancel__left__neg) # label(axiom) # label(non_clause).  [assumption].
7.49/7.49	1556 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,cos,hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),X))),one_one(real)))))) # label(fact_2243_cos__double__less__one) # label(axiom) # label(non_clause).  [assumption].
7.49/7.49	1557 (all N_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),N_1)) -> hAPP(nat,int,semiring_1_of_nat(int),hAPP(fun(int,bool),nat,finite_card(int),hAPP(fun(int,bool),fun(int,bool),collect(int),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),combs(int,bool,bool),hAPP(fun(int,bool),fun(int,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj),hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)))),hAPP(int,fun(int,bool),hAPP(fun(int,fun(int,bool)),fun(int,fun(int,bool)),combc(int,int,bool),ord_less_eq(int)),N_1))))) = ti(int,N_1))) # label(fact_3808_int__card__bdd__int__set__l__le) # label(axiom) # label(non_clause).  [assumption].
7.49/7.49	1558 (all Y_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),one_one(real)),Y_1)) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),one_one(real)),hAPP(real,real,sqrt,Y_1))))) # label(fact_1631_real__sqrt__ge__1__iff) # label(axiom) # label(non_clause).  [assumption].
7.49/7.49	1559 (all P_1 all N_1 all K (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),zero_zero(int))) -> ((all I_2 all J_1 (ti(int,N_1) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K),I_2)),J_1) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),J_1),zero_zero(int))) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),J_1)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),P_1,I_2),J_1)))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),P_1,hAPP(int,int,hAPP(int,fun(int,int),div_div(int),N_1),K)),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),N_1),K)))))) # label(fact_1007_split__neg__lemma) # label(axiom) # label(non_clause).  [assumption].
7.49/7.49	1560 (all Z_1 zero_zero(real) = hAPP(complex,real,im,hAPP(int,complex,ring_1_of_int(complex),Z_1))) # label(fact_3563_complex__Im__of__int) # label(axiom) # label(non_clause).  [assumption].
7.49/7.49	1561 (all X_a all X_1 all Y_1 all F (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(X_a,nat,F,X_1)),hAPP(X_a,nat,F,Y_1))) <-> hBOOL(hAPP(fun(product_prod(X_a,X_a),bool),bool,hAPP(product_prod(X_a,X_a),fun(fun(product_prod(X_a,X_a),bool),bool),member(product_prod(X_a,X_a)),hAPP(X_a,product_prod(X_a,X_a),hAPP(X_a,fun(X_a,product_prod(X_a,X_a)),product_Pair(X_a,X_a),X_1),Y_1)),hAPP(fun(X_a,nat),fun(product_prod(X_a,X_a),bool),measure(X_a),F))))) # label(fact_3319_in__measure) # label(axiom) # label(non_clause).  [assumption].
7.49/7.49	1562 (all X hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,cos,X)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,sin,X)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) = hAPP(real,real,cos,hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),X))) # label(fact_2395_cos__double) # label(axiom) # label(non_clause).  [assumption].
7.49/7.49	1563 (all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X_1)) <-> X_1 = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,sqrt,X_1)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) # label(fact_1641_real__sqrt__pow2__iff) # label(axiom) # label(non_clause).  [assumption].
7.49/7.49	1564 (all X all A_1 hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(real,int,archimedean_ceiling(real),X)),A_1) = hAPP(real,int,archimedean_ceiling(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),X),hAPP(int,real,real_1(int),A_1)))) # label(fact_3374_ceiling__subtract) # label(axiom) # label(non_clause).  [assumption].
7.49/7.49	1565 (all X hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,sin,X)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),one_one(real)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,cos,X)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) # label(fact_2388_sin__squared__eq) # label(axiom) # label(non_clause).  [assumption].
7.49/7.49	1566 (all X_a (order(X_a) -> (all X all Least ((all X_2 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Least),X_2))) -> ti(X_a,Least) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),Least))))) # label(fact_4835_min__leastR) # label(axiom) # label(non_clause).  [assumption].
7.49/7.49	1567 (all Ta all A_3 all D_1 all D_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),D_1),D_2)) -> (all X_2 ((all Xa (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xa),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastAtMost(int),one_one(int)),D_2))) -> (all Xb (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xb),A_3)) -> hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),Xb),Xa) != ti(int,X_2))))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),D_1),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X_2),Ta))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),D_1),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X_2),D_2)),Ta)))))))) # label(fact_4650_aset_I9_J) # label(axiom) # label(non_clause).  [assumption].
7.49/7.49	1568 (all N (hBOOL(hAPP(nat,bool,even_odd_even(nat),N)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),N),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),one_one(nat))),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) # label(fact_2470_lemma__even__div2) # label(axiom) # label(non_clause).  [assumption].
7.49/7.49	1569 (all X_1 all Y_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X_1),Y_1)) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,real_1(int),X_1)),hAPP(int,real,real_1(int),Y_1))))) # label(fact_3331_real__of__int__le__iff) # label(axiom) # label(non_clause).  [assumption].
7.49/7.49	1570 (all A_1 hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),one_one(nat)),A_1))) # label(fact_894_gcd__lcm__complete__lattice__nat_Obot__least) # label(axiom) # label(non_clause).  [assumption].
7.49/7.49	1571 (all X_a (number_ring(X_a) -> (all W hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(int,X_a,number_number_of(X_a),W)) = hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,uminus_uminus(int),W))))) # label(fact_2040_number__of__minus) # label(axiom) # label(non_clause).  [assumption].
7.49/7.49	1572 (all M all K_4 all N (hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),K_4),N) = one_one(nat) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_4),M)),N) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),M),N))) # label(fact_3268_gcd__mult__cancel__nat) # label(axiom) # label(non_clause).  [assumption].
7.49/7.49	1573 (all X_1 all Y_1 (hBOOL(hAPP(nat,bool,even_odd_even(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X_1),Y_1))) <-> -hBOOL(hAPP(nat,bool,even_odd_even(nat),X_1)) & -hBOOL(hAPP(nat,bool,even_odd_even(nat),Y_1)) | hBOOL(hAPP(nat,bool,even_odd_even(nat),Y_1)) & hBOOL(hAPP(nat,bool,even_odd_even(nat),X_1)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X_1),Y_1)))) # label(fact_2427_even__difference__nat) # label(axiom) # label(non_clause).  [assumption].
7.49/7.49	1574 (all X_a (order(X_a) -> (all X_3 ((all N_2 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(nat,X_a,X_3,hAPP(nat,nat,suc,N_2))),hAPP(nat,X_a,X_3,N_2)))) -> hBOOL(hAPP(fun(nat,X_a),bool,monoseq(X_a),X_3)))))) # label(fact_4140_mono__SucI2) # label(axiom) # label(non_clause).  [assumption].
7.49/7.49	1575 (all X_1 all N_1 all Y_1 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),Y_1),hAPP(nat,nat,suc,N_1)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),X_1),hAPP(nat,nat,suc,N_1)) <-> Y_1 = X_1)) # label(fact_1254_exp__mono__eq) # label(axiom) # label(non_clause).  [assumption].
7.49/7.49	1576 (all X_a (linordered_field(X_a) -> (all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,inverse_inverse(X_a),B)),hAPP(X_a,X_a,inverse_inverse(X_a),A_1)))))))) # label(fact_2546_less__imp__inverse__less) # label(axiom) # label(non_clause).  [assumption].
7.49/7.49	1577 (all M all N (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),N)) -> hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,N),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),M),N)) = hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,M),N))) # label(fact_3459_zgcd__non__0) # label(axiom) # label(non_clause).  [assumption].
7.49/7.49	1578 (all X_a (semiring_div(X_a) -> (all A_1 all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),A_1),B)),B) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),A_1),B)))) # label(fact_906_mod__mod__trivial) # label(axiom) # label(non_clause).  [assumption].
7.49/7.49	1579 (all P_4 hAPP(rat,int,archim2085082626_floor(rat),P_4) = hAPP(product_prod(int,int),int,hAPP(fun(int,fun(int,int)),fun(product_prod(int,int),int),product_prod_case(int,int,int),div_div(int)),hAPP(rat,product_prod(int,int),quotient_of,P_4))) # label(fact_4027_rat__floor__code) # label(axiom) # label(non_clause).  [assumption].
7.49/7.49	1580 (all X_a (linord1117847801e_zero(X_a) & number(X_a) -> (all W_1 all B_1 all C_1 ((-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_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),W_1)),C_1)))) & (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(int,X_a,number_number_of(X_a),W_1)),zero_zero(X_a))))) & (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(int,X_a,number_number_of(X_a),W_1)),C_1)),B_1))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(int,X_a,number_number_of(X_a),W_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),B_1),C_1))))))) # label(fact_1746_less__divide__eq__number__of) # label(axiom) # label(non_clause).  [assumption].
7.49/7.49	1581 (all R_4 all A_1 hAPP(real,complex,hAPP(real,fun(real,complex),rcis,hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),one_one(real)),R_4)),hAPP(real,real,uminus_uminus(real),A_1)) = hAPP(complex,complex,inverse_inverse(complex),hAPP(real,complex,hAPP(real,fun(real,complex),rcis,R_4),A_1))) # label(fact_3174_rcis__inverse) # label(axiom) # label(non_clause).  [assumption].
7.49/7.49	1582 (all Q_3 all B all R_4 all C (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),C)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),R_4)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),R_4),B)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),Q_3),C))),R_4))))))) # label(fact_1060_zmult2__lemma__aux3) # label(axiom) # label(non_clause).  [assumption].
7.49/7.49	1583 (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_1524_Suc__le__D) # label(axiom) # label(non_clause).  [assumption].
7.49/7.49	1584 (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_762_add__nonpos__neg) # label(axiom) # label(non_clause).  [assumption].
7.49/7.49	1585 (all X_a (linordered_idom(X_a) -> (all X all Y (ti(X_a,Y) != ti(X_a,X) -> (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X))))))) # label(fact_310_linorder__neqE__linordered__idom) # label(axiom) # label(non_clause).  [assumption].
7.49/7.49	1586 (all Ma (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Ma),one_one(nat))) <-> Ma = one_one(nat))) # label(fact_477_nat__dvd__1__iff__1) # label(axiom) # label(non_clause).  [assumption].
7.49/7.49	1587 (all F all B_1 all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B_1),X_1)) -> ((all X_2 (hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),X_2),hAPP(real,fun(real,bool),hAPP(real,fun(real,fun(real,bool)),ord_gr676655987ssThan(real),B_1),X_1))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(real,real,F,X_2))))) -> (hBOOL(hAPP(real,bool,hAPP(fun(real,real),fun(real,bool),isCont(real,real),F),X_1)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(real,real,F,X_1))))))) # label(fact_4924_LIM__less__bound) # label(axiom) # label(non_clause).  [assumption].
7.49/7.49	1588 (all X_a (linorder(X_a) -> (all X_1 all Y_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(X_a,fun(X_a,bool),ord_lessThan(X_a),X_1)),hAPP(X_a,fun(X_a,bool),ord_lessThan(X_a),Y_1))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),Y_1)))))) # label(fact_4319_lessThan__subset__iff) # label(axiom) # label(non_clause).  [assumption].
7.49/7.49	1589 (all X_a (archim1727834104eiling(X_a) -> (all X_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),zero_zero(X_a))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(X_a,int,archimedean_ceiling(X_a),X_1)),one_one(int))))))) # label(fact_3299_ceiling__less__one) # label(axiom) # label(non_clause).  [assumption].
7.49/7.49	1590 (all N zero_zero(nat) != hAPP(nat,nat,fact_fact(nat),N)) # label(fact_2483_fact__nonzero__nat) # label(axiom) # label(non_clause).  [assumption].
7.49/7.49	1591 (all X_a ti(fun(list(X_a),nat),size_size(list(X_a))) = size_size(list(X_a))) # label(tsy_c_Nat_Osize__class_Osize_0_res) # label(axiom) # label(non_clause).  [assumption].
7.49/7.49	1592 (all N all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(nat,real,real_1(nat),N)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),hAPP(nat,real,real_1(nat),hAPP(nat,nat,suc,N)))) -> hAPP(int,nat,nat_1,hAPP(real,int,archim2085082626_floor(real),X)) = N))) # label(fact_2877_floor__eq3) # label(axiom) # label(non_clause).  [assumption].
7.49/7.49	1593 (all X_a (archim1727834104eiling(X_a) -> (all R_4 hAPP(X_a,int,archimedean_ceiling(X_a),R_4) = hAPP(real,int,archim2085082626_floor(real),hAPP(int,real,real_1(int),hAPP(X_a,int,archimedean_ceiling(X_a),R_4)))))) # label(fact_3355_floor__ceiling) # label(axiom) # label(non_clause).  [assumption].
7.49/7.49	1594 (all L_4 all K_4 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K_4),zero_zero(int))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),L_4)) -> hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),K_4),L_4)),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),K_4),L_4)) = hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),negDivAlg,K_4),L_4)))) # label(fact_927_negDivAlg__div__mod) # label(axiom) # label(non_clause).  [assumption].
7.49/7.49	1595 (all N_1 all Ma (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(nat,real,real_1(nat),N_1)),hAPP(nat,real,real_1(nat),Ma))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),Ma)))) # label(fact_2304_real__of__nat__less__iff) # label(axiom) # label(non_clause).  [assumption].
7.49/7.49	1596 (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_1852_abs__idempotent) # label(axiom) # label(non_clause).  [assumption].
7.49/7.49	1597 (all A_1 all B hAPP(int,rat,ring_1_of_int(rat),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,sgn_sgn(int),A_1)),hAPP(int,int,sgn_sgn(int),B))) = hAPP(rat,rat,sgn_sgn(rat),hAPP(int,rat,hAPP(int,fun(int,rat),fract,A_1),B))) # label(fact_3781_sgn__rat) # label(axiom) # label(non_clause).  [assumption].
7.49/7.49	1598 (all Ma all Z (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,semiring_1_of_nat(int),Ma)),Z)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),hAPP(int,nat,nat_1,Z))))) # label(fact_1379_zless__nat__eq__int__zless) # label(axiom) # label(non_clause).  [assumption].
7.49/7.49	1599 (all X_b all X_a (topological_space(X_a) & real_normed_algebra(X_b) -> (all G all F all A_2 (hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,X_b),fun(X_a,bool),isCont(X_a,X_b),F),A_2)) -> (hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,X_b),fun(X_a,bool),isCont(X_a,X_b),G),A_2)) -> hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,X_b),fun(X_a,bool),isCont(X_a,X_b),hAPP(fun(X_a,X_b),fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,X_b)),combs(X_a,X_b,X_b),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,fun(X_b,X_b))),combb(X_b,fun(X_b,X_b),X_a),times_times(X_b)),F)),G)),A_2))))))) # label(fact_4909_isCont__mult) # label(axiom) # label(non_clause).  [assumption].
7.49/7.49	1600 (all X_a (real_normed_vector(X_a) -> (all R_1 all X_3 (hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),X_3)) -> hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(X_a,X_a),fun(fun(nat,X_a),fun(nat,X_a)),combb(X_a,X_a,nat),hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),R_1)),X_3))))))) # label(fact_4670_scaleR__right_Osummable) # label(axiom) # label(non_clause).  [assumption].
7.49/7.49	1601 (all Ma all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Ma),N_1)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,semiring_1_of_nat(int),Ma)),hAPP(nat,int,semiring_1_of_nat(int),N_1))))) # label(fact_1301_zle__int) # label(axiom) # label(non_clause).  [assumption].
7.49/7.49	1602 (all X_1 all Y_1 all P_1 ((hBOOL(P_1) -> hAPP(nat,int,semiring_1_of_nat(int),X_1) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),hAPP(bool,fun(nat,fun(nat,nat)),if(nat),P_1),X_1),Y_1))) & (-hBOOL(P_1) -> hAPP(nat,int,semiring_1_of_nat(int),Y_1) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),hAPP(bool,fun(nat,fun(nat,nat)),if(nat),P_1),X_1),Y_1))))) # label(fact_1484_int__if__cong) # label(axiom) # label(non_clause).  [assumption].
7.49/7.49	1603 (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_1843_abs__ge__self) # label(axiom) # label(non_clause).  [assumption].
7.49/7.49	1604 (all X all Y hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),X),Y)) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(nat,int,semiring_1_of_nat(int),X)),hAPP(nat,int,semiring_1_of_nat(int),Y))) # label(fact_1359_Divides_Otransfer__int__nat__functions_I2_J) # label(axiom) # label(non_clause).  [assumption].
7.49/7.49	1605 (all F all A_2 all B_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A_2),B_1)) -> ((all X_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_2),B_1)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A_2),X_2)) -> (exists Y_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),Y_2),zero_zero(real))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),F),X_2),Y_2)))))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,F,B_1)),hAPP(real,real,F,A_2)))))) # label(fact_3528_DERIV__nonpos__imp__nonincreasing) # label(axiom) # label(non_clause).  [assumption].
7.49/7.49	1606 (all X_a (real_normed_field(X_a) -> (all Y_3 all B_1 all X_3 all A_2 (hBOOL(hAPP(X_a,bool,hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),X_3),A_2)) -> (hBOOL(hAPP(X_a,bool,hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),Y_3),B_1)) -> hBOOL(hAPP(X_a,bool,hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),minus_minus(X_a)),X_3)),Y_3)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_2),B_1)))))))) # label(fact_4088_sums__diff) # label(axiom) # label(non_clause).  [assumption].
7.49/7.49	1607 (all X_a (inverse(X_a) & real_normed_vector(X_a) -> (all F all A_2 all D_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_a,fun(filter(X_a),bool),hAPP(fun(X_a,X_a),fun(X_a,fun(filter(X_a),bool)),tendsto(X_a,X_a),hAPP(fun(X_a,X_a),fun(X_a,X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,X_a),fun(X_a,X_a)),combs(X_a,X_a,X_a),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,X_a),fun(X_a,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),X_a),inverse_divide(X_a)),hAPP(X_a,fun(X_a,X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(X_a,X_a)),combc(X_a,X_a,X_a),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,X_a),fun(X_a,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),X_a),minus_minus(X_a)),hAPP(fun(X_a,X_a),fun(X_a,X_a),hAPP(fun(X_a,X_a),fun(fun(X_a,X_a),fun(X_a,X_a)),combb(X_a,X_a,X_a),F),hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2)))),hAPP(X_a,X_a,F,A_2)))),combi(X_a))),D_2),hAPP(X_a,filter(X_a),at(X_a),zero_zero(X_a)))) <-> hBOOL(hAPP(filter(X_a),bool,hAPP(X_a,fun(filter(X_a),bool),hAPP(fun(X_a,X_a),fun(X_a,fun(filter(X_a),bool)),tendsto(X_a,X_a),hAPP(fun(X_a,X_a),fun(X_a,X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,X_a),fun(X_a,X_a)),combs(X_a,X_a,X_a),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,X_a),fun(X_a,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),X_a),inverse_divide(X_a)),hAPP(X_a,fun(X_a,X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(X_a,X_a)),combc(X_a,X_a,X_a),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,X_a),fun(X_a,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),X_a),minus_minus(X_a)),F)),hAPP(X_a,X_a,F,A_2)))),hAPP(X_a,fun(X_a,X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(X_a,X_a)),combc(X_a,X_a,X_a),minus_minus(X_a)),A_2))),D_2),hAPP(X_a,filter(X_a),at(X_a),A_2))))))) # label(fact_4607_DERIV__LIM__iff) # label(axiom) # label(non_clause).  [assumption].
7.49/7.50	1608 (all Y_1 all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),Y_1),X_1)) -> hAPP(fun(real,bool),real,complete_Sup_Sup(real),hAPP(real,fun(real,bool),hAPP(real,fun(real,fun(real,bool)),ord_gr676655987ssThan(real),Y_1),X_1)) = X_1)) # label(fact_3704_Sup__greaterThanLessThan) # label(axiom) # label(non_clause).  [assumption].
7.49/7.50	1609 (all A_1 all B (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),A_1),B)),B)))) # label(fact_4398_gcd__le2__int) # label(axiom) # label(non_clause).  [assumption].
7.49/7.50	1610 (all K all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),K),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_1),K))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),K),N_1)))) # label(fact_476_dvd__reduce) # label(axiom) # label(non_clause).  [assumption].
7.49/7.50	1611 (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)) = hAPP(int,int,number_number_of(int),V)) & (hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V))) -> zero_zero(int) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(int,nat,number_number_of(nat),V))))) # label(fact_1513_int__nat__number__of) # label(axiom) # label(non_clause).  [assumption].
7.49/7.50	1612 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,fact,M)),hAPP(nat,nat,fact,N))))) # label(fact_3539_fact__mono) # label(axiom) # label(non_clause).  [assumption].
7.49/7.50	1613 (all K all I all J hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I),K)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J),K)) = hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,nat),fun(fun(nat,bool),fun(nat,bool)),image(nat,nat),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),K)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),I),J))) # label(fact_4540_image__add__atLeastAtMost) # label(axiom) # label(non_clause).  [assumption].
7.49/7.50	1614 (all X all N hAPP(real,real,tan,X) = hAPP(real,real,tan,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),N)),pi)))) # label(fact_2257_tan__periodic__n) # label(axiom) # label(non_clause).  [assumption].
7.49/7.50	1615 (all Z_1 hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(real,complex,of_real(complex),hAPP(real,real,exp(real),hAPP(complex,real,re,Z_1)))),hAPP(real,complex,cis,hAPP(complex,real,im,Z_1))) = hAPP(complex,complex,expi,Z_1)) # label(fact_3023_expi__def) # label(axiom) # label(non_clause).  [assumption].
7.49/7.50	1616 (all X_a (linorder(X_a) -> (all X_1 all Y_1 (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),Y_1)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y_1),X_1)))))) # label(fact_1583_linorder__not__le) # label(axiom) # label(non_clause).  [assumption].
7.49/7.50	1617 (all X_a (dvd(X_a) -> (all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),B),A_1)) -> -(all K_1 ti(X_a,A_1) != hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),K_1)))))) # label(fact_2772_dvdE) # label(axiom) # label(non_clause).  [assumption].
7.49/7.50	1618 (all F all A_2 all B_1 hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,F,B_1)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,F,B_1)),hAPP(real,real,F,A_2))),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),B_1),A_2))),B_1)) = hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,F,A_2)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,F,B_1)),hAPP(real,real,F,A_2))),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),B_1),A_2))),A_2))) # label(fact_1800_lemma__MVT) # label(axiom) # label(non_clause).  [assumption].
7.49/7.50	1619 (all L all K ((ti(int,K) = zero_zero(int) -> hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),zero_zero(int)),zero_zero(int)) = hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),divmod_int,K),L)) & (ti(int,K) != zero_zero(int) -> (zero_zero(int) != ti(int,L) -> hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),divmod_int,K),L) = hAPP(product_prod(int,int),product_prod(int,int),hAPP(fun(int,int),fun(product_prod(int,int),product_prod(int,int)),product_apsnd(int,int,int),hAPP(int,fun(int,int),times_times(int),hAPP(int,int,sgn_sgn(int),L))),hAPP(product_prod(int,int),product_prod(int,int),hAPP(product_prod(int,int),fun(product_prod(int,int),product_prod(int,int)),hAPP(bool,fun(product_prod(int,int),fun(product_prod(int,int),product_prod(int,int))),if(product_prod(int,int)),hAPP(int,bool,hAPP(int,fun(int,bool),fequal(int),hAPP(int,int,sgn_sgn(int),K)),hAPP(int,int,sgn_sgn(int),L))),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),pdivmod,K),L)),hAPP(product_prod(int,int),product_prod(int,int),hAPP(fun(int,fun(int,product_prod(int,int))),fun(product_prod(int,int),product_prod(int,int)),product_prod_case(int,int,product_prod(int,int)),hAPP(fun(int,fun(int,product_prod(int,int))),fun(int,fun(int,product_prod(int,int))),hAPP(fun(int,fun(fun(int,product_prod(int,int)),fun(int,product_prod(int,int)))),fun(fun(int,fun(int,product_prod(int,int))),fun(int,fun(int,product_prod(int,int)))),combs(int,fun(int,product_prod(int,int)),fun(int,product_prod(int,int))),hAPP(fun(int,fun(int,fun(product_prod(int,int),product_prod(int,int)))),fun(int,fun(fun(int,product_prod(int,int)),fun(int,product_prod(int,int)))),hAPP(fun(fun(int,fun(product_prod(int,int),product_prod(int,int))),fun(fun(int,product_prod(int,int)),fun(int,product_prod(int,int)))),fun(fun(int,fun(int,fun(product_prod(int,int),product_prod(int,int)))),fun(int,fun(fun(int,product_prod(int,int)),fun(int,product_prod(int,int))))),combb(fun(int,fun(product_prod(int,int),product_prod(int,int))),fun(fun(int,product_prod(int,int)),fun(int,product_prod(int,int))),int),combs(int,product_prod(int,int),product_prod(int,int))),hAPP(fun(int,product_prod(int,int)),fun(int,fun(int,fun(product_prod(int,int),product_prod(int,int)))),hAPP(fun(product_prod(int,int),fun(int,fun(product_prod(int,int),product_prod(int,int)))),fun(fun(int,product_prod(int,int)),fun(int,fun(int,fun(product_prod(int,int),product_prod(int,int))))),combb(product_prod(int,int),fun(int,fun(product_prod(int,int),product_prod(int,int))),int),hAPP(fun(int,fun(product_prod(int,int),fun(product_prod(int,int),product_prod(int,int)))),fun(product_prod(int,int),fun(int,fun(product_prod(int,int),product_prod(int,int)))),combc(int,product_prod(int,int),fun(product_prod(int,int),product_prod(int,int))),hAPP(fun(int,bool),fun(int,fun(product_prod(int,int),fun(product_prod(int,int),product_prod(int,int)))),hAPP(fun(bool,fun(product_prod(int,int),fun(product_prod(int,int),product_prod(int,int)))),fun(fun(int,bool),fun(int,fun(product_prod(int,int),fun(product_prod(int,int),product_prod(int,int))))),combb(bool,fun(product_prod(int,int),fun(product_prod(int,int),product_prod(int,int))),int),if(product_prod(int,int))),hAPP(int,fun(int,bool),hAPP(fun(int,fun(int,bool)),fun(int,fun(int,bool)),combc(int,int,bool),fequal(int)),zero_zero(int))))),hAPP(int,fun(int,product_prod(int,int)),hAPP(fun(int,fun(int,product_prod(int,int))),fun(int,fun(int,product_prod(int,int))),combc(int,int,product_prod(int,int)),hAPP(fun(int,int),fun(int,fun(int,product_prod(int,int))),hAPP(fun(int,fun(int,product_prod(int,int))),fun(fun(int,int),fun(int,fun(int,product_prod(int,int)))),combb(int,fun(int,product_prod(int,int)),int),product_Pair(int,int)),uminus_uminus(int))),zero_zero(int))))),hAPP(fun(int,int),fun(int,fun(int,product_prod(int,int))),hAPP(fun(int,fun(fun(int,int),fun(int,product_prod(int,int)))),fun(fun(int,int),fun(int,fun(int,product_prod(int,int)))),combc(int,fun(int,int),fun(int,product_prod(int,int))),hAPP(fun(int,fun(int,product_prod(int,int))),fun(int,fun(fun(int,int),fun(int,product_prod(int,int)))),hAPP(fun(fun(int,product_prod(int,int)),fun(fun(int,int),fun(int,product_prod(int,int)))),fun(fun(int,fun(int,product_prod(int,int))),fun(int,fun(fun(int,int),fun(int,product_prod(int,int))))),combb(fun(int,product_prod(int,int)),fun(fun(int,int),fun(int,product_prod(int,int))),int),combb(int,product_prod(int,int),int)),hAPP(fun(int,int),fun(int,fun(int,product_prod(int,int))),hAPP(fun(int,fun(int,product_prod(int,int))),fun(fun(int,int),fun(int,fun(int,product_prod(int,int)))),combb(int,fun(int,product_prod(int,int)),int),product_Pair(int,int)),hAPP(int,fun(int,int),hAPP(fun(int,fun(int,int)),fun(int,fun(int,int)),combc(int,int,int),hAPP(fun(int,int),fun(int,fun(int,int)),hAPP(fun(int,fun(int,int)),fun(fun(int,int),fun(int,fun(int,int))),combb(int,fun(int,int),int),minus_minus(int)),uminus_uminus(int))),one_one(int))))),hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,abs_abs(int),L))))),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),pdivmod,K),L))))) & (zero_zero(int) = ti(int,L) -> hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),divmod_int,K),L) = hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),zero_zero(int)),K))))) # label(fact_4069_divmod__int__code) # label(axiom) # label(non_clause).  [assumption].
7.49/7.50	1620 (all L (min_1 = ti(int,L) <-> min_1 = hAPP(int,int,bit1,L))) # label(fact_286_rel__simps_I43_J) # label(axiom) # label(non_clause).  [assumption].
7.49/7.50	1621 (all X_a (boolean_algebra(X_a) -> (all Y all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),Y)),X)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),X)),Y)))))) # label(fact_2960_compl__less__swap2) # label(axiom) # label(non_clause).  [assumption].
7.49/7.50	1622 (all X_1 all Y_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_1),Y_1)) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_1),Y_1)) & Y_1 != X_1)) # label(fact_655_real__less__def) # label(axiom) # label(non_clause).  [assumption].
7.49/7.50	1623 (all X_a (linorder(X_a) -> (all Z_1 all Y all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),X)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Z_1),X)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),Y),Z_1)),X))))))) # label(fact_4977_min__max_Osup__least) # label(axiom) # label(non_clause).  [assumption].
7.49/7.50	1624 (all B all A_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A_1),zero_zero(int))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),A_1)) -> hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_1),B) = zero_zero(int)))) # label(fact_1016_div__neg__neg__trivial) # label(axiom) # label(non_clause).  [assumption].
7.49/7.50	1625 (all X hAPP(complex,real,im,hAPP(complex,complex,uminus_uminus(complex),X)) = hAPP(real,real,uminus_uminus(real),hAPP(complex,real,im,X))) # label(fact_2980_Im_Ominus) # label(axiom) # label(non_clause).  [assumption].
7.49/7.50	1626 t = zero_zero(int) -> zero_zero(int) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),one_one(int)) # label(fact_4_calculation_I2_J) # label(axiom) # label(non_clause).  [assumption].
7.49/7.50	1627 (all A_1 all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,real_1(nat),A_1)),X)) -> hAPP(real,nat,natfloor,hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),X),hAPP(nat,real,real_1(nat),A_1))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(real,nat,natfloor,X)),A_1))) # label(fact_2348_natfloor__subtract) # label(axiom) # label(non_clause).  [assumption].
7.49/7.50	1628 (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),hAPP(nat,nat,fact_fact(nat),N))))))) # label(fact_2494_of__nat__fact__ge__zero) # label(axiom) # label(non_clause).  [assumption].
7.49/7.50	1629 (all X_1 (hAPP(real,real,cos,X_1) != zero_zero(real) -> hBOOL(hAPP(real,bool,hAPP(fun(real,real),fun(real,bool),isCont(real,real),tan),X_1)))) # label(fact_4885_isCont__tan) # label(axiom) # label(non_clause).  [assumption].
7.49/7.50	1630 (all X_a (order(X_a) -> (all F ((all X_2 all Y_2 (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y_2),X_2)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_2),Y_2)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,F,X_2)),hAPP(nat,X_a,F,Y_2))))) -> hBOOL(hAPP(fun(nat,X_a),bool,hAPP(fun(nat,fun(nat,bool)),fun(fun(nat,X_a),bool),strict_mono(nat,X_a),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),hAPP(fun(nat,fun(fun(nat,bool),fun(nat,bool))),fun(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool))),combs(nat,fun(nat,bool),fun(nat,bool)),hAPP(fun(nat,fun(nat,fun(bool,bool))),fun(nat,fun(fun(nat,bool),fun(nat,bool))),hAPP(fun(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool))),fun(fun(nat,fun(nat,fun(bool,bool))),fun(nat,fun(fun(nat,bool),fun(nat,bool)))),combb(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),nat),combs(nat,bool,bool)),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,fun(bool,bool))),hAPP(fun(fun(nat,bool),fun(nat,fun(bool,bool))),fun(fun(nat,fun(nat,bool)),fun(nat,fun(nat,fun(bool,bool)))),combb(fun(nat,bool),fun(nat,fun(bool,bool)),nat),hAPP(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fconj)),dvd_dvd(nat)))),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),hAPP(fun(fun(nat,bool),fun(nat,bool)),fun(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool))),combb(fun(nat,bool),fun(nat,bool),nat),hAPP(fun(bool,bool),fun(fun(nat,bool),fun(nat,bool)),combb(bool,bool,nat),fNot)),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),dvd_dvd(nat))))),F)))))) # label(fact_4791_dvd_Ostrict__monoI) # label(axiom) # label(non_clause).  [assumption].
7.49/7.50	1631 (all A_1 all N all P_5 (hBOOL(hAPP(nat,bool,prime,P_5)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),P_5),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A_1),N))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),P_5),A_1))))) # label(fact_3058_prime__dvd__power) # label(axiom) # label(non_clause).  [assumption].
7.49/7.50	1632 (all X_a (real_normed_algebra(X_a) -> (all A_1 all A_6 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),B)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_6),B)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),A_6)),B)))) # label(fact_882_mult_Oadd__left) # label(axiom) # label(non_clause).  [assumption].
7.49/7.50	1633 (all X_a all Q_1 all P_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),Q_1))) | hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),P_1))) -> hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,bool)),combs(X_a,bool,bool),hAPP(fun(X_a,bool),fun(X_a,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,fun(bool,bool))),combb(bool,fun(bool,bool),X_a),fconj),P_1)),Q_1)))))) # label(fact_3800_finite__Collect__conjI) # label(axiom) # label(non_clause).  [assumption].
7.49/7.50	1634 (all X_a (abs_if(X_a) -> ti(fun(X_a,X_a),abs_abs(X_a)) = abs_abs(X_a))) # label(tsy_c_Groups_Oabs__class_Oabs_0_res) # label(axiom) # label(non_clause).  [assumption].
7.49/7.50	1635 (all X_a (topological_space(X_a) -> (all G all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(complex,fun(filter(X_a),bool),hAPP(fun(X_a,complex),fun(complex,fun(filter(X_a),bool)),tendsto(X_a,complex),G),zero_zero(complex)),hAPP(X_a,filter(X_a),at(X_a),A_2))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(real,fun(filter(X_a),bool),hAPP(fun(X_a,real),fun(real,fun(filter(X_a),bool)),tendsto(X_a,real),hAPP(fun(X_a,complex),fun(X_a,real),hAPP(fun(complex,real),fun(fun(X_a,complex),fun(X_a,real)),combb(complex,real,X_a),re),G)),zero_zero(real)),hAPP(X_a,filter(X_a),at(X_a),A_2))))))) # label(fact_4615_Re_OLIM__zero) # label(axiom) # label(non_clause).  [assumption].
7.49/7.50	1636 (all Y_1 all X_1 all A_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),A_2)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Y_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_1),Y_1)) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),log,A_2),X_1)),hAPP(real,real,hAPP(real,fun(real,real),log,A_2),Y_1)))))))) # label(fact_2643_log__less__cancel__iff) # label(axiom) # label(non_clause).  [assumption].
7.49/7.50	1637 (all X_a (ring_1(X_a) -> (all Z hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),hAPP(int,X_a,ring_1_of_int(X_a),Z)),ring_1_Ints(X_a)))))) # label(fact_3804_Ints__of__int) # label(axiom) # label(non_clause).  [assumption].
7.49/7.50	1638 (all V_1 all V_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V_1),V_2)) & (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V_1),V_2)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),V_2))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(int,nat,number_number_of(nat),V_1)),hAPP(int,nat,number_number_of(nat),V_2))))) # label(fact_79_less__nat__number__of) # label(axiom) # label(non_clause).  [assumption].
7.49/7.50	1639 (all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> hAPP(nat,nat,fact_fact(nat),N) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N),hAPP(nat,nat,fact_fact(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),one_one(nat)))))) # label(fact_2501_fact__reduce__nat) # label(axiom) # label(non_clause).  [assumption].
7.49/7.50	1640 (all X_a (archim1727834104eiling(X_a) -> (all X_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),one_one(X_a))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(X_a,int,archim2085082626_floor(X_a),X_1)),one_one(int))))))) # label(fact_2883_floor__less__one) # label(axiom) # label(non_clause).  [assumption].
7.49/7.50	1641 (all X_a (real_algebra_1(X_a) -> zero_zero(X_a) = hAPP(real,X_a,of_real(X_a),zero_zero(real)))) # label(fact_2783_of__real__0) # label(axiom) # label(non_clause).  [assumption].
7.49/7.50	1642 (all X (hBOOL(hAPP(nat,bool,even_odd_even(nat),X)) -> X = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat)))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),X),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat))))))) # label(fact_2461_even__nat__div__two__times__two) # label(axiom) # label(non_clause).  [assumption].
7.49/7.50	1643 (all X_b (monoid_mult(X_b) & number(X_b) -> (all V all W hAPP(nat,X_b,hAPP(X_b,fun(nat,X_b),power_power(X_b),hAPP(int,X_b,number_number_of(X_b),V)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,W))) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(nat,X_b,hAPP(X_b,fun(nat,X_b),power_power(X_b),hAPP(int,X_b,number_number_of(X_b),V)),hAPP(int,nat,number_number_of(nat),W))),hAPP(nat,X_b,hAPP(X_b,fun(nat,X_b),power_power(X_b),hAPP(int,X_b,number_number_of(X_b),V)),hAPP(int,nat,number_number_of(nat),W)))))) # label(fact_3872_power__number__of__even__number__of) # label(axiom) # label(non_clause).  [assumption].
7.49/7.50	1644 (all X_a (metric_space(X_a) -> (all X_3 all A_2 (hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),X_3),A_2),sequentially)) -> hBOOL(hAPP(fun(nat,X_a),bool,cauchy(X_a),X_3)))))) # label(fact_4488_LIMSEQ__imp__Cauchy) # label(axiom) # label(non_clause).  [assumption].
7.49/7.50	1645 (all X_a (linorder(X_a) -> (all A_1 all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),A_1),B) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),B),A_1)))) # label(fact_4816_min__max_Oinf_Ocommute) # label(axiom) # label(non_clause).  [assumption].
7.49/7.50	1646 (all M zero_zero(nat) != hAPP(nat,nat,suc,M)) # label(fact_1227_Zero__not__Suc) # label(axiom) # label(non_clause).  [assumption].
7.49/7.50	1647 (all V_3 all V ((-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V),pls)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),V)),hAPP(int,nat,number_number_of(nat),V_3)) = hAPP(int,nat,number_number_of(nat),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),V),V_3))) & (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V),pls)) -> zero_zero(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),V)),hAPP(int,nat,number_number_of(nat),V_3))))) # label(fact_231_mult__nat__number__of) # label(axiom) # label(non_clause).  [assumption].
7.49/7.50	1648 (all Y_1 hAPP(real,real,arcsin,Y_1) = hAPP(fun(real,bool),real,the(real),hAPP(fun(real,bool),fun(real,bool),hAPP(fun(real,fun(bool,bool)),fun(fun(real,bool),fun(real,bool)),combs(real,bool,bool),hAPP(fun(real,bool),fun(real,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(real,bool),fun(real,fun(bool,bool))),combb(bool,fun(bool,bool),real),fconj),hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))),hAPP(fun(real,bool),fun(real,bool),hAPP(fun(real,fun(bool,bool)),fun(fun(real,bool),fun(real,bool)),combs(real,bool,bool),hAPP(fun(real,bool),fun(real,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(real,bool),fun(real,fun(bool,bool))),combb(bool,fun(bool,bool),real),fconj),hAPP(real,fun(real,bool),hAPP(fun(real,fun(real,bool)),fun(real,fun(real,bool)),combc(real,real,bool),ord_less_eq(real)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))),hAPP(real,fun(real,bool),hAPP(fun(real,fun(real,bool)),fun(real,fun(real,bool)),combc(real,real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),hAPP(fun(real,fun(real,bool)),fun(fun(real,real),fun(real,fun(real,bool))),combb(real,fun(real,bool),real),fequal(real)),sin)),Y_1))))) # label(fact_4133_arcsin__def) # label(axiom) # label(non_clause).  [assumption].
7.49/7.50	1649 (all X_a (number_ring(X_a) -> zero_zero(X_a) = hAPP(int,X_a,number_number_of(X_a),pls))) # label(fact_147_semiring__norm_I112_J) # label(axiom) # label(non_clause).  [assumption].
7.49/7.50	1650 (all X_a (semiring_1(X_a) -> one_one(X_a) = hAPP(nat,X_a,semiring_1_of_nat(X_a),one_one(nat)))) # label(fact_1288_of__nat__1) # label(axiom) # label(non_clause).  [assumption].
7.49/7.50	1651 (all A_2 all B_1 ((exists X_2 exists Y_2 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A_2),X_2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B_1),Y_2)) = one_one(nat) | one_one(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B_1),X_2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A_2),Y_2)))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,A_2),B_1)))) # label(fact_2896_coprime__bezout) # label(axiom) # label(non_clause).  [assumption].
7.49/7.50	1652 (all X_a (semiring_div(X_a) -> (all A_1 all C all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),C),B)) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(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),div_div(X_a),B),C)))))) # label(fact_1003_div__mult__swap) # label(axiom) # label(non_clause).  [assumption].
7.49/7.50	1653 (all X_a (semiring_div(X_a) -> (all A_1 all C all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),C)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),A_1),B)),C)))) # label(fact_932_mod__mult__mult2) # label(axiom) # label(non_clause).  [assumption].
7.49/7.50	1654 (all N_1 all P_1 (-hBOOL(hAPP(nat,bool,P_1,zero_zero(nat))) -> (hBOOL(hAPP(nat,bool,P_1,N_1)) -> (exists K_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),K_1),N_1)) & hBOOL(hAPP(nat,bool,P_1,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_1),one_one(nat)))) & (all I_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_2),K_1)) -> -hBOOL(hAPP(nat,bool,P_1,I_2))))))))) # label(fact_612_ex__least__nat__less) # label(axiom) # label(non_clause).  [assumption].
7.49/7.50	1655 (all X_a (t2_space(X_a) & comm_monoid_add(X_a) -> (all F all Sa (hBOOL(hAPP(X_a,bool,hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),F),Sa)) -> ti(X_a,Sa) = hAPP(fun(nat,X_a),X_a,suminf(X_a),F))))) # label(fact_4089_sums__unique) # label(axiom) # label(non_clause).  [assumption].
7.49/7.50	1656 (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_28_zmult__assoc) # label(axiom) # label(non_clause).  [assumption].
7.49/7.50	1657 (all X_a (field(X_a) -> (all Z all N_1 all H (ti(X_a,H) != zero_zero(X_a) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Z),H)),N_1)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),Z),N_1))),H)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),N_1)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),Z),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),hAPP(nat,nat,suc,zero_zero(nat)))))) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),H),hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),hAPP(fun(nat,fun(nat,bool)),fun(nat,X_a),hAPP(fun(fun(nat,bool),X_a),fun(fun(nat,fun(nat,bool)),fun(nat,X_a)),combb(fun(nat,bool),X_a,nat),hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),times_times(X_a)),hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Z),H)))),hAPP(fun(nat,nat),fun(nat,X_a),hAPP(fun(nat,X_a),fun(fun(nat,nat),fun(nat,X_a)),combb(nat,X_a,nat),hAPP(X_a,fun(nat,X_a),power_power(X_a),Z)),hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))))),hAPP(fun(nat,nat),fun(nat,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(nat,nat),fun(nat,fun(nat,bool))),combb(nat,fun(nat,bool),nat),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat))),hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),hAPP(nat,nat,suc,zero_zero(nat))))))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),hAPP(nat,nat,suc,zero_zero(nat)))))))))) # label(fact_4238_lemma__termdiff2) # label(axiom) # label(non_clause).  [assumption].
7.49/7.50	1658 (all X (hBOOL(hAPP(int,bool,even_odd_even(int),X)) -> hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X),one_one(int))),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(int,int,hAPP(int,fun(int,int),div_div(int),X),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) # label(fact_1473_even__plus__one__div__two) # label(axiom) # label(non_clause).  [assumption].
7.49/7.50	1659 (all B all A_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A_1)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),A_1),B)),A_1)))) # label(fact_4399_gcd__le1__int) # label(axiom) # label(non_clause).  [assumption].
7.49/7.50	1660 (all X all P_5 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),P_5)) -> (hBOOL(hAPP(int,bool,zprime,P_5)) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,X),zero_zero(int)),P_5)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(int,int,hAPP(int,fun(int,int),multInv,P_5),hAPP(int,int,hAPP(int,fun(int,int),multInv,P_5),X))),X),P_5)))))) # label(fact_846_MultInv__prop4) # label(axiom) # label(non_clause).  [assumption].
7.49/7.50	1661 (all X_a all A_2 all F all V_1 hAPP(nat,X_a,hAPP(fun(nat,fun(X_a,X_a)),fun(nat,X_a),hAPP(X_a,fun(fun(nat,fun(X_a,X_a)),fun(nat,X_a)),nat_rec(X_a),A_2),F),hAPP(int,nat,number_number_of(nat),V_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),hAPP(bool,fun(X_a,fun(X_a,X_a)),if(X_a),hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),hAPP(int,int,pred,V_1)))),A_2),hAPP(X_a,X_a,hAPP(nat,fun(X_a,X_a),F,hAPP(int,nat,nat_1,hAPP(int,int,number_number_of(int),hAPP(int,int,pred,V_1)))),hAPP(nat,X_a,hAPP(fun(nat,fun(X_a,X_a)),fun(nat,X_a),hAPP(X_a,fun(fun(nat,fun(X_a,X_a)),fun(nat,X_a)),nat_rec(X_a),A_2),F),hAPP(int,nat,nat_1,hAPP(int,int,number_number_of(int),hAPP(int,int,pred,V_1))))))) # label(fact_4157_nat__rec__number__of) # label(axiom) # label(non_clause).  [assumption].
7.49/7.50	1662 (all D_1 all F all X_1 all L (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),F),X_1),L)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),D_1)) -> ((all Y_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),X_1),Y_2))),D_1)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,F,X_1)),hAPP(real,real,F,Y_2))))) -> zero_zero(real) = L)))) # label(fact_2659_DERIV__local__min) # label(axiom) # label(non_clause).  [assumption].
7.49/7.50	1663 (all X_a (semiring_1(X_a) -> (all Z (hBOOL(hAPP(X_a,bool,iszero(X_a),Z)) <-> ti(X_a,Z) = zero_zero(X_a))))) # label(fact_2555_iszero__def) # label(axiom) # label(non_clause).  [assumption].
7.49/7.50	1664 (all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,number_number_of(real),min_1)),Y)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),Y),one_one(real))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,arcsin,Y)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),hAPP(real,real,arcsin,Y)))))) # label(fact_2129_arcsin__lt__bounded) # label(axiom) # label(non_clause).  [assumption].
7.49/7.50	1665 (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_779_add__le__imp__le__left) # label(axiom) # label(non_clause).  [assumption].
7.49/7.50	1666 (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_2950_times_Oidem) # label(axiom) # label(non_clause).  [assumption].
7.49/7.50	1667 (all M all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),hAPP(nat,nat,suc,M)),hAPP(nat,nat,suc,N)) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),M),N))) # label(fact_4808_min__Suc__Suc) # label(axiom) # label(non_clause).  [assumption].
7.49/7.50	1668 (all X_3 ((all R_2 (hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),R_2)) -> (exists K_1 all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_1),N_2)) -> hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,abs_abs(rat),hAPP(nat,rat,X_3,N_2))),R_2)))))) -> hBOOL(hAPP(fun(nat,rat),bool,vanishes,X_3)))) # label(fact_4865_vanishesI) # label(axiom) # label(non_clause).  [assumption].
7.49/7.50	1669 (all X all K_4 all N all P_5 (hBOOL(hAPP(nat,bool,prime,P_5)) -> (zero_zero(nat) != N -> (hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),P_5),K_4) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),X),N) -> (exists I_2 X = hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),P_5),I_2)))))) # label(fact_3087_prime__power__exp) # label(axiom) # label(non_clause).  [assumption].
7.49/7.50	1670 (all N_1 hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),N_1) = hAPP(nat,fun(nat,bool),ord_lessThan(nat),N_1)) # label(fact_4317_atLeast0LessThan) # label(axiom) # label(non_clause).  [assumption].
7.49/7.50	1671 (all X_a all G all A_2 all A_3 (hBOOL(hAPP(filter(X_a),bool,hAPP(complex,fun(filter(X_a),bool),hAPP(fun(X_a,complex),fun(complex,fun(filter(X_a),bool)),tendsto(X_a,complex),G),A_2),A_3)) -> hBOOL(hAPP(filter(X_a),bool,hAPP(real,fun(filter(X_a),bool),hAPP(fun(X_a,real),fun(real,fun(filter(X_a),bool)),tendsto(X_a,real),hAPP(fun(X_a,complex),fun(X_a,real),hAPP(fun(complex,real),fun(fun(X_a,complex),fun(X_a,real)),combb(complex,real,X_a),im),G)),hAPP(complex,real,im,A_2)),A_3)))) # label(fact_4508_Im_Otendsto) # label(axiom) # label(non_clause).  [assumption].
7.49/7.50	1672 (all X_a all F1 all F2 all Nat hAPP(nat,X_a,hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(X_a,fun(fun(nat,X_a),fun(nat,X_a)),nat_case(X_a),F1),F2),hAPP(nat,nat,suc,Nat)) = hAPP(nat,X_a,F2,Nat)) # label(fact_4110_nat__case__Suc) # label(axiom) # label(non_clause).  [assumption].
7.49/7.50	1673 (all Y all X (X = hAPP(real,real,exp(real),Y) -> hAPP(real,real,ln,X) = Y)) # label(fact_2507_ln__unique) # label(axiom) # label(non_clause).  [assumption].
7.49/7.50	1674 (exists K_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),K_2)) & (all X_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,norm_norm(real),hAPP(complex,real,im,X_2))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(complex,real,norm_norm(complex),X_2)),K_2)))))) # label(fact_2987_Im_Opos__bounded) # label(axiom) # label(non_clause).  [assumption].
7.49/7.50	1675 (all X_a all X_1 all A_3 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_3)) <-> hBOOL(hAPP(X_a,bool,A_3,X_1)))) # label(fact_76_mem__def) # label(axiom) # label(non_clause).  [assumption].
7.49/7.50	1676 (all X all Y hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(complex,real,im,X)),hAPP(complex,real,im,Y)) = hAPP(complex,real,im,hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),X),Y))) # label(fact_2978_Im_Oadd) # label(axiom) # label(non_clause).  [assumption].
7.49/7.50	1677 (all N -hBOOL(hAPP(int,bool,nat_neg,hAPP(nat,int,semiring_1_of_nat(int),N)))) # label(fact_1501_not__neg__int) # label(axiom) # label(non_clause).  [assumption].
7.49/7.50	1678 (all X_a (real_field(X_a) -> (all N_1 all X_1 all Y_1 hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),hAPP(real,real,inverse_inverse(real),hAPP(nat,real,real_1(nat),hAPP(nat,nat,fact_fact(nat),N_1)))),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X_1),Y_1)),N_1)) = hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),times_times(X_a)),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,real),fun(nat,fun(X_a,X_a)),hAPP(fun(real,fun(X_a,X_a)),fun(fun(nat,real),fun(nat,fun(X_a,X_a))),combb(real,fun(X_a,X_a),nat),scaleR_scaleR(X_a)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),inverse_inverse(real)),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),fact_fact(nat))))),hAPP(X_a,fun(nat,X_a),power_power(X_a),X_1)))),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,real),fun(nat,fun(X_a,X_a)),hAPP(fun(real,fun(X_a,X_a)),fun(fun(nat,real),fun(nat,fun(X_a,X_a))),combb(real,fun(X_a,X_a),nat),scaleR_scaleR(X_a)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),inverse_inverse(real)),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),hAPP(fun(nat,nat),fun(nat,nat),hAPP(fun(nat,nat),fun(fun(nat,nat),fun(nat,nat)),combb(nat,nat,nat),fact_fact(nat)),hAPP(nat,fun(nat,nat),minus_minus(nat),N_1)))))),hAPP(fun(nat,nat),fun(nat,X_a),hAPP(fun(nat,X_a),fun(fun(nat,nat),fun(nat,X_a)),combb(nat,X_a,nat),hAPP(X_a,fun(nat,X_a),power_power(X_a),Y_1)),hAPP(nat,fun(nat,nat),minus_minus(nat),N_1))))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),zero_zero(nat)),N_1))))) # label(fact_4664_exp__series__add) # label(axiom) # label(non_clause).  [assumption].
7.49/7.50	1679 (all Z_1 all W hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),Z_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,W))) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),Z_1),hAPP(int,nat,number_number_of(nat),W))),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),Z_1),hAPP(int,nat,number_number_of(nat),W)))) # label(fact_3870_zpower__number__of__even) # label(axiom) # label(non_clause).  [assumption].
7.49/7.50	1680 (all X_a (linordered_field(X_a) -> (all X all Z_1 all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),Y)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Z_1),Y))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),X),Y)),Z_1))))))) # label(fact_1739_mult__imp__div__pos__le) # label(axiom) # label(non_clause).  [assumption].
7.49/7.50	1681 (all X_a (number_ring(X_a) -> (all K_4 hAPP(int,X_a,number_number_of(X_a),K_4) = hAPP(int,X_a,ring_1_of_int(X_a),K_4)))) # label(fact_3581_number__of__eq) # label(axiom) # label(non_clause).  [assumption].
7.49/7.50	1682 (all N_1 all Ma (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Ma)) -> (N_1 = one_one(nat) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N_1),Ma)),Ma))))) # label(fact_506_dvd__mult__cancel2) # label(axiom) # label(non_clause).  [assumption].
7.49/7.50	1683 (all Ma all N_1 (zero_zero(int) = ti(int,N_1) & ti(int,Ma) = zero_zero(int) <-> zero_zero(int) = hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),Ma),N_1))) # label(fact_4361_gcd__zero__int) # label(axiom) # label(non_clause).  [assumption].
7.49/7.50	1684 (all Y all X all Z_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X),Z_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Y),Z_1))))) # label(fact_3037_termination__basic__simps_I4_J) # label(axiom) # label(non_clause).  [assumption].
7.49/7.50	1685 (all X_1 (hBOOL(hAPP(nat,bool,even_odd_even(nat),X_1)) <-> hBOOL(hAPP(int,bool,even_odd_even(int),hAPP(nat,int,semiring_1_of_nat(int),X_1))))) # label(fact_2429_even__nat__def) # label(axiom) # label(non_clause).  [assumption].
7.49/7.50	1686 (all X_a (real_n1866405975lgebra(X_a) -> (all A_1 (zero_zero(X_a) != ti(X_a,A_1) -> hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,inverse_inverse(X_a),A_1)) = hAPP(real,real,inverse_inverse(real),hAPP(X_a,real,norm_norm(X_a),A_1)))))) # label(fact_2511_nonzero__norm__inverse) # label(axiom) # label(non_clause).  [assumption].
7.49/7.50	1687 (all A_2 all A_3 all Ma (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),Ma)) -> (hBOOL(hAPP(int,bool,hAPP(fun(int,bool),fun(int,bool),is_RRset,A_3),Ma)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),A_2),A_3)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_2),hAPP(fun(int,bool),int,hilbert_Eps(int),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),combs(int,bool,bool),hAPP(fun(int,bool),fun(int,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj),hAPP(int,fun(int,bool),hAPP(fun(int,fun(int,bool)),fun(int,fun(int,bool)),combc(int,int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_2)),Ma))),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,fun(fun(int,bool),bool)),fun(fun(int,bool),fun(int,bool)),combc(int,fun(int,bool),bool),member(int)),hAPP(int,fun(int,bool),norRRset,Ma))))),Ma)) & hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),hAPP(fun(int,bool),int,hilbert_Eps(int),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),combs(int,bool,bool),hAPP(fun(int,bool),fun(int,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj),hAPP(int,fun(int,bool),hAPP(fun(int,fun(int,bool)),fun(int,fun(int,bool)),combc(int,int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_2)),Ma))),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,fun(fun(int,bool),bool)),fun(fun(int,bool),fun(int,bool)),combc(int,fun(int,bool),bool),member(int)),hAPP(int,fun(int,bool),norRRset,Ma))))),hAPP(int,fun(int,bool),norRRset,Ma))))))) # label(fact_4156_aux__some) # label(axiom) # label(non_clause).  [assumption].
7.49/7.50	1688 (all X_a (linorder(X_a) -> ord_max(X_a) = hAPP(fun(X_a,fun(X_a,bool)),fun(X_a,fun(X_a,X_a)),min(X_a),hAPP(fun(X_a,fun(X_a,bool)),fun(X_a,fun(X_a,bool)),combc(X_a,X_a,bool),ord_less_eq(X_a))))) # label(fact_4991_dual__min) # label(axiom) # label(non_clause).  [assumption].
7.49/7.50	1689 (all X all Y all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(nat,fun(real,real),root,N),X)),hAPP(real,real,hAPP(nat,fun(real,real),root,N),Y)) = hAPP(real,real,hAPP(nat,fun(real,real),root,N),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),X),Y)))) # label(fact_2687_real__root__divide) # label(axiom) # label(non_clause).  [assumption].
7.49/7.50	1690 (all V_1 all V_2 (hAPP(int,nat,number_number_of(nat),V_2) = hAPP(int,nat,number_number_of(nat),V_1) <-> (-hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V_1))) -> (hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V_2))) -> hAPP(int,int,number_number_of(int),V_1) = zero_zero(int)) & (-hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V_2))) -> ti(int,V_2) = ti(int,V_1))) & (hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V_1))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),V_2)),zero_zero(int)))))) # label(fact_1511_eq__nat__number__of) # label(axiom) # label(non_clause).  [assumption].
7.49/7.50	1691 (all A_2 all B_1 (zero_zero(real) = B_1 & A_2 = zero_zero(real) <-> zero_zero(complex) = hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,A_2),B_1))) # label(fact_2740_Complex__eq__0) # label(axiom) # label(non_clause).  [assumption].
7.49/7.50	1692 (all A_2 all B_1 (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_2),B_1)),zOdd)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),A_2),zOdd)) -> hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),B_1),zEven))))) # label(fact_1366_even__plus__odd__prop1) # label(axiom) # label(non_clause).  [assumption].
7.49/7.50	1693 (all X_a (real_normed_field(X_a) -> (all G all E_3 all F all X_1 all D_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),F),X_1),D_2)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),G),X_1),E_3)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),hAPP(fun(X_a,X_a),fun(X_a,X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,X_a),fun(X_a,X_a)),combs(X_a,X_a,X_a),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,X_a),fun(X_a,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),X_a),minus_minus(X_a)),F)),G)),X_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),D_2),E_3)))))))) # label(fact_3822_DERIV__diff) # label(axiom) # label(non_clause).  [assumption].
7.49/7.50	1694 (all X_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)) -> (hBOOL(hAPP(nat,bool,even_odd_even(nat),N_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_1),zero_zero(real))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(nat,fun(real,real),root,N_1)),X_1),hAPP(real,real,inverse_inverse(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,uminus_uminus(real),hAPP(nat,real,real_1(nat),N_1))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,hAPP(nat,fun(real,real),root,N_1),X_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),hAPP(nat,nat,suc,zero_zero(nat)))))))))))) # label(fact_2668_DERIV__even__real__root) # label(axiom) # label(non_clause).  [assumption].
7.49/7.50	1695 (all X_a (number_semiring(X_a) -> (all V (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),V)) -> hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,succ,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)))))) # label(fact_1533_semiring__number__of__add__1) # label(axiom) # label(non_clause).  [assumption].
7.49/7.50	1696 (all Code_numeral_3 zero_zero(code_code_numeral) != hAPP(code_code_numeral,code_code_numeral,code_S1047413653umeral,Code_numeral_3)) # label(fact_2947_code__numeral_Osimps_I2_J) # label(axiom) # label(non_clause).  [assumption].
7.49/7.50	1697 (all M all N all R_5 all S_4 all S_3 all T_6 all T_5 all R_4 ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),R_4),zero_zero(int))) -> hAPP(product_prod(int,int),product_prod(int,product_prod(int,int)),hAPP(int,fun(product_prod(int,int),product_prod(int,product_prod(int,int))),product_Pair(int,product_prod(int,int)),R_5),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),S_4),T_6)) = hAPP(int,product_prod(int,product_prod(int,int)),hAPP(int,fun(int,product_prod(int,product_prod(int,int))),hAPP(int,fun(int,fun(int,product_prod(int,product_prod(int,int)))),hAPP(int,fun(int,fun(int,fun(int,product_prod(int,product_prod(int,int))))),hAPP(int,fun(int,fun(int,fun(int,fun(int,product_prod(int,product_prod(int,int)))))),hAPP(int,fun(int,fun(int,fun(int,fun(int,fun(int,product_prod(int,product_prod(int,int))))))),hAPP(int,fun(int,fun(int,fun(int,fun(int,fun(int,fun(int,product_prod(int,product_prod(int,int)))))))),hAPP(int,fun(int,fun(int,fun(int,fun(int,fun(int,fun(int,fun(int,product_prod(int,product_prod(int,int))))))))),xzgcda,M),N),R_5),R_4),S_4),S_3),T_6),T_5)) & (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),R_4),zero_zero(int))) -> hAPP(int,product_prod(int,product_prod(int,int)),hAPP(int,fun(int,product_prod(int,product_prod(int,int))),hAPP(int,fun(int,fun(int,product_prod(int,product_prod(int,int)))),hAPP(int,fun(int,fun(int,fun(int,product_prod(int,product_prod(int,int))))),hAPP(int,fun(int,fun(int,fun(int,fun(int,product_prod(int,product_prod(int,int)))))),hAPP(int,fun(int,fun(int,fun(int,fun(int,fun(int,product_prod(int,product_prod(int,int))))))),hAPP(int,fun(int,fun(int,fun(int,fun(int,fun(int,fun(int,product_prod(int,product_prod(int,int)))))))),hAPP(int,fun(int,fun(int,fun(int,fun(int,fun(int,fun(int,fun(int,product_prod(int,product_prod(int,int))))))))),xzgcda,M),N),R_5),R_4),S_4),S_3),T_6),T_5) = hAPP(int,product_prod(int,product_prod(int,int)),hAPP(int,fun(int,product_prod(int,product_prod(int,int))),hAPP(int,fun(int,fun(int,product_prod(int,product_prod(int,int)))),hAPP(int,fun(int,fun(int,fun(int,product_prod(int,product_prod(int,int))))),hAPP(int,fun(int,fun(int,fun(int,fun(int,product_prod(int,product_prod(int,int)))))),hAPP(int,fun(int,fun(int,fun(int,fun(int,fun(int,product_prod(int,product_prod(int,int))))))),hAPP(int,fun(int,fun(int,fun(int,fun(int,fun(int,fun(int,product_prod(int,product_prod(int,int)))))))),hAPP(int,fun(int,fun(int,fun(int,fun(int,fun(int,fun(int,fun(int,product_prod(int,product_prod(int,int))))))))),xzgcda,M),N),R_4),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),R_5),R_4)),S_3),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),S_4),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),R_5),R_4)),S_3))),T_5),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),T_6),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),R_5),R_4)),T_5)))))) # label(fact_3083_xzgcda_Osimps) # label(axiom) # label(non_clause).  [assumption].
7.49/7.50	1698 (all N all M hAPP(quickcheck_code_int,product_prod(quickcheck_code_int,quickcheck_code_int),hAPP(quickcheck_code_int,fun(quickcheck_code_int,product_prod(quickcheck_code_int,quickcheck_code_int)),quickc495462417de_int,N),M) = hAPP(quickcheck_code_int,product_prod(quickcheck_code_int,quickcheck_code_int),hAPP(quickcheck_code_int,fun(quickcheck_code_int,product_prod(quickcheck_code_int,quickcheck_code_int)),product_Pair(quickcheck_code_int,quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),N),M)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),N),M))) # label(fact_3175_div__mod__code__int__def) # label(axiom) # label(non_clause).  [assumption].
7.49/7.50	1699 (all F all A_2 all B_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A_2),B_1)) -> ((all X_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_2),B_1)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A_2),X_2)) -> hBOOL(hAPP(real,bool,hAPP(fun(real,real),fun(real,bool),isCont(real,real),F),X_2)))) -> ((all X_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_2),B_1)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A_2),X_2)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),F),X_2),zero_zero(real))))) -> hAPP(real,real,F,A_2) = hAPP(real,real,F,B_1))))) # label(fact_4929_DERIV__isconst__end) # label(axiom) # label(non_clause).  [assumption].
7.49/7.50	1700 (all X_b all X_c all X_a (comm_monoid_add(X_a) -> (all F all B_2 all A_3 hAPP(fun(X_c,bool),X_a,hAPP(fun(X_c,X_a),fun(fun(X_c,bool),X_a),big_co1399186613setsum(X_c,X_a),hAPP(fun(X_b,bool),fun(X_c,X_a),hAPP(fun(X_c,fun(fun(X_b,bool),X_a)),fun(fun(X_b,bool),fun(X_c,X_a)),combc(X_c,fun(X_b,bool),X_a),hAPP(fun(X_c,fun(X_b,X_a)),fun(X_c,fun(fun(X_b,bool),X_a)),hAPP(fun(fun(X_b,X_a),fun(fun(X_b,bool),X_a)),fun(fun(X_c,fun(X_b,X_a)),fun(X_c,fun(fun(X_b,bool),X_a))),combb(fun(X_b,X_a),fun(fun(X_b,bool),X_a),X_c),big_co1399186613setsum(X_b,X_a)),hAPP(fun(X_b,fun(X_c,X_a)),fun(X_c,fun(X_b,X_a)),combc(X_b,X_c,X_a),F))),A_3)),B_2) = hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co1399186613setsum(X_b,X_a),hAPP(fun(X_c,bool),fun(X_b,X_a),hAPP(fun(X_b,fun(fun(X_c,bool),X_a)),fun(fun(X_c,bool),fun(X_b,X_a)),combc(X_b,fun(X_c,bool),X_a),hAPP(fun(X_b,fun(X_c,X_a)),fun(X_b,fun(fun(X_c,bool),X_a)),hAPP(fun(fun(X_c,X_a),fun(fun(X_c,bool),X_a)),fun(fun(X_b,fun(X_c,X_a)),fun(X_b,fun(fun(X_c,bool),X_a))),combb(fun(X_c,X_a),fun(fun(X_c,bool),X_a),X_b),big_co1399186613setsum(X_c,X_a)),F)),B_2)),A_3)))) # label(fact_4214_setsum__commute) # label(axiom) # label(non_clause).  [assumption].
7.49/7.50	1701 (all X_a (archim1727834104eiling(X_a) -> (all X_1 all Z (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(int,X_a,ring_1_of_int(X_a),Z)),one_one(X_a)))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(X_a,int,archim2085082626_floor(X_a),X_1)),Z)))))) # label(fact_3609_floor__le__iff) # label(axiom) # label(non_clause).  [assumption].
7.49/7.50	1702 (all X hAPP(real,real,sin,X) = hAPP(real,real,cos,hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),X))) # label(fact_2392_sin__cos__eq) # label(axiom) # label(non_clause).  [assumption].
7.49/7.50	1703 (all A_2 all B_1 all P_1 ((all A_4 all B_4 all C_4 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A_4),B_4)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B_4),C_4)) & hBOOL(hAPP(product_prod(real,real),bool,P_1,hAPP(real,product_prod(real,real),hAPP(real,fun(real,product_prod(real,real)),product_Pair(real,real),B_4),C_4))) & hBOOL(hAPP(product_prod(real,real),bool,P_1,hAPP(real,product_prod(real,real),hAPP(real,fun(real,product_prod(real,real)),product_Pair(real,real),A_4),B_4))) -> hBOOL(hAPP(product_prod(real,real),bool,P_1,hAPP(real,product_prod(real,real),hAPP(real,fun(real,product_prod(real,real)),product_Pair(real,real),A_4),C_4))))) -> (-hBOOL(hAPP(product_prod(real,real),bool,P_1,hAPP(real,product_prod(real,real),hAPP(real,fun(real,product_prod(real,real)),product_Pair(real,real),A_2),B_1))) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A_2),B_1)) -> (all N_2 -hBOOL(hAPP(product_prod(real,real),bool,P_1,hAPP(real,product_prod(real,real),hAPP(real,fun(real,product_prod(real,real)),product_Pair(real,real),hAPP(product_prod(real,real),real,product_fst(real,real),hAPP(nat,product_prod(real,real),hAPP(real,fun(nat,product_prod(real,real)),hAPP(real,fun(real,fun(nat,product_prod(real,real))),hAPP(fun(product_prod(real,real),bool),fun(real,fun(real,fun(nat,product_prod(real,real)))),bolzano_bisect,P_1),A_2),B_1),N_2))),hAPP(product_prod(real,real),real,product_snd(real,real),hAPP(nat,product_prod(real,real),hAPP(real,fun(nat,product_prod(real,real)),hAPP(real,fun(real,fun(nat,product_prod(real,real))),hAPP(fun(product_prod(real,real),bool),fun(real,fun(real,fun(nat,product_prod(real,real)))),bolzano_bisect,P_1),A_2),B_1),N_2)))))))))) # label(fact_3145_not__P__Bolzano__bisect_H) # label(axiom) # label(non_clause).  [assumption].
7.49/7.50	1704 (all U_1 all Ma all N_1 all I all J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I),J)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I),U_1)),Ma)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J),U_1)),N_1))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Ma),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J),I)),U_1)),N_1)))))) # label(fact_751_nat__le__add__iff2) # label(axiom) # label(non_clause).  [assumption].
7.49/7.50	1705 (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_427_mult__less__imp__less__left) # label(axiom) # label(non_clause).  [assumption].
7.49/7.50	1706 (all P_5 (hBOOL(hAPP(int,bool,zprime,P_5)) -> hAPP(int,nat,phi,P_5) = hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),P_5),one_one(int))))) # label(fact_1173_phi__prime) # label(axiom) # label(non_clause).  [assumption].
7.49/7.50	1707 (all X_a (real_normed_vector(X_a) -> hAPP(X_a,real,norm_norm(X_a),zero_zero(X_a)) = zero_zero(real))) # label(fact_1776_norm__zero) # label(axiom) # label(non_clause).  [assumption].
7.49/7.50	1708 (all X_a (linordered_idom(X_a) -> (all W_1 all Z (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_1),Z)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(int,X_a,ring_1_of_int(X_a),W_1)),hAPP(int,X_a,ring_1_of_int(X_a),Z))))))) # label(fact_3569_of__int__less__iff) # label(axiom) # label(non_clause).  [assumption].
7.49/7.50	1709 (all X_a (archim1804426504_field(X_a) -> (all X exists Z_2 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(int,X_a,ring_1_of_int(X_a),Z_2)),X))))) # label(fact_3624_ex__of__int__less) # label(axiom) # label(non_clause).  [assumption].
7.49/7.50	1710 (all I (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),I),zero_zero(int))) <-> zero_zero(nat) = hAPP(int,nat,nat_1,I))) # label(fact_1124_nat__0__iff) # label(axiom) # label(non_clause).  [assumption].
7.49/7.50	1711 (all P all Q (hBOOL(Q) | -hBOOL(P) | -hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fimplies,P),Q)))) # label(help_fimplies_3_1_U) # label(axiom) # label(non_clause).  [assumption].
7.49/7.50	1712 (all X_a (abs_if(X_a) -> (all A_1 ((-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),zero_zero(X_a))) -> hAPP(X_a,X_a,abs_abs(X_a),A_1) = ti(X_a,A_1)) & (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),zero_zero(X_a))) -> hAPP(X_a,X_a,abs_abs(X_a),A_1) = hAPP(X_a,X_a,uminus_uminus(X_a),A_1)))))) # label(fact_2098_abs__if) # label(axiom) # label(non_clause).  [assumption].
7.49/7.50	1713 (all X_a all X_b all F all A_3 hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),nat_tr1645093318rphism(X_a,X_b),F),A_3))) # label(fact_1176_transfer__morphismI) # label(axiom) # label(non_clause).  [assumption].
7.49/7.50	1714 (all X all Y hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),X),hAPP(real,real,sqrt,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),Y),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))))),one_one(real)))) # label(fact_1840_cos__x__y__le__one) # label(axiom) # label(non_clause).  [assumption].
7.49/7.50	1715 (all X_1 all Y_1 (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y_1),X_1)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_1),Y_1)) | Y_1 = X_1 <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_1),Y_1)))) # label(fact_621_dvd_Ole__less) # label(axiom) # label(non_clause).  [assumption].
7.49/7.50	1716 (all W hAPP(int,complex,number_number_of(complex),W) = hAPP(int,complex,ring_1_of_int(complex),W)) # label(fact_3584_complex__number__of__def) # label(axiom) # label(non_clause).  [assumption].
7.49/7.50	1717 (all X_a (comm_semiring_1(X_a) -> (all N all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),X),Y)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),N)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),Y),N))))))) # label(fact_343_dvd__power__same) # label(axiom) # label(non_clause).  [assumption].
7.49/7.50	1718 (all Ma all N_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,real_1(int),Ma)),hAPP(int,real,number_number_of(real),N_1))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Ma),hAPP(int,int,number_number_of(int),N_1))))) # label(fact_3387_number__of__less__real__of__int__iff2) # label(axiom) # label(non_clause).  [assumption].
7.49/7.50	1719 (all U (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),U)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),U),hAPP(real,real,sqrt,hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),U)))) # label(fact_1766_lemma__real__divide__sqrt__less) # label(axiom) # label(non_clause).  [assumption].
7.49/7.50	1720 (all A_2 all P_4 (hBOOL(hAPP(int,bool,zprime,P_4)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),P_4)) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_2),zero_zero(int)),P_4)) -> hAPP(int,int,zfact,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),P_4),one_one(int))) = hAPP(fun(int,bool),int,hAPP(fun(int,int),fun(fun(int,bool),int),big_co302546470etprod(int,int),combi(int)),hAPP(fun(fun(int,bool),bool),fun(int,bool),complete_Sup_Sup(fun(int,bool)),hAPP(int,fun(fun(int,bool),bool),hAPP(int,fun(int,fun(fun(int,bool),bool)),setS,A_2),P_4))))))) # label(fact_3935_Union__SetS__setprod__prop2) # label(axiom) # label(non_clause).  [assumption].
7.49/7.50	1721 (all M hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),M)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = M) # label(fact_1147_add__self__div__2) # label(axiom) # label(non_clause).  [assumption].
7.49/7.50	1722 (all X_b (number(X_b) & ord(X_b) -> (all U all V ((hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(int,X_b,number_number_of(X_b),U)),hAPP(int,X_b,number_number_of(X_b),V))) -> hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),ord_min(X_b),hAPP(int,X_b,number_number_of(X_b),U)),hAPP(int,X_b,number_number_of(X_b),V)) = hAPP(int,X_b,number_number_of(X_b),U)) & (-hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(int,X_b,number_number_of(X_b),U)),hAPP(int,X_b,number_number_of(X_b),V))) -> hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),ord_min(X_b),hAPP(int,X_b,number_number_of(X_b),U)),hAPP(int,X_b,number_number_of(X_b),V)) = hAPP(int,X_b,number_number_of(X_b),V)))))) # label(fact_4831_min__number__of) # label(axiom) # label(non_clause).  [assumption].
7.49/7.50	1723 (all X_a (comm_semiring_1(X_a) -> (all X all P_5 all Q_3 hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),P_5),Q_3)) = hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),P_5)),Q_3)))) # label(fact_200_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J) # label(axiom) # label(non_clause).  [assumption].
7.49/7.50	1724 (all X_a (linordered_semidom(X_a) -> (all M -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)),zero_zero(X_a)))))) # label(fact_1280_of__nat__less__0__iff) # label(axiom) # label(non_clause).  [assumption].
7.49/7.50	1725 (all X_a (real_normed_vector(X_a) -> (all X_3 all A_2 (hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),X_3),A_2),sequentially)) -> hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(X_a,X_a),fun(fun(nat,X_a),fun(nat,X_a)),combb(X_a,X_a,nat),uminus_uminus(X_a)),X_3)),hAPP(X_a,X_a,uminus_uminus(X_a),A_2)),sequentially)))))) # label(fact_4469_LIMSEQ__minus) # label(axiom) # label(non_clause).  [assumption].
7.49/7.50	1726 (all X_a (linordered_idom(X_a) -> (all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_1)) -> hAPP(X_a,X_a,sgn_sgn(X_a),A_1) = one_one(X_a))))) # label(fact_2223_sgn__pos) # label(axiom) # label(non_clause).  [assumption].
7.49/7.50	1727 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,ln,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),one_one(real)),X))),X)))) # label(fact_1977_ln__add__one__self__le__self) # label(axiom) # label(non_clause).  [assumption].
7.49/7.50	1728 (all X_1 all N_1 all Diff all F (hAPP(nat,fun(real,real),Diff,zero_zero(nat)) = F -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)) -> (X_1 != zero_zero(real) -> ((all M_2 all X_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(nat,fun(real,real),Diff,M_2)),X_2),hAPP(real,real,hAPP(nat,fun(real,real),Diff,hAPP(nat,nat,suc,M_2)),X_2)))) -> (exists T_4 (hAPP(real,real,F,X_1) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),inverse_divide(real)),hAPP(real,fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(real,fun(nat,real)),combc(nat,real,real),Diff),zero_zero(real)))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),fact_fact(nat))))),hAPP(real,fun(nat,real),power_power(real),X_1))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),N_1))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(nat,fun(real,real),Diff,N_1),T_4)),hAPP(nat,real,real_1(nat),hAPP(nat,nat,fact_fact(nat),N_1)))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X_1),N_1))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,abs_abs(real),T_4)),hAPP(real,real,abs_abs(real),X_1))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,abs_abs(real),T_4)))))))))) # label(fact_4276_Maclaurin__all__lt) # label(axiom) # label(non_clause).  [assumption].
7.49/7.50	1729 (all Ma all N_1 (one_one(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),Ma),N_1) <-> Ma = one_one(nat) & N_1 = one_one(nat))) # label(fact_590_nat__mult__eq__1__iff) # label(axiom) # label(non_clause).  [assumption].
7.49/7.50	1730 (all N all X hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(nat,real,real_1(nat),N)),hAPP(nat,real,real_1(nat),X))),hAPP(nat,real,real_1(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),N),X)))),one_one(real)))) # label(fact_2359_real__of__nat__div3) # label(axiom) # label(non_clause).  [assumption].
7.49/7.50	1731 (all X_a (real_normed_field(X_a) -> (all Y_1 all X_3 (hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),X_3)) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),hAPP(fun(nat,X_a),X_a,suminf(X_a),X_3)),Y_1) = hAPP(fun(nat,X_a),X_a,suminf(X_a),hAPP(X_a,fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(X_a,fun(nat,X_a)),combc(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),inverse_divide(X_a)),X_3)),Y_1)))))) # label(fact_3985_divide_Osuminf) # label(axiom) # label(non_clause).  [assumption].
7.49/7.50	1732 (all Q_3 all P_5 (hBOOL(hAPP(nat,bool,prime,P_5)) -> (hBOOL(hAPP(nat,bool,prime,Q_3)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),P_5),Q_3)) -> P_5 = Q_3)))) # label(fact_3048_primes__eq) # label(axiom) # label(non_clause).  [assumption].
7.49/7.50	1733 (all X_a all X_b product_Pair(X_a,X_b) = ti(fun(X_a,fun(X_b,product_prod(X_a,X_b))),product_Pair(X_a,X_b))) # label(tsy_c_Product__Type_OPair_res) # label(axiom) # label(non_clause).  [assumption].
7.49/7.51	1734 (all F all A_2 all B_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A_2),B_1)) -> ((all X_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_2),B_1)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A_2),X_2)) -> (exists Y_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),Y_2)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),F),X_2),Y_2)))))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,F,A_2)),hAPP(real,real,F,B_1)))))) # label(fact_3529_DERIV__nonneg__imp__nonincreasing) # label(axiom) # label(non_clause).  [assumption].
7.49/7.51	1735 (all X_b all X_a (topological_space(X_a) & real_normed_vector(X_b) -> (all G all F all A_2 (hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,X_b),fun(X_a,bool),isCont(X_a,X_b),F),A_2)) -> (hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,X_b),fun(X_a,bool),isCont(X_a,X_b),G),A_2)) -> hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,X_b),fun(X_a,bool),isCont(X_a,X_b),hAPP(fun(X_a,X_b),fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,X_b)),combs(X_a,X_b,X_b),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,fun(X_b,X_b))),combb(X_b,fun(X_b,X_b),X_a),minus_minus(X_b)),F)),G)),A_2))))))) # label(fact_4895_isCont__diff) # label(axiom) # label(non_clause).  [assumption].
7.49/7.51	1736 (all Diff all F all N_1 all H (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),H)) & hAPP(nat,fun(real,real),Diff,zero_zero(nat)) = F & (all M_2 all T_4 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),T_4),H)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),T_4)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_2),N_1)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(nat,fun(real,real),Diff,M_2)),T_4),hAPP(real,real,hAPP(nat,fun(real,real),Diff,hAPP(nat,nat,suc,M_2)),T_4))))) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)) -> (exists T_4 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),T_4)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),T_4),H)) & hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),inverse_divide(real)),hAPP(real,fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(real,fun(nat,real)),combc(nat,real,real),Diff),zero_zero(real)))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),fact_fact(nat))))),hAPP(real,fun(nat,real),power_power(real),H))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),N_1))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(nat,fun(real,real),Diff,N_1),T_4)),hAPP(nat,real,real_1(nat),hAPP(nat,nat,fact_fact(nat),N_1)))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),H),N_1))) = hAPP(real,real,F,H))))) # label(fact_4279_Maclaurin__objl) # label(axiom) # label(non_clause).  [assumption].
7.49/7.51	1737 (all X_a all C_1 all P_1 ((exists X1 hBOOL(hAPP(X_a,bool,P_1,X1))) -> (ti(X_a,C_1) = hAPP(fun(X_a,bool),X_a,hilbert_Eps(X_a),P_1) -> hBOOL(hAPP(X_a,bool,P_1,C_1))))) # label(fact_4778_exE__some) # label(axiom) # label(non_clause).  [assumption].
7.49/7.51	1738 (all X_a (field_inverse_zero(X_a) -> (all X all Y all Z_1 all W hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),X),Y)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),Z_1),W)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),Z_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Y),W))))) # label(fact_1660_times__divide__times__eq) # label(axiom) # label(non_clause).  [assumption].
7.49/7.51	1739 (all X_a (ord(X_a) -> ti(fun(fun(X_a,fun(X_a,bool)),fun(X_a,fun(X_a,X_a))),max(X_a)) = max(X_a))) # label(tsy_c_Orderings_Oord_Omax_res) # label(axiom) # label(non_clause).  [assumption].
7.49/7.51	1740 (all P (-hBOOL(P) | -hBOOL(hAPP(bool,bool,fNot,P)))) # label(help_fNot_1_1_U) # label(axiom) # label(non_clause).  [assumption].
7.49/7.51	1741 (all F ((all I_2 hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,F,hAPP(nat,nat,suc,I_2))),hAPP(nat,nat,F,I_2)))) -> (exists I_2 all K_1 hAPP(nat,nat,F,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_2),K_1)) = hAPP(nat,nat,F,I_2)))) # label(fact_3552_weak__decr__stable) # label(axiom) # label(non_clause).  [assumption].
7.49/7.51	1742 (all N all M hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,uminus_uminus(int),hAPP(nat,int,semiring_1_of_nat(int),N))),hAPP(nat,int,semiring_1_of_nat(int),M)))) # label(fact_2133_negative__zle) # label(axiom) # label(non_clause).  [assumption].
7.49/7.51	1743 (all X_a (linordered_field(X_a) -> (all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,inverse_inverse(X_a),A_1))) -> (zero_zero(X_a) != ti(X_a,A_1) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_1))))))) # label(fact_2544_inverse__positive__imp__positive) # label(axiom) # label(non_clause).  [assumption].
7.49/7.51	1744 (all X_a (linordered_idom(X_a) -> (all X_1 all Y_1 (zero_zero(X_a) = ti(X_a,Y_1) & ti(X_a,X_1) = zero_zero(X_a) <-> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),Y_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) = zero_zero(X_a))))) # label(fact_9_sum__power2__eq__zero__iff) # label(axiom) # label(non_clause).  [assumption].
7.49/7.51	1745 (all X_a (comm_semiring_1(X_a) -> (all A_1 all B hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),A_1)))))) # label(fact_333_dvd__triv__right) # label(axiom) # label(non_clause).  [assumption].
7.49/7.51	1746 (all X_b all X_a (topological_space(X_a) & real_normed_vector(X_b) & real_algebra_1(X_b) -> (all G all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(real,fun(filter(X_a),bool),hAPP(fun(X_a,real),fun(real,fun(filter(X_a),bool)),tendsto(X_a,real),G),zero_zero(real)),hAPP(X_a,filter(X_a),at(X_a),A_2))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(fun(X_a,real),fun(X_a,X_b),hAPP(fun(real,X_b),fun(fun(X_a,real),fun(X_a,X_b)),combb(real,X_b,X_a),of_real(X_b)),G)),zero_zero(X_b)),hAPP(X_a,filter(X_a),at(X_a),A_2))))))) # label(fact_4613_of__real_OLIM__zero) # label(axiom) # label(non_clause).  [assumption].
7.49/7.51	1747 (all A_1 all B all C all D all N (hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),B)),C) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),D),N) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),one_one(nat)),N)) -> (one_one(int) = hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,A_1),B) -> (hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,B),C) = one_one(int) -> (hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,C),A_1) = one_one(int) -> (exists K_1 exists L_3 exists M_2 (hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),K_1),N) = hAPP(int,int,abs_abs(int),A_1) & hAPP(int,int,abs_abs(int),B) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),L_3),N) & hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),M_2),N) = hAPP(int,int,abs_abs(int),C))))))))) # label(fact_3483_int__triple__relprime__power__divisors) # label(axiom) # label(non_clause).  [assumption].
7.49/7.51	1748 (all A_2 all Ma (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_2),Ma)) -> hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,hAPP(fun(int,bool),int,hAPP(fun(int,int),fun(fun(int,bool),int),big_co302546470etprod(int,int),combi(int)),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),bnorRset,A_2),Ma))),Ma) = one_one(int))) # label(fact_3931_Bnor__prod__zgcd) # label(axiom) # label(non_clause).  [assumption].
7.49/7.51	1749 (all Z_1 hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Z_1),one_one(int)) = ti(int,Z_1)) # label(fact_65_zmult__1__right) # label(axiom) # label(non_clause).  [assumption].
7.49/7.51	1750 (all X_a (linordered_field(X_a) -> (all A_2 all B_1 all C_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),zero_zero(X_a))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),C_1))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),B_1),C_1)))))))) # label(fact_1714_neg__less__divide__eq) # label(axiom) # label(non_clause).  [assumption].
7.49/7.51	1751 (all X_a (real_normed_vector(X_a) & real_algebra_1(X_a) -> (all X_3 (hBOOL(hAPP(fun(nat,real),bool,cauchy(real),X_3)) -> hBOOL(hAPP(fun(nat,X_a),bool,cauchy(X_a),hAPP(fun(nat,real),fun(nat,X_a),hAPP(fun(real,X_a),fun(fun(nat,real),fun(nat,X_a)),combb(real,X_a,nat),of_real(X_a)),X_3))))))) # label(fact_4077_of__real_OCauchy) # label(axiom) # label(non_clause).  [assumption].
7.49/7.51	1752 (all M (hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),M),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) = zero_zero(nat) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),M),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) = one_one(nat) | hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),M),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) | hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,hAPP(int,int,bit1,pls))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),M),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))) # label(fact_1169_mod__exhaust__less__4) # label(axiom) # label(non_clause).  [assumption].
7.49/7.51	1753 (all I all P_1 all K (hBOOL(hAPP(int,bool,P_1,K)) -> ((all I_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),K),I_2)) -> (hBOOL(hAPP(int,bool,P_1,I_2)) -> hBOOL(hAPP(int,bool,P_1,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),I_2),one_one(int))))))) -> ((all I_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),I_2),K)) -> (hBOOL(hAPP(int,bool,P_1,I_2)) -> hBOOL(hAPP(int,bool,P_1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),I_2),one_one(int))))))) -> hBOOL(hAPP(int,bool,P_1,I)))))) # label(fact_2843_int__induct) # label(axiom) # label(non_clause).  [assumption].
7.49/7.51	1754 (all W all V (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,number_number_of(int),V))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),W)),hAPP(int,int,number_number_of(int),V))) -> hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),zero_zero(int)),hAPP(int,int,number_number_of(int),W)) = hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),posDivAlg,hAPP(int,int,number_number_of(int),W)),hAPP(int,int,number_number_of(int),V))) & (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),W)),hAPP(int,int,number_number_of(int),V))) -> hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),posDivAlg,hAPP(int,int,number_number_of(int),W)),hAPP(int,int,number_number_of(int),V)) = hAPP(product_prod(int,int),product_prod(int,int),hAPP(int,fun(product_prod(int,int),product_prod(int,int)),adjust,hAPP(int,int,number_number_of(int),V)),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),posDivAlg,hAPP(int,int,number_number_of(int),W)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),hAPP(int,int,number_number_of(int),V))))))) # label(fact_1168_posDivAlg__eqn__number__of) # label(axiom) # label(non_clause).  [assumption].
7.49/7.51	1755 (all P_1 all N_1 ((exists M_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_2),N_1)) & hBOOL(hAPP(nat,bool,P_1,M_2)))) <-> (exists X_2 (hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X_2),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),zero_zero(nat)),N_1))) & hBOOL(hAPP(nat,bool,P_1,X_2)))))) # label(fact_4537_ex__nat__less) # label(axiom) # label(non_clause).  [assumption].
7.49/7.51	1756 (all M all N hAPP(nat,real,real_1(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),M),N)) = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(nat,real,real_1(nat),M)),N)) # label(fact_2310_power__real__of__nat) # label(axiom) # label(non_clause).  [assumption].
7.49/7.51	1757 (all X_a (linordered_idom(X_a) -> (all A_1 all K_4 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),K_4))),zero_zero(X_a))) -> ti(X_a,A_1) = zero_zero(X_a))))) # label(fact_234_even__power__le__0__imp__0) # label(axiom) # label(non_clause).  [assumption].
7.49/7.51	1758 (all L all U_1 hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastLessThan(int),L),U_1) = hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,int),fun(fun(int,bool),fun(int,bool)),image(int,int),hAPP(int,fun(int,int),hAPP(fun(int,fun(int,int)),fun(int,fun(int,int)),combc(int,int,int),plus_plus(int)),L)),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastLessThan(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),U_1),L)))) # label(fact_4265_image__add__int__atLeastLessThan) # label(axiom) # label(non_clause).  [assumption].
7.49/7.51	1759 (all X all A_1 all B (one_one(int) = hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),A_1),B) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),X),A_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),X),B)) -> hAPP(int,int,abs_abs(int),X) = one_one(int))))) # label(fact_4402_coprime__common__divisor__int) # label(axiom) # label(non_clause).  [assumption].
7.49/7.51	1760 (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_1575_xt1_I1_J) # label(axiom) # label(non_clause).  [assumption].
7.49/7.51	1761 (all Z_1 hAPP(real,complex,of_real(complex),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),hAPP(complex,real,re,Z_1))) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),Z_1),hAPP(complex,complex,cnj,Z_1))) # label(fact_3017_complex__add__cnj) # label(axiom) # label(non_clause).  [assumption].
7.49/7.51	1762 (all K1 all K2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),K1),K2)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,K1)),hAPP(int,int,bit1,K2))))) # label(fact_32_less__eq__int__code_I16_J) # label(axiom) # label(non_clause).  [assumption].
7.49/7.51	1763 (all X_a (semiring_0(X_a) & dvd(X_a) -> (all P_1 all L ((exists X_2 (hBOOL(hAPP(X_a,bool,P_1,X_2)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),L),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X_2),zero_zero(X_a)))))) <-> (exists X_2 hBOOL(hAPP(X_a,bool,P_1,hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),L),X_2)))))))) # label(fact_602_unity__coeff__ex) # label(axiom) # label(non_clause).  [assumption].
7.49/7.51	1764 (all U_1 all Ma all N_1 all J all I (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),J),I)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I),U_1)),Ma)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J),U_1)),N_1))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I),J)),U_1)),Ma)),N_1))))) # label(fact_738_nat__less__add__iff1) # label(axiom) # label(non_clause).  [assumption].
7.49/7.51	1765 (all M all K_4 (M != hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),K_4) -> (M != hAPP(nat,nat,suc,zero_zero(nat)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),M))))) # label(fact_1387_one__less__m) # label(axiom) # label(non_clause).  [assumption].
7.49/7.51	1766 (all A_1 all P_5 (hBOOL(hAPP(int,bool,zprime,P_5)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit1,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),P_5)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_1),P_5)) -> hAPP(int,int,hAPP(int,fun(int,int),inv,P_5),hAPP(int,int,hAPP(int,fun(int,int),inv,P_5),A_1)) = ti(int,A_1)))))) # label(fact_763_inv__inv) # label(axiom) # label(non_clause).  [assumption].
7.49/7.51	1767 (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_789_add__strict__left__mono) # label(axiom) # label(non_clause).  [assumption].
7.49/7.51	1768 (all X_a (group_add(X_a) -> zero_zero(X_a) = hAPP(X_a,X_a,uminus_uminus(X_a),zero_zero(X_a)))) # label(fact_2025_minus__zero) # label(axiom) # label(non_clause).  [assumption].
7.49/7.51	1769 (all X_a (archim1727834104eiling(X_a) -> (all X all V hAPP(X_a,int,archimedean_ceiling(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X),hAPP(int,X_a,number_number_of(X_a),V))) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(X_a,int,archimedean_ceiling(X_a),X)),hAPP(int,int,number_number_of(int),V))))) # label(fact_3306_ceiling__add__number__of) # label(axiom) # label(non_clause).  [assumption].
7.49/7.51	1770 (all Ma all K all N_1 ((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),Ma),N_1))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),Ma),K)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N_1),K))))) # label(fact_605_mult__le__cancel2) # label(axiom) # label(non_clause).  [assumption].
7.49/7.51	1771 (all M all N hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,real_1(nat),M)),hAPP(nat,real,real_1(nat),N)) = hAPP(nat,real,real_1(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),N))) # label(fact_2307_real__of__nat__mult) # label(axiom) # label(non_clause).  [assumption].
7.49/7.51	1772 (all X_1 hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),inverse_inverse(real)),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),hAPP(fun(nat,nat),fun(nat,nat),hAPP(fun(nat,nat),fun(fun(nat,nat),fun(nat,nat)),combb(nat,nat,nat),fact_fact(nat)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),hAPP(real,fun(nat,real),power_power(real),X_1)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))))) # label(fact_4034_exp__tail__after__first__two__terms__summable) # label(axiom) # label(non_clause).  [assumption].
7.49/7.51	1773 (all X_1 all Y_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),Y_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),Y_1),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),X_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_1),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),Y_1),X_1)) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,tan,Y_1)),hAPP(real,real,tan,X_1))))))))) # label(fact_2273_tan__monotone_H) # label(axiom) # label(non_clause).  [assumption].
7.49/7.51	1774 (all X_a (ring_char_0(X_a) -> (all W_1 all Z (hAPP(int,X_a,ring_1_of_int(X_a),W_1) = hAPP(int,X_a,ring_1_of_int(X_a),Z) <-> ti(int,Z) = ti(int,W_1))))) # label(fact_3574_of__int__eq__iff) # label(axiom) # label(non_clause).  [assumption].
7.49/7.51	1775 (all Y_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),Y_1)) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),hAPP(real,real,sqrt,Y_1))))) # label(fact_1633_real__sqrt__gt__1__iff) # label(axiom) # label(non_clause).  [assumption].
7.49/7.51	1776 (all A_1 zero_zero(real) = hAPP(real,real,hAPP(real,fun(real,real),log,A_1),one_one(real))) # label(fact_2638_log__one) # label(axiom) # label(non_clause).  [assumption].
7.49/7.51	1777 (all P_1 all N_1 all K (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),K)) -> ((all I_2 all J_1 (ti(int,N_1) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K),I_2)),J_1) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),J_1),K)) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),J_1)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),P_1,I_2),J_1)))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),P_1,hAPP(int,int,hAPP(int,fun(int,int),div_div(int),N_1),K)),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),N_1),K)))))) # label(fact_1008_split__pos__lemma) # label(axiom) # label(non_clause).  [assumption].
7.49/7.51	1778 (all X_a (comm_monoid_add(X_a) -> (all F all K all N_1 hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N_1),K))) = hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),hAPP(fun(nat,fun(nat,bool)),fun(nat,X_a),hAPP(fun(fun(nat,bool),X_a),fun(fun(nat,fun(nat,bool)),fun(nat,X_a)),combb(fun(nat,bool),X_a,nat),hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F)),hAPP(fun(nat,nat),fun(nat,fun(nat,bool)),hAPP(fun(nat,fun(nat,fun(nat,bool))),fun(fun(nat,nat),fun(nat,fun(nat,bool))),combs(nat,nat,fun(nat,bool)),hAPP(fun(nat,nat),fun(nat,fun(nat,fun(nat,bool))),hAPP(fun(nat,fun(nat,fun(nat,bool))),fun(fun(nat,nat),fun(nat,fun(nat,fun(nat,bool)))),combb(nat,fun(nat,fun(nat,bool)),nat),ord_atLeastLessThan(nat)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),times_times(nat)),K))),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),hAPP(fun(nat,nat),fun(nat,fun(nat,nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,nat),fun(nat,fun(nat,nat))),combb(nat,fun(nat,nat),nat),plus_plus(nat)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),times_times(nat)),K))),K)))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),N_1))))) # label(fact_4173_sumr__group) # label(axiom) # label(non_clause).  [assumption].
7.49/7.51	1779 (all K_4 all M all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_4),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_4),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_4),N))) # label(fact_580_add__mult__distrib2) # label(axiom) # label(non_clause).  [assumption].
7.49/7.51	1780 (all N -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(nat,real,real_1(nat),N)),zero_zero(real)))) # label(fact_2303_not__real__of__nat__less__zero) # label(axiom) # label(non_clause).  [assumption].
7.49/7.51	1781 (all X_a (comm_monoid_add(X_a) -> (all F all N_1 all Ma ((hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),Ma)) -> zero_zero(X_a) = hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),Ma),hAPP(nat,nat,suc,N_1)))) & (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),Ma)) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),Ma),N_1))),hAPP(nat,X_a,F,N_1)) = hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),Ma),hAPP(nat,nat,suc,N_1)))))))) # label(fact_4204_setsum__op__ivl__Suc) # label(axiom) # label(non_clause).  [assumption].
7.49/7.51	1782 (all M M = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),M),hAPP(nat,nat,suc,zero_zero(nat)))) # label(fact_1350_div__1) # label(axiom) # label(non_clause).  [assumption].
7.49/7.51	1783 (all I_1 all J_2 -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_1),J_2)),I_1))) # label(fact_554_not__add__less1) # label(axiom) # label(non_clause).  [assumption].
7.49/7.51	1784 (all X_a (linordered_semidom(X_a) -> (all M all N all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),M)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N))))))) # label(fact_442_power__le__imp__le__exp) # label(axiom) # label(non_clause).  [assumption].
7.49/7.51	1785 (all X_a all G all A_2 all A_3 (hBOOL(hAPP(filter(X_a),bool,hAPP(complex,fun(filter(X_a),bool),hAPP(fun(X_a,complex),fun(complex,fun(filter(X_a),bool)),tendsto(X_a,complex),G),A_2),A_3)) -> hBOOL(hAPP(filter(X_a),bool,hAPP(complex,fun(filter(X_a),bool),hAPP(fun(X_a,complex),fun(complex,fun(filter(X_a),bool)),tendsto(X_a,complex),hAPP(fun(X_a,complex),fun(X_a,complex),hAPP(fun(complex,complex),fun(fun(X_a,complex),fun(X_a,complex)),combb(complex,complex,X_a),cnj),G)),hAPP(complex,complex,cnj,A_2)),A_3)))) # label(fact_4507_cnj_Otendsto) # label(axiom) # label(non_clause).  [assumption].
7.49/7.51	1786 (all X all Y hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(complex,real,re,X)),hAPP(complex,real,im,Y))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(complex,real,im,X)),hAPP(complex,real,re,Y))) = hAPP(complex,real,im,hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),X),Y))) # label(fact_3010_complex__Im__mult) # label(axiom) # label(non_clause).  [assumption].
7.49/7.51	1787 (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_223_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) # label(axiom) # label(non_clause).  [assumption].
7.49/7.51	1788 (all X all Y all R_4 hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,X),Y)),hAPP(real,complex,of_real(complex),R_4)) = hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,hAPP(real,real,hAPP(real,fun(real,real),times_times(real),X),R_4)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),Y),R_4))) # label(fact_2808_Complex__mult__complex__of__real) # label(axiom) # label(non_clause).  [assumption].
7.49/7.51	1789 (all X_a (real_normed_vector(X_a) & real_algebra_1(X_a) -> (all A_2 hBOOL(hAPP(real,bool,hAPP(fun(real,X_a),fun(real,bool),isCont(real,X_a),of_real(X_a)),A_2))))) # label(fact_4903_of__real_OisCont) # label(axiom) # label(non_clause).  [assumption].
7.49/7.51	1790 (all N_1 all X_1 (zero_zero(real) != X_1 -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)) -> (exists T_4 (hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),inverse_divide(real)),hAPP(real,fun(nat,real),power_power(real),X_1))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),fact_fact(nat)))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),N_1))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,exp(real),T_4)),hAPP(nat,real,real_1(nat),hAPP(nat,nat,fact_fact(nat),N_1)))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X_1),N_1))) = hAPP(real,real,exp(real),X_1) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,abs_abs(real),T_4)),hAPP(real,real,abs_abs(real),X_1))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,abs_abs(real),T_4)))))))) # label(fact_4269_Maclaurin__exp__lt) # label(axiom) # label(non_clause).  [assumption].
7.49/7.51	1791 (all T_2 all T_1 (minus(T_1) -> minus(fun(T_2,T_1)))) # label(arity_fun___Groups_Ominus) # label(axiom) # label(non_clause).  [assumption].
7.49/7.51	1792 (all X_a (ordere236663937imp_le(X_a) -> (all C_1 all A_2 all B_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C_1),A_2)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C_1),B_1))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),B_1)))))) # label(fact_784_add__le__cancel__left) # label(axiom) # label(non_clause).  [assumption].
7.49/7.51	1793 (all X_a (linord1117847801e_zero(X_a) & number(X_a) -> (all B_1 all C_1 all W_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),B_1),C_1)),hAPP(int,X_a,number_number_of(X_a),W_1))) <-> (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C_1)) -> (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),hAPP(int,X_a,number_number_of(X_a),W_1)))) & (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(int,X_a,number_number_of(X_a),W_1)),C_1)),B_1)))) & (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_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),W_1)),C_1)))))))) # label(fact_1754_divide__le__eq__number__of) # label(axiom) # label(non_clause).  [assumption].
7.49/7.51	1794 (all X_a (real_normed_field(X_a) -> (all C_1 all X_1 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1)),X_1),C_1))))) # label(fact_2636_DERIV__cmult__Id) # label(axiom) # label(non_clause).  [assumption].
7.49/7.51	1795 (all P_1 all N_1 ((all M_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_2),N_1)) -> hBOOL(hAPP(nat,bool,P_1,M_2)))) <-> (all X_2 (hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X_2),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),zero_zero(nat)),N_1))) -> hBOOL(hAPP(nat,bool,P_1,X_2)))))) # label(fact_4536_all__nat__less) # label(axiom) # label(non_clause).  [assumption].
7.49/7.51	1796 (all Ta all A_3 all D_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D_2)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Ta),one_one(int))),A_3)) -> (all X_2 ((all Xa (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xa),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastAtMost(int),one_one(int)),D_2))) -> (all Xb (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xb),A_3)) -> ti(int,X_2) != hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),Xb),Xa))))) -> (ti(int,X_2) = ti(int,Ta) -> ti(int,Ta) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X_2),D_2))))))) # label(fact_4638_aset_I3_J) # label(axiom) # label(non_clause).  [assumption].
7.49/7.51	1797 (all X hAPP(real,real,tan,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),pi)) = hAPP(real,real,tan,X)) # label(fact_2256_tan__periodic__pi) # label(axiom) # label(non_clause).  [assumption].
7.49/7.51	1798 (all A_2 all B_1 all Ma (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),Ma)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_2),B_1),Ma)) <-> hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_2),Ma) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),B_1),Ma)))) # label(fact_1035_zcong__zmod__eq) # label(axiom) # label(non_clause).  [assumption].
7.49/7.51	1799 (all X_a (real_normed_field(X_a) -> (all Y_3 all B_1 all X_3 all A_2 (hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),X_3),A_2),sequentially)) -> (hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),Y_3),B_1),sequentially)) -> (ti(X_a,B_1) != zero_zero(X_a) -> hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),inverse_divide(X_a)),X_3)),Y_3)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),A_2),B_1)),sequentially)))))))) # label(fact_4451_LIMSEQ__divide) # label(axiom) # label(non_clause).  [assumption].
7.49/7.51	1800 (all X_a (order(X_a) -> (all Y_1 all X_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y_1),X_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),Y_1)) <-> ti(X_a,X_1) = ti(X_a,Y_1)))))) # label(fact_1554_order__antisym__conv) # label(axiom) # label(non_clause).  [assumption].
7.49/7.51	1801 (all X_a all X_b (comm_monoid_add(X_b) & ordere779506340up_add(X_b) -> (all F all A_3 ((all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_3)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),zero_zero(X_b)),hAPP(X_a,X_b,F,X_2))))) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),zero_zero(X_b)),hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),F),A_3))))))) # label(fact_4309_setsum__nonneg) # label(axiom) # label(non_clause).  [assumption].
7.49/7.51	1802 (all Y_3 all B_1 all X_3 all A_2 (hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),X_3),A_2),sequentially)) -> (hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),Y_3),B_1),sequentially)) -> hBOOL(hAPP(filter(nat),bool,hAPP(complex,fun(filter(nat),bool),hAPP(fun(nat,complex),fun(complex,fun(filter(nat),bool)),tendsto(nat,complex),hAPP(fun(nat,real),fun(nat,complex),hAPP(fun(nat,fun(real,complex)),fun(fun(nat,real),fun(nat,complex)),combs(nat,real,complex),hAPP(fun(nat,real),fun(nat,fun(real,complex)),hAPP(fun(real,fun(real,complex)),fun(fun(nat,real),fun(nat,fun(real,complex))),combb(real,fun(real,complex),nat),complex_1),X_3)),Y_3)),hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,A_2),B_1)),sequentially))))) # label(fact_4513_LIMSEQ__Complex) # label(axiom) # label(non_clause).  [assumption].
7.49/7.51	1803 (all N hAPP(nat,nat,fact_fact(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),one_one(nat))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),one_one(nat))),hAPP(nat,nat,fact_fact(nat),N))) # label(fact_2498_fact__plus__one__nat) # label(axiom) # label(non_clause).  [assumption].
7.49/7.51	1804 (all T_2 all T_1 (finite_finite(T_2) & finite_finite(T_1) -> finite_finite(product_prod(T_2,T_1)))) # label(arity_prod___Finite__Set_Ofinite) # label(axiom) # label(non_clause).  [assumption].
7.49/7.51	1805 (all X hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,uminus_uminus(real),hAPP(complex,real,norm_norm(complex),X))),hAPP(complex,real,norm_norm(complex),X)))) # label(fact_2094_complex__mod__minus__le__complex__mod) # label(axiom) # label(non_clause).  [assumption].
7.49/7.51	1806 (all X_a (linorder(X_a) -> (all T_5 exists Z_2 all X_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z_2),X_2)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),T_5),X_2)))))) # label(fact_2829_pinf_I8_J) # label(axiom) # label(non_clause).  [assumption].
7.49/7.51	1807 (all L all U_1 hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_gr676655987ssThan(int),L),U_1) = hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastLessThan(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),L),one_one(int))),U_1)) # label(fact_4261_atLeastPlusOneLessThan__greaterThanLessThan__int) # label(axiom) # label(non_clause).  [assumption].
7.49/7.51	1808 (all A_1 all B all C all D hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,A_1),B)),hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,C),D)) = hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A_1),C)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),D))),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A_1),D)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),C)))) # label(fact_2748_complex__mult) # label(axiom) # label(non_clause).  [assumption].
7.49/7.51	1809 (all X all N (-hBOOL(hAPP(nat,bool,even_odd_even(nat),N)) -> X = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,hAPP(nat,fun(real,real),root,N),X)),N))) # label(fact_2675_odd__real__root__pow) # label(axiom) # label(non_clause).  [assumption].
7.49/7.51	1810 (all X_a (topological_space(X_a) -> (all G all L all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(complex,fun(filter(X_a),bool),hAPP(fun(X_a,complex),fun(complex,fun(filter(X_a),bool)),tendsto(X_a,complex),G),L),hAPP(X_a,filter(X_a),at(X_a),A_2))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(real,fun(filter(X_a),bool),hAPP(fun(X_a,real),fun(real,fun(filter(X_a),bool)),tendsto(X_a,real),hAPP(fun(X_a,complex),fun(X_a,real),hAPP(fun(complex,real),fun(fun(X_a,complex),fun(X_a,real)),combb(complex,real,X_a),im),G)),hAPP(complex,real,im,L)),hAPP(X_a,filter(X_a),at(X_a),A_2))))))) # label(fact_4597_Im_OLIM) # label(axiom) # label(non_clause).  [assumption].
7.49/7.51	1811 (all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N),one_one(nat)) = N) # label(fact_589_nat__mult__1__right) # label(axiom) # label(non_clause).  [assumption].
7.49/7.51	1812 (all X_a (number_semiring(X_a) -> (all V_3 all V (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),V)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),V_3)) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(int,X_a,number_number_of(X_a),V)),hAPP(int,X_a,number_number_of(X_a),V_3)) = hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),V),V_3))))))) # label(fact_41_semiring__mult__number__of) # label(axiom) # label(non_clause).  [assumption].
7.49/7.51	1813 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),pi)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,sin,X)))))) # label(fact_2314_sin__gt__zero__pi) # label(axiom) # label(non_clause).  [assumption].
7.49/7.51	1814 (all X_a (real_normed_algebra(X_a) -> (all X_1 all A_2 hBOOL(hAPP(filter(X_a),bool,hAPP(X_a,fun(filter(X_a),bool),hAPP(fun(X_a,X_a),fun(X_a,fun(filter(X_a),bool)),tendsto(X_a,X_a),hAPP(X_a,fun(X_a,X_a),times_times(X_a),X_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X_1),A_2)),hAPP(X_a,filter(X_a),at(X_a),A_2)))))) # label(fact_4552_mult__right_Ocont) # label(axiom) # label(non_clause).  [assumption].
7.49/7.51	1815 (all P_1 all Y_1 all X_1 ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Y_1)) -> hBOOL(hAPP(int,bool,P_1,hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),X_1),Y_1))))) -> ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Y_1),zero_zero(int))) -> hBOOL(hAPP(int,bool,P_1,hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),X_1),hAPP(int,int,uminus_uminus(int),Y_1)))))) -> ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X_1),zero_zero(int))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Y_1)) -> hBOOL(hAPP(int,bool,P_1,hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),hAPP(int,int,uminus_uminus(int),X_1)),Y_1))))) -> ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X_1),zero_zero(int))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Y_1),zero_zero(int))) -> hBOOL(hAPP(int,bool,P_1,hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),hAPP(int,int,uminus_uminus(int),X_1)),hAPP(int,int,uminus_uminus(int),Y_1)))))) -> hBOOL(hAPP(int,bool,P_1,hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),X_1),Y_1)))))))) # label(fact_4394_gcd__cases__int) # label(axiom) # label(non_clause).  [assumption].
7.49/7.51	1816 (all P_1 all I ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),I),zero_zero(int))) -> hBOOL(hAPP(nat,bool,P_1,zero_zero(nat)))) & (all N_2 (ti(int,I) = hAPP(nat,int,semiring_1_of_nat(int),N_2) -> hBOOL(hAPP(nat,bool,P_1,N_2)))) <-> hBOOL(hAPP(nat,bool,P_1,hAPP(int,nat,nat_1,I))))) # label(fact_1405_split__nat) # label(axiom) # label(non_clause).  [assumption].
7.49/7.51	1817 (all A_1 all B hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_1),hAPP(int,int,uminus_uminus(int),B)) = hAPP(int,int,uminus_uminus(int),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,uminus_uminus(int),A_1)),B))) # label(fact_2149_zmod__zminus2) # label(axiom) # label(non_clause).  [assumption].
7.49/7.51	1818 (all A_1 all B all C hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),A_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),C)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),A_1),B)),C)) # label(fact_1090_div__mult2__eq) # label(axiom) # label(non_clause).  [assumption].
7.49/7.51	1819 (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_430_mult__right__less__imp__less) # label(axiom) # label(non_clause).  [assumption].
7.49/7.51	1820 (all X_a (number_semiring(X_a) -> (all V_3 all V (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),V)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),V_3)) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(int,X_a,number_number_of(X_a),V)),hAPP(int,X_a,number_number_of(X_a),V_3)) = hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),V),V_3))))))) # label(fact_86_semiring__add__number__of) # label(axiom) # label(non_clause).  [assumption].
7.49/7.51	1821 (all G all F all X_1 all D_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),D_1)) -> ((all Z_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),Z_2),X_1))),D_1)) -> hAPP(real,real,G,hAPP(real,real,F,Z_2)) = Z_2)) -> ((all Z_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),Z_2),X_1))),D_1)) -> hBOOL(hAPP(real,bool,hAPP(fun(real,real),fun(real,bool),isCont(real,real),F),Z_2)))) -> (exists Z_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),Z_2),X_1))),D_1)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,F,Z_2)),hAPP(real,real,F,X_1))))))))) # label(fact_4932_lemma__isCont__inj2) # label(axiom) # label(non_clause).  [assumption].
7.49/7.51	1822 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> hAPP(real,real,sgn_sgn(real),X) = one_one(real))) # label(fact_2221_real__sgn__pos) # label(axiom) # label(non_clause).  [assumption].
7.49/7.51	1823 (all X_a (linordered_field(X_a) -> (all Y all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),zero_zero(X_a))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),X),Y)))))))) # label(fact_1682_divide__neg__neg) # label(axiom) # label(non_clause).  [assumption].
7.49/7.51	1824 (all A_2 all D_1 all N_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A_2),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A_2),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),one_one(nat))),D_1)))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat)))),hAPP(fun(nat,bool),nat,hAPP(fun(nat,nat),fun(fun(nat,bool),nat),big_co1399186613setsum(nat,nat),hAPP(fun(nat,nat),fun(nat,nat),hAPP(fun(nat,nat),fun(fun(nat,nat),fun(nat,nat)),combb(nat,nat,nat),hAPP(nat,fun(nat,nat),plus_plus(nat),A_2)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),times_times(nat)),D_1))),hAPP(nat,fun(nat,bool),ord_lessThan(nat),N_1)))) # label(fact_4322_arith__series__nat) # label(axiom) # label(non_clause).  [assumption].
7.49/7.51	1825 (all X_a (linordered_idom(X_a) -> (all A_2 (zero_zero(X_a) = hAPP(X_a,X_a,sgn_sgn(X_a),A_2) <-> zero_zero(X_a) = ti(X_a,A_2))))) # label(fact_2202_sgn__0__0) # label(axiom) # label(non_clause).  [assumption].
7.49/7.51	1826 (all X_a all F1 all F2 hAPP(nat,X_a,hAPP(fun(nat,fun(X_a,X_a)),fun(nat,X_a),hAPP(X_a,fun(fun(nat,fun(X_a,X_a)),fun(nat,X_a)),nat_rec(X_a),F1),F2),zero_zero(nat)) = ti(X_a,F1)) # label(fact_4155_nat__rec__0) # label(axiom) # label(non_clause).  [assumption].
7.49/7.51	1827 (all Z (zero_zero(complex) = Z <-> hAPP(complex,complex,cnj,Z) = zero_zero(complex))) # label(fact_2930_complex__cnj__zero__iff) # label(axiom) # label(non_clause).  [assumption].
7.49/7.51	1828 (all X all Y hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(int,real,real_1(int),X)),hAPP(int,real,real_1(int),Y)) = hAPP(int,real,real_1(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X),Y))) # label(fact_3332_real__of__int__diff) # label(axiom) # label(non_clause).  [assumption].
7.49/7.51	1829 (all X_a (real_normed_vector(X_a) & real_algebra_1(X_a) -> (all R_4 all X hAPP(real,X_a,of_real(X_a),hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),R_4),X)) = hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),R_4),hAPP(real,X_a,of_real(X_a),X))))) # label(fact_4693_of__real_OscaleR) # label(axiom) # label(non_clause).  [assumption].
7.49/7.51	1830 (all X_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),X_1),N_1))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X_1)) | zero_zero(nat) = N_1)) # label(fact_198_zero__less__power__nat__eq) # label(axiom) # label(non_clause).  [assumption].
7.49/7.51	1831 (all K_4 zero_zero(rat) = hAPP(int,rat,hAPP(int,fun(int,rat),fract,K_4),zero_zero(int))) # label(fact_3740_rat__number__collapse_I4_J) # label(axiom) # label(non_clause).  [assumption].
7.49/7.51	1832 (all X_a (linord1117847801e_zero(X_a) -> (all A_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),zero_zero(X_a))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,inverse_inverse(X_a),A_2)),zero_zero(X_a))))))) # label(fact_2539_inverse__nonpositive__iff__nonpositive) # label(axiom) # label(non_clause).  [assumption].
7.49/7.51	1833 (all X_a (ordered_ring(X_a) -> (all A_2 all E_2 all C_1 all B_1 all D_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),E_2)),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B_1),E_2)),D_1))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),B_1),A_2)),E_2)),D_1))))))) # label(fact_502_le__add__iff2) # label(axiom) # label(non_clause).  [assumption].
7.49/7.51	1834 (all A_1 all B all Q_3 all R_4 (ti(int,A_1) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),Q_3)),R_4) -> ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),R_4),B)) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),R_4))) & (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),R_4)) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),R_4),zero_zero(int)))) -> hBOOL(hAPP(product_prod(int,int),bool,hAPP(int,fun(product_prod(int,int),bool),hAPP(int,fun(int,fun(product_prod(int,int),bool)),divmod_int_rel,A_1),B),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),Q_3),R_4)))))) # label(fact_1197_divmod__int__relI) # label(axiom) # label(non_clause).  [assumption].
7.49/7.51	1835 (all Z_1 hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),Z_1),hAPP(real,complex,of_real(complex),hAPP(complex,real,norm_norm(complex),Z_1))) = hAPP(complex,complex,sgn_sgn(complex),Z_1)) # label(fact_2802_sgn__eq) # label(axiom) # label(non_clause).  [assumption].
7.49/7.51	1836 (all X_b all X_a (real_normed_vector(X_b) & topological_space(X_a) -> (all X_1 all G all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(real,fun(filter(X_a),bool),hAPP(fun(X_a,real),fun(real,fun(filter(X_a),bool)),tendsto(X_a,real),G),zero_zero(real)),hAPP(X_a,filter(X_a),at(X_a),A_2))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(X_b,fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(X_b,fun(X_a,X_b)),combc(X_a,X_b,X_b),hAPP(fun(X_a,real),fun(X_a,fun(X_b,X_b)),hAPP(fun(real,fun(X_b,X_b)),fun(fun(X_a,real),fun(X_a,fun(X_b,X_b))),combb(real,fun(X_b,X_b),X_a),scaleR_scaleR(X_b)),G)),X_1)),zero_zero(X_b)),hAPP(X_a,filter(X_a),at(X_a),A_2))))))) # label(fact_4746_scaleR__left_OLIM__zero) # label(axiom) # label(non_clause).  [assumption].
7.49/7.51	1837 (all X all Y all M (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),M)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),standardRes,M),X)),hAPP(int,int,hAPP(int,fun(int,int),standardRes,M),Y))),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X),Y)),M)))) # label(fact_901_StandardRes__prop4) # label(axiom) # label(non_clause).  [assumption].
7.49/7.51	1838 (all X_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(nat,fun(real,real),root,N_1),X_1)),one_one(real))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_1),one_one(real)))))) # label(fact_2698_real__root__le__1__iff) # label(axiom) # label(non_clause).  [assumption].
7.49/7.51	1839 (all A_2 hBOOL(hAPP(complex,bool,hAPP(fun(complex,real),fun(complex,bool),isCont(complex,real),re),A_2))) # label(fact_4894_Re_OisCont) # label(axiom) # label(non_clause).  [assumption].
7.49/7.51	1840 (all X_a (metric_space(X_a) -> (all X_3 all L_2 all A_2 ((all S_2 (hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),S_2),A_2),sequentially)) & (all N_2 A_2 != hAPP(nat,real,S_2,N_2)) -> hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),hAPP(fun(nat,real),fun(nat,X_a),hAPP(fun(real,X_a),fun(fun(nat,real),fun(nat,X_a)),combb(real,X_a,nat),X_3),S_2)),L_2),sequentially)))) <-> hBOOL(hAPP(filter(real),bool,hAPP(X_a,fun(filter(real),bool),hAPP(fun(real,X_a),fun(X_a,fun(filter(real),bool)),tendsto(real,X_a),X_3),L_2),hAPP(real,filter(real),at(real),A_2))))))) # label(fact_4634_LIMSEQ__SEQ__conv) # label(axiom) # label(non_clause).  [assumption].
7.49/7.51	1841 (all X_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(real,nat,natceiling,X_1)),one_one(nat))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_1),one_one(real))))) # label(fact_1903_natceiling__le__eq__one) # label(axiom) # label(non_clause).  [assumption].
7.49/7.51	1842 (all X_a (linordered_field(X_a) -> (all Y all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),zero_zero(X_a))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),X),Y)))))))) # label(fact_1707_divide__nonpos__neg) # label(axiom) # label(non_clause).  [assumption].
7.49/7.51	1843 (all A_2 all B_1 all C_1 (zero_zero(real) != C_1 -> (A_2 = B_1 <-> hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C_1),B_1) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C_1),A_2)))) # label(fact_709_real__mult__left__cancel) # label(axiom) # label(non_clause).  [assumption].
7.49/7.51	1844 (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].
7.49/7.51	1845 (all X_a all X_b (field_inverse_zero(X_b) -> (all F all G all A_3 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_3)) -> hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),inverse_divide(X_b),hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co302546470etprod(X_a,X_b),F),A_3)),hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co302546470etprod(X_a,X_b),G),A_3)) = hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co302546470etprod(X_a,X_b),hAPP(fun(X_a,X_b),fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,X_b)),combs(X_a,X_b,X_b),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,fun(X_b,X_b))),combb(X_b,fun(X_b,X_b),X_a),inverse_divide(X_b)),F)),G)),A_3))))) # label(fact_3957_setprod__dividef) # label(axiom) # label(non_clause).  [assumption].
7.49/7.51	1846 (all A_1 hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,A_1),one_one(nat)))) # label(fact_2853_coprime__1) # label(axiom) # label(non_clause).  [assumption].
7.49/7.51	1847 (all I all J (zero_zero(int) = ti(int,I) & zero_zero(int) = ti(int,J) <-> hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,I),J) = zero_zero(int))) # label(fact_3435_zgcd0) # label(axiom) # label(non_clause).  [assumption].
7.49/7.51	1848 (all X_a (semiring_div(X_a) -> (all K_4 all M all N (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),K_4),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),M),N))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),K_4),N)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),K_4),M))))))) # label(fact_950_dvd__mod__imp__dvd) # label(axiom) # label(non_clause).  [assumption].
7.49/7.51	1849 (all X_a (number_ring(X_a) -> (all Z_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Z_1),hAPP(int,X_a,number_number_of(X_a),min_1)) = hAPP(X_a,X_a,uminus_uminus(X_a),Z_1)))) # label(fact_2102_mult__minus1__right) # label(axiom) # label(non_clause).  [assumption].
7.49/7.51	1850 (all X_a (idom(X_a) -> (all A_2 all B_1 (ti(X_a,A_2) = ti(X_a,B_1) | hAPP(X_a,X_a,uminus_uminus(X_a),B_1) = ti(X_a,A_2) <-> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B_1),B_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),A_2))))) # label(fact_2034_square__eq__iff) # label(axiom) # label(non_clause).  [assumption].
7.49/7.51	1851 (all A_1 all P_5 (hBOOL(hAPP(int,bool,zprime,P_5)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_1),P_5)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),A_1)),one_one(int)),P_5)) -> ti(int,A_1) = one_one(int) | hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),P_5),one_one(int)) = ti(int,A_1)))))) # label(fact_534_zcong__square__zless) # label(axiom) # label(non_clause).  [assumption].
7.49/7.51	1852 (all X_a all C_1 all A_3 all B_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less(fun(X_a,bool)),A_3),B_2)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),A_3)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),B_2))))) # label(fact_1972_psubsetD) # label(axiom) # label(non_clause).  [assumption].
7.49/7.51	1853 (all N all M (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),N),M)) -> ti(int,M) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),N),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),M),N)))) # label(fact_992_zdvd__mult__div__cancel) # label(axiom) # label(non_clause).  [assumption].
7.49/7.52	1854 (all X all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),Y)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),Y),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X),pi)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,cos,X)),hAPP(real,real,cos,Y))))))) # label(fact_2224_cos__monotone__0__pi) # label(axiom) # label(non_clause).  [assumption].
7.49/7.52	1855 (all X_a (ring_1(X_a) -> (all N hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),one_one(X_a))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),N)) = one_one(X_a)))) # label(fact_2121_power__minus1__even) # label(axiom) # label(non_clause).  [assumption].
7.49/7.52	1856 (all X_a (division_ring(X_a) -> (all A_1 all B hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),A_1),B)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),A_1)),B)))) # label(fact_2019_minus__divide__left) # label(axiom) # label(non_clause).  [assumption].
7.49/7.52	1857 (all A_1 all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X)) -> hAPP(real,nat,natceiling,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),hAPP(nat,real,real_1(nat),A_1))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(real,nat,natceiling,X)),A_1))) # label(fact_2364_natceiling__add) # label(axiom) # label(non_clause).  [assumption].
7.49/7.52	1858 (exists X_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X_2),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int)))) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,s1),X_2),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int)))) & (all Y_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,s1),Y_2),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int)))) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Y_2),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int)))) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Y_2)) -> ti(int,Y_2) = ti(int,X_2))) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X_2)))) # label(fact_195__096EX_B_As_O_A0_A_060_061_As_A_G_As_A_060_A4_A_K_Am_A_L_A1_A_G_A_091s1) # label(axiom) # label(non_clause).  [assumption].
7.49/7.52	1859 (all Z_1 hAPP(int,int,uminus_uminus(int),hAPP(int,int,uminus_uminus(int),Z_1)) = ti(int,Z_1)) # label(fact_2143_zminus__zminus) # label(axiom) # label(non_clause).  [assumption].
7.49/7.52	1860 (all M all N hAPP(int,product_prod(int,product_prod(int,int)),hAPP(int,fun(int,product_prod(int,product_prod(int,int))),hAPP(int,fun(int,fun(int,product_prod(int,product_prod(int,int)))),hAPP(int,fun(int,fun(int,fun(int,product_prod(int,product_prod(int,int))))),hAPP(int,fun(int,fun(int,fun(int,fun(int,product_prod(int,product_prod(int,int)))))),hAPP(int,fun(int,fun(int,fun(int,fun(int,fun(int,product_prod(int,product_prod(int,int))))))),hAPP(int,fun(int,fun(int,fun(int,fun(int,fun(int,fun(int,product_prod(int,product_prod(int,int)))))))),hAPP(int,fun(int,fun(int,fun(int,fun(int,fun(int,fun(int,fun(int,product_prod(int,product_prod(int,int))))))))),xzgcda,M),N),M),N),one_one(int)),zero_zero(int)),zero_zero(int)),one_one(int)) = hAPP(int,product_prod(int,product_prod(int,int)),hAPP(int,fun(int,product_prod(int,product_prod(int,int))),xzgcd,M),N)) # label(fact_3084_xzgcd__def) # label(axiom) # label(non_clause).  [assumption].
7.49/7.52	1861 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),hAPP(real,real,exp(real),X))))) # label(fact_2595_exp__gt__one) # label(axiom) # label(non_clause).  [assumption].
7.49/7.52	1862 (all X_a (real_normed_vector(X_a) -> (all A_1 all B hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(X_a,real,norm_norm(X_a),A_1)),hAPP(X_a,real,norm_norm(X_a),B))),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_1),B))))))) # label(fact_1796_norm__triangle__ineq2) # label(axiom) # label(non_clause).  [assumption].
7.49/7.52	1863 (all Z_1 all N (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),Z_1),N)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),N)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Z_1),N))))) # label(fact_210_zdvd__imp__le) # label(axiom) # label(non_clause).  [assumption].
7.49/7.52	1864 (all M hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),M),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,suc,hAPP(nat,nat,suc,M))),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) # label(fact_1434_mod2__Suc__Suc) # label(axiom) # label(non_clause).  [assumption].
7.49/7.52	1865 (all X_a all X_b (topological_space(X_b) -> ti(fun(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool))),tendsto(X_a,X_b)) = tendsto(X_a,X_b))) # label(tsy_c_Limits_Otendsto_res) # label(axiom) # label(non_clause).  [assumption].
7.49/7.52	1866 (all X_a (real_normed_vector(X_a) -> (all R_1 all A_2 hBOOL(hAPP(filter(X_a),bool,hAPP(X_a,fun(filter(X_a),bool),hAPP(fun(X_a,X_a),fun(X_a,fun(filter(X_a),bool)),tendsto(X_a,X_a),hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),R_1)),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),R_1),A_2)),hAPP(X_a,filter(X_a),at(X_a),A_2)))))) # label(fact_4732_scaleR__right_Ocont) # label(axiom) # label(non_clause).  [assumption].
7.49/7.52	1867 (all X_a (topological_space(X_a) -> (all F all L (hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),hAPP(fun(nat,nat),fun(nat,X_a),hAPP(fun(nat,X_a),fun(fun(nat,nat),fun(nat,X_a)),combb(nat,X_a,nat),F),suc)),L),sequentially)) -> hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),F),L),sequentially)))))) # label(fact_4463_LIMSEQ__imp__Suc) # label(axiom) # label(non_clause).  [assumption].
7.49/7.52	1868 (all X_a (comm_monoid_add(X_a) -> (all F all N_1 all K hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_1),K))) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),hAPP(fun(nat,nat),fun(nat,X_a),hAPP(fun(nat,X_a),fun(fun(nat,nat),fun(nat,X_a)),combb(nat,X_a,nat),F),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),K))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),N_1))),hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),K)))))) # label(fact_4182_sumr__offset3) # label(axiom) # label(non_clause).  [assumption].
7.49/7.52	1869 (all Real1_1 all Real2_1 zero_zero(nat) = hAPP(complex,nat,size_size(complex),hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,Real1_1),Real2_1))) # label(fact_2754_complex_Osize_I2_J) # label(axiom) # label(non_clause).  [assumption].
7.49/7.52	1870 (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_64_less__number__of__int__code) # label(axiom) # label(non_clause).  [assumption].
7.49/7.52	1871 (all X_a all C_1 all X_3 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),X_3)) -> hAPP(nat,int,semiring_1_of_nat(int),hAPP(fun(X_a,bool),nat,hAPP(fun(X_a,nat),fun(fun(X_a,bool),nat),big_co1399186613setsum(X_a,nat),hAPP(nat,fun(X_a,nat),combk(nat,X_a),C_1)),X_3)) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(nat,int,semiring_1_of_nat(int),C_1)),hAPP(nat,int,semiring_1_of_nat(int),hAPP(fun(X_a,bool),nat,finite_card(X_a),X_3))))) # label(fact_4263_setsum__const2) # label(axiom) # label(non_clause).  [assumption].
7.49/7.52	1872 (all X_a all N hAPP(product_prod(int,int),X_a,abs_Frac(X_a),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),N),one_one(int))) = hAPP(int,X_a,number_of_frac(X_a),N)) # label(fact_3685_Nitpick_Onumber__of__frac__def) # label(axiom) # label(non_clause).  [assumption].
7.49/7.52	1873 (all X_1 all Y_1 (zero_zero(int) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,number_number_of(int),Y_1)),hAPP(int,int,number_number_of(int),X_1)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(int,int,number_number_of(int),X_1)),hAPP(int,int,number_number_of(int),Y_1))))) # label(fact_1038_zdvd__iff__zmod__eq__0__number__of) # label(axiom) # label(non_clause).  [assumption].
7.49/7.52	1874 (all B_2 all A_3 (hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A_3)) -> (hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,B_2)) -> (hAPP(fun(int,bool),fun(nat,bool),hAPP(fun(int,nat),fun(fun(int,bool),fun(nat,bool)),image(int,nat),nat_1),A_3) = hAPP(fun(int,bool),fun(nat,bool),hAPP(fun(int,nat),fun(fun(int,bool),fun(nat,bool)),image(int,nat),nat_1),B_2) <-> A_3 = B_2)))) # label(fact_3664_transfer__int__nat__set__relations_I3_J) # label(axiom) # label(non_clause).  [assumption].
7.49/7.52	1875 (all A_2 all B_1 all N_1 (zero_zero(nat) != N_1 -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_2),B_1)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A_2),N_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),B_1),N_1)))))) # label(fact_871_pow__divides__eq__nat) # label(axiom) # label(non_clause).  [assumption].
7.49/7.52	1876 (all X_a (semiring_div(X_a) -> (all A_1 all B all C hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)),C) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),B),C))),C)))) # label(fact_937_zmod__simps_I2_J) # label(axiom) # label(non_clause).  [assumption].
7.49/7.52	1877 (all P (ti(bool,P) = fTrue | fFalse = ti(bool,P))) # label(help_If_3_1_T) # label(axiom) # label(non_clause).  [assumption].
7.49/7.52	1878 (all X_a (ordere236663937imp_le(X_a) -> (all A_2 all C_1 all B_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),B_1)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B_1),C_1))))))) # label(fact_785_add__le__cancel__right) # label(axiom) # label(non_clause).  [assumption].
7.49/7.52	1879 (all X_a (number_ring(X_a) -> (all A_1 ti(X_a,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)))))) # label(fact_111_mult__numeral__1__right) # label(axiom) # label(non_clause).  [assumption].
7.49/7.52	1880 (all P all Q (-hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,P),Q)) | hBOOL(Q) | hBOOL(P))) # label(help_fdisj_3_1_U) # label(axiom) # label(non_clause).  [assumption].
7.49/7.52	1881 (all X_a (real_normed_field(X_a) -> (all Y hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),zero_zero(X_a)),Y) = zero_zero(X_a)))) # label(fact_1656_divide_Ozero) # label(axiom) # label(non_clause).  [assumption].
7.49/7.52	1882 (all X_a (linordered_semidom(X_a) -> (all N all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),one_one(X_a)),A_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),one_one(X_a)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N))))))) # label(fact_412_one__le__power) # label(axiom) # label(non_clause).  [assumption].
7.49/7.52	1883 (all X_a (ring_div(X_a) -> (all Y all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),Y),X)) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),X)),Y) = hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),X),Y)))))) # label(fact_2085_dvd__neg__div) # label(axiom) # label(non_clause).  [assumption].
7.49/7.52	1884 (all X_a (ab_group_add(X_a) -> (all A_1 all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),A_1)),hAPP(X_a,X_a,uminus_uminus(X_a),B)) = hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_1),B))))) # label(fact_2052_minus__diff__minus) # label(axiom) # label(non_clause).  [assumption].
7.49/7.52	1885 (all X_a (metric_space(X_a) -> (all Y all Z_1 all X hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),Y),Z_1)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),X),Y)),hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),X),Z_1))))))) # label(fact_3507_dist__triangle__alt) # label(axiom) # label(non_clause).  [assumption].
7.49/7.52	1886 (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_398_not__square__less__zero) # label(axiom) # label(non_clause).  [assumption].
7.49/7.52	1887 (all X_1 all Y_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,semiring_1_of_nat(int),X_1)),hAPP(nat,int,semiring_1_of_nat(int),Y_1))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X_1),Y_1)))) # label(fact_1302_Nat__Transfer_Otransfer__int__nat__relations_I3_J) # label(axiom) # label(non_clause).  [assumption].
7.49/7.52	1888 (all A_1 all J_2 all K_4 all P_5 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),P_5)) -> (hBOOL(hAPP(int,bool,zprime,P_5)) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,K_4),zero_zero(int)),P_5)) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,J_2),zero_zero(int)),P_5)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,J_2),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),hAPP(int,int,hAPP(int,fun(int,int),multInv,P_5),K_4))),P_5)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,K_4),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),hAPP(int,int,hAPP(int,fun(int,int),multInv,P_5),J_2))),P_5)))))))) # label(fact_851_MultInv__zcong__prop2) # label(axiom) # label(non_clause).  [assumption].
7.49/7.52	1889 (all X_a all F all A_3 all B_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),B_2)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),B_2),A_3)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(fun(X_a,bool),nat,hAPP(fun(X_a,nat),fun(fun(X_a,bool),nat),big_co1399186613setsum(X_a,nat),F),A_3)),hAPP(fun(X_a,bool),nat,hAPP(fun(X_a,nat),fun(fun(X_a,bool),nat),big_co1399186613setsum(X_a,nat),F),B_2)) = hAPP(fun(X_a,bool),nat,hAPP(fun(X_a,nat),fun(fun(X_a,bool),nat),big_co1399186613setsum(X_a,nat),F),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_3),B_2))))) # label(fact_4260_setsum__diff__nat) # label(axiom) # label(non_clause).  [assumption].
7.49/7.52	1890 (all U_1 hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastLessThan(int),zero_zero(int)),U_1)))) # label(fact_4253_finite__atLeastZeroLessThan__int) # label(axiom) # label(non_clause).  [assumption].
7.49/7.52	1891 (all X_a (real_normed_field(X_a) -> (all X_1 (ti(X_a,X_1) != zero_zero(X_a) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),inverse_inverse(X_a)),X_1),hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(X_a,X_a,inverse_inverse(X_a),X_1)),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat))))))))))) # label(fact_3888_DERIV__inverse) # label(axiom) # label(non_clause).  [assumption].
7.49/7.52	1892 (all N hAPP(nat,nat,suc,N) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),N)) # label(fact_1344_Suc__eq__plus1__left) # label(axiom) # label(non_clause).  [assumption].
7.49/7.52	1893 (all X all Y hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),Y)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),Y),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),X)),Y))) # label(fact_609_real__sum__squared__expand) # label(axiom) # label(non_clause).  [assumption].
7.49/7.52	1894 (all X_a (topological_space(X_a) -> (all G all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(complex,fun(filter(X_a),bool),hAPP(fun(X_a,complex),fun(complex,fun(filter(X_a),bool)),tendsto(X_a,complex),G),zero_zero(complex)),hAPP(X_a,filter(X_a),at(X_a),A_2))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(real,fun(filter(X_a),bool),hAPP(fun(X_a,real),fun(real,fun(filter(X_a),bool)),tendsto(X_a,real),hAPP(fun(X_a,complex),fun(X_a,real),hAPP(fun(complex,real),fun(fun(X_a,complex),fun(X_a,real)),combb(complex,real,X_a),im),G)),zero_zero(real)),hAPP(X_a,filter(X_a),at(X_a),A_2))))))) # label(fact_4616_Im_OLIM__zero) # label(axiom) # label(non_clause).  [assumption].
7.49/7.52	1895 (all X_b all X_a (ring_1(X_a) -> (all F all A_3 hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co1399186613setsum(X_b,X_a),hAPP(fun(X_b,int),fun(X_b,X_a),hAPP(fun(int,X_a),fun(fun(X_b,int),fun(X_b,X_a)),combb(int,X_a,X_b),ring_1_of_int(X_a)),F)),A_3) = hAPP(int,X_a,ring_1_of_int(X_a),hAPP(fun(X_b,bool),int,hAPP(fun(X_b,int),fun(fun(X_b,bool),int),big_co1399186613setsum(X_b,int),F),A_3))))) # label(fact_4170_of__int__setsum) # label(axiom) # label(non_clause).  [assumption].
7.49/7.52	1896 (all B all A_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A_1)) -> hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),B))),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),A_1)) = hAPP(int,int,hAPP(int,fun(int,int),div_div(int),B),A_1))) # label(fact_905_pos__zdiv__mult__2) # label(axiom) # label(non_clause).  [assumption].
7.49/7.52	1897 (all X -(hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),X)) & -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),X)))) # label(fact_619_dvd_Oless__irrefl) # label(axiom) # label(non_clause).  [assumption].
7.49/7.52	1898 (all X_a (archim1727834104eiling(X_a) -> (all X all Z_1 hAPP(X_a,int,archimedean_ceiling(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X),hAPP(int,X_a,ring_1_of_int(X_a),Z_1))) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(X_a,int,archimedean_ceiling(X_a),X)),Z_1)))) # label(fact_3597_ceiling__add__of__int) # label(axiom) # label(non_clause).  [assumption].
7.49/7.52	1899 (all Ma (zero_zero(nat) != Ma -> hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),dvd_dvd(nat)),Ma)))))) # label(fact_3842_finite__divisors__nat) # label(axiom) # label(non_clause).  [assumption].
7.49/7.52	1900 (all X_a all X_b (ord(X_b) -> (all F all G ((all X_2 hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_a,X_b,F,X_2)),hAPP(X_a,X_b,G,X_2)))) -> hBOOL(hAPP(fun(X_a,X_b),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,X_b),bool),ord_less_eq(fun(X_a,X_b)),F),G)))))) # label(fact_1655_le__funI) # label(axiom) # label(non_clause).  [assumption].
7.49/7.52	1901 (all A_2 all B_1 all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),X_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),powr,X_1),A_2)),hAPP(real,real,hAPP(real,fun(real,real),powr,X_1),B_1))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A_2),B_1))))) # label(fact_3378_powr__le__cancel__iff) # label(axiom) # label(non_clause).  [assumption].
7.49/7.52	1902 (all X all Y hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),X),Y) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),X),hAPP(real,real,inverse_inverse(real),Y))) # label(fact_2563_divide__real__def) # label(axiom) # label(non_clause).  [assumption].
7.49/7.52	1903 (all Y_1 all X_1 (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),zEven)) -> hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X_1),Y_1)),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),X_1),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),Y_1))) # label(fact_1464_even__prod__div__2) # label(axiom) # label(non_clause).  [assumption].
7.49/7.52	1904 (all Ma all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),N_1)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,semiring_1_of_nat(int),Ma)),hAPP(nat,int,semiring_1_of_nat(int),N_1))))) # label(fact_1298_zless__int) # label(axiom) # label(non_clause).  [assumption].
7.49/7.52	1905 (all K_4 all M all N (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K_4),M)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K_4),N))) -> (zero_zero(int) != ti(int,K_4) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),M),N))))) # label(fact_206_zdvd__mult__cancel) # label(axiom) # label(non_clause).  [assumption].
7.49/7.52	1906 (all X_a (archim1727834104eiling(X_a) -> (all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),hAPP(int,X_a,ring_1_of_int(X_a),hAPP(X_a,int,archimedean_ceiling(X_a),X)))) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(int,X_a,ring_1_of_int(X_a),hAPP(X_a,int,archimedean_ceiling(X_a),X))),one_one(X_a))),X)))))) # label(fact_3607_ceiling__correct) # label(axiom) # label(non_clause).  [assumption].
7.49/7.52	1907 (all K all Ma all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),Ma)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),N_1))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Ma),N_1)) | K = zero_zero(nat))) # label(fact_748_nat__mult__dvd__cancel__disj) # label(axiom) # label(non_clause).  [assumption].
7.49/7.52	1908 (all A_2 (hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),A_2),zero_zero(real)),sequentially)) -> ((all N_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(nat,real,A_2,N_2)))) -> ((all N_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,A_2,hAPP(nat,nat,suc,N_2))),hAPP(nat,real,A_2,N_2)))) -> hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),hAPP(fun(nat,fun(nat,bool)),fun(nat,real),hAPP(fun(fun(nat,bool),real),fun(fun(nat,fun(nat,bool)),fun(nat,real)),combb(fun(nat,bool),real,nat),hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),min_1)))),A_2))),hAPP(fun(nat,nat),fun(nat,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(nat,nat),fun(nat,fun(nat,bool))),combb(nat,fun(nat,bool),nat),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat))),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),hAPP(fun(nat,nat),fun(nat,fun(nat,nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,nat),fun(nat,fun(nat,nat))),combb(nat,fun(nat,nat),nat),plus_plus(nat)),hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),one_one(nat))))),hAPP(fun(nat,real),real,suminf(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),min_1)))),A_2))),sequentially)))))) # label(fact_4503_summable__Leibniz_H_I5_J) # label(axiom) # label(non_clause).  [assumption].
7.49/7.52	1909 (all X_a (linordered_semidom(X_a) -> (all N all M (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),M)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),N)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),M),N)))))))) # label(fact_406_less__1__mult) # label(axiom) # label(non_clause).  [assumption].
7.49/7.52	1910 (all X_a (real_normed_field(X_a) -> (all X all Y hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),X),Y)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),X)),Y)))) # label(fact_2017_divide_Ominus) # label(axiom) # label(non_clause).  [assumption].
7.49/7.52	1911 (all B all A_1 all N (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),N)) -> (hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,A_1),N) = one_one(int) -> (exists X_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X_2)) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X_2),N)) & (all Y_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),Y_2)),B),N)) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Y_2),N)) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Y_2)) -> ti(int,Y_2) = ti(int,X_2))) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),X_2)),B),N))))))) # label(fact_3478_zcong__lineq__unique) # label(axiom) # label(non_clause).  [assumption].
7.49/7.52	1912 (all L all U_1 hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_gr676655987ssThan(nat),L),U_1) = hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),hAPP(nat,nat,suc,L)),U_1)) # label(fact_4222_atLeastSucLessThan__greaterThanLessThan) # label(axiom) # label(non_clause).  [assumption].
7.49/7.52	1913 (all Ta all B_2 all D_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D_2)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Ta),B_2)) -> (all X_2 ((all Xa (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xa),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastAtMost(int),one_one(int)),D_2))) -> (all Xb (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xb),B_2)) -> ti(int,X_2) != hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Xb),Xa))))) -> (ti(int,Ta) != ti(int,X_2) -> hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X_2),D_2) != ti(int,Ta))))))) # label(fact_4640_bset_I4_J) # label(axiom) # label(non_clause).  [assumption].
7.49/7.52	1914 (all X_a (real_normed_vector(X_a) -> (all R_1 all X_3 (hBOOL(hAPP(fun(nat,X_a),bool,cauchy(X_a),X_3)) -> hBOOL(hAPP(fun(nat,X_a),bool,cauchy(X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(X_a,X_a),fun(fun(nat,X_a),fun(nat,X_a)),combb(X_a,X_a,nat),hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),R_1)),X_3))))))) # label(fact_4668_scaleR__right_OCauchy) # label(axiom) # label(non_clause).  [assumption].
7.49/7.52	1915 (all K_4 hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,suc,zero_zero(nat))),K_4))) # label(fact_1209_dvd__1__left) # label(axiom) # label(non_clause).  [assumption].
7.49/7.52	1916 (all X all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),Y)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,exp(real),X)),hAPP(real,real,exp(real),Y))))) # label(fact_2506_exp__less__mono) # label(axiom) # label(non_clause).  [assumption].
7.49/7.52	1917 (all K (ti(int,K) = min_1 <-> min_1 = hAPP(int,int,bit1,K))) # label(fact_285_rel__simps_I47_J) # label(axiom) # label(non_clause).  [assumption].
7.49/7.52	1918 (all A_2 all B_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B_1)) -> (hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(int,rat,hAPP(int,fun(int,rat),fract,A_2),B_1)),zero_zero(rat))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A_2),zero_zero(int)))))) # label(fact_3791_Fract__le__zero__iff) # label(axiom) # label(non_clause).  [assumption].
7.49/7.52	1919 (all X_a (semiring_1(X_a) -> (all Inc all I hAPP(X_a,X_a,hAPP(nat,fun(X_a,X_a),hAPP(fun(X_a,X_a),fun(nat,fun(X_a,X_a)),semiri532925092at_aux(X_a),Inc),zero_zero(nat)),I) = ti(X_a,I)))) # label(fact_4160_of__nat__aux_Osimps_I1_J) # label(axiom) # label(non_clause).  [assumption].
7.49/7.52	1920 (all X_a (real_normed_field(X_a) & banach(X_a) -> (all G all X_1 all Ma (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),G),X_1),Ma)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),hAPP(fun(X_a,X_a),fun(X_a,X_a),hAPP(fun(X_a,X_a),fun(fun(X_a,X_a),fun(X_a,X_a)),combb(X_a,X_a,X_a),exp(X_a)),G)),X_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,exp(X_a),hAPP(X_a,X_a,G,X_1))),Ma))))))) # label(fact_3864_DERIV__fun__exp) # label(axiom) # label(non_clause).  [assumption].
7.49/7.52	1921 (all A_1 all B (hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),A_1),B) != zero_zero(int) -> (exists A_5 exists B_3 (hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_5),hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),A_1),B)) = ti(int,A_1) & hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),A_5),B_3) = one_one(int) & ti(int,B) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B_3),hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),A_1),B)))))) # label(fact_4777_gcd__coprime__exists__int) # label(axiom) # label(non_clause).  [assumption].
7.49/7.52	1922 (all B all A_1 (zero_zero(nat) != A_1 -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),A_1),B)),A_1)))) # label(fact_3260_gcd__le1__nat) # label(axiom) # label(non_clause).  [assumption].
7.49/7.52	1923 (all X_a (metric_space(X_a) -> (all X2_1 all X1_1 all Y all E_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),X1_1),Y)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),E_1),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),X2_1),Y)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),E_1),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),X1_1),X2_1)),E_1))))))) # label(fact_3521_dist__triangle__half__l) # label(axiom) # label(non_clause).  [assumption].
7.49/7.52	1924 (all X_a (real_normed_vector(X_a) -> (all X all Y all C (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),C),zero_zero(real))) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),X)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),hAPP(X_a,real,norm_norm(X_a),Y)))) -> ti(X_a,X) = zero_zero(X_a)))))) # label(fact_1785_norm__ratiotest__lemma) # label(axiom) # label(non_clause).  [assumption].
7.49/7.52	1925 (all A_3 all X_1 (hBOOL(hAPP(int,bool,nat_is_nat,X_1)) -> (hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A_3)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),A_3)) <-> hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),hAPP(int,nat,nat_1,X_1)),hAPP(fun(int,bool),fun(nat,bool),hAPP(fun(int,nat),fun(fun(int,bool),fun(nat,bool)),image(int,nat),nat_1),A_3))))))) # label(fact_4859_transfer__int__nat__set__relations_I2_J) # label(axiom) # label(non_clause).  [assumption].
7.49/7.52	1926 (all K_4 all L_4 all I_1 all J_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),J_2)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),K_4),L_4)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_1),K_4)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J_2),L_4)))))) # label(fact_560_add__less__mono) # label(axiom) # label(non_clause).  [assumption].
7.49/7.52	1927 (all X_a (linord219039673up_add(X_a) -> (all A_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),A_2)),zero_zero(X_a))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),zero_zero(X_a))))))) # label(fact_821_double__add__less__zero__iff__single__add__less__zero) # label(axiom) # label(non_clause).  [assumption].
7.49/7.52	1928 (all N hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,suc,N)))) # label(fact_1208_zero__less__Suc) # label(axiom) # label(non_clause).  [assumption].
7.49/7.52	1929 (all X_a (ord(X_a) -> ord_min(X_a) = hAPP(fun(X_a,fun(X_a,bool)),fun(X_a,fun(X_a,X_a)),min(X_a),ord_less_eq(X_a)))) # label(fact_4837_min__ord__min) # label(axiom) # label(non_clause).  [assumption].
7.49/7.52	1930 (all X all Y hAPP(complex,complex,cnj,hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),X),Y)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),hAPP(complex,complex,cnj,X)),hAPP(complex,complex,cnj,Y))) # label(fact_2942_cnj_Odiff) # label(axiom) # label(non_clause).  [assumption].
7.49/7.52	1931 (all A_1 -(hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),zero_zero(nat)),A_1)) & -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),zero_zero(nat))))) # label(fact_888_gcd__lcm__complete__lattice__nat_Onot__top__less) # label(axiom) # label(non_clause).  [assumption].
7.49/7.52	1932 (all A_1 hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,hAPP(int,int,bit1,pls))))) # label(fact_187_cube__square) # label(axiom) # label(non_clause).  [assumption].
7.49/7.52	1933 (all X_a all X_b all A_2 all B_1 all A_8 all B_7 all R_1 all Sa (hBOOL(hAPP(fun(product_prod(product_prod(X_a,X_b),product_prod(X_a,X_b)),bool),bool,hAPP(product_prod(product_prod(X_a,X_b),product_prod(X_a,X_b)),fun(fun(product_prod(product_prod(X_a,X_b),product_prod(X_a,X_b)),bool),bool),member(product_prod(product_prod(X_a,X_b),product_prod(X_a,X_b))),hAPP(product_prod(X_a,X_b),product_prod(product_prod(X_a,X_b),product_prod(X_a,X_b)),hAPP(product_prod(X_a,X_b),fun(product_prod(X_a,X_b),product_prod(product_prod(X_a,X_b),product_prod(X_a,X_b))),product_Pair(product_prod(X_a,X_b),product_prod(X_a,X_b)),hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),A_2),B_1)),hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),A_8),B_7))),hAPP(fun(product_prod(X_b,X_b),bool),fun(product_prod(product_prod(X_a,X_b),product_prod(X_a,X_b)),bool),hAPP(fun(product_prod(X_a,X_a),bool),fun(fun(product_prod(X_b,X_b),bool),fun(product_prod(product_prod(X_a,X_b),product_prod(X_a,X_b)),bool)),lex_prod(X_a,X_b),R_1),Sa))) <-> hBOOL(hAPP(fun(product_prod(X_b,X_b),bool),bool,hAPP(product_prod(X_b,X_b),fun(fun(product_prod(X_b,X_b),bool),bool),member(product_prod(X_b,X_b)),hAPP(X_b,product_prod(X_b,X_b),hAPP(X_b,fun(X_b,product_prod(X_b,X_b)),product_Pair(X_b,X_b),B_1),B_7)),Sa)) & ti(X_a,A_2) = ti(X_a,A_8) | hBOOL(hAPP(fun(product_prod(X_a,X_a),bool),bool,hAPP(product_prod(X_a,X_a),fun(fun(product_prod(X_a,X_a),bool),bool),member(product_prod(X_a,X_a)),hAPP(X_a,product_prod(X_a,X_a),hAPP(X_a,fun(X_a,product_prod(X_a,X_a)),product_Pair(X_a,X_a),A_2),A_8)),R_1)))) # label(fact_3487_in__lex__prod) # label(axiom) # label(non_clause).  [assumption].
7.49/7.52	1934 (all X_b all X_a all X_c all F all X_1 hAPP(product_prod(X_b,X_a),X_a,product_snd(X_b,X_a),hAPP(product_prod(X_b,X_c),product_prod(X_b,X_a),hAPP(fun(X_c,X_a),fun(product_prod(X_b,X_c),product_prod(X_b,X_a)),product_apsnd(X_c,X_a,X_b),F),X_1)) = hAPP(X_c,X_a,F,hAPP(product_prod(X_b,X_c),X_c,product_snd(X_b,X_c),X_1))) # label(fact_4067_snd__apsnd) # label(axiom) # label(non_clause).  [assumption].
7.49/7.52	1935 (all Z (zero_zero(int) = ti(int,Z) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,abs_abs(int),Z)),one_one(int))))) # label(fact_1939_zabs__less__one__iff) # label(axiom) # label(non_clause).  [assumption].
7.49/7.52	1936 (all X_a (real_vector(X_a) -> (all A_1 hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_1),zero_zero(X_a)) = zero_zero(X_a)))) # label(fact_4702_scaleR__right_Ozero) # label(axiom) # label(non_clause).  [assumption].
7.49/7.52	1937 (all X_a (linord219039673up_add(X_a) -> (all A_2 (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_2),A_2))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_2)))))) # label(fact_822_zero__less__double__add__iff__zero__less__single__add) # label(axiom) # label(non_clause).  [assumption].
7.49/7.52	1938 (all N hAPP(nat,real,real_1(nat),N) = hAPP(int,real,real_1(int),hAPP(nat,int,semiring_1_of_nat(int),N))) # label(fact_3335_real__of__int__of__nat__eq) # label(axiom) # label(non_clause).  [assumption].
7.49/7.52	1939 (all X_1 all Ma (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),Ma)) -> (one_one(int) = hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,X_1),Ma) -> hAPP(fun(int,bool),nat,finite_card(int),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),noXRRset,Ma),X_1)) = hAPP(fun(int,bool),nat,finite_card(int),hAPP(int,fun(int,bool),norRRset,Ma))))) # label(fact_3615_card__nor__eq__noX) # label(axiom) # label(non_clause).  [assumption].
7.49/7.52	1940 (all X_a (real_normed_field(X_a) & banach(X_a) -> (all X_1 hAPP(fun(nat,X_a),X_a,suminf(X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,real),fun(nat,fun(X_a,X_a)),hAPP(fun(real,fun(X_a,X_a)),fun(fun(nat,real),fun(nat,fun(X_a,X_a))),combb(real,fun(X_a,X_a),nat),scaleR_scaleR(X_a)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),inverse_inverse(real)),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),fact_fact(nat))))),hAPP(X_a,fun(nat,X_a),power_power(X_a),X_1))) = hAPP(X_a,X_a,exp(X_a),X_1)))) # label(fact_4751_exp__def) # label(axiom) # label(non_clause).  [assumption].
7.49/7.52	1941 (all X all N_5 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),N),N_5)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),one_one(real)),X)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(nat,fun(real,real),root,N_5),X)),hAPP(real,real,hAPP(nat,fun(real,real),root,N),X))))))) # label(fact_2699_real__root__decreasing) # label(axiom) # label(non_clause).  [assumption].
7.49/7.52	1942 (all A_2 all B_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A_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),div_div(int),A_2),B_1)))))) # label(fact_1025_pos__imp__zdiv__nonneg__iff) # label(axiom) # label(non_clause).  [assumption].
7.49/7.52	1943 (all N_1 all X_1 exists T_4 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),T_4)),hAPP(real,real,abs_abs(real),X_1))) & hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(real,fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(real,fun(nat,real)),combc(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(nat,fun(real,fun(real,real))),fun(fun(nat,real),fun(nat,fun(real,real))),combs(nat,real,fun(real,real)),hAPP(fun(nat,bool),fun(nat,fun(real,fun(real,real))),hAPP(fun(bool,fun(real,fun(real,real))),fun(fun(nat,bool),fun(nat,fun(real,fun(real,real)))),combb(bool,fun(real,fun(real,real)),nat),if(real)),even_odd_even(nat))),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),inverse_divide(real)),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),min_1))),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),div_div(nat)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),fact_fact(nat))))),zero_zero(real)))),hAPP(real,fun(nat,real),power_power(real),X_1))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),N_1))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,cos,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),T_4),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),one_one(real)),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,real_1(nat),N_1))),pi)))),hAPP(nat,real,real_1(nat),hAPP(nat,nat,fact_fact(nat),N_1)))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X_1),N_1))) = hAPP(real,real,cos,X_1))) # label(fact_4242_Maclaurin__cos__expansion) # label(axiom) # label(non_clause).  [assumption].
7.49/7.52	1944 (all N hAPP(complex,real,im,hAPP(nat,complex,semiring_1_of_nat(complex),N)) = zero_zero(real)) # label(fact_2982_complex__Im__of__nat) # label(axiom) # label(non_clause).  [assumption].
7.49/7.52	1945 (all X_a all X_b (real_normed_vector(X_b) -> (all F all A_2 all A_3 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),A_2),A_3)) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(fun(X_a,X_b),fun(X_a,X_b),hAPP(fun(X_b,X_b),fun(fun(X_a,X_b),fun(X_a,X_b)),combb(X_b,X_b,X_a),uminus_uminus(X_b)),F)),hAPP(X_b,X_b,uminus_uminus(X_b),A_2)),A_3)))))) # label(fact_4472_tendsto__minus) # label(axiom) # label(non_clause).  [assumption].
7.49/7.52	1946 (all X_a (linord1117847801e_zero(X_a) -> (all A_2 all C_1 all B_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),A_2),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),B_1),C_1))) <-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),B_1))) & (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_1),A_2))))))) # label(fact_1700_divide__le__cancel) # label(axiom) # label(non_clause).  [assumption].
7.49/7.52	1947 (all X_a (linorder(X_a) -> (all X_1 all Y_1 (hAPP(X_a,fun(X_a,bool),ord_lessThan(X_a),X_1) = hAPP(X_a,fun(X_a,bool),ord_lessThan(X_a),Y_1) <-> ti(X_a,Y_1) = ti(X_a,X_1))))) # label(fact_4316_lessThan__eq__iff) # label(axiom) # label(non_clause).  [assumption].
7.49/7.52	1948 (all X_a (linordered_field(X_a) -> (all C all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C),zero_zero(X_a))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),C),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),C),B))))))))) # label(fact_1717_divide__strict__left__mono__neg) # label(axiom) # label(non_clause).  [assumption].
7.49/7.52	1949 (all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,number_number_of(real),min_1)),Y)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),Y),one_one(real))) -> Y = hAPP(real,real,cos,hAPP(real,real,arccos,Y))))) # label(fact_2263_cos__arccos) # label(axiom) # label(non_clause).  [assumption].
7.49/7.52	1950 (all N all A_1 all B (one_one(int) = hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,A_1),B) -> one_one(int) = hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A_1),N)),B))) # label(fact_3449_zgcd__1__power__left__distrib) # label(axiom) # label(non_clause).  [assumption].
7.49/7.52	1951 (all L_4 min_1 != hAPP(int,int,bit0,L_4)) # label(fact_291_rel__simps_I42_J) # label(axiom) # label(non_clause).  [assumption].
7.49/7.52	1952 (all X_b all X_a (topological_space(X_a) & real_normed_algebra(X_b) -> (all C_1 all F all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),zero_zero(X_b)),hAPP(X_a,filter(X_a),at(X_a),A_2))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(X_b,fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(X_b,fun(X_a,X_b)),combc(X_a,X_b,X_b),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,fun(X_b,X_b))),combb(X_b,fun(X_b,X_b),X_a),times_times(X_b)),F)),C_1)),zero_zero(X_b)),hAPP(X_a,filter(X_a),at(X_a),A_2))))))) # label(fact_4575_LIM__mult__left__zero) # label(axiom) # label(non_clause).  [assumption].
7.49/7.52	1953 (all A_1 all B all Q_3 all R_4 (hBOOL(hAPP(product_prod(int,int),bool,hAPP(int,fun(product_prod(int,int),bool),hAPP(int,fun(int,fun(product_prod(int,int),bool)),divmod_int_rel,A_1),B),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),Q_3),R_4))) -> (zero_zero(int) != ti(int,B) -> hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_1),B) = ti(int,Q_3)))) # label(fact_1191_divmod__int__rel__div) # label(axiom) # label(non_clause).  [assumption].
7.49/7.52	1954 (all K_4 hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),K_4),one_one(int)) = hAPP(int,int,pred,K_4)) # label(fact_2905_pred__def) # label(axiom) # label(non_clause).  [assumption].
7.49/7.52	1955 (all X_a (linordered_semidom(X_a) -> (all Ma all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Ma),N_1)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),Ma)),hAPP(nat,X_a,semiring_1_of_nat(X_a),N_1))))))) # label(fact_1285_of__nat__le__iff) # label(axiom) # label(non_clause).  [assumption].
7.49/7.52	1956 (all K_4 all M all N (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),K_4),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),M),N))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),K_4),N)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),K_4),M))))) # label(fact_485_zdvd__zdiffD) # label(axiom) # label(non_clause).  [assumption].
7.49/7.52	1957 (all X_a (field_inverse_zero(X_a) -> (all A_2 all B_1 all C_1 ((ti(X_a,C_1) = zero_zero(X_a) -> ti(X_a,A_2) = zero_zero(X_a)) & (ti(X_a,C_1) != zero_zero(X_a) -> ti(X_a,B_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),C_1)) <-> ti(X_a,A_2) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),B_1),C_1))))) # label(fact_1685_eq__divide__eq) # label(axiom) # label(non_clause).  [assumption].
7.49/7.52	1958 (all F all A_3 (hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A_3)) -> ((all X_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X_2)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,F,X_2))))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(fun(int,bool),int,hAPP(fun(int,int),fun(fun(int,bool),int),big_co302546470etprod(int,int),F),A_3)))))) # label(fact_3937_transfer__nat__int__sum__prod__closure_I2_J) # label(axiom) # label(non_clause).  [assumption].
7.49/7.52	1959 (all X_a (linord1117847801e_zero(X_a) -> (all C all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),B),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),A_1),C)))))))) # label(fact_1672_divide__right__mono__neg) # label(axiom) # label(non_clause).  [assumption].
7.49/7.52	1960 (all M all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,suc,hAPP(nat,nat,suc,hAPP(nat,nat,suc,M)))),N) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,hAPP(int,int,bit1,pls)))),M)),N)) # label(fact_1437_Suc__div__eq__add3__div) # label(axiom) # label(non_clause).  [assumption].
7.49/7.52	1961 (all X_a (real_normed_field(X_a) -> (all F all X_1 all D_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),F),X_1),D_2)) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_a,fun(filter(X_a),bool),hAPP(fun(X_a,X_a),fun(X_a,fun(filter(X_a),bool)),tendsto(X_a,X_a),hAPP(fun(X_a,X_a),fun(X_a,X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,X_a),fun(X_a,X_a)),combs(X_a,X_a,X_a),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,X_a),fun(X_a,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),X_a),inverse_divide(X_a)),hAPP(X_a,fun(X_a,X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(X_a,X_a)),combc(X_a,X_a,X_a),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,X_a),fun(X_a,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),X_a),minus_minus(X_a)),hAPP(fun(X_a,X_a),fun(X_a,X_a),hAPP(fun(X_a,X_a),fun(fun(X_a,X_a),fun(X_a,X_a)),combb(X_a,X_a,X_a),F),hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X_1)))),hAPP(X_a,X_a,F,X_1)))),combi(X_a))),D_2),hAPP(X_a,filter(X_a),at(X_a),zero_zero(X_a)))))))) # label(fact_4620_DERIV__D) # label(axiom) # label(non_clause).  [assumption].
7.49/7.52	1962 (all B all A_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_1),zero_zero(int))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_1),B)),zero_zero(int)))))) # label(fact_981_div__neg__pos__less0) # label(axiom) # label(non_clause).  [assumption].
7.49/7.52	1963 (all Ma (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),Ma),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) <-> one_one(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),Ma),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) # label(fact_1153_mod2__gr__0) # label(axiom) # label(non_clause).  [assumption].
7.49/7.52	1964 (all Ma all K all N_1 (N_1 = Ma | zero_zero(nat) = K <-> hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N_1),K) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),Ma),K))) # label(fact_553_mult__cancel2) # label(axiom) # label(non_clause).  [assumption].
7.49/7.52	1965 (all X_a (ordered_ab_group_add(X_a) -> (all A_2 all B_1 all C_1 all D_1 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),C_1),D_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_2),B_1) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),D_1)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),B_1))))))) # label(fact_798_diff__eq__diff__less) # label(axiom) # label(non_clause).  [assumption].
7.49/7.52	1966 (all X_a (real_algebra_1(X_a) -> (all X all Y hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(real,X_a,of_real(X_a),X)),hAPP(real,X_a,of_real(X_a),Y)) = hAPP(real,X_a,of_real(X_a),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),Y))))) # label(fact_2788_of__real__add) # label(axiom) # label(non_clause).  [assumption].
7.49/7.52	1967 (all K_4 all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_4),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_4),N))) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K_4)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),M),N))))) # label(fact_498_dvd__mult__cancel) # label(axiom) # label(non_clause).  [assumption].
7.49/7.52	1968 (all N hAPP(int,nat,number_number_of(nat),N) = hAPP(real,nat,natceiling,hAPP(int,real,number_number_of(real),N))) # label(fact_1889_natceiling__number__of__eq) # label(axiom) # label(non_clause).  [assumption].
7.49/7.52	1969 (all X_a (ring_1(X_a) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),one_one(X_a)),ring_1_Ints(X_a))))) # label(fact_3837_Ints__1) # label(axiom) # label(non_clause).  [assumption].
7.49/7.52	1970 (all X_b all X_a (topological_space(X_a) & real_normed_vector(X_b) -> (all G all F all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),zero_zero(X_b)),hAPP(X_a,filter(X_a),at(X_a),A_2))) -> (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),G),zero_zero(X_b)),hAPP(X_a,filter(X_a),at(X_a),A_2))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(fun(X_a,X_b),fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,X_b)),combs(X_a,X_b,X_b),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,fun(X_b,X_b))),combb(X_b,fun(X_b,X_b),X_a),plus_plus(X_b)),F)),G)),zero_zero(X_b)),hAPP(X_a,filter(X_a),at(X_a),A_2)))))))) # label(fact_4579_LIM__add__zero) # label(axiom) # label(non_clause).  [assumption].
7.49/7.52	1971 (all L all U_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1),L) = hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),L),U_1))) # label(fact_4202_card__atLeastLessThan) # label(axiom) # label(non_clause).  [assumption].
7.49/7.52	1972 (all X_a (archim1727834104eiling(X_a) -> (all V hAPP(int,int,number_number_of(int),V) = hAPP(X_a,int,archim2085082626_floor(X_a),hAPP(int,X_a,number_number_of(X_a),V))))) # label(fact_2872_floor__number__of) # label(axiom) # label(non_clause).  [assumption].
7.49/7.52	1973 (all Y all U all X1_1 all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X1_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),X1_1),Y)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),X),U))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,inverse_inverse(real),X)),Y)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,inverse_inverse(real),X1_1)),U))))))) # label(fact_2590_real__mult__inverse__cancel) # label(axiom) # label(non_clause).  [assumption].
7.49/7.52	1974 (all V all W hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,number_number_of(int),V)),hAPP(int,int,number_number_of(int),W)) = hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,V))),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,W)))) # label(fact_986_zdiv__number__of__Bit0) # label(axiom) # label(non_clause).  [assumption].
7.49/7.52	1975 (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_391_zero__less__mult__pos) # label(axiom) # label(non_clause).  [assumption].
7.49/7.52	1976 (all X_a all S all T_3 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),S),T_3)) -> (-hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),S)) -> -hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),T_3))))) # label(fact_3038_infinite__super) # label(axiom) # label(non_clause).  [assumption].
7.49/7.52	1977 (all X_a (real_div_algebra(X_a) & divisi14063676e_zero(X_a) -> (all X hAPP(real,X_a,of_real(X_a),hAPP(real,real,inverse_inverse(real),X)) = hAPP(X_a,X_a,inverse_inverse(X_a),hAPP(real,X_a,of_real(X_a),X))))) # label(fact_2798_of__real__inverse) # label(axiom) # label(non_clause).  [assumption].
7.49/7.52	1978 (all A_1 all B hAPP(rat,product_prod(int,int),quotient_of,hAPP(int,rat,hAPP(int,fun(int,rat),fract,A_1),B)) = hAPP(product_prod(int,int),product_prod(int,int),normalize,hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),A_1),B))) # label(fact_3777_quotient__of__Fract) # label(axiom) # label(non_clause).  [assumption].
7.49/7.52	1979 (all T_2 all T_1 (boolean_algebra(T_1) -> boolean_algebra(fun(T_2,T_1)))) # label(arity_fun___Lattices_Oboolean__algebra) # label(axiom) # label(non_clause).  [assumption].
7.49/7.52	1980 (all X all Y hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),X),Y)) = hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),X),Y)) # label(fact_4371_abs__gcd__int) # label(axiom) # label(non_clause).  [assumption].
7.49/7.52	1981 (all X_a (metric_space(X_a) -> (all K all L (ti(X_a,L) = ti(X_a,K) <-> hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),hAPP(X_a,fun(nat,X_a),combk(X_a,nat),K)),L),sequentially)))))) # label(fact_4465_LIMSEQ__const__iff) # label(axiom) # label(non_clause).  [assumption].
7.49/7.52	1982 (all X_a (banach(X_a) -> (all F all C_1 all N_4 ((all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_4),N_2)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),hAPP(nat,X_a,F,hAPP(nat,nat,suc,N_2)))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C_1),hAPP(X_a,real,norm_norm(X_a),hAPP(nat,X_a,F,N_2))))))) -> hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),F)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),C_1)))))) # label(fact_4055_ratio__test__lemma2) # label(axiom) # label(non_clause).  [assumption].
7.49/7.52	1983 (all X_a ti(fun(X_a,fun(fun(X_a,bool),bool)),member(X_a)) = member(X_a)) # label(tsy_c_member_res) # label(axiom) # label(non_clause).  [assumption].
7.49/7.52	1984 (all N zero_zero(real) = hAPP(real,real,sin,hAPP(real,real,hAPP(real,fun(real,real),times_times(real),pi),hAPP(nat,real,real_1(nat),N)))) # label(fact_2296_sin__npi2) # label(axiom) # label(non_clause).  [assumption].
7.49/7.52	1985 (all A_1 all B (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),B)) -> zero_zero(nat) = B | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A_1),B)))) # label(fact_723_divides__ge) # label(axiom) # label(non_clause).  [assumption].
7.49/7.52	1986 (all X_a all X_b (real_normed_algebra(X_b) -> (all X_1 all G all A_2 all A_3 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),G),A_2),A_3)) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(fun(X_a,X_b),fun(X_a,X_b),hAPP(fun(X_b,X_b),fun(fun(X_a,X_b),fun(X_a,X_b)),combb(X_b,X_b,X_a),hAPP(X_b,fun(X_b,X_b),times_times(X_b),X_1)),G)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),X_1),A_2)),A_3)))))) # label(fact_4476_mult__right_Otendsto) # label(axiom) # label(non_clause).  [assumption].
7.49/7.52	1987 (all X_a (semiring_div(X_a) & number(X_a) -> (all X_1 all Y_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),hAPP(int,X_a,number_number_of(X_a),X_1)),hAPP(int,X_a,number_number_of(X_a),Y_1))) <-> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),hAPP(int,X_a,number_number_of(X_a),Y_1)),hAPP(int,X_a,number_number_of(X_a),X_1)) = zero_zero(X_a))))) # label(fact_1009_dvd__eq__mod__eq__0__number__of) # label(axiom) # label(non_clause).  [assumption].
7.49/7.52	1988 (all X_1 all N_1 all Diff all F (F = hAPP(nat,fun(real,real),Diff,zero_zero(nat)) -> ((all M_2 all T_4 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_2),N_1)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),T_4)),hAPP(real,real,abs_abs(real),X_1))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(nat,fun(real,real),Diff,M_2)),T_4),hAPP(real,real,hAPP(nat,fun(real,real),Diff,hAPP(nat,nat,suc,M_2)),T_4))))) -> (exists T_4 (hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),inverse_divide(real)),hAPP(real,fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(real,fun(nat,real)),combc(nat,real,real),Diff),zero_zero(real)))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),fact_fact(nat))))),hAPP(real,fun(nat,real),power_power(real),X_1))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),N_1))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(nat,fun(real,real),Diff,N_1),T_4)),hAPP(nat,real,real_1(nat),hAPP(nat,nat,fact_fact(nat),N_1)))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X_1),N_1))) = hAPP(real,real,F,X_1) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),T_4)),hAPP(real,real,abs_abs(real),X_1)))))))) # label(fact_4278_Maclaurin__bi__le) # label(axiom) # label(non_clause).  [assumption].
7.49/7.52	1989 (all X_a (metric_space(X_a) -> (all X all Y hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),Y),X) = hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),X),Y)))) # label(fact_3518_dist__commute) # label(axiom) # label(non_clause).  [assumption].
7.49/7.52	1990 (all N (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),N)) -> hAPP(int,int,hAPP(int,fun(int,int),times_times(int),N),hAPP(int,int,fact_fact(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),N),one_one(int)))) = hAPP(int,int,fact_fact(int),N))) # label(fact_3202_fact__reduce__int) # label(axiom) # label(non_clause).  [assumption].
7.49/7.52	1991 (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_1860_abs__of__nonneg) # label(axiom) # label(non_clause).  [assumption].
7.49/7.52	1992 (all Q_5 all R_5 all A_1 all B all Q_3 all R_4 (hBOOL(hAPP(product_prod(int,int),bool,hAPP(int,fun(product_prod(int,int),bool),hAPP(int,fun(int,fun(product_prod(int,int),bool)),divmod_int_rel,A_1),B),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),Q_3),R_4))) -> (hBOOL(hAPP(product_prod(int,int),bool,hAPP(int,fun(product_prod(int,int),bool),hAPP(int,fun(int,fun(product_prod(int,int),bool)),divmod_int_rel,A_1),B),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),Q_5),R_5))) -> (ti(int,B) != zero_zero(int) -> ti(int,R_5) = ti(int,R_4))))) # label(fact_1186_unique__remainder) # label(axiom) # label(non_clause).  [assumption].
7.49/7.52	1993 (all Y exists X_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),X_2)) & hAPP(real,real,tan,X_2) = Y & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_2),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))) # label(fact_2284_lemma__tan__total1) # label(axiom) # label(non_clause).  [assumption].
7.49/7.52	1994 (all X_a (linorder(X_a) -> (all B all A_1 all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),X)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),A_1),B)),X)))))) # label(fact_4800_min__max_Oless__infI1) # label(axiom) # label(non_clause).  [assumption].
7.49/7.52	1995 (all A_1 all M (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),M)) -> (exists X_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X_2)) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_1),X_2),M)) & (all Y_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_1),Y_2),M)) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Y_2),M)) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Y_2)) -> ti(int,X_2) = ti(int,Y_2))) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X_2),M)))))) # label(fact_616_zcong__zless__unique) # label(axiom) # label(non_clause).  [assumption].
7.49/7.52	1996 (all R_4 all A_1 hAPP(complex,real,re,hAPP(real,complex,hAPP(real,fun(real,complex),rcis,R_4),A_1)) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),R_4),hAPP(real,real,cos,A_1))) # label(fact_3169_Re__rcis) # label(axiom) # label(non_clause).  [assumption].
7.49/7.52	1997 (all F all X_1 all L (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),F),X_1),L)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),L),zero_zero(real))) -> (exists D_3 ((all H_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),H_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),H_1),D_3)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,F,X_1)),hAPP(real,real,F,hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),X_1),H_1))))))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),D_3))))))) # label(fact_2663_DERIV__neg__dec__left) # label(axiom) # label(non_clause).  [assumption].
7.49/7.53	1998 (all A_1 hAPP(real,complex,cis,hAPP(real,real,uminus_uminus(real),A_1)) = hAPP(complex,complex,inverse_inverse(complex),hAPP(real,complex,cis,A_1))) # label(fact_3030_cis__inverse) # label(axiom) # label(non_clause).  [assumption].
7.49/7.53	1999 (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_782_add__left__mono) # label(axiom) # label(non_clause).  [assumption].
7.49/7.53	2000 (all N all K_4 all M (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),K_4),M)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),K_4),N)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),K_4),hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,M),N)))))) # label(fact_3437_zgcd__greatest) # label(axiom) # label(non_clause).  [assumption].
7.49/7.53	2001 (all X_a (real_normed_field(X_a) -> (all G all E_3 all F all X_1 all D_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),F),X_1),D_2)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),G),X_1),E_3)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),hAPP(fun(X_a,X_a),fun(X_a,X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,X_a),fun(X_a,X_a)),combs(X_a,X_a,X_a),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,X_a),fun(X_a,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),X_a),plus_plus(X_a)),F)),hAPP(fun(X_a,X_a),fun(X_a,X_a),hAPP(fun(X_a,X_a),fun(fun(X_a,X_a),fun(X_a,X_a)),combb(X_a,X_a,X_a),uminus_uminus(X_a)),G))),X_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),D_2),hAPP(X_a,X_a,uminus_uminus(X_a),E_3))))))))) # label(fact_3816_DERIV__add__minus) # label(axiom) # label(non_clause).  [assumption].
7.49/7.53	2002 (all X all A_1 hAPP(real,int,archim2085082626_floor(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),hAPP(int,real,real_1(int),A_1))) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(real,int,archim2085082626_floor(real),X)),A_1)) # label(fact_3365_floor__add) # label(axiom) # label(non_clause).  [assumption].
7.49/7.53	2003 (all P_5 (hBOOL(hAPP(nat,bool,prime,P_5)) -> -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),P_5),hAPP(nat,nat,suc,zero_zero(nat)))))) # label(fact_3065_prime__nd__one) # label(axiom) # label(non_clause).  [assumption].
7.49/7.53	2004 (all M all N hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(nat,int,semiring_1_of_nat(int),M)),hAPP(nat,int,semiring_1_of_nat(int),N)) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),N))) # label(fact_1303_int__mult) # label(axiom) # label(non_clause).  [assumption].
7.49/7.53	2005 (all P_5 (hBOOL(hAPP(nat,bool,prime,P_5)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),P_5)))) # label(fact_3064_prime__g__one) # label(axiom) # label(non_clause).  [assumption].
7.49/7.53	2006 (all P_1 all N_1 all K (hBOOL(hAPP(nat,bool,P_1,hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),N_1),K))) <-> (zero_zero(nat) = K -> hBOOL(hAPP(nat,bool,P_1,N_1))) & (K != zero_zero(nat) -> (all I_2 all J_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),J_1),K)) -> (N_1 = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),I_2)),J_1) -> hBOOL(hAPP(nat,bool,P_1,J_1)))))))) # label(fact_1133_split__mod) # label(axiom) # label(non_clause).  [assumption].
7.49/7.53	2007 (all I_1 all K_4 all J_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_4),J_2)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_2),K_4)),I_1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J_2),I_1)),K_4))) # label(fact_690_add__diff__assoc2) # label(axiom) # label(non_clause).  [assumption].
7.49/7.53	2008 (all X_a (linorder(X_a) -> (all A_2 all B_1 all C_1 all D_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastLessThan(X_a),A_2),B_1)),hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastLessThan(X_a),C_1),D_1))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_1),A_2)) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C_1),A_2)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_1),D_1)))))) # label(fact_4199_atLeastLessThan__subset__iff) # label(axiom) # label(non_clause).  [assumption].
7.49/7.53	2009 (all Y hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),hAPP(real,real,arctan,Y)))) # label(fact_2126_arctan__lbound) # label(axiom) # label(non_clause).  [assumption].
7.49/7.53	2010 (all N_1 all V_1 (-hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),hAPP(int,int,pred,V_1)))) & (-hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),hAPP(int,int,pred,V_1)))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),hAPP(int,nat,nat_1,hAPP(int,int,number_number_of(int),hAPP(int,int,pred,V_1)))))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,N_1)),hAPP(int,nat,number_number_of(nat),V_1))))) # label(fact_3894_less__Suc__number__of) # label(axiom) # label(non_clause).  [assumption].
7.49/7.53	2011 (all X_a (linordered_idom(X_a) -> (all X all W (hBOOL(hAPP(nat,bool,even_odd_even(nat),hAPP(int,nat,number_number_of(nat),W))) -> hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),hAPP(int,nat,number_number_of(nat),W)) = hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(X_a,X_a,abs_abs(X_a),X)),hAPP(int,nat,number_number_of(nat),W)))))) # label(fact_2444_power__even__abs__number__of) # label(axiom) # label(non_clause).  [assumption].
7.49/7.53	2012 (all I_1 all J_2 hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,I_1),J_2) = hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,I_1),hAPP(int,int,uminus_uminus(int),J_2))) # label(fact_3443_zgcd__zminus2) # label(axiom) # label(non_clause).  [assumption].
7.49/7.53	2013 (all A_1 all N (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),N)) -> (one_one(int) = hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,A_1),N) -> (exists X_2 hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),X_2)),one_one(int)),N)))))) # label(fact_3479_zcong__lineq__ex) # label(axiom) # label(non_clause).  [assumption].
7.49/7.53	2014 (all X_a (real_algebra_1(X_a) -> (all X all N hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(real,X_a,of_real(X_a),X)),N) = hAPP(real,X_a,of_real(X_a),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),N))))) # label(fact_2789_of__real__power) # label(axiom) # label(non_clause).  [assumption].
7.49/7.53	2015 (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_1588_leI) # label(axiom) # label(non_clause).  [assumption].
7.49/7.53	2016 (all X_b all X_a (real_normed_vector(X_a) & topological_space(X_b) -> (all L all F all G all A_2 all R_3 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),R_3)) -> ((all X_2 (ti(X_a,A_2) != ti(X_a,X_2) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),X_2),A_2))),R_3)) -> hAPP(X_a,X_b,F,X_2) = hAPP(X_a,X_b,G,X_2)))) -> (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),G),L),hAPP(X_a,filter(X_a),at(X_a),A_2))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),L),hAPP(X_a,filter(X_a),at(X_a),A_2))))))))) # label(fact_4646_LIM__equal2) # label(axiom) # label(non_clause).  [assumption].
7.49/7.53	2017 (all K all L (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit0,K)),hAPP(int,int,bit1,L))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),K),L)))) # label(fact_53_rel__simps_I32_J) # label(axiom) # label(non_clause).  [assumption].
7.49/7.53	2018 (all B all D all A_1 all C (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),C)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),B),D)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),A_1),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),C),D)))))) # label(fact_3233_gcd__semilattice__nat_Oinf__mono) # label(axiom) # label(non_clause).  [assumption].
7.49/7.53	2019 (all X_a (real_normed_field(X_a) -> (all G all E_3 all F all X_1 all D_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),F),X_1),D_2)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),G),X_1),E_3)) -> (hAPP(X_a,X_a,G,X_1) != zero_zero(X_a) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),hAPP(fun(X_a,X_a),fun(X_a,X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,X_a),fun(X_a,X_a)),combs(X_a,X_a,X_a),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,X_a),fun(X_a,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),X_a),inverse_divide(X_a)),F)),G)),X_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),D_2),hAPP(X_a,X_a,G,X_1))),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,F,X_1)),E_3))),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,G,X_1)),hAPP(X_a,X_a,G,X_1))))))))))) # label(fact_3811_DERIV__divide) # label(axiom) # label(non_clause).  [assumption].
7.49/7.53	2020 (all X_a (comm_monoid_mult(X_a) & comm_monoid_add(X_a) -> (all F all G all A_3 all B_2 (A_3 = B_2 -> (hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,B_2)) -> ((all X_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X_2)) -> hAPP(int,X_a,G,X_2) = hAPP(int,X_a,F,X_2))) -> hAPP(fun(int,bool),X_a,hAPP(fun(int,X_a),fun(fun(int,bool),X_a),big_co1399186613setsum(int,X_a),G),B_2) = hAPP(fun(int,bool),X_a,hAPP(fun(int,X_a),fun(fun(int,bool),X_a),big_co1399186613setsum(int,X_a),F),A_3))))))) # label(fact_4297_transfer__nat__int__sum__prod__cong_I1_J) # label(axiom) # label(non_clause).  [assumption].
7.49/7.53	2021 (all X_a (ring_1(X_a) -> (all W all Z_1 hAPP(int,X_a,ring_1_of_int(X_a),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),W),Z_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(int,X_a,ring_1_of_int(X_a),W)),hAPP(int,X_a,ring_1_of_int(X_a),Z_1))))) # label(fact_3588_of__int__mult) # label(axiom) # label(non_clause).  [assumption].
7.49/7.53	2022 (all Y_1 all X_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),X_1)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),zOdd)) -> (exists N_2 hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),Y_1),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),N_2),X_1))))),X_1)))))) # label(fact_2005_best__odd__division__abs) # label(axiom) # label(non_clause).  [assumption].
7.49/7.53	2023 (all F all G all N_1 hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(nat,fun(real,fun(real,real))),fun(fun(nat,real),fun(nat,fun(real,real))),combs(nat,real,fun(real,real)),hAPP(fun(nat,bool),fun(nat,fun(real,fun(real,real))),hAPP(fun(bool,fun(real,fun(real,real))),fun(fun(nat,bool),fun(nat,fun(real,fun(real,real)))),combb(bool,fun(real,fun(real,real)),nat),if(real)),even_odd_even(nat))),F)),G)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),N_1))) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),F),hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),N_1))),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),G),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),hAPP(fun(nat,nat),fun(nat,fun(nat,nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,nat),fun(nat,fun(nat,nat))),combb(nat,fun(nat,nat),nat),plus_plus(nat)),hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),one_one(nat)))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),N_1)))) # label(fact_4235_sum__split__even__odd) # label(axiom) # label(non_clause).  [assumption].
7.49/7.53	2024 (all X_a (linordered_idom(X_a) -> (all Ma all K (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),hAPP(X_a,X_a,abs_abs(X_a),Ma)),K)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),Ma),K)))))) # label(fact_1846_abs__dvd__iff) # label(axiom) # label(non_clause).  [assumption].
7.49/7.53	2025 (all Qr_2 all M all N all Qr_1 (hBOOL(hAPP(product_prod(nat,nat),bool,hAPP(nat,fun(product_prod(nat,nat),bool),hAPP(nat,fun(nat,fun(product_prod(nat,nat),bool)),divmod_nat_rel,M),N),Qr_1)) -> (hBOOL(hAPP(product_prod(nat,nat),bool,hAPP(nat,fun(product_prod(nat,nat),bool),hAPP(nat,fun(nat,fun(product_prod(nat,nat),bool)),divmod_nat_rel,M),N),Qr_2)) -> Qr_1 = Qr_2))) # label(fact_3098_divmod__nat__rel__unique) # label(axiom) # label(non_clause).  [assumption].
7.49/7.53	2026 (all X_a (real_normed_field(X_a) -> (all F all X_1 all L (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),F),X_1),L)) <-> (exists G_1 ((all Z_2 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_a,X_a,F,Z_2)),hAPP(X_a,X_a,F,X_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,G_1,Z_2)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),Z_2),X_1))) & ti(X_a,L) = hAPP(X_a,X_a,G_1,X_1) & hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,X_a),fun(X_a,bool),isCont(X_a,X_a),G_1),X_1)))))))) # label(fact_4882_CARAT__DERIV) # label(axiom) # label(non_clause).  [assumption].
7.49/7.53	2027 (all X_a (real_normed_vector(X_a) -> (all A_1 all B hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),hAPP(real,real,uminus_uminus(real),A_1)),B) = hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_1),B))))) # label(fact_4685_scaleR_Ominus__left) # label(axiom) # label(non_clause).  [assumption].
7.49/7.53	2028 (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_788_add__strict__mono) # label(axiom) # label(non_clause).  [assumption].
7.49/7.53	2029 (all X all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,uminus_uminus(real),pi)),Y)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),Y),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X),zero_zero(real))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,cos,Y)),hAPP(real,real,cos,X))))))) # label(fact_2233_cos__monotone__minus__pi__0) # label(axiom) # label(non_clause).  [assumption].
7.49/7.53	2030 (all N hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(real,real,inverse_inverse(real),hAPP(nat,real,real_1(nat),hAPP(nat,nat,fact_fact(nat),N)))))) # label(fact_2614_inv__real__of__nat__fact__ge__zero) # label(axiom) # label(non_clause).  [assumption].
7.49/7.53	2031 (all X_a all A_2 all F all V_1 all N_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),hAPP(bool,fun(X_a,fun(X_a,X_a)),if(X_a),hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),hAPP(int,int,pred,V_1)))),hAPP(nat,X_a,hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(X_a,fun(fun(nat,X_a),fun(nat,X_a)),nat_case(X_a),A_2),F),N_1)),hAPP(nat,X_a,F,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,nat_1,hAPP(int,int,number_number_of(int),hAPP(int,int,pred,V_1)))),N_1))) = hAPP(nat,X_a,hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(X_a,fun(fun(nat,X_a),fun(nat,X_a)),nat_case(X_a),A_2),F),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),V_1)),N_1))) # label(fact_4108_nat__case__add__eq__if) # label(axiom) # label(non_clause).  [assumption].
7.49/7.53	2032 (all B_5 all A_6 all A_1 all B (zero_zero(int) != hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),A_1),B) -> (ti(int,A_1) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_6),hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),A_1),B)) -> (ti(int,B) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B_5),hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),A_1),B)) -> one_one(int) = hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),A_6),B_5))))) # label(fact_4351_gcd__coprime__int) # label(axiom) # label(non_clause).  [assumption].
7.49/7.53	2033 (all X_a (number_ring(X_a) -> zero_zero(X_a) = hAPP(int,X_a,number_number_of(X_a),pls))) # label(fact_146_number__of__Pls) # label(axiom) # label(non_clause).  [assumption].
7.49/7.53	2034 (all A_3 (hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A_3)) -> hAPP(fun(int,bool),nat,finite_card(int),A_3) = hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(fun(int,bool),fun(nat,bool),hAPP(fun(int,nat),fun(fun(int,bool),fun(nat,bool)),image(int,nat),nat_1),A_3)))) # label(fact_3668_Nat__Transfer_Otransfer__int__nat__set__functions_I1_J) # label(axiom) # label(non_clause).  [assumption].
7.49/7.53	2035 (all X_a all A_3 all X_3 all C_2 (hBOOL(hAPP(fun(fun(X_a,bool),bool),bool,hAPP(fun(X_a,bool),fun(fun(fun(X_a,bool),bool),bool),member(fun(X_a,bool)),X_3),C_2)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_3),X_3)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_3),hAPP(fun(fun(X_a,bool),bool),fun(X_a,bool),complete_Sup_Sup(fun(X_a,bool)),C_2)))))) # label(fact_1651_UnionI) # label(axiom) # label(non_clause).  [assumption].
7.49/7.53	2036 (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_1589_not__leE) # label(axiom) # label(non_clause).  [assumption].
7.49/7.53	2037 (all X_a all X_b (comm_monoid_add(X_b) -> (all B_1 all A_2 all S (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),S)) -> (-hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_2),S)) -> zero_zero(X_b) = hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),hAPP(X_b,fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(X_b,fun(X_a,X_b)),combc(X_a,X_b,X_b),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,X_b)),hAPP(fun(X_a,fun(X_b,fun(X_b,X_b))),fun(fun(X_a,X_b),fun(X_a,fun(X_b,X_b))),combs(X_a,X_b,fun(X_b,X_b)),hAPP(fun(X_a,bool),fun(X_a,fun(X_b,fun(X_b,X_b))),hAPP(fun(bool,fun(X_b,fun(X_b,X_b))),fun(fun(X_a,bool),fun(X_a,fun(X_b,fun(X_b,X_b)))),combb(bool,fun(X_b,fun(X_b,X_b)),X_a),if(X_b)),hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,fun(X_a,bool)),fun(X_a,fun(X_a,bool)),combc(X_a,X_a,bool),fequal(X_a)),A_2))),B_1)),zero_zero(X_b))),S)) & (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_2),S)) -> hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),hAPP(X_b,fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(X_b,fun(X_a,X_b)),combc(X_a,X_b,X_b),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,X_b)),hAPP(fun(X_a,fun(X_b,fun(X_b,X_b))),fun(fun(X_a,X_b),fun(X_a,fun(X_b,X_b))),combs(X_a,X_b,fun(X_b,X_b)),hAPP(fun(X_a,bool),fun(X_a,fun(X_b,fun(X_b,X_b))),hAPP(fun(bool,fun(X_b,fun(X_b,X_b))),fun(fun(X_a,bool),fun(X_a,fun(X_b,fun(X_b,X_b)))),combb(bool,fun(X_b,fun(X_b,X_b)),X_a),if(X_b)),hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,fun(X_a,bool)),fun(X_a,fun(X_a,bool)),combc(X_a,X_a,bool),fequal(X_a)),A_2))),B_1)),zero_zero(X_b))),S) = hAPP(X_a,X_b,B_1,A_2)))))) # label(fact_4215_setsum__delta) # label(axiom) # label(non_clause).  [assumption].
7.49/7.53	2038 (all A_1 all B hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),ii),hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,A_1),B)) = hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,hAPP(real,real,uminus_uminus(real),B)),A_1)) # label(fact_2768_i__mult__Complex) # label(axiom) # label(non_clause).  [assumption].
7.49/7.53	2039 (all Q_2 all P_1 ((all A_4 all B_4 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B_4)) -> (hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),A_4),B_4) = one_one(int) -> hBOOL(hAPP(rat,bool,P_1,hAPP(int,rat,hAPP(int,fun(int,rat),fract,A_4),B_4)))))) -> hBOOL(hAPP(rat,bool,P_1,Q_2)))) # label(fact_4413_Rat__induct) # label(axiom) # label(non_clause).  [assumption].
7.49/7.53	2040 (all T_2 all T_1 (finite_finite(T_1) & finite_finite(T_2) -> finite_finite(fun(T_2,T_1)))) # label(arity_fun___Finite__Set_Ofinite) # label(axiom) # label(non_clause).  [assumption].
7.49/7.53	2041 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,ln,X))) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),X))))) # label(fact_1951_ln__gt__zero__imp__gt__one) # label(axiom) # label(non_clause).  [assumption].
7.49/7.53	2042 (all X all A_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X),hAPP(nat,real,real_1(nat),A_1))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(real,nat,natceiling,X)),A_1)))) # label(fact_2332_natceiling__le) # label(axiom) # label(non_clause).  [assumption].
7.49/7.53	2043 (all X_a (linordered_field(X_a) -> (all Z_1 all W all Y all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),X)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),W)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),W),Z_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),X),Z_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),Y),W)))))))))) # label(fact_1703_frac__less2) # label(axiom) # label(non_clause).  [assumption].
7.49/7.53	2044 (all X_a all X_b (real_normed_vector(X_b) -> (all G all B_1 all F all A_2 all A_3 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),A_2),A_3)) -> (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),G),B_1),A_3)) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(fun(X_a,X_b),fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,X_b)),combs(X_a,X_b,X_b),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,fun(X_b,X_b))),combb(X_b,fun(X_b,X_b),X_a),plus_plus(X_b)),F)),G)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),A_2),B_1)),A_3))))))) # label(fact_4439_tendsto__add) # label(axiom) # label(non_clause).  [assumption].
7.49/7.53	2045 (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_124_less__int__code_I16_J) # label(axiom) # label(non_clause).  [assumption].
7.49/7.53	2046 (all M all N hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),N)) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(nat,int,semiring_1_of_nat(int),M)),hAPP(nat,int,semiring_1_of_nat(int),N))) # label(fact_1304_zmult__int) # label(axiom) # label(non_clause).  [assumption].
7.49/7.53	2047 (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_438_mult__right__le__one__le) # label(axiom) # label(non_clause).  [assumption].
7.49/7.53	2048 (all X_a all A_3 all B_2 hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,bool)),combs(X_a,bool,bool),hAPP(fun(X_a,bool),fun(X_a,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,fun(bool,bool))),combb(bool,fun(bool,bool),X_a),fconj),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(X_a,bool)),combc(X_a,fun(X_a,bool),bool),member(X_a)),A_3))),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(bool,bool),fun(fun(X_a,bool),fun(X_a,bool)),combb(bool,bool,X_a),fNot),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(X_a,bool)),combc(X_a,fun(X_a,bool),bool),member(X_a)),B_2)))) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_3),B_2)) # label(fact_1961_set__diff__eq) # label(axiom) # label(non_clause).  [assumption].
7.49/7.53	2049 (all X_b all X_a (topological_space(X_a) & real_normed_vector(X_b) -> (all G all M_1 all F all L_2 all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),L_2),hAPP(X_a,filter(X_a),at(X_a),A_2))) -> (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),G),M_1),hAPP(X_a,filter(X_a),at(X_a),A_2))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(fun(X_a,X_b),fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,X_b)),combs(X_a,X_b,X_b),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,fun(X_b,X_b))),combb(X_b,fun(X_b,X_b),X_a),plus_plus(X_b)),F)),G)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),L_2),M_1)),hAPP(X_a,filter(X_a),at(X_a),A_2)))))))) # label(fact_4565_LIM__add) # label(axiom) # label(non_clause).  [assumption].
7.49/7.53	2050 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,inverse_inverse(real),hAPP(real,real,sqrt,X))),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(real,real,inverse_inverse(real),X))) # label(fact_2623_real__inv__sqrt__pow2) # label(axiom) # label(non_clause).  [assumption].
7.49/7.53	2051 (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_768_add__left__imp__eq) # label(axiom) # label(non_clause).  [assumption].
7.49/7.53	2052 (all X_a (division_ring(X_a) -> (all A_2 all B_1 all C_1 (zero_zero(X_a) != ti(X_a,C_1) -> (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),C_1) = ti(X_a,B_1) <-> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),B_1),C_1) = ti(X_a,A_2)))))) # label(fact_1687_nonzero__eq__divide__eq) # label(axiom) # label(non_clause).  [assumption].
7.49/7.53	2053 (all X_a (linordered_field(X_a) -> (all Y all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),zero_zero(X_a))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),Y)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),X),Y)),zero_zero(X_a)))))))) # label(fact_1681_divide__neg__pos) # label(axiom) # label(non_clause).  [assumption].
7.49/7.53	2054 (all M all N all K_4 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),K_4)) -> hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K_4),M)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K_4),N)) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K_4),hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,M),N)))) # label(fact_3455_zgcd__zmult__distrib2) # label(axiom) # label(non_clause).  [assumption].
7.49/7.53	2055 (all X_a (linordered_field(X_a) -> (all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,inverse_inverse(X_a),A_1))))))) # label(fact_2543_positive__imp__inverse__positive) # label(axiom) # label(non_clause).  [assumption].
7.49/7.53	2056 (all Q all P (hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,P),Q)) | -hBOOL(Q) | -hBOOL(P))) # label(help_fconj_1_1_U) # label(axiom) # label(non_clause).  [assumption].
7.49/7.53	2057 (all X_a (linordered_field(X_a) -> (all C all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),C)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),C),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),C),B))))))))) # label(fact_1743_divide__left__mono) # label(axiom) # label(non_clause).  [assumption].
7.49/7.53	2058 (all A_1 all B hAPP(rat,rat,uminus_uminus(rat),hAPP(int,rat,hAPP(int,fun(int,rat),fract,A_1),B)) = hAPP(int,rat,hAPP(int,fun(int,rat),fract,hAPP(int,int,uminus_uminus(int),A_1)),B)) # label(fact_3755_minus__rat) # label(axiom) # label(non_clause).  [assumption].
7.49/7.53	2059 (all X_a (field(X_a) -> (all N all M all A_1 (ti(X_a,A_1) != zero_zero(X_a) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N),M)) -> hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),M)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N))))))) # label(fact_1751_power__diff) # label(axiom) # label(non_clause).  [assumption].
7.49/7.53	2060 (all X_b all X_a (semiring_1(X_a) -> (all F all A_3 hAPP(nat,X_a,semiring_1_of_nat(X_a),hAPP(fun(X_b,bool),nat,hAPP(fun(X_b,nat),fun(fun(X_b,bool),nat),big_co1399186613setsum(X_b,nat),F),A_3)) = hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co1399186613setsum(X_b,X_a),hAPP(fun(X_b,nat),fun(X_b,X_a),hAPP(fun(nat,X_a),fun(fun(X_b,nat),fun(X_b,X_a)),combb(nat,X_a,X_b),semiring_1_of_nat(X_a)),F)),A_3)))) # label(fact_4171_of__nat__setsum) # label(axiom) # label(non_clause).  [assumption].
7.49/7.53	2061 (all K_4 all I_1 all J_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_1),J_2)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I_1),K_4)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J_2),K_4))))) # label(fact_584_mult__le__mono1) # label(axiom) # label(non_clause).  [assumption].
7.49/7.53	2062 (all M all N all K_4 hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),M),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),N),K_4))),N) = hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,M),N)) # label(fact_3447_zgcd__zadd__zmult) # label(axiom) # label(non_clause).  [assumption].
7.49/7.53	2063 (all N all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> hAPP(real,real,hAPP(real,fun(real,real),powr,X),hAPP(nat,real,real_1(nat),N)) = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),N))) # label(fact_3404_powr__realpow) # label(axiom) # label(non_clause).  [assumption].
7.49/7.53	2064 (all X_1 all N_1 (-hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),N_1))) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(real,nat,natceiling,X_1)),hAPP(int,nat,number_number_of(nat),N_1))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_1),hAPP(int,real,number_number_of(real),N_1))))))) # label(fact_1913_natceiling__le__eq__number__of) # label(axiom) # label(non_clause).  [assumption].
7.49/7.53	2065 (all M all N all P_5 (hBOOL(hAPP(nat,bool,prime,P_5)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),P_5),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),N))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),P_5),N)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),P_5),M))))) # label(fact_3054_prime__dvd__mult) # label(axiom) # label(non_clause).  [assumption].
7.49/7.53	2066 (all X_1 all Y_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_1),Y_1)) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,exp(real),X_1)),hAPP(real,real,exp(real),Y_1))))) # label(fact_2514_exp__less__cancel__iff) # label(axiom) # label(non_clause).  [assumption].
7.49/7.53	2067 (all K (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),K),min_1)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,K)),min_1)))) # label(fact_301_rel__simps_I30_J) # label(axiom) # label(non_clause).  [assumption].
7.49/7.53	2068 (all S (hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),S)) -> (exists K_1 hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,bool),fun(fun(nat,bool),bool),ord_less_eq(fun(nat,bool)),S),hAPP(nat,fun(nat,bool),ord_lessThan(nat),K_1)))))) # label(fact_4325_finite__nat__bounded) # label(axiom) # label(non_clause).  [assumption].
7.49/7.53	2069 (all M all N all K_4 hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N)),K_4) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),K_4)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N),K_4))) # label(fact_581_add__mult__distrib) # label(axiom) # label(non_clause).  [assumption].
7.49/7.53	2070 (all X_a (metric_space(X_a) -> (all X all Y -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),X),Y)),zero_zero(real)))))) # label(fact_3515_dist__not__less__zero) # label(axiom) # label(non_clause).  [assumption].
7.49/7.53	2071 (all X_a (linordered_idom(X_a) -> (all W_1 all Z (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(int,X_a,ring_1_of_int(X_a),W_1)),hAPP(int,X_a,ring_1_of_int(X_a),Z))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),W_1),Z)))))) # label(fact_3570_of__int__le__iff) # label(axiom) # label(non_clause).  [assumption].
7.49/7.53	2072 (all X_a (group_add(X_a) -> (all A_1 all B ti(X_a,B) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),A_1)),B))))) # label(fact_2049_add__minus__cancel) # label(axiom) # label(non_clause).  [assumption].
7.49/7.53	2073 (all X_a (dvd(X_a) -> (all A_1 all B all K_4 (ti(X_a,A_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),K_4) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),B),A_1)))))) # label(fact_337_dvdI) # label(axiom) # label(non_clause).  [assumption].
7.49/7.53	2074 (all X_b all X_a (topological_space(X_a) & real_normed_vector(X_b) -> (all F all L_2 all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),L_2),hAPP(X_a,filter(X_a),at(X_a),A_2))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(fun(X_a,X_b),fun(X_a,X_b),hAPP(fun(X_b,X_b),fun(fun(X_a,X_b),fun(X_a,X_b)),combb(X_b,X_b,X_a),uminus_uminus(X_b)),F)),hAPP(X_b,X_b,uminus_uminus(X_b),L_2)),hAPP(X_a,filter(X_a),at(X_a),A_2))))))) # label(fact_4554_LIM__minus) # label(axiom) # label(non_clause).  [assumption].
7.49/7.53	2075 (all Q all P (hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,P),Q)) | -hBOOL(P))) # label(help_fdisj_1_1_U) # label(axiom) # label(non_clause).  [assumption].
7.49/7.53	2076 (all X_a all X_b (real_normed_field(X_b) -> (all F all X_1 all F_2 all S (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),S)) -> ((all N_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),N_2),S)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),hAPP(fun(X_b,X_b),fun(X_b,fun(X_b,bool)),deriv(X_b),hAPP(X_a,fun(X_b,X_b),hAPP(fun(X_b,fun(X_a,X_b)),fun(X_a,fun(X_b,X_b)),combc(X_b,X_a,X_b),F),N_2)),X_1),hAPP(X_a,X_b,hAPP(X_b,fun(X_a,X_b),F_2,X_1),N_2))))) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),hAPP(fun(X_b,X_b),fun(X_b,fun(X_b,bool)),deriv(X_b),hAPP(fun(X_a,bool),fun(X_b,X_b),hAPP(fun(X_b,fun(fun(X_a,bool),X_b)),fun(fun(X_a,bool),fun(X_b,X_b)),combc(X_b,fun(X_a,bool),X_b),hAPP(fun(X_b,fun(X_a,X_b)),fun(X_b,fun(fun(X_a,bool),X_b)),hAPP(fun(fun(X_a,X_b),fun(fun(X_a,bool),X_b)),fun(fun(X_b,fun(X_a,X_b)),fun(X_b,fun(fun(X_a,bool),X_b))),combb(fun(X_a,X_b),fun(fun(X_a,bool),X_b),X_b),big_co1399186613setsum(X_a,X_b)),F)),S)),X_1),hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),hAPP(X_b,fun(X_a,X_b),F_2,X_1)),S)))))))) # label(fact_4304_DERIV__setsum) # label(axiom) # label(non_clause).  [assumption].
7.49/7.53	2077 (all Y_1 all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_1),Y_1)) -> (exists X_2 (hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),X_2),field_char_0_Rats(real))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_2),Y_1)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_1),X_2))))))) # label(fact_3686_Rats__dense__in__nn__real) # label(axiom) # label(non_clause).  [assumption].
7.49/7.53	2078 (all Y_1 all X_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,real)),combs(real,real,real),hAPP(fun(real,real),fun(real,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,fun(real,real))),combb(real,fun(real,real),real),plus_plus(real)),hAPP(nat,fun(real,real),hAPP(fun(real,fun(nat,real)),fun(nat,fun(real,real)),combc(real,nat,real),hAPP(fun(real,real),fun(real,fun(nat,real)),hAPP(fun(real,fun(nat,real)),fun(fun(real,real),fun(real,fun(nat,real))),combb(real,fun(nat,real),real),power_power(real)),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,real)),combs(real,real,real),hAPP(fun(real,real),fun(real,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,fun(real,real))),combb(real,fun(real,real),real),minus_minus(real)),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,real),fun(fun(real,real),fun(real,real)),combb(real,real,real),sin),hAPP(real,fun(real,real),hAPP(fun(real,fun(real,real)),fun(real,fun(real,real)),combc(real,real,real),plus_plus(real)),Y_1)))),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,real)),combs(real,real,real),hAPP(fun(real,real),fun(real,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,fun(real,real))),combb(real,fun(real,real),real),plus_plus(real)),hAPP(real,fun(real,real),hAPP(fun(real,fun(real,real)),fun(real,fun(real,real)),combc(real,real,real),hAPP(fun(real,real),fun(real,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,fun(real,real))),combb(real,fun(real,real),real),times_times(real)),sin)),hAPP(real,real,cos,Y_1)))),hAPP(real,fun(real,real),hAPP(fun(real,fun(real,real)),fun(real,fun(real,real)),combc(real,real,real),hAPP(fun(real,real),fun(real,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,fun(real,real))),combb(real,fun(real,real),real),times_times(real)),cos)),hAPP(real,real,sin,Y_1)))))),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),hAPP(nat,fun(real,real),hAPP(fun(real,fun(nat,real)),fun(nat,fun(real,real)),combc(real,nat,real),hAPP(fun(real,real),fun(real,fun(nat,real)),hAPP(fun(real,fun(nat,real)),fun(fun(real,real),fun(real,fun(nat,real))),combb(real,fun(nat,real),real),power_power(real)),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,real)),combs(real,real,real),hAPP(fun(real,real),fun(real,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,fun(real,real))),combb(real,fun(real,real),real),minus_minus(real)),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,real),fun(fun(real,real),fun(real,real)),combb(real,real,real),cos),hAPP(real,fun(real,real),hAPP(fun(real,fun(real,real)),fun(real,fun(real,real)),combc(real,real,real),plus_plus(real)),Y_1)))),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,real)),combs(real,real,real),hAPP(fun(real,real),fun(real,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,fun(real,real))),combb(real,fun(real,real),real),minus_minus(real)),hAPP(real,fun(real,real),hAPP(fun(real,fun(real,real)),fun(real,fun(real,real)),combc(real,real,real),hAPP(fun(real,real),fun(real,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,fun(real,real))),combb(real,fun(real,real),real),times_times(real)),cos)),hAPP(real,real,cos,Y_1)))),hAPP(real,fun(real,real),hAPP(fun(real,fun(real,real)),fun(real,fun(real,real)),combc(real,real,real),hAPP(fun(real,real),fun(real,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,fun(real,real))),combb(real,fun(real,real),real),times_times(real)),sin)),hAPP(real,real,sin,Y_1)))))),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),X_2),zero_zero(real)))) # label(fact_3916_lemma__DERIV__sin__cos__add) # label(axiom) # label(non_clause).  [assumption].
7.49/7.53	2079 (all X_a all X_b all A_3 all B_2 all P_1 (hBOOL(hAPP(fun(product_prod(fun(X_a,bool),fun(X_b,bool)),bool),bool,hAPP(product_prod(fun(X_a,bool),fun(X_b,bool)),fun(fun(product_prod(fun(X_a,bool),fun(X_b,bool)),bool),bool),member(product_prod(fun(X_a,bool),fun(X_b,bool))),hAPP(fun(X_b,bool),product_prod(fun(X_a,bool),fun(X_b,bool)),hAPP(fun(X_a,bool),fun(fun(X_b,bool),product_prod(fun(X_a,bool),fun(X_b,bool))),product_Pair(fun(X_a,bool),fun(X_b,bool)),A_3),B_2)),hAPP(fun(X_a,fun(X_b,bool)),fun(product_prod(fun(X_a,bool),fun(X_b,bool)),bool),bijR(X_a,X_b),P_1))) -> hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_3)))) # label(fact_4876_fin__bijRl) # label(axiom) # label(non_clause).  [assumption].
7.49/7.53	2080 (all Ma all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Ma),N_1)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),hAPP(nat,nat,suc,N_1))))) # label(fact_1336_less__Suc__eq__le) # label(axiom) # label(non_clause).  [assumption].
7.49/7.53	2081 (all W_1 all Z (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),Z)) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_1),Z)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(int,nat,nat_1,W_1)),hAPP(int,nat,nat_1,Z))))) # label(fact_1125_zless__nat__conj) # label(axiom) # label(non_clause).  [assumption].
7.49/7.53	2082 (all X_a (comm_semiring_1(X_a) -> (all A_1 all M hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),M)),M) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),one_one(X_a))),M)))) # label(fact_255_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J) # label(axiom) # label(non_clause).  [assumption].
7.49/7.53	2083 (all X_a (ring_1(X_a) -> (all A_1 all N hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),A_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),N)) = hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),N))))) # label(fact_2117_ring__1__class_Opower__minus__even) # label(axiom) # label(non_clause).  [assumption].
7.49/7.53	2084 (all X_a (real_normed_vector(X_a) -> (all R_1 all A_2 hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,X_a),fun(X_a,bool),isCont(X_a,X_a),hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),R_1)),A_2))))) # label(fact_4914_scaleR__right_OisCont) # label(axiom) # label(non_clause).  [assumption].
7.49/7.53	2085 (all X_a (real_normed_algebra(X_a) -> (all X all Y all A_1 all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),Y)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),X),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),Y),B))),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),X),A_1)),B))),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),Y),B)))))) # label(fact_875_mult_Oprod__diff__prod) # label(axiom) # label(non_clause).  [assumption].
7.49/7.53	2086 (all X all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X)) -> X = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,hAPP(nat,fun(real,real),root,N),X)),N)))) # label(fact_2709_real__root__pow__pos2) # label(axiom) # label(non_clause).  [assumption].
7.49/7.53	2087 (all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> zero_zero(real) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),min_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),N),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),hAPP(nat,real,real_1(nat),hAPP(nat,nat,fact_fact(nat),N)))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),zero_zero(real)),N)))) # label(fact_2410_lemma__STAR__cos) # label(axiom) # label(non_clause).  [assumption].
7.49/7.53	2088 (all A_1 all X (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),X)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X),A_1)) -> (hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A_1),one_one(int)) != ti(int,X) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A_1),one_one(int)))))))) # label(fact_508_Euler_Oaux1) # label(axiom) # label(non_clause).  [assumption].
7.49/7.53	2089 (all X_a (metric_space(X_a) & comm_monoid_add(X_a) -> (all F hAPP(fun(nat,X_a),X_a,lim(X_a),hAPP(fun(nat,fun(nat,bool)),fun(nat,X_a),hAPP(fun(fun(nat,bool),X_a),fun(fun(nat,fun(nat,bool)),fun(nat,X_a)),combb(fun(nat,bool),X_a,nat),hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F)),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)))) = hAPP(fun(nat,X_a),X_a,suminf(X_a),F)))) # label(fact_4328_suminf__eq__lim) # label(axiom) # label(non_clause).  [assumption].
7.49/7.53	2090 (all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,number_number_of(real),min_1)),Y)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),Y),one_one(real))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,arcsin,Y)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),hAPP(real,real,arcsin,Y)))))) # label(fact_2130_arcsin__bounded) # label(axiom) # label(non_clause).  [assumption].
7.49/7.53	2091 (all X_a powp(X_a) = ti(fun(fun(X_a,bool),fun(fun(X_a,bool),bool)),powp(X_a))) # label(tsy_c_Predicate_OPowp_res) # label(axiom) # label(non_clause).  [assumption].
7.49/7.53	2092 (all Ta all A_3 all D_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D_2)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Ta),A_3)) -> (all X_2 ((all Xa (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xa),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastAtMost(int),one_one(int)),D_2))) -> (all Xb (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xb),A_3)) -> ti(int,X_2) != hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),Xb),Xa))))) -> (ti(int,X_2) != ti(int,Ta) -> ti(int,Ta) != hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X_2),D_2))))))) # label(fact_4639_aset_I4_J) # label(axiom) # label(non_clause).  [assumption].
7.49/7.53	2093 (all K_4 hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),K_4),pls) = ti(int,K_4)) # label(fact_130_add__Pls__right) # label(axiom) # label(non_clause).  [assumption].
7.49/7.53	2094 (all X all Y (Y != X -> (-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_516_linorder__neqE__nat) # label(axiom) # label(non_clause).  [assumption].
7.49/7.53	2095 (all W all V (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,number_number_of(int),V))) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,number_number_of(int),W)),hAPP(int,int,number_number_of(int),V)))) -> hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),negDivAlg,hAPP(int,int,number_number_of(int),W)),hAPP(int,int,number_number_of(int),V)) = hAPP(product_prod(int,int),product_prod(int,int),hAPP(int,fun(product_prod(int,int),product_prod(int,int)),adjust,hAPP(int,int,number_number_of(int),V)),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),negDivAlg,hAPP(int,int,number_number_of(int),W)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),hAPP(int,int,number_number_of(int),V))))) & (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,number_number_of(int),W)),hAPP(int,int,number_number_of(int),V)))) -> hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),hAPP(int,int,number_number_of(int),min_1)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,number_number_of(int),W)),hAPP(int,int,number_number_of(int),V))) = hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),negDivAlg,hAPP(int,int,number_number_of(int),W)),hAPP(int,int,number_number_of(int),V))))) # label(fact_1069_negDivAlg__eqn__number__of) # label(axiom) # label(non_clause).  [assumption].
7.49/7.53	2096 (all N hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),min_1)),N) = hAPP(real,real,sin,hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,real_1(nat),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),N)))),pi)),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) # label(fact_2367_sin__cos__npi) # label(axiom) # label(non_clause).  [assumption].
7.49/7.53	2097 (all X_a (real_normed_field(X_a) -> (all A_1 all B (zero_zero(X_a) != ti(X_a,B) -> hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),A_1),B)) = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(X_a,real,norm_norm(X_a),A_1)),hAPP(X_a,real,norm_norm(X_a),B)))))) # label(fact_1790_nonzero__norm__divide) # label(axiom) # label(non_clause).  [assumption].
7.49/7.53	2098 (all A_2 hAPP(int,int,zfact,A_2) = hAPP(fun(int,bool),int,hAPP(fun(int,int),fun(fun(int,bool),int),big_co302546470etprod(int,int),combi(int)),hAPP(int,fun(int,bool),d22set,A_2))) # label(fact_3930_d22set__prod__zfact) # label(axiom) # label(non_clause).  [assumption].
7.49/7.53	2099 (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_33_rel__simps_I34_J) # label(axiom) # label(non_clause).  [assumption].
7.49/7.53	2100 (all X_a all X_b (comm_monoid_mult(X_b) -> (all F all F_1 ((all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),F_1)) -> hAPP(X_a,X_b,F,X_2) = one_one(X_b))) -> one_one(X_b) = hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co302546470etprod(X_a,X_b),F),F_1))))) # label(fact_4772_setprod__1_H) # label(axiom) # label(non_clause).  [assumption].
7.49/7.53	2101 (all X_a (group_add(X_a) -> (all A_1 all B ti(X_a,A_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),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)))) # label(fact_808_add__diff__cancel) # label(axiom) # label(non_clause).  [assumption].
7.49/7.53	2102 (all X_a (real_normed_vector(X_a) -> (all X -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,norm_norm(X_a),X)),zero_zero(real)))))) # label(fact_1780_norm__not__less__zero) # label(axiom) # label(non_clause).  [assumption].
7.49/7.53	2103 (all A_2 (hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),A_2),zero_zero(real)),sequentially)) -> (hBOOL(hAPP(fun(nat,real),bool,monoseq(real),A_2)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(nat,real,A_2,zero_zero(nat))),zero_zero(real))) -> (all N_2 hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),hAPP(fun(nat,real),real,suminf(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),min_1)))),A_2))),hAPP(real,fun(real,bool),hAPP(real,fun(real,fun(real,bool)),ord_atLeastAtMost(real),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),min_1)))),A_2)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),N_2)),one_one(nat))))),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),min_1)))),A_2)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),N_2))))))))))) # label(fact_4522_summable__Leibniz_I3_J) # label(axiom) # label(non_clause).  [assumption].
7.49/7.53	2104 (all X_b all X_a all P_4 hAPP(product_prod(X_b,X_a),X_a,hAPP(fun(X_b,fun(X_a,X_a)),fun(product_prod(X_b,X_a),X_a),product_prod_case(X_b,X_a,X_a),hAPP(fun(X_a,X_a),fun(X_b,fun(X_a,X_a)),combk(fun(X_a,X_a),X_b),combi(X_a))),P_4) = hAPP(product_prod(X_b,X_a),X_a,product_snd(X_b,X_a),P_4)) # label(fact_4003_snd__def) # label(axiom) # label(non_clause).  [assumption].
7.49/7.53	2105 (all A_1 all B all C hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A_1),B)),C) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_1),C)),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),B),C))),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_1),C)),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),B),C))),C))) # label(fact_912_zdiv__zadd1__eq) # label(axiom) # label(non_clause).  [assumption].
7.49/7.53	2106 (all K (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),pls)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,K)),pls)))) # label(fact_154_rel__simps_I12_J) # label(axiom) # label(non_clause).  [assumption].
7.49/7.53	2107 (all X_a (linorder(X_a) -> (all A_2 all B_1 all C_1 all D_1 (hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastLessThan(X_a),C_1),D_1) = hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastLessThan(X_a),A_2),B_1) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),B_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),D_1)) -> ti(X_a,D_1) = ti(X_a,B_1))))))) # label(fact_4195_atLeastLessThan__inj_I2_J) # label(axiom) # label(non_clause).  [assumption].
7.49/7.53	2108 (all L all U_1 hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastLessThan(int),L),U_1)))) # label(fact_4243_finite__atLeastLessThan__int) # label(axiom) # label(non_clause).  [assumption].
7.49/7.53	2109 (all X_a all X_b (ab_group_add(X_b) -> (all F all B_2 all A_3 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_3)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),B_2),A_3)) -> hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),F),A_3)),hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),F),B_2)) = hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),F),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_3),B_2))))))) # label(fact_4233_setsum__diff) # label(axiom) # label(non_clause).  [assumption].
7.49/7.53	2110 (all N hAPP(complex,real,re,hAPP(nat,complex,semiring_1_of_nat(complex),N)) = hAPP(nat,real,semiring_1_of_nat(real),N)) # label(fact_3007_complex__Re__of__nat) # label(axiom) # label(non_clause).  [assumption].
7.49/7.53	2111 (all X_a all C_2 all A_3 all B_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less(fun(X_a,bool)),A_3),B_2)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),B_2),C_2)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less(fun(X_a,bool)),A_3),C_2))))) # label(fact_2002_psubset__subset__trans) # label(axiom) # label(non_clause).  [assumption].
7.49/7.53	2112 (all Y all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Y)) -> hAPP(real,real,hAPP(real,fun(real,real),times_times(real),Y),hAPP(real,real,ln,X)) = hAPP(real,real,ln,hAPP(real,real,hAPP(real,fun(real,real),powr,X),Y))))) # label(fact_3405_ln__powr) # label(axiom) # label(non_clause).  [assumption].
7.49/7.53	2113 (all N all M (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N),M)) -> hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(nat,int,semiring_1_of_nat(int),M)),hAPP(nat,int,semiring_1_of_nat(int),N)) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N)))) # label(fact_1380_zdiff__int) # label(axiom) # label(non_clause).  [assumption].
7.49/7.53	2114 (all A_1 all B ((zero_zero(int) != hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_1),B) -> hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,uminus_uminus(int),A_1)),B) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),B),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_1),B))) & (zero_zero(int) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_1),B) -> zero_zero(int) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,uminus_uminus(int),A_1)),B)))) # label(fact_2171_zmod__zminus1__eq__if) # label(axiom) # label(non_clause).  [assumption].
7.49/7.53	2115 (all A_1 all B all C (hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A_1),B) = ti(int,C) -> hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),C),B) = ti(int,A_1))) # label(fact_483_Int2_Oaux1) # label(axiom) # label(non_clause).  [assumption].
7.49/7.53	2116 (all L all U_1 hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),U_1),L)),one_one(int))) = hAPP(fun(int,bool),nat,finite_card(int),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastAtMost(int),L),U_1))) # label(fact_4605_card__atLeastAtMost__int) # label(axiom) # label(non_clause).  [assumption].
7.49/7.53	2117 (all Z_1 (hBOOL(hAPP(int,bool,nat_neg,Z_1)) -> hAPP(int,nat,nat_1,Z_1) = zero_zero(nat))) # label(fact_1507_neg__nat) # label(axiom) # label(non_clause).  [assumption].
7.49/7.53	2118 (all X_a (real_normed_algebra(X_a) -> (all A_1 all B hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),hAPP(X_a,X_a,uminus_uminus(X_a),B))))) # label(fact_2038_mult_Ominus__right) # label(axiom) # label(non_clause).  [assumption].
7.49/7.53	2119 (all X_b all X_a (real_normed_vector(X_a) & real_algebra_1(X_a) -> (all G all A_3 hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co1399186613setsum(X_b,X_a),hAPP(fun(X_b,real),fun(X_b,X_a),hAPP(fun(real,X_a),fun(fun(X_b,real),fun(X_b,X_a)),combb(real,X_a,X_b),of_real(X_a)),G)),A_3) = hAPP(real,X_a,of_real(X_a),hAPP(fun(X_b,bool),real,hAPP(fun(X_b,real),fun(fun(X_b,bool),real),big_co1399186613setsum(X_b,real),G),A_3))))) # label(fact_4189_of__real_Osetsum) # label(axiom) # label(non_clause).  [assumption].
7.49/7.53	2120 (all X_b all X_a (topological_space(X_a) & real_algebra_1(X_b) & real_normed_vector(X_b) -> (all G all L all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(real,fun(filter(X_a),bool),hAPP(fun(X_a,real),fun(real,fun(filter(X_a),bool)),tendsto(X_a,real),G),L),hAPP(X_a,filter(X_a),at(X_a),A_2))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(fun(X_a,real),fun(X_a,X_b),hAPP(fun(real,X_b),fun(fun(X_a,real),fun(X_a,X_b)),combb(real,X_b,X_a),of_real(X_b)),G)),hAPP(real,X_b,of_real(X_b),L)),hAPP(X_a,filter(X_a),at(X_a),A_2))))))) # label(fact_4595_LIM__of__real) # label(axiom) # label(non_clause).  [assumption].
7.56/7.53	2121 (all X_a (archim1727834104eiling(X_a) -> (all X_1 all V_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(int,X_a,number_number_of(X_a),V_1)),one_one(X_a)))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(X_a,int,archimedean_ceiling(X_a),X_1)),hAPP(int,int,number_number_of(int),V_1))))))) # label(fact_3311_ceiling__less__number__of) # label(axiom) # label(non_clause).  [assumption].
7.56/7.53	2122 (all X_a all C_2 all A_3 all B_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_3),B_2)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),B_2),C_2)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_3),C_2))))) # label(fact_1953_subset__trans) # label(axiom) # label(non_clause).  [assumption].
7.56/7.53	2123 (all Y all X (hBOOL(hAPP(int,bool,nat_is_nat,X)) -> (hBOOL(hAPP(int,bool,nat_is_nat,Y)) -> hBOOL(hAPP(int,bool,nat_is_nat,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X),Y)))))) # label(fact_4845_Nat__Transfer_Otransfer__int__nat__function__closures_I2_J) # label(axiom) # label(non_clause).  [assumption].
7.56/7.53	2124 (all P_1 (-hBOOL(hAPP(nat,bool,P_1,zero_zero(nat))) -> ((exists X1 hBOOL(hAPP(nat,bool,P_1,X1))) -> (exists N_2 (hBOOL(hAPP(nat,bool,P_1,hAPP(nat,nat,suc,N_2))) & -hBOOL(hAPP(nat,bool,P_1,N_2))))))) # label(fact_2738_exists__least__lemma) # label(axiom) # label(non_clause).  [assumption].
7.56/7.53	2125 (all X_a (number(X_a) & linorder(X_a) -> (all V_1 all W_1 (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(int,X_a,number_number_of(X_a),W_1)),hAPP(int,X_a,number_number_of(X_a),V_1))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(int,X_a,number_number_of(X_a),V_1)),hAPP(int,X_a,number_number_of(X_a),W_1))))))) # label(fact_50_le__number__of__eq__not__less) # label(axiom) # label(non_clause).  [assumption].
7.56/7.53	2126 (all A_1 hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,abs_abs(int),A_1)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(int,int,abs_abs(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) # label(fact_1981_abs__power2__distrib) # label(axiom) # label(non_clause).  [assumption].
7.56/7.53	2127 (all K_4 ((zero_zero(code_code_numeral) = K_4 -> zero_zero(int) = hAPP(code_code_numeral,int,code_int_of,K_4)) & (K_4 != zero_zero(code_code_numeral) -> (hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),K_4),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) != zero_zero(code_code_numeral) -> hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),hAPP(code_code_numeral,int,code_int_of,hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),K_4),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))),one_one(int)) = hAPP(code_code_numeral,int,code_int_of,K_4)) & (hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),K_4),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = zero_zero(code_code_numeral) -> hAPP(code_code_numeral,int,code_int_of,K_4) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),hAPP(code_code_numeral,int,code_int_of,hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),K_4),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))))) # label(fact_1202_Code__Numeral_Oint__of__code) # label(axiom) # label(non_clause).  [assumption].
7.56/7.53	2128 (all M one_one(int) = hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,M),one_one(int))) # label(fact_3433_zgcd__1) # label(axiom) # label(non_clause).  [assumption].
7.56/7.53	2129 (all X_a all X_b all X_c all X_d all X_e all Y -(all A_4 all B_4 all C_4 all D_3 all E hAPP(product_prod(X_b,product_prod(X_c,product_prod(X_d,X_e))),product_prod(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,X_e)))),hAPP(X_a,fun(product_prod(X_b,product_prod(X_c,product_prod(X_d,X_e))),product_prod(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,X_e))))),product_Pair(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,X_e)))),A_4),hAPP(product_prod(X_c,product_prod(X_d,X_e)),product_prod(X_b,product_prod(X_c,product_prod(X_d,X_e))),hAPP(X_b,fun(product_prod(X_c,product_prod(X_d,X_e)),product_prod(X_b,product_prod(X_c,product_prod(X_d,X_e)))),product_Pair(X_b,product_prod(X_c,product_prod(X_d,X_e))),B_4),hAPP(product_prod(X_d,X_e),product_prod(X_c,product_prod(X_d,X_e)),hAPP(X_c,fun(product_prod(X_d,X_e),product_prod(X_c,product_prod(X_d,X_e))),product_Pair(X_c,product_prod(X_d,X_e)),C_4),hAPP(X_e,product_prod(X_d,X_e),hAPP(X_d,fun(X_e,product_prod(X_d,X_e)),product_Pair(X_d,X_e),D_3),E)))) != ti(product_prod(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,X_e)))),Y))) # label(fact_3153_prod__cases5) # label(axiom) # label(non_clause).  [assumption].
7.56/7.53	2130 (all K all L (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),K),L)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),K)),hAPP(int,int,number_number_of(int),L))))) # label(fact_26_less__eq__number__of__int__code) # label(axiom) # label(non_clause).  [assumption].
7.56/7.53	2131 (all X_b all X_a all Q_1 all P_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),P_1))) -> ((all Y_2 (hBOOL(hAPP(X_a,bool,P_1,Y_2)) -> hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(X_a,fun(X_b,bool),hAPP(fun(X_b,fun(X_a,bool)),fun(X_a,fun(X_b,bool)),combc(X_b,X_a,bool),Q_1),Y_2)))))) <-> hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(fun(X_b,fun(X_a,bool)),fun(X_b,bool),hAPP(fun(fun(X_a,bool),bool),fun(fun(X_b,fun(X_a,bool)),fun(X_b,bool)),combb(fun(X_a,bool),bool,X_b),fEx(X_a)),hAPP(fun(X_b,fun(X_a,bool)),fun(X_b,fun(X_a,bool)),hAPP(fun(fun(X_a,bool),fun(X_a,bool)),fun(fun(X_b,fun(X_a,bool)),fun(X_b,fun(X_a,bool))),combb(fun(X_a,bool),fun(X_a,bool),X_b),hAPP(fun(X_a,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,bool)),combs(X_a,bool,bool),hAPP(fun(X_a,bool),fun(X_a,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,fun(bool,bool))),combb(bool,fun(bool,bool),X_a),fconj),P_1))),Q_1)))))))) # label(fact_4422_finite__Collect__bounded__ex) # label(axiom) # label(non_clause).  [assumption].
7.56/7.53	2132 (all X_a all A_3 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_3)) -> hAPP(fun(fun(X_a,bool),bool),nat,finite_card(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),pow(X_a),A_3)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat)))),hAPP(fun(X_a,bool),nat,finite_card(X_a),A_3)))) # label(fact_2773_card__Pow) # label(axiom) # label(non_clause).  [assumption].
7.56/7.53	2133 (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_390_zero__less__mult__pos2) # label(axiom) # label(non_clause).  [assumption].
7.56/7.54	2134 (all K (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),K),min_1)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit0,K)),min_1)))) # label(fact_304_rel__simps_I28_J) # label(axiom) # label(non_clause).  [assumption].
7.56/7.54	2135 (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))) -> zero_zero(X_a) = hAPP(nat,X_a,semiring_1_of_nat(X_a),hAPP(int,nat,number_number_of(nat),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)))))) # label(fact_1446_of__nat__number__of__lemma) # label(axiom) # label(non_clause).  [assumption].
7.56/7.54	2136 (all X_a (semiring_1(X_a) -> hBOOL(hAPP(X_a,bool,iszero(X_a),zero_zero(X_a))))) # label(fact_2554_iszero__0) # label(axiom) # label(non_clause).  [assumption].
7.56/7.54	2137 (all X_b all X_a (order(X_a) & order(X_b) -> (all C_1 all F all B_1 all A_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_1),A_2)) -> (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),C_1),hAPP(X_a,X_b,F,B_1))) -> ((all X_2 all Y_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y_2),X_2)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_a,X_b,F,Y_2)),hAPP(X_a,X_b,F,X_2))))) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),C_1),hAPP(X_a,X_b,F,A_2))))))))) # label(fact_2827_xt5) # label(axiom) # label(non_clause).  [assumption].
7.56/7.54	2138 (all M hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,M),zero_zero(int)),M))) # label(fact_352_zcong__id) # label(axiom) # label(non_clause).  [assumption].
7.56/7.54	2139 (all A_2 all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),X_1)) -> hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),hAPP(real,fun(real,real),inverse_divide(real),A_2)),hAPP(real,fun(nat,real),power_power(real),X_1))),zero_zero(real)),sequentially)))) # label(fact_4486_LIMSEQ__divide__realpow__zero) # label(axiom) # label(non_clause).  [assumption].
7.56/7.54	2140 (all A_2 all B_1 ((all D_3 (one_one(nat) = D_3 <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),D_3),B_1)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),D_3),A_2)))) <-> hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),A_2),B_1) = one_one(nat))) # label(fact_3265_coprime__nat) # label(axiom) # label(non_clause).  [assumption].
7.56/7.54	2141 (all N all M hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),M)) = zero_zero(nat)) # label(fact_682_diff__add__0) # label(axiom) # label(non_clause).  [assumption].
7.56/7.54	2142 (all K all L (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),K),L)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,pred,K)),L)))) # label(fact_2902_le__iff__pred__less) # label(axiom) # label(non_clause).  [assumption].
7.56/7.54	2143 (all P_5 (hBOOL(hAPP(int,bool,zprime,P_5)) -> (hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))) != ti(int,P_5) -> (hAPP(int,int,number_number_of(int),hAPP(int,int,bit1,hAPP(int,int,bit1,pls))) != ti(int,P_5) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit1,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),P_5)))))) # label(fact_274_prime__g__5) # label(axiom) # label(non_clause).  [assumption].
7.56/7.54	2144 (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_367_mult__mono) # label(axiom) # label(non_clause).  [assumption].
7.56/7.54	2145 (all K_4 hAPP(int,int,pred,hAPP(int,int,bit1,K_4)) = hAPP(int,int,bit0,K_4)) # label(fact_2900_pred__Bit1) # label(axiom) # label(non_clause).  [assumption].
7.56/7.54	2146 (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_67_plus__numeral__code_I9_J) # label(axiom) # label(non_clause).  [assumption].
7.56/7.54	2147 (all X_a (semiring_1(X_a) -> (all Inc all N_1 all I hAPP(X_a,X_a,hAPP(nat,fun(X_a,X_a),hAPP(fun(X_a,X_a),fun(nat,fun(X_a,X_a)),semiri532925092at_aux(X_a),Inc),hAPP(nat,nat,suc,N_1)),I) = hAPP(X_a,X_a,hAPP(nat,fun(X_a,X_a),hAPP(fun(X_a,X_a),fun(nat,fun(X_a,X_a)),semiri532925092at_aux(X_a),Inc),N_1),hAPP(X_a,X_a,Inc,I))))) # label(fact_4161_of__nat__aux_Osimps_I2_J) # label(axiom) # label(non_clause).  [assumption].
7.56/7.54	2148 (all R_4 all A_1 hAPP(real,real,abs_abs(real),R_4) = hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(real,complex,of_real(complex),R_4)),hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,hAPP(real,real,cos,A_1)),hAPP(real,real,sin,A_1))))) # label(fact_2816_cmod__complex__polar) # label(axiom) # label(non_clause).  [assumption].
7.56/7.54	2149 (all X_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),X_1),one_one(int))) <-> one_one(int) = hAPP(int,int,abs_abs(int),X_1))) # label(fact_1931_zdvd1__eq) # label(axiom) # label(non_clause).  [assumption].
7.56/7.54	2150 (all X_1 (hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),X_1),field_char_0_Rats(real))) -> -(all M_2 all N_2 (zero_zero(nat) != N_2 -> (hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(nat,real,real_1(nat),M_2)),hAPP(nat,real,real_1(nat),N_2)) = hAPP(real,real,abs_abs(real),X_1) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),M_2),N_2) != one_one(nat)))))) # label(fact_3679_Rats__abs__nat__div__natE) # label(axiom) # label(non_clause).  [assumption].
7.56/7.54	2151 (all B all A_1 (zero_zero(int) != ti(int,A_1) | ti(int,B) != zero_zero(int) -> hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_1),hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),A_1),B))),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),B),hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),A_1),B))) = one_one(int))) # label(fact_4390_div__gcd__coprime__int) # label(axiom) # label(non_clause).  [assumption].
7.56/7.54	2152 (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_1868_abs__triangle__ineq3) # label(axiom) # label(non_clause).  [assumption].
7.56/7.54	2153 (all X_a (linorder(X_a) -> (all B all D all A_1 all C (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),C)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),D)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),A_1),B)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),C),D)))))))) # label(fact_4976_min__max_Osup__mono) # label(axiom) # label(non_clause).  [assumption].
7.56/7.54	2154 (all X hAPP(real,real,cos,X) = hAPP(real,real,cos,hAPP(real,real,uminus_uminus(real),X))) # label(fact_2198_cos__minus) # label(axiom) # label(non_clause).  [assumption].
7.56/7.54	2155 (all B all A_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),B)) -> hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_1),B) = hAPP(product_prod(int,int),int,product_fst(int,int),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),posDivAlg,A_1),B))))) # label(fact_3109_div__pos__pos) # label(axiom) # label(non_clause).  [assumption].
7.56/7.54	2156 (all X_a (group_add(X_a) -> (all A_1 zero_zero(X_a) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_1),A_1)))) # label(fact_795_diff__self) # label(axiom) # label(non_clause).  [assumption].
7.56/7.54	2157 (all X_a all X_b (comm_monoid_mult(X_b) -> (all B_1 all A_2 all S (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),S)) -> (-hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_2),S)) -> hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co302546470etprod(X_a,X_b),hAPP(X_b,fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(X_b,fun(X_a,X_b)),combc(X_a,X_b,X_b),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,X_b)),hAPP(fun(X_a,fun(X_b,fun(X_b,X_b))),fun(fun(X_a,X_b),fun(X_a,fun(X_b,X_b))),combs(X_a,X_b,fun(X_b,X_b)),hAPP(fun(X_a,bool),fun(X_a,fun(X_b,fun(X_b,X_b))),hAPP(fun(bool,fun(X_b,fun(X_b,X_b))),fun(fun(X_a,bool),fun(X_a,fun(X_b,fun(X_b,X_b)))),combb(bool,fun(X_b,fun(X_b,X_b)),X_a),if(X_b)),hAPP(X_a,fun(X_a,bool),fequal(X_a),A_2))),B_1)),one_one(X_b))),S) = one_one(X_b)) & (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_2),S)) -> hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co302546470etprod(X_a,X_b),hAPP(X_b,fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(X_b,fun(X_a,X_b)),combc(X_a,X_b,X_b),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,X_b)),hAPP(fun(X_a,fun(X_b,fun(X_b,X_b))),fun(fun(X_a,X_b),fun(X_a,fun(X_b,X_b))),combs(X_a,X_b,fun(X_b,X_b)),hAPP(fun(X_a,bool),fun(X_a,fun(X_b,fun(X_b,X_b))),hAPP(fun(bool,fun(X_b,fun(X_b,X_b))),fun(fun(X_a,bool),fun(X_a,fun(X_b,fun(X_b,X_b)))),combb(bool,fun(X_b,fun(X_b,X_b)),X_a),if(X_b)),hAPP(X_a,fun(X_a,bool),fequal(X_a),A_2))),B_1)),one_one(X_b))),S) = hAPP(X_a,X_b,B_1,A_2)))))) # label(fact_3955_setprod__delta_H) # label(axiom) # label(non_clause).  [assumption].
7.56/7.54	2158 (all X_a (real_normed_vector(X_a) -> (all X_3 all K_3 ((all N_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),hAPP(nat,X_a,X_3,N_2))),K_3))) -> hBOOL(hAPP(fun(nat,X_a),bool,bseq(X_a),X_3)))))) # label(fact_3500_BseqI_H) # label(axiom) # label(non_clause).  [assumption].
7.56/7.54	2159 (all X_a (real_normed_field(X_a) -> (all Y_3 all X_3 (hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),X_3)) -> (hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),Y_3)) -> hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),plus_plus(X_a)),X_3)),Y_3)))))))) # label(fact_4011_summable__add) # label(axiom) # label(non_clause).  [assumption].
7.56/7.54	2160 (all X_a (real_normed_field(X_a) -> (all N all Z_1 all K_5 all H_2 (zero_zero(X_a) != ti(X_a,H_2) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),Z_1)),K_5)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Z_1),H_2))),K_5)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Z_1),H_2)),N)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),Z_1),N))),H_2)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),N)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),Z_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),hAPP(nat,nat,suc,zero_zero(nat)))))))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,semiring_1_of_nat(real),N)),hAPP(nat,real,semiring_1_of_nat(real),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),hAPP(nat,nat,suc,zero_zero(nat)))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),K_5),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))),hAPP(X_a,real,norm_norm(X_a),H_2)))))))))) # label(fact_1773_lemma__termdiff3) # label(axiom) # label(non_clause).  [assumption].
7.56/7.54	2161 (all M all P_5 (hBOOL(hAPP(nat,bool,prime,P_5)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),P_5),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),M),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),P_5),M))))) # label(fact_3044_prime__dvd__power__two) # label(axiom) # label(non_clause).  [assumption].
7.56/7.54	2162 (all X_a (ring_1(X_a) -> (all F all N_1 all R_1 hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),hAPP(X_a,fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(X_a,fun(nat,X_a)),combc(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),minus_minus(X_a)),F)),R_1)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),N_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),N_1))),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),N_1)),R_1))))) # label(fact_4172_sumr__diff__mult__const2) # label(axiom) # label(non_clause).  [assumption].
7.56/7.54	2163 (all X_a (semiring_div(X_a) -> div_div(X_a) = ti(fun(X_a,fun(X_a,X_a)),div_div(X_a)))) # label(tsy_c_Divides_Odiv__class_Odiv_res) # label(axiom) # label(non_clause).  [assumption].
7.56/7.54	2164 (all X_a (archim1727834104eiling(X_a) -> (all X_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),hAPP(X_a,int,archim2085082626_floor(X_a),X_1))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),one_one(X_a)),X_1)))))) # label(fact_2884_one__le__floor) # label(axiom) # label(non_clause).  [assumption].
7.56/7.54	2165 (all I all M_1 (hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),zero_zero(nat)),M_1)) -> zero_zero(nat) != 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_1))),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),hAPP(nat,nat,suc,I))))))) # label(fact_3874_card__less) # label(axiom) # label(non_clause).  [assumption].
7.56/7.54	2166 (all X_1 (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),zEven)) -> -(all K_1 ti(int,X_1) != hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),K_1)))) # label(fact_1477_zEvenE) # label(axiom) # label(non_clause).  [assumption].
7.56/7.54	2167 (all X all Y (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),X),Y)) -> hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),X),Y) = hAPP(int,int,abs_abs(int),X))) # label(fact_4378_gcd__proj1__if__dvd__int) # label(axiom) # label(non_clause).  [assumption].
7.56/7.54	2168 (all M all N all K_4 (one_one(int) = hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,N),K_4) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),K_4),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),M),N))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),M)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),K_4),M)))))) # label(fact_3472_zrelprime__zdvd__zmult__aux) # label(axiom) # label(non_clause).  [assumption].
7.56/7.54	2169 (all X_b all X_a (topological_space(X_b) & real_normed_vector(X_a) -> (all K all F all L_2 all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),L_2),hAPP(X_a,filter(X_a),at(X_a),A_2))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(fun(X_a,X_a),fun(X_a,X_b),hAPP(fun(X_a,X_b),fun(fun(X_a,X_a),fun(X_a,X_b)),combb(X_a,X_b,X_a),F),hAPP(X_a,fun(X_a,X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(X_a,X_a)),combc(X_a,X_a,X_a),plus_plus(X_a)),K))),L_2),hAPP(X_a,filter(X_a),at(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_2),K)))))))) # label(fact_4585_LIM__offset) # label(axiom) # label(non_clause).  [assumption].
7.56/7.54	2170 (all X_a all F1 all F2 ti(X_a,F1) = hAPP(nat,X_a,hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(X_a,fun(fun(nat,X_a),fun(nat,X_a)),nat_case(X_a),F1),F2),zero_zero(nat))) # label(fact_4112_nat__case__0) # label(axiom) # label(non_clause).  [assumption].
7.56/7.54	2171 (all N all X hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,exp(real),X)),N) = hAPP(real,real,exp(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,real_1(nat),N)),X))) # label(fact_2599_exp__real__of__nat__mult) # label(axiom) # label(non_clause).  [assumption].
7.56/7.54	2172 (all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),X_1)),one_one(real))) -> hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),min_1)))),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),hAPP(real,fun(real,real),inverse_divide(real),one_one(real))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),hAPP(fun(nat,nat),fun(nat,fun(nat,nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,nat),fun(nat,fun(nat,nat))),combb(nat,fun(nat,nat),nat),plus_plus(nat)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),times_times(nat)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),one_one(nat)))))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),hAPP(real,fun(nat,real),power_power(real),X_1)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),hAPP(fun(nat,nat),fun(nat,fun(nat,nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,nat),fun(nat,fun(nat,nat))),combb(nat,fun(nat,nat),nat),plus_plus(nat)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),times_times(nat)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),one_one(nat))))))))) # label(fact_3979_summable__arctan__series) # label(axiom) # label(non_clause).  [assumption].
7.56/7.54	2173 (all X all A_1 all B hAPP(real,real,hAPP(real,fun(real,real),powr,X),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A_1),B)) = hAPP(real,real,hAPP(real,fun(real,real),powr,hAPP(real,real,hAPP(real,fun(real,real),powr,X),A_1)),B)) # label(fact_3326_powr__powr) # label(axiom) # label(non_clause).  [assumption].
7.56/7.54	2174 (all X all Y hAPP(complex,real,re,hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),X),Y)) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(complex,real,re,X)),hAPP(complex,real,re,Y))) # label(fact_3002_Re_Oadd) # label(axiom) # label(non_clause).  [assumption].
7.56/7.54	2175 (all X_a (order(X_a) -> (all A_2 all B_1 all C_1 all D_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastAtMost(X_a),A_2),B_1)),hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastAtMost(X_a),C_1),D_1))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_1),D_1)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C_1),A_2)) | -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),B_1)))))) # label(fact_4524_atLeastatMost__subset__iff) # label(axiom) # label(non_clause).  [assumption].
7.56/7.54	2176 (all X_a (real_normed_field(X_a) -> (all N_1 all F all X_1 all D_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),F),X_1),D_2)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),hAPP(nat,fun(X_a,X_a),hAPP(fun(X_a,fun(nat,X_a)),fun(nat,fun(X_a,X_a)),combc(X_a,nat,X_a),hAPP(fun(X_a,X_a),fun(X_a,fun(nat,X_a)),hAPP(fun(X_a,fun(nat,X_a)),fun(fun(X_a,X_a),fun(X_a,fun(nat,X_a))),combb(X_a,fun(nat,X_a),X_a),power_power(X_a)),F)),hAPP(nat,nat,suc,N_1))),X_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),one_one(X_a)),hAPP(nat,X_a,semiring_1_of_nat(X_a),N_1))),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),D_2),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(X_a,X_a,F,X_1)),N_1))))))))) # label(fact_3887_DERIV__power__Suc) # label(axiom) # label(non_clause).  [assumption].
7.56/7.54	2177 (all Y all X all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),Y)) -> hAPP(real,real,hAPP(nat,fun(real,real),root,N),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),X),Y)) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(nat,fun(real,real),root,N),X)),hAPP(real,real,hAPP(nat,fun(real,real),root,N),Y)))))) # label(fact_2706_real__root__mult__lemma) # label(axiom) # label(non_clause).  [assumption].
7.56/7.54	2178 (all X_a (semiring_div(X_a) -> (all B all A_1 all C hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_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),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),A_1),B))),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),A_1),B))),C)))) # label(fact_916_div__mod__equality2) # label(axiom) # label(non_clause).  [assumption].
7.56/7.54	2179 (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_1413_Suc__pred_H) # label(axiom) # label(non_clause).  [assumption].
7.56/7.54	2180 (all N all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> hAPP(real,real,ln,hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),N)) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,real_1(nat),N)),hAPP(real,real,ln,X)))) # label(fact_2355_ln__realpow) # label(axiom) # label(non_clause).  [assumption].
7.56/7.54	2181 (all X_a all F all S (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),S)) -> ((all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),S)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(X_a,nat,F,X_2))))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(fun(X_a,bool),nat,hAPP(fun(X_a,nat),fun(fun(X_a,bool),nat),big_co302546470etprod(X_a,nat),F),S)))))) # label(fact_3963_setprod__pos__nat) # label(axiom) # label(non_clause).  [assumption].
7.56/7.54	2182 (all X_a (archim1727834104eiling(X_a) -> one_one(int) = hAPP(X_a,int,archim2085082626_floor(X_a),one_one(X_a)))) # label(fact_2870_floor__one) # label(axiom) # label(non_clause).  [assumption].
7.56/7.54	2183 (all X_a (ordered_ab_group_add(X_a) -> (all A_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),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,uminus_uminus(X_a),A_2))))))) # label(fact_2059_neg__0__le__iff__le) # label(axiom) # label(non_clause).  [assumption].
7.56/7.54	2184 (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_1862_abs__ge__zero) # label(axiom) # label(non_clause).  [assumption].
7.56/7.54	2185 (all Y all X (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Y)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),hAPP(int,nat,nat_1,X)),hAPP(int,nat,nat_1,Y)) = hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),X),Y))))) # label(fact_4406_transfer__nat__int__gcd_I1_J) # label(axiom) # label(non_clause).  [assumption].
7.56/7.54	2186 (all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,abs_abs(real),X_1)),one_one(real))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(fun(real,fun(nat,real)),fun(real,real),hAPP(fun(fun(nat,real),real),fun(fun(real,fun(nat,real)),fun(real,real)),combb(fun(nat,real),real,real),suminf(real)),hAPP(fun(real,fun(nat,real)),fun(real,fun(nat,real)),hAPP(fun(fun(nat,real),fun(nat,real)),fun(fun(real,fun(nat,real)),fun(real,fun(nat,real))),combb(fun(nat,real),fun(nat,real),real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),min_1))))),hAPP(fun(real,fun(nat,real)),fun(real,fun(nat,real)),hAPP(fun(fun(nat,real),fun(nat,real)),fun(fun(real,fun(nat,real)),fun(real,fun(nat,real))),combb(fun(nat,real),fun(nat,real),real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),hAPP(real,fun(real,real),inverse_divide(real),one_one(real))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),hAPP(fun(nat,nat),fun(nat,fun(nat,nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,nat),fun(nat,fun(nat,nat))),combb(nat,fun(nat,nat),nat),plus_plus(nat)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),times_times(nat)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),one_one(nat))))))),hAPP(fun(nat,nat),fun(real,fun(nat,real)),hAPP(fun(real,fun(fun(nat,nat),fun(nat,real))),fun(fun(nat,nat),fun(real,fun(nat,real))),combc(real,fun(nat,nat),fun(nat,real)),hAPP(fun(real,fun(nat,real)),fun(real,fun(fun(nat,nat),fun(nat,real))),hAPP(fun(fun(nat,real),fun(fun(nat,nat),fun(nat,real))),fun(fun(real,fun(nat,real)),fun(real,fun(fun(nat,nat),fun(nat,real)))),combb(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),real),combb(nat,real,nat)),power_power(real))),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),hAPP(fun(nat,nat),fun(nat,fun(nat,nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,nat),fun(nat,fun(nat,nat))),combb(nat,fun(nat,nat),nat),plus_plus(nat)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),times_times(nat)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),one_one(nat))))))),X_1),hAPP(fun(nat,real),real,suminf(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),min_1)))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),hAPP(real,fun(nat,real),power_power(real),X_1)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),times_times(nat)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))))))) # label(fact_3967_DERIV__arctan__series) # label(axiom) # label(non_clause).  [assumption].
7.56/7.54	2187 (all X_a (real_normed_vector(X_a) -> (exists K_2 ((all A_4 all B_4 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_4),B_4))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,norm_norm(real),A_4)),hAPP(X_a,real,norm_norm(X_a),B_4))),K_2)))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),K_2)))))) # label(fact_4754_scaleR_Opos__bounded) # label(axiom) # label(non_clause).  [assumption].
7.56/7.54	2188 (all N_1 all Ma (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),Ma)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),Ma),N_1)) <-> ti(int,Ma) = hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,N_1),Ma)))) # label(fact_3457_zdvd__iff__zgcd) # label(axiom) # label(non_clause).  [assumption].
7.56/7.54	2189 (all X_a (linord1117847801e_zero(X_a) -> (all C all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C),zero_zero(X_a))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),C),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),C),B))))))))) # label(fact_1744_divide__left__mono__neg) # label(axiom) # label(non_clause).  [assumption].
7.56/7.54	2190 (all X_a all X_b (comm_monoid_mult(X_b) -> (all F all S all T_3 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),T_3)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),S),T_3)) -> ((all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),T_3),S))) -> one_one(X_b) = hAPP(X_a,X_b,F,X_2))) -> hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co302546470etprod(X_a,X_b),F),T_3) = hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co302546470etprod(X_a,X_b),F),S))))))) # label(fact_3961_setprod__mono__one__right) # label(axiom) # label(non_clause).  [assumption].
7.56/7.54	2191 (all X_a (field_char_0(X_a) -> (all B_1 all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_2),field_char_0_Rats(X_a))) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),B_1),field_char_0_Rats(X_a))) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_2),B_1)),field_char_0_Rats(X_a)))))))) # label(fact_3696_Rats__diff) # label(axiom) # label(non_clause).  [assumption].
7.56/7.54	2192 (all N_1 all K all Ma (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K),Ma)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K),N_1)) -> (hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),K) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),Ma),K) <-> N_1 = Ma)))) # label(fact_673_eq__diff__iff) # label(axiom) # label(non_clause).  [assumption].
7.56/7.54	2193 (all A_1 all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A_1)) -> (exists R_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),R_2)) & A_1 = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),R_2),N)))))) # label(fact_734_realpow__pos__nth) # label(axiom) # label(non_clause).  [assumption].
7.56/7.54	2194 (all A_2 all X_1 (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),zOdd)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X_1)) -> hAPP(int,int,uminus_uminus(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A_2),hAPP(int,nat,nat_1,X_1))) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,uminus_uminus(int),A_2)),hAPP(int,nat,nat_1,X_1))))) # label(fact_2182_neg__odd__power) # label(axiom) # label(non_clause).  [assumption].
7.56/7.54	2195 (all X_a (linordered_idom(X_a) -> (all Z (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(int,X_a,ring_1_of_int(X_a),Z))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),Z)))))) # label(fact_3600_of__int__0__less__iff) # label(axiom) # label(non_clause).  [assumption].
7.56/7.54	2196 (all N hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),one_one(real)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),N)))) # label(fact_614_two__realpow__ge__one) # label(axiom) # label(non_clause).  [assumption].
7.56/7.54	2197 (all K_4 hAPP(nat,rat,semiring_1_of_nat(rat),K_4) = hAPP(int,rat,hAPP(int,fun(int,rat),fract,hAPP(nat,int,semiring_1_of_nat(int),K_4)),one_one(int))) # label(fact_3742_of__nat__rat) # label(axiom) # label(non_clause).  [assumption].
7.56/7.54	2198 (all N_1 hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),hAPP(nat,real,real_1(nat),N_1)),ring_1_Ints(real)))) # label(fact_3852_Ints__real__of__nat) # label(axiom) # label(non_clause).  [assumption].
7.56/7.54	2199 (all X_a (real_normed_field(X_a) -> (all G all E_3 all F all X_1 all D_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),F),X_1),D_2)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),G),hAPP(X_a,X_a,F,X_1)),E_3)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),hAPP(fun(X_a,X_a),fun(X_a,X_a),hAPP(fun(X_a,X_a),fun(fun(X_a,X_a),fun(X_a,X_a)),combb(X_a,X_a,X_a),G),F)),X_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),E_3),D_2)))))))) # label(fact_3862_DERIV__chain_H) # label(axiom) # label(non_clause).  [assumption].
7.56/7.54	2200 (all A_2 all P_4 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_2),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),P_4),one_one(int))),P_4)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_2),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),P_4),one_one(int)))),one_one(int)),P_4)))) # label(fact_513_inv__not__p__minus__1__aux) # label(axiom) # label(non_clause).  [assumption].
7.56/7.54	2201 (all N_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,real_1(nat),N_1)),zero_zero(real))) <-> N_1 = zero_zero(nat))) # label(fact_2315_real__of__nat__le__zero__cancel__iff) # label(axiom) # label(non_clause).  [assumption].
7.56/7.54	2202 (all X_a (semiring_div(X_a) -> (all A_1 zero_zero(X_a) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),A_1),one_one(X_a))))) # label(fact_975_mod__by__1) # label(axiom) # label(non_clause).  [assumption].
7.56/7.54	2203 (all X_b all X_a (comm_monoid_mult(X_a) & ring_1(X_a) -> (all F all A_3 hAPP(int,X_a,ring_1_of_int(X_a),hAPP(fun(X_b,bool),int,hAPP(fun(X_b,int),fun(fun(X_b,bool),int),big_co302546470etprod(X_b,int),F),A_3)) = hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co302546470etprod(X_b,X_a),hAPP(fun(X_b,int),fun(X_b,X_a),hAPP(fun(int,X_a),fun(fun(X_b,int),fun(X_b,X_a)),combb(int,X_a,X_b),ring_1_of_int(X_a)),F)),A_3)))) # label(fact_3929_of__int__setprod) # label(axiom) # label(non_clause).  [assumption].
7.56/7.54	2204 (all X_a (real_normed_algebra(X_a) -> (exists K_2 ((all A_4 all B_4 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_4),B_4))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(X_a,real,norm_norm(X_a),A_4)),hAPP(X_a,real,norm_norm(X_a),B_4))),K_2)))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),K_2)))))) # label(fact_1807_mult_Ononneg__bounded) # label(axiom) # label(non_clause).  [assumption].
7.56/7.54	2205 (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),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))))) # label(fact_2952_mult__left__idem) # label(axiom) # label(non_clause).  [assumption].
7.56/7.54	2206 (all K_4 all I_1 all J_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),J_2)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_1),K_4)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J_2),K_4))))) # label(fact_559_add__less__mono1) # label(axiom) # label(non_clause).  [assumption].
7.56/7.54	2207 (all X_a (real_normed_algebra(X_a) -> (all Y_1 all X_3 all A_2 (hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),X_3),A_2),sequentially)) -> hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),hAPP(X_a,fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(X_a,fun(nat,X_a)),combc(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),times_times(X_a)),X_3)),Y_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),Y_1)),sequentially)))))) # label(fact_4478_mult__left_OLIMSEQ) # label(axiom) # label(non_clause).  [assumption].
7.56/7.54	2208 (all X_a (real_normed_field(X_a) -> (all Y_1 all X_3 (hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),X_3)) -> hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),hAPP(X_a,fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(X_a,fun(nat,X_a)),combc(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),inverse_divide(X_a)),X_3)),Y_1))))))) # label(fact_4008_divide_Osummable) # label(axiom) # label(non_clause).  [assumption].
7.56/7.54	2209 (all X_a all X_b in_rel(X_a,X_b) = ti(fun(fun(product_prod(X_a,X_b),bool),fun(X_a,fun(X_b,bool))),in_rel(X_a,X_b))) # label(tsy_c_FunDef_Oin__rel_res) # label(axiom) # label(non_clause).  [assumption].
7.56/7.54	2210 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,sqrt,X))))) # label(fact_1625_real__sqrt__gt__zero) # label(axiom) # label(non_clause).  [assumption].
7.56/7.54	2211 (all X_a (number_ring(X_a) -> (all Z_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,bit0,hAPP(int,int,bit1,pls)))),Z_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Z_1),Z_1)))) # label(fact_140_mult__2) # label(axiom) # label(non_clause).  [assumption].
7.56/7.54	2212 (all N_1 hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),hAPP(nat,real,real_1(nat),N_1)),field_char_0_Rats(real)))) # label(fact_3682_Rats__real__nat) # label(axiom) # label(non_clause).  [assumption].
7.56/7.54	2213 (all X_a (real_algebra_1(X_a) & real_normed_vector(X_a) -> (all X all Y hAPP(real,X_a,of_real(X_a),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),X),Y)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(real,X_a,of_real(X_a),X)),hAPP(real,X_a,of_real(X_a),Y))))) # label(fact_2794_of__real_Odiff) # label(axiom) # label(non_clause).  [assumption].
7.56/7.54	2214 (all I_1 hAPP(quickcheck_code_int,nat,quickcheck_nat_of,I_1) = hAPP(int,nat,nat_1,hAPP(quickcheck_code_int,int,quickcheck_int_of,I_1))) # label(fact_3176_nat__of__def) # label(axiom) # label(non_clause).  [assumption].
7.56/7.54	2215 (all X_a (linordered_field(X_a) -> (all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,inverse_inverse(X_a),A_1)),zero_zero(X_a))) -> (zero_zero(X_a) != ti(X_a,A_1) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),zero_zero(X_a)))))))) # label(fact_2548_inverse__negative__imp__negative) # label(axiom) # label(non_clause).  [assumption].
7.56/7.54	2216 (all X_a (linordered_field(X_a) -> (all C all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),C),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),C),B))))))))) # label(fact_1716_divide__strict__left__mono) # label(axiom) # label(non_clause).  [assumption].
7.56/7.54	2217 (all L_4 hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),pls),hAPP(int,int,bit1,L_4)) = hAPP(int,int,bit1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),min_1),L_4))) # label(fact_510_diff__bin__simps_I4_J) # label(axiom) # label(non_clause).  [assumption].
7.56/7.54	2218 (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_1558_linorder__linear) # label(axiom) # label(non_clause).  [assumption].
7.56/7.54	2219 (all A_1 all B all C (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),C)) -> hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_1),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),C)) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_1),B)),C))),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_1),B)))) # label(fact_976_zmod__zmult2__eq) # label(axiom) # label(non_clause).  [assumption].
7.56/7.54	2220 (all X_3 ((all R_2 exists N_3 all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_3),N_2)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),R_2),hAPP(nat,real,X_3,N_2))))) -> hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),inverse_inverse(real)),X_3)),zero_zero(real)),sequentially)))) # label(fact_4660_LIMSEQ__inverse__zero) # label(axiom) # label(non_clause).  [assumption].
7.56/7.54	2221 (all X_a (comm_monoid_add(X_a) -> (all F all N_1 all Ma ((hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,N_1)),Ma)) -> zero_zero(X_a) = hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),Ma),hAPP(nat,nat,suc,N_1)))) & (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,N_1)),Ma)) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(nat,X_a,F,Ma)),hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),hAPP(fun(nat,nat),fun(nat,X_a),hAPP(fun(nat,X_a),fun(fun(nat,nat),fun(nat,X_a)),combb(nat,X_a,nat),F),suc)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),Ma),N_1))) = hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),Ma),hAPP(nat,nat,suc,N_1)))))))) # label(fact_4606_setsum__cl__ivl__Suc2) # label(axiom) # label(non_clause).  [assumption].
7.56/7.54	2222 (all M all V (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),V)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,M)),hAPP(int,nat,number_number_of(nat),V)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),hAPP(int,nat,number_number_of(nat),hAPP(int,int,pred,V))))) # label(fact_2912_Suc__diff__number__of) # label(axiom) # label(non_clause).  [assumption].
7.56/7.54	2223 (all X_a all X_b (comm_monoid_mult(X_b) -> (all G all H all A_3 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_3)) -> ((all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_3)) -> hAPP(X_a,X_b,G,X_2) = hAPP(X_a,X_b,H,X_2))) -> hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co302546470etprod(X_a,X_b),G),A_3) = hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co302546470etprod(X_a,X_b),H),A_3)))))) # label(fact_4769_setprod_Ocong) # label(axiom) # label(non_clause).  [assumption].
7.56/7.54	2224 (all X_a (archim1727834104eiling(X_a) -> zero_zero(int) = hAPP(X_a,int,archimedean_ceiling(X_a),zero_zero(X_a)))) # label(fact_3279_ceiling__zero) # label(axiom) # label(non_clause).  [assumption].
7.56/7.54	2225 (all D all A_1 all B (one_one(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),D),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A_1),B)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),D),B) = one_one(nat))) # label(fact_3272_coprime__rmult__nat) # label(axiom) # label(non_clause).  [assumption].
7.56/7.54	2226 (all X_a (real_normed_field(X_a) -> (all F all X_1 all D_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),F),X_1),D_2)) <-> hBOOL(hAPP(filter(X_a),bool,hAPP(X_a,fun(filter(X_a),bool),hAPP(fun(X_a,X_a),fun(X_a,fun(filter(X_a),bool)),tendsto(X_a,X_a),hAPP(fun(X_a,X_a),fun(X_a,X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,X_a),fun(X_a,X_a)),combs(X_a,X_a,X_a),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,X_a),fun(X_a,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),X_a),inverse_divide(X_a)),hAPP(X_a,fun(X_a,X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(X_a,X_a)),combc(X_a,X_a,X_a),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,X_a),fun(X_a,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),X_a),minus_minus(X_a)),hAPP(fun(X_a,X_a),fun(X_a,X_a),hAPP(fun(X_a,X_a),fun(fun(X_a,X_a),fun(X_a,X_a)),combb(X_a,X_a,X_a),F),hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X_1)))),hAPP(X_a,X_a,F,X_1)))),combi(X_a))),D_2),hAPP(X_a,filter(X_a),at(X_a),zero_zero(X_a)))))))) # label(fact_4619_DERIV__iff) # label(axiom) # label(non_clause).  [assumption].
7.56/7.54	2227 (all Q_3 ((all A_4 all B_4 (hAPP(int,rat,hAPP(int,fun(int,rat),fract,A_4),B_4) = Q_3 -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B_4)) -> (ti(int,A_4) != zero_zero(int) -> hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),A_4),B_4) != one_one(int))))) -> zero_zero(rat) = Q_3)) # label(fact_4411_Rat__cases__nonzero) # label(axiom) # label(non_clause).  [assumption].
7.56/7.54	2228 (all M all I_1 all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),I_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),I_1)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),M),N)),I_1)) # label(fact_4804_min__diff) # label(axiom) # label(non_clause).  [assumption].
7.56/7.54	2229 (all X_a (real_normed_field(X_a) -> (all X_3 all A_2 (hBOOL(hAPP(X_a,bool,hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),X_3),A_2)) -> hBOOL(hAPP(X_a,bool,hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(X_a,X_a),fun(fun(nat,X_a),fun(nat,X_a)),combb(X_a,X_a,nat),uminus_uminus(X_a)),X_3)),hAPP(X_a,X_a,uminus_uminus(X_a),A_2))))))) # label(fact_4083_sums__minus) # label(axiom) # label(non_clause).  [assumption].
7.56/7.54	2230 (all R_4 all A_1 hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),R_4),A_1)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),R_4),R_4)) = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A_1),R_4)) # label(fact_1667_real__divide__square__eq) # label(axiom) # label(non_clause).  [assumption].
7.56/7.54	2231 (all X_a all X_b (real_normed_vector(X_b) -> (all X_1 all G all A_2 all A_3 (hBOOL(hAPP(filter(X_a),bool,hAPP(real,fun(filter(X_a),bool),hAPP(fun(X_a,real),fun(real,fun(filter(X_a),bool)),tendsto(X_a,real),G),A_2),A_3)) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(X_b,fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(X_b,fun(X_a,X_b)),combc(X_a,X_b,X_b),hAPP(fun(X_a,real),fun(X_a,fun(X_b,X_b)),hAPP(fun(real,fun(X_b,X_b)),fun(fun(X_a,real),fun(X_a,fun(X_b,X_b))),combb(real,fun(X_b,X_b),X_a),scaleR_scaleR(X_b)),G)),X_1)),hAPP(X_b,X_b,hAPP(real,fun(X_b,X_b),scaleR_scaleR(X_b),A_2),X_1)),A_3)))))) # label(fact_4727_scaleR__left_Otendsto) # label(axiom) # label(non_clause).  [assumption].
7.56/7.54	2232 (all Sa all Ta all A_2 all B_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A_2),B_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Sa),Ta)) -> hBOOL(hAPP(fun(product_prod(product_prod(nat,nat),product_prod(nat,nat)),bool),bool,hAPP(product_prod(product_prod(nat,nat),product_prod(nat,nat)),fun(fun(product_prod(product_prod(nat,nat),product_prod(nat,nat)),bool),bool),member(product_prod(product_prod(nat,nat),product_prod(nat,nat))),hAPP(product_prod(nat,nat),product_prod(product_prod(nat,nat),product_prod(nat,nat)),hAPP(product_prod(nat,nat),fun(product_prod(nat,nat),product_prod(product_prod(nat,nat),product_prod(nat,nat))),product_Pair(product_prod(nat,nat),product_prod(nat,nat)),hAPP(nat,product_prod(nat,nat),hAPP(nat,fun(nat,product_prod(nat,nat)),product_Pair(nat,nat),A_2),Sa)),hAPP(nat,product_prod(nat,nat),hAPP(nat,fun(nat,product_prod(nat,nat)),product_Pair(nat,nat),B_1),Ta))),pair_less))))) # label(fact_3485_pair__lessI2) # label(axiom) # label(non_clause).  [assumption].
7.56/7.54	2233 (all X_a (field(X_a) -> (all X all Y all Z_1 (zero_zero(X_a) != ti(X_a,Z_1) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),X),Z_1)),Y) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Z_1),Y))),Z_1))))) # label(fact_1721_divide__add__eq__iff) # label(axiom) # label(non_clause).  [assumption].
7.56/7.54	2234 (all X_1 hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less_eq(nat)),X_1))))) # label(fact_3827_bdd__nat__set__le__finite) # label(axiom) # label(non_clause).  [assumption].
7.56/7.54	2235 (all X_a (monoid_add(X_a) -> (all A_1 ti(X_a,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)))) # label(fact_778_add__0__left) # label(axiom) # label(non_clause).  [assumption].
7.56/7.54	2236 (all P_1 all N_1 all K ((zero_zero(int) = ti(int,K) -> hBOOL(hAPP(int,bool,P_1,N_1))) & (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),K)) -> (all I_2 all J_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),J_1)) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),J_1),K)) & ti(int,N_1) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K),I_2)),J_1) -> hBOOL(hAPP(int,bool,P_1,J_1))))) & (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),zero_zero(int))) -> (all I_2 all J_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),J_1)) & ti(int,N_1) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K),I_2)),J_1) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),J_1),zero_zero(int))) -> hBOOL(hAPP(int,bool,P_1,J_1))))) <-> hBOOL(hAPP(int,bool,P_1,hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),N_1),K))))) # label(fact_1061_split__zmod) # label(axiom) # label(non_clause).  [assumption].
7.56/7.54	2237 (all N all M all A_1 all B (hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),A_1),B) = one_one(nat) -> one_one(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A_1),N)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),B),M)))) # label(fact_3216_coprime__exp2__nat) # label(axiom) # label(non_clause).  [assumption].
7.56/7.54	2238 (all N_1 zero_zero(real) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),hAPP(bool,fun(real,fun(real,real)),if(real),hAPP(nat,bool,even_odd_even(nat),N_1)),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),min_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),hAPP(nat,nat,suc,zero_zero(nat)))),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),hAPP(nat,real,real_1(nat),hAPP(nat,nat,fact_fact(nat),N_1))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),zero_zero(real)),N_1))) # label(fact_2471_lemma__STAR__sin) # label(axiom) # label(non_clause).  [assumption].
7.56/7.54	2239 (all K_4 all L_4 hAPP(int,int,bit1,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),K_4),L_4)) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,bit0,K_4)),hAPP(int,int,bit1,L_4))) # label(fact_163_add__Bit0__Bit1) # label(axiom) # label(non_clause).  [assumption].
7.56/7.54	2240 (all X_3 (hBOOL(hAPP(fun(nat,complex),bool,summable(complex),X_3)) -> hBOOL(hAPP(fun(nat,complex),bool,summable(complex),hAPP(fun(nat,complex),fun(nat,complex),hAPP(fun(complex,complex),fun(fun(nat,complex),fun(nat,complex)),combb(complex,complex,nat),cnj),X_3))))) # label(fact_4045_cnj_Osummable) # label(axiom) # label(non_clause).  [assumption].
7.56/7.54	2241 (all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,number_number_of(real),min_1)),Y)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),Y),one_one(real))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),hAPP(real,real,arcsin,Y))) & hAPP(real,real,sin,hAPP(real,real,arcsin,Y)) = Y & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,arcsin,Y)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))))) # label(fact_2403_arcsin) # label(axiom) # label(non_clause).  [assumption].
7.56/7.54	2242 (all N all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,real_1(nat),N)),X)),one_one(real))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),one_one(real))),N))))) # label(fact_2370_LIMSEQ__inverse__realpow__zero__lemma) # label(axiom) # label(non_clause).  [assumption].
7.56/7.54	2243 (all X_a all F all A_3 hAPP(int,real,real_1(int),hAPP(fun(X_a,bool),int,hAPP(fun(X_a,int),fun(fun(X_a,bool),int),big_co302546470etprod(X_a,int),F),A_3)) = hAPP(fun(X_a,bool),real,hAPP(fun(X_a,real),fun(fun(X_a,bool),real),big_co302546470etprod(X_a,real),hAPP(fun(X_a,int),fun(X_a,real),hAPP(fun(int,real),fun(fun(X_a,int),fun(X_a,real)),combb(int,real,X_a),real_1(int)),F)),A_3)) # label(fact_3940_real__of__int__setprod) # label(axiom) # label(non_clause).  [assumption].
7.56/7.54	2244 (all X_a (archim1727834104eiling(X_a) -> (all X_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),zero_zero(X_a))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(X_a,int,archimedean_ceiling(X_a),X_1)),zero_zero(int))))))) # label(fact_3298_ceiling__le__zero) # label(axiom) # label(non_clause).  [assumption].
7.56/7.54	2245 (all X_b all X_a all F all A_3 (-hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_3)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),A_3))) -> (exists X_2 (-hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,bool)),combs(X_a,bool,bool),hAPP(fun(X_a,bool),fun(X_a,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,fun(bool,bool))),combb(bool,fun(bool,bool),X_a),fconj),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(X_a,bool)),combc(X_a,fun(X_a,bool),bool),member(X_a)),A_3))),hAPP(X_b,fun(X_a,bool),hAPP(fun(X_a,fun(X_b,bool)),fun(X_b,fun(X_a,bool)),combc(X_a,X_b,bool),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,bool)),hAPP(fun(X_b,fun(X_b,bool)),fun(fun(X_a,X_b),fun(X_a,fun(X_b,bool))),combb(X_b,fun(X_b,bool),X_a),fequal(X_b)),F)),hAPP(X_a,X_b,F,X_2)))))) & hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_3))))))) # label(fact_4331_pigeonhole__infinite) # label(axiom) # label(non_clause).  [assumption].
7.56/7.54	2246 (all X_a (ring_1(X_a) -> (all C_1 all X_2 hAPP(nat,X_a,hAPP(fun(nat,X_a),fun(nat,X_a),diffs(X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(X_a,X_a),fun(fun(nat,X_a),fun(nat,X_a)),combb(X_a,X_a,nat),uminus_uminus(X_a)),C_1)),X_2) = hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(nat,X_a,hAPP(fun(nat,X_a),fun(nat,X_a),diffs(X_a),C_1),X_2))))) # label(fact_4113_diffs__minus) # label(axiom) # label(non_clause).  [assumption].
7.56/7.54	2247 (all X_a (archim1804426504_field(X_a) -> (all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),X)) -> (exists N_2 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,inverse_inverse(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),hAPP(nat,nat,suc,N_2)))),X))))))) # label(fact_2723_ex__inverse__of__nat__Suc__less) # label(axiom) # label(non_clause).  [assumption].
7.56/7.54	2248 (all X_a (banach(X_a) -> (all F all G ((exists N_3 all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_3),N_2)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),hAPP(nat,X_a,F,N_2))),hAPP(nat,real,G,N_2))))) -> (hBOOL(hAPP(fun(nat,real),bool,summable(real),G)) -> hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,X_a),fun(nat,real),hAPP(fun(X_a,real),fun(fun(nat,X_a),fun(nat,real)),combb(X_a,real,nat),norm_norm(X_a)),F)))))))) # label(fact_4017_summable__norm__comparison__test) # label(axiom) # label(non_clause).  [assumption].
7.56/7.54	2249 (all Ma (one_one(int) = hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,zero_zero(int)),Ma) <-> hAPP(int,int,abs_abs(int),Ma) = one_one(int))) # label(fact_3464_zgcd__0__1__iff) # label(axiom) # label(non_clause).  [assumption].
7.56/7.54	2250 (all X_a (topological_space(X_a) -> (all K hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),hAPP(X_a,fun(nat,X_a),combk(X_a,nat),K)),K),sequentially))))) # label(fact_4464_LIMSEQ__const) # label(axiom) # label(non_clause).  [assumption].
7.56/7.54	2251 (all X_a (field(X_a) -> (all X_1 all W_1 all Z all Y_1 (zero_zero(X_a) != ti(X_a,Y_1) -> (ti(X_a,Z) != zero_zero(X_a) -> (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),X_1),Y_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),W_1),Z) <-> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X_1),Z) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),W_1),Y_1))))))) # label(fact_1691_frac__eq__eq) # label(axiom) # label(non_clause).  [assumption].
7.56/7.54	2252 (all X_a (linordered_idom(X_a) -> (all X all Y hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),Y),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))))) # label(fact_107_sum__power2__ge__zero) # label(axiom) # label(non_clause).  [assumption].
7.56/7.54	2253 (all X_a (ordered_ab_group_add(X_a) -> (all A_2 all B_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_1),hAPP(X_a,X_a,uminus_uminus(X_a),A_2))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),hAPP(X_a,X_a,uminus_uminus(X_a),B_1))))))) # label(fact_2014_less__minus__iff) # label(axiom) # label(non_clause).  [assumption].
7.56/7.54	2254 (all F all X_1 all L (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),F),X_1),L)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),L)) -> (exists D_3 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),D_3)) & (all H_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),H_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),H_1),D_3)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,F,X_1)),hAPP(real,real,F,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X_1),H_1)))))))))))) # label(fact_2665_DERIV__pos__inc__right) # label(axiom) # label(non_clause).  [assumption].
7.56/7.54	2255 (all Y_3 all Y_1 all X_3 all X_1 (hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),X_3),X_1),sequentially)) -> (hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),Y_3),Y_1),sequentially)) -> ((exists N_3 all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_3),N_2)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,X_3,N_2)),hAPP(nat,real,Y_3,N_2))))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_1),Y_1)))))) # label(fact_4431_LIMSEQ__le) # label(axiom) # label(non_clause).  [assumption].
7.56/7.54	2256 (all N_1 (hBOOL(hAPP(nat,bool,even_odd_even(nat),N_1)) <-> hBOOL(hAPP(nat,bool,even_odd_even(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),N_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))))) # label(fact_2468_even__even__mod__4__iff) # label(axiom) # label(non_clause).  [assumption].
7.56/7.54	2257 (all Y all X (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Y)) -> hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),nat_tsub,X),Y)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(int,nat,nat_1,X)),hAPP(int,nat,nat_1,Y))))) # label(fact_1199_Nat__Transfer_Otransfer__nat__int__functions_I3_J) # label(axiom) # label(non_clause).  [assumption].
7.56/7.54	2258 (all X_a (order(X_a) -> (all X_1 all Y_1 (ti(X_a,Y_1) = ti(X_a,X_1) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y_1)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),Y_1)))))) # label(fact_1587_order__le__less) # label(axiom) # label(non_clause).  [assumption].
7.56/7.54	2259 (all X_a (field_char_0(X_a) -> (all B_1 all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_2),field_char_0_Rats(X_a))) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),B_1),field_char_0_Rats(X_a))) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),B_1)),field_char_0_Rats(X_a)))))))) # label(fact_3692_Rats__mult) # label(axiom) # label(non_clause).  [assumption].
7.56/7.55	2260 (all X_a all A_3 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_3)) <-> (exists N_2 exists F_3 ti(fun(X_a,bool),A_3) = hAPP(fun(nat,bool),fun(X_a,bool),hAPP(fun(nat,X_a),fun(fun(nat,bool),fun(X_a,bool)),image(nat,X_a),F_3),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),N_2)))))) # label(fact_4127_finite__conv__nat__seg__image) # label(axiom) # label(non_clause).  [assumption].
7.56/7.55	2261 (all B all A_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A_1),zero_zero(int))) -> hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),B),one_one(int))),A_1))),one_one(int)) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),B))),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),A_1)))) # label(fact_900_neg__zmod__mult__2) # label(axiom) # label(non_clause).  [assumption].
7.56/7.55	2262 (all L all U_1 hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_gr676655987ssThan(int),L),U_1)))) # label(fact_3677_finite__greaterThanLessThan__int) # label(axiom) # label(non_clause).  [assumption].
7.56/7.55	2263 (all X all M hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,uminus_uminus(int),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),X),M))),M) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,uminus_uminus(int),X)),M)) # label(fact_2151_zminus__zmod) # label(axiom) # label(non_clause).  [assumption].
7.56/7.55	2264 (all W_1 (hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),W_1))) <-> hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,W_1)))))) # label(fact_1506_neg__number__of__Bit0) # label(axiom) # label(non_clause).  [assumption].
7.56/7.55	2265 (all A_1 all Y all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Y)) -> hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),powr,X),A_1)),hAPP(real,real,hAPP(real,fun(real,real),powr,Y),A_1)) = hAPP(real,real,hAPP(real,fun(real,real),powr,hAPP(real,real,hAPP(real,fun(real,real),times_times(real),X),Y)),A_1)))) # label(fact_3376_powr__mult) # label(axiom) # label(non_clause).  [assumption].
7.56/7.55	2266 (all R_4 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),R_4),zero_zero(real))) -> (exists N_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,real_1(int),N_2)),R_4)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),R_4),hAPP(int,real,real_1(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),N_2),one_one(int))))))))) # label(fact_3423_reals__Archimedean__6c__int) # label(axiom) # label(non_clause).  [assumption].
7.56/7.55	2267 (all X_a all X_b all P_4 hAPP(product_prod(X_a,X_b),X_a,product_fst(X_a,X_b),P_4) = hAPP(product_prod(X_a,X_b),X_a,hAPP(fun(X_a,fun(X_b,X_a)),fun(product_prod(X_a,X_b),X_a),product_prod_case(X_a,X_b,X_a),combk(X_a,X_b)),P_4)) # label(fact_4004_fst__def) # label(axiom) # label(non_clause).  [assumption].
7.57/7.55	2268 (all A_1 all B (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,A_1),B)) -> (B != one_one(nat) -> (exists X_2 exists Y_2 hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),Y_2)),one_one(nat)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A_1),X_2))))) # label(fact_2897_coprime__bezout__strong) # label(axiom) # label(non_clause).  [assumption].
7.57/7.55	2269 (all X hAPP(real,real,exp(real),X) = hAPP(real,real,abs_abs(real),hAPP(real,real,exp(real),X))) # label(fact_2532_abs__exp__cancel) # label(axiom) # label(non_clause).  [assumption].
7.57/7.55	2270 (all X_a (linorder(X_a) -> (all X_1 all Y_1 (ti(X_a,X_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X_1),Y_1) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),Y_1)))))) # label(fact_4827_min__max_Ole__iff__inf) # label(axiom) # label(non_clause).  [assumption].
7.57/7.55	2271 (all M all N all K_4 hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),M),N)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_4),N)))) # label(fact_3215_gcd__dvd__prod__nat) # label(axiom) # label(non_clause).  [assumption].
7.57/7.55	2272 (all X_a trivial_limit(X_a) = ti(fun(filter(X_a),bool),trivial_limit(X_a))) # label(tsy_c_Limits_Otrivial__limit_res) # label(axiom) # label(non_clause).  [assumption].
7.57/7.55	2273 (all X_a ti(fun(fun(X_a,fun(X_a,bool)),fun(X_a,bool)),accp(X_a)) = accp(X_a)) # label(tsy_c_Wellfounded_Oaccp_res) # label(axiom) # label(non_clause).  [assumption].
7.57/7.55	2274 (all X_b all X_a all B_2 all A_3 ((hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_3)) & hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),B_2)) -> hAPP(fun(sum_sum(X_a,X_b),bool),nat,finite_card(sum_sum(X_a,X_b)),hAPP(fun(X_b,bool),fun(sum_sum(X_a,X_b),bool),hAPP(fun(X_a,bool),fun(fun(X_b,bool),fun(sum_sum(X_a,X_b),bool)),sum_Plus(X_a,X_b),A_3),B_2)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(fun(X_a,bool),nat,finite_card(X_a),A_3)),hAPP(fun(X_b,bool),nat,finite_card(X_b),B_2))) & (-(hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_3)) & hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),B_2))) -> hAPP(fun(sum_sum(X_a,X_b),bool),nat,finite_card(sum_sum(X_a,X_b)),hAPP(fun(X_b,bool),fun(sum_sum(X_a,X_b),bool),hAPP(fun(X_a,bool),fun(fun(X_b,bool),fun(sum_sum(X_a,X_b),bool)),sum_Plus(X_a,X_b),A_3),B_2)) = zero_zero(nat)))) # label(fact_3180_card__Plus__conv__if) # label(axiom) # label(non_clause).  [assumption].
7.57/7.55	2275 (all E_1 all B all D all A_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),D),A_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),E_1),B)) -> (hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),A_1),B) = one_one(int) -> one_one(int) = hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),D),E_1))))) # label(fact_4358_coprime__divisors__nat) # label(axiom) # label(non_clause).  [assumption].
7.57/7.55	2276 (all N all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> hAPP(real,real,hAPP(nat,fun(real,real),root,hAPP(nat,nat,suc,N)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),hAPP(nat,nat,suc,N))) = X)) # label(fact_2703_real__root__pos) # label(axiom) # label(non_clause).  [assumption].
7.57/7.55	2277 (all X_a (ring_1(X_a) -> (all K ((zero_zero(int) = ti(int,K) -> hAPP(int,X_a,ring_1_of_int(X_a),K) = zero_zero(X_a)) & (zero_zero(int) != ti(int,K) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),zero_zero(int))) -> hAPP(int,X_a,ring_1_of_int(X_a),K) = hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(int,X_a,ring_1_of_int(X_a),hAPP(int,int,uminus_uminus(int),K)))) & (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),zero_zero(int))) -> hAPP(int,X_a,ring_1_of_int(X_a),K) = hAPP(product_prod(int,int),X_a,hAPP(fun(int,fun(int,X_a)),fun(product_prod(int,int),X_a),product_prod_case(int,int,X_a),hAPP(fun(int,X_a),fun(int,fun(int,X_a)),hAPP(fun(int,fun(X_a,fun(int,X_a))),fun(fun(int,X_a),fun(int,fun(int,X_a))),combs(int,X_a,fun(int,X_a)),hAPP(fun(int,fun(int,fun(X_a,X_a))),fun(int,fun(X_a,fun(int,X_a))),hAPP(fun(fun(int,fun(X_a,X_a)),fun(X_a,fun(int,X_a))),fun(fun(int,fun(int,fun(X_a,X_a))),fun(int,fun(X_a,fun(int,X_a)))),combb(fun(int,fun(X_a,X_a)),fun(X_a,fun(int,X_a)),int),combc(int,X_a,X_a)),hAPP(fun(int,X_a),fun(int,fun(int,fun(X_a,X_a))),hAPP(fun(X_a,fun(int,fun(X_a,X_a))),fun(fun(int,X_a),fun(int,fun(int,fun(X_a,X_a)))),combb(X_a,fun(int,fun(X_a,X_a)),int),hAPP(fun(int,fun(X_a,fun(X_a,X_a))),fun(X_a,fun(int,fun(X_a,X_a))),combc(int,X_a,fun(X_a,X_a)),hAPP(fun(int,bool),fun(int,fun(X_a,fun(X_a,X_a))),hAPP(fun(bool,fun(X_a,fun(X_a,X_a))),fun(fun(int,bool),fun(int,fun(X_a,fun(X_a,X_a)))),combb(bool,fun(X_a,fun(X_a,X_a)),int),if(X_a)),hAPP(int,fun(int,bool),hAPP(fun(int,fun(int,bool)),fun(int,fun(int,bool)),combc(int,int,bool),fequal(int)),zero_zero(int))))),hAPP(fun(int,X_a),fun(int,X_a),hAPP(fun(int,fun(X_a,X_a)),fun(fun(int,X_a),fun(int,X_a)),combs(int,X_a,X_a),hAPP(fun(int,X_a),fun(int,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(int,X_a),fun(int,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),int),plus_plus(X_a)),ring_1_of_int(X_a))),ring_1_of_int(X_a))))),hAPP(X_a,fun(int,X_a),hAPP(fun(int,fun(X_a,X_a)),fun(X_a,fun(int,X_a)),combc(int,X_a,X_a),hAPP(fun(int,X_a),fun(int,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(int,X_a),fun(int,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),int),plus_plus(X_a)),hAPP(fun(int,X_a),fun(int,X_a),hAPP(fun(int,fun(X_a,X_a)),fun(fun(int,X_a),fun(int,X_a)),combs(int,X_a,X_a),hAPP(fun(int,X_a),fun(int,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(int,X_a),fun(int,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),int),plus_plus(X_a)),ring_1_of_int(X_a))),ring_1_of_int(X_a)))),one_one(X_a)))),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),divmod_int,K),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))))))) # label(fact_3978_of__int__num) # label(axiom) # label(non_clause).  [assumption].
7.57/7.55	2278 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N)) -> zero_zero(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N))) # label(fact_683_diff__is__0__eq_H) # label(axiom) # label(non_clause).  [assumption].
7.57/7.55	2279 (all X_a (semiring_char_0(X_a) -> (all N zero_zero(X_a) != hAPP(nat,X_a,semiring_1_of_nat(X_a),hAPP(nat,nat,fact_fact(nat),N))))) # label(fact_2486_of__nat__fact__not__zero) # label(axiom) # label(non_clause).  [assumption].
7.57/7.55	2280 (all F all F_2 all A_2 all B_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A_2),B_1)) -> ((all X_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A_2),X_2)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_2),B_1)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),F),X_2),hAPP(real,real,F_2,X_2))))) -> (exists Z_2 (hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,F,B_1)),hAPP(real,real,F,A_2)) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),B_1),A_2)),hAPP(real,real,F_2,Z_2)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),Z_2),B_1)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A_2),Z_2))))))) # label(fact_2721_MVT2) # label(axiom) # label(non_clause).  [assumption].
7.57/7.55	2281 (all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),N),zero_zero(nat)) = N) # label(fact_4960_max__0R) # label(axiom) # label(non_clause).  [assumption].
7.57/7.55	2282 (all X_a (field_inverse_zero(X_a) & real_normed_field(X_a) -> (all A_1 all B hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),A_1),B)) = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(X_a,real,norm_norm(X_a),A_1)),hAPP(X_a,real,norm_norm(X_a),B))))) # label(fact_1783_norm__divide) # label(axiom) # label(non_clause).  [assumption].
7.57/7.55	2283 (all X_b all X_a (comm_monoid_add(X_a) -> (all F all G all A_3 hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co1399186613setsum(X_b,X_a),hAPP(fun(X_b,X_a),fun(X_b,X_a),hAPP(fun(X_b,fun(X_a,X_a)),fun(fun(X_b,X_a),fun(X_b,X_a)),combs(X_b,X_a,X_a),hAPP(fun(X_b,X_a),fun(X_b,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_b,X_a),fun(X_b,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),X_b),plus_plus(X_a)),F)),G)),A_3) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co1399186613setsum(X_b,X_a),F),A_3)),hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co1399186613setsum(X_b,X_a),G),A_3))))) # label(fact_4220_setsum__addf) # label(axiom) # label(non_clause).  [assumption].
7.57/7.55	2284 (all X_a (archim1727834104eiling(X_a) -> (all X hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(int,X_a,ring_1_of_int(X_a),hAPP(X_a,int,archim2085082626_floor(X_a),X))),X))))) # label(fact_3567_of__int__floor__le) # label(axiom) # label(non_clause).  [assumption].
7.57/7.55	2285 (all X_a (linorder(X_a) -> (all X_1 all Y_1 all Z (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y_1),Z)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Z)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X_1),Y_1)),Z)))))) # label(fact_4949_max__less__iff__conj) # label(axiom) # label(non_clause).  [assumption].
7.57/7.55	2286 (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_1858_abs__minus__commute) # label(axiom) # label(non_clause).  [assumption].
7.57/7.55	2287 (all A_3 all P_2 all P_1 all D_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D_2)) -> ((exists Z_2 all X_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Z_2),X_2)) -> (hBOOL(hAPP(int,bool,P_2,X_2)) <-> hBOOL(hAPP(int,bool,P_1,X_2))))) -> ((all X_2 ((all Xa (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xa),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastAtMost(int),one_one(int)),D_2))) -> (all Xb (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xb),A_3)) -> ti(int,X_2) != hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),Xb),Xa))))) -> (hBOOL(hAPP(int,bool,P_1,X_2)) -> hBOOL(hAPP(int,bool,P_1,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X_2),D_2)))))) -> ((all X_2 all K_1 (hBOOL(hAPP(int,bool,P_2,X_2)) <-> hBOOL(hAPP(int,bool,P_2,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X_2),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K_1),D_2)))))) -> ((exists X1 hBOOL(hAPP(int,bool,P_1,X1))) <-> (exists X_2 ((exists Xa (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xa),A_3)) & hBOOL(hAPP(int,bool,P_1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),Xa),X_2))))) & hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_2),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastAtMost(int),one_one(int)),D_2))))) | (exists X_2 (hBOOL(hAPP(int,bool,P_2,X_2)) & hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_2),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastAtMost(int),one_one(int)),D_2))))))))))) # label(fact_4875_cppi) # label(axiom) # label(non_clause).  [assumption].
7.57/7.55	2288 (all Z1 all Z2 all Z3 hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),Z1),Z2)),Z3) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),Z1),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),Z2),Z3))) # label(fact_705_real__mult__assoc) # label(axiom) # label(non_clause).  [assumption].
7.57/7.55	2289 (all X_a (archim1727834104eiling(X_a) -> (all Z all X_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(int,X_a,ring_1_of_int(X_a),Z)),one_one(X_a))),X_1)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Z),hAPP(X_a,int,archimedean_ceiling(X_a),X_1))))))) # label(fact_3611_le__ceiling__iff) # label(axiom) # label(non_clause).  [assumption].
7.57/7.55	2290 (all A_1 all P_5 (hBOOL(hAPP(int,bool,zprime,P_5)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),A_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_1),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),P_5),one_one(int)))) -> ti(int,A_1) != hAPP(int,int,hAPP(int,fun(int,int),inv,P_5),A_1))))) # label(fact_807_inv__distinct) # label(axiom) # label(non_clause).  [assumption].
7.57/7.55	2291 (all Y_1 all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Y_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,ln,X_1)),hAPP(real,real,ln,Y_1))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_1),Y_1)))))) # label(fact_1935_ln__less__cancel__iff) # label(axiom) # label(non_clause).  [assumption].
7.57/7.55	2292 (all N N = hAPP(nat,nat,size_size(nat),N)) # label(fact_2923_nat__size) # label(axiom) # label(non_clause).  [assumption].
7.57/7.55	2293 (all W all Z1 all 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)) = 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))) # label(fact_69_zadd__zmult__distrib2) # label(axiom) # label(non_clause).  [assumption].
7.57/7.55	2294 (all X all Y hAPP(complex,complex,cnj,hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),X),Y)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(complex,complex,cnj,X)),hAPP(complex,complex,cnj,Y))) # label(fact_2936_cnj_Oadd) # label(axiom) # label(non_clause).  [assumption].
7.57/7.55	2295 (all X all N hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(nat,int,semiring_1_of_nat(int),X)),N) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),X),N))) # label(fact_1357_Nat__Transfer_Otransfer__int__nat__functions_I4_J) # label(axiom) # label(non_clause).  [assumption].
7.57/7.55	2296 (all X_a (ring_1(X_a) -> (all Z_1 all N hAPP(int,X_a,ring_1_of_int(X_a),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),Z_1),N)) = hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(int,X_a,ring_1_of_int(X_a),Z_1)),N)))) # label(fact_3566_of__int__power) # label(axiom) # label(non_clause).  [assumption].
7.57/7.55	2297 (all X_1 all N_1 (-hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),N_1))) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,number_number_of(real),N_1)),X_1)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(int,nat,number_number_of(nat),N_1)),hAPP(real,nat,natfloor,X_1))))))) # label(fact_1912_le__natfloor__eq__number__of) # label(axiom) # label(non_clause).  [assumption].
7.57/7.55	2298 (all G all F all X_1 all D_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),D_1)) -> ((all Z_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),Z_2),X_1))),D_1)) -> Z_2 = hAPP(real,real,G,hAPP(real,real,F,Z_2)))) -> ((all Z_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),Z_2),X_1))),D_1)) -> hBOOL(hAPP(real,bool,hAPP(fun(real,real),fun(real,bool),isCont(real,real),F),Z_2)))) -> (exists E (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),E)) & (all Y_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),Y_2),hAPP(real,real,F,X_1)))),E)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),Y_2),hAPP(real,real,F,X_1))))) -> Y_2 = hAPP(real,real,F,hAPP(real,real,G,Y_2)))))))))) # label(fact_4931_isCont__inv__fun__inv) # label(axiom) # label(non_clause).  [assumption].
7.57/7.55	2299 (all X_b all X_a image(X_b,X_a) = ti(fun(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool))),image(X_b,X_a))) # label(tsy_c_Set_Oimage_res) # label(axiom) # label(non_clause).  [assumption].
7.57/7.55	2300 (all K all Ma all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),N_1)) & 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),Ma)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),N_1))))) # label(fact_596_mult__less__cancel1) # label(axiom) # label(non_clause).  [assumption].
7.57/7.55	2301 (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_174_semiring__norm_I110_J) # label(axiom) # label(non_clause).  [assumption].
7.57/7.55	2302 (all Y all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Y)) -> hAPP(real,real,ln,hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),X),Y)) = hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,ln,X)),hAPP(real,real,ln,Y))))) # label(fact_1978_ln__div) # label(axiom) # label(non_clause).  [assumption].
7.57/7.55	2303 (all X_a (linordered_semidom(X_a) -> (all A_1 all N all B (hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N) = hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),B),N) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),B)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> ti(X_a,B) = ti(X_a,A_1)))))))) # label(fact_460_power__eq__imp__eq__base) # label(axiom) # label(non_clause).  [assumption].
7.57/7.55	2304 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,ln,X)),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),X),one_one(real)))))) # label(fact_1966_ln__le__minus__one) # label(axiom) # label(non_clause).  [assumption].
7.57/7.55	2305 (all Ma all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,N_1)),Ma)) <-> -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Ma),N_1)))) # label(fact_1244_not__less__eq__eq) # label(axiom) # label(non_clause).  [assumption].
7.57/7.55	2306 (all K1 all K2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K1),K2)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,K1)),hAPP(int,int,bit0,K2))))) # label(fact_155_less__int__code_I15_J) # label(axiom) # label(non_clause).  [assumption].
7.57/7.55	2307 (all X all Y hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),X),Y) = hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),Y),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),X),Y))) # label(fact_4370_gcd__red__int) # label(axiom) # label(non_clause).  [assumption].
7.57/7.55	2308 (all X_a (ordered_ab_group_add(X_a) -> (all X_1 all Y_1 hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,X_a),fun(fun(X_a,bool),fun(X_a,bool)),image(X_a,X_a),uminus_uminus(X_a)),hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastAtMost(X_a),X_1),Y_1)) = hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastAtMost(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),Y_1)),hAPP(X_a,X_a,uminus_uminus(X_a),X_1))))) # label(fact_4526_image__uminus__atLeastAtMost) # label(axiom) # label(non_clause).  [assumption].
7.57/7.55	2309 (all K_4 all M all N hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K_4),M)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K_4),N)) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,abs_abs(int),K_4)),hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),M),N))) # label(fact_4380_gcd__mult__distrib__int) # label(axiom) # label(non_clause).  [assumption].
7.57/7.55	2310 (all X_1 all A_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(real,int,archimedean_ceiling(real),X_1)),A_2)) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_1),hAPP(int,real,real_1(int),A_2))))) # label(fact_3367_ceiling__le__eq) # label(axiom) # label(non_clause).  [assumption].
7.57/7.55	2311 (all X_b all X_a (metric_space(X_a) & metric_space(X_b) -> (all F all L_2 all A_2 ((all R_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),R_2)) -> (exists S_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),S_1)) & (all X_2 (ti(X_a,A_2) != ti(X_a,X_2) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),X_2),A_2)),S_1)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_b,real,hAPP(X_b,fun(X_b,real),dist_dist(X_b),hAPP(X_a,X_b,F,X_2)),L_2)),R_2)))))))) <-> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),L_2),hAPP(X_a,filter(X_a),at(X_a),A_2))))))) # label(fact_4653_LIM__def) # label(axiom) # label(non_clause).  [assumption].
7.57/7.55	2312 (all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),X_1)),one_one(real))) -> hAPP(fun(nat,real),real,suminf(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),min_1)))),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),hAPP(real,fun(real,real),inverse_divide(real),one_one(real))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),hAPP(fun(nat,nat),fun(nat,fun(nat,nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,nat),fun(nat,fun(nat,nat))),combb(nat,fun(nat,nat),nat),plus_plus(nat)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),times_times(nat)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),one_one(nat)))))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),hAPP(real,fun(nat,real),power_power(real),X_1)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),hAPP(fun(nat,nat),fun(nat,fun(nat,nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,nat),fun(nat,fun(nat,nat))),combb(nat,fun(nat,nat),nat),plus_plus(nat)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),times_times(nat)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),one_one(nat)))))) = hAPP(real,real,arctan,X_1))) # label(fact_3966_arctan__series) # label(axiom) # label(non_clause).  [assumption].
7.57/7.55	2313 (all X all D (ti(int,D) != zero_zero(int) -> hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(int,real,real_1(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),X),D))),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(int,real,real_1(int),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),X),D))),hAPP(int,real,real_1(int),D))) = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(int,real,real_1(int),X)),hAPP(int,real,real_1(int),D)))) # label(fact_3411_real__of__int__div__aux) # label(axiom) # label(non_clause).  [assumption].
7.57/7.55	2314 (all X_a (zero(X_a) -> (all X_1 (ti(X_a,X_1) = zero_zero(X_a) <-> ti(X_a,X_1) = zero_zero(X_a))))) # label(fact_764_zero__reorient) # label(axiom) # label(non_clause).  [assumption].
7.57/7.55	2315 (all X_a (linord581940658strict(X_a) -> (all A_2 all B_1 all C_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),B_1)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1),A_2)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1),B_1)))))))) # label(fact_436_mult__le__cancel__left__pos) # label(axiom) # label(non_clause).  [assumption].
7.57/7.55	2316 (all X_a (field_char_0(X_a) -> field_char_0_Rats(X_a) = ti(fun(X_a,bool),field_char_0_Rats(X_a)))) # label(tsy_c_Rat_Ofield__char__0__class_ORats_res) # label(axiom) # label(non_clause).  [assumption].
7.57/7.55	2317 (all K_4 hAPP(nat,rat,semiring_1_of_nat(rat),K_4) = hAPP(int,rat,hAPP(int,fun(int,rat),fract,hAPP(nat,int,semiring_1_of_nat(int),K_4)),one_one(int))) # label(fact_3743_Fract__of__nat__eq) # label(axiom) # label(non_clause).  [assumption].
7.57/7.55	2318 (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_1544_linorder__le__cases) # label(axiom) # label(non_clause).  [assumption].
7.57/7.55	2319 (all A_1 all B (hAPP(rat,product_prod(int,int),quotient_of,A_1) = hAPP(rat,product_prod(int,int),quotient_of,B) -> B = A_1)) # label(fact_3720_quotient__of__inject) # label(axiom) # label(non_clause).  [assumption].
7.57/7.55	2320 (all N all P_5 (hBOOL(hAPP(int,bool,zprime,P_5)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),N)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),N),P_5)) -> hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,N),P_5) = one_one(int))))) # label(fact_3469_zless__zprime__imp__zrelprime) # label(axiom) # label(non_clause).  [assumption].
7.57/7.55	2321 (all X_a all X_b (order(X_a) & order(X_b) -> (all C_1 all A_2 all F all B_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),hAPP(X_b,X_a,F,B_1))) -> (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),B_1),C_1)) -> ((all X_2 all Y_2 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_2),Y_2)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_b,X_a,F,X_2)),hAPP(X_b,X_a,F,Y_2))))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),hAPP(X_b,X_a,F,C_1))))))))) # label(fact_2836_order__le__less__subst1) # label(axiom) # label(non_clause).  [assumption].
7.57/7.55	2322 (all K all L hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),hAPP(bool,fun(int,fun(int,int)),if(int),hAPP(int,bool,hAPP(int,fun(int,bool),fequal(int),L),zero_zero(int))),K),hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),L),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,abs_abs(int),K)),hAPP(int,int,abs_abs(int),L))))) = hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),K),L)) # label(fact_4401_gcd__code__int) # label(axiom) # label(non_clause).  [assumption].
7.57/7.55	2323 (all R_1 hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),hAPP(real,fun(real,real),times_times(real),R_1)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),hAPP(real,fun(real,real),plus_plus(real),one_one(real))),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),uminus_uminus(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),inverse_inverse(real)),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),suc)))))),R_1),sequentially))) # label(fact_4498_LIMSEQ__inverse__real__of__nat__add__minus__mult) # label(axiom) # label(non_clause).  [assumption].
7.57/7.55	2324 (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_149_add__numeral__0__right) # label(axiom) # label(non_clause).  [assumption].
7.57/7.55	2325 (all X_a (ordere142940540dd_abs(X_a) -> (all A_1 hAPP(X_a,X_a,abs_abs(X_a),A_1) = hAPP(X_a,X_a,abs_abs(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),A_1))))) # label(fact_2010_abs__minus__cancel) # label(axiom) # label(non_clause).  [assumption].
7.57/7.55	2326 (all N all A_1 all B all P_5 (hBOOL(hAPP(nat,bool,prime,P_5)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,A_1),B)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),P_5),N)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A_1),B))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),P_5),N)),A_1)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),P_5),N)),B)))))) # label(fact_3077_prime__divprod__pow) # label(axiom) # label(non_clause).  [assumption].
7.57/7.55	2327 (all X_a (real_normed_vector(X_a) -> (all Y all S_3 all X all R_4 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,norm_norm(X_a),X)),R_4)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,norm_norm(X_a),Y)),S_3)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X),Y))),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),R_4),S_3)))))))) # label(fact_1792_norm__add__less) # label(axiom) # label(non_clause).  [assumption].
7.57/7.55	2328 (all X_a (field(X_a) -> (all X all W all Z_1 all Y (zero_zero(X_a) != ti(X_a,Y) -> (zero_zero(X_a) != ti(X_a,Z_1) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),Z_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),W),Y))),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Y),Z_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),inverse_divide(X_a),X),Y)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),W),Z_1))))))) # label(fact_1722_add__frac__eq) # label(axiom) # label(non_clause).  [assumption].
7.57/7.55	2329 (all Z_1 all W (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),W),Z_1)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),Z_1),W)))) # label(fact_656_real__le__linear) # label(axiom) # label(non_clause).  [assumption].
7.57/7.55	2330 (all Y all X (hBOOL(hAPP(int,bool,nat_is_nat,X)) -> (hBOOL(hAPP(int,bool,nat_is_nat,Y)) -> hBOOL(hAPP(int,bool,nat_is_nat,hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),X),Y)))))) # label(fact_4847_Divides_Otransfer__int__nat__function__closures_I2_J) # label(axiom) # label(non_clause).  [assumption].
7.57/7.55	2331 (all X_a (divisi14063676e_zero(X_a) -> (all A_1 ((zero_zero(X_a) = ti(X_a,A_1) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),A_1),A_1) = zero_zero(X_a)) & (ti(X_a,A_1) != zero_zero(X_a) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),A_1),A_1) = one_one(X_a)))))) # label(fact_1694_divide__self__if) # label(axiom) # label(non_clause).  [assumption].
7.57/7.55	2332 (all X_a all X_b all P_1 hAPP(fun(product_prod(X_a,X_b),bool),product_prod(X_a,X_b),the(product_prod(X_a,X_b)),P_1) = hAPP(fun(product_prod(X_a,X_b),bool),product_prod(X_a,X_b),the(product_prod(X_a,X_b)),hAPP(fun(X_a,fun(X_b,bool)),fun(product_prod(X_a,X_b),bool),product_prod_case(X_a,X_b,bool),hAPP(fun(X_a,fun(X_b,product_prod(X_a,X_b))),fun(X_a,fun(X_b,bool)),hAPP(fun(fun(X_b,product_prod(X_a,X_b)),fun(X_b,bool)),fun(fun(X_a,fun(X_b,product_prod(X_a,X_b))),fun(X_a,fun(X_b,bool))),combb(fun(X_b,product_prod(X_a,X_b)),fun(X_b,bool),X_a),hAPP(fun(product_prod(X_a,X_b),bool),fun(fun(X_b,product_prod(X_a,X_b)),fun(X_b,bool)),combb(product_prod(X_a,X_b),bool,X_b),P_1)),product_Pair(X_a,X_b))))) # label(fact_4143_split__paired__The) # label(axiom) # label(non_clause).  [assumption].
7.57/7.55	2333 (all X_a (real_normed_algebra(X_a) -> (all Y_3 all B_1 all X_3 all A_2 (hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),X_3),A_2),sequentially)) -> (hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),Y_3),B_1),sequentially)) -> hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),times_times(X_a)),X_3)),Y_3)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),B_1)),sequentially))))))) # label(fact_4477_LIMSEQ__mult) # label(axiom) # label(non_clause).  [assumption].
7.57/7.55	2334 (all X_1 all Y_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_1),Y_1)) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,sqrt,X_1)),hAPP(real,real,sqrt,Y_1))))) # label(fact_1616_real__sqrt__less__iff) # label(axiom) # label(non_clause).  [assumption].
7.57/7.55	2335 (all N all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(int,real,real_1(int),N)),one_one(real))),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X),hAPP(int,real,real_1(int),N))) -> hAPP(real,int,archimedean_ceiling(real),X) = ti(int,N)))) # label(fact_3415_ceiling__eq3) # label(axiom) # label(non_clause).  [assumption].
7.57/7.55	2336 (all X_a (real_div_algebra(X_a) & divisi14063676e_zero(X_a) -> (all A_1 all X hAPP(X_a,X_a,inverse_inverse(X_a),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_1),X)) = hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),hAPP(real,real,inverse_inverse(real),A_1)),hAPP(X_a,X_a,inverse_inverse(X_a),X))))) # label(fact_4684_inverse__scaleR__distrib) # label(axiom) # label(non_clause).  [assumption].
7.57/7.55	2337 (all N all K_4 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),K_4)) -> hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K_4),N)),K_4) = ti(int,K_4))) # label(fact_3456_zgcd__zmult__eq__self2) # label(axiom) # label(non_clause).  [assumption].
7.57/7.55	2338 (all N_1 all Ma (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,number_number_of(real),N_1)),hAPP(int,real,real_1(int),Ma))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),N_1)),Ma)))) # label(fact_3388_number__of__less__real__of__int__iff) # label(axiom) # label(non_clause).  [assumption].
7.57/7.55	2339 (all X_a (power(X_a) -> (all A_1 all N hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N)) = hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),hAPP(nat,nat,suc,N))))) # label(fact_1308_power__Suc) # label(axiom) # label(non_clause).  [assumption].
7.57/7.55	2340 (all X_a (real_normed_vector(X_a) -> (all X_1 all X_3 (hBOOL(hAPP(fun(nat,real),bool,summable(real),X_3)) -> hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),hAPP(X_a,fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(X_a,fun(nat,X_a)),combc(nat,X_a,X_a),hAPP(fun(nat,real),fun(nat,fun(X_a,X_a)),hAPP(fun(real,fun(X_a,X_a)),fun(fun(nat,real),fun(nat,fun(X_a,X_a))),combb(real,fun(X_a,X_a),nat),scaleR_scaleR(X_a)),X_3)),X_1))))))) # label(fact_4671_scaleR__left_Osummable) # label(axiom) # label(non_clause).  [assumption].
7.57/7.55	2341 (all X_b all X_a (topological_space(X_a) & real_normed_vector(X_b) -> (all G all F all A_2 (hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,X_b),fun(X_a,bool),isCont(X_a,X_b),F),A_2)) -> (hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,X_b),fun(X_a,bool),isCont(X_a,X_b),G),A_2)) -> hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,X_b),fun(X_a,bool),isCont(X_a,X_b),hAPP(fun(X_a,X_b),fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,X_b)),combs(X_a,X_b,X_b),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,fun(X_b,X_b))),combb(X_b,fun(X_b,X_b),X_a),plus_plus(X_b)),F)),G)),A_2))))))) # label(fact_4896_isCont__add) # label(axiom) # label(non_clause).  [assumption].
7.57/7.55	2342 (all X all P_5 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),P_5)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),standardRes,P_5),X))))) # label(fact_1049_StandardRes__lbound) # label(axiom) # label(non_clause).  [assumption].
7.57/7.55	2343 (all Y all X all U (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),U)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),U),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),Y),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),U),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),Y)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,sqrt,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),Y),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))),U)))))))) # label(fact_1650_lemma__sqrt__hcomplex__capprox) # label(axiom) # label(non_clause).  [assumption].
7.57/7.55	2344 (all X_a (comm_ring_1(X_a) -> (all X all N ((-hBOOL(hAPP(nat,bool,even_odd_even(nat),N)) -> hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),N)) = hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),X)),N)) & (hBOOL(hAPP(nat,bool,even_odd_even(nat),N)) -> hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),X)),N) = hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),N)))))) # label(fact_2423_neg__power__if) # label(axiom) # label(non_clause).  [assumption].
7.57/7.55	2345 (all X all Y hAPP(real,real,cos,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),Y)) = hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,cos,X)),hAPP(real,real,cos,Y))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,sin,X)),hAPP(real,real,sin,Y)))) # label(fact_2340_cos__add) # label(axiom) # label(non_clause).  [assumption].
7.57/7.55	2346 (all X_a (real_vector(X_a) -> (all A_1 all B all X hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A_1),B)),X) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_1),X)),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),B),X))))) # label(fact_4714_scaleR__left__diff__distrib) # label(axiom) # label(non_clause).  [assumption].
7.57/7.55	2347 (all X_a (real_algebra_1(X_a) & real_normed_vector(X_a) -> (all A_2 hBOOL(hAPP(filter(real),bool,hAPP(X_a,fun(filter(real),bool),hAPP(fun(real,X_a),fun(X_a,fun(filter(real),bool)),tendsto(real,X_a),of_real(X_a)),hAPP(real,X_a,of_real(X_a),A_2)),hAPP(real,filter(real),at(real),A_2)))))) # label(fact_4555_of__real_Ocont) # label(axiom) # label(non_clause).  [assumption].
7.57/7.55	2348 (all N hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),N),one_one(int))),N) = one_one(int)) # label(fact_4357_coprime__minus__one__int) # label(axiom) # label(non_clause).  [assumption].
7.57/7.55	2349 (all N (one_one(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),N),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) -> hBOOL(hAPP(nat,bool,even_odd_even(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),one_one(nat))),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))) # label(fact_2474_lemma__even__mod__4__div__2) # label(axiom) # label(non_clause).  [assumption].
7.57/7.56	2350 (all Z_5 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Z_5),zero_zero(int))) <-> hBOOL(hAPP(int,bool,nat_neg,Z_5)))) # label(fact_1502_neg__def) # label(axiom) # label(non_clause).  [assumption].
7.57/7.56	2351 (all Ta all B_2 all D_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D_2)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Ta),B_2)) -> (all X_2 ((all Xa (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xa),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastAtMost(int),one_one(int)),D_2))) -> (all Xb (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xb),B_2)) -> hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Xb),Xa) != ti(int,X_2))))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Ta),X_2)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Ta),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X_2),D_2))))))))) # label(fact_4642_bset_I7_J) # label(axiom) # label(non_clause).  [assumption].
7.57/7.56	2352 (all X_a (banach(X_a) & real_normed_field(X_a) -> (all X_1 hBOOL(hAPP(X_a,bool,hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,real),fun(nat,fun(X_a,X_a)),hAPP(fun(real,fun(X_a,X_a)),fun(fun(nat,real),fun(nat,fun(X_a,X_a))),combb(real,fun(X_a,X_a),nat),scaleR_scaleR(X_a)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),inverse_inverse(real)),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),fact_fact(nat))))),hAPP(X_a,fun(nat,X_a),power_power(X_a),X_1))),hAPP(X_a,X_a,exp(X_a),X_1)))))) # label(fact_4752_exp__converges) # label(axiom) # label(non_clause).  [assumption].
7.57/7.56	2353 (all X_a (ring_1(X_a) -> (all Z_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Z_1)) -> hAPP(int,X_a,ring_1_of_int(X_a),Z_1) = hAPP(nat,X_a,semiring_1_of_nat(X_a),hAPP(int,nat,nat_1,Z_1)))))) # label(fact_3604_of__nat__nat) # label(axiom) # label(non_clause).  [assumption].
7.57/7.56	2354 (all W hAPP(int,int,ring_1_of_int(int),W) = hAPP(int,int,number_number_of(int),W)) # label(fact_3583_int__number__of__def) # label(axiom) # label(non_clause).  [assumption].
7.57/7.56	2355 (all A_2 all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_1),hAPP(nat,real,real_1(nat),A_2))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(real,nat,natceiling,X_1)),A_2))))) # label(fact_2345_natceiling__le__eq) # label(axiom) # label(non_clause).  [assumption].
7.57/7.56	2356 (all X all A_1 hAPP(real,real,exp(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A_1),hAPP(real,real,ln,X))) = hAPP(real,real,hAPP(real,fun(real,real),powr,X),A_1)) # label(fact_3382_powr__def) # label(axiom) # label(non_clause).  [assumption].
7.57/7.56	2357 (all T_2 all T_1 (uminus(T_1) -> uminus(fun(T_2,T_1)))) # label(arity_fun___Groups_Ouminus) # label(axiom) # label(non_clause).  [assumption].
7.57/7.56	2358 (all Z_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Z_1)) -> -(all M_2 hAPP(nat,int,semiring_1_of_nat(int),M_2) != ti(int,Z_1)))) # label(fact_1488_nonneg__eq__int) # label(axiom) # label(non_clause).  [assumption].
7.57/7.56	2359 (all X_a (linordered_field(X_a) -> (all A_2 all B_1 all C_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),zero_zero(X_a))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),B_1),C_1))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),C_1)))))))) # label(fact_1741_neg__le__divide__eq) # label(axiom) # label(non_clause).  [assumption].
7.57/7.56	2360 (all P_1 all A0 all A1 (hBOOL(hAPP(product_prod(int,int),bool,hAPP(fun(product_prod(int,int),fun(product_prod(int,int),bool)),fun(product_prod(int,int),bool),accp(product_prod(int,int)),negDivAlg_rel),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),A0),A1))) -> ((all A_4 all B_4 (hBOOL(hAPP(product_prod(int,int),bool,hAPP(fun(product_prod(int,int),fun(product_prod(int,int),bool)),fun(product_prod(int,int),bool),accp(product_prod(int,int)),negDivAlg_rel),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),A_4),B_4))) -> ((-(hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A_4),B_4))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B_4),zero_zero(int)))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),P_1,A_4),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),B_4)))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),P_1,A_4),B_4))))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),P_1,A0),A1))))) # label(fact_1179_negDivAlg_Opinduct) # label(axiom) # label(non_clause).  [assumption].
7.57/7.56	2361 (all X_a (real_normed_vector(X_a) -> (all X_1 all A_2 hBOOL(hAPP(filter(real),bool,hAPP(X_a,fun(filter(real),bool),hAPP(fun(real,X_a),fun(X_a,fun(filter(real),bool)),tendsto(real,X_a),hAPP(X_a,fun(real,X_a),hAPP(fun(real,fun(X_a,X_a)),fun(X_a,fun(real,X_a)),combc(real,X_a,X_a),scaleR_scaleR(X_a)),X_1)),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_2),X_1)),hAPP(real,filter(real),at(real),A_2)))))) # label(fact_4733_scaleR__left_Ocont) # label(axiom) # label(non_clause).  [assumption].
7.57/7.56	2362 (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_246_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J) # label(axiom) # label(non_clause).  [assumption].
7.57/7.56	2363 (all Ma all K all N_1 (Ma = N_1 <-> hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Ma),K) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_1),K))) # label(fact_525_nat__add__right__cancel) # label(axiom) # label(non_clause).  [assumption].
7.57/7.56	2364 (all A_1 all B all P_5 all Q_3 (hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),P_5),Q_3) = hAPP(rat,product_prod(int,int),quotient_of,hAPP(int,rat,hAPP(int,fun(int,rat),fract,A_1),B)) -> hAPP(int,rat,hAPP(int,fun(int,rat),fract,A_1),B) = hAPP(int,rat,hAPP(int,fun(int,rat),fract,P_5),Q_3))) # label(fact_3735_quotient__of__eq) # label(axiom) # label(non_clause).  [assumption].
7.57/7.56	2365 (all X_b all X_c all X_a (semiring_0(X_a) -> (all F all A_3 all G all B_2 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co1399186613setsum(X_b,X_a),F),A_3)),hAPP(fun(X_c,bool),X_a,hAPP(fun(X_c,X_a),fun(fun(X_c,bool),X_a),big_co1399186613setsum(X_c,X_a),G),B_2)) = hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co1399186613setsum(X_b,X_a),hAPP(fun(X_c,bool),fun(X_b,X_a),hAPP(fun(X_b,fun(fun(X_c,bool),X_a)),fun(fun(X_c,bool),fun(X_b,X_a)),combc(X_b,fun(X_c,bool),X_a),hAPP(fun(X_b,fun(X_c,X_a)),fun(X_b,fun(fun(X_c,bool),X_a)),hAPP(fun(fun(X_c,X_a),fun(fun(X_c,bool),X_a)),fun(fun(X_b,fun(X_c,X_a)),fun(X_b,fun(fun(X_c,bool),X_a))),combb(fun(X_c,X_a),fun(fun(X_c,bool),X_a),X_b),big_co1399186613setsum(X_c,X_a)),hAPP(fun(X_c,X_a),fun(X_b,fun(X_c,X_a)),hAPP(fun(X_b,fun(fun(X_c,X_a),fun(X_c,X_a))),fun(fun(X_c,X_a),fun(X_b,fun(X_c,X_a))),combc(X_b,fun(X_c,X_a),fun(X_c,X_a)),hAPP(fun(X_b,fun(X_a,X_a)),fun(X_b,fun(fun(X_c,X_a),fun(X_c,X_a))),hAPP(fun(fun(X_a,X_a),fun(fun(X_c,X_a),fun(X_c,X_a))),fun(fun(X_b,fun(X_a,X_a)),fun(X_b,fun(fun(X_c,X_a),fun(X_c,X_a)))),combb(fun(X_a,X_a),fun(fun(X_c,X_a),fun(X_c,X_a)),X_b),combb(X_a,X_a,X_c)),hAPP(fun(X_b,X_a),fun(X_b,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_b,X_a),fun(X_b,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),X_b),times_times(X_a)),F))),G))),B_2)),A_3)))) # label(fact_4209_setsum__product) # label(axiom) # label(non_clause).  [assumption].
7.57/7.56	2366 (all X_a (real_normed_algebra(X_a) -> (exists K_2 all A_4 all B_4 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_4),B_4))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(X_a,real,norm_norm(X_a),A_4)),hAPP(X_a,real,norm_norm(X_a),B_4))),K_2)))))) # label(fact_1811_mult_Obounded) # label(axiom) # label(non_clause).  [assumption].
7.57/7.56	2367 (all X_a (real_normed_field(X_a) -> (all X_1 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),combi(X_a)),X_1),one_one(X_a)))))) # label(fact_3839_DERIV__ident) # label(axiom) # label(non_clause).  [assumption].
7.57/7.56	2368 (all B all A_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_1),zero_zero(int))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B)) -> hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_1),B) = hAPP(product_prod(int,int),int,product_fst(int,int),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),negDivAlg,A_1),B))))) # label(fact_3108_div__neg__pos) # label(axiom) # label(non_clause).  [assumption].
7.57/7.56	2369 (all X_a (linord1117847801e_zero(X_a) -> (all A_2 all C_1 all B_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),A_2),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),B_1),C_1))) <-> zero_zero(X_a) != ti(X_a,C_1) & (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_1),A_2))) & (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),B_1))))))) # label(fact_1678_divide__less__cancel) # label(axiom) # label(non_clause).  [assumption].
7.57/7.56	2370 (all X_a (real_normed_algebra(X_a) -> (all A_1 all R_4 all B hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),R_4),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),R_4),B))))) # label(fact_4674_mult_OscaleR__right) # label(axiom) # label(non_clause).  [assumption].
7.57/7.56	2371 (all Z_1 all W (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Z_1),W)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),W),Z_1)) -> ti(int,W) = ti(int,Z_1)))) # label(fact_30_zle__antisym) # label(axiom) # label(non_clause).  [assumption].
7.57/7.56	2372 (all X all N hAPP(int,real,real_1(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),X),N)) = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,real_1(int),X)),N)) # label(fact_3334_real__of__int__power) # label(axiom) # label(non_clause).  [assumption].
7.57/7.56	2373 (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_819_add__neg__neg) # label(axiom) # label(non_clause).  [assumption].
7.57/7.56	2374 (all X_a (semiring_div(X_a) -> (all A_1 all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)),B) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),A_1),B)))) # label(fact_942_mod__add__self2) # label(axiom) # label(non_clause).  [assumption].
7.57/7.56	2375 (all A_1 all B all K_4 hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_1),B)),B)),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_1),B))),K_4) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A_1),K_4)) # label(fact_921_zdiv__zmod__equality2) # label(axiom) # label(non_clause).  [assumption].
7.57/7.56	2376 (all X_a (field_inverse_zero(X_a) -> (all X_1 (ti(X_a,X_1) = one_one(X_a) <-> hAPP(X_a,X_a,inverse_inverse(X_a),X_1) = one_one(X_a))))) # label(fact_2517_inverse__eq__1__iff) # label(axiom) # label(non_clause).  [assumption].
7.57/7.56	2377 (all X_a (monoid_mult(X_a) & comm_semiring_0(X_a) -> (all X_1 all Y_1 all N_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Y_1),hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),times_times(X_a)),hAPP(X_a,fun(nat,X_a),power_power(X_a),X_1))),hAPP(fun(nat,nat),fun(nat,X_a),hAPP(fun(nat,X_a),fun(fun(nat,nat),fun(nat,X_a)),combb(nat,X_a,nat),hAPP(X_a,fun(nat,X_a),power_power(X_a),Y_1)),hAPP(nat,fun(nat,nat),minus_minus(nat),N_1)))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,suc,N_1)))) = hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),times_times(X_a)),hAPP(X_a,fun(nat,X_a),power_power(X_a),X_1))),hAPP(fun(nat,nat),fun(nat,X_a),hAPP(fun(nat,X_a),fun(fun(nat,nat),fun(nat,X_a)),combb(nat,X_a,nat),hAPP(X_a,fun(nat,X_a),power_power(X_a),Y_1)),hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,N_1))))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,suc,N_1)))))) # label(fact_4174_lemma__realpow__diff__sumr) # label(axiom) # label(non_clause).  [assumption].
7.57/7.56	2378 (all X all Y hAPP(real,real,cos,hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),X),Y)) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,cos,X)),hAPP(real,real,cos,Y))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,sin,X)),hAPP(real,real,sin,Y)))) # label(fact_2339_cos__diff) # label(axiom) # label(non_clause).  [assumption].
7.57/7.56	2379 (all X_a (ordered_ab_group_add(X_a) -> (all B_1 all A_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),B_1)),hAPP(X_a,X_a,uminus_uminus(X_a),A_2))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),B_1)))))) # label(fact_2016_neg__less__iff__less) # label(axiom) # label(non_clause).  [assumption].
7.57/7.56	2380 (all Real1 all Real2 all Real1_2 all Real2_2 (Real2_2 = Real2 & Real1 = Real1_2 <-> hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,Real1),Real2) = hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,Real1_2),Real2_2))) # label(fact_2739_complex_Oinject) # label(axiom) # label(non_clause).  [assumption].
7.57/7.56	2381 (all X_a (comm_semiring_1(X_a) -> (all X all Q_3 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),Q_3)) = hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),hAPP(nat,nat,suc,Q_3))))) # label(fact_1311_comm__semiring__1__class_Onormalizing__semiring__rules_I35_J) # label(axiom) # label(non_clause).  [assumption].
7.57/7.56	2382 (all X_a (archim1727834104eiling(X_a) -> (all X_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(X_a,int,archimedean_ceiling(X_a),X_1))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(int,X_a,number_number_of(X_a),min_1)),X_1)))))) # label(fact_3310_zero__le__ceiling) # label(axiom) # label(non_clause).  [assumption].
7.57/7.56	2383 (all M all N hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N)) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,semiring_1_of_nat(int),M)),hAPP(nat,int,semiring_1_of_nat(int),N))) # label(fact_1312_zadd__int) # label(axiom) # label(non_clause).  [assumption].
7.57/7.56	2384 (all X_a (linordered_semidom(X_a) -> (all A_1 all N all N_5 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N),N_5)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),one_one(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N_5)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N))))))))) # label(fact_441_power__decreasing) # label(axiom) # label(non_clause).  [assumption].
7.57/7.56	2385 (all X_b all X_c all X_a all F1 all A_2 all B_1 hAPP(product_prod(X_b,X_c),X_a,hAPP(fun(X_b,fun(X_c,X_a)),fun(product_prod(X_b,X_c),X_a),product_prod_rec(X_b,X_c,X_a),F1),hAPP(X_c,product_prod(X_b,X_c),hAPP(X_b,fun(X_c,product_prod(X_b,X_c)),product_Pair(X_b,X_c),A_2),B_1)) = hAPP(X_c,X_a,hAPP(X_b,fun(X_c,X_a),F1,A_2),B_1)) # label(fact_3155_prod_Orecs) # label(axiom) # label(non_clause).  [assumption].
7.57/7.56	2386 (all L (hAPP(int,int,bit0,L) = pls <-> ti(int,L) = pls)) # label(fact_121_rel__simps_I38_J) # label(axiom) # label(non_clause).  [assumption].
7.57/7.56	2387 (all A_1 all B hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_1),B) = hAPP(product_prod(int,int),int,product_snd(int,int),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),divmod_int,A_1),B))) # label(fact_3116_mod__int__def) # label(axiom) # label(non_clause).  [assumption].
7.57/7.56	2388 (all X hAPP(int,int,abs_abs(int),X) = hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),X),X)) # label(fact_4372_gcd__idem__int) # label(axiom) # label(non_clause).  [assumption].
7.57/7.56	2389 (all X_a (division_ring(X_a) -> one_one(X_a) = hAPP(X_a,X_a,inverse_inverse(X_a),one_one(X_a)))) # label(fact_2516_inverse__1) # label(axiom) # label(non_clause).  [assumption].
7.57/7.56	2390 (all X_a (linord581940658strict(X_a) -> (all A_2 all B_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_2),B_1))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),B_1)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),A_2)) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),zero_zero(X_a))) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_1),zero_zero(X_a))))))) # label(fact_380_zero__le__mult__iff) # label(axiom) # label(non_clause).  [assumption].
7.57/7.56	2391 (all X all P_5 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),P_5)) -> (hBOOL(hAPP(int,bool,zprime,P_5)) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,X),zero_zero(int)),P_5)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X),hAPP(int,int,hAPP(int,fun(int,int),multInv,P_5),X))),one_one(int)),P_5)))))) # label(fact_854_MultInv__prop2) # label(axiom) # label(non_clause).  [assumption].
7.57/7.56	2392 (all X_a (linordered_idom(X_a) -> (all X_1 all N_1 (-hBOOL(hAPP(nat,bool,even_odd_even(nat),N_1)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),X_1)) | hBOOL(hAPP(nat,bool,even_odd_even(nat),N_1)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X_1),N_1))))))) # label(fact_2435_zero__le__power__eq) # label(axiom) # label(non_clause).  [assumption].
7.57/7.56	2393 (all X_a all P_1 (hBOOL(hAPP(X_a,bool,P_1,hAPP(fun(X_a,bool),X_a,hilbert_Eps(X_a),P_1))) <-> (exists X1 hBOOL(hAPP(X_a,bool,P_1,X1))))) # label(fact_4786_some__eq__ex) # label(axiom) # label(non_clause).  [assumption].
7.57/7.56	2394 (all X (hBOOL(hAPP(int,bool,nat_is_nat,X)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,fact_fact(int),X))))) # label(fact_4858_transfer__int__nat__factorial__closure) # label(axiom) # label(non_clause).  [assumption].
7.57/7.56	2395 (all X_b all X_a all F all A_3 all B_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),B_2)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),B_2),hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),A_3))) -> (exists C_3 (hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),C_3) = ti(fun(X_a,bool),B_2) & hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),C_3)) & hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),C_3),A_3))))))) # label(fact_3645_finite__subset__image) # label(axiom) # label(non_clause).  [assumption].
7.57/7.56	2396 (all Y all X exists R_2 exists A_4 (Y = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),R_2),hAPP(real,real,sin,A_4)) & X = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),R_2),hAPP(real,real,cos,A_4)))) # label(fact_3492_polar__Ex) # label(axiom) # label(non_clause).  [assumption].
7.57/7.56	2397 (all X_a (zero_neq_one(X_a) -> one_one(X_a) != zero_zero(X_a))) # label(fact_325_one__neq__zero) # label(axiom) # label(non_clause).  [assumption].
7.57/7.56	2398 (all X all M all Y (hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),Y),M) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),X),M) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,X),Y),M)))) # label(fact_959_Residues_Oaux) # label(axiom) # label(non_clause).  [assumption].
7.57/7.56	2399 (all X_a (topological_space(X_a) -> (all F all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(real,fun(filter(X_a),bool),hAPP(fun(X_a,real),fun(real,fun(filter(X_a),bool)),tendsto(X_a,real),hAPP(fun(X_a,real),fun(X_a,real),hAPP(fun(real,real),fun(fun(X_a,real),fun(X_a,real)),combb(real,real,X_a),abs_abs(real)),F)),zero_zero(real)),hAPP(X_a,filter(X_a),at(X_a),A_2))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(real,fun(filter(X_a),bool),hAPP(fun(X_a,real),fun(real,fun(filter(X_a),bool)),tendsto(X_a,real),F),zero_zero(real)),hAPP(X_a,filter(X_a),at(X_a),A_2))))))) # label(fact_4592_LIM__rabs__zero__cancel) # label(axiom) # label(non_clause).  [assumption].
7.57/7.56	2400 (all R_4 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),R_4)) -> (exists N_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,real_1(nat),N_2)),R_4)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),R_4),hAPP(nat,real,real_1(nat),hAPP(nat,nat,suc,N_2)))))))) # label(fact_2408_reals__Archimedean6a) # label(axiom) # label(non_clause).  [assumption].
7.57/7.56	2401 (all X_a (real_normed_vector(X_a) -> (all R_1 all X_3 all A_2 (hBOOL(hAPP(X_a,bool,hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),X_3),A_2)) -> hBOOL(hAPP(X_a,bool,hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(X_a,X_a),fun(fun(nat,X_a),fun(nat,X_a)),combb(X_a,X_a,nat),hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),R_1)),X_3)),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),R_1),A_2))))))) # label(fact_4667_scaleR__right_Osums) # label(axiom) # label(non_clause).  [assumption].
7.57/7.56	2402 (all X all Y hAPP(rat,real,ratreal,hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),X),Y)) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(rat,real,ratreal,X)),hAPP(rat,real,ratreal,Y))) # label(fact_3771_real__times__code) # label(axiom) # label(non_clause).  [assumption].
7.57/7.56	2403 (all A_1 all P_5 (hBOOL(hAPP(int,bool,zprime,P_5)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),A_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_1),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),P_5),one_one(int)))) -> zero_zero(int) != hAPP(int,int,hAPP(int,fun(int,int),inv,P_5),A_1))))) # label(fact_810_inv__not__0) # label(axiom) # label(non_clause).  [assumption].
7.57/7.56	2404 (all M all N all S_4 all S_3 all T_6 all T_5 all R_5 all R_4 all K_4 (hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,R_5),R_4) = ti(int,K_4) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),R_4)) -> (exists Sn exists Tn hAPP(product_prod(int,int),product_prod(int,product_prod(int,int)),hAPP(int,fun(product_prod(int,int),product_prod(int,product_prod(int,int))),product_Pair(int,product_prod(int,int)),K_4),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),Sn),Tn)) = hAPP(int,product_prod(int,product_prod(int,int)),hAPP(int,fun(int,product_prod(int,product_prod(int,int))),hAPP(int,fun(int,fun(int,product_prod(int,product_prod(int,int)))),hAPP(int,fun(int,fun(int,fun(int,product_prod(int,product_prod(int,int))))),hAPP(int,fun(int,fun(int,fun(int,fun(int,product_prod(int,product_prod(int,int)))))),hAPP(int,fun(int,fun(int,fun(int,fun(int,fun(int,product_prod(int,product_prod(int,int))))))),hAPP(int,fun(int,fun(int,fun(int,fun(int,fun(int,fun(int,product_prod(int,product_prod(int,int)))))))),hAPP(int,fun(int,fun(int,fun(int,fun(int,fun(int,fun(int,fun(int,product_prod(int,product_prod(int,int))))))))),xzgcda,M),N),R_5),R_4),S_4),S_3),T_6),T_5))))) # label(fact_3480_xzgcd__correct__aux1) # label(axiom) # label(non_clause).  [assumption].
7.57/7.56	2405 (all X_a (number_ring(X_a) & real_n2089651433ebra_1(X_a) -> (all W hAPP(X_a,real,norm_norm(X_a),hAPP(int,X_a,number_number_of(X_a),W)) = hAPP(real,real,abs_abs(real),hAPP(int,real,number_number_of(real),W))))) # label(fact_1892_norm__number__of) # label(axiom) # label(non_clause).  [assumption].
7.57/7.56	2406 (all X_a (number_semiring(X_a) -> one_one(X_a) = hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,bit1,pls)))) # label(fact_172_semiring__numeral__1__eq__1) # label(axiom) # label(non_clause).  [assumption].
7.57/7.56	2407 (all X_a (semiring_div(X_a) -> (all C all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_1),B)) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),C)),A_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),B),A_1)),C))))) # label(fact_1001_dvd__div__mult) # label(axiom) # label(non_clause).  [assumption].
7.57/7.56	2408 (all L all U_1 hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastAtMost(int),L),U_1) = hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastLessThan(int),L),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),U_1),one_one(int)))) # label(fact_4572_atLeastLessThanPlusOne__atLeastAtMost__int) # label(axiom) # label(non_clause).  [assumption].
7.57/7.56	2409 (all X_a (ab_group_add(X_a) -> (all F all K all N_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_1),K)))),hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),K))) = hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),hAPP(fun(nat,nat),fun(nat,X_a),hAPP(fun(nat,X_a),fun(fun(nat,nat),fun(nat,X_a)),combb(nat,X_a,nat),F),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),K))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),N_1))))) # label(fact_4180_sumr__offset) # label(axiom) # label(non_clause).  [assumption].
7.57/7.56	2410 (all X_a (zero(X_a) -> (all Diff all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)) -> hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),inverse_divide(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(X_a,fun(nat,real),hAPP(fun(nat,fun(X_a,real)),fun(X_a,fun(nat,real)),combc(nat,X_a,real),Diff),zero_zero(X_a)))),hAPP(real,fun(nat,real),power_power(real),zero_zero(real))))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),fact_fact(nat)))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),N_1))),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(X_a,real,hAPP(nat,fun(X_a,real),Diff,N_1),zero_zero(X_a))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),zero_zero(real)),N_1))),hAPP(nat,real,real_1(nat),hAPP(nat,nat,fact_fact(nat),N_1)))) = hAPP(X_a,real,hAPP(nat,fun(X_a,real),Diff,zero_zero(nat)),zero_zero(X_a)))))) # label(fact_4236_Maclaurin__bi__le__lemma) # label(axiom) # label(non_clause).  [assumption].
7.57/7.56	2411 (all A_2 (hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),A_2),zero_zero(real)),sequentially)) -> ((all N_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(nat,real,A_2,N_2)))) -> ((all N_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,A_2,hAPP(nat,nat,suc,N_2))),hAPP(nat,real,A_2,N_2)))) -> hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),hAPP(fun(nat,fun(nat,bool)),fun(nat,real),hAPP(fun(fun(nat,bool),real),fun(fun(nat,fun(nat,bool)),fun(nat,real)),combb(fun(nat,bool),real,nat),hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),min_1)))),A_2))),hAPP(fun(nat,nat),fun(nat,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(nat,nat),fun(nat,fun(nat,bool))),combb(nat,fun(nat,bool),nat),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat))),hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))),hAPP(fun(nat,real),real,suminf(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),min_1)))),A_2))),sequentially)))))) # label(fact_4515_summable__Leibniz_H_I3_J) # label(axiom) # label(non_clause).  [assumption].
7.57/7.56	2412 (all X hAPP(real,real,uminus_uminus(real),hAPP(complex,real,re,X)) = hAPP(complex,real,re,hAPP(complex,complex,uminus_uminus(complex),X))) # label(fact_3004_Re_Ominus) # label(axiom) # label(non_clause).  [assumption].
7.57/7.56	2413 (all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,number_number_of(real),min_1)),X_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_1),one_one(real))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),arccos),X_1),hAPP(real,real,inverse_inverse(real),hAPP(real,real,uminus_uminus(real),hAPP(real,real,sqrt,hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),one_one(real)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))))))))) # label(fact_2631_DERIV__arccos) # label(axiom) # label(non_clause).  [assumption].
7.57/7.56	2414 (all X_a (real_vector(X_a) -> (all A_1 all X all Y hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X),Y)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_1),X)),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_1),Y))))) # label(fact_4718_scaleR__right_Oadd) # label(axiom) # label(non_clause).  [assumption].
7.57/7.56	2415 (all X_a (linorder(X_a) -> (all X all Y all Z_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),Y)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),Z_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),Y),Z_1))))) # label(fact_4940_min__max_Osup__inf__distrib1) # label(axiom) # label(non_clause).  [assumption].
7.57/7.56	2416 (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_125_rel__simps_I17_J) # label(axiom) # label(non_clause).  [assumption].
7.57/7.56	2417 (all Ma all K all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),Ma),K)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N_1),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),Ma),N_1)))) # label(fact_597_mult__less__cancel2) # label(axiom) # label(non_clause).  [assumption].
7.57/7.56	2418 (all U all X (X = hAPP(real,real,exp(real),U) -> hAPP(real,real,ln,X) = U)) # label(fact_2508_exp__ln__eq) # label(axiom) # label(non_clause).  [assumption].
7.57/7.56	2419 (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,Y) = ti(X_a,X)))))) # label(fact_1549_order__antisym) # label(axiom) # label(non_clause).  [assumption].
7.57/7.56	2420 (all X_a (linord1117847801e_zero(X_a) -> (all X_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),one_one(X_a)),hAPP(X_a,X_a,inverse_inverse(X_a),X_1))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),one_one(X_a))) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),X_1)))))) # label(fact_2608_one__le__inverse__iff) # label(axiom) # label(non_clause).  [assumption].
7.57/7.56	2421 (all X_a (real_normed_algebra(X_a) -> (all A_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),zero_zero(X_a)) = zero_zero(X_a)))) # label(fact_878_mult_Ozero__right) # label(axiom) # label(non_clause).  [assumption].
7.57/7.56	2422 (all X_a (linorder(X_a) -> (all T_5 exists Z_2 all X_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_2),Z_2)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_2),T_5)))))) # label(fact_2828_minf_I6_J) # label(axiom) # label(non_clause).  [assumption].
7.57/7.56	2423 (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_820_add__pos__pos) # label(axiom) # label(non_clause).  [assumption].
7.57/7.56	2424 (all X all Y hAPP(real,real,sqrt,hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),X),Y)) = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,sqrt,X)),hAPP(real,real,sqrt,Y))) # label(fact_1668_real__sqrt__divide) # label(axiom) # label(non_clause).  [assumption].
7.57/7.56	2425 (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),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),zero_zero(X_a)),A_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B))))))) # label(fact_366_split__mult__pos__le) # label(axiom) # label(non_clause).  [assumption].
7.57/7.56	2426 (all X (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X)) -> hAPP(int,nat,nat_1,hAPP(int,int,fact_fact(int),X)) = hAPP(nat,nat,fact_fact(nat),hAPP(int,nat,nat_1,X)))) # label(fact_3199_transfer__nat__int__factorial) # label(axiom) # label(non_clause).  [assumption].
7.57/7.56	2427 (all K_4 all N all M (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),M)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),K_4),N)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),K_4),M)))))) # label(fact_1117_div__le__mono2) # label(axiom) # label(non_clause).  [assumption].
7.57/7.56	2428 (all Y_1 all X_1 (hBOOL(hAPP(int,bool,nat_is_nat,X_1)) -> hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastAtMost(int),X_1),Y_1))))) # label(fact_4855_SetInterval_Otransfer__int__nat__set__function__closures) # label(axiom) # label(non_clause).  [assumption].
7.57/7.56	2429 (all K_4 all L_4 hAPP(int,int,bit0,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),K_4),hAPP(int,int,succ,L_4))) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,bit1,K_4)),hAPP(int,int,bit1,L_4))) # label(fact_1532_add__Bit1__Bit1) # label(axiom) # label(non_clause).  [assumption].
7.57/7.56	2430 (all X_a (comm_monoid_mult(X_a) & comm_monoid_add(X_a) -> (all F all A_3 (hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A_3)) -> hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),hAPP(fun(nat,int),fun(nat,X_a),hAPP(fun(int,X_a),fun(fun(nat,int),fun(nat,X_a)),combb(int,X_a,nat),F),semiring_1_of_nat(int))),hAPP(fun(int,bool),fun(nat,bool),hAPP(fun(int,nat),fun(fun(int,bool),fun(nat,bool)),image(int,nat),nat_1),A_3)) = hAPP(fun(int,bool),X_a,hAPP(fun(int,X_a),fun(fun(int,bool),X_a),big_co1399186613setsum(int,X_a),F),A_3))))) # label(fact_4266_transfer__int__nat__sum__prod_I1_J) # label(axiom) # label(non_clause).  [assumption].
7.57/7.56	2431 (all X_a (ring_div(X_a) -> (all A_1 all B all A_6 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),A_6),B) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),A_1),B) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),A_6)),B) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),A_1)),B))))) # label(fact_2011_mod__minus__cong) # label(axiom) # label(non_clause).  [assumption].
7.57/7.56	2432 (all X_a (linord219039673up_add(X_a) -> (all A_2 (zero_zero(X_a) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),A_2) <-> zero_zero(X_a) = ti(X_a,A_2))))) # label(fact_115_double__eq__0__iff) # label(axiom) # label(non_clause).  [assumption].
7.57/7.56	2433 (all Y_1 all X_1 (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),zOdd)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Y_1),zOdd)) -> hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X_1),Y_1)),zEven))))) # label(fact_1370_odd__minus__odd) # label(axiom) # label(non_clause).  [assumption].
7.57/7.56	2434 (all X all Y all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(nat,fun(real,real),root,N),X)),hAPP(real,real,hAPP(nat,fun(real,real),root,N),Y)) = hAPP(real,real,hAPP(nat,fun(real,real),root,N),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),X),Y)))) # label(fact_2682_real__root__mult) # label(axiom) # label(non_clause).  [assumption].
7.57/7.56	2435 (all X_a (linorder(X_a) -> (all B all D all A_1 all C (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),C)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),D)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),A_1),B)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),C),D)))))))) # label(fact_4819_min__max_Oinf__mono) # label(axiom) # label(non_clause).  [assumption].
7.57/7.56	2436 (all X all Y all Z_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Y),Z_1)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Y),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X),Z_1))) # label(fact_522_nat__add__left__commute) # label(axiom) # label(non_clause).  [assumption].
7.57/7.56	2437 (all N_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),N_1),zero_zero(int))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,real_1(int),N_1)),zero_zero(real))))) # label(fact_3386_real__of__int__le__zero__cancel__iff) # label(axiom) # label(non_clause).  [assumption].
7.57/7.56	2438 (all X_a (real_normed_vector(X_a) & real_algebra_1(X_a) -> (all X_3 all A_2 (hBOOL(hAPP(real,bool,hAPP(fun(nat,real),fun(real,bool),sums(real),X_3),A_2)) -> hBOOL(hAPP(X_a,bool,hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),hAPP(fun(nat,real),fun(nat,X_a),hAPP(fun(real,X_a),fun(fun(nat,real),fun(nat,X_a)),combb(real,X_a,nat),of_real(X_a)),X_3)),hAPP(real,X_a,of_real(X_a),A_2))))))) # label(fact_4084_of__real_Osums) # label(axiom) # label(non_clause).  [assumption].
7.57/7.56	2439 (all X all N_5 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),N),N_5)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),X)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(nat,fun(real,real),root,N_5),X)),hAPP(real,real,hAPP(nat,fun(real,real),root,N),X))))))) # label(fact_2702_real__root__strict__decreasing) # label(axiom) # label(non_clause).  [assumption].
7.57/7.56	2440 (all X_a all A_3 all B_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),B_2),A_3)) & hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_3),B_2)) <-> ti(fun(X_a,bool),A_3) = ti(fun(X_a,bool),B_2))) # label(fact_1959_set__eq__subset) # label(axiom) # label(non_clause).  [assumption].
7.57/7.56	2441 (all X_1 ((exists Y_2 ti(int,X_1) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),Y_2)),one_one(int))) <-> -hBOOL(hAPP(int,bool,even_odd_even(int),X_1)))) # label(fact_1469_odd__equiv__def) # label(axiom) # label(non_clause).  [assumption].
7.57/7.56	2442 (all N_1 (hBOOL(hAPP(nat,bool,even_odd_even(nat),N_1)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),N_1)))) # label(fact_2465_even__dvd) # label(axiom) # label(non_clause).  [assumption].
7.57/7.56	2443 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),M),N)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),M))))) # label(fact_874_dvd__pos__nat) # label(axiom) # label(non_clause).  [assumption].
7.57/7.56	2444 (all N_1 all X_1 all Diff all F (hAPP(nat,fun(real,real),Diff,zero_zero(nat)) = F -> ((all M_2 all X_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(nat,fun(real,real),Diff,M_2)),X_2),hAPP(real,real,hAPP(nat,fun(real,real),Diff,hAPP(nat,nat,suc,M_2)),X_2)))) -> (exists T_4 (hAPP(real,real,F,X_1) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),inverse_divide(real)),hAPP(real,fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(real,fun(nat,real)),combc(nat,real,real),Diff),zero_zero(real)))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),fact_fact(nat))))),hAPP(real,fun(nat,real),power_power(real),X_1))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),N_1))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(nat,fun(real,real),Diff,N_1),T_4)),hAPP(nat,real,real_1(nat),hAPP(nat,nat,fact_fact(nat),N_1)))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X_1),N_1))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),T_4)),hAPP(real,real,abs_abs(real),X_1)))))))) # label(fact_4286_Maclaurin__all__le) # label(axiom) # label(non_clause).  [assumption].
7.57/7.56	2445 (all X_a all X_b (order(X_a) & order(X_b) -> (all F all C_1 all A_2 all B_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),B_1)) -> (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_a,X_b,F,B_1)),C_1)) -> ((all X_2 all Y_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_2),Y_2)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_a,X_b,F,X_2)),hAPP(X_a,X_b,F,Y_2))))) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_a,X_b,F,A_2)),C_1)))))))) # label(fact_2832_order__less__le__subst2) # label(axiom) # label(non_clause).  [assumption].
7.57/7.56	2446 (all X_a all Q_1 all P_1 ((exists X1 hBOOL(hAPP(X_a,bool,P_1,X1))) -> ((all X_2 (hBOOL(hAPP(X_a,bool,P_1,X_2)) -> hBOOL(hAPP(X_a,bool,Q_1,X_2)))) -> hBOOL(hAPP(X_a,bool,Q_1,hAPP(fun(X_a,bool),X_a,hilbert_Eps(X_a),P_1)))))) # label(fact_4869_someI2__ex) # label(axiom) # label(non_clause).  [assumption].
7.57/7.56	2447 (all X all Y hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),X),Y) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),X),hAPP(complex,complex,uminus_uminus(complex),Y))) # label(fact_2153_complex__diff__def) # label(axiom) # label(non_clause).  [assumption].
7.57/7.56	2448 (all X_a (monoid_mult(X_a) -> (all X all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),N) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),one_one(nat)))),X))))) # label(fact_717_realpow__minus__mult) # label(axiom) # label(non_clause).  [assumption].
7.57/7.56	2449 (all X_a (semiri456707255roduct(X_a) -> (all B_1 all A_2 (ti(X_a,B_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B_1),A_2) <-> zero_zero(X_a) = ti(X_a,A_2))))) # label(fact_239_add__0__iff) # label(axiom) # label(non_clause).  [assumption].
7.57/7.56	2450 (all X_a (real_normed_field(X_a) -> (all C_1 all F (hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),F)) -> hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),hAPP(X_a,fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(X_a,fun(nat,X_a)),combc(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),inverse_divide(X_a)),F)),C_1))))))) # label(fact_4009_summable__divide) # label(axiom) # label(non_clause).  [assumption].
7.57/7.56	2451 (all X_a all F all C_1 all H ((all N_2 hAPP(nat,X_a,F,N_2) = hAPP(nat,X_a,hAPP(fun(nat,fun(X_a,X_a)),fun(nat,X_a),hAPP(X_a,fun(fun(nat,fun(X_a,X_a)),fun(nat,X_a)),nat_rec(X_a),C_1),H),N_2)) -> hAPP(nat,X_a,F,zero_zero(nat)) = ti(X_a,C_1))) # label(fact_4332_def__nat__rec__0) # label(axiom) # label(non_clause).  [assumption].
7.57/7.56	2452 (all A_2 all B_1 all C_1 all X_1 (hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),C_1),hAPP(int,nat,nat_1,X_1)) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_2),B_1) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),one_one(nat)),hAPP(int,nat,nat_1,X_1))) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),zOdd)) -> (one_one(int) = hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,A_2),B_1) -> (exists K_1 ti(int,A_2) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),K_1),hAPP(int,nat,nat_1,X_1)))))))) # label(fact_3474_int__relprime__odd__power__divisors) # label(axiom) # label(non_clause).  [assumption].
7.57/7.56	2453 (all X_a (linord1117847801e_zero(X_a) & number_ring(X_a) -> (all R_4 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),R_4)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),R_4),hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))))) # label(fact_1757_half__gt__zero) # label(axiom) # label(non_clause).  [assumption].
7.57/7.56	2454 (all X_a (linordered_idom(X_a) -> (all X_1 all A_2 all R_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,abs_abs(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),X_1),A_2))),R_1)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),R_1))) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_2),R_1)),X_1)))))) # label(fact_1883_abs__diff__less__iff) # label(axiom) # label(non_clause).  [assumption].
7.57/7.56	2455 (all M all V hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,hAPP(int,int,bit1,pls)))),M)),hAPP(int,nat,number_number_of(nat),V)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,suc,hAPP(nat,nat,suc,hAPP(nat,nat,suc,M)))),hAPP(int,nat,number_number_of(nat),V))) # label(fact_1439_Suc__mod__eq__add3__mod__number__of) # label(axiom) # label(non_clause).  [assumption].
7.57/7.56	2456 (all X_a all X_b ti(fun(fun(X_a,bool),fun(fun(X_b,bool),fun(product_prod(X_a,X_b),bool))),prod(X_a,X_b)) = prod(X_a,X_b)) # label(tsy_c_Nitpick_Oprod_res) # label(axiom) # label(non_clause).  [assumption].
7.57/7.56	2457 (all R_4 all Q_3 all A_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A_1)) -> (hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),R_4),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),Q_3)) = ti(int,A_1) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),R_4),A_1)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),Q_3)))))) # label(fact_189_self__quotient__aux1) # label(axiom) # label(non_clause).  [assumption].
7.57/7.56	2458 (all K_4 hAPP(int,rat,number_number_of(rat),K_4) = hAPP(int,rat,hAPP(int,fun(int,rat),fract,hAPP(int,int,number_number_of(int),K_4)),one_one(int))) # label(fact_3774_rat__number__expand_I3_J) # label(axiom) # label(non_clause).  [assumption].
7.57/7.56	2459 (all M all A_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_1),M)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_1),zero_zero(int)),M)) -> ti(int,A_1) = zero_zero(int))))) # label(fact_452_zcong__zless__0) # label(axiom) # label(non_clause).  [assumption].
7.57/7.56	2460 (all X_a (number_ring(X_a) & linord1117847801e_zero(X_a) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),one_one(X_a)),hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))) # label(fact_1768_half) # label(axiom) # label(non_clause).  [assumption].
7.57/7.56	2461 (all X_a (archim1727834104eiling(X_a) -> (all X_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),hAPP(X_a,int,archimedean_ceiling(X_a),X_1))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),X_1)))))) # label(fact_3300_one__le__ceiling) # label(axiom) # label(non_clause).  [assumption].
7.57/7.56	2462 (all B hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),hAPP(int,int,number_number_of(int),min_1)),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),B),one_one(int))) = hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),negDivAlg,hAPP(int,int,number_number_of(int),min_1)),B)) # label(fact_1066_negDivAlg__minus1) # label(axiom) # label(non_clause).  [assumption].
7.57/7.56	2463 (all X_a (linorder(X_a) -> (all X all Y all Z_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),Y),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),Z_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),Y),Z_1))))) # label(fact_4811_min__max_Oinf__left__commute) # label(axiom) # label(non_clause).  [assumption].
7.57/7.56	2464 (all Y_1 all X_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Y_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X_1),Y_1)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(int,nat,nat_1,X_1)),hAPP(int,nat,nat_1,Y_1))))))) # label(fact_1136_transfer__nat__int__relations_I2_J) # label(axiom) # label(non_clause).  [assumption].
7.57/7.56	2465 (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_1541_order__refl) # label(axiom) # label(non_clause).  [assumption].
7.57/7.56	2466 (all X_a (topological_space(X_a) -> (all F all L (hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),F),L),sequentially)) -> hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),hAPP(fun(nat,nat),fun(nat,X_a),hAPP(fun(nat,X_a),fun(fun(nat,nat),fun(nat,X_a)),combb(nat,X_a,nat),F),suc)),L),sequentially)))))) # label(fact_4462_LIMSEQ__Suc) # label(axiom) # label(non_clause).  [assumption].
7.57/7.56	2467 (all X all Y hAPP(real,real,hAPP(real,fun(real,real),dist_dist(real),X),Y) = hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),X),Y))) # label(fact_3519_dist__real__def) # label(axiom) # label(non_clause).  [assumption].
7.57/7.56	2468 (all Z all W_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),W_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_1),Z)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(int,nat,nat_1,W_1)),hAPP(int,nat,nat_1,Z)))))) # label(fact_1137_nat__less__eq__zless) # label(axiom) # label(non_clause).  [assumption].
7.57/7.56	2469 (all A_1 all P_5 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),P_5)) -> hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A_1),hAPP(int,nat,nat_1,P_5)) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(int,nat,nat_1,P_5)),one_one(nat)))))) # label(fact_1149_Euler_Oaux__1) # label(axiom) # label(non_clause).  [assumption].
7.57/7.56	2470 (all X_a (linordered_field(X_a) -> (all B_1 all A_2 all C_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),zero_zero(X_a))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),C_1)),B_1)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),B_1),C_1)),A_2))))))) # label(fact_1715_neg__divide__less__eq) # label(axiom) # label(non_clause).  [assumption].
7.57/7.56	2471 (all X all M hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,X),hAPP(int,int,hAPP(int,fun(int,int),standardRes,M),X)),M))) # label(fact_972_StandardRes__prop1) # label(axiom) # label(non_clause).  [assumption].
7.57/7.56	2472 (all X_a all X_b (comm_monoid_add(X_b) -> ti(fun(fun(X_a,X_b),fun(fun(X_a,bool),X_b)),big_co1399186613setsum(X_a,X_b)) = big_co1399186613setsum(X_a,X_b))) # label(tsy_c_Big__Operators_Ocomm__monoid__add__class_Osetsum_res) # label(axiom) # label(non_clause).  [assumption].
7.57/7.56	2473 (all X_a (field_inverse_zero(X_a) -> (all A_1 all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),A_1)),hAPP(X_a,X_a,uminus_uminus(X_a),B)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),A_1),B)))) # label(fact_2018_minus__divide__divide) # label(axiom) # label(non_clause).  [assumption].
7.57/7.56	2474 (all X_1 all W_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),X_1),hAPP(int,nat,number_number_of(nat),W_1)))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X_1)) | hAPP(int,nat,number_number_of(nat),W_1) = zero_zero(nat))) # label(fact_228_zero__less__power__nat__eq__number__of) # label(axiom) # label(non_clause).  [assumption].
7.57/7.56	2475 (all X_a (linord1117847801e_zero(X_a) -> (all A_2 all B_1 ((hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),B_1)),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),B_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),A_2),B_1))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_1),A_2))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,inverse_inverse(X_a),A_2)),hAPP(X_a,X_a,inverse_inverse(X_a),B_1))))))) # label(fact_2607_inverse__le__iff) # label(axiom) # label(non_clause).  [assumption].
7.57/7.56	2476 (all X_a (topological_space(X_a) & comm_monoid_add(X_a) -> (all F hAPP(fun(nat,X_a),X_a,suminf(X_a),F) = hAPP(fun(X_a,bool),X_a,the(X_a),hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),F))))) # label(fact_4135_suminf__def) # label(axiom) # label(non_clause).  [assumption].
7.57/7.56	2477 (all X_a all G all B_1 all F all A_2 all Net (hBOOL(hAPP(filter(X_a),bool,hAPP(real,fun(filter(X_a),bool),hAPP(fun(X_a,real),fun(real,fun(filter(X_a),bool)),tendsto(X_a,real),F),A_2),Net)) -> (hBOOL(hAPP(filter(X_a),bool,hAPP(real,fun(filter(X_a),bool),hAPP(fun(X_a,real),fun(real,fun(filter(X_a),bool)),tendsto(X_a,real),G),B_1),Net)) -> hBOOL(hAPP(filter(X_a),bool,hAPP(complex,fun(filter(X_a),bool),hAPP(fun(X_a,complex),fun(complex,fun(filter(X_a),bool)),tendsto(X_a,complex),hAPP(fun(X_a,real),fun(X_a,complex),hAPP(fun(X_a,fun(real,complex)),fun(fun(X_a,real),fun(X_a,complex)),combs(X_a,real,complex),hAPP(fun(X_a,real),fun(X_a,fun(real,complex)),hAPP(fun(real,fun(real,complex)),fun(fun(X_a,real),fun(X_a,fun(real,complex))),combb(real,fun(real,complex),X_a),complex_1),F)),G)),hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,A_2),B_1)),Net))))) # label(fact_4505_tendsto__Complex) # label(axiom) # label(non_clause).  [assumption].
7.57/7.56	2478 (all B_1 all C_1 all A_2 all D_1 (one_one(int) = hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),A_2),D_1) -> (one_one(int) = hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),B_1),C_1) -> (hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,abs_abs(int),B_1)),hAPP(int,int,abs_abs(int),D_1)) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,abs_abs(int),A_2)),hAPP(int,int,abs_abs(int),C_1)) <-> hAPP(int,int,abs_abs(int),B_1) = hAPP(int,int,abs_abs(int),A_2) & hAPP(int,int,abs_abs(int),C_1) = hAPP(int,int,abs_abs(int),D_1))))) # label(fact_4400_coprime__crossproduct__int) # label(axiom) # label(non_clause).  [assumption].
7.57/7.56	2479 (all P_5 ((-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(product_prod(int,int),int,product_snd(int,int),P_5))) -> (hAPP(product_prod(int,int),int,product_snd(int,int),P_5) = zero_zero(int) -> hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),zero_zero(int)),one_one(int)) = hAPP(product_prod(int,int),product_prod(int,int),normalize,P_5)) & (zero_zero(int) != hAPP(product_prod(int,int),int,product_snd(int,int),P_5) -> hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(product_prod(int,int),int,product_fst(int,int),P_5)),hAPP(int,int,uminus_uminus(int),hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),hAPP(product_prod(int,int),int,product_fst(int,int),P_5)),hAPP(product_prod(int,int),int,product_snd(int,int),P_5))))),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(product_prod(int,int),int,product_snd(int,int),P_5)),hAPP(int,int,uminus_uminus(int),hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),hAPP(product_prod(int,int),int,product_fst(int,int),P_5)),hAPP(product_prod(int,int),int,product_snd(int,int),P_5))))) = hAPP(product_prod(int,int),product_prod(int,int),normalize,P_5))) & (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(product_prod(int,int),int,product_snd(int,int),P_5))) -> hAPP(product_prod(int,int),product_prod(int,int),normalize,P_5) = hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(product_prod(int,int),int,product_fst(int,int),P_5)),hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),hAPP(product_prod(int,int),int,product_fst(int,int),P_5)),hAPP(product_prod(int,int),int,product_snd(int,int),P_5)))),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(product_prod(int,int),int,product_snd(int,int),P_5)),hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),hAPP(product_prod(int,int),int,product_fst(int,int),P_5)),hAPP(product_prod(int,int),int,product_snd(int,int),P_5))))))) # label(fact_4344_normalize__def) # label(axiom) # label(non_clause).  [assumption].
7.57/7.56	2480 (all C all A_1 all B (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),B)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),C),A_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),C),B))))) # label(fact_715_divides__mul__l) # label(axiom) # label(non_clause).  [assumption].
7.57/7.56	2481 (all N all M (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N),M)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),M),N) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N)),N))) # label(fact_1114_le__mod__geq) # label(axiom) # label(non_clause).  [assumption].
7.57/7.56	2482 (all N_1 one_one(real) = hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(real,fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(real,fun(nat,real)),combc(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(nat,fun(real,fun(real,real))),fun(fun(nat,real),fun(nat,fun(real,real))),combs(nat,real,fun(real,real)),hAPP(fun(nat,bool),fun(nat,fun(real,fun(real,real))),hAPP(fun(bool,fun(real,fun(real,real))),fun(fun(nat,bool),fun(nat,fun(real,fun(real,real)))),combb(bool,fun(real,fun(real,real)),nat),if(real)),even_odd_even(nat))),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),inverse_divide(real)),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),min_1))),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),div_div(nat)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),fact_fact(nat))))),zero_zero(real)))),hAPP(real,fun(nat,real),power_power(real),zero_zero(real)))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,suc,N_1)))) # label(fact_4240_sumr__cos__zero__one) # label(axiom) # label(non_clause).  [assumption].
7.57/7.56	2483 (all A_1 all B (zero_zero(nat) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),A_1),B) -> (exists A_5 exists B_3 (A_1 = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A_5),hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),A_1),B)) & B = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B_3),hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),A_1),B)) & one_one(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),A_5),B_3))))) # label(fact_3312_gcd__coprime__exists__nat) # label(axiom) # label(non_clause).  [assumption].
7.57/7.56	2484 (all N all M all R_4 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),M),R_4)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),N),R_4)) -> (hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),M),N) = one_one(nat) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),N)),R_4)))))) # label(fact_3288_divides__mult__nat) # label(axiom) # label(non_clause).  [assumption].
7.57/7.56	2485 (all X_a all F all S (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),S)) -> ((all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),S)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(X_a,nat,F,X_2))))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(fun(X_a,bool),nat,hAPP(fun(X_a,nat),fun(fun(X_a,bool),nat),big_co302546470etprod(X_a,nat),F),S)))))) # label(fact_3939_setprod__pos__nat__iff) # label(axiom) # label(non_clause).  [assumption].
7.57/7.56	2486 (all X_1 all Y_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),X_1),Y_1))) <-> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_1),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),Y_1))) & (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X_1)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),Y_1),zero_zero(real)))))) # label(fact_1699_real__0__le__divide__iff) # label(axiom) # label(non_clause).  [assumption].
7.57/7.56	2487 (all X_5 all N_6 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_6)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X_5)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(real,real,hAPP(nat,fun(real,real),root,N_6),X_5)))))) # label(fact_2704_real__root__pos__pos) # label(axiom) # label(non_clause).  [assumption].
7.57/7.56	2488 (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,B) != ti(X_a,A_1) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),A_1))))))) # label(fact_1598_xt1_I11_J) # label(axiom) # label(non_clause).  [assumption].
7.57/7.56	2489 (all A_1 all J_2 all K_4 all P_5 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),P_5)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,J_2),K_4),P_5)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),hAPP(int,int,hAPP(int,fun(int,int),multInv,P_5),J_2))),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),hAPP(int,int,hAPP(int,fun(int,int),multInv,P_5),K_4))),P_5))))) # label(fact_844_MultInv__zcong__prop1) # label(axiom) # label(non_clause).  [assumption].
7.57/7.57	2490 (all X_a (real_normed_vector(X_a) -> (all X ((zero_zero(X_a) != ti(X_a,X) -> one_one(real) = hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,sgn_sgn(X_a),X))) & (zero_zero(X_a) = ti(X_a,X) -> zero_zero(real) = hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,sgn_sgn(X_a),X))))))) # label(fact_2234_norm__sgn) # label(axiom) # label(non_clause).  [assumption].
7.57/7.57	2491 (all X_a all X_b (ord(X_b) -> (all X_1 all F all G (hBOOL(hAPP(fun(X_a,X_b),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,X_b),bool),ord_less_eq(fun(X_a,X_b)),F),G)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_a,X_b,F,X_1)),hAPP(X_a,X_b,G,X_1))))))) # label(fact_1545_le__funE) # label(axiom) # label(non_clause).  [assumption].
7.57/7.57	2492 (all X_5 all Y_4 hAPP(real,real,cos,hAPP(real,real,arccos,hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),X_5),hAPP(real,real,sqrt,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X_5),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),Y_4),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))))) = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),X_5),hAPP(real,real,sqrt,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X_5),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),Y_4),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))) # label(fact_2251_cos__arccos__lemma1) # label(axiom) # label(non_clause).  [assumption].
7.57/7.57	2493 (all Sa all Ta all A_2 all B_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A_2),B_1)) -> hBOOL(hAPP(fun(product_prod(product_prod(nat,nat),product_prod(nat,nat)),bool),bool,hAPP(product_prod(product_prod(nat,nat),product_prod(nat,nat)),fun(fun(product_prod(product_prod(nat,nat),product_prod(nat,nat)),bool),bool),member(product_prod(product_prod(nat,nat),product_prod(nat,nat))),hAPP(product_prod(nat,nat),product_prod(product_prod(nat,nat),product_prod(nat,nat)),hAPP(product_prod(nat,nat),fun(product_prod(nat,nat),product_prod(product_prod(nat,nat),product_prod(nat,nat))),product_Pair(product_prod(nat,nat),product_prod(nat,nat)),hAPP(nat,product_prod(nat,nat),hAPP(nat,fun(nat,product_prod(nat,nat)),product_Pair(nat,nat),A_2),Sa)),hAPP(nat,product_prod(nat,nat),hAPP(nat,fun(nat,product_prod(nat,nat)),product_Pair(nat,nat),B_1),Ta))),pair_less)))) # label(fact_3486_pair__lessI1) # label(axiom) # label(non_clause).  [assumption].
7.57/7.57	2494 (all X_a (archim1727834104eiling(X_a) -> (all X_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),X_1)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),hAPP(X_a,int,archimedean_ceiling(X_a),X_1))))))) # label(fact_3301_one__less__ceiling) # label(axiom) # label(non_clause).  [assumption].
7.57/7.57	2495 (all Z_1 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_1),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_1))),one_one(int))),D)))))) # label(fact_1987_incr__lemma) # label(axiom) # label(non_clause).  [assumption].
7.57/7.57	2496 (all N one_one(int) = hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),N),one_one(int))),N)) # label(fact_4356_coprime__plus__one__int) # label(axiom) # label(non_clause).  [assumption].
7.57/7.57	2497 (all I_1 all J_2 hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,I_1),J_2)),I_1))) # label(fact_3428_zgcd__zdvd1) # label(axiom) # label(non_clause).  [assumption].
7.57/7.57	2498 (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(int,X_a,number_number_of(X_a),V) = hAPP(nat,X_a,semiring_1_of_nat(X_a),hAPP(int,nat,number_number_of(nat),V))))))) # label(fact_1514_of__nat__number__of__eq) # label(axiom) # label(non_clause).  [assumption].
7.57/7.57	2499 (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_781_add__mono) # label(axiom) # label(non_clause).  [assumption].
7.57/7.57	2500 (all X_a (real_normed_vector(X_a) -> (all X_3 (hBOOL(hAPP(fun(nat,X_a),bool,cauchy(X_a),X_3)) -> hBOOL(hAPP(fun(nat,X_a),bool,bseq(X_a),X_3)))))) # label(fact_3493_Cauchy__Bseq) # label(axiom) # label(non_clause).  [assumption].
7.57/7.57	2501 (all Z (hAPP(int,int,abs_abs(int),Z) = one_one(int) <-> one_one(int) = ti(int,Z) | ti(int,Z) = hAPP(int,int,number_number_of(int),min_1))) # label(fact_1943_abs__eq__1__iff) # label(axiom) # label(non_clause).  [assumption].
7.57/7.57	2502 (all X_a all X_c all X_b (real_normed_vector(X_c) & topological_space(X_b) -> (all F all X_1 all A_3 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_3)) -> ((all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_3)) -> hBOOL(hAPP(X_b,bool,hAPP(fun(X_b,X_c),fun(X_b,bool),isCont(X_b,X_c),hAPP(X_a,fun(X_b,X_c),F,X_2)),X_1)))) -> hBOOL(hAPP(X_b,bool,hAPP(fun(X_b,X_c),fun(X_b,bool),isCont(X_b,X_c),hAPP(fun(X_a,bool),fun(X_b,X_c),hAPP(fun(X_b,fun(fun(X_a,bool),X_c)),fun(fun(X_a,bool),fun(X_b,X_c)),combc(X_b,fun(X_a,bool),X_c),hAPP(fun(X_b,fun(X_a,X_c)),fun(X_b,fun(fun(X_a,bool),X_c)),hAPP(fun(fun(X_a,X_c),fun(fun(X_a,bool),X_c)),fun(fun(X_b,fun(X_a,X_c)),fun(X_b,fun(fun(X_a,bool),X_c))),combb(fun(X_a,X_c),fun(fun(X_a,bool),X_c),X_b),big_co1399186613setsum(X_a,X_c)),hAPP(fun(X_a,fun(X_b,X_c)),fun(X_b,fun(X_a,X_c)),combc(X_a,X_b,X_c),F))),A_3)),X_1))))))) # label(fact_4926_isCont__setsum) # label(axiom) # label(non_clause).  [assumption].
7.57/7.57	2503 (all Y_1 all X_1 (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),zEven)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Y_1),zEven)) -> hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X_1),Y_1)),zEven))))) # label(fact_1271_EvenOdd_Oeven__plus__even) # label(axiom) # label(non_clause).  [assumption].
7.57/7.57	2504 (all X_b all X_a all F all X_1 all A_3 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_3)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),hAPP(X_a,X_b,F,X_1)),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),A_3))))) # label(fact_3638_imageI) # label(axiom) # label(non_clause).  [assumption].
7.57/7.57	2505 (all A_1 all B (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),B)) & -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),B),A_1)) -> -(-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),B)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),B),A_1))))) # label(fact_647_dvd_Oless__asym_H) # label(axiom) # label(non_clause).  [assumption].
7.57/7.57	2506 (all X_3 (hBOOL(hAPP(fun(nat,complex),bool,summable(complex),X_3)) -> hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,complex),fun(nat,real),hAPP(fun(complex,real),fun(fun(nat,complex),fun(nat,real)),combb(complex,real,nat),im),X_3))))) # label(fact_4047_Im_Osummable) # label(axiom) # label(non_clause).  [assumption].
7.57/7.57	2507 (all L all U_1 hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastAtMost(int),L),U_1)))) # label(fact_4534_finite__atLeastAtMost__int) # label(axiom) # label(non_clause).  [assumption].
7.57/7.57	2508 (all X_a (banach(X_a) -> (all F (hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),F)) <-> (all E (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),E)) -> (exists N_3 all M_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_3),M_2)) -> (all N_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,norm_norm(X_a),hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),M_2),N_2)))),E))))))))))) # label(fact_4287_summable__Cauchy) # label(axiom) # label(non_clause).  [assumption].
7.57/7.57	2509 (all Z_1 all W (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),W),Z_1)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Z_1),W)))) # label(fact_24_zle__linear) # label(axiom) # label(non_clause).  [assumption].
7.57/7.57	2510 (all X_a (dvd(X_a) & comm_ring(X_a) -> (all Ta all D_1 all D_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),D_1),D_2)) -> (all X_2 all K_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),D_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),X_2),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),K_1),D_2))),Ta))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),D_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X_2),Ta))))))))) # label(fact_487_inf__period_I3_J) # label(axiom) # label(non_clause).  [assumption].
7.57/7.57	2511 (all K_4 all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),K_4),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N))) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),K_4),M)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N),M)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),K_4),N)))))) # label(fact_677_dvd__diffD1) # label(axiom) # label(non_clause).  [assumption].
7.57/7.57	2512 (all X_a (field_char_0(X_a) -> (all N_1 all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_2),field_char_0_Rats(X_a))) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_2),N_1)),field_char_0_Rats(X_a))))))) # label(fact_3697_Rats__power) # label(axiom) # label(non_clause).  [assumption].
7.57/7.57	2513 (all B_1 all A_2 all P_4 (hBOOL(hAPP(int,bool,zprime,P_4)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_2),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),P_4),one_one(int)))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),B_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B_1),A_2)) -> hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),B_1),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),wset,A_2),P_4)))))))) # label(fact_843_wset__mem) # label(axiom) # label(non_clause).  [assumption].
7.57/7.57	2514 (all X_a (comm_monoid_add(X_a) -> (all F all Ma all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),N_1)) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(nat,X_a,F,Ma)),hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),hAPP(nat,nat,suc,Ma)),N_1))) = hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),Ma),N_1)))))) # label(fact_4203_setsum__head__upt__Suc) # label(axiom) # label(non_clause).  [assumption].
7.57/7.57	2515 (all X_a all A_3 ti(fun(X_a,bool),A_3) = hAPP(fun(X_a,bool),fun(X_a,bool),uminus_uminus(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),uminus_uminus(fun(X_a,bool)),A_3))) # label(fact_2193_double__complement) # label(axiom) # label(non_clause).  [assumption].
7.57/7.57	2516 (all N_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(nat,int,semiring_1_of_nat(int),N_1))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)))) # label(fact_1399_zero__less__int__conv) # label(axiom) # label(non_clause).  [assumption].
7.57/7.57	2517 (all X_b all X_a (real_normed_field(X_a) -> (all G all A_3 all Y_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co1399186613setsum(X_b,X_a),G),A_3)),Y_1) = hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co1399186613setsum(X_b,X_a),hAPP(X_a,fun(X_b,X_a),hAPP(fun(X_b,fun(X_a,X_a)),fun(X_a,fun(X_b,X_a)),combc(X_b,X_a,X_a),hAPP(fun(X_b,X_a),fun(X_b,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_b,X_a),fun(X_b,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),X_b),inverse_divide(X_a)),G)),Y_1)),A_3)))) # label(fact_4184_divide_Osetsum) # label(axiom) # label(non_clause).  [assumption].
7.57/7.57	2518 (all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_1),zero_zero(real))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,sqrt,X_1)),zero_zero(real))))) # label(fact_1627_real__sqrt__lt__0__iff) # label(axiom) # label(non_clause).  [assumption].
7.57/7.57	2519 (all X_a (real_normed_vector(X_a) -> (all F all G all L_2 (hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),G),L_2),sequentially)) -> (hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),minus_minus(X_a)),F)),G)),zero_zero(X_a)),sequentially)) -> hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),F),L_2),sequentially))))))) # label(fact_4448_LIMSEQ__diff__approach__zero) # label(axiom) # label(non_clause).  [assumption].
7.57/7.57	2520 (all X_1 all A_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(real,int,archimedean_ceiling(real),X_1)),A_2)) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_1),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(int,real,real_1(int),A_2)),one_one(real)))))) # label(fact_3416_ceiling__less__eq) # label(axiom) # label(non_clause).  [assumption].
7.57/7.57	2521 (all K (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),min_1),K)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),min_1),hAPP(int,int,bit1,K))))) # label(fact_295_rel__simps_I9_J) # label(axiom) # label(non_clause).  [assumption].
7.57/7.57	2522 (all X (hBOOL(hAPP(nat,bool,even_odd_even(nat),X)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),X),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat)))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,suc,X)),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat)))))) # label(fact_2446_even__nat__plus__one__div__two) # label(axiom) # label(non_clause).  [assumption].
7.57/7.57	2523 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(int,nat,number_number_of(nat),pls)),N)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,M)),N) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,pls)))))) # label(fact_1430_Suc__diff__eq__diff__pred) # label(axiom) # label(non_clause).  [assumption].
7.57/7.57	2524 (all X_a all X_b all X_c ti(fun(fun(X_a,fun(X_b,X_c)),fun(product_prod(X_a,X_b),X_c)),product_prod_case(X_a,X_b,X_c)) = product_prod_case(X_a,X_b,X_c)) # label(tsy_c_Product__Type_Oprod_Oprod__case_res) # label(axiom) # label(non_clause).  [assumption].
7.57/7.57	2525 (all X_a (number(X_a) & linord1117847801e_zero(X_a) -> (all B_1 all C_1 all W_1 ((-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(int,X_a,number_number_of(X_a),W_1)),C_1)),B_1))) & (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(int,X_a,number_number_of(X_a),W_1))))) & (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_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),W_1)),C_1)))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),B_1),C_1)),hAPP(int,X_a,number_number_of(X_a),W_1))))))) # label(fact_1747_divide__less__eq__number__of) # label(axiom) # label(non_clause).  [assumption].
7.57/7.57	2526 (all X hAPP(complex,complex,cnj,hAPP(complex,complex,uminus_uminus(complex),X)) = hAPP(complex,complex,uminus_uminus(complex),hAPP(complex,complex,cnj,X))) # label(fact_2935_cnj_Ominus) # label(axiom) # label(non_clause).  [assumption].
7.57/7.57	2527 (all X_a all A_3 hAPP(fun(fun(X_a,bool),bool),fun(fun(X_a,bool),bool),collect(fun(X_a,bool)),hAPP(fun(fun(X_a,bool),fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),bool),hAPP(fun(fun(fun(X_a,bool),bool),bool),fun(fun(fun(X_a,bool),fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),bool)),combb(fun(fun(X_a,bool),bool),bool,fun(X_a,bool)),fEx(fun(X_a,bool))),hAPP(fun(fun(X_a,bool),bool),fun(fun(X_a,bool),fun(fun(X_a,bool),bool)),hAPP(fun(fun(X_a,bool),fun(fun(fun(X_a,bool),bool),fun(fun(X_a,bool),bool))),fun(fun(fun(X_a,bool),bool),fun(fun(X_a,bool),fun(fun(X_a,bool),bool))),combc(fun(X_a,bool),fun(fun(X_a,bool),bool),fun(fun(X_a,bool),bool)),hAPP(fun(fun(X_a,bool),fun(fun(X_a,bool),fun(bool,bool))),fun(fun(X_a,bool),fun(fun(fun(X_a,bool),bool),fun(fun(X_a,bool),bool))),hAPP(fun(fun(fun(X_a,bool),fun(bool,bool)),fun(fun(fun(X_a,bool),bool),fun(fun(X_a,bool),bool))),fun(fun(fun(X_a,bool),fun(fun(X_a,bool),fun(bool,bool))),fun(fun(X_a,bool),fun(fun(fun(X_a,bool),bool),fun(fun(X_a,bool),bool)))),combb(fun(fun(X_a,bool),fun(bool,bool)),fun(fun(fun(X_a,bool),bool),fun(fun(X_a,bool),bool)),fun(X_a,bool)),combs(fun(X_a,bool),bool,bool)),hAPP(fun(fun(X_a,bool),fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(fun(X_a,bool),fun(bool,bool))),hAPP(fun(fun(fun(X_a,bool),bool),fun(fun(X_a,bool),fun(bool,bool))),fun(fun(fun(X_a,bool),fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(fun(X_a,bool),fun(bool,bool)))),combb(fun(fun(X_a,bool),bool),fun(fun(X_a,bool),fun(bool,bool)),fun(X_a,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(fun(X_a,bool),bool),fun(fun(X_a,bool),fun(bool,bool))),combb(bool,fun(bool,bool),fun(X_a,bool)),fconj)),hAPP(fun(fun(X_a,bool),fun(X_a,bool)),fun(fun(X_a,bool),fun(fun(X_a,bool),bool)),hAPP(fun(fun(X_a,bool),fun(fun(fun(X_a,bool),fun(X_a,bool)),fun(fun(X_a,bool),bool))),fun(fun(fun(X_a,bool),fun(X_a,bool)),fun(fun(X_a,bool),fun(fun(X_a,bool),bool))),combc(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),fun(fun(X_a,bool),bool)),hAPP(fun(fun(X_a,bool),fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(fun(fun(X_a,bool),fun(X_a,bool)),fun(fun(X_a,bool),bool))),hAPP(fun(fun(fun(X_a,bool),bool),fun(fun(fun(X_a,bool),fun(X_a,bool)),fun(fun(X_a,bool),bool))),fun(fun(fun(X_a,bool),fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(fun(fun(X_a,bool),fun(X_a,bool)),fun(fun(X_a,bool),bool)))),combb(fun(fun(X_a,bool),bool),fun(fun(fun(X_a,bool),fun(X_a,bool)),fun(fun(X_a,bool),bool)),fun(X_a,bool)),combb(fun(X_a,bool),bool,fun(X_a,bool))),fequal(fun(X_a,bool)))),uminus_uminus(fun(X_a,bool)))))),hAPP(fun(fun(X_a,bool),fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),bool),hAPP(fun(fun(fun(X_a,bool),bool),bool),fun(fun(fun(X_a,bool),fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),bool)),combb(fun(fun(X_a,bool),bool),bool,fun(X_a,bool)),hAPP(fun(X_a,bool),fun(fun(fun(X_a,bool),bool),bool),member(fun(X_a,bool)),A_3)),pow(X_a))))) = hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),pow(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),uminus_uminus(fun(X_a,bool)),A_3))) # label(fact_4428_Pow__Compl) # label(axiom) # label(non_clause).  [assumption].
7.57/7.57	2528 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,M)),N)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N)))) # label(fact_1249_Suc__leD) # label(axiom) # label(non_clause).  [assumption].
7.57/7.57	2529 (all N all B all A_1 all P_5 (hBOOL(hAPP(int,bool,zprime,P_5)) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),P_5),A_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),P_5),N)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),B))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),P_5),N)),B)))))) # label(fact_202_zprime__power__zdvd__cancel__left) # label(axiom) # label(non_clause).  [assumption].
7.57/7.57	2530 (all M all I_1 all J_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),J_2)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),J_2))))) # label(fact_558_trans__less__add2) # label(axiom) # label(non_clause).  [assumption].
7.57/7.57	2531 (all Ma all N_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Ma),hAPP(int,int,number_number_of(int),N_1))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,real_1(int),Ma)),hAPP(int,real,number_number_of(real),N_1))))) # label(fact_3389_number__of__le__real__of__int__iff2) # label(axiom) # label(non_clause).  [assumption].
7.57/7.57	2532 (all X_a (archim1727834104eiling(X_a) -> (all X_1 all V_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),hAPP(int,X_a,number_number_of(X_a),V_1))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(X_a,int,archim2085082626_floor(X_a),X_1)),hAPP(int,int,number_number_of(int),V_1))))))) # label(fact_2885_floor__less__number__of) # label(axiom) # label(non_clause).  [assumption].
7.57/7.57	2533 (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_220_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) # label(axiom) # label(non_clause).  [assumption].
7.57/7.57	2534 (all A_2 all B_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A_2)) <-> hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(int,rat,hAPP(int,fun(int,rat),fract,A_2),B_1)))))) # label(fact_3783_zero__less__Fract__iff) # label(axiom) # label(non_clause).  [assumption].
7.57/7.57	2535 (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_374_mult__nonpos__nonpos) # label(axiom) # label(non_clause).  [assumption].
7.57/7.57	2536 (all X_a (comm_semiring_1(X_a) -> (all A_1 zero_zero(X_a) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),zero_zero(X_a)),A_1)))) # label(fact_235_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J) # label(axiom) # label(non_clause).  [assumption].
7.57/7.57	2537 (all A_1 all B all C all N (hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),C),N) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),B) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),one_one(nat)),N)) -> (hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,A_1),B) = one_one(int) -> (exists K_1 hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),K_1),N) = hAPP(int,int,abs_abs(int),A_1)))))) # label(fact_3476_int__relprime__power__divisors) # label(axiom) # label(non_clause).  [assumption].
7.57/7.57	2538 (all X_a (real_normed_vector(X_a) -> (all X_3 (hBOOL(hAPP(fun(nat,X_a),bool,bseq(X_a),X_3)) <-> (exists K_1 ((exists N_3 all N_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(nat,X_a,X_3,N_2)),hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(nat,X_a,X_3,N_3))))),K_1))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),K_1)))))))) # label(fact_3490_Bseq__iff3) # label(axiom) # label(non_clause).  [assumption].
7.57/7.57	2539 (all X_a all X_b (real_normed_algebra(X_b) & comm_ring_1(X_b) -> (all X_3 all L_2 all S ((all N_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),N_2),S)) -> hBOOL(hAPP(filter(nat),bool,hAPP(X_b,fun(filter(nat),bool),hAPP(fun(nat,X_b),fun(X_b,fun(filter(nat),bool)),tendsto(nat,X_b),hAPP(X_a,fun(nat,X_b),X_3,N_2)),hAPP(X_a,X_b,L_2,N_2)),sequentially)))) -> hBOOL(hAPP(filter(nat),bool,hAPP(X_b,fun(filter(nat),bool),hAPP(fun(nat,X_b),fun(X_b,fun(filter(nat),bool)),tendsto(nat,X_b),hAPP(fun(X_a,bool),fun(nat,X_b),hAPP(fun(nat,fun(fun(X_a,bool),X_b)),fun(fun(X_a,bool),fun(nat,X_b)),combc(nat,fun(X_a,bool),X_b),hAPP(fun(nat,fun(X_a,X_b)),fun(nat,fun(fun(X_a,bool),X_b)),hAPP(fun(fun(X_a,X_b),fun(fun(X_a,bool),X_b)),fun(fun(nat,fun(X_a,X_b)),fun(nat,fun(fun(X_a,bool),X_b))),combb(fun(X_a,X_b),fun(fun(X_a,bool),X_b),nat),big_co302546470etprod(X_a,X_b)),hAPP(fun(X_a,fun(nat,X_b)),fun(nat,fun(X_a,X_b)),combc(X_a,nat,X_b),X_3))),S)),hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co302546470etprod(X_a,X_b),L_2),S)),sequentially)))))) # label(fact_4657_LIMSEQ__setprod) # label(axiom) # label(non_clause).  [assumption].
7.57/7.57	2540 (all P_1 all I hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),combs(nat,bool,bool),hAPP(fun(nat,bool),fun(nat,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fconj),P_1)),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),I)))))) # label(fact_3869_finite__M__bounded__by__nat) # label(axiom) # label(non_clause).  [assumption].
7.57/7.57	2541 (all K_4 all L_4 hAPP(int,int,bit1,K_4) != hAPP(int,int,bit0,L_4)) # label(fact_118_rel__simps_I50_J) # label(axiom) # label(non_clause).  [assumption].
7.57/7.57	2542 (all K_4 hAPP(int,int,bit0,K_4) != min_1) # label(fact_290_rel__simps_I45_J) # label(axiom) # label(non_clause).  [assumption].
7.57/7.57	2543 (all N all A_1 all B all P_5 (hBOOL(hAPP(int,bool,zprime,P_5)) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),P_5),B)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),P_5),N)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),B))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),P_5),N)),A_1)))))) # label(fact_201_zprime__power__zdvd__cancel__right) # label(axiom) # label(non_clause).  [assumption].
7.57/7.57	2544 (all C_2 hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),C_2)))) # label(fact_3663_Nat__Transfer_Otransfer__int__nat__set__function__closures_I5_J) # label(axiom) # label(non_clause).  [assumption].
7.57/7.57	2545 (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_1869_abs__triangle__ineq2) # label(axiom) # label(non_clause).  [assumption].
7.57/7.57	2546 (all X_a (topological_space(X_a) -> (all K all F all A_2 (hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),F),A_2),sequentially)) -> hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),hAPP(fun(nat,nat),fun(nat,X_a),hAPP(fun(nat,X_a),fun(fun(nat,nat),fun(nat,X_a)),combb(nat,X_a,nat),F),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),K))),A_2),sequentially)))))) # label(fact_4446_LIMSEQ__ignore__initial__segment) # label(axiom) # label(non_clause).  [assumption].
7.57/7.57	2547 (all P_1 all N_1 all K ((zero_zero(nat) != K -> (all I_2 all J_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),J_1),K)) -> (N_1 = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),I_2)),J_1) -> hBOOL(hAPP(nat,bool,P_1,I_2)))))) & (zero_zero(nat) = K -> hBOOL(hAPP(nat,bool,P_1,zero_zero(nat)))) <-> hBOOL(hAPP(nat,bool,P_1,hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),N_1),K))))) # label(fact_1131_split__div) # label(axiom) # label(non_clause).  [assumption].
7.57/7.57	2548 (all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,number_number_of(real),min_1)),Y)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),Y),one_one(real))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,arccos,Y))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,arccos,Y)),pi))))) # label(fact_2274_arccos__lt__bounded) # label(axiom) # label(non_clause).  [assumption].
7.57/7.57	2549 (all M zero_zero(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),M)) # label(fact_659_diff__self__eq__0) # label(axiom) # label(non_clause).  [assumption].
7.57/7.57	2550 (all A_2 all R_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),R_1)) -> (hBOOL(hAPP(fun(nat,real),bool,summable(real),A_2)) -> (exists N_3 all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_3),N_2)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,abs_abs(real),hAPP(fun(nat,real),real,suminf(real),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),A_2),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),N_2))))),R_1))))))) # label(fact_4056_suminf__exist__split) # label(axiom) # label(non_clause).  [assumption].
7.57/7.57	2551 (all P_1 all A_2 all B_1 ((all D_3 (A_2 = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B_1),D_3) -> hBOOL(hAPP(nat,bool,P_1,D_3)))) & (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A_2),B_1)) -> hBOOL(hAPP(nat,bool,P_1,zero_zero(nat)))) <-> hBOOL(hAPP(nat,bool,P_1,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),A_2),B_1))))) # label(fact_700_nat__diff__split) # label(axiom) # label(non_clause).  [assumption].
7.57/7.57	2552 (all Y_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(real,real,hAPP(nat,fun(real,real),root,N_1),Y_1))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),Y_1))))) # label(fact_2691_real__root__ge__0__iff) # label(axiom) # label(non_clause).  [assumption].
7.57/7.57	2553 (all X_a (real_normed_vector(X_a) -> (all K all F (hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),F)) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),K))),hAPP(fun(nat,X_a),X_a,suminf(X_a),hAPP(fun(nat,nat),fun(nat,X_a),hAPP(fun(nat,X_a),fun(fun(nat,nat),fun(nat,X_a)),combb(nat,X_a,nat),F),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),K)))) = hAPP(fun(nat,X_a),X_a,suminf(X_a),F))))) # label(fact_4169_suminf__split__initial__segment) # label(axiom) # label(non_clause).  [assumption].
7.57/7.57	2554 (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_1881_abs__diff__triangle__ineq) # label(axiom) # label(non_clause).  [assumption].
7.57/7.57	2555 (all Z_1 all W (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),Z_1),W)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),W),Z_1)) -> W = Z_1))) # label(fact_651_real__le__antisym) # label(axiom) # label(non_clause).  [assumption].
7.57/7.57	2556 (all X all Y (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Y)) -> hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),hAPP(product_prod(int,int),int,product_snd(int,int),hAPP(nat,product_prod(int,int),hAPP(nat,fun(nat,product_prod(int,int)),bezw,Y),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),X),Y)))),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(product_prod(int,int),int,product_fst(int,int),hAPP(nat,product_prod(int,int),hAPP(nat,fun(nat,product_prod(int,int)),bezw,Y),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),X),Y)))),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(product_prod(int,int),int,product_snd(int,int),hAPP(nat,product_prod(int,int),hAPP(nat,fun(nat,product_prod(int,int)),bezw,Y),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),X),Y)))),hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),X),Y))))) = hAPP(nat,product_prod(int,int),hAPP(nat,fun(nat,product_prod(int,int)),bezw,X),Y))) # label(fact_3114_bezw__non__0) # label(axiom) # label(non_clause).  [assumption].
7.57/7.57	2557 (all X_a (real_normed_vector(X_a) -> (all X_3 (hBOOL(hAPP(fun(nat,X_a),bool,bseq(X_a),X_3)) <-> (exists K_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),K_2)) & (all N_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),hAPP(nat,X_a,X_3,N_2))),K_2))))))))) # label(fact_3494_Bseq__def) # label(axiom) # label(non_clause).  [assumption].
7.57/7.57	2558 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X),one_one(real))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,exp(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),X),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),one_one(real)),X)))))) # label(fact_2505_aux4) # label(axiom) # label(non_clause).  [assumption].
7.57/7.57	2559 (all 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)) = hAPP(fun(nat,bool),nat,finite_card(nat),A_3)) # label(fact_3651_Nat__Transfer_Otransfer__nat__int__set__functions_I1_J) # label(axiom) # label(non_clause).  [assumption].
7.57/7.57	2560 (all A_2 all Ma (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_2),Ma)) -> hBOOL(hAPP(fun(fun(int,bool),bool),bool,hAPP(fun(int,bool),fun(fun(fun(int,bool),bool),bool),member(fun(int,bool)),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),bnorRset,A_2),Ma)),hAPP(int,fun(fun(int,bool),bool),rsetR,Ma))))) # label(fact_3629_Bnor__in__RsetR) # label(axiom) # label(non_clause).  [assumption].
7.57/7.57	2561 (all K_4 hAPP(int,rat,number_number_of(rat),K_4) = hAPP(int,rat,hAPP(int,fun(int,rat),fract,hAPP(int,int,number_number_of(int),K_4)),one_one(int))) # label(fact_3775_rat__number__collapse_I3_J) # label(axiom) # label(non_clause).  [assumption].
7.57/7.57	2562 (all A_1 all B all C hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A_1),B)),C) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),B),C))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),B),C))),C))) # label(fact_1083_div__mult1__eq) # label(axiom) # label(non_clause).  [assumption].
7.57/7.57	2563 (all Q_2 all P_1 ((all A_4 all B_4 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B_4)) -> hBOOL(hAPP(rat,bool,P_1,hAPP(int,rat,hAPP(int,fun(int,rat),fract,A_4),B_4))))) -> hBOOL(hAPP(rat,bool,P_1,Q_2)))) # label(fact_3795_Rat__induct__pos) # label(axiom) # label(non_clause).  [assumption].
7.57/7.57	2564 (all X_a hAPP(product_prod(int,int),X_a,abs_Frac(X_a),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),zero_zero(int)),one_one(int))) = zero_frac(X_a)) # label(fact_3680_Nitpick_Ozero__frac__def) # label(axiom) # label(non_clause).  [assumption].
7.57/7.57	2565 (all X_a (number_ring(X_a) & ring_char_0(X_a) -> (all X_1 all Y_1 (ti(int,X_1) = ti(int,Y_1) <-> hAPP(int,X_a,number_number_of(X_a),X_1) = hAPP(int,X_a,number_number_of(X_a),Y_1))))) # label(fact_89_eq__number__of) # label(axiom) # label(non_clause).  [assumption].
7.57/7.57	2566 (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_383_mult__strict__right__mono__neg) # label(axiom) # label(non_clause).  [assumption].
7.57/7.57	2567 (all X_a (linorder(X_a) -> (all X all Y hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),Y)),Y))))) # label(fact_4828_min__max_Oinf__le2) # label(axiom) # label(non_clause).  [assumption].
7.57/7.57	2568 (all Ma all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),N_1)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,Ma)),hAPP(nat,nat,suc,N_1))))) # label(fact_1237_Suc__less__eq) # label(axiom) # label(non_clause).  [assumption].
7.57/7.57	2569 (all X_b all X_a (field(X_a) -> (all F all A_3 all R_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co1399186613setsum(X_b,X_a),F),A_3)),R_1) = hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co1399186613setsum(X_b,X_a),hAPP(X_a,fun(X_b,X_a),hAPP(fun(X_b,fun(X_a,X_a)),fun(X_a,fun(X_b,X_a)),combc(X_b,X_a,X_a),hAPP(fun(X_b,X_a),fun(X_b,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_b,X_a),fun(X_b,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),X_b),inverse_divide(X_a)),F)),R_1)),A_3)))) # label(fact_4218_setsum__divide__distrib) # label(axiom) # label(non_clause).  [assumption].
7.57/7.57	2570 (all M all K_4 all J_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_4),J_2)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_2),K_4))),M) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,J_2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_4),M)))) # label(fact_1393_diff__Suc__diff__eq2) # label(axiom) # label(non_clause).  [assumption].
7.57/7.57	2571 (all X_1 (X_1 = hAPP(real,real,hAPP(real,fun(real,real),powr,X_1),one_one(real)) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X_1)))) # label(fact_3379_powr__one__gt__zero__iff) # label(axiom) # label(non_clause).  [assumption].
7.57/7.57	2572 (all A_1 all B all P_5 (hBOOL(hAPP(nat,bool,prime,P_5)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),P_5),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A_1),B))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),P_5),A_1)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),P_5),B))))) # label(fact_3053_prime__divprod) # label(axiom) # label(non_clause).  [assumption].
7.57/7.57	2573 (all P_2 all P_1 all X_1 ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X_1)) -> (hBOOL(P_1) <-> hBOOL(P_2))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X_1)) & hBOOL(P_1) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X_1)) & hBOOL(P_2)))) # label(fact_545_conj__le__cong) # label(axiom) # label(non_clause).  [assumption].
7.57/7.57	2574 (all X_a (semiring_div(X_a) -> (all A_1 all B all C hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),C))),B) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),A_1),B)))) # label(fact_978_mod__mult__self2) # label(axiom) # label(non_clause).  [assumption].
7.57/7.57	2575 (all X_a (real_normed_vector(X_a) -> (all R_1 all X_3 all L_2 (hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),X_3),L_2),sequentially)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),R_1)) -> (exists No all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),No),N_2)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(nat,X_a,X_3,N_2)),L_2))),R_1))))))))) # label(fact_4519_LIMSEQ__D) # label(axiom) # label(non_clause).  [assumption].
7.57/7.57	2576 (all V_1 all V_2 ((-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),V_1),V_2)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),V_1),pls))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(int,nat,number_number_of(nat),V_1)),hAPP(int,nat,number_number_of(nat),V_2))))) # label(fact_212_le__nat__number__of) # label(axiom) # label(non_clause).  [assumption].
7.57/7.57	2577 (all X_a all X_b (comm_monoid_add(X_b) -> (all B_1 all A_2 all S (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),S)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_2),S)) -> hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),hAPP(X_b,fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(X_b,fun(X_a,X_b)),combc(X_a,X_b,X_b),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,X_b)),hAPP(fun(X_a,fun(X_b,fun(X_b,X_b))),fun(fun(X_a,X_b),fun(X_a,fun(X_b,X_b))),combs(X_a,X_b,fun(X_b,X_b)),hAPP(fun(X_a,bool),fun(X_a,fun(X_b,fun(X_b,X_b))),hAPP(fun(bool,fun(X_b,fun(X_b,X_b))),fun(fun(X_a,bool),fun(X_a,fun(X_b,fun(X_b,X_b)))),combb(bool,fun(X_b,fun(X_b,X_b)),X_a),if(X_b)),hAPP(X_a,fun(X_a,bool),fequal(X_a),A_2))),B_1)),zero_zero(X_b))),S) = hAPP(X_a,X_b,B_1,A_2)) & (-hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_2),S)) -> hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),hAPP(X_b,fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(X_b,fun(X_a,X_b)),combc(X_a,X_b,X_b),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,X_b)),hAPP(fun(X_a,fun(X_b,fun(X_b,X_b))),fun(fun(X_a,X_b),fun(X_a,fun(X_b,X_b))),combs(X_a,X_b,fun(X_b,X_b)),hAPP(fun(X_a,bool),fun(X_a,fun(X_b,fun(X_b,X_b))),hAPP(fun(bool,fun(X_b,fun(X_b,X_b))),fun(fun(X_a,bool),fun(X_a,fun(X_b,fun(X_b,X_b)))),combb(bool,fun(X_b,fun(X_b,X_b)),X_a),if(X_b)),hAPP(X_a,fun(X_a,bool),fequal(X_a),A_2))),B_1)),zero_zero(X_b))),S) = zero_zero(X_b)))))) # label(fact_4216_setsum__delta_H) # label(axiom) # label(non_clause).  [assumption].
7.57/7.57	2578 (all X hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),hAPP(complex,real,re,X))),hAPP(complex,real,norm_norm(complex),X)))) # label(fact_3008_abs__Re__le__cmod) # label(axiom) # label(non_clause).  [assumption].
7.57/7.57	2579 (all K all 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))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),L)))) # label(fact_496_less__bin__lemma) # label(axiom) # label(non_clause).  [assumption].
7.57/7.57	2580 (all Ma all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Ma)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),Ma),N_1))))) # label(fact_595_nat__0__less__mult__iff) # label(axiom) # label(non_clause).  [assumption].
7.57/7.57	2581 (all V hAPP(complex,real,im,hAPP(int,complex,number_number_of(complex),V)) = zero_zero(real)) # label(fact_2979_complex__Im__number__of) # label(axiom) # label(non_clause).  [assumption].
7.57/7.57	2582 (all X_a (real_normed_vector(X_a) -> (all A_1 all B all B_5 hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B),B_5)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_1),B)),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_1),B_5))))) # label(fact_4717_scaleR_Oadd__right) # label(axiom) # label(non_clause).  [assumption].
7.57/7.57	2583 (all N_1 all X_1 exists T_4 (hAPP(real,real,exp(real),X_1) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),inverse_divide(real)),hAPP(real,fun(nat,real),power_power(real),X_1))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),fact_fact(nat)))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),N_1))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,exp(real),T_4)),hAPP(nat,real,real_1(nat),hAPP(nat,nat,fact_fact(nat),N_1)))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X_1),N_1))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),T_4)),hAPP(real,real,abs_abs(real),X_1))))) # label(fact_4270_Maclaurin__exp__le) # label(axiom) # label(non_clause).  [assumption].
7.57/7.57	2584 (all X_a all X_b (real_normed_vector(X_b) -> (all F all A_3 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),zero_zero(X_b)),A_3)) -> hBOOL(hAPP(filter(X_a),bool,hAPP(real,fun(filter(X_a),bool),hAPP(fun(X_a,real),fun(real,fun(filter(X_a),bool)),tendsto(X_a,real),hAPP(fun(X_a,X_b),fun(X_a,real),hAPP(fun(X_b,real),fun(fun(X_a,X_b),fun(X_a,real)),combb(X_b,real,X_a),norm_norm(X_b)),F)),zero_zero(real)),A_3)))))) # label(fact_4454_tendsto__norm__zero) # label(axiom) # label(non_clause).  [assumption].
7.57/7.57	2585 (all N all X hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(int,real,real_1(int),N)),hAPP(int,real,real_1(int),X))),hAPP(int,real,real_1(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),N),X)))))) # label(fact_3409_real__of__int__div2) # label(axiom) # label(non_clause).  [assumption].
7.57/7.57	2586 (all N hAPP(int,nat,nat_1,hAPP(int,int,uminus_uminus(int),hAPP(nat,int,semiring_1_of_nat(int),N))) = zero_zero(nat)) # label(fact_2167_nat__zminus__int) # label(axiom) # label(non_clause).  [assumption].
7.57/7.57	2587 (all N (zero_zero(nat) != N -> one_one(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),one_one(nat))),N))) # label(fact_3287_coprime__minus__one__nat) # label(axiom) # label(non_clause).  [assumption].
7.57/7.57	2588 (all X_a (metric_space(X_a) -> dist_dist(X_a) = ti(fun(X_a,fun(X_a,real)),dist_dist(X_a)))) # label(tsy_c_RealVector_Odist__class_Odist_1_res) # label(axiom) # label(non_clause).  [assumption].
7.57/7.57	2589 (all Y all X all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),Y)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(nat,fun(real,real),root,N),X)),hAPP(real,real,hAPP(nat,fun(real,real),root,N),Y))))))) # label(fact_2705_real__root__less__mono__lemma) # label(axiom) # label(non_clause).  [assumption].
7.57/7.57	2590 (all X_a (semiring_1(X_a) -> ti(fun(X_a,bool),iszero(X_a)) = iszero(X_a))) # label(tsy_c_Int_Oiszero_res) # label(axiom) # label(non_clause).  [assumption].
7.57/7.57	2591 (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_217_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J) # label(axiom) # label(non_clause).  [assumption].
7.57/7.57	2592 (all X_a all M_1 (hBOOL(hAPP(fun(list(X_a),bool),bool,finite_finite_1(list(X_a)),M_1)) -> (exists N_2 all X_2 (hBOOL(hAPP(fun(list(X_a),bool),bool,hAPP(list(X_a),fun(fun(list(X_a),bool),bool),member(list(X_a)),X_2),M_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(list(X_a),nat,size_size(list(X_a)),X_2)),N_2)))))) # label(fact_3558_finite__maxlen) # label(axiom) # label(non_clause).  [assumption].
7.57/7.57	2593 (all X all Y hAPP(nat,nat,hAPP(nat,fun(nat,nat),nat_lcm,X),Y) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X),Y)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),nat_gcd,X),Y))) # label(fact_3658_Nitpick_Onat__lcm__def) # label(axiom) # label(non_clause).  [assumption].
7.57/7.57	2594 (all X_1 hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),X_1))))) # label(fact_3865_bdd__nat__set__l__finite) # label(axiom) # label(non_clause).  [assumption].
7.57/7.57	2595 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),M),N) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N)),N))))) # label(fact_1416_div__geq) # label(axiom) # label(non_clause).  [assumption].
7.57/7.57	2596 (all X_a (order(X_a) -> (all X_1 all Y_1 all F (hBOOL(hAPP(fun(nat,X_a),bool,hAPP(fun(nat,fun(nat,bool)),fun(fun(nat,X_a),bool),mono(nat,X_a),dvd_dvd(nat)),F)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_1),Y_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(nat,X_a,F,X_1)),hAPP(nat,X_a,F,Y_1)))))))) # label(fact_4793_dvd_OmonoD) # label(axiom) # label(non_clause).  [assumption].
7.57/7.57	2597 (all X_a (real_normed_vector(X_a) -> (all R_1 all X_3 all A_2 (hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),X_3),A_2),sequentially)) -> hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(X_a,X_a),fun(fun(nat,X_a),fun(nat,X_a)),combb(X_a,X_a,nat),hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),R_1)),X_3)),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),R_1),A_2)),sequentially)))))) # label(fact_4729_scaleR__right_OLIMSEQ) # label(axiom) # label(non_clause).  [assumption].
7.57/7.57	2598 (all P_4 (hBOOL(hAPP(int,bool,zprime,P_4)) <-> (all M_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),M_2),P_4)) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),M_2)) -> ti(int,P_4) = ti(int,M_2) | ti(int,M_2) = one_one(int))) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),P_4)))) # label(fact_273_zprime__def) # label(axiom) # label(non_clause).  [assumption].
7.57/7.57	2599 (all Ma all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,zero_zero(nat))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),Ma),N_1))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,zero_zero(nat))),N_1)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,zero_zero(nat))),Ma)))) # label(fact_1390_one__le__mult__iff) # label(axiom) # label(non_clause).  [assumption].
7.57/7.57	2600 (all X_1 all Y_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(nat,int,semiring_1_of_nat(int),X_1)),hAPP(nat,int,semiring_1_of_nat(int),Y_1))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_1),Y_1)))) # label(fact_1317_Nat__Transfer_Otransfer__int__nat__relations_I4_J) # label(axiom) # label(non_clause).  [assumption].
7.57/7.57	2601 (all X all Y hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),Y),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X),Y)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X),Y))) # label(fact_721_diff__square) # label(axiom) # label(non_clause).  [assumption].
7.57/7.57	2602 (all M all K_4 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)),K_4)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),M)) -> (hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),N) = K_4 -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),K_4))))))) # label(fact_1385_prod__mn__less__k) # label(axiom) # label(non_clause).  [assumption].
7.57/7.57	2603 (all F all A_2 all B_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A_2),B_1)) -> ((all X_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_2),B_1)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A_2),X_2)) -> hBOOL(hAPP(real,bool,hAPP(fun(real,real),fun(real,bool),isCont(real,real),F),X_2)))) -> ((all X_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A_2),X_2)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_2),B_1)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),F),X_2),zero_zero(real))))) -> (all X_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A_2),X_2)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_2),B_1)) -> hAPP(real,real,F,A_2) = hAPP(real,real,F,X_2))))))) # label(fact_4930_DERIV__isconst1) # label(axiom) # label(non_clause).  [assumption].
7.57/7.57	2604 (all X_a (archim1804426504_field(X_a) -> (all X exists N_2 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),hAPP(nat,X_a,semiring_1_of_nat(X_a),N_2)))))) # label(fact_2737_ex__le__of__nat) # label(axiom) # label(non_clause).  [assumption].
7.57/7.57	2605 (all X_a all X_b (comm_monoid_add(X_b) -> (all F all B_2 all A_3 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_3)) -> hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),F),hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,bool)),combs(X_a,bool,bool),hAPP(fun(X_a,bool),fun(X_a,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,fun(bool,bool))),combb(bool,fun(bool,bool),X_a),fconj),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(X_a,bool)),combc(X_a,fun(X_a,bool),bool),member(X_a)),A_3))),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(X_a,bool)),combc(X_a,fun(X_a,bool),bool),member(X_a)),B_2)))) = hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),hAPP(X_b,fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(X_b,fun(X_a,X_b)),combc(X_a,X_b,X_b),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,X_b)),hAPP(fun(X_a,fun(X_b,fun(X_b,X_b))),fun(fun(X_a,X_b),fun(X_a,fun(X_b,X_b))),combs(X_a,X_b,fun(X_b,X_b)),hAPP(fun(X_a,bool),fun(X_a,fun(X_b,fun(X_b,X_b))),hAPP(fun(bool,fun(X_b,fun(X_b,X_b))),fun(fun(X_a,bool),fun(X_a,fun(X_b,fun(X_b,X_b)))),combb(bool,fun(X_b,fun(X_b,X_b)),X_a),if(X_b)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(X_a,bool)),combc(X_a,fun(X_a,bool),bool),member(X_a)),B_2))),F)),zero_zero(X_b))),A_3))))) # label(fact_4185_setsum__restrict__set_H) # label(axiom) # label(non_clause).  [assumption].
7.57/7.57	2606 (all Z_4 all Z_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Z_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Z_4)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,nat_1,Z_1)),hAPP(int,nat,nat_1,Z_4)) = hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Z_1),Z_4))))) # label(fact_1142_nat__add__distrib) # label(axiom) # label(non_clause).  [assumption].
7.57/7.57	2607 (all N all M (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),M)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),M),N)) -> -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),N),M))))) # label(fact_204_zdvd__not__zless) # label(axiom) # label(non_clause).  [assumption].
7.57/7.57	2608 (all X_1 all Y_1 all Z (hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X_1),Z) = Y_1 <-> hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),Y_1),Z) = X_1)) # label(fact_1178_eq__diff__eq_H) # label(axiom) # label(non_clause).  [assumption].
7.57/7.57	2609 (all X_a (real_normed_field(X_a) -> (all Y_1 all X_3 (hBOOL(hAPP(fun(nat,X_a),bool,cauchy(X_a),X_3)) -> hBOOL(hAPP(fun(nat,X_a),bool,cauchy(X_a),hAPP(X_a,fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(X_a,fun(nat,X_a)),combc(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),inverse_divide(X_a)),X_3)),Y_1))))))) # label(fact_4102_divide_OCauchy) # label(axiom) # label(non_clause).  [assumption].
7.57/7.57	2610 (all X_a (real_normed_vector(X_a) -> (all X_3 (hBOOL(hAPP(fun(nat,X_a),bool,bseq(X_a),X_3)) -> (exists K_2 ((all N_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),hAPP(nat,X_a,X_3,N_2))),K_2))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),K_2)))))))) # label(fact_3498_BseqD) # label(axiom) # label(non_clause).  [assumption].
7.57/7.57	2611 (all X_a all X_b (comm_monoid_add(X_b) -> (all G all F all S all T_3 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),T_3)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),S),T_3)) -> ((all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),T_3),S))) -> zero_zero(X_b) = hAPP(X_a,X_b,F,X_2))) -> ((all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),S)) -> hAPP(X_a,X_b,G,X_2) = hAPP(X_a,X_b,F,X_2))) -> hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),F),T_3) = hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),G),S)))))))) # label(fact_4417_setsum__mono__zero__cong__right) # label(axiom) # label(non_clause).  [assumption].
7.57/7.57	2612 (all X all Y hAPP(complex,complex,cnj,hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),X),Y)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),hAPP(complex,complex,cnj,X)),hAPP(complex,complex,cnj,Y))) # label(fact_2944_complex__cnj__divide) # label(axiom) # label(non_clause).  [assumption].
7.57/7.57	2613 (all Y_1 all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),Y_1),X_1)) -> hAPP(fun(real,bool),real,complete_Sup_Sup(real),hAPP(real,fun(real,bool),hAPP(real,fun(real,fun(real,bool)),ord_atLeastAtMost(real),Y_1),X_1)) = X_1)) # label(fact_4525_Sup__atLeastAtMost) # label(axiom) # label(non_clause).  [assumption].
7.57/7.57	2614 (all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,sqrt,X_1)),one_one(real))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_1),one_one(real))))) # label(fact_1630_real__sqrt__le__1__iff) # label(axiom) # label(non_clause).  [assumption].
7.57/7.57	2615 (all X_a (real_normed_vector(X_a) -> (all X_3 ((exists K_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),K_1)) & (exists X_2 all N_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(nat,X_a,X_3,N_2)),hAPP(X_a,X_a,uminus_uminus(X_a),X_2)))),K_1))))) <-> hBOOL(hAPP(fun(nat,X_a),bool,bseq(X_a),X_3)))))) # label(fact_3491_Bseq__iff2) # label(axiom) # label(non_clause).  [assumption].
7.57/7.57	2616 (all A_1 all B ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_1),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),zero_zero(int))) -> hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),zero_zero(int)),A_1) = hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),posDivAlg,A_1),B)) & (-(hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_1),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),zero_zero(int)))) -> hAPP(product_prod(int,int),product_prod(int,int),hAPP(int,fun(product_prod(int,int),product_prod(int,int)),adjust,B),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),posDivAlg,A_1),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),B))) = hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),posDivAlg,A_1),B)))) # label(fact_1077_posDivAlg_Osimps) # label(axiom) # label(non_clause).  [assumption].
7.57/7.57	2617 (all X_3 (hBOOL(hAPP(fun(nat,complex),bool,summable(complex),X_3)) -> hAPP(complex,real,re,hAPP(fun(nat,complex),complex,suminf(complex),X_3)) = hAPP(fun(nat,real),real,suminf(real),hAPP(fun(nat,complex),fun(nat,real),hAPP(fun(complex,real),fun(fun(nat,complex),fun(nat,real)),combb(complex,real,nat),re),X_3)))) # label(fact_4048_Re_Osuminf) # label(axiom) # label(non_clause).  [assumption].
7.57/7.57	2618 (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_1294_zero__zle__int) # label(axiom) # label(non_clause).  [assumption].
7.57/7.57	2619 (all X_a (real_normed_algebra(X_a) -> (all A_1 all B all B_5 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B),B_5)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B_5))))) # label(fact_880_mult_Oadd__right) # label(axiom) # label(non_clause).  [assumption].
7.57/7.57	2620 (all F all L all C_1 (hBOOL(hAPP(filter(real),bool,hAPP(real,fun(filter(real),bool),hAPP(fun(real,real),fun(real,fun(filter(real),bool)),tendsto(real,real),F),L),hAPP(real,filter(real),at(real),C_1))) -> (zero_zero(real) != L -> (exists R_2 ((all X_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),C_1),X_2))),R_2)) & X_2 != C_1 -> hAPP(real,real,F,X_2) != zero_zero(real))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),R_2))))))) # label(fact_4627_LIM__fun__not__zero) # label(axiom) # label(non_clause).  [assumption].
7.57/7.58	2621 (all X_1 all N_1 all Y_1 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),X_1),N_1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),Y_1),N_1) <-> (exists Q1 exists Q2 hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N_1),Q1)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Y_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N_1),Q2))))) # label(fact_1183_nat__mod__eq__iff) # label(axiom) # label(non_clause).  [assumption].
7.57/7.58	2622 (all X_a (banach(X_a) & real_normed_field(X_a) -> (all X all Y hAPP(X_a,X_a,exp(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X),Y)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,exp(X_a),X)),hAPP(X_a,X_a,exp(X_a),Y))))) # label(fact_2585_exp__add) # label(axiom) # label(non_clause).  [assumption].
7.57/7.58	2623 (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_370_mult__right__mono__neg) # label(axiom) # label(non_clause).  [assumption].
7.57/7.58	2624 (all X_a (real_normed_vector(X_a) -> (all A_1 all B all C all D hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),D)))),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_1),C))),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),B),D)))))))) # label(fact_1797_norm__diff__triangle__ineq) # label(axiom) # label(non_clause).  [assumption].
7.57/7.58	2625 (all Z_1 hAPP(complex,complex,cnj,hAPP(complex,complex,cnj,Z_1)) = Z_1) # label(fact_2938_complex__cnj__cnj) # label(axiom) # label(non_clause).  [assumption].
7.57/7.58	2626 (all A_1 all B hAPP(int,rat,hAPP(int,fun(int,rat),fract,hAPP(int,int,abs_abs(int),A_1)),hAPP(int,int,abs_abs(int),B)) = hAPP(rat,rat,abs_abs(rat),hAPP(int,rat,hAPP(int,fun(int,rat),fract,A_1),B))) # label(fact_3757_abs__rat) # label(axiom) # label(non_clause).  [assumption].
7.57/7.58	2627 (all X_3 ((all J_1 exists M_3 all M_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_3),M_2)) -> (all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_3),N_2)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(nat,real,X_3,M_2)),hAPP(nat,real,X_3,N_2)))),hAPP(real,real,inverse_inverse(real),hAPP(nat,real,real_1(nat),hAPP(nat,nat,suc,J_1))))))))) <-> hBOOL(hAPP(fun(nat,real),bool,cauchy(real),X_3)))) # label(fact_3314_Cauchy__iff2) # label(axiom) # label(non_clause).  [assumption].
7.57/7.58	2628 (all I_1 all M hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_1),M))))) # label(fact_1329_less__add__Suc1) # label(axiom) # label(non_clause).  [assumption].
7.57/7.58	2629 (all A_1 hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,hAPP(nat,nat,suc,zero_zero(nat))),A_1))) # label(fact_2861_coprime__Suc0_H) # label(axiom) # label(non_clause).  [assumption].
7.57/7.58	2630 (all X_a all A_1 all B hAPP(product_prod(int,int),X_a,abs_Frac(X_a),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),norm_frac,A_1),B)) = hAPP(int,X_a,hAPP(int,fun(int,X_a),frac(X_a),A_1),B)) # label(fact_4420_Nitpick_Ofrac__def) # label(axiom) # label(non_clause).  [assumption].
7.57/7.58	2631 (all Z_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Z_1)) -> hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),Z_1)) = hAPP(nat,nat,suc,hAPP(int,nat,nat_1,Z_1)))) # label(fact_1435_Suc__nat__eq__nat__zadd1) # label(axiom) # label(non_clause).  [assumption].
7.57/7.58	2632 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),one_one(real)),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X),zero_zero(real))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,ln,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),one_one(real)),X))),X))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))))) # label(fact_2007_abs__ln__one__plus__x__minus__x__bound__nonpos) # label(axiom) # label(non_clause).  [assumption].
7.57/7.58	2633 (all C all A_1 all B all Q_3 all R_4 (hBOOL(hAPP(product_prod(nat,nat),bool,hAPP(nat,fun(product_prod(nat,nat),bool),hAPP(nat,fun(nat,fun(product_prod(nat,nat),bool)),divmod_nat_rel,A_1),B),hAPP(nat,product_prod(nat,nat),hAPP(nat,fun(nat,product_prod(nat,nat)),product_Pair(nat,nat),Q_3),R_4))) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),B)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),C)) -> hBOOL(hAPP(product_prod(nat,nat),bool,hAPP(nat,fun(product_prod(nat,nat),bool),hAPP(nat,fun(nat,fun(product_prod(nat,nat),bool)),divmod_nat_rel,A_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),C)),hAPP(nat,product_prod(nat,nat),hAPP(nat,fun(nat,product_prod(nat,nat)),product_Pair(nat,nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),Q_3),C)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),Q_3),C))),R_4)))))))) # label(fact_3096_divmod__nat__rel__mult2__eq) # label(axiom) # label(non_clause).  [assumption].
7.57/7.58	2634 (all X_a (monoid_mult(X_a) -> (all A_1 all N hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),N))))) # label(fact_233_power__even__eq) # label(axiom) # label(non_clause).  [assumption].
7.57/7.58	2635 (all M all N all R_5 all R_4 all S_4 all S_3 all T_6 all T_5 all K_4 ((exists Sn exists Tn hAPP(int,product_prod(int,product_prod(int,int)),hAPP(int,fun(int,product_prod(int,product_prod(int,int))),hAPP(int,fun(int,fun(int,product_prod(int,product_prod(int,int)))),hAPP(int,fun(int,fun(int,fun(int,product_prod(int,product_prod(int,int))))),hAPP(int,fun(int,fun(int,fun(int,fun(int,product_prod(int,product_prod(int,int)))))),hAPP(int,fun(int,fun(int,fun(int,fun(int,fun(int,product_prod(int,product_prod(int,int))))))),hAPP(int,fun(int,fun(int,fun(int,fun(int,fun(int,fun(int,product_prod(int,product_prod(int,int)))))))),hAPP(int,fun(int,fun(int,fun(int,fun(int,fun(int,fun(int,fun(int,product_prod(int,product_prod(int,int))))))))),xzgcda,M),N),R_5),R_4),S_4),S_3),T_6),T_5) = hAPP(product_prod(int,int),product_prod(int,product_prod(int,int)),hAPP(int,fun(product_prod(int,int),product_prod(int,product_prod(int,int))),product_Pair(int,product_prod(int,int)),K_4),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),Sn),Tn))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),R_4)) -> ti(int,K_4) = hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,R_5),R_4)))) # label(fact_3477_xzgcd__correct__aux2) # label(axiom) # label(non_clause).  [assumption].
7.57/7.58	2636 (all X_a all X_b all P_1 hAPP(fun(product_prod(X_a,X_b),bool),product_prod(X_a,X_b),hilbert_Eps(product_prod(X_a,X_b)),hAPP(fun(product_prod(X_a,X_b),X_b),fun(product_prod(X_a,X_b),bool),hAPP(fun(product_prod(X_a,X_b),fun(X_b,bool)),fun(fun(product_prod(X_a,X_b),X_b),fun(product_prod(X_a,X_b),bool)),combs(product_prod(X_a,X_b),X_b,bool),hAPP(fun(product_prod(X_a,X_b),X_a),fun(product_prod(X_a,X_b),fun(X_b,bool)),hAPP(fun(X_a,fun(X_b,bool)),fun(fun(product_prod(X_a,X_b),X_a),fun(product_prod(X_a,X_b),fun(X_b,bool))),combb(X_a,fun(X_b,bool),product_prod(X_a,X_b)),P_1),product_fst(X_a,X_b))),product_snd(X_a,X_b))) = hAPP(fun(product_prod(X_a,X_b),bool),product_prod(X_a,X_b),hilbert_Eps(product_prod(X_a,X_b)),hAPP(fun(X_a,fun(X_b,bool)),fun(product_prod(X_a,X_b),bool),product_prod_case(X_a,X_b,bool),P_1))) # label(fact_4782_Eps__split) # label(axiom) # label(non_clause).  [assumption].
7.57/7.58	2637 (all X_a (order(X_a) -> (all X_1 all Y_1 (ti(X_a,Y_1) = ti(X_a,X_1) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),Y_1)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y_1),X_1)))))) # label(fact_1557_order__eq__iff) # label(axiom) # label(non_clause).  [assumption].
7.57/7.58	2638 (all N all V ((-hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V))) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),hAPP(int,nat,number_number_of(nat),V)),N) = hAPP(int,nat,nat_1,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,number_number_of(int),V)),N))) & (hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V))) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),zero_zero(nat)),N) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),hAPP(int,nat,number_number_of(nat),V)),N)))) # label(fact_1517_power__nat__number__of) # label(axiom) # label(non_clause).  [assumption].
7.57/7.58	2639 (all X_a all F all A_3 ((all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_3)) -> hBOOL(hAPP(int,bool,nat_is_nat,hAPP(X_a,int,F,X_2))))) -> hAPP(fun(X_a,bool),int,hAPP(fun(X_a,int),fun(fun(X_a,bool),int),big_co302546470etprod(X_a,int),F),A_3) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(fun(X_a,bool),nat,hAPP(fun(X_a,nat),fun(fun(X_a,bool),nat),big_co302546470etprod(X_a,nat),hAPP(fun(X_a,int),fun(X_a,nat),hAPP(fun(int,nat),fun(fun(X_a,int),fun(X_a,nat)),combb(int,nat,X_a),nat_1),F)),A_3)))) # label(fact_4861_transfer__int__nat__sum__prod2_I2_J) # label(axiom) # label(non_clause).  [assumption].
7.57/7.58	2640 (all X_a (linorder(X_a) -> (all A_1 all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),A_1),B) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),A_1),B))))) # label(fact_4814_min__max_Oinf_Oleft__idem) # label(axiom) # label(non_clause).  [assumption].
7.57/7.58	2641 (all X_1 all Y_1 (ti(int,Y_1) = ti(int,X_1) <-> hAPP(int,real,real_1(int),X_1) = hAPP(int,real,real_1(int),Y_1))) # label(fact_3328_real__of__int__inject) # label(axiom) # label(non_clause).  [assumption].
7.57/7.58	2642 (all X_a (linorder(X_a) -> (all A_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),A_1),A_1) = ti(X_a,A_1)))) # label(fact_4972_min__max_Osup_Oidem) # label(axiom) # label(non_clause).  [assumption].
7.57/7.58	2643 (all X_a (semiring_div(X_a) -> (all Y all Z_1 all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),Z_1),X)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),Z_1),Y)) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X),Y)),Z_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),div_div(X_a),X),Z_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),Y),Z_1))))))) # label(fact_1005_div__add) # label(axiom) # label(non_clause).  [assumption].
7.57/7.58	2644 (all X_a (real_normed_vector(X_a) -> (all X exists K_2 ((all X_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),X_2),X))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,norm_norm(real),X_2)),K_2)))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),K_2)))))) # label(fact_4753_scaleR__left_Opos__bounded) # label(axiom) # label(non_clause).  [assumption].
7.57/7.58	2645 (all Ta all A_3 all D_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D_2)) -> (all X_2 ((all Xa (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xa),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastAtMost(int),one_one(int)),D_2))) -> (all Xb (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xb),A_3)) -> ti(int,X_2) != hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),Xb),Xa))))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Ta),X_2)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Ta),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X_2),D_2)))))))) # label(fact_4635_aset_I7_J) # label(axiom) # label(non_clause).  [assumption].
7.57/7.58	2646 (all X all Y hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),hAPP(int,int,abs_abs(int),X)),Y) = hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),X),Y)) # label(fact_4375_gcd__abs1__int) # label(axiom) # label(non_clause).  [assumption].
7.57/7.58	2647 (all D_1 hAPP(int,fun(product_prod(int,int),bool),int_ge_less_than2,D_1) = hAPP(fun(product_prod(int,int),bool),fun(product_prod(int,int),bool),collect(product_prod(int,int)),hAPP(fun(int,fun(int,bool)),fun(product_prod(int,int),bool),product_prod_case(int,int,bool),hAPP(fun(int,fun(int,bool)),fun(int,fun(int,bool)),hAPP(fun(fun(int,bool),fun(int,bool)),fun(fun(int,fun(int,bool)),fun(int,fun(int,bool))),combb(fun(int,bool),fun(int,bool),int),hAPP(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),combs(int,bool,bool),hAPP(fun(int,bool),fun(int,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj),hAPP(int,fun(int,bool),ord_less_eq(int),D_1)))),ord_less(int))))) # label(fact_4075_int__ge__less__than2__def) # label(axiom) # label(non_clause).  [assumption].
7.57/7.58	2648 (all X_a (real_normed_field(X_a) -> (all Db all F all G all X_1 all Da (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),F),hAPP(X_a,X_a,G,X_1)),Da)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),G),X_1),Db)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),hAPP(fun(X_a,X_a),fun(X_a,X_a),hAPP(fun(X_a,X_a),fun(fun(X_a,X_a),fun(X_a,X_a)),combb(X_a,X_a,X_a),F),G)),X_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Da),Db)))))))) # label(fact_3861_DERIV__chain2) # label(axiom) # label(non_clause).  [assumption].
7.57/7.58	2649 (all X_a (semiring_div(X_a) -> (all A_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),A_1),zero_zero(X_a)) = zero_zero(X_a)))) # label(fact_964_div__by__0) # label(axiom) # label(non_clause).  [assumption].
7.57/7.58	2650 (all M all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),hAPP(nat,nat,suc,N)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),N))) # label(fact_1341_mult__Suc__right) # label(axiom) # label(non_clause).  [assumption].
7.57/7.58	2651 (all X_a (real_normed_vector(X_a) -> (all F all L (hBOOL(hAPP(X_a,bool,hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),hAPP(fun(nat,nat),fun(nat,X_a),hAPP(fun(nat,X_a),fun(fun(nat,nat),fun(nat,X_a)),combb(nat,X_a,nat),F),suc)),L)) -> hBOOL(hAPP(X_a,bool,hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),F),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),L),hAPP(nat,X_a,F,zero_zero(nat))))))))) # label(fact_4095_sums__Suc) # label(axiom) # label(non_clause).  [assumption].
7.57/7.58	2652 (all X_a (linord219039673up_add(X_a) -> (all A_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),A_2)),A_2)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_2)))))) # label(fact_2063_neg__less__nonneg) # label(axiom) # label(non_clause).  [assumption].
7.57/7.58	2653 (all Y all X all A_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A_1)) -> (A_1 != one_one(real) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Y)) -> hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,hAPP(real,fun(real,real),log,A_1),X)),hAPP(real,real,hAPP(real,fun(real,real),log,A_1),Y)) = hAPP(real,real,hAPP(real,fun(real,real),log,A_1),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),X),Y))))))) # label(fact_2649_log__divide) # label(axiom) # label(non_clause).  [assumption].
7.57/7.58	2654 (all X_a (number_ring(X_a) -> (all X_1 all Y_1 (hAPP(int,X_a,number_number_of(X_a),Y_1) = hAPP(int,X_a,number_number_of(X_a),X_1) <-> hBOOL(hAPP(X_a,bool,iszero(X_a),hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X_1),hAPP(int,int,uminus_uminus(int),Y_1))))))))) # label(fact_2622_eq__number__of__eq) # label(axiom) # label(non_clause).  [assumption].
7.57/7.58	2655 (all X_a (linordered_field(X_a) -> (all Y all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),X)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),X),Y)),zero_zero(X_a)))))))) # label(fact_1702_divide__nonneg__neg) # label(axiom) # label(non_clause).  [assumption].
7.57/7.58	2656 (all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,exp(real),X_1)),one_one(real))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_1),zero_zero(real))))) # label(fact_2596_exp__less__one__iff) # label(axiom) # label(non_clause).  [assumption].
7.57/7.58	2657 (all Ma all Z (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(nat,int,semiring_1_of_nat(int),Ma)),Z)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Ma),hAPP(int,nat,nat_1,hAPP(int,int,abs_abs(int),Z)))))) # label(fact_1971_int__dvd__iff) # label(axiom) # label(non_clause).  [assumption].
7.57/7.58	2658 (all X_a (real_normed_field(X_a) -> (all F all X_1 all D_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),F),X_1),D_2)) -> hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,X_a),fun(X_a,bool),isCont(X_a,X_a),F),X_1)))))) # label(fact_4886_DERIV__isCont) # label(axiom) # label(non_clause).  [assumption].
7.57/7.58	2659 (all A_2 all P_4 (hBOOL(hAPP(int,bool,zprime,P_4)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),P_4)) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_2),zero_zero(int)),P_4)) -> hAPP(fun(fun(int,bool),bool),fun(int,bool),complete_Sup_Sup(fun(int,bool)),hAPP(int,fun(fun(int,bool),bool),hAPP(int,fun(int,fun(fun(int,bool),bool)),setS,A_2),P_4)) = hAPP(int,fun(int,bool),sRStar,P_4))))) # label(fact_1604_MultInvPair__prop2) # label(axiom) # label(non_clause).  [assumption].
7.57/7.58	2660 (all X_a ti(fun(fun(X_a,nat),fun(product_prod(X_a,X_a),bool)),measure(X_a)) = measure(X_a)) # label(tsy_c_Wellfounded_Omeasure_res) # label(axiom) # label(non_clause).  [assumption].
7.57/7.58	2661 (all X_a (number_ring(X_a) -> (all K_4 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),one_one(X_a)),hAPP(int,X_a,number_number_of(X_a),K_4)) = hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,succ,K_4))))) # label(fact_1531_number__of__succ) # label(axiom) # label(non_clause).  [assumption].
7.57/7.58	2662 (all X_a all X_b (comm_monoid_mult(X_b) -> (all G all H all A_3 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_3)) -> hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co302546470etprod(X_a,X_b),hAPP(fun(X_a,X_b),fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,X_b)),combs(X_a,X_b,X_b),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,fun(X_b,X_b))),combb(X_b,fun(X_b,X_b),X_a),times_times(X_b)),G)),H)),A_3) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co302546470etprod(X_a,X_b),G),A_3)),hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co302546470etprod(X_a,X_b),H),A_3)))))) # label(fact_3954_setprod_Odistrib) # label(axiom) # label(non_clause).  [assumption].
7.57/7.58	2663 (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_1593_leD) # label(axiom) # label(non_clause).  [assumption].
7.57/7.58	2664 (all X_b all X_a all P all Q hAPP(X_b,X_a,hAPP(X_a,fun(X_b,X_a),combk(X_a,X_b),P),Q) = ti(X_a,P)) # label(help_COMBK_1_1_U) # label(axiom) # label(non_clause).  [assumption].
7.57/7.58	2665 (all Ma all X_1 hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,int),fun(fun(int,bool),fun(int,bool)),image(int,int),hAPP(int,fun(int,int),hAPP(fun(int,fun(int,int)),fun(int,fun(int,int)),combc(int,int,int),times_times(int)),X_1)),hAPP(int,fun(int,bool),norRRset,Ma)) = hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),noXRRset,Ma),X_1)) # label(fact_3878_noXRRset__def) # label(axiom) # label(non_clause).  [assumption].
7.57/7.58	2666 (all N hAPP(real,real,cos,hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,real_1(nat),N)),pi)) = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),min_1)),N)) # label(fact_2373_cos__npi) # label(axiom) # label(non_clause).  [assumption].
7.57/7.58	2667 (all X_a (number_ring(X_a) & linordered_idom(X_a) -> (all X_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(int,X_a,number_number_of(X_a),X_1)),zero_zero(X_a))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X_1),pls)))))) # label(fact_47_le__special_I3_J) # label(axiom) # label(non_clause).  [assumption].
7.57/7.58	2668 (all X_a (semiring_div(X_a) -> (all A_1 all C all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),C),B)) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),A_1),C) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),A_1),B)),C))))) # label(fact_948_mod__mod__cancel) # label(axiom) # label(non_clause).  [assumption].
7.57/7.58	2669 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),one_one(nat)),N)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),M)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),M),N)),M))))) # label(fact_1121_div__less__dividend) # label(axiom) # label(non_clause).  [assumption].
7.57/7.58	2670 (all X all K_4 all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> hAPP(real,real,hAPP(nat,fun(real,real),root,N),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),K_4)) = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,hAPP(nat,fun(real,real),root,N),X)),K_4))) # label(fact_2684_real__root__power) # label(axiom) # label(non_clause).  [assumption].
7.57/7.58	2671 (all X_a (comm_semiring_1(X_a) -> (all A_1 all B all C (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)),C)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),B),C)))))) # label(fact_339_dvd__mult__right) # label(axiom) # label(non_clause).  [assumption].
7.57/7.58	2672 (all X_a (real_vector(X_a) -> scaleR_scaleR(X_a) = ti(fun(real,fun(X_a,X_a)),scaleR_scaleR(X_a)))) # label(tsy_c_RealVector_OscaleR__class_OscaleR_1_res) # label(axiom) # label(non_clause).  [assumption].
7.57/7.58	2673 (all A_1 all N all B hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),A_1),B)),N) = hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A_1),N)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),B),N))) # label(fact_4362_gcd__exp__int) # label(axiom) # label(non_clause).  [assumption].
7.57/7.58	2674 (all A_1 A_1 = hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),A_1),A_1)) # label(fact_3218_gcd__semilattice__nat_Oinf_Oidem) # label(axiom) # label(non_clause).  [assumption].
7.57/7.58	2675 (all M all K_4 all N (hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),K_4),N) = one_one(nat) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),K_4),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),N))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),K_4),M))))) # label(fact_3290_coprime__dvd__mult__nat) # label(axiom) # label(non_clause).  [assumption].
7.57/7.58	2676 (all I all J hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,nat),fun(fun(nat,bool),fun(nat,bool)),image(nat,nat),suc),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),I),J)) = hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),hAPP(nat,nat,suc,I)),hAPP(nat,nat,suc,J))) # label(fact_4225_image__Suc__atLeastLessThan) # label(axiom) # label(non_clause).  [assumption].
7.57/7.58	2677 (all K (hBOOL(hAPP(int,bool,iszero(int),hAPP(int,int,number_number_of(int),K))) <-> hBOOL(hAPP(rat,bool,iszero(rat),hAPP(int,rat,number_number_of(rat),K))))) # label(fact_3690_iszero__rat) # label(axiom) # label(non_clause).  [assumption].
7.57/7.58	2678 (all A_1 all B (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A_1),B)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),B),A_1)) -> hAPP(int,int,abs_abs(int),B) = hAPP(int,int,abs_abs(int),A_1)))) # label(fact_1924_zdvd__antisym__abs) # label(axiom) # label(non_clause).  [assumption].
7.57/7.58	2679 (all X_a (ordere236663937imp_le(X_a) -> (all A_2 all C_1 all B_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B_1),C_1))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),B_1)))))) # label(fact_792_add__less__cancel__right) # label(axiom) # label(non_clause).  [assumption].
7.57/7.58	2680 (all X_a (order(X_a) -> (all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y)) -> (ti(X_a,X) != ti(X_a,Y) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y))))))) # label(fact_318_order__le__neq__implies__less) # label(axiom) # label(non_clause).  [assumption].
7.57/7.58	2681 (all X_1 all Y_1 (ii = hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,X_1),Y_1) <-> zero_zero(real) = X_1 & Y_1 = one_one(real))) # label(fact_2766_Complex__eq__i) # label(axiom) # label(non_clause).  [assumption].
7.57/7.58	2682 (all W (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),W))) -> hAPP(product_prod(int,int),int,product_snd(int,int),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),posDivAlg,one_one(int)),hAPP(int,int,number_number_of(int),W))) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),one_one(int)),hAPP(int,int,number_number_of(int),W)))) # label(fact_3119_mod__pos__pos__1__number__of) # label(axiom) # label(non_clause).  [assumption].
7.57/7.58	2683 (all X_a all X_b (real_normed_vector(X_b) -> (all G all B_1 all F all A_2 all A_3 (hBOOL(hAPP(filter(X_a),bool,hAPP(real,fun(filter(X_a),bool),hAPP(fun(X_a,real),fun(real,fun(filter(X_a),bool)),tendsto(X_a,real),F),A_2),A_3)) -> (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),G),B_1),A_3)) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(fun(X_a,X_b),fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,X_b)),combs(X_a,X_b,X_b),hAPP(fun(X_a,real),fun(X_a,fun(X_b,X_b)),hAPP(fun(real,fun(X_b,X_b)),fun(fun(X_a,real),fun(X_a,fun(X_b,X_b))),combb(real,fun(X_b,X_b),X_a),scaleR_scaleR(X_b)),F)),G)),hAPP(X_b,X_b,hAPP(real,fun(X_b,X_b),scaleR_scaleR(X_b),A_2),B_1)),A_3))))))) # label(fact_4726_scaleR_Otendsto) # label(axiom) # label(non_clause).  [assumption].
7.57/7.58	2684 (all X_a (number_ring(X_a) -> (all W hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),one_one(X_a)),hAPP(int,X_a,number_number_of(X_a),W)) = hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,bit1,pls)),hAPP(int,int,uminus_uminus(int),W)))))) # label(fact_2185_diff__special_I1_J) # label(axiom) # label(non_clause).  [assumption].
7.57/7.58	2685 (all P_5 all Q_3 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Q_3),zero_zero(int))) -> hAPP(product_prod(int,int),product_prod(int,int),normalize,hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),P_5),Q_3)) = hAPP(product_prod(int,int),product_prod(int,int),normalize,hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),hAPP(int,int,uminus_uminus(int),P_5)),hAPP(int,int,uminus_uminus(int),Q_3))))) # label(fact_3718_normalize__negative) # label(axiom) # label(non_clause).  [assumption].
7.57/7.58	2686 (all K (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),min_1)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,K)),min_1)))) # label(fact_294_rel__simps_I13_J) # label(axiom) # label(non_clause).  [assumption].
7.57/7.58	2687 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(real,nat,natfloor,X)),one_one(nat)) = hAPP(real,nat,natfloor,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),one_one(real))))) # label(fact_1907_natfloor__add__one) # label(axiom) # label(non_clause).  [assumption].
7.57/7.58	2688 (all F all G ((exists N_3 all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_3),N_2)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),hAPP(nat,real,F,N_2))),hAPP(nat,real,G,N_2))))) -> (hBOOL(hAPP(fun(nat,real),bool,summable(real),G)) -> hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),abs_abs(real)),F)))))) # label(fact_4018_summable__rabs__comparison__test) # label(axiom) # label(non_clause).  [assumption].
7.57/7.58	2689 (all B all D all A_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,D),A_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,D),B)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,D),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A_1),B)))))) # label(fact_2850_coprime__mul) # label(axiom) # label(non_clause).  [assumption].
7.57/7.58	2690 (all X_a all N_1 all F all C_1 all H ((all N_2 hAPP(nat,X_a,hAPP(fun(nat,fun(X_a,X_a)),fun(nat,X_a),hAPP(X_a,fun(fun(nat,fun(X_a,X_a)),fun(nat,X_a)),nat_rec(X_a),C_1),H),N_2) = hAPP(nat,X_a,F,N_2)) -> hAPP(nat,X_a,F,hAPP(nat,nat,suc,N_1)) = hAPP(X_a,X_a,hAPP(nat,fun(X_a,X_a),H,N_1),hAPP(nat,X_a,F,N_1)))) # label(fact_4330_def__nat__rec__Suc) # label(axiom) # label(non_clause).  [assumption].
7.57/7.58	2691 (all Y all X (hBOOL(hAPP(int,bool,nat_is_nat,X)) -> (hBOOL(hAPP(int,bool,nat_is_nat,Y)) -> hBOOL(hAPP(int,bool,nat_is_nat,hAPP(int,int,hAPP(int,fun(int,int),nat_tsub,X),Y)))))) # label(fact_4849_Nat__Transfer_Otransfer__int__nat__function__closures_I3_J) # label(axiom) # label(non_clause).  [assumption].
7.57/7.58	2692 (all X_1 all Y_1 (X_1 = Y_1 <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_1),Y_1)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y_1),X_1)))) # label(fact_624_divides__antisym) # label(axiom) # label(non_clause).  [assumption].
7.57/7.58	2693 (all X_a (linordered_idom(X_a) -> (all A_1 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))))) # label(fact_104_zero__le__power2) # label(axiom) # label(non_clause).  [assumption].
7.57/7.58	2694 (all X_a (ring_1(X_a) -> (all Q_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Q_2),ring_1_Ints(X_a))) -> -(all Z_2 hAPP(int,X_a,ring_1_of_int(X_a),Z_2) != ti(X_a,Q_2)))))) # label(fact_4345_Ints__cases) # label(axiom) # label(non_clause).  [assumption].
7.57/7.58	2695 (all A_1 hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,A_1),hAPP(nat,nat,suc,zero_zero(nat))))) # label(fact_2862_coprime__Suc0) # label(axiom) # label(non_clause).  [assumption].
7.57/7.58	2696 (all X_a all X_b all A_3 all B_2 (hBOOL(hAPP(fun(sum_sum(X_a,X_b),bool),bool,finite_finite_1(sum_sum(X_a,X_b)),hAPP(fun(X_b,bool),fun(sum_sum(X_a,X_b),bool),hAPP(fun(X_a,bool),fun(fun(X_b,bool),fun(sum_sum(X_a,X_b),bool)),sum_Plus(X_a,X_b),A_3),B_2))) <-> hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_3)) & hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),B_2)))) # label(fact_3185_finite__Plus__iff) # label(axiom) # label(non_clause).  [assumption].
7.57/7.58	2697 (all X_a (preorder(X_a) -> (all Z_1 all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),Z_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Z_1))))))) # label(fact_1601_order__le__less__trans) # label(axiom) # label(non_clause).  [assumption].
7.57/7.58	2698 (all X_a all X_b (comm_monoid_add(X_b) -> (all F all A_3 (-hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_3)) -> zero_zero(X_b) = hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),F),A_3))))) # label(fact_4208_setsum__infinite) # label(axiom) # label(non_clause).  [assumption].
7.57/7.58	2699 (all X_a all C_1 all A_3 (-hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),A_3)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),hAPP(fun(X_a,bool),fun(X_a,bool),uminus_uminus(fun(X_a,bool)),A_3))))) # label(fact_2191_ComplI) # label(axiom) # label(non_clause).  [assumption].
7.57/7.58	2700 (all X_a (semiring_0(X_a) & power(X_a) -> (all N ((N != zero_zero(nat) -> hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),zero_zero(X_a)),N) = zero_zero(X_a)) & (N = zero_zero(nat) -> one_one(X_a) = hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),zero_zero(X_a)),N)))))) # label(fact_446_power__0__left) # label(axiom) # label(non_clause).  [assumption].
7.57/7.58	2701 (all D_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,D_1),zero_zero(nat))) <-> one_one(nat) = D_1)) # label(fact_2866_coprime__0) # label(axiom) # label(non_clause).  [assumption].
7.57/7.58	2702 (all X_a (real_vector(X_a) -> (all X all Y all Xa_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),X),Xa_1)),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),Y),Xa_1)) = hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),X),Y)),Xa_1)))) # label(fact_4716_scaleR__left_Odiff) # label(axiom) # label(non_clause).  [assumption].
7.57/7.58	2703 (all X_a finite_psubset(X_a) = hAPP(fun(product_prod(fun(X_a,bool),fun(X_a,bool)),bool),fun(product_prod(fun(X_a,bool),fun(X_a,bool)),bool),collect(product_prod(fun(X_a,bool),fun(X_a,bool))),hAPP(fun(fun(X_a,bool),fun(fun(X_a,bool),bool)),fun(product_prod(fun(X_a,bool),fun(X_a,bool)),bool),product_prod_case(fun(X_a,bool),fun(X_a,bool),bool),hAPP(fun(fun(X_a,bool),bool),fun(fun(X_a,bool),fun(fun(X_a,bool),bool)),hAPP(fun(fun(X_a,bool),fun(fun(fun(X_a,bool),bool),fun(fun(X_a,bool),bool))),fun(fun(fun(X_a,bool),bool),fun(fun(X_a,bool),fun(fun(X_a,bool),bool))),combc(fun(X_a,bool),fun(fun(X_a,bool),bool),fun(fun(X_a,bool),bool)),hAPP(fun(fun(X_a,bool),fun(fun(X_a,bool),fun(bool,bool))),fun(fun(X_a,bool),fun(fun(fun(X_a,bool),bool),fun(fun(X_a,bool),bool))),hAPP(fun(fun(fun(X_a,bool),fun(bool,bool)),fun(fun(fun(X_a,bool),bool),fun(fun(X_a,bool),bool))),fun(fun(fun(X_a,bool),fun(fun(X_a,bool),fun(bool,bool))),fun(fun(X_a,bool),fun(fun(fun(X_a,bool),bool),fun(fun(X_a,bool),bool)))),combb(fun(fun(X_a,bool),fun(bool,bool)),fun(fun(fun(X_a,bool),bool),fun(fun(X_a,bool),bool)),fun(X_a,bool)),combs(fun(X_a,bool),bool,bool)),hAPP(fun(fun(X_a,bool),fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(fun(X_a,bool),fun(bool,bool))),hAPP(fun(fun(fun(X_a,bool),bool),fun(fun(X_a,bool),fun(bool,bool))),fun(fun(fun(X_a,bool),fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(fun(X_a,bool),fun(bool,bool)))),combb(fun(fun(X_a,bool),bool),fun(fun(X_a,bool),fun(bool,bool)),fun(X_a,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(fun(X_a,bool),bool),fun(fun(X_a,bool),fun(bool,bool))),combb(bool,fun(bool,bool),fun(X_a,bool)),fconj)),ord_less(fun(X_a,bool))))),finite_finite_1(X_a))))) # label(fact_4050_finite__psubset__def) # label(axiom) # label(non_clause).  [assumption].
7.57/7.58	2704 (all X_a (number_ring(X_a) -> (all Y_1 (hBOOL(hAPP(X_a,bool,iszero(X_a),hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),pls),hAPP(int,int,uminus_uminus(int),Y_1))))) <-> zero_zero(X_a) = hAPP(int,X_a,number_number_of(X_a),Y_1))))) # label(fact_2624_eq__special_I1_J) # label(axiom) # label(non_clause).  [assumption].
7.57/7.58	2705 (all X_b all X_c all X_a (topological_space(X_a) & topological_space(X_b) & topological_space(X_c) -> (all G all F all A_2 (hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,X_b),fun(X_a,bool),isCont(X_a,X_b),F),A_2)) -> (hBOOL(hAPP(X_b,bool,hAPP(fun(X_b,X_c),fun(X_b,bool),isCont(X_b,X_c),G),hAPP(X_a,X_b,F,A_2))) -> hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,X_c),fun(X_a,bool),isCont(X_a,X_c),hAPP(fun(X_a,X_b),fun(X_a,X_c),hAPP(fun(X_b,X_c),fun(fun(X_a,X_b),fun(X_a,X_c)),combb(X_b,X_c,X_a),G),F)),A_2))))))) # label(fact_4900_isCont__o2) # label(axiom) # label(non_clause).  [assumption].
7.57/7.58	2706 (all X_b all X_a (topological_space(X_a) & real_normed_vector(X_b) -> (all F all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(real,fun(filter(X_a),bool),hAPP(fun(X_a,real),fun(real,fun(filter(X_a),bool)),tendsto(X_a,real),hAPP(fun(X_a,X_b),fun(X_a,real),hAPP(fun(X_b,real),fun(fun(X_a,X_b),fun(X_a,real)),combb(X_b,real,X_a),norm_norm(X_b)),F)),zero_zero(real)),hAPP(X_a,filter(X_a),at(X_a),A_2))) <-> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),zero_zero(X_b)),hAPP(X_a,filter(X_a),at(X_a),A_2))))))) # label(fact_4609_LIM__norm__zero__iff) # label(axiom) # label(non_clause).  [assumption].
7.57/7.58	2707 (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].
7.57/7.58	2708 (all X_a (linord1117847801e_zero(X_a) -> (all A_2 all B_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),B_1)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),A_2)) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_1),zero_zero(X_a))) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),zero_zero(X_a))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),A_2),B_1))))))) # label(fact_1675_zero__le__divide__iff) # label(axiom) # label(non_clause).  [assumption].
7.57/7.58	2709 (all Nat_1 hAPP(nat,nat,nat_size,hAPP(nat,nat,suc,Nat_1)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,nat_size,Nat_1)),hAPP(nat,nat,suc,zero_zero(nat)))) # label(fact_2920_nat_Osize_I2_J) # label(axiom) # label(non_clause).  [assumption].
7.57/7.58	2710 (all X_1 all Y_1 (hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),Y_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) = zero_zero(real) <-> zero_zero(real) = X_1 & Y_1 = zero_zero(real))) # label(fact_615_realpow__two__sum__zero__iff) # label(axiom) # label(non_clause).  [assumption].
7.57/7.58	2711 (all N_1 all X_1 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(nat,fun(real,real),hAPP(fun(real,fun(nat,real)),fun(nat,fun(real,real)),combc(real,nat,real),power_power(real)),N_1)),X_1),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,real_1(nat),N_1)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),hAPP(nat,nat,suc,zero_zero(nat)))))))) # label(fact_3891_DERIV__pow) # label(axiom) # label(non_clause).  [assumption].
7.57/7.58	2712 (all X_a (comm_semiring_1(X_a) -> (all A_1 all B hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)))))) # label(fact_332_dvd__triv__left) # label(axiom) # label(non_clause).  [assumption].
7.57/7.58	2713 (all K_4 all N all M hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),M),N) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_4),N)),M)),N)) # label(fact_1111_mod__mult__self3) # label(axiom) # label(non_clause).  [assumption].
7.57/7.58	2714 (all X hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(complex,real,re,X)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(complex,real,re,X)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(complex,real,im,X)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) = hAPP(complex,real,re,hAPP(complex,complex,inverse_inverse(complex),X))) # label(fact_3019_complex__Re__inverse) # label(axiom) # label(non_clause).  [assumption].
7.57/7.58	2715 (all X_a all A_2 all F all V_1 all N_1 hAPP(nat,X_a,hAPP(fun(nat,fun(X_a,X_a)),fun(nat,X_a),hAPP(X_a,fun(fun(nat,fun(X_a,X_a)),fun(nat,X_a)),nat_rec(X_a),A_2),F),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),V_1)),N_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),hAPP(bool,fun(X_a,fun(X_a,X_a)),if(X_a),hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),hAPP(int,int,pred,V_1)))),hAPP(nat,X_a,hAPP(fun(nat,fun(X_a,X_a)),fun(nat,X_a),hAPP(X_a,fun(fun(nat,fun(X_a,X_a)),fun(nat,X_a)),nat_rec(X_a),A_2),F),N_1)),hAPP(X_a,X_a,hAPP(nat,fun(X_a,X_a),F,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,nat_1,hAPP(int,int,number_number_of(int),hAPP(int,int,pred,V_1)))),N_1)),hAPP(nat,X_a,hAPP(fun(nat,fun(X_a,X_a)),fun(nat,X_a),hAPP(X_a,fun(fun(nat,fun(X_a,X_a)),fun(nat,X_a)),nat_rec(X_a),A_2),F),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,nat_1,hAPP(int,int,number_number_of(int),hAPP(int,int,pred,V_1)))),N_1))))) # label(fact_4152_nat__rec__add__eq__if) # label(axiom) # label(non_clause).  [assumption].
7.57/7.58	2716 (all X_a (linord626643107strict(X_a) -> (all V all U all Y all X all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),U)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),V)) -> (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),U),V) = one_one(X_a) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),U),X)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),V),Y))),A_1)))))))))) # label(fact_277_convex__bound__lt) # label(axiom) # label(non_clause).  [assumption].
7.57/7.58	2717 (all Y all X (X = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),Y),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),Y)) -> hAPP(real,real,sqrt,X) = Y))) # label(fact_1639_real__sqrt__unique) # label(axiom) # label(non_clause).  [assumption].
7.57/7.58	2718 (all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),zero_zero(nat)),N) = N) # label(fact_541_plus__nat_Oadd__0) # label(axiom) # label(non_clause).  [assumption].
7.57/7.58	2719 (all X_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),X_1)) <-> hBOOL(hAPP(int,bool,even_odd_even(int),X_1)))) # label(fact_1448_int__even__iff__2__dvd) # label(axiom) # label(non_clause).  [assumption].
7.57/7.58	2720 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,M)),N)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N)))) # label(fact_1230_Suc__lessD) # label(axiom) # label(non_clause).  [assumption].
7.57/7.58	2721 (all X_a (field_inverse_zero(X_a) -> (all A_1 all B all C (ti(X_a,C) != zero_zero(X_a) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),A_1),B) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),hAPP(X_a,X_a,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_1689_mult__divide__mult__cancel__right) # label(axiom) # label(non_clause).  [assumption].
7.57/7.58	2722 (all X_a (metric_space(X_a) -> (all X_3 all L_2 ((all R_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),R_2)) -> (exists No all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),No),N_2)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),hAPP(nat,X_a,X_3,N_2)),L_2)),R_2)))))) -> hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),X_3),L_2),sequentially)))))) # label(fact_4662_metric__LIMSEQ__I) # label(axiom) # label(non_clause).  [assumption].
7.57/7.58	2723 (all N_1 hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),hAPP(fun(int,bool),fun(int,bool),collect(int),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),combs(int,bool,bool),hAPP(fun(int,bool),fun(int,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj),hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)))),hAPP(int,fun(int,bool),hAPP(fun(int,fun(int,bool)),fun(int,fun(int,bool)),combc(int,int,bool),ord_less(int)),N_1)))))) # label(fact_3813_bdd__int__set__l__finite) # label(axiom) # label(non_clause).  [assumption].
7.57/7.58	2724 (all X_a (semiring_div(X_a) -> (all B all A_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),A_1),B))),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),A_1),B)) = ti(X_a,A_1)))) # label(fact_914_mod__div__equality2) # label(axiom) # label(non_clause).  [assumption].
7.57/7.58	2725 (all X_a (sgn_div_norm(X_a) -> (all X hAPP(X_a,X_a,sgn_sgn(X_a),X) = hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),hAPP(real,real,inverse_inverse(real),hAPP(X_a,real,norm_norm(X_a),X))),X)))) # label(fact_4725_sgn__div__norm) # label(axiom) # label(non_clause).  [assumption].
7.57/7.58	2726 (all X_a (topological_space(X_a) & comm_monoid_add(X_a) -> ti(fun(fun(nat,X_a),bool),summable(X_a)) = summable(X_a))) # label(tsy_c_Series_Osummable_res) # label(axiom) # label(non_clause).  [assumption].
7.57/7.58	2727 (all B all A_1 all X (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),X)) & -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),A_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),A_1),B)),X)) & -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),A_1),B))))) # label(fact_3229_gcd__semilattice__nat_Oless__infI1) # label(axiom) # label(non_clause).  [assumption].
7.57/7.58	2728 (all A_1 all B (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_1),B)),B)) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_1),B))))) # label(fact_1033_pos__mod__conj) # label(axiom) # label(non_clause).  [assumption].
7.57/7.58	2729 (all K all Ma all N_1 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),Ma) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),N_1) <-> Ma = N_1 | zero_zero(nat) = K)) # label(fact_744_nat__mult__eq__cancel__disj) # label(axiom) # label(non_clause).  [assumption].
7.57/7.58	2730 (all I_1 all K_4 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),K_4)) -> (K_4 != hAPP(nat,nat,suc,I_1) -> -(all J_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),J_1)) -> K_4 != hAPP(nat,nat,suc,J_1)))))) # label(fact_1542_lessE) # label(axiom) # label(non_clause).  [assumption].
7.57/7.58	2731 (all X hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),hAPP(real,real,inverse_inverse(real),hAPP(complex,real,norm_norm(complex),X))),X) = hAPP(complex,complex,sgn_sgn(complex),X)) # label(fact_4742_complex__sgn__def) # label(axiom) # label(non_clause).  [assumption].
7.57/7.58	2732 (all X_1 (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),zEven)) -> hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),X_1),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = zero_zero(int))) # label(fact_1461_even__div__2__prop1) # label(axiom) # label(non_clause).  [assumption].
7.57/7.58	2733 (all A_1 all B all C hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),B)),C) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),B),C))),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),B),C))),C))) # label(fact_919_zdiv__zmult1__eq) # label(axiom) # label(non_clause).  [assumption].
7.57/7.58	2734 (all B_1 all A_2 (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),A_2),zEven)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),B_1),zOdd)) -> hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A_2),B_1)),zOdd))))) # label(fact_1365_IntNatAux_Oeven__plus__odd) # label(axiom) # label(non_clause).  [assumption].
7.57/7.58	2735 (all X_a (ordere142940540dd_abs(X_a) -> ti(fun(X_a,X_a),abs_abs(X_a)) = abs_abs(X_a))) # label(tsy_c_Groups_Oabs__class_Oabs_1_res) # label(axiom) # label(non_clause).  [assumption].
7.57/7.58	2736 (all Y all X all A_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A_1),zero_zero(real))) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),Y)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),powr,Y),A_1)),hAPP(real,real,hAPP(real,fun(real,real),powr,X),A_1))))))) # label(fact_3349_powr__less__mono2__neg) # label(axiom) # label(non_clause).  [assumption].
7.57/7.58	2737 (all M_5 all D_4 (zero_zero(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),M_5),D_4) -> (exists Q_4 M_5 = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),D_4),Q_4)))) # label(fact_1184_mod__eq__0D) # label(axiom) # label(non_clause).  [assumption].
7.57/7.58	2738 (all C all A_1 all B (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),B)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A_1),C)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),C))))) # label(fact_716_divides__mul__r) # label(axiom) # label(non_clause).  [assumption].
7.57/7.58	2739 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),M)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N)),M))))) # label(fact_680_diff__less) # label(axiom) # label(non_clause).  [assumption].
7.57/7.58	2740 (all X_a (linorder(X_a) -> (all B all X all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),B)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),A_1),B)))))))) # label(fact_4821_min__max_Ole__infI) # label(axiom) # label(non_clause).  [assumption].
7.57/7.58	2741 (all X_a (comm_semiring_1(X_a) -> (all C all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_1),B)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_1),C)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B),C)))))))) # label(fact_340_dvd__add) # label(axiom) # label(non_clause).  [assumption].
7.57/7.58	2742 (all K_4 -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,semiring_1_of_nat(int),K_4)),zero_zero(int)))) # label(fact_1293_int__less__0__conv) # label(axiom) # label(non_clause).  [assumption].
7.57/7.58	2743 (all K_4 hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),min_1),K_4) = hAPP(int,int,pred,K_4)) # label(fact_2908_add__Min) # label(axiom) # label(non_clause).  [assumption].
7.57/7.58	2744 (all X_a (semiring_div(X_a) -> (all A_1 all C all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)),C) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),A_1),C)),B)),C)))) # label(fact_936_zmod__simps_I1_J) # label(axiom) # label(non_clause).  [assumption].
7.57/7.58	2745 (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) = zero_zero(int)) & (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_1458_tsub__def) # label(axiom) # label(non_clause).  [assumption].
7.57/7.58	2746 (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_1863_abs__not__less__zero) # label(axiom) # label(non_clause).  [assumption].
7.57/7.58	2747 (all M (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),M),zero_zero(int))) -> zero_zero(int) = hAPP(int,int,fact_fact(int),M))) # label(fact_3188_fact__neg__int) # label(axiom) # label(non_clause).  [assumption].
7.57/7.58	2748 (all X hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,exp(real),X)))) # label(fact_2567_exp__gt__zero) # label(axiom) # label(non_clause).  [assumption].
7.57/7.58	2749 (all R_4 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,real_1(int),hAPP(real,int,archim2085082626_floor(real),R_4))),R_4))) # label(fact_3344_real__of__int__floor__le) # label(axiom) # label(non_clause).  [assumption].
7.57/7.58	2750 (all C all A_1 all B (A_1 = B -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),B),C)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),C))))) # label(fact_630_dvd_Oord__eq__le__trans) # label(axiom) # label(non_clause).  [assumption].
7.57/7.58	2751 (all X_a (t2_space(X_a) & comm_monoid_add(X_a) -> (all F all X_1 (hBOOL(hAPP(X_a,bool,hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),F),X_1)) <-> ti(X_a,X_1) = hAPP(fun(nat,X_a),X_a,suminf(X_a),F) & hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),F)))))) # label(fact_4093_sums__iff) # label(axiom) # label(non_clause).  [assumption].
7.57/7.58	2752 (all X (-hBOOL(hAPP(nat,bool,even_odd_even(nat),X)) -> hAPP(nat,nat,suc,zero_zero(nat)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),X),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat)))))) # label(fact_2447_odd__nat__mod__two__eq__one) # label(axiom) # label(non_clause).  [assumption].
7.57/7.58	2753 (all X_a all C_1 all A_3 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),hAPP(fun(X_a,bool),fun(X_a,bool),uminus_uminus(fun(X_a,bool)),A_3))) -> -hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),A_3)))) # label(fact_2196_ComplD) # label(axiom) # label(non_clause).  [assumption].
7.57/7.58	2754 (all X_a (real_normed_vector(X_a) -> (all X_1 (hAPP(X_a,X_a,sgn_sgn(X_a),X_1) = zero_zero(X_a) <-> ti(X_a,X_1) = zero_zero(X_a))))) # label(fact_2200_sgn__zero__iff) # label(axiom) # label(non_clause).  [assumption].
7.57/7.58	2755 (all X_a (divisi14063676e_zero(X_a) -> (all A_1 ti(X_a,A_1) = hAPP(X_a,X_a,inverse_inverse(X_a),hAPP(X_a,X_a,inverse_inverse(X_a),A_1))))) # label(fact_2521_inverse__inverse__eq) # label(axiom) # label(non_clause).  [assumption].
7.57/7.58	2756 (all X_a (ab_group_add(X_a) -> (all A_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),A_1)),A_1) = zero_zero(X_a)))) # label(fact_2068_ab__left__minus) # label(axiom) # label(non_clause).  [assumption].
7.57/7.58	2757 (all X_b all X_a all H all F_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),F_1)) -> hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),H),F_1))))) # label(fact_3633_finite__imageI) # label(axiom) # label(non_clause).  [assumption].
7.57/7.58	2758 (all X_a (number_ring(X_a) & ring_char_0(X_a) -> (all W_1 (hBOOL(hAPP(X_a,bool,iszero(X_a),hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,bit0,W_1)))) <-> hBOOL(hAPP(X_a,bool,iszero(X_a),hAPP(int,X_a,number_number_of(X_a),W_1))))))) # label(fact_2604_iszero__number__of__Bit0) # label(axiom) # label(non_clause).  [assumption].
7.57/7.58	2759 (all L_4 all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),L_4)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),L_4))))) # label(fact_671_diff__le__mono) # label(axiom) # label(non_clause).  [assumption].
7.57/7.58	2760 (all X_a (linorder(X_a) -> (all X all Y hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),Y) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),Y),X)))) # label(fact_4815_min__max_Oinf__commute) # label(axiom) # label(non_clause).  [assumption].
7.57/7.58	2761 (all X_a (topological_space(X_a) -> ti(fun(X_a,filter(X_a)),at(X_a)) = at(X_a))) # label(tsy_c_Limits_Oat_res) # label(axiom) # label(non_clause).  [assumption].
7.57/7.58	2762 (all A_2 (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_2),one_one(nat))) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),one_one(nat)),A_2)) <-> A_2 != one_one(nat))) # label(fact_895_gcd__lcm__complete__lattice__nat_Obot__less) # label(axiom) # label(non_clause).  [assumption].
7.57/7.58	2763 (all R_4 all A_1 all B hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),R_4),hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,A_1),B)) = hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,hAPP(real,real,hAPP(real,fun(real,real),times_times(real),R_4),A_1)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),R_4),B))) # label(fact_4683_complex__scaleR) # label(axiom) # label(non_clause).  [assumption].
7.57/7.58	2764 (all Y all U all X1_1 all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X1_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),X1_1),Y)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),X),U))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),Y),hAPP(real,real,inverse_inverse(real),X))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),U),hAPP(real,real,inverse_inverse(real),X1_1)))))))) # label(fact_2591_real__mult__inverse__cancel2) # label(axiom) # label(non_clause).  [assumption].
7.57/7.58	2765 (all X_a (ordered_ab_group_add(X_a) -> (all A_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),A_2)),zero_zero(X_a))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_2)))))) # label(fact_2062_neg__less__0__iff__less) # label(axiom) # label(non_clause).  [assumption].
7.57/7.58	2766 (all R_4 all X all Y hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(real,complex,of_real(complex),R_4)),hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,X),Y)) = hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),R_4),X)),Y)) # label(fact_2811_complex__of__real__add__Complex) # label(axiom) # label(non_clause).  [assumption].
7.57/7.59	2767 (all X_1 all Y_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_1),Y_1)) -> (exists X_2 (hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),X_2),field_char_0_Rats(real))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_2),Y_1)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_1),X_2)))))) # label(fact_3703_Rats__dense__in__real) # label(axiom) # label(non_clause).  [assumption].
7.57/7.59	2768 (all X_1 (hBOOL(hAPP(int,bool,even_odd_even(int),X_1)) <-> hBOOL(hAPP(int,bool,even_odd_even(int),hAPP(int,int,uminus_uminus(int),X_1))))) # label(fact_2152_even__neg) # label(axiom) # label(non_clause).  [assumption].
7.57/7.59	2769 (all P_1 all N_1 ((exists X_2 (hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X_2),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),N_1))) & hBOOL(hAPP(nat,bool,P_1,X_2)))) <-> (exists M_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_2),N_1)) & hBOOL(hAPP(nat,bool,P_1,M_2)))))) # label(fact_4193_ex__nat__less__eq) # label(axiom) # label(non_clause).  [assumption].
7.57/7.59	2770 (all F all A_2 all B_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A_2),B_1)) -> ((all X_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_2),B_1)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A_2),X_2)) -> (exists Y_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Y_2)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),F),X_2),Y_2)))))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,F,A_2)),hAPP(real,real,F,B_1)))))) # label(fact_2839_DERIV__pos__imp__increasing) # label(axiom) # label(non_clause).  [assumption].
7.57/7.59	2771 (all Z_1 hAPP(complex,complex,cnj,hAPP(int,complex,ring_1_of_int(complex),Z_1)) = hAPP(int,complex,ring_1_of_int(complex),Z_1)) # label(fact_3572_complex__cnj__of__int) # label(axiom) # label(non_clause).  [assumption].
7.57/7.59	2772 (all B all N all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> hAPP(real,real,hAPP(real,fun(real,real),log,B),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),N)) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,real_1(nat),N)),hAPP(real,real,hAPP(real,fun(real,real),log,B),X)))) # label(fact_2647_log__nat__power) # label(axiom) # label(non_clause).  [assumption].
7.57/7.59	2773 (all X_1 all N_1 (N_1 = zero_zero(nat) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X_1)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),X_1),N_1))))) # label(fact_348_nat__zero__less__power__iff) # label(axiom) # label(non_clause).  [assumption].
7.57/7.59	2774 (all X_a (boolean_algebra(X_a) -> (all Y all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),hAPP(X_a,X_a,uminus_uminus(X_a),X))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),hAPP(X_a,X_a,uminus_uminus(X_a),Y))))))) # label(fact_2961_compl__less__swap1) # label(axiom) # label(non_clause).  [assumption].
7.57/7.59	2775 (all K_4 all M all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_4),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),M),N)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_4),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_4),N))) # label(fact_1092_mod__mult__distrib2) # label(axiom) # label(non_clause).  [assumption].
7.57/7.59	2776 (all X_a (boolean_algebra(X_a) -> (all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),Y)),hAPP(X_a,X_a,uminus_uminus(X_a),X))))))) # label(fact_2957_compl__mono) # label(axiom) # label(non_clause).  [assumption].
7.57/7.59	2777 (exists K_2 all X_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,cnj,X_2))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(complex,real,norm_norm(complex),X_2)),K_2)))) # label(fact_2968_cnj_Obounded) # label(axiom) # label(non_clause).  [assumption].
7.57/7.59	2778 (all X_a (linordered_idom(X_a) -> (all A_1 hAPP(X_a,X_a,abs_abs(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) = hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))) # label(fact_1900_abs__power2) # label(axiom) # label(non_clause).  [assumption].
7.57/7.59	2779 (all X_1 all R_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),X_1)),R_1)) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_1),R_1)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,uminus_uminus(real),R_1)),X_1)))) # label(fact_2090_abs__le__interval__iff) # label(axiom) # label(non_clause).  [assumption].
7.57/7.59	2780 (all X_a (ring_1(X_a) -> (all N_1 all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_2),ring_1_Ints(X_a))) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_2),N_1)),ring_1_Ints(X_a))))))) # label(fact_3851_Ints__power) # label(axiom) # label(non_clause).  [assumption].
7.57/7.59	2781 (all G all X_1 all Ma (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),G),X_1),Ma)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,real),fun(fun(real,real),fun(real,real)),combb(real,real,real),sin),G)),X_1),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,cos,hAPP(real,real,G,X_1))),Ma))))) # label(fact_3859_DERIV__fun__sin) # label(axiom) # label(non_clause).  [assumption].
7.57/7.59	2782 (all X hAPP(int,real,ring_1_of_int(real),X) = hAPP(int,real,number_number_of(real),X)) # label(fact_3582_number__of__real__def) # label(axiom) # label(non_clause).  [assumption].
7.57/7.59	2783 (all X_a (ab_group_add(X_a) -> (all A_1 all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_1),B) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),hAPP(X_a,X_a,uminus_uminus(X_a),B))))) # label(fact_2075_ab__diff__minus) # label(axiom) # label(non_clause).  [assumption].
7.57/7.59	2784 (all X_a (real_normed_field(X_a) & banach(X_a) -> (all X_1 hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,X_a),fun(X_a,bool),isCont(X_a,X_a),exp(X_a)),X_1))))) # label(fact_4891_isCont__exp) # label(axiom) # label(non_clause).  [assumption].
7.57/7.59	2785 (all X_a (number_ring(X_a) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),one_one(X_a)),one_one(X_a)) = hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) # label(fact_179_one__add__one__is__two) # label(axiom) # label(non_clause).  [assumption].
7.57/7.59	2786 (all M hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,M),zero_zero(int)) = hAPP(int,int,abs_abs(int),M)) # label(fact_3452_zgcd__0) # label(axiom) # label(non_clause).  [assumption].
7.57/7.59	2787 (all X all M hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,X),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),X),M)),M))) # label(fact_958_mod__mod__is__mod) # label(axiom) # label(non_clause).  [assumption].
7.57/7.59	2788 (all X_1 all N_1 (X_1 = one_one(nat) | N_1 = zero_zero(nat) <-> one_one(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),X_1),N_1))) # label(fact_730_exp__eq__1) # label(axiom) # label(non_clause).  [assumption].
7.57/7.59	2789 (all X_a (linordered_semidom(X_a) -> (all M all N all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),M)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N))))))) # label(fact_448_power__less__imp__less__exp) # label(axiom) # label(non_clause).  [assumption].
7.57/7.59	2790 (all X hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(complex,real,re,X)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(complex,real,re,X)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(complex,real,im,X)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,uminus_uminus(real),hAPP(complex,real,im,X))),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(complex,real,re,X)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(complex,real,im,X)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))) = hAPP(complex,complex,inverse_inverse(complex),X)) # label(fact_2990_complex__inverse__def) # label(axiom) # label(non_clause).  [assumption].
7.57/7.59	2791 (all X_a (number_ring(X_a) -> (all W_1 hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),hAPP(int,X_a,number_number_of(X_a),W_1)),ring_1_Ints(X_a)))))) # label(fact_3843_Ints__number__of) # label(axiom) # label(non_clause).  [assumption].
7.57/7.59	2792 (all N all M hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),minus_minus(quickcheck_code_int),N),M) = hAPP(int,quickcheck_code_int,quickcheck_of_int,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(quickcheck_code_int,int,quickcheck_int_of,N)),hAPP(quickcheck_code_int,int,quickcheck_int_of,M)))) # label(fact_3542_minus__code__int__def) # label(axiom) # label(non_clause).  [assumption].
7.57/7.59	2793 (all X_a (comm_semiring_1(X_a) -> (all C all D all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_1),B)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),C),D)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),D)))))))) # label(fact_336_mult__dvd__mono) # label(axiom) # label(non_clause).  [assumption].
7.57/7.59	2794 (all X_a (metric_space(X_a) -> (all X_1 all Y_1 (ti(X_a,Y_1) != ti(X_a,X_1) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),X_1),Y_1))))))) # label(fact_3514_dist__nz) # label(axiom) # label(non_clause).  [assumption].
7.57/7.59	2795 (all B_1 all Q_2 all R_1 hAPP(product_prod(int,int),product_prod(int,int),hAPP(product_prod(int,int),fun(product_prod(int,int),product_prod(int,int)),hAPP(bool,fun(product_prod(int,int),fun(product_prod(int,int),product_prod(int,int))),if(product_prod(int,int)),hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),R_1),B_1))),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),Q_2)),one_one(int))),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),R_1),B_1))),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),Q_2)),R_1)) = hAPP(product_prod(int,int),product_prod(int,int),hAPP(int,fun(product_prod(int,int),product_prod(int,int)),adjust,B_1),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),Q_2),R_1))) # label(fact_3798_adjust__eq) # label(axiom) # label(non_clause).  [assumption].
7.57/7.59	2796 (all X_a (preorder(X_a) -> (all P_1 all X_1 all Y_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y_1),X_1)) -> hBOOL(P_1)))))) # label(fact_1571_order__less__imp__triv) # label(axiom) # label(non_clause).  [assumption].
7.57/7.59	2797 (all K1 all K2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit0,K1)),hAPP(int,int,bit1,K2))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),K1),K2)))) # label(fact_74_less__int__code_I14_J) # label(axiom) # label(non_clause).  [assumption].
7.57/7.59	2798 (all N all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,real_1(int),N)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(int,real,real_1(int),N)),one_one(real)))) -> ti(int,N) = hAPP(real,int,archim2085082626_floor(real),X)))) # label(fact_3412_floor__eq2) # label(axiom) # label(non_clause).  [assumption].
7.57/7.59	2799 (all Ma all N_1 hAPP(fun(int,bool),fun(nat,bool),hAPP(fun(int,nat),fun(fun(int,bool),fun(nat,bool)),image(int,nat),nat_1),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastAtMost(int),hAPP(nat,int,semiring_1_of_nat(int),Ma)),hAPP(nat,int,semiring_1_of_nat(int),N_1))) = hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),Ma),N_1)) # label(fact_4538_SetInterval_Otransfer__nat__int__set__functions_I2_J) # label(axiom) # label(non_clause).  [assumption].
7.57/7.59	2800 (all X all Y all Z_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),Z_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Y),Z_1)),Z_1))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),X),Z_1)),Y))))) # label(fact_1053_div__prop2) # label(axiom) # label(non_clause).  [assumption].
7.57/7.59	2801 (all X_a (no_zero_divisors(X_a) -> (all B all A_1 (zero_zero(X_a) != ti(X_a,A_1) -> (zero_zero(X_a) != ti(X_a,B) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B) != zero_zero(X_a)))))) # label(fact_320_no__zero__divisors) # label(axiom) # label(non_clause).  [assumption].
7.57/7.59	2802 (all M hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,zero_zero(int)),M) = hAPP(int,int,abs_abs(int),M)) # label(fact_3451_zgcd__0__left) # label(axiom) # label(non_clause).  [assumption].
7.57/7.59	2803 (all X_a (real_normed_vector(X_a) -> (all X_1 all A_2 hBOOL(hAPP(real,bool,hAPP(fun(real,X_a),fun(real,bool),isCont(real,X_a),hAPP(X_a,fun(real,X_a),hAPP(fun(real,fun(X_a,X_a)),fun(X_a,fun(real,X_a)),combc(real,X_a,X_a),scaleR_scaleR(X_a)),X_1)),A_2))))) # label(fact_4915_scaleR__left_OisCont) # label(axiom) # label(non_clause).  [assumption].
7.57/7.59	2804 (all X_a all P_1 all A_2 (hBOOL(hAPP(X_a,bool,P_1,A_2)) -> ((all X_2 (hBOOL(hAPP(X_a,bool,P_1,X_2)) -> ti(X_a,A_2) = ti(X_a,X_2))) -> ti(X_a,A_2) = hAPP(fun(X_a,bool),X_a,hilbert_Eps(X_a),P_1)))) # label(fact_4789_some__equality) # label(axiom) # label(non_clause).  [assumption].
7.57/7.59	2805 (all X_a (linordered_idom(X_a) -> (all A_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),hAPP(X_a,X_a,uminus_uminus(X_a),A_2))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),zero_zero(X_a))))))) # label(fact_2060_less__minus__self__iff) # label(axiom) # label(non_clause).  [assumption].
7.57/7.59	2806 (all Z_4 all Z_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Z_1)) -> hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Z_1),Z_4)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,nat_1,Z_1)),hAPP(int,nat,nat_1,Z_4)))) # label(fact_1139_nat__mult__distrib) # label(axiom) # label(non_clause).  [assumption].
7.57/7.59	2807 (all X_a (comm_semiring_1(X_a) -> (all N_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))),hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),semiring_1_of_nat(X_a)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),one_one(nat)),N_1))) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),N_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),N_1)),one_one(X_a)))))) # label(fact_4617_gauss__sum) # label(axiom) # label(non_clause).  [assumption].
7.57/7.59	2808 (all X_a (linord581940658strict(X_a) -> (all X_1 all Y_1 (zero_zero(X_a) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X_1),X_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Y_1),Y_1)) <-> ti(X_a,X_1) = zero_zero(X_a) & ti(X_a,Y_1) = zero_zero(X_a))))) # label(fact_94_sum__squares__eq__zero__iff) # label(axiom) # label(non_clause).  [assumption].
7.57/7.59	2809 (all X_1 hAPP(fun(int,bool),int,the(int),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),combs(int,bool,bool),hAPP(fun(int,bool),fun(int,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj),hAPP(rat,fun(int,bool),hAPP(fun(int,fun(rat,bool)),fun(rat,fun(int,bool)),combc(int,rat,bool),hAPP(fun(int,rat),fun(int,fun(rat,bool)),hAPP(fun(rat,fun(rat,bool)),fun(fun(int,rat),fun(int,fun(rat,bool))),combb(rat,fun(rat,bool),int),ord_less_eq(rat)),ring_1_of_int(rat))),X_1))),hAPP(fun(int,rat),fun(int,bool),hAPP(fun(rat,bool),fun(fun(int,rat),fun(int,bool)),combb(rat,bool,int),hAPP(rat,fun(rat,bool),ord_less(rat),X_1)),hAPP(fun(int,int),fun(int,rat),hAPP(fun(int,rat),fun(fun(int,int),fun(int,rat)),combb(int,rat,int),ring_1_of_int(rat)),hAPP(int,fun(int,int),hAPP(fun(int,fun(int,int)),fun(int,fun(int,int)),combc(int,int,int),plus_plus(int)),one_one(int)))))) = hAPP(rat,int,archim2085082626_floor(rat),X_1)) # label(fact_4147_floor__rat__def) # label(axiom) # label(non_clause).  [assumption].
7.57/7.59	2810 (all K_4 all A_1 all B all M (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_1),B),M)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K_4),A_1)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K_4),B)),M)))) # label(fact_359_zcong__scalar2) # label(axiom) # label(non_clause).  [assumption].
7.57/7.59	2811 (all X_a (ab_group_add(X_a) -> (all A_1 all B hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_1),B)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),B),A_1)))) # label(fact_2053_minus__diff__eq) # label(axiom) # label(non_clause).  [assumption].
7.57/7.59	2812 (all Z all P_1 ((all N_2 hBOOL(hAPP(int,bool,P_1,hAPP(nat,int,semiring_1_of_nat(int),N_2)))) -> ((all N_2 hBOOL(hAPP(int,bool,P_1,hAPP(int,int,uminus_uminus(int),hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,N_2)))))) -> hBOOL(hAPP(int,bool,P_1,Z))))) # label(fact_3527_int__of__nat__induct) # label(axiom) # label(non_clause).  [assumption].
7.57/7.59	2813 (all Z_1 all X all Y (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),Y)) & -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y),X)) -> (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Z_1),Y)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y),Z_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),Z_1)) & -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Z_1),X))))) # label(fact_648_dvd_Oless__trans) # label(axiom) # label(non_clause).  [assumption].
7.57/7.59	2814 (all N_1 all X_1 ((hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X_1)) -> hAPP(real,real,hAPP(nat,fun(real,real),root,N_1),X_1) = hAPP(fun(real,bool),real,the(real),hAPP(fun(real,bool),fun(real,bool),hAPP(fun(real,fun(bool,bool)),fun(fun(real,bool),fun(real,bool)),combs(real,bool,bool),hAPP(fun(real,bool),fun(real,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(real,bool),fun(real,fun(bool,bool))),combb(bool,fun(bool,bool),real),fconj),hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)))),hAPP(real,fun(real,bool),hAPP(fun(real,fun(real,bool)),fun(real,fun(real,bool)),combc(real,real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),hAPP(fun(real,fun(real,bool)),fun(fun(real,real),fun(real,fun(real,bool))),combb(real,fun(real,bool),real),fequal(real)),hAPP(nat,fun(real,real),hAPP(fun(real,fun(nat,real)),fun(nat,fun(real,real)),combc(real,nat,real),power_power(real)),N_1))),X_1)))) & (-hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X_1)) -> (-hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_1),zero_zero(real))) -> zero_zero(real) = hAPP(real,real,hAPP(nat,fun(real,real),root,N_1),X_1)) & (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_1),zero_zero(real))) -> hAPP(real,real,uminus_uminus(real),hAPP(fun(real,bool),real,the(real),hAPP(fun(real,bool),fun(real,bool),hAPP(fun(real,fun(bool,bool)),fun(fun(real,bool),fun(real,bool)),combs(real,bool,bool),hAPP(fun(real,bool),fun(real,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(real,bool),fun(real,fun(bool,bool))),combb(bool,fun(bool,bool),real),fconj),hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)))),hAPP(real,fun(real,bool),hAPP(fun(real,fun(real,bool)),fun(real,fun(real,bool)),combc(real,real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),hAPP(fun(real,fun(real,bool)),fun(fun(real,real),fun(real,fun(real,bool))),combb(real,fun(real,bool),real),fequal(real)),hAPP(nat,fun(real,real),hAPP(fun(real,fun(nat,real)),fun(nat,fun(real,real)),combc(real,nat,real),power_power(real)),N_1))),hAPP(real,real,uminus_uminus(real),X_1))))) = hAPP(real,real,hAPP(nat,fun(real,real),root,N_1),X_1))))) # label(fact_4136_root__def) # label(axiom) # label(non_clause).  [assumption].
7.57/7.59	2815 (all D_1 all Ta (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),D_1),hAPP(int,int,uminus_uminus(int),Ta))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),D_1),Ta)))) # label(fact_2146_uminus__dvd__conv_I2_J) # label(axiom) # label(non_clause).  [assumption].
7.57/7.59	2816 (all X_a (number_ring(X_a) & linordered_idom(X_a) -> (all Y_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(int,X_a,number_number_of(X_a),Y_1))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),Y_1)))))) # label(fact_177_less__special_I1_J) # label(axiom) # label(non_clause).  [assumption].
7.57/7.59	2817 (all X_1 all N_1 all Y_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X_1),Y_1)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),X_1),hAPP(nat,nat,suc,N_1))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),Y_1),hAPP(nat,nat,suc,N_1)))))) # label(fact_1360_exp__mono__lt) # label(axiom) # label(non_clause).  [assumption].
7.57/7.59	2818 (all N hAPP(nat,int,semiring_1_of_nat(int),N) = hAPP(real,int,archim2085082626_floor(real),hAPP(nat,real,real_1(nat),N))) # label(fact_2859_floor__real__of__nat) # label(axiom) # label(non_clause).  [assumption].
7.57/7.59	2819 (all A_1 all P_5 ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_1),zero_zero(int)),P_5)) -> hAPP(int,int,hAPP(int,fun(int,int),legendre,A_1),P_5) = zero_zero(int)) & (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_1),zero_zero(int)),P_5)) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),quadRes,P_5),A_1)) -> hAPP(int,int,number_number_of(int),min_1) = hAPP(int,int,hAPP(int,fun(int,int),legendre,A_1),P_5)) & (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),quadRes,P_5),A_1)) -> hAPP(int,int,hAPP(int,fun(int,int),legendre,A_1),P_5) = one_one(int))))) # label(fact_607_Legendre__def) # label(axiom) # label(non_clause).  [assumption].
7.57/7.59	2820 (all P_1 all A0 (hBOOL(hAPP(int,bool,hAPP(fun(int,fun(int,bool)),fun(int,bool),accp(int),quickc1265749348ro_rel),A0)) -> ((all I_2 (hBOOL(hAPP(int,bool,hAPP(fun(int,fun(int,bool)),fun(int,bool),accp(int),quickc1265749348ro_rel),I_2)) -> ((-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),I_2),zero_zero(int))) -> (ti(int,I_2) != zero_zero(int) -> hBOOL(hAPP(int,bool,P_1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),I_2),one_one(int)))))) -> hBOOL(hAPP(int,bool,P_1,I_2))))) -> hBOOL(hAPP(int,bool,P_1,A0))))) # label(fact_3177_around__zero_Opinduct) # label(axiom) # label(non_clause).  [assumption].
7.57/7.59	2821 (all M hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),zero_zero(nat)) = zero_zero(nat)) # label(fact_550_mult__0__right) # label(axiom) # label(non_clause).  [assumption].
7.57/7.59	2822 (all X_a all A_3 all B_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),B_2)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_3),B_2)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(X_a,bool),nat,finite_card(X_a),A_3)),hAPP(fun(X_a,bool),nat,finite_card(X_a),B_2))) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less(fun(X_a,bool)),A_3),B_2)))))) # label(fact_1827_card__psubset) # label(axiom) # label(non_clause).  [assumption].
7.57/7.59	2823 (all M all D all R_4 (R_4 = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),M),D) -> (exists Q_4 M = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),R_4),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),Q_4),D))))) # label(fact_1182_mod__eqD) # label(axiom) # label(non_clause).  [assumption].
7.57/7.59	2824 (all X all Y all Z_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),X),hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),Y),Z_1)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),X),Y)),Z_1)) # label(fact_3227_gcd__semilattice__nat_Oinf__assoc) # label(axiom) # label(non_clause).  [assumption].
7.57/7.59	2825 (all X_a (comm_monoid_add(X_a) -> (all K all F (zero_zero(X_a) = hAPP(nat,X_a,F,zero_zero(nat)) -> hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),K)) = hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),hAPP(nat,nat,suc,zero_zero(nat))),K)))))) # label(fact_4198_setsum__shift__lb__Suc0__0__upt) # label(axiom) # label(non_clause).  [assumption].
7.57/7.59	2826 (all X_a (number_ring(X_a) -> (all V hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),V),hAPP(int,int,uminus_uminus(int),hAPP(int,int,bit1,pls)))) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(int,X_a,number_number_of(X_a),V)),one_one(X_a))))) # label(fact_2184_diff__special_I2_J) # label(axiom) # label(non_clause).  [assumption].
7.57/7.59	2827 (all X_a (linordered_idom(X_a) -> (all X_1 all N_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X_1),N_1)),zero_zero(X_a))) <-> zero_zero(nat) != N_1 & (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),zero_zero(X_a))) & -hBOOL(hAPP(nat,bool,even_odd_even(nat),N_1)) | ti(X_a,X_1) = zero_zero(X_a) & hBOOL(hAPP(nat,bool,even_odd_even(nat),N_1))))))) # label(fact_2453_power__le__zero__eq) # label(axiom) # label(non_clause).  [assumption].
7.57/7.59	2828 (all X_a (real_normed_algebra(X_a) -> (all X_1 all X_3 (hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),X_3)) -> hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(X_a,X_a),fun(fun(nat,X_a),fun(nat,X_a)),combb(X_a,X_a,nat),hAPP(X_a,fun(X_a,X_a),times_times(X_a),X_1)),X_3))))))) # label(fact_3999_mult__right_Osummable) # label(axiom) # label(non_clause).  [assumption].
7.57/7.59	2829 (all K_4 all L_4 hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),pdivmod,K_4),L_4) = hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,abs_abs(int),K_4)),hAPP(int,int,abs_abs(int),L_4))),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,abs_abs(int),K_4)),hAPP(int,int,abs_abs(int),L_4)))) # label(fact_2722_pdivmod__def) # label(axiom) # label(non_clause).  [assumption].
7.57/7.59	2830 (all X_a hilbert_Eps(X_a) = ti(fun(fun(X_a,bool),X_a),hilbert_Eps(X_a))) # label(tsy_c_Hilbert__Choice_OEps_res) # label(axiom) # label(non_clause).  [assumption].
7.57/7.59	2831 (all X_a (comple44059174attice(X_a) -> (all V_1 all U_1 all A_3 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),U_1),A_3)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),V_1),U_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),V_1),hAPP(fun(X_a,bool),X_a,complete_Sup_Sup(X_a),A_3)))))))) # label(fact_1765_complete__lattice__class_OSup__upper2) # label(axiom) # label(non_clause).  [assumption].
7.57/7.59	2832 (all K_4 all I_1 all J_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),J_2)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K_4)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_4),I_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_4),J_2)))))) # label(fact_599_mult__less__mono2) # label(axiom) # label(non_clause).  [assumption].
7.57/7.59	2833 (all P_1 all X_1 all Y_1 (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y_1),X_1)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_1),Y_1)) -> (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_1),Y_1)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y_1),X_1)) -> hBOOL(P_1)))) # label(fact_644_dvd_Oless__imp__triv) # label(axiom) # label(non_clause).  [assumption].
7.57/7.59	2834 (all X_a (real_normed_algebra(X_a) -> (all Y_1 all A_2 hBOOL(hAPP(filter(X_a),bool,hAPP(X_a,fun(filter(X_a),bool),hAPP(fun(X_a,X_a),fun(X_a,fun(filter(X_a),bool)),tendsto(X_a,X_a),hAPP(X_a,fun(X_a,X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(X_a,X_a)),combc(X_a,X_a,X_a),times_times(X_a)),Y_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),Y_1)),hAPP(X_a,filter(X_a),at(X_a),A_2)))))) # label(fact_4551_mult__left_Ocont) # label(axiom) # label(non_clause).  [assumption].
7.57/7.59	2835 (all X_a all A_3 all B_2 (ti(fun(X_a,bool),A_3) = ti(fun(X_a,bool),B_2) -> -(hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_3),B_2)) -> -hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),B_2),A_3))))) # label(fact_1952_equalityE) # label(axiom) # label(non_clause).  [assumption].
7.57/7.59	2836 (all X_a (real_normed_vector(X_a) -> (all X_1 all X_3 all A_2 (hBOOL(hAPP(real,bool,hAPP(fun(nat,real),fun(real,bool),sums(real),X_3),A_2)) -> hBOOL(hAPP(X_a,bool,hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),hAPP(X_a,fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(X_a,fun(nat,X_a)),combc(nat,X_a,X_a),hAPP(fun(nat,real),fun(nat,fun(X_a,X_a)),hAPP(fun(real,fun(X_a,X_a)),fun(fun(nat,real),fun(nat,fun(X_a,X_a))),combb(real,fun(X_a,X_a),nat),scaleR_scaleR(X_a)),X_3)),X_1)),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_2),X_1))))))) # label(fact_4666_scaleR__left_Osums) # label(axiom) # label(non_clause).  [assumption].
7.57/7.59	2837 (all X_a (division_ring(X_a) -> (all A_1 all B all C hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_1),B)),C) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),B),C))))) # label(fact_1665_diff__divide__distrib) # label(axiom) # label(non_clause).  [assumption].
7.57/7.59	2838 (all N_1 all X_1 exists T_4 (hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(real,fun(nat,fun(real,real)),hAPP(fun(nat,fun(real,fun(real,real))),fun(real,fun(nat,fun(real,real))),combc(nat,real,fun(real,real)),hAPP(fun(nat,bool),fun(nat,fun(real,fun(real,real))),hAPP(fun(bool,fun(real,fun(real,real))),fun(fun(nat,bool),fun(nat,fun(real,fun(real,real)))),combb(bool,fun(real,fun(real,real)),nat),if(real)),even_odd_even(nat))),zero_zero(real))),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),inverse_divide(real)),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),min_1))),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),hAPP(fun(nat,nat),fun(nat,fun(nat,nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,nat),fun(nat,fun(nat,nat))),combb(nat,fun(nat,nat),nat),div_div(nat)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),minus_minus(nat)),hAPP(nat,nat,suc,zero_zero(nat))))),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),fact_fact(nat)))))),hAPP(real,fun(nat,real),power_power(real),X_1))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),N_1))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,sin,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),T_4),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),one_one(real)),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,real_1(nat),N_1))),pi)))),hAPP(nat,real,real_1(nat),hAPP(nat,nat,fact_fact(nat),N_1)))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X_1),N_1))) = hAPP(real,real,sin,X_1) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),T_4)),hAPP(real,real,abs_abs(real),X_1))))) # label(fact_4241_Maclaurin__sin__expansion2) # label(axiom) # label(non_clause).  [assumption].
7.57/7.59	2839 (all X_a ti(X_a,zero_frac(X_a)) = zero_frac(X_a)) # label(tsy_c_Nitpick_Ozero__frac_res) # label(axiom) # label(non_clause).  [assumption].
7.57/7.59	2840 (all X_a all A_3 hAPP(fun(fun(X_a,bool),bool),fun(X_a,bool),complete_Sup_Sup(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),pow(X_a),A_3)) = ti(fun(X_a,bool),A_3)) # label(fact_2775_Union__Pow__eq) # label(axiom) # label(non_clause).  [assumption].
7.57/7.59	2841 (all X_a (semiring_div(X_a) -> (all A_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),A_1),zero_zero(X_a)) = ti(X_a,A_1)))) # label(fact_925_mod__by__0) # label(axiom) # label(non_clause).  [assumption].
7.57/7.59	2842 (all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),zero_zero(nat)),N) = zero_zero(nat)) # label(fact_661_diff__0__eq__0) # label(axiom) # label(non_clause).  [assumption].
7.57/7.59	2843 (all X all Y all Z_1 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_1)) = 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_1))) # label(fact_98_zadd__left__commute) # label(axiom) # label(non_clause).  [assumption].
7.57/7.59	2844 (all X_a (power(X_a) -> (all A_1 hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),zero_zero(nat)) = one_one(X_a)))) # label(fact_415_power__0) # label(axiom) # label(non_clause).  [assumption].
7.57/7.59	2845 (all B (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B)) -> hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,number_number_of(int),min_1)),B) = hAPP(int,int,number_number_of(int),min_1))) # label(fact_1047_div__eq__minus1) # label(axiom) # label(non_clause).  [assumption].
7.57/7.59	2846 (all X_a all X_b all P_1 hAPP(fun(product_prod(X_a,X_b),bool),product_prod(X_a,X_b),the(product_prod(X_a,X_b)),hAPP(fun(product_prod(X_a,X_b),X_b),fun(product_prod(X_a,X_b),bool),hAPP(fun(product_prod(X_a,X_b),fun(X_b,bool)),fun(fun(product_prod(X_a,X_b),X_b),fun(product_prod(X_a,X_b),bool)),combs(product_prod(X_a,X_b),X_b,bool),hAPP(fun(product_prod(X_a,X_b),X_a),fun(product_prod(X_a,X_b),fun(X_b,bool)),hAPP(fun(X_a,fun(X_b,bool)),fun(fun(product_prod(X_a,X_b),X_a),fun(product_prod(X_a,X_b),fun(X_b,bool))),combb(X_a,fun(X_b,bool),product_prod(X_a,X_b)),P_1),product_fst(X_a,X_b))),product_snd(X_a,X_b))) = hAPP(fun(product_prod(X_a,X_b),bool),product_prod(X_a,X_b),the(product_prod(X_a,X_b)),hAPP(fun(X_a,fun(X_b,bool)),fun(product_prod(X_a,X_b),bool),product_prod_case(X_a,X_b,bool),P_1))) # label(fact_4145_The__split) # label(axiom) # label(non_clause).  [assumption].
7.57/7.59	2847 (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_432_mult__less__le__imp__less) # label(axiom) # label(non_clause).  [assumption].
7.57/7.59	2848 (all X_a (linordered_field(X_a) -> (all Y all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),X)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),Y)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),X),Y)))))))) # label(fact_1701_divide__nonneg__pos) # label(axiom) # label(non_clause).  [assumption].
7.57/7.59	2849 (all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),Y)) -> (exists X_2 (hAPP(real,real,tan,X_2) = Y & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_2),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X_2)))))) # label(fact_2282_tan__total__pos) # label(axiom) # label(non_clause).  [assumption].
7.57/7.59	2850 (all X_a (power(X_a) & mult_zero(X_a) & zero_neq_one(X_a) & no_zero_divisors(X_a) -> (all A_2 all W_1 (hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_2),hAPP(int,nat,number_number_of(nat),W_1)) = zero_zero(X_a) <-> zero_zero(X_a) = ti(X_a,A_2) & zero_zero(nat) != hAPP(int,nat,number_number_of(nat),W_1))))) # label(fact_256_power__eq__0__iff__number__of) # label(axiom) # label(non_clause).  [assumption].
7.57/7.59	2851 (all A_1 all Q_3 all R_4 (hBOOL(hAPP(product_prod(int,int),bool,hAPP(int,fun(product_prod(int,int),bool),hAPP(int,fun(int,fun(product_prod(int,int),bool)),divmod_int_rel,A_1),A_1),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),Q_3),R_4))) -> (ti(int,A_1) != zero_zero(int) -> zero_zero(int) = ti(int,R_4)))) # label(fact_1188_self__remainder) # label(axiom) # label(non_clause).  [assumption].
7.57/7.59	2852 (all W (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,number_number_of(int),W))) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),hAPP(int,int,number_number_of(int),W)))) -> hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),negDivAlg,one_one(int)),hAPP(int,int,number_number_of(int),W)) = hAPP(product_prod(int,int),product_prod(int,int),hAPP(int,fun(product_prod(int,int),product_prod(int,int)),adjust,hAPP(int,int,number_number_of(int),W)),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),negDivAlg,one_one(int)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),hAPP(int,int,number_number_of(int),W))))) & (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),hAPP(int,int,number_number_of(int),W)))) -> hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),negDivAlg,one_one(int)),hAPP(int,int,number_number_of(int),W)) = hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),hAPP(int,int,number_number_of(int),min_1)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),hAPP(int,int,number_number_of(int),W)))))) # label(fact_902_negDivAlg__eqn__1__number__of) # label(axiom) # label(non_clause).  [assumption].
7.57/7.59	2853 (all Ma all N_1 (hBOOL(hAPP(nat,bool,even_odd_even(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Ma),N_1))) <-> (hBOOL(hAPP(nat,bool,even_odd_even(nat),N_1)) <-> hBOOL(hAPP(nat,bool,even_odd_even(nat),Ma))))) # label(fact_2414_even__add) # label(axiom) # label(non_clause).  [assumption].
7.57/7.59	2854 (all K all I all J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I),J)) -> (hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J),I) = K <-> J = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K),I)))) # label(fact_692_le__imp__diff__is__add) # label(axiom) # label(non_clause).  [assumption].
7.57/7.59	2855 (all K (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit0,K)),pls)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),K),pls)))) # label(fact_54_rel__simps_I27_J) # label(axiom) # label(non_clause).  [assumption].
7.57/7.59	2856 (all X all P_5 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),P_5)) -> (hBOOL(hAPP(int,bool,zprime,P_5)) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,X),zero_zero(int)),P_5)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X),hAPP(int,int,hAPP(int,fun(int,int),multInv,P_5),X))),hAPP(int,int,hAPP(int,fun(int,int),multInv,P_5),hAPP(int,int,hAPP(int,fun(int,int),multInv,P_5),X)))),X),P_5)))))) # label(fact_849_Int2_Oaux____2) # label(axiom) # label(non_clause).  [assumption].
7.57/7.59	2857 (all F all A_3 (hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A_3)) -> ((all X_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X_2)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,F,X_2))))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(fun(int,bool),int,hAPP(fun(int,int),fun(fun(int,bool),int),big_co1399186613setsum(int,int),F),A_3)))))) # label(fact_4305_transfer__nat__int__sum__prod__closure_I1_J) # label(axiom) # label(non_clause).  [assumption].
7.57/7.59	2858 (all N all D all A_1 (one_one(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),D),A_1) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),D),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A_1),N)) = one_one(nat))) # label(fact_3277_coprime__exp__nat) # label(axiom) # label(non_clause).  [assumption].
7.57/7.59	2859 (all X all Y hAPP(complex,real,hAPP(complex,fun(complex,real),dist_dist(complex),X),Y) = hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),X),Y))) # label(fact_3520_dist__complex__def) # label(axiom) # label(non_clause).  [assumption].
7.57/7.59	2860 (all X_a all A_3 all B_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(filter(X_a),fun(filter(X_a),bool),ord_less_eq(filter(X_a)),A_3),B_2)) & -hBOOL(hAPP(filter(X_a),bool,hAPP(filter(X_a),fun(filter(X_a),bool),ord_less_eq(filter(X_a)),B_2),A_3)) <-> hBOOL(hAPP(filter(X_a),bool,hAPP(filter(X_a),fun(filter(X_a),bool),ord_less(filter(X_a)),A_3),B_2)))) # label(fact_4510_less__filter__def) # label(axiom) # label(non_clause).  [assumption].
7.57/7.59	2861 (all A_1 all B all C all D hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A_1),C)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),B),D)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,A_1),B)),hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,C),D))) # label(fact_2745_complex__add) # label(axiom) # label(non_clause).  [assumption].
7.57/7.59	2862 (all X_b all X_a (topological_space(X_a) & real_n1866405975lgebra(X_b) -> (all F all A_2 (hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,X_b),fun(X_a,bool),isCont(X_a,X_b),F),A_2)) -> (hAPP(X_a,X_b,F,A_2) != zero_zero(X_b) -> hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,X_b),fun(X_a,bool),isCont(X_a,X_b),hAPP(fun(X_a,X_b),fun(X_a,X_b),hAPP(fun(X_b,X_b),fun(fun(X_a,X_b),fun(X_a,X_b)),combb(X_b,X_b,X_a),inverse_inverse(X_b)),F)),A_2))))))) # label(fact_4912_isCont__inverse) # label(axiom) # label(non_clause).  [assumption].
7.57/7.59	2863 (all X_a (comm_monoid_mult(X_a) -> (all A_1 ti(X_a,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)))) # label(fact_801_mult__1) # label(axiom) # label(non_clause).  [assumption].
7.57/7.59	2864 (all X_a (linorder(X_a) -> (all Y_1 all X_1 (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y_1),X_1)) -> (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y_1)) <-> ti(X_a,X_1) = ti(X_a,Y_1)))))) # label(fact_1564_linorder__antisym__conv3) # label(axiom) # label(non_clause).  [assumption].
7.57/7.59	2865 (all X_a all F all X_1 all A_3 ((all I_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),I_2),A_3)) -> hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),hAPP(X_a,int,F,I_2)),X_1) = one_one(int))) -> hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),hAPP(fun(X_a,bool),int,hAPP(fun(X_a,int),fun(fun(X_a,bool),int),big_co302546470etprod(X_a,int),F),A_3)),X_1) = one_one(int))) # label(fact_4414_setprod__coprime__int) # label(axiom) # label(non_clause).  [assumption].
7.57/7.59	2866 (all X_a (linordered_semidom(X_a) -> (all N all R_4 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),R_4)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),R_4),one_one(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),R_4),hAPP(nat,nat,suc,N))),R_4))))))) # label(fact_1403_realpow__Suc__le__self) # label(axiom) # label(non_clause).  [assumption].
7.57/7.59	2867 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) -> X = hAPP(real,real,arcsin,hAPP(real,real,sin,X))))) # label(fact_2398_arcsin__sin) # label(axiom) # label(non_clause).  [assumption].
7.57/7.59	2868 (all X_1 (hAPP(int,real,real_1(int),X_1) = zero_zero(real) <-> ti(int,X_1) = zero_zero(int))) # label(fact_3330_real__of__int__zero__cancel) # label(axiom) # label(non_clause).  [assumption].
7.57/7.59	2869 (all X_a (semiring_div(X_a) -> (all C all A_1 all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),B)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),A_1),B))))) # label(fact_931_mod__mult__mult1) # label(axiom) # label(non_clause).  [assumption].
7.57/7.59	2870 (all X_a (plus(X_a) & dvd(X_a) & linorder(X_a) -> (all D_1 all Sa exists Z_2 all X_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z_2),X_2)) -> (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),D_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X_2),Sa))) <-> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),D_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X_2),Sa)))))))) # label(fact_862_pinf_I10_J) # label(axiom) # label(non_clause).  [assumption].
7.57/7.59	2871 (all A_1 all B all X (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),B),X)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),A_1),B)),X)))) # label(fact_3239_gcd__semilattice__nat_Ole__infI2) # label(axiom) # label(non_clause).  [assumption].
7.57/7.59	2872 (all X_a (ord(X_a) -> (all I all K (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),I),K)) <-> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),I),hAPP(X_a,fun(X_a,bool),ord_atMost(X_a),K))))))) # label(fact_4988_atMost__iff) # label(axiom) # label(non_clause).  [assumption].
7.57/7.59	2873 (all X_a (group_add(X_a) -> (all A_2 all B_1 (ti(X_a,A_2) = hAPP(X_a,X_a,uminus_uminus(X_a),B_1) <-> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),B_1) = zero_zero(X_a))))) # label(fact_2066_eq__neg__iff__add__eq__0) # label(axiom) # label(non_clause).  [assumption].
7.57/7.59	2874 (all Z_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),hAPP(real,nat,natfloor,Z_1)),one_one(nat))),N)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),Z_1),hAPP(nat,real,real_1(nat),N))))) # label(fact_2362_ge__natfloor__plus__one__imp__gt) # label(axiom) # label(non_clause).  [assumption].
7.57/7.59	2875 (all Y (Y != zero_zero(nat) -> -(all Nat_2 Y != hAPP(nat,nat,suc,Nat_2)))) # label(fact_1607_nat_Oexhaust) # label(axiom) # label(non_clause).  [assumption].
7.57/7.59	2876 (all Z_1 hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),zero_zero(int)),Z_1) = ti(int,Z_1)) # label(fact_135_zadd__0) # label(axiom) # label(non_clause).  [assumption].
7.57/7.59	2877 (all X_a (linorder(X_a) -> (all Ma all I all N_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),I),N_1)) -> hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastLessThan(X_a),N_1),Ma) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastLessThan(X_a),I),Ma)),hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastLessThan(X_a),I),N_1)))))) # label(fact_4205_ivl__diff) # label(axiom) # label(non_clause).  [assumption].
7.57/7.59	2878 (all X_a (number_ring(X_a) & linordered_idom(X_a) -> (all Y_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),hAPP(int,X_a,number_number_of(X_a),Y_1))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,pls)),Y_1)))))) # label(fact_181_less__special_I2_J) # label(axiom) # label(non_clause).  [assumption].
7.57/7.59	2879 (all X_a (real_normed_vector(X_a) -> (all A_1 hAPP(real,real,abs_abs(real),hAPP(X_a,real,norm_norm(X_a),A_1)) = hAPP(X_a,real,norm_norm(X_a),A_1)))) # label(fact_1859_abs__norm__cancel) # label(axiom) # label(non_clause).  [assumption].
7.57/7.59	2880 (all X_a all A_3 all B_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less(fun(X_a,bool)),A_3),B_2)) | ti(fun(X_a,bool),A_3) = ti(fun(X_a,bool),B_2) <-> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_3),B_2)))) # label(fact_2000_subset__iff__psubset__eq) # label(axiom) # label(non_clause).  [assumption].
7.57/7.59	2881 (all J_2 all A_1 all P_5 all K_4 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,J_2),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),hAPP(int,int,hAPP(int,fun(int,int),multInv,P_5),K_4))),P_5)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),J_2),K_4)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),hAPP(int,int,hAPP(int,fun(int,int),multInv,P_5),K_4))),K_4)),P_5)))) # label(fact_835_aux______1) # label(axiom) # label(non_clause).  [assumption].
7.57/7.59	2882 (all B_1 all D_1 all A_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),D_1),A_2)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),D_1),B_1)) & (all E (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),E),B_1)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),E),A_2)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),E),D_1)))) <-> D_1 = hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),A_2),B_1))) # label(fact_3241_gcd__unique__nat) # label(axiom) # label(non_clause).  [assumption].
7.57/7.59	2883 (all X_a (number(X_a) & field_inverse_zero(X_a) -> (all W_1 all B_1 all C_1 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),B_1),C_1) = hAPP(int,X_a,number_number_of(X_a),W_1) <-> (zero_zero(X_a) = ti(X_a,C_1) -> hAPP(int,X_a,number_number_of(X_a),W_1) = zero_zero(X_a)) & (zero_zero(X_a) != ti(X_a,C_1) -> ti(X_a,B_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),W_1)),C_1)))))) # label(fact_1724_eq__divide__eq__number__of) # label(axiom) # label(non_clause).  [assumption].
7.57/7.59	2884 (all X_a all G all A_2 all A_3 (hBOOL(hAPP(filter(X_a),bool,hAPP(complex,fun(filter(X_a),bool),hAPP(fun(X_a,complex),fun(complex,fun(filter(X_a),bool)),tendsto(X_a,complex),G),A_2),A_3)) -> hBOOL(hAPP(filter(X_a),bool,hAPP(real,fun(filter(X_a),bool),hAPP(fun(X_a,real),fun(real,fun(filter(X_a),bool)),tendsto(X_a,real),hAPP(fun(X_a,complex),fun(X_a,real),hAPP(fun(complex,real),fun(fun(X_a,complex),fun(X_a,real)),combb(complex,real,X_a),re),G)),hAPP(complex,real,re,A_2)),A_3)))) # label(fact_4509_Re_Otendsto) # label(axiom) # label(non_clause).  [assumption].
7.57/7.59	2885 (all X_a (ordered_ab_group_add(X_a) -> (all A_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),A_2)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),A_2)),zero_zero(X_a))))))) # label(fact_2057_neg__le__0__iff__le) # label(axiom) # label(non_clause).  [assumption].
7.57/7.59	2886 (exists K_2 all X_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,norm_norm(real),hAPP(complex,real,re,X_2))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(complex,real,norm_norm(complex),X_2)),K_2)))) # label(fact_3022_Re_Obounded) # label(axiom) # label(non_clause).  [assumption].
7.57/7.59	2887 (all X_a (archim1727834104eiling(X_a) -> (all X_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),one_one(X_a))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(X_a,int,archim2085082626_floor(X_a),X_1)),zero_zero(int))))))) # label(fact_2882_floor__le__zero) # label(axiom) # label(non_clause).  [assumption].
7.57/7.59	2888 (all X_1 (-hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),X_1),X_1))) <-> X_1 = zero_zero(real))) # label(fact_474_not__real__square__gt__zero) # label(axiom) # label(non_clause).  [assumption].
7.57/7.59	2889 (all Diff all F all N_1 all H (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),H),zero_zero(real))) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)) -> (hAPP(nat,fun(real,real),Diff,zero_zero(nat)) = F -> ((all M_2 all T_4 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),H),T_4)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),T_4),zero_zero(real))) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_2),N_1)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(nat,fun(real,real),Diff,M_2)),T_4),hAPP(real,real,hAPP(nat,fun(real,real),Diff,hAPP(nat,nat,suc,M_2)),T_4))))) -> (exists T_4 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),H),T_4)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),T_4),zero_zero(real))) & hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),inverse_divide(real)),hAPP(real,fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(real,fun(nat,real)),combc(nat,real,real),Diff),zero_zero(real)))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),fact_fact(nat))))),hAPP(real,fun(nat,real),power_power(real),H))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),N_1))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(nat,fun(real,real),Diff,N_1),T_4)),hAPP(nat,real,real_1(nat),hAPP(nat,nat,fact_fact(nat),N_1)))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),H),N_1))) = hAPP(real,real,F,H)))))))) # label(fact_4281_Maclaurin__minus) # label(axiom) # label(non_clause).  [assumption].
7.57/7.59	2890 (all A_1 all P_5 (hBOOL(hAPP(int,bool,zprime,P_5)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),A_1)),one_one(int)),P_5)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_1),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),P_5),one_one(int))),P_5)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_1),one_one(int)),P_5)))))) # label(fact_535_zcong__square) # label(axiom) # label(non_clause).  [assumption].
7.57/7.59	2891 (all X hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,number_number_of(real),min_1)),hAPP(real,real,sin,X)))) # label(fact_2316_sin__ge__minus__one) # label(axiom) # label(non_clause).  [assumption].
7.57/7.59	2892 (all X_a (linordered_idom(X_a) -> (all N all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),N)))),zero_zero(X_a))))))) # label(fact_1471_odd__power__less__zero) # label(axiom) # label(non_clause).  [assumption].
7.57/7.59	2893 (all X all Y hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(rat,real,ratreal,X)),hAPP(rat,real,ratreal,Y)) = hAPP(rat,real,ratreal,hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),X),Y))) # label(fact_3768_real__minus__code) # label(axiom) # label(non_clause).  [assumption].
7.57/7.59	2894 (all X hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),X))) # label(fact_617_dvd_Oorder__refl) # label(axiom) # label(non_clause).  [assumption].
7.57/7.59	2895 (all X_a (linordered_field(X_a) -> (all C all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),B),C)))))))) # label(fact_1684_divide__strict__right__mono__neg) # label(axiom) # label(non_clause).  [assumption].
7.57/7.59	2896 (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].
7.57/7.59	2897 (all Y_1 all X_1 (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),zOdd)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Y_1),zEven)) -> hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X_1),Y_1)),zOdd))))) # label(fact_1369_odd__minus__even) # label(axiom) # label(non_clause).  [assumption].
7.57/7.59	2898 (all X_a (semiring_div(X_a) -> (all A_1 all B ti(X_a,A_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),A_1),B)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),A_1),B)),B))))) # label(fact_913_semiring__div__class_Omod__div__equality_H) # label(axiom) # label(non_clause).  [assumption].
7.57/7.59	2899 (all A_1 all B (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),gcd_gcd(nat),A_1),B)),B)))) # label(fact_3261_gcd__le2__nat) # label(axiom) # label(non_clause).  [assumption].
7.57/7.59	2900 (all X -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,abs_abs(real),X)),one_one(real))),X))) # label(fact_1893_abs__add__one__not__less__self) # label(axiom) # label(non_clause).  [assumption].
7.57/7.59	2901 (all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,number_number_of(real),min_1)),Y)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),Y),one_one(real))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(real,real,arccos,Y))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,arccos,Y)),pi)) & Y = hAPP(real,real,cos,hAPP(real,real,arccos,Y))))) # label(fact_2280_arccos) # label(axiom) # label(non_clause).  [assumption].
7.57/7.59	2902 (all X X = hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),X),X)) # label(fact_3219_gcd__idem__nat) # label(axiom) # label(non_clause).  [assumption].
7.57/7.59	2903 (all X_a all B_2 all A_3 (hBOOL(hAPP(fun(fun(X_a,bool),bool),bool,hAPP(fun(X_a,bool),fun(fun(fun(X_a,bool),bool),bool),member(fun(X_a,bool)),B_2),A_3)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),B_2),hAPP(fun(fun(X_a,bool),bool),fun(X_a,bool),complete_Sup_Sup(fun(X_a,bool)),A_3))))) # label(fact_1750_Union__upper) # label(axiom) # label(non_clause).  [assumption].
7.57/7.59	2904 (all X_a all X_b (real_normed_field(X_b) -> (all G all B_1 all F all A_2 all A_3 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),A_2),A_3)) -> (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),G),B_1),A_3)) -> (ti(X_b,B_1) != zero_zero(X_b) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(fun(X_a,X_b),fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,X_b)),combs(X_a,X_b,X_b),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,fun(X_b,X_b))),combb(X_b,fun(X_b,X_b),X_a),inverse_divide(X_b)),F)),G)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),inverse_divide(X_b),A_2),B_1)),A_3)))))))) # label(fact_4452_tendsto__divide) # label(axiom) # label(non_clause).  [assumption].
7.57/7.59	2905 (all X hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),hAPP(real,real,arctan,hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),X),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),one_one(real)),hAPP(real,real,sqrt,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),one_one(real)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))))) = hAPP(real,real,arctan,X)) # label(fact_1831_arctan__half) # label(axiom) # label(non_clause).  [assumption].
7.57/7.59	2906 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,uminus_uminus(real),pi)),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),zero_zero(real))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,sin,X)),zero_zero(real)))))) # label(fact_2394_sin__less__zero) # label(axiom) # label(non_clause).  [assumption].
7.57/7.59	2907 (all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(real,real,ln,X_1))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),one_one(real)),X_1))))) # label(fact_1975_ln__ge__zero__iff) # label(axiom) # label(non_clause).  [assumption].
7.57/7.59	2908 (all X_a (order(X_a) -> (all A_1 all B (ti(X_a,B) != ti(X_a,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(X_a),B),A_1))))))) # label(fact_1592_xt1_I12_J) # label(axiom) # label(non_clause).  [assumption].
7.57/7.59	2909 (all Ma hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),bnorRset,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),Ma),one_one(int))),Ma) = hAPP(int,fun(int,bool),norRRset,Ma)) # label(fact_3560_norRRset__def) # label(axiom) # label(non_clause).  [assumption].
7.57/7.59	2910 (all X_a (linordered_idom(X_a) -> (all X_1 all N_1 (-hBOOL(hAPP(nat,bool,even_odd_even(nat),N_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),X_1)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X_1),N_1)))))))) # label(fact_2432_zero__le__odd__power) # label(axiom) # label(non_clause).  [assumption].
7.57/7.59	2911 (all Ta all A_3 all D_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D_2)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Ta),A_3)) -> (all X_2 ((all Xa (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xa),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastAtMost(int),one_one(int)),D_2))) -> (all Xb (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xb),A_3)) -> hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),Xb),Xa) != ti(int,X_2))))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X_2),Ta)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X_2),D_2)),Ta)))))))) # label(fact_4641_aset_I5_J) # label(axiom) # label(non_clause).  [assumption].
7.57/7.59	2912 (all A_2 all B_1 (B_1 = A_2 <-> hAPP(rat,product_prod(int,int),quotient_of,A_2) = hAPP(rat,product_prod(int,int),quotient_of,B_1))) # label(fact_3721_quotient__of__inject__eq) # label(axiom) # label(non_clause).  [assumption].
7.57/7.59	2913 (all X_a all A_3 all B_2 hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_3),B_2) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_3),B_2)),B_2)) # label(fact_1963_Diff__idemp) # label(axiom) # label(non_clause).  [assumption].
7.57/7.59	2914 (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_1870_abs__triangle__ineq2__sym) # label(axiom) # label(non_clause).  [assumption].
7.57/7.59	2915 (all X_a (linordered_field(X_a) -> (all A_2 all B_1 all C_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),C_1)),B_1)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),B_1),C_1)))))))) # label(fact_1737_pos__le__divide__eq) # label(axiom) # label(non_clause).  [assumption].
7.57/7.60	2916 (all X_a (ord(X_a) -> (all C all A_1 all B (ti(X_a,B) = ti(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),A_1),C))))))) # label(fact_1574_ord__eq__less__trans) # label(axiom) # label(non_clause).  [assumption].
7.57/7.60	2917 (all X hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),one_one(real)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,sin,X)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,cos,X)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) # label(fact_2389_cos__squared__eq) # label(axiom) # label(non_clause).  [assumption].
7.57/7.60	2918 (all Ma all D_1 (hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),Ma),D_1) = zero_zero(int) <-> (exists Q_4 hAPP(int,int,hAPP(int,fun(int,int),times_times(int),D_1),Q_4) = ti(int,Ma)))) # label(fact_991_zmod__eq__0__iff) # label(axiom) # label(non_clause).  [assumption].
7.57/7.60	2919 (all X all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X),Y)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(real,nat,natceiling,X)),hAPP(real,nat,natceiling,Y))))) # label(fact_1888_natceiling__mono) # label(axiom) # label(non_clause).  [assumption].
7.57/7.60	2920 (all X_a (comm_monoid_add(X_a) & topological_space(X_a) -> (all F all L (hBOOL(hAPP(X_a,bool,hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),F),L)) -> hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),F)))))) # label(fact_4091_sums__summable) # label(axiom) # label(non_clause).  [assumption].
7.57/7.60	2921 (all X_1 all P_4 (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),hAPP(int,fun(int,bool),sRStar,P_4))) -> ti(int,X_1) = hAPP(int,int,hAPP(int,fun(int,int),standardRes,P_4),X_1))) # label(fact_1100_StandardRes__SRStar__prop3) # label(axiom) # label(non_clause).  [assumption].
7.57/7.60	2922 (all X_a (t2_space(X_a) & comm_monoid_add(X_a) -> (all F (hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),F)) -> hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),hAPP(fun(nat,fun(nat,bool)),fun(nat,X_a),hAPP(fun(fun(nat,bool),X_a),fun(fun(nat,fun(nat,bool)),fun(nat,X_a)),combb(fun(nat,bool),X_a,nat),hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F)),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)))),hAPP(fun(nat,X_a),X_a,suminf(X_a),F)),sequentially)))))) # label(fact_4497_summable__sumr__LIMSEQ__suminf) # label(axiom) # label(non_clause).  [assumption].
7.57/7.60	2923 (all C all A_1 all B (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),B)) & -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),B),A_1)) -> (C = B -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),C)) & -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),C),A_1))))) # label(fact_645_dvd_Oord__less__eq__trans) # label(axiom) # label(non_clause).  [assumption].
7.57/7.60	2924 (all X_a all X_b (metric_space(X_b) & real_n2089651433ebra_1(X_a) -> (all M_1 all F all L_2 all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),L_2),hAPP(X_a,filter(X_a),at(X_a),A_2))) -> (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),M_1),hAPP(X_a,filter(X_a),at(X_a),A_2))) -> ti(X_b,L_2) = ti(X_b,M_1)))))) # label(fact_4546_LIM__unique) # label(axiom) # label(non_clause).  [assumption].
7.57/7.60	2925 (all X_b all X_a (topological_space(X_a) & real_normed_vector(X_b) -> (all F all L all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),L),hAPP(X_a,filter(X_a),at(X_a),A_2))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(real,fun(filter(X_a),bool),hAPP(fun(X_a,real),fun(real,fun(filter(X_a),bool)),tendsto(X_a,real),hAPP(fun(X_a,X_b),fun(X_a,real),hAPP(fun(X_b,real),fun(fun(X_a,X_b),fun(X_a,real)),combb(X_b,real,X_a),norm_norm(X_b)),F)),hAPP(X_b,real,norm_norm(X_b),L)),hAPP(X_a,filter(X_a),at(X_a),A_2))))))) # label(fact_4591_LIM__norm) # label(axiom) # label(non_clause).  [assumption].
7.57/7.60	2926 (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_375_mult__nonpos__nonneg) # label(axiom) # label(non_clause).  [assumption].
7.57/7.60	2927 (all X_1 (hBOOL(hAPP(nat,bool,even_odd_even(nat),X_1)) <-> hBOOL(hAPP(int,bool,even_odd_even(int),hAPP(nat,int,semiring_1_of_nat(int),X_1))))) # label(fact_2428_Parity_Otransfer__int__nat__relations) # label(axiom) # label(non_clause).  [assumption].
7.57/7.60	2928 (all X_a all F all A_3 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_3)) -> (hAPP(nat,nat,suc,zero_zero(nat)) = hAPP(fun(X_a,bool),nat,hAPP(fun(X_a,nat),fun(fun(X_a,bool),nat),big_co1399186613setsum(X_a,nat),F),A_3) <-> (exists X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_3)) & hAPP(X_a,nat,F,X_2) = hAPP(nat,nat,suc,zero_zero(nat)) & (all Xa (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Xa),A_3)) -> (ti(X_a,X_2) != ti(X_a,Xa) -> zero_zero(nat) = hAPP(X_a,nat,F,Xa))))))))) # label(fact_4256_setsum__eq__Suc0__iff) # label(axiom) # label(non_clause).  [assumption].
7.57/7.60	2929 (all X_a (comm_semiring_1(X_a) -> (all X all Y all Q_3 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),Q_3)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),Y),Q_3)) = hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),Y)),Q_3)))) # label(fact_247_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J) # label(axiom) # label(non_clause).  [assumption].
7.57/7.60	2930 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,tan,X)))))) # label(fact_2270_tan__gt__zero) # label(axiom) # label(non_clause).  [assumption].
7.57/7.60	2931 (all X_a (metric_space(X_a) -> the(X_a) = ti(fun(fun(X_a,bool),X_a),the(X_a)))) # label(tsy_c_HOL_OThe_0_res) # label(axiom) # label(non_clause).  [assumption].
7.57/7.60	2932 (all X_a all X_b all X_c all X_d all X_e all X_f all Y -(all A_4 all B_4 all C_4 all D_3 all E all F_3 ti(product_prod(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f))))),Y) != hAPP(product_prod(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f)))),product_prod(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f))))),hAPP(X_a,fun(product_prod(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f)))),product_prod(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f)))))),product_Pair(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f))))),A_4),hAPP(product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f))),product_prod(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f)))),hAPP(X_b,fun(product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f))),product_prod(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f))))),product_Pair(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f)))),B_4),hAPP(product_prod(X_d,product_prod(X_e,X_f)),product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f))),hAPP(X_c,fun(product_prod(X_d,product_prod(X_e,X_f)),product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f)))),product_Pair(X_c,product_prod(X_d,product_prod(X_e,X_f))),C_4),hAPP(product_prod(X_e,X_f),product_prod(X_d,product_prod(X_e,X_f)),hAPP(X_d,fun(product_prod(X_e,X_f),product_prod(X_d,product_prod(X_e,X_f))),product_Pair(X_d,product_prod(X_e,X_f)),D_3),hAPP(X_f,product_prod(X_e,X_f),hAPP(X_e,fun(X_f,product_prod(X_e,X_f)),product_Pair(X_e,X_f),E),F_3))))))) # label(fact_3151_prod__cases6) # label(axiom) # label(non_clause).  [assumption].
7.57/7.60	2933 (all X_a (linord581940658strict(X_a) -> (all C_1 all A_2 all B_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1),A_2)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1),B_1))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),zero_zero(X_a))) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_1),A_2)) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),B_1)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C_1)))))) # label(fact_396_mult__less__cancel__left__disj) # label(axiom) # label(non_clause).  [assumption].
7.57/7.60	2934 (all X_a (field(X_a) -> (all X all Y all Z_1 (ti(X_a,Z_1) != zero_zero(X_a) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),Y),Z_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Z_1),X)),Y)),Z_1))))) # label(fact_1729_diff__divide__eq__iff) # label(axiom) # label(non_clause).  [assumption].
7.57/7.60	2935 (all X_a (number_ring(X_a) -> (all X_1 (hBOOL(hAPP(X_a,bool,iszero(X_a),hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X_1),hAPP(int,int,uminus_uminus(int),hAPP(int,int,bit1,pls)))))) <-> hAPP(int,X_a,number_number_of(X_a),X_1) = one_one(X_a))))) # label(fact_2503_eq__special_I4_J) # label(axiom) # label(non_clause).  [assumption].
7.57/7.60	2936 (all X hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),hAPP(real,nat,natfloor,X)))) # label(fact_1874_zero__le__natfloor) # label(axiom) # label(non_clause).  [assumption].
7.57/7.60	2937 (all K all Ma all N_1 (N_1 = Ma <-> hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,K)),N_1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,K)),Ma))) # label(fact_1250_Suc__mult__cancel1) # label(axiom) # label(non_clause).  [assumption].
7.57/7.60	2938 (all X_a (linordered_field(X_a) -> (all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,inverse_inverse(X_a),A_1)),hAPP(X_a,X_a,inverse_inverse(X_a),B))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),A_1))))))) # label(fact_2549_inverse__less__imp__less) # label(axiom) # label(non_clause).  [assumption].
7.57/7.60	2939 (all N hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(nat,real,real_1(nat),hAPP(nat,nat,suc,N))))) # label(fact_2317_real__of__nat__Suc__gt__zero) # label(axiom) # label(non_clause).  [assumption].
7.57/7.60	2940 (all K_4 hAPP(product_prod(int,int),rat,frct,hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),one_one(int)),hAPP(int,int,number_number_of(int),K_4))) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),one_one(rat)),hAPP(int,rat,number_number_of(rat),K_4))) # label(fact_3712_Frct__code__post_I5_J) # label(axiom) # label(non_clause).  [assumption].
7.57/7.60	2941 (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_814_add__increasing) # label(axiom) # label(non_clause).  [assumption].
7.57/7.60	2942 (all K_4 hAPP(int,int,uminus_uminus(int),hAPP(int,int,bit0,K_4)) = hAPP(int,int,bit0,hAPP(int,int,uminus_uminus(int),K_4))) # label(fact_2138_minus__Bit0) # label(axiom) # label(non_clause).  [assumption].
7.57/7.60	2943 (all N_1 all Ma (hAPP(int,quickcheck_code_int,quickcheck_of_int,N_1) = hAPP(int,quickcheck_code_int,quickcheck_of_int,Ma) <-> ti(int,Ma) = ti(int,N_1))) # label(fact_3534_Quickcheck__Narrowing_Oof__int__inject) # label(axiom) # label(non_clause).  [assumption].
7.57/7.60	2944 (all N all A_1 all B (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,A_1),B)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A_1),N)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),B),N))))) # label(fact_2857_coprime__exp__imp) # label(axiom) # label(non_clause).  [assumption].
7.57/7.60	2945 (all X_a (ordere142940540dd_abs(X_a) -> (all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),A_1)),B)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,abs_abs(X_a),A_1)),B))))))) # label(fact_2081_abs__leI) # label(axiom) # label(non_clause).  [assumption].
7.57/7.60	2946 (all X_b (number(X_b) & division_ring(X_b) -> (all W hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),inverse_divide(X_b),one_one(X_b)),hAPP(int,X_b,number_number_of(X_b),W)) = hAPP(X_b,X_b,inverse_inverse(X_b),hAPP(int,X_b,number_number_of(X_b),W))))) # label(fact_2588_inverse__eq__divide__number__of) # label(axiom) # label(non_clause).  [assumption].
7.57/7.60	2947 (all X_a (archim1727834104eiling(X_a) -> (all X_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),hAPP(int,X_a,number_number_of(X_a),min_1))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(X_a,int,archimedean_ceiling(X_a),X_1)),zero_zero(int))))))) # label(fact_3309_ceiling__less__zero) # label(axiom) # label(non_clause).  [assumption].
7.57/7.60	2948 (all N all X hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(nat,real,real_1(nat),N)),hAPP(nat,real,real_1(nat),X))),hAPP(nat,real,real_1(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),N),X)))))) # label(fact_2357_real__of__nat__div2) # label(axiom) # label(non_clause).  [assumption].
7.57/7.60	2949 (all X all Y (hAPP(complex,real,re,X) = hAPP(complex,real,re,Y) -> (hAPP(complex,real,im,Y) = hAPP(complex,real,im,X) -> Y = X))) # label(fact_2997_complex__eqI) # label(axiom) # label(non_clause).  [assumption].
7.57/7.60	2950 (all X_a (real_n1866405975lgebra(X_a) -> (all X all Y hAPP(X_a,X_a,sgn_sgn(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),Y)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,sgn_sgn(X_a),X)),hAPP(X_a,X_a,sgn_sgn(X_a),Y))))) # label(fact_2204_sgn__mult) # label(axiom) # label(non_clause).  [assumption].
7.57/7.60	2951 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N)) -> (hAPP(nat,nat,suc,M) != N -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,M)),N))))) # label(fact_1233_Suc__lessI) # label(axiom) # label(non_clause).  [assumption].
7.57/7.60	2952 (all X_a (linord1117847801e_zero(X_a) & number_ring(X_a) -> (all R_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),R_1)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),R_1),hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))))) # label(fact_1756_half__gt__zero__iff) # label(axiom) # label(non_clause).  [assumption].
7.57/7.60	2953 (all N all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> (zero_zero(real) != X -> hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),N) = hAPP(real,real,hAPP(real,fun(real,real),powr,X),hAPP(nat,real,real_1(nat),N))) & (zero_zero(real) = X -> hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),N) = zero_zero(real))))) # label(fact_3420_powr__realpow2) # label(axiom) # label(non_clause).  [assumption].
7.57/7.60	2954 (all B all A_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A_1),B)),zero_zero(int))) -> hAPP(int,int,number_number_of(int),min_1) = hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_1),B)))) # label(fact_1063_div__pos__neg__trivial) # label(axiom) # label(non_clause).  [assumption].
7.57/7.60	2955 (all K all Ma all N_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),K),N_1)) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),K),Ma)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),K),hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),Ma),N_1))))) # label(fact_4369_gcd__greatest__iff__int) # label(axiom) # label(non_clause).  [assumption].
7.57/7.60	2956 (all X_c all X_b all X_a (topological_space(X_b) & topological_space(X_c) & metric_space(X_a) -> (all G all C_1 all F all B_1 all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),B_1),hAPP(X_a,filter(X_a),at(X_a),A_2))) -> (hBOOL(hAPP(filter(X_b),bool,hAPP(X_c,fun(filter(X_b),bool),hAPP(fun(X_b,X_c),fun(X_c,fun(filter(X_b),bool)),tendsto(X_b,X_c),G),C_1),hAPP(X_b,filter(X_b),at(X_b),B_1))) -> ((exists D_3 ((all X_2 (ti(X_a,X_2) != ti(X_a,A_2) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),X_2),A_2)),D_3)) -> ti(X_b,B_1) != hAPP(X_a,X_b,F,X_2))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),D_3)))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_c,fun(filter(X_a),bool),hAPP(fun(X_a,X_c),fun(X_c,fun(filter(X_a),bool)),tendsto(X_a,X_c),hAPP(fun(X_a,X_b),fun(X_a,X_c),hAPP(fun(X_b,X_c),fun(fun(X_a,X_b),fun(X_a,X_c)),combb(X_b,X_c,X_a),G),F)),C_1),hAPP(X_a,filter(X_a),at(X_a),A_2))))))))) # label(fact_4602_metric__LIM__compose2) # label(axiom) # label(non_clause).  [assumption].
7.57/7.60	2957 (all X_a (ordere142940540dd_abs(X_a) -> (all A_1 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),A_1)),hAPP(X_a,X_a,abs_abs(X_a),A_1)))))) # label(fact_2079_abs__ge__minus__self) # label(axiom) # label(non_clause).  [assumption].
7.57/7.60	2958 (all X_a (real_algebra_1(X_a) & real_normed_vector(X_a) -> (all X_3 (hBOOL(hAPP(fun(nat,real),bool,summable(real),X_3)) -> hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),hAPP(fun(nat,real),fun(nat,X_a),hAPP(fun(real,X_a),fun(fun(nat,real),fun(nat,X_a)),combb(real,X_a,nat),of_real(X_a)),X_3))))))) # label(fact_4006_of__real_Osummable) # label(axiom) # label(non_clause).  [assumption].
7.57/7.60	2959 (all P_4 all N_1 (hBOOL(hAPP(nat,bool,prime,hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),P_4),N_1))) <-> hBOOL(hAPP(nat,bool,prime,P_4)) & one_one(nat) = N_1)) # label(fact_3059_prime__exp) # label(axiom) # label(non_clause).  [assumption].
7.57/7.60	2960 (all A_2 all B_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B_1),A_2)) <-> hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),one_one(rat)),hAPP(int,rat,hAPP(int,fun(int,rat),fract,A_2),B_1)))))) # label(fact_3788_one__less__Fract__iff) # label(axiom) # label(non_clause).  [assumption].
7.57/7.60	2961 (all M all P_5 (hBOOL(hAPP(nat,bool,prime,P_5)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),P_5),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),M),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat)))))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),P_5),M))))) # label(fact_3076_prime__dvd__square) # label(axiom) # label(non_clause).  [assumption].
7.57/7.60	2962 (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_688_diff__less__mono) # label(axiom) # label(non_clause).  [assumption].
7.57/7.60	2963 (all Ma all Ta all K (zero_zero(int) != ti(int,K) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K),Ma)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K),Ta))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),Ma),Ta))))) # label(fact_601_zdvd__mono) # label(axiom) # label(non_clause).  [assumption].
7.57/7.60	2964 (all X_3 ((all R_2 (hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),R_2)) -> (exists K_1 all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_1),N_2)) -> hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,abs_abs(rat),hAPP(nat,rat,X_3,N_2))),R_2)))))) <-> hBOOL(hAPP(fun(nat,rat),bool,vanishes,X_3)))) # label(fact_4863_vanishes__def) # label(axiom) # label(non_clause).  [assumption].
7.57/7.60	2965 (all P_1 all P_2 all D_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D_1)) -> ((all X_2 all K_1 (hBOOL(hAPP(int,bool,P_2,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X_2),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K_1),D_1)))) <-> hBOOL(hAPP(int,bool,P_2,X_2)))) -> ((exists Z_2 all X_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Z_2),X_2)) -> (hBOOL(hAPP(int,bool,P_1,X_2)) <-> hBOOL(hAPP(int,bool,P_2,X_2))))) -> ((exists X1 hBOOL(hAPP(int,bool,P_2,X1))) -> (exists X1 hBOOL(hAPP(int,bool,P_1,X1)))))))) # label(fact_2845_plusinfinity) # label(axiom) # label(non_clause).  [assumption].
7.57/7.60	2966 (all X_a (real_normed_algebra(X_a) -> (all X zero_zero(X_a) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),zero_zero(X_a))))) # label(fact_879_mult__right_Ozero) # label(axiom) # label(non_clause).  [assumption].
7.57/7.60	2967 (all X_1 hBOOL(hAPP(real,bool,hAPP(fun(nat,real),fun(real,bool),sums(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),sin_coeff)),hAPP(real,fun(nat,real),power_power(real),X_1))),hAPP(real,real,sin,X_1)))) # label(fact_4096_sin__converges) # label(axiom) # label(non_clause).  [assumption].
7.57/7.60	2968 (all D all A_1 all B (one_one(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),D),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A_1),B)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),D),A_1) = one_one(nat))) # label(fact_3271_coprime__lmult__nat) # label(axiom) # label(non_clause).  [assumption].
7.57/7.60	2969 (all A_2 all D_1 all N_1 hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),hAPP(fun(nat,bool),int,hAPP(fun(nat,int),fun(fun(nat,bool),int),big_co1399186613setsum(nat,int),hAPP(fun(nat,int),fun(nat,int),hAPP(fun(int,int),fun(fun(nat,int),fun(nat,int)),combb(int,int,nat),hAPP(int,fun(int,int),plus_plus(int),A_2)),hAPP(int,fun(nat,int),hAPP(fun(nat,fun(int,int)),fun(int,fun(nat,int)),combc(nat,int,int),hAPP(fun(nat,int),fun(nat,fun(int,int)),hAPP(fun(int,fun(int,int)),fun(fun(nat,int),fun(nat,fun(int,int))),combb(int,fun(int,int),nat),times_times(int)),semiring_1_of_nat(int))),D_1))),hAPP(nat,fun(nat,bool),ord_lessThan(nat),N_1))) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(nat,int,semiring_1_of_nat(int),N_1)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A_2),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A_2),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),one_one(nat)))),D_1))))) # label(fact_4311_arith__series__int) # label(axiom) # label(non_clause).  [assumption].
7.57/7.60	2970 (all X_3 (hBOOL(hAPP(fun(nat,complex),bool,cauchy(complex),X_3)) -> hBOOL(hAPP(fun(nat,complex),bool,cauchy(complex),hAPP(fun(nat,complex),fun(nat,complex),hAPP(fun(complex,complex),fun(fun(nat,complex),fun(nat,complex)),combb(complex,complex,nat),cnj),X_3))))) # label(fact_3848_cnj_OCauchy) # label(axiom) # label(non_clause).  [assumption].
7.57/7.60	2971 (all X_a (comm_monoid_add(X_a) & topological_space(X_a) -> hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),hAPP(X_a,fun(nat,X_a),combk(X_a,nat),zero_zero(X_a)))))) # label(fact_3980_summable__zero) # label(axiom) # label(non_clause).  [assumption].
7.57/7.60	2972 (all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,arctan,Y)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) & hAPP(real,real,tan,hAPP(real,real,arctan,Y)) = Y & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),hAPP(real,real,arctan,Y))))) # label(fact_2278_arctan) # label(axiom) # label(non_clause).  [assumption].
7.57/7.60	2973 (all X_a all F all X_1 all A_3 ((all I_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),I_2),A_3)) -> one_one(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),hAPP(X_a,nat,F,I_2)),X_1))) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),hAPP(fun(X_a,bool),nat,hAPP(fun(X_a,nat),fun(fun(X_a,bool),nat),big_co302546470etprod(X_a,nat),F),A_3)),X_1) = one_one(nat))) # label(fact_4128_setprod__coprime__nat) # label(axiom) # label(non_clause).  [assumption].
7.57/7.60	2974 (all M all N hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(nat,int,semiring_1_of_nat(int),M)),N) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),M),N))) # label(fact_1355_int__power) # label(axiom) # label(non_clause).  [assumption].
7.57/7.60	2975 (all X_b all X_a (comm_monoid_mult(X_a) -> (all H all G all S all R_3 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),R_3,one_one(X_a)),one_one(X_a))) -> ((all X1 all Y1 all X2 all Y2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),R_3,X1),X2)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),R_3,Y1),Y2)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),R_3,hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X1),Y1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X2),Y2))))) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),S)) -> ((all X_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),S)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),R_3,hAPP(X_b,X_a,H,X_2)),hAPP(X_b,X_a,G,X_2))))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),R_3,hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co302546470etprod(X_b,X_a),H),S)),hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co302546470etprod(X_b,X_a),G),S)))))))))) # label(fact_4779_setprod_Orelated) # label(axiom) # label(non_clause).  [assumption].
7.57/7.60	2976 (all X hAPP(real,real,hAPP(nat,fun(real,real),root,hAPP(nat,nat,suc,zero_zero(nat))),X) = X) # label(fact_2671_real__root__Suc__0) # label(axiom) # label(non_clause).  [assumption].
7.57/7.60	2977 (all Y all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Y)) -> hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,ln,X)),hAPP(real,real,ln,Y)) = hAPP(real,real,ln,hAPP(real,real,hAPP(real,fun(real,real),times_times(real),X),Y))))) # label(fact_1976_ln__mult) # label(axiom) # label(non_clause).  [assumption].
7.57/7.60	2978 (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),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)) = 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))))) # label(fact_214_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J) # label(axiom) # label(non_clause).  [assumption].
7.57/7.60	2979 (all X_1 hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less_eq(nat)),X_1))) = hAPP(nat,nat,suc,X_1)) # label(fact_3829_card__bdd__nat__set__le) # label(axiom) # label(non_clause).  [assumption].
7.57/7.60	2980 (all R_4 all P_5 all Q_3 (hAPP(rat,product_prod(int,int),quotient_of,R_4) = hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),P_5),Q_3) -> hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),P_5),Q_3) = one_one(int))) # label(fact_4403_quotient__of__coprime) # label(axiom) # label(non_clause).  [assumption].
7.57/7.60	2981 (all K all L hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),hAPP(bool,fun(int,fun(int,int)),if(int),hAPP(int,bool,hAPP(int,fun(int,bool),fequal(int),L),zero_zero(int))),K),hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,L),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,abs_abs(int),K)),hAPP(int,int,abs_abs(int),L))))) = hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,K),L)) # label(fact_3465_zgcd__code) # label(axiom) # label(non_clause).  [assumption].
7.57/7.60	2982 (all X_a (group_add(X_a) -> (all A_1 all B hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),B)),hAPP(X_a,X_a,uminus_uminus(X_a),A_1))))) # label(fact_2050_minus__add) # label(axiom) # label(non_clause).  [assumption].
7.57/7.60	2983 (all N_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(int,real,real_1(int),N_1))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),N_1)))) # label(fact_3385_real__of__int__ge__zero__cancel__iff) # label(axiom) # label(non_clause).  [assumption].
7.57/7.60	2984 (all X_a (real_vector(X_a) -> (all X all Y all A_1 (zero_zero(real) != A_1 -> (hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_1),Y) = hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_1),X) -> ti(X_a,X) = ti(X_a,Y)))))) # label(fact_4701_scaleR__left__imp__eq) # label(axiom) # label(non_clause).  [assumption].
7.57/7.60	2985 (all K_4 hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),K_4),pls) = ti(int,K_4)) # label(fact_479_diff__bin__simps_I1_J) # label(axiom) # label(non_clause).  [assumption].
7.57/7.60	2986 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,fact_fact(nat),N)),hAPP(nat,nat,fact_fact(nat),M)) = zero_zero(nat))) # label(fact_2499_fact__mod) # label(axiom) # label(non_clause).  [assumption].
7.57/7.60	2987 (all X_a (semiring_1(X_a) -> -hBOOL(hAPP(X_a,bool,iszero(X_a),one_one(X_a))))) # label(fact_2562_not__iszero__1) # label(axiom) # label(non_clause).  [assumption].
7.57/7.60	2988 (all X_c all X_a all X_b all C_1 all P_4 all Z (hBOOL(hAPP(X_c,bool,hAPP(product_prod(X_a,X_b),fun(X_c,bool),hAPP(fun(X_a,fun(X_b,fun(X_c,bool))),fun(product_prod(X_a,X_b),fun(X_c,bool)),product_prod_case(X_a,X_b,fun(X_c,bool)),C_1),P_4),Z)) -> -(all X_2 all Y_2 (ti(product_prod(X_a,X_b),P_4) = hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),X_2),Y_2) -> -hBOOL(hAPP(X_c,bool,hAPP(X_b,fun(X_c,bool),hAPP(X_a,fun(X_b,fun(X_c,bool)),C_1,X_2),Y_2),Z)))))) # label(fact_4058_splitE_H) # label(axiom) # label(non_clause).  [assumption].
7.57/7.60	2989 (all X_a (ring_1(X_a) -> (all N hAPP(nat,X_a,semiring_1_of_nat(X_a),N) = hAPP(int,X_a,ring_1_of_int(X_a),hAPP(nat,int,semiring_1_of_nat(int),N))))) # label(fact_3587_of__int__of__nat__eq) # label(axiom) # label(non_clause).  [assumption].
7.57/7.60	2990 (all X_a (ordere142940540dd_abs(X_a) -> (all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),zero_zero(X_a))) -> hAPP(X_a,X_a,uminus_uminus(X_a),A_1) = hAPP(X_a,X_a,abs_abs(X_a),A_1))))) # label(fact_2095_abs__of__nonpos) # label(axiom) # label(non_clause).  [assumption].
7.57/7.60	2991 (all A_2 all P_4 hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),wset,A_2),P_4)))) # label(fact_1669_wset__fin) # label(axiom) # label(non_clause).  [assumption].
7.57/7.60	2992 (all X_1 (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),zEven)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X_1)) -> hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,number_number_of(int),min_1)),hAPP(int,nat,nat_1,X_1)) = one_one(int)))) # label(fact_1203_EvenOdd_Oneg__one__even__power) # label(axiom) # label(non_clause).  [assumption].
7.57/7.60	2993 (all X_a all Q_1 all P_1 all A_2 (hBOOL(hAPP(X_a,bool,P_1,A_2)) -> ((all X_2 (hBOOL(hAPP(X_a,bool,P_1,X_2)) -> hBOOL(hAPP(X_a,bool,Q_1,X_2)))) -> hBOOL(hAPP(X_a,bool,Q_1,hAPP(fun(X_a,bool),X_a,hilbert_Eps(X_a),P_1)))))) # label(fact_4867_someI2) # label(axiom) # label(non_clause).  [assumption].
7.57/7.60	2994 (all N zero_zero(real) = hAPP(real,real,hAPP(nat,fun(real,real),root,N),zero_zero(real))) # label(fact_2670_real__root__zero) # label(axiom) # label(non_clause).  [assumption].
7.57/7.60	2995 (all X_1 all Y_1 (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Y_1),zEven)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X_1),Y_1)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),X_1),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),Y_1),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))))) # label(fact_1462_even__div__2__l) # label(axiom) # label(non_clause).  [assumption].
7.57/7.60	2996 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),one_one(real))) -> hAPP(real,real,uminus_uminus(real),hAPP(real,real,ln,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),one_one(real)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),X),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),one_one(real)),X))))) = hAPP(real,real,ln,hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),one_one(real)),X)))) # label(fact_2120_aux5) # label(axiom) # label(non_clause).  [assumption].
7.57/7.60	2997 (all X_a all X_b (comm_monoid_mult(X_b) -> (all G all A_3 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_3)) -> ((all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_3)) -> hAPP(X_a,X_b,G,X_2) = one_one(X_b))) -> one_one(X_b) = hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co302546470etprod(X_a,X_b),G),A_3)))))) # label(fact_4148_setprod_Oneutral) # label(axiom) # label(non_clause).  [assumption].
7.57/7.60	2998 (all X_a (order(X_a) -> (all Z_1 all Y all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),X)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z_1),Y)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z_1),X))))))) # label(fact_1602_xt1_I8_J) # label(axiom) # label(non_clause).  [assumption].
7.57/7.60	2999 (all N ti(int,N) = hAPP(real,int,archim2085082626_floor(real),hAPP(int,real,real_1(int),N))) # label(fact_3324_floor__real__of__int) # label(axiom) # label(non_clause).  [assumption].
7.57/7.60	3000 (all X all M hAPP(real,real,sin,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,real_1(nat),hAPP(nat,nat,suc,M))),pi)),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) = hAPP(real,real,cos,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,real_1(nat),M)),pi)),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))) # label(fact_2351_sin__expansion__lemma) # label(axiom) # label(non_clause).  [assumption].
7.57/7.60	3001 (all X_a (dense_linorder(X_a) -> (all A_2 all B_1 all C_1 all D_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_gr676655987ssThan(X_a),A_2),B_1)),hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastLessThan(X_a),C_1),D_1))) <-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),B_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_1),D_1)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C_1),A_2))))))) # label(fact_4234_greaterThanLessThan__subseteq__atLeastLessThan__iff) # label(axiom) # label(non_clause).  [assumption].
7.57/7.60	3002 (all A_1 hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,uminus_uminus(int),A_1)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,hAPP(int,int,bit1,pls)))) = hAPP(int,int,uminus_uminus(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,hAPP(int,int,bit1,pls)))))) # label(fact_2177_power3__minus) # label(axiom) # label(non_clause).  [assumption].
7.57/7.60	3003 (all B_1 all A_2 all P_4 (hBOOL(hAPP(int,bool,zprime,P_4)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit1,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),P_4)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_2),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),P_4),one_one(int)))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),B_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B_1),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),P_4),one_one(int)))) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),hAPP(int,int,hAPP(int,fun(int,int),inv,P_4),B_1)),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),wset,A_2),P_4))) -> hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),B_1),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),wset,A_2),P_4)))))))))) # label(fact_829_wset__inv__mem__mem) # label(axiom) # label(non_clause).  [assumption].
7.57/7.60	3004 (all X_a (dist_norm(X_a) -> norm_norm(X_a) = ti(fun(X_a,real),norm_norm(X_a)))) # label(tsy_c_RealVector_Onorm__class_Onorm_1_res) # label(axiom) # label(non_clause).  [assumption].
7.57/7.60	3005 (all K_4 all L_4 ((-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),L_4)) -> hAPP(int,int,uminus_uminus(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),K_4),hAPP(int,int,uminus_uminus(int),L_4))) = hAPP(int,int,hAPP(int,fun(int,int),z3div,K_4),L_4)) & (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),L_4)) -> hAPP(int,int,hAPP(int,fun(int,int),div_div(int),K_4),L_4) = hAPP(int,int,hAPP(int,fun(int,int),z3div,K_4),L_4)))) # label(fact_2729_z3div__def) # label(axiom) # label(non_clause).  [assumption].
7.57/7.60	3006 (all A_2 all B_1 all C_1 (C_1 != zero_zero(real) -> (hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B_1),C_1) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A_2),C_1) <-> A_2 = B_1))) # label(fact_708_real__mult__right__cancel) # label(axiom) # label(non_clause).  [assumption].
7.57/7.60	3007 (all X_1 (zero_zero(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),X_1),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat)))) <-> hBOOL(hAPP(nat,bool,even_odd_even(nat),X_1)))) # label(fact_2450_even__nat__equiv__def) # label(axiom) # label(non_clause).  [assumption].
7.57/7.60	3008 (all X_a all X_b (ord(X_b) -> (all F all G ((all X_2 hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_a,X_b,F,X_2)),hAPP(X_a,X_b,G,X_2)))) <-> hBOOL(hAPP(fun(X_a,X_b),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,X_b),bool),ord_less_eq(fun(X_a,X_b)),F),G)))))) # label(fact_1559_le__fun__def) # label(axiom) # label(non_clause).  [assumption].
7.57/7.60	3009 (all X_a (ordered_ab_group_add(X_a) -> (all A_2 all B_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),B_1)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_2),B_1)),zero_zero(X_a))))))) # label(fact_825_le__iff__diff__le__0) # label(axiom) # label(non_clause).  [assumption].
7.57/7.60	3010 (all A_1 all B hAPP(product_prod(int,int),int,product_fst(int,int),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),divmod_int,A_1),B)) = hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_1),B)) # label(fact_3107_div__int__def) # label(axiom) # label(non_clause).  [assumption].
7.57/7.60	3011 (all N hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),minus_minus(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,code_S1047413653umeral,N)),one_one(code_code_numeral)) = N) # label(fact_2955_Suc__code__numeral__minus__one) # label(axiom) # label(non_clause).  [assumption].
7.57/7.60	3012 (all X_a (linordered_idom(X_a) -> (all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),zero_zero(X_a))) -> hAPP(X_a,X_a,uminus_uminus(X_a),one_one(X_a)) = hAPP(X_a,X_a,sgn_sgn(X_a),A_1))))) # label(fact_2231_sgn__neg) # label(axiom) # label(non_clause).  [assumption].
7.57/7.60	3013 (all X_a all A_3 all B_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),B_2),A_3)) <-> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),uminus_uminus(fun(X_a,bool)),A_3)),hAPP(fun(X_a,bool),fun(X_a,bool),uminus_uminus(fun(X_a,bool)),B_2))))) # label(fact_2135_Compl__subset__Compl__iff) # label(axiom) # label(non_clause).  [assumption].
7.57/7.60	3014 (all N_4 (hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),N_4)) <-> (exists M_2 all X_2 (hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X_2),N_4)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X_2),M_2)))))) # label(fact_3673_finite__nat__set__iff__bounded__le) # label(axiom) # label(non_clause).  [assumption].
7.57/7.60	3015 (all B_1 all A_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A_2)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_2),B_1))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B_1),A_2)) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B_1))))) # label(fact_1023_nonneg1__imp__zdiv__pos__iff) # label(axiom) # label(non_clause).  [assumption].
7.57/7.60	3016 (all N all M hAPP(code_code_numeral,product_prod(code_code_numeral,code_code_numeral),hAPP(code_code_numeral,fun(code_code_numeral,product_prod(code_code_numeral,code_code_numeral)),code_d418564891umeral,N),M) = hAPP(code_code_numeral,product_prod(code_code_numeral,code_code_numeral),hAPP(code_code_numeral,fun(code_code_numeral,product_prod(code_code_numeral,code_code_numeral)),product_Pair(code_code_numeral,code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),N),M)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),N),M))) # label(fact_3081_div__mod__code__numeral__def) # label(axiom) # label(non_clause).  [assumption].
7.57/7.60	3017 (all X_a (field_char_0(X_a) -> (all Z hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),hAPP(int,X_a,ring_1_of_int(X_a),Z)),field_char_0_Rats(X_a)))))) # label(fact_3702_Rats__of__int) # label(axiom) # label(non_clause).  [assumption].
7.57/7.60	3018 (all B_1 all A_2 all F all G all X_1 all D_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),F),hAPP(real,real,G,X_1)),D_2)) -> (zero_zero(real) != D_2 -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A_2),X_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_1),B_1)) -> ((all Y_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),Y_2),B_1)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A_2),Y_2)) -> Y_2 = hAPP(real,real,F,hAPP(real,real,G,Y_2)))) -> (hBOOL(hAPP(real,bool,hAPP(fun(real,real),fun(real,bool),isCont(real,real),G),X_1)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),G),X_1),hAPP(real,real,inverse_inverse(real),D_2)))))))))) # label(fact_4925_DERIV__inverse__function) # label(axiom) # label(non_clause).  [assumption].
7.57/7.60	3019 (all B_2 all A_3 (hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A_3)) -> (hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,B_2)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(fun(int,bool),fun(fun(int,bool),bool),ord_less(fun(int,bool)),A_3),B_2)) <-> hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,bool),fun(fun(nat,bool),bool),ord_less(fun(nat,bool)),hAPP(fun(int,bool),fun(nat,bool),hAPP(fun(int,nat),fun(fun(int,bool),fun(nat,bool)),image(int,nat),nat_1),A_3)),hAPP(fun(int,bool),fun(nat,bool),hAPP(fun(int,nat),fun(fun(int,bool),fun(nat,bool)),image(int,nat),nat_1),B_2))))))) # label(fact_3659_transfer__int__nat__set__relations_I4_J) # label(axiom) # label(non_clause).  [assumption].
7.57/7.60	3020 (all X_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)) -> hBOOL(hAPP(real,bool,hAPP(fun(real,real),fun(real,bool),isCont(real,real),hAPP(nat,fun(real,real),root,N_1)),X_1)))) # label(fact_4884_isCont__real__root) # label(axiom) # label(non_clause).  [assumption].
7.57/7.60	3021 (all X_1 hBOOL(hAPP(real,bool,hAPP(fun(real,real),fun(real,bool),isCont(real,real),arctan),X_1))) # label(fact_4888_isCont__arctan) # label(axiom) # label(non_clause).  [assumption].
7.57/7.60	3022 (all X_a all P_1 hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(bool,bool),fun(fun(X_a,bool),fun(X_a,bool)),combb(bool,bool,X_a),fNot),P_1)) = hAPP(fun(X_a,bool),fun(X_a,bool),uminus_uminus(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),P_1))) # label(fact_3857_Collect__neg__eq) # label(axiom) # label(non_clause).  [assumption].
7.57/7.60	3023 (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),hAPP(int,int,uminus_uminus(int),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_2163_diff__number__of__eq) # label(axiom) # label(non_clause).  [assumption].
7.57/7.60	3024 (all X_1 all A_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(real,int,archim2085082626_floor(real),X_1)),A_2)) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_1),hAPP(int,real,real_1(int),A_2))))) # label(fact_3361_floor__less__eq) # label(axiom) # label(non_clause).  [assumption].
7.57/7.60	3025 (all X_a all A_3 all B_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),B_2)) -> (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_3),B_2))) <-> hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_3))))) # label(fact_1820_finite__Diff2) # label(axiom) # label(non_clause).  [assumption].
7.57/7.60	3026 (all X_a (real_algebra_1(X_a) -> (all N hAPP(real,X_a,of_real(X_a),hAPP(nat,real,semiring_1_of_nat(real),N)) = hAPP(nat,X_a,semiring_1_of_nat(X_a),N)))) # label(fact_2800_of__real__of__nat__eq) # label(axiom) # label(non_clause).  [assumption].
7.57/7.60	3027 (all M all K_4 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),K_4) != M -> (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),K_4))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),K_4))))) # label(fact_1386_one__less__k) # label(axiom) # label(non_clause).  [assumption].
7.57/7.60	3028 (all R_1 all X_3 (hBOOL(hAPP(fun(nat,rat),bool,vanishes,X_3)) -> (hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),R_1)) -> (exists K_1 all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_1),N_2)) -> hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,abs_abs(rat),hAPP(nat,rat,X_3,N_2))),R_1))))))) # label(fact_4864_vanishesD) # label(axiom) # label(non_clause).  [assumption].
7.57/7.60	3029 (all X_1 all Y_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(rat,real,ratreal,X_1)),hAPP(rat,real,ratreal,Y_1))) <-> hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),X_1),Y_1)))) # label(fact_3766_real__less__eq__code) # label(axiom) # label(non_clause).  [assumption].
7.57/7.60	3030 (all B all A_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),zero_zero(int))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_1),B)),zero_zero(int)))))) # label(fact_1021_div__nonneg__neg__le0) # label(axiom) # label(non_clause).  [assumption].
7.57/7.60	3031 (all X_a (semiring_1(X_a) -> (all M all 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)),hAPP(nat,X_a,semiring_1_of_nat(X_a),N)) = hAPP(nat,X_a,semiring_1_of_nat(X_a),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N))))) # label(fact_1286_of__nat__add) # label(axiom) # label(non_clause).  [assumption].
7.57/7.60	3032 (all X_a (semiring_1(X_a) -> (all M all 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)),hAPP(nat,X_a,semiring_1_of_nat(X_a),N)) = hAPP(nat,X_a,semiring_1_of_nat(X_a),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),N))))) # label(fact_1287_of__nat__mult) # label(axiom) # label(non_clause).  [assumption].
7.57/7.60	3033 (all P all Q (hBOOL(P) | -hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,P),Q)))) # label(help_fconj_2_1_U) # label(axiom) # label(non_clause).  [assumption].
7.57/7.60	3034 (all X_a (comm_ring(X_a) & monoid_mult(X_a) -> (all X_1 all N_1 all Y_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X_1),hAPP(nat,nat,suc,N_1))),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),Y_1),hAPP(nat,nat,suc,N_1))) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),X_1),Y_1)),hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),times_times(X_a)),hAPP(X_a,fun(nat,X_a),power_power(X_a),X_1))),hAPP(fun(nat,nat),fun(nat,X_a),hAPP(fun(nat,X_a),fun(fun(nat,nat),fun(nat,X_a)),combb(nat,X_a,nat),hAPP(X_a,fun(nat,X_a),power_power(X_a),Y_1)),hAPP(nat,fun(nat,nat),minus_minus(nat),N_1)))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,suc,N_1))))))) # label(fact_4227_lemma__realpow__diff__sumr2) # label(axiom) # label(non_clause).  [assumption].
7.57/7.60	3035 (all A_1 all N all B (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A_1),N)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),B),N))) -> (N != zero_zero(nat) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A_1),B))))) # label(fact_870_pow__divides__pow__int) # label(axiom) # label(non_clause).  [assumption].
7.57/7.60	3036 (all X_a (comm_ring_1(X_a) -> (all X (hBOOL(hAPP(nat,bool,even_odd_even(nat),X)) -> one_one(X_a) = hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),one_one(X_a))),X))))) # label(fact_2438_minus__one__even__power) # label(axiom) # label(non_clause).  [assumption].
7.57/7.60	3037 (all X_a (archim1727834104eiling(X_a) -> (all V_1 all X_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(int,X_a,number_number_of(X_a),V_1)),X_1)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),V_1)),hAPP(X_a,int,archimedean_ceiling(X_a),X_1))))))) # label(fact_3303_number__of__less__ceiling) # label(axiom) # label(non_clause).  [assumption].
7.57/7.60	3038 (all Y_1 all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),Y_1),X_1)) -> X_1 = hAPP(fun(real,bool),real,complete_Sup_Sup(real),hAPP(real,fun(real,bool),hAPP(real,fun(real,fun(real,bool)),ord_atLeastLessThan(real),Y_1),X_1)))) # label(fact_4244_Sup__atLeastLessThan) # label(axiom) # label(non_clause).  [assumption].
7.57/7.60	3039 (all A_2 all B_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,A_2),B_1)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,B_1),A_2)))) # label(fact_2855_coprime__commute) # label(axiom) # label(non_clause).  [assumption].
7.57/7.60	3040 (all X_a all X_b all X_c all X_2 all Xa hAPP(X_b,X_c,hAPP(X_a,fun(X_b,X_c),X_2,hAPP(product_prod(X_a,X_b),X_a,product_fst(X_a,X_b),Xa)),hAPP(product_prod(X_a,X_b),X_b,product_snd(X_a,X_b),Xa)) = hAPP(product_prod(X_a,X_b),X_c,hAPP(fun(X_a,fun(X_b,X_c)),fun(product_prod(X_a,X_b),X_c),product_prod_case(X_a,X_b,X_c),X_2),Xa)) # label(fact_4014_split__def) # label(axiom) # label(non_clause).  [assumption].
7.57/7.60	3041 (all R_4 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),R_4)) -> (exists N_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,real_1(int),N_2)),R_4)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),R_4),hAPP(int,real,real_1(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),N_2),one_one(int))))))))) # label(fact_3422_reals__Archimedean__6b__int) # label(axiom) # label(non_clause).  [assumption].
7.57/7.60	3042 (all X hAPP(real,real,hAPP(real,fun(real,real),log,hAPP(real,real,exp(real),one_one(real))),X) = hAPP(real,real,ln,X)) # label(fact_2644_log__ln) # label(axiom) # label(non_clause).  [assumption].
7.57/7.60	3043 (all X hAPP(real,real,uminus_uminus(real),hAPP(rat,real,ratreal,X)) = hAPP(rat,real,ratreal,hAPP(rat,rat,uminus_uminus(rat),X))) # label(fact_3769_real__uminus__code) # label(axiom) # label(non_clause).  [assumption].
7.57/7.60	3044 (all Nat_3 zero_zero(nat) != hAPP(nat,nat,suc,Nat_3)) # label(fact_1226_nat_Osimps_I2_J) # label(axiom) # label(non_clause).  [assumption].
7.57/7.60	3045 (all X_a (real_n2089651433ebra_1(X_a) -> (all F hAPP(fun(nat,X_a),X_a,suminf(X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),times_times(X_a)),F)),hAPP(X_a,fun(nat,X_a),power_power(X_a),zero_zero(X_a)))) = hAPP(nat,X_a,F,zero_zero(nat))))) # label(fact_3973_powser__zero) # label(axiom) # label(non_clause).  [assumption].
7.57/7.60	3046 (all X_a (metric_space(X_a) -> (all X_3 hAPP(fun(nat,X_a),X_a,lim(X_a),X_3) = hAPP(fun(X_a,bool),X_a,the(X_a),hAPP(filter(nat),fun(X_a,bool),hAPP(fun(X_a,fun(filter(nat),bool)),fun(filter(nat),fun(X_a,bool)),combc(X_a,filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),X_3)),sequentially))))) # label(fact_4495_lim__def) # label(axiom) # label(non_clause).  [assumption].
7.57/7.60	3047 (all W hAPP(int,rat,hAPP(int,fun(int,rat),fract,W),one_one(int)) = hAPP(int,rat,number_number_of(rat),W)) # label(fact_3747_rat__number__of__def) # label(axiom) # label(non_clause).  [assumption].
7.57/7.60	3048 (all X_b (minus(X_b) -> minus_minus(X_b) = ti(fun(X_b,fun(X_b,X_b)),minus_minus(X_b)))) # label(tsy_c_Groups_Ominus__class_Ominus_res) # label(axiom) # label(non_clause).  [assumption].
7.57/7.60	3049 (all X_a all X_b all B_1 all F all A_3 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),B_1),hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),A_3))) -> -(all X_2 (hAPP(X_b,X_a,F,X_2) = ti(X_a,B_1) -> -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_3)))))) # label(fact_3964_imageE) # label(axiom) # label(non_clause).  [assumption].
7.57/7.60	3050 (all X_a (real_normed_vector(X_a) -> (all A_1 all B hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_1),B)) = hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_1),hAPP(X_a,X_a,uminus_uminus(X_a),B))))) # label(fact_4689_scaleR_Ominus__right) # label(axiom) # label(non_clause).  [assumption].
7.57/7.60	3051 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X)) -> X = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,sqrt,X)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) # label(fact_1640_real__sqrt__pow2) # label(axiom) # label(non_clause).  [assumption].
7.57/7.60	3052 (all N (-hBOOL(hAPP(nat,bool,even_odd_even(nat),N)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)))) # label(fact_2422_odd__pos) # label(axiom) # label(non_clause).  [assumption].
7.57/7.60	3053 (all X all N_5 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),N),N_5)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),one_one(real))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(nat,fun(real,real),root,N),X)),hAPP(real,real,hAPP(nat,fun(real,real),root,N_5),X)))))))) # label(fact_2713_real__root__strict__increasing) # label(axiom) # label(non_clause).  [assumption].
7.57/7.60	3054 (all X_a (linorder(X_a) -> (all B all X all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),A_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),A_1),B))))))) # label(fact_4951_min__max_Oless__supI1) # label(axiom) # label(non_clause).  [assumption].
7.57/7.60	3055 (all X_a collect(X_a) = ti(fun(fun(X_a,bool),fun(X_a,bool)),collect(X_a))) # label(tsy_c_Set_OCollect_res) # label(axiom) # label(non_clause).  [assumption].
7.57/7.60	3056 (all X_a (preorder(X_a) -> (all Z_1 all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),Z_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Z_1))))))) # label(fact_1578_order__less__trans) # label(axiom) # label(non_clause).  [assumption].
7.57/7.60	3057 (all N all M hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),M)))) # label(fact_570_le__add1) # label(axiom) # label(non_clause).  [assumption].
7.57/7.60	3058 (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_1212_number__of__int) # label(axiom) # label(non_clause).  [assumption].
7.57/7.60	3059 (all X_a (archim1727834104eiling(X_a) -> (all Z_1 ti(int,Z_1) = hAPP(X_a,int,archim2085082626_floor(X_a),hAPP(int,X_a,ring_1_of_int(X_a),Z_1))))) # label(fact_3576_floor__of__int) # label(axiom) # label(non_clause).  [assumption].
7.57/7.60	3060 (all X_1 hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),sin_coeff)),hAPP(real,fun(nat,real),power_power(real),X_1))))) # label(fact_4021_summable__sin) # label(axiom) # label(non_clause).  [assumption].
7.57/7.60	3061 (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_425_mult__left__le__imp__le) # label(axiom) # label(non_clause).  [assumption].
7.57/7.60	3062 (all X_a all G all A_3 hAPP(complex,real,im,hAPP(fun(X_a,bool),complex,hAPP(fun(X_a,complex),fun(fun(X_a,bool),complex),big_co1399186613setsum(X_a,complex),G),A_3)) = hAPP(fun(X_a,bool),real,hAPP(fun(X_a,real),fun(fun(X_a,bool),real),big_co1399186613setsum(X_a,real),hAPP(fun(X_a,complex),fun(X_a,real),hAPP(fun(complex,real),fun(fun(X_a,complex),fun(X_a,real)),combb(complex,real,X_a),im),G)),A_3)) # label(fact_4248_Im_Osetsum) # label(axiom) # label(non_clause).  [assumption].
7.57/7.60	3063 (all T_2 all T_1 (order(T_1) -> order(fun(T_2,T_1)))) # label(arity_fun___Orderings_Oorder) # label(axiom) # label(non_clause).  [assumption].
7.57/7.60	3064 (all K_4 all L_4 hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,bit1,K_4)),hAPP(int,int,bit0,L_4)) = hAPP(int,int,bit1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),K_4),L_4))) # label(fact_493_diff__bin__simps_I9_J) # label(axiom) # label(non_clause).  [assumption].
7.57/7.60	3065 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) -> hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,sin,hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),X))),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,cos,hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),X))),one_one(real))) = hAPP(real,real,tan,X)))) # label(fact_2286_tan__half) # label(axiom) # label(non_clause).  [assumption].
7.57/7.60	3066 (all X_a (real_normed_vector(X_a) & real_algebra_1(X_a) -> (all X hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(real,X_a,of_real(X_a),X)) = hAPP(real,X_a,of_real(X_a),hAPP(real,real,uminus_uminus(real),X))))) # label(fact_2796_of__real_Ominus) # label(axiom) # label(non_clause).  [assumption].
7.57/7.60	3067 (all X hAPP(real,real,tan,hAPP(real,real,uminus_uminus(real),X)) = hAPP(real,real,uminus_uminus(real),hAPP(real,real,tan,X))) # label(fact_2252_tan__minus) # label(axiom) # label(non_clause).  [assumption].
7.57/7.60	3068 (all X all Y all P_5 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),P_5)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,X),Y),P_5)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(int,int,hAPP(int,fun(int,int),multInv,P_5),X)),hAPP(int,int,hAPP(int,fun(int,int),multInv,P_5),Y)),P_5))))) # label(fact_842_MultInv__prop1) # label(axiom) # label(non_clause).  [assumption].
7.57/7.60	3069 (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_403_not__one__less__zero) # label(axiom) # label(non_clause).  [assumption].
7.57/7.60	3070 (all X_a all C_1 all F all A_3 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_3)) -> hAPP(fun(X_a,bool),int,hAPP(fun(X_a,int),fun(fun(X_a,bool),int),big_co1399186613setsum(X_a,int),hAPP(fun(X_a,int),fun(X_a,int),hAPP(fun(int,int),fun(fun(X_a,int),fun(X_a,int)),combb(int,int,X_a),hAPP(int,fun(int,int),times_times(int),C_1)),F)),A_3) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C_1),hAPP(fun(X_a,bool),int,hAPP(fun(X_a,int),fun(fun(X_a,bool),int),big_co1399186613setsum(X_a,int),F),A_3)))) # label(fact_4252_setsum__const__mult) # label(axiom) # label(non_clause).  [assumption].
7.57/7.60	3071 (all X all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),Y),zero_zero(real))) -> (exists R_2 exists A_4 (X = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),R_2),hAPP(real,real,cos,A_4)) & Y = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),R_2),hAPP(real,real,sin,A_4)))))) # label(fact_2725_polar__ex2) # label(axiom) # label(non_clause).  [assumption].
7.57/7.60	3072 (all X_a all X_b all A_3 all B_1 all F all X_1 (hAPP(X_b,X_a,F,X_1) = ti(X_a,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_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),B_1),hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),A_3)))))) # label(fact_3632_image__eqI) # label(axiom) # label(non_clause).  [assumption].
7.57/7.61	3073 (all A_2 all P_4 (hBOOL(hAPP(int,bool,zprime,P_4)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_2),P_4)) -> hAPP(fun(int,bool),nat,finite_card(int),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),bnorRset,A_2),P_4)) = hAPP(int,nat,nat_1,A_2)))) # label(fact_3204_Bnor__prime) # label(axiom) # label(non_clause).  [assumption].
7.57/7.61	3074 (all B all A_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_1),B)) -> hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_1),B) = zero_zero(int)))) # label(fact_1020_div__pos__pos__trivial) # label(axiom) # label(non_clause).  [assumption].
7.57/7.61	3075 (all B all D all A_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),D),A_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),D),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A_1),B))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),D),B))))) # label(fact_702_divides__add__revr) # label(axiom) # label(non_clause).  [assumption].
7.57/7.61	3076 (all X_a (linordered_semidom(X_a) -> (all X_1 all Y_1 all B_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),B_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),B_1),X_1)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),B_1),Y_1))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X_1),Y_1))))))) # label(fact_449_power__strict__increasing__iff) # label(axiom) # label(non_clause).  [assumption].
7.57/7.61	3077 (all N_1 all V_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),hAPP(nat,nat,suc,N_1)),hAPP(int,nat,number_number_of(nat),V_1)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),hAPP(bool,fun(nat,fun(nat,nat)),if(nat),hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),hAPP(int,int,pred,V_1)))),hAPP(nat,nat,suc,N_1)),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),N_1),hAPP(int,nat,nat_1,hAPP(int,int,number_number_of(int),hAPP(int,int,pred,V_1))))))) # label(fact_4935_max__number__of__Suc) # label(axiom) # label(non_clause).  [assumption].
7.57/7.61	3078 (all M all N (hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),N) = M -> N = one_one(nat) | M = zero_zero(nat))) # label(fact_600_mult__eq__self__implies__10) # label(axiom) # label(non_clause).  [assumption].
7.57/7.61	3079 (all X_a (linorder(X_a) -> (all T_5 exists Z_2 all X_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z_2),X_2)) -> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_2),T_5)))))) # label(fact_2824_pinf_I6_J) # label(axiom) # label(non_clause).  [assumption].
7.57/7.61	3080 (all X_a (comm_semiring_1(X_a) -> (all X all P_5 all Q_3 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),P_5)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),Q_3)) = hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),P_5),Q_3))))) # label(fact_248_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J) # label(axiom) # label(non_clause).  [assumption].
7.57/7.61	3081 (all B_5 all A_6 all A_1 all B (hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),A_1),B) != zero_zero(nat) -> (A_1 = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A_6),hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),A_1),B)) -> (B = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B_5),hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),A_1),B)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),A_6),B_5) = one_one(nat))))) # label(fact_3286_gcd__coprime__nat) # label(axiom) # label(non_clause).  [assumption].
7.57/7.61	3082 (all X all Y hAPP(real,real,sin,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),Y)) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,sin,X)),hAPP(real,real,cos,Y))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,cos,X)),hAPP(real,real,sin,Y)))) # label(fact_2321_sin__add) # label(axiom) # label(non_clause).  [assumption].
7.57/7.61	3083 (all X_a all X_b (comm_monoid_add(X_b) -> (all F all G all S all T_3 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),T_3)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),S),T_3)) -> ((all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),T_3),S))) -> hAPP(X_a,X_b,G,X_2) = zero_zero(X_b))) -> ((all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),S)) -> hAPP(X_a,X_b,F,X_2) = hAPP(X_a,X_b,G,X_2))) -> hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),F),S) = hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),G),T_3)))))))) # label(fact_4416_setsum__mono__zero__cong__left) # label(axiom) # label(non_clause).  [assumption].
7.57/7.61	3084 (all X_a (banach(X_a) -> (all F all G ((exists N_3 all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_3),N_2)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),hAPP(nat,X_a,F,N_2))),hAPP(nat,real,G,N_2))))) -> (hBOOL(hAPP(fun(nat,real),bool,summable(real),G)) -> hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),F))))))) # label(fact_3994_summable__comparison__test) # label(axiom) # label(non_clause).  [assumption].
7.57/7.61	3085 (all X all A_1 all B hAPP(real,real,hAPP(real,fun(real,real),powr,hAPP(real,real,hAPP(real,fun(real,real),powr,X),A_1)),B) = hAPP(real,real,hAPP(real,fun(real,real),powr,hAPP(real,real,hAPP(real,fun(real,real),powr,X),B)),A_1)) # label(fact_3327_powr__powr__swap) # label(axiom) # label(non_clause).  [assumption].
7.57/7.61	3086 (all X_a (archim1727834104eiling(X_a) -> (all X hAPP(int,int,uminus_uminus(int),hAPP(X_a,int,archim2085082626_floor(X_a),X)) = hAPP(X_a,int,archimedean_ceiling(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),X))))) # label(fact_3294_ceiling__minus) # label(axiom) # label(non_clause).  [assumption].
7.57/7.61	3087 (all X_a (banach(X_a) & real_normed_field(X_a) -> (all X all Y hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,exp(X_a),X)),hAPP(X_a,X_a,exp(X_a),Y)) = hAPP(X_a,X_a,exp(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X),Y))))) # label(fact_2586_mult__exp__exp) # label(axiom) # label(non_clause).  [assumption].
7.57/7.61	3088 (all J_2 all K_4 all A_1 all P_5 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),J_2),K_4)),A_1),P_5)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),multInv,P_5),J_2)),J_2)),K_4)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),multInv,P_5),J_2)),A_1)),P_5)))) # label(fact_836_aux______3) # label(axiom) # label(non_clause).  [assumption].
7.57/7.61	3089 (all X_a (group_add(X_a) -> (all A_2 all B_1 (ti(X_a,B_1) = ti(X_a,A_2) <-> hAPP(X_a,X_a,uminus_uminus(X_a),B_1) = hAPP(X_a,X_a,uminus_uminus(X_a),A_2))))) # label(fact_2044_neg__equal__iff__equal) # label(axiom) # label(non_clause).  [assumption].
7.57/7.61	3090 (all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,number_number_of(real),min_1)),X_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_1),one_one(real))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),arcsin),X_1),hAPP(real,real,inverse_inverse(real),hAPP(real,real,sqrt,hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),one_one(real)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))))))) # label(fact_2656_DERIV__arcsin) # label(axiom) # label(non_clause).  [assumption].
7.57/7.61	3091 (all A_2 all B_1 (one_one(real) = A_2 & zero_zero(real) = B_1 <-> hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,A_2),B_1) = one_one(complex))) # label(fact_2744_Complex__eq__1) # label(axiom) # label(non_clause).  [assumption].
7.57/7.61	3092 (all X_1 hAPP(fun(int,bool),int,the(int),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),combs(int,bool,bool),hAPP(fun(int,bool),fun(int,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj),hAPP(real,fun(int,bool),hAPP(fun(int,fun(real,bool)),fun(real,fun(int,bool)),combc(int,real,bool),hAPP(fun(int,real),fun(int,fun(real,bool)),hAPP(fun(real,fun(real,bool)),fun(fun(int,real),fun(int,fun(real,bool))),combb(real,fun(real,bool),int),ord_less_eq(real)),ring_1_of_int(real))),X_1))),hAPP(fun(int,real),fun(int,bool),hAPP(fun(real,bool),fun(fun(int,real),fun(int,bool)),combb(real,bool,int),hAPP(real,fun(real,bool),ord_less(real),X_1)),hAPP(fun(int,int),fun(int,real),hAPP(fun(int,real),fun(fun(int,int),fun(int,real)),combb(int,real,int),ring_1_of_int(real)),hAPP(int,fun(int,int),hAPP(fun(int,fun(int,int)),fun(int,fun(int,int)),combc(int,int,int),plus_plus(int)),one_one(int)))))) = hAPP(real,int,archim2085082626_floor(real),X_1)) # label(fact_4146_floor__real__def) # label(axiom) # label(non_clause).  [assumption].
7.57/7.61	3093 (all X all A_1 hAPP(real,int,archim2085082626_floor(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),X),hAPP(int,real,real_1(int),A_1))) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(real,int,archim2085082626_floor(real),X)),A_1)) # label(fact_3371_floor__subtract) # label(axiom) # label(non_clause).  [assumption].
7.57/7.61	3094 (all X_a (real_normed_vector(X_a) -> (all X hAPP(X_a,real,norm_norm(X_a),X) = hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),X),zero_zero(X_a))))) # label(fact_3524_norm__conv__dist) # label(axiom) # label(non_clause).  [assumption].
7.57/7.61	3095 (all X_c all X_a all X_b all C_1 all P_4 all Q_2 (ti(product_prod(X_a,X_b),P_4) = ti(product_prod(X_a,X_b),Q_2) -> hAPP(product_prod(X_a,X_b),X_c,hAPP(fun(X_a,fun(X_b,X_c)),fun(product_prod(X_a,X_b),X_c),product_prod_case(X_a,X_b,X_c),C_1),Q_2) = hAPP(product_prod(X_a,X_b),X_c,hAPP(fun(X_a,fun(X_b,X_c)),fun(product_prod(X_a,X_b),X_c),product_prod_case(X_a,X_b,X_c),C_1),P_4))) # label(fact_3995_split__weak__cong) # label(axiom) # label(non_clause).  [assumption].
7.57/7.61	3096 (all X_a (comm_semiring_1(X_a) -> (all A_1 all M all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),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) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),M)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),M))))) # label(fact_243_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J) # label(axiom) # label(non_clause).  [assumption].
7.57/7.61	3097 (all R_1 hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),hAPP(real,fun(real,real),plus_plus(real),R_1)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),uminus_uminus(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),inverse_inverse(real)),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),suc))))),R_1),sequentially))) # label(fact_4492_LIMSEQ__inverse__real__of__nat__add__minus) # label(axiom) # label(non_clause).  [assumption].
7.57/7.61	3098 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,real_1(nat),hAPP(real,nat,natfloor,X))),X)))) # label(fact_2330_real__natfloor__le) # label(axiom) # label(non_clause).  [assumption].
7.57/7.61	3099 (all X_b all X_a (real_vector(X_a) -> (all A_2 all G all A_3 hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_2),hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co1399186613setsum(X_b,X_a),G),A_3)) = hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co1399186613setsum(X_b,X_a),hAPP(fun(X_b,X_a),fun(X_b,X_a),hAPP(fun(X_a,X_a),fun(fun(X_b,X_a),fun(X_b,X_a)),combb(X_a,X_a,X_b),hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_2)),G)),A_3)))) # label(fact_4730_scaleR__right_Osetsum) # label(axiom) # label(non_clause).  [assumption].
7.57/7.61	3100 (all X_a (semiring_div(X_a) -> (all Ma all K all N_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),K),N_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),K),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),Ma),N_1))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),K),Ma))))))) # label(fact_947_dvd__mod__iff) # label(axiom) # label(non_clause).  [assumption].
7.57/7.61	3101 (all X_a all X_b all A_3 all B_2 (hBOOL(hAPP(fun(sum_sum(X_a,X_b),bool),bool,finite_finite_1(sum_sum(X_a,X_b)),hAPP(fun(X_b,bool),fun(sum_sum(X_a,X_b),bool),hAPP(fun(X_a,bool),fun(fun(X_b,bool),fun(sum_sum(X_a,X_b),bool)),sum_Plus(X_a,X_b),A_3),B_2))) -> hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),B_2)))) # label(fact_3182_finite__PlusD_I2_J) # label(axiom) # label(non_clause).  [assumption].
7.57/7.61	3102 (all X_b all X_a (topological_space(X_b) & topological_space(X_a) -> (all L all F all G all A_2 ((all X_2 (ti(X_a,X_2) != ti(X_a,A_2) -> hAPP(X_a,X_b,F,X_2) = hAPP(X_a,X_b,G,X_2))) -> (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),G),L),hAPP(X_a,filter(X_a),at(X_a),A_2))) <-> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),L),hAPP(X_a,filter(X_a),at(X_a),A_2)))))))) # label(fact_4766_LIM__equal) # label(axiom) # label(non_clause).  [assumption].
7.57/7.61	3103 (all X_b all X_a (real_normed_vector(X_b) & ord(X_a) -> (all X_3 all M_1 ((all N_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),M_1),N_2)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_b,real,norm_norm(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),hAPP(X_a,X_b,X_3,M_1)),hAPP(X_a,X_b,X_3,N_2)))),one_one(real))))) -> (all N_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),M_1),N_2)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_b,real,norm_norm(X_b),hAPP(X_a,X_b,X_3,N_2))),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),one_one(real)),hAPP(X_b,real,norm_norm(X_b),hAPP(X_a,X_b,X_3,M_1))))))))))) # label(fact_1838_lemmaCauchy) # label(axiom) # label(non_clause).  [assumption].
7.57/7.61	3104 (all X_1 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),sin),X_1),hAPP(real,real,cos,X_1)))) # label(fact_2637_DERIV__sin) # label(axiom) # label(non_clause).  [assumption].
7.57/7.61	3105 (all X_a (real_normed_field(X_a) -> (all H_2 all B all A_1 (ti(X_a,A_1) != zero_zero(X_a) -> (zero_zero(X_a) != ti(X_a,B) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_a,X_a,inverse_inverse(X_a),A_1)),hAPP(X_a,X_a,inverse_inverse(X_a),B))),H_2) = hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,inverse_inverse(X_a),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_1),B)),H_2))),hAPP(X_a,X_a,inverse_inverse(X_a),B)))))))) # label(fact_2620_DERIV__inverse__lemma) # label(axiom) # label(non_clause).  [assumption].
7.57/7.61	3106 (all X_a all X_b (comm_monoid_add(X_b) -> (all G all H all A_3 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_3)) -> ((all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_3)) -> hAPP(X_a,X_b,G,X_2) = hAPP(X_a,X_b,H,X_2))) -> hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),H),A_3) = hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),G),A_3)))))) # label(fact_4774_setsum_Ocong) # label(axiom) # label(non_clause).  [assumption].
7.57/7.61	3107 (all Ma all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Ma),N_1))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Ma)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)))) # label(fact_594_add__gr__0) # label(axiom) # label(non_clause).  [assumption].
7.57/7.61	3108 (all Code_numeral_2 hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(code_code_numeral,nat,code_c271388182l_size,Code_numeral_2)),hAPP(nat,nat,suc,zero_zero(nat))) = hAPP(code_code_numeral,nat,code_c271388182l_size,hAPP(code_code_numeral,code_code_numeral,code_S1047413653umeral,Code_numeral_2))) # label(fact_2926_code__numeral_Osize_I2_J) # label(axiom) # label(non_clause).  [assumption].
7.57/7.61	3109 (all X_a (real_normed_algebra(X_a) -> (all X_1 all X_3 all A_2 (hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),X_3),A_2),sequentially)) -> hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(X_a,X_a),fun(fun(nat,X_a),fun(nat,X_a)),combb(X_a,X_a,nat),hAPP(X_a,fun(X_a,X_a),times_times(X_a),X_1)),X_3)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X_1),A_2)),sequentially)))))) # label(fact_4479_mult__right_OLIMSEQ) # label(axiom) # label(non_clause).  [assumption].
7.57/7.61	3110 (all X_a (number_ring(X_a) & linordered_idom(X_a) -> (all X_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(int,X_a,number_number_of(X_a),X_1)),one_one(X_a))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X_1),hAPP(int,int,bit1,pls))))))) # label(fact_59_le__special_I4_J) # label(axiom) # label(non_clause).  [assumption].
7.57/7.61	3111 (all X_a (real_normed_vector(X_a) -> (all E_2 all X_3 (hBOOL(hAPP(fun(nat,X_a),bool,cauchy(X_a),X_3)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),E_2)) -> (exists M_3 all M_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_3),M_2)) -> (all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_3),N_2)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(nat,X_a,X_3,M_2)),hAPP(nat,X_a,X_3,N_2)))),E_2))))))))))) # label(fact_3315_CauchyD) # label(axiom) # label(non_clause).  [assumption].
7.57/7.61	3112 (all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_1),zero_zero(nat))) <-> zero_zero(nat) = N_1)) # label(fact_548_le__0__eq) # label(axiom) # label(non_clause).  [assumption].
7.57/7.61	3113 (all Z_1 all X all Y (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),Y)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y),Z_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),Z_1))))) # label(fact_634_dvd_Oorder__trans) # label(axiom) # label(non_clause).  [assumption].
7.57/7.61	3114 (all X_a (division_ring(X_a) -> (all A_1 all B (ti(X_a,B) != zero_zero(X_a) -> hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),A_1),B)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),A_1),hAPP(X_a,X_a,uminus_uminus(X_a),B)))))) # label(fact_2077_nonzero__minus__divide__right) # label(axiom) # label(non_clause).  [assumption].
7.57/7.61	3115 (all A_1 all P_5 (hBOOL(hAPP(int,bool,zprime,P_5)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_1),P_5)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),hAPP(int,int,hAPP(int,fun(int,int),inv,P_5),A_1))),one_one(int)),P_5)))))) # label(fact_811_inv__is__inv) # label(axiom) # label(non_clause).  [assumption].
7.57/7.61	3116 (all A_2 all B_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B_1)) -> (hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),hAPP(int,rat,hAPP(int,fun(int,rat),fract,A_2),B_1))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A_2))))) # label(fact_3790_zero__le__Fract__iff) # label(axiom) # label(non_clause).  [assumption].
7.57/7.61	3117 (all A_2 hBOOL(hAPP(filter(complex),bool,hAPP(real,fun(filter(complex),bool),hAPP(fun(complex,real),fun(real,fun(filter(complex),bool)),tendsto(complex,real),re),hAPP(complex,real,re,A_2)),hAPP(complex,filter(complex),at(complex),A_2)))) # label(fact_4568_Re_Ocont) # label(axiom) # label(non_clause).  [assumption].
7.57/7.61	3118 (all D all I_1 (zero_zero(int) != ti(int,I_1) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),D),I_1)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,abs_abs(int),D)),hAPP(int,int,abs_abs(int),I_1)))))) # label(fact_1940_dvd__imp__le__int) # label(axiom) # label(non_clause).  [assumption].
7.57/7.61	3119 (all N all K_4 all M (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),K_4),M)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),K_4),N)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),K_4),hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),M),N)))))) # label(fact_3236_gcd__greatest__nat) # label(axiom) # label(non_clause).  [assumption].
7.57/7.61	3120 (all X_a all X_c all X_b all P all Q all R hAPP(X_a,X_c,hAPP(fun(X_a,X_b),fun(X_a,X_c),hAPP(fun(X_a,fun(X_b,X_c)),fun(fun(X_a,X_b),fun(X_a,X_c)),combs(X_a,X_b,X_c),P),Q),R) = hAPP(X_b,X_c,hAPP(X_a,fun(X_b,X_c),P,R),hAPP(X_a,X_b,Q,R))) # label(help_COMBS_1_1_U) # label(axiom) # label(non_clause).  [assumption].
7.57/7.61	3121 (all X_a all X_b (comm_monoid_add(X_b) -> (all G all A_3 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_3)) -> ((all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_3)) -> hAPP(X_a,X_b,G,X_2) = zero_zero(X_b))) -> zero_zero(X_b) = hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),G),A_3)))))) # label(fact_4307_setsum_Oneutral) # label(axiom) # label(non_clause).  [assumption].
7.57/7.61	3122 (all M all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),M)) # label(fact_521_nat__add__commute) # label(axiom) # label(non_clause).  [assumption].
7.57/7.61	3123 (all Y (Y != zero_zero(code_code_numeral) -> -(all Code_numeral_1 hAPP(code_code_numeral,code_code_numeral,code_S1047413653umeral,Code_numeral_1) != Y))) # label(fact_2971_code__numeral_Oexhaust) # label(axiom) # label(non_clause).  [assumption].
7.57/7.61	3124 (all Y all X (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Y)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),X),Y)))))) # label(fact_985_Divides_Otransfer__nat__int__function__closures_I1_J) # label(axiom) # label(non_clause).  [assumption].
7.57/7.61	3125 (all B all D all A_1 (hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),D),A_1) = one_one(int) -> (hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),D),B) = one_one(int) -> one_one(int) = hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),D),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),B))))) # label(fact_4384_coprime__mult__int) # label(axiom) # label(non_clause).  [assumption].
7.57/7.61	3126 (all X_a (linorder(X_a) -> (all X_1 all Y_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y_1)) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y_1),X_1)) <-> ti(X_a,Y_1) != ti(X_a,X_1))))) # label(fact_1561_linorder__neq__iff) # label(axiom) # label(non_clause).  [assumption].
7.57/7.61	3127 (all A_1 all B all C hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A_1),B)),C) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),A_1),C)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),B),C))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),A_1),C)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),B),C))),C))) # label(fact_1080_div__add1__eq) # label(axiom) # label(non_clause).  [assumption].
7.57/7.61	3128 (all K_4 all L_4 ((ti(int,L_4) != zero_zero(int) -> hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),pdivmod,K_4),L_4) = hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),posDivAlg,hAPP(int,int,abs_abs(int),K_4)),hAPP(int,int,abs_abs(int),L_4))) & (zero_zero(int) = ti(int,L_4) -> hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),pdivmod,K_4),L_4) = hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),zero_zero(int)),hAPP(int,int,abs_abs(int),K_4))))) # label(fact_2720_pdivmod__posDivAlg) # label(axiom) # label(non_clause).  [assumption].
7.57/7.61	3129 (all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_1),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) -> hAPP(fun(nat,real),real,suminf(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),min_1)))),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),hAPP(real,fun(real,real),inverse_divide(real),one_one(real))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),one_one(nat))))))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),X_1),one_one(real)))),suc))) = hAPP(real,real,ln,X_1)))) # label(fact_3977_ln__series) # label(axiom) # label(non_clause).  [assumption].
7.57/7.61	3130 (all Z_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Z_1),zero_zero(int))) -> zero_zero(nat) = hAPP(int,nat,nat_1,Z_1))) # label(fact_1123_nat__le__0) # label(axiom) # label(non_clause).  [assumption].
7.57/7.61	3131 (all X_a (linordered_idom(X_a) -> (all X all N (hBOOL(hAPP(nat,bool,even_odd_even(nat),N)) -> hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(X_a,X_a,abs_abs(X_a),X)),N) = hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),N))))) # label(fact_2426_power__even__abs) # label(axiom) # label(non_clause).  [assumption].
7.57/7.61	3132 (all N all X all Y (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),Y)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),Y),hAPP(nat,nat,suc,N)))))) # label(fact_1361_divides__rexp) # label(axiom) # label(non_clause).  [assumption].
7.57/7.61	3133 (all N hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),one_one(nat))),N))) # label(fact_2873_coprime__plus1) # label(axiom) # label(non_clause).  [assumption].
7.57/7.61	3134 (all X_a (semiring_div(X_a) -> (all A_1 all B all C hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_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),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),A_1),B)),B)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),A_1),B))),C)))) # label(fact_917_div__mod__equality) # label(axiom) # label(non_clause).  [assumption].
7.57/7.61	3135 (all R_4 hAPP(real,complex,of_real(complex),R_4) = hAPP(real,complex,hAPP(real,fun(real,complex),rcis,R_4),zero_zero(real))) # label(fact_3165_rcis__zero__arg) # label(axiom) # label(non_clause).  [assumption].
7.57/7.61	3136 (all X_1 all Y_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_1),Y_1)) & -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y_1),X_1)) <-> Y_1 != X_1 & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_1),Y_1)))) # label(fact_622_dvd_Oless__le) # label(axiom) # label(non_clause).  [assumption].
7.57/7.61	3137 (all X_a (real_n2089651433ebra_1(X_a) -> (all R_4 hAPP(X_a,real,norm_norm(X_a),hAPP(real,X_a,of_real(X_a),R_4)) = hAPP(real,real,abs_abs(real),R_4)))) # label(fact_2797_norm__of__real) # label(axiom) # label(non_clause).  [assumption].
7.57/7.61	3138 (all T_1 order(filter(T_1))) # label(arity_Limits_Ofilter___Orderings_Oorder) # label(axiom) # label(non_clause).  [assumption].
7.57/7.61	3139 (all X X = hAPP(int,quickcheck_code_int,quickcheck_of_int,hAPP(quickcheck_code_int,int,quickcheck_int_of,X))) # label(fact_3535_int__of__inverse) # label(axiom) # label(non_clause).  [assumption].
7.57/7.61	3140 (all X_a (banach(X_a) & real_normed_field(X_a) -> (all X_1 all C_1 all K_3 (hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),times_times(X_a)),hAPP(fun(nat,X_a),fun(nat,X_a),diffs(X_a),hAPP(fun(nat,X_a),fun(nat,X_a),diffs(X_a),C_1)))),hAPP(X_a,fun(nat,X_a),power_power(X_a),K_3)))) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,norm_norm(X_a),X_1)),hAPP(X_a,real,norm_norm(X_a),K_3))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_a,fun(filter(X_a),bool),hAPP(fun(X_a,X_a),fun(X_a,fun(filter(X_a),bool)),tendsto(X_a,X_a),hAPP(fun(X_a,fun(nat,X_a)),fun(X_a,X_a),hAPP(fun(fun(nat,X_a),X_a),fun(fun(X_a,fun(nat,X_a)),fun(X_a,X_a)),combb(fun(nat,X_a),X_a,X_a),suminf(X_a)),hAPP(fun(X_a,fun(nat,X_a)),fun(X_a,fun(nat,X_a)),hAPP(fun(fun(nat,X_a),fun(nat,X_a)),fun(fun(X_a,fun(nat,X_a)),fun(X_a,fun(nat,X_a))),combb(fun(nat,X_a),fun(nat,X_a),X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),times_times(X_a)),C_1))),hAPP(fun(nat,X_a),fun(X_a,fun(nat,X_a)),hAPP(fun(X_a,fun(fun(nat,X_a),fun(nat,X_a))),fun(fun(nat,X_a),fun(X_a,fun(nat,X_a))),combc(X_a,fun(nat,X_a),fun(nat,X_a)),hAPP(fun(X_a,fun(nat,fun(X_a,X_a))),fun(X_a,fun(fun(nat,X_a),fun(nat,X_a))),hAPP(fun(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a))),fun(fun(X_a,fun(nat,fun(X_a,X_a))),fun(X_a,fun(fun(nat,X_a),fun(nat,X_a)))),combb(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),X_a),combs(nat,X_a,X_a)),hAPP(fun(X_a,fun(nat,X_a)),fun(X_a,fun(nat,fun(X_a,X_a))),hAPP(fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),fun(fun(X_a,fun(nat,X_a)),fun(X_a,fun(nat,fun(X_a,X_a)))),combb(fun(nat,X_a),fun(nat,fun(X_a,X_a)),X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),minus_minus(X_a))),hAPP(fun(X_a,X_a),fun(X_a,fun(nat,X_a)),hAPP(fun(X_a,fun(X_a,fun(nat,X_a))),fun(fun(X_a,X_a),fun(X_a,fun(nat,X_a))),combs(X_a,X_a,fun(nat,X_a)),hAPP(fun(X_a,fun(nat,fun(X_a,X_a))),fun(X_a,fun(X_a,fun(nat,X_a))),hAPP(fun(fun(nat,fun(X_a,X_a)),fun(X_a,fun(nat,X_a))),fun(fun(X_a,fun(nat,fun(X_a,X_a))),fun(X_a,fun(X_a,fun(nat,X_a)))),combb(fun(nat,fun(X_a,X_a)),fun(X_a,fun(nat,X_a)),X_a),combc(nat,X_a,X_a)),hAPP(fun(X_a,fun(nat,X_a)),fun(X_a,fun(nat,fun(X_a,X_a))),hAPP(fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),fun(fun(X_a,fun(nat,X_a)),fun(X_a,fun(nat,fun(X_a,X_a)))),combb(fun(nat,X_a),fun(nat,fun(X_a,X_a)),X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),inverse_divide(X_a))),hAPP(fun(nat,X_a),fun(X_a,fun(nat,X_a)),hAPP(fun(X_a,fun(fun(nat,X_a),fun(nat,X_a))),fun(fun(nat,X_a),fun(X_a,fun(nat,X_a))),combc(X_a,fun(nat,X_a),fun(nat,X_a)),hAPP(fun(X_a,fun(nat,fun(X_a,X_a))),fun(X_a,fun(fun(nat,X_a),fun(nat,X_a))),hAPP(fun(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a))),fun(fun(X_a,fun(nat,fun(X_a,X_a))),fun(X_a,fun(fun(nat,X_a),fun(nat,X_a)))),combb(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),X_a),combs(nat,X_a,X_a)),hAPP(fun(X_a,fun(nat,X_a)),fun(X_a,fun(nat,fun(X_a,X_a))),hAPP(fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),fun(fun(X_a,fun(nat,X_a)),fun(X_a,fun(nat,fun(X_a,X_a)))),combb(fun(nat,X_a),fun(nat,fun(X_a,X_a)),X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),minus_minus(X_a))),hAPP(fun(X_a,X_a),fun(X_a,fun(nat,X_a)),hAPP(fun(X_a,fun(nat,X_a)),fun(fun(X_a,X_a),fun(X_a,fun(nat,X_a))),combb(X_a,fun(nat,X_a),X_a),power_power(X_a)),hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X_1))))),hAPP(X_a,fun(nat,X_a),power_power(X_a),X_1))))),combi(X_a))))),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),times_times(X_a)),semiring_1_of_nat(X_a))),hAPP(fun(nat,nat),fun(nat,X_a),hAPP(fun(nat,X_a),fun(fun(nat,nat),fun(nat,X_a)),combb(nat,X_a,nat),hAPP(X_a,fun(nat,X_a),power_power(X_a),X_1)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),minus_minus(nat)),hAPP(nat,nat,suc,zero_zero(nat))))))))),zero_zero(X_a)),hAPP(X_a,filter(X_a),at(X_a),zero_zero(X_a))))))))) # label(fact_4532_termdiffs__aux) # label(axiom) # label(non_clause).  [assumption].
7.57/7.61	3141 (all X all N hAPP(int,real,real_1(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),X),N)) = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,real_1(int),X)),N)) # label(fact_3333_power__real__of__int) # label(axiom) # label(non_clause).  [assumption].
7.57/7.61	3142 (all X_a all X_1 ti(X_a,X_1) = hAPP(fun(X_a,bool),X_a,hilbert_Eps(X_a),hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,fun(X_a,bool)),fun(X_a,fun(X_a,bool)),combc(X_a,X_a,bool),fequal(X_a)),X_1))) # label(fact_4787_some__eq__trivial) # label(axiom) # label(non_clause).  [assumption].
7.57/7.61	3143 (all A_1 all B all P_5 all Q_3 hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(product_prod(int,int),int,twoSqu1094008024sum2sq,hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),A_1),B))),hAPP(product_prod(int,int),int,twoSqu1094008024sum2sq,hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),P_5),Q_3))) = hAPP(product_prod(int,int),int,twoSqu1094008024sum2sq,hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),P_5)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),Q_3))),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),Q_3)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),P_5))))) # label(fact_743_mult__sum2sq) # label(axiom) # label(non_clause).  [assumption].
7.57/7.61	3144 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X),zero_zero(real))) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,uminus_uminus(real),pi)),X)) -> hAPP(real,real,arccos,hAPP(real,real,cos,X)) = hAPP(real,real,uminus_uminus(real),X)))) # label(fact_2265_arccos__cos2) # label(axiom) # label(non_clause).  [assumption].
7.57/7.61	3145 (all A_1 all M all B hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),M)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),M)),M))) # label(fact_355_zcong__zmult__self) # label(axiom) # label(non_clause).  [assumption].
7.57/7.61	3146 (all X_a (linorder(X_a) -> (all A_1 all B all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),X)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),A_1),B)),X)))))) # label(fact_4801_min__max_Oless__infI2) # label(axiom) # label(non_clause).  [assumption].
7.57/7.61	3147 (all Ma all K all N_1 (one_one(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),K),N_1) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),K),Ma)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),K),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),Ma),N_1)))))) # label(fact_3289_coprime__dvd__mult__iff__nat) # label(axiom) # label(non_clause).  [assumption].
7.57/7.61	3148 (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_1563_linorder__less__linear) # label(axiom) # label(non_clause).  [assumption].
7.57/7.61	3149 (all X_a (real_normed_field(X_a) & banach(X_a) -> (all X zero_zero(X_a) != hAPP(X_a,X_a,exp(X_a),X)))) # label(fact_2537_exp__not__eq__zero) # label(axiom) # label(non_clause).  [assumption].
7.57/7.61	3150 (all X_b all X_a (comm_monoid_add(X_b) & ord(X_a) -> (all F all G all B_1 all D_1 all A_2 all C_1 (ti(X_a,C_1) = ti(X_a,A_2) -> (ti(X_a,D_1) = ti(X_a,B_1) -> ((all X_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C_1),X_2)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_2),D_1)) -> hAPP(X_a,X_b,F,X_2) = hAPP(X_a,X_b,G,X_2)))) -> hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),G),hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastLessThan(X_a),C_1),D_1)) = hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),F),hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastLessThan(X_a),A_2),B_1)))))))) # label(fact_4302_setsum__ivl__cong) # label(axiom) # label(non_clause).  [assumption].
7.57/7.61	3151 (all P_5 all Q_3 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),Q_3)) -> (hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),P_5),Q_3) = one_one(int) -> hAPP(product_prod(int,int),product_prod(int,int),normalize,hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),P_5),Q_3)) = hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),P_5),Q_3)))) # label(fact_4408_normalize__stable) # label(axiom) # label(non_clause).  [assumption].
7.57/7.61	3152 (all X_3 (hBOOL(hAPP(fun(nat,complex),bool,summable(complex),X_3)) -> hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,complex),fun(nat,real),hAPP(fun(complex,real),fun(fun(nat,complex),fun(nat,real)),combb(complex,real,nat),re),X_3))))) # label(fact_4046_Re_Osummable) # label(axiom) # label(non_clause).  [assumption].
7.57/7.61	3153 (all X_a all A_3 all B_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),B_2)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less(fun(X_a,bool)),A_3),B_2)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(X_a,bool),nat,finite_card(X_a),A_3)),hAPP(fun(X_a,bool),nat,finite_card(X_a),B_2)))))) # label(fact_1824_psubset__card__mono) # label(axiom) # label(non_clause).  [assumption].
7.57/7.61	3154 (all X_b all X_a (ordere142940540dd_abs(X_a) -> (all F all A_3 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,abs_abs(X_a),hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co1399186613setsum(X_b,X_a),F),A_3))),hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co1399186613setsum(X_b,X_a),hAPP(fun(X_b,X_a),fun(X_b,X_a),hAPP(fun(X_a,X_a),fun(fun(X_b,X_a),fun(X_b,X_a)),combb(X_a,X_a,X_b),abs_abs(X_a)),F)),A_3)))))) # label(fact_4165_setsum__abs) # label(axiom) # label(non_clause).  [assumption].
7.57/7.61	3155 (all E_1 all B all D all A_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),D),A_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),E_1),B)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,A_1),B)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,D),E_1)))))) # label(fact_2856_coprime__divisors) # label(axiom) # label(non_clause).  [assumption].
7.57/7.61	3156 (all X all Y hAPP(real,real,cos,hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),X),Y)) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,cos,Y)),hAPP(real,real,cos,X))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,sin,Y)),hAPP(real,real,sin,X)))) # label(fact_2338_cos__diff2) # label(axiom) # label(non_clause).  [assumption].
7.57/7.61	3157 (all X_b all X_a (topological_space(X_a) & real_normed_vector(X_b) -> (all C_1 all F all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),zero_zero(X_b)),hAPP(X_a,filter(X_a),at(X_a),A_2))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(fun(X_a,X_b),fun(X_a,X_b),hAPP(fun(X_b,X_b),fun(fun(X_a,X_b),fun(X_a,X_b)),combb(X_b,X_b,X_a),hAPP(real,fun(X_b,X_b),scaleR_scaleR(X_b),C_1)),F)),zero_zero(X_b)),hAPP(X_a,filter(X_a),at(X_a),A_2))))))) # label(fact_4736_scaleR_OLIM__right__zero) # label(axiom) # label(non_clause).  [assumption].
7.57/7.61	3158 (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_758_add__nonneg__pos) # label(axiom) # label(non_clause).  [assumption].
7.57/7.61	3159 (all N_1 all Ma (Ma = zero_zero(nat) & N_1 = zero_zero(nat) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,semiring_1_of_nat(int),N_1)),hAPP(int,int,uminus_uminus(int),hAPP(nat,int,semiring_1_of_nat(int),Ma)))))) # label(fact_2165_int__zle__neg) # label(axiom) # label(non_clause).  [assumption].
7.57/7.61	3160 (all Y hAPP(real,real,tan,hAPP(real,real,arctan,Y)) = Y) # label(fact_2254_tan__arctan) # label(axiom) # label(non_clause).  [assumption].
7.57/7.61	3161 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> hAPP(real,real,hAPP(real,fun(real,real),log,hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),X) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),log,hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),hAPP(real,real,exp(real),one_one(real)))),hAPP(real,real,ln,X)))) # label(fact_2657_log__base__10__eq2) # label(axiom) # label(non_clause).  [assumption].
7.57/7.61	3162 (all Q_3 -(all A_4 all B_4 (Q_3 = hAPP(int,rat,hAPP(int,fun(int,rat),fract,A_4),B_4) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B_4)) -> one_one(int) != hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),A_4),B_4))))) # label(fact_4412_Rat__cases) # label(axiom) # label(non_clause).  [assumption].
7.57/7.61	3163 (all X all A_1 all B (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),A_1),B))) -> -(hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),A_1)) -> -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),B))))) # label(fact_3230_gcd__semilattice__nat_Ole__infE) # label(axiom) # label(non_clause).  [assumption].
7.57/7.61	3164 (all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_1),zero_zero(real))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,sqrt,X_1)),zero_zero(real))))) # label(fact_1623_real__sqrt__le__0__iff) # label(axiom) # label(non_clause).  [assumption].
7.57/7.61	3165 (all X_a (ordere142940540dd_abs(X_a) -> (all A_2 (zero_zero(X_a) = ti(X_a,A_2) <-> hAPP(X_a,X_a,abs_abs(X_a),A_2) = zero_zero(X_a))))) # label(fact_1850_abs__eq__0) # label(axiom) # label(non_clause).  [assumption].
7.57/7.61	3166 (all X_a all X_b all X_c all F all X_1 hAPP(product_prod(X_a,X_b),X_a,product_fst(X_a,X_b),hAPP(product_prod(X_a,X_c),product_prod(X_a,X_b),hAPP(fun(X_c,X_b),fun(product_prod(X_a,X_c),product_prod(X_a,X_b)),product_apsnd(X_c,X_b,X_a),F),X_1)) = hAPP(product_prod(X_a,X_c),X_a,product_fst(X_a,X_c),X_1)) # label(fact_4065_fst__apsnd) # label(axiom) # label(non_clause).  [assumption].
7.57/7.61	3167 (all Ma all No_1 all F ((all N_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,F,N_2)),hAPP(nat,real,F,hAPP(nat,nat,suc,N_2))))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,F,Ma)),hAPP(nat,real,F,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Ma),No_1)))))) # label(fact_1833_lemma__f__mono__add) # label(axiom) # label(non_clause).  [assumption].
7.57/7.61	3168 (all A_1 all B all C hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),A_1),B)),C))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),A_1),B)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),A_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),C))) # label(fact_1082_mod__mult2__eq) # label(axiom) # label(non_clause).  [assumption].
7.57/7.61	3169 (all Q_3 ((zero_zero(rat) != Q_3 -> (hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),Q_3)) -> hAPP(rat,rat,sgn_sgn(rat),Q_3) = one_one(rat)) & (-hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),Q_3)) -> hAPP(rat,rat,sgn_sgn(rat),Q_3) = hAPP(rat,rat,uminus_uminus(rat),one_one(rat)))) & (zero_zero(rat) = Q_3 -> hAPP(rat,rat,sgn_sgn(rat),Q_3) = zero_zero(rat)))) # label(fact_3716_sgn__rat__def) # label(axiom) # label(non_clause).  [assumption].
7.57/7.61	3170 (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_384_comm__mult__strict__left__mono) # label(axiom) # label(non_clause).  [assumption].
7.57/7.61	3171 (all X_a (ring_div(X_a) -> (all Y all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),Y),X)) -> hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),X),Y)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),X),hAPP(X_a,X_a,uminus_uminus(X_a),Y)))))) # label(fact_2086_dvd__div__neg) # label(axiom) # label(non_clause).  [assumption].
7.57/7.61	3172 (all X_a (metric_space(X_a) -> (all X_3 all L_2 all A_2 ((all S_2 (hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),S_2),A_2),sequentially)) & (all N_2 A_2 != hAPP(nat,real,S_2,N_2)) -> hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),hAPP(fun(nat,real),fun(nat,X_a),hAPP(fun(real,X_a),fun(fun(nat,real),fun(nat,X_a)),combb(real,X_a,nat),X_3),S_2)),L_2),sequentially)))) -> hBOOL(hAPP(filter(real),bool,hAPP(X_a,fun(filter(real),bool),hAPP(fun(real,X_a),fun(X_a,fun(filter(real),bool)),tendsto(real,X_a),X_3),L_2),hAPP(real,filter(real),at(real),A_2))))))) # label(fact_4661_LIMSEQ__SEQ__conv2) # label(axiom) # label(non_clause).  [assumption].
7.57/7.61	3173 (all X_a (real_vector(X_a) -> (all A_1 all B all X (zero_zero(X_a) != ti(X_a,X) -> (hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),B),X) = hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_1),X) -> B = A_1))))) # label(fact_4705_scaleR__right__imp__eq) # label(axiom) # label(non_clause).  [assumption].
7.57/7.61	3174 (all X_a (division_ring(X_a) -> (all B_1 all A_2 all C_1 (ti(X_a,C_1) != zero_zero(X_a) -> (ti(X_a,A_2) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),B_1),C_1) <-> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),C_1) = ti(X_a,B_1)))))) # label(fact_1688_nonzero__divide__eq__eq) # label(axiom) # label(non_clause).  [assumption].
7.57/7.61	3175 (all Sa (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Sa)) -> hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),hAPP(real,fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(real,fun(nat,real)),combc(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),powr),real_1(nat))),hAPP(real,real,uminus_uminus(real),Sa))),zero_zero(real)),sequentially)))) # label(fact_4493_LIMSEQ__neg__powr) # label(axiom) # label(non_clause).  [assumption].
7.57/7.61	3176 (all X_a (metric_space(X_a) -> (all R_1 all X_3 all L_2 (hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),X_3),L_2),sequentially)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),R_1)) -> (exists No all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),No),N_2)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),hAPP(nat,X_a,X_3,N_2)),L_2)),R_1))))))))) # label(fact_4521_metric__LIMSEQ__D) # label(axiom) # label(non_clause).  [assumption].
7.57/7.61	3177 (all N hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),one_one(nat)),hAPP(nat,nat,fact_fact(nat),N)))) # label(fact_2493_fact__ge__one__nat) # label(axiom) # label(non_clause).  [assumption].
7.57/7.61	3178 (all N all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,real_1(int),N)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(int,real,real_1(int),X)),one_one(real)))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),N),X)))) # label(fact_3392_lemma__floor2) # label(axiom) # label(non_clause).  [assumption].
7.57/7.61	3179 (all Q_5 all R_5 all A_1 all B all Q_3 all R_4 (hBOOL(hAPP(product_prod(int,int),bool,hAPP(int,fun(product_prod(int,int),bool),hAPP(int,fun(int,fun(product_prod(int,int),bool)),divmod_int_rel,A_1),B),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),Q_3),R_4))) -> (hBOOL(hAPP(product_prod(int,int),bool,hAPP(int,fun(product_prod(int,int),bool),hAPP(int,fun(int,fun(product_prod(int,int),bool)),divmod_int_rel,A_1),B),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),Q_5),R_5))) -> (zero_zero(int) != ti(int,B) -> ti(int,Q_5) = ti(int,Q_3))))) # label(fact_1187_unique__quotient) # label(axiom) # label(non_clause).  [assumption].
7.57/7.61	3180 (all X_a (mult_zero(X_a) & no_zero_divisors(X_a) & zero_neq_one(X_a) & power(X_a) -> (all A_2 all N_1 (zero_zero(X_a) = hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_2),N_1) <-> zero_zero(X_a) = ti(X_a,A_2) & zero_zero(nat) != N_1)))) # label(fact_414_power__eq__0__iff) # label(axiom) # label(non_clause).  [assumption].
7.57/7.61	3181 (all X_a (semiring(X_a) -> times_times(X_a) = ti(fun(X_a,fun(X_a,X_a)),times_times(X_a)))) # label(tsy_c_Groups_Otimes__class_Otimes_3_res) # label(axiom) # label(non_clause).  [assumption].
7.57/7.61	3182 (all X_a (archim1727834104eiling(X_a) -> (all V_1 all X_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),V_1)),hAPP(X_a,int,archimedean_ceiling(X_a),X_1))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(int,X_a,number_number_of(X_a),V_1)),one_one(X_a))),X_1)))))) # label(fact_3212_number__of__le__ceiling) # label(axiom) # label(non_clause).  [assumption].
7.57/7.61	3183 (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),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),C)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)),C)))) # label(fact_765_ab__semigroup__mult__class_Omult__ac_I1_J) # label(axiom) # label(non_clause).  [assumption].
7.57/7.61	3184 (all A_1 all Q_3 all R_4 (hBOOL(hAPP(product_prod(int,int),bool,hAPP(int,fun(product_prod(int,int),bool),hAPP(int,fun(int,fun(product_prod(int,int),bool)),divmod_int_rel,A_1),A_1),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),Q_3),R_4))) -> (zero_zero(int) != ti(int,A_1) -> one_one(int) = ti(int,Q_3)))) # label(fact_1190_self__quotient) # label(axiom) # label(non_clause).  [assumption].
7.57/7.61	3185 (all A_2 all B_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B_1),zero_zero(int))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A_2),zero_zero(int))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_2),B_1)))))) # label(fact_1019_neg__imp__zdiv__nonneg__iff) # label(axiom) # label(non_clause).  [assumption].
7.57/7.61	3186 (all X_a (semiring_1(X_a) -> (all X (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X)) -> hAPP(nat,X_a,semiring_1_of_nat(X_a),hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),X))) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),hAPP(int,nat,nat_1,X))),hAPP(nat,X_a,semiring_1_of_nat(X_a),hAPP(int,nat,nat_1,X))))))) # label(fact_1204_of__nat__double) # label(axiom) # label(non_clause).  [assumption].
7.57/7.61	3187 (all S (hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),S)) <-> (exists K_1 hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,bool),fun(fun(nat,bool),bool),ord_less_eq(fun(nat,bool)),S),hAPP(nat,fun(nat,bool),ord_atMost(nat),K_1)))))) # label(fact_4974_finite__nat__iff__bounded__le) # label(axiom) # label(non_clause).  [assumption].
7.57/7.61	3188 (all X -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,exp(real),X)),zero_zero(real)))) # label(fact_2568_not__exp__less__zero) # label(axiom) # label(non_clause).  [assumption].
7.57/7.61	3189 (all X_a (archim1727834104eiling(X_a) -> (all X all Z_1 hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(X_a,int,archim2085082626_floor(X_a),X)),Z_1) = hAPP(X_a,int,archim2085082626_floor(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X),hAPP(int,X_a,ring_1_of_int(X_a),Z_1)))))) # label(fact_3596_floor__add__of__int) # label(axiom) # label(non_clause).  [assumption].
7.57/7.61	3190 (all P_1 all A0 all A1 (hBOOL(hAPP(product_prod(int,int),bool,hAPP(fun(product_prod(int,int),fun(product_prod(int,int),bool)),fun(product_prod(int,int),bool),accp(product_prod(int,int)),lazy_small_lazy_rel),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),A0),A1))) -> ((all D_3 all I_2 (hBOOL(hAPP(product_prod(int,int),bool,hAPP(fun(product_prod(int,int),fun(product_prod(int,int),bool)),fun(product_prod(int,int),bool),accp(product_prod(int,int)),lazy_small_lazy_rel),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),D_3),I_2))) -> ((-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),D_3),I_2)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),P_1,D_3),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),I_2),one_one(int))))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),P_1,D_3),I_2))))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),P_1,A0),A1))))) # label(fact_3556_small__lazy_H_Opinduct) # label(axiom) # label(non_clause).  [assumption].
7.57/7.61	3191 (exists K_2 ((all X_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,cnj,X_2))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(complex,real,norm_norm(complex),X_2)),K_2)))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),K_2)))) # label(fact_2967_cnj_Ononneg__bounded) # label(axiom) # label(non_clause).  [assumption].
7.57/7.61	3192 (all Z_1 zero_zero(real) = hAPP(complex,real,im,hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),Z_1),hAPP(complex,complex,cnj,Z_1)))) # label(fact_2984_complex__In__mult__cnj__zero) # label(axiom) # label(non_clause).  [assumption].
7.57/7.61	3193 (all N_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),N_1)) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(int,real,real_1(int),N_1))))) # label(fact_3384_real__of__int__gt__zero__cancel__iff) # label(axiom) # label(non_clause).  [assumption].
7.57/7.61	3194 (all X all Y Y = hAPP(complex,real,im,hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,X),Y))) # label(fact_2972_Im) # label(axiom) # label(non_clause).  [assumption].
7.57/7.61	3195 (all I_1 all M hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),I_1))))) # label(fact_1328_less__add__Suc2) # label(axiom) # label(non_clause).  [assumption].
7.57/7.61	3196 (all X_2 hAPP(fun(nat,real),real,suminf(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),cos_coeff)),hAPP(real,fun(nat,real),power_power(real),X_2))) = hAPP(real,real,cos,X_2)) # label(fact_3971_lemma__cos__ext) # label(axiom) # label(non_clause).  [assumption].
7.57/7.61	3197 (all X_a (linordered_idom(X_a) -> (all A_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_2)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,sgn_sgn(X_a),A_2))))))) # label(fact_2211_sgn__greater) # label(axiom) # label(non_clause).  [assumption].
7.57/7.61	3198 (all X_a (ord(X_a) -> ti(fun(X_a,fun(X_a,fun(X_a,bool))),ord_atLeastLessThan(X_a)) = ord_atLeastLessThan(X_a))) # label(tsy_c_SetInterval_Oord__class_OatLeastLessThan_res) # label(axiom) # label(non_clause).  [assumption].
7.57/7.61	3199 (all N (N != zero_zero(nat) -> hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),N)),one_one(nat))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),N))) # label(fact_1475_Suc__mult__two__diff__one) # label(axiom) # label(non_clause).  [assumption].
7.57/7.61	3200 (all X_a (real_normed_algebra(X_a) -> (exists K_2 ((all A_4 all B_4 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_4),B_4))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(X_a,real,norm_norm(X_a),A_4)),hAPP(X_a,real,norm_norm(X_a),B_4))),K_2)))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),K_2)))))) # label(fact_1805_mult_Opos__bounded) # label(axiom) # label(non_clause).  [assumption].
7.57/7.61	3201 (all X_1 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(nat,fun(real,real),hAPP(fun(real,fun(nat,real)),fun(nat,fun(real,real)),combc(real,nat,real),hAPP(fun(real,real),fun(real,fun(nat,real)),hAPP(fun(real,fun(nat,real)),fun(fun(real,real),fun(real,fun(nat,real))),combb(real,fun(nat,real),real),power_power(real)),cos)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),X_1),hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),hAPP(real,real,cos,X_1))),hAPP(real,real,sin,X_1)))))) # label(fact_3913_DERIV__cos__realpow2b) # label(axiom) # label(non_clause).  [assumption].
7.57/7.61	3202 (all P_5 all R_4 all S_3 all Q_3 (ti(int,Q_3) != zero_zero(int) -> (ti(int,S_3) != zero_zero(int) -> (hAPP(product_prod(int,int),product_prod(int,int),normalize,hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),R_4),S_3)) = hAPP(product_prod(int,int),product_prod(int,int),normalize,hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),P_5),Q_3)) -> hAPP(int,int,hAPP(int,fun(int,int),times_times(int),P_5),S_3) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),R_4),Q_3))))) # label(fact_3728_normalize__crossproduct) # label(axiom) # label(non_clause).  [assumption].
7.57/7.61	3203 (all X_3 (hBOOL(hAPP(fun(nat,complex),bool,cauchy(complex),X_3)) -> hBOOL(hAPP(fun(nat,real),bool,cauchy(real),hAPP(fun(nat,complex),fun(nat,real),hAPP(fun(complex,real),fun(fun(nat,complex),fun(nat,real)),combb(complex,real,nat),im),X_3))))) # label(fact_3849_Im_OCauchy) # label(axiom) # label(non_clause).  [assumption].
7.57/7.61	3204 (all I all M_1 (-hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),zero_zero(nat)),M_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_1))),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),hAPP(nat,nat,suc,I))))) = hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),combs(nat,bool,bool),hAPP(fun(nat,bool),fun(nat,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fconj),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,bool),fun(nat,bool)),combc(nat,fun(nat,bool),bool),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_1))),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),I)))))) # label(fact_3873_card__less__Suc2) # label(axiom) # label(non_clause).  [assumption].
7.57/7.61	3205 (all X_a (real_n2089651433ebra_1(X_a) -> (all R_4 hAPP(real,X_a,of_real(X_a),hAPP(real,real,sgn_sgn(real),R_4)) = hAPP(X_a,X_a,sgn_sgn(X_a),hAPP(real,X_a,of_real(X_a),R_4))))) # label(fact_2801_sgn__of__real) # label(axiom) # label(non_clause).  [assumption].
7.57/7.61	3206 (all A_1 all R_4 all B all M all C all D all N hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A_1),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),R_4),B))),M)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),C),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),R_4),D))),N)) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),M)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),N))),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),R_4),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),M)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),D),N))))) # label(fact_499_xzgcda__linear__aux1) # label(axiom) # label(non_clause).  [assumption].
7.57/7.61	3207 (all X_a (ordere142940540dd_abs(X_a) -> (all A_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,abs_abs(X_a),A_2))) <-> zero_zero(X_a) != ti(X_a,A_2))))) # label(fact_1864_zero__less__abs__iff) # label(axiom) # label(non_clause).  [assumption].
7.57/7.61	3208 (all X_a all A_3 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_3)) -> hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,number_number_of(int),min_1)),hAPP(fun(X_a,bool),nat,finite_card(X_a),A_3))),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,number_number_of(int),min_1)),hAPP(fun(X_a,bool),nat,finite_card(X_a),A_3))) = one_one(int))) # label(fact_1760_neg__one__special) # label(axiom) # label(non_clause).  [assumption].
7.57/7.61	3209 (all X_1 all F all A_2 all B_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A_2),B_1)) -> ((all X_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_2),B_1)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A_2),X_2)) -> hBOOL(hAPP(real,bool,hAPP(fun(real,real),fun(real,bool),isCont(real,real),F),X_2)))) -> ((all X_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_2),B_1)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A_2),X_2)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),F),X_2),zero_zero(real))))) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A_2),X_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_1),B_1)) -> hAPP(real,real,F,A_2) = hAPP(real,real,F,X_1))))))) # label(fact_4928_DERIV__isconst2) # label(axiom) # label(non_clause).  [assumption].
7.57/7.61	3210 (all X_3 (hBOOL(hAPP(fun(nat,complex),bool,cauchy(complex),X_3)) -> hBOOL(hAPP(fun(nat,real),bool,cauchy(real),hAPP(fun(nat,complex),fun(nat,real),hAPP(fun(complex,real),fun(fun(nat,complex),fun(nat,real)),combb(complex,real,nat),re),X_3))))) # label(fact_3850_Re_OCauchy) # label(axiom) # label(non_clause).  [assumption].
7.57/7.61	3211 (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_2951_mult__idem) # label(axiom) # label(non_clause).  [assumption].
7.57/7.61	3212 (all Z all Ma (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),Z),hAPP(nat,int,semiring_1_of_nat(int),Ma))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(int,nat,nat_1,hAPP(int,int,abs_abs(int),Z))),Ma)))) # label(fact_1970_dvd__int__iff) # label(axiom) # label(non_clause).  [assumption].
7.57/7.61	3213 (all X_a (archim1804426504_field(X_a) -> (all X exists X_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(int,X_a,ring_1_of_int(X_a),X_2)),X)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),hAPP(int,X_a,ring_1_of_int(X_a),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X_2),one_one(int))))) & (all Y_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),hAPP(int,X_a,ring_1_of_int(X_a),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Y_2),one_one(int))))) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(int,X_a,ring_1_of_int(X_a),Y_2)),X)) -> ti(int,X_2) = ti(int,Y_2))))))) # label(fact_3617_floor__exists1) # label(axiom) # label(non_clause).  [assumption].
7.57/7.61	3214 (all X_b all X_a (topological_space(X_a) & real_normed_vector(X_b) -> (all F all L all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),L),hAPP(X_a,filter(X_a),at(X_a),A_2))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(X_b,fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(X_b,fun(X_a,X_b)),combc(X_a,X_b,X_b),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,fun(X_b,X_b))),combb(X_b,fun(X_b,X_b),X_a),minus_minus(X_b)),F)),L)),zero_zero(X_b)),hAPP(X_a,filter(X_a),at(X_a),A_2))))))) # label(fact_4583_LIM__zero) # label(axiom) # label(non_clause).  [assumption].
7.57/7.62	3215 (all X_a all C_1 all A_3 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),hAPP(fun(X_a,bool),fun(X_a,bool),uminus_uminus(fun(X_a,bool)),A_3))) -> -hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),A_3)))) # label(fact_2197_ComplE) # label(axiom) # label(non_clause).  [assumption].
7.57/7.62	3216 (all X_a (linordered_semidom(X_a) -> (all X_1 all Y_1 all B_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),B_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X_1),Y_1)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),B_1),X_1)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),B_1),Y_1)))))))) # label(fact_443_power__increasing__iff) # label(axiom) # label(non_clause).  [assumption].
7.57/7.62	3217 (all X_a (ring_div(X_a) -> (all B all B_5 all A_1 all C all A_6 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),A_1),C) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),A_6),C) -> (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),B),C) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),B_5),C) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_6),B_5)),C) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_1),B)),C)))))) # label(fact_943_mod__diff__cong) # label(axiom) # label(non_clause).  [assumption].
7.57/7.62	3218 (all X hAPP(real,real,uminus_uminus(real),hAPP(real,real,sin,X)) = hAPP(real,real,sin,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),pi))) # label(fact_2326_sin__periodic__pi) # label(axiom) # label(non_clause).  [assumption].
7.57/7.62	3219 (all X hAPP(real,real,ln,hAPP(real,real,exp(real),X)) = X) # label(fact_2509_ln__exp) # label(axiom) # label(non_clause).  [assumption].
7.57/7.62	3220 (all A_2 all B_1 all Ma (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_2),B_1),Ma)) <-> (exists K_1 ti(int,B_1) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A_2),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Ma),K_1))))) # label(fact_421_zcong__iff__lin) # label(axiom) # label(non_clause).  [assumption].
7.57/7.62	3221 (all X_a all X_b nat_tr1645093318rphism(X_a,X_b) = ti(fun(fun(X_a,X_b),fun(fun(X_a,bool),bool)),nat_tr1645093318rphism(X_a,X_b))) # label(tsy_c_Nat__Transfer_Otransfer__morphism_res) # label(axiom) # label(non_clause).  [assumption].
7.57/7.62	3222 (all M all 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),N)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,M)),N)) # label(fact_1340_mult__Suc) # label(axiom) # label(non_clause).  [assumption].
7.57/7.62	3223 (all X_1 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(nat,fun(real,real),hAPP(fun(real,fun(nat,real)),fun(nat,fun(real,real)),combc(real,nat,real),hAPP(fun(real,real),fun(real,fun(nat,real)),hAPP(fun(real,fun(nat,real)),fun(fun(real,real),fun(real,fun(nat,real))),combb(real,fun(nat,real),real),power_power(real)),cos)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),X_1),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,min_1))),hAPP(real,real,cos,X_1))),hAPP(real,real,sin,X_1))))) # label(fact_3912_DERIV__cos__realpow2a) # label(axiom) # label(non_clause).  [assumption].
7.57/7.62	3224 (all X all Y hAPP(nat,nat,hAPP(nat,fun(nat,nat),nat_gcd,X),Y) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),X),Y)) # label(fact_3660_gcd__eq__nitpick__gcd) # label(axiom) # label(non_clause).  [assumption].
7.57/7.62	3225 (all X_a (ord(X_a) -> ord_min(X_a) = ti(fun(X_a,fun(X_a,X_a)),ord_min(X_a)))) # label(tsy_c_Orderings_Oord__class_Omin_res) # label(axiom) # label(non_clause).  [assumption].
7.57/7.62	3226 (all X_a (monoid_mult(X_a) -> (all Z_1 all W ((-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),W))) -> hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),Z_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,W))) = one_one(X_a)) & (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),W))) -> hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),Z_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,W))) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Z_1),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),Z_1),hAPP(int,nat,number_number_of(nat),W)))),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),Z_1),hAPP(int,nat,number_number_of(nat),W)))))))) # label(fact_3898_power__number__of__odd) # label(axiom) # label(non_clause).  [assumption].
7.57/7.62	3227 (all N_1 (zero_zero(nat) != N_1 <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)))) # label(fact_537_neq0__conv) # label(axiom) # label(non_clause).  [assumption].
7.57/7.62	3228 (all X_a (ordere236663937imp_le(X_a) -> (all X all Y all Z_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X),Z_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Y),Z_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),Y)),Z_1)))) # label(fact_4959_max__add__distrib__left) # label(axiom) # label(non_clause).  [assumption].
7.57/7.62	3229 (all X_a (semiring_div(X_a) -> (all A_1 all B all C (ti(X_a,C) != zero_zero(X_a) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),A_1),B) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),C)))))) # label(fact_995_div__mult__mult2) # label(axiom) # label(non_clause).  [assumption].
7.57/7.62	3230 (all Ma all N_1 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),Ma),N_1) = hAPP(nat,nat,suc,zero_zero(nat)) <-> Ma = hAPP(nat,nat,suc,zero_zero(nat)) & N_1 = hAPP(nat,nat,suc,zero_zero(nat)))) # label(fact_1326_mult__eq__1__iff) # label(axiom) # label(non_clause).  [assumption].
7.57/7.62	3231 (all X_a (comm_semiring_1(X_a) -> (all A_1 all B all C (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)),C)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_1),C)))))) # label(fact_338_dvd__mult__left) # label(axiom) # label(non_clause).  [assumption].
7.57/7.62	3232 (all W_1 all Z (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),W_1),Z)) <-> 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),one_one(int)))))) # label(fact_85_zle__add1__eq__le) # label(axiom) # label(non_clause).  [assumption].
7.57/7.62	3233 (all X_b all X_a (real_normed_vector(X_b) & topological_space(X_a) -> (all F all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(real,fun(filter(X_a),bool),hAPP(fun(X_a,real),fun(real,fun(filter(X_a),bool)),tendsto(X_a,real),hAPP(fun(X_a,X_b),fun(X_a,real),hAPP(fun(X_b,real),fun(fun(X_a,X_b),fun(X_a,real)),combb(X_b,real,X_a),norm_norm(X_b)),F)),zero_zero(real)),hAPP(X_a,filter(X_a),at(X_a),A_2))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),zero_zero(X_b)),hAPP(X_a,filter(X_a),at(X_a),A_2))))))) # label(fact_4611_LIM__norm__zero__cancel) # label(axiom) # label(non_clause).  [assumption].
7.57/7.62	3234 (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_1572_order__less__asym_H) # label(axiom) # label(non_clause).  [assumption].
7.57/7.62	3235 (all X_a all X_b (metric_space(X_b) & real_n2089651433ebra_1(X_a) -> (all K all L_2 all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(X_b,fun(X_a,X_b),combk(X_b,X_a),K)),L_2),hAPP(X_a,filter(X_a),at(X_a),A_2))) -> ti(X_b,L_2) = ti(X_b,K))))) # label(fact_4557_LIM__const__eq) # label(axiom) # label(non_clause).  [assumption].
7.57/7.62	3236 (all X_a all X_b (comm_monoid_add(X_b) -> (all F all P_1 all A_3 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_3)) -> hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),F),hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,bool)),combs(X_a,bool,bool),hAPP(fun(X_a,bool),fun(X_a,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,fun(bool,bool))),combb(bool,fun(bool,bool),X_a),fconj),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(X_a,bool)),combc(X_a,fun(X_a,bool),bool),member(X_a)),A_3))),P_1))) = hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),hAPP(X_b,fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(X_b,fun(X_a,X_b)),combc(X_a,X_b,X_b),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,X_b)),hAPP(fun(X_a,fun(X_b,fun(X_b,X_b))),fun(fun(X_a,X_b),fun(X_a,fun(X_b,X_b))),combs(X_a,X_b,fun(X_b,X_b)),hAPP(fun(X_a,bool),fun(X_a,fun(X_b,fun(X_b,X_b))),hAPP(fun(bool,fun(X_b,fun(X_b,X_b))),fun(fun(X_a,bool),fun(X_a,fun(X_b,fun(X_b,X_b)))),combb(bool,fun(X_b,fun(X_b,X_b)),X_a),if(X_b)),P_1)),F)),zero_zero(X_b))),A_3))))) # label(fact_4186_setsum__restrict__set_H_H) # label(axiom) # label(non_clause).  [assumption].
7.57/7.62	3237 (all R_4 exists X_2 (hAPP(int,rat,hAPP(int,fun(int,rat),fract,hAPP(product_prod(int,int),int,product_fst(int,int),X_2)),hAPP(product_prod(int,int),int,product_snd(int,int),X_2)) = R_4 & one_one(int) = hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),hAPP(product_prod(int,int),int,product_fst(int,int),X_2)),hAPP(product_prod(int,int),int,product_snd(int,int),X_2)) & (all Y_2 (hAPP(int,rat,hAPP(int,fun(int,rat),fract,hAPP(product_prod(int,int),int,product_fst(int,int),Y_2)),hAPP(product_prod(int,int),int,product_snd(int,int),Y_2)) = R_4 & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(product_prod(int,int),int,product_snd(int,int),Y_2))) & one_one(int) = hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),hAPP(product_prod(int,int),int,product_fst(int,int),Y_2)),hAPP(product_prod(int,int),int,product_snd(int,int),Y_2)) -> X_2 = Y_2)) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(product_prod(int,int),int,product_snd(int,int),X_2))))) # label(fact_4410_quotient__of__unique) # label(axiom) # label(non_clause).  [assumption].
7.57/7.62	3238 (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_70_rel__simps_I29_J) # label(axiom) # label(non_clause).  [assumption].
7.57/7.62	3239 (all Y all X (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y),X)) -> Y = hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),X),Y))) # label(fact_3237_gcd__proj2__if__dvd__nat) # label(axiom) # label(non_clause).  [assumption].
7.57/7.62	3240 (all X hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),hAPP(complex,real,im,X))),hAPP(complex,real,norm_norm(complex),X)))) # label(fact_2983_abs__Im__le__cmod) # label(axiom) # label(non_clause).  [assumption].
7.57/7.62	3241 (all N all M ((M = zero_zero(nat) -> zero_zero(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),N)) & (zero_zero(nat) != M -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),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),one_one(nat))),N))))) # label(fact_719_mult__eq__if) # label(axiom) # label(non_clause).  [assumption].
7.57/7.62	3242 (all J_2 all K_4 all A_1 all P_5 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),P_5)) -> (hBOOL(hAPP(int,bool,zprime,P_5)) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_1),zero_zero(int)),P_5)) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,K_4),zero_zero(int)),P_5)) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,J_2),zero_zero(int)),P_5)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),hAPP(int,int,hAPP(int,fun(int,int),multInv,P_5),J_2))),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),hAPP(int,int,hAPP(int,fun(int,int),multInv,P_5),K_4))),P_5)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,J_2),K_4),P_5))))))))) # label(fact_850_MultInv__zcong__prop3) # label(axiom) # label(non_clause).  [assumption].
7.57/7.62	3243 (all K (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),hAPP(int,int,bit0,K))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),K)))) # label(fact_55_rel__simps_I21_J) # label(axiom) # label(non_clause).  [assumption].
7.57/7.62	3244 (all A_2 all B_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B_1),A_2)) <-> hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),one_one(rat)),hAPP(int,rat,hAPP(int,fun(int,rat),fract,A_2),B_1)))))) # label(fact_3793_one__le__Fract__iff) # label(axiom) # label(non_clause).  [assumption].
7.57/7.62	3245 (all B all A_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),B)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(real,nat,natfloor,A_1)),hAPP(real,nat,natfloor,B))),hAPP(real,nat,natfloor,hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A_1),B))))))) # label(fact_1905_le__mult__natfloor) # label(axiom) # label(non_clause).  [assumption].
7.57/7.62	3246 (all X_b all X_a all B_2 all F all A_3 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_3)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),B_2),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),A_3))) -> hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),B_2))))) # label(fact_3642_finite__surj) # label(axiom) # label(non_clause).  [assumption].
7.57/7.62	3247 (all X_a (archim1727834104eiling(X_a) -> (all X all V hAPP(X_a,int,archim2085082626_floor(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X),hAPP(int,X_a,number_number_of(X_a),V))) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(X_a,int,archim2085082626_floor(X_a),X)),hAPP(int,int,number_number_of(int),V))))) # label(fact_2888_floor__add__number__of) # label(axiom) # label(non_clause).  [assumption].
7.57/7.62	3248 (all Z_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Z_1)) -> ti(int,Z_1) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(int,nat,nat_1,Z_1)))) # label(fact_1378_nat__0__le) # label(axiom) # label(non_clause).  [assumption].
7.57/7.62	3249 (all Ma all W_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),W_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_1),hAPP(nat,int,semiring_1_of_nat(int),Ma))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(int,nat,nat_1,W_1)),Ma))))) # label(fact_1423_nat__less__iff) # label(axiom) # label(non_clause).  [assumption].
7.57/7.62	3250 (all X all Y all L_4 all M hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),Y)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,uminus_uminus(real),L_4)),hAPP(real,real,uminus_uminus(real),M))))),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),hAPP(real,real,uminus_uminus(real),L_4)))),hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),Y),hAPP(real,real,uminus_uminus(real),M))))))) # label(fact_2112_abs__sum__triangle__ineq) # label(axiom) # label(non_clause).  [assumption].
7.57/7.62	3251 (all X_a all X_c all X_b all F all X_1 all G (hAPP(X_c,X_b,G,hAPP(product_prod(X_a,X_c),X_c,product_snd(X_a,X_c),X_1)) = hAPP(X_c,X_b,F,hAPP(product_prod(X_a,X_c),X_c,product_snd(X_a,X_c),X_1)) <-> hAPP(product_prod(X_a,X_c),product_prod(X_a,X_b),hAPP(fun(X_c,X_b),fun(product_prod(X_a,X_c),product_prod(X_a,X_b)),product_apsnd(X_c,X_b,X_a),G),X_1) = hAPP(product_prod(X_a,X_c),product_prod(X_a,X_b),hAPP(fun(X_c,X_b),fun(product_prod(X_a,X_c),product_prod(X_a,X_b)),product_apsnd(X_c,X_b,X_a),F),X_1))) # label(fact_4066_apsnd__eq__conv) # label(axiom) # label(non_clause).  [assumption].
7.57/7.62	3252 (all T_1 preorder(filter(T_1))) # label(arity_Limits_Ofilter___Orderings_Opreorder) # label(axiom) # label(non_clause).  [assumption].
7.57/7.62	3253 (all K_4 all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),M),K_4)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),N),K_4))))) # label(fact_1087_div__le__mono) # label(axiom) # label(non_clause).  [assumption].
7.57/7.62	3254 (all M all N hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),M),N)),M))) # label(fact_3214_gcd__dvd1__nat) # label(axiom) # label(non_clause).  [assumption].
7.57/7.62	3255 (all X_a (comm_ring_1(X_a) -> (all X hAPP(X_a,X_a,uminus_uminus(X_a),X) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),one_one(X_a))),X)))) # label(fact_2071_comm__ring__1__class_Onormalizing__ring__rules_I1_J) # label(axiom) # label(non_clause).  [assumption].
7.57/7.62	3256 (all U_1 hAPP(nat,nat,suc,U_1) = hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(nat,fun(nat,bool),ord_atMost(nat),U_1))) # label(fact_4973_card__atMost) # label(axiom) # label(non_clause).  [assumption].
7.57/7.62	3257 (all X_a all X_b (ordere216010020id_add(X_b) -> (all F all A_3 all B_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),B_2)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_3),B_2)) -> ((all B_4 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),B_4),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),B_2),A_3))) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),zero_zero(X_b)),hAPP(X_a,X_b,F,B_4))))) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),F),A_3)),hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),F),B_2))))))))) # label(fact_4293_setsum__mono2) # label(axiom) # label(non_clause).  [assumption].
7.57/7.62	3258 (all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),X_1)),one_one(real))) -> hBOOL(hAPP(fun(nat,real),bool,monoseq(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),hAPP(real,fun(real,real),inverse_divide(real),one_one(real))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),hAPP(fun(nat,nat),fun(nat,fun(nat,nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,nat),fun(nat,fun(nat,nat))),combb(nat,fun(nat,nat),nat),plus_plus(nat)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),times_times(nat)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),one_one(nat)))))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),hAPP(real,fun(nat,real),power_power(real),X_1)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),hAPP(fun(nat,nat),fun(nat,fun(nat,nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,nat),fun(nat,fun(nat,nat))),combb(nat,fun(nat,nat),nat),plus_plus(nat)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),times_times(nat)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),one_one(nat)))))))) # label(fact_3920_monoseq__arctan__series) # label(axiom) # label(non_clause).  [assumption].
7.57/7.62	3259 (all X_b all X_a all B_2 all A_3 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_3)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),B_2)) -> hBOOL(hAPP(fun(sum_sum(X_a,X_b),bool),bool,finite_finite_1(sum_sum(X_a,X_b)),hAPP(fun(X_b,bool),fun(sum_sum(X_a,X_b),bool),hAPP(fun(X_a,bool),fun(fun(X_b,bool),fun(sum_sum(X_a,X_b),bool)),sum_Plus(X_a,X_b),A_3),B_2)))))) # label(fact_3184_finite__Plus) # label(axiom) # label(non_clause).  [assumption].
7.57/7.62	3260 (all X all A_1 all B (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A_1),B)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),one_one(real)),X)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),powr,X),A_1)),hAPP(real,real,hAPP(real,fun(real,real),powr,X),B)))))) # label(fact_3350_powr__mono) # label(axiom) # label(non_clause).  [assumption].
7.57/7.62	3261 (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_1569_order__less__imp__not__eq) # label(axiom) # label(non_clause).  [assumption].
7.57/7.62	3262 (all X_a (linord1117847801e_zero(X_a) -> (all A_1 hAPP(X_a,X_a,abs_abs(X_a),hAPP(X_a,X_a,inverse_inverse(X_a),A_1)) = hAPP(X_a,X_a,inverse_inverse(X_a),hAPP(X_a,X_a,abs_abs(X_a),A_1))))) # label(fact_2534_abs__inverse) # label(axiom) # label(non_clause).  [assumption].
7.57/7.62	3263 (all X_a (real_normed_vector(X_a) -> (all R_4 all X hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),hAPP(real,real,sgn_sgn(real),R_4)),hAPP(X_a,X_a,sgn_sgn(X_a),X)) = hAPP(X_a,X_a,sgn_sgn(X_a),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),R_4),X))))) # label(fact_4721_sgn__scaleR) # label(axiom) # label(non_clause).  [assumption].
7.57/7.62	3264 (all P_5 all A_1 hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A_1),hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),P_5),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))),P_5) = hAPP(int,int,hAPP(int,fun(int,int),inv,P_5),A_1)) # label(fact_1159_WilsonRuss_Oinv__def) # label(axiom) # label(non_clause).  [assumption].
7.57/7.62	3265 (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_475_number__of__diff) # label(axiom) # label(non_clause).  [assumption].
7.57/7.62	3266 (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_507_add__number__of__diff1) # label(axiom) # label(non_clause).  [assumption].
7.57/7.62	3267 (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_215_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J) # label(axiom) # label(non_clause).  [assumption].
7.57/7.62	3268 (all X_a (idom(X_a) -> (all X_1 all Y_1 (hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X_1),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat)))) = hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),Y_1),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat)))) <-> ti(X_a,X_1) = hAPP(X_a,X_a,uminus_uminus(X_a),Y_1) | ti(X_a,Y_1) = ti(X_a,X_1))))) # label(fact_2100_realpow__two__disj) # label(axiom) # label(non_clause).  [assumption].
7.57/7.62	3269 (all F all L (hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),F),L),sequentially)) -> hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),abs_abs(real)),F)),hAPP(real,real,abs_abs(real),L)),sequentially)))) # label(fact_4471_LIMSEQ__imp__rabs) # label(axiom) # label(non_clause).  [assumption].
7.57/7.62	3270 (all N all M hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,uminus_uminus(int),hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,N)))),hAPP(nat,int,semiring_1_of_nat(int),M)))) # label(fact_2134_negative__zless) # label(axiom) # label(non_clause).  [assumption].
7.57/7.62	3271 (all X_a (real_normed_vector(X_a) -> (all X_3 (hBOOL(hAPP(fun(nat,X_a),bool,cauchy(X_a),X_3)) <-> (all E (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),E)) -> (exists M_3 all M_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_3),M_2)) -> (all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_3),N_2)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(nat,X_a,X_3,M_2)),hAPP(nat,X_a,X_3,N_2)))),E)))))))))))) # label(fact_3316_Cauchy__iff) # label(axiom) # label(non_clause).  [assumption].
7.57/7.62	3272 (all X_a (ring_1(X_a) -> (all W all Z_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(int,X_a,ring_1_of_int(X_a),W)),hAPP(int,X_a,ring_1_of_int(X_a),Z_1)) = hAPP(int,X_a,ring_1_of_int(X_a),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),W),Z_1))))) # label(fact_3589_of__int__diff) # label(axiom) # label(non_clause).  [assumption].
7.57/7.62	3273 (all N all A_1 all B (hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,A_1),B) = one_one(int) -> hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A_1),N)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),B),N)) = one_one(int))) # label(fact_3450_zgcd__1__power__distrib) # label(axiom) # label(non_clause).  [assumption].
7.57/7.62	3274 (all X_a all A_3 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_3)) -> (((exists X_2 hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_3))) -> one_one(nat) = zero_zero(nat)) -> hAPP(fun(X_a,bool),nat,finite_card(X_a),A_3) = zero_zero(nat)))) # label(fact_1830_card_Oneutral) # label(axiom) # label(non_clause).  [assumption].
7.57/7.62	3275 (all N_1 hAPP(nat,fun(nat,bool),ord_atMost(nat),N_1) = hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),zero_zero(nat)),N_1)) # label(fact_4948_atLeast0AtMost) # label(axiom) # label(non_clause).  [assumption].
7.57/7.62	3276 (all N_1 all P_1 (-hBOOL(hAPP(nat,bool,P_1,zero_zero(nat))) -> (hBOOL(hAPP(nat,bool,P_1,N_1)) -> (exists K_1 (hBOOL(hAPP(nat,bool,P_1,K_1)) & (all I_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),K_1)) -> -hBOOL(hAPP(nat,bool,P_1,I_2)))) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_1),N_1))))))) # label(fact_859_ex__least__nat__le) # label(axiom) # label(non_clause).  [assumption].
7.57/7.62	3277 (all M all N (hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N) = M -> N = zero_zero(nat))) # label(fact_544_add__eq__self__zero) # label(axiom) # label(non_clause).  [assumption].
7.57/7.62	3278 (all N_1 all K all Ma (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K),Ma)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K),N_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),N_1)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),Ma),K)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),K))))))) # label(fact_687_less__diff__iff) # label(axiom) # label(non_clause).  [assumption].
7.57/7.62	3279 (all M all N all Z_1 hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,semiring_1_of_nat(int),M)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,semiring_1_of_nat(int),N)),Z_1)) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N))),Z_1)) # label(fact_1313_zadd__int__left) # label(axiom) # label(non_clause).  [assumption].
7.57/7.62	3280 (all N all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X),one_one(real))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,inverse_inverse(real),hAPP(nat,real,real_1(nat),hAPP(nat,nat,fact_fact(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),one_one(real)),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),N))))))) # label(fact_2502_Ln_Oaux1) # label(axiom) # label(non_clause).  [assumption].
7.57/7.62	3281 (all F all X_1 all L (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),F),X_1),L)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),L),zero_zero(real))) -> (exists D_3 ((all H_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),H_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),H_1),D_3)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,F,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X_1),H_1))),hAPP(real,real,F,X_1)))))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),D_3))))))) # label(fact_2664_DERIV__neg__dec__right) # label(axiom) # label(non_clause).  [assumption].
7.57/7.62	3282 (all Y all X all A_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X),Y)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),powr,X),A_1)),hAPP(real,real,hAPP(real,fun(real,real),powr,Y),A_1))))))) # label(fact_3375_powr__mono2) # label(axiom) # label(non_clause).  [assumption].
7.57/7.62	3283 (all Q_3 all B all R_4 all C (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),C)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),R_4)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),R_4),zero_zero(int))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),C)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),Q_3),C))),R_4))))))) # label(fact_1058_zmult2__lemma__aux1) # label(axiom) # label(non_clause).  [assumption].
7.57/7.62	3284 (all N all M (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N),M)) -> hAPP(nat,real,real_1(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N)) = hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(nat,real,real_1(nat),M)),hAPP(nat,real,real_1(nat),N)))) # label(fact_2327_real__of__nat__diff) # label(axiom) # label(non_clause).  [assumption].
7.57/7.62	3285 (all N all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,real_1(int),N)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(int,real,real_1(int),N)),one_one(real)))) -> hAPP(real,int,archimedean_ceiling(real),X) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),N),one_one(int))))) # label(fact_3318_ceiling__eq2) # label(axiom) # label(non_clause).  [assumption].
7.57/7.62	3286 (all X all Y all Z_1 hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),X),Y)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),X),Z_1)) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),X),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Y),Z_1))) # label(fact_31_zpower__zadd__distrib) # label(axiom) # label(non_clause).  [assumption].
7.57/7.62	3287 (all A_1 all B ((hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_1),B) = zero_zero(int) -> zero_zero(int) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_1),hAPP(int,int,uminus_uminus(int),B))) & (zero_zero(int) != hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_1),B) -> hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_1),hAPP(int,int,uminus_uminus(int),B)) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_1),B)),B)))) # label(fact_2170_zmod__zminus2__eq__if) # label(axiom) # label(non_clause).  [assumption].
7.57/7.62	3288 (all B all A_1 all A_6 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A_1),A_6)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_1),B)),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_6),B)))))) # label(fact_1015_zdiv__mono1) # label(axiom) # label(non_clause).  [assumption].
7.57/7.62	3289 (all X_b all X_c all X_a all F1 all A_2 all B_1 hAPP(X_c,X_a,hAPP(X_b,fun(X_c,X_a),F1,A_2),B_1) = hAPP(product_prod(X_b,X_c),X_a,hAPP(fun(X_b,fun(X_c,X_a)),fun(product_prod(X_b,X_c),X_a),product_prod_case(X_b,X_c,X_a),F1),hAPP(X_c,product_prod(X_b,X_c),hAPP(X_b,fun(X_c,product_prod(X_b,X_c)),product_Pair(X_b,X_c),A_2),B_1))) # label(fact_3992_Product__Type_Oprod_Osimps_I2_J) # label(axiom) # label(non_clause).  [assumption].
7.57/7.62	3290 (all X_a (linordered_idom(X_a) -> (all X ti(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,sgn_sgn(X_a),X)),hAPP(X_a,X_a,abs_abs(X_a),X))))) # label(fact_2215_mult__sgn__abs) # label(axiom) # label(non_clause).  [assumption].
7.57/7.62	3291 (all X_a (real_normed_vector(X_a) -> (all K all Sa all F (hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),F)) -> (ti(X_a,Sa) = hAPP(fun(nat,X_a),X_a,suminf(X_a),F) -> hAPP(fun(nat,X_a),X_a,suminf(X_a),hAPP(fun(nat,nat),fun(nat,X_a),hAPP(fun(nat,X_a),fun(fun(nat,nat),fun(nat,X_a)),combb(nat,X_a,nat),F),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),K))) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),Sa),hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),K)))))))) # label(fact_4168_suminf__minus__initial__segment) # label(axiom) # label(non_clause).  [assumption].
7.57/7.62	3292 (all Diff all F all N_1 all H (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),H)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)) -> (F = hAPP(nat,fun(real,real),Diff,zero_zero(nat)) -> ((all M_2 all T_4 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_2),N_1)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),T_4)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),T_4),H)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(nat,fun(real,real),Diff,M_2)),T_4),hAPP(real,real,hAPP(nat,fun(real,real),Diff,hAPP(nat,nat,suc,M_2)),T_4))))) -> (exists T_4 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),T_4)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),T_4),H)) & hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),inverse_divide(real)),hAPP(real,fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(real,fun(nat,real)),combc(nat,real,real),Diff),zero_zero(real)))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),fact_fact(nat))))),hAPP(real,fun(nat,real),power_power(real),H))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),N_1))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(nat,fun(real,real),Diff,N_1),T_4)),hAPP(nat,real,real_1(nat),hAPP(nat,nat,fact_fact(nat),N_1)))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),H),N_1))) = hAPP(real,real,F,H)))))))) # label(fact_4284_Maclaurin) # label(axiom) # label(non_clause).  [assumption].
7.57/7.62	3293 (all M hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,suc,hAPP(nat,nat,suc,M))),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),M),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) # label(fact_1433_div2__Suc__Suc) # label(axiom) # label(non_clause).  [assumption].
7.57/7.62	3294 (all R_4 all A_1 all N hAPP(real,complex,hAPP(real,fun(real,complex),rcis,hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),R_4),N)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,real_1(nat),N)),A_1)) = hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),hAPP(real,complex,hAPP(real,fun(real,complex),rcis,R_4),A_1)),N)) # label(fact_3158_DeMoivre2) # label(axiom) # label(non_clause).  [assumption].
7.57/7.62	3295 (all X_a finite_finite_1(X_a) = ti(fun(fun(X_a,bool),bool),finite_finite_1(X_a))) # label(tsy_c_Finite__Set_Ofinite_res) # label(axiom) # label(non_clause).  [assumption].
7.57/7.62	3296 (all N hAPP(real,int,archimedean_ceiling(real),hAPP(int,real,real_1(int),N)) = ti(int,N)) # label(fact_3340_ceiling__real__of__int) # label(axiom) # label(non_clause).  [assumption].
7.57/7.62	3297 (all X_a (real_normed_algebra(X_a) -> (all C_1 all F all A_2 (hBOOL(hAPP(X_a,bool,hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),F),A_2)) -> hBOOL(hAPP(X_a,bool,hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(X_a,X_a),fun(fun(nat,X_a),fun(nat,X_a)),combb(X_a,X_a,nat),hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1)),F)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1),A_2))))))) # label(fact_4079_sums__mult) # label(axiom) # label(non_clause).  [assumption].
7.57/7.62	3298 (all K_4 all M all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_4),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_4),N)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_4),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N))) # label(fact_679_diff__mult__distrib2) # label(axiom) # label(non_clause).  [assumption].
7.57/7.62	3299 (all N_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),N_1)) -> hAPP(int,int,fact_fact(int),N_1) = hAPP(fun(int,bool),int,hAPP(fun(int,int),fun(fun(int,bool),int),big_co302546470etprod(int,int),combi(int)),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastAtMost(int),one_one(int)),N_1)))) # label(fact_4614_fact__altdef__int) # label(axiom) # label(non_clause).  [assumption].
7.57/7.62	3300 (all B all B_5 all A_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_1),zero_zero(int))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B_5)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B_5),B)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_1),B_5)),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_1),B))))))) # label(fact_1017_zdiv__mono2__neg) # label(axiom) # label(non_clause).  [assumption].
7.57/7.62	3301 (all B_5 all Q_5 all R_5 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B_5),Q_5)),R_5)),zero_zero(int))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),R_5)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B_5)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Q_5),zero_zero(int))))))) # label(fact_265_q__neg__lemma) # label(axiom) # label(non_clause).  [assumption].
7.57/7.62	3302 (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),Rx)),Ly) = 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)))) # label(fact_216_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J) # label(axiom) # label(non_clause).  [assumption].
7.57/7.62	3303 (all X_c all X_b all X_a all C_1 all X_1 all P_4 ((all A_4 all B_4 (ti(product_prod(X_a,X_b),P_4) = hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),A_4),B_4) -> hBOOL(hAPP(X_c,bool,hAPP(X_b,fun(X_c,bool),hAPP(X_a,fun(X_b,fun(X_c,bool)),C_1,A_4),B_4),X_1)))) -> hBOOL(hAPP(X_c,bool,hAPP(product_prod(X_a,X_b),fun(X_c,bool),hAPP(fun(X_a,fun(X_b,fun(X_c,bool))),fun(product_prod(X_a,X_b),fun(X_c,bool)),product_prod_case(X_a,X_b,fun(X_c,bool)),C_1),P_4),X_1)))) # label(fact_4060_splitI2_H) # label(axiom) # label(non_clause).  [assumption].
7.57/7.62	3304 (all Y all X all A_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),Y)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),powr,X),A_1)),hAPP(real,real,hAPP(real,fun(real,real),powr,Y),A_1))))))) # label(fact_3348_powr__less__mono2) # label(axiom) # label(non_clause).  [assumption].
7.57/7.62	3305 (all B all A_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A_1)) -> hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),B),A_1))) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),B))),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),A_1)))) # label(fact_904_pos__zmod__mult__2) # label(axiom) # label(non_clause).  [assumption].
7.57/7.62	3306 (all X_a (comm_semiring_1(X_a) -> (all A_1 zero_zero(X_a) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),zero_zero(X_a))))) # label(fact_236_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J) # label(axiom) # label(non_clause).  [assumption].
7.57/7.62	3307 (all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Y)) -> (exists X_2 Y = hAPP(real,real,exp(real),X_2)))) # label(fact_2718_exp__total) # label(axiom) # label(non_clause).  [assumption].
7.57/7.62	3308 (all X_a (ordered_ab_group_add(X_a) -> (all A_2 all B_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),A_2)),B_1)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),B_1)),A_2)))))) # label(fact_2027_minus__le__iff) # label(axiom) # label(non_clause).  [assumption].
7.57/7.62	3309 (all X (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X),zero_zero(int))) -> (exists N_2 ti(int,X) = hAPP(int,int,uminus_uminus(int),hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,N_2)))))) # label(fact_2186_negD) # label(axiom) # label(non_clause).  [assumption].
7.57/7.62	3310 (all X_b all X_a (real_normed_field(X_a) & banach(X_b) -> (all G all F all K (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),K)) -> (hBOOL(hAPP(fun(nat,real),bool,summable(real),F)) -> ((all H_1 all N_2 (ti(X_a,H_1) != zero_zero(X_a) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,norm_norm(X_a),H_1)),K)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_b,real,norm_norm(X_b),hAPP(nat,X_b,hAPP(X_a,fun(nat,X_b),G,H_1),N_2))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,F,N_2)),hAPP(X_a,real,norm_norm(X_a),H_1))))))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(fun(X_a,fun(nat,X_b)),fun(X_a,X_b),hAPP(fun(fun(nat,X_b),X_b),fun(fun(X_a,fun(nat,X_b)),fun(X_a,X_b)),combb(fun(nat,X_b),X_b,X_a),suminf(X_b)),G)),zero_zero(X_b)),hAPP(X_a,filter(X_a),at(X_a),zero_zero(X_a)))))))))) # label(fact_4625_lemma__termdiff5) # label(axiom) # label(non_clause).  [assumption].
7.57/7.62	3311 (all X_a (archim1804426504_field(X_a) -> (all X exists Z_2 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),hAPP(int,X_a,ring_1_of_int(X_a),Z_2)))))) # label(fact_3626_ex__le__of__int) # label(axiom) # label(non_clause).  [assumption].
7.57/7.62	3312 (all I all P_1 all K (hBOOL(hAPP(nat,bool,P_1,K)) -> ((all N_2 (hBOOL(hAPP(nat,bool,P_1,hAPP(nat,nat,suc,N_2))) -> hBOOL(hAPP(nat,bool,P_1,N_2)))) -> hBOOL(hAPP(nat,bool,P_1,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),K),I)))))) # label(fact_1522_zero__induct__lemma) # label(axiom) # label(non_clause).  [assumption].
7.57/7.62	3313 (all X_a (comm_monoid_add(X_a) & comm_monoid_mult(X_a) -> (all F all A_3 hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co302546470etprod(nat,X_a),F),A_3) = hAPP(fun(int,bool),X_a,hAPP(fun(int,X_a),fun(fun(int,bool),X_a),big_co302546470etprod(int,X_a),hAPP(fun(int,nat),fun(int,X_a),hAPP(fun(nat,X_a),fun(fun(int,nat),fun(int,X_a)),combb(nat,X_a,int),F),nat_1)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),A_3))))) # label(fact_3944_transfer__nat__int__sum__prod_I2_J) # label(axiom) # label(non_clause).  [assumption].
7.57/7.62	3314 (all X_b all X_a (metric_space(X_b) & metric_space(X_a) -> (all F all L_2 all A_2 ((all R_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),R_2)) -> (exists S_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),S_1)) & (all X_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),X_2),A_2)),S_1)) & ti(X_a,X_2) != ti(X_a,A_2) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_b,real,hAPP(X_b,fun(X_b,real),dist_dist(X_b),hAPP(X_a,X_b,F,X_2)),L_2)),R_2)))))))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),L_2),hAPP(X_a,filter(X_a),at(X_a),A_2))))))) # label(fact_4764_metric__LIM__I) # label(axiom) # label(non_clause).  [assumption].
7.57/7.62	3315 (all X_a (linord1117847801e_zero(X_a) -> (all A_2 all B_1 all C_1 ((hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),C_1)),B_1))) & (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),C_1)))) & (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),zero_zero(X_a))))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),B_1),C_1))))))) # label(fact_1708_less__divide__eq) # label(axiom) # label(non_clause).  [assumption].
7.57/7.62	3316 (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_1570_order__less__imp__not__eq2) # label(axiom) # label(non_clause).  [assumption].
7.57/7.62	3317 (all Ta all B_2 all D_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D_2)) -> (all X_2 ((all Xa (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xa),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastAtMost(int),one_one(int)),D_2))) -> (all Xb (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xb),B_2)) -> ti(int,X_2) != hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Xb),Xa))))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X_2),Ta)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X_2),D_2)),Ta))))))) # label(fact_4636_bset_I5_J) # label(axiom) # label(non_clause).  [assumption].
7.57/7.62	3318 (all X_a (comm_monoid_add(X_a) -> (all F all N_1 hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),hAPP(fun(nat,fun(nat,bool)),fun(nat,X_a),hAPP(fun(nat,fun(fun(nat,bool),X_a)),fun(fun(nat,fun(nat,bool)),fun(nat,X_a)),combs(nat,fun(nat,bool),X_a),hAPP(fun(nat,fun(nat,X_a)),fun(nat,fun(fun(nat,bool),X_a)),hAPP(fun(fun(nat,X_a),fun(fun(nat,bool),X_a)),fun(fun(nat,fun(nat,X_a)),fun(nat,fun(fun(nat,bool),X_a))),combb(fun(nat,X_a),fun(fun(nat,bool),X_a),nat),big_co1399186613setsum(nat,X_a)),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,X_a)),hAPP(fun(fun(nat,nat),fun(nat,X_a)),fun(fun(nat,fun(nat,nat)),fun(nat,fun(nat,X_a))),combb(fun(nat,nat),fun(nat,X_a),nat),hAPP(fun(nat,fun(nat,X_a)),fun(fun(nat,nat),fun(nat,X_a)),combs(nat,nat,X_a),F)),minus_minus(nat)))),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),zero_zero(nat)))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),N_1)) = hAPP(fun(product_prod(nat,nat),bool),X_a,hAPP(fun(product_prod(nat,nat),X_a),fun(fun(product_prod(nat,nat),bool),X_a),big_co1399186613setsum(product_prod(nat,nat),X_a),hAPP(fun(nat,fun(nat,X_a)),fun(product_prod(nat,nat),X_a),product_prod_case(nat,nat,X_a),F)),hAPP(fun(product_prod(nat,nat),bool),fun(product_prod(nat,nat),bool),collect(product_prod(nat,nat)),hAPP(fun(nat,fun(nat,bool)),fun(product_prod(nat,nat),bool),product_prod_case(nat,nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),hAPP(fun(nat,fun(nat,fun(nat,bool))),fun(nat,fun(nat,fun(nat,bool))),combc(nat,nat,fun(nat,bool)),hAPP(fun(nat,fun(nat,fun(nat,bool))),fun(nat,fun(nat,fun(nat,bool))),hAPP(fun(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool))),fun(fun(nat,fun(nat,fun(nat,bool))),fun(nat,fun(nat,fun(nat,bool)))),combb(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),nat),combc(nat,nat,bool)),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,fun(nat,bool))),hAPP(fun(fun(nat,nat),fun(nat,fun(nat,bool))),fun(fun(nat,fun(nat,nat)),fun(nat,fun(nat,fun(nat,bool)))),combb(fun(nat,nat),fun(nat,fun(nat,bool)),nat),hAPP(fun(nat,fun(nat,bool)),fun(fun(nat,nat),fun(nat,fun(nat,bool))),combb(nat,fun(nat,bool),nat),ord_less(nat))),plus_plus(nat)))),N_1))))))) # label(fact_4622_setsum__triangle__reindex) # label(axiom) # label(non_clause).  [assumption].
7.57/7.62	3319 (all K_4 all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),K_4),hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),M),N))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),K_4),M)))) # label(fact_3232_dvd__gcd__D1__nat) # label(axiom) # label(non_clause).  [assumption].
7.57/7.62	3320 (all X_a (t2_space(X_a) & comm_monoid_add(X_a) -> (all F all N_1 ((all M_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_1),M_2)) -> zero_zero(X_a) = hAPP(nat,X_a,F,M_2))) -> hBOOL(hAPP(X_a,bool,hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),F),hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),N_1)))))))) # label(fact_4291_series__zero) # label(axiom) # label(non_clause).  [assumption].
7.57/7.62	3321 (all N all M all K_4 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K_4)) -> (hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_4),N) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_4),M) -> M = N))) # label(fact_873_mult__left__cancel) # label(axiom) # label(non_clause).  [assumption].
7.57/7.62	3322 (all N hAPP(nat,real,real_1(nat),hAPP(nat,nat,suc,N)) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,real_1(nat),N)),one_one(real))) # label(fact_2324_real__of__nat__Suc) # label(axiom) # label(non_clause).  [assumption].
7.57/7.62	3323 (all X ((zero_zero(real) != X -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> one_one(real) = hAPP(real,real,sgn_sgn(real),X)) & (-hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> hAPP(real,real,uminus_uminus(real),one_one(real)) = hAPP(real,real,sgn_sgn(real),X))) & (X = zero_zero(real) -> hAPP(real,real,sgn_sgn(real),X) = zero_zero(real)))) # label(fact_2227_real__sgn__def) # label(axiom) # label(non_clause).  [assumption].
7.57/7.62	3324 (all K_4 all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),K_4),hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),M),N))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),K_4),N)))) # label(fact_3231_dvd__gcd__D2__nat) # label(axiom) # label(non_clause).  [assumption].
7.57/7.62	3325 (all X_a (sgn_div_norm(X_a) -> ti(fun(real,fun(X_a,X_a)),scaleR_scaleR(X_a)) = scaleR_scaleR(X_a))) # label(tsy_c_RealVector_OscaleR__class_OscaleR_0_res) # label(axiom) # label(non_clause).  [assumption].
7.57/7.62	3326 (all I_1 all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,nat_1,I_1)),N) = hAPP(nat,nat,hAPP(int,fun(nat,nat),nat_aux,I_1),N)) # label(fact_1170_nat__aux__def) # label(axiom) # label(non_clause).  [assumption].
7.57/7.62	3327 (all Z (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),hAPP(int,nat,nat_1,Z))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),Z)))) # label(fact_1431_one__less__nat__eq) # label(axiom) # label(non_clause).  [assumption].
7.57/7.62	3328 (all X (X != zero_zero(real) -> hAPP(real,real,arctan,hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),one_one(real)),X)) = hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,sgn_sgn(real),X)),pi)),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(real,real,arctan,X)))) # label(fact_2187_arctan__inverse) # label(axiom) # label(non_clause).  [assumption].
7.57/7.62	3329 (all X_a (semiring_div(X_a) -> (all A_1 all C all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),A_1),B) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),B))),B)))) # label(fact_977_mod__mult__self1) # label(axiom) # label(non_clause).  [assumption].
7.57/7.62	3330 (all X_b all X_a (topological_space(X_b) & real_normed_vector(X_a) -> (all F all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(fun(X_a,X_a),fun(X_a,X_b),hAPP(fun(X_a,X_b),fun(fun(X_a,X_a),fun(X_a,X_b)),combb(X_a,X_b,X_a),F),hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2))),hAPP(X_a,X_b,F,A_2)),hAPP(X_a,filter(X_a),at(X_a),zero_zero(X_a)))) <-> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),hAPP(X_a,X_b,F,A_2)),hAPP(X_a,filter(X_a),at(X_a),A_2))))))) # label(fact_4578_LIM__isCont__iff) # label(axiom) # label(non_clause).  [assumption].
7.57/7.62	3331 (all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X_1)) <-> hAPP(real,real,exp(real),hAPP(real,real,ln,X_1)) = X_1)) # label(fact_2600_exp__ln__iff) # label(axiom) # label(non_clause).  [assumption].
7.57/7.62	3332 (all X_a (real_normed_vector(X_a) -> (all A_1 all A_6 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(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_1),B)),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_6),B)) = hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A_1),A_6)),B)))) # label(fact_4712_scaleR_Oadd__left) # label(axiom) # label(non_clause).  [assumption].
7.57/7.62	3333 (all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_1),one_one(real))) -> hBOOL(hAPP(fun(nat,real),bool,monoseq(real),hAPP(real,fun(nat,real),power_power(real),X_1)))))) # label(fact_3924_monoseq__realpow) # label(axiom) # label(non_clause).  [assumption].
7.57/7.62	3334 (all X_a (plus(X_a) & dvd(X_a) & linorder(X_a) -> ti(fun(X_a,fun(X_a,X_a)),plus_plus(X_a)) = plus_plus(X_a))) # label(tsy_c_Groups_Oplus__class_Oplus_0_res) # label(axiom) # label(non_clause).  [assumption].
7.57/7.62	3335 (all A_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),A_1)) -> (exists P_6 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),P_6),A_1)) & hBOOL(hAPP(int,bool,zprime,P_6)))))) # label(fact_473_zprime__factor__exists) # label(axiom) # label(non_clause).  [assumption].
7.57/7.62	3336 (all X hAPP(real,real,uminus_uminus(real),hAPP(real,real,sin,X)) = hAPP(real,real,sin,hAPP(real,real,uminus_uminus(real),X))) # label(fact_2290_sin__minus) # label(axiom) # label(non_clause).  [assumption].
7.57/7.62	3337 (all X_a (real_normed_vector(X_a) & real_algebra_1(X_a) -> (all X all Y hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(real,X_a,of_real(X_a),X)),hAPP(real,X_a,of_real(X_a),Y)) = hAPP(real,X_a,of_real(X_a),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),Y))))) # label(fact_2787_of__real_Oadd) # label(axiom) # label(non_clause).  [assumption].
7.57/7.62	3338 (all R_4 all S_3 hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),R_4),hAPP(real,real,uminus_uminus(real),S_3)) = hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),R_4),S_3)) # label(fact_2091_real__diff__def) # label(axiom) # label(non_clause).  [assumption].
7.57/7.62	3339 (all X_a all X_c all X_b all Z all C_1 all A_2 all B_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Z),hAPP(X_c,fun(X_a,bool),hAPP(X_b,fun(X_c,fun(X_a,bool)),C_1,A_2),B_1))) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Z),hAPP(product_prod(X_b,X_c),fun(X_a,bool),hAPP(fun(X_b,fun(X_c,fun(X_a,bool))),fun(product_prod(X_b,X_c),fun(X_a,bool)),product_prod_case(X_b,X_c,fun(X_a,bool)),C_1),hAPP(X_c,product_prod(X_b,X_c),hAPP(X_b,fun(X_c,product_prod(X_b,X_c)),product_Pair(X_b,X_c),A_2),B_1)))))) # label(fact_4038_mem__splitI) # label(axiom) # label(non_clause).  [assumption].
7.57/7.63	3340 (all A_1 (zero_zero(int) != ti(int,A_1) -> one_one(int) = hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_1),A_1))) # label(fact_984_zdiv__self) # label(axiom) # label(non_clause).  [assumption].
7.57/7.63	3341 (all X_b all X_a (real_normed_vector(X_b) & topological_space(X_a) -> (all F all A_2 (hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,X_b),fun(X_a,bool),isCont(X_a,X_b),F),A_2)) -> (zero_zero(X_b) != hAPP(X_a,X_b,F,A_2) -> hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,X_b),fun(X_a,bool),isCont(X_a,X_b),hAPP(fun(X_a,X_b),fun(X_a,X_b),hAPP(fun(X_b,X_b),fun(fun(X_a,X_b),fun(X_a,X_b)),combb(X_b,X_b,X_a),sgn_sgn(X_b)),F)),A_2))))))) # label(fact_4911_isCont__sgn) # label(axiom) # label(non_clause).  [assumption].
7.57/7.63	3342 (all X_a (comm_monoid_add(X_a) -> (all F all N_1 all Ma ((hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,N_1)),Ma)) -> zero_zero(X_a) = hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),Ma),hAPP(nat,nat,suc,N_1)))) & (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,N_1)),Ma)) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),Ma),N_1))),hAPP(nat,X_a,F,hAPP(nat,nat,suc,N_1))) = hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),Ma),hAPP(nat,nat,suc,N_1)))))))) # label(fact_4603_setsum__cl__ivl__Suc) # label(axiom) # label(non_clause).  [assumption].
7.57/7.63	3343 (all C_1 all D_1 all A_2 all B_1 all Ma (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_2),B_1),Ma)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,C_1),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),D_1),B_1)),Ma)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,C_1),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),D_1),A_2)),Ma))))) # label(fact_357_zcong__zmult__prop2) # label(axiom) # label(non_clause).  [assumption].
7.57/7.63	3344 (all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),one_one(nat))),N) = one_one(nat)) # label(fact_3266_coprime__plus__one__nat) # label(axiom) # label(non_clause).  [assumption].
7.57/7.63	3345 (all Z_1 ti(int,Z_1) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Z_1),zero_zero(int))) # label(fact_134_zadd__0__right) # label(axiom) # label(non_clause).  [assumption].
7.57/7.63	3346 (all X_a (divisi14063676e_zero(X_a) -> (all A_1 all B (hAPP(X_a,X_a,inverse_inverse(X_a),B) = hAPP(X_a,X_a,inverse_inverse(X_a),A_1) -> ti(X_a,B) = ti(X_a,A_1))))) # label(fact_2523_inverse__eq__imp__eq) # label(axiom) # label(non_clause).  [assumption].
7.57/7.63	3347 (all X_1 all Y_1 (hBOOL(hAPP(int,bool,even_odd_even(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X_1),Y_1))) <-> hBOOL(hAPP(int,bool,even_odd_even(int),Y_1)) | hBOOL(hAPP(int,bool,even_odd_even(int),X_1)))) # label(fact_1257_Parity_Oeven__product) # label(axiom) # label(non_clause).  [assumption].
7.57/7.63	3348 (all A_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A_1)) -> (A_1 != one_one(real) -> hAPP(real,real,hAPP(real,fun(real,real),log,A_1),A_1) = one_one(real)))) # label(fact_2642_log__eq__one) # label(axiom) # label(non_clause).  [assumption].
7.57/7.63	3349 (all R_4 all X hAPP(real,real,hAPP(real,fun(real,real),times_times(real),R_4),hAPP(complex,real,im,X)) = hAPP(complex,real,im,hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),R_4),X))) # label(fact_4681_complex__Im__scaleR) # label(axiom) # label(non_clause).  [assumption].
7.57/7.63	3350 (all X_a all X_b all X_c all X_d all F all G hAPP(fun(product_prod(X_a,X_b),X_b),fun(product_prod(X_a,X_b),X_c),hAPP(fun(product_prod(X_a,X_b),fun(X_b,X_c)),fun(fun(product_prod(X_a,X_b),X_b),fun(product_prod(X_a,X_b),X_c)),combs(product_prod(X_a,X_b),X_b,X_c),hAPP(fun(product_prod(X_a,X_b),X_d),fun(product_prod(X_a,X_b),fun(X_b,X_c)),hAPP(fun(X_d,fun(X_b,X_c)),fun(fun(product_prod(X_a,X_b),X_d),fun(product_prod(X_a,X_b),fun(X_b,X_c))),combb(X_d,fun(X_b,X_c),product_prod(X_a,X_b)),F),hAPP(fun(product_prod(X_a,X_b),X_a),fun(product_prod(X_a,X_b),X_d),hAPP(fun(X_a,X_d),fun(fun(product_prod(X_a,X_b),X_a),fun(product_prod(X_a,X_b),X_d)),combb(X_a,X_d,product_prod(X_a,X_b)),G),product_fst(X_a,X_b)))),product_snd(X_a,X_b)) = hAPP(fun(X_a,fun(X_b,X_c)),fun(product_prod(X_a,X_b),X_c),product_prod_case(X_a,X_b,X_c),hAPP(fun(X_a,X_d),fun(X_a,fun(X_b,X_c)),hAPP(fun(X_d,fun(X_b,X_c)),fun(fun(X_a,X_d),fun(X_a,fun(X_b,X_c))),combb(X_d,fun(X_b,X_c),X_a),F),G))) # label(fact_4015_split__comp__eq) # label(axiom) # label(non_clause).  [assumption].
7.57/7.63	3351 (all X_a (number_semiring(X_a) -> (all Z_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Z_1),Z_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,bit0,hAPP(int,int,bit1,pls)))),Z_1)))) # label(fact_139_semiring__mult__2) # label(axiom) # label(non_clause).  [assumption].
7.57/7.63	3352 (all A_1 all B hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),B),A_1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),A_1),B)) # label(fact_3220_gcd__commute__nat) # label(axiom) # label(non_clause).  [assumption].
7.57/7.63	3353 (all P_4 (hBOOL(hAPP(int,bool,zprime,P_4)) -> hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),wset,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),P_4),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),P_4) = hAPP(int,fun(int,bool),d22set,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),P_4),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))) # label(fact_858_d22set__eq__wset) # label(axiom) # label(non_clause).  [assumption].
7.57/7.63	3354 (all K_4 all L_4 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_4),L_4)) -> (exists N_2 L_4 = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_4),N_2)))) # label(fact_2733_le__Suc__ex) # label(axiom) # label(non_clause).  [assumption].
7.57/7.63	3355 (all X_a (dvd(X_a) & linorder(X_a) & plus(X_a) -> (all D_1 all Sa exists Z_2 all X_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z_2),X_2)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),D_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X_2),Sa))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),D_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X_2),Sa)))))))) # label(fact_868_pinf_I9_J) # label(axiom) # label(non_clause).  [assumption].
7.57/7.63	3356 (all X_a (real_algebra_1(X_a) -> (all X_1 all Y_1 (hAPP(real,X_a,of_real(X_a),Y_1) = hAPP(real,X_a,of_real(X_a),X_1) <-> Y_1 = X_1)))) # label(fact_2777_of__real__eq__iff) # label(axiom) # label(non_clause).  [assumption].
7.57/7.63	3357 (all M all N (ti(int,N) != zero_zero(int) -> hAPP(int,rat,hAPP(int,fun(int,rat),fract,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),M),N)),N) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(int,rat,hAPP(int,fun(int,rat),fract,M),N)),one_one(rat)))) # label(fact_3789_Fract__add__one) # label(axiom) # label(non_clause).  [assumption].
7.57/7.63	3358 (all X_b all X_a (topological_space(X_a) & real_normed_algebra(X_b) & power(X_b) -> (all N_1 all F all L all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),L),hAPP(X_a,filter(X_a),at(X_a),A_2))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(nat,fun(X_a,X_b),hAPP(fun(X_a,fun(nat,X_b)),fun(nat,fun(X_a,X_b)),combc(X_a,nat,X_b),hAPP(fun(X_a,X_b),fun(X_a,fun(nat,X_b)),hAPP(fun(X_b,fun(nat,X_b)),fun(fun(X_a,X_b),fun(X_a,fun(nat,X_b))),combb(X_b,fun(nat,X_b),X_a),power_power(X_b)),F)),N_1)),hAPP(nat,X_b,hAPP(X_b,fun(nat,X_b),power_power(X_b),L),N_1)),hAPP(X_a,filter(X_a),at(X_a),A_2))))))) # label(fact_4556_LIM__power) # label(axiom) # label(non_clause).  [assumption].
7.57/7.63	3359 (all X_a all X_b (topological_space(X_b) -> (all F all L all A_3 all A_7 (hBOOL(hAPP(filter(X_a),bool,hAPP(filter(X_a),fun(filter(X_a),bool),ord_less_eq(filter(X_a)),A_3),A_7)) -> (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),L),A_7)) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),L),A_3))))))) # label(fact_4430_tendsto__mono) # label(axiom) # label(non_clause).  [assumption].
7.57/7.63	3360 (all T_2 all T_1 (ord(T_1) -> ord(fun(T_2,T_1)))) # label(arity_fun___Orderings_Oord) # label(axiom) # label(non_clause).  [assumption].
7.57/7.63	3361 (all X_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X_1)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(nat,fun(real,real),root,N_1)),X_1),hAPP(real,real,inverse_inverse(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,real_1(nat),N_1)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,hAPP(nat,fun(real,real),root,N_1),X_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),hAPP(nat,nat,suc,zero_zero(nat))))))))))) # label(fact_2717_DERIV__real__root) # label(axiom) # label(non_clause).  [assumption].
7.57/7.63	3362 (all D_1 all F all X_1 all L (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),F),X_1),L)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),D_1)) -> ((all Y_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),X_1),Y_2))),D_1)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,F,Y_2)),hAPP(real,real,F,X_1))))) -> zero_zero(real) = L)))) # label(fact_2660_DERIV__local__max) # label(axiom) # label(non_clause).  [assumption].
7.57/7.63	3363 (all D all A_1 all B (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,D),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A_1),B))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,D),B)))) # label(fact_2848_coprime__lmul2) # label(axiom) # label(non_clause).  [assumption].
7.57/7.63	3364 (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),hAPP(X_a,X_a,uminus_uminus(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,pred,W))))) # label(fact_2910_number__of__pred) # label(axiom) # label(non_clause).  [assumption].
7.57/7.63	3365 (all M all N all K_4 ((zero_zero(nat) = K_4 -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_4),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_4),N)) = zero_zero(nat)) & (zero_zero(nat) != K_4 -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_4),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_4),N)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),M),N)))) # label(fact_1099_nat__mult__div__cancel__disj) # label(axiom) # label(non_clause).  [assumption].
7.57/7.63	3366 (all X all Y hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),X)),hAPP(real,real,sqrt,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),Y),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))))) # label(fact_1908_real__sqrt__ge__abs1) # label(axiom) # label(non_clause).  [assumption].
7.57/7.63	3367 (all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,number_number_of(real),min_1)),Y)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),Y),one_one(real))) -> hAPP(real,real,sin,hAPP(real,real,arcsin,Y)) = Y))) # label(fact_2361_sin__arcsin) # label(axiom) # label(non_clause).  [assumption].
7.57/7.63	3368 (all Y all X all P_5 (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,X),zero_zero(int)),P_5)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),Y),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),X),P_5)) -> -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),P_5),Y))))) # label(fact_272_Euler_Oaux____1) # label(axiom) # label(non_clause).  [assumption].
7.57/7.63	3369 (all X_a (archim1727834104eiling(X_a) -> archim2085082626_floor(X_a) = ti(fun(X_a,int),archim2085082626_floor(X_a)))) # label(tsy_c_Archimedean__Field_Ofloor__ceiling__class_Ofloor_res) # label(axiom) # label(non_clause).  [assumption].
7.57/7.63	3370 (all W all Z1 all 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)) = 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))) # label(fact_482_zdiff__zmult__distrib2) # label(axiom) # label(non_clause).  [assumption].
7.57/7.63	3371 (all X_a (linordered_idom(X_a) -> (all A_1 all B hAPP(X_a,X_a,sgn_sgn(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,sgn_sgn(X_a),A_1)),hAPP(X_a,X_a,sgn_sgn(X_a),B))))) # label(fact_2205_sgn__times) # label(axiom) # label(non_clause).  [assumption].
7.57/7.63	3372 (all X_a (linord1117847801e_zero(X_a) -> (all B_1 all C_1 all A_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),B_1),C_1)),A_2)) <-> (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C_1)) -> (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),A_2))) & (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),C_1)),B_1)))) & (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),C_1)))))))) # label(fact_1736_divide__le__eq) # label(axiom) # label(non_clause).  [assumption].
7.57/7.63	3373 (all X_a (linorder(X_a) -> (all Y all Z_1 all X hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),Y),Z_1)),X) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),Y),X)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),Z_1),X))))) # label(fact_4938_min__max_Osup__inf__distrib2) # label(axiom) # label(non_clause).  [assumption].
7.57/7.63	3374 (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_824_add__less__le__mono) # label(axiom) # label(non_clause).  [assumption].
7.57/7.63	3375 (all Z_1 all W hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Z_1),W) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),W),Z_1)) # label(fact_23_zmult__commute) # label(axiom) # label(non_clause).  [assumption].
7.57/7.63	3376 (all X_a all X_b all X_c all X_d all X_e all X_1 all P_1 ((all A_4 all B_4 all C_4 all D_3 all E hBOOL(hAPP(product_prod(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,X_e)))),bool,P_1,hAPP(product_prod(X_b,product_prod(X_c,product_prod(X_d,X_e))),product_prod(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,X_e)))),hAPP(X_a,fun(product_prod(X_b,product_prod(X_c,product_prod(X_d,X_e))),product_prod(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,X_e))))),product_Pair(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,X_e)))),A_4),hAPP(product_prod(X_c,product_prod(X_d,X_e)),product_prod(X_b,product_prod(X_c,product_prod(X_d,X_e))),hAPP(X_b,fun(product_prod(X_c,product_prod(X_d,X_e)),product_prod(X_b,product_prod(X_c,product_prod(X_d,X_e)))),product_Pair(X_b,product_prod(X_c,product_prod(X_d,X_e))),B_4),hAPP(product_prod(X_d,X_e),product_prod(X_c,product_prod(X_d,X_e)),hAPP(X_c,fun(product_prod(X_d,X_e),product_prod(X_c,product_prod(X_d,X_e))),product_Pair(X_c,product_prod(X_d,X_e)),C_4),hAPP(X_e,product_prod(X_d,X_e),hAPP(X_d,fun(X_e,product_prod(X_d,X_e)),product_Pair(X_d,X_e),D_3),E))))))) -> hBOOL(hAPP(product_prod(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,X_e)))),bool,P_1,X_1)))) # label(fact_3152_prod__induct5) # label(axiom) # label(non_clause).  [assumption].
7.57/7.63	3377 (all X_a (comm_ring_1(X_a) -> (all X_1 all Y_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),X_1),hAPP(X_a,X_a,uminus_uminus(X_a),Y_1))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),X_1),Y_1)))))) # label(fact_2046_dvd__minus__iff) # label(axiom) # label(non_clause).  [assumption].
7.57/7.63	3378 (all X_a (group_add(X_a) -> (all A_1 all B ti(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,uminus_uminus(X_a),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B))))) # label(fact_2048_minus__add__cancel) # label(axiom) # label(non_clause).  [assumption].
7.57/7.63	3379 (all X_a all X_1 all P_1 all Q_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),P_1),Q_1)) -> (hBOOL(hAPP(X_a,bool,P_1,X_1)) -> hBOOL(hAPP(X_a,bool,Q_1,X_1))))) # label(fact_4336_predicate1D) # label(axiom) # label(non_clause).  [assumption].
7.57/7.63	3380 (all K_4 all I_1 all J_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),I_1),J_2)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),K_4),I_1)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),K_4),J_2))))) # label(fact_38_zadd__left__mono) # label(axiom) # label(non_clause).  [assumption].
7.57/7.63	3381 (all X_1 all Y_1 (hAPP(quickcheck_code_int,int,quickcheck_int_of,Y_1) = hAPP(quickcheck_code_int,int,quickcheck_int_of,X_1) <-> Y_1 = X_1)) # label(fact_3161_code__int_Oint__of__inject) # label(axiom) # label(non_clause).  [assumption].
7.57/7.63	3382 (all X_a all A_3 all B_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_3),B_2)) -> (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),B_2)) -> hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_3))))) # label(fact_1822_finite__subset) # label(axiom) # label(non_clause).  [assumption].
7.57/7.63	3383 (all X_a (linordered_idom(X_a) & number_ring(X_a) -> (all X_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X_1),hAPP(int,int,bit1,pls))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(int,X_a,number_number_of(X_a),X_1)),one_one(X_a))))))) # label(fact_180_less__special_I4_J) # label(axiom) # label(non_clause).  [assumption].
7.57/7.63	3384 (all N_1 hAPP(fun(int,bool),fun(nat,bool),hAPP(fun(int,nat),fun(fun(int,bool),fun(nat,bool)),image(int,nat),nat_1),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastAtMost(int),zero_zero(int)),hAPP(nat,int,semiring_1_of_nat(int),N_1))) = hAPP(nat,fun(nat,bool),ord_atMost(nat),N_1)) # label(fact_4934_SetInterval_Otransfer__nat__int__set__functions_I1_J) # label(axiom) # label(non_clause).  [assumption].
7.57/7.63	3385 (all X_a (semiring_div(X_a) -> (all A_1 all B ti(X_a,A_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),A_1),B)),B)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),A_1),B))))) # label(fact_1074_mod__div__decomp) # label(axiom) # label(non_clause).  [assumption].
7.57/7.63	3386 (all N hAPP(real,int,archim2085082626_floor(real),hAPP(real,real,uminus_uminus(real),hAPP(int,real,real_1(int),N))) = hAPP(int,int,uminus_uminus(int),N)) # label(fact_3373_floor__minus__real__of__int) # label(axiom) # label(non_clause).  [assumption].
7.57/7.63	3387 (all X all A_1 all B hAPP(real,real,hAPP(real,fun(real,real),powr,X),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A_1),B)) = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(real,fun(real,real),powr,X),A_1)),hAPP(real,real,hAPP(real,fun(real,real),powr,X),B))) # label(fact_3358_powr__divide2) # label(axiom) # label(non_clause).  [assumption].
7.57/7.63	3388 (all F (hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),abs_abs(real)),F)),zero_zero(real)),sequentially)) <-> hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),F),zero_zero(real)),sequentially)))) # label(fact_4482_LIMSEQ__rabs__zero) # label(axiom) # label(non_clause).  [assumption].
7.57/7.63	3389 (all X_a (linorder(X_a) -> (all X ti(X_a,X) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),X)))) # label(fact_4802_Min_Oidem) # label(axiom) # label(non_clause).  [assumption].
7.57/7.63	3390 (all X_a (real_normed_field(X_a) -> (all G all E_3 all F all X_1 all D_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),F),X_1),D_2)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),G),X_1),E_3)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),hAPP(fun(X_a,X_a),fun(X_a,X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,X_a),fun(X_a,X_a)),combs(X_a,X_a,X_a),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,X_a),fun(X_a,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),X_a),times_times(X_a)),F)),G)),X_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,F,X_1)),E_3)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),D_2),hAPP(X_a,X_a,G,X_1)))))))))) # label(fact_3818_DERIV__mult_H) # label(axiom) # label(non_clause).  [assumption].
7.57/7.63	3391 (all A_2 all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,real_1(int),A_2)),X_1)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_2),hAPP(real,int,archimedean_ceiling(real),X_1))))) # label(fact_3366_less__ceiling__eq) # label(axiom) # label(non_clause).  [assumption].
7.57/7.63	3392 (all K_4 all M all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_4),hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),M),N)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_4),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_4),N))) # label(fact_3249_gcd__mult__distrib__nat) # label(axiom) # label(non_clause).  [assumption].
7.57/7.63	3393 (all X_a (number_semiring(X_a) -> hAPP(int,X_a,number_number_of(X_a),pls) = zero_zero(X_a))) # label(fact_145_semiring__numeral__0__eq__0) # label(axiom) # label(non_clause).  [assumption].
7.57/7.63	3394 (all X_a (semiring_div(X_a) -> (all A_1 (zero_zero(X_a) != ti(X_a,A_1) -> one_one(X_a) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),A_1),A_1))))) # label(fact_999_div__self) # label(axiom) # label(non_clause).  [assumption].
7.57/7.63	3395 (all N all M all A_1 all B (hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),A_1),B) = one_one(int) -> hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A_1),N)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),B),M)) = one_one(int))) # label(fact_4348_coprime__exp2__int) # label(axiom) # label(non_clause).  [assumption].
7.57/7.63	3396 (all Y all X hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),Y)),hAPP(real,real,sqrt,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),Y),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))))) # label(fact_1909_real__sqrt__ge__abs2) # label(axiom) # label(non_clause).  [assumption].
7.57/7.63	3397 (all X all Y all R_4 hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,X),Y)),hAPP(real,complex,of_real(complex),R_4)) = hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),R_4)),Y)) # label(fact_2810_Complex__add__complex__of__real) # label(axiom) # label(non_clause).  [assumption].
7.57/7.63	3398 (all Y all X (hBOOL(hAPP(int,bool,twoSqu1091635170sum2sq,X)) -> (hBOOL(hAPP(int,bool,twoSqu1091635170sum2sq,Y)) -> hBOOL(hAPP(int,bool,twoSqu1091635170sum2sq,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X),Y)))))) # label(fact_211_is__mult__sum2sq) # label(axiom) # label(non_clause).  [assumption].
7.57/7.63	3399 (all N_1 all X_1 all Diff all F (hAPP(nat,fun(real,real),Diff,zero_zero(nat)) = F & (all M_2 all X_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(nat,fun(real,real),Diff,M_2)),X_2),hAPP(real,real,hAPP(nat,fun(real,real),Diff,hAPP(nat,nat,suc,M_2)),X_2)))) & zero_zero(real) != X_1 & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)) -> (exists T_4 (hAPP(real,real,F,X_1) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),inverse_divide(real)),hAPP(real,fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(real,fun(nat,real)),combc(nat,real,real),Diff),zero_zero(real)))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),fact_fact(nat))))),hAPP(real,fun(nat,real),power_power(real),X_1))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),N_1))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(nat,fun(real,real),Diff,N_1),T_4)),hAPP(nat,real,real_1(nat),hAPP(nat,nat,fact_fact(nat),N_1)))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X_1),N_1))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,abs_abs(real),T_4)),hAPP(real,real,abs_abs(real),X_1))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,abs_abs(real),T_4))))))) # label(fact_4277_Maclaurin__all__lt__objl) # label(axiom) # label(non_clause).  [assumption].
7.57/7.63	3400 (all X_a (linordered_idom(X_a) & number_ring(X_a) -> (all N hAPP(X_a,X_a,abs_abs(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(int,X_a,number_number_of(X_a),min_1)),N)) = one_one(X_a)))) # label(fact_1896_abs__power__minus__one) # label(axiom) # label(non_clause).  [assumption].
7.57/7.63	3401 (all X_a all One all Times all A_2 ti(X_a,One) = hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(nat,X_a)),hAPP(X_a,fun(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(nat,X_a))),power_1(X_a),One),Times),A_2),zero_zero(nat))) # label(fact_2840_power_Opower_Opower__0) # label(axiom) # label(non_clause).  [assumption].
7.57/7.63	3402 (all X_a (linorder(X_a) -> (all X_1 all Y_1 all Z (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),Y_1),Z))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),Y_1)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),Z)))))) # label(fact_4826_min__max_Ole__inf__iff) # label(axiom) # label(non_clause).  [assumption].
7.57/7.63	3403 (all A_1 hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,hAPP(real,real,cos,A_1)),hAPP(real,real,sin,A_1)) = hAPP(real,complex,cis,A_1)) # label(fact_3032_cis__def) # label(axiom) # label(non_clause).  [assumption].
7.57/7.63	3404 (all X (hBOOL(hAPP(nat,bool,even_odd_even(nat),X)) -> zero_zero(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),X),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat)))))) # label(fact_2448_even__nat__mod__two__eq__zero) # label(axiom) # label(non_clause).  [assumption].
7.57/7.63	3405 (all X_a (linordered_field(X_a) -> (all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,inverse_inverse(X_a),A_1)),hAPP(X_a,X_a,inverse_inverse(X_a),B))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),A_1))))))) # label(fact_2573_inverse__le__imp__le__neg) # label(axiom) # label(non_clause).  [assumption].
7.57/7.63	3406 (all X all Y hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X),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))) # label(fact_1305_Nat__Transfer_Otransfer__int__nat__functions_I2_J) # label(axiom) # label(non_clause).  [assumption].
7.57/7.63	3407 (all X_a (number_ring(X_a) -> (all X_1 (hBOOL(hAPP(X_a,bool,iszero(X_a),hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X_1),hAPP(int,int,uminus_uminus(int),pls))))) <-> hAPP(int,X_a,number_number_of(X_a),X_1) = zero_zero(X_a))))) # label(fact_2625_eq__special_I3_J) # label(axiom) # label(non_clause).  [assumption].
7.57/7.63	3408 (all A_2 all B_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B_1)) -> (hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(int,rat,hAPP(int,fun(int,rat),fract,A_2),B_1)),one_one(rat))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_2),B_1))))) # label(fact_3787_Fract__less__one__iff) # label(axiom) # label(non_clause).  [assumption].
7.57/7.63	3409 (all W (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),W))) -> hAPP(product_prod(int,int),int,product_fst(int,int),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),posDivAlg,one_one(int)),hAPP(int,int,number_number_of(int),W))) = hAPP(int,int,hAPP(int,fun(int,int),div_div(int),one_one(int)),hAPP(int,int,number_number_of(int),W)))) # label(fact_3110_div__pos__pos__1__number__of) # label(axiom) # label(non_clause).  [assumption].
7.57/7.63	3410 (all X_a (linordered_idom(X_a) -> (all A_2 (ti(X_a,A_2) != 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(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_2),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))))) # label(fact_11_zero__less__power2) # label(axiom) # label(non_clause).  [assumption].
7.57/7.63	3411 (all X_a (real_normed_vector(X_a) -> (all X_3 all K_3 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),K_3)) -> ((all N_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),hAPP(nat,X_a,X_3,N_2))),K_3))) -> hBOOL(hAPP(fun(nat,X_a),bool,bseq(X_a),X_3))))))) # label(fact_3497_BseqI) # label(axiom) # label(non_clause).  [assumption].
7.57/7.63	3412 (all Y all X all U (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,abs_abs(real),X)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),U),hAPP(real,real,sqrt,hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,abs_abs(real),Y)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),U),hAPP(real,real,sqrt,hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,sqrt,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),Y),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))),U))))) # label(fact_1839_real__sqrt__sum__squares__less) # label(axiom) # label(non_clause).  [assumption].
7.57/7.63	3413 (all A_1 all B all N hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A_1),N)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),B),N)) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,A_1),B)),N)) # label(fact_3441_zgcd__power__distrib) # label(axiom) # label(non_clause).  [assumption].
7.57/7.63	3414 (all X all N hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),hAPP(complex,complex,cnj,X)),N) = hAPP(complex,complex,cnj,hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),X),N))) # label(fact_2943_complex__cnj__power) # label(axiom) # label(non_clause).  [assumption].
7.57/7.63	3415 (all K_4 hAPP(int,quickcheck_code_int,quickcheck_of_int,hAPP(quickcheck_code_int,int,quickcheck_int_of,K_4)) = K_4) # label(fact_3536_of__int__int__of) # label(axiom) # label(non_clause).  [assumption].
7.57/7.63	3416 (all K all F all N_1 ((all I_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),N_1)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(nat,int,F,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_2),one_one(nat)))),hAPP(nat,int,F,I_2)))),one_one(int))))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,F,zero_zero(nat))),K)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),K),hAPP(nat,int,F,N_1))) -> (exists I_2 (ti(int,K) = hAPP(nat,int,F,I_2) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_2),N_1)))))))) # label(fact_2009_nat0__intermed__int__val) # label(axiom) # label(non_clause).  [assumption].
7.57/7.63	3417 (all X_a (real_normed_algebra(X_a) -> (all A_1 all B hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),A_1)),B)))) # label(fact_2036_mult_Ominus__left) # label(axiom) # label(non_clause).  [assumption].
7.57/7.63	3418 (all X_1 all F (hBOOL(hAPP(fun(nat,real),bool,summable(real),F)) -> ((all N_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),N_2))),X_1))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(fun(nat,real),real,suminf(real),F)),X_1))))) # label(fact_4290_suminf__le) # label(axiom) # label(non_clause).  [assumption].
7.57/7.63	3419 (all A_2 all B_1 all Q_2 all R_1 (hBOOL(hAPP(product_prod(int,int),bool,hAPP(int,fun(product_prod(int,int),bool),hAPP(int,fun(int,fun(product_prod(int,int),bool)),divmod_int_rel,A_2),B_1),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),Q_2),R_1))) -> hBOOL(hAPP(product_prod(int,int),bool,hAPP(int,fun(product_prod(int,int),bool),hAPP(int,fun(int,fun(product_prod(int,int),bool)),divmod_int_rel,hAPP(int,int,uminus_uminus(int),A_2)),B_1),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),hAPP(int,int,hAPP(int,fun(int,int),hAPP(bool,fun(int,fun(int,int)),if(int),hAPP(int,bool,hAPP(int,fun(int,bool),fequal(int),R_1),zero_zero(int))),hAPP(int,int,uminus_uminus(int),Q_2)),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,uminus_uminus(int),Q_2)),one_one(int)))),hAPP(int,int,hAPP(int,fun(int,int),hAPP(bool,fun(int,fun(int,int)),if(int),hAPP(int,bool,hAPP(int,fun(int,bool),fequal(int),R_1),zero_zero(int))),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),B_1),R_1))))))) # label(fact_2183_zminus1__lemma) # label(axiom) # label(non_clause).  [assumption].
7.57/7.63	3420 (all X_a (linordered_semidom(X_a) -> (all N all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),one_one(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N))),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N)))))))) # label(fact_458_power__Suc__less) # label(axiom) # label(non_clause).  [assumption].
7.57/7.63	3421 (all N_1 all V_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,N_1)),hAPP(int,nat,number_number_of(nat),V_1))) <-> (-hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),hAPP(int,int,pred,V_1)))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_1),hAPP(int,nat,nat_1,hAPP(int,int,number_number_of(int),hAPP(int,int,pred,V_1)))))) & -hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),hAPP(int,int,pred,V_1)))))) # label(fact_3895_le__Suc__number__of) # label(axiom) # label(non_clause).  [assumption].
7.57/7.63	3422 (all X_3 all Ma (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),Ma)) -> hBOOL(hAPP(fun(int,bool),bool,hAPP(fun(int,bool),fun(fun(int,bool),bool),ord_less_eq(fun(int,bool)),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,int),fun(fun(int,bool),fun(int,bool)),image(int,int),hAPP(int,fun(int,int),standardRes,Ma)),X_3)),hAPP(fun(int,bool),fun(int,bool),collect(int),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),combs(int,bool,bool),hAPP(fun(int,bool),fun(int,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj),hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)))),hAPP(int,fun(int,bool),hAPP(fun(int,fun(int,bool)),fun(int,fun(int,bool)),combc(int,int,bool),ord_less(int)),Ma))))))) # label(fact_3897_SR__pos) # label(axiom) # label(non_clause).  [assumption].
7.57/7.63	3423 (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_388_mult__neg__pos) # label(axiom) # label(non_clause).  [assumption].
7.57/7.63	3424 (all X_a all X_b all X_c all X_d all Y -(all A_4 all B_4 all C_4 all D_3 ti(product_prod(X_a,product_prod(X_b,product_prod(X_c,X_d))),Y) != hAPP(product_prod(X_b,product_prod(X_c,X_d)),product_prod(X_a,product_prod(X_b,product_prod(X_c,X_d))),hAPP(X_a,fun(product_prod(X_b,product_prod(X_c,X_d)),product_prod(X_a,product_prod(X_b,product_prod(X_c,X_d)))),product_Pair(X_a,product_prod(X_b,product_prod(X_c,X_d))),A_4),hAPP(product_prod(X_c,X_d),product_prod(X_b,product_prod(X_c,X_d)),hAPP(X_b,fun(product_prod(X_c,X_d),product_prod(X_b,product_prod(X_c,X_d))),product_Pair(X_b,product_prod(X_c,X_d)),B_4),hAPP(X_d,product_prod(X_c,X_d),hAPP(X_c,fun(X_d,product_prod(X_c,X_d)),product_Pair(X_c,X_d),C_4),D_3))))) # label(fact_3149_prod__cases4) # label(axiom) # label(non_clause).  [assumption].
7.57/7.63	3425 (all X_2 hAPP(real,real,uminus_uminus(real),hAPP(nat,real,sin_coeff,X_2)) = hAPP(nat,real,hAPP(fun(nat,real),fun(nat,real),diffs(real),cos_coeff),X_2)) # label(fact_4122_cos__fdiffs) # label(axiom) # label(non_clause).  [assumption].
7.57/7.63	3426 (all A_1 all Y all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Y)) -> hAPP(real,real,hAPP(real,fun(real,real),powr,hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),X),Y)),A_1) = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(real,fun(real,real),powr,X),A_1)),hAPP(real,real,hAPP(real,fun(real,real),powr,Y),A_1))))) # label(fact_3380_powr__divide) # label(axiom) # label(non_clause).  [assumption].
7.57/7.63	3427 (all Ta all B_2 all D_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D_2)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),Ta),one_one(int))),B_2)) -> (all X_2 ((all Xa (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xa),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastAtMost(int),one_one(int)),D_2))) -> (all Xb (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xb),B_2)) -> hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Xb),Xa) != ti(int,X_2))))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Ta),X_2)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Ta),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X_2),D_2))))))))) # label(fact_4633_bset_I8_J) # label(axiom) # label(non_clause).  [assumption].
7.57/7.63	3428 (all Y all X (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Y)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(int,nat,nat_1,X)),hAPP(int,nat,nat_1,Y)) = hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),div_div(int),X),Y))))) # label(fact_1095_Divides_Otransfer__nat__int__functions_I1_J) # label(axiom) # label(non_clause).  [assumption].
7.57/7.63	3429 (all X_a (linordered_idom(X_a) -> (all A_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,sgn_sgn(X_a),A_2)),zero_zero(X_a))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),zero_zero(X_a))))))) # label(fact_2212_sgn__less) # label(axiom) # label(non_clause).  [assumption].
7.57/7.63	3430 (all X_1 (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),zEven)) -> hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),X_1),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) = ti(int,X_1))) # label(fact_1465_even__div__2__prop2) # label(axiom) # label(non_clause).  [assumption].
7.57/7.63	3431 (all X_a (linordered_idom(X_a) -> (all X_1 all W_1 (hAPP(int,nat,number_number_of(nat),W_1) != zero_zero(nat) & (ti(X_a,X_1) = zero_zero(X_a) & hBOOL(hAPP(nat,bool,even_odd_even(nat),hAPP(int,nat,number_number_of(nat),W_1))) | -hBOOL(hAPP(nat,bool,even_odd_even(nat),hAPP(int,nat,number_number_of(nat),W_1))) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),zero_zero(X_a)))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X_1),hAPP(int,nat,number_number_of(nat),W_1))),zero_zero(X_a))))))) # label(fact_2463_power__le__zero__eq__number__of) # label(axiom) # label(non_clause).  [assumption].
7.57/7.63	3432 (all X all Y hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),X),Y)),X))) # label(fact_4346_gcd__dvd1__int) # label(axiom) # label(non_clause).  [assumption].
7.57/7.63	3433 (all X_a (real_normed_field(X_a) -> (all C_1 all F all X_1 all D_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),F),X_1),D_2)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),hAPP(X_a,fun(X_a,X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(X_a,X_a)),combc(X_a,X_a,X_a),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,X_a),fun(X_a,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),X_a),inverse_divide(X_a)),F)),C_1)),X_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),D_2),C_1))))))) # label(fact_3836_DERIV__cdivide) # label(axiom) # label(non_clause).  [assumption].
7.57/7.63	3434 (all X_a (linorder(X_a) -> (all C_1 all D_1 all A_2 all B_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),B_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),D_1)) -> (ti(X_a,D_1) = ti(X_a,B_1) & ti(X_a,C_1) = ti(X_a,A_2) <-> hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastLessThan(X_a),A_2),B_1) = hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastLessThan(X_a),C_1),D_1))))))) # label(fact_4197_atLeastLessThan__eq__iff) # label(axiom) # label(non_clause).  [assumption].
7.57/7.63	3435 (all X_a all X_b (comm_semiring_1(X_b) -> (all F all I all A_3 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_3)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),I),A_3)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),dvd_dvd(X_b),hAPP(X_a,X_b,F,I)),hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co302546470etprod(X_a,X_b),F),A_3)))))))) # label(fact_3953_dvd__setprod) # label(axiom) # label(non_clause).  [assumption].
7.57/7.63	3436 (all X_a (linord219039673up_add(X_a) -> (all A_2 (ti(X_a,A_2) = hAPP(X_a,X_a,uminus_uminus(X_a),A_2) <-> ti(X_a,A_2) = zero_zero(X_a))))) # label(fact_2023_equal__neg__zero) # label(axiom) # label(non_clause).  [assumption].
7.57/7.63	3437 (all Z_1 all W hAPP(int,int,uminus_uminus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Z_1),W)) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,uminus_uminus(int),Z_1)),hAPP(int,int,uminus_uminus(int),W))) # label(fact_2142_zminus__zadd__distrib) # label(axiom) # label(non_clause).  [assumption].
7.57/7.63	3438 (all X_a (uminus(X_a) -> uminus_uminus(X_a) = ti(fun(X_a,X_a),uminus_uminus(X_a)))) # label(tsy_c_Groups_Ouminus__class_Ouminus_res) # label(axiom) # label(non_clause).  [assumption].
7.57/7.63	3439 (all V all W ((-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),W))) -> hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit1,V))),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,W))) = hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,number_number_of(int),V)),one_one(int))),hAPP(int,int,number_number_of(int),W))) & (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),W))) -> hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,number_number_of(int),V)),hAPP(int,int,number_number_of(int),W)) = hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit1,V))),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,W)))))) # label(fact_1065_zdiv__number__of__Bit1) # label(axiom) # label(non_clause).  [assumption].
7.57/7.63	3440 (all M all I_1 all J_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_1),J_2)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J_2),M))))) # label(fact_573_trans__le__add1) # label(axiom) # label(non_clause).  [assumption].
7.57/7.63	3441 (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),C),A_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)))) # label(fact_221_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) # label(axiom) # label(non_clause).  [assumption].
7.57/7.63	3442 (all X_a (linordered_field(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(X_a,X_a,inverse_inverse(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),hAPP(nat,nat,fact_fact(nat),N)))))))) # label(fact_2612_inv__of__nat__fact__ge__zero) # label(axiom) # label(non_clause).  [assumption].
7.57/7.63	3443 (all A_2 hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),hAPP(int,fun(int,bool),d22set,A_2)))) # label(fact_1671_d22set__fin) # label(axiom) # label(non_clause).  [assumption].
7.57/7.63	3444 (all X_a (ord(X_a) -> ti(fun(X_a,fun(X_a,X_a)),ord_max(X_a)) = ord_max(X_a))) # label(tsy_c_Orderings_Oord__class_Omax_res) # label(axiom) # label(non_clause).  [assumption].
7.57/7.63	3445 (all A_3 (hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A_3)) <-> hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),A_3))))) # label(fact_3652_transfer__nat__int__set__relations_I1_J) # label(axiom) # label(non_clause).  [assumption].
7.57/7.63	3446 (all X_a (semiring_0(X_a) & power(X_a) -> (all N hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),zero_zero(X_a)),hAPP(nat,nat,suc,N)) = zero_zero(X_a)))) # label(fact_1300_power__0__Suc) # label(axiom) # label(non_clause).  [assumption].
7.57/7.63	3447 (all X_a all C_1 all A_3 all B_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_3),B_2))) -> -hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),B_2)))) # label(fact_1965_DiffD2) # label(axiom) # label(non_clause).  [assumption].
7.57/7.63	3448 (all X_a (linorder(X_a) -> (all X all Y all Z_1 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),Y)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),Z_1))),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),Y),Z_1))))))) # label(fact_4945_min__max_Odistrib__inf__le) # label(axiom) # label(non_clause).  [assumption].
7.57/7.63	3449 (all X_a (division_ring(X_a) -> (all B all A_1 (ti(X_a,A_1) != zero_zero(X_a) -> (zero_zero(X_a) != ti(X_a,B) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,inverse_inverse(X_a),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B))),hAPP(X_a,X_a,inverse_inverse(X_a),B)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,inverse_inverse(X_a),A_1)),hAPP(X_a,X_a,inverse_inverse(X_a),B))))))) # label(fact_2577_division__ring__inverse__add) # label(axiom) # label(non_clause).  [assumption].
7.57/7.63	3450 (all I all K all J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K),J)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J),K))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I),K)),J))))) # label(fact_694_le__diff__conv2) # label(axiom) # label(non_clause).  [assumption].
7.57/7.63	3451 (all N_1 all F (hBOOL(hAPP(fun(nat,real),bool,summable(real),F)) -> ((all M_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_1),M_2)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(nat,real,F,M_2))))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),N_1))),hAPP(fun(nat,real),real,suminf(real),F)))))) # label(fact_4274_series__pos__less) # label(axiom) # label(non_clause).  [assumption].
7.57/7.63	3452 (all X_b all X_a (topological_space(X_a) & real_normed_algebra(X_b) -> (all C_1 all F all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),zero_zero(X_b)),hAPP(X_a,filter(X_a),at(X_a),A_2))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(fun(X_a,X_b),fun(X_a,X_b),hAPP(fun(X_b,X_b),fun(fun(X_a,X_b),fun(X_a,X_b)),combb(X_b,X_b,X_a),hAPP(X_b,fun(X_b,X_b),times_times(X_b),C_1)),F)),zero_zero(X_b)),hAPP(X_a,filter(X_a),at(X_a),A_2))))))) # label(fact_4573_LIM__mult__right__zero) # label(axiom) # label(non_clause).  [assumption].
7.57/7.63	3453 (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_1851_abs__zero) # label(axiom) # label(non_clause).  [assumption].
7.57/7.63	3454 (all I (zero_zero(int) != ti(int,I) -> hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),hAPP(fun(int,bool),fun(int,bool),collect(int),hAPP(int,fun(int,bool),hAPP(fun(int,fun(int,bool)),fun(int,fun(int,bool)),combc(int,int,bool),dvd_dvd(int)),I)))))) # label(fact_3841_finite__divisors__int) # label(axiom) # label(non_clause).  [assumption].
7.57/7.63	3455 (all U all X hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,uminus_uminus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),U),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))) # label(fact_2118_realpow__square__minus__le) # label(axiom) # label(non_clause).  [assumption].
7.57/7.63	3456 (all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_1),one_one(real))) -> hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),hAPP(real,fun(nat,real),power_power(real),X_1)),zero_zero(real)),sequentially))))) # label(fact_4429_LIMSEQ__realpow__zero) # label(axiom) # label(non_clause).  [assumption].
7.57/7.63	3457 (all R_4 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),R_4),hAPP(int,real,real_1(int),hAPP(real,int,archimedean_ceiling(real),R_4))))) # label(fact_3345_real__of__int__ceiling__ge) # label(axiom) # label(non_clause).  [assumption].
7.57/7.63	3458 (all X_a (comm_semiring_1(X_a) -> (all X all Q_3 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),Q_3)) = hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),hAPP(nat,nat,suc,Q_3))))) # label(fact_1310_comm__semiring__1__class_Onormalizing__semiring__rules_I27_J) # label(axiom) # label(non_clause).  [assumption].
7.57/7.63	3459 (all X_a all F1 all F2 all Code_numeral hAPP(code_code_numeral,X_a,hAPP(fun(code_code_numeral,X_a),fun(code_code_numeral,X_a),hAPP(X_a,fun(fun(code_code_numeral,X_a),fun(code_code_numeral,X_a)),code_c600343653l_case(X_a),F1),F2),hAPP(code_code_numeral,code_code_numeral,code_S1047413653umeral,Code_numeral)) = hAPP(code_code_numeral,X_a,F2,Code_numeral)) # label(fact_3531_code__numeral_Osimps_I5_J) # label(axiom) # label(non_clause).  [assumption].
7.57/7.63	3460 (all X all M all Y hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),X),M)),Y)),M) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X),Y)),M)) # label(fact_956_zdiff__zmod__left) # label(axiom) # label(non_clause).  [assumption].
7.57/7.63	3461 (all Y_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Y_1)) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,sqrt,Y_1))))) # label(fact_1628_real__sqrt__gt__0__iff) # label(axiom) # label(non_clause).  [assumption].
7.57/7.63	3462 (all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X_1)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),sqrt),X_1),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,inverse_inverse(real),hAPP(real,real,sqrt,X_1))),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))) # label(fact_2652_DERIV__real__sqrt) # label(axiom) # label(non_clause).  [assumption].
7.57/7.63	3463 (all X_a (number_ring(X_a) -> (all A_1 ti(X_a,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)))) # label(fact_148_add__numeral__0) # label(axiom) # label(non_clause).  [assumption].
7.57/7.63	3464 (all X_b all X_a (semiring_0(X_a) -> (all F all A_3 all R_1 hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co1399186613setsum(X_b,X_a),hAPP(X_a,fun(X_b,X_a),hAPP(fun(X_b,fun(X_a,X_a)),fun(X_a,fun(X_b,X_a)),combc(X_b,X_a,X_a),hAPP(fun(X_b,X_a),fun(X_b,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_b,X_a),fun(X_b,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),X_b),times_times(X_a)),F)),R_1)),A_3) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co1399186613setsum(X_b,X_a),F),A_3)),R_1)))) # label(fact_4210_setsum__left__distrib) # label(axiom) # label(non_clause).  [assumption].
7.57/7.63	3465 (all V (hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V))) -> zero_zero(nat) = hAPP(int,nat,number_number_of(nat),V))) # label(fact_1510_neg__imp__number__of__eq__0) # label(axiom) # label(non_clause).  [assumption].
7.57/7.63	3466 (all X_a (ordered_ab_group_add(X_a) -> (all B_1 all A_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),B_1)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),B_1)),hAPP(X_a,X_a,uminus_uminus(X_a),A_2))))))) # label(fact_2028_neg__le__iff__le) # label(axiom) # label(non_clause).  [assumption].
7.57/7.63	3467 (all Ma all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),Ma),N_1))) <-> N_1 != zero_zero(nat) | zero_zero(nat) != Ma)) # label(fact_3259_gcd__pos__nat) # label(axiom) # label(non_clause).  [assumption].
7.57/7.63	3468 (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_434_mult__strict__mono) # label(axiom) # label(non_clause).  [assumption].
7.57/7.63	3469 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),hAPP(nat,nat,suc,N))) -> (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N)) -> hAPP(nat,nat,suc,N) = M))) # label(fact_1248_le__SucE) # label(axiom) # label(non_clause).  [assumption].
7.57/7.63	3470 (all X_a all A_3 all B_2 (hBOOL(hAPP(fun(fun(X_a,bool),bool),bool,hAPP(fun(X_a,bool),fun(fun(fun(X_a,bool),bool),bool),member(fun(X_a,bool)),A_3),hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),pow(X_a),B_2))) <-> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_3),B_2)))) # label(fact_2779_Pow__iff) # label(axiom) # label(non_clause).  [assumption].
7.57/7.63	3471 (all X all Y (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,X),Y)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X),Y)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),Y),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))))) # label(fact_2846_coprime__sos) # label(axiom) # label(non_clause).  [assumption].
7.57/7.63	3472 (all A_1 all B all M (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),M)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),M),B)) -> hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_1),B)),M) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_1),M)))) # label(fact_1036_zmod__zdvd__zmod) # label(axiom) # label(non_clause).  [assumption].
7.57/7.63	3473 (all Y all X (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Y)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),X),Y)))))) # label(fact_990_Divides_Otransfer__nat__int__function__closures_I2_J) # label(axiom) # label(non_clause).  [assumption].
7.57/7.63	3474 (all X_a (topological_space(X_a) -> (all G all F all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(real,fun(filter(X_a),bool),hAPP(fun(X_a,real),fun(real,fun(filter(X_a),bool)),tendsto(X_a,real),F),zero_zero(real)),hAPP(X_a,filter(X_a),at(X_a),A_2))) -> ((all X_2 (ti(X_a,A_2) != ti(X_a,X_2) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(X_a,real,G,X_2))))) -> ((all X_2 (ti(X_a,X_2) != ti(X_a,A_2) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,G,X_2)),hAPP(X_a,real,F,X_2))))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(real,fun(filter(X_a),bool),hAPP(fun(X_a,real),fun(real,fun(filter(X_a),bool)),tendsto(X_a,real),G),zero_zero(real)),hAPP(X_a,filter(X_a),at(X_a),A_2))))))))) # label(fact_4776_real__LIM__sandwich__zero) # label(axiom) # label(non_clause).  [assumption].
7.57/7.63	3475 (all K_4 all L_4 (zero_zero(int) != hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),K_4),hAPP(int,int,uminus_uminus(int),L_4)) -> zero_zero(int) != hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),K_4),L_4))) # label(fact_2159_zmod__zminus2__not__zero) # label(axiom) # label(non_clause).  [assumption].
7.57/7.63	3476 (all A_2 all B_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B_1)) -> (hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(int,rat,hAPP(int,fun(int,rat),fract,A_2),B_1)),one_one(rat))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A_2),B_1))))) # label(fact_3794_Fract__le__one__iff) # label(axiom) # label(non_clause).  [assumption].
7.57/7.63	3477 (all W hAPP(int,int,hAPP(int,fun(int,int),times_times(int),pls),W) = pls) # label(fact_62_mult__Pls) # label(axiom) # label(non_clause).  [assumption].
7.57/7.63	3478 (all X_a (ring(X_a) -> (all A_1 all B hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),A_1)),B)))) # label(fact_2031_minus__mult__left) # label(axiom) # label(non_clause).  [assumption].
7.57/7.63	3479 (all P_5 all X hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),X),hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),P_5),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) = hAPP(int,int,hAPP(int,fun(int,int),multInv,P_5),X)) # label(fact_1154_MultInv__def) # label(axiom) # label(non_clause).  [assumption].
7.57/7.63	3480 (all X_a (linordered_idom(X_a) -> (all A_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),A_2)),zero_zero(X_a))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),zero_zero(X_a))))))) # label(fact_144_even__less__0__iff) # label(axiom) # label(non_clause).  [assumption].
7.57/7.63	3481 (all V all W ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),W))) -> hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit1,V))),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,W))) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,number_number_of(int),V)),hAPP(int,int,number_number_of(int),W)))),one_one(int))) & (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),W))) -> hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,number_number_of(int),V)),one_one(int))),hAPP(int,int,number_number_of(int),W)))),one_one(int)) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit1,V))),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,W)))))) # label(fact_899_zmod__number__of__Bit1) # label(axiom) # label(non_clause).  [assumption].
7.57/7.63	3482 (all B all Q_3 all R_4 all B_5 all Q_5 all R_5 (hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B_5),Q_5)),R_5) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),Q_3)),R_4) -> (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_5),Q_5)),R_5)),zero_zero(int))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),R_4),B)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),R_5)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B_5)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B_5),B)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Q_5),Q_3))))))))) # label(fact_269_zdiv__mono2__neg__lemma) # label(axiom) # label(non_clause).  [assumption].
7.57/7.63	3483 (all K_4 all I_1 all J_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),I_1),J_2)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),I_1),K_4)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),J_2),K_4))))) # label(fact_136_zadd__strict__right__mono) # label(axiom) # label(non_clause).  [assumption].
7.57/7.63	3484 (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_237_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) # label(axiom) # label(non_clause).  [assumption].
7.57/7.63	3485 (all X_a all X_b the(product_prod(X_a,X_b)) = ti(fun(fun(product_prod(X_a,X_b),bool),product_prod(X_a,X_b)),the(product_prod(X_a,X_b)))) # label(tsy_c_HOL_OThe_2_res) # label(axiom) # label(non_clause).  [assumption].
7.57/7.63	3486 (all Ma all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Ma),N_1)) <-> zero_zero(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),Ma),N_1))) # label(fact_684_diff__is__0__eq) # label(axiom) # label(non_clause).  [assumption].
7.57/7.63	3487 (all P_1 all A_2 all B_1 hAPP(real,product_prod(real,real),hAPP(real,fun(real,product_prod(real,real)),product_Pair(real,real),A_2),B_1) = hAPP(nat,product_prod(real,real),hAPP(real,fun(nat,product_prod(real,real)),hAPP(real,fun(real,fun(nat,product_prod(real,real))),hAPP(fun(product_prod(real,real),bool),fun(real,fun(real,fun(nat,product_prod(real,real)))),bolzano_bisect,P_1),A_2),B_1),zero_zero(nat))) # label(fact_3132_Bolzano__bisect_Osimps_I1_J) # label(axiom) # label(non_clause).  [assumption].
7.57/7.63	3488 (all X_a (archim1727834104eiling(X_a) -> (all X_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),hAPP(X_a,int,archim2085082626_floor(X_a),X_1))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),X_1)))))) # label(fact_2895_one__less__floor) # label(axiom) # label(non_clause).  [assumption].
7.57/7.63	3489 (all A_2 all B_1 all P_1 ((all A_4 all B_4 all C_4 (hBOOL(hAPP(product_prod(real,real),bool,P_1,hAPP(real,product_prod(real,real),hAPP(real,fun(real,product_prod(real,real)),product_Pair(real,real),A_4),B_4))) & hBOOL(hAPP(product_prod(real,real),bool,P_1,hAPP(real,product_prod(real,real),hAPP(real,fun(real,product_prod(real,real)),product_Pair(real,real),B_4),C_4))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A_4),B_4)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B_4),C_4)) -> hBOOL(hAPP(product_prod(real,real),bool,P_1,hAPP(real,product_prod(real,real),hAPP(real,fun(real,product_prod(real,real)),product_Pair(real,real),A_4),C_4))))) -> ((all X_2 exists D_3 ((all A_4 all B_4 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A_4),X_2)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_2),B_4)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),B_4),A_4)),D_3)) -> hBOOL(hAPP(product_prod(real,real),bool,P_1,hAPP(real,product_prod(real,real),hAPP(real,fun(real,product_prod(real,real)),product_Pair(real,real),A_4),B_4))))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),D_3)))) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A_2),B_1)) -> hBOOL(hAPP(product_prod(real,real),bool,P_1,hAPP(real,product_prod(real,real),hAPP(real,fun(real,product_prod(real,real)),product_Pair(real,real),A_2),B_1))))))) # label(fact_3205_lemma__BOLZANO) # label(axiom) # label(non_clause).  [assumption].
7.57/7.64	3490 (all X ((-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X)) -> zero_zero(int) = hAPP(int,int,fact_fact(int),X)) & (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X)) -> hAPP(int,int,fact_fact(int),X) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,fact_fact(nat),hAPP(int,nat,nat_1,X)))))) # label(fact_3178_fact__int__def) # label(axiom) # label(non_clause).  [assumption].
7.57/7.64	3491 (all X_a (linordered_field(X_a) -> (all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),one_one(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),hAPP(X_a,X_a,inverse_inverse(X_a),A_1)))))))) # label(fact_2576_one__less__inverse) # label(axiom) # label(non_clause).  [assumption].
7.57/7.64	3492 (all K all Ma all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K),Ma)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K),N_1))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),N_1)))) # label(fact_556_nat__add__left__cancel__less) # label(axiom) # label(non_clause).  [assumption].
7.57/7.64	3493 (all A_2 all B_1 all A_3 all Ma (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),Ma)) -> (hBOOL(hAPP(int,bool,hAPP(fun(int,bool),fun(int,bool),is_RRset,A_3),Ma)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_2),B_1),Ma)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),A_2),A_3)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),B_1),A_3)) -> ti(int,B_1) = ti(int,A_2))))))) # label(fact_3620_RRset__zcong__eq) # label(axiom) # label(non_clause).  [assumption].
7.57/7.64	3494 (all X_a (banach(X_a) & real_normed_field(X_a) -> ti(fun(X_a,X_a),exp(X_a)) = exp(X_a))) # label(tsy_c_Transcendental_Oexp_res) # label(axiom) # label(non_clause).  [assumption].
7.57/7.64	3495 (all X_a (comm_monoid_add(X_a) -> (all F all P_4 all Ma all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Ma),N_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_1),P_4)) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),Ma),N_1))),hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),N_1),P_4))) = hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),Ma),P_4))))))) # label(fact_4201_setsum__add__nat__ivl) # label(axiom) # label(non_clause).  [assumption].
7.57/7.64	3496 (all X_a (ring_1(X_a) -> ring_1_of_int(X_a) = ti(fun(int,X_a),ring_1_of_int(X_a)))) # label(tsy_c_Int_Oring__1__class_Oof__int_res) # label(axiom) # label(non_clause).  [assumption].
7.57/7.64	3497 (all X_1 ((exists N_2 X_1 = hAPP(int,real,real_1(int),N_2)) <-> X_1 = hAPP(int,real,real_1(int),hAPP(real,int,archim2085082626_floor(real),X_1)))) # label(fact_3325_real__of__int__floor__cancel) # label(axiom) # label(non_clause).  [assumption].
7.57/7.64	3498 (all X_a (cancel_semigroup_add(X_a) -> ti(fun(X_a,fun(X_a,X_a)),plus_plus(X_a)) = plus_plus(X_a))) # label(tsy_c_Groups_Oplus__class_Oplus_3_res) # label(axiom) # label(non_clause).  [assumption].
7.57/7.64	3499 (all Y_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),one_one(real)),Y_1)) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),one_one(real)),hAPP(real,real,hAPP(nat,fun(real,real),root,N_1),Y_1)))))) # label(fact_2697_real__root__ge__1__iff) # label(axiom) # label(non_clause).  [assumption].
7.57/7.64	3500 (all Ma all N_1 (Ma = zero_zero(nat) & zero_zero(nat) != N_1 <-> hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),Ma),N_1) = zero_zero(nat))) # label(fact_726_nat__power__eq__0__iff) # label(axiom) # label(non_clause).  [assumption].
7.57/7.64	3501 (all X_a (real_field(X_a) -> (all A_1 all B all C all D all H_2 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),B),D)),H_2))),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_1),C)),H_2)),D)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),D))),H_2)))) # label(fact_1801_DERIV__mult__lemma) # label(axiom) # label(non_clause).  [assumption].
7.57/7.64	3502 (all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X_1)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),ln),X_1),hAPP(real,real,inverse_inverse(real),X_1))))) # label(fact_2641_DERIV__ln) # label(axiom) # label(non_clause).  [assumption].
7.57/7.64	3503 (all R_4 all A_1 hAPP(real,real,hAPP(real,fun(real,real),times_times(real),R_4),hAPP(real,real,sin,A_1)) = hAPP(complex,real,im,hAPP(real,complex,hAPP(real,fun(real,complex),rcis,R_4),A_1))) # label(fact_3170_Im__rcis) # label(axiom) # label(non_clause).  [assumption].
7.57/7.64	3504 (all X_a all Q_1 all P_1 (hBOOL(hAPP(X_a,bool,P_1,hAPP(fun(X_a,bool),X_a,hilbert_Eps(X_a),P_1))) -> (hBOOL(hAPP(X_a,bool,Q_1,hAPP(fun(X_a,bool),X_a,hilbert_Eps(X_a),Q_1))) -> (hAPP(fun(X_a,bool),X_a,hilbert_Eps(X_a),Q_1) = hAPP(fun(X_a,bool),X_a,hilbert_Eps(X_a),P_1) -> (exists A_4 (hBOOL(hAPP(X_a,bool,Q_1,A_4)) & hBOOL(hAPP(X_a,bool,P_1,A_4)))))))) # label(fact_4866_EulerFermat_Oaux) # label(axiom) # label(non_clause).  [assumption].
7.57/7.64	3505 (all Z_1 ti(int,Z_1) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),one_one(int)),Z_1)) # label(fact_66_zmult__1) # label(axiom) # label(non_clause).  [assumption].
7.57/7.64	3506 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,number_number_of(real),min_1)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X),one_one(real))) -> hAPP(real,real,cos,hAPP(real,real,arcsin,X)) = hAPP(real,real,sqrt,hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),one_one(real)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))))) # label(fact_2189_cos__arcsin) # label(axiom) # label(non_clause).  [assumption].
7.57/7.64	3507 (all Z_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),Z_1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Z_1),Z_1)) # label(fact_230_nat__mult__2) # label(axiom) # label(non_clause).  [assumption].
7.57/7.64	3508 (exists K_2 all X_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,norm_norm(real),hAPP(complex,real,im,X_2))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(complex,real,norm_norm(complex),X_2)),K_2)))) # label(fact_2989_Im_Obounded) # label(axiom) # label(non_clause).  [assumption].
7.57/7.64	3509 (all Z_1 hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(nat,int,semiring_1_of_nat(int),Z_1)))) # label(fact_1295_Nat__Transfer_Otransfer__nat__int__function__closures_I9_J) # label(axiom) # label(non_clause).  [assumption].
7.57/7.64	3510 (all Y all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Y)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),X),Y)))))) # label(fact_711_real__mult__order) # label(axiom) # label(non_clause).  [assumption].
7.57/7.64	3511 (all Ma all K all N_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),N_1)) -> ((exists S_1 exists T_4 hAPP(product_prod(int,int),product_prod(int,product_prod(int,int)),hAPP(int,fun(product_prod(int,int),product_prod(int,product_prod(int,int))),product_Pair(int,product_prod(int,int)),K),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),S_1),T_4)) = hAPP(int,product_prod(int,product_prod(int,int)),hAPP(int,fun(int,product_prod(int,product_prod(int,int))),xzgcd,Ma),N_1)) <-> hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,Ma),N_1) = ti(int,K)))) # label(fact_3475_xzgcd__correct) # label(axiom) # label(non_clause).  [assumption].
7.57/7.64	3512 (all X_a (linord581940658strict(X_a) -> (all X_1 all Y_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X_1),X_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Y_1),Y_1))),zero_zero(X_a))) <-> zero_zero(X_a) = ti(X_a,X_1) & ti(X_a,Y_1) = zero_zero(X_a))))) # label(fact_45_sum__squares__le__zero__iff) # label(axiom) # label(non_clause).  [assumption].
7.57/7.64	3513 (all X_a (ord(X_a) -> (all C all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)) -> (ti(X_a,C) = ti(X_a,B) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),C))))))) # label(fact_1576_ord__less__eq__trans) # label(axiom) # label(non_clause).  [assumption].
7.57/7.64	3514 (all I all J all K (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J),K))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I),K)),J)))) # label(fact_686_less__diff__conv) # label(axiom) # label(non_clause).  [assumption].
7.57/7.64	3515 (all X all A_1 all B (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A_1),B)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),X)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),powr,X),A_1)),hAPP(real,real,hAPP(real,fun(real,real),powr,X),B)))))) # label(fact_3353_powr__less__mono) # label(axiom) # label(non_clause).  [assumption].
7.57/7.64	3516 (all X_a (linordered_idom(X_a) -> (all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_2),ring_1_Ints(X_a))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),one_one(X_a)),A_2)),A_2)),zero_zero(X_a))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),zero_zero(X_a)))))))) # label(fact_3799_Ints__odd__less__0) # label(axiom) # label(non_clause).  [assumption].
7.57/7.64	3517 (all X hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),hAPP(real,real,sin,X))),one_one(real)))) # label(fact_2319_abs__sin__le__one) # label(axiom) # label(non_clause).  [assumption].
7.57/7.64	3518 (all X_a (number_ring(X_a) & field(X_a) -> (all X ti(X_a,X) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),X),hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,bit1,pls)))))) # label(fact_1734_divide__Numeral1) # label(axiom) # label(non_clause).  [assumption].
7.57/7.64	3519 (all N all M ((M != zero_zero(nat) -> hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),one_one(nat))),N)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N)) & (M = zero_zero(nat) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N) = N))) # label(fact_1415_add__eq__if) # label(axiom) # label(non_clause).  [assumption].
7.57/7.64	3520 (all R_4 hAPP(real,real,norm_norm(real),R_4) = hAPP(real,real,abs_abs(real),R_4)) # label(fact_1857_real__norm__def) # label(axiom) # label(non_clause).  [assumption].
7.57/7.64	3521 (all X_a (archim1727834104eiling(X_a) -> (all V hAPP(int,int,number_number_of(int),V) = hAPP(X_a,int,archimedean_ceiling(X_a),hAPP(int,X_a,number_number_of(X_a),V))))) # label(fact_3283_ceiling__number__of) # label(axiom) # label(non_clause).  [assumption].
7.57/7.64	3522 (all X_a (number_ring(X_a) & linordered_idom(X_a) -> (all X_1 all Y_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X_1),Y_1)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(int,X_a,number_number_of(X_a),X_1)),hAPP(int,X_a,number_number_of(X_a),Y_1))))))) # label(fact_150_less__number__of) # label(axiom) # label(non_clause).  [assumption].
7.57/7.64	3523 (all R_4 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),R_4),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(int,real,real_1(int),hAPP(real,int,archim2085082626_floor(real),R_4))),one_one(real))))) # label(fact_3396_real__of__int__floor__add__one__ge) # label(axiom) # label(non_clause).  [assumption].
7.57/7.64	3524 (all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) -> hAPP(nat,nat,suc,zero_zero(nat)) = N | N = zero_zero(nat))) # label(fact_1451_less__2__cases) # label(axiom) # label(non_clause).  [assumption].
7.57/7.64	3525 (all X_2 ((-hBOOL(hAPP(nat,bool,even_odd_even(nat),X_2)) -> hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),min_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X_2),hAPP(nat,nat,suc,zero_zero(nat)))),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),hAPP(nat,real,real_1(nat),hAPP(nat,nat,fact_fact(nat),X_2))) = hAPP(nat,real,sin_coeff,X_2)) & (hBOOL(hAPP(nat,bool,even_odd_even(nat),X_2)) -> hAPP(nat,real,sin_coeff,X_2) = zero_zero(real)))) # label(fact_2478_sin__coeff__def) # label(axiom) # label(non_clause).  [assumption].
7.57/7.64	3526 (all Y all X (-hBOOL(hAPP(int,bool,even_odd_even(int),X)) -> (-hBOOL(hAPP(int,bool,even_odd_even(int),Y)) -> hBOOL(hAPP(int,bool,even_odd_even(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X),Y)))))) # label(fact_1261_Parity_Oodd__plus__odd) # label(axiom) # label(non_clause).  [assumption].
7.57/7.64	3527 (all X_a (linord1117847801e_zero(X_a) -> (all C all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),C)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),B),C)))))))) # label(fact_1673_divide__right__mono) # label(axiom) # label(non_clause).  [assumption].
7.57/7.64	3528 (all S ((all M_2 exists N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_2),N_2)) & hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),N_2),S)))) <-> -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),S)))) # label(fact_3656_infinite__nat__iff__unbounded__le) # label(axiom) # label(non_clause).  [assumption].
7.57/7.64	3529 (all A_2 all C_1 all D_1 all B_1 (ti(int,B_1) != zero_zero(int) -> (ti(int,D_1) != zero_zero(int) -> (hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_2),D_1) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C_1),B_1) <-> hAPP(int,rat,hAPP(int,fun(int,rat),fract,C_1),D_1) = hAPP(int,rat,hAPP(int,fun(int,rat),fract,A_2),B_1))))) # label(fact_3753_eq__rat_I1_J) # label(axiom) # label(non_clause).  [assumption].
7.57/7.64	3530 (all N (hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,number_number_of(int),min_1)),N) = one_one(int) | hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,number_number_of(int),min_1)),N) = hAPP(int,int,number_number_of(int),min_1))) # label(fact_606_neg__one__power) # label(axiom) # label(non_clause).  [assumption].
7.57/7.64	3531 (all P_1 hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,hAPP(fun(int,bool),fun(int,bool),collect(int),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),combs(int,bool,bool),hAPP(fun(int,bool),fun(int,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj),hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)))),P_1))))) # label(fact_3831_Nat__Transfer_Otransfer__int__nat__set__function__closures_I4_J) # label(axiom) # label(non_clause).  [assumption].
7.57/7.64	3532 (all X_a (ring_1(X_a) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),zero_zero(X_a)),ring_1_Ints(X_a))))) # label(fact_3838_Ints__0) # label(axiom) # label(non_clause).  [assumption].
7.57/7.64	3533 (all N_1 all X_1 (X_1 != one_one(real) -> hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(real,fun(nat,real),power_power(real),X_1)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),N_1)) = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X_1),N_1)),one_one(real))),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),X_1),one_one(real))))) # label(fact_4206_sumr__geometric) # label(axiom) # label(non_clause).  [assumption].
7.57/7.64	3534 (all X_c all X_b all X_a product_apsnd(X_c,X_b,X_a) = ti(fun(fun(X_c,X_b),fun(product_prod(X_a,X_c),product_prod(X_a,X_b))),product_apsnd(X_c,X_b,X_a))) # label(tsy_c_Product__Type_Oapsnd_res) # label(axiom) # label(non_clause).  [assumption].
7.57/7.64	3535 (all X all Y hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),X),Y) = hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),X),hAPP(int,int,abs_abs(int),Y))) # label(fact_4374_gcd__abs2__int) # label(axiom) # label(non_clause).  [assumption].
7.57/7.64	3536 (all X_a (ring_1(X_a) -> (all K_4 ((-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K_4),zero_zero(int))) -> hAPP(nat,X_a,semiring_1_of_nat(X_a),hAPP(int,nat,nat_1,K_4)) = hAPP(int,X_a,ring_1_of_int(X_a),K_4)) & (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K_4),zero_zero(int))) -> hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),hAPP(int,nat,nat_1,hAPP(int,int,uminus_uminus(int),K_4)))) = hAPP(int,X_a,ring_1_of_int(X_a),K_4)))))) # label(fact_3559_of__int__of__nat) # label(axiom) # label(non_clause).  [assumption].
7.57/7.64	3537 (all X_a all A_3 all B_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),B_2)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(fun(X_a,bool),nat,finite_card(X_a),A_3)),hAPP(fun(X_a,bool),nat,finite_card(X_a),B_2))),hAPP(fun(X_a,bool),nat,finite_card(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_3),B_2)))))) # label(fact_1814_diff__card__le__card__Diff) # label(axiom) # label(non_clause).  [assumption].
7.57/7.64	3538 (all X all N all P_5 (hBOOL(hAPP(nat,bool,prime,P_5)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),P_5),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),X),N))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),P_5),X))))) # label(fact_3057_prime__divexp) # label(axiom) # label(non_clause).  [assumption].
7.57/7.64	3539 (all X_a (linordered_field(X_a) -> (all Z_1 all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),Y)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Z_1),Y)),X)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),X),Y)))))))) # label(fact_1713_mult__imp__less__div__pos) # label(axiom) # label(non_clause).  [assumption].
7.57/7.64	3540 (all X all Y (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),Y)) -> hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),Y),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),X),Y)) = hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),X),Y))) # label(fact_4350_gcd__non__0__int) # label(axiom) # label(non_clause).  [assumption].
7.57/7.64	3541 (all X_a (semiring_1(X_a) -> hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),one_one(X_a)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = one_one(X_a))) # label(fact_12_one__power2) # label(axiom) # label(non_clause).  [assumption].
7.57/7.64	3542 (all M all K_4 all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_4),N)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),M)),K_4))))) # label(fact_697_le__add__diff) # label(axiom) # label(non_clause).  [assumption].
7.57/7.64	3543 (all Y all X (hBOOL(hAPP(int,bool,even_odd_even(int),X)) -> (-hBOOL(hAPP(int,bool,even_odd_even(int),Y)) -> -hBOOL(hAPP(int,bool,even_odd_even(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X),Y)))))) # label(fact_1263_Parity_Oeven__plus__odd) # label(axiom) # label(non_clause).  [assumption].
7.57/7.64	3544 (all K_4 hAPP(product_prod(int,int),rat,frct,hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),zero_zero(int)),K_4)) = zero_zero(rat)) # label(fact_3709_Frct__code__post_I1_J) # label(axiom) # label(non_clause).  [assumption].
7.57/7.64	3545 (all Z all Z_3 ((hBOOL(hAPP(int,bool,nat_neg,Z_3)) -> hAPP(int,nat,nat_1,Z) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(int,nat,nat_1,Z)),hAPP(int,nat,nat_1,Z_3))) & (-hBOOL(hAPP(int,bool,nat_neg,Z_3)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),hAPP(bool,fun(nat,fun(nat,nat)),if(nat),hAPP(int,bool,nat_neg,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),Z),Z_3))),zero_zero(nat)),hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),Z),Z_3))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(int,nat,nat_1,Z)),hAPP(int,nat,nat_1,Z_3))))) # label(fact_3835_diff__nat__eq__if) # label(axiom) # label(non_clause).  [assumption].
7.57/7.64	3546 (all X_a all A_3 hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_3),A_3))) # label(fact_1960_subset__refl) # label(axiom) # label(non_clause).  [assumption].
7.57/7.64	3547 (all X_a (archim1804426504_field(X_a) -> (all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),X)) -> (exists N_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,inverse_inverse(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),N_2))),X)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_2)))))))) # label(fact_2719_ex__inverse__of__nat__less) # label(axiom) # label(non_clause).  [assumption].
7.57/7.64	3548 (all X_a (division_ring(X_a) -> (all A_1 all B (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B) = one_one(X_a) -> ti(X_a,B) = hAPP(X_a,X_a,inverse_inverse(X_a),A_1))))) # label(fact_2552_inverse__unique) # label(axiom) # label(non_clause).  [assumption].
7.57/7.64	3549 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,number_number_of(real),min_1)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X),one_one(real))) -> hAPP(real,real,sin,hAPP(real,real,arccos,X)) = hAPP(real,real,sqrt,hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),one_one(real)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))))) # label(fact_2288_sin__arccos) # label(axiom) # label(non_clause).  [assumption].
7.57/7.64	3550 (all X_b all X_a all F all A_3 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),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_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),A_3))),hAPP(fun(X_a,bool),nat,finite_card(X_a),A_3))))) # label(fact_3643_card__image__le) # label(axiom) # label(non_clause).  [assumption].
7.57/7.64	3551 (all R_4 all S_3 all T_5 all R_5 all S_4 all M all T_6 all N (hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),S_4),M)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),T_6),N)) = ti(int,R_5) -> (ti(int,R_4) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),S_3),M)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),T_5),N)) -> hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),S_4),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),R_5),R_4)),S_3))),M)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),T_6),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),R_5),R_4)),T_5))),N)) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),R_5),R_4)))) # label(fact_968_xzgcda__linear__aux2) # label(axiom) # label(non_clause).  [assumption].
7.57/7.64	3552 (all A_1 all B hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,uminus_uminus(int),A_1)),B) = hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_1),hAPP(int,int,uminus_uminus(int),B))) # label(fact_2147_zdiv__zminus2) # label(axiom) # label(non_clause).  [assumption].
7.57/7.64	3553 (all Q_3 all B all R_4 all C (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),C)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),R_4)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),R_4),B)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),Q_3),C))),R_4)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),C))))))) # label(fact_1059_zmult2__lemma__aux4) # label(axiom) # label(non_clause).  [assumption].
7.57/7.64	3554 (all X_a all X_b all X_c all X_1 all P_1 ((all A_4 all B_4 all C_4 hBOOL(hAPP(product_prod(X_a,product_prod(X_b,X_c)),bool,P_1,hAPP(product_prod(X_b,X_c),product_prod(X_a,product_prod(X_b,X_c)),hAPP(X_a,fun(product_prod(X_b,X_c),product_prod(X_a,product_prod(X_b,X_c))),product_Pair(X_a,product_prod(X_b,X_c)),A_4),hAPP(X_c,product_prod(X_b,X_c),hAPP(X_b,fun(X_c,product_prod(X_b,X_c)),product_Pair(X_b,X_c),B_4),C_4))))) -> hBOOL(hAPP(product_prod(X_a,product_prod(X_b,X_c)),bool,P_1,X_1)))) # label(fact_3148_prod__induct3) # label(axiom) # label(non_clause).  [assumption].
7.57/7.64	3555 (all M all K_4 all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),K_4)),N)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N)))) # label(fact_578_add__leD1) # label(axiom) # label(non_clause).  [assumption].
7.57/7.64	3556 (all X_a (linord1117847801e_zero(X_a) -> (all A_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,inverse_inverse(X_a),A_2)),zero_zero(X_a))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),zero_zero(X_a))))))) # label(fact_2542_inverse__negative__iff__negative) # label(axiom) # label(non_clause).  [assumption].
7.57/7.64	3557 (all X_a all X_b (ord(X_b) -> (all X_1 all F all G (hBOOL(hAPP(fun(X_a,X_b),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,X_b),bool),ord_less_eq(fun(X_a,X_b)),F),G)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_a,X_b,F,X_1)),hAPP(X_a,X_b,G,X_1))))))) # label(fact_1555_le__funD) # label(axiom) # label(non_clause).  [assumption].
7.57/7.64	3558 (all X_a (real_n2089651433ebra_1(X_a) & banach(X_a) -> (all X_1 hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,real),fun(nat,fun(X_a,X_a)),hAPP(fun(real,fun(X_a,X_a)),fun(fun(nat,real),fun(nat,fun(X_a,X_a))),combb(real,fun(X_a,X_a),nat),scaleR_scaleR(X_a)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),inverse_inverse(real)),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),fact_fact(nat))))),hAPP(X_a,fun(nat,X_a),power_power(X_a),X_1))))))) # label(fact_4748_summable__exp__generic) # label(axiom) # label(non_clause).  [assumption].
7.57/7.64	3559 (all Ma all V_1 (hAPP(int,int,number_number_of(int),V_1) = hAPP(nat,int,semiring_1_of_nat(int),Ma) <-> Ma = hAPP(int,nat,nat_1,hAPP(int,int,number_number_of(int),V_1)) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),V_1))))) # label(fact_1408_int__eq__iff__number__of) # label(axiom) # label(non_clause).  [assumption].
7.57/7.64	3560 (all X_a (real_normed_vector(X_a) -> (all A_1 all A_6 all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_1),B)),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_6),B)) = hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A_1),A_6)),B)))) # label(fact_4715_scaleR_Odiff__left) # label(axiom) # label(non_clause).  [assumption].
7.57/7.64	3561 (all X_b all X_a (real_normed_vector(X_b) & real_normed_vector(X_a) -> (all F all L_2 all A_2 ((all R_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),R_2)) -> (exists S_1 ((all X_2 (ti(X_a,A_2) != ti(X_a,X_2) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),X_2),A_2))),S_1)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_b,real,norm_norm(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),hAPP(X_a,X_b,F,X_2)),L_2))),R_2)))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),S_1)))))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),L_2),hAPP(X_a,filter(X_a),at(X_a),A_2))))))) # label(fact_4663_LIM__I) # label(axiom) # label(non_clause).  [assumption].
7.57/7.64	3562 (all X_a (ordered_ab_group_add(X_a) -> (all X all Y all Z_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),Y)),Z_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),X),Z_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),Y),Z_1))))) # label(fact_4958_max__diff__distrib__left) # label(axiom) # label(non_clause).  [assumption].
7.57/7.64	3563 (all Z_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Z_1)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),Z_1))))) # label(fact_88_le__imp__0__less) # label(axiom) # label(non_clause).  [assumption].
7.57/7.64	3564 (all X_a (comm_ring_1(X_a) -> (all X all N (hBOOL(hAPP(nat,bool,even_odd_even(nat),N)) -> hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),X)),N) = hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),N))))) # label(fact_2424_Parity_Opower__minus__even) # label(axiom) # label(non_clause).  [assumption].
7.57/7.64	3565 (all X_b all X_a (topological_space(X_a) & topological_space(X_b) -> (all K all X_1 hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(X_b,fun(X_a,X_b),combk(X_b,X_a),K)),K),hAPP(X_a,filter(X_a),at(X_a),X_1)))))) # label(fact_4561_LIM__const) # label(axiom) # label(non_clause).  [assumption].
7.57/7.64	3566 (all U all M all N all J_2 all I_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),J_2),I_1)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I_1),J_2)),U)),M)),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),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_2),U)),N)))) # label(fact_753_nat__diff__add__eq1) # label(axiom) # label(non_clause).  [assumption].
7.57/7.64	3567 (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)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),one_one(nat))),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))) # label(fact_1156_Suc__n__div__2__gt__zero) # label(axiom) # label(non_clause).  [assumption].
7.57/7.64	3568 (all L all U_1 hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),U_1),L)) = hAPP(fun(int,bool),nat,finite_card(int),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastLessThan(int),L),U_1))) # label(fact_4259_card__atLeastLessThan__int) # label(axiom) # label(non_clause).  [assumption].
7.57/7.64	3569 (all X_a (ab_group_add(X_a) -> (all A_1 all C all B all D hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B),D)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_1),B)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),C),D))))) # label(fact_722_add__diff__add) # label(axiom) # label(non_clause).  [assumption].
7.57/7.64	3570 (all B all X all A_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),A_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),B)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),A_1),B)))))) # label(fact_3235_gcd__semilattice__nat_Ole__infI) # label(axiom) # label(non_clause).  [assumption].
7.57/7.64	3571 (all T_1 comple44059174attice(filter(T_1))) # label(arity_Limits_Ofilter___Complete__Lattice_Ocomplete__lattice) # label(axiom) # label(non_clause).  [assumption].
7.57/7.64	3572 (all X_a all A_3 all B_2 (hBOOL(hAPP(fun(fun(X_a,bool),bool),bool,hAPP(fun(X_a,bool),fun(fun(fun(X_a,bool),bool),bool),member(fun(X_a,bool)),A_3),hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),pow(X_a),B_2))) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_3),B_2)))) # label(fact_2780_PowD) # label(axiom) # label(non_clause).  [assumption].
7.57/7.64	3573 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X)) -> (zero_zero(real) = hAPP(real,real,sqrt,X) -> X = zero_zero(real)))) # label(fact_1621_real__sqrt__eq__zero__cancel) # label(axiom) # label(non_clause).  [assumption].
7.57/7.64	3574 (all X_a (linorder(X_a) -> (all X all Y ti(X_a,X) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),Y))))) # label(fact_4941_min__max_Oinf__sup__absorb) # label(axiom) # label(non_clause).  [assumption].
7.57/7.64	3575 (all Ma all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),hAPP(nat,nat,suc,N_1))) <-> N_1 = Ma | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),N_1)))) # label(fact_1238_less__Suc__eq) # label(axiom) # label(non_clause).  [assumption].
7.57/7.64	3576 (all A_2 all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,real_1(int),A_2)),X_1)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A_2),hAPP(real,int,archim2085082626_floor(real),X_1))))) # label(fact_3364_le__floor__eq) # label(axiom) # label(non_clause).  [assumption].
7.57/7.64	3577 (all B all A_1 (B != zero_zero(nat) | A_1 != zero_zero(nat) -> one_one(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),A_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),A_1),B))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),A_1),B))))) # label(fact_3291_div__gcd__coprime__nat) # label(axiom) # label(non_clause).  [assumption].
7.57/7.64	3578 (all A_2 (hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),A_2),zero_zero(real)),sequentially)) -> (hBOOL(hAPP(fun(nat,real),bool,monoseq(real),A_2)) -> hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),min_1)))),A_2)))))) # label(fact_4499_summable__Leibniz_I1_J) # label(axiom) # label(non_clause).  [assumption].
7.57/7.64	3579 (all X_a (number_ring(X_a) -> (all Y_1 (hBOOL(hAPP(X_a,bool,iszero(X_a),hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,bit1,pls)),hAPP(int,int,uminus_uminus(int),Y_1))))) <-> one_one(X_a) = hAPP(int,X_a,number_number_of(X_a),Y_1))))) # label(fact_2504_eq__special_I2_J) # label(axiom) # label(non_clause).  [assumption].
7.57/7.64	3580 (all X hAPP(int,int,abs_abs(int),X) = hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),X),zero_zero(int))) # label(fact_4388_gcd__0__int) # label(axiom) # label(non_clause).  [assumption].
7.57/7.64	3581 (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_796_diff__0__right) # label(axiom) # label(non_clause).  [assumption].
7.57/7.64	3582 (all A_1 all X hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),A_1),X) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A_1),X)) # label(fact_4673_real__scaleR__def) # label(axiom) # label(non_clause).  [assumption].
7.57/7.64	3583 -(all S_1 -(hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),S_1),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int)))) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,s1),S_1),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int)))) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),S_1)))) # label(fact_196__096_B_Bthesis_O_A_I_B_Bs_O_A0_A_060_061_As_A_G_As_A_060_A4_A_K_Am_A_L_) # label(axiom) # label(non_clause).  [assumption].
7.57/7.64	3584 (all Ma all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Ma),N_1)) <-> (exists K_1 N_1 = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Ma),K_1)))) # label(fact_571_le__iff__add) # label(axiom) # label(non_clause).  [assumption].
7.57/7.64	3585 (all X_a (order(X_a) -> (all X_1 all Y_1 all F (hBOOL(hAPP(fun(nat,X_a),bool,hAPP(fun(nat,fun(nat,bool)),fun(fun(nat,X_a),bool),strict_mono(nat,X_a),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),hAPP(fun(nat,fun(fun(nat,bool),fun(nat,bool))),fun(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool))),combs(nat,fun(nat,bool),fun(nat,bool)),hAPP(fun(nat,fun(nat,fun(bool,bool))),fun(nat,fun(fun(nat,bool),fun(nat,bool))),hAPP(fun(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool))),fun(fun(nat,fun(nat,fun(bool,bool))),fun(nat,fun(fun(nat,bool),fun(nat,bool)))),combb(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),nat),combs(nat,bool,bool)),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,fun(bool,bool))),hAPP(fun(fun(nat,bool),fun(nat,fun(bool,bool))),fun(fun(nat,fun(nat,bool)),fun(nat,fun(nat,fun(bool,bool)))),combb(fun(nat,bool),fun(nat,fun(bool,bool)),nat),hAPP(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fconj)),dvd_dvd(nat)))),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),hAPP(fun(fun(nat,bool),fun(nat,bool)),fun(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool))),combb(fun(nat,bool),fun(nat,bool),nat),hAPP(fun(bool,bool),fun(fun(nat,bool),fun(nat,bool)),combb(bool,bool,nat),fNot)),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),dvd_dvd(nat))))),F)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_1),Y_1)) & -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y_1),X_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,F,X_1)),hAPP(nat,X_a,F,Y_1)))))))) # label(fact_4790_dvd_Ostrict__monoD) # label(axiom) # label(non_clause).  [assumption].
7.57/7.64	3586 (all X_a (linorder(X_a) -> (all A_1 all X all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),B)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),A_1),B))))))) # label(fact_4981_min__max_Ole__supI2) # label(axiom) # label(non_clause).  [assumption].
7.57/7.64	3587 (all X_a complex_case(X_a) = ti(fun(fun(real,fun(real,X_a)),fun(complex,X_a)),complex_case(X_a))) # label(tsy_c_Complex_Ocomplex_Ocomplex__case_res) # label(axiom) # label(non_clause).  [assumption].
7.57/7.64	3588 (all A_1 all N all P_5 (hBOOL(hAPP(int,bool,zprime,P_5)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),P_5),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A_1),N))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),P_5),A_1))))) # label(fact_199_zprime__zdvd__power) # label(axiom) # label(non_clause).  [assumption].
7.57/7.64	3589 (all N_1 all A_2 (hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),A_2),zero_zero(real)),sequentially)) -> ((all N_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(nat,real,A_2,N_2)))) -> ((all N_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,A_2,hAPP(nat,nat,suc,N_2))),hAPP(nat,real,A_2,N_2)))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),min_1)))),A_2)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),N_1)))),hAPP(fun(nat,real),real,suminf(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),min_1)))),A_2)))))))) # label(fact_4516_summable__Leibniz_H_I2_J) # label(axiom) # label(non_clause).  [assumption].
7.57/7.64	3590 (all L_4 all K_4 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),K_4)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),L_4)) -> hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),posDivAlg,K_4),L_4) = hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),K_4),L_4)),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),K_4),L_4))))) # label(fact_1155_posDivAlg__div__mod) # label(axiom) # label(non_clause).  [assumption].
7.57/7.64	3591 (all I_1 all J_2 hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,I_1),J_2)))) # label(fact_3445_zgcd__pos) # label(axiom) # label(non_clause).  [assumption].
7.57/7.64	3592 (all X_b all X_a (real_normed_algebra(X_b) & topological_space(X_a) -> (all G all M_1 all F all L_2 all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),L_2),hAPP(X_a,filter(X_a),at(X_a),A_2))) -> (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),G),M_1),hAPP(X_a,filter(X_a),at(X_a),A_2))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(fun(X_a,X_b),fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,X_b)),combs(X_a,X_b,X_b),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,fun(X_b,X_b))),combb(X_b,fun(X_b,X_b),X_a),times_times(X_b)),F)),G)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),L_2),M_1)),hAPP(X_a,filter(X_a),at(X_a),A_2)))))))) # label(fact_4548_LIM__mult) # label(axiom) # label(non_clause).  [assumption].
7.57/7.64	3593 (all X hAPP(real,real,cos,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),pi)) = hAPP(real,real,uminus_uminus(real),hAPP(real,real,cos,X))) # label(fact_2220_cos__periodic__pi) # label(axiom) # label(non_clause).  [assumption].
7.57/7.64	3594 (all N_4 (hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),N_4)) <-> (exists M_2 all X_2 (hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X_2),N_4)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X_2),M_2)))))) # label(fact_3674_finite__nat__set__iff__bounded) # label(axiom) # label(non_clause).  [assumption].
7.57/7.64	3595 (all Y all X (hBOOL(hAPP(int,bool,even_odd_even(int),X)) -> (hBOOL(hAPP(int,bool,even_odd_even(int),Y)) -> hBOOL(hAPP(int,bool,even_odd_even(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X),Y)))))) # label(fact_1264_Parity_Oeven__plus__even) # label(axiom) # label(non_clause).  [assumption].
7.57/7.64	3596 (all N all D (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),D)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),D),N)) -> hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(nat,real,real_1(nat),N)),hAPP(nat,real,real_1(nat),D)) = hAPP(nat,real,real_1(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),N),D))))) # label(fact_2354_real__of__nat__div) # label(axiom) # label(non_clause).  [assumption].
7.57/7.64	3597 (all N all X all Y (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),Y)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),X),N)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),Y),N))))) # label(fact_718_divides__exp) # label(axiom) # label(non_clause).  [assumption].
7.57/7.64	3598 (all W all Z_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W),Z_1)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),W),one_one(int))),Z_1)))) # label(fact_83_zless__imp__add1__zle) # label(axiom) # label(non_clause).  [assumption].
7.57/7.64	3599 (all A_3 hAPP(fun(int,bool),fun(nat,bool),hAPP(fun(int,nat),fun(fun(int,bool),fun(nat,bool)),image(int,nat),nat_1),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),A_3)) = A_3) # label(fact_3650_transfer__int__nat__set__return__embed) # label(axiom) # label(non_clause).  [assumption].
7.57/7.64	3600 (all X_b (ord(X_b) -> ord_less_eq(X_b) = ti(fun(X_b,fun(X_b,bool)),ord_less_eq(X_b)))) # label(tsy_c_Orderings_Oord__class_Oless__eq_res) # label(axiom) # label(non_clause).  [assumption].
7.57/7.64	3601 (all X_1 all K (ti(int,X_1) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),K)),one_one(int)) -> hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),zOdd)))) # label(fact_903_zOddI) # label(axiom) # label(non_clause).  [assumption].
7.57/7.64	3602 (all K_4 all L_4 hAPP(int,int,bit0,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),K_4),L_4)) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,bit1,K_4)),hAPP(int,int,bit1,L_4))) # label(fact_494_diff__bin__simps_I10_J) # label(axiom) # label(non_clause).  [assumption].
7.57/7.64	3603 (all X_1 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(nat,fun(real,real),hAPP(fun(real,fun(nat,real)),fun(nat,fun(real,real)),combc(real,nat,real),hAPP(fun(real,real),fun(real,fun(nat,real)),hAPP(fun(real,fun(nat,real)),fun(fun(real,real),fun(real,fun(nat,real))),combb(real,fun(nat,real),real),power_power(real)),cos)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),X_1),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,uminus_uminus(real),hAPP(real,real,sin,X_1))),hAPP(real,real,cos,X_1))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,uminus_uminus(real),hAPP(real,real,sin,X_1))),hAPP(real,real,cos,X_1)))))) # label(fact_3914_DERIV__cos__realpow2) # label(axiom) # label(non_clause).  [assumption].
7.57/7.64	3604 (all N_1 all Ma (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(quickcheck_code_int,int,quickcheck_int_of,N_1)),hAPP(quickcheck_code_int,int,quickcheck_int_of,Ma))) <-> hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),N_1),Ma)))) # label(fact_3160_less__code__int__def) # label(axiom) # label(non_clause).  [assumption].
7.57/7.64	3605 (all X_a (real_normed_algebra(X_a) -> (all Y_1 all X_3 (hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),X_3)) -> hAPP(fun(nat,X_a),X_a,suminf(X_a),hAPP(X_a,fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(X_a,fun(nat,X_a)),combc(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),times_times(X_a)),X_3)),Y_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(fun(nat,X_a),X_a,suminf(X_a),X_3)),Y_1))))) # label(fact_3987_mult__left_Osuminf) # label(axiom) # label(non_clause).  [assumption].
7.57/7.64	3606 (all K_4 all L_4 hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,bit0,K_4)),hAPP(int,int,bit1,L_4)) = hAPP(int,int,bit1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,pred,K_4)),L_4))) # label(fact_2909_diff__bin__simps_I8_J) # label(axiom) # label(non_clause).  [assumption].
7.57/7.64	3607 (all X_a (real_normed_algebra(X_a) -> (all C_1 all F (hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),F)) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(fun(nat,X_a),X_a,suminf(X_a),F)),C_1) = hAPP(fun(nat,X_a),X_a,suminf(X_a),hAPP(X_a,fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(X_a,fun(nat,X_a)),combc(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),times_times(X_a)),F)),C_1)))))) # label(fact_3989_suminf__mult2) # label(axiom) # label(non_clause).  [assumption].
7.57/7.64	3608 (all X all Y hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),X),Y)),X))) # label(fact_3246_gcd__semilattice__nat_Oinf__le1) # label(axiom) # label(non_clause).  [assumption].
7.57/7.64	3609 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),M),N) = zero_zero(nat)) & (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N)) -> hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N)),N)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),M),N)))) # label(fact_1417_div__if) # label(axiom) # label(non_clause).  [assumption].
7.57/7.64	3610 (all X_a (field_char_0(X_a) -> (all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_2),field_char_0_Rats(X_a))) -> (ti(X_a,A_2) != zero_zero(X_a) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),hAPP(X_a,X_a,inverse_inverse(X_a),A_2)),field_char_0_Rats(X_a)))))))) # label(fact_3688_nonzero__Rats__inverse) # label(axiom) # label(non_clause).  [assumption].
7.57/7.64	3611 (all X_b all X_a (comm_monoid_mult(X_a) -> (all A_3 one_one(X_a) = hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co302546470etprod(X_b,X_a),hAPP(X_a,fun(X_b,X_a),combk(X_a,X_b),one_one(X_a))),A_3)))) # label(fact_3947_setprod__1) # label(axiom) # label(non_clause).  [assumption].
7.57/7.64	3612 (all X_a (number_ring(X_a) -> hAPP(X_a,X_a,uminus_uminus(X_a),one_one(X_a)) = hAPP(int,X_a,number_number_of(X_a),min_1))) # label(fact_2103_arith__simps_I31_J) # label(axiom) # label(non_clause).  [assumption].
7.57/7.64	3613 (all Y_3 all X_3 (hBOOL(hAPP(fun(nat,rat),bool,vanishes,X_3)) -> (hBOOL(hAPP(fun(nat,rat),bool,vanishes,Y_3)) -> hBOOL(hAPP(fun(nat,rat),bool,vanishes,hAPP(fun(nat,rat),fun(nat,rat),hAPP(fun(nat,fun(rat,rat)),fun(fun(nat,rat),fun(nat,rat)),combs(nat,rat,rat),hAPP(fun(nat,rat),fun(nat,fun(rat,rat)),hAPP(fun(rat,fun(rat,rat)),fun(fun(nat,rat),fun(nat,fun(rat,rat))),combb(rat,fun(rat,rat),nat),plus_plus(rat)),X_3)),Y_3)))))) # label(fact_4842_vanishes__add) # label(axiom) # label(non_clause).  [assumption].
7.57/7.64	3614 (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)) -> ti(X_a,X) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),Y))))) # label(fact_4823_min__max_Oinf__absorb1) # label(axiom) # label(non_clause).  [assumption].
7.57/7.64	3615 (all X_a (monoid_mult(X_a) -> (all Y all P_5 all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),P_5),N)) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),Y),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),P_5))),Y) = hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),Y),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,N)),P_5)))))) # label(fact_1412_lemma__realpow__diff) # label(axiom) # label(non_clause).  [assumption].
7.57/7.64	3616 (all X_a (linordered_idom(X_a) -> (all K_4 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),K_4),hAPP(X_a,X_a,sgn_sgn(X_a),K_4)) = hAPP(X_a,X_a,abs_abs(X_a),K_4)))) # label(fact_2214_abs__sgn) # label(axiom) # label(non_clause).  [assumption].
7.57/7.64	3617 (all N_1 (-hBOOL(hAPP(nat,bool,even_odd_even(nat),N_1)) <-> (exists M_2 hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),M_2)) = N_1))) # label(fact_2469_odd__Suc__mult__two__ex) # label(axiom) # label(non_clause).  [assumption].
7.57/7.64	3618 (all R_4 hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,R_4),zero_zero(real)) = hAPP(real,complex,of_real(complex),R_4)) # label(fact_2791_complex__of__real__def) # label(axiom) # label(non_clause).  [assumption].
7.57/7.64	3619 (all A_2 all P_4 all X_2 (hBOOL(hAPP(fun(fun(int,bool),bool),bool,hAPP(fun(int,bool),fun(fun(fun(int,bool),bool),bool),member(fun(int,bool)),X_2),hAPP(int,fun(fun(int,bool),bool),hAPP(int,fun(int,fun(fun(int,bool),bool)),setS,A_2),P_4))) -> hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),X_2)))) # label(fact_1670_SetS__elems__finite) # label(axiom) # label(non_clause).  [assumption].
7.57/7.64	3620 (all X_a (real_normed_vector(X_a) -> (all X all Y hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X),Y))),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(X_a,real,norm_norm(X_a),X)),hAPP(X_a,real,norm_norm(X_a),Y))))))) # label(fact_1791_norm__triangle__ineq) # label(axiom) # label(non_clause).  [assumption].
7.57/7.64	3621 (all X_a (comm_monoid_add(X_a) -> (all F all Ma all N_1 hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,suc,Ma)),hAPP(nat,nat,suc,N_1))) = hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),hAPP(fun(nat,nat),fun(nat,X_a),hAPP(fun(nat,X_a),fun(fun(nat,nat),fun(nat,X_a)),combb(nat,X_a,nat),F),suc)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),Ma),N_1))))) # label(fact_4544_setsum__shift__bounds__cl__Suc__ivl) # label(axiom) # label(non_clause).  [assumption].
7.57/7.64	3622 (all X_a (real_normed_vector(X_a) -> (all X_3 all L_2 (hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),X_3),L_2),sequentially)) <-> (all R_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),R_2)) -> (exists No all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),No),N_2)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(nat,X_a,X_3,N_2)),L_2))),R_2)))))))))) # label(fact_4518_LIMSEQ__iff) # label(axiom) # label(non_clause).  [assumption].
7.57/7.64	3623 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),M),N) = M)) # label(fact_1089_mod__less) # label(axiom) # label(non_clause).  [assumption].
7.57/7.64	3624 (all X_b all X_a (real_normed_field(X_a) & real_normed_vector(X_b) -> (all F all K_3 all K (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),K)) -> ((all H_1 (zero_zero(X_a) != ti(X_a,H_1) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,norm_norm(X_a),H_1)),K)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_b,real,norm_norm(X_b),hAPP(X_a,X_b,F,H_1))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),K_3),hAPP(X_a,real,norm_norm(X_a),H_1))))))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),zero_zero(X_b)),hAPP(X_a,filter(X_a),at(X_a),zero_zero(X_a))))))))) # label(fact_4626_lemma__termdiff4) # label(axiom) # label(non_clause).  [assumption].
7.57/7.64	3625 (all X_a (linordered_semidom(X_a) -> (all N all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),one_one(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),hAPP(nat,nat,suc,N))),one_one(X_a)))))))) # label(fact_1404_power__Suc__less__one) # label(axiom) # label(non_clause).  [assumption].
7.57/7.64	3626 (all X_a (metric_space(X_a) -> (all X_3 (hBOOL(hAPP(fun(nat,X_a),bool,cauchy(X_a),X_3)) <-> (all E (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),E)) -> (exists M_3 all M_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_3),M_2)) -> (all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_3),N_2)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),hAPP(nat,X_a,X_3,M_2)),hAPP(nat,X_a,X_3,N_2))),E)))))))))))) # label(fact_3522_Cauchy__def) # label(axiom) # label(non_clause).  [assumption].
7.57/7.64	3627 (all X hAPP(real,real,tan,X) = hAPP(real,real,tan,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),pi)))) # label(fact_2266_tan__periodic) # label(axiom) # label(non_clause).  [assumption].
7.57/7.64	3628 (all X_b all X_a (real_normed_algebra(X_b) & topological_space(X_a) -> (all X_1 all G all L all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),G),L),hAPP(X_a,filter(X_a),at(X_a),A_2))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(fun(X_a,X_b),fun(X_a,X_b),hAPP(fun(X_b,X_b),fun(fun(X_a,X_b),fun(X_a,X_b)),combb(X_b,X_b,X_a),hAPP(X_b,fun(X_b,X_b),times_times(X_b),X_1)),G)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),X_1),L)),hAPP(X_a,filter(X_a),at(X_a),A_2))))))) # label(fact_4550_mult__right_OLIM) # label(axiom) # label(non_clause).  [assumption].
7.57/7.64	3629 (all X_a all C_2 all A_3 all B_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less(fun(X_a,bool)),A_3),B_2)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less(fun(X_a,bool)),B_2),C_2)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less(fun(X_a,bool)),A_3),C_2))))) # label(fact_1973_psubset__trans) # label(axiom) # label(non_clause).  [assumption].
7.57/7.64	3630 (all N N = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,N)),one_one(nat))) # label(fact_1346_diff__Suc__1) # label(axiom) # label(non_clause).  [assumption].
7.57/7.64	3631 (all X_1 ((exists N_2 (hBOOL(hAPP(nat,bool,even_odd_even(nat),N_2)) & hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,real_1(nat),N_2)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) = X_1)) | (exists N_2 (X_1 = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,real_1(nat),N_2)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) & hBOOL(hAPP(nat,bool,even_odd_even(nat),N_2)))) <-> hAPP(real,real,sin,X_1) = zero_zero(real))) # label(fact_2411_sin__zero__iff) # label(axiom) # label(non_clause).  [assumption].
7.57/7.64	3632 (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_238_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) # label(axiom) # label(non_clause).  [assumption].
7.57/7.64	3633 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(real,real,ln,X))) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),one_one(real)),X))))) # label(fact_1974_ln__ge__zero__imp__ge__one) # label(axiom) # label(non_clause).  [assumption].
7.57/7.64	3634 (all Y all X (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Y)) -> hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),X),Y)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(int,nat,nat_1,X)),hAPP(int,nat,nat_1,Y))))) # label(fact_1097_Divides_Otransfer__nat__int__functions_I2_J) # label(axiom) # label(non_clause).  [assumption].
7.57/7.64	3635 (all X_a (comm_semiring_1(X_a) -> (all X hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),one_one(nat)) = ti(X_a,X)))) # label(fact_227_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J) # label(axiom) # label(non_clause).  [assumption].
7.57/7.64	3636 (all N_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),N_1)) -> hAPP(nat,int,semiring_1_of_nat(int),hAPP(fun(int,bool),nat,finite_card(int),hAPP(fun(int,bool),fun(int,bool),collect(int),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),combs(int,bool,bool),hAPP(fun(int,bool),fun(int,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj),hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)))),hAPP(int,fun(int,bool),hAPP(fun(int,fun(int,bool)),fun(int,fun(int,bool)),combc(int,int,bool),ord_less(int)),N_1))))) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),N_1),one_one(int)))) # label(fact_3881_int__card__bdd__int__set__l__l) # label(axiom) # label(non_clause).  [assumption].
7.57/7.64	3637 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,sqrt,X)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))) # label(fact_1642_real__sqrt__pow2__gt__zero) # label(axiom) # label(non_clause).  [assumption].
7.57/7.64	3638 (all A_2 all B_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B_1)) -> (hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(int,rat,hAPP(int,fun(int,rat),fract,A_2),B_1)),zero_zero(rat))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_2),zero_zero(int)))))) # label(fact_3782_Fract__less__zero__iff) # label(axiom) # label(non_clause).  [assumption].
7.57/7.64	3639 (all X_a (real_vector(X_a) -> (all A_1 all X all Y hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_1),X)),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_1),Y)) = hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),X),Y))))) # label(fact_4720_scaleR__right_Odiff) # label(axiom) # label(non_clause).  [assumption].
7.57/7.64	3640 (all X_a (linorder(X_a) -> (all Y all Z_1 all X hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),Y),Z_1)),X) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),Y),X)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),Z_1),X))))) # label(fact_4937_min__max_Oinf__sup__distrib2) # label(axiom) # label(non_clause).  [assumption].
7.57/7.64	3641 (all X_b all X_a (uminus(X_a) -> (all A_3 all X_1 hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(X_b,X_a,A_3,X_1)) = hAPP(X_b,X_a,hAPP(fun(X_b,X_a),fun(X_b,X_a),uminus_uminus(fun(X_b,X_a)),A_3),X_1)))) # label(fact_2928_uminus__apply) # label(axiom) # label(non_clause).  [assumption].
7.57/7.64	3642 (all X_a (semiring_div(X_a) -> (all Z_1 all W all Y all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),Y),X)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),Z_1),W)) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),W)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Y),Z_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),div_div(X_a),X),Y)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),W),Z_1))))))) # label(fact_1000_div__mult__div__if__dvd) # label(axiom) # label(non_clause).  [assumption].
7.57/7.64	3643 (all B_1 all A_2 all D_1 (ti(int,D_1) = hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),A_2),B_1) <-> (all E (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),E),B_1)) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),E),A_2)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),E),D_1)))) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),D_1),B_1)) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),D_1),A_2)) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),D_1)))) # label(fact_4395_gcd__unique__int) # label(axiom) # label(non_clause).  [assumption].
7.57/7.64	3644 (all X_b all X_a (topological_space(X_a) & real_normed_vector(X_b) -> (all G all F all A_2 (hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,real),fun(X_a,bool),isCont(X_a,real),F),A_2)) -> (hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,X_b),fun(X_a,bool),isCont(X_a,X_b),G),A_2)) -> hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,X_b),fun(X_a,bool),isCont(X_a,X_b),hAPP(fun(X_a,X_b),fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,X_b)),combs(X_a,X_b,X_b),hAPP(fun(X_a,real),fun(X_a,fun(X_b,X_b)),hAPP(fun(real,fun(X_b,X_b)),fun(fun(X_a,real),fun(X_a,fun(X_b,X_b))),combb(real,fun(X_b,X_b),X_a),scaleR_scaleR(X_b)),F)),G)),A_2))))))) # label(fact_4916_isCont__scaleR) # label(axiom) # label(non_clause).  [assumption].
7.57/7.64	3645 (all X_a all A_3 all B_2 (ti(fun(X_a,bool),A_3) = ti(fun(X_a,bool),B_2) <-> hAPP(fun(X_a,bool),fun(X_a,bool),uminus_uminus(fun(X_a,bool)),A_3) = hAPP(fun(X_a,bool),fun(X_a,bool),uminus_uminus(fun(X_a,bool)),B_2))) # label(fact_2195_Compl__eq__Compl__iff) # label(axiom) # label(non_clause).  [assumption].
7.57/7.65	3646 (all M (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),M)) -> hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,M),M) = ti(int,M))) # label(fact_3444_zgcd__self) # label(axiom) # label(non_clause).  [assumption].
7.57/7.65	3647 (all Ma all N_1 (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),Ma)),N_1)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,Ma)),N_1)))) # label(fact_4120_less__eq__nat_Osimps_I2_J) # label(axiom) # label(non_clause).  [assumption].
7.57/7.65	3648 (all W_1 all Z (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),Z)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(int,nat,nat_1,W_1)),hAPP(int,nat,nat_1,Z))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_1),Z))))) # label(fact_1126_nat__mono__iff) # label(axiom) # label(non_clause).  [assumption].
7.57/7.65	3649 (all X_a all X_b (comm_monoid_add(X_b) -> (all F all S (hBOOL(hAPP(fun(fun(X_a,bool),bool),bool,finite_finite_1(fun(X_a,bool)),S)) -> ((all X_2 (hBOOL(hAPP(fun(fun(X_a,bool),bool),bool,hAPP(fun(X_a,bool),fun(fun(fun(X_a,bool),bool),bool),member(fun(X_a,bool)),X_2),S)) -> hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),X_2)))) -> ((all T1 (hBOOL(hAPP(fun(fun(X_a,bool),bool),bool,hAPP(fun(X_a,bool),fun(fun(fun(X_a,bool),bool),bool),member(fun(X_a,bool)),T1),S)) -> (all T2 (hBOOL(hAPP(fun(fun(X_a,bool),bool),bool,hAPP(fun(X_a,bool),fun(fun(fun(X_a,bool),bool),bool),member(fun(X_a,bool)),T2),S)) -> (ti(fun(X_a,bool),T2) != ti(fun(X_a,bool),T1) -> (all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),T1)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),T2)) -> zero_zero(X_b) = hAPP(X_a,X_b,F,X_2))))))))) -> hAPP(fun(fun(X_a,bool),bool),X_b,hAPP(fun(fun(X_a,bool),X_b),fun(fun(fun(X_a,bool),bool),X_b),big_co1399186613setsum(fun(X_a,bool),X_b),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),F)),S) = hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),F),hAPP(fun(fun(X_a,bool),bool),fun(X_a,bool),complete_Sup_Sup(fun(X_a,bool)),S)))))))) # label(fact_4310_setsum__UNION__zero) # label(axiom) # label(non_clause).  [assumption].
7.57/7.65	3650 (all X_a (linorder(X_a) -> (all A_1 all X all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),B)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),A_1),B))))))) # label(fact_4952_min__max_Oless__supI2) # label(axiom) # label(non_clause).  [assumption].
7.57/7.65	3651 (all A_2 all B_1 all Ma (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_2),B_1),Ma)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_2),Ma)),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),B_1),Ma)),Ma)))) # label(fact_960_zcong__zmod) # label(axiom) # label(non_clause).  [assumption].
7.57/7.65	3652 (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_400_zero__le__one) # label(axiom) # label(non_clause).  [assumption].
7.57/7.65	3653 (all A_2 (hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),A_2),zero_zero(real)),sequentially)) -> (hBOOL(hAPP(fun(nat,real),bool,monoseq(real),A_2)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(nat,real,A_2,zero_zero(nat)))) -> (all N_2 hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),hAPP(fun(nat,real),real,suminf(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),min_1)))),A_2))),hAPP(real,fun(real,bool),hAPP(real,fun(real,fun(real,bool)),ord_atLeastAtMost(real),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),min_1)))),A_2)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),N_2)))),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),min_1)))),A_2)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),N_2)),one_one(nat)))))))))))) # label(fact_4523_summable__Leibniz_I2_J) # label(axiom) # label(non_clause).  [assumption].
7.57/7.65	3654 (all X all P_5 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),P_5)) -> (hBOOL(hAPP(int,bool,zprime,P_5)) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,X),zero_zero(int)),P_5)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),quadRes,P_5),X)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),X),hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),P_5),one_one(int))),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))),one_one(int)),P_5))))))) # label(fact_1079_Euler__part3) # label(axiom) # label(non_clause).  [assumption].
7.57/7.65	3655 (all M all N hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(nat,real,real_1(nat),M)),N) = hAPP(nat,real,real_1(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),M),N))) # label(fact_2311_real__of__nat__power) # label(axiom) # label(non_clause).  [assumption].
7.57/7.65	3656 (all X_b all X_a (real_normed_vector(X_b) & topological_space(X_a) -> (all F all L all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),L),hAPP(X_a,filter(X_a),at(X_a),A_2))) -> (ti(X_b,L) != zero_zero(X_b) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(fun(X_a,X_b),fun(X_a,X_b),hAPP(fun(X_b,X_b),fun(fun(X_a,X_b),fun(X_a,X_b)),combb(X_b,X_b,X_a),sgn_sgn(X_b)),F)),hAPP(X_b,X_b,sgn_sgn(X_b),L)),hAPP(X_a,filter(X_a),at(X_a),A_2)))))))) # label(fact_4590_LIM__sgn) # label(axiom) # label(non_clause).  [assumption].
7.57/7.65	3657 (all X_1 hBOOL(hAPP(real,bool,hAPP(fun(nat,real),fun(real,bool),sums(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),one_one(real)),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))) # label(fact_4103_Ln_Oaux2) # label(axiom) # label(non_clause).  [assumption].
7.57/7.65	3658 (all X_a all X_c all X_b all P all Q all R hAPP(X_b,X_c,hAPP(X_a,fun(X_b,X_c),P,R),Q) = 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)) # label(help_COMBC_1_1_U) # label(axiom) # label(non_clause).  [assumption].
7.57/7.65	3659 (all X_b all X_a all A_1 all B hAPP(product_prod(X_b,X_a),X_a,product_snd(X_b,X_a),hAPP(X_a,product_prod(X_b,X_a),hAPP(X_b,fun(X_a,product_prod(X_b,X_a)),product_Pair(X_b,X_a),A_1),B)) = ti(X_a,B)) # label(fact_3138_snd__conv) # label(axiom) # label(non_clause).  [assumption].
7.57/7.65	3660 (all Z (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Z),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),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),Z)),Z)),zero_zero(int))))) # label(fact_175_odd__less__0) # label(axiom) # label(non_clause).  [assumption].
7.57/7.65	3661 (all X_a (linordered_semidom(X_a) -> (all N hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(nat,X_a,semiring_1_of_nat(X_a),hAPP(nat,nat,fact_fact(nat),N))))))) # label(fact_2495_of__nat__fact__gt__zero) # label(axiom) # label(non_clause).  [assumption].
7.57/7.65	3662 (all Z_1 hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),Z_1),hAPP(complex,complex,cnj,Z_1))) = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(complex,real,norm_norm(complex),Z_1)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) # label(fact_2927_complex__mod__mult__cnj) # label(axiom) # label(non_clause).  [assumption].
7.57/7.65	3663 (all X all Y hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),X),Y) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),hAPP(real,real,uminus_uminus(real),Y))) # label(fact_2092_minus__real__def) # label(axiom) # label(non_clause).  [assumption].
7.57/7.65	3664 (all X_a (field_inverse_zero(X_a) -> zero_zero(X_a) = hAPP(X_a,X_a,inverse_inverse(X_a),zero_zero(X_a)))) # label(fact_2525_field__inverse__zero) # label(axiom) # label(non_clause).  [assumption].
7.57/7.65	3665 (all N all K_4 all M (hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,K_4),M) = one_one(int) -> (one_one(int) = hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,N),M) -> one_one(int) = hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K_4),N)),M)))) # label(fact_3431_zgcd__zgcd__zmult) # label(axiom) # label(non_clause).  [assumption].
7.57/7.65	3666 (all X_a all X_b (comm_monoid_add(X_b) -> (all G all H all A_3 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_3)) -> hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),hAPP(fun(X_a,X_b),fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,X_b)),combs(X_a,X_b,X_b),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,fun(X_b,X_b))),combb(X_b,fun(X_b,X_b),X_a),plus_plus(X_b)),G)),H)),A_3) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),G),A_3)),hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),H),A_3)))))) # label(fact_4219_setsum_Odistrib) # label(axiom) # label(non_clause).  [assumption].
7.57/7.65	3667 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),one_one(real)),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,uminus_uminus(real),X)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))),hAPP(real,real,ln,hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),one_one(real)),X))))))) # label(fact_2127_ln__one__minus__pos__lower__bound) # label(axiom) # label(non_clause).  [assumption].
7.57/7.65	3668 (all Y all X (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Y)) -> hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X),Y)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,nat_1,X)),hAPP(int,nat,nat_1,Y))))) # label(fact_1140_Nat__Transfer_Otransfer__nat__int__functions_I2_J) # label(axiom) # label(non_clause).  [assumption].
7.57/7.65	3669 (all X_b all X_a all F all A_2 all B_1 (hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),F,A_2),B_1)) -> hBOOL(hAPP(product_prod(X_a,X_b),bool,hAPP(fun(X_a,fun(X_b,bool)),fun(product_prod(X_a,X_b),bool),product_prod_case(X_a,X_b,bool),F),hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),A_2),B_1))))) # label(fact_4040_splitI) # label(axiom) # label(non_clause).  [assumption].
7.57/7.65	3670 (all X_a (monoid_mult(X_a) -> (all N hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),one_one(X_a)),N) = one_one(X_a)))) # label(fact_341_power__one) # label(axiom) # label(non_clause).  [assumption].
7.57/7.65	3671 (all X_a (real_algebra_1(X_a) & number_ring(X_a) -> (all W hAPP(int,X_a,number_number_of(X_a),W) = hAPP(real,X_a,of_real(X_a),hAPP(int,real,number_number_of(real),W))))) # label(fact_2785_of__real__number__of__eq) # label(axiom) # label(non_clause).  [assumption].
7.57/7.65	3672 (all X_a (real_normed_field(X_a) & banach(X_a) -> (all X hAPP(X_a,X_a,exp(X_a),hAPP(real,X_a,of_real(X_a),X)) = hAPP(real,X_a,of_real(X_a),hAPP(real,real,exp(real),X))))) # label(fact_2799_exp__of__real) # label(axiom) # label(non_clause).  [assumption].
7.57/7.65	3673 (all M all K_4 all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),K_4)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),K_4)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N)) # label(fact_664_diff__cancel2) # label(axiom) # label(non_clause).  [assumption].
7.57/7.65	3674 (all X1_2 all X2_2 all Ma (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),Ma)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,X1_2),X2_2),Ma)) <-> hAPP(int,int,hAPP(int,fun(int,int),standardRes,Ma),X1_2) = hAPP(int,int,hAPP(int,fun(int,int),standardRes,Ma),X2_2)))) # label(fact_1051_StandardRes__prop2) # label(axiom) # label(non_clause).  [assumption].
7.57/7.65	3675 (all B (ti(int,B) != zero_zero(int) -> hBOOL(hAPP(product_prod(int,int),bool,hAPP(int,fun(product_prod(int,int),bool),hAPP(int,fun(int,fun(product_prod(int,int),bool)),divmod_int_rel,zero_zero(int)),B),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),zero_zero(int)),zero_zero(int)))))) # label(fact_1189_divmod__int__rel__0) # label(axiom) # label(non_clause).  [assumption].
7.57/7.65	3676 (all Z_1 all X all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X),Y)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),Z_1),X)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),Z_1),Y))))) # label(fact_653_real__add__left__mono) # label(axiom) # label(non_clause).  [assumption].
7.57/7.65	3677 (all J all K all I (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),J),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I),K))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J),K)),I)))) # label(fact_698_le__diff__conv) # label(axiom) # label(non_clause).  [assumption].
7.57/7.65	3678 (all X_a (dense_linorder(X_a) -> ord_gr676655987ssThan(X_a) = ti(fun(X_a,fun(X_a,fun(X_a,bool))),ord_gr676655987ssThan(X_a)))) # label(tsy_c_SetInterval_Oord__class_OgreaterThanLessThan_0_res) # label(axiom) # label(non_clause).  [assumption].
7.57/7.65	3679 (all X all A_1 hAPP(real,real,hAPP(real,fun(real,real),powr,X),hAPP(real,real,uminus_uminus(real),A_1)) = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),one_one(real)),hAPP(real,real,hAPP(real,fun(real,real),powr,X),A_1))) # label(fact_3381_powr__minus__divide) # label(axiom) # label(non_clause).  [assumption].
7.57/7.65	3680 (all N all X (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),X),N))))) # label(fact_261_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J) # label(axiom) # label(non_clause).  [assumption].
7.57/7.65	3681 (all X_1 all A_3 (hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A_3)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),A_3)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X_1))))) # label(fact_3661_Nat__Transfer_Otransfer__nat__int__set__function__closures_I6_J) # label(axiom) # label(non_clause).  [assumption].
7.57/7.65	3682 (all M hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),M),one_one(int)) = one_one(int)) # label(fact_4360_gcd__1__int) # label(axiom) # label(non_clause).  [assumption].
7.57/7.65	3683 (all X_a (linord219039673up_add(X_a) -> (all A_2 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),A_2) = zero_zero(X_a) <-> ti(X_a,A_2) = zero_zero(X_a))))) # label(fact_776_double__zero__sym) # label(axiom) # label(non_clause).  [assumption].
7.57/7.65	3684 (all X_a (real_normed_algebra(X_a) -> (all Y exists K_2 all X_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X_2),Y))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(X_a,real,norm_norm(X_a),X_2)),K_2)))))) # label(fact_1812_mult__left_Obounded) # label(axiom) # label(non_clause).  [assumption].
7.57/7.65	3685 (all P_1 hAPP(fun(int,bool),fun(int,bool),collect(int),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),combs(int,bool,bool),hAPP(fun(int,bool),fun(int,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj),hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)))),P_1)) = hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(fun(nat,int),fun(nat,bool),hAPP(fun(int,bool),fun(fun(nat,int),fun(nat,bool)),combb(int,bool,nat),P_1),semiring_1_of_nat(int))))) # label(fact_3807_Nat__Transfer_Otransfer__int__nat__set__functions_I5_J) # label(axiom) # label(non_clause).  [assumption].
7.57/7.65	3686 (all A_1 all B all Q_3 all R_4 (hBOOL(hAPP(product_prod(int,int),bool,hAPP(int,fun(product_prod(int,int),bool),hAPP(int,fun(int,fun(product_prod(int,int),bool)),divmod_int_rel,A_1),B),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),Q_3),R_4))) -> (zero_zero(int) != ti(int,B) -> hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_1),B) = ti(int,R_4)))) # label(fact_1192_divmod__int__rel__mod) # label(axiom) # label(non_clause).  [assumption].
7.57/7.65	3687 (all X_a (monoid_mult(X_a) -> (all A_1 ti(X_a,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))))) # label(fact_800_mult__1__right) # label(axiom) # label(non_clause).  [assumption].
7.57/7.65	3688 (all X_a (one(X_a) -> one_one(X_a) = ti(X_a,one_one(X_a)))) # label(tsy_c_Groups_Oone__class_Oone_res) # label(axiom) # label(non_clause).  [assumption].
7.57/7.65	3689 (all X_a all P hAPP(X_a,X_a,combi(X_a),P) = ti(X_a,P)) # label(help_COMBI_1_1_U) # label(axiom) # label(non_clause).  [assumption].
7.57/7.65	3690 (all X_a undefined(X_a) = ti(X_a,undefined(X_a))) # label(tsy_c_HOL_Oundefined_res) # label(axiom) # label(non_clause).  [assumption].
7.57/7.65	3691 (all N hAPP(real,nat,natceiling,hAPP(nat,real,real_1(nat),N)) = N) # label(fact_2295_natceiling__real__of__nat) # label(axiom) # label(non_clause).  [assumption].
7.57/7.65	3692 (all B all A_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),zero_zero(int))) -> hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_1),B) = hAPP(product_prod(int,int),int,product_fst(int,int),hAPP(product_prod(int,int),product_prod(int,int),negateSnd,hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),negDivAlg,hAPP(int,int,uminus_uminus(int),A_1)),hAPP(int,int,uminus_uminus(int),B))))))) # label(fact_3111_div__pos__neg) # label(axiom) # label(non_clause).  [assumption].
7.57/7.65	3693 (all B zero_zero(int) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),zero_zero(int)),B)) # label(fact_953_zmod__zero) # label(axiom) # label(non_clause).  [assumption].
7.57/7.65	3694 (all N_1 hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),hAPP(fun(int,bool),fun(int,bool),collect(int),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),combs(int,bool,bool),hAPP(fun(int,bool),fun(int,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj),hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)))),hAPP(int,fun(int,bool),hAPP(fun(int,fun(int,bool)),fun(int,fun(int,bool)),combc(int,int,bool),ord_less_eq(int)),N_1)))))) # label(fact_3834_bdd__int__set__le__finite) # label(axiom) # label(non_clause).  [assumption].
7.57/7.65	3695 (all X_a (linordered_idom(X_a) -> (all Z (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),hAPP(int,X_a,ring_1_of_int(X_a),Z))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Z)))))) # label(fact_3602_of__int__0__le__iff) # label(axiom) # label(non_clause).  [assumption].
7.57/7.65	3696 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,M)),N)))) # label(fact_1333_Suc__leI) # label(axiom) # label(non_clause).  [assumption].
7.57/7.65	3697 (all N -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),N))) # label(fact_514_less__not__refl) # label(axiom) # label(non_clause).  [assumption].
7.57/7.65	3698 (all X_a all A_3 all B_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less(fun(X_a,bool)),A_3),B_2)) -> (exists B_4 hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),B_4),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),B_2),A_3)))))) # label(fact_2727_psubset__imp__ex__mem) # label(axiom) # label(non_clause).  [assumption].
7.57/7.65	3699 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N),M)) -> hAPP(nat,product_prod(nat,nat),hAPP(nat,fun(nat,product_prod(nat,nat)),divmod_nat,M),N) = hAPP(nat,product_prod(nat,nat),hAPP(nat,fun(nat,product_prod(nat,nat)),product_Pair(nat,nat),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N)),N))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N)),N))))) # label(fact_3089_divmod__nat__step) # label(axiom) # label(non_clause).  [assumption].
7.57/7.65	3700 (all X_a (ring_1(X_a) -> (all N hAPP(X_a,X_a,uminus_uminus(X_a),one_one(X_a)) = hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),one_one(X_a))),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),N)))))) # label(fact_2123_power__minus1__odd) # label(axiom) # label(non_clause).  [assumption].
7.57/7.65	3701 (all B all A_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_1),zero_zero(int))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),zero_zero(int))) -> hAPP(product_prod(int,int),int,product_fst(int,int),hAPP(product_prod(int,int),product_prod(int,int),negateSnd,hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),posDivAlg,hAPP(int,int,uminus_uminus(int),A_1)),hAPP(int,int,uminus_uminus(int),B)))) = hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_1),B)))) # label(fact_3112_div__neg__neg) # label(axiom) # label(non_clause).  [assumption].
7.57/7.65	3702 (all X_a (archim1727834104eiling(X_a) -> archimedean_ceiling(X_a) = ti(fun(X_a,int),archimedean_ceiling(X_a)))) # label(tsy_c_Archimedean__Field_Oceiling_res) # label(axiom) # label(non_clause).  [assumption].
7.57/7.65	3703 (all K hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),K))))) # label(fact_3801_finite__Collect__less__nat) # label(axiom) # label(non_clause).  [assumption].
7.57/7.65	3704 (all X_a (divisi14063676e_zero(X_a) -> (all A_2 (ti(X_a,A_2) = zero_zero(X_a) <-> zero_zero(X_a) = hAPP(X_a,X_a,inverse_inverse(X_a),A_2))))) # label(fact_2527_inverse__nonzero__iff__nonzero) # label(axiom) # label(non_clause).  [assumption].
7.57/7.65	3705 (all X_a (linordered_idom(X_a) -> (all A_1 hAPP(X_a,X_a,sgn_sgn(X_a),A_1) = hAPP(X_a,X_a,sgn_sgn(X_a),hAPP(X_a,X_a,sgn_sgn(X_a),A_1))))) # label(fact_2199_sgn__sgn) # label(axiom) # label(non_clause).  [assumption].
7.57/7.65	3706 (all K_4 all M all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_4),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_4),N)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N)) # label(fact_665_Nat_Odiff__cancel) # label(axiom) # label(non_clause).  [assumption].
7.57/7.65	3707 (all X_a (archim1727834104eiling(X_a) -> (all X_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),one_one(X_a))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(X_a,int,archimedean_ceiling(X_a),X_1)),one_one(int))))))) # label(fact_3302_ceiling__le__one) # label(axiom) # label(non_clause).  [assumption].
7.57/7.65	3708 (all K_4 hAPP(quickcheck_code_int,int,quickcheck_int_of,hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),K_4)) = hAPP(int,int,number_number_of(int),K_4)) # label(fact_3163_int__of__number) # label(axiom) # label(non_clause).  [assumption].
7.57/7.65	3709 (all N all M ((M = zero_zero(nat) -> hAPP(nat,nat,fact_fact(nat),N) = hAPP(nat,nat,fact_fact(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N))) & (M != zero_zero(nat) -> hAPP(nat,nat,fact_fact(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N)),hAPP(nat,nat,fact_fact(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),one_one(nat))),N)))))) # label(fact_2481_fact__add__num__eq__if2__nat) # label(axiom) # label(non_clause).  [assumption].
7.57/7.65	3710 (all D_2 all X_1 (zero_zero(real) != X_1 -> ((hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X_1)) -> hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,inverse_inverse(real),hAPP(real,real,sqrt,X_1))),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = D_2) -> ((hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_1),zero_zero(real))) -> hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,uminus_uminus(real),hAPP(real,real,inverse_inverse(real),hAPP(real,real,sqrt,X_1)))),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = D_2) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),sqrt),X_1),D_2)))))) # label(fact_2655_DERIV__real__sqrt__generic) # label(axiom) # label(non_clause).  [assumption].
7.57/7.65	3711 (all X_b all X_a (topological_space(X_a) & real_normed_vector(X_b) -> (all C_1 all F all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(real,fun(filter(X_a),bool),hAPP(fun(X_a,real),fun(real,fun(filter(X_a),bool)),tendsto(X_a,real),F),zero_zero(real)),hAPP(X_a,filter(X_a),at(X_a),A_2))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(X_b,fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(X_b,fun(X_a,X_b)),combc(X_a,X_b,X_b),hAPP(fun(X_a,real),fun(X_a,fun(X_b,X_b)),hAPP(fun(real,fun(X_b,X_b)),fun(fun(X_a,real),fun(X_a,fun(X_b,X_b))),combb(real,fun(X_b,X_b),X_a),scaleR_scaleR(X_b)),F)),C_1)),zero_zero(X_b)),hAPP(X_a,filter(X_a),at(X_a),A_2))))))) # label(fact_4747_scaleR_OLIM__left__zero) # label(axiom) # label(non_clause).  [assumption].
7.57/7.65	3712 (all X_a (ring_11004092258visors(X_a) -> (all A_2 (one_one(X_a) = ti(X_a,A_2) | ti(X_a,A_2) = hAPP(X_a,X_a,uminus_uminus(X_a),one_one(X_a)) <-> one_one(X_a) = hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_2),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))) # label(fact_2116_power2__eq__1__iff) # label(axiom) # label(non_clause).  [assumption].
7.57/7.65	3713 (all N -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,uminus_uminus(int),hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,N)))))) # label(fact_2176_not__zle__0__negative) # label(axiom) # label(non_clause).  [assumption].
7.57/7.65	3714 (all X_a all X_b (real_normed_vector(X_b) -> (all G all B_1 all F all A_2 all A_3 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),A_2),A_3)) -> (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),G),B_1),A_3)) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(fun(X_a,X_b),fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,X_b)),combs(X_a,X_b,X_b),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,fun(X_b,X_b))),combb(X_b,fun(X_b,X_b),X_a),minus_minus(X_b)),F)),G)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),A_2),B_1)),A_3))))))) # label(fact_4440_tendsto__diff) # label(axiom) # label(non_clause).  [assumption].
7.57/7.65	3715 (all X all Y hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),X),Y) = hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),X),hAPP(int,int,uminus_uminus(int),Y))) # label(fact_4377_gcd__neg2__int) # label(axiom) # label(non_clause).  [assumption].
7.57/7.65	3716 (all Ma all N_1 (-hBOOL(hAPP(nat,bool,even_odd_even(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Ma),N_1))) <-> -(-hBOOL(hAPP(nat,bool,even_odd_even(nat),Ma)) <-> -hBOOL(hAPP(nat,bool,even_odd_even(nat),N_1))))) # label(fact_2413_odd__add) # label(axiom) # label(non_clause).  [assumption].
7.57/7.65	3717 (all Z_1 hBOOL(hAPP(int,bool,nat_is_nat,hAPP(nat,int,semiring_1_of_nat(int),Z_1)))) # label(fact_4854_Nat__Transfer_Otransfer__int__nat__function__closures_I9_J) # label(axiom) # label(non_clause).  [assumption].
7.57/7.65	3718 (all X_a (ordere142940540dd_abs(X_a) -> (all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,abs_abs(X_a),A_1)),B)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),A_1)),B)))))) # label(fact_2082_abs__le__D2) # label(axiom) # label(non_clause).  [assumption].
7.57/7.65	3719 (all A_2 all B_1 all Ma (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_2),B_1),Ma)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_2),B_1),hAPP(int,int,uminus_uminus(int),Ma))))) # label(fact_2144_zcong__zminus) # label(axiom) # label(non_clause).  [assumption].
7.57/7.65	3720 (all F all A_3 all Ma (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),Ma)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),resSet,Ma),A_3)) -> ((all X_2 (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_2),A_3)) -> (all Xa (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xa),A_3)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(int,int,F,X_2)),hAPP(int,int,F,Xa)),Ma)) -> ti(int,Xa) = ti(int,X_2)))))) -> hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),resSet,Ma),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,int),fun(fun(int,bool),fun(int,bool)),image(int,int),F),A_3))))))) # label(fact_3644_ResSet__image) # label(axiom) # label(non_clause).  [assumption].
7.57/7.65	3721 (all X_1 all Y_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_1),Y_1)) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),X_1),Y_1)),zero_zero(real))))) # label(fact_618_real__le__eq__diff) # label(axiom) # label(non_clause).  [assumption].
7.57/7.65	3722 (all X_a all F all A_3 hAPP(nat,int,semiring_1_of_nat(int),hAPP(fun(X_a,bool),nat,hAPP(fun(X_a,nat),fun(fun(X_a,bool),nat),big_co302546470etprod(X_a,nat),F),A_3)) = hAPP(fun(X_a,bool),int,hAPP(fun(X_a,int),fun(fun(X_a,bool),int),big_co302546470etprod(X_a,int),hAPP(fun(X_a,nat),fun(X_a,int),hAPP(fun(nat,int),fun(fun(X_a,nat),fun(X_a,int)),combb(nat,int,X_a),semiring_1_of_nat(int)),F)),A_3)) # label(fact_3942_int__setprod) # label(axiom) # label(non_clause).  [assumption].
7.57/7.65	3723 (all X_a all X_b all X_1 all Y_1 hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),X_1),Y_1) = hAPP(fun(product_prod(X_a,X_b),bool),product_prod(X_a,X_b),the(product_prod(X_a,X_b)),hAPP(fun(X_a,fun(X_b,bool)),fun(product_prod(X_a,X_b),bool),product_prod_case(X_a,X_b,bool),hAPP(fun(X_b,bool),fun(X_a,fun(X_b,bool)),hAPP(fun(X_a,fun(fun(X_b,bool),fun(X_b,bool))),fun(fun(X_b,bool),fun(X_a,fun(X_b,bool))),combc(X_a,fun(X_b,bool),fun(X_b,bool)),hAPP(fun(X_a,fun(bool,bool)),fun(X_a,fun(fun(X_b,bool),fun(X_b,bool))),hAPP(fun(fun(bool,bool),fun(fun(X_b,bool),fun(X_b,bool))),fun(fun(X_a,fun(bool,bool)),fun(X_a,fun(fun(X_b,bool),fun(X_b,bool)))),combb(fun(bool,bool),fun(fun(X_b,bool),fun(X_b,bool)),X_a),combb(bool,bool,X_b)),hAPP(fun(X_a,bool),fun(X_a,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,fun(bool,bool))),combb(bool,fun(bool,bool),X_a),fconj),hAPP(X_a,fun(X_a,bool),fequal(X_a),X_1)))),hAPP(X_b,fun(X_b,bool),fequal(X_b),Y_1))))) # label(fact_4142_The__split__eq) # label(axiom) # label(non_clause).  [assumption].
7.57/7.65	3724 (all Z_1 hAPP(real,complex,of_real(complex),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(complex,real,re,Z_1)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(complex,real,im,Z_1)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),Z_1),hAPP(complex,complex,cnj,Z_1))) # label(fact_2991_complex__mult__cnj) # label(axiom) # label(non_clause).  [assumption].
7.57/7.65	3725 (all X_a (number_ring(X_a) & linordered_idom(X_a) -> hAPP(X_a,X_a,abs_abs(X_a),hAPP(int,X_a,number_number_of(X_a),min_1)) = one_one(X_a))) # label(fact_1885_abs__minus__one) # label(axiom) # label(non_clause).  [assumption].
7.57/7.65	3726 (all K all L (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit0,K)),hAPP(int,int,bit0,L))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),L)))) # label(fact_128_rel__simps_I14_J) # label(axiom) # label(non_clause).  [assumption].
7.57/7.65	3727 (all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_1),one_one(real))) -> hBOOL(hAPP(fun(nat,real),bool,bseq(real),hAPP(real,fun(nat,real),power_power(real),X_1)))))) # label(fact_3833_Bseq__realpow) # label(axiom) # label(non_clause).  [assumption].
7.57/7.65	3728 (all K_4 all L_4 hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,bit1,K_4)),L_4) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,bit0,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K_4),L_4))),L_4)) # label(fact_113_mult__Bit1) # label(axiom) # label(non_clause).  [assumption].
7.57/7.65	3729 (all X_a all X_b all X_1 all Y_1 hAPP(fun(product_prod(X_a,X_b),bool),product_prod(X_a,X_b),hilbert_Eps(product_prod(X_a,X_b)),hAPP(fun(X_a,fun(X_b,bool)),fun(product_prod(X_a,X_b),bool),product_prod_case(X_a,X_b,bool),hAPP(fun(X_b,bool),fun(X_a,fun(X_b,bool)),hAPP(fun(X_a,fun(fun(X_b,bool),fun(X_b,bool))),fun(fun(X_b,bool),fun(X_a,fun(X_b,bool))),combc(X_a,fun(X_b,bool),fun(X_b,bool)),hAPP(fun(X_a,fun(bool,bool)),fun(X_a,fun(fun(X_b,bool),fun(X_b,bool))),hAPP(fun(fun(bool,bool),fun(fun(X_b,bool),fun(X_b,bool))),fun(fun(X_a,fun(bool,bool)),fun(X_a,fun(fun(X_b,bool),fun(X_b,bool)))),combb(fun(bool,bool),fun(fun(X_b,bool),fun(X_b,bool)),X_a),combb(bool,bool,X_b)),hAPP(fun(X_a,bool),fun(X_a,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,fun(bool,bool))),combb(bool,fun(bool,bool),X_a),fconj),hAPP(X_a,fun(X_a,bool),fequal(X_a),X_1)))),hAPP(X_b,fun(X_b,bool),fequal(X_b),Y_1)))) = hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),X_1),Y_1)) # label(fact_4780_Eps__split__eq) # label(axiom) # label(non_clause).  [assumption].
7.57/7.65	3730 (all K_4 hAPP(int,int,bit1,hAPP(int,int,pred,K_4)) = hAPP(int,int,pred,hAPP(int,int,bit0,K_4))) # label(fact_2901_pred__Bit0) # label(axiom) # label(non_clause).  [assumption].
7.57/7.65	3731 (all N (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),N)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),hAPP(int,int,fact_fact(int),N))))) # label(fact_3195_fact__ge__one__int) # label(axiom) # label(non_clause).  [assumption].
7.57/7.65	3732 (all K_4 all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),K_4),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N))) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),K_4),N)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N),M)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),K_4),M)))))) # label(fact_676_dvd__diffD) # label(axiom) # label(non_clause).  [assumption].
7.57/7.65	3733 (all X_a all C_2 all A_3 ((all X_4 (hBOOL(hAPP(fun(fun(X_a,bool),bool),bool,hAPP(fun(X_a,bool),fun(fun(fun(X_a,bool),bool),bool),member(fun(X_a,bool)),X_4),A_3)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),X_4),C_2)))) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(fun(fun(X_a,bool),bool),fun(X_a,bool),complete_Sup_Sup(fun(X_a,bool)),A_3)),C_2)))) # label(fact_2730_Union__least) # label(axiom) # label(non_clause).  [assumption].
7.57/7.65	3734 (all Y all X all P_5 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),P_5)) -> (hBOOL(hAPP(int,bool,zprime,P_5)) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,X),zero_zero(int)),P_5)) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,Y),zero_zero(int)),P_5)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(int,int,hAPP(int,fun(int,int),multInv,P_5),X)),hAPP(int,int,hAPP(int,fun(int,int),multInv,P_5),Y)),P_5)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,X),Y),P_5)))))))) # label(fact_847_MultInv__prop5) # label(axiom) # label(non_clause).  [assumption].
7.57/7.65	3735 (all X_a (semiring_div(X_a) -> (all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_1),B)) -> ti(X_a,B) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),B),A_1)))))) # label(fact_1004_dvd__mult__div__cancel) # label(axiom) # label(non_clause).  [assumption].
7.57/7.65	3736 (all X_1 hAPP(fun(nat,real),real,suminf(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),uminus_uminus(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),sin_coeff)),hAPP(real,fun(nat,real),power_power(real),X_1)))) = hAPP(real,real,uminus_uminus(real),hAPP(real,real,sin,X_1))) # label(fact_3974_lemma__sin__minus) # label(axiom) # label(non_clause).  [assumption].
7.57/7.65	3737 (all N_1 hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),hAPP(fun(int,bool),fun(int,bool),collect(int),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),combs(int,bool,bool),hAPP(fun(int,bool),fun(int,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj),hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)))),hAPP(int,fun(int,bool),hAPP(fun(int,fun(int,bool)),fun(int,fun(int,bool)),combc(int,int,bool),ord_less(int)),N_1)))))) # label(fact_3876_bdd__int__set__l__l__finite) # label(axiom) # label(non_clause).  [assumption].
7.57/7.65	3738 (all A_1 all B hAPP(complex,complex,cnj,hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,A_1),B)) = hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,A_1),hAPP(real,real,uminus_uminus(real),B))) # label(fact_2948_complex__cnj) # label(axiom) # label(non_clause).  [assumption].
7.57/7.65	3739 (all V_1 all V_2 ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V_2),pls)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(int,nat,number_number_of(nat),V_1)),hAPP(int,nat,number_number_of(nat),V_2)) = hAPP(int,nat,number_number_of(nat),V_1)) & (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V_2),pls)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),hAPP(bool,fun(nat,fun(nat,nat)),if(nat),hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),V_1),hAPP(int,int,uminus_uminus(int),V_2))))),zero_zero(nat)),hAPP(int,nat,nat_1,hAPP(int,int,number_number_of(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),V_1),hAPP(int,int,uminus_uminus(int),V_2))))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(int,nat,number_number_of(nat),V_1)),hAPP(int,nat,number_number_of(nat),V_2))))) # label(fact_3911_diff__nat__number__of) # label(axiom) # label(non_clause).  [assumption].
7.57/7.65	3740 (all X_a (linord1117847801e_zero(X_a) & number(X_a) -> (all A_2 all B_1 all W_1 ((-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(int,X_a,number_number_of(X_a),W_1))) -> (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(int,X_a,number_number_of(X_a),W_1)),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),zero_zero(X_a)))) & (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(int,X_a,number_number_of(X_a),W_1)),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),hAPP(int,X_a,number_number_of(X_a),W_1)))))) & (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(int,X_a,number_number_of(X_a),W_1))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),hAPP(int,X_a,number_number_of(X_a),W_1))),B_1))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),B_1),hAPP(int,X_a,number_number_of(X_a),W_1)))))))) # label(fact_1745_less__divide__eq__number__of1) # label(axiom) # label(non_clause).  [assumption].
7.57/7.65	3741 (all X_a all X_b all X_c all Q_1 all P_1 all Z (hBOOL(hAPP(X_a,bool,Q_1,hAPP(product_prod(X_b,X_c),X_a,hAPP(fun(X_b,fun(X_c,X_a)),fun(product_prod(X_b,X_c),X_a),product_prod_case(X_b,X_c,X_a),P_1),Z))) -> -(all X_2 all Y_2 (ti(product_prod(X_b,X_c),Z) = hAPP(X_c,product_prod(X_b,X_c),hAPP(X_b,fun(X_c,product_prod(X_b,X_c)),product_Pair(X_b,X_c),X_2),Y_2) -> -hBOOL(hAPP(X_a,bool,Q_1,hAPP(X_c,X_a,hAPP(X_b,fun(X_c,X_a),P_1,X_2),Y_2))))))) # label(fact_4770_splitE2) # label(axiom) # label(non_clause).  [assumption].
7.57/7.65	3742 (all X_1 X_1 = hAPP(fun(real,bool),real,complete_Sup_Sup(real),hAPP(real,fun(real,bool),ord_lessThan(real),X_1))) # label(fact_4327_Sup__lessThan) # label(axiom) # label(non_clause).  [assumption].
7.57/7.65	3743 (all X_a (real_normed_vector(X_a) -> (all A_1 all B hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(X_a,real,norm_norm(X_a),A_1)),hAPP(X_a,real,norm_norm(X_a),B)))),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_1),B))))))) # label(fact_1898_norm__triangle__ineq3) # label(axiom) # label(non_clause).  [assumption].
7.57/7.65	3744 (all X_a all X_b (ordere779506340up_add(X_b) & comm_monoid_add(X_b) -> (all F all G all K_3 ((all I_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),I_2),K_3)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_a,X_b,F,I_2)),hAPP(X_a,X_b,G,I_2))))) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),F),K_3)),hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),G),K_3))))))) # label(fact_4343_setsum__mono) # label(axiom) # label(non_clause).  [assumption].
7.57/7.65	3745 (all X_b all X_a (real_normed_vector(X_b) & real_normed_vector(X_a) -> (all F all L_2 all A_2 ((all R_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),R_2)) -> (exists S_1 ((all X_2 (ti(X_a,X_2) != ti(X_a,A_2) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),X_2),A_2))),S_1)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_b,real,norm_norm(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),hAPP(X_a,X_b,F,X_2)),L_2))),R_2)))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),S_1)))))) <-> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),L_2),hAPP(X_a,filter(X_a),at(X_a),A_2))))))) # label(fact_4644_LIM__eq) # label(axiom) # label(non_clause).  [assumption].
7.57/7.65	3746 (all V_3 all V ((-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V),pls)) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V_3),pls)) -> hAPP(int,nat,number_number_of(nat),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),V),V_3)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),V)),hAPP(int,nat,number_number_of(nat),V_3))) & (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V_3),pls)) -> 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)),hAPP(int,nat,number_number_of(nat),V_3)))) & (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V),pls)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),V)),hAPP(int,nat,number_number_of(nat),V_3)) = hAPP(int,nat,number_number_of(nat),V_3)))) # label(fact_87_add__nat__number__of) # label(axiom) # label(non_clause).  [assumption].
7.57/7.65	3747 (all P_5 (hBOOL(hAPP(nat,bool,prime,P_5)) -> hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))) = P_5 | -hBOOL(hAPP(nat,bool,even_odd_even(nat),P_5)))) # label(fact_3079_prime__odd) # label(axiom) # label(non_clause).  [assumption].
7.57/7.65	3748 (all X_a (ring_1(X_a) -> ti(fun(X_a,bool),ring_1_Ints(X_a)) = ring_1_Ints(X_a))) # label(tsy_c_Int_Oring__1__class_OInts_res) # label(axiom) # label(non_clause).  [assumption].
7.57/7.65	3749 (all X all Y hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),hAPP(int,int,abs_abs(int),X)),hAPP(int,int,abs_abs(int),Y)) = hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),X),Y)) # label(fact_4373_gcd__abs__int) # label(axiom) # label(non_clause).  [assumption].
7.57/7.65	3750 (all X_a (group_add(X_a) -> (all A_1 all B ti(X_a,A_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_1),B)),B)))) # label(fact_809_diff__add__cancel) # label(axiom) # label(non_clause).  [assumption].
7.57/7.65	3751 (all X_a (linordered_semidom(X_a) -> (all A_1 all N all B (hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),hAPP(nat,nat,suc,N)) = hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),B),hAPP(nat,nat,suc,N)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),B)) -> ti(X_a,B) = ti(X_a,A_1))))))) # label(fact_1373_power__inject__base) # label(axiom) # label(non_clause).  [assumption].
7.57/7.65	3752 (all X_a all X_b (comm_monoid_mult(X_b) -> (all G all A_3 (-hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_3)) -> hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co302546470etprod(X_a,X_b),G),A_3) = one_one(X_b))))) # label(fact_3952_setprod_Oinfinite) # label(axiom) # label(non_clause).  [assumption].
7.57/7.65	3753 (all V_3 all K_4 all V ((-hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V))) -> (-hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V_3))) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),V)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),V_3)),K_4)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),V),V_3))),K_4)) & (hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V_3))) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),V)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),V_3)),K_4)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),V)),K_4))) & (hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V))) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),V)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),V_3)),K_4)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),V_3)),K_4)))) # label(fact_1512_nat__number__of__add__left) # label(axiom) # label(non_clause).  [assumption].
7.57/7.65	3754 (all X_a (archim1727834104eiling(X_a) -> (all X_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(X_a,int,archimedean_ceiling(X_a),X_1))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),X_1)))))) # label(fact_3297_zero__less__ceiling) # label(axiom) # label(non_clause).  [assumption].
7.57/7.65	3755 (all X_a all X_b (real_normed_vector(X_b) -> (all X_3 ((exists N_3 all N_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_b,real,norm_norm(X_b),hAPP(X_a,X_b,X_3,N_2))),hAPP(nat,real,real_1(nat),hAPP(nat,nat,suc,N_3))))) <-> (exists K_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),K_2)) & (all N_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_b,real,norm_norm(X_b),hAPP(X_a,X_b,X_3,N_2))),K_2))))))))) # label(fact_2353_lemma__NBseq__def) # label(axiom) # label(non_clause).  [assumption].
7.57/7.65	3756 (all Q_3 all R_4 hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),Q_3),hAPP(int,int,uminus_uminus(int),R_4)) = hAPP(product_prod(int,int),product_prod(int,int),negateSnd,hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),Q_3),R_4))) # label(fact_3072_negateSnd__eq) # label(axiom) # label(non_clause).  [assumption].
7.57/7.65	3757 (all N all K_4 all M (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),K_4),M)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),K_4),N)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),K_4),hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),M),N)))))) # label(fact_4368_gcd__greatest__int) # label(axiom) # label(non_clause).  [assumption].
7.57/7.65	3758 (all X_1 all N_1 (N_1 != zero_zero(nat) & hBOOL(hAPP(int,bool,even_odd_even(int),X_1)) <-> hBOOL(hAPP(int,bool,even_odd_even(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),X_1),N_1))))) # label(fact_1363_even__power) # label(axiom) # label(non_clause).  [assumption].
7.57/7.65	3759 (all X_a (linordered_field(X_a) -> (all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,inverse_inverse(X_a),A_1)),zero_zero(X_a))))))) # label(fact_2545_negative__imp__inverse__negative) # label(axiom) # label(non_clause).  [assumption].
7.57/7.65	3760 (all S (hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),S)) <-> (exists K_1 hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,bool),fun(fun(nat,bool),bool),ord_less_eq(fun(nat,bool)),S),hAPP(nat,fun(nat,bool),ord_lessThan(nat),K_1)))))) # label(fact_4318_finite__nat__iff__bounded) # label(axiom) # label(non_clause).  [assumption].
7.57/7.65	3761 (all N_1 hAPP(nat,real,hAPP(fun(nat,real),fun(nat,real),diffs(real),sin_coeff),N_1) = hAPP(nat,real,cos_coeff,N_1)) # label(fact_4116_sin__fdiffs2) # label(axiom) # label(non_clause).  [assumption].
7.57/7.65	3762 (all C all N all A_1 all B (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,A_1),B)) -> (hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A_1),B) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),C),N) -> (exists R_2 exists S_1 (B = hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),S_1),N) & A_1 = hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),R_2),N)))))) # label(fact_3425_coprime__pow) # label(axiom) # label(non_clause).  [assumption].
7.57/7.65	3763 (all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> (exists M_2 hAPP(nat,nat,suc,M_2) = N))) # label(fact_1494_gr0__implies__Suc) # label(axiom) # label(non_clause).  [assumption].
7.57/7.65	3764 (all X (hAPP(real,real,cos,X) = one_one(real) -> zero_zero(real) = hAPP(real,real,sin,X))) # label(fact_2318_cos__one__sin__zero) # label(axiom) # label(non_clause).  [assumption].
7.57/7.65	3765 (all X_a (metric_space(X_a) -> (all X all Y hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),X),Y)))))) # label(fact_3510_zero__le__dist) # label(axiom) # label(non_clause).  [assumption].
7.57/7.65	3766 (all N all A_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A_1)) -> (exists R_2 (hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),R_2),hAPP(nat,nat,suc,N)) = A_1 & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),R_2)))))) # label(fact_1479_realpow__pos__nth2) # label(axiom) # label(non_clause).  [assumption].
7.57/7.65	3767 (all X_a (metric_space(X_a) -> (all X2_1 all Y all X1_1 all E_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),Y),X1_1)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),E_1),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),Y),X2_1)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),E_1),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),X1_1),X2_1)),E_1))))))) # label(fact_3502_dist__triangle__half__r) # label(axiom) # label(non_clause).  [assumption].
7.57/7.65	3768 (all X_a (topological_space(X_a) -> (all G all L all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(complex,fun(filter(X_a),bool),hAPP(fun(X_a,complex),fun(complex,fun(filter(X_a),bool)),tendsto(X_a,complex),G),L),hAPP(X_a,filter(X_a),at(X_a),A_2))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(real,fun(filter(X_a),bool),hAPP(fun(X_a,real),fun(real,fun(filter(X_a),bool)),tendsto(X_a,real),hAPP(fun(X_a,complex),fun(X_a,real),hAPP(fun(complex,real),fun(fun(X_a,complex),fun(X_a,real)),combb(complex,real,X_a),re),G)),hAPP(complex,real,re,L)),hAPP(X_a,filter(X_a),at(X_a),A_2))))))) # label(fact_4596_Re_OLIM) # label(axiom) # label(non_clause).  [assumption].
7.57/7.65	3769 (all X_a (divisi14063676e_zero(X_a) -> (all A_1 zero_zero(X_a) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),A_1),zero_zero(X_a))))) # label(fact_1657_divide__zero) # label(axiom) # label(non_clause).  [assumption].
7.57/7.65	3770 (all X_a (linordered_field(X_a) -> (all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),one_one(X_a)),one_one(X_a))))))))) # label(fact_1730_less__half__sum) # label(axiom) # label(non_clause).  [assumption].
7.57/7.65	3771 (all X_a (real_normed_field(X_a) -> (all F all X_1 all D_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_a,fun(filter(X_a),bool),hAPP(fun(X_a,X_a),fun(X_a,fun(filter(X_a),bool)),tendsto(X_a,X_a),hAPP(fun(X_a,X_a),fun(X_a,X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,X_a),fun(X_a,X_a)),combs(X_a,X_a,X_a),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,X_a),fun(X_a,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),X_a),inverse_divide(X_a)),hAPP(X_a,fun(X_a,X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(X_a,X_a)),combc(X_a,X_a,X_a),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,X_a),fun(X_a,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),X_a),minus_minus(X_a)),F)),hAPP(X_a,X_a,F,X_1)))),hAPP(X_a,fun(X_a,X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(X_a,X_a)),combc(X_a,X_a,X_a),minus_minus(X_a)),X_1))),D_2),hAPP(X_a,filter(X_a),at(X_a),X_1))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),F),X_1),D_2)))))) # label(fact_4601_DERIV__iff2) # label(axiom) # label(non_clause).  [assumption].
7.57/7.65	3772 (all X_a (comm_semiring_1(X_a) -> (all N all M all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),X),Y)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N),M)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),N)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),Y),M)))))))) # label(fact_345_dvd__power__le) # label(axiom) # label(non_clause).  [assumption].
7.57/7.65	3773 (all K_4 all L_4 hAPP(int,int,bit1,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),K_4),L_4)) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,bit1,K_4)),hAPP(int,int,bit0,L_4))) # label(fact_162_add__Bit1__Bit0) # label(axiom) # label(non_clause).  [assumption].
7.57/7.65	3774 (all P_1 all A_2 all B_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A_2),B_1)) -> (all N_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(product_prod(real,real),real,product_fst(real,real),hAPP(nat,product_prod(real,real),hAPP(real,fun(nat,product_prod(real,real)),hAPP(real,fun(real,fun(nat,product_prod(real,real))),hAPP(fun(product_prod(real,real),bool),fun(real,fun(real,fun(nat,product_prod(real,real)))),bolzano_bisect,P_1),A_2),B_1),N_2))),hAPP(product_prod(real,real),real,product_snd(real,real),hAPP(nat,product_prod(real,real),hAPP(real,fun(nat,product_prod(real,real)),hAPP(real,fun(real,fun(nat,product_prod(real,real))),hAPP(fun(product_prod(real,real),bool),fun(real,fun(real,fun(nat,product_prod(real,real)))),bolzano_bisect,P_1),A_2),B_1),N_2))))))) # label(fact_3131_Bolzano__bisect__le) # label(axiom) # label(non_clause).  [assumption].
7.57/7.65	3775 (all X_a all X_b (comm_semiring_1(X_b) -> (all D_1 all F all A_3 ((all I_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),I_2),A_3)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),dvd_dvd(X_b),D_1),hAPP(X_a,X_b,F,I_2))))) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),dvd_dvd(X_b),D_1),hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),F),A_3))))))) # label(fact_4773_dvd__setsum) # label(axiom) # label(non_clause).  [assumption].
7.57/7.65	3776 (all A_1 hAPP(real,real,sin,A_1) = hAPP(complex,real,im,hAPP(real,complex,cis,A_1))) # label(fact_3027_Im__cis) # label(axiom) # label(non_clause).  [assumption].
7.57/7.65	3777 (all X_a (real_algebra_1(X_a) -> (all F all X_2 hAPP(real,X_a,of_real(X_a),hAPP(nat,real,hAPP(fun(nat,real),fun(nat,real),diffs(real),F),X_2)) = hAPP(nat,X_a,hAPP(fun(nat,X_a),fun(nat,X_a),diffs(X_a),hAPP(fun(nat,real),fun(nat,X_a),hAPP(fun(real,X_a),fun(fun(nat,real),fun(nat,X_a)),combb(real,X_a,nat),of_real(X_a)),F)),X_2)))) # label(fact_4111_diffs__of__real) # label(axiom) # label(non_clause).  [assumption].
7.57/7.65	3778 (all X_a (linordered_idom(X_a) & number_ring(X_a) -> (all X ((hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(int,X_a,number_number_of(X_a),X)),zero_zero(X_a))) -> hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(int,X_a,number_number_of(X_a),X)) = hAPP(X_a,X_a,abs_abs(X_a),hAPP(int,X_a,number_number_of(X_a),X))) & (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(int,X_a,number_number_of(X_a),X)),zero_zero(X_a))) -> hAPP(int,X_a,number_number_of(X_a),X) = hAPP(X_a,X_a,abs_abs(X_a),hAPP(int,X_a,number_number_of(X_a),X))))))) # label(fact_2113_abs__number__of) # label(axiom) # label(non_clause).  [assumption].
7.57/7.65	3779 (all X_a (number_ring(X_a) & linordered_idom(X_a) -> (all X_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X_1),pls)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(int,X_a,number_number_of(X_a),X_1)),zero_zero(X_a))))))) # label(fact_176_less__special_I3_J) # label(axiom) # label(non_clause).  [assumption].
7.57/7.65	3780 (all K_4 all M (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),M)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),M),K_4)),M)))) # label(fact_989_zmod__le__nonneg__dividend) # label(axiom) # label(non_clause).  [assumption].
7.57/7.65	3781 (all X_a (real_normed_field(X_a) -> (all F all X_1 all D_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),F),X_1),D_2)) -> (zero_zero(X_a) != hAPP(X_a,X_a,F,X_1) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),hAPP(fun(X_a,X_a),fun(X_a,X_a),hAPP(fun(X_a,X_a),fun(fun(X_a,X_a),fun(X_a,X_a)),combb(X_a,X_a,X_a),inverse_inverse(X_a)),F)),X_1),hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,inverse_inverse(X_a),hAPP(X_a,X_a,F,X_1))),D_2)),hAPP(X_a,X_a,inverse_inverse(X_a),hAPP(X_a,X_a,F,X_1))))))))))) # label(fact_3877_DERIV__inverse_H) # label(axiom) # label(non_clause).  [assumption].
7.57/7.65	3782 (all X_a (number(X_a) & linord1117847801e_zero(X_a) -> (all B_1 all W_1 all A_2 ((hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(int,X_a,number_number_of(X_a),W_1))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),hAPP(int,X_a,number_number_of(X_a),W_1))))) & (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(int,X_a,number_number_of(X_a),W_1))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(int,X_a,number_number_of(X_a),W_1)),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),hAPP(int,X_a,number_number_of(X_a),W_1))),B_1))) & (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(int,X_a,number_number_of(X_a),W_1)),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_2)))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),B_1),hAPP(int,X_a,number_number_of(X_a),W_1))),A_2)))))) # label(fact_1748_divide__less__eq__number__of1) # label(axiom) # label(non_clause).  [assumption].
7.57/7.66	3783 (all X_a all X_b all P_1 all Q_1 all X_2 (hBOOL(hAPP(product_prod(X_a,X_b),bool,hAPP(fun(X_a,fun(X_b,bool)),fun(product_prod(X_a,X_b),bool),product_prod_case(X_a,X_b,bool),Q_1),X_2)) & hBOOL(P_1) <-> hBOOL(hAPP(product_prod(X_a,X_b),bool,hAPP(fun(X_a,fun(X_b,bool)),fun(product_prod(X_a,X_b),bool),product_prod_case(X_a,X_b,bool),hAPP(fun(X_a,fun(X_b,bool)),fun(X_a,fun(X_b,bool)),hAPP(fun(fun(X_b,bool),fun(X_b,bool)),fun(fun(X_a,fun(X_b,bool)),fun(X_a,fun(X_b,bool))),combb(fun(X_b,bool),fun(X_b,bool),X_a),hAPP(fun(bool,bool),fun(fun(X_b,bool),fun(X_b,bool)),combb(bool,bool,X_b),hAPP(bool,fun(bool,bool),fconj,P_1))),Q_1)),X_2)))) # label(fact_4044_split__part) # label(axiom) # label(non_clause).  [assumption].
7.57/7.66	3784 (all X_a all X_b (real_normed_vector(X_b) -> (all R_1 all G all A_2 all A_3 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),G),A_2),A_3)) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(fun(X_a,X_b),fun(X_a,X_b),hAPP(fun(X_b,X_b),fun(fun(X_a,X_b),fun(X_a,X_b)),combb(X_b,X_b,X_a),hAPP(real,fun(X_b,X_b),scaleR_scaleR(X_b),R_1)),G)),hAPP(X_b,X_b,hAPP(real,fun(X_b,X_b),scaleR_scaleR(X_b),R_1),A_2)),A_3)))))) # label(fact_4728_scaleR__right_Otendsto) # label(axiom) # label(non_clause).  [assumption].
7.57/7.66	3785 (all X hAPP(real,real,uminus_uminus(real),hAPP(complex,real,im,X)) = hAPP(complex,real,im,hAPP(complex,complex,cnj,X))) # label(fact_2973_complex__Im__cnj) # label(axiom) # label(non_clause).  [assumption].
7.57/7.66	3786 (all X_a (dvd(X_a) & comm_ring(X_a) -> (all Ta all D_1 all D_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),D_1),D_2)) -> (all X_2 all K_1 (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),D_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X_2),Ta))) <-> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),D_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),X_2),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),K_1),D_2))),Ta))))))))) # label(fact_488_inf__period_I4_J) # label(axiom) # label(non_clause).  [assumption].
7.57/7.66	3787 (all K_4 hAPP(int,rat,ring_1_of_int(rat),K_4) = hAPP(int,rat,hAPP(int,fun(int,rat),fract,K_4),one_one(int))) # label(fact_3744_of__int__rat) # label(axiom) # label(non_clause).  [assumption].
7.57/7.66	3788 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N),M)) -> N = M))) # label(fact_526_le__antisym) # label(axiom) # label(non_clause).  [assumption].
7.57/7.66	3789 (all A_1 all B hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,hAPP(int,int,bit1,pls))))),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit1,hAPP(int,int,bit1,pls)))),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),B))),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit1,hAPP(int,int,bit1,pls)))),A_1)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,hAPP(int,int,bit1,pls))))) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A_1),B)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,hAPP(int,int,bit1,pls))))) # label(fact_593_zdiff__power3) # label(axiom) # label(non_clause).  [assumption].
7.57/7.66	3790 (all Y all N all P_5 (hBOOL(hAPP(int,bool,zprime,P_5)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),P_5),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),Y),N))) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),P_5),Y)))))) # label(fact_278_zpower__zdvd__prop2) # label(axiom) # label(non_clause).  [assumption].
7.57/7.66	3791 (all X_1 (zero_zero(real) != hAPP(real,real,cos,X_1) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,real)),combs(real,real,real),hAPP(fun(real,real),fun(real,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,fun(real,real))),combb(real,fun(real,real),real),inverse_divide(real)),sin)),cos)),X_1),hAPP(real,real,inverse_inverse(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,cos,X_1)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))))) # label(fact_3915_lemma__DERIV__tan) # label(axiom) # label(non_clause).  [assumption].
7.57/7.66	3792 (all X hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),one_one(int)),zero_zero(int)) = hAPP(nat,product_prod(int,int),hAPP(nat,fun(nat,product_prod(int,int)),bezw,X),zero_zero(nat))) # label(fact_3035_bezw__0) # label(axiom) # label(non_clause).  [assumption].
7.57/7.66	3793 (all X all Y hAPP(rat,real,ratreal,hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),X),Y)) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(rat,real,ratreal,X)),hAPP(rat,real,ratreal,Y))) # label(fact_3767_real__plus__code) # label(axiom) # label(non_clause).  [assumption].
7.57/7.66	3794 (all X_a all A_2 all F all V_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),hAPP(bool,fun(X_a,fun(X_a,X_a)),if(X_a),hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),hAPP(int,int,pred,V_1)))),A_2),hAPP(nat,X_a,F,hAPP(int,nat,nat_1,hAPP(int,int,number_number_of(int),hAPP(int,int,pred,V_1))))) = hAPP(nat,X_a,hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(X_a,fun(fun(nat,X_a),fun(nat,X_a)),nat_case(X_a),A_2),F),hAPP(int,nat,number_number_of(nat),V_1))) # label(fact_4125_nat__case__number__of) # label(axiom) # label(non_clause).  [assumption].
7.57/7.66	3795 (all X_a (monoid_mult(X_a) -> (all A_1 all N hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),hAPP(nat,nat,suc,N)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N)),A_1)))) # label(fact_1307_power__Suc2) # label(axiom) # label(non_clause).  [assumption].
7.57/7.66	3796 (all X_a (real_normed_vector(X_a) -> (all X_1 all X_3 all A_2 (hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),X_3),A_2),sequentially)) -> hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),hAPP(X_a,fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(X_a,fun(nat,X_a)),combc(nat,X_a,X_a),hAPP(fun(nat,real),fun(nat,fun(X_a,X_a)),hAPP(fun(real,fun(X_a,X_a)),fun(fun(nat,real),fun(nat,fun(X_a,X_a))),combb(real,fun(X_a,X_a),nat),scaleR_scaleR(X_a)),X_3)),X_1)),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_2),X_1)),sequentially)))))) # label(fact_4740_scaleR__left_OLIMSEQ) # label(axiom) # label(non_clause).  [assumption].
7.57/7.66	3797 (all X_a (real_normed_vector(X_a) -> (all X_3 all A_2 (hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(X_a,X_a),fun(fun(nat,X_a),fun(nat,X_a)),combb(X_a,X_a,nat),uminus_uminus(X_a)),X_3)),hAPP(X_a,X_a,uminus_uminus(X_a),A_2)),sequentially)) -> hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),X_3),A_2),sequentially)))))) # label(fact_4470_LIMSEQ__minus__cancel) # label(axiom) # label(non_clause).  [assumption].
7.57/7.66	3798 (all V ((-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),V),pls)) -> hAPP(int,nat,number_number_of(nat),hAPP(int,int,pred,V)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(int,nat,number_number_of(nat),V)),one_one(nat))) & (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),V),pls)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(int,nat,number_number_of(nat),V)),one_one(nat)) = zero_zero(nat)))) # label(fact_2898_nat__number__of__diff__1) # label(axiom) # label(non_clause).  [assumption].
7.57/7.66	3799 (all X all Y all Xa_1 all Ya hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(real,real,sqrt,hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),Y),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),Xa_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),Ya),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))))) # label(fact_1606_real__sqrt__sum__squares__mult__ge__zero) # label(axiom) # label(non_clause).  [assumption].
7.57/7.66	3800 (all N all M (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N),M)) -> hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,M)),N))) # label(fact_1345_Suc__diff__le) # label(axiom) # label(non_clause).  [assumption].
7.57/7.66	3801 (all X_a (real_normed_field(X_a) & banach(X_a) -> (all X_2 hAPP(X_a,X_a,exp(X_a),X_2) = hAPP(fun(nat,X_a),X_a,suminf(X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,real),fun(nat,fun(X_a,X_a)),hAPP(fun(real,fun(X_a,X_a)),fun(fun(nat,real),fun(nat,fun(X_a,X_a))),combb(real,fun(X_a,X_a),nat),scaleR_scaleR(X_a)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),inverse_inverse(real)),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),fact_fact(nat))))),hAPP(X_a,fun(nat,X_a),power_power(X_a),X_2)))))) # label(fact_4750_lemma__exp__ext) # label(axiom) # label(non_clause).  [assumption].
7.57/7.66	3802 (all X_a all X_b (comm_monoid_mult(X_b) -> (all B_1 all A_2 all S (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),S)) -> (-hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_2),S)) -> one_one(X_b) = hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co302546470etprod(X_a,X_b),hAPP(X_b,fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(X_b,fun(X_a,X_b)),combc(X_a,X_b,X_b),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,X_b)),hAPP(fun(X_a,fun(X_b,fun(X_b,X_b))),fun(fun(X_a,X_b),fun(X_a,fun(X_b,X_b))),combs(X_a,X_b,fun(X_b,X_b)),hAPP(fun(X_a,bool),fun(X_a,fun(X_b,fun(X_b,X_b))),hAPP(fun(bool,fun(X_b,fun(X_b,X_b))),fun(fun(X_a,bool),fun(X_a,fun(X_b,fun(X_b,X_b)))),combb(bool,fun(X_b,fun(X_b,X_b)),X_a),if(X_b)),hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,fun(X_a,bool)),fun(X_a,fun(X_a,bool)),combc(X_a,X_a,bool),fequal(X_a)),A_2))),B_1)),one_one(X_b))),S)) & (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_2),S)) -> hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co302546470etprod(X_a,X_b),hAPP(X_b,fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(X_b,fun(X_a,X_b)),combc(X_a,X_b,X_b),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,X_b)),hAPP(fun(X_a,fun(X_b,fun(X_b,X_b))),fun(fun(X_a,X_b),fun(X_a,fun(X_b,X_b))),combs(X_a,X_b,fun(X_b,X_b)),hAPP(fun(X_a,bool),fun(X_a,fun(X_b,fun(X_b,X_b))),hAPP(fun(bool,fun(X_b,fun(X_b,X_b))),fun(fun(X_a,bool),fun(X_a,fun(X_b,fun(X_b,X_b)))),combb(bool,fun(X_b,fun(X_b,X_b)),X_a),if(X_b)),hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,fun(X_a,bool)),fun(X_a,fun(X_a,bool)),combc(X_a,X_a,bool),fequal(X_a)),A_2))),B_1)),one_one(X_b))),S) = hAPP(X_a,X_b,B_1,A_2)))))) # label(fact_3956_setprod__delta) # label(axiom) # label(non_clause).  [assumption].
7.67/7.66	3803 (all K_4 all L_4 hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,bit0,K_4)),hAPP(int,int,bit0,L_4)) = hAPP(int,int,bit0,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),K_4),L_4))) # label(fact_132_add__Bit0__Bit0) # label(axiom) # label(non_clause).  [assumption].
7.67/7.66	3804 (all X_a (ord(X_a) -> ord_max(X_a) = hAPP(fun(X_a,fun(X_a,bool)),fun(X_a,fun(X_a,X_a)),max(X_a),ord_less_eq(X_a)))) # label(fact_4947_max__ord__max) # label(axiom) # label(non_clause).  [assumption].
7.67/7.66	3805 (all Ma all N_1 (Ma = N_1 <-> hAPP(nat,int,semiring_1_of_nat(int),N_1) = hAPP(nat,int,semiring_1_of_nat(int),Ma))) # label(fact_1486_int__int__eq) # label(axiom) # label(non_clause).  [assumption].
7.67/7.66	3806 (all X_a (number_ring(X_a) -> (all X (hBOOL(hAPP(nat,bool,even_odd_even(nat),X)) -> hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(int,X_a,number_number_of(X_a),min_1)),X) = one_one(X_a))))) # label(fact_2457_Parity_Oneg__one__even__power) # label(axiom) # label(non_clause).  [assumption].
7.67/7.66	3807 (all X_a (topological_space(X_a) -> (all F all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(real,fun(filter(X_a),bool),hAPP(fun(X_a,real),fun(real,fun(filter(X_a),bool)),tendsto(X_a,real),hAPP(fun(X_a,real),fun(X_a,real),hAPP(fun(real,real),fun(fun(X_a,real),fun(X_a,real)),combb(real,real,X_a),abs_abs(real)),F)),zero_zero(real)),hAPP(X_a,filter(X_a),at(X_a),A_2))) <-> hBOOL(hAPP(filter(X_a),bool,hAPP(real,fun(filter(X_a),bool),hAPP(fun(X_a,real),fun(real,fun(filter(X_a),bool)),tendsto(X_a,real),F),zero_zero(real)),hAPP(X_a,filter(X_a),at(X_a),A_2))))))) # label(fact_4594_LIM__rabs__zero__iff) # label(axiom) # label(non_clause).  [assumption].
7.67/7.66	3808 (all X_a all C_2 all A_3 all B_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_3),B_2)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),B_2),C_2)) -> ti(fun(X_a,bool),A_3) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),B_2),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),C_2),A_3))))) # label(fact_1997_double__diff) # label(axiom) # label(non_clause).  [assumption].
7.67/7.66	3809 (all X_a (real_normed_field(X_a) -> (all Y_3 all X_3 (hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),X_3)) -> (hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),Y_3)) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(fun(nat,X_a),X_a,suminf(X_a),X_3)),hAPP(fun(nat,X_a),X_a,suminf(X_a),Y_3)) = hAPP(fun(nat,X_a),X_a,suminf(X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),minus_minus(X_a)),X_3)),Y_3))))))) # label(fact_3982_suminf__diff) # label(axiom) # label(non_clause).  [assumption].
7.67/7.66	3810 (all X_a (order(X_a) -> (all X_3 ((all M_2 all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_2),N_2)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(nat,X_a,X_3,N_2)),hAPP(nat,X_a,X_3,M_2))))) -> hBOOL(hAPP(fun(nat,X_a),bool,monoseq(X_a),X_3)))))) # label(fact_4130_monoI2) # label(axiom) # label(non_clause).  [assumption].
7.67/7.66	3811 (all K all Ma all N_1 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K),Ma) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K),N_1) <-> Ma = N_1)) # label(fact_524_nat__add__left__cancel) # label(axiom) # label(non_clause).  [assumption].
7.67/7.66	3812 (all N hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),hAPP(nat,nat,suc,N)))) # label(fact_1207_lessI) # label(axiom) # label(non_clause).  [assumption].
7.67/7.66	3813 (all X_1 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,real)),combs(real,real,real),hAPP(fun(real,real),fun(real,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,fun(real,real))),combb(real,fun(real,real),real),times_times(real)),sin)),sin)),X_1),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),hAPP(real,real,cos,X_1))),hAPP(real,real,sin,X_1))))) # label(fact_3903_DERIV__sin__sin__mult2) # label(axiom) # label(non_clause).  [assumption].
7.67/7.66	3814 (all X_a (field(X_a) & number_ring(X_a) -> (all A_1 ti(X_a,A_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),A_1),hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,bit1,pls)))))) # label(fact_1733_divide__numeral__1) # label(axiom) # label(non_clause).  [assumption].
7.67/7.66	3815 (all R_4 hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(real,complex,of_real(complex),R_4)),ii) = hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,zero_zero(real)),R_4)) # label(fact_2813_complex__of__real__i) # label(axiom) # label(non_clause).  [assumption].
7.67/7.66	3816 (all X hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),ii),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),ii),X)) = hAPP(complex,complex,uminus_uminus(complex),X)) # label(fact_2763_complex__i__mult__minus) # label(axiom) # label(non_clause).  [assumption].
7.67/7.66	3817 (all V_1 (hAPP(int,nat,number_number_of(nat),V_1) = zero_zero(nat) <-> hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),hAPP(int,int,pred,V_1)))))) # label(fact_2911_neg__number__of__pred__iff__0) # label(axiom) # label(non_clause).  [assumption].
7.67/7.66	3818 (all X_a (real_normed_field(X_a) -> (all C_1 all F (hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),F)) -> hAPP(fun(nat,X_a),X_a,suminf(X_a),hAPP(X_a,fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(X_a,fun(nat,X_a)),combc(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),inverse_divide(X_a)),F)),C_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),hAPP(fun(nat,X_a),X_a,suminf(X_a),F)),C_1))))) # label(fact_3984_suminf__divide) # label(axiom) # label(non_clause).  [assumption].
7.67/7.66	3819 (all X_a (ordere216010020id_add(X_a) -> (all Y_1 all X_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),X_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),Y_1)) -> (ti(X_a,X_1) = zero_zero(X_a) & ti(X_a,Y_1) = zero_zero(X_a) <-> zero_zero(X_a) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X_1),Y_1))))))) # label(fact_815_add__nonneg__eq__0__iff) # label(axiom) # label(non_clause).  [assumption].
7.67/7.66	3820 (all M all Y all X (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),X)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),Y)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),M)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,X),Y),M)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X),M)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Y),M)) -> ti(int,X) = ti(int,Y)))))))) # label(fact_419_zcong__less__eq) # label(axiom) # label(non_clause).  [assumption].
7.67/7.66	3821 (all Ma all K all F ((all M_2 all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_2),N_2)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,F,M_2)),hAPP(nat,nat,F,N_2))))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,F,Ma)),K)),hAPP(nat,nat,F,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Ma),K)))))) # label(fact_857_mono__nat__linear__lb) # label(axiom) # label(non_clause).  [assumption].
7.67/7.66	3822 (all X_a all B_2 all A_3 ((all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_3)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),B_2)))) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_3),B_2)))) # label(fact_2188_subsetI) # label(axiom) # label(non_clause).  [assumption].
7.67/7.66	3823 (all X_a (semiring_div(X_a) -> (all A_1 all B all C hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)),C) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),B),C))),C)))) # label(fact_940_mod__add__right__eq) # label(axiom) # label(non_clause).  [assumption].
7.67/7.66	3824 (all X_a (real_normed_algebra(X_a) -> (all Y exists K_2 ((all X_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X_2),Y))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(X_a,real,norm_norm(X_a),X_2)),K_2)))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),K_2)))))) # label(fact_1809_mult__left_Ononneg__bounded) # label(axiom) # label(non_clause).  [assumption].
7.67/7.66	3825 (all X_1 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,real)),combs(real,real,real),hAPP(fun(real,real),fun(real,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,fun(real,real))),combb(real,fun(real,real),real),times_times(real)),cos)),cos)),X_1),hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),hAPP(real,real,cos,X_1))),hAPP(real,real,sin,X_1)))))) # label(fact_3906_DERIV__cos__cos__mult3) # label(axiom) # label(non_clause).  [assumption].
7.67/7.66	3826 (all X_a all P_1 all Q_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,bool)),combs(X_a,bool,bool),hAPP(fun(X_a,bool),fun(X_a,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,fun(bool,bool))),combb(bool,fun(bool,bool),X_a),fdisj),P_1)),Q_1)))) <-> hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),Q_1))) & hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),P_1))))) # label(fact_3847_finite__Collect__disjI) # label(axiom) # label(non_clause).  [assumption].
7.67/7.66	3827 (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_1865_abs__of__pos) # label(axiom) # label(non_clause).  [assumption].
7.67/7.66	3828 (all I_1 all J_2 hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,I_1),J_2)),J_2))) # label(fact_3429_zgcd__zdvd2) # label(axiom) # label(non_clause).  [assumption].
7.67/7.66	3829 (all X_a (linorder(X_a) -> (all A_1 all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),A_1),B)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),A_1),B)))) # label(fact_4969_min__max_Osup_Oleft__idem) # label(axiom) # label(non_clause).  [assumption].
7.67/7.66	3830 (all X all Y (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,X),Y)) -> (exists P_6 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),P_6),X)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),P_6),Y)) & hBOOL(hAPP(nat,bool,prime,P_6)))))) # label(fact_3086_coprime__prime__dvd__ex) # label(axiom) # label(non_clause).  [assumption].
7.67/7.66	3831 (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_5_res) # label(axiom) # label(non_clause).  [assumption].
7.67/7.66	3832 (all X_a all X_b all X_c (topological_space(X_b) & topological_space(X_a) & topological_space(X_c) -> (all F all A_2 all G all L (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),G),hAPP(X_a,X_b,G,L)),hAPP(X_a,filter(X_a),at(X_a),L))) -> (hBOOL(hAPP(filter(X_c),bool,hAPP(X_a,fun(filter(X_c),bool),hAPP(fun(X_c,X_a),fun(X_a,fun(filter(X_c),bool)),tendsto(X_c,X_a),F),L),hAPP(X_c,filter(X_c),at(X_c),A_2))) -> hBOOL(hAPP(filter(X_c),bool,hAPP(X_b,fun(filter(X_c),bool),hAPP(fun(X_c,X_b),fun(X_b,fun(filter(X_c),bool)),tendsto(X_c,X_b),hAPP(fun(X_c,X_a),fun(X_c,X_b),hAPP(fun(X_a,X_b),fun(fun(X_c,X_a),fun(X_c,X_b)),combb(X_a,X_b,X_c),G),F)),hAPP(X_a,X_b,G,L)),hAPP(X_c,filter(X_c),at(X_c),A_2)))))))) # label(fact_4558_LIM__compose) # label(axiom) # label(non_clause).  [assumption].
7.67/7.66	3833 (all N_1 N_1 = hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),N_1)))) # label(fact_3866_card__Collect__less__nat) # label(axiom) # label(non_clause).  [assumption].
7.67/7.66	3834 (all X_a (archim1727834104eiling(X_a) -> (all V_1 all X_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(int,X_a,number_number_of(X_a),V_1)),one_one(X_a))),X_1)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),V_1)),hAPP(X_a,int,archim2085082626_floor(X_a),X_1))))))) # label(fact_2893_number__of__less__floor) # label(axiom) # label(non_clause).  [assumption].
7.67/7.66	3835 (all X_a all X_b all Z all F all A_3 ((exists X_2 (hAPP(X_b,X_a,F,X_2) = ti(X_a,Z) & 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_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Z),hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),A_3))))) # label(fact_3637_image__iff) # label(axiom) # label(non_clause).  [assumption].
7.67/7.66	3836 (all P_4 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),P_4)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),P_4),zOdd)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),P_4),one_one(int))),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))))) # label(fact_1050_Euler_Oaux__2) # label(axiom) # label(non_clause).  [assumption].
7.67/7.66	3837 (all X_a (ord(X_a) -> min(X_a) = ti(fun(fun(X_a,fun(X_a,bool)),fun(X_a,fun(X_a,X_a))),min(X_a)))) # label(tsy_c_Orderings_Oord_Omin_res) # label(axiom) # label(non_clause).  [assumption].
7.67/7.66	3838 (all X_a (no_zero_divisors(X_a) -> (all A_1 all 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) = ti(X_a,A_1) | zero_zero(X_a) = ti(X_a,B))))) # label(fact_319_divisors__zero) # label(axiom) # label(non_clause).  [assumption].
7.67/7.66	3839 (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_3041_termination__basic__simps_I5_J) # label(axiom) # label(non_clause).  [assumption].
7.67/7.66	3840 (all X_a (comm_semiring_1(X_a) -> (all M hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),one_one(X_a)),one_one(X_a))),M) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),M),M)))) # label(fact_253_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J) # label(axiom) # label(non_clause).  [assumption].
7.67/7.66	3841 (all X_1 all Y_1 (hAPP(real,real,sqrt,Y_1) = hAPP(real,real,sqrt,X_1) <-> Y_1 = X_1)) # label(fact_1610_real__sqrt__eq__iff) # label(axiom) # label(non_clause).  [assumption].
7.67/7.66	3842 (all Z all X_3 (hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),Z),X_3)) -> ((all X_2 (hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),X_2),X_3)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_2),Z)))) -> Z = hAPP(fun(real,bool),real,complete_Sup_Sup(real),X_3)))) # label(fact_3713_Sup__eq__maximum) # label(axiom) # label(non_clause).  [assumption].
7.67/7.66	3843 (all A_1 all B all C (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),C)) -> hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_1),B)),C) = hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_1),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),C)))) # label(fact_1028_zdiv__zmult2__eq) # label(axiom) # label(non_clause).  [assumption].
7.67/7.66	3844 (all Ma all N_1 hAPP(nat,product_prod(nat,nat),hAPP(nat,fun(nat,product_prod(nat,nat)),divmod_nat,Ma),N_1) = hAPP(fun(product_prod(nat,nat),bool),product_prod(nat,nat),the(product_prod(nat,nat)),hAPP(nat,fun(product_prod(nat,nat),bool),hAPP(nat,fun(nat,fun(product_prod(nat,nat),bool)),divmod_nat_rel,Ma),N_1))) # label(fact_4144_divmod__nat__def) # label(axiom) # label(non_clause).  [assumption].
7.67/7.66	3845 (all X_a (ring_1(X_a) -> (all P_1 all Q_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Q_2),ring_1_Ints(X_a))) -> ((all Z_2 hBOOL(hAPP(X_a,bool,P_1,hAPP(int,X_a,ring_1_of_int(X_a),Z_2)))) -> hBOOL(hAPP(X_a,bool,P_1,Q_2))))))) # label(fact_4415_Ints__induct) # label(axiom) # label(non_clause).  [assumption].
7.67/7.66	3846 (all Y all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),one_one(real)),X)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Y)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(real,nat,natfloor,X)),Y) = hAPP(real,nat,natfloor,hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),X),hAPP(nat,real,real_1(nat),Y)))))) # label(fact_2382_natfloor__div__nat) # label(axiom) # label(non_clause).  [assumption].
7.67/7.66	3847 (all X_a ti(fun(fun(X_a,bool),nat),finite_card(X_a)) = finite_card(X_a)) # label(tsy_c_Finite__Set_Ocard_res) # label(axiom) # label(non_clause).  [assumption].
7.67/7.66	3848 (all X_a all X_b (t2_space(X_b) -> (all L_1 all F all L all A_3 (-hBOOL(hAPP(filter(X_a),bool,trivial_limit(X_a),A_3)) -> (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),L),A_3)) -> (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),L_1),A_3)) -> ti(X_b,L) = ti(X_b,L_1))))))) # label(fact_4767_tendsto__unique) # label(axiom) # label(non_clause).  [assumption].
7.67/7.66	3849 (all X_a (ab_group_add(X_a) -> (all A_2 all B_1 all C_1 all D_1 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_2),B_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),C_1),D_1) -> (ti(X_a,D_1) = ti(X_a,C_1) <-> ti(X_a,A_2) = ti(X_a,B_1)))))) # label(fact_773_diff__eq__diff__eq) # label(axiom) # label(non_clause).  [assumption].
7.67/7.66	3850 (all K all L (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K),L)) <-> (exists N_2 hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K),N_2) = L))) # label(fact_1799_le__Suc__ex__iff) # label(axiom) # label(non_clause).  [assumption].
7.67/7.66	3851 (all I_1 all J_2 hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,I_1),J_2) = hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,J_2),I_1)) # label(fact_3440_zgcd__commute) # label(axiom) # label(non_clause).  [assumption].
7.67/7.66	3852 (all N (N != zero_zero(nat) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),N) = hAPP(nat,nat,suc,hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),N)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))) # label(fact_1460_Suc__Suc__mult__two__diff__two) # label(axiom) # label(non_clause).  [assumption].
7.67/7.66	3853 (all X_a (comm_ring_1(X_a) -> (all Z_1 all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),X),Y)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),X),Z_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),Y),Z_1)))))))) # label(fact_478_dvd__diff) # label(axiom) # label(non_clause).  [assumption].
7.67/7.66	3854 (all S (hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,S)) <-> (all X_2 (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_2),S)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X_2)))))) # label(fact_3662_nat__set__def) # label(axiom) # label(non_clause).  [assumption].
7.67/7.66	3855 (all X_a (order(X_a) -> (all X_3 ((all N_2 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(nat,X_a,X_3,N_2)),hAPP(nat,X_a,X_3,hAPP(nat,nat,suc,N_2))))) -> hBOOL(hAPP(fun(nat,X_a),bool,monoseq(X_a),X_3)))))) # label(fact_4141_mono__SucI1) # label(axiom) # label(non_clause).  [assumption].
7.67/7.66	3856 (all X_1 all Ma (X_1 = hAPP(nat,nat,suc,zero_zero(nat)) | Ma = zero_zero(nat) <-> hAPP(nat,nat,suc,zero_zero(nat)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),X_1),Ma))) # label(fact_1353_nat__power__eq__Suc__0__iff) # label(axiom) # label(non_clause).  [assumption].
7.67/7.66	3857 (all P_1 all N_1 ((all X_2 (hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X_2),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),N_1))) -> hBOOL(hAPP(nat,bool,P_1,X_2)))) <-> (all M_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_2),N_1)) -> hBOOL(hAPP(nat,bool,P_1,M_2)))))) # label(fact_4194_all__nat__less__eq) # label(axiom) # label(non_clause).  [assumption].
7.67/7.66	3858 (all X all Y all Xa_1 all Ya hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),Y),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),Xa_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),Ya),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,sqrt,hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),Y),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),Xa_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),Ya),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) # label(fact_1648_real__sqrt__sum__squares__mult__squared__eq) # label(axiom) # label(non_clause).  [assumption].
7.67/7.66	3859 (all X_a (real_vector(X_a) -> (all A_1 all B all X hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_1),X)),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),B),X)) = hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A_1),B)),X)))) # label(fact_4711_real__vector_Oscale__left__distrib) # label(axiom) # label(non_clause).  [assumption].
7.67/7.66	3860 (all U all M all N all I_1 all J_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_1),J_2)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I_1),U)),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J_2),U)),N)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_2),I_1)),U)),N)))) # label(fact_750_nat__diff__add__eq2) # label(axiom) # label(non_clause).  [assumption].
7.67/7.66	3861 (all F all X_1 all F_2 all N_1 all Ma ((all R_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Ma),R_2)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),R_2),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Ma),N_1))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(nat,fun(real,real),F,R_2)),X_1),hAPP(real,real,hAPP(nat,fun(real,real),F_2,R_2),X_1))))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(fun(nat,bool),fun(real,real),hAPP(fun(real,fun(fun(nat,bool),real)),fun(fun(nat,bool),fun(real,real)),combc(real,fun(nat,bool),real),hAPP(fun(real,fun(nat,real)),fun(real,fun(fun(nat,bool),real)),hAPP(fun(fun(nat,real),fun(fun(nat,bool),real)),fun(fun(real,fun(nat,real)),fun(real,fun(fun(nat,bool),real))),combb(fun(nat,real),fun(fun(nat,bool),real),real),big_co1399186613setsum(nat,real)),hAPP(fun(nat,fun(real,real)),fun(real,fun(nat,real)),combc(nat,real,real),F))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),Ma),N_1))),X_1),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(real,fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(real,fun(nat,real)),combc(nat,real,real),F_2),X_1)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),Ma),N_1)))))) # label(fact_4289_DERIV__sumr) # label(axiom) # label(non_clause).  [assumption].
7.67/7.66	3862 (all P_5 all Y all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),P_5),Y)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),P_5),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),Y),N)))))) # label(fact_454_zpower__zdvd__prop1) # label(axiom) # label(non_clause).  [assumption].
7.67/7.66	3863 (all A_1 all B (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B)) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A_1),B))) -> hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),negDivAlg,A_1),B) = hAPP(product_prod(int,int),product_prod(int,int),hAPP(int,fun(product_prod(int,int),product_prod(int,int)),adjust,B),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),negDivAlg,A_1),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),B)))) & (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A_1),B))) -> hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),negDivAlg,A_1),B) = hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),hAPP(int,int,number_number_of(int),min_1)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A_1),B))))) # label(fact_1070_negDivAlg__eqn) # label(axiom) # label(non_clause).  [assumption].
7.67/7.66	3864 (all N all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,real_1(int),N)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(int,real,real_1(int),N)),one_one(real)))) -> hAPP(real,int,archimedean_ceiling(real),X) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),N),one_one(int))))) # label(fact_3419_ceiling__eq) # label(axiom) # label(non_clause).  [assumption].
7.67/7.66	3865 (all X_a (ring_1(X_a) -> (all W all Z_1 hAPP(int,X_a,ring_1_of_int(X_a),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),W),Z_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(int,X_a,ring_1_of_int(X_a),W)),hAPP(int,X_a,ring_1_of_int(X_a),Z_1))))) # label(fact_3590_of__int__add) # label(axiom) # label(non_clause).  [assumption].
7.67/7.66	3866 (all X_a (comm_semiring_1(X_a) -> (all X all N hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),N)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),N)) = hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),N))))) # label(fact_192_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J) # label(axiom) # label(non_clause).  [assumption].
7.67/7.66	3867 (all K_4 all M (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),M)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),K_4)) -> hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),K_4),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),hAPP(nat,nat,suc,zero_zero(nat)))) = hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),K_4),M)),K_4)))) # label(fact_1463_int__power__div__base) # label(axiom) # label(non_clause).  [assumption].
7.67/7.66	3868 (all X_b all X_a (semiring_1(X_a) & comm_monoid_mult(X_a) -> (all F all A_3 hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co302546470etprod(X_b,X_a),hAPP(fun(X_b,nat),fun(X_b,X_a),hAPP(fun(nat,X_a),fun(fun(X_b,nat),fun(X_b,X_a)),combb(nat,X_a,X_b),semiring_1_of_nat(X_a)),F)),A_3) = hAPP(nat,X_a,semiring_1_of_nat(X_a),hAPP(fun(X_b,bool),nat,hAPP(fun(X_b,nat),fun(fun(X_b,bool),nat),big_co302546470etprod(X_b,nat),F),A_3))))) # label(fact_3928_of__nat__setprod) # label(axiom) # label(non_clause).  [assumption].
7.67/7.66	3869 (all N_1 all Ma (hAPP(nat,real,real_1(nat),N_1) = hAPP(nat,real,real_1(nat),Ma) <-> N_1 = Ma)) # label(fact_2292_real__of__nat__inject) # label(axiom) # label(non_clause).  [assumption].
7.67/7.66	3870 (all X all Y (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),Y)) -> -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y),X)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),Y)) | Y = X)) # label(fact_628_dvd_Ole__imp__less__or__eq) # label(axiom) # label(non_clause).  [assumption].
7.67/7.66	3871 (all X_a (monoid_mult(X_a) -> (all A_1 hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,hAPP(int,int,bit1,pls)))) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),A_1)),A_1)))) # label(fact_138_power3__eq__cube) # label(axiom) # label(non_clause).  [assumption].
7.67/7.66	3872 (all Ma all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,Ma)),N_1)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),N_1)))) # label(fact_1335_Suc__le__eq) # label(axiom) # label(non_clause).  [assumption].
7.67/7.66	3873 (all X_a (group_add(X_a) -> (all A_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),zero_zero(X_a)),A_1) = hAPP(X_a,X_a,uminus_uminus(X_a),A_1)))) # label(fact_2070_diff__0) # label(axiom) # label(non_clause).  [assumption].
7.67/7.66	3874 (all K_4 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),K_4)) -> (exists N_2 ti(int,K_4) = hAPP(nat,int,semiring_1_of_nat(int),N_2)))) # label(fact_1490_zero__le__imp__eq__int) # label(axiom) # label(non_clause).  [assumption].
7.67/7.66	3875 (all X hAPP(rat,real,ratreal,hAPP(rat,rat,inverse_inverse(rat),X)) = hAPP(real,real,inverse_inverse(real),hAPP(rat,real,ratreal,X))) # label(fact_3772_real__inverse__code) # label(axiom) # label(non_clause).  [assumption].
7.67/7.66	3876 (all A_1 all B hAPP(real,complex,cis,hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A_1),B)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),hAPP(real,complex,cis,A_1)),hAPP(real,complex,cis,B))) # label(fact_3031_cis__divide) # label(axiom) # label(non_clause).  [assumption].
7.67/7.66	3877 (all X_a (divisi14063676e_zero(X_a) -> hAPP(X_a,X_a,inverse_inverse(X_a),zero_zero(X_a)) = zero_zero(X_a))) # label(fact_2526_inverse__zero) # label(axiom) # label(non_clause).  [assumption].
7.67/7.66	3878 (all N hAPP(nat,complex,semiring_1_of_nat(complex),N) = hAPP(complex,complex,cnj,hAPP(nat,complex,semiring_1_of_nat(complex),N))) # label(fact_2940_complex__cnj__of__nat) # label(axiom) # label(non_clause).  [assumption].
7.67/7.66	3879 (all A_2 all B_1 ((all D_3 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),D_3),B_1)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),D_3),A_2)) <-> D_3 = one_one(nat))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,A_2),B_1)))) # label(fact_2871_coprime) # label(axiom) # label(non_clause).  [assumption].
7.67/7.66	3880 (all X_a (real_normed_algebra(X_a) -> (all X_1 all X_3 (hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),X_3)) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X_1),hAPP(fun(nat,X_a),X_a,suminf(X_a),X_3)) = hAPP(fun(nat,X_a),X_a,suminf(X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(X_a,X_a),fun(fun(nat,X_a),fun(nat,X_a)),combb(X_a,X_a,nat),hAPP(X_a,fun(X_a,X_a),times_times(X_a),X_1)),X_3)))))) # label(fact_3988_mult__right_Osuminf) # label(axiom) # label(non_clause).  [assumption].
7.67/7.66	3881 (all X_b all X_a (metric_space(X_a) & metric_space(X_b) -> (all X_3 all L_2 all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),X_3),L_2),hAPP(X_a,filter(X_a),at(X_a),A_2))) -> (all S_2 (hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),S_2),A_2),sequentially)) & (all N_2 ti(X_a,A_2) != hAPP(nat,X_a,S_2,N_2)) -> hBOOL(hAPP(filter(nat),bool,hAPP(X_b,fun(filter(nat),bool),hAPP(fun(nat,X_b),fun(X_b,fun(filter(nat),bool)),tendsto(nat,X_b),hAPP(fun(nat,X_a),fun(nat,X_b),hAPP(fun(X_a,X_b),fun(fun(nat,X_a),fun(nat,X_b)),combb(X_a,X_b,nat),X_3),S_2)),L_2),sequentially)))))))) # label(fact_4655_LIMSEQ__SEQ__conv1) # label(axiom) # label(non_clause).  [assumption].
7.67/7.66	3882 (all X_a (linorder(X_a) -> (all A_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),A_1),A_1) = ti(X_a,A_1)))) # label(fact_4817_min__max_Oinf_Oidem) # label(axiom) # label(non_clause).  [assumption].
7.67/7.66	3883 (all X all N (-hBOOL(hAPP(nat,bool,even_odd_even(nat),N)) -> X = hAPP(real,real,hAPP(nat,fun(real,real),root,N),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),N)))) # label(fact_2676_odd__real__root__power__cancel) # label(axiom) # label(non_clause).  [assumption].
7.67/7.66	3884 (all X hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),hAPP(real,real,sin,X))),hAPP(real,real,cos,X)) = hAPP(real,real,sin,hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),X))) # label(fact_2368_sin__double) # label(axiom) # label(non_clause).  [assumption].
7.67/7.66	3885 (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_381_zero__le__square) # label(axiom) # label(non_clause).  [assumption].
7.67/7.66	3886 (all Ta all B_2 all D_1 all D_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),D_1),D_2)) -> (all X_2 ((all Xa (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xa),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastAtMost(int),one_one(int)),D_2))) -> (all Xb (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xb),B_2)) -> ti(int,X_2) != hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Xb),Xa))))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),D_1),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X_2),Ta))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),D_1),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X_2),D_2)),Ta)))))))) # label(fact_4649_bset_I9_J) # label(axiom) # label(non_clause).  [assumption].
7.67/7.66	3887 (all B_2 all A_3 (hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A_3)) -> (hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,B_2)) -> (hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,bool),fun(fun(nat,bool),bool),ord_less_eq(fun(nat,bool)),hAPP(fun(int,bool),fun(nat,bool),hAPP(fun(int,nat),fun(fun(int,bool),fun(nat,bool)),image(int,nat),nat_1),A_3)),hAPP(fun(int,bool),fun(nat,bool),hAPP(fun(int,nat),fun(fun(int,bool),fun(nat,bool)),image(int,nat),nat_1),B_2))) <-> hBOOL(hAPP(fun(int,bool),bool,hAPP(fun(int,bool),fun(fun(int,bool),bool),ord_less_eq(fun(int,bool)),A_3),B_2)))))) # label(fact_3669_transfer__int__nat__set__relations_I5_J) # label(axiom) # label(non_clause).  [assumption].
7.67/7.66	3888 (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_153_number__of__add) # label(axiom) # label(non_clause).  [assumption].
7.67/7.66	3889 (all X_c all X_a all X_b (comm_monoid_add(X_b) -> (all G all F all S (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),S)) -> hAPP(fun(X_c,bool),X_b,hAPP(fun(X_c,X_b),fun(fun(X_c,bool),X_b),big_co1399186613setsum(X_c,X_b),hAPP(fun(X_c,fun(X_a,bool)),fun(X_c,X_b),hAPP(fun(fun(X_a,bool),X_b),fun(fun(X_c,fun(X_a,bool)),fun(X_c,X_b)),combb(fun(X_a,bool),X_b,X_c),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),G)),hAPP(fun(X_c,fun(X_a,bool)),fun(X_c,fun(X_a,bool)),hAPP(fun(fun(X_a,bool),fun(X_a,bool)),fun(fun(X_c,fun(X_a,bool)),fun(X_c,fun(X_a,bool))),combb(fun(X_a,bool),fun(X_a,bool),X_c),collect(X_a)),hAPP(fun(X_c,fun(X_a,bool)),fun(X_c,fun(X_a,bool)),hAPP(fun(fun(X_a,bool),fun(X_a,bool)),fun(fun(X_c,fun(X_a,bool)),fun(X_c,fun(X_a,bool))),combb(fun(X_a,bool),fun(X_a,bool),X_c),hAPP(fun(X_a,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,bool)),combs(X_a,bool,bool),hAPP(fun(X_a,bool),fun(X_a,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,fun(bool,bool))),combb(bool,fun(bool,bool),X_a),fconj),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(X_a,bool)),combc(X_a,fun(X_a,bool),bool),member(X_a)),S)))),hAPP(fun(X_a,fun(X_c,bool)),fun(X_c,fun(X_a,bool)),combc(X_a,X_c,bool),hAPP(fun(X_a,X_c),fun(X_a,fun(X_c,bool)),hAPP(fun(X_c,fun(X_c,bool)),fun(fun(X_a,X_c),fun(X_a,fun(X_c,bool))),combb(X_c,fun(X_c,bool),X_a),fequal(X_c)),F)))))),hAPP(fun(X_a,bool),fun(X_c,bool),hAPP(fun(X_a,X_c),fun(fun(X_a,bool),fun(X_c,bool)),image(X_a,X_c),F),S)) = hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),G),S))))) # label(fact_4224_setsum__image__gen) # label(axiom) # label(non_clause).  [assumption].
7.67/7.66	3890 (all X hAPP(int,int,fact_fact(int),hAPP(nat,int,semiring_1_of_nat(int),X)) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,fact_fact(nat),X))) # label(fact_3193_transfer__int__nat__factorial) # label(axiom) # label(non_clause).  [assumption].
7.67/7.66	3891 (all K_4 all L_4 hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,bit0,K_4)),L_4) = hAPP(int,int,bit0,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K_4),L_4))) # label(fact_63_mult__Bit0) # label(axiom) # label(non_clause).  [assumption].
7.67/7.66	3892 (all M 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)) -> 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),N)))))) # label(fact_1383_n__less__m__mult__n) # label(axiom) # label(non_clause).  [assumption].
7.67/7.66	3893 (all X_a all X_b all P_1 hAPP(fun(product_prod(X_a,X_b),bool),product_prod(X_a,X_b),hilbert_Eps(product_prod(X_a,X_b)),hAPP(fun(X_a,fun(X_b,bool)),fun(product_prod(X_a,X_b),bool),product_prod_case(X_a,X_b,bool),hAPP(fun(X_a,fun(X_b,product_prod(X_a,X_b))),fun(X_a,fun(X_b,bool)),hAPP(fun(fun(X_b,product_prod(X_a,X_b)),fun(X_b,bool)),fun(fun(X_a,fun(X_b,product_prod(X_a,X_b))),fun(X_a,fun(X_b,bool))),combb(fun(X_b,product_prod(X_a,X_b)),fun(X_b,bool),X_a),hAPP(fun(product_prod(X_a,X_b),bool),fun(fun(X_b,product_prod(X_a,X_b)),fun(X_b,bool)),combb(product_prod(X_a,X_b),bool,X_b),P_1)),product_Pair(X_a,X_b)))) = hAPP(fun(product_prod(X_a,X_b),bool),product_prod(X_a,X_b),hilbert_Eps(product_prod(X_a,X_b)),P_1)) # label(fact_4781_split__paired__Eps) # label(axiom) # label(non_clause).  [assumption].
7.67/7.66	3894 (all N hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,inverse_inverse(real),hAPP(nat,real,real_1(nat),hAPP(nat,nat,fact_fact(nat),N)))))) # label(fact_2616_inv__real__of__nat__fact__gt__zero) # label(axiom) # label(non_clause).  [assumption].
7.67/7.66	3895 (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_369_mult__left__mono__neg) # label(axiom) # label(non_clause).  [assumption].
7.67/7.66	3896 (all X hAPP(real,real,uminus_uminus(real),hAPP(int,real,real_1(int),X)) = hAPP(int,real,real_1(int),hAPP(int,int,uminus_uminus(int),X))) # label(fact_3342_real__of__int__minus) # label(axiom) # label(non_clause).  [assumption].
7.67/7.66	3897 (all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),Y),zero_zero(real))) -> hAPP(real,real,cos,hAPP(complex,real,arg,hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,zero_zero(real)),Y))) = zero_zero(real))) # label(fact_2753_cos__arg__i__mult__zero__neg) # label(axiom) # label(non_clause).  [assumption].
7.67/7.66	3898 (all X_a (ring_div(X_a) -> (all A_1 all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),A_1)),B) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),A_1),B))),B)))) # label(fact_2012_mod__minus__eq) # label(axiom) # label(non_clause).  [assumption].
7.67/7.66	3899 (all X hAPP(int,real,real_1(int),hAPP(int,int,abs_abs(int),X)) = hAPP(real,real,abs_abs(real),hAPP(int,real,real_1(int),X))) # label(fact_3343_real__of__int__abs) # label(axiom) # label(non_clause).  [assumption].
7.67/7.66	3900 (all X_a all X_b (comm_monoid_mult(X_b) -> (all F all S all T_3 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),T_3)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),S),T_3)) -> ((all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),T_3),S))) -> one_one(X_b) = hAPP(X_a,X_b,F,X_2))) -> hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co302546470etprod(X_a,X_b),F),S) = hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co302546470etprod(X_a,X_b),F),T_3))))))) # label(fact_3960_setprod__mono__one__left) # label(axiom) # label(non_clause).  [assumption].
7.67/7.66	3901 (all X all M hAPP(real,real,uminus_uminus(real),hAPP(real,real,sin,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,real_1(nat),M)),pi)),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))) = hAPP(real,real,cos,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,real_1(nat),hAPP(nat,nat,suc,M))),pi)),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))) # label(fact_2365_cos__expansion__lemma) # label(axiom) # label(non_clause).  [assumption].
7.67/7.66	3902 (all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),hAPP(real,real,arctan,Y))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,arctan,Y)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))) # label(fact_2125_arctan__bounded) # label(axiom) # label(non_clause).  [assumption].
7.67/7.66	3903 (all K all F (zero_zero(nat) = hAPP(nat,nat,F,zero_zero(nat)) -> hAPP(fun(nat,bool),nat,hAPP(fun(nat,nat),fun(fun(nat,bool),nat),big_co1399186613setsum(nat,nat),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),zero_zero(nat)),K)) = hAPP(fun(nat,bool),nat,hAPP(fun(nat,nat),fun(fun(nat,bool),nat),big_co1399186613setsum(nat,nat),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,suc,zero_zero(nat))),K)))) # label(fact_4589_setsum__shift__lb__Suc0__0) # label(axiom) # label(non_clause).  [assumption].
7.67/7.66	3904 (all X all Y ((zero_zero(nat) != Y -> hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),hAPP(product_prod(int,int),int,product_snd(int,int),hAPP(nat,product_prod(int,int),hAPP(nat,fun(nat,product_prod(int,int)),bezw,Y),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),X),Y)))),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(product_prod(int,int),int,product_fst(int,int),hAPP(nat,product_prod(int,int),hAPP(nat,fun(nat,product_prod(int,int)),bezw,Y),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),X),Y)))),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(product_prod(int,int),int,product_snd(int,int),hAPP(nat,product_prod(int,int),hAPP(nat,fun(nat,product_prod(int,int)),bezw,Y),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),X),Y)))),hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),X),Y))))) = hAPP(nat,product_prod(int,int),hAPP(nat,fun(nat,product_prod(int,int)),bezw,X),Y)) & (zero_zero(nat) = Y -> hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),one_one(int)),zero_zero(int)) = hAPP(nat,product_prod(int,int),hAPP(nat,fun(nat,product_prod(int,int)),bezw,X),Y)))) # label(fact_3113_bezw_Osimps) # label(axiom) # label(non_clause).  [assumption].
7.67/7.66	3905 (all X_1 all Y_1 all Xa_2 (X_1 = Xa_2 & Y_1 = zero_zero(real) <-> hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,X_1),Y_1) = hAPP(real,complex,of_real(complex),Xa_2))) # label(fact_2790_complex__eq__cancel__iff2) # label(axiom) # label(non_clause).  [assumption].
7.67/7.66	3906 (all F (hBOOL(hAPP(fun(nat,real),bool,summable(real),F)) -> ((all N_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(nat,real,F,N_2)))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(fun(nat,real),real,suminf(real),F)))))) # label(fact_4071_suminf__gt__zero) # label(axiom) # label(non_clause).  [assumption].
7.67/7.66	3907 (all A_1 all B hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),A_1),B) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),A_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),A_1),B))) # label(fact_3222_gcd__semilattice__nat_Oinf_Oleft__idem) # label(axiom) # label(non_clause).  [assumption].
7.67/7.66	3908 (all Z_1 all X all Y (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X),Y)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Y),Z_1))))) # label(fact_3039_termination__basic__simps_I1_J) # label(axiom) # label(non_clause).  [assumption].
7.67/7.66	3909 (all X_a all X_b (comm_monoid_add(X_b) -> (all F all S all T_3 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),T_3)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),S),T_3)) -> ((all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),T_3),S))) -> hAPP(X_a,X_b,F,X_2) = zero_zero(X_b))) -> hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),F),T_3) = hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),F),S))))))) # label(fact_4295_setsum__mono__zero__left) # label(axiom) # label(non_clause).  [assumption].
7.67/7.66	3910 (all C all D all A_1 all B all M (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_1),B),M)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,C),D),M)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A_1),C)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),B),D)),M))))) # label(fact_361_zcong__zadd) # label(axiom) # label(non_clause).  [assumption].
7.67/7.66	3911 (all X_a all P_1 hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),P_1) = ti(fun(X_a,bool),P_1)) # label(fact_77_Collect__def) # label(axiom) # label(non_clause).  [assumption].
7.67/7.66	3912 (all X_a (real_normed_field(X_a) -> (all Y_1 all X_3 all A_2 (hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),X_3),A_2),sequentially)) -> hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),hAPP(X_a,fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(X_a,fun(nat,X_a)),combc(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),inverse_divide(X_a)),X_3)),Y_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),A_2),Y_1)),sequentially)))))) # label(fact_4449_divide_OLIMSEQ) # label(axiom) # label(non_clause).  [assumption].
7.67/7.66	3913 (all X_a all A_3 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),hAPP(fun(fun(X_a,bool),bool),fun(X_a,bool),complete_Sup_Sup(fun(X_a,bool)),A_3))) -> hBOOL(hAPP(fun(fun(X_a,bool),bool),bool,finite_finite_1(fun(X_a,bool)),A_3)))) # label(fact_1825_finite__UnionD) # label(axiom) # label(non_clause).  [assumption].
7.67/7.66	3914 (all X_a (linorder(X_a) -> (all Y all X hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),Y)))))) # label(fact_4985_le__maxI2) # label(axiom) # label(non_clause).  [assumption].
7.67/7.66	3915 (all X_a all C_1 all A_3 all B_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_3),B_2))) <-> -hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),B_2)) & hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),A_3)))) # label(fact_1962_Diff__iff) # label(axiom) # label(non_clause).  [assumption].
7.67/7.66	3916 (all N_1 all Ma (N_1 = one_one(nat) & one_one(nat) = Ma <-> hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N_1),Ma) = one_one(nat))) # label(fact_725_nat__mult__eq__one) # label(axiom) # label(non_clause).  [assumption].
7.67/7.66	3917 (all I all J all F ((all I_2 all J_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),J_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,F,I_2)),hAPP(nat,nat,F,J_1))))) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I),J)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,F,I)),hAPP(nat,nat,F,J)))))) # label(fact_1205_less__mono__imp__le__mono) # label(axiom) # label(non_clause).  [assumption].
7.67/7.67	3918 (all X_a (comm_monoid_add(X_a) -> (all F all Ma all K all N_1 hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Ma),K)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_1),K))) = hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),hAPP(fun(nat,nat),fun(nat,X_a),hAPP(fun(nat,X_a),fun(fun(nat,nat),fun(nat,X_a)),combb(nat,X_a,nat),F),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),K))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),Ma),N_1))))) # label(fact_4178_setsum__shift__bounds__nat__ivl) # label(axiom) # label(non_clause).  [assumption].
7.67/7.67	3919 (all X_b all X_a all X all Y all A_1 (ti(X_a,A_1) = hAPP(product_prod(X_b,X_a),X_a,product_snd(X_b,X_a),hAPP(X_a,product_prod(X_b,X_a),hAPP(X_b,fun(X_a,product_prod(X_b,X_a)),product_Pair(X_b,X_a),X),Y)) -> ti(X_a,A_1) = ti(X_a,Y))) # label(fact_3139_snd__eqD) # label(axiom) # label(non_clause).  [assumption].
7.67/7.67	3920 (all M zero_zero(nat) != hAPP(nat,nat,suc,M)) # label(fact_1225_Suc__not__Zero) # label(axiom) # label(non_clause).  [assumption].
7.67/7.67	3921 (all X_a (archim1727834104eiling(X_a) -> (all X hAPP(int,int,uminus_uminus(int),hAPP(X_a,int,archimedean_ceiling(X_a),X)) = hAPP(X_a,int,archim2085082626_floor(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),X))))) # label(fact_3293_floor__minus) # label(axiom) # label(non_clause).  [assumption].
7.67/7.67	3922 (all X_a (archim1727834104eiling(X_a) -> (all X_1 all V_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(X_a,int,archim2085082626_floor(X_a),X_1)),hAPP(int,int,number_number_of(int),V_1))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(int,X_a,number_number_of(X_a),V_1)),one_one(X_a)))))))) # label(fact_2894_floor__le__number__of) # label(axiom) # label(non_clause).  [assumption].
7.67/7.67	3923 (all B_2 all P_2 all P_1 all D_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D_2)) -> ((exists Z_2 all X_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X_2),Z_2)) -> (hBOOL(hAPP(int,bool,P_2,X_2)) <-> hBOOL(hAPP(int,bool,P_1,X_2))))) -> ((all X_2 ((all Xa (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xa),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastAtMost(int),one_one(int)),D_2))) -> (all Xb (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xb),B_2)) -> ti(int,X_2) != hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Xb),Xa))))) -> (hBOOL(hAPP(int,bool,P_1,X_2)) -> hBOOL(hAPP(int,bool,P_1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X_2),D_2)))))) -> ((all X_2 all K_1 (hBOOL(hAPP(int,bool,P_2,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X_2),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K_1),D_2)))) <-> hBOOL(hAPP(int,bool,P_2,X_2)))) -> ((exists X1 hBOOL(hAPP(int,bool,P_1,X1))) <-> (exists X_2 (hBOOL(hAPP(int,bool,P_2,X_2)) & hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_2),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastAtMost(int),one_one(int)),D_2))))) | (exists X_2 (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_2),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastAtMost(int),one_one(int)),D_2))) & (exists Xa (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xa),B_2)) & hBOOL(hAPP(int,bool,P_1,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Xa),X_2))))))))))))) # label(fact_4873_cpmi) # label(axiom) # label(non_clause).  [assumption].
7.67/7.67	3924 (all X_a (archim1804426504_field(X_a) -> (all X exists N_2 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),hAPP(nat,X_a,semiring_1_of_nat(X_a),N_2)))))) # label(fact_2736_ex__less__of__nat) # label(axiom) # label(non_clause).  [assumption].
7.67/7.67	3925 (exists K_2 ((all X_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,norm_norm(real),hAPP(complex,real,re,X_2))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(complex,real,norm_norm(complex),X_2)),K_2)))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),K_2)))) # label(fact_3021_Re_Ononneg__bounded) # label(axiom) # label(non_clause).  [assumption].
7.67/7.67	3926 (all X_a (comple44059174attice(X_a) -> complete_Sup_Sup(X_a) = ti(fun(fun(X_a,bool),X_a),complete_Sup_Sup(X_a)))) # label(tsy_c_Complete__Lattice_OSup__class_OSup_1_res) # label(axiom) # label(non_clause).  [assumption].
7.67/7.67	3927 (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_1882_abs__triangle__ineq4) # label(axiom) # label(non_clause).  [assumption].
7.67/7.67	3928 (all X_a (real_normed_vector(X_a) -> (all X_3 all K_3 all N_4 ((all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_4),N_2)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),hAPP(nat,X_a,X_3,N_2))),K_3)))) -> hBOOL(hAPP(fun(nat,X_a),bool,bseq(X_a),X_3)))))) # label(fact_3499_BseqI2_H) # label(axiom) # label(non_clause).  [assumption].
7.67/7.67	3929 (all X_a (metric_space(X_a) -> (all X_1 all Y_1 (ti(X_a,Y_1) = ti(X_a,X_1) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),X_1),Y_1)),zero_zero(real))))))) # label(fact_3511_dist__le__zero__iff) # label(axiom) # label(non_clause).  [assumption].
7.67/7.67	3930 (all X_a (number_ring(X_a) & field_inverse_zero(X_a) -> (all X hAPP(X_a,X_a,uminus_uminus(X_a),X) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),X),hAPP(int,X_a,number_number_of(X_a),min_1))))) # label(fact_2105_divide__minus1) # label(axiom) # label(non_clause).  [assumption].
7.67/7.67	3931 (all X_c all X_b all X_a (topological_space(X_c) & topological_space(X_b) & metric_space(X_a) -> (all G all L all F all A_2 (hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,X_b),fun(X_a,bool),isCont(X_a,X_b),F),A_2)) -> (hBOOL(hAPP(filter(X_b),bool,hAPP(X_c,fun(filter(X_b),bool),hAPP(fun(X_b,X_c),fun(X_c,fun(filter(X_b),bool)),tendsto(X_b,X_c),G),L),hAPP(X_b,filter(X_b),at(X_b),hAPP(X_a,X_b,F,A_2)))) -> ((exists D_3 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),D_3)) & (all X_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),X_2),A_2)),D_3)) & ti(X_a,X_2) != ti(X_a,A_2) -> hAPP(X_a,X_b,F,X_2) != hAPP(X_a,X_b,F,A_2))))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_c,fun(filter(X_a),bool),hAPP(fun(X_a,X_c),fun(X_c,fun(filter(X_a),bool)),tendsto(X_a,X_c),hAPP(fun(X_a,X_b),fun(X_a,X_c),hAPP(fun(X_b,X_c),fun(fun(X_a,X_b),fun(X_a,X_c)),combb(X_b,X_c,X_a),G),F)),L),hAPP(X_a,filter(X_a),at(X_a),A_2))))))))) # label(fact_4923_metric__isCont__LIM__compose2) # label(axiom) # label(non_clause).  [assumption].
7.67/7.67	3932 (all K all N_1 all Ma (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),K),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),N_1),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K),Ma)))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),K),N_1)))) # label(fact_207_zdvd__reduce) # label(axiom) # label(non_clause).  [assumption].
7.67/7.67	3933 (all I all K (hAPP(int,int,hAPP(int,fun(int,int),div_div(int),I),K) = zero_zero(int) <-> zero_zero(int) = ti(int,K) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),I)) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),I),zero_zero(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),I),K)) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),I)))) # label(fact_1026_zdiv__eq__0__iff) # label(axiom) # label(non_clause).  [assumption].
7.67/7.67	3934 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),one_one(real))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,ln,hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),one_one(real)),X))),hAPP(real,real,uminus_uminus(real),X)))))) # label(fact_2119_ln__one__minus__pos__upper__bound) # label(axiom) # label(non_clause).  [assumption].
7.67/7.67	3935 (all W hAPP(int,nat,number_number_of(nat),W) = hAPP(int,nat,nat_1,hAPP(int,int,number_number_of(int),W))) # label(fact_1113_nat__number__of) # label(axiom) # label(non_clause).  [assumption].
7.67/7.67	3936 (all X all Y hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X),hAPP(real,real,sqrt,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),X),X)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),Y),Y)))))) # label(fact_1634_le__real__sqrt__sumsq) # label(axiom) # label(non_clause).  [assumption].
7.67/7.67	3937 (all X_a all X_b all P_1 ((all X1 hBOOL(hAPP(product_prod(X_a,X_b),bool,P_1,X1))) <-> (all A_4 all B_4 hBOOL(hAPP(product_prod(X_a,X_b),bool,P_1,hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),A_4),B_4)))))) # label(fact_3135_split__paired__All) # label(axiom) # label(non_clause).  [assumption].
7.67/7.67	3938 (all M hAPP(nat,product_prod(nat,nat),hAPP(nat,fun(nat,product_prod(nat,nat)),product_Pair(nat,nat),zero_zero(nat)),M) = hAPP(nat,product_prod(nat,nat),hAPP(nat,fun(nat,product_prod(nat,nat)),divmod_nat,M),zero_zero(nat))) # label(fact_3092_divmod__nat__zero) # label(axiom) # label(non_clause).  [assumption].
7.67/7.67	3939 (all X all Y (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),Y)) & -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y),X)) -> -(-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),Y)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y),X))))) # label(fact_641_dvd_Oless__imp__not__less) # label(axiom) # label(non_clause).  [assumption].
7.67/7.67	3940 (all Y all X (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X)) -> hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),div_div(int),X),Y)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(int,nat,nat_1,X)),hAPP(int,nat,nat_1,Y)))) # label(fact_1094_nat__div__distrib) # label(axiom) # label(non_clause).  [assumption].
7.67/7.67	3941 (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].
7.67/7.67	3942 (all X all Y (hBOOL(hAPP(int,bool,even_odd_even(int),Y)) -> hBOOL(hAPP(int,bool,even_odd_even(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X),Y))))) # label(fact_1259_anything__times__even) # label(axiom) # label(non_clause).  [assumption].
7.67/7.67	3943 (all X_a (linordered_idom(X_a) -> (all A_1 all N hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),N))))))) # label(fact_251_zero__le__even__power_H) # label(axiom) # label(non_clause).  [assumption].
7.67/7.67	3944 (all X_a power_1(X_a) = ti(fun(X_a,fun(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(nat,X_a)))),power_1(X_a))) # label(tsy_c_Power_Opower_Opower_res) # label(axiom) # label(non_clause).  [assumption].
7.67/7.67	3945 (all X_a (semiring_1(X_a) -> ti(fun(fun(X_a,X_a),fun(nat,fun(X_a,X_a))),semiri532925092at_aux(X_a)) = semiri532925092at_aux(X_a))) # label(tsy_c_Nat_Osemiring__1__class_Oof__nat__aux_res) # label(axiom) # label(non_clause).  [assumption].
7.67/7.67	3946 (all X_b all X_a (topological_space(X_a) & real_normed_vector(X_b) -> (all X_1 all G all L all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(real,fun(filter(X_a),bool),hAPP(fun(X_a,real),fun(real,fun(filter(X_a),bool)),tendsto(X_a,real),G),L),hAPP(X_a,filter(X_a),at(X_a),A_2))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(X_b,fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(X_b,fun(X_a,X_b)),combc(X_a,X_b,X_b),hAPP(fun(X_a,real),fun(X_a,fun(X_b,X_b)),hAPP(fun(real,fun(X_b,X_b)),fun(fun(X_a,real),fun(X_a,fun(X_b,X_b))),combb(real,fun(X_b,X_b),X_a),scaleR_scaleR(X_b)),G)),X_1)),hAPP(X_b,X_b,hAPP(real,fun(X_b,X_b),scaleR_scaleR(X_b),L),X_1)),hAPP(X_a,filter(X_a),at(X_a),A_2))))))) # label(fact_4737_scaleR__left_OLIM) # label(axiom) # label(non_clause).  [assumption].
7.67/7.67	3947 (all N (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),N)) -> zero_zero(int) != hAPP(int,int,fact_fact(int),N))) # label(fact_3191_fact__nonzero__int) # label(axiom) # label(non_clause).  [assumption].
7.67/7.67	3948 (all X all Y (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),Y)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Y),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),X),Y))),X)))) # label(fact_1045_zdiv__leq__prop) # label(axiom) # label(non_clause).  [assumption].
7.67/7.67	3949 (all X_a (metric_space(X_a) -> (all X_1 all Y_1 (zero_zero(real) = hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),X_1),Y_1) <-> ti(X_a,X_1) = ti(X_a,Y_1))))) # label(fact_3517_dist__eq__0__iff) # label(axiom) # label(non_clause).  [assumption].
7.67/7.67	3950 (all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,number_number_of(real),min_1)),Y)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),Y),one_one(real))) -> (exists X_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X_2)) & hAPP(real,real,cos,X_2) = Y & (all Y_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),Y_2)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),Y_2),pi)) & Y = hAPP(real,real,cos,Y_2) -> X_2 = Y_2)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_2),pi))))))) # label(fact_2248_cos__total) # label(axiom) # label(non_clause).  [assumption].
7.67/7.67	3951 (all X_1 all Y_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,uminus_uminus(real),X_1)),Y_1)) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X_1),Y_1))))) # label(fact_2106_real__0__le__add__iff) # label(axiom) # label(non_clause).  [assumption].
7.67/7.67	3952 (all X_a (field_inverse_zero(X_a) -> (all A_1 all N hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),one_one(X_a)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N)) = hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),one_one(X_a)),A_1)),N)))) # label(fact_1698_power__one__over) # label(axiom) # label(non_clause).  [assumption].
7.67/7.67	3953 (all Ma all N_1 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),Ma),N_1)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),Ma),hAPP(nat,nat,suc,N_1))) # label(fact_4123_diff__Suc) # label(axiom) # label(non_clause).  [assumption].
7.67/7.67	3954 (all X_a (number_ring(X_a) -> (all V all W all Z_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),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_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,hAPP(int,fun(int,int),times_times(int),V),W))),Z_1)))) # label(fact_42_mult__number__of__left) # label(axiom) # label(non_clause).  [assumption].
7.67/7.67	3955 (all X_a (monoid_mult(X_a) -> (all A_1 all N hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),N))) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))) # label(fact_1456_power__odd__eq) # label(axiom) # label(non_clause).  [assumption].
7.67/7.67	3956 (all U_1 all Ma all N_1 all I all J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I),J)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I),U_1)),Ma)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J),U_1)),N_1))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J),I)),U_1)),N_1)))))) # label(fact_739_nat__less__add__iff2) # label(axiom) # label(non_clause).  [assumption].
7.67/7.67	3957 (all X_a all F all A_3 hAPP(fun(X_a,bool),int,hAPP(fun(X_a,int),fun(fun(X_a,bool),int),big_co1399186613setsum(X_a,int),hAPP(fun(X_a,nat),fun(X_a,int),hAPP(fun(nat,int),fun(fun(X_a,nat),fun(X_a,int)),combb(nat,int,X_a),semiring_1_of_nat(int)),F)),A_3) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(fun(X_a,bool),nat,hAPP(fun(X_a,nat),fun(fun(X_a,bool),nat),big_co1399186613setsum(X_a,nat),F),A_3))) # label(fact_4245_int__setsum) # label(axiom) # label(non_clause).  [assumption].
7.67/7.67	3958 (all I_1 all J_2 hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,hAPP(int,int,uminus_uminus(int),I_1)),J_2) = hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,I_1),J_2)) # label(fact_3442_zgcd__zminus) # label(axiom) # label(non_clause).  [assumption].
7.67/7.67	3959 (all X all A_1 all B (one_one(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),A_1),B) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),A_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),B)) -> one_one(nat) = X)))) # label(fact_3264_coprime__common__divisor__nat) # label(axiom) # label(non_clause).  [assumption].
7.67/7.67	3960 (all X_a (linordered_idom(X_a) -> (all A_1 all N hAPP(X_a,X_a,abs_abs(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),A_1)),N)) = hAPP(X_a,X_a,abs_abs(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N))))) # label(fact_2084_abs__power__minus) # label(axiom) # label(non_clause).  [assumption].
7.67/7.67	3961 (all A_3 all Ma (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),Ma)) -> (hBOOL(hAPP(int,bool,hAPP(fun(int,bool),fun(int,bool),is_RRset,A_3),Ma)) -> hAPP(int,fun(int,bool),norRRset,Ma) = hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,int),fun(fun(int,bool),fun(int,bool)),image(int,int),hAPP(int,fun(int,int),hAPP(fun(int,bool),fun(int,fun(int,int)),rRset2norRR,A_3),Ma)),A_3)))) # label(fact_3630_RRset2norRR__eq__norR) # label(axiom) # label(non_clause).  [assumption].
7.67/7.67	3962 (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)) = 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)))) & (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)))) # label(fact_3890_nat__number__of__Bit1) # label(axiom) # label(non_clause).  [assumption].
7.67/7.67	3963 (all X_a (linord1117847801e_zero(X_a) -> (all X all Y ((all Z_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),Z_2)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z_2),one_one(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Z_2),X)),Y))))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y)))))) # label(fact_1523_field__le__mult__one__interval) # label(axiom) # label(non_clause).  [assumption].
7.67/7.67	3964 (all X_a (archim1727834104eiling(X_a) -> (all X hAPP(X_a,int,archimedean_ceiling(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X),one_one(X_a))) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(X_a,int,archimedean_ceiling(X_a),X)),one_one(int))))) # label(fact_3305_ceiling__add__one) # label(axiom) # label(non_clause).  [assumption].
7.67/7.67	3965 (all A_2 hBOOL(hAPP(filter(complex),bool,hAPP(complex,fun(filter(complex),bool),hAPP(fun(complex,complex),fun(complex,fun(filter(complex),bool)),tendsto(complex,complex),cnj),hAPP(complex,complex,cnj,A_2)),hAPP(complex,filter(complex),at(complex),A_2)))) # label(fact_4570_cnj_Ocont) # label(axiom) # label(non_clause).  [assumption].
7.67/7.67	3966 (all X all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> X = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,hAPP(nat,fun(real,real),root,N),X)),N)))) # label(fact_2711_real__root__pow__pos) # label(axiom) # label(non_clause).  [assumption].
7.67/7.67	3967 (all X_a (linordered_semidom(X_a) -> (all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(nat,X_a,semiring_1_of_nat(X_a),N_1))))))) # label(fact_1397_of__nat__0__less__iff) # label(axiom) # label(non_clause).  [assumption].
7.67/7.67	3968 (all X_a all X_b all X_c ti(fun(fun(X_a,fun(X_b,X_c)),fun(X_b,fun(X_a,X_c))),combc(X_a,X_b,X_c)) = combc(X_a,X_b,X_c)) # label(tsy_c_COMBC_res) # label(axiom) # label(non_clause).  [assumption].
7.67/7.67	3969 (all X_a (comple1803745165norder(X_a) -> (all A_2 all S (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),hAPP(fun(X_a,bool),X_a,complete_Sup_Sup(X_a),S))) <-> (exists X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),S)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),X_2)))))))) # label(fact_1767_less__Sup__iff) # label(axiom) # label(non_clause).  [assumption].
7.67/7.67	3970 (all X_a (ring(X_a) -> (all A_1 all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),A_1)),hAPP(X_a,X_a,uminus_uminus(X_a),B))))) # label(fact_2033_minus__mult__minus) # label(axiom) # label(non_clause).  [assumption].
7.67/7.67	3971 (all M all N (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N)) = M)) # label(fact_685_add__diff__inverse) # label(axiom) # label(non_clause).  [assumption].
7.67/7.67	3972 (all N hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),one_one(nat)),hAPP(nat,nat,fact,N)))) # label(fact_3547_fact__le) # label(axiom) # label(non_clause).  [assumption].
7.67/7.67	3973 (all X_1 all Y_1 (Y_1 = hAPP(real,real,uminus_uminus(real),X_1) <-> hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X_1),Y_1) = zero_zero(real))) # label(fact_2089_real__add__eq__0__iff) # label(axiom) # label(non_clause).  [assumption].
7.67/7.67	3974 (all P_2 all P_1 all X_1 ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X_1)) -> (hBOOL(P_1) <-> hBOOL(P_2))) -> ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X_1)) -> hBOOL(P_1)) <-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X_1)) -> hBOOL(P_2))))) # label(fact_546_imp__le__cong) # label(axiom) # label(non_clause).  [assumption].
7.67/7.67	3975 (all D_2 all X_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)) -> (X_1 != zero_zero(real) -> ((hBOOL(hAPP(nat,bool,even_odd_even(nat),N_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X_1)) -> hAPP(real,real,inverse_inverse(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,real_1(nat),N_1)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,hAPP(nat,fun(real,real),root,N_1),X_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),hAPP(nat,nat,suc,zero_zero(nat)))))) = D_2)) -> ((hBOOL(hAPP(nat,bool,even_odd_even(nat),N_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_1),zero_zero(real))) -> D_2 = hAPP(real,real,uminus_uminus(real),hAPP(real,real,inverse_inverse(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,real_1(nat),N_1)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,hAPP(nat,fun(real,real),root,N_1),X_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),hAPP(nat,nat,suc,zero_zero(nat))))))))) -> ((-hBOOL(hAPP(nat,bool,even_odd_even(nat),N_1)) -> D_2 = hAPP(real,real,inverse_inverse(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,real_1(nat),N_1)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,hAPP(nat,fun(real,real),root,N_1),X_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),hAPP(nat,nat,suc,zero_zero(nat))))))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(nat,fun(real,real),root,N_1)),X_1),D_2)))))))) # label(fact_2669_DERIV__real__root__generic) # label(axiom) # label(non_clause).  [assumption].
7.67/7.67	3976 (all X all Y hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),hAPP(real,complex,of_real(complex),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),X),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),Y),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),ii),hAPP(real,complex,of_real(complex),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),Y),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),Y),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))))) = hAPP(complex,complex,inverse_inverse(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(real,complex,of_real(complex),X)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),ii),hAPP(real,complex,of_real(complex),Y))))) # label(fact_2771_complex__inverse__complex__split) # label(axiom) # label(non_clause).  [assumption].
7.67/7.67	3977 (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_401_not__one__le__zero) # label(axiom) # label(non_clause).  [assumption].
7.67/7.67	3978 (all R_4 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),R_4)) -> (exists N_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),R_4),hAPP(nat,real,real_1(nat),N_2))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,real_1(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_2),one_one(nat)))),R_4)))))) # label(fact_2406_reals__Archimedean6) # label(axiom) # label(non_clause).  [assumption].
7.67/7.67	3979 (all X_a (real_normed_vector(X_a) -> (all R_1 all X_3 (hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),X_3)) -> hAPP(fun(nat,X_a),X_a,suminf(X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(X_a,X_a),fun(fun(nat,X_a),fun(nat,X_a)),combb(X_a,X_a,nat),hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),R_1)),X_3)) = hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),R_1),hAPP(fun(nat,X_a),X_a,suminf(X_a),X_3)))))) # label(fact_4669_scaleR__right_Osuminf) # label(axiom) # label(non_clause).  [assumption].
7.67/7.67	3980 (all B all A_1 all M (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),M)) -> (one_one(int) = hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,A_1),M) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_1),B),M)) -> hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,B),M) = one_one(int))))) # label(fact_3468_zgcd__zcong__zgcd) # label(axiom) # label(non_clause).  [assumption].
7.67/7.67	3981 (all X_a (archim1727834104eiling(X_a) -> (all X all V hAPP(X_a,int,archim2085082626_floor(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),X),hAPP(int,X_a,number_number_of(X_a),V))) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(X_a,int,archim2085082626_floor(X_a),X)),hAPP(int,int,number_number_of(int),V))))) # label(fact_2890_floor__diff__number__of) # label(axiom) # label(non_clause).  [assumption].
7.67/7.67	3982 (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_408_less__add__one) # label(axiom) # label(non_clause).  [assumption].
7.67/7.67	3983 (all A_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),one_one(nat))) -> one_one(nat) = A_1)) # label(fact_897_gcd__lcm__complete__lattice__nat_Ole__bot) # label(axiom) # label(non_clause).  [assumption].
7.67/7.67	3984 (all X_1 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(nat,fun(real,real),hAPP(fun(real,fun(nat,real)),fun(nat,fun(real,real)),combc(real,nat,real),hAPP(fun(real,real),fun(real,fun(nat,real)),hAPP(fun(real,fun(nat,real)),fun(fun(real,real),fun(real,fun(nat,real))),combb(real,fun(nat,real),real),power_power(real)),sin)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),X_1),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),hAPP(real,real,cos,X_1))),hAPP(real,real,sin,X_1))))) # label(fact_3909_DERIV__sin__realpow2a) # label(axiom) # label(non_clause).  [assumption].
7.67/7.67	3985 (all X_1 all N_1 (-hBOOL(hAPP(nat,bool,even_odd_even(nat),N_1)) -> (zero_zero(real) != X_1 -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(nat,fun(real,real),root,N_1)),X_1),hAPP(real,real,inverse_inverse(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,real_1(nat),N_1)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,hAPP(nat,fun(real,real),root,N_1),X_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),hAPP(nat,nat,suc,zero_zero(nat))))))))))) # label(fact_2716_DERIV__odd__real__root) # label(axiom) # label(non_clause).  [assumption].
7.67/7.67	3986 (all X hAPP(int,int,abs_abs(int),X) = hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),zero_zero(int)),X)) # label(fact_4387_gcd__0__left__int) # label(axiom) # label(non_clause).  [assumption].
7.67/7.67	3987 (all Ma all N_1 ((exists K_1 hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Ma),K_1)) = N_1) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),N_1)))) # label(fact_1327_less__iff__Suc__add) # label(axiom) # label(non_clause).  [assumption].
7.67/7.67	3988 (all X_b all X_a (real_normed_algebra(X_b) & topological_space(X_a) -> (all Y_1 all G all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),G),zero_zero(X_b)),hAPP(X_a,filter(X_a),at(X_a),A_2))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(X_b,fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(X_b,fun(X_a,X_b)),combc(X_a,X_b,X_b),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,fun(X_b,X_b))),combb(X_b,fun(X_b,X_b),X_a),times_times(X_b)),G)),Y_1)),zero_zero(X_b)),hAPP(X_a,filter(X_a),at(X_a),A_2))))))) # label(fact_4576_mult__left_OLIM__zero) # label(axiom) # label(non_clause).  [assumption].
7.67/7.67	3989 (all X_a (sgn_if(X_a) -> sgn_sgn(X_a) = ti(fun(X_a,X_a),sgn_sgn(X_a)))) # label(tsy_c_Groups_Osgn__class_Osgn_1_res) # label(axiom) # label(non_clause).  [assumption].
7.67/7.67	3990 (all X hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))) # label(fact_188_power2__ge__self) # label(axiom) # label(non_clause).  [assumption].
7.67/7.67	3991 (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_3649_transfer__nat__int__set__relations_I2_J) # label(axiom) # label(non_clause).  [assumption].
7.67/7.67	3992 (all M hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,one_one(int)),M) = one_one(int)) # label(fact_3434_zgcd__1__left) # label(axiom) # label(non_clause).  [assumption].
7.67/7.67	3993 (all X_a (linordered_idom(X_a) -> (all Ma all K (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),Ma),K)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),Ma),hAPP(X_a,X_a,abs_abs(X_a),K))))))) # label(fact_1845_dvd__abs__iff) # label(axiom) # label(non_clause).  [assumption].
7.67/7.67	3994 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),M),N)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N)) | zero_zero(nat) = N)) # label(fact_872_divides__le) # label(axiom) # label(non_clause).  [assumption].
7.67/7.67	3995 (all X_a (preorder(X_a) -> (all X_1 all Y_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y_1)) <-> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y_1),X_1)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),Y_1)))))) # label(fact_1586_less__le__not__le) # label(axiom) # label(non_clause).  [assumption].
7.67/7.67	3996 (all X_b all X_a (metric_space(X_a) & real_normed_vector(X_b) -> (all L all F all G all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(fun(X_a,X_b),fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,X_b)),combs(X_a,X_b,X_b),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,fun(X_b,X_b))),combb(X_b,fun(X_b,X_b),X_a),plus_plus(X_b)),F)),hAPP(fun(X_a,X_b),fun(X_a,X_b),hAPP(fun(X_b,X_b),fun(fun(X_a,X_b),fun(X_a,X_b)),combb(X_b,X_b,X_a),uminus_uminus(X_b)),G))),zero_zero(X_b)),hAPP(X_a,filter(X_a),at(X_a),A_2))) -> (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),G),L),hAPP(X_a,filter(X_a),at(X_a),A_2))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),L),hAPP(X_a,filter(X_a),at(X_a),A_2)))))))) # label(fact_4600_LIM__trans) # label(axiom) # label(non_clause).  [assumption].
7.67/7.67	3997 (all X_b all X_a (real_normed_vector(X_b) & topological_space(X_a) -> (all G all Ma all F all L all X_1 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),L),hAPP(X_a,filter(X_a),at(X_a),X_1))) -> (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),G),Ma),hAPP(X_a,filter(X_a),at(X_a),X_1))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(fun(X_a,X_b),fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,X_b)),combs(X_a,X_b,X_b),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,fun(X_b,X_b))),combb(X_b,fun(X_b,X_b),X_a),minus_minus(X_b)),F)),G)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),L),Ma)),hAPP(X_a,filter(X_a),at(X_a),X_1)))))))) # label(fact_4566_LIM__diff) # label(axiom) # label(non_clause).  [assumption].
7.67/7.67	3998 (all X_a (semiring_div(X_a) -> (all A_1 all B all C hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),B),C))),C) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)),C)))) # label(fact_930_mod__mult__eq) # label(axiom) # label(non_clause).  [assumption].
7.67/7.67	3999 (all Z (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),Z)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),Z)))) # label(fact_80_int__one__le__iff__zero__less) # label(axiom) # label(non_clause).  [assumption].
7.67/7.67	4000 (all A_1 all P_5 (hBOOL(hAPP(int,bool,zprime,P_5)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),P_5)) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_1),zero_zero(int)),P_5)) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),quadRes,P_5),A_1)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(int,int,zfact,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),P_5),one_one(int)))),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A_1),hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),P_5),one_one(int))),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))),P_5))))))) # label(fact_1075_zfact__prop) # label(axiom) # label(non_clause).  [assumption].
7.67/7.67	4001 (all A_1 all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),one_one(real)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A_1)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),one_one(real)),hAPP(real,real,hAPP(real,fun(real,real),powr,X),A_1)))))) # label(fact_3377_ge__one__powr__ge__zero) # label(axiom) # label(non_clause).  [assumption].
7.67/7.67	4002 (all Z_1 hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,hAPP(complex,real,re,Z_1)),hAPP(real,real,uminus_uminus(real),hAPP(complex,real,im,Z_1))) = hAPP(complex,complex,cnj,Z_1)) # label(fact_3012_cnj__def) # label(axiom) # label(non_clause).  [assumption].
7.67/7.67	4003 (all X_a (order(X_a) -> (all X_1 all Y_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y_1)) <-> ti(X_a,Y_1) != ti(X_a,X_1) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),Y_1)))))) # label(fact_1585_order__less__le) # label(axiom) # label(non_clause).  [assumption].
7.67/7.67	4004 (all X_3 (hBOOL(hAPP(fun(nat,complex),bool,summable(complex),X_3)) -> hAPP(fun(nat,complex),complex,suminf(complex),hAPP(fun(nat,complex),fun(nat,complex),hAPP(fun(complex,complex),fun(fun(nat,complex),fun(nat,complex)),combb(complex,complex,nat),cnj),X_3)) = hAPP(complex,complex,cnj,hAPP(fun(nat,complex),complex,suminf(complex),X_3)))) # label(fact_4041_cnj_Osuminf) # label(axiom) # label(non_clause).  [assumption].
7.67/7.67	4005 (all X_a (real_normed_algebra(X_a) -> (all Y_1 all X_3 all A_2 (hBOOL(hAPP(X_a,bool,hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),X_3),A_2)) -> hBOOL(hAPP(X_a,bool,hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),hAPP(X_a,fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(X_a,fun(nat,X_a)),combc(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),times_times(X_a)),X_3)),Y_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),Y_1))))))) # label(fact_4082_mult__left_Osums) # label(axiom) # label(non_clause).  [assumption].
7.67/7.67	4006 (all X hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),one_one(nat)),X) = one_one(nat)) # label(fact_3250_gcd__lcm__complete__lattice__nat_Oinf__bot__left) # label(axiom) # label(non_clause).  [assumption].
7.67/7.67	4007 (all K1 all K2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),K1),K2)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit0,K1)),hAPP(int,int,bit1,K2))))) # label(fact_52_less__eq__int__code_I14_J) # label(axiom) # label(non_clause).  [assumption].
7.67/7.67	4008 (all X_a (real_normed_field(X_a) -> (all Y_3 all X_3 (hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),X_3)) -> (hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),Y_3)) -> hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),minus_minus(X_a)),X_3)),Y_3)))))))) # label(fact_4012_summable__diff) # label(axiom) # label(non_clause).  [assumption].
7.67/7.67	4009 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,abs_abs(real),X)),one_one(real))) -> (exists Z_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),Z_2),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))) & hAPP(real,real,tan,Z_2) = X & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))),Z_2)))))) # label(fact_2281_tan__total__pi4) # label(axiom) # label(non_clause).  [assumption].
7.67/7.67	4010 (all X_3 all A_2 (hBOOL(hAPP(complex,bool,hAPP(fun(nat,complex),fun(complex,bool),sums(complex),X_3),A_2)) -> hBOOL(hAPP(complex,bool,hAPP(fun(nat,complex),fun(complex,bool),sums(complex),hAPP(fun(nat,complex),fun(nat,complex),hAPP(fun(complex,complex),fun(fun(nat,complex),fun(nat,complex)),combb(complex,complex,nat),cnj),X_3)),hAPP(complex,complex,cnj,A_2))))) # label(fact_4109_cnj_Osums) # label(axiom) # label(non_clause).  [assumption].
7.67/7.67	4011 (all N all K_4 all M (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),K_4),M)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),K_4),N)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),K_4),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N)))))) # label(fact_635_dvd__diff__nat) # label(axiom) # label(non_clause).  [assumption].
7.67/7.67	4012 (all Z_1 all W hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Z_1),hAPP(int,int,uminus_uminus(int),W)) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),Z_1),W)) # label(fact_2162_diff__int__def__symmetric) # label(axiom) # label(non_clause).  [assumption].
7.67/7.67	4013 (all X_a (linordered_semidom(X_a) -> (all N all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),A_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N))))))) # label(fact_405_zero__le__power) # label(axiom) # label(non_clause).  [assumption].
7.67/7.67	4014 (all X_a (linordered_idom(X_a) -> (all A_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_2)) <-> hAPP(X_a,X_a,sgn_sgn(X_a),A_2) = one_one(X_a))))) # label(fact_2222_sgn__1__pos) # label(axiom) # label(non_clause).  [assumption].
7.67/7.67	4015 (all X_1 ((exists A_4 exists B_4 ti(int,X_1) = hAPP(product_prod(int,int),int,twoSqu1094008024sum2sq,hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),A_4),B_4))) <-> hBOOL(hAPP(int,bool,twoSqu1091635170sum2sq,X_1)))) # label(fact_755_is__sum2sq__def) # label(axiom) # label(non_clause).  [assumption].
7.67/7.67	4016 (all X_a all X_b (order(X_a) & order(X_b) -> (all F all C_1 all A_2 all B_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),B_1)) -> (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_a,X_b,F,B_1)),C_1)) -> ((all X_2 all Y_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_2),Y_2)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_a,X_b,F,X_2)),hAPP(X_a,X_b,F,Y_2))))) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_a,X_b,F,A_2)),C_1)))))))) # label(fact_2833_order__le__less__subst2) # label(axiom) # label(non_clause).  [assumption].
7.67/7.67	4017 (all X_a (real_normed_vector(X_a) -> (all X hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(X_a,real,norm_norm(X_a),X)))))) # label(fact_1779_norm__ge__zero) # label(axiom) # label(non_clause).  [assumption].
7.67/7.67	4018 (all K all F (hBOOL(hAPP(fun(nat,real),bool,summable(real),F)) -> ((all D_3 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,F,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat)))),D_3)))),hAPP(nat,real,F,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat)))),D_3)),one_one(nat)))))))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),K))),hAPP(fun(nat,real),real,suminf(real),F)))))) # label(fact_4271_sumr__pos__lt__pair) # label(axiom) # label(non_clause).  [assumption].
7.67/7.67	4019 (all P_4 hAPP(rat,product_prod(int,int),quotient_of,hAPP(rat,rat,uminus_uminus(rat),P_4)) = hAPP(product_prod(int,int),product_prod(int,int),hAPP(fun(int,fun(int,product_prod(int,int))),fun(product_prod(int,int),product_prod(int,int)),product_prod_case(int,int,product_prod(int,int)),hAPP(fun(int,int),fun(int,fun(int,product_prod(int,int))),hAPP(fun(int,fun(int,product_prod(int,int))),fun(fun(int,int),fun(int,fun(int,product_prod(int,int)))),combb(int,fun(int,product_prod(int,int)),int),product_Pair(int,int)),uminus_uminus(int))),hAPP(rat,product_prod(int,int),quotient_of,P_4))) # label(fact_4028_rat__uminus__code) # label(axiom) # label(non_clause).  [assumption].
7.67/7.67	4020 (all X_a (archim1727834104eiling(X_a) -> (all X all Y (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(X_a,int,archimedean_ceiling(X_a),X)),hAPP(X_a,int,archimedean_ceiling(X_a),Y))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)))))) # label(fact_3280_ceiling__less__cancel) # label(axiom) # label(non_clause).  [assumption].
7.67/7.67	4021 (all B all A_1 all P_5 (hBOOL(hAPP(int,bool,zprime,P_5)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),B)),zero_zero(int)),P_5)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_1),zero_zero(int)),P_5)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,B),zero_zero(int)),P_5)))))) # label(fact_281_zcong__zprime__prod__zero) # label(axiom) # label(non_clause).  [assumption].
7.67/7.67	4022 (all X all A_1 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),powr,X),A_1)))) # label(fact_3347_powr__gt__zero) # label(axiom) # label(non_clause).  [assumption].
7.67/7.67	4023 (all X_1 all Y_1 (hBOOL(hAPP(product_prod(nat,nat),bool,hAPP(fun(product_prod(nat,nat),fun(product_prod(nat,nat),bool)),fun(product_prod(nat,nat),bool),accp(product_prod(nat,nat)),nat_gcd_rel),hAPP(nat,product_prod(nat,nat),hAPP(nat,fun(nat,product_prod(nat,nat)),product_Pair(nat,nat),X_1),Y_1))) -> (Y_1 = zero_zero(nat) -> X_1 = hAPP(nat,nat,hAPP(nat,fun(nat,nat),nat_gcd,X_1),Y_1)) & (Y_1 != zero_zero(nat) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),nat_gcd,Y_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),X_1),Y_1)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),nat_gcd,X_1),Y_1)))) # label(fact_3670_nat__gcd_Opsimps) # label(axiom) # label(non_clause).  [assumption].
7.67/7.67	4024 (all X_1 all Y_1 (Y_1 = X_1 <-> hAPP(real,real,exp(real),X_1) = hAPP(real,real,exp(real),Y_1))) # label(fact_2524_exp__inj__iff) # label(axiom) # label(non_clause).  [assumption].
7.67/7.68	4025 (all X_a (semiring_div(X_a) -> (all D_1 all B_1 all C_1 all A_2 (zero_zero(X_a) != ti(X_a,A_2) -> (ti(X_a,C_1) != zero_zero(X_a) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_2),B_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),C_1),D_1)) -> (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),D_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B_1),C_1) <-> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),B_1),A_2) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),D_1),C_1))))))))) # label(fact_1043_dvd__div__div__eq__mult) # label(axiom) # label(non_clause).  [assumption].
7.67/7.68	4026 (all X_a (real_normed_algebra(X_a) -> (all Xa_1 all X hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Xa_1),X)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Xa_1),hAPP(X_a,X_a,uminus_uminus(X_a),X))))) # label(fact_2037_mult__right_Ominus) # label(axiom) # label(non_clause).  [assumption].
7.67/7.68	4027 (all X all Y all M hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),Y),M))),M) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X),Y)),M)) # label(fact_957_zdiff__zmod__right) # label(axiom) # label(non_clause).  [assumption].
7.67/7.68	4028 (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_1849_abs__of__nat) # label(axiom) # label(non_clause).  [assumption].
7.67/7.68	4029 (all X_a (real_algebra_1(X_a) -> (all X all Y hAPP(real,X_a,of_real(X_a),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),X),Y)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(real,X_a,of_real(X_a),X)),hAPP(real,X_a,of_real(X_a),Y))))) # label(fact_2793_of__real__diff) # label(axiom) # label(non_clause).  [assumption].
7.67/7.68	4030 (all A_1 hAPP(complex,real,norm_norm(complex),hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,hAPP(real,real,cos,A_1)),hAPP(real,real,sin,A_1))) = one_one(real)) # label(fact_2749_cmod__unit__one) # label(axiom) # label(non_clause).  [assumption].
7.67/7.68	4031 (all X all Y all C (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),C),zero_zero(real))) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),X)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),hAPP(real,real,abs_abs(real),Y)))) -> zero_zero(real) = X))) # label(fact_1891_rabs__ratiotest__lemma) # label(axiom) # label(non_clause).  [assumption].
7.67/7.68	4032 (all X all A_1 hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(real,int,archimedean_ceiling(real),X)),A_1) = hAPP(real,int,archimedean_ceiling(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),hAPP(int,real,real_1(int),A_1)))) # label(fact_3372_ceiling__add) # label(axiom) # label(non_clause).  [assumption].
7.67/7.68	4033 (all X all Y (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),Y)) & -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y),X)) -> X != Y)) # label(fact_643_dvd_Oless__imp__not__eq2) # label(axiom) # label(non_clause).  [assumption].
7.67/7.68	4034 (all X (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,fact_fact(int),X))))) # label(fact_3190_transfer__nat__int__factorial__closure) # label(axiom) # label(non_clause).  [assumption].
7.67/7.68	4035 (all Y hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,arctan,Y)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))) # label(fact_1993_arctan__ubound) # label(axiom) # label(non_clause).  [assumption].
7.67/7.68	4036 (all X_b all X_a (topological_space(X_a) & real_normed_vector(X_b) -> (all F all L all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(X_b,fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(X_b,fun(X_a,X_b)),combc(X_a,X_b,X_b),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,fun(X_b,X_b))),combb(X_b,fun(X_b,X_b),X_a),minus_minus(X_b)),F)),L)),zero_zero(X_b)),hAPP(X_a,filter(X_a),at(X_a),A_2))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),L),hAPP(X_a,filter(X_a),at(X_a),A_2))))))) # label(fact_4582_LIM__zero__cancel) # label(axiom) # label(non_clause).  [assumption].
7.67/7.68	4037 (all N all P_5 (hBOOL(hAPP(nat,bool,prime,P_5)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,P_5),N)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),P_5),N)) | N = one_one(nat))) # label(fact_3071_prime__coprime) # label(axiom) # label(non_clause).  [assumption].
7.67/7.68	4038 (all L_4 pls != hAPP(int,int,bit1,L_4)) # label(fact_117_rel__simps_I39_J) # label(axiom) # label(non_clause).  [assumption].
7.67/7.68	4039 (all K_4 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),K_4)) -> -(all N_2 hAPP(nat,int,semiring_1_of_nat(int),N_2) != ti(int,K_4)))) # label(fact_1489_nonneg__int__cases) # label(axiom) # label(non_clause).  [assumption].
7.67/7.68	4040 (all F all K all A_2 all B_1 (A_2 != B_1 -> ((all X_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),F),X_2),K))) -> hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,F,B_1)),hAPP(real,real,F,A_2))),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),B_1),A_2)) = K))) # label(fact_2666_DERIV__const__ratio__const2) # label(axiom) # label(non_clause).  [assumption].
7.67/7.68	4041 (all L_4 all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),L_4),N)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),L_4),M))))) # label(fact_670_diff__le__mono2) # label(axiom) # label(non_clause).  [assumption].
7.67/7.68	4042 (all X_a (linordered_field(X_a) -> (all Y all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),X)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),Y)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),X),Y)))))))) # label(fact_1679_divide__pos__pos) # label(axiom) # label(non_clause).  [assumption].
7.67/7.68	4043 (all X_b all X_a (semiring_1(X_a) -> (all Y_1 all A_3 hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co1399186613setsum(X_b,X_a),hAPP(X_a,fun(X_b,X_a),combk(X_a,X_b),Y_1)),A_3) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3))),Y_1)))) # label(fact_4228_setsum__constant) # label(axiom) # label(non_clause).  [assumption].
7.67/7.68	4044 (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_1594_order__less__imp__le) # label(axiom) # label(non_clause).  [assumption].
7.67/7.68	4045 (all X_a all F all A_3 hAPP(fun(X_a,bool),nat,hAPP(fun(X_a,nat),fun(fun(X_a,bool),nat),big_co1399186613setsum(X_a,nat),F),A_3) = hAPP(int,nat,nat_1,hAPP(fun(X_a,bool),int,hAPP(fun(X_a,int),fun(fun(X_a,bool),int),big_co1399186613setsum(X_a,int),hAPP(fun(X_a,nat),fun(X_a,int),hAPP(fun(nat,int),fun(fun(X_a,nat),fun(X_a,int)),combb(nat,int,X_a),semiring_1_of_nat(int)),F)),A_3))) # label(fact_4246_transfer__nat__int__sum__prod2_I1_J) # label(axiom) # label(non_clause).  [assumption].
7.67/7.68	4046 (all X_a (monoid_mult(X_a) -> (all Z_1 all W hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),Z_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,W))) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),Z_1),hAPP(int,nat,number_number_of(nat),W))),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),Z_1),hAPP(int,nat,number_number_of(nat),W)))))) # label(fact_3871_power__number__of__even) # label(axiom) # label(non_clause).  [assumption].
7.67/7.68	4047 (all N_1 all N_4 ((all X_2 (hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X_2),N_4)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X_2),N_1)))) -> hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),N_4)))) # label(fact_3675_bounded__nat__set__is__finite) # label(axiom) # label(non_clause).  [assumption].
7.67/7.68	4048 (all X all Y hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),X),Y)),Y))) # label(fact_4347_gcd__dvd2__int) # label(axiom) # label(non_clause).  [assumption].
7.67/7.68	4049 (all Y_1 all X_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Y_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(int,nat,nat_1,X_1)),hAPP(int,nat,nat_1,Y_1))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X_1),Y_1)))))) # label(fact_1127_transfer__nat__int__relations_I3_J) # label(axiom) # label(non_clause).  [assumption].
7.67/7.68	4050 (all X_a (linordered_field(X_a) -> (all A_1 all B (ti(X_a,B) != zero_zero(X_a) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),hAPP(X_a,X_a,abs_abs(X_a),A_1)),hAPP(X_a,X_a,abs_abs(X_a),B)) = hAPP(X_a,X_a,abs_abs(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),A_1),B)))))) # label(fact_1871_nonzero__abs__divide) # label(axiom) # label(non_clause).  [assumption].
7.67/7.68	4051 (all G all F all X_1 all D_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),D_1)) -> ((all Z_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),Z_2),X_1))),D_1)) -> Z_2 = hAPP(real,real,G,hAPP(real,real,F,Z_2)))) -> ((all Z_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),Z_2),X_1))),D_1)) -> hBOOL(hAPP(real,bool,hAPP(fun(real,real),fun(real,bool),isCont(real,real),F),Z_2)))) -> hBOOL(hAPP(real,bool,hAPP(fun(real,real),fun(real,bool),isCont(real,real),G),hAPP(real,real,F,X_1))))))) # label(fact_4927_isCont__inv__fun) # label(axiom) # label(non_clause).  [assumption].
7.67/7.68	4052 (all X_a (linordered_semidom(X_a) -> (all Ma all N_1 all A_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),A_2)) -> (Ma = N_1 <-> hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_2),N_1) = hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_2),Ma)))))) # label(fact_413_power__inject__exp) # label(axiom) # label(non_clause).  [assumption].
7.67/7.68	4053 (all X_a all A_3 all B_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_3),B_2)) -> hBOOL(hAPP(fun(fun(X_a,bool),bool),bool,hAPP(fun(fun(X_a,bool),bool),fun(fun(fun(X_a,bool),bool),bool),ord_less_eq(fun(fun(X_a,bool),bool)),hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),pow(X_a),A_3)),hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),pow(X_a),B_2))))) # label(fact_2803_Pow__mono) # label(axiom) # label(non_clause).  [assumption].
7.67/7.68	4054 (all Y all X (-hBOOL(hAPP(int,bool,even_odd_even(int),X)) -> (-hBOOL(hAPP(int,bool,even_odd_even(int),Y)) -> -hBOOL(hAPP(int,bool,even_odd_even(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X),Y)))))) # label(fact_1260_Parity_Oodd__times__odd) # label(axiom) # label(non_clause).  [assumption].
7.67/7.68	4055 (all X_b all X_a (topological_space(X_a) & real_n2089651433ebra_1(X_b) -> (all F all A_2 (hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,real),fun(X_a,bool),isCont(X_a,real),F),A_2)) -> hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,X_b),fun(X_a,bool),isCont(X_a,X_b),hAPP(fun(X_a,real),fun(X_a,X_b),hAPP(fun(real,X_b),fun(fun(X_a,real),fun(X_a,X_b)),combb(real,X_b,X_a),of_real(X_b)),F)),A_2)))))) # label(fact_4904_isCont__of__real) # label(axiom) # label(non_clause).  [assumption].
7.67/7.68	4056 (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_51_rel__simps_I22_J) # label(axiom) # label(non_clause).  [assumption].
7.67/7.68	4057 (all X_1 hAPP(rat,product_prod(int,int),quotient_of,X_1) = hAPP(fun(product_prod(int,int),bool),product_prod(int,int),the(product_prod(int,int)),hAPP(fun(product_prod(int,int),bool),fun(product_prod(int,int),bool),hAPP(fun(product_prod(int,int),fun(bool,bool)),fun(fun(product_prod(int,int),bool),fun(product_prod(int,int),bool)),combs(product_prod(int,int),bool,bool),hAPP(fun(product_prod(int,int),bool),fun(product_prod(int,int),fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(product_prod(int,int),bool),fun(product_prod(int,int),fun(bool,bool))),combb(bool,fun(bool,bool),product_prod(int,int)),fconj),hAPP(fun(product_prod(int,int),rat),fun(product_prod(int,int),bool),hAPP(fun(rat,bool),fun(fun(product_prod(int,int),rat),fun(product_prod(int,int),bool)),combb(rat,bool,product_prod(int,int)),hAPP(rat,fun(rat,bool),fequal(rat),X_1)),hAPP(fun(product_prod(int,int),int),fun(product_prod(int,int),rat),hAPP(fun(product_prod(int,int),fun(int,rat)),fun(fun(product_prod(int,int),int),fun(product_prod(int,int),rat)),combs(product_prod(int,int),int,rat),hAPP(fun(product_prod(int,int),int),fun(product_prod(int,int),fun(int,rat)),hAPP(fun(int,fun(int,rat)),fun(fun(product_prod(int,int),int),fun(product_prod(int,int),fun(int,rat))),combb(int,fun(int,rat),product_prod(int,int)),fract),product_fst(int,int))),product_snd(int,int))))),hAPP(fun(product_prod(int,int),bool),fun(product_prod(int,int),bool),hAPP(fun(product_prod(int,int),fun(bool,bool)),fun(fun(product_prod(int,int),bool),fun(product_prod(int,int),bool)),combs(product_prod(int,int),bool,bool),hAPP(fun(product_prod(int,int),bool),fun(product_prod(int,int),fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(product_prod(int,int),bool),fun(product_prod(int,int),fun(bool,bool))),combb(bool,fun(bool,bool),product_prod(int,int)),fconj),hAPP(fun(product_prod(int,int),int),fun(product_prod(int,int),bool),hAPP(fun(int,bool),fun(fun(product_prod(int,int),int),fun(product_prod(int,int),bool)),combb(int,bool,product_prod(int,int)),hAPP(int,fun(int,bool),ord_less(int),zero_zero(int))),product_snd(int,int)))),hAPP(int,fun(product_prod(int,int),bool),hAPP(fun(product_prod(int,int),fun(int,bool)),fun(int,fun(product_prod(int,int),bool)),combc(product_prod(int,int),int,bool),hAPP(fun(product_prod(int,int),int),fun(product_prod(int,int),fun(int,bool)),hAPP(fun(int,fun(int,bool)),fun(fun(product_prod(int,int),int),fun(product_prod(int,int),fun(int,bool))),combb(int,fun(int,bool),product_prod(int,int)),fequal(int)),hAPP(fun(product_prod(int,int),int),fun(product_prod(int,int),int),hAPP(fun(product_prod(int,int),fun(int,int)),fun(fun(product_prod(int,int),int),fun(product_prod(int,int),int)),combs(product_prod(int,int),int,int),hAPP(fun(product_prod(int,int),int),fun(product_prod(int,int),fun(int,int)),hAPP(fun(int,fun(int,int)),fun(fun(product_prod(int,int),int),fun(product_prod(int,int),fun(int,int))),combb(int,fun(int,int),product_prod(int,int)),gcd_gcd(int)),product_fst(int,int))),product_snd(int,int)))),one_one(int)))))) # label(fact_4409_quotient__of__def) # label(axiom) # label(non_clause).  [assumption].
7.67/7.68	4058 (all X_a (linorder(X_a) -> (all X hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),X) = ti(X_a,X)))) # label(fact_4956_Max_Oidem) # label(axiom) # label(non_clause).  [assumption].
7.67/7.68	4059 (all U_1 all Ma all N_1 all J all I (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),J),I)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I),U_1)),Ma)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J),U_1)),N_1))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I),J)),U_1)),Ma)),N_1))))) # label(fact_754_nat__le__add__iff1) # label(axiom) # label(non_clause).  [assumption].
7.67/7.68	4060 (all P_4 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),P_4)) -> hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),hAPP(int,fun(int,bool),sRStar,P_4))))) # label(fact_1761_SRStar__finite) # label(axiom) # label(non_clause).  [assumption].
7.67/7.68	4061 (all A_1 all B hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),A_1),B)) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(nat,int,semiring_1_of_nat(int),A_1)),hAPP(nat,int,semiring_1_of_nat(int),B))) # label(fact_1358_zmod__int) # label(axiom) # label(non_clause).  [assumption].
7.67/7.68	4062 (all X_a (linorder(X_a) -> (all X all Y all Z_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),Y)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),Z_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),Y),Z_1))))) # label(fact_4939_min__max_Oinf__sup__distrib1) # label(axiom) # label(non_clause).  [assumption].
7.67/7.68	4063 (all X_a (archim1727834104eiling(X_a) -> (all X_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),zero_zero(X_a))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(X_a,int,archim2085082626_floor(X_a),X_1)),zero_zero(int))))))) # label(fact_2879_floor__less__zero) # label(axiom) # label(non_clause).  [assumption].
7.67/7.68	4064 (all X_a (order(X_a) -> (all N_1 all Ma all F ((all N_2 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,F,N_2)),hAPP(nat,X_a,F,hAPP(nat,nat,suc,N_2))))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,F,N_1)),hAPP(nat,X_a,F,Ma))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),Ma))))))) # label(fact_1497_lift__Suc__mono__less__iff) # label(axiom) # label(non_clause).  [assumption].
7.67/7.68	4065 (all A_1 all N all B hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),A_1),B)),N) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A_1),N)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),B),N))) # label(fact_3217_gcd__exp__nat) # label(axiom) # label(non_clause).  [assumption].
7.67/7.68	4066 (all N -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,N)),N))) # label(fact_1243_Suc__n__not__le__n) # label(axiom) # label(non_clause).  [assumption].
7.67/7.68	4067 (all X_1 hBOOL(hAPP(real,bool,hAPP(fun(real,real),fun(real,bool),isCont(real,real),sin),X_1))) # label(fact_4890_isCont__sin) # label(axiom) # label(non_clause).  [assumption].
7.67/7.68	4068 (all X_a (real_normed_field(X_a) -> (all Y_1 all X_3 all A_2 (hBOOL(hAPP(X_a,bool,hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),X_3),A_2)) -> hBOOL(hAPP(X_a,bool,hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),hAPP(X_a,fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(X_a,fun(nat,X_a)),combc(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),inverse_divide(X_a)),X_3)),Y_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),A_2),Y_1))))))) # label(fact_4085_divide_Osums) # label(axiom) # label(non_clause).  [assumption].
7.67/7.68	4069 (all B_2 all K all Diff all H all N_1 ((all M_2 all T_4 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_2),N_1)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),T_4)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),T_4),H)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(nat,fun(real,real),Diff,M_2)),T_4),hAPP(real,real,hAPP(nat,fun(real,real),Diff,hAPP(nat,nat,suc,M_2)),T_4))))) -> (N_1 = hAPP(nat,nat,suc,K) -> (all M_2 all T_4 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_2),N_1)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),T_4),H)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),T_4)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,real)),combs(real,real,real),hAPP(fun(real,real),fun(real,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,fun(real,real))),combb(real,fun(real,real),real),minus_minus(real)),hAPP(nat,fun(real,real),Diff,M_2))),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,real)),combs(real,real,real),hAPP(fun(real,real),fun(real,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,fun(real,real))),combb(real,fun(real,real),real),plus_plus(real)),hAPP(fun(nat,bool),fun(real,real),hAPP(fun(real,fun(fun(nat,bool),real)),fun(fun(nat,bool),fun(real,real)),combc(real,fun(nat,bool),real),hAPP(fun(real,fun(nat,real)),fun(real,fun(fun(nat,bool),real)),hAPP(fun(fun(nat,real),fun(fun(nat,bool),real)),fun(fun(real,fun(nat,real)),fun(real,fun(fun(nat,bool),real))),combb(fun(nat,real),fun(fun(nat,bool),real),real),big_co1399186613setsum(nat,real)),hAPP(fun(real,fun(nat,real)),fun(real,fun(nat,real)),hAPP(fun(fun(nat,real),fun(nat,real)),fun(fun(real,fun(nat,real)),fun(real,fun(nat,real))),combb(fun(nat,real),fun(nat,real),real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),inverse_divide(real)),hAPP(real,fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(real,fun(nat,real)),combc(nat,real,real),hAPP(fun(nat,nat),fun(nat,fun(real,real)),hAPP(fun(nat,fun(real,real)),fun(fun(nat,nat),fun(nat,fun(real,real))),combb(nat,fun(real,real),nat),Diff),hAPP(nat,fun(nat,nat),plus_plus(nat),M_2))),zero_zero(real)))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),fact_fact(nat)))))),power_power(real)))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),M_2))))),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,real),fun(fun(real,real),fun(real,real)),combb(real,real,real),hAPP(real,fun(real,real),times_times(real),B_2)),hAPP(real,fun(real,real),hAPP(fun(real,fun(real,real)),fun(real,fun(real,real)),combc(real,real,real),hAPP(fun(real,real),fun(real,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,fun(real,real))),combb(real,fun(real,real),real),inverse_divide(real)),hAPP(nat,fun(real,real),hAPP(fun(real,fun(nat,real)),fun(nat,fun(real,real)),combc(real,nat,real),power_power(real)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),M_2)))),hAPP(nat,real,real_1(nat),hAPP(nat,nat,fact_fact(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),M_2)))))))),T_4),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,hAPP(nat,fun(real,real),Diff,hAPP(nat,nat,suc,M_2)),T_4)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),inverse_divide(real)),hAPP(real,fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(real,fun(nat,real)),combc(nat,real,real),hAPP(fun(nat,nat),fun(nat,fun(real,real)),hAPP(fun(nat,fun(real,real)),fun(fun(nat,nat),fun(nat,fun(real,real))),combb(nat,fun(real,real),nat),Diff),hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,suc,M_2)))),zero_zero(real)))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),fact_fact(nat))))),hAPP(real,fun(nat,real),power_power(real),T_4))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),hAPP(nat,nat,suc,M_2))))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B_2),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),T_4),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),hAPP(nat,nat,suc,M_2)))),hAPP(nat,real,real_1(nat),hAPP(nat,nat,fact_fact(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),hAPP(nat,nat,suc,M_2))))))))))))))) # label(fact_4268_Maclaurin__lemma2) # label(axiom) # label(non_clause).  [assumption].
7.67/7.68	4070 (all X_a (metric_space(X_a) -> (all X_1 all Y_1 (ti(X_a,X_1) != ti(X_a,Y_1) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),X_1),Y_1))))))) # label(fact_3513_zero__less__dist__iff) # label(axiom) # label(non_clause).  [assumption].
7.67/7.68	4071 (all X_a (group_add(X_a) -> (all A_1 all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_1),hAPP(X_a,X_a,uminus_uminus(X_a),B)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)))) # label(fact_2074_diff__minus__eq__add) # label(axiom) # label(non_clause).  [assumption].
7.67/7.68	4072 (all X_a all X_b all X_c all F hAPP(fun(X_a,fun(X_b,X_c)),fun(product_prod(X_a,X_b),X_c),product_prod_case(X_a,X_b,X_c),hAPP(fun(X_a,fun(X_b,product_prod(X_a,X_b))),fun(X_a,fun(X_b,X_c)),hAPP(fun(fun(X_b,product_prod(X_a,X_b)),fun(X_b,X_c)),fun(fun(X_a,fun(X_b,product_prod(X_a,X_b))),fun(X_a,fun(X_b,X_c))),combb(fun(X_b,product_prod(X_a,X_b)),fun(X_b,X_c),X_a),hAPP(fun(product_prod(X_a,X_b),X_c),fun(fun(X_b,product_prod(X_a,X_b)),fun(X_b,X_c)),combb(product_prod(X_a,X_b),X_c,X_b),F)),product_Pair(X_a,X_b))) = ti(fun(product_prod(X_a,X_b),X_c),F)) # label(fact_4013_split__eta) # label(axiom) # label(non_clause).  [assumption].
7.67/7.68	4073 (all M all N all K_4 hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),K_4)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N),K_4)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),M),N)),K_4)) # label(fact_1093_mod__mult__distrib) # label(axiom) # label(non_clause).  [assumption].
7.67/7.68	4074 (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_816_add__nonneg__nonneg) # label(axiom) # label(non_clause).  [assumption].
7.67/7.68	4075 (all X_1 all A_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(real,int,archim2085082626_floor(real),X_1)),A_2)) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_1),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(int,real,real_1(int),A_2)),one_one(real)))))) # label(fact_3414_floor__le__eq) # label(axiom) # label(non_clause).  [assumption].
7.67/7.68	4076 (all X_a (real_normed_vector(X_a) & real_algebra_1(X_a) -> (all X_3 all A_2 (hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),X_3),A_2),sequentially)) -> hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),hAPP(fun(nat,real),fun(nat,X_a),hAPP(fun(real,X_a),fun(fun(nat,real),fun(nat,X_a)),combb(real,X_a,nat),of_real(X_a)),X_3)),hAPP(real,X_a,of_real(X_a),A_2)),sequentially)))))) # label(fact_4468_of__real_OLIMSEQ) # label(axiom) # label(non_clause).  [assumption].
7.67/7.68	4077 (all X_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)) -> (one_one(real) = X_1 <-> hAPP(real,real,hAPP(nat,fun(real,real),root,N_1),X_1) = one_one(real)))) # label(fact_2686_real__root__eq__1__iff) # label(axiom) # label(non_clause).  [assumption].
7.67/7.68	4078 (all P_4 all A_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),A_2)) -> hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),A_2),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),wset,A_2),P_4))))) # label(fact_837_wset__mem__mem) # label(axiom) # label(non_clause).  [assumption].
7.67/7.68	4079 (all X_a all X_b ti(fun(product_prod(X_a,X_b),X_a),product_fst(X_a,X_b)) = product_fst(X_a,X_b)) # label(tsy_c_Product__Type_Ofst_res) # label(axiom) # label(non_clause).  [assumption].
7.67/7.68	4080 (all X_1 all Y_1 (hAPP(complex,complex,cnj,Y_1) = hAPP(complex,complex,cnj,X_1) <-> Y_1 = X_1)) # label(fact_2937_complex__cnj__cancel__iff) # label(axiom) # label(non_clause).  [assumption].
7.67/7.68	4081 (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_1560_order__less__irrefl) # label(axiom) # label(non_clause).  [assumption].
7.67/7.68	4082 (all X all P_5 (hBOOL(hAPP(nat,bool,prime,P_5)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X),P_5)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,X),P_5)))))) # label(fact_3070_prime__coprime__lt) # label(axiom) # label(non_clause).  [assumption].
7.67/7.68	4083 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,abs_abs(real),X)),one_one(real))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),one_one(real))))) # label(fact_1906_less__one__imp__sqr__less__one) # label(axiom) # label(non_clause).  [assumption].
7.67/7.68	4084 (all K (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),min_1),K)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),min_1),hAPP(int,int,bit0,K))))) # label(fact_307_rel__simps_I25_J) # label(axiom) # label(non_clause).  [assumption].
7.67/7.68	4085 (all X_a (linord1117847801e_zero(X_a) -> (all A_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),hAPP(X_a,X_a,inverse_inverse(X_a),A_2))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),A_2)))))) # label(fact_2540_inverse__nonnegative__iff__nonnegative) # label(axiom) # label(non_clause).  [assumption].
7.67/7.68	4086 (all X_a all X_b (real_normed_vector(X_b) -> (all F all A_3 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),zero_zero(X_b)),A_3)) <-> hBOOL(hAPP(filter(X_a),bool,hAPP(real,fun(filter(X_a),bool),hAPP(fun(X_a,real),fun(real,fun(filter(X_a),bool)),tendsto(X_a,real),hAPP(fun(X_a,X_b),fun(X_a,real),hAPP(fun(X_b,real),fun(fun(X_a,X_b),fun(X_a,real)),combb(X_b,real,X_a),norm_norm(X_b)),F)),zero_zero(real)),A_3)))))) # label(fact_4455_tendsto__norm__zero__iff) # label(axiom) # label(non_clause).  [assumption].
7.67/7.68	4087 (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_393_mult__pos__neg) # label(axiom) # label(non_clause).  [assumption].
7.67/7.68	4088 (all P all Q (hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,P),Q)) | -hBOOL(Q))) # label(help_fdisj_2_1_U) # label(axiom) # label(non_clause).  [assumption].
7.67/7.68	4089 (all K all Ma all N_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),K),hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,Ma),N_1))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),K),Ma)) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),K),N_1)))) # label(fact_3436_zgcd__greatest__iff) # label(axiom) # label(non_clause).  [assumption].
7.67/7.68	4090 (all X_1 (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),zOdd)) -> -(all K_1 hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),K_1)),one_one(int)) != ti(int,X_1)))) # label(fact_1072_zOddE) # label(axiom) # label(non_clause).  [assumption].
7.67/7.68	4091 (all X all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Y)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X)) -> (exists N_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,real_1(nat),N_2)),Y)),X)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,real_1(nat),hAPP(nat,nat,suc,N_2))),Y)))))))) # label(fact_2407_reals__Archimedean4) # label(axiom) # label(non_clause).  [assumption].
7.67/7.68	4092 (all X all N all M (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),M)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> hAPP(real,real,hAPP(nat,fun(real,real),root,N),hAPP(real,real,hAPP(nat,fun(real,real),root,M),X)) = hAPP(real,real,hAPP(nat,fun(real,real),root,M),hAPP(real,real,hAPP(nat,fun(real,real),root,N),X))))) # label(fact_2673_real__root__commute) # label(axiom) # label(non_clause).  [assumption].
7.67/7.68	4093 (all K_4 hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),K_4),K_4) = hAPP(int,int,bit0,K_4)) # label(fact_133_Bit0__def) # label(axiom) # label(non_clause).  [assumption].
7.67/7.68	4094 (all X_1 all P_4 (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),hAPP(int,fun(int,bool),sRStar,P_4))) -> hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),hAPP(int,fun(int,bool),sr,P_4))))) # label(fact_1116_SRStar__SR__prop) # label(axiom) # label(non_clause).  [assumption].
7.67/7.68	4095 (all D_1 (one_one(nat) = D_1 <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,zero_zero(nat)),D_1)))) # label(fact_2867_coprime__0_H) # label(axiom) # label(non_clause).  [assumption].
7.67/7.68	4096 (all X_a (real_normed_field(X_a) & banach(X_a) -> (all X all Y hAPP(X_a,X_a,exp(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),X),Y)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),hAPP(X_a,X_a,exp(X_a),X)),hAPP(X_a,X_a,exp(X_a),Y))))) # label(fact_2589_exp__diff) # label(axiom) # label(non_clause).  [assumption].
7.67/7.68	4097 (all Ma all N_1 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),Ma),N_1) = zero_zero(nat) <-> N_1 = zero_zero(nat) | zero_zero(nat) = Ma)) # label(fact_551_mult__is__0) # label(axiom) # label(non_clause).  [assumption].
7.67/7.68	4098 (all X_a nat_case(X_a) = ti(fun(X_a,fun(fun(nat,X_a),fun(nat,X_a))),nat_case(X_a))) # label(tsy_c_Nat_Onat_Onat__case_res) # label(axiom) # label(non_clause).  [assumption].
7.67/7.68	4099 (all X all Y all Z_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),Y),hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),X),Z_1)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),X),hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),Y),Z_1))) # label(fact_3225_gcd__semilattice__nat_Oinf__left__commute) # label(axiom) # label(non_clause).  [assumption].
7.67/7.68	4100 (all B all A_1 all K_4 hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A_1),K_4) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_1),B))),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_1),B))),K_4)) # label(fact_920_zdiv__zmod__equality) # label(axiom) # label(non_clause).  [assumption].
7.67/7.68	4101 (all K_4 all L_4 hAPP(int,rat,hAPP(int,fun(int,rat),fract,hAPP(int,int,number_number_of(int),K_4)),hAPP(int,int,number_number_of(int),L_4)) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),hAPP(int,rat,number_number_of(rat),K_4)),hAPP(int,rat,number_number_of(rat),L_4))) # label(fact_3776_Fract__number__of__quotient) # label(axiom) # label(non_clause).  [assumption].
7.67/7.68	4102 (all X_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),X_1),N_1)),zEven)) <-> hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),zEven))))) # label(fact_1398_power__preserves__even) # label(axiom) # label(non_clause).  [assumption].
7.67/7.68	4103 (all X_a all A_3 all B_2 hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_3),B_2)),A_3))) # label(fact_1995_Diff__subset) # label(axiom) # label(non_clause).  [assumption].
7.67/7.68	4104 (all X_a (real_normed_vector(X_a) -> (all X_3 ((all E (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),E)) -> (exists M_3 all M_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_3),M_2)) -> (all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_3),N_2)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(nat,X_a,X_3,M_2)),hAPP(nat,X_a,X_3,N_2)))),E)))))))) -> hBOOL(hAPP(fun(nat,X_a),bool,cauchy(X_a),X_3)))))) # label(fact_3317_CauchyI) # label(axiom) # label(non_clause).  [assumption].
7.67/7.68	4105 (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)) = hAPP(int,nat,number_number_of(nat),hAPP(int,int,succ,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)))) # label(fact_1537_Suc__nat__number__of) # label(axiom) # label(non_clause).  [assumption].
7.67/7.68	4106 (all X hAPP(real,real,uminus_uminus(real),hAPP(real,real,sin,X)) = hAPP(real,real,cos,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))) # label(fact_2397_minus__sin__cos__eq) # label(axiom) # label(non_clause).  [assumption].
7.67/7.68	4107 (all X_a (semiring_div(X_a) -> (all B all A_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),A_1),B) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B),A_1)),B)))) # label(fact_941_mod__add__self1) # label(axiom) # label(non_clause).  [assumption].
7.67/7.68	4108 (all X_a (group_add(X_a) -> (all X_1 all Y_1 (zero_zero(X_a) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X_1),Y_1) <-> hAPP(X_a,X_a,uminus_uminus(X_a),X_1) = ti(X_a,Y_1))))) # label(fact_2064_add__eq__0__iff) # label(axiom) # label(non_clause).  [assumption].
7.67/7.68	4109 (all K_4 ti(int,K_4) = hAPP(int,int,number_number_of(int),K_4)) # label(fact_22_number__of__is__id) # label(axiom) # label(non_clause).  [assumption].
7.67/7.68	4110 (all X_a (ring(X_a) -> (all A_2 all E_2 all C_1 all B_1 all D_1 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_2),B_1)),E_2)),C_1) = ti(X_a,D_1) <-> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),E_2)),C_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B_1),E_2)),D_1))))) # label(fact_490_eq__add__iff1) # label(axiom) # label(non_clause).  [assumption].
7.67/7.68	4111 (all X_a all B_2 all C_1 all A_3 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),A_3)) -> (-hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),B_2)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_3),B_2)))))) # label(fact_1921_DiffI) # label(axiom) # label(non_clause).  [assumption].
7.67/7.68	4112 (all X_a (real_normed_algebra(X_a) -> (all X exists K_2 all X_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),X_2))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(X_a,real,norm_norm(X_a),X_2)),K_2)))))) # label(fact_1813_mult__right_Obounded) # label(axiom) # label(non_clause).  [assumption].
7.67/7.68	4113 (all N (zero_zero(nat) != N -> hAPP(nat,nat,suc,hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),N)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),N))) # label(fact_1459_lemma__Suc__Suc__4n__diff__2) # label(axiom) # label(non_clause).  [assumption].
7.67/7.68	4114 (all C_1 all X_1 all Ta all A_2 all D_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A_2),D_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A_2),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X_1),Ta))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A_2),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X_1),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C_1),D_1))),Ta)))))) # label(fact_208_zdvd__period) # label(axiom) # label(non_clause).  [assumption].
7.67/7.68	4115 (all X0 all F all R_3 ((all X_2 (hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),X_2),hAPP(real,fun(real,bool),hAPP(real,fun(real,fun(real,bool)),ord_gr676655987ssThan(real),hAPP(real,real,uminus_uminus(real),R_3)),R_3))) -> hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),F)),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),suc)))),hAPP(real,fun(nat,real),power_power(real),X_2)))))) -> (hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),X0),hAPP(real,fun(real,bool),hAPP(real,fun(real,fun(real,bool)),ord_gr676655987ssThan(real),hAPP(real,real,uminus_uminus(real),R_3)),R_3))) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),R_3)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(fun(real,fun(nat,real)),fun(real,real),hAPP(fun(fun(nat,real),real),fun(fun(real,fun(nat,real)),fun(real,real)),combb(fun(nat,real),real,real),suminf(real)),hAPP(fun(real,fun(nat,real)),fun(real,fun(nat,real)),hAPP(fun(fun(nat,real),fun(nat,real)),fun(fun(real,fun(nat,real)),fun(real,fun(nat,real))),combb(fun(nat,real),fun(nat,real),real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),F))),hAPP(fun(nat,nat),fun(real,fun(nat,real)),hAPP(fun(real,fun(fun(nat,nat),fun(nat,real))),fun(fun(nat,nat),fun(real,fun(nat,real))),combc(real,fun(nat,nat),fun(nat,real)),hAPP(fun(real,fun(nat,real)),fun(real,fun(fun(nat,nat),fun(nat,real))),hAPP(fun(fun(nat,real),fun(fun(nat,nat),fun(nat,real))),fun(fun(real,fun(nat,real)),fun(real,fun(fun(nat,nat),fun(nat,real)))),combb(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),real),combb(nat,real,nat)),power_power(real))),suc)))),X0),hAPP(fun(nat,real),real,suminf(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),F)),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),suc)))),hAPP(real,fun(nat,real),power_power(real),X0))))))))) # label(fact_4036_DERIV__power__series_H) # label(axiom) # label(non_clause).  [assumption].
7.67/7.68	4116 (all X all Y hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(complex,real,im,X)),hAPP(complex,real,im,Y)) = hAPP(complex,real,im,hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),X),Y))) # label(fact_2981_Im_Odiff) # label(axiom) # label(non_clause).  [assumption].
7.67/7.68	4117 (all X_a all P all X (-hBOOL(hAPP(X_a,bool,P,X)) | hBOOL(hAPP(fun(X_a,bool),bool,fEx(X_a),P)))) # label(help_fEx_1_1_U) # label(axiom) # label(non_clause).  [assumption].
7.67/7.68	4118 (all A_1 all B hAPP(int,rat,hAPP(int,fun(int,rat),fract,hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_1),hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),A_1),B))),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),B),hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),A_1),B))) = hAPP(int,rat,hAPP(int,fun(int,rat),fract,A_1),B)) # label(fact_4389_Fract__coprime) # label(axiom) # label(non_clause).  [assumption].
7.67/7.68	4119 (all A_2 all B_1 (ti(int,A_2) = ti(int,B_1) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_2),B_1),zero_zero(int))))) # label(fact_353_IntPrimes_Ozcong__zero) # label(axiom) # label(non_clause).  [assumption].
7.67/7.68	4120 (all X_a (sgn_if(X_a) -> (all X ((zero_zero(X_a) != ti(X_a,X) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),X)) -> hAPP(X_a,X_a,sgn_sgn(X_a),X) = one_one(X_a)) & (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),X)) -> hAPP(X_a,X_a,uminus_uminus(X_a),one_one(X_a)) = hAPP(X_a,X_a,sgn_sgn(X_a),X))) & (ti(X_a,X) = zero_zero(X_a) -> zero_zero(X_a) = hAPP(X_a,X_a,sgn_sgn(X_a),X)))))) # label(fact_2232_sgn__if) # label(axiom) # label(non_clause).  [assumption].
7.67/7.68	4121 (all X_a (topological_space(X_a) & comm_monoid_add(X_a) -> (all F (hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),F)) <-> (exists X1 hBOOL(hAPP(X_a,bool,hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),F),X1))))))) # label(fact_4090_summable__def) # label(axiom) # label(non_clause).  [assumption].
7.67/7.68	4122 (all X_1 all N_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,abs_abs(int),X_1)),N_1))) <-> zero_zero(nat) = N_1 | zero_zero(int) != ti(int,X_1))) # label(fact_1967_zero__less__zpower__abs__iff) # label(axiom) # label(non_clause).  [assumption].
7.67/7.68	4123 (all X_a (comm_ring_1(X_a) -> (all X ((-hBOOL(hAPP(nat,bool,even_odd_even(nat),X)) -> hAPP(X_a,X_a,uminus_uminus(X_a),one_one(X_a)) = hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),one_one(X_a))),X)) & (hBOOL(hAPP(nat,bool,even_odd_even(nat),X)) -> one_one(X_a) = hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),one_one(X_a))),X)))))) # label(fact_2437_minus__one__even__odd__power) # label(axiom) # label(non_clause).  [assumption].
7.67/7.68	4124 (all X_a (dvd(X_a) & linorder(X_a) & plus(X_a) -> (all D_1 all Sa exists Z_2 all X_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_2),Z_2)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),D_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X_2),Sa))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),D_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X_2),Sa)))))))) # label(fact_863_minf_I9_J) # label(axiom) # label(non_clause).  [assumption].
7.67/7.68	4125 (all M all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),M),N) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),M),N)),N))) # label(fact_1086_Divides_Omod__div__equality_H) # label(axiom) # label(non_clause).  [assumption].
7.67/7.68	4126 (all Z_1 hAPP(complex,real,re,hAPP(int,complex,ring_1_of_int(complex),Z_1)) = hAPP(int,real,ring_1_of_int(real),Z_1)) # label(fact_3571_complex__Re__of__int) # label(axiom) # label(non_clause).  [assumption].
7.67/7.68	4127 (all X_a (dense_linorder(X_a) -> (all A_2 all B_1 all C_1 all D_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_gr676655987ssThan(X_a),A_2),B_1)),hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastAtMost(X_a),C_1),D_1))) <-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),B_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_1),D_1)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C_1),A_2))))))) # label(fact_4530_greaterThanLessThan__subseteq__atLeastAtMost__iff) # label(axiom) # label(non_clause).  [assumption].
7.67/7.68	4128 (all V_1 all N_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),hAPP(bool,fun(nat,fun(nat,nat)),if(nat),hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),hAPP(int,int,pred,V_1)))),zero_zero(nat)),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),hAPP(int,nat,nat_1,hAPP(int,int,number_number_of(int),hAPP(int,int,pred,V_1)))),N_1))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),hAPP(int,nat,number_number_of(nat),V_1)),hAPP(nat,nat,suc,N_1))) # label(fact_4797_min__Suc__number__of) # label(axiom) # label(non_clause).  [assumption].
7.67/7.68	4129 (all X_a (archim1727834104eiling(X_a) -> (all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(X_a,int,archim2085082626_floor(X_a),X)),hAPP(X_a,int,archim2085082626_floor(X_a),Y))))))) # label(fact_2865_floor__mono) # label(axiom) # label(non_clause).  [assumption].
7.67/7.68	4130 (all X all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(nat,fun(real,real),root,N),X)) = hAPP(real,real,hAPP(nat,fun(real,real),root,N),hAPP(real,real,uminus_uminus(real),X)))) # label(fact_2688_real__root__minus) # label(axiom) # label(non_clause).  [assumption].
7.67/7.68	4131 (all X_a (linordered_idom(X_a) -> (all X all Y all N (hBOOL(hAPP(nat,bool,even_odd_even(nat),N)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,abs_abs(X_a),X)),hAPP(X_a,X_a,abs_abs(X_a),Y))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),N)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),Y),N)))))))) # label(fact_2440_power__mono__even) # label(axiom) # label(non_clause).  [assumption].
7.67/7.68	4132 (all U all V all X all Y (Y = X -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),U)),V)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),U)),Y))),V))))) # label(fact_1894_sin__bound__lemma) # label(axiom) # label(non_clause).  [assumption].
7.67/7.68	4133 (all J_2 all K_4 all M (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),M)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,number_number_of(int),min_1)),J_2)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,number_number_of(int),min_1)),K_4)),M)) -> hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,number_number_of(int),min_1)),K_4) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,number_number_of(int),min_1)),J_2)))) # label(fact_465_neg__one__power__eq__mod__m) # label(axiom) # label(non_clause).  [assumption].
7.67/7.68	4134 (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_43_arith__simps_I32_J) # label(axiom) # label(non_clause).  [assumption].
7.67/7.68	4135 (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_1573_xt1_I9_J) # label(axiom) # label(non_clause).  [assumption].
7.67/7.68	4136 (all W ii != hAPP(int,complex,number_number_of(complex),W)) # label(fact_2762_complex__i__not__number__of) # label(axiom) # label(non_clause).  [assumption].
7.67/7.68	4137 (all X_a (semiring_div(X_a) -> (all A_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),zero_zero(X_a)),A_1) = zero_zero(X_a)))) # label(fact_926_mod__0) # label(axiom) # label(non_clause).  [assumption].
7.67/7.68	4138 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),M),N)),N)))) # label(fact_1122_mod__le__divisor) # label(axiom) # label(non_clause).  [assumption].
7.67/7.68	4139 (all X_a (power(X_a) & comm_monoid_add(X_a) -> (all X_1 all Y_1 all N_1 hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),times_times(X_a)),hAPP(X_a,fun(nat,X_a),power_power(X_a),X_1))),hAPP(fun(nat,nat),fun(nat,X_a),hAPP(fun(nat,X_a),fun(fun(nat,nat),fun(nat,X_a)),combb(nat,X_a,nat),hAPP(X_a,fun(nat,X_a),power_power(X_a),Y_1)),hAPP(nat,fun(nat,nat),minus_minus(nat),N_1)))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,suc,N_1))) = hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),times_times(X_a)),hAPP(fun(nat,nat),fun(nat,X_a),hAPP(fun(nat,X_a),fun(fun(nat,nat),fun(nat,X_a)),combb(nat,X_a,nat),hAPP(X_a,fun(nat,X_a),power_power(X_a),X_1)),hAPP(nat,fun(nat,nat),minus_minus(nat),N_1)))),hAPP(X_a,fun(nat,X_a),power_power(X_a),Y_1))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,suc,N_1)))))) # label(fact_4175_lemma__realpow__rev__sumr) # label(axiom) # label(non_clause).  [assumption].
7.67/7.68	4140 (all Nat all Nat_5 (Nat = Nat_5 <-> hAPP(nat,nat,suc,Nat_5) = hAPP(nat,nat,suc,Nat))) # label(fact_1215_nat_Oinject) # label(axiom) # label(non_clause).  [assumption].
7.67/7.68	4141 (all N hAPP(int,nat,number_number_of(nat),N) = hAPP(real,nat,natfloor,hAPP(int,real,number_number_of(real),N))) # label(fact_1876_natfloor__number__of__eq) # label(axiom) # label(non_clause).  [assumption].
7.67/7.68	4142 (all I_1 all J_2 all K_4 hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I_1),K_4)),J_2) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I_1),J_2)),K_4)) # label(fact_742_diff__commute) # label(axiom) # label(non_clause).  [assumption].
7.67/7.68	4143 (all P_1 all P1 all D_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D_1)) -> ((all X_2 all K_1 (hBOOL(hAPP(int,bool,P1,X_2)) <-> hBOOL(hAPP(int,bool,P1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X_2),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K_1),D_1)))))) -> ((exists Z_2 all X_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X_2),Z_2)) -> (hBOOL(hAPP(int,bool,P1,X_2)) <-> hBOOL(hAPP(int,bool,P_1,X_2))))) -> ((exists X1 hBOOL(hAPP(int,bool,P1,X1))) -> (exists X1 hBOOL(hAPP(int,bool,P_1,X1)))))))) # label(fact_2844_minusinfinity) # label(axiom) # label(non_clause).  [assumption].
7.67/7.68	4144 (all X_a (linordered_field(X_a) -> (all A_1 (zero_zero(X_a) != ti(X_a,A_1) -> hAPP(X_a,X_a,inverse_inverse(X_a),hAPP(X_a,X_a,abs_abs(X_a),A_1)) = hAPP(X_a,X_a,abs_abs(X_a),hAPP(X_a,X_a,inverse_inverse(X_a),A_1)))))) # label(fact_2559_nonzero__abs__inverse) # label(axiom) # label(non_clause).  [assumption].
7.67/7.68	4145 (all Y all X all A_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A_1)) -> (A_1 != one_one(real) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Y)) -> hAPP(real,real,hAPP(real,fun(real,real),log,A_1),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),X),Y)) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),log,A_1),X)),hAPP(real,real,hAPP(real,fun(real,real),log,A_1),Y))))))) # label(fact_2648_log__mult) # label(axiom) # label(non_clause).  [assumption].
7.67/7.68	4146 (all P_1 all A0 all A1 (hBOOL(hAPP(product_prod(int,int),bool,hAPP(fun(product_prod(int,int),fun(product_prod(int,int),bool)),fun(product_prod(int,int),bool),accp(product_prod(int,int)),posDivAlg_rel),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),A0),A1))) -> ((all A_4 all B_4 (hBOOL(hAPP(product_prod(int,int),bool,hAPP(fun(product_prod(int,int),fun(product_prod(int,int),bool)),fun(product_prod(int,int),bool),accp(product_prod(int,int)),posDivAlg_rel),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),A_4),B_4))) -> ((-(hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_4),B_4)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B_4),zero_zero(int)))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),P_1,A_4),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),B_4)))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),P_1,A_4),B_4))))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),P_1,A0),A1))))) # label(fact_1181_posDivAlg_Opinduct) # label(axiom) # label(non_clause).  [assumption].
7.67/7.68	4147 (all X_a (linordered_idom(X_a) -> (all X_1 all N_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X_1),N_1)),zero_zero(X_a))) <-> -hBOOL(hAPP(nat,bool,even_odd_even(nat),N_1)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),zero_zero(X_a))))))) # label(fact_2436_power__less__zero__eq) # label(axiom) # label(non_clause).  [assumption].
7.67/7.68	4148 (all X_b all X_a (topological_space(X_a) & real_normed_field(X_b) -> (all Y_1 all G all L all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),G),L),hAPP(X_a,filter(X_a),at(X_a),A_2))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(X_b,fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(X_b,fun(X_a,X_b)),combc(X_a,X_b,X_b),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,fun(X_b,X_b))),combb(X_b,fun(X_b,X_b),X_a),inverse_divide(X_b)),G)),Y_1)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),inverse_divide(X_b),L),Y_1)),hAPP(X_a,filter(X_a),at(X_a),A_2))))))) # label(fact_4563_divide_OLIM) # label(axiom) # label(non_clause).  [assumption].
7.67/7.68	4149 (all N hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(nat,real,real_1(nat),N)))) # label(fact_2289_real__of__nat__ge__zero) # label(axiom) # label(non_clause).  [assumption].
7.67/7.68	4150 (all K_4 all I_1 all J_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),J_2)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K_4)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I_1),K_4)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J_2),K_4)))))) # label(fact_598_mult__less__mono1) # label(axiom) # label(non_clause).  [assumption].
7.67/7.68	4151 (all Y (Y != zero_zero(real) -> zero_zero(real) = hAPP(real,real,cos,hAPP(complex,real,arg,hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,zero_zero(real)),Y))))) # label(fact_2756_cos__arg__i__mult__zero) # label(axiom) # label(non_clause).  [assumption].
7.67/7.68	4152 (all X all Y hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),Y),hAPP(real,real,uminus_uminus(real),X))) = hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),hAPP(real,real,uminus_uminus(real),Y)))) # label(fact_2093_abs__minus__add__cancel) # label(axiom) # label(non_clause).  [assumption].
7.67/7.68	4153 (all N hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,fact_fact(nat),N)))) # label(fact_2489_fact__gt__zero__nat) # label(axiom) # label(non_clause).  [assumption].
7.67/7.68	4154 (all M all N ((hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N) != zero_zero(nat) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N)),hAPP(nat,nat,fact_fact(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N)),one_one(nat)))) = hAPP(nat,nat,fact_fact(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N))) & (hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N) = zero_zero(nat) -> one_one(nat) = hAPP(nat,nat,fact_fact(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N))))) # label(fact_2482_fact__add__num__eq__if__nat) # label(axiom) # label(non_clause).  [assumption].
7.67/7.68	4155 (all M hAPP(nat,nat,suc,zero_zero(nat)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),M),hAPP(nat,nat,suc,zero_zero(nat)))) # label(fact_3258_gcd__Suc__0) # label(axiom) # label(non_clause).  [assumption].
7.67/7.68	4156 (all X_a (ordered_ab_group_add(X_a) -> (all A_2 all B_1 all C_1 all D_1 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),C_1),D_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_2),B_1) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C_1),D_1)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),B_1))))))) # label(fact_797_diff__eq__diff__less__eq) # label(axiom) # label(non_clause).  [assumption].
7.67/7.68	4157 (all X_a (linordered_semidom(X_a) -> (all N all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),A_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N)))))))) # label(fact_461_one__less__power) # label(axiom) # label(non_clause).  [assumption].
7.67/7.68	4158 (all X_a (linord1117847801e_zero(X_a) -> (all B_1 all C_1 all A_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),B_1),C_1)),A_2)) <-> (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C_1)) -> (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_2))) & (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),C_1)),B_1)))) & (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),C_1)))))))) # label(fact_1709_divide__less__eq) # label(axiom) # label(non_clause).  [assumption].
7.67/7.68	4159 (all X_a (comple44059174attice(X_a) -> (all X_1 all A_3 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_3)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),hAPP(fun(X_a,bool),X_a,complete_Sup_Sup(X_a),A_3))))))) # label(fact_1763_complete__lattice__class_OSup__upper) # label(axiom) # label(non_clause).  [assumption].
7.67/7.68	4160 (all X_a all X_c all X_b all F all X_1 all Y_1 hAPP(product_prod(X_a,X_c),product_prod(X_a,X_b),hAPP(fun(X_c,X_b),fun(product_prod(X_a,X_c),product_prod(X_a,X_b)),product_apsnd(X_c,X_b,X_a),F),hAPP(X_c,product_prod(X_a,X_c),hAPP(X_a,fun(X_c,product_prod(X_a,X_c)),product_Pair(X_a,X_c),X_1),Y_1)) = hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),X_1),hAPP(X_c,X_b,F,Y_1))) # label(fact_4064_apsnd__conv) # label(axiom) # label(non_clause).  [assumption].
7.67/7.68	4161 (all V_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),V_1),pls)) <-> zero_zero(nat) = hAPP(int,nat,number_number_of(nat),V_1))) # label(fact_40_eq__0__number__of) # label(axiom) # label(non_clause).  [assumption].
7.67/7.68	4162 (all X_a (real_normed_field(X_a) -> (all X all Y all Ya hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X),Y)),Ya) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),X),Ya)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),Y),Ya))))) # label(fact_1661_divide_Oadd) # label(axiom) # label(non_clause).  [assumption].
7.67/7.68	4163 (all K_4 hAPP(int,int,succ,hAPP(int,int,bit0,K_4)) = hAPP(int,int,bit1,K_4)) # label(fact_1527_succ__Bit0) # label(axiom) # label(non_clause).  [assumption].
7.67/7.68	4164 (all X all N_5 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),N),N_5)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X),one_one(real))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(nat,fun(real,real),root,N),X)),hAPP(real,real,hAPP(nat,fun(real,real),root,N_5),X)))))))) # label(fact_2712_real__root__increasing) # label(axiom) # label(non_clause).  [assumption].
7.67/7.68	4165 (all M all N hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),M),N)) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(nat,int,semiring_1_of_nat(int),M)),N)) # label(fact_1356_zpower__int) # label(axiom) # label(non_clause).  [assumption].
7.67/7.68	4166 (all X all M all Y hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),X),Y)),M) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),X),M)),Y)),M)) # label(fact_963_zpower__zmod) # label(axiom) # label(non_clause).  [assumption].
7.67/7.68	4167 (all X all Y (hAPP(real,real,sqrt,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),Y),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) = X -> Y = zero_zero(real))) # label(fact_1647_real__sqrt__sum__squares__eq__cancel) # label(axiom) # label(non_clause).  [assumption].
7.67/7.69	4168 (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),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Lx),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),Rx),Ry))))) # label(fact_218_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J) # label(axiom) # label(non_clause).  [assumption].
7.67/7.69	4169 (all A_3 all Ma (hBOOL(hAPP(fun(fun(int,bool),bool),bool,hAPP(fun(int,bool),fun(fun(fun(int,bool),bool),bool),member(fun(int,bool)),A_3),hAPP(int,fun(fun(int,bool),bool),rsetR,Ma))) -> hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A_3)))) # label(fact_3628_RsetR__fin) # label(axiom) # label(non_clause).  [assumption].
7.67/7.69	4170 (all L all K ((zero_zero(int) != ti(int,K) -> (ti(int,L) != zero_zero(int) -> hAPP(product_prod(int,int),product_prod(int,int),hAPP(fun(int,int),fun(product_prod(int,int),product_prod(int,int)),product_apsnd(int,int,int),hAPP(int,fun(int,int),times_times(int),hAPP(int,int,sgn_sgn(int),L))),hAPP(product_prod(int,int),product_prod(int,int),hAPP(product_prod(int,int),fun(product_prod(int,int),product_prod(int,int)),hAPP(bool,fun(product_prod(int,int),fun(product_prod(int,int),product_prod(int,int))),if(product_prod(int,int)),hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),L)),hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),K))),hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),L),zero_zero(int))),hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),zero_zero(int))))),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),pdivmod,K),L)),hAPP(product_prod(int,int),product_prod(int,int),hAPP(fun(int,fun(int,product_prod(int,int))),fun(product_prod(int,int),product_prod(int,int)),product_prod_case(int,int,product_prod(int,int)),hAPP(fun(int,fun(int,product_prod(int,int))),fun(int,fun(int,product_prod(int,int))),hAPP(fun(int,fun(fun(int,product_prod(int,int)),fun(int,product_prod(int,int)))),fun(fun(int,fun(int,product_prod(int,int))),fun(int,fun(int,product_prod(int,int)))),combs(int,fun(int,product_prod(int,int)),fun(int,product_prod(int,int))),hAPP(fun(int,fun(int,fun(product_prod(int,int),product_prod(int,int)))),fun(int,fun(fun(int,product_prod(int,int)),fun(int,product_prod(int,int)))),hAPP(fun(fun(int,fun(product_prod(int,int),product_prod(int,int))),fun(fun(int,product_prod(int,int)),fun(int,product_prod(int,int)))),fun(fun(int,fun(int,fun(product_prod(int,int),product_prod(int,int)))),fun(int,fun(fun(int,product_prod(int,int)),fun(int,product_prod(int,int))))),combb(fun(int,fun(product_prod(int,int),product_prod(int,int))),fun(fun(int,product_prod(int,int)),fun(int,product_prod(int,int))),int),combs(int,product_prod(int,int),product_prod(int,int))),hAPP(fun(int,product_prod(int,int)),fun(int,fun(int,fun(product_prod(int,int),product_prod(int,int)))),hAPP(fun(product_prod(int,int),fun(int,fun(product_prod(int,int),product_prod(int,int)))),fun(fun(int,product_prod(int,int)),fun(int,fun(int,fun(product_prod(int,int),product_prod(int,int))))),combb(product_prod(int,int),fun(int,fun(product_prod(int,int),product_prod(int,int))),int),hAPP(fun(int,fun(product_prod(int,int),fun(product_prod(int,int),product_prod(int,int)))),fun(product_prod(int,int),fun(int,fun(product_prod(int,int),product_prod(int,int)))),combc(int,product_prod(int,int),fun(product_prod(int,int),product_prod(int,int))),hAPP(fun(int,bool),fun(int,fun(product_prod(int,int),fun(product_prod(int,int),product_prod(int,int)))),hAPP(fun(bool,fun(product_prod(int,int),fun(product_prod(int,int),product_prod(int,int)))),fun(fun(int,bool),fun(int,fun(product_prod(int,int),fun(product_prod(int,int),product_prod(int,int))))),combb(bool,fun(product_prod(int,int),fun(product_prod(int,int),product_prod(int,int))),int),if(product_prod(int,int))),hAPP(int,fun(int,bool),hAPP(fun(int,fun(int,bool)),fun(int,fun(int,bool)),combc(int,int,bool),fequal(int)),zero_zero(int))))),hAPP(int,fun(int,product_prod(int,int)),hAPP(fun(int,fun(int,product_prod(int,int))),fun(int,fun(int,product_prod(int,int))),combc(int,int,product_prod(int,int)),hAPP(fun(int,int),fun(int,fun(int,product_prod(int,int))),hAPP(fun(int,fun(int,product_prod(int,int))),fun(fun(int,int),fun(int,fun(int,product_prod(int,int)))),combb(int,fun(int,product_prod(int,int)),int),product_Pair(int,int)),uminus_uminus(int))),zero_zero(int))))),hAPP(fun(int,int),fun(int,fun(int,product_prod(int,int))),hAPP(fun(int,fun(fun(int,int),fun(int,product_prod(int,int)))),fun(fun(int,int),fun(int,fun(int,product_prod(int,int)))),combc(int,fun(int,int),fun(int,product_prod(int,int))),hAPP(fun(int,fun(int,product_prod(int,int))),fun(int,fun(fun(int,int),fun(int,product_prod(int,int)))),hAPP(fun(fun(int,product_prod(int,int)),fun(fun(int,int),fun(int,product_prod(int,int)))),fun(fun(int,fun(int,product_prod(int,int))),fun(int,fun(fun(int,int),fun(int,product_prod(int,int))))),combb(fun(int,product_prod(int,int)),fun(fun(int,int),fun(int,product_prod(int,int))),int),combb(int,product_prod(int,int),int)),hAPP(fun(int,int),fun(int,fun(int,product_prod(int,int))),hAPP(fun(int,fun(int,product_prod(int,int))),fun(fun(int,int),fun(int,fun(int,product_prod(int,int)))),combb(int,fun(int,product_prod(int,int)),int),product_Pair(int,int)),hAPP(int,fun(int,int),hAPP(fun(int,fun(int,int)),fun(int,fun(int,int)),combc(int,int,int),hAPP(fun(int,int),fun(int,fun(int,int)),hAPP(fun(int,fun(int,int)),fun(fun(int,int),fun(int,fun(int,int))),combb(int,fun(int,int),int),minus_minus(int)),uminus_uminus(int))),one_one(int))))),hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,abs_abs(int),L))))),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),pdivmod,K),L)))) = hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),divmod_int,K),L)) & (ti(int,L) = zero_zero(int) -> hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),zero_zero(int)),K) = hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),divmod_int,K),L))) & (ti(int,K) = zero_zero(int) -> hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),zero_zero(int)),zero_zero(int)) = hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),divmod_int,K),L)))) # label(fact_4063_divmod__int__pdivmod) # label(axiom) # label(non_clause).  [assumption].
7.67/7.69	4171 (all G all X_1 all Ma (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),G),X_1),Ma)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,real),fun(fun(real,real),fun(real,real)),combb(real,real,real),cos),G)),X_1),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,uminus_uminus(real),hAPP(real,real,sin,hAPP(real,real,G,X_1)))),Ma))))) # label(fact_3854_DERIV__fun__cos) # label(axiom) # label(non_clause).  [assumption].
7.67/7.69	4172 (all X_a (ordered_ab_group_add(X_a) -> (all X all Y all Z_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),X),Z_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),Y),Z_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),Y)),Z_1)))) # label(fact_4803_min__diff__distrib__left) # label(axiom) # label(non_clause).  [assumption].
7.67/7.69	4173 (all X_a (preorder(X_a) -> (all Z_1 all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),Z_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Z_1))))))) # label(fact_1548_order__trans) # label(axiom) # label(non_clause).  [assumption].
7.67/7.69	4174 (all R_4 all S_3 hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(rat,real,ratreal,hAPP(int,rat,number_number_of(rat),R_4))),hAPP(rat,real,ratreal,hAPP(int,rat,number_number_of(rat),S_3))) = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(int,real,number_number_of(real),R_4)),hAPP(int,real,number_number_of(real),S_3))) # label(fact_3780_Ratreal__number__of__quotient) # label(axiom) # label(non_clause).  [assumption].
7.67/7.69	4175 (all Diff all F all N_1 all H (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)) & (all M_2 all T_4 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),H),T_4)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),T_4),zero_zero(real))) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_2),N_1)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(nat,fun(real,real),Diff,M_2)),T_4),hAPP(real,real,hAPP(nat,fun(real,real),Diff,hAPP(nat,nat,suc,M_2)),T_4))))) & F = hAPP(nat,fun(real,real),Diff,zero_zero(nat)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),H),zero_zero(real))) -> (exists T_4 (hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),inverse_divide(real)),hAPP(real,fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(real,fun(nat,real)),combc(nat,real,real),Diff),zero_zero(real)))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),fact_fact(nat))))),hAPP(real,fun(nat,real),power_power(real),H))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),N_1))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(nat,fun(real,real),Diff,N_1),T_4)),hAPP(nat,real,real_1(nat),hAPP(nat,nat,fact_fact(nat),N_1)))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),H),N_1))) = hAPP(real,real,F,H) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),T_4),zero_zero(real))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),H),T_4)))))) # label(fact_4283_Maclaurin__minus__objl) # label(axiom) # label(non_clause).  [assumption].
7.67/7.69	4176 (all X_a (field_inverse_zero(X_a) -> (all Z_1 all X all Y (ti(X_a,Y) != zero_zero(X_a) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Z_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),X),Y)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Z_1),Y))),Y))))) # label(fact_1718_add__num__frac) # label(axiom) # label(non_clause).  [assumption].
7.67/7.69	4177 (all X_a (real_normed_algebra(X_a) -> (all X_1 all A_2 hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,X_a),fun(X_a,bool),isCont(X_a,X_a),hAPP(X_a,fun(X_a,X_a),times_times(X_a),X_1)),A_2))))) # label(fact_4907_mult__right_OisCont) # label(axiom) # label(non_clause).  [assumption].
7.67/7.69	4178 (all A_3 all B_2 (hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,bool),fun(fun(nat,bool),bool),ord_less(fun(nat,bool)),A_3),B_2)) <-> hBOOL(hAPP(fun(int,bool),bool,hAPP(fun(int,bool),fun(fun(int,bool),bool),ord_less(fun(int,bool)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),A_3)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),B_2))))) # label(fact_3647_transfer__nat__int__set__relations_I4_J) # label(axiom) # label(non_clause).  [assumption].
7.67/7.69	4179 (all M all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),M),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),M),N)) # label(fact_3247_gcd__add2__nat) # label(axiom) # label(non_clause).  [assumption].
7.67/7.69	4180 (all X_a (comm_monoid_add(X_a) -> (all F all N_1 hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),ord_lessThan(nat),hAPP(nat,nat,suc,N_1))) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),ord_lessThan(nat),N_1))),hAPP(nat,X_a,F,N_1))))) # label(fact_4321_setsum__lessThan__Suc) # label(axiom) # label(non_clause).  [assumption].
7.67/7.69	4181 (all Q_3 all R_4 hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),Q_3),hAPP(rat,rat,inverse_inverse(rat),R_4)) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),Q_3),R_4)) # label(fact_3717_divide__rat__def) # label(axiom) # label(non_clause).  [assumption].
7.67/7.69	4182 (all P all Q (hBOOL(Q) | -hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,P),Q)))) # label(help_fconj_3_1_U) # label(axiom) # label(non_clause).  [assumption].
7.67/7.69	4183 (all M all N all K_4 hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N)),K_4) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,M)),N)),hAPP(nat,nat,suc,K_4))) # label(fact_1252_Suc__diff__diff) # label(axiom) # label(non_clause).  [assumption].
7.67/7.69	4184 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> (hAPP(real,real,ln,X) = hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),X),one_one(real)) -> one_one(real) = X))) # label(fact_1938_ln__eq__minus__one) # label(axiom) # label(non_clause).  [assumption].
7.67/7.69	4185 (all N_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),N_1)) -> hAPP(fun(int,bool),nat,finite_card(int),hAPP(fun(int,bool),fun(int,bool),collect(int),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),combs(int,bool,bool),hAPP(fun(int,bool),fun(int,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj),hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)))),hAPP(int,fun(int,bool),hAPP(fun(int,fun(int,bool)),fun(int,fun(int,bool)),combc(int,int,bool),ord_less_eq(int)),N_1)))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,nat_1,N_1)),one_one(nat)))) # label(fact_3880_card__bdd__int__set__le) # label(axiom) # label(non_clause).  [assumption].
7.67/7.69	4186 (all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,N)),hAPP(nat,nat,fact,N)) = hAPP(nat,nat,fact,hAPP(nat,nat,suc,N))) # label(fact_3546_fact_Osimps_I2_J) # label(axiom) # label(non_clause).  [assumption].
7.67/7.69	4187 (all X_a (real_normed_vector(X_a) -> (all X_1 (zero_zero(X_a) = ti(X_a,X_1) <-> hAPP(X_a,real,norm_norm(X_a),X_1) = zero_zero(real))))) # label(fact_1777_norm__eq__zero) # label(axiom) # label(non_clause).  [assumption].
7.67/7.69	4188 (all N ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),N),zero_zero(int))) -> hAPP(int,int,zfact,N) = one_one(int)) & (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),N),zero_zero(int))) -> hAPP(int,int,zfact,N) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),N),hAPP(int,int,zfact,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),N),one_one(int))))))) # label(fact_827_zfact_Osimps) # label(axiom) # label(non_clause).  [assumption].
7.67/7.69	4189 (all X_1 (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),zOdd)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X_1)) -> hAPP(int,int,number_number_of(int),min_1) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,number_number_of(int),min_1)),hAPP(int,nat,nat_1,X_1))))) # label(fact_1150_EvenOdd_Oneg__one__odd__power) # label(axiom) # label(non_clause).  [assumption].
7.67/7.69	4190 (all X_1 all Y_1 (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X_1),Y_1)),zEven)) <-> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Y_1),zEven)) <-> hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),zEven))))) # label(fact_1272_even__diff) # label(axiom) # label(non_clause).  [assumption].
7.67/7.69	4191 (all M all K_4 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),K_4)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,fact_fact(int),M)),hAPP(int,int,fact_fact(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),M),K_4)))))) # label(fact_3196_fact__mono__int__aux) # label(axiom) # label(non_clause).  [assumption].
7.67/7.69	4192 (all X_a (number_ring(X_a) -> -hBOOL(hAPP(X_a,bool,iszero(X_a),hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,bit1,pls)))))) # label(fact_2621_not__iszero__Numeral1) # label(axiom) # label(non_clause).  [assumption].
7.67/7.69	4193 (all X_a (dense_linorder(X_a) -> (all Z_1 all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)) -> ((all W_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),W_2)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),W_2),Y)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),W_2),Z_1))))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),Z_1))))))) # label(fact_2826_dense__le__bounded) # label(axiom) # label(non_clause).  [assumption].
7.67/7.69	4194 (all X all Y ((Y = zero_zero(nat) -> X = hAPP(nat,nat,hAPP(nat,fun(nat,nat),nat_gcd,X),Y)) & (Y != zero_zero(nat) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),nat_gcd,X),Y) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),nat_gcd,Y),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),X),Y))))) # label(fact_3665_nat__gcd_Osimps) # label(axiom) # label(non_clause).  [assumption].
7.67/7.69	4195 (all Y_1 all X_1 (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),zOdd)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Y_1),zOdd)) -> hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X_1),Y_1)),zOdd))))) # label(fact_970_EvenOdd_Oodd__times__odd) # label(axiom) # label(non_clause).  [assumption].
7.67/7.69	4196 (all X all A_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X),hAPP(int,real,real_1(int),A_1))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(real,int,archimedean_ceiling(real),X)),A_1)))) # label(fact_3368_ceiling__le) # label(axiom) # label(non_clause).  [assumption].
7.67/7.69	4197 (all X all Y (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y),X)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),Y)) -> Y != X)) # label(fact_638_dvd_Oless__imp__neq) # label(axiom) # label(non_clause).  [assumption].
7.67/7.69	4198 (all N all M (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N),M)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,fact_fact(nat),N)),hAPP(nat,nat,fact_fact(nat),M))))) # label(fact_2492_fact__dvd) # label(axiom) # label(non_clause).  [assumption].
7.67/7.69	4199 (all B all A_1 (ti(int,B) != zero_zero(int) | zero_zero(int) != ti(int,A_1) -> one_one(int) = hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_1),hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,A_1),B))),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),B),hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,A_1),B))))) # label(fact_3458_div__zgcd__relprime) # label(axiom) # label(non_clause).  [assumption].
7.67/7.69	4200 (all A_1 all B (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_1),B))))) # label(fact_1034_pos__mod__sign) # label(axiom) # label(non_clause).  [assumption].
7.67/7.69	4201 (all N N = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),zero_zero(nat)),N)) # label(fact_4961_max__0L) # label(axiom) # label(non_clause).  [assumption].
7.67/7.69	4202 (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_813_add__increasing2) # label(axiom) # label(non_clause).  [assumption].
7.67/7.69	4203 (all X_a (real_normed_vector(X_a) -> (all A_1 all R_4 all B hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),R_4),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_1),B)) = hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_1),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),R_4),B))))) # label(fact_4695_scaleR_OscaleR__right) # label(axiom) # label(non_clause).  [assumption].
7.67/7.69	4204 (all X all Y hAPP(complex,complex,cnj,hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),X),Y)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,cnj,X)),hAPP(complex,complex,cnj,Y))) # label(fact_2933_complex__cnj__mult) # label(axiom) # label(non_clause).  [assumption].
7.67/7.69	4205 (all X_a (linordered_field(X_a) -> (all B_1 all A_2 all C_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),B_1),C_1)),A_2)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),C_1)))))))) # label(fact_1738_pos__divide__le__eq) # label(axiom) # label(non_clause).  [assumption].
7.67/7.69	4206 (all N_1 all S (hBOOL(hAPP(fun(fun(int,bool),bool),bool,finite_finite_1(fun(int,bool)),S)) -> ((all X_2 (hBOOL(hAPP(fun(fun(int,bool),bool),bool,hAPP(fun(int,bool),fun(fun(fun(int,bool),bool),bool),member(fun(int,bool)),X_2),S)) -> hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),X_2)))) -> ((all X_2 (hBOOL(hAPP(fun(fun(int,bool),bool),bool,hAPP(fun(int,bool),fun(fun(fun(int,bool),bool),bool),member(fun(int,bool)),X_2),S)) -> N_1 = hAPP(fun(int,bool),nat,finite_card(int),X_2))) -> hAPP(fun(fun(int,bool),bool),nat,hAPP(fun(fun(int,bool),nat),fun(fun(fun(int,bool),bool),nat),big_co1399186613setsum(fun(int,bool),nat),hAPP(nat,fun(fun(int,bool),nat),combk(nat,fun(int,bool)),N_1)),S) = hAPP(fun(fun(int,bool),bool),nat,hAPP(fun(fun(int,bool),nat),fun(fun(fun(int,bool),bool),nat),big_co1399186613setsum(fun(int,bool),nat),finite_card(int)),S))))) # label(fact_4418_card__setsum__aux) # label(axiom) # label(non_clause).  [assumption].
7.67/7.69	4207 (all F all X_1 all L (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),F),X_1),L)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),L)) -> (exists D_3 ((all H_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),H_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),H_1),D_3)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,F,hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),X_1),H_1))),hAPP(real,real,F,X_1)))))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),D_3))))))) # label(fact_2662_DERIV__pos__inc__left) # label(axiom) # label(non_clause).  [assumption].
7.67/7.69	4208 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(real,real,cos,X)))))) # label(fact_2246_cos__ge__zero) # label(axiom) # label(non_clause).  [assumption].
7.67/7.69	4209 (all X all Y all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),Y)) -> (X = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),Y),N) -> hAPP(real,real,hAPP(nat,fun(real,real),root,N),X) = Y)))) # label(fact_2710_real__root__pos__unique) # label(axiom) # label(non_clause).  [assumption].
7.67/7.69	4210 (all B_1 all A_2 all P_4 (hBOOL(hAPP(int,bool,zprime,P_4)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit1,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),P_4)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_2),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),P_4),one_one(int)))) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),B_1),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),wset,A_2),P_4))) -> hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),hAPP(int,int,hAPP(int,fun(int,int),inv,P_4),B_1)),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),wset,A_2),P_4)))))))) # label(fact_828_wset__mem__inv__mem) # label(axiom) # label(non_clause).  [assumption].
7.67/7.69	4211 (all N_1 hAPP(nat,nat,fact_fact(nat),N_1) = hAPP(fun(nat,bool),nat,hAPP(fun(nat,nat),fun(fun(nat,bool),nat),big_co302546470etprod(nat,nat),combi(nat)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),one_one(nat)),N_1))) # label(fact_4541_fact__altdef__nat) # label(axiom) # label(non_clause).  [assumption].
7.67/7.69	4212 (all X_a (zero_neq_one(X_a) -> zero_zero(X_a) != one_one(X_a))) # label(fact_324_zero__neq__one) # label(axiom) # label(non_clause).  [assumption].
7.67/7.69	4213 (all X all Y hAPP(real,real,sin,hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),X),Y)) = hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,cos,Y)),hAPP(real,real,sin,X))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,sin,Y)),hAPP(real,real,cos,X)))) # label(fact_2322_sin__diff2) # label(axiom) # label(non_clause).  [assumption].
7.67/7.69	4214 (all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)) -> (-hBOOL(hAPP(nat,bool,even_odd_even(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),one_one(nat)))) <-> hBOOL(hAPP(nat,bool,even_odd_even(nat),N_1))))) # label(fact_2459_even__num__iff) # label(axiom) # label(non_clause).  [assumption].
7.67/7.69	4215 (all B_1 all A_2 (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),A_2),zOdd)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),B_1),zOdd)) -> hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A_2),B_1)),zEven))))) # label(fact_1364_IntNatAux_Oodd__plus__odd) # label(axiom) # label(non_clause).  [assumption].
7.67/7.69	4216 (all X_b all X_c all X_a combb(X_b,X_c,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))) # label(tsy_c_COMBB_res) # label(axiom) # label(non_clause).  [assumption].
7.67/7.69	4217 (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),A_1),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))))) # label(fact_1855_abs__mult__self) # label(axiom) # label(non_clause).  [assumption].
7.67/7.69	4218 (all X_a (linordered_semidom(X_a) -> (all N all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N))))))) # label(fact_407_zero__less__power) # label(axiom) # label(non_clause).  [assumption].
7.67/7.69	4219 (all X_c all X_b all X_a all P_4 all F all G all Q_2 ((all X_2 all Y_2 (ti(product_prod(X_a,X_b),Q_2) = hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),X_2),Y_2) -> hAPP(X_b,X_c,hAPP(X_a,fun(X_b,X_c),F,X_2),Y_2) = hAPP(X_b,X_c,hAPP(X_a,fun(X_b,X_c),G,X_2),Y_2))) -> (ti(product_prod(X_a,X_b),P_4) = ti(product_prod(X_a,X_b),Q_2) -> hAPP(product_prod(X_a,X_b),X_c,hAPP(fun(X_a,fun(X_b,X_c)),fun(product_prod(X_a,X_b),X_c),product_prod_case(X_a,X_b,X_c),F),P_4) = hAPP(product_prod(X_a,X_b),X_c,hAPP(fun(X_a,fun(X_b,X_c)),fun(product_prod(X_a,X_b),X_c),product_prod_case(X_a,X_b,X_c),G),Q_2)))) # label(fact_4771_split__cong) # label(axiom) # label(non_clause).  [assumption].
7.67/7.69	4220 (all N_1 all Ma (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Ma)) -> (one_one(nat) = N_1 <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),Ma),N_1)),Ma))))) # label(fact_505_dvd__mult__cancel1) # label(axiom) # label(non_clause).  [assumption].
7.67/7.69	4221 (all R_4 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),R_4),one_one(real))),hAPP(int,real,real_1(int),hAPP(real,int,archim2085082626_floor(real),R_4))))) # label(fact_3401_real__of__int__floor__gt__diff__one) # label(axiom) # label(non_clause).  [assumption].
7.67/7.69	4222 (all Z_1 hAPP(real,real,sqrt,hAPP(complex,real,re,hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),Z_1),hAPP(complex,complex,cnj,Z_1)))) = hAPP(complex,real,norm_norm(complex),Z_1)) # label(fact_3013_complex__mod__sqrt__Re__mult__cnj) # label(axiom) # label(non_clause).  [assumption].
7.67/7.69	4223 (all K all P_1 all D_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D_1)) -> ((all X_2 (hBOOL(hAPP(int,bool,P_1,X_2)) -> hBOOL(hAPP(int,bool,P_1,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X_2),D_1))))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),K)) -> (all X_2 (hBOOL(hAPP(int,bool,P_1,X_2)) -> hBOOL(hAPP(int,bool,P_1,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X_2),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K),D_1)))))))))) # label(fact_613_incr__mult__lemma) # label(axiom) # label(non_clause).  [assumption].
7.67/7.69	4224 (all X_b all X_a (ord(X_b) & order(X_a) -> (all C_1 all F all B_1 all A_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_b,X_a,F,B_1)),A_2)) -> (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),C_1),B_1)) -> ((all X_2 all Y_2 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Y_2),X_2)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_b,X_a,F,Y_2)),hAPP(X_b,X_a,F,X_2))))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_b,X_a,F,C_1)),A_2)))))))) # label(fact_2834_xt6) # label(axiom) # label(non_clause).  [assumption].
7.67/7.69	4225 (all X_a (banach(X_a) & real_normed_field(X_a) -> (all X_1 all C_1 all K_3 (hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),times_times(X_a)),C_1)),hAPP(X_a,fun(nat,X_a),power_power(X_a),K_3)))) -> (hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),times_times(X_a)),hAPP(fun(nat,X_a),fun(nat,X_a),diffs(X_a),C_1))),hAPP(X_a,fun(nat,X_a),power_power(X_a),K_3)))) -> (hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),times_times(X_a)),hAPP(fun(nat,X_a),fun(nat,X_a),diffs(X_a),hAPP(fun(nat,X_a),fun(nat,X_a),diffs(X_a),C_1)))),hAPP(X_a,fun(nat,X_a),power_power(X_a),K_3)))) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,norm_norm(X_a),X_1)),hAPP(X_a,real,norm_norm(X_a),K_3))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),hAPP(fun(X_a,fun(nat,X_a)),fun(X_a,X_a),hAPP(fun(fun(nat,X_a),X_a),fun(fun(X_a,fun(nat,X_a)),fun(X_a,X_a)),combb(fun(nat,X_a),X_a,X_a),suminf(X_a)),hAPP(fun(X_a,fun(nat,X_a)),fun(X_a,fun(nat,X_a)),hAPP(fun(fun(nat,X_a),fun(nat,X_a)),fun(fun(X_a,fun(nat,X_a)),fun(X_a,fun(nat,X_a))),combb(fun(nat,X_a),fun(nat,X_a),X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),times_times(X_a)),C_1))),power_power(X_a)))),X_1),hAPP(fun(nat,X_a),X_a,suminf(X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),times_times(X_a)),hAPP(fun(nat,X_a),fun(nat,X_a),diffs(X_a),C_1))),hAPP(X_a,fun(nat,X_a),power_power(X_a),X_1)))))))))))) # label(fact_4124_termdiffs) # label(axiom) # label(non_clause).  [assumption].
7.67/7.69	4226 (all X_a (semiring_div(X_a) -> (all A_1 all B (zero_zero(X_a) != ti(X_a,B) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)),B) = ti(X_a,A_1))))) # label(fact_997_div__mult__self2__is__id) # label(axiom) # label(non_clause).  [assumption].
7.67/7.69	4227 (all M zero_zero(real) = hAPP(real,real,cos,hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),pi),hAPP(nat,real,real_1(nat),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),M))))),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) # label(fact_2287_cos__pi__eq__zero) # label(axiom) # label(non_clause).  [assumption].
7.67/7.69	4228 (all X all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),Y)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),Y)),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),Y)))) # label(fact_1759_real__gt__half__sum) # label(axiom) # label(non_clause).  [assumption].
7.67/7.69	4229 (all M all K_4 all N (one_one(int) = hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),K_4),N) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),K_4),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),M),N))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),K_4),M))))) # label(fact_4391_coprime__dvd__mult__int) # label(axiom) # label(non_clause).  [assumption].
7.67/7.69	4230 (all A_1 all B ti(int,A_1) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_1),B))),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_1),B))) # label(fact_918_zmod__zdiv__equality) # label(axiom) # label(non_clause).  [assumption].
7.67/7.69	4231 (all P_5 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit1,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),P_5)) -> hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),P_5),one_one(int)))),hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),P_5),hAPP(int,int,number_number_of(int),hAPP(int,int,bit1,hAPP(int,int,bit1,pls))))))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),P_5),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),P_5),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))) # label(fact_1200_inv__inv__aux) # label(axiom) # label(non_clause).  [assumption].
7.67/7.69	4232 (all X_a (real_normed_algebra(X_a) -> (all A_1 all A_6 all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_6),B)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_1),A_6)),B)))) # label(fact_885_mult_Odiff__left) # label(axiom) # label(non_clause).  [assumption].
7.67/7.69	4233 (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_1420_Nat__Transfer_Otransfer__nat__int__function__closures_I3_J) # label(axiom) # label(non_clause).  [assumption].
7.67/7.69	4234 (all M all N all P_5 (hBOOL(hAPP(nat,bool,prime,P_5)) -> (zero_zero(nat) != N -> (N = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),P_5),M) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N)))))) # label(fact_3066_prime__factor__lt) # label(axiom) # label(non_clause).  [assumption].
7.67/7.69	4235 (all X all P_5 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),P_5)) -> (hBOOL(hAPP(int,bool,zprime,P_5)) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,X),zero_zero(int)),P_5)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),multInv,P_5),X)),X)),one_one(int)),P_5)))))) # label(fact_855_MultInv__prop2a) # label(axiom) # label(non_clause).  [assumption].
7.67/7.69	4236 (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_327_comm__semiring__class_Odistrib) # label(axiom) # label(non_clause).  [assumption].
7.67/7.69	4237 (all K_4 all N all M hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,suc,M)),N) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_4),N)),M))),N)) # label(fact_1395_mod__mult__self4) # label(axiom) # label(non_clause).  [assumption].
7.67/7.69	4238 (all N_1 all Ma (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),Ma)) -> (hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Ma),N_1) = one_one(int) <-> one_one(int) = ti(int,Ma) & ti(int,N_1) = one_one(int)))) # label(fact_114_pos__zmult__eq__1__iff) # label(axiom) # label(non_clause).  [assumption].
7.67/7.69	4239 (all Z1 all Z2 all W hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),Z1),Z2)),W) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),Z1),W)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),Z2),W))) # label(fact_706_real__add__mult__distrib) # label(axiom) # label(non_clause).  [assumption].
7.67/7.69	4240 (all X_a all X_b all F all A_2 all B_1 (hBOOL(hAPP(product_prod(X_a,X_b),bool,hAPP(fun(X_a,fun(X_b,bool)),fun(product_prod(X_a,X_b),bool),product_prod_case(X_a,X_b,bool),F),hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),A_2),B_1))) -> hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),F,A_2),B_1)))) # label(fact_4043_splitD) # label(axiom) # label(non_clause).  [assumption].
7.67/7.69	4241 (all X_a (dense_linorder(X_a) -> (all A_2 all B_1 all C_1 all D_1 ((hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),B_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C_1),A_2)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_1),D_1))) <-> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastAtMost(X_a),A_2),B_1)),hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastLessThan(X_a),C_1),D_1))))))) # label(fact_4529_atLeastAtMost__subseteq__atLeastLessThan__iff) # label(axiom) # label(non_clause).  [assumption].
7.67/7.69	4242 (all X_a all A_3 (hBOOL(hAPP(fun(fun(X_a,bool),bool),bool,finite_finite_1(fun(X_a,bool)),A_3)) -> ((all M_3 (hBOOL(hAPP(fun(fun(X_a,bool),bool),bool,hAPP(fun(X_a,bool),fun(fun(fun(X_a,bool),bool),bool),member(fun(X_a,bool)),M_3),A_3)) -> hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),M_3)))) -> hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),hAPP(fun(fun(X_a,bool),bool),fun(X_a,bool),complete_Sup_Sup(fun(X_a,bool)),A_3)))))) # label(fact_1829_finite__Union) # label(axiom) # label(non_clause).  [assumption].
7.67/7.69	4243 (all X_a (division_ring(X_a) -> (all A_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),zero_zero(X_a)),A_1) = zero_zero(X_a)))) # label(fact_1658_divide__zero__left) # label(axiom) # label(non_clause).  [assumption].
7.67/7.69	4244 (all X_b (number(X_b) & monoid_mult(X_b) -> (all W hAPP(nat,X_b,hAPP(X_b,fun(nat,X_b),power_power(X_b),hAPP(int,X_b,number_number_of(X_b),W)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(int,X_b,number_number_of(X_b),W)),hAPP(int,X_b,number_number_of(X_b),W))))) # label(fact_168_power2__eq__square__number__of) # label(axiom) # label(non_clause).  [assumption].
7.67/7.69	4245 (all X_a all X_b all S all R_3 (ti(fun(product_prod(X_a,X_b),bool),S) = ti(fun(product_prod(X_a,X_b),bool),R_3) <-> (all X_2 all Xa (hBOOL(hAPP(fun(product_prod(X_a,X_b),bool),bool,hAPP(product_prod(X_a,X_b),fun(fun(product_prod(X_a,X_b),bool),bool),member(product_prod(X_a,X_b)),hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),X_2),Xa)),R_3)) <-> hBOOL(hAPP(fun(product_prod(X_a,X_b),bool),bool,hAPP(product_prod(X_a,X_b),fun(fun(product_prod(X_a,X_b),bool),bool),member(product_prod(X_a,X_b)),hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),X_2),Xa)),S)))))) # label(fact_4338_pred__equals__eq2) # label(axiom) # label(non_clause).  [assumption].
7.67/7.69	4246 (all X hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),X),zero_zero(nat)) = X) # label(fact_3254_gcd__0__nat) # label(axiom) # label(non_clause).  [assumption].
7.67/7.69	4247 (all X_a (linord1117847801e_zero(X_a) -> (all A_2 all B_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),B_1)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),zero_zero(X_a))) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_2)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_1),zero_zero(X_a))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),A_2),B_1)),zero_zero(X_a))))))) # label(fact_1677_divide__less__0__iff) # label(axiom) # label(non_clause).  [assumption].
7.67/7.69	4248 (all X_a (archim1727834104eiling(X_a) -> (all X_1 all Z (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(X_a,int,archim2085082626_floor(X_a),X_1)),Z)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),hAPP(int,X_a,ring_1_of_int(X_a),Z))))))) # label(fact_3592_floor__less__iff) # label(axiom) # label(non_clause).  [assumption].
7.67/7.69	4249 (all N (zero_zero(nat) != N -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)))) # label(fact_540_gr0I) # label(axiom) # label(non_clause).  [assumption].
7.67/7.69	4250 (all P_5 hAPP(product_prod(int,int),product_prod(int,int),normalize,hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),P_5),zero_zero(int))) = hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),zero_zero(int)),one_one(int))) # label(fact_3727_normalize__denom__zero) # label(axiom) # label(non_clause).  [assumption].
7.67/7.69	4251 (all M all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,suc,M)),N) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N))) # label(fact_1241_add__Suc) # label(axiom) # label(non_clause).  [assumption].
7.67/7.69	4252 (all K1 all K2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K1),K2)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,K1)),hAPP(int,int,bit0,K2))))) # label(fact_72_less__eq__int__code_I15_J) # label(axiom) # label(non_clause).  [assumption].
7.67/7.69	4253 (all P_1 all I all K (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),I),K)) -> (hBOOL(hAPP(int,bool,P_1,K)) -> ((all I_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),I_2),K)) -> (hBOOL(hAPP(int,bool,P_1,I_2)) -> hBOOL(hAPP(int,bool,P_1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),I_2),one_one(int))))))) -> hBOOL(hAPP(int,bool,P_1,I)))))) # label(fact_831_int__le__induct) # label(axiom) # label(non_clause).  [assumption].
7.67/7.69	4254 (all X_1 (hAPP(nat,nat,suc,zero_zero(nat)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),X_1),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat)))) <-> -hBOOL(hAPP(nat,bool,even_odd_even(nat),X_1)))) # label(fact_2449_odd__nat__equiv__def) # label(axiom) # label(non_clause).  [assumption].
7.67/7.69	4255 (all X_b all X_a (real_normed_vector(X_b) & real_normed_vector(X_a) -> (all R_1 all F all L_2 all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),L_2),hAPP(X_a,filter(X_a),at(X_a),A_2))) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),R_1)) -> (exists S_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),S_1)) & (all X_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),X_2),A_2))),S_1)) & ti(X_a,A_2) != ti(X_a,X_2) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_b,real,norm_norm(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),hAPP(X_a,X_b,F,X_2)),L_2))),R_1))))))))))) # label(fact_4645_LIM__D) # label(axiom) # label(non_clause).  [assumption].
7.67/7.69	4256 (all K all Ma all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Ma),N_1)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,K)),Ma)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,K)),N_1))))) # label(fact_1342_Suc__mult__le__cancel1) # label(axiom) # label(non_clause).  [assumption].
7.67/7.69	4257 (all A_1 all B all Qr_1 (hBOOL(hAPP(product_prod(int,int),bool,hAPP(int,fun(product_prod(int,int),bool),hAPP(int,fun(int,fun(product_prod(int,int),bool)),divmod_int_rel,hAPP(int,int,uminus_uminus(int),A_1)),hAPP(int,int,uminus_uminus(int),B)),Qr_1)) -> hBOOL(hAPP(product_prod(int,int),bool,hAPP(int,fun(product_prod(int,int),bool),hAPP(int,fun(int,fun(product_prod(int,int),bool)),divmod_int_rel,A_1),B),hAPP(product_prod(int,int),product_prod(int,int),negateSnd,Qr_1))))) # label(fact_3073_divmod__int__rel__neg) # label(axiom) # label(non_clause).  [assumption].
7.67/7.69	4258 (all W (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,number_number_of(int),W))) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),hAPP(int,int,number_number_of(int),W))) -> hAPP(product_prod(int,int),product_prod(int,int),hAPP(int,fun(product_prod(int,int),product_prod(int,int)),adjust,hAPP(int,int,number_number_of(int),W)),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),posDivAlg,one_one(int)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),hAPP(int,int,number_number_of(int),W)))) = hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),posDivAlg,one_one(int)),hAPP(int,int,number_number_of(int),W))) & (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),hAPP(int,int,number_number_of(int),W))) -> hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),posDivAlg,one_one(int)),hAPP(int,int,number_number_of(int),W)) = hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),zero_zero(int)),one_one(int))))) # label(fact_1078_posDivAlg__eqn__1__number__of) # label(axiom) # label(non_clause).  [assumption].
7.67/7.69	4259 (all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(nat,real,real_1(nat),N_1))))) # label(fact_2335_real__of__nat__gt__zero__cancel__iff) # label(axiom) # label(non_clause).  [assumption].
7.67/7.69	4260 (all X_a (metric_space(X_a) -> (all X_3 all L_2 (hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),X_3),L_2),sequentially)) <-> (all R_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),R_2)) -> (exists No all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),No),N_2)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),hAPP(nat,X_a,X_3,N_2)),L_2)),R_2)))))))))) # label(fact_4520_LIMSEQ__def) # label(axiom) # label(non_clause).  [assumption].
7.67/7.69	4261 (all P_1 all N_1 all A_2 all B_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A_2),B_1)) -> hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),B_1),A_2)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),N_1)) = hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(product_prod(real,real),real,product_snd(real,real),hAPP(nat,product_prod(real,real),hAPP(real,fun(nat,product_prod(real,real)),hAPP(real,fun(real,fun(nat,product_prod(real,real))),hAPP(fun(product_prod(real,real),bool),fun(real,fun(real,fun(nat,product_prod(real,real)))),bolzano_bisect,P_1),A_2),B_1),N_1))),hAPP(product_prod(real,real),real,product_fst(real,real),hAPP(nat,product_prod(real,real),hAPP(real,fun(nat,product_prod(real,real)),hAPP(real,fun(real,fun(nat,product_prod(real,real))),hAPP(fun(product_prod(real,real),bool),fun(real,fun(real,fun(nat,product_prod(real,real)))),bolzano_bisect,P_1),A_2),B_1),N_1))))) # label(fact_3128_Bolzano__bisect__diff) # label(axiom) # label(non_clause).  [assumption].
7.67/7.69	4262 (all X_a (comm_monoid_add(X_a) -> (all A_1 ti(X_a,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))))) # label(fact_774_add_Ocomm__neutral) # label(axiom) # label(non_clause).  [assumption].
7.67/7.69	4263 (all X all A_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(real,int,archimedean_ceiling(real),X)),A_1)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X),hAPP(int,real,real_1(int),A_1))))) # label(fact_3369_ceiling__le__real) # label(axiom) # label(non_clause).  [assumption].
7.67/7.69	4264 (all X_a (real_normed_vector(X_a) -> (all B zero_zero(X_a) = hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),zero_zero(real)),B)))) # label(fact_4710_scaleR_Ozero__left) # label(axiom) # label(non_clause).  [assumption].
7.67/7.69	4265 (all X_a (field_inverse_zero(X_a) & number(X_a) -> (all A_2 all B_1 all W_1 ((hAPP(int,X_a,number_number_of(X_a),W_1) = zero_zero(X_a) -> zero_zero(X_a) = ti(X_a,A_2)) & (zero_zero(X_a) != hAPP(int,X_a,number_number_of(X_a),W_1) -> ti(X_a,B_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),hAPP(int,X_a,number_number_of(X_a),W_1))) <-> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),B_1),hAPP(int,X_a,number_number_of(X_a),W_1)) = ti(X_a,A_2))))) # label(fact_1723_eq__divide__eq__number__of1) # label(axiom) # label(non_clause).  [assumption].
7.67/7.69	4266 (all A_1 all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,real_1(nat),A_1)),X)) -> hAPP(real,nat,natceiling,hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),X),hAPP(nat,real,real_1(nat),A_1))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(real,nat,natceiling,X)),A_1))) # label(fact_2350_natceiling__subtract) # label(axiom) # label(non_clause).  [assumption].
7.67/7.69	4267 (all X -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,exp(real),X)),zero_zero(real)))) # label(fact_2565_not__exp__le__zero) # label(axiom) # label(non_clause).  [assumption].
7.67/7.69	4268 (all X_a (division_ring(X_a) -> (all B all A_1 all C (zero_zero(X_a) != ti(X_a,C) -> (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),C) = ti(X_a,B) -> ti(X_a,A_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),B),C)))))) # label(fact_1692_divide__eq__imp) # label(axiom) # label(non_clause).  [assumption].
7.67/7.69	4269 (all A_1 all B ((-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),zero_zero(int))) -> (-(ti(int,B) = zero_zero(int) | ti(int,A_1) = zero_zero(int)) -> hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),norm_frac,A_1),B) = hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_1),hAPP(int,int,hAPP(int,fun(int,int),int_gcd,A_1),B))),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),B),hAPP(int,int,hAPP(int,fun(int,int),int_gcd,A_1),B)))) & (ti(int,B) = zero_zero(int) | ti(int,A_1) = zero_zero(int) -> hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),zero_zero(int)),one_one(int)) = hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),norm_frac,A_1),B))) & (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),zero_zero(int))) -> hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),norm_frac,hAPP(int,int,uminus_uminus(int),A_1)),hAPP(int,int,uminus_uminus(int),B)) = hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),norm_frac,A_1),B)))) # label(fact_3925_norm__frac_Osimps) # label(axiom) # label(non_clause).  [assumption].
7.67/7.69	4270 (all X all Q_3 all N all R_4 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),Q_3),N)),R_4) = X -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),R_4)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),R_4),N)) -> -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),N),X)))))) # label(fact_732_divides__div__not) # label(axiom) # label(non_clause).  [assumption].
7.67/7.69	4271 (all X_b all X_a (real_normed_vector(X_b) & topological_space(X_a) -> (all R_1 all G all L all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),G),L),hAPP(X_a,filter(X_a),at(X_a),A_2))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(fun(X_a,X_b),fun(X_a,X_b),hAPP(fun(X_b,X_b),fun(fun(X_a,X_b),fun(X_a,X_b)),combb(X_b,X_b,X_a),hAPP(real,fun(X_b,X_b),scaleR_scaleR(X_b),R_1)),G)),hAPP(X_b,X_b,hAPP(real,fun(X_b,X_b),scaleR_scaleR(X_b),R_1),L)),hAPP(X_a,filter(X_a),at(X_a),A_2))))))) # label(fact_4734_scaleR__right_OLIM) # label(axiom) # label(non_clause).  [assumption].
7.67/7.69	4272 (all X_1 all Y_1 (hBOOL(hAPP(nat,bool,even_odd_even(nat),X_1)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Y_1)) <-> hBOOL(hAPP(nat,bool,even_odd_even(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),X_1),Y_1))))) # label(fact_2451_even__power__nat) # label(axiom) # label(non_clause).  [assumption].
7.67/7.69	4273 (all X_a (real_algebra_1(X_a) -> (all X hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(real,X_a,of_real(X_a),X)) = hAPP(real,X_a,of_real(X_a),hAPP(real,real,uminus_uminus(real),X))))) # label(fact_2795_of__real__minus) # label(axiom) # label(non_clause).  [assumption].
7.67/7.69	4274 (all X hAPP(nat,nat,fact_fact(nat),hAPP(nat,nat,suc,X)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,X)),hAPP(nat,nat,fact_fact(nat),X))) # label(fact_2491_Fact_Ofact__Suc) # label(axiom) # label(non_clause).  [assumption].
7.67/7.69	4275 (all K_4 all L_4 all I_1 all J_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_1),J_2)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_4),L_4)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_1),K_4)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J_2),L_4)))))) # label(fact_576_add__le__mono) # label(axiom) # label(non_clause).  [assumption].
7.67/7.69	4276 (all X_a (archim1727834104eiling(X_a) -> (all X all Z_1 hAPP(X_a,int,archimedean_ceiling(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),X),hAPP(int,X_a,ring_1_of_int(X_a),Z_1))) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(X_a,int,archimedean_ceiling(X_a),X)),Z_1)))) # label(fact_3599_ceiling__diff__of__int) # label(axiom) # label(non_clause).  [assumption].
7.67/7.69	4277 (all X_a (real_n2089651433ebra_1(X_a) -> (all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,norm_norm(X_a),X_1)),one_one(real))) -> hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),hAPP(X_a,fun(nat,X_a),power_power(X_a),X_1)),zero_zero(X_a)),sequentially)))))) # label(fact_4487_LIMSEQ__power__zero) # label(axiom) # label(non_clause).  [assumption].
7.67/7.69	4278 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),one_one(real)),X)),hAPP(real,real,exp(real),X))))) # label(fact_2618_exp__ge__add__one__self__aux) # label(axiom) # label(non_clause).  [assumption].
7.67/7.69	4279 (all N hAPP(real,real,tan,hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,real_1(nat),N)),pi)) = zero_zero(real)) # label(fact_2344_tan__npi) # label(axiom) # label(non_clause).  [assumption].
7.67/7.69	4280 (all Ta all B_2 all D_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D_2)) -> (all X_2 ((all Xa (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xa),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastAtMost(int),one_one(int)),D_2))) -> (all Xb (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xb),B_2)) -> ti(int,X_2) != hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Xb),Xa))))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X_2),Ta)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X_2),D_2)),Ta))))))) # label(fact_4632_bset_I6_J) # label(axiom) # label(non_clause).  [assumption].
7.67/7.69	4281 (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_95_left__distrib__number__of) # label(axiom) # label(non_clause).  [assumption].
7.67/7.69	4282 (all X_b all X_a (topological_space(X_a) & real_normed_algebra(X_b) -> (all X_1 all G all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),G),zero_zero(X_b)),hAPP(X_a,filter(X_a),at(X_a),A_2))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(fun(X_a,X_b),fun(X_a,X_b),hAPP(fun(X_b,X_b),fun(fun(X_a,X_b),fun(X_a,X_b)),combb(X_b,X_b,X_a),hAPP(X_b,fun(X_b,X_b),times_times(X_b),X_1)),G)),zero_zero(X_b)),hAPP(X_a,filter(X_a),at(X_a),A_2))))))) # label(fact_4574_mult__right_OLIM__zero) # label(axiom) # label(non_clause).  [assumption].
7.67/7.70	4283 (all X_a (ordered_ab_group_add(X_a) -> (all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),B)),hAPP(X_a,X_a,uminus_uminus(X_a),A_1))))))) # label(fact_2029_le__imp__neg__le) # label(axiom) # label(non_clause).  [assumption].
7.67/7.70	4284 (all X_a (division_ring(X_a) -> inverse_inverse(X_a) = ti(fun(X_a,X_a),inverse_inverse(X_a)))) # label(tsy_c_Fields_Oinverse__class_Oinverse_res) # label(axiom) # label(non_clause).  [assumption].
7.67/7.70	4285 (all X_a (ab_group_add(X_a) -> (all A_1 all B hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),A_1)),hAPP(X_a,X_a,uminus_uminus(X_a),B))))) # label(fact_2051_minus__add__distrib) # label(axiom) # label(non_clause).  [assumption].
7.67/7.70	4286 (all X_1 all Y_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,semiring_1_of_nat(int),X_1)),hAPP(nat,int,semiring_1_of_nat(int),Y_1))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X_1),Y_1)))) # label(fact_1299_Nat__Transfer_Otransfer__int__nat__relations_I2_J) # label(axiom) # label(non_clause).  [assumption].
7.67/7.70	4287 (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_433_mult__strict__mono_H) # label(axiom) # label(non_clause).  [assumption].
7.67/7.70	4288 (all X_a all X_b (comm_semiring_1(X_b) -> (all F all A_3 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_3)) -> ((exists X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_3)) & zero_zero(X_b) = hAPP(X_a,X_b,F,X_2))) -> zero_zero(X_b) = hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co302546470etprod(X_a,X_b),F),A_3)))))) # label(fact_3950_setprod__zero) # label(axiom) # label(non_clause).  [assumption].
7.67/7.70	4289 (all X_a all F all A_3 hAPP(fun(X_a,bool),nat,hAPP(fun(X_a,nat),fun(fun(X_a,bool),nat),big_co302546470etprod(X_a,nat),F),A_3) = hAPP(int,nat,nat_1,hAPP(fun(X_a,bool),int,hAPP(fun(X_a,int),fun(fun(X_a,bool),int),big_co302546470etprod(X_a,int),hAPP(fun(X_a,nat),fun(X_a,int),hAPP(fun(nat,int),fun(fun(X_a,nat),fun(X_a,int)),combb(nat,int,X_a),semiring_1_of_nat(int)),F)),A_3))) # label(fact_3943_transfer__nat__int__sum__prod2_I2_J) # label(axiom) # label(non_clause).  [assumption].
7.67/7.70	4290 (all L_4 hAPP(int,int,bit1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),min_1),L_4)) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),min_1),hAPP(int,int,bit0,L_4))) # label(fact_511_diff__bin__simps_I5_J) # label(axiom) # label(non_clause).  [assumption].
7.67/7.70	4291 (all X_a (real_normed_field(X_a) -> (all E_3 all F all X_1 all D_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),F),X_1),D_2)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),F),X_1),E_3)) -> ti(X_a,E_3) = ti(X_a,D_2)))))) # label(fact_2633_DERIV__unique) # label(axiom) # label(non_clause).  [assumption].
7.67/7.70	4292 (all X_a (group_add(X_a) -> (all A_1 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,uminus_uminus(X_a),A_1)),A_1)))) # label(fact_2067_left__minus) # label(axiom) # label(non_clause).  [assumption].
7.67/7.70	4293 (all A_1 all B all P_5 all Q_3 (hAPP(product_prod(int,int),product_prod(int,int),normalize,hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),A_1),B)) = hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),P_5),Q_3) -> hAPP(int,rat,hAPP(int,fun(int,rat),fract,P_5),Q_3) = hAPP(int,rat,hAPP(int,fun(int,rat),fract,A_1),B))) # label(fact_3758_normalize__eq) # label(axiom) # label(non_clause).  [assumption].
7.67/7.70	4294 (all X_a (field(X_a) -> (all A_1 (zero_zero(X_a) != ti(X_a,A_1) -> one_one(X_a) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,inverse_inverse(X_a),A_1)),A_1))))) # label(fact_2580_field__inverse) # label(axiom) # label(non_clause).  [assumption].
7.67/7.70	4295 (all X_b all X_a (topological_space(X_a) & real_normed_vector(X_b) -> (all F all A_2 (hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,X_b),fun(X_a,bool),isCont(X_a,X_b),F),A_2)) -> hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,real),fun(X_a,bool),isCont(X_a,real),hAPP(fun(X_a,X_b),fun(X_a,real),hAPP(fun(X_b,real),fun(fun(X_a,X_b),fun(X_a,real)),combb(X_b,real,X_a),norm_norm(X_b)),F)),A_2)))))) # label(fact_4901_isCont__norm) # label(axiom) # label(non_clause).  [assumption].
7.67/7.70	4296 (all Z_1 hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,uminus_uminus(int),Z_1)),Z_1) = zero_zero(int)) # label(fact_2154_zadd__zminus__inverse2) # label(axiom) # label(non_clause).  [assumption].
7.67/7.70	4297 (all X_a (order(X_a) -> (all N_1 all N_7 all F ((all N_2 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(nat,X_a,F,N_2)),hAPP(nat,X_a,F,hAPP(nat,nat,suc,N_2))))) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_1),N_7)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(nat,X_a,F,N_1)),hAPP(nat,X_a,F,N_7)))))))) # label(fact_1495_lift__Suc__mono__le) # label(axiom) # label(non_clause).  [assumption].
7.67/7.70	4298 (all X_a (archim1727834104eiling(X_a) -> hAPP(X_a,int,archim2085082626_floor(X_a),zero_zero(X_a)) = zero_zero(int))) # label(fact_2863_floor__zero) # label(axiom) # label(non_clause).  [assumption].
7.67/7.70	4299 (all I_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),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),hAPP(nat,nat,suc,I_1))),N)))) # label(fact_1388_diff__Suc__less) # label(axiom) # label(non_clause).  [assumption].
7.67/7.70	4300 (all X_a all X_b (linordered_semidom(X_b) -> (all G all F all A_3 ((all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_3)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_a,X_b,F,X_2)),hAPP(X_a,X_b,G,X_2))) & hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),zero_zero(X_b)),hAPP(X_a,X_b,F,X_2))))) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co302546470etprod(X_a,X_b),F),A_3)),hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co302546470etprod(X_a,X_b),G),A_3))))))) # label(fact_4150_setprod__mono) # label(axiom) # label(non_clause).  [assumption].
7.67/7.70	4301 (all X_a (ring_1(X_a) -> (all B_1 all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_2),ring_1_Ints(X_a))) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),B_1),ring_1_Ints(X_a))) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),B_1)),ring_1_Ints(X_a)))))))) # label(fact_3860_Ints__mult) # label(axiom) # label(non_clause).  [assumption].
7.67/7.70	4302 (all Y all X (zero_zero(real) != hAPP(real,real,cos,X) -> (zero_zero(real) != hAPP(real,real,cos,Y) -> hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),one_one(real)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,tan,X)),hAPP(real,real,tan,Y))) = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,cos,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),Y))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,cos,X)),hAPP(real,real,cos,Y)))))) # label(fact_2269_lemma__tan__add1) # label(axiom) # label(non_clause).  [assumption].
7.67/7.70	4303 (all X_a all X_b all F all A_3 hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),nat_tr1645093318rphism(X_a,X_b),F),A_3))) # label(fact_1177_transfer__morphism__def) # label(axiom) # label(non_clause).  [assumption].
7.67/7.70	4304 (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_783_add__right__mono) # label(axiom) # label(non_clause).  [assumption].
7.67/7.70	4305 (all X_a (monoid_mult(X_a) -> (all A_1 ti(X_a,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)))) # label(fact_802_mult__1__left) # label(axiom) # label(non_clause).  [assumption].
7.67/7.70	4306 (all X_a all X_b (real_normed_field(X_b) -> (all Y_1 all G all A_2 all A_3 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),G),A_2),A_3)) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(X_b,fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(X_b,fun(X_a,X_b)),combc(X_a,X_b,X_b),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,fun(X_b,X_b))),combb(X_b,fun(X_b,X_b),X_a),inverse_divide(X_b)),G)),Y_1)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),inverse_divide(X_b),A_2),Y_1)),A_3)))))) # label(fact_4456_divide_Otendsto) # label(axiom) # label(non_clause).  [assumption].
7.67/7.70	4307 (all X_a (order(X_a) -> (all Z_1 all Y all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Z_1),Y)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z_1),X))))))) # label(fact_1600_xt1_I7_J) # label(axiom) # label(non_clause).  [assumption].
7.67/7.70	4308 (all X_a (linorder(X_a) -> (all A_1 all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),B),A_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),A_1),B)))) # label(fact_4971_min__max_Osup_Ocommute) # label(axiom) # label(non_clause).  [assumption].
7.67/7.70	4309 (all X_1 all Y_1 all Z (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Z)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_1),Y_1)) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),X_1),Z)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),Y_1),Z)))))) # label(fact_710_real__mult__less__iff1) # label(axiom) # label(non_clause).  [assumption].
7.67/7.70	4310 (all N all P_5 (hBOOL(hAPP(nat,bool,prime,P_5)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,P_5),N)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),P_5),N)))) # label(fact_3061_prime__coprime__strong) # label(axiom) # label(non_clause).  [assumption].
7.67/7.70	4311 (all V_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),V_1)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(int,nat,number_number_of(nat),V_1))))) # label(fact_49_less__0__number__of) # label(axiom) # label(non_clause).  [assumption].
7.67/7.70	4312 (all X_a (real_normed_field(X_a) -> (all G all Db all F all X_1 all Da (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),F),X_1),Da)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),G),X_1),Db)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),hAPP(fun(X_a,X_a),fun(X_a,X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,X_a),fun(X_a,X_a)),combs(X_a,X_a,X_a),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,X_a),fun(X_a,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),X_a),times_times(X_a)),F)),G)),X_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Da),hAPP(X_a,X_a,G,X_1))),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Db),hAPP(X_a,X_a,F,X_1)))))))))) # label(fact_3817_DERIV__mult) # label(axiom) # label(non_clause).  [assumption].
7.67/7.70	4313 (all K (hAPP(int,int,bit0,K) = pls <-> pls = ti(int,K))) # label(fact_120_rel__simps_I44_J) # label(axiom) # label(non_clause).  [assumption].
7.67/7.70	4314 (all X all Y hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),X),Y)) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(product_prod(int,int),int,product_fst(int,int),hAPP(nat,product_prod(int,int),hAPP(nat,fun(nat,product_prod(int,int)),bezw,X),Y))),hAPP(nat,int,semiring_1_of_nat(int),X))),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(product_prod(int,int),int,product_snd(int,int),hAPP(nat,product_prod(int,int),hAPP(nat,fun(nat,product_prod(int,int)),bezw,X),Y))),hAPP(nat,int,semiring_1_of_nat(int),Y)))) # label(fact_3211_bezw__aux) # label(axiom) # label(non_clause).  [assumption].
7.67/7.70	4315 (all X_a (semiring_div(X_a) -> (all B all A_1 zero_zero(X_a) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),A_1)),B)))) # label(fact_973_mod__mult__self1__is__0) # label(axiom) # label(non_clause).  [assumption].
7.67/7.70	4316 (all X_a (field(X_a) -> (all N_1 all X_1 (ti(X_a,X_1) != one_one(X_a) -> hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),hAPP(X_a,fun(nat,X_a),power_power(X_a),X_1)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),N_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X_1),N_1)),one_one(X_a))),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),X_1),one_one(X_a))))))) # label(fact_4179_geometric__sum) # label(axiom) # label(non_clause).  [assumption].
7.67/7.70	4317 (all B all A_1 all P_5 (hBOOL(hAPP(int,bool,zprime,P_5)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A_1)) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,B),zero_zero(int)),P_5)) & -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_1),zero_zero(int)),P_5)) -> -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),B)),zero_zero(int)),P_5)))))) # label(fact_280_zcong__zprime__prod__zero__contra) # label(axiom) # label(non_clause).  [assumption].
7.67/7.70	4318 (all A_1 all C hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,suc,A_1)),C) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),A_1),C)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,suc,zero_zero(nat))),C))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),A_1),C)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,suc,zero_zero(nat))),C))),C))) # label(fact_1419_div__Suc) # label(axiom) # label(non_clause).  [assumption].
7.67/7.70	4319 (all Y all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),X)),one_one(real))) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,abs_abs(real),Y)),one_one(real))) -> hAPP(real,real,arctan,hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),Y)),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),one_one(real)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),X),Y)))) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,arctan,X)),hAPP(real,real,arctan,Y))))) # label(fact_1910_arctan__add) # label(axiom) # label(non_clause).  [assumption].
7.67/7.70	4320 (all X_a all X_b all F all G ((all X_2 hAPP(X_a,X_b,G,X_2) = hAPP(X_a,X_b,F,X_2)) -> ti(fun(X_a,X_b),F) = ti(fun(X_a,X_b),G))) # label(fact_75_ext) # label(axiom) # label(non_clause).  [assumption].
7.67/7.70	4321 (all X_b all X_a (ordere142940540dd_abs(X_a) -> (all F all A_3 hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co1399186613setsum(X_b,X_a),hAPP(fun(X_b,X_a),fun(X_b,X_a),hAPP(fun(X_a,X_a),fun(fun(X_b,X_a),fun(X_b,X_a)),combb(X_a,X_a,X_b),abs_abs(X_a)),F)),A_3) = hAPP(X_a,X_a,abs_abs(X_a),hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co1399186613setsum(X_b,X_a),hAPP(fun(X_b,X_a),fun(X_b,X_a),hAPP(fun(X_a,X_a),fun(fun(X_b,X_a),fun(X_b,X_a)),combb(X_a,X_a,X_b),abs_abs(X_a)),F)),A_3))))) # label(fact_4212_abs__setsum__abs) # label(axiom) # label(non_clause).  [assumption].
7.67/7.70	4322 (all X_a (linorder(X_a) -> ord_min(X_a) = hAPP(fun(X_a,fun(X_a,bool)),fun(X_a,fun(X_a,X_a)),max(X_a),hAPP(fun(X_a,fun(X_a,bool)),fun(X_a,fun(X_a,bool)),combc(X_a,X_a,bool),ord_less_eq(X_a))))) # label(fact_4834_dual__max) # label(axiom) # label(non_clause).  [assumption].
7.67/7.70	4323 (all X_a (real_normed_field(X_a) -> (all X_3 (hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),X_3)) -> hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(fun(nat,X_a),X_a,suminf(X_a),X_3)) = hAPP(fun(nat,X_a),X_a,suminf(X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(X_a,X_a),fun(fun(nat,X_a),fun(nat,X_a)),combb(X_a,X_a,nat),uminus_uminus(X_a)),X_3)))))) # label(fact_3986_suminf__minus) # label(axiom) # label(non_clause).  [assumption].
7.67/7.70	4324 (all X_a (division_ring(X_a) -> (all A_1 (ti(X_a,A_1) != zero_zero(X_a) -> hAPP(X_a,X_a,inverse_inverse(X_a),hAPP(X_a,X_a,inverse_inverse(X_a),A_1)) = ti(X_a,A_1))))) # label(fact_2529_nonzero__inverse__inverse__eq) # label(axiom) # label(non_clause).  [assumption].
7.67/7.70	4325 (all R all S_5 hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),R),S_5) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),R),hAPP(real,real,inverse_inverse(real),S_5))) # label(fact_2564_real__divide__def) # label(axiom) # label(non_clause).  [assumption].
7.67/7.70	4326 (all X_a all A_3 all B_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_3),B_2)) & ti(fun(X_a,bool),A_3) != ti(fun(X_a,bool),B_2) <-> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less(fun(X_a,bool)),A_3),B_2)))) # label(fact_1999_psubset__eq) # label(axiom) # label(non_clause).  [assumption].
7.67/7.70	4327 (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_245_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J) # label(axiom) # label(non_clause).  [assumption].
7.67/7.70	4328 (all A_2 all B_1 (one_one(int) = hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,A_2),B_1) <-> -(exists P_6 (hBOOL(hAPP(int,bool,zprime,P_6)) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),P_6),A_2)) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),P_6),B_1)))))) # label(fact_3467_zgcd1__iff__no__common__primedivisor) # label(axiom) # label(non_clause).  [assumption].
7.67/7.70	4329 (all N all M hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N)))) # label(fact_569_le__add2) # label(axiom) # label(non_clause).  [assumption].
7.67/7.70	4330 (all U all X hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),U),U))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),X),X)))) # label(fact_2087_real__minus__mult__self__le) # label(axiom) # label(non_clause).  [assumption].
7.67/7.70	4331 (all X_a (ordere142940540dd_abs(X_a) -> (all A_2 all B_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),A_2)),B_1)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),B_1)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,abs_abs(X_a),A_2)),B_1)))))) # label(fact_2080_abs__le__iff) # label(axiom) # label(non_clause).  [assumption].
7.67/7.70	4332 (all N all M (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),M)) -> (M = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),N) -> N = hAPP(nat,nat,suc,zero_zero(nat))))) # label(fact_1384_mn__eq__m__one) # label(axiom) # label(non_clause).  [assumption].
7.67/7.70	4333 (all M all I_1 all J_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),J_2)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J_2),M))))) # label(fact_557_trans__less__add1) # label(axiom) # label(non_clause).  [assumption].
7.67/7.70	4334 (all X_a (archim1727834104eiling(X_a) -> (all Z_1 hAPP(X_a,int,archimedean_ceiling(X_a),hAPP(int,X_a,ring_1_of_int(X_a),Z_1)) = ti(int,Z_1)))) # label(fact_3564_ceiling__of__int) # label(axiom) # label(non_clause).  [assumption].
7.67/7.70	4335 (all X_a (division_ring(X_a) -> (all A_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),one_one(X_a)),A_1) = hAPP(X_a,X_a,inverse_inverse(X_a),A_1)))) # label(fact_2560_inverse__eq__divide) # label(axiom) # label(non_clause).  [assumption].
7.67/7.70	4336 (all X_a (linorder(X_a) -> (all A_1 all B all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),A_1),B)),X)) -> -(hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),X)) -> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),X))))))) # label(fact_4975_min__max_Ole__supE) # label(axiom) # label(non_clause).  [assumption].
7.67/7.70	4337 (all X_a (linordered_idom(X_a) -> (all X_1 all W_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X_1),hAPP(int,nat,number_number_of(nat),W_1))),zero_zero(X_a))) <-> -hBOOL(hAPP(nat,bool,even_odd_even(nat),hAPP(int,nat,number_number_of(nat),W_1))) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),zero_zero(X_a))))))) # label(fact_2456_power__less__zero__eq__number__of) # label(axiom) # label(non_clause).  [assumption].
7.67/7.70	4338 (all X_a (ordered_ring(X_a) -> (all A_2 all E_2 all C_1 all B_1 all D_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),E_2)),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B_1),E_2)),D_1))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),B_1),A_2)),E_2)),D_1))))))) # label(fact_503_less__add__iff2) # label(axiom) # label(non_clause).  [assumption].
7.67/7.70	4339 (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_260_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J) # label(axiom) # label(non_clause).  [assumption].
7.67/7.70	4340 (all M all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,suc,M)),N) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),M),N))),N)) # label(fact_1253_mod__Suc__eq__Suc__mod) # label(axiom) # label(non_clause).  [assumption].
7.67/7.70	4341 (all V ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V),pls)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),V)),one_one(nat)) = one_one(nat)) & (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V),pls)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),V)),one_one(nat)) = hAPP(int,nat,number_number_of(nat),hAPP(int,int,succ,V))))) # label(fact_1535_nat__number__of__add__1) # label(axiom) # label(non_clause).  [assumption].
7.67/7.70	4342 (all Y all X (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),Y),X)) -> hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),X),Y)) = hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,abs_abs(int),X)),hAPP(int,int,abs_abs(int),Y)))) # label(fact_1936_abs__div) # label(axiom) # label(non_clause).  [assumption].
7.67/7.70	4343 (all V_3 ((hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V_3))) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,suc,zero_zero(nat))),hAPP(int,nat,number_number_of(nat),V_3)) = hAPP(nat,nat,suc,zero_zero(nat))) & (-hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V_3))) -> hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),one_one(int)),hAPP(int,int,number_number_of(int),V_3))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,suc,zero_zero(nat))),hAPP(int,nat,number_number_of(nat),V_3))))) # label(fact_1498_one__mod__nat__number__of) # label(axiom) # label(non_clause).  [assumption].
7.67/7.70	4344 (all R_4 all A_1 hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(real,complex,of_real(complex),R_4)),hAPP(real,complex,cis,A_1)) = hAPP(real,complex,hAPP(real,fun(real,complex),rcis,R_4),A_1)) # label(fact_3173_rcis__def) # label(axiom) # label(non_clause).  [assumption].
7.67/7.70	4345 (all X all N all Y (hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),X),N) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),Y),N) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Y),X)) -> (exists Q_4 hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Y),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N),Q_4)) = X)))) # label(fact_1172_nat__mod__eq__lemma) # label(axiom) # label(non_clause).  [assumption].
7.67/7.70	4346 (all B_1 all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X_1)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(real,fun(real,real),log,B_1)),X_1),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),one_one(real)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,ln,B_1)),X_1)))))) # label(fact_3904_DERIV__log) # label(axiom) # label(non_clause).  [assumption].
7.67/7.70	4347 (all X_a (linord1117847801e_zero(X_a) -> (all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),Y)) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),hAPP(X_a,X_a,abs_abs(X_a),X)),Y) = hAPP(X_a,X_a,abs_abs(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),X),Y)))))) # label(fact_1884_abs__div__pos) # label(axiom) # label(non_clause).  [assumption].
7.67/7.70	4348 (all X_a all X_b (real_n2089651433ebra_1(X_b) & metric_space(X_a) -> (all A_2 all K all L_2 (ti(X_a,L_2) != ti(X_a,K) -> -hBOOL(hAPP(filter(X_b),bool,hAPP(X_a,fun(filter(X_b),bool),hAPP(fun(X_b,X_a),fun(X_a,fun(filter(X_b),bool)),tendsto(X_b,X_a),hAPP(X_a,fun(X_b,X_a),combk(X_a,X_b),K)),L_2),hAPP(X_b,filter(X_b),at(X_b),A_2))))))) # label(fact_4559_LIM__const__not__eq) # label(axiom) # label(non_clause).  [assumption].
7.67/7.70	4349 (all Ma all N_1 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),N_1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),Ma) <-> N_1 = Ma))) # label(fact_746_nat__mult__eq__cancel1) # label(axiom) # label(non_clause).  [assumption].
7.67/7.70	4350 (all K_4 all L_4 hAPP(int,rat,hAPP(int,fun(int,rat),fract,K_4),L_4) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),hAPP(int,rat,ring_1_of_int(rat),K_4)),hAPP(int,rat,ring_1_of_int(rat),L_4))) # label(fact_3746_Fract__of__int__quotient) # label(axiom) # label(non_clause).  [assumption].
7.67/7.70	4351 (all D all A_1 all B (hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),D),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),B)) = one_one(int) -> one_one(int) = hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),D),A_1))) # label(fact_4383_coprime__lmult__int) # label(axiom) # label(non_clause).  [assumption].
7.67/7.70	4352 (all A_1 hAPP(real,complex,hAPP(real,fun(real,complex),rcis,zero_zero(real)),A_1) = zero_zero(complex)) # label(fact_3168_rcis__zero__mod) # label(axiom) # label(non_clause).  [assumption].
7.67/7.70	4353 (all X_a (real_normed_vector(X_a) -> (all Y_3 all B_1 all X_3 all A_2 (hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),X_3),A_2),sequentially)) -> (hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),Y_3),B_1),sequentially)) -> hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),plus_plus(X_a)),X_3)),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(X_a,X_a),fun(fun(nat,X_a),fun(nat,X_a)),combb(X_a,X_a,nat),uminus_uminus(X_a)),Y_3))),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),hAPP(X_a,X_a,uminus_uminus(X_a),B_1))),sequentially))))))) # label(fact_4438_LIMSEQ__add__minus) # label(axiom) # label(non_clause).  [assumption].
7.67/7.70	4354 (all A_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),zero_zero(nat)),A_2)) <-> A_2 = zero_zero(nat))) # label(fact_891_gcd__lcm__complete__lattice__nat_Otop__unique) # label(axiom) # label(non_clause).  [assumption].
7.67/7.70	4355 (all F ((all N_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(nat,real,F,N_2)))) -> (hBOOL(hAPP(fun(nat,real),bool,summable(real),F)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(fun(nat,real),real,suminf(real),F)))))) # label(fact_4073_suminf__0__le) # label(axiom) # label(non_clause).  [assumption].
7.67/7.70	4356 (all X_a (semiring_div(X_a) -> (all A_1 all B all C hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),B),C))),C) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)),C)))) # label(fact_928_mod__mult__right__eq) # label(axiom) # label(non_clause).  [assumption].
7.67/7.70	4357 (all X_a all X_b (ordered_ab_group_add(X_b) -> (all I all F all Sa (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),Sa)) -> ((all I_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),I_2),Sa)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),zero_zero(X_b)),hAPP(X_a,X_b,F,I_2))))) -> (zero_zero(X_b) = hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),F),Sa) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),I),Sa)) -> zero_zero(X_b) = hAPP(X_a,X_b,F,I)))))))) # label(fact_4300_setsum__nonneg__0) # label(axiom) # label(non_clause).  [assumption].
7.67/7.70	4358 (all A_2 all B_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B_1),zero_zero(int))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A_2)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_2),B_1)),zero_zero(int)))))) # label(fact_982_neg__imp__zdiv__neg__iff) # label(axiom) # label(non_clause).  [assumption].
7.67/7.70	4359 (all L all U_1 hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),L),U_1)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,U_1)),L)) # label(fact_4571_card__atLeastAtMost) # label(axiom) # label(non_clause).  [assumption].
7.67/7.70	4360 (all X_a (real_normed_vector(X_a) -> (all K all X_3 (hBOOL(hAPP(fun(nat,X_a),bool,bseq(X_a),X_3)) -> hBOOL(hAPP(fun(nat,X_a),bool,bseq(X_a),hAPP(fun(nat,nat),fun(nat,X_a),hAPP(fun(nat,X_a),fun(fun(nat,nat),fun(nat,X_a)),combb(nat,X_a,nat),X_3),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),K)))))))) # label(fact_3825_Bseq__ignore__initial__segment) # label(axiom) # label(non_clause).  [assumption].
7.67/7.70	4361 (all X_a (linord1117847801e_zero(X_a) & number(X_a) -> (all B_1 all W_1 all A_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),B_1),hAPP(int,X_a,number_number_of(X_a),W_1))),A_2)) <-> (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(int,X_a,number_number_of(X_a),W_1))) -> (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(int,X_a,number_number_of(X_a),W_1)),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),A_2))) & (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(int,X_a,number_number_of(X_a),W_1)),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),hAPP(int,X_a,number_number_of(X_a),W_1))),B_1)))) & (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(int,X_a,number_number_of(X_a),W_1))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),hAPP(int,X_a,number_number_of(X_a),W_1))))))))) # label(fact_1755_divide__le__eq__number__of1) # label(axiom) # label(non_clause).  [assumption].
7.67/7.70	4362 (all X (-hBOOL(hAPP(nat,bool,even_odd_even(nat),X)) -> X = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat)))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),X),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat)))))))) # label(fact_2460_odd__nat__div__two__times__two__plus__one) # label(axiom) # label(non_clause).  [assumption].
7.67/7.70	4363 (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_323_mult__zero__left) # label(axiom) # label(non_clause).  [assumption].
7.67/7.70	4364 (all X_a (ordere142940540dd_abs(X_a) -> (all A_1 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(X_a,X_a,abs_abs(X_a),A_1))),zero_zero(X_a)))))) # label(fact_2096_abs__minus__le__zero) # label(axiom) # label(non_clause).  [assumption].
7.67/7.70	4365 (all K_4 hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),K_4),min_1) = hAPP(int,int,pred,K_4)) # label(fact_2907_add__Min__right) # label(axiom) # label(non_clause).  [assumption].
7.67/7.70	4366 (all X_b all X_a (topological_space(X_b) & real_normed_vector(X_a) -> (all F all L_2 all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),L_2),hAPP(X_a,filter(X_a),at(X_a),A_2))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(fun(X_a,X_a),fun(X_a,X_b),hAPP(fun(X_a,X_b),fun(fun(X_a,X_a),fun(X_a,X_b)),combb(X_a,X_b,X_a),F),hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2))),L_2),hAPP(X_a,filter(X_a),at(X_a),zero_zero(X_a)))))))) # label(fact_4580_LIM__offset__zero) # label(axiom) # label(non_clause).  [assumption].
7.67/7.70	4367 (all N hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(nat,real,real_1(nat),hAPP(nat,nat,fact_fact(nat),N))))) # label(fact_2431_real__of__nat__fact__gt__zero) # label(axiom) # label(non_clause).  [assumption].
7.67/7.70	4368 (all X_a (semiring_div(X_a) -> (all N all Y all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),Y),X)) -> hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),X),Y)),N) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),N)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),Y),N)))))) # label(fact_1006_div__power) # label(axiom) # label(non_clause).  [assumption].
7.67/7.70	4369 (all X_b all X_a (topological_space(X_a) & real_normed_vector(X_b) -> (all G all Ma all F all L all X_1 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),L),hAPP(X_a,filter(X_a),at(X_a),X_1))) -> (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),G),Ma),hAPP(X_a,filter(X_a),at(X_a),X_1))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(fun(X_a,X_b),fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,X_b)),combs(X_a,X_b,X_b),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,fun(X_b,X_b))),combb(X_b,fun(X_b,X_b),X_a),plus_plus(X_b)),F)),hAPP(fun(X_a,X_b),fun(X_a,X_b),hAPP(fun(X_b,X_b),fun(fun(X_a,X_b),fun(X_a,X_b)),combb(X_b,X_b,X_a),uminus_uminus(X_b)),G))),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),L),hAPP(X_b,X_b,uminus_uminus(X_b),Ma))),hAPP(X_a,filter(X_a),at(X_a),X_1)))))))) # label(fact_4587_LIM__add__minus) # label(axiom) # label(non_clause).  [assumption].
7.67/7.70	4370 (all B zero_zero(int) = hAPP(int,int,hAPP(int,fun(int,int),div_div(int),zero_zero(int)),B)) # label(fact_951_zdiv__zero) # label(axiom) # label(non_clause).  [assumption].
7.67/7.70	4371 (all X_a (archim1727834104eiling(X_a) -> (all X all Z_1 hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(X_a,int,archim2085082626_floor(X_a),X)),Z_1) = hAPP(X_a,int,archim2085082626_floor(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),X),hAPP(int,X_a,ring_1_of_int(X_a),Z_1)))))) # label(fact_3598_floor__diff__of__int) # label(axiom) # label(non_clause).  [assumption].
7.67/7.70	4372 (all X_a hAPP(product_prod(int,int),X_a,abs_Frac(X_a),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),one_one(int)),one_one(int))) = one_frac(X_a)) # label(fact_3684_Nitpick_Oone__frac__def) # label(axiom) # label(non_clause).  [assumption].
7.67/7.70	4373 (all N all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),hAPP(nat,real,real_1(nat),N))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(real,nat,natfloor,X)),N))))) # label(fact_2356_less__natfloor) # label(axiom) # label(non_clause).  [assumption].
7.67/7.70	4374 (all X_a (ring_char_0(X_a) -> (all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_2),ring_1_Ints(X_a))) -> (zero_zero(X_a) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),A_2) <-> ti(X_a,A_2) = zero_zero(X_a)))))) # label(fact_3886_Ints__double__eq__0__iff) # label(axiom) # label(non_clause).  [assumption].
7.67/7.70	4375 (all A_1 all B hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),B),A_1) = hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),A_1),B)) # label(fact_4363_gcd__commute__int) # label(axiom) # label(non_clause).  [assumption].
7.67/7.70	4376 (all X_a (real_n2089651433ebra_1(X_a) -> (all N hAPP(X_a,real,norm_norm(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),N)) = hAPP(nat,real,semiring_1_of_nat(real),N)))) # label(fact_1775_norm__of__nat) # label(axiom) # label(non_clause).  [assumption].
7.67/7.70	4377 (all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),hAPP(nat,nat,suc,zero_zero(nat))),N) = hAPP(nat,nat,suc,zero_zero(nat))) # label(fact_1354_power__Suc__0) # label(axiom) # label(non_clause).  [assumption].
7.67/7.70	4378 (all X_a (monoid_mult(X_a) -> (all A_1 hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),one_one(nat)) = ti(X_a,A_1)))) # label(fact_351_power__one__right) # label(axiom) # label(non_clause).  [assumption].
7.67/7.70	4379 (all X_a (archim1727834104eiling(X_a) -> (all R_4 hAPP(real,int,archimedean_ceiling(real),hAPP(int,real,real_1(int),hAPP(X_a,int,archim2085082626_floor(X_a),R_4))) = hAPP(X_a,int,archim2085082626_floor(X_a),R_4)))) # label(fact_3357_ceiling__floor) # label(axiom) # label(non_clause).  [assumption].
7.67/7.70	4380 (all X_b (monoid_mult(X_b) & number(X_b) -> (all V all W ((-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),W))) -> one_one(X_b) = hAPP(nat,X_b,hAPP(X_b,fun(nat,X_b),power_power(X_b),hAPP(int,X_b,number_number_of(X_b),V)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,W)))) & (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),W))) -> hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(int,X_b,number_number_of(X_b),V)),hAPP(nat,X_b,hAPP(X_b,fun(nat,X_b),power_power(X_b),hAPP(int,X_b,number_number_of(X_b),V)),hAPP(int,nat,number_number_of(nat),W)))),hAPP(nat,X_b,hAPP(X_b,fun(nat,X_b),power_power(X_b),hAPP(int,X_b,number_number_of(X_b),V)),hAPP(int,nat,number_number_of(nat),W))) = hAPP(nat,X_b,hAPP(X_b,fun(nat,X_b),power_power(X_b),hAPP(int,X_b,number_number_of(X_b),V)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,W)))))))) # label(fact_3905_power__number__of__odd__number__of) # label(axiom) # label(non_clause).  [assumption].
7.67/7.70	4381 (all X_a (linorder(X_a) -> (all B all A_1 all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),X)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),X)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),A_1),B)),X))))))) # label(fact_4978_min__max_Ole__supI) # label(axiom) # label(non_clause).  [assumption].
7.67/7.70	4382 (all X_a (linorder(X_a) -> (all X_1 all Y_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),Y_1)) <-> ti(X_a,Y_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X_1),Y_1))))) # label(fact_4984_min__max_Ole__iff__sup) # label(axiom) # label(non_clause).  [assumption].
7.67/7.70	4383 (exists K_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),K_2)) & (all X_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,norm_norm(real),hAPP(complex,real,im,X_2))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(complex,real,norm_norm(complex),X_2)),K_2)))))) # label(fact_2988_Im_Ononneg__bounded) # label(axiom) # label(non_clause).  [assumption].
7.67/7.70	4384 (all X_a (semiring_div(X_a) -> (all A_1 all C all B (zero_zero(X_a) != ti(X_a,B) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),A_1),B)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),C))),B))))) # label(fact_1040_div__mult__self2) # label(axiom) # label(non_clause).  [assumption].
7.67/7.70	4385 (all X_1 all N_1 all Y_1 (hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),X_1),N_1) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),Y_1),N_1) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),N_1),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X_1),Y_1))))) # label(fact_993_zmod__eq__dvd__iff) # label(axiom) # label(non_clause).  [assumption].
7.67/7.70	4386 (all P_1 ((all X_2 exists D_3 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),D_3)) & (all A_4 all B_4 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_2),B_4)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),B_4),A_4)),D_3)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A_4),X_2)) -> hBOOL(hAPP(product_prod(real,real),bool,P_1,hAPP(real,product_prod(real,real),hAPP(real,fun(real,product_prod(real,real)),product_Pair(real,real),A_4),B_4))))))) & (all A_4 all B_4 all C_4 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B_4),C_4)) & hBOOL(hAPP(product_prod(real,real),bool,P_1,hAPP(real,product_prod(real,real),hAPP(real,fun(real,product_prod(real,real)),product_Pair(real,real),A_4),B_4))) & hBOOL(hAPP(product_prod(real,real),bool,P_1,hAPP(real,product_prod(real,real),hAPP(real,fun(real,product_prod(real,real)),product_Pair(real,real),B_4),C_4))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A_4),B_4)) -> hBOOL(hAPP(product_prod(real,real),bool,P_1,hAPP(real,product_prod(real,real),hAPP(real,fun(real,product_prod(real,real)),product_Pair(real,real),A_4),C_4))))) -> (all A_4 all B_4 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A_4),B_4)) -> hBOOL(hAPP(product_prod(real,real),bool,P_1,hAPP(real,product_prod(real,real),hAPP(real,fun(real,product_prod(real,real)),product_Pair(real,real),A_4),B_4))))))) # label(fact_3210_lemma__BOLZANO2) # label(axiom) # label(non_clause).  [assumption].
7.67/7.70	4387 (all X_a (ord(X_a) -> ord_atMost(X_a) = ti(fun(X_a,fun(X_a,bool)),ord_atMost(X_a)))) # label(tsy_c_SetInterval_Oord__class_OatMost_res) # label(axiom) # label(non_clause).  [assumption].
7.67/7.70	4388 (all N all M (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),N),M)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),N),M)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),M),zero_zero(int))))) # label(fact_420_zdvd__bounds) # label(axiom) # label(non_clause).  [assumption].
7.67/7.70	4389 (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_371_comm__mult__left__mono) # label(axiom) # label(non_clause).  [assumption].
7.67/7.70	4390 (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_372_mult__left__mono) # label(axiom) # label(non_clause).  [assumption].
7.67/7.70	4391 (all X all Y (hAPP(nat,nat,suc,X) = hAPP(nat,nat,suc,Y) -> X = Y)) # label(fact_1213_Suc__inject) # label(axiom) # label(non_clause).  [assumption].
7.67/7.70	4392 (all K_4 hAPP(int,int,uminus_uminus(int),hAPP(int,int,bit1,K_4)) = hAPP(int,int,bit1,hAPP(int,int,pred,hAPP(int,int,uminus_uminus(int),K_4)))) # label(fact_2906_minus__Bit1) # label(axiom) # label(non_clause).  [assumption].
7.67/7.70	4393 (all N all M -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,semiring_1_of_nat(int),N)),hAPP(int,int,uminus_uminus(int),hAPP(nat,int,semiring_1_of_nat(int),M))))) # label(fact_2156_not__int__zless__negative) # label(axiom) # label(non_clause).  [assumption].
7.67/7.70	4394 (all X_a (real_normed_vector(X_a) -> (all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(X_a,real,norm_norm(X_a),X_1))) <-> zero_zero(X_a) != ti(X_a,X_1))))) # label(fact_1787_zero__less__norm__iff) # label(axiom) # label(non_clause).  [assumption].
7.67/7.70	4395 (all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Y)) -> hAPP(real,real,cos,hAPP(complex,real,arg,hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,zero_zero(real)),Y))) = zero_zero(real))) # label(fact_2752_cos__arg__i__mult__zero__pos) # label(axiom) # label(non_clause).  [assumption].
7.67/7.70	4396 (all X_a all X_b all C_1 all P_4 ((all A_4 all B_4 (hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),A_4),B_4) = ti(product_prod(X_a,X_b),P_4) -> hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),C_1,A_4),B_4)))) -> hBOOL(hAPP(product_prod(X_a,X_b),bool,hAPP(fun(X_a,fun(X_b,bool)),fun(product_prod(X_a,X_b),bool),product_prod_case(X_a,X_b,bool),C_1),P_4)))) # label(fact_4061_splitI2) # label(axiom) # label(non_clause).  [assumption].
7.67/7.70	4397 (all X_a (boolean_algebra(X_a) -> (all X_1 all Y_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y_1),X_1)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),X_1)),hAPP(X_a,X_a,uminus_uminus(X_a),Y_1))))))) # label(fact_2956_compl__le__compl__iff) # label(axiom) # label(non_clause).  [assumption].
7.67/7.70	4398 (all N hAPP(real,real,cos,hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),hAPP(nat,real,real_1(nat),N))),pi)) = one_one(real)) # label(fact_2393_cos__2npi) # label(axiom) # label(non_clause).  [assumption].
7.67/7.70	4399 (all M all N hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N)),M))) # label(fact_669_Nat_Odiff__le__self) # label(axiom) # label(non_clause).  [assumption].
7.67/7.70	4400 (all P_1 ((exists X_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X_2)) & hBOOL(hAPP(int,bool,P_1,X_2)))) <-> (exists X_2 hBOOL(hAPP(int,bool,P_1,hAPP(nat,int,semiring_1_of_nat(int),X_2)))))) # label(fact_1296_transfer__int__nat__quantifiers_I2_J) # label(axiom) # label(non_clause).  [assumption].
7.67/7.70	4401 (all A_2 all B_1 all Ma (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),Ma),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A_2),B_1))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_2),B_1),Ma)))) # label(fact_500_zcong__def) # label(axiom) # label(non_clause).  [assumption].
7.67/7.70	4402 (all X_a all G all A_3 hAPP(fun(X_a,bool),real,hAPP(fun(X_a,real),fun(fun(X_a,bool),real),big_co1399186613setsum(X_a,real),hAPP(fun(X_a,complex),fun(X_a,real),hAPP(fun(complex,real),fun(fun(X_a,complex),fun(X_a,real)),combb(complex,real,X_a),re),G)),A_3) = hAPP(complex,real,re,hAPP(fun(X_a,bool),complex,hAPP(fun(X_a,complex),fun(fun(X_a,bool),complex),big_co1399186613setsum(X_a,complex),G),A_3))) # label(fact_4249_Re_Osetsum) # label(axiom) # label(non_clause).  [assumption].
7.67/7.70	4403 (all X hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,sin,hAPP(real,real,uminus_uminus(real),X))),hAPP(real,real,sin,X))),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,cos,hAPP(real,real,uminus_uminus(real),X))),hAPP(real,real,cos,X))),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) = zero_zero(real)) # label(fact_2400_sin__cos__minus) # label(axiom) # label(non_clause).  [assumption].
7.67/7.70	4404 (all X all A_1 hAPP(real,real,hAPP(real,fun(real,real),powr,X),A_1) != zero_zero(real)) # label(fact_3322_powr__not__zero) # label(axiom) # label(non_clause).  [assumption].
7.67/7.70	4405 (all X_a (real_normed_vector(X_a) -> (exists K_2 all A_4 all B_4 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_4),B_4))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,norm_norm(real),A_4)),hAPP(X_a,real,norm_norm(X_a),B_4))),K_2)))))) # label(fact_4759_scaleR_Obounded) # label(axiom) # label(non_clause).  [assumption].
7.67/7.70	4406 (all X_5 all Y_4 hAPP(real,real,sqrt,hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),one_one(real)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),X_5),hAPP(real,real,sqrt,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X_5),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),Y_4),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) = hAPP(real,real,sin,hAPP(real,real,arccos,hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),X_5),hAPP(real,real,sqrt,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X_5),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),Y_4),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))))) # label(fact_2404_sin__arccos__lemma1) # label(axiom) # label(non_clause).  [assumption].
7.67/7.70	4407 (all K_4 all I_1 all J_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),I_1),J_2)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K_4)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(nat,int,semiring_1_of_nat(int),K_4)),I_1)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(nat,int,semiring_1_of_nat(int),K_4)),J_2)))))) # label(fact_1402_zmult__zless__mono2__lemma) # label(axiom) # label(non_clause).  [assumption].
7.67/7.70	4408 (all C_1 all D_1 all A_2 all B_1 all Ma (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_2),B_1),Ma)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,C_1),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_2),D_1)),Ma)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,C_1),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B_1),D_1)),Ma))))) # label(fact_356_zcong__zmult__prop1) # label(axiom) # label(non_clause).  [assumption].
7.67/7.70	4409 (all X_a (order(X_a) -> (all X_3 (hBOOL(hAPP(fun(nat,X_a),bool,monoseq(X_a),X_3)) <-> (all N_2 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(nat,X_a,X_3,hAPP(nat,nat,suc,N_2))),hAPP(nat,X_a,X_3,N_2)))) | (all N_2 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(nat,X_a,X_3,N_2)),hAPP(nat,X_a,X_3,hAPP(nat,nat,suc,N_2))))))))) # label(fact_3922_monoseq__Suc) # label(axiom) # label(non_clause).  [assumption].
7.67/7.70	4410 (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)) -> ti(X_a,X) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),Y))))) # label(fact_4979_min__max_Osup__absorb1) # label(axiom) # label(non_clause).  [assumption].
7.67/7.70	4411 (all X_a (inverse(X_a) & real_normed_vector(X_a) -> ti(fun(X_a,fun(X_a,X_a)),inverse_divide(X_a)) = inverse_divide(X_a))) # label(tsy_c_Fields_Oinverse__class_Odivide_0_res) # label(axiom) # label(non_clause).  [assumption].
7.67/7.70	4412 (all X_a (comm_monoid_add(X_a) -> (all F all Ma all K all N_1 hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),hAPP(fun(nat,nat),fun(nat,X_a),hAPP(fun(nat,X_a),fun(fun(nat,nat),fun(nat,X_a)),combb(nat,X_a,nat),F),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),K))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),Ma),N_1)) = hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Ma),K)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_1),K)))))) # label(fact_4543_setsum__shift__bounds__cl__nat__ivl) # label(axiom) # label(non_clause).  [assumption].
7.67/7.70	4413 (all X_a (field(X_a) -> (all A_1 all N all B (zero_zero(X_a) != ti(X_a,B) -> hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),A_1),B)),N) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),B),N)))))) # label(fact_1697_nonzero__power__divide) # label(axiom) # label(non_clause).  [assumption].
7.67/7.70	4414 (all X_a (linord1117847801e_zero(X_a) -> (all A_2 all B_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),B_1)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_2)) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),zero_zero(X_a))) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_1),zero_zero(X_a))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),A_2),B_1))))))) # label(fact_1676_zero__less__divide__iff) # label(axiom) # label(non_clause).  [assumption].
7.67/7.70	4415 (all K all P_1 all D_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D_1)) -> ((all X_2 (hBOOL(hAPP(int,bool,P_1,X_2)) -> hBOOL(hAPP(int,bool,P_1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X_2),D_1))))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),K)) -> (all X_2 (hBOOL(hAPP(int,bool,P_1,X_2)) -> hBOOL(hAPP(int,bool,P_1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X_2),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K),D_1)))))))))) # label(fact_611_decr__mult__lemma) # label(axiom) # label(non_clause).  [assumption].
7.67/7.70	4416 (all T_2 all T_1 (comple44059174attice(T_1) -> comple44059174attice(fun(T_2,T_1)))) # label(arity_fun___Complete__Lattice_Ocomplete__lattice) # label(axiom) # label(non_clause).  [assumption].
7.67/7.70	4417 (all X_a (ring_1(X_a) -> (all X hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),X)),one_one(X_a)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X),one_one(X_a))),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),X),one_one(X_a)))))) # label(fact_731_real__squared__diff__one__factored) # label(axiom) # label(non_clause).  [assumption].
7.67/7.70	4418 (all T_2 all T_1 (preorder(T_1) -> preorder(fun(T_2,T_1)))) # label(arity_fun___Orderings_Opreorder) # label(axiom) # label(non_clause).  [assumption].
7.67/7.70	4419 (all X_a (monoid_mult(X_a) -> (all A_1 all M all N hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),M)),N) = hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),N))))) # label(fact_349_power__mult) # label(axiom) # label(non_clause).  [assumption].
7.67/7.70	4420 (all X_a (real_algebra_1(X_a) -> one_one(X_a) = hAPP(real,X_a,of_real(X_a),one_one(real)))) # label(fact_2786_of__real__1) # label(axiom) # label(non_clause).  [assumption].
7.67/7.70	4421 (all X_a (comm_monoid_add(X_a) -> (all F all Ma all N_1 hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),hAPP(fun(nat,nat),fun(nat,X_a),hAPP(fun(nat,X_a),fun(fun(nat,nat),fun(nat,X_a)),combb(nat,X_a,nat),F),suc)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),Ma),N_1)) = hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),hAPP(nat,nat,suc,Ma)),hAPP(nat,nat,suc,N_1)))))) # label(fact_4187_setsum__shift__bounds__Suc__ivl) # label(axiom) # label(non_clause).  [assumption].
7.67/7.70	4422 (all X_a (ring_1(X_a) -> hAPP(int,X_a,ring_1_of_int(X_a),one_one(int)) = one_one(X_a))) # label(fact_3585_of__int__1) # label(axiom) # label(non_clause).  [assumption].
7.67/7.70	4423 (all X all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> hAPP(real,real,hAPP(nat,fun(real,real),root,N),hAPP(real,real,inverse_inverse(real),X)) = hAPP(real,real,inverse_inverse(real),hAPP(real,real,hAPP(nat,fun(real,real),root,N),X)))) # label(fact_2690_real__root__inverse) # label(axiom) # label(non_clause).  [assumption].
7.67/7.70	4424 (all K all L (hAPP(int,int,bit0,K) = hAPP(int,int,bit0,L) <-> ti(int,L) = ti(int,K))) # label(fact_92_rel__simps_I48_J) # label(axiom) # label(non_clause).  [assumption].
7.67/7.70	4425 (all N hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,uminus_uminus(int),hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,N)))))) # label(fact_2173_neg__zminus__int) # label(axiom) # label(non_clause).  [assumption].
7.67/7.70	4426 (all X all P_5 (hBOOL(hAPP(int,bool,zprime,P_5)) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),P_5),X)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),X),hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),P_5),one_one(int))))),one_one(int)),P_5))))) # label(fact_1151_Little__Fermat) # label(axiom) # label(non_clause).  [assumption].
7.67/7.70	4427 (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_387_mult__neg__neg) # label(axiom) # label(non_clause).  [assumption].
7.67/7.70	4428 (all A_2 hBOOL(hAPP(complex,bool,hAPP(fun(complex,complex),fun(complex,bool),isCont(complex,complex),cnj),A_2))) # label(fact_4892_cnj_OisCont) # label(axiom) # label(non_clause).  [assumption].
7.67/7.70	4429 (all X_a (field_inverse_zero(X_a) & number(X_a) -> (all B_1 all C_1 all W_1 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),B_1),C_1) = hAPP(int,X_a,number_number_of(X_a),W_1) <-> (zero_zero(X_a) != ti(X_a,C_1) -> ti(X_a,B_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),W_1)),C_1)) & (zero_zero(X_a) = ti(X_a,C_1) -> hAPP(int,X_a,number_number_of(X_a),W_1) = zero_zero(X_a)))))) # label(fact_1725_divide__eq__eq__number__of) # label(axiom) # label(non_clause).  [assumption].
7.67/7.70	4430 (all F all N_1 hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),F)),hAPP(real,fun(nat,real),power_power(real),zero_zero(real)))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),hAPP(nat,nat,suc,zero_zero(nat))),N_1)) = zero_zero(real)) # label(fact_4192_sumr__one__lb__realpow__zero) # label(axiom) # label(non_clause).  [assumption].
7.67/7.70	4431 (all X_a all F all A_3 ((all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_3)) -> hBOOL(hAPP(int,bool,nat_is_nat,hAPP(X_a,int,F,X_2))))) -> hAPP(fun(X_a,bool),int,hAPP(fun(X_a,int),fun(fun(X_a,bool),int),big_co1399186613setsum(X_a,int),F),A_3) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(fun(X_a,bool),nat,hAPP(fun(X_a,nat),fun(fun(X_a,bool),nat),big_co1399186613setsum(X_a,nat),hAPP(fun(X_a,int),fun(X_a,nat),hAPP(fun(int,nat),fun(fun(X_a,int),fun(X_a,nat)),combb(int,nat,X_a),nat_1),F)),A_3)))) # label(fact_4862_transfer__int__nat__sum__prod2_I1_J) # label(axiom) # label(non_clause).  [assumption].
7.67/7.70	4432 (all X all Y hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),hAPP(int,nat,nat_1,hAPP(int,int,abs_abs(int),X))),hAPP(int,nat,nat_1,hAPP(int,int,abs_abs(int),Y)))) = hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),X),Y)) # label(fact_4407_gcd__int__def) # label(axiom) # label(non_clause).  [assumption].
7.67/7.70	4433 (all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_1),one_one(real))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,ln,X_1)),zero_zero(real)))))) # label(fact_1949_ln__less__zero__iff) # label(axiom) # label(non_clause).  [assumption].
7.67/7.70	4434 (all X_a (group_add(X_a) -> (all A_1 all B (zero_zero(X_a) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B) -> ti(X_a,B) = hAPP(X_a,X_a,uminus_uminus(X_a),A_1))))) # label(fact_2069_minus__unique) # label(axiom) # label(non_clause).  [assumption].
7.67/7.70	4435 (all X_a all A_3 (-hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_3)) -> zero_zero(nat) = hAPP(fun(X_a,bool),nat,finite_card(X_a),A_3))) # label(fact_1823_card__infinite) # label(axiom) # label(non_clause).  [assumption].
7.67/7.70	4436 (all X_b all X_c all X_a all X_d all X_e all F all G all P_4 hAPP(product_prod(X_d,X_e),X_a,hAPP(fun(X_d,fun(X_e,X_a)),fun(product_prod(X_d,X_e),X_a),product_prod_case(X_d,X_e,X_a),hAPP(fun(X_d,fun(X_e,product_prod(X_b,X_c))),fun(X_d,fun(X_e,X_a)),hAPP(fun(fun(X_e,product_prod(X_b,X_c)),fun(X_e,X_a)),fun(fun(X_d,fun(X_e,product_prod(X_b,X_c))),fun(X_d,fun(X_e,X_a))),combb(fun(X_e,product_prod(X_b,X_c)),fun(X_e,X_a),X_d),hAPP(fun(product_prod(X_b,X_c),X_a),fun(fun(X_e,product_prod(X_b,X_c)),fun(X_e,X_a)),combb(product_prod(X_b,X_c),X_a,X_e),hAPP(fun(X_b,fun(X_c,X_a)),fun(product_prod(X_b,X_c),X_a),product_prod_case(X_b,X_c,X_a),F))),G)),P_4) = hAPP(product_prod(X_b,X_c),X_a,hAPP(fun(X_b,fun(X_c,X_a)),fun(product_prod(X_b,X_c),X_a),product_prod_case(X_b,X_c,X_a),F),hAPP(product_prod(X_d,X_e),product_prod(X_b,X_c),hAPP(fun(X_d,fun(X_e,product_prod(X_b,X_c))),fun(product_prod(X_d,X_e),product_prod(X_b,X_c)),product_prod_case(X_d,X_e,product_prod(X_b,X_c)),G),P_4))) # label(fact_4005_split__twice) # label(axiom) # label(non_clause).  [assumption].
7.67/7.70	4437 (all X_a (division_ring(X_a) -> (all A_1 all B (hAPP(X_a,X_a,inverse_inverse(X_a),A_1) = hAPP(X_a,X_a,inverse_inverse(X_a),B) -> (zero_zero(X_a) != ti(X_a,A_1) -> (zero_zero(X_a) != ti(X_a,B) -> ti(X_a,A_1) = ti(X_a,B))))))) # label(fact_2531_nonzero__inverse__eq__imp__eq) # label(axiom) # label(non_clause).  [assumption].
7.67/7.70	4438 (all X_b all X_a all X_c (comm_monoid_add(X_c) -> (all F all R_3 all T_3 all S (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),S)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),T_3)) -> hAPP(fun(X_a,bool),X_c,hAPP(fun(X_a,X_c),fun(fun(X_a,bool),X_c),big_co1399186613setsum(X_a,X_c),hAPP(fun(X_a,fun(X_b,bool)),fun(X_a,X_c),hAPP(fun(X_a,fun(fun(X_b,bool),X_c)),fun(fun(X_a,fun(X_b,bool)),fun(X_a,X_c)),combs(X_a,fun(X_b,bool),X_c),hAPP(fun(X_a,fun(X_b,X_c)),fun(X_a,fun(fun(X_b,bool),X_c)),hAPP(fun(fun(X_b,X_c),fun(fun(X_b,bool),X_c)),fun(fun(X_a,fun(X_b,X_c)),fun(X_a,fun(fun(X_b,bool),X_c))),combb(fun(X_b,X_c),fun(fun(X_b,bool),X_c),X_a),big_co1399186613setsum(X_b,X_c)),F)),hAPP(fun(X_a,fun(X_b,bool)),fun(X_a,fun(X_b,bool)),hAPP(fun(fun(X_b,bool),fun(X_b,bool)),fun(fun(X_a,fun(X_b,bool)),fun(X_a,fun(X_b,bool))),combb(fun(X_b,bool),fun(X_b,bool),X_a),collect(X_b)),hAPP(fun(X_a,fun(X_b,bool)),fun(X_a,fun(X_b,bool)),hAPP(fun(fun(X_b,bool),fun(X_b,bool)),fun(fun(X_a,fun(X_b,bool)),fun(X_a,fun(X_b,bool))),combb(fun(X_b,bool),fun(X_b,bool),X_a),hAPP(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),combs(X_b,bool,bool),hAPP(fun(X_b,bool),fun(X_b,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fconj),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(fun(X_b,bool),bool)),fun(fun(X_b,bool),fun(X_b,bool)),combc(X_b,fun(X_b,bool),bool),member(X_b)),T_3)))),R_3)))),S) = hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co1399186613setsum(X_b,X_c),hAPP(fun(X_b,fun(X_a,bool)),fun(X_b,X_c),hAPP(fun(X_b,fun(fun(X_a,bool),X_c)),fun(fun(X_b,fun(X_a,bool)),fun(X_b,X_c)),combs(X_b,fun(X_a,bool),X_c),hAPP(fun(X_b,fun(X_a,X_c)),fun(X_b,fun(fun(X_a,bool),X_c)),hAPP(fun(fun(X_a,X_c),fun(fun(X_a,bool),X_c)),fun(fun(X_b,fun(X_a,X_c)),fun(X_b,fun(fun(X_a,bool),X_c))),combb(fun(X_a,X_c),fun(fun(X_a,bool),X_c),X_b),big_co1399186613setsum(X_a,X_c)),hAPP(fun(X_a,fun(X_b,X_c)),fun(X_b,fun(X_a,X_c)),combc(X_a,X_b,X_c),F))),hAPP(fun(X_b,fun(X_a,bool)),fun(X_b,fun(X_a,bool)),hAPP(fun(fun(X_a,bool),fun(X_a,bool)),fun(fun(X_b,fun(X_a,bool)),fun(X_b,fun(X_a,bool))),combb(fun(X_a,bool),fun(X_a,bool),X_b),collect(X_a)),hAPP(fun(X_b,fun(X_a,bool)),fun(X_b,fun(X_a,bool)),hAPP(fun(fun(X_a,bool),fun(X_a,bool)),fun(fun(X_b,fun(X_a,bool)),fun(X_b,fun(X_a,bool))),combb(fun(X_a,bool),fun(X_a,bool),X_b),hAPP(fun(X_a,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,bool)),combs(X_a,bool,bool),hAPP(fun(X_a,bool),fun(X_a,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,fun(bool,bool))),combb(bool,fun(bool,bool),X_a),fconj),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(X_a,bool)),combc(X_a,fun(X_a,bool),bool),member(X_a)),S)))),hAPP(fun(X_a,fun(X_b,bool)),fun(X_b,fun(X_a,bool)),combc(X_a,X_b,bool),R_3))))),T_3)))))) # label(fact_4188_setsum__setsum__restrict) # label(axiom) # label(non_clause).  [assumption].
7.67/7.71	4439 (all N (hBOOL(hAPP(nat,bool,even_odd_even(nat),N)) -> (exists X_2 hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),N),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),X_2)))) # label(fact_2479_even__square) # label(axiom) # label(non_clause).  [assumption].
7.67/7.71	4440 (all X_a (real_normed_field(X_a) -> (all Y_3 all F all X_1 all X_3 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),F),X_1),X_3)) -> (ti(X_a,Y_3) = ti(X_a,X_3) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),F),X_1),Y_3))))))) # label(fact_2634_DERIV__cong) # label(axiom) # label(non_clause).  [assumption].
7.67/7.71	4441 (all X_a all C_1 all A_3 all B_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_3),B_2))) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),A_3)))) # label(fact_1964_DiffD1) # label(axiom) # label(non_clause).  [assumption].
7.67/7.71	4442 (all X_a all S all T_3 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),T_3)) -> (-hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),S)) -> -hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),S),T_3)))))) # label(fact_3036_Diff__infinite__finite) # label(axiom) # label(non_clause).  [assumption].
7.67/7.71	4443 (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_761_add__neg__nonpos) # label(axiom) # label(non_clause).  [assumption].
7.67/7.71	4444 (all D_1 all K all P_4 (hBOOL(hAPP(nat,bool,prime,P_4)) -> ((exists I_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_2),K)) & hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),P_4),I_2) = D_1)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),D_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),P_4),K)))))) # label(fact_3068_divides__primepow) # label(axiom) # label(non_clause).  [assumption].
7.67/7.71	4445 (all X_a (ordere236663937imp_le(X_a) -> (all X all Y all Z_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X),Z_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Y),Z_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),Y)),Z_1)))) # label(fact_4805_min__add__distrib__left) # label(axiom) # label(non_clause).  [assumption].
7.67/7.71	4446 (all N hAPP(nat,nat,suc,N) != N) # label(fact_1217_n__not__Suc__n) # label(axiom) # label(non_clause).  [assumption].
7.67/7.71	4447 (all X hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,uminus_uminus(real),hAPP(complex,real,im,X))),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(complex,real,re,X)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(complex,real,im,X)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) = hAPP(complex,real,im,hAPP(complex,complex,inverse_inverse(complex),X))) # label(fact_2992_complex__Im__inverse) # label(axiom) # label(non_clause).  [assumption].
7.67/7.71	4448 (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].
7.67/7.71	4449 (all X_b all X_a all B_1 all F all X_1 all A_3 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_3)) -> (hAPP(X_a,X_b,F,X_1) = ti(X_b,B_1) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),B_1),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),A_3)))))) # label(fact_3639_rev__image__eqI) # label(axiom) # label(non_clause).  [assumption].
7.67/7.71	4450 (all X_b all X_a all A_2 all B_1 all A_8 all B_7 (ti(X_a,A_2) = ti(X_a,A_8) & ti(X_b,B_7) = ti(X_b,B_1) <-> hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),A_8),B_7) = hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),A_2),B_1))) # label(fact_3136_Pair__eq) # label(axiom) # label(non_clause).  [assumption].
7.67/7.71	4451 (all Z_1 zero_zero(real) = hAPP(complex,real,im,hAPP(real,complex,of_real(complex),Z_1))) # label(fact_2974_Im__complex__of__real) # label(axiom) # label(non_clause).  [assumption].
7.67/7.71	4452 (all N (-hBOOL(hAPP(nat,bool,even_odd_even(nat),N)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),one_one(nat))),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),N),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))) # label(fact_2472_lemma__not__even__div2) # label(axiom) # label(non_clause).  [assumption].
7.67/7.71	4453 (all F all L all C_1 (hBOOL(hAPP(filter(real),bool,hAPP(real,fun(filter(real),bool),hAPP(fun(real,real),fun(real,fun(filter(real),bool)),tendsto(real,real),F),L),hAPP(real,filter(real),at(real),C_1))) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),L),zero_zero(real))) -> (exists R_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),R_2)) & (all X_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),C_1),X_2))),R_2)) & X_2 != C_1 -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,F,X_2)),zero_zero(real)))))))))) # label(fact_4629_LIM__fun__less__zero) # label(axiom) # label(non_clause).  [assumption].
7.67/7.71	4454 (all X_a (division_ring(X_a) -> (all A_1 (zero_zero(X_a) != ti(X_a,A_1) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,inverse_inverse(X_a),A_1)),A_1) = one_one(X_a))))) # label(fact_2581_left__inverse) # label(axiom) # label(non_clause).  [assumption].
7.67/7.71	4455 (all X_a (real_normed_vector(X_a) -> (all A_1 all X hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_1),X)) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,abs_abs(real),A_1)),hAPP(X_a,real,norm_norm(X_a),X))))) # label(fact_4665_norm__scaleR) # label(axiom) # label(non_clause).  [assumption].
7.67/7.71	4456 (all X hAPP(real,real,sin,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),pi))) = hAPP(real,real,sin,X)) # label(fact_2376_sin__periodic) # label(axiom) # label(non_clause).  [assumption].
7.67/7.71	4457 (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_787_add__less__imp__less__right) # label(axiom) # label(non_clause).  [assumption].
7.67/7.71	4458 (all B all M all A_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_1),M)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),B)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),M)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_1),B),M)) -> ti(int,A_1) = ti(int,B))))))) # label(fact_453_zcong__zless__imp__eq) # label(axiom) # label(non_clause).  [assumption].
7.67/7.71	4459 (all K_4 hAPP(int,rat,hAPP(int,fun(int,rat),fract,K_4),one_one(int)) = hAPP(int,rat,ring_1_of_int(rat),K_4)) # label(fact_3745_Fract__of__int__eq) # label(axiom) # label(non_clause).  [assumption].
7.67/7.71	4460 (all Nat_1 hAPP(nat,nat,size_size(nat),hAPP(nat,nat,suc,Nat_1)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,size_size(nat),Nat_1)),hAPP(nat,nat,suc,zero_zero(nat)))) # label(fact_2921_nat_Osize_I4_J) # label(axiom) # label(non_clause).  [assumption].
7.67/7.71	4461 (all X_a (linordered_semidom(X_a) -> (all N all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),A_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),hAPP(nat,nat,suc,N)))))))) # label(fact_1375_power__gt1) # label(axiom) # label(non_clause).  [assumption].
7.67/7.71	4462 (all M all K_4 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),K_4)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),M)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,fact_fact(int),M)),hAPP(int,int,fact_fact(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),M),one_one(int))),K_4))))))) # label(fact_3200_fact__less__mono__int__aux) # label(axiom) # label(non_clause).  [assumption].
7.67/7.71	4463 (all X_a (cancel_semigroup_add(X_a) -> (all B_1 all A_2 all C_1 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B_1),A_2) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C_1),A_2) <-> ti(X_a,C_1) = ti(X_a,B_1))))) # label(fact_769_add__right__cancel) # label(axiom) # label(non_clause).  [assumption].
7.67/7.71	4464 (all X_a all X_b (linordered_semidom(X_b) -> (all F all A_3 ((all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_3)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),zero_zero(X_b)),hAPP(X_a,X_b,F,X_2))))) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),zero_zero(X_b)),hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co302546470etprod(X_a,X_b),F),A_3))))))) # label(fact_4151_setprod__nonneg) # label(axiom) # label(non_clause).  [assumption].
7.67/7.71	4465 (all A_2 all P_4 (hBOOL(hAPP(int,bool,zprime,P_4)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),P_4)) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_2),zero_zero(int)),P_4)) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),quadRes,P_4),A_2)) -> hAPP(nat,int,semiring_1_of_nat(int),hAPP(fun(fun(int,bool),bool),nat,finite_card(fun(int,bool)),hAPP(int,fun(fun(int,bool),bool),hAPP(int,fun(int,fun(fun(int,bool),bool)),setS,A_2),P_4))) = hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),P_4),one_one(int))),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))))) # label(fact_1603_SetS__card) # label(axiom) # label(non_clause).  [assumption].
7.67/7.71	4466 (all A_2 all P_4 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),P_4)) -> hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),hAPP(fun(fun(int,bool),bool),fun(int,bool),complete_Sup_Sup(fun(int,bool)),hAPP(int,fun(fun(int,bool),bool),hAPP(int,fun(int,fun(fun(int,bool),bool)),setS,A_2),P_4)))))) # label(fact_1652_Union__SetS__finite) # label(axiom) # label(non_clause).  [assumption].
7.67/7.71	4467 (all X_a (group_add(X_a) -> (all A_2 all B_1 (ti(X_a,B_1) = ti(X_a,A_2) <-> zero_zero(X_a) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_2),B_1))))) # label(fact_793_right__minus__eq) # label(axiom) # label(non_clause).  [assumption].
7.67/7.71	4468 (all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),one_one(real)),Y)) -> (exists X_2 (Y = hAPP(real,real,exp(real),X_2) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_2),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),Y),one_one(real)))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X_2)))))) # label(fact_2628_lemma__exp__total) # label(axiom) # label(non_clause).  [assumption].
7.74/7.71	4469 (all X_3 all A_2 (hBOOL(hAPP(filter(nat),bool,hAPP(complex,fun(filter(nat),bool),hAPP(fun(nat,complex),fun(complex,fun(filter(nat),bool)),tendsto(nat,complex),X_3),A_2),sequentially)) -> hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),hAPP(fun(nat,complex),fun(nat,real),hAPP(fun(complex,real),fun(fun(nat,complex),fun(nat,real)),combb(complex,real,nat),re),X_3)),hAPP(complex,real,re,A_2)),sequentially)))) # label(fact_4511_Re_OLIMSEQ) # label(axiom) # label(non_clause).  [assumption].
7.74/7.71	4470 (all R_4 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(int,real,real_1(int),hAPP(real,int,archimedean_ceiling(real),R_4))),one_one(real))),R_4))) # label(fact_3403_real__of__int__ceiling__diff__one__le) # label(axiom) # label(non_clause).  [assumption].
7.74/7.71	4471 (all N hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),N))) # label(fact_470_le0) # label(axiom) # label(non_clause).  [assumption].
7.74/7.71	4472 (all P_5 hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),P_5),one_one(int))),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) = hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),P_5),one_one(int))),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))) # label(fact_1160_Euler_Oaux____2) # label(axiom) # label(non_clause).  [assumption].
7.74/7.71	4473 (all F all N_1 all R_1 hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),N_1))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,real_1(nat),N_1)),R_1)) = hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(real,fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(real,fun(nat,real)),combc(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),minus_minus(real)),F)),R_1)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),N_1))) # label(fact_4176_sumr__diff__mult__const) # label(axiom) # label(non_clause).  [assumption].
7.74/7.71	4474 (all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,number_number_of(real),min_1)),Y)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),Y),one_one(real))) -> (exists X_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),X_2)) & (all Y_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),Y_2)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),Y_2),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) & hAPP(real,real,sin,Y_2) = Y -> Y_2 = X_2)) & hAPP(real,real,sin,X_2) = Y & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_2),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))))))) # label(fact_2405_sin__total) # label(axiom) # label(non_clause).  [assumption].
7.74/7.71	4475 (all M all N (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),M),N)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,fact_fact(int),M)),hAPP(int,int,fact_fact(int),N))))) # label(fact_3181_fact__mono__int) # label(axiom) # label(non_clause).  [assumption].
7.74/7.71	4476 (all Z_1 ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Z_1)) -> ti(int,Z_1) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(int,nat,nat_1,Z_1))) & (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Z_1)) -> zero_zero(int) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(int,nat,nat_1,Z_1))))) # label(fact_1376_int__nat__eq) # label(axiom) # label(non_clause).  [assumption].
7.74/7.71	4477 (all M all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),M),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)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),M),hAPP(nat,nat,suc,hAPP(nat,nat,suc,hAPP(nat,nat,suc,N))))) # label(fact_1438_div__Suc__eq__div__add3) # label(axiom) # label(non_clause).  [assumption].
7.74/7.71	4478 (all N_1 all Ma (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,N_1)),Ma)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),Ma)))) # label(fact_1337_less__eq__Suc__le) # label(axiom) # label(non_clause).  [assumption].
7.74/7.71	4479 (all X_a all F all G all Ma all S ((all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),S)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(X_a,int,F,X_2)),hAPP(X_a,int,G,X_2)),Ma)))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(fun(X_a,bool),int,hAPP(fun(X_a,int),fun(fun(X_a,bool),int),big_co302546470etprod(X_a,int),F),S)),hAPP(fun(X_a,bool),int,hAPP(fun(X_a,int),fun(fun(X_a,bool),int),big_co302546470etprod(X_a,int),G),S)),Ma)))) # label(fact_4419_setprod__same__function__zcong) # label(axiom) # label(non_clause).  [assumption].
7.74/7.71	4480 (all X_b all X_a (metric_space(X_a) & metric_space(X_b) -> (all R_1 all F all L_2 all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),L_2),hAPP(X_a,filter(X_a),at(X_a),A_2))) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),R_1)) -> (exists S_1 ((all X_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),X_2),A_2)),S_1)) & ti(X_a,X_2) != ti(X_a,A_2) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_b,real,hAPP(X_b,fun(X_b,real),dist_dist(X_b),hAPP(X_a,X_b,F,X_2)),L_2)),R_1)))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),S_1))))))))) # label(fact_4651_metric__LIM__D) # label(axiom) # label(non_clause).  [assumption].
7.74/7.71	4481 (all X_a (linord219039673up_add(X_a) -> (all A_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),A_2)),zero_zero(X_a))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),zero_zero(X_a))))))) # label(fact_817_double__add__le__zero__iff__single__add__le__zero) # label(axiom) # label(non_clause).  [assumption].
7.74/7.71	4482 (all P_4 hAPP(product_prod(int,int),product_prod(int,int),hAPP(fun(int,fun(int,product_prod(int,int))),fun(product_prod(int,int),product_prod(int,int)),product_prod_case(int,int,product_prod(int,int)),hAPP(fun(int,fun(int,product_prod(int,int))),fun(int,fun(int,product_prod(int,int))),hAPP(fun(int,fun(fun(int,product_prod(int,int)),fun(int,product_prod(int,int)))),fun(fun(int,fun(int,product_prod(int,int))),fun(int,fun(int,product_prod(int,int)))),combs(int,fun(int,product_prod(int,int)),fun(int,product_prod(int,int))),hAPP(fun(int,fun(product_prod(int,int),product_prod(int,int))),fun(int,fun(fun(int,product_prod(int,int)),fun(int,product_prod(int,int)))),hAPP(fun(fun(product_prod(int,int),product_prod(int,int)),fun(fun(int,product_prod(int,int)),fun(int,product_prod(int,int)))),fun(fun(int,fun(product_prod(int,int),product_prod(int,int))),fun(int,fun(fun(int,product_prod(int,int)),fun(int,product_prod(int,int))))),combb(fun(product_prod(int,int),product_prod(int,int)),fun(fun(int,product_prod(int,int)),fun(int,product_prod(int,int))),int),combb(product_prod(int,int),product_prod(int,int),int)),hAPP(product_prod(int,int),fun(int,fun(product_prod(int,int),product_prod(int,int))),hAPP(fun(int,fun(product_prod(int,int),fun(product_prod(int,int),product_prod(int,int)))),fun(product_prod(int,int),fun(int,fun(product_prod(int,int),product_prod(int,int)))),combc(int,product_prod(int,int),fun(product_prod(int,int),product_prod(int,int))),hAPP(fun(int,bool),fun(int,fun(product_prod(int,int),fun(product_prod(int,int),product_prod(int,int)))),hAPP(fun(bool,fun(product_prod(int,int),fun(product_prod(int,int),product_prod(int,int)))),fun(fun(int,bool),fun(int,fun(product_prod(int,int),fun(product_prod(int,int),product_prod(int,int))))),combb(bool,fun(product_prod(int,int),fun(product_prod(int,int),product_prod(int,int))),int),if(product_prod(int,int))),hAPP(int,fun(int,bool),hAPP(fun(int,fun(int,bool)),fun(int,fun(int,bool)),combc(int,int,bool),fequal(int)),zero_zero(int)))),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),zero_zero(int)),one_one(int))))),hAPP(fun(int,int),fun(int,fun(int,product_prod(int,int))),hAPP(fun(int,fun(int,fun(int,product_prod(int,int)))),fun(fun(int,int),fun(int,fun(int,product_prod(int,int)))),combs(int,int,fun(int,product_prod(int,int))),hAPP(fun(int,fun(int,fun(int,product_prod(int,int)))),fun(int,fun(int,fun(int,product_prod(int,int)))),hAPP(fun(fun(int,fun(int,product_prod(int,int))),fun(int,fun(int,product_prod(int,int)))),fun(fun(int,fun(int,fun(int,product_prod(int,int)))),fun(int,fun(int,fun(int,product_prod(int,int))))),combb(fun(int,fun(int,product_prod(int,int))),fun(int,fun(int,product_prod(int,int))),int),combc(int,int,product_prod(int,int))),hAPP(fun(int,fun(int,int)),fun(int,fun(int,fun(int,product_prod(int,int)))),hAPP(fun(fun(int,int),fun(int,fun(int,product_prod(int,int)))),fun(fun(int,fun(int,int)),fun(int,fun(int,fun(int,product_prod(int,int))))),combb(fun(int,int),fun(int,fun(int,product_prod(int,int))),int),hAPP(fun(int,fun(int,product_prod(int,int))),fun(fun(int,int),fun(int,fun(int,product_prod(int,int)))),combb(int,fun(int,product_prod(int,int)),int),product_Pair(int,int))),hAPP(fun(int,int),fun(int,fun(int,int)),hAPP(fun(int,fun(int,int)),fun(fun(int,int),fun(int,fun(int,int))),combb(int,fun(int,int),int),times_times(int)),sgn_sgn(int))))),abs_abs(int)))),hAPP(rat,product_prod(int,int),quotient_of,P_4)) = hAPP(rat,product_prod(int,int),quotient_of,hAPP(rat,rat,inverse_inverse(rat),P_4))) # label(fact_4033_rat__inverse__code) # label(axiom) # label(non_clause).  [assumption].
7.74/7.71	4483 (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_1565_linorder__neqE) # label(axiom) # label(non_clause).  [assumption].
7.74/7.71	4484 (all A_1 all B all C hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),B),C))),C) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),B)),C)) # label(fact_954_zmod__zmult1__eq) # label(axiom) # label(non_clause).  [assumption].
7.74/7.71	4485 (all X_b all X_a (real_n1866405975lgebra(X_b) & topological_space(X_a) -> (all F all L_2 all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),L_2),hAPP(X_a,filter(X_a),at(X_a),A_2))) -> (ti(X_b,L_2) != zero_zero(X_b) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(fun(X_a,X_b),fun(X_a,X_b),hAPP(fun(X_b,X_b),fun(fun(X_a,X_b),fun(X_a,X_b)),combb(X_b,X_b,X_a),inverse_inverse(X_b)),F)),hAPP(X_b,X_b,inverse_inverse(X_b),L_2)),hAPP(X_a,filter(X_a),at(X_a),A_2)))))))) # label(fact_4588_LIM__inverse) # label(axiom) # label(non_clause).  [assumption].
7.74/7.71	4486 (all X_a (real_normed_vector(X_a) -> (all Y_3 all B_1 all X_3 all A_2 (hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),X_3),A_2),sequentially)) -> (hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),Y_3),B_1),sequentially)) -> hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),plus_plus(X_a)),X_3)),Y_3)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),B_1)),sequentially))))))) # label(fact_4444_LIMSEQ__add) # label(axiom) # label(non_clause).  [assumption].
7.74/7.71	4487 (all X_a (real_algebra(X_a) -> (all A_1 all X all Y hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),Y)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_1),X)),Y)))) # label(fact_4677_mult__scaleR__left) # label(axiom) # label(non_clause).  [assumption].
7.74/7.71	4488 (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,Y) != ti(X_a,X) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X))))))) # label(fact_1581_linorder__cases) # label(axiom) # label(non_clause).  [assumption].
7.74/7.71	4489 (all X_a (division_ring(X_a) -> (all N all A_1 (ti(X_a,A_1) != zero_zero(X_a) -> hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(X_a,X_a,inverse_inverse(X_a),A_1)),N) = hAPP(X_a,X_a,inverse_inverse(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N)))))) # label(fact_2553_nonzero__power__inverse) # label(axiom) # label(non_clause).  [assumption].
7.74/7.71	4490 (all M all N all K_4 hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,M),N)),hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K_4),M)),N)))) # label(fact_3453_zgcd__zdvd__zgcd__zmult) # label(axiom) # label(non_clause).  [assumption].
7.74/7.71	4491 (all P (hBOOL(P) | hBOOL(hAPP(bool,bool,fNot,P)))) # label(help_fNot_2_1_U) # label(axiom) # label(non_clause).  [assumption].
7.74/7.71	4492 (all Y all X (hBOOL(hAPP(int,bool,nat_is_nat,X)) -> (hBOOL(hAPP(int,bool,nat_is_nat,Y)) -> hBOOL(hAPP(int,bool,nat_is_nat,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X),Y)))))) # label(fact_4853_Nat__Transfer_Otransfer__int__nat__function__closures_I1_J) # label(axiom) # label(non_clause).  [assumption].
7.74/7.71	4493 (all A_1 hAPP(real,complex,cis,A_1) = hAPP(real,complex,hAPP(real,fun(real,complex),rcis,one_one(real)),A_1)) # label(fact_3167_cis__rcis__eq) # label(axiom) # label(non_clause).  [assumption].
7.74/7.71	4494 (all K all L (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit0,K)),hAPP(int,int,bit0,L))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),K),L)))) # label(fact_36_rel__simps_I31_J) # label(axiom) # label(non_clause).  [assumption].
7.74/7.71	4495 (all K_4 all L_4 hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),hAPP(int,rat,number_number_of(rat),K_4)),hAPP(int,rat,number_number_of(rat),L_4)) = hAPP(product_prod(int,int),rat,frct,hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),hAPP(int,int,number_number_of(int),K_4)),hAPP(int,int,number_number_of(int),L_4)))) # label(fact_3711_Frct__code__post_I6_J) # label(axiom) # label(non_clause).  [assumption].
7.74/7.71	4496 (all X_a (order(X_a) -> (all X_3 (hBOOL(hAPP(fun(nat,X_a),bool,monoseq(X_a),X_3)) <-> (all M_2 all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_2),N_2)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(nat,X_a,X_3,M_2)),hAPP(nat,X_a,X_3,N_2))))) | (all M_2 all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_2),N_2)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(nat,X_a,X_3,N_2)),hAPP(nat,X_a,X_3,M_2))))))))) # label(fact_3923_monoseq__def) # label(axiom) # label(non_clause).  [assumption].
7.74/7.71	4497 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N)))) # label(fact_565_less__imp__le__nat) # label(axiom) # label(non_clause).  [assumption].
7.74/7.71	4498 (all X_a (division_ring(X_a) -> (all A_1 (zero_zero(X_a) != ti(X_a,A_1) -> one_one(X_a) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),A_1),A_1))))) # label(fact_1695_divide__self) # label(axiom) # label(non_clause).  [assumption].
7.74/7.71	4499 (all B_1 all P_4 all A_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),A_2)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),B_1),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),wset,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A_2),one_one(int))),P_4))) -> hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),B_1),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),wset,A_2),P_4)))))) # label(fact_838_wset__subset) # label(axiom) # label(non_clause).  [assumption].
7.74/7.71	4500 (all X_a (preorder(X_a) -> (all Z_1 all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),Z_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Z_1))))))) # label(fact_1599_order__less__le__trans) # label(axiom) # label(non_clause).  [assumption].
7.74/7.71	4501 (all X_a (archim1804426504_field(X_a) -> (all X exists Z_2 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),hAPP(int,X_a,ring_1_of_int(X_a),Z_2)))))) # label(fact_3625_ex__less__of__int) # label(axiom) # label(non_clause).  [assumption].
7.74/7.71	4502 (all Z_1 (-hBOOL(hAPP(int,bool,nat_neg,Z_1)) -> ti(int,Z_1) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(int,nat,nat_1,Z_1)))) # label(fact_1509_not__neg__nat) # label(axiom) # label(non_clause).  [assumption].
7.74/7.71	4503 (all X_a (comm_semiring_1(X_a) -> (all A_1 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),one_one(X_a)),A_1))))) # label(fact_342_one__dvd) # label(axiom) # label(non_clause).  [assumption].
7.74/7.71	4504 (all A_2 all B_1 (hAPP(int,int,abs_abs(int),A_2) = hAPP(int,int,abs_abs(int),B_1) <-> hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A_2),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),B_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) # label(fact_1980_power2__eq__iff__abs__eq) # label(axiom) # label(non_clause).  [assumption].
7.74/7.71	4505 (all X_a (real_normed_field(X_a) & banach(X_a) -> (all X hAPP(X_a,X_a,exp(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),X)) = hAPP(X_a,X_a,inverse_inverse(X_a),hAPP(X_a,X_a,exp(X_a),X))))) # label(fact_2535_exp__minus) # label(axiom) # label(non_clause).  [assumption].
7.74/7.71	4506 (all I_1 all M all N (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),I_1),hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),M),N))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),I_1),N)))) # label(fact_4366_dvd__gcd__D2__int) # label(axiom) # label(non_clause).  [assumption].
7.74/7.71	4507 (all X_a (group_add(X_a) -> (all A_2 all B_1 (ti(X_a,B_1) = hAPP(X_a,X_a,uminus_uminus(X_a),A_2) <-> hAPP(X_a,X_a,uminus_uminus(X_a),B_1) = ti(X_a,A_2))))) # label(fact_2043_minus__equation__iff) # label(axiom) # label(non_clause).  [assumption].
7.74/7.71	4508 (all N all A_1 hAPP(complex,real,re,hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),hAPP(real,complex,cis,A_1)),N)) = hAPP(real,real,cos,hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,real_1(nat),N)),A_1))) # label(fact_3025_cos__n__Re__cis__pow__n) # label(axiom) # label(non_clause).  [assumption].
7.74/7.71	4509 (all X_a all X_b (real_normed_vector(X_b) -> (all X_3 ((exists N_3 all N_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_b,real,norm_norm(X_b),hAPP(X_a,X_b,X_3,N_2))),hAPP(nat,real,real_1(nat),hAPP(nat,nat,suc,N_3))))) <-> (exists K_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),K_2)) & (all N_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_b,real,norm_norm(X_b),hAPP(X_a,X_b,X_3,N_2))),K_2))))))))) # label(fact_2352_lemma__NBseq__def2) # label(axiom) # label(non_clause).  [assumption].
7.74/7.71	4510 (all X_a all A_3 all B_2 (ti(fun(X_a,bool),A_3) = ti(fun(X_a,bool),B_2) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),B_2),A_3)))) # label(fact_1957_equalityD2) # label(axiom) # label(non_clause).  [assumption].
7.74/7.71	4511 (all X_a all F all A_3 hAPP(nat,real,real_1(nat),hAPP(fun(X_a,bool),nat,hAPP(fun(X_a,nat),fun(fun(X_a,bool),nat),big_co1399186613setsum(X_a,nat),F),A_3)) = hAPP(fun(X_a,bool),real,hAPP(fun(X_a,real),fun(fun(X_a,bool),real),big_co1399186613setsum(X_a,real),hAPP(fun(X_a,nat),fun(X_a,real),hAPP(fun(nat,real),fun(fun(X_a,nat),fun(X_a,real)),combb(nat,real,X_a),real_1(nat)),F)),A_3)) # label(fact_4250_real__of__nat__setsum) # label(axiom) # label(non_clause).  [assumption].
7.74/7.71	4512 (all K all Xa_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,real),fun(fun(real,real),fun(real,real)),combb(real,real,real),cos),hAPP(real,fun(real,real),hAPP(fun(real,fun(real,real)),fun(real,fun(real,real)),combc(real,real,real),plus_plus(real)),K))),Xa_2),hAPP(real,real,uminus_uminus(real),hAPP(real,real,sin,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),Xa_2),K)))))) # label(fact_3814_DERIV__cos__add) # label(axiom) # label(non_clause).  [assumption].
7.74/7.71	4513 (all N hAPP(quickcheck_code_int,int,quickcheck_int_of,hAPP(int,quickcheck_code_int,quickcheck_of_int,N)) = ti(int,N)) # label(fact_3537_int__of__of__int) # label(axiom) # label(non_clause).  [assumption].
7.74/7.71	4514 (all X_a one_frac(X_a) = ti(X_a,one_frac(X_a))) # label(tsy_c_Nitpick_Oone__frac_res) # label(axiom) # label(non_clause).  [assumption].
7.74/7.71	4515 (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_760_add__strict__increasing2) # label(axiom) # label(non_clause).  [assumption].
7.74/7.71	4516 (all X_3 all A_2 (hBOOL(hAPP(complex,bool,hAPP(fun(nat,complex),fun(complex,bool),sums(complex),X_3),A_2)) -> hBOOL(hAPP(real,bool,hAPP(fun(nat,real),fun(real,bool),sums(real),hAPP(fun(nat,complex),fun(nat,real),hAPP(fun(complex,real),fun(fun(nat,complex),fun(nat,real)),combb(complex,real,nat),im),X_3)),hAPP(complex,real,im,A_2))))) # label(fact_4115_Im_Osums) # label(axiom) # label(non_clause).  [assumption].
7.74/7.71	4517 (all X (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X)) -> hAPP(int,real,real_1(int),X) = hAPP(nat,real,real_1(nat),hAPP(int,nat,nat_1,X)))) # label(fact_3394_real__nat__eq__real) # label(axiom) # label(non_clause).  [assumption].
7.74/7.71	4518 (all I_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),I_1)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),hAPP(int,nat,nat_1,I_1))),one_one(nat)) = hAPP(list(int),nat,size_size(list(int)),hAPP(int,list(int),quickc666637781d_zero,I_1)))) # label(fact_3203_length__around__zero) # label(axiom) # label(non_clause).  [assumption].
7.74/7.71	4519 (all X_b all X_a all F all P_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),P_1))) -> hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(fun(X_b,fun(X_a,bool)),fun(X_b,bool),hAPP(fun(fun(X_a,bool),bool),fun(fun(X_b,fun(X_a,bool)),fun(X_b,bool)),combb(fun(X_a,bool),bool,X_b),fEx(X_a)),hAPP(fun(X_a,bool),fun(X_b,fun(X_a,bool)),hAPP(fun(X_b,fun(fun(X_a,bool),fun(X_a,bool))),fun(fun(X_a,bool),fun(X_b,fun(X_a,bool))),combc(X_b,fun(X_a,bool),fun(X_a,bool)),hAPP(fun(X_b,fun(X_a,fun(bool,bool))),fun(X_b,fun(fun(X_a,bool),fun(X_a,bool))),hAPP(fun(fun(X_a,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,bool))),fun(fun(X_b,fun(X_a,fun(bool,bool))),fun(X_b,fun(fun(X_a,bool),fun(X_a,bool)))),combb(fun(X_a,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,bool)),X_b),combs(X_a,bool,bool)),hAPP(fun(X_b,fun(X_a,bool)),fun(X_b,fun(X_a,fun(bool,bool))),hAPP(fun(fun(X_a,bool),fun(X_a,fun(bool,bool))),fun(fun(X_b,fun(X_a,bool)),fun(X_b,fun(X_a,fun(bool,bool)))),combb(fun(X_a,bool),fun(X_a,fun(bool,bool)),X_b),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,fun(bool,bool))),combb(bool,fun(bool,bool),X_a),fconj)),hAPP(fun(X_a,X_b),fun(X_b,fun(X_a,bool)),hAPP(fun(X_b,fun(fun(X_a,X_b),fun(X_a,bool))),fun(fun(X_a,X_b),fun(X_b,fun(X_a,bool))),combc(X_b,fun(X_a,X_b),fun(X_a,bool)),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(fun(X_a,X_b),fun(X_a,bool))),hAPP(fun(fun(X_b,bool),fun(fun(X_a,X_b),fun(X_a,bool))),fun(fun(X_b,fun(X_b,bool)),fun(X_b,fun(fun(X_a,X_b),fun(X_a,bool)))),combb(fun(X_b,bool),fun(fun(X_a,X_b),fun(X_a,bool)),X_b),combb(X_b,bool,X_a)),fequal(X_b))),F)))),P_1))))))) # label(fact_4423_finite__image__set) # label(axiom) # label(non_clause).  [assumption].
7.74/7.71	4520 (all M all N hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,N),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),M),N)) = hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,M),N)) # label(fact_3432_zgcd__eq) # label(axiom) # label(non_clause).  [assumption].
7.74/7.71	4521 (all X_a (linordered_field(X_a) -> (all A_2 all B_1 all C_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),C_1)),B_1)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),B_1),C_1)))))))) # label(fact_1710_pos__less__divide__eq) # label(axiom) # label(non_clause).  [assumption].
7.74/7.71	4522 (all X all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),Y)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),Y),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,sin,Y)),hAPP(real,real,sin,X))))))) # label(fact_2390_sin__monotone__2pi_H) # label(axiom) # label(non_clause).  [assumption].
7.74/7.71	4523 (all A_1 all B hAPP(complex,complex,uminus_uminus(complex),hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,A_1),B)) = hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,hAPP(real,real,uminus_uminus(real),A_1)),hAPP(real,real,uminus_uminus(real),B))) # label(fact_2746_complex__minus) # label(axiom) # label(non_clause).  [assumption].
7.74/7.71	4524 (all P_1 all A_2 all B_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A_2),B_1)) -> (all N_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(product_prod(real,real),real,product_snd(real,real),hAPP(nat,product_prod(real,real),hAPP(real,fun(nat,product_prod(real,real)),hAPP(real,fun(real,fun(nat,product_prod(real,real))),hAPP(fun(product_prod(real,real),bool),fun(real,fun(real,fun(nat,product_prod(real,real)))),bolzano_bisect,P_1),A_2),B_1),hAPP(nat,nat,suc,N_2)))),hAPP(product_prod(real,real),real,product_snd(real,real),hAPP(nat,product_prod(real,real),hAPP(real,fun(nat,product_prod(real,real)),hAPP(real,fun(real,fun(nat,product_prod(real,real))),hAPP(fun(product_prod(real,real),bool),fun(real,fun(real,fun(nat,product_prod(real,real)))),bolzano_bisect,P_1),A_2),B_1),N_2))))))) # label(fact_3134_Bolzano__bisect__Suc__le__snd) # label(axiom) # label(non_clause).  [assumption].
7.74/7.71	4525 (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_759_add__strict__increasing) # label(axiom) # label(non_clause).  [assumption].
7.74/7.71	4526 (all X_a (boolean_algebra(X_a) -> (all X_1 all Y_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y_1),X_1)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),X_1)),hAPP(X_a,X_a,uminus_uminus(X_a),Y_1))))))) # label(fact_2962_compl__less__compl__iff) # label(axiom) # label(non_clause).  [assumption].
7.74/7.71	4527 (all X_1 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,real)),combs(real,real,real),hAPP(fun(real,real),fun(real,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,fun(real,real))),combb(real,fun(real,real),real),times_times(real)),cos)),cos)),X_1),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,uminus_uminus(real),hAPP(real,real,sin,X_1))),hAPP(real,real,cos,X_1))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,uminus_uminus(real),hAPP(real,real,sin,X_1))),hAPP(real,real,cos,X_1)))))) # label(fact_3883_DERIV__cos__cos__mult) # label(axiom) # label(non_clause).  [assumption].
7.74/7.71	4528 (all X_1 all X_3 (hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),X_1),X_3)) -> ((exists Z_2 all X_2 (hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),X_2),X_3)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_2),Z_2)))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_1),hAPP(fun(real,bool),real,complete_Sup_Sup(real),X_3)))))) # label(fact_3705_Sup__upper__EX) # label(axiom) # label(non_clause).  [assumption].
7.74/7.71	4529 (all X_a all X_b (real_normed_algebra(X_b) -> (all Y_1 all G all A_2 all A_3 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),G),A_2),A_3)) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(X_b,fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(X_b,fun(X_a,X_b)),combc(X_a,X_b,X_b),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,fun(X_b,X_b))),combb(X_b,fun(X_b,X_b),X_a),times_times(X_b)),G)),Y_1)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),A_2),Y_1)),A_3)))))) # label(fact_4475_mult__left_Otendsto) # label(axiom) # label(non_clause).  [assumption].
7.74/7.71	4530 (all X_a (semiring_1(X_a) -> zero_zero(X_a) = hAPP(nat,X_a,semiring_1_of_nat(X_a),zero_zero(nat)))) # label(fact_1281_of__nat__0) # label(axiom) # label(non_clause).  [assumption].
7.74/7.71	4531 (all M all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N)),N) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),M),N)) # label(fact_3248_gcd__add1__nat) # label(axiom) # label(non_clause).  [assumption].
7.74/7.71	4532 (all X all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X),Y)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(real,nat,natfloor,X)),hAPP(real,nat,natfloor,Y))))) # label(fact_1875_natfloor__mono) # label(axiom) # label(non_clause).  [assumption].
7.74/7.71	4533 (all X_a (comm_semiring_1(X_a) -> (all X all Y all Z_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Y),Z_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),Y)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),Z_1))))) # label(fact_240_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J) # label(axiom) # label(non_clause).  [assumption].
7.74/7.71	4534 (all X_1 all P_4 (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,X_1),zero_zero(int)),P_4)) <-> hAPP(int,int,hAPP(int,fun(int,int),standardRes,P_4),X_1) != zero_zero(int))) # label(fact_1012_StandardRes__prop3) # label(axiom) # label(non_clause).  [assumption].
7.74/7.71	4535 (all X_a (linordered_semidom(X_a) -> (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),M)),hAPP(nat,X_a,semiring_1_of_nat(X_a),N))))))) # label(fact_1283_less__imp__of__nat__less) # label(axiom) # label(non_clause).  [assumption].
7.74/7.71	4536 (all M (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),M)) -> -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,one_one(int)),hAPP(int,int,number_number_of(int),min_1)),M)))) # label(fact_466_one__not__neg__one__mod__m) # label(axiom) # label(non_clause).  [assumption].
7.74/7.71	4537 (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_426_mult__right__le__imp__le) # label(axiom) # label(non_clause).  [assumption].
7.74/7.71	4538 (all X all Y (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),Y)) & -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y),X)) -> -(hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y),X)) & -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),Y))))) # label(fact_639_dvd_Oless__not__sym) # label(axiom) # label(non_clause).  [assumption].
7.74/7.71	4539 (all X_a (ring_1(X_a) -> (all B_1 all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_2),ring_1_Ints(X_a))) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),B_1),ring_1_Ints(X_a))) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_2),B_1)),ring_1_Ints(X_a)))))))) # label(fact_3821_Ints__diff) # label(axiom) # label(non_clause).  [assumption].
7.74/7.71	4540 (all X_a (real_normed_vector(X_a) -> (all X_3 ((exists N_3 all N_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,norm_norm(X_a),hAPP(nat,X_a,X_3,N_2))),hAPP(nat,real,real_1(nat),hAPP(nat,nat,suc,N_3))))) <-> hBOOL(hAPP(fun(nat,X_a),bool,bseq(X_a),X_3)))))) # label(fact_3496_Bseq__iff1a) # label(axiom) # label(non_clause).  [assumption].
7.74/7.71	4541 (all W_1 (hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),W_1))) <-> hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),hAPP(int,int,bit1,W_1)))))) # label(fact_1504_neg__number__of__Bit1) # label(axiom) # label(non_clause).  [assumption].
7.74/7.71	4542 (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,abs_abs(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Y),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))))) # label(fact_1879_abs__mult__pos) # label(axiom) # label(non_clause).  [assumption].
7.74/7.71	4543 (all K_4 hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),K_4),one_one(int)) = hAPP(int,int,succ,K_4)) # label(fact_1528_succ__def) # label(axiom) # label(non_clause).  [assumption].
7.74/7.71	4544 (all X_a all F1 all Real1 all Real2 hAPP(real,X_a,hAPP(real,fun(real,X_a),F1,Real1),Real2) = hAPP(complex,X_a,hAPP(fun(real,fun(real,X_a)),fun(complex,X_a),complex_rec(X_a),F1),hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,Real1),Real2))) # label(fact_2758_complex_Orecs) # label(axiom) # label(non_clause).  [assumption].
7.74/7.71	4545 (all X_a (real_normed_algebra(X_a) -> (all R_4 all X all Y hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),R_4),X)),Y) = hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),R_4),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),Y))))) # label(fact_4679_mult__left_OscaleR) # label(axiom) # label(non_clause).  [assumption].
7.74/7.71	4546 (all L_4 hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),min_1),hAPP(int,int,bit1,L_4)) = hAPP(int,int,bit0,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),min_1),L_4))) # label(fact_512_diff__bin__simps_I6_J) # label(axiom) # label(non_clause).  [assumption].
7.74/7.71	4547 (all X_a (real_normed_vector(X_a) -> (all X hAPP(X_a,real,norm_norm(X_a),X) = hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),X))))) # label(fact_2013_norm__minus__cancel) # label(axiom) # label(non_clause).  [assumption].
7.74/7.71	4548 (all Y all X (hAPP(real,real,cos,X) != zero_zero(real) -> (hAPP(real,real,cos,Y) != zero_zero(real) -> (zero_zero(real) != hAPP(real,real,cos,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),Y)) -> hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,tan,X)),hAPP(real,real,tan,Y))),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),one_one(real)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,tan,X)),hAPP(real,real,tan,Y)))) = hAPP(real,real,tan,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),Y)))))) # label(fact_2268_tan__add) # label(axiom) # label(non_clause).  [assumption].
7.74/7.71	4549 (all K_4 all M all N hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,M),hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,K_4),N)) = hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,K_4),hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,M),N))) # label(fact_3439_zgcd__left__commute) # label(axiom) # label(non_clause).  [assumption].
7.74/7.71	4550 (all A_2 (A_2 = one_one(nat) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_2),one_one(nat))))) # label(fact_896_gcd__lcm__complete__lattice__nat_Obot__unique) # label(axiom) # label(non_clause).  [assumption].
7.74/7.71	4551 (all X_1 all A_2 (hBOOL(hAPP(fun(nat,real),bool,monoseq(real),A_2)) -> (hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),A_2),X_1),sequentially)) -> (all N_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_1),hAPP(nat,real,A_2,N_2)))) & (all M_2 all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_2),N_2)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,A_2,N_2)),hAPP(nat,real,A_2,M_2))))) | (all N_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,A_2,N_2)),X_1))) & (all M_2 all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_2),N_2)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,A_2,M_2)),hAPP(nat,real,A_2,N_2)))))))) # label(fact_4434_monoseq__le) # label(axiom) # label(non_clause).  [assumption].
7.74/7.71	4552 (all V all W hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,V))),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,W))) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,number_number_of(int),V)),hAPP(int,int,number_number_of(int),W)))) # label(fact_1052_zmod__number__of__Bit0) # label(axiom) # label(non_clause).  [assumption].
7.74/7.71	4553 (all X_a (linordered_idom(X_a) -> (all X_1 all Y_1 (ti(X_a,Y_1) != zero_zero(X_a) | zero_zero(X_a) != ti(X_a,X_1) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),Y_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))))))) # label(fact_8_sum__power2__gt__zero__iff) # label(axiom) # label(non_clause).  [assumption].
7.74/7.71	4554 (all X_a (semiring_1(X_a) -> (all N_1 hAPP(X_a,X_a,hAPP(nat,fun(X_a,X_a),hAPP(fun(X_a,X_a),fun(nat,fun(X_a,X_a)),semiri532925092at_aux(X_a),hAPP(X_a,fun(X_a,X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(X_a,X_a)),combc(X_a,X_a,X_a),plus_plus(X_a)),one_one(X_a))),N_1),zero_zero(X_a)) = hAPP(nat,X_a,semiring_1_of_nat(X_a),N_1)))) # label(fact_4158_semiring__1__class_Oof__nat__code) # label(axiom) # label(non_clause).  [assumption].
7.74/7.71	4555 (all Y all X hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),Y),hAPP(real,real,sqrt,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),Y),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))))) # label(fact_1644_real__sqrt__sum__squares__ge2) # label(axiom) # label(non_clause).  [assumption].
7.74/7.71	4556 (all X_a (real_normed_vector(X_a) -> (all R_4 exists K_2 all X_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),R_4),X_2))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(X_a,real,norm_norm(X_a),X_2)),K_2)))))) # label(fact_4761_scaleR__right_Obounded) # label(axiom) # label(non_clause).  [assumption].
7.74/7.71	4557 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,ln,hAPP(real,real,exp(real),one_one(real)))),hAPP(real,real,ln,hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))),hAPP(real,real,ln,X)) = hAPP(real,real,hAPP(real,fun(real,real),log,hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),X))) # label(fact_2630_log__base__10__eq1) # label(axiom) # label(non_clause).  [assumption].
7.74/7.71	4558 (all X hAPP(complex,complex,uminus_uminus(complex),X) = hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,hAPP(real,real,uminus_uminus(real),hAPP(complex,real,re,X))),hAPP(real,real,uminus_uminus(real),hAPP(complex,real,im,X)))) # label(fact_3015_complex__minus__def) # label(axiom) # label(non_clause).  [assumption].
7.74/7.71	4559 (all X_a (linord219039673up_add(X_a) -> (all A_2 (hAPP(X_a,X_a,uminus_uminus(X_a),A_2) = ti(X_a,A_2) <-> zero_zero(X_a) = ti(X_a,A_2))))) # label(fact_2021_neg__equal__zero) # label(axiom) # label(non_clause).  [assumption].
7.74/7.71	4560 (all X_a (linordered_field(X_a) -> (all Z_1 all W all Y all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),X)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),W)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),W),Z_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),X),Z_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),Y),W)))))))))) # label(fact_1705_frac__le) # label(axiom) # label(non_clause).  [assumption].
7.74/7.71	4561 (all X_a (real_normed_vector(X_a) -> (all A_1 zero_zero(X_a) = hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_1),zero_zero(X_a))))) # label(fact_4703_scaleR_Ozero__right) # label(axiom) # label(non_clause).  [assumption].
7.74/7.71	4562 (all I_1 all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_1),N)) -> I_1 = 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_1)))) # label(fact_672_diff__diff__cancel) # label(axiom) # label(non_clause).  [assumption].
7.74/7.71	4563 (all B all A_1 ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A_1)) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),B)) -> (ti(int,A_1) != zero_zero(int) -> hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),divmod_int,A_1),B) = hAPP(product_prod(int,int),product_prod(int,int),negateSnd,hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),negDivAlg,hAPP(int,int,uminus_uminus(int),A_1)),hAPP(int,int,uminus_uminus(int),B)))) & (zero_zero(int) = ti(int,A_1) -> hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),divmod_int,A_1),B) = hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),zero_zero(int)),zero_zero(int)))) & (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),B)) -> hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),posDivAlg,A_1),B) = hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),divmod_int,A_1),B))) & (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B)) -> hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),negDivAlg,A_1),B) = hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),divmod_int,A_1),B)) & (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B)) -> hAPP(product_prod(int,int),product_prod(int,int),negateSnd,hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),posDivAlg,hAPP(int,int,uminus_uminus(int),A_1)),hAPP(int,int,uminus_uminus(int),B))) = hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),divmod_int,A_1),B))))) # label(fact_3045_divmod__int__def) # label(axiom) # label(non_clause).  [assumption].
7.74/7.71	4564 (all X_a (linord1117847801e_zero(X_a) -> (all X_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,inverse_inverse(X_a),X_1)),one_one(X_a))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),X_1)) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),zero_zero(X_a))))))) # label(fact_2609_inverse__less__1__iff) # label(axiom) # label(non_clause).  [assumption].
7.74/7.71	4565 (all X_a (real_normed_vector(X_a) -> (all X_1 all X_3 (hBOOL(hAPP(fun(nat,real),bool,summable(real),X_3)) -> hAPP(fun(nat,X_a),X_a,suminf(X_a),hAPP(X_a,fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(X_a,fun(nat,X_a)),combc(nat,X_a,X_a),hAPP(fun(nat,real),fun(nat,fun(X_a,X_a)),hAPP(fun(real,fun(X_a,X_a)),fun(fun(nat,real),fun(nat,fun(X_a,X_a))),combb(real,fun(X_a,X_a),nat),scaleR_scaleR(X_a)),X_3)),X_1)) = hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),hAPP(fun(nat,real),real,suminf(real),X_3)),X_1))))) # label(fact_4741_scaleR__left_Osuminf) # label(axiom) # label(non_clause).  [assumption].
7.74/7.71	4566 (all X_1 (hBOOL(hAPP(int,bool,nat_is_nat,X_1)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X_1)))) # label(fact_4840_is__nat__def) # label(axiom) # label(non_clause).  [assumption].
7.74/7.71	4567 (all N_1 all X_1 all Diff all F ((all M_2 all X_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(nat,fun(real,real),Diff,M_2)),X_2),hAPP(real,real,hAPP(nat,fun(real,real),Diff,hAPP(nat,nat,suc,M_2)),X_2)))) & F = hAPP(nat,fun(real,real),Diff,zero_zero(nat)) -> (exists T_4 (hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),inverse_divide(real)),hAPP(real,fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(real,fun(nat,real)),combc(nat,real,real),Diff),zero_zero(real)))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),fact_fact(nat))))),hAPP(real,fun(nat,real),power_power(real),X_1))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),N_1))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(nat,fun(real,real),Diff,N_1),T_4)),hAPP(nat,real,real_1(nat),hAPP(nat,nat,fact_fact(nat),N_1)))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X_1),N_1))) = hAPP(real,real,F,X_1) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),T_4)),hAPP(real,real,abs_abs(real),X_1))))))) # label(fact_4285_Maclaurin__all__le__objl) # label(axiom) # label(non_clause).  [assumption].
7.74/7.71	4568 (all X_a (real_normed_algebra(X_a) -> (all Y exists K_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),K_2)) & (all X_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X_2),Y))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(X_a,real,norm_norm(X_a),X_2)),K_2)))))))) # label(fact_1803_mult__left_Opos__bounded) # label(axiom) # label(non_clause).  [assumption].
7.74/7.71	4569 (all M all N hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),M),N)),M))) # label(fact_1088_div__le__dividend) # label(axiom) # label(non_clause).  [assumption].
7.74/7.71	4570 (all X_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),one_one(nat)),hAPP(real,nat,natfloor,X_1))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),one_one(real)),X_1)))) # label(fact_1902_le__natfloor__eq__one) # label(axiom) # label(non_clause).  [assumption].
7.74/7.71	4571 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),hAPP(nat,nat,suc,N))) -> (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N)) -> M = N))) # label(fact_1231_less__SucE) # label(axiom) # label(non_clause).  [assumption].
7.74/7.71	4572 (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,B) != ti(X_a,A_1) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B))))))) # label(fact_1597_order__le__neq__trans) # label(axiom) # label(non_clause).  [assumption].
7.74/7.71	4573 (all X_a all R_3 all F all X_1 all Y_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(X_a,nat,F,X_1)),hAPP(X_a,nat,F,Y_1))) -> hBOOL(hAPP(fun(product_prod(X_a,X_a),bool),bool,hAPP(product_prod(X_a,X_a),fun(fun(product_prod(X_a,X_a),bool),bool),member(product_prod(X_a,X_a)),hAPP(X_a,product_prod(X_a,X_a),hAPP(X_a,fun(X_a,product_prod(X_a,X_a)),product_Pair(X_a,X_a),X_1),Y_1)),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(X_a,X_a),bool),hAPP(fun(X_a,nat),fun(fun(product_prod(X_a,X_a),bool),fun(product_prod(X_a,X_a),bool)),mlex_prod(X_a),F),R_3))))) # label(fact_3797_mlex__less) # label(axiom) # label(non_clause).  [assumption].
7.74/7.71	4574 (all Z_4 all Z_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Z_1),zero_zero(int))) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,nat_1,hAPP(int,int,uminus_uminus(int),Z_1))),hAPP(int,nat,nat_1,hAPP(int,int,uminus_uminus(int),Z_4))) = hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Z_1),Z_4)))) # label(fact_2178_nat__mult__distrib__neg) # label(axiom) # label(non_clause).  [assumption].
7.74/7.71	4575 (all A_3 all B_2 all Ma (hBOOL(hAPP(fun(product_prod(fun(int,bool),fun(int,bool)),bool),bool,hAPP(product_prod(fun(int,bool),fun(int,bool)),fun(fun(product_prod(fun(int,bool),fun(int,bool)),bool),bool),member(product_prod(fun(int,bool),fun(int,bool))),hAPP(fun(int,bool),product_prod(fun(int,bool),fun(int,bool)),hAPP(fun(int,bool),fun(fun(int,bool),product_prod(fun(int,bool),fun(int,bool))),product_Pair(fun(int,bool),fun(int,bool)),A_3),B_2)),hAPP(fun(int,fun(int,bool)),fun(product_prod(fun(int,bool),fun(int,bool)),bool),bijR(int,int),hAPP(int,fun(int,fun(int,bool)),zcongm,Ma)))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(fun(int,bool),int,hAPP(fun(int,int),fun(fun(int,bool),int),big_co302546470etprod(int,int),combi(int)),A_3)),hAPP(fun(int,bool),int,hAPP(fun(int,int),fun(fun(int,bool),int),big_co302546470etprod(int,int),combi(int)),B_2)),Ma)))) # label(fact_4874_bijzcong__zcong__prod) # label(axiom) # label(non_clause).  [assumption].
7.74/7.71	4576 (exists K_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),K_2)) & (all X_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,cnj,X_2))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(complex,real,norm_norm(complex),X_2)),K_2)))))) # label(fact_2966_cnj_Opos__bounded) # label(axiom) # label(non_clause).  [assumption].
7.74/7.71	4577 (all M all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,suc,M)),N) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),hAPP(nat,nat,suc,N))) # label(fact_1240_add__Suc__shift) # label(axiom) # label(non_clause).  [assumption].
7.74/7.71	4578 (all N all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,real_1(int),N)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(int,real,real_1(int),N)),one_one(real)))) -> ti(int,N) = hAPP(real,int,archim2085082626_floor(real),X)))) # label(fact_3398_floor__eq) # label(axiom) # label(non_clause).  [assumption].
7.74/7.71	4579 (all A_2 all B_1 hAPP(int,fun(product_prod(int,int),bool),hAPP(int,fun(int,fun(product_prod(int,int),bool)),divmod_int_rel,A_2),B_1) = hAPP(fun(int,fun(int,bool)),fun(product_prod(int,int),bool),product_prod_case(int,int,bool),hAPP(fun(int,bool),fun(int,fun(int,bool)),hAPP(fun(int,fun(fun(int,bool),fun(int,bool))),fun(fun(int,bool),fun(int,fun(int,bool))),combc(int,fun(int,bool),fun(int,bool)),hAPP(fun(int,fun(int,fun(bool,bool))),fun(int,fun(fun(int,bool),fun(int,bool))),hAPP(fun(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool))),fun(fun(int,fun(int,fun(bool,bool))),fun(int,fun(fun(int,bool),fun(int,bool)))),combb(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),int),combs(int,bool,bool)),hAPP(fun(int,fun(int,bool)),fun(int,fun(int,fun(bool,bool))),hAPP(fun(fun(int,bool),fun(int,fun(bool,bool))),fun(fun(int,fun(int,bool)),fun(int,fun(int,fun(bool,bool)))),combb(fun(int,bool),fun(int,fun(bool,bool)),int),hAPP(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj)),hAPP(fun(int,fun(int,int)),fun(int,fun(int,bool)),hAPP(fun(fun(int,int),fun(int,bool)),fun(fun(int,fun(int,int)),fun(int,fun(int,bool))),combb(fun(int,int),fun(int,bool),int),hAPP(fun(int,bool),fun(fun(int,int),fun(int,bool)),combb(int,bool,int),hAPP(int,fun(int,bool),fequal(int),A_2))),hAPP(fun(int,int),fun(int,fun(int,int)),hAPP(fun(int,fun(int,int)),fun(fun(int,int),fun(int,fun(int,int))),combb(int,fun(int,int),int),plus_plus(int)),hAPP(int,fun(int,int),times_times(int),B_1)))))),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),combs(int,bool,bool),hAPP(fun(int,bool),fun(int,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(bool,bool),fun(fun(int,bool),fun(int,bool)),combb(bool,bool,int),hAPP(bool,fun(bool,bool),fimplies,hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B_1))),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),combs(int,bool,bool),hAPP(fun(int,bool),fun(int,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj),hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)))),hAPP(int,fun(int,bool),hAPP(fun(int,fun(int,bool)),fun(int,fun(int,bool)),combc(int,int,bool),ord_less(int)),B_1))))),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(bool,bool),fun(fun(int,bool),fun(int,bool)),combb(bool,bool,int),hAPP(bool,fun(bool,bool),fimplies,hAPP(bool,bool,fNot,hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B_1)))),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),combs(int,bool,bool),hAPP(fun(int,bool),fun(int,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj),hAPP(int,fun(int,bool),ord_less(int),B_1))),hAPP(int,fun(int,bool),hAPP(fun(int,fun(int,bool)),fun(int,fun(int,bool)),combc(int,int,bool),ord_less_eq(int)),zero_zero(int)))))))) # label(fact_4031_divmod__int__rel__def) # label(axiom) # label(non_clause).  [assumption].
7.74/7.71	4580 (all Q_3 all R_4 hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),Q_3),R_4) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),Q_3),hAPP(rat,rat,uminus_uminus(rat),R_4))) # label(fact_3722_diff__rat__def) # label(axiom) # label(non_clause).  [assumption].
7.74/7.71	4581 (all X_a (field_char_0(X_a) & field_inverse_zero(X_a) -> (all B_1 all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_2),field_char_0_Rats(X_a))) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),B_1),field_char_0_Rats(X_a))) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),A_2),B_1)),field_char_0_Rats(X_a)))))))) # label(fact_3699_Rats__divide) # label(axiom) # label(non_clause).  [assumption].
7.74/7.71	4582 (all X_a (real_normed_vector(X_a) -> (all B_1 all F all A_2 (hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),F),A_2),sequentially)) -> hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),hAPP(X_a,fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(X_a,fun(nat,X_a)),combc(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),minus_minus(X_a)),F)),B_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_2),B_1)),sequentially)))))) # label(fact_4441_LIMSEQ__diff__const) # label(axiom) # label(non_clause).  [assumption].
7.74/7.71	4583 (all A_2 all P_4 (hBOOL(hAPP(int,bool,zprime,P_4)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),P_4)) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_2),zero_zero(int)),P_4)) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),quadRes,P_4),A_2)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(fun(int,bool),int,hAPP(fun(int,int),fun(fun(int,bool),int),big_co302546470etprod(int,int),combi(int)),hAPP(fun(fun(int,bool),bool),fun(int,bool),complete_Sup_Sup(fun(int,bool)),hAPP(int,fun(fun(int,bool),bool),hAPP(int,fun(int,fun(fun(int,bool),bool)),setS,A_2),P_4)))),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A_2),hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),P_4),one_one(int))),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))),P_4))))))) # label(fact_3927_Union__SetS__setprod__prop1) # label(axiom) # label(non_clause).  [assumption].
7.74/7.72	4584 (all X_a (archim1727834104eiling(X_a) -> (all X hAPP(X_a,int,archim2085082626_floor(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X),one_one(X_a))) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(X_a,int,archim2085082626_floor(X_a),X)),one_one(int))))) # label(fact_2887_floor__add__one) # label(axiom) # label(non_clause).  [assumption].
7.74/7.72	4585 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),zero_zero(real))) -> hAPP(real,real,sgn_sgn(real),X) = hAPP(int,real,number_number_of(real),min_1))) # label(fact_2226_real__sgn__neg) # label(axiom) # label(non_clause).  [assumption].
7.74/7.72	4586 (all B_1 all A_2 all Ma (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),B_1),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),bnorRset,A_2),Ma))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B_1)))) # label(fact_3209_Bnor__mem__zg) # label(axiom) # label(non_clause).  [assumption].
7.74/7.72	4587 (all M all N hBOOL(hAPP(product_prod(nat,nat),bool,hAPP(nat,fun(product_prod(nat,nat),bool),hAPP(nat,fun(nat,fun(product_prod(nat,nat),bool)),divmod_nat_rel,M),N),hAPP(nat,product_prod(nat,nat),hAPP(nat,fun(nat,product_prod(nat,nat)),product_Pair(nat,nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),M),N)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),M),N))))) # label(fact_3103_divmod__nat__rel) # label(axiom) # label(non_clause).  [assumption].
7.74/7.72	4588 (all X_a (real_normed_field(X_a) -> (all Y exists K_2 all X_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),X_2),Y))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(X_a,real,norm_norm(X_a),X_2)),K_2)))))) # label(fact_1810_divide_Obounded) # label(axiom) # label(non_clause).  [assumption].
7.74/7.72	4589 (all K (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit0,K)),min_1)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),K),min_1)))) # label(fact_306_rel__simps_I11_J) # label(axiom) # label(non_clause).  [assumption].
7.74/7.72	4590 (all Ma all N_1 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),Ma)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),N_1))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),N_1))))) # label(fact_747_nat__mult__less__cancel1) # label(axiom) # label(non_clause).  [assumption].
7.74/7.72	4591 (all X_a (metric_space(X_a) -> (all X all Z_1 all Y all E_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),X),Z_1)),hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),Y),Z_1))),E_1)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),X),Y)),E_1)))))) # label(fact_3509_dist__triangle__lt) # label(axiom) # label(non_clause).  [assumption].
7.74/7.72	4592 (all V_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),V_1),pls)) <-> zero_zero(nat) = hAPP(int,nat,number_number_of(nat),V_1))) # label(fact_39_eq__number__of__0) # label(axiom) # label(non_clause).  [assumption].
7.74/7.72	4593 (all X_a (archim1727834104eiling(X_a) -> (all X all Y (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(X_a,int,archim2085082626_floor(X_a),X)),hAPP(X_a,int,archim2085082626_floor(X_a),Y))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)))))) # label(fact_2864_floor__less__cancel) # label(axiom) # label(non_clause).  [assumption].
7.74/7.72	4594 (all X_a (linorder(X_a) -> (all Z all X_1 all Y_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Z),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X_1),Y_1))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Z),X_1)) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Z),Y_1)))))) # label(fact_4987_le__max__iff__disj) # label(axiom) # label(non_clause).  [assumption].
7.74/7.72	4595 (all Code_numeral all Code_numeral_5 (Code_numeral = Code_numeral_5 <-> hAPP(code_code_numeral,code_code_numeral,code_S1047413653umeral,Code_numeral) = hAPP(code_code_numeral,code_code_numeral,code_S1047413653umeral,Code_numeral_5))) # label(fact_2939_code__numeral_Oinject) # label(axiom) # label(non_clause).  [assumption].
7.74/7.72	4596 (all Z_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),Z_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Z_1),Z_1)) # label(fact_229_nat__mult__2__right) # label(axiom) # label(non_clause).  [assumption].
7.74/7.72	4597 (all X_a all X_b all T_5 ti(product_prod(X_a,X_b),T_5) = hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),hAPP(product_prod(X_a,X_b),X_a,product_fst(X_a,X_b),T_5)),hAPP(product_prod(X_a,X_b),X_b,product_snd(X_a,X_b),T_5))) # label(fact_3129_surjective__pairing) # label(axiom) # label(non_clause).  [assumption].
7.74/7.72	4598 (all M hAPP(nat,nat,suc,M) != zero_zero(nat)) # label(fact_1222_Suc__neq__Zero) # label(axiom) # label(non_clause).  [assumption].
7.74/7.72	4599 (all X_b (semiring(X_b) & number(X_b) -> (all V all B all 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)) = 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))))) # label(fact_96_right__distrib__number__of) # label(axiom) # label(non_clause).  [assumption].
7.74/7.72	4600 (all P_1 all K (hBOOL(hAPP(nat,bool,P_1,K)) -> ((all N_2 (hBOOL(hAPP(nat,bool,P_1,hAPP(nat,nat,suc,N_2))) -> hBOOL(hAPP(nat,bool,P_1,N_2)))) -> hBOOL(hAPP(nat,bool,P_1,zero_zero(nat)))))) # label(fact_1608_zero__induct) # label(axiom) # label(non_clause).  [assumption].
7.74/7.72	4601 (all N all X (hAPP(int,real,real_1(int),hAPP(real,int,archim2085082626_floor(real),X)) = X -> hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(real,int,archim2085082626_floor(real),X)),N) = hAPP(real,int,archim2085082626_floor(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),N)))) # label(fact_3370_floor__power) # label(axiom) # label(non_clause).  [assumption].
7.74/7.72	4602 (all X_a (boolean_algebra(X_a) -> (all X_1 all Y_1 (hAPP(X_a,X_a,uminus_uminus(X_a),X_1) = hAPP(X_a,X_a,uminus_uminus(X_a),Y_1) <-> ti(X_a,X_1) = ti(X_a,Y_1))))) # label(fact_2954_compl__eq__compl__iff) # label(axiom) # label(non_clause).  [assumption].
7.74/7.72	4603 (all X_a all X_1 all A_3 all B_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_3),B_2)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_3)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),B_2))))) # label(fact_1954_set__mp) # label(axiom) # label(non_clause).  [assumption].
7.74/7.72	4604 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),one_one(real))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,ln,X)),zero_zero(real)))))) # label(fact_1950_ln__less__zero) # label(axiom) # label(non_clause).  [assumption].
7.74/7.72	4605 (all X_a (number_ring(X_a) & field_char_0(X_a) -> (all W_1 hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),hAPP(int,X_a,number_number_of(X_a),W_1)),field_char_0_Rats(X_a)))))) # label(fact_3694_Rats__number__of) # label(axiom) # label(non_clause).  [assumption].
7.74/7.72	4606 (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_402_zero__less__one) # label(axiom) # label(non_clause).  [assumption].
7.74/7.72	4607 (all X_a (ordered_ring(X_a) -> (all A_2 all E_2 all C_1 all B_1 all D_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_2),B_1)),E_2)),C_1)),D_1)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),E_2)),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B_1),E_2)),D_1))))))) # label(fact_501_le__add__iff1) # label(axiom) # label(non_clause).  [assumption].
7.74/7.72	4608 (all X_a (real_normed_vector(X_a) & real_algebra_1(X_a) -> hAPP(real,X_a,of_real(X_a),zero_zero(real)) = zero_zero(X_a))) # label(fact_2782_of__real_Ozero) # label(axiom) # label(non_clause).  [assumption].
7.74/7.72	4609 (all B all D all A_1 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),D),A_1) = one_one(nat) -> (hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),D),B) = one_one(nat) -> one_one(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),D),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A_1),B))))) # label(fact_3269_coprime__mult__nat) # label(axiom) # label(non_clause).  [assumption].
7.74/7.72	4610 (all M all N (M = N -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N)))) # label(fact_528_eq__imp__le) # label(axiom) # label(non_clause).  [assumption].
7.74/7.72	4611 (all M all K_4 all N (hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,K_4),N) = one_one(int) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K_4),M)),N)),hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,M),N))))) # label(fact_3461_zgcd__zmult__zdvd__zgcd) # label(axiom) # label(non_clause).  [assumption].
7.74/7.72	4612 (all X_a pow(X_a) = ti(fun(fun(X_a,bool),fun(fun(X_a,bool),bool)),pow(X_a))) # label(tsy_c_Set_OPow_res) # label(axiom) # label(non_clause).  [assumption].
7.74/7.72	4613 (all X all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,exp(real),X)),hAPP(real,real,exp(real),Y))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),Y)))) # label(fact_2513_exp__less__cancel) # label(axiom) # label(non_clause).  [assumption].
7.74/7.72	4614 (all X_1 all A_2 (hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X_1),hAPP(real,real,uminus_uminus(real),A_2)) = zero_zero(real) <-> A_2 = X_1)) # label(fact_2088_real__add__minus__iff) # label(axiom) # label(non_clause).  [assumption].
7.74/7.72	4615 (all X_a all X_c all X_b all P all Q all R hAPP(X_a,X_c,hAPP(fun(X_a,X_b),fun(X_a,X_c),hAPP(fun(X_b,X_c),fun(fun(X_a,X_b),fun(X_a,X_c)),combb(X_b,X_c,X_a),P),Q),R) = hAPP(X_b,X_c,P,hAPP(X_a,X_b,Q,R))) # label(help_COMBB_1_1_U) # label(axiom) # label(non_clause).  [assumption].
7.74/7.72	4616 (all M all N all P_5 (hBOOL(hAPP(int,bool,zprime,P_5)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),P_5),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),M),N))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),P_5),N)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),P_5),M))))) # label(fact_424_zprime__zdvd__zmult__better) # label(axiom) # label(non_clause).  [assumption].
7.74/7.72	4617 (all X_a (semiring_div(X_a) -> (all A_2 all B_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_2),B_1)) <-> zero_zero(X_a) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),B_1),A_2))))) # label(fact_980_dvd__eq__mod__eq__0) # label(axiom) # label(non_clause).  [assumption].
7.74/7.72	4618 (all M hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),M))))) # label(fact_583_le__cube) # label(axiom) # label(non_clause).  [assumption].
7.74/7.72	4619 (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_392_mult__pos__neg2) # label(axiom) # label(non_clause).  [assumption].
7.74/7.72	4620 (all X_a all A_2 all P_1 ((exists X_2 ((all Y_2 (hBOOL(hAPP(X_a,bool,P_1,Y_2)) -> ti(X_a,Y_2) = ti(X_a,X_2))) & hBOOL(hAPP(X_a,bool,P_1,X_2)))) -> (hBOOL(hAPP(X_a,bool,P_1,A_2)) -> ti(X_a,A_2) = hAPP(fun(X_a,bool),X_a,hilbert_Eps(X_a),P_1)))) # label(fact_4868_some1__equality) # label(axiom) # label(non_clause).  [assumption].
7.74/7.72	4621 (all X_a (linorder(X_a) -> (all B all A_1 all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),X)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),A_1),B)),X)))))) # label(fact_4825_min__max_Ole__infI1) # label(axiom) # label(non_clause).  [assumption].
7.74/7.72	4622 (all X_a (ring_11004092258visors(X_a) -> (all X_1 (hAPP(X_a,X_a,uminus_uminus(X_a),one_one(X_a)) = ti(X_a,X_1) | one_one(X_a) = ti(X_a,X_1) <-> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X_1),X_1) = one_one(X_a))))) # label(fact_2072_square__eq__1__iff) # label(axiom) # label(non_clause).  [assumption].
7.74/7.72	4623 (all X hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),X),one_one(real))),hAPP(nat,real,real_1(nat),hAPP(real,nat,natfloor,X))))) # label(fact_2349_real__natfloor__gt__diff__one) # label(axiom) # label(non_clause).  [assumption].
7.74/7.72	4624 (all N (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),N)) -> hAPP(int,int,fact_fact(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),N),one_one(int))) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),N),one_one(int))),hAPP(int,int,fact_fact(int),N)))) # label(fact_3201_fact__plus__one__int) # label(axiom) # label(non_clause).  [assumption].
7.74/7.72	4625 (all Y all X (-hBOOL(hAPP(int,bool,even_odd_even(int),X)) -> (hBOOL(hAPP(int,bool,even_odd_even(int),Y)) -> -hBOOL(hAPP(int,bool,even_odd_even(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X),Y)))))) # label(fact_1262_odd__plus__even) # label(axiom) # label(non_clause).  [assumption].
7.74/7.72	4626 (all K_4 all X (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),X)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),K_4)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),X),K_4)),X))))) # label(fact_1013_int__div__less__self) # label(axiom) # label(non_clause).  [assumption].
7.74/7.72	4627 (all X_a (division_ring(X_a) -> (all A_1 (ti(X_a,A_1) != zero_zero(X_a) -> hAPP(X_a,X_a,inverse_inverse(X_a),A_1) != zero_zero(X_a))))) # label(fact_2528_nonzero__imp__inverse__nonzero) # label(axiom) # label(non_clause).  [assumption].
7.74/7.72	4628 (all M 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)) -> 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)))))) # label(fact_1382_n__less__n__mult__m) # label(axiom) # label(non_clause).  [assumption].
7.74/7.72	4629 (all X_1 all Y_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,exp(real),X_1)),hAPP(real,real,exp(real),Y_1))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_1),Y_1)))) # label(fact_2512_exp__le__cancel__iff) # label(axiom) # label(non_clause).  [assumption].
7.74/7.72	4630 (all A_1 all B hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A_1),B)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),A_1)),B))),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) # label(fact_184_zadd__power2) # label(axiom) # label(non_clause).  [assumption].
7.74/7.72	4631 -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),quadRes,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))),hAPP(int,int,number_number_of(int),min_1))) -> one_one(int) != hAPP(int,int,hAPP(int,fun(int,int),legendre,hAPP(int,int,number_number_of(int),min_1)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))) # label(fact_468__096_126_AQuadRes_A_I4_A_K_Am_A_L_A1_J_A_N1_A_061_061_062_ALegendre_A_N) # label(axiom) # label(non_clause).  [assumption].
7.74/7.72	4632 (all X hAPP(real,nat,natceiling,X) = hAPP(int,nat,nat_1,hAPP(real,int,archimedean_ceiling(real),X))) # label(fact_3284_natceiling__def) # label(axiom) # label(non_clause).  [assumption].
7.74/7.72	4633 (all B_1 all A_2 (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),B_1),hAPP(int,fun(int,bool),d22set,A_2))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B_1),A_2)))) # label(fact_865_d22set__le) # label(axiom) # label(non_clause).  [assumption].
7.74/7.72	4634 (all X_a (ord(X_a) -> (all C all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B)) -> (ti(X_a,C) = ti(X_a,B) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),C))))))) # label(fact_1551_ord__le__eq__trans) # label(axiom) # label(non_clause).  [assumption].
7.74/7.72	4635 (all X (hBOOL(hAPP(int,bool,even_odd_even(int),X)) -> hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),X),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) = ti(int,X))) # label(fact_1454_two__times__even__div__two) # label(axiom) # label(non_clause).  [assumption].
7.74/7.72	4636 (all R_4 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,real_1(int),hAPP(real,int,archimedean_ceiling(real),R_4))),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),R_4),one_one(real))))) # label(fact_3402_real__of__int__ceiling__le__add__one) # label(axiom) # label(non_clause).  [assumption].
7.74/7.72	4637 (all X_a (comm_monoid_mult(X_a) & comm_monoid_add(X_a) -> (all F all G all A_3 all B_2 (B_2 = A_3 -> (hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,B_2)) -> ((all X_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X_2)) -> hAPP(int,X_a,F,X_2) = hAPP(int,X_a,G,X_2))) -> hAPP(fun(int,bool),X_a,hAPP(fun(int,X_a),fun(fun(int,bool),X_a),big_co302546470etprod(int,X_a),F),A_3) = hAPP(fun(int,bool),X_a,hAPP(fun(int,X_a),fun(fun(int,bool),X_a),big_co302546470etprod(int,X_a),G),B_2))))))) # label(fact_3962_transfer__nat__int__sum__prod__cong_I2_J) # label(axiom) # label(non_clause).  [assumption].
7.74/7.72	4638 (all N all M hAPP(int,quickcheck_code_int,quickcheck_of_int,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(quickcheck_code_int,int,quickcheck_int_of,N)),hAPP(quickcheck_code_int,int,quickcheck_int_of,M))) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),N),M)) # label(fact_3540_times__code__int__def) # label(axiom) # label(non_clause).  [assumption].
7.74/7.72	4639 (all X all Z_1 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_1))),one_one(int))),D))),Z_1)))) # label(fact_1986_decr__lemma) # label(axiom) # label(non_clause).  [assumption].
7.74/7.72	4640 (all X_a (field_inverse_zero(X_a) -> (all A_1 all B hAPP(X_a,X_a,inverse_inverse(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,inverse_inverse(X_a),A_1)),hAPP(X_a,X_a,inverse_inverse(X_a),B))))) # label(fact_2515_inverse__mult__distrib) # label(axiom) # label(non_clause).  [assumption].
7.74/7.72	4641 (all N_1 hAPP(nat,real,hAPP(fun(nat,real),fun(nat,real),diffs(real),cos_coeff),N_1) = hAPP(real,real,uminus_uminus(real),hAPP(nat,real,sin_coeff,N_1))) # label(fact_4121_cos__fdiffs2) # label(axiom) # label(non_clause).  [assumption].
7.74/7.72	4642 (all V hAPP(complex,real,re,hAPP(int,complex,number_number_of(complex),V)) = hAPP(int,real,number_number_of(real),V)) # label(fact_3005_complex__Re__number__of) # label(axiom) # label(non_clause).  [assumption].
7.74/7.72	4643 (all X_a (linordered_semidom(X_a) -> (all M 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)))))) # label(fact_1278_zero__le__imp__of__nat) # label(axiom) # label(non_clause).  [assumption].
7.74/7.72	4644 (all Y all X (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Y)) -> hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),X),Y)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(int,nat,nat_1,X)),hAPP(int,nat,nat_1,Y))))) # label(fact_1096_nat__mod__distrib) # label(axiom) # label(non_clause).  [assumption].
7.74/7.72	4645 (all Z_1 all X all Y (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X),Y)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Y),Z_1))))) # label(fact_3042_termination__basic__simps_I3_J) # label(axiom) # label(non_clause).  [assumption].
7.74/7.72	4646 (all A_2 (hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),A_2),zero_zero(real)),sequentially)) -> ((all N_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(nat,real,A_2,N_2)))) -> ((all N_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,A_2,hAPP(nat,nat,suc,N_2))),hAPP(nat,real,A_2,N_2)))) -> hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),min_1)))),A_2))))))) # label(fact_4531_summable) # label(axiom) # label(non_clause).  [assumption].
7.74/7.72	4647 (all X_a (ring_char_0(X_a) & number_ring(X_a) -> (all W -hBOOL(hAPP(X_a,bool,iszero(X_a),hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,bit1,W))))))) # label(fact_2602_iszero__number__of__Bit1) # label(axiom) # label(non_clause).  [assumption].
7.74/7.72	4648 (all X_a (linorder(X_a) -> (all A_1 all B all C hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),B),C)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),A_1),B)),C)))) # label(fact_4965_min__max_Osup_Oassoc) # label(axiom) # label(non_clause).  [assumption].
7.74/7.72	4649 (all Z_1 all W hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,uminus_uminus(int),Z_1)),W) = hAPP(int,int,uminus_uminus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Z_1),W))) # label(fact_2140_zmult__zminus) # label(axiom) # label(non_clause).  [assumption].
7.74/7.72	4650 (all X all Y hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(real,real,sqrt,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),Y),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))))) # label(fact_1649_real__sqrt__sum__squares__ge__zero) # label(axiom) # label(non_clause).  [assumption].
7.74/7.72	4651 (all X_a all X_b (comm_monoid_mult(X_b) -> (all Y_1 all A_3 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_3)) -> hAPP(nat,X_b,hAPP(X_b,fun(nat,X_b),power_power(X_b),Y_1),hAPP(fun(X_a,bool),nat,finite_card(X_a),A_3)) = hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co302546470etprod(X_a,X_b),hAPP(X_b,fun(X_a,X_b),combk(X_b,X_a),Y_1)),A_3))))) # label(fact_3959_setprod__constant) # label(axiom) # label(non_clause).  [assumption].
7.74/7.72	4652 (all X_1 all Y_1 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),X_1),Y_1) = X_1 <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_1),Y_1)))) # label(fact_3244_gcd__semilattice__nat_Ole__iff__inf) # label(axiom) # label(non_clause).  [assumption].
7.74/7.72	4653 (all X all Y (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X),Y)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Y),X)) | ti(int,Y) = ti(int,X))) # label(fact_93_zless__linear) # label(axiom) # label(non_clause).  [assumption].
7.74/7.72	4654 (all X_a (number_ring(X_a) -> -hBOOL(hAPP(X_a,bool,iszero(X_a),hAPP(int,X_a,number_number_of(X_a),min_1))))) # label(fact_2605_nonzero__number__of__Min) # label(axiom) # label(non_clause).  [assumption].
7.74/7.72	4655 (all X_a (linorder(X_a) -> (all X all Y all Z_1 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),Y),Z_1))),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),Y)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),Z_1))))))) # label(fact_4946_min__max_Odistrib__sup__le) # label(axiom) # label(non_clause).  [assumption].
7.74/7.72	4656 (all X_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,real)),combs(real,real,real),hAPP(fun(real,real),fun(real,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,fun(real,real))),combb(real,fun(real,real),real),plus_plus(real)),hAPP(nat,fun(real,real),hAPP(fun(real,fun(nat,real)),fun(nat,fun(real,real)),combc(real,nat,real),hAPP(fun(real,real),fun(real,fun(nat,real)),hAPP(fun(real,fun(nat,real)),fun(fun(real,real),fun(real,fun(nat,real))),combb(real,fun(nat,real),real),power_power(real)),sin)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),hAPP(nat,fun(real,real),hAPP(fun(real,fun(nat,real)),fun(nat,fun(real,real)),combc(real,nat,real),hAPP(fun(real,real),fun(real,fun(nat,real)),hAPP(fun(real,fun(nat,real)),fun(fun(real,real),fun(real,fun(nat,real))),combb(real,fun(nat,real),real),power_power(real)),cos)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),X_2),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),hAPP(real,real,cos,X_2))),hAPP(real,real,sin,X_2))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),hAPP(real,real,cos,X_2))),hAPP(real,real,sin,X_2)))))) # label(fact_3917_DERIV__sin__circle__all) # label(axiom) # label(non_clause).  [assumption].
7.74/7.72	4657 (all X_a all Q_1 all P_1 all X_1 (hBOOL(hAPP(X_a,bool,P_1,X_1)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),P_1),Q_1)) -> hBOOL(hAPP(X_a,bool,Q_1,X_1))))) # label(fact_4337_rev__predicate1D) # label(axiom) # label(non_clause).  [assumption].
7.74/7.72	4658 (all X_a all F1 all F2 all Nat hAPP(X_a,X_a,hAPP(nat,fun(X_a,X_a),F2,Nat),hAPP(nat,X_a,hAPP(fun(nat,fun(X_a,X_a)),fun(nat,X_a),hAPP(X_a,fun(fun(nat,fun(X_a,X_a)),fun(nat,X_a)),nat_rec(X_a),F1),F2),Nat)) = hAPP(nat,X_a,hAPP(fun(nat,fun(X_a,X_a)),fun(nat,X_a),hAPP(X_a,fun(fun(nat,fun(X_a,X_a)),fun(nat,X_a)),nat_rec(X_a),F1),F2),hAPP(nat,nat,suc,Nat))) # label(fact_4154_nat__rec__Suc) # label(axiom) # label(non_clause).  [assumption].
7.74/7.72	4659 (all X_1 hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),cos_coeff)),hAPP(real,fun(nat,real),power_power(real),X_1))))) # label(fact_4022_summable__cos) # label(axiom) # label(non_clause).  [assumption].
7.74/7.72	4660 (all N hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(nat,real,real_1(nat),hAPP(nat,nat,fact_fact(nat),N))))) # label(fact_2430_real__of__nat__fact__ge__zero) # label(axiom) # label(non_clause).  [assumption].
7.74/7.72	4661 (all X all Y all K_4 all P_5 (hBOOL(hAPP(nat,bool,prime,P_5)) -> (hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),P_5),K_4) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X),Y) -> (exists I_2 exists J_1 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),P_5),J_1) = Y & hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),P_5),I_2) = X))))) # label(fact_3426_prime__power__mult) # label(axiom) # label(non_clause).  [assumption].
7.74/7.72	4662 (all A_1 all N hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),hAPP(real,complex,cis,A_1)),N) = hAPP(real,complex,cis,hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,real_1(nat),N)),A_1))) # label(fact_3033_DeMoivre) # label(axiom) # label(non_clause).  [assumption].
7.74/7.72	4663 (all A_2 all B_1 (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_2),B_1)),zOdd)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),A_2),zEven)) -> hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),B_1),zOdd))))) # label(fact_1367_even__plus__odd__prop2) # label(axiom) # label(non_clause).  [assumption].
7.74/7.72	4664 (all X hAPP(real,real,abs_abs(real),X) = hAPP(real,real,sqrt,hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) # label(fact_1904_real__sqrt__abs) # label(axiom) # label(non_clause).  [assumption].
7.74/7.72	4665 (all X_a (real_normed_vector(X_a) -> (all X_3 (hBOOL(hAPP(fun(nat,X_a),bool,bseq(X_a),X_3)) <-> hBOOL(hAPP(fun(nat,X_a),bool,bseq(X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(X_a,X_a),fun(fun(nat,X_a),fun(nat,X_a)),combb(X_a,X_a,nat),uminus_uminus(X_a)),X_3))))))) # label(fact_3855_Bseq__minus__iff) # label(axiom) # label(non_clause).  [assumption].
7.74/7.72	4666 (all X_a (field_char_0(X_a) -> (all N_1 hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),N_1)),field_char_0_Rats(X_a)))))) # label(fact_3700_Rats__of__nat) # label(axiom) # label(non_clause).  [assumption].
7.74/7.72	4667 (all A_1 all B all C hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),A_1),B)),C) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),A_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),B),C))) # label(fact_3226_gcd__assoc__nat) # label(axiom) # label(non_clause).  [assumption].
7.74/7.72	4668 (all X all P_5 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),P_5)) -> (hBOOL(hAPP(int,bool,zprime,P_5)) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,X),zero_zero(int)),P_5)) -> -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(int,int,hAPP(int,fun(int,int),multInv,P_5),X)),zero_zero(int)),P_5)))))) # label(fact_845_MultInv__prop3) # label(axiom) # label(non_clause).  [assumption].
7.74/7.72	4669 (all A_2 all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(int,real,real_1(int),A_2)),one_one(real))),X_1)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A_2),hAPP(real,int,archimedean_ceiling(real),X_1))))) # label(fact_3417_le__ceiling__eq) # label(axiom) # label(non_clause).  [assumption].
7.74/7.72	4670 (all X X = hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),zero_zero(nat)),X)) # label(fact_3253_gcd__0__left__nat) # label(axiom) # label(non_clause).  [assumption].
7.74/7.72	4671 (all X_a (real_n1866405975lgebra(X_a) -> (all A_2 (ti(X_a,A_2) != zero_zero(X_a) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_a,fun(filter(X_a),bool),hAPP(fun(X_a,X_a),fun(X_a,fun(filter(X_a),bool)),tendsto(X_a,X_a),inverse_inverse(X_a)),hAPP(X_a,X_a,inverse_inverse(X_a),A_2)),hAPP(X_a,filter(X_a),at(X_a),A_2))))))) # label(fact_4547_LIM__inverse__fun) # label(axiom) # label(non_clause).  [assumption].
7.74/7.72	4672 (all X_a (real_vector(X_a) -> (all A_1 all B all X hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A_1),B)),X) = hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_1),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),B),X))))) # label(fact_4672_real__vector_Oscale__scale) # label(axiom) # label(non_clause).  [assumption].
7.74/7.72	4673 (all X_a (field(X_a) -> (all A_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),one_one(X_a)),A_1) = hAPP(X_a,X_a,inverse_inverse(X_a),A_1)))) # label(fact_2561_field__class_Onormalizing__field__rules_I2_J) # label(axiom) # label(non_clause).  [assumption].
7.74/7.72	4674 (all X_a (archim1727834104eiling(X_a) -> (all X_1 all V_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),hAPP(int,X_a,number_number_of(X_a),V_1))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(X_a,int,archimedean_ceiling(X_a),X_1)),hAPP(int,int,number_number_of(int),V_1))))))) # label(fact_3304_ceiling__le__number__of) # label(axiom) # label(non_clause).  [assumption].
7.74/7.72	4675 (all X_a (real_algebra_1(X_a) & real_normed_vector(X_a) -> (exists K_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),K_2)) & (all X_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),hAPP(real,X_a,of_real(X_a),X_2))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,norm_norm(real),X_2)),K_2)))))))) # label(fact_2817_of__real_Opos__bounded) # label(axiom) # label(non_clause).  [assumption].
7.74/7.72	4676 (all X_a (topological_space(X_a) -> (all F all K all A_2 (hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),hAPP(fun(nat,nat),fun(nat,X_a),hAPP(fun(nat,X_a),fun(fun(nat,nat),fun(nat,X_a)),combb(nat,X_a,nat),F),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),K))),A_2),sequentially)) -> hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),F),A_2),sequentially)))))) # label(fact_4443_LIMSEQ__offset) # label(axiom) # label(non_clause).  [assumption].
7.74/7.72	4677 (all X_a (topological_space(X_a) -> (all L all X_3 all X_1 (hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),X_3),X_1),sequentially)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),L)) -> hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),hAPP(fun(nat,nat),fun(nat,X_a),hAPP(fun(nat,X_a),fun(fun(nat,nat),fun(nat,X_a)),combb(nat,X_a,nat),X_3),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),times_times(nat)),L))),X_1),sequentially))))))) # label(fact_4480_LIMSEQ__linear) # label(axiom) # label(non_clause).  [assumption].
7.74/7.72	4678 (all X_a all R_3 all F all X_1 all Y_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(X_a,nat,F,X_1)),hAPP(X_a,nat,F,Y_1))) -> (hBOOL(hAPP(fun(product_prod(X_a,X_a),bool),bool,hAPP(product_prod(X_a,X_a),fun(fun(product_prod(X_a,X_a),bool),bool),member(product_prod(X_a,X_a)),hAPP(X_a,product_prod(X_a,X_a),hAPP(X_a,fun(X_a,product_prod(X_a,X_a)),product_Pair(X_a,X_a),X_1),Y_1)),R_3)) -> hBOOL(hAPP(fun(product_prod(X_a,X_a),bool),bool,hAPP(product_prod(X_a,X_a),fun(fun(product_prod(X_a,X_a),bool),bool),member(product_prod(X_a,X_a)),hAPP(X_a,product_prod(X_a,X_a),hAPP(X_a,fun(X_a,product_prod(X_a,X_a)),product_Pair(X_a,X_a),X_1),Y_1)),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(X_a,X_a),bool),hAPP(fun(X_a,nat),fun(fun(product_prod(X_a,X_a),bool),fun(product_prod(X_a,X_a),bool)),mlex_prod(X_a),F),R_3)))))) # label(fact_3796_mlex__leq) # label(axiom) # label(non_clause).  [assumption].
7.74/7.72	4679 (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_1580_order__less__asym) # label(axiom) # label(non_clause).  [assumption].
7.74/7.72	4680 (all X hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X),hAPP(nat,real,real_1(nat),hAPP(real,nat,natceiling,X))))) # label(fact_2312_real__natceiling__ge) # label(axiom) # label(non_clause).  [assumption].
7.74/7.72	4681 (all X_1 all Y_1 (hBOOL(hAPP(nat,bool,even_odd_even(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X_1),Y_1))) <-> -hBOOL(hAPP(nat,bool,even_odd_even(nat),X_1)) & -hBOOL(hAPP(nat,bool,even_odd_even(nat),Y_1)) | hBOOL(hAPP(nat,bool,even_odd_even(nat),X_1)) & hBOOL(hAPP(nat,bool,even_odd_even(nat),Y_1)))) # label(fact_2415_even__sum__nat) # label(axiom) # label(non_clause).  [assumption].
7.74/7.72	4682 (all C_1 (C_1 = zero_zero(rat) <-> hBOOL(hAPP(fun(nat,rat),bool,vanishes,hAPP(rat,fun(nat,rat),combk(rat,nat),C_1))))) # label(fact_4843_vanishes__const) # label(axiom) # label(non_clause).  [assumption].
7.74/7.72	4683 (all X_b all X_a all X_c all F all G all A_3 hAPP(fun(X_c,bool),fun(X_a,bool),hAPP(fun(X_c,X_a),fun(fun(X_c,bool),fun(X_a,bool)),image(X_c,X_a),hAPP(fun(X_c,X_b),fun(X_c,X_a),hAPP(fun(X_b,X_a),fun(fun(X_c,X_b),fun(X_c,X_a)),combb(X_b,X_a,X_c),F),G)),A_3) = hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),G),A_3))) # label(fact_3844_image__image) # label(axiom) # label(non_clause).  [assumption].
7.74/7.72	4684 (all X_a (semiring_div(X_a) -> (all A_1 all B all C (zero_zero(X_a) != ti(X_a,C) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),A_1),B) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),B)))))) # label(fact_994_div__mult__mult1) # label(axiom) # label(non_clause).  [assumption].
7.74/7.72	4685 (all X_b all X_c all X_a product_prod_rec(X_b,X_c,X_a) = ti(fun(fun(X_b,fun(X_c,X_a)),fun(product_prod(X_b,X_c),X_a)),product_prod_rec(X_b,X_c,X_a))) # label(tsy_c_Product__Type_Oprod_Oprod__rec_res) # label(axiom) # label(non_clause).  [assumption].
7.74/7.72	4686 (all K_4 all L_4 ((-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),L_4)) -> hAPP(int,int,hAPP(int,fun(int,int),z3mod,K_4),L_4) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),K_4),hAPP(int,int,uminus_uminus(int),L_4))) & (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),L_4)) -> hAPP(int,int,hAPP(int,fun(int,int),z3mod,K_4),L_4) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),K_4),L_4)))) # label(fact_2728_z3mod__def) # label(axiom) # label(non_clause).  [assumption].
7.74/7.72	4687 (all X_1 all P_4 (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),hAPP(int,fun(int,bool),sRStar,P_4))) -> -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,X_1),zero_zero(int)),P_4)))) # label(fact_1130_StandardRes__SRStar__prop1a) # label(axiom) # label(non_clause).  [assumption].
7.74/7.72	4688 (all X_a (comm_semiring_1(X_a) -> (all M all A_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),M),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),M)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),one_one(X_a))),M)))) # label(fact_254_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J) # label(axiom) # label(non_clause).  [assumption].
7.74/7.72	4689 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),N)),N) = M)) # label(fact_1119_div__mult__self__is__m) # label(axiom) # label(non_clause).  [assumption].
7.74/7.72	4690 (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_1432_expand__Suc) # label(axiom) # label(non_clause).  [assumption].
7.74/7.72	4691 (all X_a all Xs all Ys (hAPP(list(X_a),nat,size_size(list(X_a)),Xs) != hAPP(list(X_a),nat,size_size(list(X_a)),Ys) -> Xs != Ys)) # label(fact_3557_neq__if__length__neq) # label(axiom) # label(non_clause).  [assumption].
7.74/7.72	4692 (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_1566_less__imp__neq) # label(axiom) # label(non_clause).  [assumption].
7.74/7.72	4693 (all A_2 all P_4 (hBOOL(hAPP(int,bool,zprime,P_4)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),P_4)) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_2),zero_zero(int)),P_4)) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),quadRes,P_4),A_2)) -> (all X_2 (hBOOL(hAPP(fun(fun(int,bool),bool),bool,hAPP(fun(int,bool),fun(fun(fun(int,bool),bool),bool),member(fun(int,bool)),X_2),hAPP(int,fun(fun(int,bool),bool),hAPP(int,fun(int,fun(fun(int,bool),bool)),setS,A_2),P_4))) -> hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))) = hAPP(fun(int,bool),nat,finite_card(int),X_2)))))))) # label(fact_1539_SetS__elems__card) # label(axiom) # label(non_clause).  [assumption].
7.74/7.72	4694 (all Z1 all Z2 all 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)) = 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)) # label(fact_481_zdiff__zmult__distrib) # label(axiom) # label(non_clause).  [assumption].
7.74/7.72	4695 (all Y all X all N (-hBOOL(hAPP(nat,bool,even_odd_even(nat),N)) -> (X = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),Y),N) -> Y = hAPP(real,real,hAPP(nat,fun(real,real),root,N),X)))) # label(fact_2674_odd__real__root__unique) # label(axiom) # label(non_clause).  [assumption].
7.74/7.72	4696 (all X_a (linordered_idom(X_a) -> (all A_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),zero_zero(X_a))) <-> hAPP(X_a,X_a,sgn_sgn(X_a),A_2) = hAPP(X_a,X_a,uminus_uminus(X_a),one_one(X_a)))))) # label(fact_2230_sgn__1__neg) # label(axiom) # label(non_clause).  [assumption].
7.74/7.72	4697 (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)) -> ti(X_a,Y) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),Y))))) # label(fact_4980_min__max_Osup__absorb2) # label(axiom) # label(non_clause).  [assumption].
7.74/7.72	4698 (all X_a all F all A_3 hAPP(fun(X_a,bool),real,hAPP(fun(X_a,real),fun(fun(X_a,bool),real),big_co302546470etprod(X_a,real),hAPP(fun(X_a,nat),fun(X_a,real),hAPP(fun(nat,real),fun(fun(X_a,nat),fun(X_a,real)),combb(nat,real,X_a),real_1(nat)),F)),A_3) = hAPP(nat,real,real_1(nat),hAPP(fun(X_a,bool),nat,hAPP(fun(X_a,nat),fun(fun(X_a,bool),nat),big_co302546470etprod(X_a,nat),F),A_3))) # label(fact_3941_real__of__nat__setprod) # label(axiom) # label(non_clause).  [assumption].
7.74/7.72	4699 (all R_4 exists N_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,real_1(int),N_2)),R_4)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),R_4),hAPP(int,real,real_1(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),N_2),one_one(int))))))) # label(fact_3424_real__lb__ub__int) # label(axiom) # label(non_clause).  [assumption].
7.74/7.72	4700 (all B hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),posDivAlg,zero_zero(int)),B) = hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),zero_zero(int)),zero_zero(int))) # label(fact_1128_posDivAlg__0) # label(axiom) # label(non_clause).  [assumption].
7.74/7.72	4701 (all B_1 all A_2 all P_4 (hBOOL(hAPP(int,bool,zprime,P_4)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_2),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),P_4),one_one(int)))) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),B_1),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),wset,A_2),P_4))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),B_1)))))) # label(fact_839_wset__g__1) # label(axiom) # label(non_clause).  [assumption].
7.74/7.72	4702 (all X all N (-hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),N))) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X)) -> hAPP(real,nat,natceiling,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),hAPP(int,real,number_number_of(real),N))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(real,nat,natceiling,X)),hAPP(int,nat,number_number_of(nat),N))))) # label(fact_1837_natceiling__add__number__of) # label(axiom) # label(non_clause).  [assumption].
7.74/7.72	4703 (all X_a all R1_1 all R2_1 (hBOOL(hAPP(fun(X_a,fun(X_a,bool)),bool,hAPP(fun(X_a,fun(X_a,bool)),fun(fun(X_a,fun(X_a,bool)),bool),ord_less_eq(fun(X_a,fun(X_a,bool))),R1_1),R2_1)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(fun(X_a,fun(X_a,bool)),fun(X_a,bool),accp(X_a),R2_1)),hAPP(fun(X_a,fun(X_a,bool)),fun(X_a,bool),accp(X_a),R1_1))))) # label(fact_2913_accp__subset) # label(axiom) # label(non_clause).  [assumption].
7.74/7.72	4704 (all X_a ti(fun(product_prod(int,int),X_a),abs_Frac(X_a)) = abs_Frac(X_a)) # label(tsy_c_Nitpick_OAbs__Frac_res) # label(axiom) # label(non_clause).  [assumption].
7.74/7.72	4705 (all X_a all X_b (metric_space(X_b) -> (all G all Ma all F all L all A_3 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),L),A_3)) -> (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),G),Ma),A_3)) -> hBOOL(hAPP(filter(X_a),bool,hAPP(real,fun(filter(X_a),bool),hAPP(fun(X_a,real),fun(real,fun(filter(X_a),bool)),tendsto(X_a,real),hAPP(fun(X_a,X_b),fun(X_a,real),hAPP(fun(X_a,fun(X_b,real)),fun(fun(X_a,X_b),fun(X_a,real)),combs(X_a,X_b,real),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,real)),hAPP(fun(X_b,fun(X_b,real)),fun(fun(X_a,X_b),fun(X_a,fun(X_b,real))),combb(X_b,fun(X_b,real),X_a),dist_dist(X_b)),F)),G)),hAPP(X_b,real,hAPP(X_b,fun(X_b,real),dist_dist(X_b),L),Ma)),A_3))))))) # label(fact_4457_tendsto__dist) # label(axiom) # label(non_clause).  [assumption].
7.74/7.72	4706 (all X_a (number_ring(X_a) -> (all W all Z_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,uminus_uminus(int),W))),Z_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(int,X_a,number_number_of(X_a),W))),Z_1)))) # label(fact_2045_minus__number__of__mult) # label(axiom) # label(non_clause).  [assumption].
7.74/7.72	4707 (all X_a (order(X_a) -> ord_atLeastAtMost(X_a) = ti(fun(X_a,fun(X_a,fun(X_a,bool))),ord_atLeastAtMost(X_a)))) # label(tsy_c_SetInterval_Oord__class_OatLeastAtMost_res) # label(axiom) # label(non_clause).  [assumption].
7.74/7.72	4708 (all L all U_1 hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),L),U_1)))) # label(fact_4164_finite__atLeastLessThan) # label(axiom) # label(non_clause).  [assumption].
7.74/7.72	4709 (all X (hAPP(real,real,cos,X) != zero_zero(real) -> hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),one_one(real)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,tan,X)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,inverse_inverse(real),hAPP(real,real,cos,X))),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) # label(fact_2627_tan__sec) # label(axiom) # label(non_clause).  [assumption].
7.74/7.72	4710 (all X_a (linord1117847801e_zero(X_a) -> (all X_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,inverse_inverse(X_a),X_1)),one_one(X_a))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),one_one(X_a)),X_1)) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),zero_zero(X_a))))))) # label(fact_2574_inverse__le__1__iff) # label(axiom) # label(non_clause).  [assumption].
7.74/7.72	4711 (all X_a (real_normed_algebra(X_a) -> (all C_1 all F (hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),F)) -> hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(X_a,X_a),fun(fun(nat,X_a),fun(nat,X_a)),combb(X_a,X_a,nat),hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1)),F))))))) # label(fact_3997_summable__mult) # label(axiom) # label(non_clause).  [assumption].
7.74/7.72	4712 (all N all M hAPP(int,quickcheck_code_int,quickcheck_of_int,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(quickcheck_code_int,int,quickcheck_int_of,N)),hAPP(quickcheck_code_int,int,quickcheck_int_of,M))) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),N),M)) # label(fact_3541_plus__code__int__def) # label(axiom) # label(non_clause).  [assumption].
7.74/7.72	4713 (all X_a (finite_finite(X_a) -> (all A_3 hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_3))))) # label(fact_1818_finite__code) # label(axiom) # label(non_clause).  [assumption].
7.74/7.72	4714 (all X_1 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(nat,fun(real,real),hAPP(fun(real,fun(nat,real)),fun(nat,fun(real,real)),combc(real,nat,real),hAPP(fun(real,real),fun(real,fun(nat,real)),hAPP(fun(real,fun(nat,real)),fun(fun(real,real),fun(real,fun(nat,real))),combb(real,fun(nat,real),real),power_power(real)),sin)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),X_1),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,cos,X_1)),hAPP(real,real,sin,X_1))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,cos,X_1)),hAPP(real,real,sin,X_1)))))) # label(fact_3910_DERIV__sin__realpow2) # label(axiom) # label(non_clause).  [assumption].
7.74/7.72	4715 (all X all P_5 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),P_5)) -> (hBOOL(hAPP(int,bool,zprime,P_5)) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,X),zero_zero(int)),P_5)) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),quadRes,P_5),X)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),X),hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),P_5),one_one(int))),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))),hAPP(int,int,number_number_of(int),min_1)),P_5))))))) # label(fact_1076_Euler__part1) # label(axiom) # label(non_clause).  [assumption].
7.74/7.72	4716 (all N_1 all Ma (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),Ma)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),hAPP(nat,nat,suc,Ma))) <-> N_1 = Ma))) # label(fact_1236_not__less__less__Suc__eq) # label(axiom) # label(non_clause).  [assumption].
7.74/7.72	4717 (all X_a (linordered_semidom(X_a) -> (all N all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),A_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),B),N)))))))) # label(fact_404_power__mono) # label(axiom) # label(non_clause).  [assumption].
7.74/7.72	4718 (all X_a (linordered_field(X_a) -> (all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,inverse_inverse(X_a),A_1)),hAPP(X_a,X_a,inverse_inverse(X_a),B))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),A_1))))))) # label(fact_2572_inverse__le__imp__le) # label(axiom) # label(non_clause).  [assumption].
7.74/7.72	4719 (all X_a (ring_char_0(X_a) -> (all Z (hAPP(int,X_a,ring_1_of_int(X_a),Z) = zero_zero(X_a) <-> zero_zero(int) = ti(int,Z))))) # label(fact_3578_of__int__eq__0__iff) # label(axiom) # label(non_clause).  [assumption].
7.74/7.72	4720 (all Y_1 hAPP(fun(real,bool),real,the(real),hAPP(fun(real,bool),fun(real,bool),hAPP(fun(real,fun(bool,bool)),fun(fun(real,bool),fun(real,bool)),combs(real,bool,bool),hAPP(fun(real,bool),fun(real,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(real,bool),fun(real,fun(bool,bool))),combb(bool,fun(bool,bool),real),fconj),hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))),hAPP(fun(real,bool),fun(real,bool),hAPP(fun(real,fun(bool,bool)),fun(fun(real,bool),fun(real,bool)),combs(real,bool,bool),hAPP(fun(real,bool),fun(real,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(real,bool),fun(real,fun(bool,bool))),combb(bool,fun(bool,bool),real),fconj),hAPP(real,fun(real,bool),hAPP(fun(real,fun(real,bool)),fun(real,fun(real,bool)),combc(real,real,bool),ord_less(real)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))),hAPP(real,fun(real,bool),hAPP(fun(real,fun(real,bool)),fun(real,fun(real,bool)),combc(real,real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),hAPP(fun(real,fun(real,bool)),fun(fun(real,real),fun(real,fun(real,bool))),combb(real,fun(real,bool),real),fequal(real)),tan)),Y_1)))) = hAPP(real,real,arctan,Y_1)) # label(fact_4132_arctan__def) # label(axiom) # label(non_clause).  [assumption].
7.74/7.72	4721 (all X_a (linordered_field(X_a) -> (all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),one_one(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),one_one(X_a)),hAPP(X_a,X_a,inverse_inverse(X_a),A_1)))))))) # label(fact_2610_one__le__inverse) # label(axiom) # label(non_clause).  [assumption].
7.74/7.72	4722 (all X_a (boolean_algebra(X_a) -> (all Y all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),hAPP(X_a,X_a,uminus_uminus(X_a),X))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),hAPP(X_a,X_a,uminus_uminus(X_a),Y))))))) # label(fact_2958_compl__le__swap1) # label(axiom) # label(non_clause).  [assumption].
7.74/7.72	4723 (all R_4 all S_3 hAPP(rat,real,ratreal,hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),hAPP(int,rat,number_number_of(rat),R_4)),hAPP(int,rat,number_number_of(rat),S_3))) = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(int,real,number_number_of(real),R_4)),hAPP(int,real,number_number_of(real),S_3))) # label(fact_3734_Ratreal__number__of__quotient2) # label(axiom) # label(non_clause).  [assumption].
7.74/7.72	4724 (all Y all X all P_5 (hBOOL(hAPP(int,bool,zprime,P_5)) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,X),zero_zero(int)),P_5)) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,Y),zero_zero(int)),P_5)) -> -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X),Y)),zero_zero(int)),P_5)))))) # label(fact_456_zcong__zmult__prop3) # label(axiom) # label(non_clause).  [assumption].
7.74/7.72	4725 (all X_1 ((exists N_2 hAPP(int,real,real_1(int),N_2) = X_1) <-> X_1 = hAPP(int,real,real_1(int),hAPP(real,int,archimedean_ceiling(real),X_1)))) # label(fact_3341_real__of__int__ceiling__cancel) # label(axiom) # label(non_clause).  [assumption].
7.74/7.72	4726 (all Y all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,exp(real),one_one(real))),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X),Y)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,ln,Y)),Y)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,ln,X)),X)))))) # label(fact_2619_ln__x__over__x__mono) # label(axiom) # label(non_clause).  [assumption].
7.74/7.72	4727 (all X_a all X_b all F all A_3 all B_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),A_3)),B_2)) -> hBOOL(hAPP(fun(fun(X_a,bool),bool),bool,hAPP(fun(fun(X_a,bool),bool),fun(fun(fun(X_a,bool),bool),bool),ord_less_eq(fun(fun(X_a,bool),bool)),hAPP(fun(fun(X_b,bool),bool),fun(fun(X_a,bool),bool),hAPP(fun(fun(X_b,bool),fun(X_a,bool)),fun(fun(fun(X_b,bool),bool),fun(fun(X_a,bool),bool)),image(fun(X_b,bool),fun(X_a,bool)),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F)),hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),pow(X_b),A_3))),hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),pow(X_a),B_2))))) # label(fact_3636_image__Pow__mono) # label(axiom) # label(non_clause).  [assumption].
7.74/7.72	4728 (all Z (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(int,nat,nat_1,Z))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),Z)))) # label(fact_1132_zero__less__nat__eq) # label(axiom) # label(non_clause).  [assumption].
7.74/7.72	4729 (all X_a (archim1727834104eiling(X_a) -> (all X_1 all Z (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(X_a,int,archimedean_ceiling(X_a),X_1)),Z)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(int,X_a,ring_1_of_int(X_a),Z)),one_one(X_a)))))))) # label(fact_3610_ceiling__less__iff) # label(axiom) # label(non_clause).  [assumption].
7.74/7.72	4730 (all X all Y hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(complex,real,re,X)),hAPP(complex,real,re,Y))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(complex,real,im,X)),hAPP(complex,real,im,Y)))),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(complex,real,re,X)),hAPP(complex,real,im,Y))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(complex,real,im,X)),hAPP(complex,real,re,Y)))) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),X),Y)) # label(fact_3016_complex__mult__def) # label(axiom) # label(non_clause).  [assumption].
7.74/7.72	4731 (all X_b all X_a (real_normed_vector(X_b) & topological_space(X_a) -> (all G all M_1 all F all L_2 all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(real,fun(filter(X_a),bool),hAPP(fun(X_a,real),fun(real,fun(filter(X_a),bool)),tendsto(X_a,real),F),L_2),hAPP(X_a,filter(X_a),at(X_a),A_2))) -> (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),G),M_1),hAPP(X_a,filter(X_a),at(X_a),A_2))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(fun(X_a,X_b),fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,X_b)),combs(X_a,X_b,X_b),hAPP(fun(X_a,real),fun(X_a,fun(X_b,X_b)),hAPP(fun(real,fun(X_b,X_b)),fun(fun(X_a,real),fun(X_a,fun(X_b,X_b))),combb(real,fun(X_b,X_b),X_a),scaleR_scaleR(X_b)),F)),G)),hAPP(X_b,X_b,hAPP(real,fun(X_b,X_b),scaleR_scaleR(X_b),L_2),M_1)),hAPP(X_a,filter(X_a),at(X_a),A_2)))))))) # label(fact_4738_LIM__scaleR) # label(axiom) # label(non_clause).  [assumption].
7.74/7.72	4732 (all X_a all X all Y hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),hAPP(bool,fun(X_a,fun(X_a,X_a)),if(X_a),fTrue),X),Y) = ti(X_a,X)) # label(help_If_1_1_T) # label(axiom) # label(non_clause).  [assumption].
7.74/7.72	4733 (all X_a all X_b (ordere779506340up_add(X_b) & semiring_1(X_b) -> (all F all K_3 all A_3 ((all I_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),I_2),A_3)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_a,X_b,F,I_2)),K_3)))) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),F),A_3)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(nat,X_b,semiring_1_of_nat(X_b),hAPP(fun(X_a,bool),nat,finite_card(X_a),A_3))),K_3))))))) # label(fact_4296_setsum__bounded) # label(axiom) # label(non_clause).  [assumption].
7.74/7.72	4734 (all X_a (linorder(X_a) -> (all X_1 all Y_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),Y_1)) -> (ti(X_a,Y_1) = ti(X_a,X_1) <-> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y_1))))))) # label(fact_1595_linorder__antisym__conv2) # label(axiom) # label(non_clause).  [assumption].
7.74/7.72	4735 (all K_4 all I_1 all J_2 (hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,I_1),J_2) = one_one(int) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),I_1),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K_4),J_2))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),I_1),K_4))))) # label(fact_3463_zrelprime__dvd__mult) # label(axiom) # label(non_clause).  [assumption].
7.74/7.72	4736 (all X_c all X_b all X_a all Q_1 all F all P_1 all P_4 (hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),P_1,hAPP(product_prod(X_b,X_a),X_a,product_snd(X_b,X_a),P_4)),hAPP(product_prod(X_b,X_a),X_b,product_fst(X_b,X_a),P_4))) -> ((all X_2 all Y_2 (hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),P_1,Y_2),X_2)) -> hBOOL(hAPP(X_c,bool,Q_1,hAPP(X_a,X_c,hAPP(X_b,fun(X_a,X_c),F,X_2),Y_2))))) -> hBOOL(hAPP(X_c,bool,Q_1,hAPP(product_prod(X_b,X_a),X_c,hAPP(fun(X_b,fun(X_a,X_c)),fun(product_prod(X_b,X_a),X_c),product_prod_case(X_b,X_a,X_c),F),P_4)))))) # label(fact_4126_exE__realizer) # label(axiom) # label(non_clause).  [assumption].
7.74/7.72	4737 (all P_1 all I all J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I),J)) -> (hBOOL(hAPP(nat,bool,P_1,J)) -> ((all I_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),J)) -> (hBOOL(hAPP(nat,bool,P_1,hAPP(nat,nat,suc,I_2))) -> hBOOL(hAPP(nat,bool,P_1,I_2))))) -> hBOOL(hAPP(nat,bool,P_1,I)))))) # label(fact_1483_inc__induct) # label(axiom) # label(non_clause).  [assumption].
7.74/7.72	4738 (all A_1 all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A_1)) -> (exists X_2 ((all Y_2 (A_1 = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),Y_2),N) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Y_2)) -> Y_2 = X_2)) & hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X_2),N) = A_1 & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X_2))))))) # label(fact_733_realpow__pos__nth__unique) # label(axiom) # label(non_clause).  [assumption].
7.74/7.72	4739 (all X_a (ab_group_add(X_a) -> (all A_2 all B_1 (zero_zero(X_a) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_2),B_1) <-> ti(X_a,A_2) = ti(X_a,B_1))))) # label(fact_794_eq__iff__diff__eq__0) # label(axiom) # label(non_clause).  [assumption].
7.74/7.72	4740 (all W_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit0,W_1)),zero_zero(int))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_1),zero_zero(int))))) # label(fact_161_bin__less__0__simps_I3_J) # label(axiom) # label(non_clause).  [assumption].
7.74/7.72	4741 (all X_1 all Y_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_1),Y_1)) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,sqrt,X_1)),hAPP(real,real,sqrt,Y_1))))) # label(fact_1612_real__sqrt__le__iff) # label(axiom) # label(non_clause).  [assumption].
7.74/7.72	4742 (all N all I_1 ((zero_zero(code_code_numeral) != I_1 -> hAPP(nat,nat,hAPP(code_code_numeral,fun(nat,nat),code_nat_of_aux,I_1),N) = hAPP(nat,nat,hAPP(code_code_numeral,fun(nat,nat),code_nat_of_aux,hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),minus_minus(code_code_numeral),I_1),one_one(code_code_numeral))),hAPP(nat,nat,suc,N))) & (I_1 = zero_zero(code_code_numeral) -> N = hAPP(nat,nat,hAPP(code_code_numeral,fun(nat,nat),code_nat_of_aux,I_1),N)))) # label(fact_1487_nat__of__aux__code) # label(axiom) # label(non_clause).  [assumption].
7.74/7.72	4743 (all N hAPP(real,real,sin,hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),hAPP(nat,real,real_1(nat),N))),pi)) = zero_zero(real)) # label(fact_2333_sin__2npi) # label(axiom) # label(non_clause).  [assumption].
7.74/7.72	4744 (all X all Y (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),Y)) -> X = hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),X),Y))) # label(fact_3238_gcd__proj1__if__dvd__nat) # label(axiom) # label(non_clause).  [assumption].
7.74/7.72	4745 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> hAPP(real,real,uminus_uminus(real),hAPP(real,real,ln,X)) = hAPP(real,real,ln,hAPP(real,real,inverse_inverse(real),X)))) # label(fact_2617_ln__inverse) # label(axiom) # label(non_clause).  [assumption].
7.74/7.72	4746 (all A_1 all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),one_one(real)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A_1)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,ln,X)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(real,fun(real,real),powr,X),A_1)),A_1)))))) # label(fact_3320_ln__powr__bound) # label(axiom) # label(non_clause).  [assumption].
7.74/7.72	4747 (all Y all X (hBOOL(hAPP(int,bool,nat_is_nat,X)) -> (hBOOL(hAPP(int,bool,nat_is_nat,Y)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),X),Y)))))) # label(fact_4857_transfer__int__nat__gcd__closures_I1_J) # label(axiom) # label(non_clause).  [assumption].
7.74/7.72	4748 (all A_2 all B_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),B_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B_1),A_2)) -> hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),B_1),hAPP(int,fun(int,bool),d22set,A_2)))))) # label(fact_867_d22set__mem) # label(axiom) # label(non_clause).  [assumption].
7.74/7.72	4749 (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),hAPP(int,nat,number_number_of(nat),hAPP(int,int,succ,V))),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),one_one(nat)),N)))) # label(fact_1519_Suc__nat__number__of__add) # label(axiom) # label(non_clause).  [assumption].
7.74/7.73	4750 (all C_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,abs_abs(real),C_1)),one_one(real))) -> hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,abs_abs(real),C_1))),zero_zero(real)),sequentially)))) # label(fact_4490_LIMSEQ__rabs__realpow__zero) # label(axiom) # label(non_clause).  [assumption].
7.74/7.73	4751 (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_386_mult__strict__right__mono) # label(axiom) # label(non_clause).  [assumption].
7.74/7.73	4752 (all X_1 all N_1 exists T_4 hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(real,fun(nat,fun(real,real)),hAPP(fun(nat,fun(real,fun(real,real))),fun(real,fun(nat,fun(real,real))),combc(nat,real,fun(real,real)),hAPP(fun(nat,bool),fun(nat,fun(real,fun(real,real))),hAPP(fun(bool,fun(real,fun(real,real))),fun(fun(nat,bool),fun(nat,fun(real,fun(real,real)))),combb(bool,fun(real,fun(real,real)),nat),if(real)),even_odd_even(nat))),zero_zero(real))),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),inverse_divide(real)),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),min_1))),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),hAPP(fun(nat,nat),fun(nat,fun(nat,nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,nat),fun(nat,fun(nat,nat))),combb(nat,fun(nat,nat),nat),div_div(nat)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),minus_minus(nat)),hAPP(nat,nat,suc,zero_zero(nat))))),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),fact_fact(nat)))))),hAPP(real,fun(nat,real),power_power(real),X_1))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),N_1))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,sin,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),T_4),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),one_one(real)),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,real_1(nat),N_1))),pi)))),hAPP(nat,real,real_1(nat),hAPP(nat,nat,fact_fact(nat),N_1)))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X_1),N_1))) = hAPP(real,real,sin,X_1)) # label(fact_4267_Maclaurin__sin__expansion) # label(axiom) # label(non_clause).  [assumption].
7.74/7.73	4753 (all M (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),M)) -> hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),M),one_one(int))) = hAPP(nat,nat,suc,hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),M),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))) # label(fact_1476_inv__is__inv__aux) # label(axiom) # label(non_clause).  [assumption].
7.74/7.73	4754 (all X_a all G all A_3 hAPP(fun(X_a,bool),complex,hAPP(fun(X_a,complex),fun(fun(X_a,bool),complex),big_co1399186613setsum(X_a,complex),hAPP(fun(X_a,complex),fun(X_a,complex),hAPP(fun(complex,complex),fun(fun(X_a,complex),fun(X_a,complex)),combb(complex,complex,X_a),cnj),G)),A_3) = hAPP(complex,complex,cnj,hAPP(fun(X_a,bool),complex,hAPP(fun(X_a,complex),fun(fun(X_a,bool),complex),big_co1399186613setsum(X_a,complex),G),A_3))) # label(fact_4247_cnj_Osetsum) # label(axiom) # label(non_clause).  [assumption].
7.74/7.73	4755 (all X_1 all Y_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X_1),Y_1))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,uminus_uminus(real),X_1)),Y_1)))) # label(fact_2109_real__0__less__add__iff) # label(axiom) # label(non_clause).  [assumption].
7.74/7.73	4756 (all X_a (number(X_a) & field_inverse_zero(X_a) -> (all B_1 all W_1 all A_2 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),B_1),hAPP(int,X_a,number_number_of(X_a),W_1)) = ti(X_a,A_2) <-> (hAPP(int,X_a,number_number_of(X_a),W_1) != zero_zero(X_a) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),hAPP(int,X_a,number_number_of(X_a),W_1)) = ti(X_a,B_1)) & (zero_zero(X_a) = hAPP(int,X_a,number_number_of(X_a),W_1) -> zero_zero(X_a) = ti(X_a,A_2)))))) # label(fact_1726_divide__eq__eq__number__of1) # label(axiom) # label(non_clause).  [assumption].
7.74/7.73	4757 (all X hAPP(real,real,sgn_sgn(real),X) = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),X),hAPP(real,real,abs_abs(real),X))) # label(fact_2213_real__sgn__eq) # label(axiom) # label(non_clause).  [assumption].
7.74/7.73	4758 (all N all M (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),M)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),M),N)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),M),hAPP(int,int,fact_fact(int),N)))))) # label(fact_3197_dvd__fact__int) # label(axiom) # label(non_clause).  [assumption].
7.74/7.73	4759 (all X_a (number_semiring(X_a) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),one_one(X_a)),one_one(X_a)) = hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) # label(fact_178_semiring__one__add__one__is__two) # label(axiom) # label(non_clause).  [assumption].
7.74/7.73	4760 (all X_a ti(fun(fun(product_prod(X_a,X_a),bool),bool),refl(X_a)) = refl(X_a)) # label(tsy_c_Nitpick_Orefl_H_res) # label(axiom) # label(non_clause).  [assumption].
7.74/7.73	4761 (all X_a (real_normed_vector(X_a) -> (all A_1 all B hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(X_a,real,norm_norm(X_a),A_1)),hAPP(X_a,real,norm_norm(X_a),B))),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B))))))) # label(fact_1795_norm__diff__ineq) # label(axiom) # label(non_clause).  [assumption].
7.74/7.73	4762 (all N_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),N_1),zero_zero(int))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,real_1(int),N_1)),zero_zero(real))))) # label(fact_3383_real__of__int__lt__zero__cancel__iff) # label(axiom) # label(non_clause).  [assumption].
7.74/7.73	4763 (all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X_1)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),ln),X_1),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),one_one(real)),X_1))))) # label(fact_2645_DERIV__ln__divide) # label(axiom) # label(non_clause).  [assumption].
7.74/7.73	4764 (all Ma (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Ma),hAPP(nat,nat,suc,zero_zero(nat)))) <-> hAPP(nat,nat,suc,zero_zero(nat)) = Ma)) # label(fact_1323_dvd__1__iff__1) # label(axiom) # label(non_clause).  [assumption].
7.74/7.73	4765 (all X_a (linorder(X_a) -> (all Y all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),X)) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),Y) = ti(X_a,Y))))) # label(fact_4822_min__max_Oinf__absorb2) # label(axiom) # label(non_clause).  [assumption].
7.74/7.73	4766 (all X_a (number_ring(X_a) -> (all N hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(int,X_a,number_number_of(X_a),min_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),N)) = one_one(X_a)))) # label(fact_364_power__m1__even) # label(axiom) # label(non_clause).  [assumption].
7.74/7.73	4767 (all P_1 hAPP(fun(nat,bool),fun(nat,bool),collect(nat),P_1) = hAPP(fun(int,bool),fun(nat,bool),hAPP(fun(int,nat),fun(fun(int,bool),fun(nat,bool)),image(int,nat),nat_1),hAPP(fun(int,bool),fun(int,bool),collect(int),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),combs(int,bool,bool),hAPP(fun(int,bool),fun(int,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj),hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)))),hAPP(fun(int,nat),fun(int,bool),hAPP(fun(nat,bool),fun(fun(int,nat),fun(int,bool)),combb(nat,bool,int),P_1),nat_1))))) # label(fact_3832_Nat__Transfer_Otransfer__nat__int__set__functions_I5_J) # label(axiom) # label(non_clause).  [assumption].
7.74/7.73	4768 (all X_1 all A_2 all P_4 (hBOOL(hAPP(int,bool,zprime,P_4)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),P_4)) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_2),zero_zero(int)),P_4)) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),quadRes,P_4),A_2)) -> (hBOOL(hAPP(fun(fun(int,bool),bool),bool,hAPP(fun(int,bool),fun(fun(fun(int,bool),bool),bool),member(fun(int,bool)),X_1),hAPP(int,fun(fun(int,bool),bool),hAPP(int,fun(int,fun(fun(int,bool),bool)),setS,A_2),P_4))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(fun(int,bool),int,hAPP(fun(int,int),fun(fun(int,bool),int),big_co302546470etprod(int,int),combi(int)),X_1)),A_2),P_4)))))))) # label(fact_3933_SetS__setprod__prop) # label(axiom) # label(non_clause).  [assumption].
7.74/7.73	4769 (all A_1 all B hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),B),A_1)),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A_1),B)),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),A_1)) # label(fact_1769_real__average__minus__first) # label(axiom) # label(non_clause).  [assumption].
7.74/7.73	4770 (all X_3 (hBOOL(hAPP(fun(nat,rat),bool,vanishes,X_3)) -> hBOOL(hAPP(fun(nat,rat),bool,vanishes,hAPP(fun(nat,rat),fun(nat,rat),hAPP(fun(rat,rat),fun(fun(nat,rat),fun(nat,rat)),combb(rat,rat,nat),uminus_uminus(rat)),X_3))))) # label(fact_4844_vanishes__minus) # label(axiom) # label(non_clause).  [assumption].
7.74/7.73	4771 (all X_a (real_normed_field(X_a) -> (all Y_1 all A_2 hBOOL(hAPP(filter(X_a),bool,hAPP(X_a,fun(filter(X_a),bool),hAPP(fun(X_a,X_a),fun(X_a,fun(filter(X_a),bool)),tendsto(X_a,X_a),hAPP(X_a,fun(X_a,X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(X_a,X_a)),combc(X_a,X_a,X_a),inverse_divide(X_a)),Y_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),A_2),Y_1)),hAPP(X_a,filter(X_a),at(X_a),A_2)))))) # label(fact_4564_divide_Ocont) # label(axiom) # label(non_clause).  [assumption].
7.74/7.73	4772 (all X_a (real_normed_algebra(X_a) -> (all Xa_1 all X all Y hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Xa_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),X),Y)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Xa_1),X)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Xa_1),Y))))) # label(fact_886_mult__right_Odiff) # label(axiom) # label(non_clause).  [assumption].
7.74/7.73	4773 (all X_1 all P_4 (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),hAPP(int,fun(int,bool),sr,P_4))) -> hAPP(int,int,hAPP(int,fun(int,int),standardRes,P_4),X_1) = ti(int,X_1))) # label(fact_910_StandardRes__SR__prop) # label(axiom) # label(non_clause).  [assumption].
7.74/7.73	4774 (all X_b (ring(X_b) & number(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_492_left__diff__distrib__number__of) # label(axiom) # label(non_clause).  [assumption].
7.74/7.73	4775 (all X_a (semiri456707255roduct(X_a) -> (all C_1 all D_1 all A_2 all B_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_2),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B_1),D_1)) != hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),D_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B_1),C_1)) <-> ti(X_a,D_1) != ti(X_a,C_1) & ti(X_a,B_1) != ti(X_a,A_2))))) # label(fact_241_crossproduct__noteq) # label(axiom) # label(non_clause).  [assumption].
7.74/7.73	4776 (all X_a (linordered_idom(X_a) -> (all X_1 all N_1 (zero_zero(nat) = N_1 | hBOOL(hAPP(nat,bool,even_odd_even(nat),N_1)) & zero_zero(X_a) != ti(X_a,X_1) | -hBOOL(hAPP(nat,bool,even_odd_even(nat),N_1)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),X_1)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X_1),N_1))))))) # label(fact_2454_zero__less__power__eq) # label(axiom) # label(non_clause).  [assumption].
7.74/7.73	4777 (all X_a (linorder(X_a) -> (all A_1 all B all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),X)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),A_1),B)),X)))))) # label(fact_4824_min__max_Ole__infI2) # label(axiom) # label(non_clause).  [assumption].
7.74/7.73	4778 (all X_1 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),cos),X_1),hAPP(real,real,uminus_uminus(real),hAPP(real,real,sin,X_1))))) # label(fact_2640_DERIV__cos) # label(axiom) # label(non_clause).  [assumption].
7.74/7.73	4779 (all D_1 all A_2 all B_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,D_1),B_1)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,D_1),A_2)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,D_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A_2),B_1))))) # label(fact_2851_coprime__mul__eq) # label(axiom) # label(non_clause).  [assumption].
7.74/7.73	4780 (all A_3 (hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,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)),hAPP(fun(int,bool),fun(nat,bool),hAPP(fun(int,nat),fun(fun(int,bool),fun(nat,bool)),image(int,nat),nat_1),A_3)) = A_3)) # label(fact_3666_transfer__nat__int__set__return__embed) # label(axiom) # label(non_clause).  [assumption].
7.74/7.73	4781 (all X_a (linordered_idom(X_a) -> (all A_1 all N hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(X_a,X_a,abs_abs(X_a),A_1)),N)))))) # label(fact_1880_zero__le__power__abs) # label(axiom) # label(non_clause).  [assumption].
7.74/7.73	4782 (all A_1 all P_5 (hBOOL(hAPP(int,bool,zprime,P_5)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),A_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_1),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),P_5),one_one(int)))) -> hAPP(int,int,hAPP(int,fun(int,int),inv,P_5),A_1) != one_one(int))))) # label(fact_806_inv__not__1) # label(axiom) # label(non_clause).  [assumption].
7.74/7.73	4783 (all B all A_1 all C hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),B),hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),A_1),C)) = hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),A_1),hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),B),C))) # label(fact_4364_gcd__int_Oleft__commute) # label(axiom) # label(non_clause).  [assumption].
7.74/7.73	4784 (all N all M (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),M)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),hAPP(nat,nat,suc,M))) -> M = N))) # label(fact_1235_less__antisym) # label(axiom) # label(non_clause).  [assumption].
7.74/7.73	4785 (all A_1 (hBOOL(hAPP(nat,bool,prime,A_1)) -> hBOOL(hAPP(int,bool,zprime,hAPP(nat,int,semiring_1_of_nat(int),A_1))))) # label(fact_3063_prime__impl__zprime__int) # label(axiom) # label(non_clause).  [assumption].
7.74/7.73	4786 (all R_4 all X hAPP(complex,real,re,hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),R_4),X)) = hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),R_4),hAPP(complex,real,re,X))) # label(fact_4690_Re_OscaleR) # label(axiom) # label(non_clause).  [assumption].
7.74/7.73	4787 (all X_a (real_normed_vector(X_a) -> (all X_1 all X_3 (hBOOL(hAPP(fun(nat,real),bool,cauchy(real),X_3)) -> hBOOL(hAPP(fun(nat,X_a),bool,cauchy(X_a),hAPP(X_a,fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(X_a,fun(nat,X_a)),combc(nat,X_a,X_a),hAPP(fun(nat,real),fun(nat,fun(X_a,X_a)),hAPP(fun(real,fun(X_a,X_a)),fun(fun(nat,real),fun(nat,fun(X_a,X_a))),combb(real,fun(X_a,X_a),nat),scaleR_scaleR(X_a)),X_3)),X_1))))))) # label(fact_4723_scaleR__left_OCauchy) # label(axiom) # label(non_clause).  [assumption].
7.74/7.73	4788 (all A_1 all B ((-(hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A_1),B))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),zero_zero(int)))) -> hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),negDivAlg,A_1),B) = hAPP(product_prod(int,int),product_prod(int,int),hAPP(int,fun(product_prod(int,int),product_prod(int,int)),adjust,B),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),negDivAlg,A_1),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),B)))) & (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A_1),B))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),zero_zero(int))) -> hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),hAPP(int,int,number_number_of(int),min_1)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A_1),B)) = hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),negDivAlg,A_1),B)))) # label(fact_1067_negDivAlg_Osimps) # label(axiom) # label(non_clause).  [assumption].
7.74/7.73	4789 (all X_b all X_a all F all B_2 all A_3 ((all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_3)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),hAPP(X_a,X_b,F,X_2)),B_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_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),A_3)),B_2)))) # label(fact_3655_image__subsetI) # label(axiom) # label(non_clause).  [assumption].
7.74/7.73	4790 (all I_1 all K_4 all J_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_4),J_2)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_1),J_2)),K_4) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_2),K_4)))) # label(fact_695_add__diff__assoc) # label(axiom) # label(non_clause).  [assumption].
7.74/7.73	4791 (all X_a all A_3 all B_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_3),B_2)) -> hBOOL(hAPP(fun(fun(X_a,bool),bool),bool,hAPP(fun(X_a,bool),fun(fun(fun(X_a,bool),bool),bool),member(fun(X_a,bool)),A_3),hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),pow(X_a),B_2))))) # label(fact_2774_PowI) # label(axiom) # label(non_clause).  [assumption].
7.74/7.73	4792 (all M all N (zero_zero(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N) -> (hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),M) = zero_zero(nat) -> M = N))) # label(fact_658_diffs0__imp__equal) # label(axiom) # label(non_clause).  [assumption].
7.74/7.73	4793 (all X_b all X_a (minus(X_a) -> (all A_3 all B_2 all X_1 hAPP(X_b,X_a,hAPP(fun(X_b,X_a),fun(X_b,X_a),hAPP(fun(X_b,X_a),fun(fun(X_b,X_a),fun(X_b,X_a)),minus_minus(fun(X_b,X_a)),A_3),B_2),X_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_b,X_a,A_3,X_1)),hAPP(X_b,X_a,B_2,X_1))))) # label(fact_2964_minus__apply) # label(axiom) # label(non_clause).  [assumption].
7.74/7.73	4794 (all K_4 hAPP(int,int,bit1,K_4) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),K_4)),K_4)) # label(fact_165_Bit1__def) # label(axiom) # label(non_clause).  [assumption].
7.74/7.73	4795 (all X_1 (hBOOL(hAPP(nat,bool,even_odd_even(nat),X_1)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),X_1)))) # label(fact_2466_nat__even__iff__2__dvd) # label(axiom) # label(non_clause).  [assumption].
7.74/7.73	4796 (all Q_3 all R_4 all B all C (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),C)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),R_4),B)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),Q_3),C))),R_4)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),C)))))) # label(fact_1134_mod__lemma) # label(axiom) # label(non_clause).  [assumption].
7.74/7.73	4797 (all X_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X_1)) <-> -hBOOL(hAPP(int,bool,nat_neg,X_1)))) # label(fact_1503_not__neg__eq__ge__0) # label(axiom) # label(non_clause).  [assumption].
7.74/7.73	4798 (all M hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),M),hAPP(nat,nat,suc,zero_zero(nat))) = zero_zero(nat)) # label(fact_1351_mod__1) # label(axiom) # label(non_clause).  [assumption].
7.74/7.73	4799 (all A_9 all B_8 all Y all R_6 (ti(int,A_9) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B_8),Y)),R_6) -> ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B_8)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),R_6),B_8)) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),R_6))) & (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B_8)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),R_6),zero_zero(int))) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B_8),R_6))) -> (ti(int,B_8) != zero_zero(int) -> hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_9),B_8) = ti(int,Y))))) # label(fact_1054_divmod__int__rel__div__eq) # label(axiom) # label(non_clause).  [assumption].
7.74/7.73	4800 (all Ma all N_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),Ma),hAPP(nat,nat,suc,N_1)) = hAPP(nat,nat,hAPP(fun(nat,nat),fun(nat,nat),hAPP(nat,fun(fun(nat,nat),fun(nat,nat)),nat_case(nat),zero_zero(nat)),hAPP(fun(nat,nat),fun(nat,nat),hAPP(fun(nat,nat),fun(fun(nat,nat),fun(nat,nat)),combb(nat,nat,nat),suc),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),ord_min(nat)),N_1))),Ma)) # label(fact_4832_min__Suc2) # label(axiom) # label(non_clause).  [assumption].
7.74/7.73	4801 (all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,number_number_of(real),min_1)),Y)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),Y),one_one(real))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),hAPP(real,real,arcsin,Y)))))) # label(fact_2131_arcsin__lbound) # label(axiom) # label(non_clause).  [assumption].
7.74/7.73	4802 (all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X_1)) -> hBOOL(hAPP(real,bool,hAPP(fun(real,real),fun(real,bool),isCont(real,real),ln),X_1)))) # label(fact_4883_isCont__ln) # label(axiom) # label(non_clause).  [assumption].
7.74/7.73	4803 (all X_a all A_3 all B_2 (hBOOL(hAPP(fun(product_prod(fun(X_a,bool),fun(X_a,bool)),bool),bool,hAPP(product_prod(fun(X_a,bool),fun(X_a,bool)),fun(fun(product_prod(fun(X_a,bool),fun(X_a,bool)),bool),bool),member(product_prod(fun(X_a,bool),fun(X_a,bool))),hAPP(fun(X_a,bool),product_prod(fun(X_a,bool),fun(X_a,bool)),hAPP(fun(X_a,bool),fun(fun(X_a,bool),product_prod(fun(X_a,bool),fun(X_a,bool))),product_Pair(fun(X_a,bool),fun(X_a,bool)),A_3),B_2)),finite_psubset(X_a))) <-> hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),B_2)) & hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less(fun(X_a,bool)),A_3),B_2)))) # label(fact_3179_in__finite__psubset) # label(axiom) # label(non_clause).  [assumption].
7.74/7.73	4804 (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_429_mult__less__imp__less__right) # label(axiom) # label(non_clause).  [assumption].
7.74/7.73	4805 (all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),zero_zero(nat)),N) = zero_zero(nat)) # label(fact_4807_min__0L) # label(axiom) # label(non_clause).  [assumption].
7.74/7.73	4806 (all C all D all A_1 all B all M (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_1),B),M)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,C),D),M)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A_1),C)),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),B),D)),M))))) # label(fact_484_zcong__zdiff) # label(axiom) # label(non_clause).  [assumption].
7.74/7.73	4807 (all X_a (linord581940658strict(X_a) -> (all X_1 all Y_1 (zero_zero(X_a) != ti(X_a,Y_1) | ti(X_a,X_1) != zero_zero(X_a) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X_1),X_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Y_1),Y_1)))))))) # label(fact_108_sum__squares__gt__zero__iff) # label(axiom) # label(non_clause).  [assumption].
7.74/7.73	4808 (all X_1 all Y_1 (hAPP(complex,real,re,Y_1) = hAPP(complex,real,re,X_1) & hAPP(complex,real,im,X_1) = hAPP(complex,real,im,Y_1) <-> X_1 = Y_1)) # label(fact_2996_complex__eq__iff) # label(axiom) # label(non_clause).  [assumption].
7.74/7.73	4809 (all N_1 hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),min_1))),suc)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),N_1))) = zero_zero(real)) # label(fact_4237_sumr__minus__one__realpow__zero) # label(axiom) # label(non_clause).  [assumption].
7.74/7.73	4810 (all X_a all R_3 all S (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),R_3),S)) <-> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(X_a,bool)),combc(X_a,fun(X_a,bool),bool),member(X_a)),R_3)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(X_a,bool)),combc(X_a,fun(X_a,bool),bool),member(X_a)),S))))) # label(fact_4339_pred__subset__eq) # label(axiom) # label(non_clause).  [assumption].
7.74/7.73	4811 (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_771_ab__semigroup__add__class_Oadd__ac_I1_J) # label(axiom) # label(non_clause).  [assumption].
7.74/7.73	4812 (all Sa all Ta all A_2 all B_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A_2),B_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Sa),Ta)) -> hBOOL(hAPP(fun(product_prod(product_prod(nat,nat),product_prod(nat,nat)),bool),bool,hAPP(product_prod(product_prod(nat,nat),product_prod(nat,nat)),fun(fun(product_prod(product_prod(nat,nat),product_prod(nat,nat)),bool),bool),member(product_prod(product_prod(nat,nat),product_prod(nat,nat))),hAPP(product_prod(nat,nat),product_prod(product_prod(nat,nat),product_prod(nat,nat)),hAPP(product_prod(nat,nat),fun(product_prod(nat,nat),product_prod(product_prod(nat,nat),product_prod(nat,nat))),product_Pair(product_prod(nat,nat),product_prod(nat,nat)),hAPP(nat,product_prod(nat,nat),hAPP(nat,fun(nat,product_prod(nat,nat)),product_Pair(nat,nat),A_2),Sa)),hAPP(nat,product_prod(nat,nat),hAPP(nat,fun(nat,product_prod(nat,nat)),product_Pair(nat,nat),B_1),Ta))),pair_leq))))) # label(fact_3488_pair__leqI2) # label(axiom) # label(non_clause).  [assumption].
7.74/7.73	4813 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,M)),hAPP(nat,nat,suc,N))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N)))) # label(fact_1229_Suc__less__SucD) # label(axiom) # label(non_clause).  [assumption].
7.74/7.73	4814 (all A_3 all Ma (hAPP(int,nat,phi,Ma) = hAPP(fun(int,bool),nat,finite_card(int),A_3) & hBOOL(hAPP(fun(fun(int,bool),bool),bool,hAPP(fun(int,bool),fun(fun(fun(int,bool),bool),bool),member(fun(int,bool)),A_3),hAPP(int,fun(fun(int,bool),bool),rsetR,Ma))) <-> hBOOL(hAPP(int,bool,hAPP(fun(int,bool),fun(int,bool),is_RRset,A_3),Ma)))) # label(fact_3627_is__RRset__def) # label(axiom) # label(non_clause).  [assumption].
7.74/7.73	4815 (all X_a (real_normed_field(X_a) -> (all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,norm_norm(X_a),X_1)),one_one(real))) -> hBOOL(hAPP(X_a,bool,hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),hAPP(X_a,fun(nat,X_a),power_power(X_a),X_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),one_one(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),one_one(X_a)),X_1)))))))) # label(fact_4098_geometric__sums) # label(axiom) # label(non_clause).  [assumption].
7.74/7.73	4816 (all X_a (field_inverse_zero(X_a) & field_char_0(X_a) -> (all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_2),field_char_0_Rats(X_a))) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),hAPP(X_a,X_a,inverse_inverse(X_a),A_2)),field_char_0_Rats(X_a))))))) # label(fact_3701_Rats__inverse) # label(axiom) # label(non_clause).  [assumption].
7.74/7.73	4817 (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_399_pos__add__strict) # label(axiom) # label(non_clause).  [assumption].
7.74/7.73	4818 (all X_a ti(fun(int,fun(int,X_a)),frac(X_a)) = frac(X_a)) # label(tsy_c_Nitpick_Ofrac_res) # label(axiom) # label(non_clause).  [assumption].
7.74/7.73	4819 (all X_a (real_normed_field(X_a) -> (all C_1 all F all A_2 (hBOOL(hAPP(X_a,bool,hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),F),A_2)) -> hBOOL(hAPP(X_a,bool,hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),hAPP(X_a,fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(X_a,fun(nat,X_a)),combc(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),inverse_divide(X_a)),F)),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),A_2),C_1))))))) # label(fact_4086_sums__divide) # label(axiom) # label(non_clause).  [assumption].
7.74/7.73	4820 (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_46_sum__squares__ge__zero) # label(axiom) # label(non_clause).  [assumption].
7.74/7.73	4821 (all N hAPP(int,int,ring_1_of_int(int),hAPP(nat,int,semiring_1_of_nat(int),N)) = hAPP(nat,int,semiring_1_of_nat(int),N)) # label(fact_3577_of__int__int__eq) # label(axiom) # label(non_clause).  [assumption].
7.74/7.73	4822 (all L all U_1 hAPP(fun(int,bool),nat,finite_card(int),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_gr676655987ssThan(int),L),U_1)) = hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),U_1),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),L),one_one(int))))) # label(fact_3676_card__greaterThanLessThan__int) # label(axiom) # label(non_clause).  [assumption].
7.74/7.73	4823 (all X_1 -(hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),zEven)) & hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),zOdd)))) # label(fact_1277_even__odd__conj) # label(axiom) # label(non_clause).  [assumption].
7.74/7.73	4824 (all X_a (divisi14063676e_zero(X_a) -> (all A_1 all N hAPP(X_a,X_a,inverse_inverse(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N)) = hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(X_a,X_a,inverse_inverse(X_a),A_1)),N)))) # label(fact_2518_power__inverse) # label(axiom) # label(non_clause).  [assumption].
7.74/7.73	4825 (all A_1 ((A_1 = zero_zero(real) -> hAPP(real,real,sgn_sgn(real),A_1) = zero_zero(real)) & (A_1 != zero_zero(real) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A_1)) -> hAPP(real,real,sgn_sgn(real),A_1) = one_one(real)) & (-hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A_1)) -> hAPP(real,real,sgn_sgn(real),A_1) = hAPP(real,real,uminus_uminus(real),one_one(real)))))) # label(fact_2228_sgn__real__def) # label(axiom) # label(non_clause).  [assumption].
7.74/7.73	4826 (all X_a all A_3 all B_2 (ti(fun(X_a,bool),B_2) = ti(fun(X_a,bool),A_3) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_3),B_2)))) # label(fact_1958_equalityD1) # label(axiom) # label(non_clause).  [assumption].
7.74/7.73	4827 (all X_a (order(X_a) -> (all A_1 all B (ti(X_a,B) != ti(X_a,A_1) -> (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_1591_order__neq__le__trans) # label(axiom) # label(non_clause).  [assumption].
7.74/7.73	4828 (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),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),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_365_split__mult__neg__le) # label(axiom) # label(non_clause).  [assumption].
7.74/7.73	4829 (all X_a (field_char_0(X_a) -> (all B_1 all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_2),field_char_0_Rats(X_a))) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),B_1),field_char_0_Rats(X_a))) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),B_1)),field_char_0_Rats(X_a)))))))) # label(fact_3693_Rats__add) # label(axiom) # label(non_clause).  [assumption].
7.74/7.73	4830 (all D_1 all A_2 all B_1 (hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),D_1),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_2),B_1)) = one_one(int) <-> hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),D_1),A_2) = one_one(int) & hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),D_1),B_1) = one_one(int))) # label(fact_4386_coprime__mul__eq__int) # label(axiom) # label(non_clause).  [assumption].
7.74/7.73	4831 (all X_a (real_normed_vector(X_a) -> (all A_1 all B all B_5 hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),B),B_5)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_1),B)),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_1),B_5))))) # label(fact_4719_scaleR_Odiff__right) # label(axiom) # label(non_clause).  [assumption].
7.74/7.73	4832 (all X hAPP(nat,int,semiring_1_of_nat(int),hAPP(int,nat,nat_1,hAPP(int,int,abs_abs(int),X))) = hAPP(int,int,abs_abs(int),X)) # label(fact_1932_int__nat__abs) # label(axiom) # label(non_clause).  [assumption].
7.74/7.73	4833 (all X_a (real_n1866405975lgebra(X_a) -> (all X_3 all A_2 (hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),X_3),A_2),sequentially)) -> (zero_zero(X_a) != ti(X_a,A_2) -> hBOOL(hAPP(fun(nat,X_a),bool,bseq(X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(X_a,X_a),fun(fun(nat,X_a),fun(nat,X_a)),combb(X_a,X_a,nat),inverse_inverse(X_a)),X_3)))))))) # label(fact_4489_Bseq__inverse) # label(axiom) # label(non_clause).  [assumption].
7.74/7.73	4834 (all X_a (ring_1(X_a) -> ti(fun(fun(nat,X_a),fun(nat,X_a)),diffs(X_a)) = diffs(X_a))) # label(tsy_c_Transcendental_Odiffs_res) # label(axiom) # label(non_clause).  [assumption].
7.74/7.73	4835 (all X_b all X_a (comm_monoid_mult(X_a) -> (all F all G all A_3 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co302546470etprod(X_b,X_a),F),A_3)),hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co302546470etprod(X_b,X_a),G),A_3)) = hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co302546470etprod(X_b,X_a),hAPP(fun(X_b,X_a),fun(X_b,X_a),hAPP(fun(X_b,fun(X_a,X_a)),fun(fun(X_b,X_a),fun(X_b,X_a)),combs(X_b,X_a,X_a),hAPP(fun(X_b,X_a),fun(X_b,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_b,X_a),fun(X_b,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),X_b),times_times(X_a)),F)),G)),A_3)))) # label(fact_3946_setprod__timesf) # label(axiom) # label(non_clause).  [assumption].
7.74/7.73	4836 (all X_a (archim1727834104eiling(X_a) -> hAPP(X_a,int,archimedean_ceiling(X_a),one_one(X_a)) = one_one(int))) # label(fact_3282_ceiling__one) # label(axiom) # label(non_clause).  [assumption].
7.74/7.73	4837 (all X_b all X_a all A_1 all B all A_6 all B_5 (hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),A_1),B) = hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),A_6),B_5) -> -(ti(X_a,A_1) = ti(X_a,A_6) -> ti(X_b,B) != ti(X_b,B_5)))) # label(fact_3137_Pair__inject) # label(axiom) # label(non_clause).  [assumption].
7.74/7.73	4838 (all X_a (metric_space(X_a) -> (all X all Y all Z_1 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),X),Y)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),X),Z_1)),hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),Y),Z_1))))))) # label(fact_3505_dist__triangle2) # label(axiom) # label(non_clause).  [assumption].
7.74/7.73	4839 (all D hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),D),hAPP(int,int,abs_abs(int),D)))) # label(fact_1926_zdvd__self__abs1) # label(axiom) # label(non_clause).  [assumption].
7.74/7.73	4840 (all B all A_1 all C (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_1),C)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),C)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A_1),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),A_1))))) # label(fact_350_Euler_Oaux2) # label(axiom) # label(non_clause).  [assumption].
7.74/7.73	4841 (all X all Y hAPP(int,real,real_1(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X),Y)) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(int,real,real_1(int),X)),hAPP(int,real,real_1(int),Y))) # label(fact_3336_real__of__int__add) # label(axiom) # label(non_clause).  [assumption].
7.74/7.73	4842 (all K_4 all L_4 hAPP(int,int,bit1,L_4) != hAPP(int,int,bit0,K_4)) # label(fact_119_rel__simps_I49_J) # label(axiom) # label(non_clause).  [assumption].
7.74/7.73	4843 (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_1279_of__nat__0__le__iff) # label(axiom) # label(non_clause).  [assumption].
7.74/7.73	4844 (all X_a (real_normed_vector(X_a) -> (all A_1 all B hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_1),B)) = hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),B),A_1))))) # label(fact_1774_norm__minus__commute) # label(axiom) # label(non_clause).  [assumption].
7.74/7.73	4845 (all Ma all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),N_1)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),Ma)) <-> N_1 != Ma)) # label(fact_515_nat__neq__iff) # label(axiom) # label(non_clause).  [assumption].
7.74/7.73	4846 (all X_a (linordered_idom(X_a) -> (all A_1 hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(X_a,X_a,abs_abs(X_a),A_1)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))) # label(fact_1901_power2__abs) # label(axiom) # label(non_clause).  [assumption].
7.74/7.73	4847 (all K_4 hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),pls),K_4) = ti(int,K_4)) # label(fact_131_add__Pls) # label(axiom) # label(non_clause).  [assumption].
7.74/7.73	4848 (all N all J_2 all K_4 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),J_2),K_4)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_2),N)),K_4)))) # label(fact_663_less__imp__diff__less) # label(axiom) # label(non_clause).  [assumption].
7.74/7.73	4849 (all X_a all F all G all Ma all S ((all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),S)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(X_a,int,F,X_2)),hAPP(X_a,int,G,X_2)),Ma)))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(fun(X_a,bool),int,hAPP(fun(X_a,int),fun(fun(X_a,bool),int),big_co1399186613setsum(X_a,int),F),S)),hAPP(fun(X_a,bool),int,hAPP(fun(X_a,int),fun(fun(X_a,bool),int),big_co1399186613setsum(X_a,int),G),S)),Ma)))) # label(fact_4333_setsum__same__function__zcong) # label(axiom) # label(non_clause).  [assumption].
7.74/7.73	4850 (all X_a (real_vector(X_a) -> (all X zero_zero(X_a) = hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),zero_zero(real)),X)))) # label(fact_4709_scaleR__left_Ozero) # label(axiom) # label(non_clause).  [assumption].
7.74/7.73	4851 (all B_5 all Q_5 all R_5 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B_5),Q_5)),R_5))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),R_5),B_5)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B_5)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Q_5)))))) # label(fact_264_q__pos__lemma) # label(axiom) # label(non_clause).  [assumption].
7.74/7.73	4852 (all X_a (number_semiring(X_a) -> (all X all Y hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),Y),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),X)),Y)) = hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X),Y)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))) # label(fact_169_power2__sum) # label(axiom) # label(non_clause).  [assumption].
7.74/7.73	4853 (all K all Xa_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,real),fun(fun(real,real),fun(real,real)),combb(real,real,real),sin),hAPP(real,fun(real,real),hAPP(fun(real,fun(real,real)),fun(real,fun(real,real)),combc(real,real,real),plus_plus(real)),K))),Xa_2),hAPP(real,real,cos,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),Xa_2),K))))) # label(fact_3820_DERIV__sin__add) # label(axiom) # label(non_clause).  [assumption].
7.74/7.73	4854 (all X_a (topological_space(X_a) -> (all G all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(complex,fun(filter(X_a),bool),hAPP(fun(X_a,complex),fun(complex,fun(filter(X_a),bool)),tendsto(X_a,complex),G),zero_zero(complex)),hAPP(X_a,filter(X_a),at(X_a),A_2))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(complex,fun(filter(X_a),bool),hAPP(fun(X_a,complex),fun(complex,fun(filter(X_a),bool)),tendsto(X_a,complex),hAPP(fun(X_a,complex),fun(X_a,complex),hAPP(fun(complex,complex),fun(fun(X_a,complex),fun(X_a,complex)),combb(complex,complex,X_a),cnj),G)),zero_zero(complex)),hAPP(X_a,filter(X_a),at(X_a),A_2))))))) # label(fact_4599_cnj_OLIM__zero) # label(axiom) # label(non_clause).  [assumption].
7.74/7.73	4855 (all X_b all X_a all F all A_3 all B_2 (hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),A_3) = ti(fun(X_a,bool),B_2) -> hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),pow(X_a),B_2) = hAPP(fun(fun(X_b,bool),bool),fun(fun(X_a,bool),bool),hAPP(fun(fun(X_b,bool),fun(X_a,bool)),fun(fun(fun(X_b,bool),bool),fun(fun(X_a,bool),bool)),image(fun(X_b,bool),fun(X_a,bool)),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F)),hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),pow(X_b),A_3)))) # label(fact_3640_image__Pow__surj) # label(axiom) # label(non_clause).  [assumption].
7.74/7.73	4856 (all X_a (real_normed_algebra(X_a) -> (all X all Y all Ya hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),Ya)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Y),Ya)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X),Y)),Ya)))) # label(fact_883_mult__left_Oadd) # label(axiom) # label(non_clause).  [assumption].
7.74/7.73	4857 (all X_a (real_normed_vector(X_a) -> (all R_4 exists K_2 ((all X_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),R_4),X_2))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(X_a,real,norm_norm(X_a),X_2)),K_2)))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),K_2)))))) # label(fact_4760_scaleR__right_Ononneg__bounded) # label(axiom) # label(non_clause).  [assumption].
7.74/7.73	4858 (all M all N hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),hAPP(nat,nat,suc,N))) # label(fact_1242_add__Suc__right) # label(axiom) # label(non_clause).  [assumption].
7.74/7.73	4859 (all F all K_3 all N_1 ((all P_6 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),P_6),N_1)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,F,P_6)),K_3)))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),N_1))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,real_1(nat),N_1)),K_3))))) # label(fact_4288_real__setsum__nat__ivl__bounded) # label(axiom) # label(non_clause).  [assumption].
7.74/7.73	4860 (all K all Ma all N_1 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),Ma) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),N_1) <-> zero_zero(nat) = K | Ma = N_1)) # label(fact_552_mult__cancel1) # label(axiom) # label(non_clause).  [assumption].
7.74/7.73	4861 (all N all D (zero_zero(int) != ti(int,D) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),D),N)) -> hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(int,real,real_1(int),N)),hAPP(int,real,real_1(int),D)) = hAPP(int,real,real_1(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),N),D))))) # label(fact_3395_real__of__int__div) # label(axiom) # label(non_clause).  [assumption].
7.74/7.73	4862 (all A_1 all P_5 (hBOOL(hAPP(nat,bool,prime,P_5)) -> (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),P_5),A_1)) -> (exists X_2 exists Y_2 hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),P_5),Y_2)),one_one(nat)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A_1),X_2))))) # label(fact_3090_bezout__prime) # label(axiom) # label(non_clause).  [assumption].
7.74/7.73	4863 (all X_1 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,real)),combs(real,real,real),hAPP(fun(real,real),fun(real,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,fun(real,real))),combb(real,fun(real,real),real),times_times(real)),cos)),cos)),X_1),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,min_1))),hAPP(real,real,cos,X_1))),hAPP(real,real,sin,X_1))))) # label(fact_3892_DERIV__cos__cos__mult2) # label(axiom) # label(non_clause).  [assumption].
7.74/7.73	4864 (all X_1 all P_4 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),P_4),X_1)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,X_1),zero_zero(int)),P_4)))) # label(fact_422_zcong__eq__zdvd__prop) # label(axiom) # label(non_clause).  [assumption].
7.74/7.73	4865 (all X_a (comm_monoid_mult(X_a) & comm_monoid_add(X_a) -> (all F all A_3 hAPP(fun(int,bool),X_a,hAPP(fun(int,X_a),fun(fun(int,bool),X_a),big_co1399186613setsum(int,X_a),hAPP(fun(int,nat),fun(int,X_a),hAPP(fun(nat,X_a),fun(fun(int,nat),fun(int,X_a)),combb(nat,X_a,int),F),nat_1)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),A_3)) = hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),A_3)))) # label(fact_4264_transfer__nat__int__sum__prod_I1_J) # label(axiom) # label(non_clause).  [assumption].
7.74/7.73	4866 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),M),N) = zero_zero(nat))) # label(fact_1098_div__less) # label(axiom) # label(non_clause).  [assumption].
7.74/7.73	4867 (all M all K_4 all N hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),M),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K_4),M)),N)) = hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),M),N)) # label(fact_4353_gcd__add__mult__int) # label(axiom) # label(non_clause).  [assumption].
7.74/7.73	4868 (all X_a (linordered_semidom(X_a) -> (all N all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),A_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),B),N))))))))) # label(fact_276_power__strict__mono) # label(axiom) # label(non_clause).  [assumption].
7.74/7.73	4869 (all X_a all F all A_3 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_3)) -> ((exists X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_3)) & (all Xa (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Xa),A_3)) -> (ti(X_a,X_2) != ti(X_a,Xa) -> hAPP(X_a,nat,F,Xa) = zero_zero(nat)))) & one_one(nat) = hAPP(X_a,nat,F,X_2))) <-> one_one(nat) = hAPP(fun(X_a,bool),nat,hAPP(fun(X_a,nat),fun(fun(X_a,bool),nat),big_co1399186613setsum(X_a,nat),F),A_3)))) # label(fact_4257_setsum__eq__1__iff) # label(axiom) # label(non_clause).  [assumption].
7.74/7.73	4870 (all B all Q_5 all R_5 all Q_3 all R_4 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),Q_5)),R_5)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),Q_3)),R_4))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),R_4),zero_zero(int))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),R_4)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),R_5)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Q_3),Q_5))))))) # label(fact_268_unique__quotient__lemma__neg) # label(axiom) # label(non_clause).  [assumption].
7.74/7.73	4871 (all A_3 (hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A_3)) -> (hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),hAPP(fun(int,bool),fun(nat,bool),hAPP(fun(int,nat),fun(fun(int,bool),fun(nat,bool)),image(int,nat),nat_1),A_3))) <-> hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A_3))))) # label(fact_3667_transfer__int__nat__set__relations_I1_J) # label(axiom) # label(non_clause).  [assumption].
7.74/7.73	4872 (all X_a all P_3 all X_2 (hBOOL(hAPP(X_a,bool,P_3,X_2)) -> hBOOL(hAPP(X_a,bool,P_3,hAPP(fun(X_a,bool),X_a,hilbert_Eps(X_a),P_3))))) # label(fact_4783_tfl__some) # label(axiom) # label(non_clause).  [assumption].
7.74/7.73	4873 (all X_a (semiring_div(X_a) -> (all A_1 all B (ti(X_a,B) != zero_zero(X_a) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B),A_1)),B) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),A_1),B)),one_one(X_a)))))) # label(fact_1041_div__add__self1) # label(axiom) # label(non_clause).  [assumption].
7.74/7.73	4874 (all X_a (order(X_a) -> strict_mono(nat,X_a) = ti(fun(fun(nat,fun(nat,bool)),fun(fun(nat,X_a),bool)),strict_mono(nat,X_a)))) # label(tsy_c_Orderings_Oorder_Ostrict__mono_res) # label(axiom) # label(non_clause).  [assumption].
7.74/7.73	4875 (all N all X hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(int,real,real_1(int),N)),hAPP(int,real,real_1(int),X))),hAPP(int,real,real_1(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),N),X)))),one_one(real)))) # label(fact_3410_real__of__int__div3) # label(axiom) # label(non_clause).  [assumption].
7.74/7.73	4876 (all X_a (linord581940658strict(X_a) -> (all A_2 all B_1 all C_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),B_1)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1),A_2)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1),B_1)))))))) # label(fact_395_mult__less__cancel__left__pos) # label(axiom) # label(non_clause).  [assumption].
7.74/7.73	4877 (all X_a (ordered_ring(X_a) -> (all A_2 all E_2 all C_1 all B_1 all D_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),E_2)),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B_1),E_2)),D_1))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_2),B_1)),E_2)),C_1)),D_1)))))) # label(fact_504_less__add__iff1) # label(axiom) # label(non_clause).  [assumption].
7.74/7.73	4878 (all N all X (X = hAPP(nat,real,real_1(nat),hAPP(real,nat,natfloor,X)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),hAPP(real,nat,natfloor,X)),N) = hAPP(real,nat,natfloor,hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),N)))) # label(fact_2334_natfloor__power) # label(axiom) # label(non_clause).  [assumption].
7.74/7.73	4879 (all F (hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),abs_abs(real)),F))) -> hBOOL(hAPP(fun(nat,real),bool,summable(real),F)))) # label(fact_4001_summable__rabs__cancel) # label(axiom) # label(non_clause).  [assumption].
7.74/7.73	4880 (all D2 all D1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),D1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),D2)) -> (exists E (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),E)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),E),D2)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),E),D1))))))) # label(fact_1605_real__lbound__gt__zero) # label(axiom) # label(non_clause).  [assumption].
7.74/7.73	4881 (all X_a (comm_monoid_mult(X_a) & comm_monoid_add(X_a) -> (all F all A_3 (hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A_3)) -> hAPP(fun(int,bool),X_a,hAPP(fun(int,X_a),fun(fun(int,bool),X_a),big_co302546470etprod(int,X_a),F),A_3) = hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co302546470etprod(nat,X_a),hAPP(fun(nat,int),fun(nat,X_a),hAPP(fun(int,X_a),fun(fun(nat,int),fun(nat,X_a)),combb(int,X_a,nat),F),semiring_1_of_nat(int))),hAPP(fun(int,bool),fun(nat,bool),hAPP(fun(int,nat),fun(fun(int,bool),fun(nat,bool)),image(int,nat),nat_1),A_3)))))) # label(fact_3945_transfer__int__nat__sum__prod_I2_J) # label(axiom) # label(non_clause).  [assumption].
7.74/7.73	4882 (all X_a (metric_space(X_a) -> (all X all Y (ti(X_a,Y) != ti(X_a,X) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),X),Y))))))) # label(fact_3512_dist__pos__lt) # label(axiom) # label(non_clause).  [assumption].
7.74/7.73	4883 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N),M)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),M),N) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N)),N))))) # label(fact_1444_le__div__geq) # label(axiom) # label(non_clause).  [assumption].
7.74/7.73	4884 (all X_1 all A_3 (hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A_3)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),A_3)) -> hBOOL(hAPP(int,bool,nat_is_nat,X_1))))) # label(fact_4850_Nat__Transfer_Otransfer__int__nat__set__function__closures_I6_J) # label(axiom) # label(non_clause).  [assumption].
7.74/7.73	4885 (all X_a (semiring_div(X_a) -> (all A_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),A_1),one_one(X_a)) = ti(X_a,A_1)))) # label(fact_966_div__by__1) # label(axiom) # label(non_clause).  [assumption].
7.74/7.73	4886 (all Y all A_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A_1)) -> (one_one(real) != A_1 -> hAPP(real,real,hAPP(real,fun(real,real),log,A_1),hAPP(real,real,hAPP(real,fun(real,real),powr,A_1),Y)) = Y))) # label(fact_3407_log__powr__cancel) # label(axiom) # label(non_clause).  [assumption].
7.74/7.73	4887 (all X_2 ((hBOOL(hAPP(nat,bool,even_odd_even(nat),X_2)) -> hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),min_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),X_2),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),hAPP(nat,real,real_1(nat),hAPP(nat,nat,fact_fact(nat),X_2))) = hAPP(nat,real,cos_coeff,X_2)) & (-hBOOL(hAPP(nat,bool,even_odd_even(nat),X_2)) -> zero_zero(real) = hAPP(nat,real,cos_coeff,X_2)))) # label(fact_2480_cos__coeff__def) # label(axiom) # label(non_clause).  [assumption].
7.74/7.73	4888 (all M all N all R_5 all S_4 all S_3 all T_6 all T_5 all Rn all Sn_1 all Tn_1 all R_4 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),R_4)) -> (hAPP(product_prod(int,int),product_prod(int,product_prod(int,int)),hAPP(int,fun(product_prod(int,int),product_prod(int,product_prod(int,int))),product_Pair(int,product_prod(int,int)),Rn),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),Sn_1),Tn_1)) = hAPP(int,product_prod(int,product_prod(int,int)),hAPP(int,fun(int,product_prod(int,product_prod(int,int))),hAPP(int,fun(int,fun(int,product_prod(int,product_prod(int,int)))),hAPP(int,fun(int,fun(int,fun(int,product_prod(int,product_prod(int,int))))),hAPP(int,fun(int,fun(int,fun(int,fun(int,product_prod(int,product_prod(int,int)))))),hAPP(int,fun(int,fun(int,fun(int,fun(int,fun(int,product_prod(int,product_prod(int,int))))))),hAPP(int,fun(int,fun(int,fun(int,fun(int,fun(int,fun(int,product_prod(int,product_prod(int,int)))))))),hAPP(int,fun(int,fun(int,fun(int,fun(int,fun(int,fun(int,fun(int,product_prod(int,product_prod(int,int))))))))),xzgcda,M),N),R_5),R_4),S_4),S_3),T_6),T_5) -> (hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),S_4),M)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),T_6),N)) = ti(int,R_5) -> (ti(int,R_4) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),S_3),M)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),T_5),N)) -> hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Sn_1),M)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Tn_1),N)) = ti(int,Rn)))))) # label(fact_3085_xzgcda__linear) # label(axiom) # label(non_clause).  [assumption].
7.74/7.73	4889 (all X all Y hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),X),Y) = hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(complex,real,re,X)),hAPP(complex,real,re,Y))),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(complex,real,im,X)),hAPP(complex,real,im,Y)))) # label(fact_3014_complex__add__def) # label(axiom) # label(non_clause).  [assumption].
7.74/7.73	4890 (all X_a (archim1727834104eiling(X_a) -> (all X hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(X_a,int,archim2085082626_floor(X_a),X)),one_one(int)) = hAPP(X_a,int,archim2085082626_floor(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),X),one_one(X_a)))))) # label(fact_2889_floor__diff__one) # label(axiom) # label(non_clause).  [assumption].
7.74/7.73	4891 (all B all A_1 all X (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),X)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),A_1),B)),X)))) # label(fact_3240_gcd__semilattice__nat_Ole__infI1) # label(axiom) # label(non_clause).  [assumption].
7.74/7.73	4892 (all M all K_4 all N (one_one(int) = hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),K_4),N) -> hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K_4),M)),N) = hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),M),N))) # label(fact_4385_gcd__mult__cancel__int) # label(axiom) # label(non_clause).  [assumption].
7.74/7.73	4893 (all X_a (field_inverse_zero(X_a) -> (all A_1 all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),A_1),hAPP(X_a,X_a,uminus_uminus(X_a),B)) = hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),A_1),B))))) # label(fact_2020_minus__divide__right) # label(axiom) # label(non_clause).  [assumption].
7.74/7.73	4894 (all C_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,abs_abs(real),C_1)),one_one(real))) -> hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),hAPP(real,fun(nat,real),power_power(real),C_1)),zero_zero(real)),sequentially)))) # label(fact_4491_LIMSEQ__rabs__realpow__zero2) # label(axiom) # label(non_clause).  [assumption].
7.74/7.73	4895 (all X_a all X_b (comm_monoid_mult(X_b) & dvd(X_b) -> (all F all A_3 all B_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),B_2)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_3),B_2)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),dvd_dvd(X_b),hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co302546470etprod(X_a,X_b),F),A_3)),hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co302546470etprod(X_a,X_b),F),B_2)))))))) # label(fact_3958_setprod__dvd__setprod__subset) # label(axiom) # label(non_clause).  [assumption].
7.74/7.73	4896 (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_373_mult__right__mono) # label(axiom) # label(non_clause).  [assumption].
7.74/7.73	4897 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,uminus_uminus(real),pi)),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),zero_zero(real))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,tan,X)),zero_zero(real)))))) # label(fact_2277_tan__less__zero) # label(axiom) # label(non_clause).  [assumption].
7.74/7.73	4898 (all X_1 all N_1 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,sin,X_1)),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(real,fun(nat,fun(real,real)),hAPP(fun(nat,fun(real,fun(real,real))),fun(real,fun(nat,fun(real,real))),combc(nat,real,fun(real,real)),hAPP(fun(nat,bool),fun(nat,fun(real,fun(real,real))),hAPP(fun(bool,fun(real,fun(real,real))),fun(fun(nat,bool),fun(nat,fun(real,fun(real,real)))),combb(bool,fun(real,fun(real,real)),nat),if(real)),even_odd_even(nat))),zero_zero(real))),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),inverse_divide(real)),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),min_1))),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),hAPP(fun(nat,nat),fun(nat,fun(nat,nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,nat),fun(nat,fun(nat,nat))),combb(nat,fun(nat,nat),nat),div_div(nat)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),minus_minus(nat)),hAPP(nat,nat,suc,zero_zero(nat))))),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),fact_fact(nat)))))),hAPP(real,fun(nat,real),power_power(real),X_1))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),N_1))))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,inverse_inverse(real),hAPP(nat,real,real_1(nat),hAPP(nat,nat,fact_fact(nat),N_1)))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,abs_abs(real),X_1)),N_1))))) # label(fact_4162_Maclaurin__sin__bound) # label(axiom) # label(non_clause).  [assumption].
7.74/7.74	4899 (all X_a (ord(X_a) -> (all C all A_1 all B (ti(X_a,A_1) = ti(X_a,B) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),C)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),C))))))) # label(fact_1553_ord__eq__le__trans) # label(axiom) # label(non_clause).  [assumption].
7.74/7.74	4900 (all Z_1 all X all Y (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),Y)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),Z_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),Y),Z_1)))))) # label(fact_3234_gcd__semilattice__nat_Oinf__greatest) # label(axiom) # label(non_clause).  [assumption].
7.74/7.74	4901 (all X_a all A_3 all B_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_3),B_2)) -> hBOOL(hAPP(fun(fun(X_a,bool),bool),bool,hAPP(fun(fun(X_a,bool),bool),fun(fun(fun(X_a,bool),bool),bool),ord_less_eq(fun(fun(X_a,bool),bool)),hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),powp(X_a),A_3)),hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),powp(X_a),B_2))))) # label(fact_4870_Powp__mono) # label(axiom) # label(non_clause).  [assumption].
7.74/7.74	4902 (all M one_one(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),M),one_one(nat))) # label(fact_3251_gcd__1__nat) # label(axiom) # label(non_clause).  [assumption].
7.74/7.74	4903 (all X_a (mult_zero(X_a) -> (all A_1 zero_zero(X_a) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),zero_zero(X_a))))) # label(fact_322_mult__zero__right) # label(axiom) # label(non_clause).  [assumption].
7.74/7.74	4904 (all P (fFalse = ti(bool,P) | fTrue = ti(bool,P))) # label(help_fFalse_1_1_T) # label(axiom) # label(non_clause).  [assumption].
7.74/7.74	4905 (all Y_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),hAPP(real,real,hAPP(nat,fun(real,real),root,N_1),Y_1))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),Y_1))))) # label(fact_2700_real__root__gt__1__iff) # label(axiom) # label(non_clause).  [assumption].
7.74/7.74	4906 (all X_b all X_a (order(X_a) & order(X_b) -> (all C_1 all F all B_1 all A_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_b,X_a,F,B_1)),A_2)) -> (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),C_1),B_1)) -> ((all X_2 all Y_2 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),Y_2),X_2)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_b,X_a,F,Y_2)),hAPP(X_b,X_a,F,X_2))))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_b,X_a,F,C_1)),A_2)))))))) # label(fact_2835_xt4) # label(axiom) # label(non_clause).  [assumption].
7.74/7.74	4907 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),X)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),one_one(real)),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,ln,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),one_one(real)),X))),X))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))))) # label(fact_1916_abs__ln__one__plus__x__minus__x__bound) # label(axiom) # label(non_clause).  [assumption].
7.74/7.74	4908 (all X all A_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,real_1(nat),X)),A_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X),hAPP(real,nat,natfloor,A_1))))) # label(fact_2331_le__natfloor) # label(axiom) # label(non_clause).  [assumption].
7.74/7.74	4909 (all A_1 all B (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),B)) -> (B != A_1 -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),B)) & -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),B),A_1))))) # label(fact_629_dvd_Ole__neq__trans) # label(axiom) # label(non_clause).  [assumption].
7.74/7.74	4910 (all W all Z_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,nat_1,hAPP(int,int,abs_abs(int),W))),hAPP(int,nat,nat_1,hAPP(int,int,abs_abs(int),Z_1))) = hAPP(int,nat,nat_1,hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),W),Z_1)))) # label(fact_1942_nat__abs__mult__distrib) # label(axiom) # label(non_clause).  [assumption].
7.74/7.74	4911 (all B all A_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),B)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(real,int,archim2085082626_floor(real),A_1)),hAPP(real,int,archim2085082626_floor(real),B))),hAPP(real,int,archim2085082626_floor(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A_1),B))))))) # label(fact_2891_le__mult__floor) # label(axiom) # label(non_clause).  [assumption].
7.74/7.74	4912 (all X_a (comm_semiring_1(X_a) -> (all X all Q_3 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),Q_3)),X) = hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),hAPP(nat,nat,suc,Q_3))))) # label(fact_1309_comm__semiring__1__class_Onormalizing__semiring__rules_I28_J) # label(axiom) # label(non_clause).  [assumption].
7.74/7.74	4913 (all X_a (real_normed_vector(X_a) -> (all X_3 all A_2 (hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),X_3),A_2),sequentially)) -> hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),hAPP(fun(nat,X_a),fun(nat,real),hAPP(fun(X_a,real),fun(fun(nat,X_a),fun(nat,real)),combb(X_a,real,nat),norm_norm(X_a)),X_3)),hAPP(X_a,real,norm_norm(X_a),A_2)),sequentially)))))) # label(fact_4466_LIMSEQ__norm) # label(axiom) # label(non_clause).  [assumption].
7.74/7.74	4914 (all X_a (real_algebra_1(X_a) -> (all X all Y hAPP(real,X_a,of_real(X_a),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),X),Y)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(real,X_a,of_real(X_a),X)),hAPP(real,X_a,of_real(X_a),Y))))) # label(fact_2784_of__real__mult) # label(axiom) # label(non_clause).  [assumption].
7.74/7.74	4915 (all X_a (real_normed_algebra(X_a) -> (all R_4 all A_1 all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),R_4),A_1)),B) = hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),R_4),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B))))) # label(fact_4678_mult_OscaleR__left) # label(axiom) # label(non_clause).  [assumption].
7.74/7.74	4916 (all X_a (comm_monoid_mult(X_a) -> (all A_1 ti(X_a,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))))) # label(fact_799_mult_Ocomm__neutral) # label(axiom) # label(non_clause).  [assumption].
7.74/7.74	4917 (all X all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X)) -> hAPP(real,real,hAPP(nat,fun(real,real),root,N),hAPP(real,real,inverse_inverse(real),X)) = hAPP(real,real,inverse_inverse(real),hAPP(real,real,hAPP(nat,fun(real,real),root,N),X))))) # label(fact_2715_real__root__inverse__lemma) # label(axiom) # label(non_clause).  [assumption].
7.74/7.74	4918 (all N_1 all Ma (hAPP(nat,int,semiring_1_of_nat(int),Ma) = hAPP(int,int,uminus_uminus(int),hAPP(nat,int,semiring_1_of_nat(int),N_1)) <-> Ma = zero_zero(nat) & zero_zero(nat) = N_1)) # label(fact_2155_negative__eq__positive) # label(axiom) # label(non_clause).  [assumption].
7.74/7.74	4919 (all A_2 all B_1 all W_1 (zero_zero(real) = B_1 & A_2 = hAPP(int,real,number_number_of(real),W_1) <-> hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,A_2),B_1) = hAPP(int,complex,number_number_of(complex),W_1))) # label(fact_2742_Complex__eq__number__of) # label(axiom) # label(non_clause).  [assumption].
7.74/7.74	4920 (all Y_1 all X_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X_1)) -> hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastAtMost(int),X_1),Y_1))))) # label(fact_4535_SetInterval_Otransfer__nat__int__set__function__closures) # label(axiom) # label(non_clause).  [assumption].
7.74/7.74	4921 (all A_1 all X hAPP(real,real,hAPP(real,fun(real,real),log,A_1),X) = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,ln,X)),hAPP(real,real,ln,A_1))) # label(fact_2639_Log_Olog__def) # label(axiom) # label(non_clause).  [assumption].
7.74/7.74	4922 (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_382_mult__strict__left__mono__neg) # label(axiom) # label(non_clause).  [assumption].
7.74/7.74	4923 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N),M)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N)))) # label(fact_529_nat__le__linear) # label(axiom) # label(non_clause).  [assumption].
7.74/7.74	4924 (all X_a (archim1727834104eiling(X_a) -> (all X all V hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(X_a,int,archimedean_ceiling(X_a),X)),hAPP(int,int,number_number_of(int),V)) = hAPP(X_a,int,archimedean_ceiling(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),X),hAPP(int,X_a,number_number_of(X_a),V)))))) # label(fact_3308_ceiling__diff__number__of) # label(axiom) # label(non_clause).  [assumption].
7.74/7.74	4925 (all X all Y all M (one_one(int) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X),Y)),M) -> hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),X),M) = one_one(int))) # label(fact_4349_invertible__coprime__int) # label(axiom) # label(non_clause).  [assumption].
7.74/7.74	4926 (all X all Y hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(real,real,sqrt,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),X),X)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),Y),Y)))))) # label(fact_1635_real__sqrt__mult__self__sum__ge__zero) # label(axiom) # label(non_clause).  [assumption].
7.74/7.74	4927 (all X_a (real_normed_field(X_a) -> (all G all E_2 all F all X_1 all D_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),F),X_1),D_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),G),X_1),E_2)) -> (zero_zero(X_a) != hAPP(X_a,X_a,G,X_1) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),hAPP(fun(X_a,X_a),fun(X_a,X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,X_a),fun(X_a,X_a)),combs(X_a,X_a,X_a),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,X_a),fun(X_a,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),X_a),inverse_divide(X_a)),F)),G)),X_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),D_1),hAPP(X_a,X_a,G,X_1))),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),E_2),hAPP(X_a,X_a,F,X_1)))),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(X_a,X_a,G,X_1)),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat))))))))))))) # label(fact_3899_DERIV__quotient) # label(axiom) # label(non_clause).  [assumption].
7.84/7.84	4928 (all X_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_1),zero_zero(real))) -> hBOOL(hAPP(real,bool,hAPP(fun(real,real),fun(real,bool),isCont(real,real),hAPP(nat,fun(real,real),root,N_1)),X_1))))) # label(fact_4918_isCont__root__neg) # label(axiom) # label(non_clause).  [assumption].
7.84/7.84	
7.84/7.84	============================== end of process non-clausal formulas ===
7.84/7.84	
7.84/7.84	============================== PROCESS INITIAL CLAUSES ===============
7.84/7.84	
7.84/7.84	============================== PREDICATE ELIMINATION =================
7.84/7.84	4929 -comm_monoid_mult(A) | -dvd(A) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f9(B,A,C,D,E)),E)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),C),E)),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),D),E))) # label(fact_4427_setprod__dvd__setprod) # label(axiom).  [clausify(38)].
7.84/7.84	4930 dvd(rat) # label(arity_Rat_Orat___Rings_Odvd) # label(axiom).  [assumption].
7.84/7.84	Derived: -comm_monoid_mult(rat) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f9(A,rat,B,C,D)),D)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),dvd_dvd(rat),hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co302546470etprod(A,rat),B),D)),hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co302546470etprod(A,rat),C),D))).  [resolve(4929,b,4930,a)].
7.84/7.84	4931 -comm_monoid_mult(A) | -dvd(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),hAPP(B,A,C,f9(B,A,C,D,E))),hAPP(B,A,D,f9(B,A,C,D,E)))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),C),E)),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),D),E))) # label(fact_4427_setprod__dvd__setprod) # label(axiom).  [clausify(38)].
7.84/7.84	Derived: -comm_monoid_mult(rat) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),dvd_dvd(rat),hAPP(A,rat,B,f9(A,rat,B,C,D))),hAPP(A,rat,C,f9(A,rat,B,C,D)))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),dvd_dvd(rat),hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co302546470etprod(A,rat),B),D)),hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co302546470etprod(A,rat),C),D))).  [resolve(4931,b,4930,a)].
7.84/7.84	4932 dvd(real) # label(arity_RealDef_Oreal___Rings_Odvd) # label(axiom).  [assumption].
7.84/7.84	Derived: -comm_monoid_mult(real) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f9(A,real,B,C,D)),D)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),dvd_dvd(real),hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co302546470etprod(A,real),B),D)),hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co302546470etprod(A,real),C),D))).  [resolve(4932,a,4929,b)].
7.84/7.84	Derived: -comm_monoid_mult(real) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),dvd_dvd(real),hAPP(A,real,B,f9(A,real,B,C,D))),hAPP(A,real,C,f9(A,real,B,C,D)))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),dvd_dvd(real),hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co302546470etprod(A,real),B),D)),hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co302546470etprod(A,real),C),D))).  [resolve(4932,a,4931,b)].
8.14/8.15	4933 -dvd(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(192)].
8.14/8.15	Derived: times_times(rat) = ti(fun(rat,fun(rat,rat)),times_times(rat)).  [resolve(4933,a,4930,a)].
8.14/8.15	Derived: times_times(real) = ti(fun(real,fun(real,real)),times_times(real)).  [resolve(4933,a,4932,a)].
8.14/8.15	4934 dvd(nat) # label(arity_Nat_Onat___Rings_Odvd) # label(axiom).  [assumption].
8.14/8.15	Derived: -comm_monoid_mult(nat) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f9(A,nat,B,C,D)),D)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),B),D)),hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),C),D))).  [resolve(4934,a,4929,b)].
8.14/8.15	Derived: -comm_monoid_mult(nat) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(A,nat,B,f9(A,nat,B,C,D))),hAPP(A,nat,C,f9(A,nat,B,C,D)))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),B),D)),hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),C),D))).  [resolve(4934,a,4931,b)].
8.14/8.15	Derived: times_times(nat) = ti(fun(nat,fun(nat,nat)),times_times(nat)).  [resolve(4934,a,4933,a)].
8.14/8.15	4935 dvd(int) # label(arity_Int_Oint___Rings_Odvd) # label(axiom).  [assumption].
8.14/8.15	Derived: -comm_monoid_mult(int) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f9(A,int,B,C,D)),D)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),B),D)),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),C),D))).  [resolve(4935,a,4929,b)].
8.14/8.15	Derived: -comm_monoid_mult(int) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(A,int,B,f9(A,int,B,C,D))),hAPP(A,int,C,f9(A,int,B,C,D)))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),B),D)),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),C),D))).  [resolve(4935,a,4931,b)].
8.14/8.15	Derived: times_times(int) = ti(fun(int,fun(int,int)),times_times(int)).  [resolve(4935,a,4933,a)].
8.14/8.15	4936 -dvd(A) | dvd_dvd(A) = ti(fun(A,fun(A,bool)),dvd_dvd(A)) # label(tsy_c_Rings_Odvd__class_Odvd_res) # label(axiom).  [clausify(1302)].
8.14/8.15	Derived: dvd_dvd(rat) = ti(fun(rat,fun(rat,bool)),dvd_dvd(rat)).  [resolve(4936,a,4930,a)].
8.14/8.15	Derived: dvd_dvd(real) = ti(fun(real,fun(real,bool)),dvd_dvd(real)).  [resolve(4936,a,4932,a)].
8.14/8.15	Derived: dvd_dvd(nat) = ti(fun(nat,fun(nat,bool)),dvd_dvd(nat)).  [resolve(4936,a,4934,a)].
8.14/8.15	Derived: dvd_dvd(int) = ti(fun(int,fun(int,bool)),dvd_dvd(int)).  [resolve(4936,a,4935,a)].
8.14/8.15	4937 -dvd(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),C)) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),f265(A,B,C)) = ti(A,C) # label(fact_2772_dvdE) # label(axiom).  [clausify(1617)].
8.14/8.15	Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),dvd_dvd(rat),A),B)) | hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),f265(rat,A,B)) = ti(rat,B).  [resolve(4937,a,4930,a)].
8.14/8.15	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),dvd_dvd(real),A),B)) | hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),f265(real,A,B)) = ti(real,B).  [resolve(4937,a,4932,a)].
8.14/8.15	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A),B)) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),f265(nat,A,B)) = ti(nat,B).  [resolve(4937,a,4934,a)].
8.14/8.15	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),B)) | hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),f265(int,A,B)) = ti(int,B).  [resolve(4937,a,4935,a)].
8.30/8.28	4938 -semiring_0(A) | -dvd(A) | -hBOOL(hAPP(A,bool,B,C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),D),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),zero_zero(A)))) | hBOOL(hAPP(A,bool,B,hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),f297(A,B,D)))) # label(fact_602_unity__coeff__ex) # label(axiom).  [clausify(1763)].
8.30/8.28	Derived: -semiring_0(rat) | -hBOOL(hAPP(rat,bool,A,B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),dvd_dvd(rat),C),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),B),zero_zero(rat)))) | hBOOL(hAPP(rat,bool,A,hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),C),f297(rat,A,C)))).  [resolve(4938,b,4930,a)].
8.30/8.28	Derived: -semiring_0(real) | -hBOOL(hAPP(real,bool,A,B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),dvd_dvd(real),C),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),B),zero_zero(real)))) | hBOOL(hAPP(real,bool,A,hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),f297(real,A,C)))).  [resolve(4938,b,4932,a)].
8.30/8.28	Derived: -semiring_0(nat) | -hBOOL(hAPP(nat,bool,A,B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),C),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),zero_zero(nat)))) | hBOOL(hAPP(nat,bool,A,hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),C),f297(nat,A,C)))).  [resolve(4938,b,4934,a)].
8.30/8.28	Derived: -semiring_0(int) | -hBOOL(hAPP(int,bool,A,B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),C),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),B),zero_zero(int)))) | hBOOL(hAPP(int,bool,A,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),f297(int,A,C)))).  [resolve(4938,b,4935,a)].
8.30/8.28	4939 -semiring_0(A) | -dvd(A) | hBOOL(hAPP(A,bool,B,f298(A,B,C))) | -hBOOL(hAPP(A,bool,B,hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),D))) # label(fact_602_unity__coeff__ex) # label(axiom).  [clausify(1763)].
8.30/8.28	Derived: -semiring_0(rat) | hBOOL(hAPP(rat,bool,A,f298(rat,A,B))) | -hBOOL(hAPP(rat,bool,A,hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),B),C))).  [resolve(4939,b,4930,a)].
8.30/8.28	Derived: -semiring_0(real) | hBOOL(hAPP(real,bool,A,f298(real,A,B))) | -hBOOL(hAPP(real,bool,A,hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),C))).  [resolve(4939,b,4932,a)].
8.30/8.28	Derived: -semiring_0(nat) | hBOOL(hAPP(nat,bool,A,f298(nat,A,B))) | -hBOOL(hAPP(nat,bool,A,hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),C))).  [resolve(4939,b,4934,a)].
8.30/8.28	Derived: -semiring_0(int) | hBOOL(hAPP(int,bool,A,f298(int,A,B))) | -hBOOL(hAPP(int,bool,A,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),C))).  [resolve(4939,b,4935,a)].
8.30/8.28	4940 -semiring_0(A) | -dvd(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),f298(A,C,B)),zero_zero(A)))) | -hBOOL(hAPP(A,bool,C,hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D))) # label(fact_602_unity__coeff__ex) # label(axiom).  [clausify(1763)].
8.30/8.28	Derived: -semiring_0(rat) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),dvd_dvd(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),f298(rat,B,A)),zero_zero(rat)))) | -hBOOL(hAPP(rat,bool,B,hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),C))).  [resolve(4940,b,4930,a)].
8.30/8.28	Derived: -semiring_0(real) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),dvd_dvd(real),A),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),f298(real,B,A)),zero_zero(real)))) | -hBOOL(hAPP(real,bool,B,hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),C))).  [resolve(4940,b,4932,a)].
8.30/8.28	Derived: -semiring_0(nat) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),f298(nat,B,A)),zero_zero(nat)))) | -hBOOL(hAPP(nat,bool,B,hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),C))).  [resolve(4940,b,4934,a)].
8.30/8.28	Derived: -semiring_0(int) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),f298(int,B,A)),zero_zero(int)))) | -hBOOL(hAPP(int,bool,B,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),C))).  [resolve(4940,b,4935,a)].
8.30/8.28	4941 -dvd(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C) != ti(A,D) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),D)) # label(fact_337_dvdI) # label(axiom).  [clausify(2073)].
8.60/8.60	Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B) != ti(rat,C) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),dvd_dvd(rat),A),C)).  [resolve(4941,a,4930,a)].
8.60/8.60	Derived: hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B) != ti(real,C) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),dvd_dvd(real),A),C)).  [resolve(4941,a,4932,a)].
8.60/8.60	Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),B) != ti(nat,C) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A),C)).  [resolve(4941,a,4934,a)].
8.60/8.60	Derived: hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B) != ti(int,C) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),C)).  [resolve(4941,a,4935,a)].
8.60/8.60	4942 -dvd(A) | -comm_ring(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),D),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),E),C))),F))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),D),F))) # label(fact_487_inf__period_I3_J) # label(axiom).  [clausify(2510)].
8.60/8.60	Derived: -comm_ring(rat) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),dvd_dvd(rat),A),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),dvd_dvd(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),C),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),D),B))),E))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),dvd_dvd(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),C),E))).  [resolve(4942,a,4930,a)].
8.60/8.60	Derived: -comm_ring(real) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),dvd_dvd(real),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),dvd_dvd(real),A),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),C),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),D),B))),E))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),dvd_dvd(real),A),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),C),E))).  [resolve(4942,a,4932,a)].
8.60/8.60	Derived: -comm_ring(nat) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),C),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),D),B))),E))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),C),E))).  [resolve(4942,a,4934,a)].
8.60/8.60	Derived: -comm_ring(int) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),C),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),D),B))),E))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),C),E))).  [resolve(4942,a,4935,a)].
8.60/8.60	4943 -dvd(A) | -comm_ring(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),D),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),E),C))),F))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),D),F))) # label(fact_487_inf__period_I3_J) # label(axiom).  [clausify(2510)].
8.60/8.60	Derived: -comm_ring(rat) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),dvd_dvd(rat),A),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),dvd_dvd(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),C),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),D),B))),E))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),dvd_dvd(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),C),E))).  [resolve(4943,a,4930,a)].
8.60/8.60	Derived: -comm_ring(real) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),dvd_dvd(real),A),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),dvd_dvd(real),A),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),C),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),D),B))),E))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),dvd_dvd(real),A),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),C),E))).  [resolve(4943,a,4932,a)].
8.79/8.76	Derived: -comm_ring(nat) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),C),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),D),B))),E))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),C),E))).  [resolve(4943,a,4934,a)].
8.79/8.76	Derived: -comm_ring(int) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),C),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),D),B))),E))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),C),E))).  [resolve(4943,a,4935,a)].
8.79/8.76	4944 dvd(complex) # label(arity_Complex_Ocomplex___Rings_Odvd) # label(axiom).  [assumption].
8.79/8.76	Derived: -comm_monoid_mult(complex) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f9(A,complex,B,C,D)),D)) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),dvd_dvd(complex),hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co302546470etprod(A,complex),B),D)),hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co302546470etprod(A,complex),C),D))).  [resolve(4944,a,4929,b)].
8.79/8.76	Derived: -comm_monoid_mult(complex) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),dvd_dvd(complex),hAPP(A,complex,B,f9(A,complex,B,C,D))),hAPP(A,complex,C,f9(A,complex,B,C,D)))) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),dvd_dvd(complex),hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co302546470etprod(A,complex),B),D)),hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co302546470etprod(A,complex),C),D))).  [resolve(4944,a,4931,b)].
8.79/8.76	Derived: times_times(complex) = ti(fun(complex,fun(complex,complex)),times_times(complex)).  [resolve(4944,a,4933,a)].
8.79/8.76	Derived: dvd_dvd(complex) = ti(fun(complex,fun(complex,bool)),dvd_dvd(complex)).  [resolve(4944,a,4936,a)].
8.79/8.76	Derived: -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),dvd_dvd(complex),A),B)) | hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),f265(complex,A,B)) = ti(complex,B).  [resolve(4944,a,4937,a)].
8.79/8.76	Derived: -semiring_0(complex) | -hBOOL(hAPP(complex,bool,A,B)) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),dvd_dvd(complex),C),hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),B),zero_zero(complex)))) | hBOOL(hAPP(complex,bool,A,hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),C),f297(complex,A,C)))).  [resolve(4944,a,4938,b)].
8.79/8.76	Derived: -semiring_0(complex) | hBOOL(hAPP(complex,bool,A,f298(complex,A,B))) | -hBOOL(hAPP(complex,bool,A,hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),B),C))).  [resolve(4944,a,4939,b)].
8.79/8.76	Derived: -semiring_0(complex) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),dvd_dvd(complex),A),hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),f298(complex,B,A)),zero_zero(complex)))) | -hBOOL(hAPP(complex,bool,B,hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),C))).  [resolve(4944,a,4940,b)].
8.79/8.76	Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),B) != ti(complex,C) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),dvd_dvd(complex),A),C)).  [resolve(4944,a,4941,a)].
9.55/9.50	Derived: -comm_ring(complex) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),dvd_dvd(complex),A),B)) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),dvd_dvd(complex),A),hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),C),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),D),B))),E))) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),dvd_dvd(complex),A),hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),C),E))).  [resolve(4944,a,4942,a)].
9.55/9.50	Derived: -comm_ring(complex) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),dvd_dvd(complex),A),B)) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),dvd_dvd(complex),A),hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),C),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),D),B))),E))) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),dvd_dvd(complex),A),hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),C),E))).  [resolve(4944,a,4943,a)].
9.55/9.50	4945 -plus(A) | -dvd(A) | -linorder(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(3334)].
9.55/9.50	Derived: -plus(rat) | -linorder(rat) | plus_plus(rat) = ti(fun(rat,fun(rat,rat)),plus_plus(rat)).  [resolve(4945,b,4930,a)].
9.55/9.50	Derived: -plus(real) | -linorder(real) | plus_plus(real) = ti(fun(real,fun(real,real)),plus_plus(real)).  [resolve(4945,b,4932,a)].
9.55/9.50	Derived: -plus(nat) | -linorder(nat) | plus_plus(nat) = ti(fun(nat,fun(nat,nat)),plus_plus(nat)).  [resolve(4945,b,4934,a)].
9.55/9.50	Derived: -plus(int) | -linorder(int) | plus_plus(int) = ti(fun(int,fun(int,int)),plus_plus(int)).  [resolve(4945,b,4935,a)].
9.55/9.50	Derived: -plus(complex) | -linorder(complex) | plus_plus(complex) = ti(fun(complex,fun(complex,complex)),plus_plus(complex)).  [resolve(4945,b,4944,a)].
9.55/9.50	4946 dvd(code_code_numeral) # label(arity_Code__Numeral_Ocode__numeral___Rings_Odvd) # label(axiom).  [assumption].
9.55/9.50	Derived: -comm_monoid_mult(code_code_numeral) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f9(A,code_code_numeral,B,C,D)),D)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co302546470etprod(A,code_code_numeral),B),D)),hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co302546470etprod(A,code_code_numeral),C),D))).  [resolve(4946,a,4929,b)].
9.55/9.50	Derived: -comm_monoid_mult(code_code_numeral) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),hAPP(A,code_code_numeral,B,f9(A,code_code_numeral,B,C,D))),hAPP(A,code_code_numeral,C,f9(A,code_code_numeral,B,C,D)))) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co302546470etprod(A,code_code_numeral),B),D)),hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co302546470etprod(A,code_code_numeral),C),D))).  [resolve(4946,a,4931,b)].
9.55/9.50	Derived: times_times(code_code_numeral) = ti(fun(code_code_numeral,fun(code_code_numeral,code_code_numeral)),times_times(code_code_numeral)).  [resolve(4946,a,4933,a)].
9.55/9.50	Derived: dvd_dvd(code_code_numeral) = ti(fun(code_code_numeral,fun(code_code_numeral,bool)),dvd_dvd(code_code_numeral)).  [resolve(4946,a,4936,a)].
9.55/9.50	Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),A),B)) | hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),f265(code_code_numeral,A,B)) = ti(code_code_numeral,B).  [resolve(4946,a,4937,a)].
9.56/9.57	Derived: -semiring_0(code_code_numeral) | -hBOOL(hAPP(code_code_numeral,bool,A,B)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),C),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),B),zero_zero(code_code_numeral)))) | hBOOL(hAPP(code_code_numeral,bool,A,hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),C),f297(code_code_numeral,A,C)))).  [resolve(4946,a,4938,b)].
9.56/9.57	Derived: -semiring_0(code_code_numeral) | hBOOL(hAPP(code_code_numeral,bool,A,f298(code_code_numeral,A,B))) | -hBOOL(hAPP(code_code_numeral,bool,A,hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),B),C))).  [resolve(4946,a,4939,b)].
9.56/9.57	Derived: -semiring_0(code_code_numeral) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),A),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),f298(code_code_numeral,B,A)),zero_zero(code_code_numeral)))) | -hBOOL(hAPP(code_code_numeral,bool,B,hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),C))).  [resolve(4946,a,4940,b)].
9.56/9.57	Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),B) != ti(code_code_numeral,C) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),A),C)).  [resolve(4946,a,4941,a)].
9.56/9.57	Derived: -comm_ring(code_code_numeral) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),A),B)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),A),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),minus_minus(code_code_numeral),C),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),D),B))),E))) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),A),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),C),E))).  [resolve(4946,a,4942,a)].
9.56/9.57	Derived: -comm_ring(code_code_numeral) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),A),B)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),A),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),minus_minus(code_code_numeral),C),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),D),B))),E))) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),A),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),C),E))).  [resolve(4946,a,4943,a)].
9.56/9.57	Derived: -plus(code_code_numeral) | -linorder(code_code_numeral) | plus_plus(code_code_numeral) = ti(fun(code_code_numeral,fun(code_code_numeral,code_code_numeral)),plus_plus(code_code_numeral)).  [resolve(4946,a,4945,b)].
9.56/9.57	4947 -dvd(A) | -comm_ring(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),D),E))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),D),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),F),C))),E))) # label(fact_488_inf__period_I4_J) # label(axiom).  [clausify(3786)].
10.39/10.37	4948 -dvd(A) | -comm_ring(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),D),E))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),D),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),F),C))),E))) # label(fact_488_inf__period_I4_J) # label(axiom).  [clausify(3786)].
10.39/10.37	4949 dvd(quickcheck_code_int) # label(arity_Quickcheck__Narrowing_Ocode__int___Rings_Odvd) # label(axiom).  [assumption].
10.39/10.37	Derived: -comm_monoid_mult(quickcheck_code_int) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f9(A,quickcheck_code_int,B,C,D)),D)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co302546470etprod(A,quickcheck_code_int),B),D)),hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co302546470etprod(A,quickcheck_code_int),C),D))).  [resolve(4949,a,4929,b)].
10.39/10.37	Derived: -comm_monoid_mult(quickcheck_code_int) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),hAPP(A,quickcheck_code_int,B,f9(A,quickcheck_code_int,B,C,D))),hAPP(A,quickcheck_code_int,C,f9(A,quickcheck_code_int,B,C,D)))) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co302546470etprod(A,quickcheck_code_int),B),D)),hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co302546470etprod(A,quickcheck_code_int),C),D))).  [resolve(4949,a,4931,b)].
10.39/10.37	Derived: times_times(quickcheck_code_int) = ti(fun(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int)),times_times(quickcheck_code_int)).  [resolve(4949,a,4933,a)].
10.39/10.37	Derived: dvd_dvd(quickcheck_code_int) = ti(fun(quickcheck_code_int,fun(quickcheck_code_int,bool)),dvd_dvd(quickcheck_code_int)).  [resolve(4949,a,4936,a)].
10.39/10.37	Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),A),B)) | hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),f265(quickcheck_code_int,A,B)) = ti(quickcheck_code_int,B).  [resolve(4949,a,4937,a)].
10.39/10.37	Derived: -semiring_0(quickcheck_code_int) | -hBOOL(hAPP(quickcheck_code_int,bool,A,B)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),C),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),B),zero_zero(quickcheck_code_int)))) | hBOOL(hAPP(quickcheck_code_int,bool,A,hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),C),f297(quickcheck_code_int,A,C)))).  [resolve(4949,a,4938,b)].
10.39/10.37	Derived: -semiring_0(quickcheck_code_int) | hBOOL(hAPP(quickcheck_code_int,bool,A,f298(quickcheck_code_int,A,B))) | -hBOOL(hAPP(quickcheck_code_int,bool,A,hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),B),C))).  [resolve(4949,a,4939,b)].
10.39/10.37	Derived: -semiring_0(quickcheck_code_int) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),A),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),f298(quickcheck_code_int,B,A)),zero_zero(quickcheck_code_int)))) | -hBOOL(hAPP(quickcheck_code_int,bool,B,hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),C))).  [resolve(4949,a,4940,b)].
10.83/10.84	Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),B) != ti(quickcheck_code_int,C) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),A),C)).  [resolve(4949,a,4941,a)].
10.83/10.84	Derived: -comm_ring(quickcheck_code_int) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),A),B)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),A),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),minus_minus(quickcheck_code_int),C),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),D),B))),E))) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),A),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),C),E))).  [resolve(4949,a,4942,a)].
10.83/10.84	Derived: -comm_ring(quickcheck_code_int) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),A),B)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),A),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),minus_minus(quickcheck_code_int),C),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),D),B))),E))) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),A),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),C),E))).  [resolve(4949,a,4943,a)].
10.83/10.84	Derived: -plus(quickcheck_code_int) | -linorder(quickcheck_code_int) | plus_plus(quickcheck_code_int) = ti(fun(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int)),plus_plus(quickcheck_code_int)).  [resolve(4949,a,4945,b)].
10.83/10.84	4950 -comm_monoid_mult(A) | -dvd(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | -hBOOL(hAPP(fun(B,bool),bool,hAPP(fun(B,bool),fun(fun(B,bool),bool),ord_less_eq(fun(B,bool)),D),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),E),D)),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),E),C))) # label(fact_3958_setprod__dvd__setprod__subset) # label(axiom).  [clausify(4895)].
10.83/10.84	Derived: -comm_monoid_mult(rat) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),dvd_dvd(rat),hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co302546470etprod(A,rat),D),C)),hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co302546470etprod(A,rat),D),B))).  [resolve(4950,b,4930,a)].
11.27/11.27	Derived: -comm_monoid_mult(real) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),dvd_dvd(real),hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co302546470etprod(A,real),D),C)),hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co302546470etprod(A,real),D),B))).  [resolve(4950,b,4932,a)].
11.27/11.27	Derived: -comm_monoid_mult(nat) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),D),C)),hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),D),B))).  [resolve(4950,b,4934,a)].
11.27/11.27	Derived: -comm_monoid_mult(int) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),D),C)),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),D),B))).  [resolve(4950,b,4935,a)].
11.27/11.27	Derived: -comm_monoid_mult(complex) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),dvd_dvd(complex),hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co302546470etprod(A,complex),D),C)),hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co302546470etprod(A,complex),D),B))).  [resolve(4950,b,4944,a)].
11.27/11.27	Derived: -comm_monoid_mult(code_code_numeral) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co302546470etprod(A,code_code_numeral),D),C)),hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co302546470etprod(A,code_code_numeral),D),B))).  [resolve(4950,b,4946,a)].
11.27/11.27	Derived: -comm_monoid_mult(quickcheck_code_int) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co302546470etprod(A,quickcheck_code_int),D),C)),hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co302546470etprod(A,quickcheck_code_int),D),B))).  [resolve(4950,b,4949,a)].
11.27/11.27	4951 field_char_0(rat) # label(arity_Rat_Orat___Rat_Ofield__char__0) # label(axiom).  [assumption].
11.27/11.27	4952 -field_char_0(A) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),B),field_char_0_Rats(A))) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),field_char_0_Rats(A))) | zero_zero(A) = ti(A,C) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)),field_char_0_Rats(A))) # label(fact_3689_nonzero__Rats__divide) # label(axiom).  [clausify(3)].
11.27/11.27	4953 -field_char_0(A) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),zero_zero(A)),field_char_0_Rats(A))) # label(fact_3691_Rats__0) # label(axiom).  [clausify(128)].
11.92/11.92	4954 -field_char_0(A) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),one_one(A)),field_char_0_Rats(A))) # label(fact_3695_Rats__1) # label(axiom).  [clausify(261)].
11.92/11.92	Derived: -hBOOL(hAPP(fun(rat,bool),bool,hAPP(rat,fun(fun(rat,bool),bool),member(rat),A),field_char_0_Rats(rat))) | -hBOOL(hAPP(fun(rat,bool),bool,hAPP(rat,fun(fun(rat,bool),bool),member(rat),B),field_char_0_Rats(rat))) | zero_zero(rat) = ti(rat,B) | hBOOL(hAPP(fun(rat,bool),bool,hAPP(rat,fun(fun(rat,bool),bool),member(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),B)),field_char_0_Rats(rat))).  [resolve(4951,a,4952,a)].
11.92/11.92	Derived: hBOOL(hAPP(fun(rat,bool),bool,hAPP(rat,fun(fun(rat,bool),bool),member(rat),zero_zero(rat)),field_char_0_Rats(rat))).  [resolve(4951,a,4953,a)].
11.92/11.92	Derived: hBOOL(hAPP(fun(rat,bool),bool,hAPP(rat,fun(fun(rat,bool),bool),member(rat),one_one(rat)),field_char_0_Rats(rat))).  [resolve(4951,a,4954,a)].
11.92/11.92	4955 -field_char_0(A) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),B),field_char_0_Rats(A))) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),hAPP(A,A,uminus_uminus(A),B)),field_char_0_Rats(A))) # label(fact_3698_Rats__minus) # label(axiom).  [clausify(515)].
11.92/11.92	Derived: -hBOOL(hAPP(fun(rat,bool),bool,hAPP(rat,fun(fun(rat,bool),bool),member(rat),A),field_char_0_Rats(rat))) | hBOOL(hAPP(fun(rat,bool),bool,hAPP(rat,fun(fun(rat,bool),bool),member(rat),hAPP(rat,rat,uminus_uminus(rat),A)),field_char_0_Rats(rat))).  [resolve(4955,a,4951,a)].
11.92/11.92	4956 -field_char_0(A) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),B),field_char_0_Rats(A))) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),field_char_0_Rats(A))) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C)),field_char_0_Rats(A))) # label(fact_3696_Rats__diff) # label(axiom).  [clausify(2191)].
11.92/11.92	Derived: -hBOOL(hAPP(fun(rat,bool),bool,hAPP(rat,fun(fun(rat,bool),bool),member(rat),A),field_char_0_Rats(rat))) | -hBOOL(hAPP(fun(rat,bool),bool,hAPP(rat,fun(fun(rat,bool),bool),member(rat),B),field_char_0_Rats(rat))) | hBOOL(hAPP(fun(rat,bool),bool,hAPP(rat,fun(fun(rat,bool),bool),member(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),A),B)),field_char_0_Rats(rat))).  [resolve(4956,a,4951,a)].
11.92/11.92	4957 -field_char_0(A) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),B),field_char_0_Rats(A))) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),field_char_0_Rats(A))) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),field_char_0_Rats(A))) # label(fact_3692_Rats__mult) # label(axiom).  [clausify(2259)].
11.92/11.92	Derived: -hBOOL(hAPP(fun(rat,bool),bool,hAPP(rat,fun(fun(rat,bool),bool),member(rat),A),field_char_0_Rats(rat))) | -hBOOL(hAPP(fun(rat,bool),bool,hAPP(rat,fun(fun(rat,bool),bool),member(rat),B),field_char_0_Rats(rat))) | hBOOL(hAPP(fun(rat,bool),bool,hAPP(rat,fun(fun(rat,bool),bool),member(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B)),field_char_0_Rats(rat))).  [resolve(4957,a,4951,a)].
11.92/11.92	4958 -field_char_0(A) | field_char_0_Rats(A) = ti(fun(A,bool),field_char_0_Rats(A)) # label(tsy_c_Rat_Ofield__char__0__class_ORats_res) # label(axiom).  [clausify(2316)].
11.92/11.92	Derived: field_char_0_Rats(rat) = ti(fun(rat,bool),field_char_0_Rats(rat)).  [resolve(4958,a,4951,a)].
11.92/11.92	4959 field_char_0(complex) # label(arity_Complex_Ocomplex___Rat_Ofield__char__0) # label(axiom).  [assumption].
11.92/11.92	Derived: -hBOOL(hAPP(fun(complex,bool),bool,hAPP(complex,fun(fun(complex,bool),bool),member(complex),A),field_char_0_Rats(complex))) | -hBOOL(hAPP(fun(complex,bool),bool,hAPP(complex,fun(fun(complex,bool),bool),member(complex),B),field_char_0_Rats(complex))) | zero_zero(complex) = ti(complex,B) | hBOOL(hAPP(fun(complex,bool),bool,hAPP(complex,fun(fun(complex,bool),bool),member(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),A),B)),field_char_0_Rats(complex))).  [resolve(4959,a,4952,a)].
12.67/12.64	Derived: hBOOL(hAPP(fun(complex,bool),bool,hAPP(complex,fun(fun(complex,bool),bool),member(complex),zero_zero(complex)),field_char_0_Rats(complex))).  [resolve(4959,a,4953,a)].
12.67/12.64	Derived: hBOOL(hAPP(fun(complex,bool),bool,hAPP(complex,fun(fun(complex,bool),bool),member(complex),one_one(complex)),field_char_0_Rats(complex))).  [resolve(4959,a,4954,a)].
12.67/12.64	Derived: -hBOOL(hAPP(fun(complex,bool),bool,hAPP(complex,fun(fun(complex,bool),bool),member(complex),A),field_char_0_Rats(complex))) | hBOOL(hAPP(fun(complex,bool),bool,hAPP(complex,fun(fun(complex,bool),bool),member(complex),hAPP(complex,complex,uminus_uminus(complex),A)),field_char_0_Rats(complex))).  [resolve(4959,a,4955,a)].
12.67/12.64	Derived: -hBOOL(hAPP(fun(complex,bool),bool,hAPP(complex,fun(fun(complex,bool),bool),member(complex),A),field_char_0_Rats(complex))) | -hBOOL(hAPP(fun(complex,bool),bool,hAPP(complex,fun(fun(complex,bool),bool),member(complex),B),field_char_0_Rats(complex))) | hBOOL(hAPP(fun(complex,bool),bool,hAPP(complex,fun(fun(complex,bool),bool),member(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),A),B)),field_char_0_Rats(complex))).  [resolve(4959,a,4956,a)].
12.67/12.64	Derived: -hBOOL(hAPP(fun(complex,bool),bool,hAPP(complex,fun(fun(complex,bool),bool),member(complex),A),field_char_0_Rats(complex))) | -hBOOL(hAPP(fun(complex,bool),bool,hAPP(complex,fun(fun(complex,bool),bool),member(complex),B),field_char_0_Rats(complex))) | hBOOL(hAPP(fun(complex,bool),bool,hAPP(complex,fun(fun(complex,bool),bool),member(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),B)),field_char_0_Rats(complex))).  [resolve(4959,a,4957,a)].
12.67/12.64	Derived: field_char_0_Rats(complex) = ti(fun(complex,bool),field_char_0_Rats(complex)).  [resolve(4959,a,4958,a)].
12.67/12.64	4960 -field_char_0(A) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),B),field_char_0_Rats(A))) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C)),field_char_0_Rats(A))) # label(fact_3697_Rats__power) # label(axiom).  [clausify(2512)].
12.67/12.64	Derived: -hBOOL(hAPP(fun(rat,bool),bool,hAPP(rat,fun(fun(rat,bool),bool),member(rat),A),field_char_0_Rats(rat))) | hBOOL(hAPP(fun(rat,bool),bool,hAPP(rat,fun(fun(rat,bool),bool),member(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),B)),field_char_0_Rats(rat))).  [resolve(4960,a,4951,a)].
12.67/12.64	Derived: -hBOOL(hAPP(fun(complex,bool),bool,hAPP(complex,fun(fun(complex,bool),bool),member(complex),A),field_char_0_Rats(complex))) | hBOOL(hAPP(fun(complex,bool),bool,hAPP(complex,fun(fun(complex,bool),bool),member(complex),hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),A),B)),field_char_0_Rats(complex))).  [resolve(4960,a,4959,a)].
12.67/12.64	4961 -field_char_0(A) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),hAPP(int,A,ring_1_of_int(A),B)),field_char_0_Rats(A))) # label(fact_3702_Rats__of__int) # label(axiom).  [clausify(3017)].
12.67/12.64	Derived: hBOOL(hAPP(fun(rat,bool),bool,hAPP(rat,fun(fun(rat,bool),bool),member(rat),hAPP(int,rat,ring_1_of_int(rat),A)),field_char_0_Rats(rat))).  [resolve(4961,a,4951,a)].
12.67/12.64	Derived: hBOOL(hAPP(fun(complex,bool),bool,hAPP(complex,fun(fun(complex,bool),bool),member(complex),hAPP(int,complex,ring_1_of_int(complex),A)),field_char_0_Rats(complex))).  [resolve(4961,a,4959,a)].
12.67/12.64	4962 -field_char_0(A) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),B),field_char_0_Rats(A))) | zero_zero(A) = ti(A,B) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),hAPP(A,A,inverse_inverse(A),B)),field_char_0_Rats(A))) # label(fact_3688_nonzero__Rats__inverse) # label(axiom).  [clausify(3610)].
12.67/12.64	Derived: -hBOOL(hAPP(fun(rat,bool),bool,hAPP(rat,fun(fun(rat,bool),bool),member(rat),A),field_char_0_Rats(rat))) | zero_zero(rat) = ti(rat,A) | hBOOL(hAPP(fun(rat,bool),bool,hAPP(rat,fun(fun(rat,bool),bool),member(rat),hAPP(rat,rat,inverse_inverse(rat),A)),field_char_0_Rats(rat))).  [resolve(4962,a,4951,a)].
12.67/12.64	Derived: -hBOOL(hAPP(fun(complex,bool),bool,hAPP(complex,fun(fun(complex,bool),bool),member(complex),A),field_char_0_Rats(complex))) | zero_zero(complex) = ti(complex,A) | hBOOL(hAPP(fun(complex,bool),bool,hAPP(complex,fun(fun(complex,bool),bool),member(complex),hAPP(complex,complex,inverse_inverse(complex),A)),field_char_0_Rats(complex))).  [resolve(4962,a,4959,a)].
13.55/13.58	4963 field_char_0(real) # label(arity_RealDef_Oreal___Rat_Ofield__char__0) # label(axiom).  [assumption].
13.55/13.58	Derived: -hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),A),field_char_0_Rats(real))) | -hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),B),field_char_0_Rats(real))) | zero_zero(real) = ti(real,B) | hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B)),field_char_0_Rats(real))).  [resolve(4963,a,4952,a)].
13.55/13.58	Derived: hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),zero_zero(real)),field_char_0_Rats(real))).  [resolve(4963,a,4953,a)].
13.55/13.58	Derived: hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),one_one(real)),field_char_0_Rats(real))).  [resolve(4963,a,4954,a)].
13.55/13.58	Derived: -hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),A),field_char_0_Rats(real))) | hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),hAPP(real,real,uminus_uminus(real),A)),field_char_0_Rats(real))).  [resolve(4963,a,4955,a)].
13.55/13.58	Derived: -hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),A),field_char_0_Rats(real))) | -hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),B),field_char_0_Rats(real))) | hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),B)),field_char_0_Rats(real))).  [resolve(4963,a,4956,a)].
13.55/13.58	Derived: -hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),A),field_char_0_Rats(real))) | -hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),B),field_char_0_Rats(real))) | hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),field_char_0_Rats(real))).  [resolve(4963,a,4957,a)].
13.55/13.58	Derived: field_char_0_Rats(real) = ti(fun(real,bool),field_char_0_Rats(real)).  [resolve(4963,a,4958,a)].
13.55/13.58	Derived: -hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),A),field_char_0_Rats(real))) | hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),B)),field_char_0_Rats(real))).  [resolve(4963,a,4960,a)].
13.55/13.58	Derived: hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),hAPP(int,real,ring_1_of_int(real),A)),field_char_0_Rats(real))).  [resolve(4963,a,4961,a)].
13.55/13.58	Derived: -hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),A),field_char_0_Rats(real))) | zero_zero(real) = ti(real,A) | hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),hAPP(real,real,inverse_inverse(real),A)),field_char_0_Rats(real))).  [resolve(4963,a,4962,a)].
13.55/13.58	4964 -field_char_0(A) | -field_inverse_zero(A) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),B),field_char_0_Rats(A))) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),field_char_0_Rats(A))) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)),field_char_0_Rats(A))) # label(fact_3699_Rats__divide) # label(axiom).  [clausify(4581)].
13.55/13.58	Derived: -field_inverse_zero(rat) | -hBOOL(hAPP(fun(rat,bool),bool,hAPP(rat,fun(fun(rat,bool),bool),member(rat),A),field_char_0_Rats(rat))) | -hBOOL(hAPP(fun(rat,bool),bool,hAPP(rat,fun(fun(rat,bool),bool),member(rat),B),field_char_0_Rats(rat))) | hBOOL(hAPP(fun(rat,bool),bool,hAPP(rat,fun(fun(rat,bool),bool),member(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),B)),field_char_0_Rats(rat))).  [resolve(4964,a,4951,a)].
13.78/13.79	Derived: -field_inverse_zero(complex) | -hBOOL(hAPP(fun(complex,bool),bool,hAPP(complex,fun(fun(complex,bool),bool),member(complex),A),field_char_0_Rats(complex))) | -hBOOL(hAPP(fun(complex,bool),bool,hAPP(complex,fun(fun(complex,bool),bool),member(complex),B),field_char_0_Rats(complex))) | hBOOL(hAPP(fun(complex,bool),bool,hAPP(complex,fun(fun(complex,bool),bool),member(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),A),B)),field_char_0_Rats(complex))).  [resolve(4964,a,4959,a)].
13.78/13.79	Derived: -field_inverse_zero(real) | -hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),A),field_char_0_Rats(real))) | -hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),B),field_char_0_Rats(real))) | hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B)),field_char_0_Rats(real))).  [resolve(4964,a,4963,a)].
13.78/13.79	4965 -number_ring(A) | -field_char_0(A) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),hAPP(int,A,number_number_of(A),B)),field_char_0_Rats(A))) # label(fact_3694_Rats__number__of) # label(axiom).  [clausify(4605)].
13.78/13.79	Derived: -number_ring(rat) | hBOOL(hAPP(fun(rat,bool),bool,hAPP(rat,fun(fun(rat,bool),bool),member(rat),hAPP(int,rat,number_number_of(rat),A)),field_char_0_Rats(rat))).  [resolve(4965,b,4951,a)].
13.78/13.79	Derived: -number_ring(complex) | hBOOL(hAPP(fun(complex,bool),bool,hAPP(complex,fun(fun(complex,bool),bool),member(complex),hAPP(int,complex,number_number_of(complex),A)),field_char_0_Rats(complex))).  [resolve(4965,b,4959,a)].
13.78/13.79	Derived: -number_ring(real) | hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),hAPP(int,real,number_number_of(real),A)),field_char_0_Rats(real))).  [resolve(4965,b,4963,a)].
13.78/13.79	4966 -field_char_0(A) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),hAPP(nat,A,semiring_1_of_nat(A),B)),field_char_0_Rats(A))) # label(fact_3700_Rats__of__nat) # label(axiom).  [clausify(4666)].
13.78/13.79	Derived: hBOOL(hAPP(fun(rat,bool),bool,hAPP(rat,fun(fun(rat,bool),bool),member(rat),hAPP(nat,rat,semiring_1_of_nat(rat),A)),field_char_0_Rats(rat))).  [resolve(4966,a,4951,a)].
13.78/13.79	Derived: hBOOL(hAPP(fun(complex,bool),bool,hAPP(complex,fun(fun(complex,bool),bool),member(complex),hAPP(nat,complex,semiring_1_of_nat(complex),A)),field_char_0_Rats(complex))).  [resolve(4966,a,4959,a)].
13.78/13.79	Derived: hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),hAPP(nat,real,semiring_1_of_nat(real),A)),field_char_0_Rats(real))).  [resolve(4966,a,4963,a)].
13.78/13.79	4967 -field_inverse_zero(A) | -field_char_0(A) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),B),field_char_0_Rats(A))) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),hAPP(A,A,inverse_inverse(A),B)),field_char_0_Rats(A))) # label(fact_3701_Rats__inverse) # label(axiom).  [clausify(4816)].
13.78/13.79	Derived: -field_inverse_zero(rat) | -hBOOL(hAPP(fun(rat,bool),bool,hAPP(rat,fun(fun(rat,bool),bool),member(rat),A),field_char_0_Rats(rat))) | hBOOL(hAPP(fun(rat,bool),bool,hAPP(rat,fun(fun(rat,bool),bool),member(rat),hAPP(rat,rat,inverse_inverse(rat),A)),field_char_0_Rats(rat))).  [resolve(4967,b,4951,a)].
13.78/13.79	Derived: -field_inverse_zero(complex) | -hBOOL(hAPP(fun(complex,bool),bool,hAPP(complex,fun(fun(complex,bool),bool),member(complex),A),field_char_0_Rats(complex))) | hBOOL(hAPP(fun(complex,bool),bool,hAPP(complex,fun(fun(complex,bool),bool),member(complex),hAPP(complex,complex,inverse_inverse(complex),A)),field_char_0_Rats(complex))).  [resolve(4967,b,4959,a)].
13.78/13.79	Derived: -field_inverse_zero(real) | -hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),A),field_char_0_Rats(real))) | hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),hAPP(real,real,inverse_inverse(real),A)),field_char_0_Rats(real))).  [resolve(4967,b,4963,a)].
13.78/13.79	4968 -field_char_0(A) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),B),field_char_0_Rats(A))) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),field_char_0_Rats(A))) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),field_char_0_Rats(A))) # label(fact_3693_Rats__add) # label(axiom).  [clausify(4829)].
14.60/14.58	Derived: -hBOOL(hAPP(fun(rat,bool),bool,hAPP(rat,fun(fun(rat,bool),bool),member(rat),A),field_char_0_Rats(rat))) | -hBOOL(hAPP(fun(rat,bool),bool,hAPP(rat,fun(fun(rat,bool),bool),member(rat),B),field_char_0_Rats(rat))) | hBOOL(hAPP(fun(rat,bool),bool,hAPP(rat,fun(fun(rat,bool),bool),member(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),B)),field_char_0_Rats(rat))).  [resolve(4968,a,4951,a)].
14.60/14.58	Derived: -hBOOL(hAPP(fun(complex,bool),bool,hAPP(complex,fun(fun(complex,bool),bool),member(complex),A),field_char_0_Rats(complex))) | -hBOOL(hAPP(fun(complex,bool),bool,hAPP(complex,fun(fun(complex,bool),bool),member(complex),B),field_char_0_Rats(complex))) | hBOOL(hAPP(fun(complex,bool),bool,hAPP(complex,fun(fun(complex,bool),bool),member(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),A),B)),field_char_0_Rats(complex))).  [resolve(4968,a,4959,a)].
14.60/14.58	Derived: -hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),A),field_char_0_Rats(real))) | -hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),B),field_char_0_Rats(real))) | hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),B)),field_char_0_Rats(real))).  [resolve(4968,a,4963,a)].
14.60/14.58	4969 archim1727834104eiling(real) # label(arity_RealDef_Oreal___Archimedean__Field_Ofloor__ceiling) # label(axiom).  [assumption].
14.60/14.58	4970 -archim1727834104eiling(A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(A,int,archimedean_ceiling(A),B)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(int,A,ring_1_of_int(A),C))) # label(fact_3595_ceiling__le__iff) # label(axiom).  [clausify(6)].
14.60/14.58	4971 -archim1727834104eiling(A) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(A,int,archimedean_ceiling(A),B)),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(int,A,ring_1_of_int(A),C))) # label(fact_3595_ceiling__le__iff) # label(axiom).  [clausify(6)].
14.60/14.58	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(real,int,archimedean_ceiling(real),A)),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),hAPP(int,real,ring_1_of_int(real),B))).  [resolve(4969,a,4970,a)].
14.60/14.58	Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(real,int,archimedean_ceiling(real),A)),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),hAPP(int,real,ring_1_of_int(real),B))).  [resolve(4969,a,4971,a)].
14.60/14.58	4972 -archim1727834104eiling(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(int,A,number_number_of(A),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(A,int,archim2085082626_floor(A),B)),one_one(int))) # label(fact_2847_floor__le__one) # label(axiom).  [clausify(20)].
14.60/14.58	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(real,int,archim2085082626_floor(real),A)),one_one(int))).  [resolve(4972,a,4969,a)].
14.60/14.58	4973 -archim1727834104eiling(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(int,A,number_number_of(A),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(A,int,archim2085082626_floor(A),B)),one_one(int))) # label(fact_2847_floor__le__one) # label(axiom).  [clausify(20)].
14.60/14.58	Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(real,int,archim2085082626_floor(real),A)),one_one(int))).  [resolve(4973,a,4969,a)].
14.60/14.61	4974 -archim1727834104eiling(A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),hAPP(A,int,archim2085082626_floor(A),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(int,A,ring_1_of_int(A),B)),C)) # label(fact_3593_le__floor__iff) # label(axiom).  [clausify(77)].
14.60/14.61	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),hAPP(real,int,archim2085082626_floor(real),B))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,ring_1_of_int(real),A)),B)).  [resolve(4974,a,4969,a)].
14.60/14.61	4975 -archim1727834104eiling(A) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),hAPP(A,int,archim2085082626_floor(A),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(int,A,ring_1_of_int(A),B)),C)) # label(fact_3593_le__floor__iff) # label(axiom).  [clausify(77)].
14.60/14.61	Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),hAPP(real,int,archim2085082626_floor(real),B))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,ring_1_of_int(real),A)),B)).  [resolve(4975,a,4969,a)].
14.60/14.61	4976 -archim1727834104eiling(A) | hAPP(A,int,archimedean_ceiling(A),hAPP(nat,A,semiring_1_of_nat(A),B)) = hAPP(nat,int,semiring_1_of_nat(int),B) # label(fact_3285_ceiling__of__nat) # label(axiom).  [clausify(101)].
14.60/14.61	Derived: hAPP(real,int,archimedean_ceiling(real),hAPP(nat,real,semiring_1_of_nat(real),A)) = hAPP(nat,int,semiring_1_of_nat(int),A).  [resolve(4976,a,4969,a)].
14.60/14.61	4977 -archim1727834104eiling(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,ring_1_of_int(A),B)),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),hAPP(A,int,archimedean_ceiling(A),C))) # label(fact_3594_less__ceiling__iff) # label(axiom).  [clausify(159)].
14.60/14.61	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,ring_1_of_int(real),A)),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),hAPP(real,int,archimedean_ceiling(real),B))).  [resolve(4977,a,4969,a)].
14.60/14.61	4978 -archim1727834104eiling(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,ring_1_of_int(A),B)),C)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),hAPP(A,int,archimedean_ceiling(A),C))) # label(fact_3594_less__ceiling__iff) # label(axiom).  [clausify(159)].
14.60/14.61	Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,ring_1_of_int(real),A)),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),hAPP(real,int,archimedean_ceiling(real),B))).  [resolve(4978,a,4969,a)].
14.60/14.61	4979 -archim1727834104eiling(A) | hAPP(A,int,archimedean_ceiling(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),one_one(A))) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(A,int,archimedean_ceiling(A),B)),one_one(int)) # label(fact_3307_ceiling__diff__one) # label(axiom).  [clausify(346)].
14.60/14.61	Derived: hAPP(real,int,archimedean_ceiling(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),one_one(real))) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(real,int,archimedean_ceiling(real),A)),one_one(int)).  [resolve(4979,a,4969,a)].
14.60/14.61	4980 -archim1727834104eiling(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(int,A,ring_1_of_int(A),hAPP(A,int,archim2085082626_floor(A),B))),B)) # label(fact_3612_floor__correct) # label(axiom).  [clausify(420)].
14.60/14.61	Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,ring_1_of_int(real),hAPP(real,int,archim2085082626_floor(real),A))),A)).  [resolve(4980,a,4969,a)].
14.60/14.61	4981 -archim1727834104eiling(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(int,A,ring_1_of_int(A),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(A,int,archim2085082626_floor(A),B)),one_one(int))))) # label(fact_3612_floor__correct) # label(axiom).  [clausify(420)].
14.60/14.61	Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),hAPP(int,real,ring_1_of_int(real),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(real,int,archim2085082626_floor(real),A)),one_one(int))))).  [resolve(4981,a,4969,a)].
14.71/14.68	4982 -archim1727834104eiling(A) | hAPP(A,int,archim2085082626_floor(A),hAPP(nat,A,semiring_1_of_nat(A),B)) = hAPP(nat,int,semiring_1_of_nat(int),B) # label(fact_2875_floor__of__nat) # label(axiom).  [clausify(451)].
14.71/14.68	Derived: hAPP(real,int,archim2085082626_floor(real),hAPP(nat,real,semiring_1_of_nat(real),A)) = hAPP(nat,int,semiring_1_of_nat(int),A).  [resolve(4982,a,4969,a)].
14.71/14.68	4983 -archim1727834104eiling(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),one_one(A)),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(A,int,archim2085082626_floor(A),B))) # label(fact_2881_zero__less__floor) # label(axiom).  [clausify(568)].
14.71/14.68	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),one_one(real)),A)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(real,int,archim2085082626_floor(real),A))).  [resolve(4983,a,4969,a)].
14.71/14.68	4984 -archim1727834104eiling(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),one_one(A)),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(A,int,archim2085082626_floor(A),B))) # label(fact_2881_zero__less__floor) # label(axiom).  [clausify(568)].
14.71/14.68	Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),one_one(real)),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(real,int,archim2085082626_floor(real),A))).  [resolve(4984,a,4969,a)].
14.71/14.68	4985 -archim1727834104eiling(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(int,A,ring_1_of_int(A),B)),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(int,A,ring_1_of_int(A),B)),one_one(A)))) | hAPP(A,int,archim2085082626_floor(A),C) = ti(int,B) # label(fact_3605_floor__unique) # label(axiom).  [clausify(630)].
14.71/14.68	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,ring_1_of_int(real),A)),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(int,real,ring_1_of_int(real),A)),one_one(real)))) | hAPP(real,int,archim2085082626_floor(real),B) = ti(int,A).  [resolve(4985,a,4969,a)].
14.71/14.68	4986 -archim1727834104eiling(A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(A,int,archim2085082626_floor(A),B))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) # label(fact_2880_zero__le__floor) # label(axiom).  [clausify(703)].
14.71/14.68	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(real,int,archim2085082626_floor(real),A))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A)).  [resolve(4986,a,4969,a)].
14.71/14.68	4987 -archim1727834104eiling(A) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(A,int,archim2085082626_floor(A),B))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) # label(fact_2880_zero__le__floor) # label(axiom).  [clausify(703)].
14.71/14.68	Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(real,int,archim2085082626_floor(real),A))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A)).  [resolve(4987,a,4969,a)].
14.71/14.68	4988 -archim1727834104eiling(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(A,int,archimedean_ceiling(A),B)),hAPP(A,int,archimedean_ceiling(A),C))) # label(fact_3281_ceiling__mono) # label(axiom).  [clausify(760)].
14.71/14.68	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(real,int,archimedean_ceiling(real),A)),hAPP(real,int,archimedean_ceiling(real),B))).  [resolve(4988,a,4969,a)].
14.71/14.68	4989 -archim1727834104eiling(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(int,A,ring_1_of_int(A),B)),one_one(A))),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),hAPP(int,A,ring_1_of_int(A),B))) | hAPP(A,int,archimedean_ceiling(A),C) = ti(int,B) # label(fact_3606_ceiling__unique) # label(axiom).  [clausify(840)].
14.84/14.84	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(int,real,ring_1_of_int(real),A)),one_one(real))),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),hAPP(int,real,ring_1_of_int(real),A))) | hAPP(real,int,archimedean_ceiling(real),B) = ti(int,A).  [resolve(4989,a,4969,a)].
14.84/14.84	4990 -archim1727834104eiling(A) | hAPP(A,int,archimedean_ceiling(A),B) = hAPP(int,int,uminus_uminus(int),hAPP(A,int,archim2085082626_floor(A),hAPP(A,A,uminus_uminus(A),B))) # label(fact_3295_ceiling__def) # label(axiom).  [clausify(976)].
14.84/14.84	Derived: hAPP(real,int,archimedean_ceiling(real),A) = hAPP(int,int,uminus_uminus(int),hAPP(real,int,archim2085082626_floor(real),hAPP(real,real,uminus_uminus(real),A))).  [resolve(4990,a,4969,a)].
14.84/14.84	4991 -archim1727834104eiling(A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),B)),hAPP(A,int,archim2085082626_floor(A),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(int,A,number_number_of(A),B)),C)) # label(fact_2886_number__of__le__floor) # label(axiom).  [clausify(1056)].
14.84/14.84	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),A)),hAPP(real,int,archim2085082626_floor(real),B))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,number_number_of(real),A)),B)).  [resolve(4991,a,4969,a)].
14.84/14.84	4992 -archim1727834104eiling(A) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),B)),hAPP(A,int,archim2085082626_floor(A),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(int,A,number_number_of(A),B)),C)) # label(fact_2886_number__of__le__floor) # label(axiom).  [clausify(1056)].
14.84/14.84	Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),A)),hAPP(real,int,archim2085082626_floor(real),B))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,number_number_of(real),A)),B)).  [resolve(4992,a,4969,a)].
14.84/14.84	4993 -archim1727834104eiling(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(int,A,ring_1_of_int(A),hAPP(A,int,archimedean_ceiling(A),B)))) # label(fact_3586_le__of__int__ceiling) # label(axiom).  [clausify(1353)].
14.84/14.84	Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),hAPP(int,real,ring_1_of_int(real),hAPP(real,int,archimedean_ceiling(real),A)))).  [resolve(4993,a,4969,a)].
14.84/14.84	4994 -archim1727834104eiling(A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),hAPP(A,int,archim2085082626_floor(A),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(int,A,ring_1_of_int(A),B)),one_one(A))),C)) # label(fact_3608_less__floor__iff) # label(axiom).  [clausify(1400)].
14.84/14.84	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),hAPP(real,int,archim2085082626_floor(real),B))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(int,real,ring_1_of_int(real),A)),one_one(real))),B)).  [resolve(4994,a,4969,a)].
14.84/14.84	4995 -archim1727834104eiling(A) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),hAPP(A,int,archim2085082626_floor(A),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(int,A,ring_1_of_int(A),B)),one_one(A))),C)) # label(fact_3608_less__floor__iff) # label(axiom).  [clausify(1400)].
14.84/14.84	Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),hAPP(real,int,archim2085082626_floor(real),B))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(int,real,ring_1_of_int(real),A)),one_one(real))),B)).  [resolve(4995,a,4969,a)].
15.01/14.98	4996 -archim1727834104eiling(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),zero_zero(A))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(A,int,archimedean_ceiling(A),B)),one_one(int))) # label(fact_3299_ceiling__less__one) # label(axiom).  [clausify(1589)].
15.01/14.98	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),zero_zero(real))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(real,int,archimedean_ceiling(real),A)),one_one(int))).  [resolve(4996,a,4969,a)].
15.01/14.98	4997 -archim1727834104eiling(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),zero_zero(A))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(A,int,archimedean_ceiling(A),B)),one_one(int))) # label(fact_3299_ceiling__less__one) # label(axiom).  [clausify(1589)].
15.01/14.98	Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),zero_zero(real))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(real,int,archimedean_ceiling(real),A)),one_one(int))).  [resolve(4997,a,4969,a)].
15.01/14.98	4998 -archim1727834104eiling(A) | hAPP(A,int,archimedean_ceiling(A),B) = hAPP(real,int,archim2085082626_floor(real),hAPP(int,real,real_1(int),hAPP(A,int,archimedean_ceiling(A),B))) # label(fact_3355_floor__ceiling) # label(axiom).  [clausify(1593)].
15.01/14.98	Derived: hAPP(real,int,archimedean_ceiling(real),A) = hAPP(real,int,archim2085082626_floor(real),hAPP(int,real,real_1(int),hAPP(real,int,archimedean_ceiling(real),A))).  [resolve(4998,a,4969,a)].
15.01/14.98	4999 -archim1727834104eiling(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),one_one(A))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(A,int,archim2085082626_floor(A),B)),one_one(int))) # label(fact_2883_floor__less__one) # label(axiom).  [clausify(1640)].
15.01/14.98	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),one_one(real))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(real,int,archim2085082626_floor(real),A)),one_one(int))).  [resolve(4999,a,4969,a)].
15.01/14.98	5000 -archim1727834104eiling(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),one_one(A))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(A,int,archim2085082626_floor(A),B)),one_one(int))) # label(fact_2883_floor__less__one) # label(axiom).  [clausify(1640)].
15.01/14.98	Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),one_one(real))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(real,int,archim2085082626_floor(real),A)),one_one(int))).  [resolve(5000,a,4969,a)].
15.01/14.98	5001 -archim1727834104eiling(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),hAPP(int,A,ring_1_of_int(A),C)),one_one(A)))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(A,int,archim2085082626_floor(A),B)),C)) # label(fact_3609_floor__le__iff) # label(axiom).  [clausify(1701)].
15.01/14.98	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(int,real,ring_1_of_int(real),B)),one_one(real)))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(real,int,archim2085082626_floor(real),A)),B)).  [resolve(5001,a,4969,a)].
15.01/14.98	5002 -archim1727834104eiling(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),hAPP(int,A,ring_1_of_int(A),C)),one_one(A)))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(A,int,archim2085082626_floor(A),B)),C)) # label(fact_3609_floor__le__iff) # label(axiom).  [clausify(1701)].
15.01/14.98	Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(int,real,ring_1_of_int(real),B)),one_one(real)))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(real,int,archim2085082626_floor(real),A)),B)).  [resolve(5002,a,4969,a)].
15.01/14.98	5003 -archim1727834104eiling(A) | hAPP(A,int,archimedean_ceiling(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),hAPP(int,A,number_number_of(A),C))) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(A,int,archimedean_ceiling(A),B)),hAPP(int,int,number_number_of(int),C)) # label(fact_3306_ceiling__add__number__of) # label(axiom).  [clausify(1769)].
15.19/15.18	Derived: hAPP(real,int,archimedean_ceiling(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),hAPP(int,real,number_number_of(real),B))) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(real,int,archimedean_ceiling(real),A)),hAPP(int,int,number_number_of(int),B)).  [resolve(5003,a,4969,a)].
15.19/15.18	5004 -archim1727834104eiling(A) | hAPP(A,int,archimedean_ceiling(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),hAPP(int,A,ring_1_of_int(A),C))) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(A,int,archimedean_ceiling(A),B)),C) # label(fact_3597_ceiling__add__of__int) # label(axiom).  [clausify(1898)].
15.19/15.18	Derived: hAPP(real,int,archimedean_ceiling(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),hAPP(int,real,ring_1_of_int(real),B))) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(real,int,archimedean_ceiling(real),A)),B).  [resolve(5004,a,4969,a)].
15.19/15.18	5005 -archim1727834104eiling(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(int,A,ring_1_of_int(A),hAPP(A,int,archimedean_ceiling(A),B)))) # label(fact_3607_ceiling__correct) # label(axiom).  [clausify(1906)].
15.19/15.18	5006 -archim1727834104eiling(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(int,A,ring_1_of_int(A),hAPP(A,int,archimedean_ceiling(A),B))),one_one(A))),B)) # label(fact_3607_ceiling__correct) # label(axiom).  [clausify(1906)].
15.19/15.18	Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(int,real,ring_1_of_int(real),hAPP(real,int,archimedean_ceiling(real),A))),one_one(real))),A)).  [resolve(5006,a,4969,a)].
15.19/15.18	5007 -archim1727834104eiling(A) | hAPP(A,int,archim2085082626_floor(A),hAPP(int,A,number_number_of(A),B)) = hAPP(int,int,number_number_of(int),B) # label(fact_2872_floor__number__of) # label(axiom).  [clausify(1972)].
15.19/15.18	Derived: hAPP(real,int,archim2085082626_floor(real),hAPP(int,real,number_number_of(real),A)) = hAPP(int,int,number_number_of(int),A).  [resolve(5007,a,4969,a)].
15.19/15.18	5008 -archim1727834104eiling(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(int,A,number_number_of(A),C)),one_one(A)))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(A,int,archimedean_ceiling(A),B)),hAPP(int,int,number_number_of(int),C))) # label(fact_3311_ceiling__less__number__of) # label(axiom).  [clausify(2121)].
15.19/15.18	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(int,real,number_number_of(real),B)),one_one(real)))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(real,int,archimedean_ceiling(real),A)),hAPP(int,int,number_number_of(int),B))).  [resolve(5008,a,4969,a)].
15.19/15.18	5009 -archim1727834104eiling(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(int,A,number_number_of(A),C)),one_one(A)))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(A,int,archimedean_ceiling(A),B)),hAPP(int,int,number_number_of(int),C))) # label(fact_3311_ceiling__less__number__of) # label(axiom).  [clausify(2121)].
15.19/15.18	Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(int,real,number_number_of(real),B)),one_one(real)))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(real,int,archimedean_ceiling(real),A)),hAPP(int,int,number_number_of(int),B))).  [resolve(5009,a,4969,a)].
15.19/15.18	5010 -archim1727834104eiling(A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),hAPP(A,int,archim2085082626_floor(A),B))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),one_one(A)),B)) # label(fact_2884_one__le__floor) # label(axiom).  [clausify(2164)].
15.19/15.18	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),hAPP(real,int,archim2085082626_floor(real),A))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),one_one(real)),A)).  [resolve(5010,a,4969,a)].
15.31/15.26	5011 -archim1727834104eiling(A) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),hAPP(A,int,archim2085082626_floor(A),B))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),one_one(A)),B)) # label(fact_2884_one__le__floor) # label(axiom).  [clausify(2164)].
15.31/15.26	Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),hAPP(real,int,archim2085082626_floor(real),A))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),one_one(real)),A)).  [resolve(5011,a,4969,a)].
15.31/15.26	5012 -archim1727834104eiling(A) | one_one(int) = hAPP(A,int,archim2085082626_floor(A),one_one(A)) # label(fact_2870_floor__one) # label(axiom).  [clausify(2182)].
15.31/15.26	Derived: one_one(int) = hAPP(real,int,archim2085082626_floor(real),one_one(real)).  [resolve(5012,a,4969,a)].
15.31/15.26	5013 -archim1727834104eiling(A) | zero_zero(int) = hAPP(A,int,archimedean_ceiling(A),zero_zero(A)) # label(fact_3279_ceiling__zero) # label(axiom).  [clausify(2224)].
15.31/15.26	Derived: zero_zero(int) = hAPP(real,int,archimedean_ceiling(real),zero_zero(real)).  [resolve(5013,a,4969,a)].
15.31/15.26	5014 -archim1727834104eiling(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),zero_zero(A))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(A,int,archimedean_ceiling(A),B)),zero_zero(int))) # label(fact_3298_ceiling__le__zero) # label(axiom).  [clausify(2244)].
15.31/15.26	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),zero_zero(real))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(real,int,archimedean_ceiling(real),A)),zero_zero(int))).  [resolve(5014,a,4969,a)].
15.31/15.26	5015 -archim1727834104eiling(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),zero_zero(A))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(A,int,archimedean_ceiling(A),B)),zero_zero(int))) # label(fact_3298_ceiling__le__zero) # label(axiom).  [clausify(2244)].
15.31/15.26	Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),zero_zero(real))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(real,int,archimedean_ceiling(real),A)),zero_zero(int))).  [resolve(5015,a,4969,a)].
15.31/15.26	5016 archim1727834104eiling(rat) # label(arity_Rat_Orat___Archimedean__Field_Ofloor__ceiling) # label(axiom).  [assumption].
15.31/15.26	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(rat,int,archimedean_ceiling(rat),A)),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),hAPP(int,rat,ring_1_of_int(rat),B))).  [resolve(5016,a,4970,a)].
15.31/15.26	Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(rat,int,archimedean_ceiling(rat),A)),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),hAPP(int,rat,ring_1_of_int(rat),B))).  [resolve(5016,a,4971,a)].
15.31/15.26	Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),hAPP(int,rat,number_number_of(rat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(rat,int,archim2085082626_floor(rat),A)),one_one(int))).  [resolve(5016,a,4972,a)].
15.31/15.26	Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),hAPP(int,rat,number_number_of(rat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(rat,int,archim2085082626_floor(rat),A)),one_one(int))).  [resolve(5016,a,4973,a)].
15.31/15.26	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),hAPP(rat,int,archim2085082626_floor(rat),B))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(int,rat,ring_1_of_int(rat),A)),B)).  [resolve(5016,a,4974,a)].
15.31/15.26	Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),hAPP(rat,int,archim2085082626_floor(rat),B))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(int,rat,ring_1_of_int(rat),A)),B)).  [resolve(5016,a,4975,a)].
15.31/15.26	Derived: hAPP(rat,int,archimedean_ceiling(rat),hAPP(nat,rat,semiring_1_of_nat(rat),A)) = hAPP(nat,int,semiring_1_of_nat(int),A).  [resolve(5016,a,4976,a)].
15.31/15.28	Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(int,rat,ring_1_of_int(rat),A)),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),hAPP(rat,int,archimedean_ceiling(rat),B))).  [resolve(5016,a,4977,a)].
15.31/15.28	Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(int,rat,ring_1_of_int(rat),A)),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),hAPP(rat,int,archimedean_ceiling(rat),B))).  [resolve(5016,a,4978,a)].
15.31/15.28	Derived: hAPP(rat,int,archimedean_ceiling(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),A),one_one(rat))) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(rat,int,archimedean_ceiling(rat),A)),one_one(int)).  [resolve(5016,a,4979,a)].
15.31/15.28	Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(int,rat,ring_1_of_int(rat),hAPP(rat,int,archim2085082626_floor(rat),A))),A)).  [resolve(5016,a,4980,a)].
15.31/15.28	Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),hAPP(int,rat,ring_1_of_int(rat),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(rat,int,archim2085082626_floor(rat),A)),one_one(int))))).  [resolve(5016,a,4981,a)].
15.31/15.28	Derived: hAPP(rat,int,archim2085082626_floor(rat),hAPP(nat,rat,semiring_1_of_nat(rat),A)) = hAPP(nat,int,semiring_1_of_nat(int),A).  [resolve(5016,a,4982,a)].
15.31/15.28	Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),one_one(rat)),A)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(rat,int,archim2085082626_floor(rat),A))).  [resolve(5016,a,4983,a)].
15.31/15.28	Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),one_one(rat)),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(rat,int,archim2085082626_floor(rat),A))).  [resolve(5016,a,4984,a)].
15.31/15.28	Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(int,rat,ring_1_of_int(rat),A)),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(int,rat,ring_1_of_int(rat),A)),one_one(rat)))) | hAPP(rat,int,archim2085082626_floor(rat),B) = ti(int,A).  [resolve(5016,a,4985,a)].
15.31/15.28	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(rat,int,archim2085082626_floor(rat),A))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),A)).  [resolve(5016,a,4986,a)].
15.31/15.28	Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(rat,int,archim2085082626_floor(rat),A))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),A)).  [resolve(5016,a,4987,a)].
15.31/15.28	Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(rat,int,archimedean_ceiling(rat),A)),hAPP(rat,int,archimedean_ceiling(rat),B))).  [resolve(5016,a,4988,a)].
15.31/15.28	Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),hAPP(int,rat,ring_1_of_int(rat),A)),one_one(rat))),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),B),hAPP(int,rat,ring_1_of_int(rat),A))) | hAPP(rat,int,archimedean_ceiling(rat),B) = ti(int,A).  [resolve(5016,a,4989,a)].
15.31/15.28	Derived: hAPP(rat,int,archimedean_ceiling(rat),A) = hAPP(int,int,uminus_uminus(int),hAPP(rat,int,archim2085082626_floor(rat),hAPP(rat,rat,uminus_uminus(rat),A))).  [resolve(5016,a,4990,a)].
15.31/15.28	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),A)),hAPP(rat,int,archim2085082626_floor(rat),B))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(int,rat,number_number_of(rat),A)),B)).  [resolve(5016,a,4991,a)].
15.31/15.28	Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),A)),hAPP(rat,int,archim2085082626_floor(rat),B))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(int,rat,number_number_of(rat),A)),B)).  [resolve(5016,a,4992,a)].
15.31/15.29	Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),hAPP(int,rat,ring_1_of_int(rat),hAPP(rat,int,archimedean_ceiling(rat),A)))).  [resolve(5016,a,4993,a)].
15.31/15.29	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),hAPP(rat,int,archim2085082626_floor(rat),B))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(int,rat,ring_1_of_int(rat),A)),one_one(rat))),B)).  [resolve(5016,a,4994,a)].
15.31/15.29	Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),hAPP(rat,int,archim2085082626_floor(rat),B))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(int,rat,ring_1_of_int(rat),A)),one_one(rat))),B)).  [resolve(5016,a,4995,a)].
15.31/15.29	Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),zero_zero(rat))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(rat,int,archimedean_ceiling(rat),A)),one_one(int))).  [resolve(5016,a,4996,a)].
15.31/15.29	Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),zero_zero(rat))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(rat,int,archimedean_ceiling(rat),A)),one_one(int))).  [resolve(5016,a,4997,a)].
15.31/15.29	Derived: hAPP(rat,int,archimedean_ceiling(rat),A) = hAPP(real,int,archim2085082626_floor(real),hAPP(int,real,real_1(int),hAPP(rat,int,archimedean_ceiling(rat),A))).  [resolve(5016,a,4998,a)].
15.31/15.29	Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),one_one(rat))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(rat,int,archim2085082626_floor(rat),A)),one_one(int))).  [resolve(5016,a,4999,a)].
15.31/15.29	Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),one_one(rat))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(rat,int,archim2085082626_floor(rat),A)),one_one(int))).  [resolve(5016,a,5000,a)].
15.31/15.29	Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(int,rat,ring_1_of_int(rat),B)),one_one(rat)))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(rat,int,archim2085082626_floor(rat),A)),B)).  [resolve(5016,a,5001,a)].
15.31/15.29	Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(int,rat,ring_1_of_int(rat),B)),one_one(rat)))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(rat,int,archim2085082626_floor(rat),A)),B)).  [resolve(5016,a,5002,a)].
15.31/15.29	Derived: hAPP(rat,int,archimedean_ceiling(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),hAPP(int,rat,number_number_of(rat),B))) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(rat,int,archimedean_ceiling(rat),A)),hAPP(int,int,number_number_of(int),B)).  [resolve(5016,a,5003,a)].
15.31/15.29	Derived: hAPP(rat,int,archimedean_ceiling(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),hAPP(int,rat,ring_1_of_int(rat),B))) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(rat,int,archimedean_ceiling(rat),A)),B).  [resolve(5016,a,5004,a)].
15.31/15.29	Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),hAPP(int,rat,ring_1_of_int(rat),hAPP(rat,int,archimedean_ceiling(rat),A))),one_one(rat))),A)).  [resolve(5016,a,5006,a)].
15.31/15.29	Derived: hAPP(rat,int,archim2085082626_floor(rat),hAPP(int,rat,number_number_of(rat),A)) = hAPP(int,int,number_number_of(int),A).  [resolve(5016,a,5007,a)].
15.31/15.29	Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),hAPP(int,rat,number_number_of(rat),B)),one_one(rat)))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(rat,int,archimedean_ceiling(rat),A)),hAPP(int,int,number_number_of(int),B))).  [resolve(5016,a,5008,a)].
15.31/15.29	Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),hAPP(int,rat,number_number_of(rat),B)),one_one(rat)))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(rat,int,archimedean_ceiling(rat),A)),hAPP(int,int,number_number_of(int),B))).  [resolve(5016,a,5009,a)].
15.45/15.46	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),hAPP(rat,int,archim2085082626_floor(rat),A))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),one_one(rat)),A)).  [resolve(5016,a,5010,a)].
15.45/15.46	Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),hAPP(rat,int,archim2085082626_floor(rat),A))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),one_one(rat)),A)).  [resolve(5016,a,5011,a)].
15.45/15.46	Derived: one_one(int) = hAPP(rat,int,archim2085082626_floor(rat),one_one(rat)).  [resolve(5016,a,5012,a)].
15.45/15.46	Derived: zero_zero(int) = hAPP(rat,int,archimedean_ceiling(rat),zero_zero(rat)).  [resolve(5016,a,5013,a)].
15.45/15.46	Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),zero_zero(rat))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(rat,int,archimedean_ceiling(rat),A)),zero_zero(int))).  [resolve(5016,a,5014,a)].
15.45/15.46	Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),zero_zero(rat))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(rat,int,archimedean_ceiling(rat),A)),zero_zero(int))).  [resolve(5016,a,5015,a)].
15.45/15.46	5017 -archim1727834104eiling(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(int,A,ring_1_of_int(A),hAPP(A,int,archim2085082626_floor(A),B))),B)) # label(fact_3567_of__int__floor__le) # label(axiom).  [clausify(2284)].
15.45/15.46	5018 -archim1727834104eiling(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(int,A,ring_1_of_int(A),B)),one_one(A))),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),hAPP(A,int,archimedean_ceiling(A),C))) # label(fact_3611_le__ceiling__iff) # label(axiom).  [clausify(2289)].
15.45/15.46	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(int,real,ring_1_of_int(real),A)),one_one(real))),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),hAPP(real,int,archimedean_ceiling(real),B))).  [resolve(5018,a,4969,a)].
15.45/15.46	Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),hAPP(int,rat,ring_1_of_int(rat),A)),one_one(rat))),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),hAPP(rat,int,archimedean_ceiling(rat),B))).  [resolve(5018,a,5016,a)].
15.45/15.46	5019 -archim1727834104eiling(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(int,A,ring_1_of_int(A),B)),one_one(A))),C)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),hAPP(A,int,archimedean_ceiling(A),C))) # label(fact_3611_le__ceiling__iff) # label(axiom).  [clausify(2289)].
15.45/15.46	Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(int,real,ring_1_of_int(real),A)),one_one(real))),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),hAPP(real,int,archimedean_ceiling(real),B))).  [resolve(5019,a,4969,a)].
15.45/15.46	Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),hAPP(int,rat,ring_1_of_int(rat),A)),one_one(rat))),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),hAPP(rat,int,archimedean_ceiling(rat),B))).  [resolve(5019,a,5016,a)].
15.45/15.46	5020 -archim1727834104eiling(A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(A,int,archimedean_ceiling(A),B))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),min_1)),B)) # label(fact_3310_zero__le__ceiling) # label(axiom).  [clausify(2382)].
15.45/15.46	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(real,int,archimedean_ceiling(real),A))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,number_number_of(real),min_1)),A)).  [resolve(5020,a,4969,a)].
15.60/15.55	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(rat,int,archimedean_ceiling(rat),A))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(int,rat,number_number_of(rat),min_1)),A)).  [resolve(5020,a,5016,a)].
15.60/15.55	5021 -archim1727834104eiling(A) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(A,int,archimedean_ceiling(A),B))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),min_1)),B)) # label(fact_3310_zero__le__ceiling) # label(axiom).  [clausify(2382)].
15.60/15.55	Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(real,int,archimedean_ceiling(real),A))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,number_number_of(real),min_1)),A)).  [resolve(5021,a,4969,a)].
15.60/15.55	Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(rat,int,archimedean_ceiling(rat),A))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(int,rat,number_number_of(rat),min_1)),A)).  [resolve(5021,a,5016,a)].
15.60/15.55	5022 -archim1727834104eiling(A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),hAPP(A,int,archimedean_ceiling(A),B))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) # label(fact_3300_one__le__ceiling) # label(axiom).  [clausify(2461)].
15.60/15.55	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),hAPP(real,int,archimedean_ceiling(real),A))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)).  [resolve(5022,a,4969,a)].
15.60/15.55	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),hAPP(rat,int,archimedean_ceiling(rat),A))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)).  [resolve(5022,a,5016,a)].
15.60/15.55	5023 -archim1727834104eiling(A) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),hAPP(A,int,archimedean_ceiling(A),B))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) # label(fact_3300_one__le__ceiling) # label(axiom).  [clausify(2461)].
15.60/15.55	Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),hAPP(real,int,archimedean_ceiling(real),A))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)).  [resolve(5023,a,4969,a)].
15.60/15.55	Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),hAPP(rat,int,archimedean_ceiling(rat),A))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)).  [resolve(5023,a,5016,a)].
15.60/15.55	5024 -archim1727834104eiling(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),hAPP(A,int,archimedean_ceiling(A),B))) # label(fact_3301_one__less__ceiling) # label(axiom).  [clausify(2494)].
15.60/15.55	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),A)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),hAPP(real,int,archimedean_ceiling(real),A))).  [resolve(5024,a,4969,a)].
15.60/15.55	Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),one_one(rat)),A)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),hAPP(rat,int,archimedean_ceiling(rat),A))).  [resolve(5024,a,5016,a)].
15.60/15.55	5025 -archim1727834104eiling(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),hAPP(A,int,archimedean_ceiling(A),B))) # label(fact_3301_one__less__ceiling) # label(axiom).  [clausify(2494)].
15.60/15.55	Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),hAPP(real,int,archimedean_ceiling(real),A))).  [resolve(5025,a,4969,a)].
15.60/15.55	Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),one_one(rat)),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),hAPP(rat,int,archimedean_ceiling(rat),A))).  [resolve(5025,a,5016,a)].
15.92/15.89	5026 -archim1727834104eiling(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(int,A,number_number_of(A),C))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(A,int,archim2085082626_floor(A),B)),hAPP(int,int,number_number_of(int),C))) # label(fact_2885_floor__less__number__of) # label(axiom).  [clausify(2532)].
15.92/15.89	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),hAPP(int,real,number_number_of(real),B))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(real,int,archim2085082626_floor(real),A)),hAPP(int,int,number_number_of(int),B))).  [resolve(5026,a,4969,a)].
15.92/15.89	Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),hAPP(int,rat,number_number_of(rat),B))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(rat,int,archim2085082626_floor(rat),A)),hAPP(int,int,number_number_of(int),B))).  [resolve(5026,a,5016,a)].
15.92/15.89	5027 -archim1727834104eiling(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(int,A,number_number_of(A),C))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(A,int,archim2085082626_floor(A),B)),hAPP(int,int,number_number_of(int),C))) # label(fact_2885_floor__less__number__of) # label(axiom).  [clausify(2532)].
15.92/15.89	Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),hAPP(int,real,number_number_of(real),B))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(real,int,archim2085082626_floor(real),A)),hAPP(int,int,number_number_of(int),B))).  [resolve(5027,a,4969,a)].
15.92/15.89	Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),hAPP(int,rat,number_number_of(rat),B))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(rat,int,archim2085082626_floor(rat),A)),hAPP(int,int,number_number_of(int),B))).  [resolve(5027,a,5016,a)].
15.92/15.89	5028 -archim1727834104eiling(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),one_one(A))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(A,int,archim2085082626_floor(A),B)),zero_zero(int))) # label(fact_2882_floor__le__zero) # label(axiom).  [clausify(2887)].
15.92/15.89	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),one_one(real))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(real,int,archim2085082626_floor(real),A)),zero_zero(int))).  [resolve(5028,a,4969,a)].
15.92/15.89	Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),one_one(rat))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(rat,int,archim2085082626_floor(rat),A)),zero_zero(int))).  [resolve(5028,a,5016,a)].
15.92/15.89	5029 -archim1727834104eiling(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),one_one(A))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(A,int,archim2085082626_floor(A),B)),zero_zero(int))) # label(fact_2882_floor__le__zero) # label(axiom).  [clausify(2887)].
15.92/15.89	Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),one_one(real))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(real,int,archim2085082626_floor(real),A)),zero_zero(int))).  [resolve(5029,a,4969,a)].
15.92/15.89	Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),one_one(rat))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(rat,int,archim2085082626_floor(rat),A)),zero_zero(int))).  [resolve(5029,a,5016,a)].
15.92/15.89	5030 -archim1727834104eiling(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(int,A,number_number_of(A),min_1))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(A,int,archimedean_ceiling(A),B)),zero_zero(int))) # label(fact_3309_ceiling__less__zero) # label(axiom).  [clausify(2947)].
15.92/15.89	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),hAPP(int,real,number_number_of(real),min_1))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(real,int,archimedean_ceiling(real),A)),zero_zero(int))).  [resolve(5030,a,4969,a)].
15.92/15.89	Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),hAPP(int,rat,number_number_of(rat),min_1))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(rat,int,archimedean_ceiling(rat),A)),zero_zero(int))).  [resolve(5030,a,5016,a)].
16.03/16.07	5031 -archim1727834104eiling(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(int,A,number_number_of(A),min_1))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(A,int,archimedean_ceiling(A),B)),zero_zero(int))) # label(fact_3309_ceiling__less__zero) # label(axiom).  [clausify(2947)].
16.03/16.07	Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),hAPP(int,real,number_number_of(real),min_1))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(real,int,archimedean_ceiling(real),A)),zero_zero(int))).  [resolve(5031,a,4969,a)].
16.03/16.07	Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),hAPP(int,rat,number_number_of(rat),min_1))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(rat,int,archimedean_ceiling(rat),A)),zero_zero(int))).  [resolve(5031,a,5016,a)].
16.03/16.07	5032 -archim1727834104eiling(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),B)),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),B)),hAPP(A,int,archimedean_ceiling(A),C))) # label(fact_3303_number__of__less__ceiling) # label(axiom).  [clausify(3037)].
16.03/16.07	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,number_number_of(real),A)),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),A)),hAPP(real,int,archimedean_ceiling(real),B))).  [resolve(5032,a,4969,a)].
16.03/16.07	Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(int,rat,number_number_of(rat),A)),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),A)),hAPP(rat,int,archimedean_ceiling(rat),B))).  [resolve(5032,a,5016,a)].
16.03/16.07	5033 -archim1727834104eiling(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),B)),C)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),B)),hAPP(A,int,archimedean_ceiling(A),C))) # label(fact_3303_number__of__less__ceiling) # label(axiom).  [clausify(3037)].
16.03/16.07	Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,number_number_of(real),A)),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),A)),hAPP(real,int,archimedean_ceiling(real),B))).  [resolve(5033,a,4969,a)].
16.03/16.07	Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(int,rat,number_number_of(rat),A)),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),A)),hAPP(rat,int,archimedean_ceiling(rat),B))).  [resolve(5033,a,5016,a)].
16.03/16.07	5034 -archim1727834104eiling(A) | hAPP(A,int,archim2085082626_floor(A),hAPP(int,A,ring_1_of_int(A),B)) = ti(int,B) # label(fact_3576_floor__of__int) # label(axiom).  [clausify(3059)].
16.03/16.07	Derived: hAPP(real,int,archim2085082626_floor(real),hAPP(int,real,ring_1_of_int(real),A)) = ti(int,A).  [resolve(5034,a,4969,a)].
16.03/16.07	Derived: hAPP(rat,int,archim2085082626_floor(rat),hAPP(int,rat,ring_1_of_int(rat),A)) = ti(int,A).  [resolve(5034,a,5016,a)].
16.03/16.07	5035 -archim1727834104eiling(A) | hAPP(A,int,archimedean_ceiling(A),hAPP(A,A,uminus_uminus(A),B)) = hAPP(int,int,uminus_uminus(int),hAPP(A,int,archim2085082626_floor(A),B)) # label(fact_3294_ceiling__minus) # label(axiom).  [clausify(3086)].
16.03/16.07	Derived: hAPP(real,int,archimedean_ceiling(real),hAPP(real,real,uminus_uminus(real),A)) = hAPP(int,int,uminus_uminus(int),hAPP(real,int,archim2085082626_floor(real),A)).  [resolve(5035,a,4969,a)].
16.03/16.07	Derived: hAPP(rat,int,archimedean_ceiling(rat),hAPP(rat,rat,uminus_uminus(rat),A)) = hAPP(int,int,uminus_uminus(int),hAPP(rat,int,archim2085082626_floor(rat),A)).  [resolve(5035,a,5016,a)].
16.03/16.07	5036 -archim1727834104eiling(A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),B)),hAPP(A,int,archimedean_ceiling(A),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(int,A,number_number_of(A),B)),one_one(A))),C)) # label(fact_3212_number__of__le__ceiling) # label(axiom).  [clausify(3182)].
16.21/16.24	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),A)),hAPP(real,int,archimedean_ceiling(real),B))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(int,real,number_number_of(real),A)),one_one(real))),B)).  [resolve(5036,a,4969,a)].
16.21/16.24	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),A)),hAPP(rat,int,archimedean_ceiling(rat),B))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),hAPP(int,rat,number_number_of(rat),A)),one_one(rat))),B)).  [resolve(5036,a,5016,a)].
16.21/16.24	5037 -archim1727834104eiling(A) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),B)),hAPP(A,int,archimedean_ceiling(A),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(int,A,number_number_of(A),B)),one_one(A))),C)) # label(fact_3212_number__of__le__ceiling) # label(axiom).  [clausify(3182)].
16.21/16.24	Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),A)),hAPP(real,int,archimedean_ceiling(real),B))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(int,real,number_number_of(real),A)),one_one(real))),B)).  [resolve(5037,a,4969,a)].
16.21/16.24	Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),A)),hAPP(rat,int,archimedean_ceiling(rat),B))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),hAPP(int,rat,number_number_of(rat),A)),one_one(rat))),B)).  [resolve(5037,a,5016,a)].
16.21/16.24	5038 -archim1727834104eiling(A) | hAPP(A,int,archim2085082626_floor(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),hAPP(int,A,ring_1_of_int(A),C))) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(A,int,archim2085082626_floor(A),B)),C) # label(fact_3596_floor__add__of__int) # label(axiom).  [clausify(3189)].
16.21/16.24	Derived: hAPP(real,int,archim2085082626_floor(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),hAPP(int,real,ring_1_of_int(real),B))) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(real,int,archim2085082626_floor(real),A)),B).  [resolve(5038,a,4969,a)].
16.21/16.24	Derived: hAPP(rat,int,archim2085082626_floor(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),hAPP(int,rat,ring_1_of_int(rat),B))) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(rat,int,archim2085082626_floor(rat),A)),B).  [resolve(5038,a,5016,a)].
16.21/16.24	5039 -archim1727834104eiling(A) | hAPP(A,int,archim2085082626_floor(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),hAPP(int,A,number_number_of(A),C))) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(A,int,archim2085082626_floor(A),B)),hAPP(int,int,number_number_of(int),C)) # label(fact_2888_floor__add__number__of) # label(axiom).  [clausify(3247)].
16.21/16.24	Derived: hAPP(real,int,archim2085082626_floor(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),hAPP(int,real,number_number_of(real),B))) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(real,int,archim2085082626_floor(real),A)),hAPP(int,int,number_number_of(int),B)).  [resolve(5039,a,4969,a)].
16.21/16.24	Derived: hAPP(rat,int,archim2085082626_floor(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),hAPP(int,rat,number_number_of(rat),B))) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(rat,int,archim2085082626_floor(rat),A)),hAPP(int,int,number_number_of(int),B)).  [resolve(5039,a,5016,a)].
16.21/16.24	5040 -archim1727834104eiling(A) | archim2085082626_floor(A) = ti(fun(A,int),archim2085082626_floor(A)) # label(tsy_c_Archimedean__Field_Ofloor__ceiling__class_Ofloor_res) # label(axiom).  [clausify(3369)].
16.21/16.24	Derived: archim2085082626_floor(real) = ti(fun(real,int),archim2085082626_floor(real)).  [resolve(5040,a,4969,a)].
16.51/16.54	Derived: archim2085082626_floor(rat) = ti(fun(rat,int),archim2085082626_floor(rat)).  [resolve(5040,a,5016,a)].
16.51/16.54	5041 -archim1727834104eiling(A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),hAPP(A,int,archim2085082626_floor(A),B))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(int,A,number_number_of(A),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),B)) # label(fact_2895_one__less__floor) # label(axiom).  [clausify(3488)].
16.51/16.54	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),hAPP(real,int,archim2085082626_floor(real),A))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),A)).  [resolve(5041,a,4969,a)].
16.51/16.54	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),hAPP(rat,int,archim2085082626_floor(rat),A))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(int,rat,number_number_of(rat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),A)).  [resolve(5041,a,5016,a)].
16.51/16.54	5042 -archim1727834104eiling(A) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),hAPP(A,int,archim2085082626_floor(A),B))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(int,A,number_number_of(A),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),B)) # label(fact_2895_one__less__floor) # label(axiom).  [clausify(3488)].
16.51/16.54	Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),hAPP(real,int,archim2085082626_floor(real),A))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),A)).  [resolve(5042,a,4969,a)].
16.51/16.54	Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),hAPP(rat,int,archim2085082626_floor(rat),A))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(int,rat,number_number_of(rat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),A)).  [resolve(5042,a,5016,a)].
16.51/16.54	5043 -archim1727834104eiling(A) | hAPP(A,int,archimedean_ceiling(A),hAPP(int,A,number_number_of(A),B)) = hAPP(int,int,number_number_of(int),B) # label(fact_3283_ceiling__number__of) # label(axiom).  [clausify(3521)].
16.51/16.54	Derived: hAPP(real,int,archimedean_ceiling(real),hAPP(int,real,number_number_of(real),A)) = hAPP(int,int,number_number_of(int),A).  [resolve(5043,a,4969,a)].
16.51/16.54	Derived: hAPP(rat,int,archimedean_ceiling(rat),hAPP(int,rat,number_number_of(rat),A)) = hAPP(int,int,number_number_of(int),A).  [resolve(5043,a,5016,a)].
16.51/16.54	5044 -archim1727834104eiling(A) | archimedean_ceiling(A) = ti(fun(A,int),archimedean_ceiling(A)) # label(tsy_c_Archimedean__Field_Oceiling_res) # label(axiom).  [clausify(3702)].
16.51/16.54	Derived: archimedean_ceiling(real) = ti(fun(real,int),archimedean_ceiling(real)).  [resolve(5044,a,4969,a)].
16.51/16.54	Derived: archimedean_ceiling(rat) = ti(fun(rat,int),archimedean_ceiling(rat)).  [resolve(5044,a,5016,a)].
16.51/16.54	5045 -archim1727834104eiling(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),one_one(A))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(A,int,archimedean_ceiling(A),B)),one_one(int))) # label(fact_3302_ceiling__le__one) # label(axiom).  [clausify(3707)].
16.51/16.54	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),one_one(real))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(real,int,archimedean_ceiling(real),A)),one_one(int))).  [resolve(5045,a,4969,a)].
16.51/16.54	Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),one_one(rat))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(rat,int,archimedean_ceiling(rat),A)),one_one(int))).  [resolve(5045,a,5016,a)].
16.51/16.54	5046 -archim1727834104eiling(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),one_one(A))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(A,int,archimedean_ceiling(A),B)),one_one(int))) # label(fact_3302_ceiling__le__one) # label(axiom).  [clausify(3707)].
16.66/16.67	Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),one_one(real))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(real,int,archimedean_ceiling(real),A)),one_one(int))).  [resolve(5046,a,4969,a)].
16.66/16.67	Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),one_one(rat))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(rat,int,archimedean_ceiling(rat),A)),one_one(int))).  [resolve(5046,a,5016,a)].
16.66/16.67	5047 -archim1727834104eiling(A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(A,int,archimedean_ceiling(A),B))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) # label(fact_3297_zero__less__ceiling) # label(axiom).  [clausify(3754)].
16.66/16.67	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(real,int,archimedean_ceiling(real),A))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)).  [resolve(5047,a,4969,a)].
16.66/16.67	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(rat,int,archimedean_ceiling(rat),A))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)).  [resolve(5047,a,5016,a)].
16.66/16.67	5048 -archim1727834104eiling(A) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(A,int,archimedean_ceiling(A),B))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) # label(fact_3297_zero__less__ceiling) # label(axiom).  [clausify(3754)].
16.66/16.67	Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(real,int,archimedean_ceiling(real),A))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)).  [resolve(5048,a,4969,a)].
16.66/16.67	Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(rat,int,archimedean_ceiling(rat),A))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)).  [resolve(5048,a,5016,a)].
16.66/16.67	5049 -archim1727834104eiling(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(int,A,number_number_of(A),B)),one_one(A))),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),B)),hAPP(A,int,archim2085082626_floor(A),C))) # label(fact_2893_number__of__less__floor) # label(axiom).  [clausify(3834)].
16.66/16.67	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(int,real,number_number_of(real),A)),one_one(real))),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),A)),hAPP(real,int,archim2085082626_floor(real),B))).  [resolve(5049,a,4969,a)].
16.66/16.67	Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(int,rat,number_number_of(rat),A)),one_one(rat))),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),A)),hAPP(rat,int,archim2085082626_floor(rat),B))).  [resolve(5049,a,5016,a)].
16.66/16.67	5050 -archim1727834104eiling(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(int,A,number_number_of(A),B)),one_one(A))),C)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),B)),hAPP(A,int,archim2085082626_floor(A),C))) # label(fact_2893_number__of__less__floor) # label(axiom).  [clausify(3834)].
16.66/16.67	Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(int,real,number_number_of(real),A)),one_one(real))),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),A)),hAPP(real,int,archim2085082626_floor(real),B))).  [resolve(5050,a,4969,a)].
16.66/16.67	Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(int,rat,number_number_of(rat),A)),one_one(rat))),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),A)),hAPP(rat,int,archim2085082626_floor(rat),B))).  [resolve(5050,a,5016,a)].
17.01/16.97	5051 -archim1727834104eiling(A) | hAPP(A,int,archim2085082626_floor(A),hAPP(A,A,uminus_uminus(A),B)) = hAPP(int,int,uminus_uminus(int),hAPP(A,int,archimedean_ceiling(A),B)) # label(fact_3293_floor__minus) # label(axiom).  [clausify(3921)].
17.01/16.97	Derived: hAPP(real,int,archim2085082626_floor(real),hAPP(real,real,uminus_uminus(real),A)) = hAPP(int,int,uminus_uminus(int),hAPP(real,int,archimedean_ceiling(real),A)).  [resolve(5051,a,4969,a)].
17.01/16.97	Derived: hAPP(rat,int,archim2085082626_floor(rat),hAPP(rat,rat,uminus_uminus(rat),A)) = hAPP(int,int,uminus_uminus(int),hAPP(rat,int,archimedean_ceiling(rat),A)).  [resolve(5051,a,5016,a)].
17.01/16.97	5052 -archim1727834104eiling(A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(A,int,archim2085082626_floor(A),B)),hAPP(int,int,number_number_of(int),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(int,A,number_number_of(A),C)),one_one(A)))) # label(fact_2894_floor__le__number__of) # label(axiom).  [clausify(3922)].
17.01/16.97	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(real,int,archim2085082626_floor(real),A)),hAPP(int,int,number_number_of(int),B))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(int,real,number_number_of(real),B)),one_one(real)))).  [resolve(5052,a,4969,a)].
17.01/16.97	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(rat,int,archim2085082626_floor(rat),A)),hAPP(int,int,number_number_of(int),B))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(int,rat,number_number_of(rat),B)),one_one(rat)))).  [resolve(5052,a,5016,a)].
17.01/16.97	5053 -archim1727834104eiling(A) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(A,int,archim2085082626_floor(A),B)),hAPP(int,int,number_number_of(int),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(int,A,number_number_of(A),C)),one_one(A)))) # label(fact_2894_floor__le__number__of) # label(axiom).  [clausify(3922)].
17.01/16.97	Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(real,int,archim2085082626_floor(real),A)),hAPP(int,int,number_number_of(int),B))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(int,real,number_number_of(real),B)),one_one(real)))).  [resolve(5053,a,4969,a)].
17.01/16.97	Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(rat,int,archim2085082626_floor(rat),A)),hAPP(int,int,number_number_of(int),B))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(int,rat,number_number_of(rat),B)),one_one(rat)))).  [resolve(5053,a,5016,a)].
17.01/16.97	5054 -archim1727834104eiling(A) | hAPP(A,int,archimedean_ceiling(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),one_one(A))) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(A,int,archimedean_ceiling(A),B)),one_one(int)) # label(fact_3305_ceiling__add__one) # label(axiom).  [clausify(3964)].
17.01/16.97	Derived: hAPP(real,int,archimedean_ceiling(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),one_one(real))) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(real,int,archimedean_ceiling(real),A)),one_one(int)).  [resolve(5054,a,4969,a)].
17.01/16.97	Derived: hAPP(rat,int,archimedean_ceiling(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),one_one(rat))) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(rat,int,archimedean_ceiling(rat),A)),one_one(int)).  [resolve(5054,a,5016,a)].
17.01/16.97	5055 -archim1727834104eiling(A) | hAPP(A,int,archim2085082626_floor(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),hAPP(int,A,number_number_of(A),C))) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(A,int,archim2085082626_floor(A),B)),hAPP(int,int,number_number_of(int),C)) # label(fact_2890_floor__diff__number__of) # label(axiom).  [clausify(3981)].
17.23/17.26	Derived: hAPP(real,int,archim2085082626_floor(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),hAPP(int,real,number_number_of(real),B))) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(real,int,archim2085082626_floor(real),A)),hAPP(int,int,number_number_of(int),B)).  [resolve(5055,a,4969,a)].
17.23/17.26	Derived: hAPP(rat,int,archim2085082626_floor(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),A),hAPP(int,rat,number_number_of(rat),B))) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(rat,int,archim2085082626_floor(rat),A)),hAPP(int,int,number_number_of(int),B)).  [resolve(5055,a,5016,a)].
17.23/17.26	5056 -archim1727834104eiling(A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(A,int,archimedean_ceiling(A),B)),hAPP(A,int,archimedean_ceiling(A),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) # label(fact_3280_ceiling__less__cancel) # label(axiom).  [clausify(4020)].
17.23/17.26	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(real,int,archimedean_ceiling(real),A)),hAPP(real,int,archimedean_ceiling(real),B))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)).  [resolve(5056,a,4969,a)].
17.23/17.26	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(rat,int,archimedean_ceiling(rat),A)),hAPP(rat,int,archimedean_ceiling(rat),B))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),B)).  [resolve(5056,a,5016,a)].
17.23/17.26	5057 -archim1727834104eiling(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(A,int,archim2085082626_floor(A),B)),zero_zero(int))) # label(fact_2879_floor__less__zero) # label(axiom).  [clausify(4063)].
17.23/17.26	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(real,int,archim2085082626_floor(real),A)),zero_zero(int))).  [resolve(5057,a,4969,a)].
17.23/17.26	Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),zero_zero(rat))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(rat,int,archim2085082626_floor(rat),A)),zero_zero(int))).  [resolve(5057,a,5016,a)].
17.23/17.26	5058 -archim1727834104eiling(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(A,int,archim2085082626_floor(A),B)),zero_zero(int))) # label(fact_2879_floor__less__zero) # label(axiom).  [clausify(4063)].
17.23/17.26	Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(real,int,archim2085082626_floor(real),A)),zero_zero(int))).  [resolve(5058,a,4969,a)].
17.23/17.26	Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),zero_zero(rat))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(rat,int,archim2085082626_floor(rat),A)),zero_zero(int))).  [resolve(5058,a,5016,a)].
17.23/17.26	5059 -archim1727834104eiling(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(A,int,archim2085082626_floor(A),B)),hAPP(A,int,archim2085082626_floor(A),C))) # label(fact_2865_floor__mono) # label(axiom).  [clausify(4129)].
17.23/17.26	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(real,int,archim2085082626_floor(real),A)),hAPP(real,int,archim2085082626_floor(real),B))).  [resolve(5059,a,4969,a)].
17.23/17.26	Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(rat,int,archim2085082626_floor(rat),A)),hAPP(rat,int,archim2085082626_floor(rat),B))).  [resolve(5059,a,5016,a)].
17.23/17.26	5060 -archim1727834104eiling(A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(A,int,archim2085082626_floor(A),B)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(int,A,ring_1_of_int(A),C))) # label(fact_3592_floor__less__iff) # label(axiom).  [clausify(4248)].
17.41/17.40	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(real,int,archim2085082626_floor(real),A)),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),hAPP(int,real,ring_1_of_int(real),B))).  [resolve(5060,a,4969,a)].
17.41/17.40	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(rat,int,archim2085082626_floor(rat),A)),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),hAPP(int,rat,ring_1_of_int(rat),B))).  [resolve(5060,a,5016,a)].
17.41/17.40	5061 -archim1727834104eiling(A) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(A,int,archim2085082626_floor(A),B)),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(int,A,ring_1_of_int(A),C))) # label(fact_3592_floor__less__iff) # label(axiom).  [clausify(4248)].
17.41/17.40	Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(real,int,archim2085082626_floor(real),A)),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),hAPP(int,real,ring_1_of_int(real),B))).  [resolve(5061,a,4969,a)].
17.41/17.40	Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(rat,int,archim2085082626_floor(rat),A)),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),hAPP(int,rat,ring_1_of_int(rat),B))).  [resolve(5061,a,5016,a)].
17.41/17.40	5062 -archim1727834104eiling(A) | hAPP(A,int,archimedean_ceiling(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),hAPP(int,A,ring_1_of_int(A),C))) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(A,int,archimedean_ceiling(A),B)),C) # label(fact_3599_ceiling__diff__of__int) # label(axiom).  [clausify(4276)].
17.41/17.40	Derived: hAPP(real,int,archimedean_ceiling(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),hAPP(int,real,ring_1_of_int(real),B))) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(real,int,archimedean_ceiling(real),A)),B).  [resolve(5062,a,4969,a)].
17.41/17.40	Derived: hAPP(rat,int,archimedean_ceiling(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),A),hAPP(int,rat,ring_1_of_int(rat),B))) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(rat,int,archimedean_ceiling(rat),A)),B).  [resolve(5062,a,5016,a)].
17.41/17.40	5063 -archim1727834104eiling(A) | zero_zero(int) = hAPP(A,int,archim2085082626_floor(A),zero_zero(A)) # label(fact_2863_floor__zero) # label(axiom).  [clausify(4298)].
17.41/17.40	Derived: zero_zero(int) = hAPP(real,int,archim2085082626_floor(real),zero_zero(real)).  [resolve(5063,a,4969,a)].
17.41/17.40	Derived: zero_zero(int) = hAPP(rat,int,archim2085082626_floor(rat),zero_zero(rat)).  [resolve(5063,a,5016,a)].
17.41/17.40	5064 -archim1727834104eiling(A) | hAPP(A,int,archimedean_ceiling(A),hAPP(int,A,ring_1_of_int(A),B)) = ti(int,B) # label(fact_3564_ceiling__of__int) # label(axiom).  [clausify(4334)].
17.41/17.40	Derived: hAPP(real,int,archimedean_ceiling(real),hAPP(int,real,ring_1_of_int(real),A)) = ti(int,A).  [resolve(5064,a,4969,a)].
17.41/17.40	Derived: hAPP(rat,int,archimedean_ceiling(rat),hAPP(int,rat,ring_1_of_int(rat),A)) = ti(int,A).  [resolve(5064,a,5016,a)].
17.41/17.40	5065 -archim1727834104eiling(A) | hAPP(A,int,archim2085082626_floor(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),hAPP(int,A,ring_1_of_int(A),C))) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(A,int,archim2085082626_floor(A),B)),C) # label(fact_3598_floor__diff__of__int) # label(axiom).  [clausify(4371)].
17.41/17.40	Derived: hAPP(real,int,archim2085082626_floor(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),hAPP(int,real,ring_1_of_int(real),B))) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(real,int,archim2085082626_floor(real),A)),B).  [resolve(5065,a,4969,a)].
17.41/17.40	Derived: hAPP(rat,int,archim2085082626_floor(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),A),hAPP(int,rat,ring_1_of_int(rat),B))) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(rat,int,archim2085082626_floor(rat),A)),B).  [resolve(5065,a,5016,a)].
17.41/17.40	5066 -archim1727834104eiling(A) | hAPP(A,int,archim2085082626_floor(A),B) = hAPP(real,int,archimedean_ceiling(real),hAPP(int,real,real_1(int),hAPP(A,int,archim2085082626_floor(A),B))) # label(fact_3357_ceiling__floor) # label(axiom).  [clausify(4379)].
17.77/17.75	Derived: hAPP(real,int,archim2085082626_floor(real),A) = hAPP(real,int,archimedean_ceiling(real),hAPP(int,real,real_1(int),hAPP(real,int,archim2085082626_floor(real),A))).  [resolve(5066,a,4969,a)].
17.77/17.75	Derived: hAPP(rat,int,archim2085082626_floor(rat),A) = hAPP(real,int,archimedean_ceiling(real),hAPP(int,real,real_1(int),hAPP(rat,int,archim2085082626_floor(rat),A))).  [resolve(5066,a,5016,a)].
17.77/17.75	5067 -archim1727834104eiling(A) | hAPP(A,int,archim2085082626_floor(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),one_one(A))) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(A,int,archim2085082626_floor(A),B)),one_one(int)) # label(fact_2887_floor__add__one) # label(axiom).  [clausify(4584)].
17.77/17.75	Derived: hAPP(real,int,archim2085082626_floor(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),one_one(real))) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(real,int,archim2085082626_floor(real),A)),one_one(int)).  [resolve(5067,a,4969,a)].
17.77/17.75	Derived: hAPP(rat,int,archim2085082626_floor(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),one_one(rat))) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(rat,int,archim2085082626_floor(rat),A)),one_one(int)).  [resolve(5067,a,5016,a)].
17.77/17.75	5068 -archim1727834104eiling(A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(A,int,archim2085082626_floor(A),B)),hAPP(A,int,archim2085082626_floor(A),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) # label(fact_2864_floor__less__cancel) # label(axiom).  [clausify(4593)].
17.77/17.75	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(real,int,archim2085082626_floor(real),A)),hAPP(real,int,archim2085082626_floor(real),B))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)).  [resolve(5068,a,4969,a)].
17.77/17.75	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(rat,int,archim2085082626_floor(rat),A)),hAPP(rat,int,archim2085082626_floor(rat),B))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),B)).  [resolve(5068,a,5016,a)].
17.77/17.75	5069 -archim1727834104eiling(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(int,A,number_number_of(A),C))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(A,int,archimedean_ceiling(A),B)),hAPP(int,int,number_number_of(int),C))) # label(fact_3304_ceiling__le__number__of) # label(axiom).  [clausify(4674)].
17.77/17.75	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),hAPP(int,real,number_number_of(real),B))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(real,int,archimedean_ceiling(real),A)),hAPP(int,int,number_number_of(int),B))).  [resolve(5069,a,4969,a)].
17.77/17.75	Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),hAPP(int,rat,number_number_of(rat),B))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(rat,int,archimedean_ceiling(rat),A)),hAPP(int,int,number_number_of(int),B))).  [resolve(5069,a,5016,a)].
17.77/17.75	5070 -archim1727834104eiling(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(int,A,number_number_of(A),C))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(A,int,archimedean_ceiling(A),B)),hAPP(int,int,number_number_of(int),C))) # label(fact_3304_ceiling__le__number__of) # label(axiom).  [clausify(4674)].
17.77/17.75	Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),hAPP(int,real,number_number_of(real),B))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(real,int,archimedean_ceiling(real),A)),hAPP(int,int,number_number_of(int),B))).  [resolve(5070,a,4969,a)].
17.77/17.75	Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),hAPP(int,rat,number_number_of(rat),B))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(rat,int,archimedean_ceiling(rat),A)),hAPP(int,int,number_number_of(int),B))).  [resolve(5070,a,5016,a)].
17.77/17.75	5071 -archim1727834104eiling(A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(A,int,archimedean_ceiling(A),B)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(int,A,ring_1_of_int(A),C)),one_one(A)))) # label(fact_3610_ceiling__less__iff) # label(axiom).  [clausify(4729)].
18.57/18.52	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(real,int,archimedean_ceiling(real),A)),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(int,real,ring_1_of_int(real),B)),one_one(real)))).  [resolve(5071,a,4969,a)].
18.57/18.52	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(rat,int,archimedean_ceiling(rat),A)),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),hAPP(int,rat,ring_1_of_int(rat),B)),one_one(rat)))).  [resolve(5071,a,5016,a)].
18.57/18.52	5072 -archim1727834104eiling(A) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(A,int,archimedean_ceiling(A),B)),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(int,A,ring_1_of_int(A),C)),one_one(A)))) # label(fact_3610_ceiling__less__iff) # label(axiom).  [clausify(4729)].
18.57/18.52	Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(real,int,archimedean_ceiling(real),A)),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(int,real,ring_1_of_int(real),B)),one_one(real)))).  [resolve(5072,a,4969,a)].
18.57/18.52	Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(rat,int,archimedean_ceiling(rat),A)),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),hAPP(int,rat,ring_1_of_int(rat),B)),one_one(rat)))).  [resolve(5072,a,5016,a)].
18.57/18.52	5073 -archim1727834104eiling(A) | one_one(int) = hAPP(A,int,archimedean_ceiling(A),one_one(A)) # label(fact_3282_ceiling__one) # label(axiom).  [clausify(4836)].
18.57/18.52	Derived: one_one(int) = hAPP(real,int,archimedean_ceiling(real),one_one(real)).  [resolve(5073,a,4969,a)].
18.57/18.52	Derived: one_one(int) = hAPP(rat,int,archimedean_ceiling(rat),one_one(rat)).  [resolve(5073,a,5016,a)].
18.57/18.52	5074 -archim1727834104eiling(A) | hAPP(A,int,archim2085082626_floor(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),one_one(A))) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(A,int,archim2085082626_floor(A),B)),one_one(int)) # label(fact_2889_floor__diff__one) # label(axiom).  [clausify(4890)].
18.57/18.52	Derived: hAPP(real,int,archim2085082626_floor(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),one_one(real))) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(real,int,archim2085082626_floor(real),A)),one_one(int)).  [resolve(5074,a,4969,a)].
18.57/18.52	Derived: hAPP(rat,int,archim2085082626_floor(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),A),one_one(rat))) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(rat,int,archim2085082626_floor(rat),A)),one_one(int)).  [resolve(5074,a,5016,a)].
18.57/18.52	5075 -archim1727834104eiling(A) | hAPP(A,int,archimedean_ceiling(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),hAPP(int,A,number_number_of(A),C))) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(A,int,archimedean_ceiling(A),B)),hAPP(int,int,number_number_of(int),C)) # label(fact_3308_ceiling__diff__number__of) # label(axiom).  [clausify(4924)].
18.57/18.52	Derived: hAPP(real,int,archimedean_ceiling(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),hAPP(int,real,number_number_of(real),B))) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(real,int,archimedean_ceiling(real),A)),hAPP(int,int,number_number_of(int),B)).  [resolve(5075,a,4969,a)].
18.57/18.52	Derived: hAPP(rat,int,archimedean_ceiling(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),A),hAPP(int,rat,number_number_of(rat),B))) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(rat,int,archimedean_ceiling(rat),A)),hAPP(int,int,number_number_of(int),B)).  [resolve(5075,a,5016,a)].
18.57/18.52	5076 real_normed_field(real) # label(arity_RealDef_Oreal___RealVector_Oreal__normed__field) # label(axiom).  [assumption].
18.57/18.52	5077 -real_normed_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),B),C),D)) | zero_zero(A) = hAPP(A,A,B,C) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),hAPP(fun(A,A),fun(A,A),hAPP(fun(A,A),fun(fun(A,A),fun(A,A)),combb(A,A,A),inverse_inverse(A)),B)),C),hAPP(A,A,uminus_uminus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),hAPP(A,A,inverse_inverse(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),hAPP(A,A,B,C)),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat))))))))) # label(fact_3901_DERIV__inverse__fun) # label(axiom).  [clausify(7)].
18.57/18.52	5078 -real_normed_field(A) | -hBOOL(hAPP(fun(nat,A),bool,summable(A),B)) | hBOOL(hAPP(fun(nat,A),bool,summable(A),hAPP(fun(nat,A),fun(nat,A),hAPP(fun(A,A),fun(fun(nat,A),fun(nat,A)),combb(A,A,nat),uminus_uminus(A)),B))) # label(fact_4002_summable__minus) # label(axiom).  [clausify(63)].
18.57/18.52	5079 -real_normed_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),B),C),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),E),C),F)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),hAPP(fun(A,A),fun(A,A),hAPP(fun(A,fun(A,A)),fun(fun(A,A),fun(A,A)),combs(A,A,A),hAPP(fun(A,A),fun(A,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(A,A),fun(A,fun(A,A))),combb(A,fun(A,A),A),plus_plus(A)),B)),E)),C),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),D),F))) # label(fact_3823_DERIV__add) # label(axiom).  [clausify(64)].
18.57/18.52	5080 -real_normed_field(A) | -banach(A) | -hBOOL(hAPP(fun(nat,A),bool,summable(A),hAPP(fun(nat,A),fun(nat,A),hAPP(fun(nat,fun(A,A)),fun(fun(nat,A),fun(nat,A)),combs(nat,A,A),hAPP(fun(nat,A),fun(nat,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(nat,A),fun(nat,fun(A,A))),combb(A,fun(A,A),nat),times_times(A)),B)),hAPP(A,fun(nat,A),power_power(A),C)))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(A,real,norm_norm(A),D)),hAPP(A,real,norm_norm(A),C))) | hBOOL(hAPP(fun(nat,A),bool,summable(A),hAPP(fun(nat,A),fun(nat,A),hAPP(fun(nat,fun(A,A)),fun(fun(nat,A),fun(nat,A)),combs(nat,A,A),hAPP(fun(nat,A),fun(nat,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(nat,A),fun(nat,fun(A,A))),combb(A,fun(A,A),nat),times_times(A)),B)),hAPP(A,fun(nat,A),power_power(A),D)))) # label(fact_4024_powser__inside) # label(axiom).  [clausify(81)].
18.57/18.52	5081 -real_normed_field(A) | hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),C)) = hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),D)),C) # label(fact_1664_divide_Odiff) # label(axiom).  [clausify(84)].
18.57/18.52	5082 -real_normed_field(A) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(A,real,norm_norm(A),B)),one_one(real))) | hBOOL(hAPP(fun(nat,A),bool,summable(A),hAPP(A,fun(nat,A),power_power(A),B))) # label(fact_4026_summable__geometric) # label(axiom).  [clausify(140)].
18.57/18.52	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),A),B),C)) | zero_zero(real) = hAPP(real,real,A,B) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,real),fun(fun(real,real),fun(real,real)),combb(real,real,real),inverse_inverse(real)),A)),B),hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),hAPP(real,real,inverse_inverse(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,A,B)),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat))))))))).  [resolve(5076,a,5077,a)].
18.57/18.52	Derived: -hBOOL(hAPP(fun(nat,real),bool,summable(real),A)) | hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),uminus_uminus(real)),A))).  [resolve(5076,a,5078,a)].
18.57/18.52	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),A),B),C)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),D),B),E)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,real)),combs(real,real,real),hAPP(fun(real,real),fun(real,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,fun(real,real))),combb(real,fun(real,real),real),plus_plus(real)),A)),D)),B),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),C),E))).  [resolve(5076,a,5079,a)].
18.57/18.54	Derived: -banach(real) | -hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),A)),hAPP(real,fun(nat,real),power_power(real),B)))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,norm_norm(real),C)),hAPP(real,real,norm_norm(real),B))) | hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),A)),hAPP(real,fun(nat,real),power_power(real),C)))).  [resolve(5076,a,5080,a)].
18.57/18.54	Derived: hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),C),B)) = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),C)),B).  [resolve(5076,a,5081,a)].
18.57/18.54	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,norm_norm(real),A)),one_one(real))) | hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(real,fun(nat,real),power_power(real),A))).  [resolve(5076,a,5082,a)].
18.57/18.54	5083 -real_normed_field(A) | -banach(A) | -hBOOL(hAPP(fun(nat,A),bool,summable(A),hAPP(fun(nat,A),fun(nat,A),hAPP(fun(nat,fun(A,A)),fun(fun(nat,A),fun(nat,A)),combs(nat,A,A),hAPP(fun(nat,A),fun(nat,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(nat,A),fun(nat,fun(A,A))),combb(A,fun(A,A),nat),times_times(A)),B)),hAPP(A,fun(nat,A),power_power(A),C)))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(A,real,norm_norm(A),D)),hAPP(A,real,norm_norm(A),C))) | hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,A),fun(nat,real),hAPP(fun(A,real),fun(fun(nat,A),fun(nat,real)),combb(A,real,nat),norm_norm(A)),hAPP(fun(nat,A),fun(nat,A),hAPP(fun(nat,fun(A,A)),fun(fun(nat,A),fun(nat,A)),combs(nat,A,A),hAPP(fun(nat,A),fun(nat,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(nat,A),fun(nat,fun(A,A))),combb(A,fun(A,A),nat),times_times(A)),B)),hAPP(A,fun(nat,A),power_power(A),D))))) # label(fact_3996_powser__insidea) # label(axiom).  [clausify(468)].
18.57/18.54	Derived: -banach(real) | -hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),A)),hAPP(real,fun(nat,real),power_power(real),B)))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,norm_norm(real),C)),hAPP(real,real,norm_norm(real),B))) | hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),norm_norm(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),A)),hAPP(real,fun(nat,real),power_power(real),C))))).  [resolve(5083,a,5076,a)].
18.61/18.59	5084 -real_normed_field(A) | hBOOL(hAPP(A,bool,hAPP(fun(A,A),fun(A,bool),isCont(A,A),hAPP(A,fun(A,A),hAPP(fun(A,fun(A,A)),fun(A,fun(A,A)),combc(A,A,A),inverse_divide(A)),B)),C)) # label(fact_4897_divide_OisCont) # label(axiom).  [clausify(484)].
18.61/18.59	Derived: hBOOL(hAPP(real,bool,hAPP(fun(real,real),fun(real,bool),isCont(real,real),hAPP(real,fun(real,real),hAPP(fun(real,fun(real,real)),fun(real,fun(real,real)),combc(real,real,real),inverse_divide(real)),A)),B)).  [resolve(5084,a,5076,a)].
18.61/18.59	5085 -real_normed_field(A) | -hBOOL(hAPP(fun(nat,A),bool,summable(A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),C)) | hBOOL(hAPP(A,bool,hAPP(fun(nat,A),fun(A,bool),sums(A),hAPP(fun(nat,fun(nat,bool)),fun(nat,A),hAPP(fun(fun(nat,bool),A),fun(fun(nat,fun(nat,bool)),fun(nat,A)),combb(fun(nat,bool),A,nat),hAPP(fun(nat,A),fun(fun(nat,bool),A),big_co1399186613setsum(nat,A),B)),hAPP(fun(nat,nat),fun(nat,fun(nat,bool)),hAPP(fun(nat,fun(nat,fun(nat,bool))),fun(fun(nat,nat),fun(nat,fun(nat,bool))),combs(nat,nat,fun(nat,bool)),hAPP(fun(nat,nat),fun(nat,fun(nat,fun(nat,bool))),hAPP(fun(nat,fun(nat,fun(nat,bool))),fun(fun(nat,nat),fun(nat,fun(nat,fun(nat,bool)))),combb(nat,fun(nat,fun(nat,bool)),nat),ord_atLeastLessThan(nat)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),times_times(nat)),C))),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),hAPP(fun(nat,nat),fun(nat,fun(nat,nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,nat),fun(nat,fun(nat,nat))),combb(nat,fun(nat,nat),nat),plus_plus(nat)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),times_times(nat)),C))),C)))),hAPP(fun(nat,A),A,suminf(A),B))) # label(fact_4231_sums__group) # label(axiom).  [clausify(682)].
18.61/18.59	Derived: -hBOOL(hAPP(fun(nat,real),bool,summable(real),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),B)) | hBOOL(hAPP(real,bool,hAPP(fun(nat,real),fun(real,bool),sums(real),hAPP(fun(nat,fun(nat,bool)),fun(nat,real),hAPP(fun(fun(nat,bool),real),fun(fun(nat,fun(nat,bool)),fun(nat,real)),combb(fun(nat,bool),real,nat),hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),A)),hAPP(fun(nat,nat),fun(nat,fun(nat,bool)),hAPP(fun(nat,fun(nat,fun(nat,bool))),fun(fun(nat,nat),fun(nat,fun(nat,bool))),combs(nat,nat,fun(nat,bool)),hAPP(fun(nat,nat),fun(nat,fun(nat,fun(nat,bool))),hAPP(fun(nat,fun(nat,fun(nat,bool))),fun(fun(nat,nat),fun(nat,fun(nat,fun(nat,bool)))),combb(nat,fun(nat,fun(nat,bool)),nat),ord_atLeastLessThan(nat)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),times_times(nat)),B))),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),hAPP(fun(nat,nat),fun(nat,fun(nat,nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,nat),fun(nat,fun(nat,nat))),combb(nat,fun(nat,nat),nat),plus_plus(nat)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),times_times(nat)),B))),B)))),hAPP(fun(nat,real),real,suminf(real),A))).  [resolve(5085,a,5076,a)].
18.61/18.59	5086 -real_normed_field(A) | -hBOOL(hAPP(fun(nat,A),bool,summable(A),B)) | hBOOL(hAPP(filter(nat),bool,hAPP(A,fun(filter(nat),bool),hAPP(fun(nat,A),fun(A,fun(filter(nat),bool)),tendsto(nat,A),B),zero_zero(A)),sequentially)) # label(fact_4435_summable__LIMSEQ__zero) # label(axiom).  [clausify(725)].
18.61/18.59	Derived: -hBOOL(hAPP(fun(nat,real),bool,summable(real),A)) | hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),A),zero_zero(real)),sequentially)).  [resolve(5086,a,5076,a)].
18.61/18.59	5087 -real_normed_field(A) | -banach(A) | one_one(A) = hAPP(A,A,exp(A),zero_zero(A)) # label(fact_2583_exp__zero) # label(axiom).  [clausify(843)].
18.61/18.59	Derived: -banach(real) | one_one(real) = hAPP(real,real,exp(real),zero_zero(real)).  [resolve(5087,a,5076,a)].
18.61/18.59	5088 -real_normed_field(A) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),f135(A,B))) # label(fact_1802_divide_Opos__bounded) # label(axiom).  [clausify(869)].
18.70/18.65	Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),f135(real,A))).  [resolve(5088,a,5076,a)].
18.70/18.65	5089 -real_normed_field(A) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(A,real,norm_norm(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(A,real,norm_norm(A),B)),f135(A,C)))) # label(fact_1802_divide_Opos__bounded) # label(axiom).  [clausify(869)].
18.70/18.65	Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,norm_norm(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,norm_norm(real),A)),f135(real,B)))).  [resolve(5089,a,5076,a)].
18.70/18.65	5090 -real_normed_field(A) | -hBOOL(hAPP(A,bool,hAPP(fun(nat,A),fun(A,bool),sums(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(fun(nat,A),fun(A,bool),sums(A),D),E)) | hBOOL(hAPP(A,bool,hAPP(fun(nat,A),fun(A,bool),sums(A),hAPP(fun(nat,A),fun(nat,A),hAPP(fun(nat,fun(A,A)),fun(fun(nat,A),fun(nat,A)),combs(nat,A,A),hAPP(fun(nat,A),fun(nat,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(nat,A),fun(nat,fun(A,A))),combb(A,fun(A,A),nat),plus_plus(A)),B)),D)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),E))) # label(fact_4087_sums__add) # label(axiom).  [clausify(999)].
18.70/18.65	Derived: -hBOOL(hAPP(real,bool,hAPP(fun(nat,real),fun(real,bool),sums(real),A),B)) | -hBOOL(hAPP(real,bool,hAPP(fun(nat,real),fun(real,bool),sums(real),C),D)) | hBOOL(hAPP(real,bool,hAPP(fun(nat,real),fun(real,bool),sums(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),plus_plus(real)),A)),C)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),B),D))).  [resolve(5090,a,5076,a)].
18.70/18.65	5091 -banach(A) | -real_normed_field(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),exp(A)),B),hAPP(A,A,exp(A),B))) # label(fact_2632_DERIV__exp) # label(axiom).  [clausify(1088)].
18.70/18.65	Derived: -banach(real) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),exp(real)),A),hAPP(real,real,exp(real),A))).  [resolve(5091,b,5076,a)].
18.70/18.65	5092 -real_normed_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),B),C),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),hAPP(fun(A,A),fun(A,A),hAPP(fun(A,A),fun(fun(A,A),fun(A,A)),combb(A,A,A),uminus_uminus(A)),B)),C),hAPP(A,A,uminus_uminus(A),D))) # label(fact_3856_DERIV__minus) # label(axiom).  [clausify(1157)].
18.70/18.65	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),A),B),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,real),fun(fun(real,real),fun(real,real)),combb(real,real,real),uminus_uminus(real)),A)),B),hAPP(real,real,uminus_uminus(real),C))).  [resolve(5092,a,5076,a)].
18.70/18.65	5093 -real_normed_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),B),C),D)) | ti(A,D) != ti(A,E) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),B),C),E)) # label(fact_2635_Deriv_Olemma__DERIV__subst) # label(axiom).  [clausify(1162)].
18.70/18.65	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),A),B),C)) | ti(real,C) != ti(real,D) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),A),B),D)).  [resolve(5093,a,5076,a)].
18.70/18.65	5094 -real_normed_field(A) | -hBOOL(hAPP(fun(nat,A),bool,summable(A),B)) | -hBOOL(hAPP(fun(nat,A),bool,summable(A),C)) | hAPP(fun(nat,A),A,suminf(A),hAPP(fun(nat,A),fun(nat,A),hAPP(fun(nat,fun(A,A)),fun(fun(nat,A),fun(nat,A)),combs(nat,A,A),hAPP(fun(nat,A),fun(nat,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(nat,A),fun(nat,fun(A,A))),combb(A,fun(A,A),nat),plus_plus(A)),B)),C)) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(fun(nat,A),A,suminf(A),B)),hAPP(fun(nat,A),A,suminf(A),C)) # label(fact_3983_suminf__add) # label(axiom).  [clausify(1188)].
18.70/18.68	Derived: -hBOOL(hAPP(fun(nat,real),bool,summable(real),A)) | -hBOOL(hAPP(fun(nat,real),bool,summable(real),B)) | hAPP(fun(nat,real),real,suminf(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),plus_plus(real)),A)),B)) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(fun(nat,real),real,suminf(real),A)),hAPP(fun(nat,real),real,suminf(real),B)).  [resolve(5094,a,5076,a)].
18.70/18.68	5095 -real_normed_field(A) | deriv(A) = ti(fun(fun(A,A),fun(A,fun(A,bool))),deriv(A)) # label(tsy_c_Deriv_Oderiv_res) # label(axiom).  [clausify(1219)].
18.70/18.68	Derived: deriv(real) = ti(fun(fun(real,real),fun(real,fun(real,bool))),deriv(real)).  [resolve(5095,a,5076,a)].
18.70/18.68	5096 -real_normed_field(A) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(A,real,norm_norm(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(A,real,norm_norm(A),B)),f193(A,C)))) # label(fact_1806_divide_Ononneg__bounded) # label(axiom).  [clausify(1240)].
18.70/18.68	Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,norm_norm(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,norm_norm(real),A)),f193(real,B)))).  [resolve(5096,a,5076,a)].
18.70/18.68	5097 -real_normed_field(A) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),f193(A,B))) # label(fact_1806_divide_Ononneg__bounded) # label(axiom).  [clausify(1240)].
18.70/18.68	Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),f193(real,A))).  [resolve(5097,a,5076,a)].
18.70/18.68	5098 -real_normed_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),B),C),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),hAPP(fun(A,A),fun(A,A),hAPP(fun(A,A),fun(fun(A,A),fun(A,A)),combb(A,A,A),hAPP(A,fun(A,A),times_times(A),E)),B)),C),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),E),D))) # label(fact_3863_DERIV__cmult) # label(axiom).  [clausify(1282)].
18.70/18.68	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),A),B),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,real),fun(fun(real,real),fun(real,real)),combb(real,real,real),hAPP(real,fun(real,real),times_times(real),D)),A)),B),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),D),C))).  [resolve(5098,a,5076,a)].
18.70/18.68	5099 -real_normed_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),B),C),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),hAPP(nat,fun(A,A),hAPP(fun(A,fun(nat,A)),fun(nat,fun(A,A)),combc(A,nat,A),hAPP(fun(A,A),fun(A,fun(nat,A)),hAPP(fun(A,fun(nat,A)),fun(fun(A,A),fun(A,fun(nat,A))),combb(A,fun(nat,A),A),power_power(A)),B)),E)),C),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(nat,A,semiring_1_of_nat(A),E)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),hAPP(A,A,B,C)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),E),hAPP(nat,nat,suc,zero_zero(nat)))))))) # label(fact_3889_DERIV__power) # label(axiom).  [clausify(1286)].
18.70/18.68	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),A),B),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(nat,fun(real,real),hAPP(fun(real,fun(nat,real)),fun(nat,fun(real,real)),combc(real,nat,real),hAPP(fun(real,real),fun(real,fun(nat,real)),hAPP(fun(real,fun(nat,real)),fun(fun(real,real),fun(real,fun(nat,real))),combb(real,fun(nat,real),real),power_power(real)),A)),D)),B),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,semiring_1_of_nat(real),D)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,A,B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),D),hAPP(nat,nat,suc,zero_zero(nat)))))))).  [resolve(5099,a,5076,a)].
18.82/18.76	5100 -real_normed_field(A) | hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),B),C)),D) = hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),B),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),D)) # label(fact_4707_divide_OscaleR) # label(axiom).  [clausify(1350)].
18.82/18.76	Derived: hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),A),B)),C) = hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),A),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),B),C)).  [resolve(5100,a,5076,a)].
18.82/18.76	5101 -real_normed_field(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),hAPP(A,fun(A,A),combk(A,A),B)),C),zero_zero(A))) # label(fact_3840_DERIV__const) # label(axiom).  [clausify(1410)].
18.82/18.76	Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(real,fun(real,real),combk(real,real),A)),B),zero_zero(real))).  [resolve(5101,a,5076,a)].
18.82/18.76	5102 -real_normed_field(A) | -topological_space(B) | -hBOOL(hAPP(filter(B),bool,hAPP(A,fun(filter(B),bool),hAPP(fun(B,A),fun(A,fun(filter(B),bool)),tendsto(B,A),C),zero_zero(A)),hAPP(B,filter(B),at(B),D))) | hBOOL(hAPP(filter(B),bool,hAPP(A,fun(filter(B),bool),hAPP(fun(B,A),fun(A,fun(filter(B),bool)),tendsto(B,A),hAPP(A,fun(B,A),hAPP(fun(B,fun(A,A)),fun(A,fun(B,A)),combc(B,A,A),hAPP(fun(B,A),fun(B,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(B,A),fun(B,fun(A,A))),combb(A,fun(A,A),B),inverse_divide(A)),C)),E)),zero_zero(A)),hAPP(B,filter(B),at(B),D))) # label(fact_4586_divide_OLIM__zero) # label(axiom).  [clausify(1473)].
18.82/18.76	Derived: -topological_space(A) | -hBOOL(hAPP(filter(A),bool,hAPP(real,fun(filter(A),bool),hAPP(fun(A,real),fun(real,fun(filter(A),bool)),tendsto(A,real),B),zero_zero(real)),hAPP(A,filter(A),at(A),C))) | hBOOL(hAPP(filter(A),bool,hAPP(real,fun(filter(A),bool),hAPP(fun(A,real),fun(real,fun(filter(A),bool)),tendsto(A,real),hAPP(real,fun(A,real),hAPP(fun(A,fun(real,real)),fun(real,fun(A,real)),combc(A,real,real),hAPP(fun(A,real),fun(A,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(A,real),fun(A,fun(real,real))),combb(real,fun(real,real),A),inverse_divide(real)),B)),D)),zero_zero(real)),hAPP(A,filter(A),at(A),C))).  [resolve(5102,a,5076,a)].
18.82/18.76	5103 real_normed_field(complex) # label(arity_Complex_Ocomplex___RealVector_Oreal__normed__field) # label(axiom).  [assumption].
18.82/18.76	Derived: -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),A),B),C)) | zero_zero(complex) = hAPP(complex,complex,A,B) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),hAPP(fun(complex,complex),fun(complex,complex),hAPP(fun(complex,complex),fun(fun(complex,complex),fun(complex,complex)),combb(complex,complex,complex),inverse_inverse(complex)),A)),B),hAPP(complex,complex,uminus_uminus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),C),hAPP(complex,complex,inverse_inverse(complex),hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),hAPP(complex,complex,A,B)),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat))))))))).  [resolve(5103,a,5077,a)].
18.82/18.76	Derived: -hBOOL(hAPP(fun(nat,complex),bool,summable(complex),A)) | hBOOL(hAPP(fun(nat,complex),bool,summable(complex),hAPP(fun(nat,complex),fun(nat,complex),hAPP(fun(complex,complex),fun(fun(nat,complex),fun(nat,complex)),combb(complex,complex,nat),uminus_uminus(complex)),A))).  [resolve(5103,a,5078,a)].
18.82/18.77	Derived: -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),A),B),C)) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),D),B),E)) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),hAPP(fun(complex,complex),fun(complex,complex),hAPP(fun(complex,fun(complex,complex)),fun(fun(complex,complex),fun(complex,complex)),combs(complex,complex,complex),hAPP(fun(complex,complex),fun(complex,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(complex,complex),fun(complex,fun(complex,complex))),combb(complex,fun(complex,complex),complex),plus_plus(complex)),A)),D)),B),hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),C),E))).  [resolve(5103,a,5079,a)].
18.82/18.77	Derived: -banach(complex) | -hBOOL(hAPP(fun(nat,complex),bool,summable(complex),hAPP(fun(nat,complex),fun(nat,complex),hAPP(fun(nat,fun(complex,complex)),fun(fun(nat,complex),fun(nat,complex)),combs(nat,complex,complex),hAPP(fun(nat,complex),fun(nat,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(nat,complex),fun(nat,fun(complex,complex))),combb(complex,fun(complex,complex),nat),times_times(complex)),A)),hAPP(complex,fun(nat,complex),power_power(complex),B)))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(complex,real,norm_norm(complex),C)),hAPP(complex,real,norm_norm(complex),B))) | hBOOL(hAPP(fun(nat,complex),bool,summable(complex),hAPP(fun(nat,complex),fun(nat,complex),hAPP(fun(nat,fun(complex,complex)),fun(fun(nat,complex),fun(nat,complex)),combs(nat,complex,complex),hAPP(fun(nat,complex),fun(nat,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(nat,complex),fun(nat,fun(complex,complex))),combb(complex,fun(complex,complex),nat),times_times(complex)),A)),hAPP(complex,fun(nat,complex),power_power(complex),C)))).  [resolve(5103,a,5080,a)].
18.82/18.77	Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),A),B)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),C),B)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),A),C)),B).  [resolve(5103,a,5081,a)].
18.82/18.77	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(complex,real,norm_norm(complex),A)),one_one(real))) | hBOOL(hAPP(fun(nat,complex),bool,summable(complex),hAPP(complex,fun(nat,complex),power_power(complex),A))).  [resolve(5103,a,5082,a)].
18.82/18.77	Derived: -banach(complex) | -hBOOL(hAPP(fun(nat,complex),bool,summable(complex),hAPP(fun(nat,complex),fun(nat,complex),hAPP(fun(nat,fun(complex,complex)),fun(fun(nat,complex),fun(nat,complex)),combs(nat,complex,complex),hAPP(fun(nat,complex),fun(nat,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(nat,complex),fun(nat,fun(complex,complex))),combb(complex,fun(complex,complex),nat),times_times(complex)),A)),hAPP(complex,fun(nat,complex),power_power(complex),B)))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(complex,real,norm_norm(complex),C)),hAPP(complex,real,norm_norm(complex),B))) | hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,complex),fun(nat,real),hAPP(fun(complex,real),fun(fun(nat,complex),fun(nat,real)),combb(complex,real,nat),norm_norm(complex)),hAPP(fun(nat,complex),fun(nat,complex),hAPP(fun(nat,fun(complex,complex)),fun(fun(nat,complex),fun(nat,complex)),combs(nat,complex,complex),hAPP(fun(nat,complex),fun(nat,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(nat,complex),fun(nat,fun(complex,complex))),combb(complex,fun(complex,complex),nat),times_times(complex)),A)),hAPP(complex,fun(nat,complex),power_power(complex),C))))).  [resolve(5103,a,5083,a)].
18.82/18.78	Derived: hBOOL(hAPP(complex,bool,hAPP(fun(complex,complex),fun(complex,bool),isCont(complex,complex),hAPP(complex,fun(complex,complex),hAPP(fun(complex,fun(complex,complex)),fun(complex,fun(complex,complex)),combc(complex,complex,complex),inverse_divide(complex)),A)),B)).  [resolve(5103,a,5084,a)].
18.82/18.78	Derived: -hBOOL(hAPP(fun(nat,complex),bool,summable(complex),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),B)) | hBOOL(hAPP(complex,bool,hAPP(fun(nat,complex),fun(complex,bool),sums(complex),hAPP(fun(nat,fun(nat,bool)),fun(nat,complex),hAPP(fun(fun(nat,bool),complex),fun(fun(nat,fun(nat,bool)),fun(nat,complex)),combb(fun(nat,bool),complex,nat),hAPP(fun(nat,complex),fun(fun(nat,bool),complex),big_co1399186613setsum(nat,complex),A)),hAPP(fun(nat,nat),fun(nat,fun(nat,bool)),hAPP(fun(nat,fun(nat,fun(nat,bool))),fun(fun(nat,nat),fun(nat,fun(nat,bool))),combs(nat,nat,fun(nat,bool)),hAPP(fun(nat,nat),fun(nat,fun(nat,fun(nat,bool))),hAPP(fun(nat,fun(nat,fun(nat,bool))),fun(fun(nat,nat),fun(nat,fun(nat,fun(nat,bool)))),combb(nat,fun(nat,fun(nat,bool)),nat),ord_atLeastLessThan(nat)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),times_times(nat)),B))),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),hAPP(fun(nat,nat),fun(nat,fun(nat,nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,nat),fun(nat,fun(nat,nat))),combb(nat,fun(nat,nat),nat),plus_plus(nat)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),times_times(nat)),B))),B)))),hAPP(fun(nat,complex),complex,suminf(complex),A))).  [resolve(5103,a,5085,a)].
18.82/18.78	Derived: -hBOOL(hAPP(fun(nat,complex),bool,summable(complex),A)) | hBOOL(hAPP(filter(nat),bool,hAPP(complex,fun(filter(nat),bool),hAPP(fun(nat,complex),fun(complex,fun(filter(nat),bool)),tendsto(nat,complex),A),zero_zero(complex)),sequentially)).  [resolve(5103,a,5086,a)].
18.82/18.78	Derived: -banach(complex) | one_one(complex) = hAPP(complex,complex,exp(complex),zero_zero(complex)).  [resolve(5103,a,5087,a)].
18.82/18.78	Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),f135(complex,A))).  [resolve(5103,a,5088,a)].
18.82/18.78	Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),A),B))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(complex,real,norm_norm(complex),A)),f135(complex,B)))).  [resolve(5103,a,5089,a)].
18.82/18.78	Derived: -hBOOL(hAPP(complex,bool,hAPP(fun(nat,complex),fun(complex,bool),sums(complex),A),B)) | -hBOOL(hAPP(complex,bool,hAPP(fun(nat,complex),fun(complex,bool),sums(complex),C),D)) | hBOOL(hAPP(complex,bool,hAPP(fun(nat,complex),fun(complex,bool),sums(complex),hAPP(fun(nat,complex),fun(nat,complex),hAPP(fun(nat,fun(complex,complex)),fun(fun(nat,complex),fun(nat,complex)),combs(nat,complex,complex),hAPP(fun(nat,complex),fun(nat,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(nat,complex),fun(nat,fun(complex,complex))),combb(complex,fun(complex,complex),nat),plus_plus(complex)),A)),C)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),B),D))).  [resolve(5103,a,5090,a)].
18.82/18.78	Derived: -banach(complex) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),exp(complex)),A),hAPP(complex,complex,exp(complex),A))).  [resolve(5103,a,5091,b)].
18.82/18.78	Derived: -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),A),B),C)) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),hAPP(fun(complex,complex),fun(complex,complex),hAPP(fun(complex,complex),fun(fun(complex,complex),fun(complex,complex)),combb(complex,complex,complex),uminus_uminus(complex)),A)),B),hAPP(complex,complex,uminus_uminus(complex),C))).  [resolve(5103,a,5092,a)].
18.82/18.79	Derived: -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),A),B),C)) | ti(complex,C) != ti(complex,D) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),A),B),D)).  [resolve(5103,a,5093,a)].
18.82/18.79	Derived: -hBOOL(hAPP(fun(nat,complex),bool,summable(complex),A)) | -hBOOL(hAPP(fun(nat,complex),bool,summable(complex),B)) | hAPP(fun(nat,complex),complex,suminf(complex),hAPP(fun(nat,complex),fun(nat,complex),hAPP(fun(nat,fun(complex,complex)),fun(fun(nat,complex),fun(nat,complex)),combs(nat,complex,complex),hAPP(fun(nat,complex),fun(nat,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(nat,complex),fun(nat,fun(complex,complex))),combb(complex,fun(complex,complex),nat),plus_plus(complex)),A)),B)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(fun(nat,complex),complex,suminf(complex),A)),hAPP(fun(nat,complex),complex,suminf(complex),B)).  [resolve(5103,a,5094,a)].
18.82/18.79	Derived: deriv(complex) = ti(fun(fun(complex,complex),fun(complex,fun(complex,bool))),deriv(complex)).  [resolve(5103,a,5095,a)].
18.82/18.79	Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),A),B))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(complex,real,norm_norm(complex),A)),f193(complex,B)))).  [resolve(5103,a,5096,a)].
18.82/18.79	Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),f193(complex,A))).  [resolve(5103,a,5097,a)].
18.82/18.79	Derived: -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),A),B),C)) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),hAPP(fun(complex,complex),fun(complex,complex),hAPP(fun(complex,complex),fun(fun(complex,complex),fun(complex,complex)),combb(complex,complex,complex),hAPP(complex,fun(complex,complex),times_times(complex),D)),A)),B),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),D),C))).  [resolve(5103,a,5098,a)].
18.82/18.79	Derived: -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),A),B),C)) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),hAPP(nat,fun(complex,complex),hAPP(fun(complex,fun(nat,complex)),fun(nat,fun(complex,complex)),combc(complex,nat,complex),hAPP(fun(complex,complex),fun(complex,fun(nat,complex)),hAPP(fun(complex,fun(nat,complex)),fun(fun(complex,complex),fun(complex,fun(nat,complex))),combb(complex,fun(nat,complex),complex),power_power(complex)),A)),D)),B),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(nat,complex,semiring_1_of_nat(complex),D)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),C),hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),hAPP(complex,complex,A,B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),D),hAPP(nat,nat,suc,zero_zero(nat)))))))).  [resolve(5103,a,5099,a)].
18.82/18.79	Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),A),B)),C) = hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),A),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),B),C)).  [resolve(5103,a,5100,a)].
18.82/18.79	Derived: hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),hAPP(complex,fun(complex,complex),combk(complex,complex),A)),B),zero_zero(complex))).  [resolve(5103,a,5101,a)].
18.82/18.79	Derived: -topological_space(A) | -hBOOL(hAPP(filter(A),bool,hAPP(complex,fun(filter(A),bool),hAPP(fun(A,complex),fun(complex,fun(filter(A),bool)),tendsto(A,complex),B),zero_zero(complex)),hAPP(A,filter(A),at(A),C))) | hBOOL(hAPP(filter(A),bool,hAPP(complex,fun(filter(A),bool),hAPP(fun(A,complex),fun(complex,fun(filter(A),bool)),tendsto(A,complex),hAPP(complex,fun(A,complex),hAPP(fun(A,fun(complex,complex)),fun(complex,fun(A,complex)),combc(A,complex,complex),hAPP(fun(A,complex),fun(A,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(A,complex),fun(A,fun(complex,complex))),combb(complex,fun(complex,complex),A),inverse_divide(complex)),B)),D)),zero_zero(complex)),hAPP(A,filter(A),at(A),C))).  [resolve(5103,a,5102,a)].
18.87/18.83	5104 -real_normed_field(A) | -hBOOL(hAPP(A,bool,hAPP(fun(nat,A),fun(A,bool),sums(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(fun(nat,A),fun(A,bool),sums(A),D),E)) | hBOOL(hAPP(A,bool,hAPP(fun(nat,A),fun(A,bool),sums(A),hAPP(fun(nat,A),fun(nat,A),hAPP(fun(nat,fun(A,A)),fun(fun(nat,A),fun(nat,A)),combs(nat,A,A),hAPP(fun(nat,A),fun(nat,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(nat,A),fun(nat,fun(A,A))),combb(A,fun(A,A),nat),minus_minus(A)),B)),D)),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),C),E))) # label(fact_4088_sums__diff) # label(axiom).  [clausify(1606)].
18.87/18.83	Derived: -hBOOL(hAPP(real,bool,hAPP(fun(nat,real),fun(real,bool),sums(real),A),B)) | -hBOOL(hAPP(real,bool,hAPP(fun(nat,real),fun(real,bool),sums(real),C),D)) | hBOOL(hAPP(real,bool,hAPP(fun(nat,real),fun(real,bool),sums(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),minus_minus(real)),A)),C)),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),B),D))).  [resolve(5104,a,5076,a)].
18.87/18.83	Derived: -hBOOL(hAPP(complex,bool,hAPP(fun(nat,complex),fun(complex,bool),sums(complex),A),B)) | -hBOOL(hAPP(complex,bool,hAPP(fun(nat,complex),fun(complex,bool),sums(complex),C),D)) | hBOOL(hAPP(complex,bool,hAPP(fun(nat,complex),fun(complex,bool),sums(complex),hAPP(fun(nat,complex),fun(nat,complex),hAPP(fun(nat,fun(complex,complex)),fun(fun(nat,complex),fun(nat,complex)),combs(nat,complex,complex),hAPP(fun(nat,complex),fun(nat,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(nat,complex),fun(nat,fun(complex,complex))),combb(complex,fun(complex,complex),nat),minus_minus(complex)),A)),C)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),B),D))).  [resolve(5104,a,5103,a)].
18.87/18.83	5105 -real_normed_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),B),C),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),E),C),F)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),hAPP(fun(A,A),fun(A,A),hAPP(fun(A,fun(A,A)),fun(fun(A,A),fun(A,A)),combs(A,A,A),hAPP(fun(A,A),fun(A,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(A,A),fun(A,fun(A,A))),combb(A,fun(A,A),A),minus_minus(A)),B)),E)),C),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),D),F))) # label(fact_3822_DERIV__diff) # label(axiom).  [clausify(1693)].
18.87/18.83	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),A),B),C)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),D),B),E)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,real)),combs(real,real,real),hAPP(fun(real,real),fun(real,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,fun(real,real))),combb(real,fun(real,real),real),minus_minus(real)),A)),D)),B),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),C),E))).  [resolve(5105,a,5076,a)].
18.87/18.83	Derived: -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),A),B),C)) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),D),B),E)) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),hAPP(fun(complex,complex),fun(complex,complex),hAPP(fun(complex,fun(complex,complex)),fun(fun(complex,complex),fun(complex,complex)),combs(complex,complex,complex),hAPP(fun(complex,complex),fun(complex,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(complex,complex),fun(complex,fun(complex,complex))),combb(complex,fun(complex,complex),complex),minus_minus(complex)),A)),D)),B),hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),C),E))).  [resolve(5105,a,5103,a)].
18.91/18.88	5106 -real_normed_field(A) | -hBOOL(hAPP(fun(nat,A),bool,summable(A),B)) | hAPP(fun(nat,A),A,suminf(A),hAPP(A,fun(nat,A),hAPP(fun(nat,fun(A,A)),fun(A,fun(nat,A)),combc(nat,A,A),hAPP(fun(nat,A),fun(nat,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(nat,A),fun(nat,fun(A,A))),combb(A,fun(A,A),nat),inverse_divide(A)),B)),C)) = hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),hAPP(fun(nat,A),A,suminf(A),B)),C) # label(fact_3985_divide_Osuminf) # label(axiom).  [clausify(1731)].
18.91/18.88	Derived: -hBOOL(hAPP(fun(nat,real),bool,summable(real),A)) | hAPP(fun(nat,real),real,suminf(real),hAPP(real,fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(real,fun(nat,real)),combc(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),inverse_divide(real)),A)),B)) = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(fun(nat,real),real,suminf(real),A)),B).  [resolve(5106,a,5076,a)].
18.91/18.88	Derived: -hBOOL(hAPP(fun(nat,complex),bool,summable(complex),A)) | hAPP(fun(nat,complex),complex,suminf(complex),hAPP(complex,fun(nat,complex),hAPP(fun(nat,fun(complex,complex)),fun(complex,fun(nat,complex)),combc(nat,complex,complex),hAPP(fun(nat,complex),fun(nat,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(nat,complex),fun(nat,fun(complex,complex))),combb(complex,fun(complex,complex),nat),inverse_divide(complex)),A)),B)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),hAPP(fun(nat,complex),complex,suminf(complex),A)),B).  [resolve(5106,a,5103,a)].
18.91/18.88	5107 -real_normed_field(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),hAPP(A,fun(A,A),times_times(A),B)),C),B)) # label(fact_2636_DERIV__cmult__Id) # label(axiom).  [clausify(1794)].
18.91/18.88	Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(real,fun(real,real),times_times(real),A)),B),A)).  [resolve(5107,a,5076,a)].
18.91/18.88	Derived: hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),hAPP(complex,fun(complex,complex),times_times(complex),A)),B),A)).  [resolve(5107,a,5103,a)].
18.91/18.88	5108 -real_normed_field(A) | -hBOOL(hAPP(filter(nat),bool,hAPP(A,fun(filter(nat),bool),hAPP(fun(nat,A),fun(A,fun(filter(nat),bool)),tendsto(nat,A),B),C),sequentially)) | -hBOOL(hAPP(filter(nat),bool,hAPP(A,fun(filter(nat),bool),hAPP(fun(nat,A),fun(A,fun(filter(nat),bool)),tendsto(nat,A),D),E),sequentially)) | zero_zero(A) = ti(A,E) | hBOOL(hAPP(filter(nat),bool,hAPP(A,fun(filter(nat),bool),hAPP(fun(nat,A),fun(A,fun(filter(nat),bool)),tendsto(nat,A),hAPP(fun(nat,A),fun(nat,A),hAPP(fun(nat,fun(A,A)),fun(fun(nat,A),fun(nat,A)),combs(nat,A,A),hAPP(fun(nat,A),fun(nat,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(nat,A),fun(nat,fun(A,A))),combb(A,fun(A,A),nat),inverse_divide(A)),B)),D)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),E)),sequentially)) # label(fact_4451_LIMSEQ__divide) # label(axiom).  [clausify(1799)].
18.91/18.88	Derived: -hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),A),B),sequentially)) | -hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),C),D),sequentially)) | zero_zero(real) = ti(real,D) | hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),inverse_divide(real)),A)),C)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),B),D)),sequentially)).  [resolve(5108,a,5076,a)].
18.91/18.93	Derived: -hBOOL(hAPP(filter(nat),bool,hAPP(complex,fun(filter(nat),bool),hAPP(fun(nat,complex),fun(complex,fun(filter(nat),bool)),tendsto(nat,complex),A),B),sequentially)) | -hBOOL(hAPP(filter(nat),bool,hAPP(complex,fun(filter(nat),bool),hAPP(fun(nat,complex),fun(complex,fun(filter(nat),bool)),tendsto(nat,complex),C),D),sequentially)) | zero_zero(complex) = ti(complex,D) | hBOOL(hAPP(filter(nat),bool,hAPP(complex,fun(filter(nat),bool),hAPP(fun(nat,complex),fun(complex,fun(filter(nat),bool)),tendsto(nat,complex),hAPP(fun(nat,complex),fun(nat,complex),hAPP(fun(nat,fun(complex,complex)),fun(fun(nat,complex),fun(nat,complex)),combs(nat,complex,complex),hAPP(fun(nat,complex),fun(nat,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(nat,complex),fun(nat,fun(complex,complex))),combb(complex,fun(complex,complex),nat),inverse_divide(complex)),A)),C)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),B),D)),sequentially)).  [resolve(5108,a,5103,a)].
18.91/18.93	5109 -real_normed_field(A) | zero_zero(A) = hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),zero_zero(A)),B) # label(fact_1656_divide_Ozero) # label(axiom).  [clausify(1881)].
18.91/18.93	Derived: zero_zero(real) = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),zero_zero(real)),A).  [resolve(5109,a,5076,a)].
18.91/18.93	Derived: zero_zero(complex) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),zero_zero(complex)),A).  [resolve(5109,a,5103,a)].
18.91/18.93	5110 -real_normed_field(A) | zero_zero(A) = ti(A,B) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),inverse_inverse(A)),B),hAPP(A,A,uminus_uminus(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),hAPP(A,A,inverse_inverse(A),B)),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat))))))) # label(fact_3888_DERIV__inverse) # label(axiom).  [clausify(1891)].
18.91/18.93	Derived: zero_zero(real) = ti(real,A) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),inverse_inverse(real)),A),hAPP(real,real,uminus_uminus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,inverse_inverse(real),A)),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat))))))).  [resolve(5110,a,5076,a)].
18.91/18.93	Derived: zero_zero(complex) = ti(complex,A) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),inverse_inverse(complex)),A),hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),hAPP(complex,complex,inverse_inverse(complex),A)),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat))))))).  [resolve(5110,a,5103,a)].
18.91/18.93	5111 -real_normed_field(A) | hAPP(A,A,uminus_uminus(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)) = hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),hAPP(A,A,uminus_uminus(A),B)),C) # label(fact_2017_divide_Ominus) # label(axiom).  [clausify(1910)].
18.91/18.93	Derived: hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B)) = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,uminus_uminus(real),A)),B).  [resolve(5111,a,5076,a)].
18.91/18.93	Derived: hAPP(complex,complex,uminus_uminus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),A),B)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),hAPP(complex,complex,uminus_uminus(complex),A)),B).  [resolve(5111,a,5103,a)].
18.91/18.93	5112 -real_normed_field(A) | -banach(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),B),C),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),hAPP(fun(A,A),fun(A,A),hAPP(fun(A,A),fun(fun(A,A),fun(A,A)),combb(A,A,A),exp(A)),B)),C),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,exp(A),hAPP(A,A,B,C))),D))) # label(fact_3864_DERIV__fun__exp) # label(axiom).  [clausify(1920)].
19.00/18.95	Derived: -banach(real) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),A),B),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,real),fun(fun(real,real),fun(real,real)),combb(real,real,real),exp(real)),A)),B),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,exp(real),hAPP(real,real,A,B))),C))).  [resolve(5112,a,5076,a)].
19.00/18.95	Derived: -banach(complex) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),A),B),C)) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),hAPP(fun(complex,complex),fun(complex,complex),hAPP(fun(complex,complex),fun(fun(complex,complex),fun(complex,complex)),combb(complex,complex,complex),exp(complex)),A)),B),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,exp(complex),hAPP(complex,complex,A,B))),C))).  [resolve(5112,a,5103,a)].
19.00/18.95	5113 -real_normed_field(A) | -banach(A) | hAPP(fun(nat,A),A,suminf(A),hAPP(fun(nat,A),fun(nat,A),hAPP(fun(nat,fun(A,A)),fun(fun(nat,A),fun(nat,A)),combs(nat,A,A),hAPP(fun(nat,real),fun(nat,fun(A,A)),hAPP(fun(real,fun(A,A)),fun(fun(nat,real),fun(nat,fun(A,A))),combb(real,fun(A,A),nat),scaleR_scaleR(A)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),inverse_inverse(real)),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),fact_fact(nat))))),hAPP(A,fun(nat,A),power_power(A),B))) = hAPP(A,A,exp(A),B) # label(fact_4751_exp__def) # label(axiom).  [clausify(1940)].
19.00/18.95	Derived: -banach(real) | hAPP(fun(nat,real),real,suminf(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),scaleR_scaleR(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),inverse_inverse(real)),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),fact_fact(nat))))),hAPP(real,fun(nat,real),power_power(real),A))) = hAPP(real,real,exp(real),A).  [resolve(5113,a,5076,a)].
19.00/18.95	Derived: -banach(complex) | hAPP(fun(nat,complex),complex,suminf(complex),hAPP(fun(nat,complex),fun(nat,complex),hAPP(fun(nat,fun(complex,complex)),fun(fun(nat,complex),fun(nat,complex)),combs(nat,complex,complex),hAPP(fun(nat,real),fun(nat,fun(complex,complex)),hAPP(fun(real,fun(complex,complex)),fun(fun(nat,real),fun(nat,fun(complex,complex))),combb(real,fun(complex,complex),nat),scaleR_scaleR(complex)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),inverse_inverse(real)),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),fact_fact(nat))))),hAPP(complex,fun(nat,complex),power_power(complex),A))) = hAPP(complex,complex,exp(complex),A).  [resolve(5113,a,5103,a)].
19.00/18.95	5114 -real_normed_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),B),C),D)) | hBOOL(hAPP(filter(A),bool,hAPP(A,fun(filter(A),bool),hAPP(fun(A,A),fun(A,fun(filter(A),bool)),tendsto(A,A),hAPP(fun(A,A),fun(A,A),hAPP(fun(A,fun(A,A)),fun(fun(A,A),fun(A,A)),combs(A,A,A),hAPP(fun(A,A),fun(A,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(A,A),fun(A,fun(A,A))),combb(A,fun(A,A),A),inverse_divide(A)),hAPP(A,fun(A,A),hAPP(fun(A,fun(A,A)),fun(A,fun(A,A)),combc(A,A,A),hAPP(fun(A,A),fun(A,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(A,A),fun(A,fun(A,A))),combb(A,fun(A,A),A),minus_minus(A)),hAPP(fun(A,A),fun(A,A),hAPP(fun(A,A),fun(fun(A,A),fun(A,A)),combb(A,A,A),B),hAPP(A,fun(A,A),plus_plus(A),C)))),hAPP(A,A,B,C)))),combi(A))),D),hAPP(A,filter(A),at(A),zero_zero(A)))) # label(fact_4620_DERIV__D) # label(axiom).  [clausify(1961)].
19.00/18.96	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),A),B),C)) | hBOOL(hAPP(filter(real),bool,hAPP(real,fun(filter(real),bool),hAPP(fun(real,real),fun(real,fun(filter(real),bool)),tendsto(real,real),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,real)),combs(real,real,real),hAPP(fun(real,real),fun(real,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,fun(real,real))),combb(real,fun(real,real),real),inverse_divide(real)),hAPP(real,fun(real,real),hAPP(fun(real,fun(real,real)),fun(real,fun(real,real)),combc(real,real,real),hAPP(fun(real,real),fun(real,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,fun(real,real))),combb(real,fun(real,real),real),minus_minus(real)),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,real),fun(fun(real,real),fun(real,real)),combb(real,real,real),A),hAPP(real,fun(real,real),plus_plus(real),B)))),hAPP(real,real,A,B)))),combi(real))),C),hAPP(real,filter(real),at(real),zero_zero(real)))).  [resolve(5114,a,5076,a)].
19.00/18.96	Derived: -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),A),B),C)) | hBOOL(hAPP(filter(complex),bool,hAPP(complex,fun(filter(complex),bool),hAPP(fun(complex,complex),fun(complex,fun(filter(complex),bool)),tendsto(complex,complex),hAPP(fun(complex,complex),fun(complex,complex),hAPP(fun(complex,fun(complex,complex)),fun(fun(complex,complex),fun(complex,complex)),combs(complex,complex,complex),hAPP(fun(complex,complex),fun(complex,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(complex,complex),fun(complex,fun(complex,complex))),combb(complex,fun(complex,complex),complex),inverse_divide(complex)),hAPP(complex,fun(complex,complex),hAPP(fun(complex,fun(complex,complex)),fun(complex,fun(complex,complex)),combc(complex,complex,complex),hAPP(fun(complex,complex),fun(complex,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(complex,complex),fun(complex,fun(complex,complex))),combb(complex,fun(complex,complex),complex),minus_minus(complex)),hAPP(fun(complex,complex),fun(complex,complex),hAPP(fun(complex,complex),fun(fun(complex,complex),fun(complex,complex)),combb(complex,complex,complex),A),hAPP(complex,fun(complex,complex),plus_plus(complex),B)))),hAPP(complex,complex,A,B)))),combi(complex))),C),hAPP(complex,filter(complex),at(complex),zero_zero(complex)))).  [resolve(5114,a,5103,a)].
19.00/18.96	5115 -real_normed_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),B),C),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),E),C),F)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),hAPP(fun(A,A),fun(A,A),hAPP(fun(A,fun(A,A)),fun(fun(A,A),fun(A,A)),combs(A,A,A),hAPP(fun(A,A),fun(A,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(A,A),fun(A,fun(A,A))),combb(A,fun(A,A),A),plus_plus(A)),B)),hAPP(fun(A,A),fun(A,A),hAPP(fun(A,A),fun(fun(A,A),fun(A,A)),combb(A,A,A),uminus_uminus(A)),E))),C),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),D),hAPP(A,A,uminus_uminus(A),F)))) # label(fact_3816_DERIV__add__minus) # label(axiom).  [clausify(2001)].
19.00/18.96	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),A),B),C)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),D),B),E)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,real)),combs(real,real,real),hAPP(fun(real,real),fun(real,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,fun(real,real))),combb(real,fun(real,real),real),plus_plus(real)),A)),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,real),fun(fun(real,real),fun(real,real)),combb(real,real,real),uminus_uminus(real)),D))),B),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),C),hAPP(real,real,uminus_uminus(real),E)))).  [resolve(5115,a,5076,a)].
19.00/18.98	Derived: -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),A),B),C)) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),D),B),E)) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),hAPP(fun(complex,complex),fun(complex,complex),hAPP(fun(complex,fun(complex,complex)),fun(fun(complex,complex),fun(complex,complex)),combs(complex,complex,complex),hAPP(fun(complex,complex),fun(complex,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(complex,complex),fun(complex,fun(complex,complex))),combb(complex,fun(complex,complex),complex),plus_plus(complex)),A)),hAPP(fun(complex,complex),fun(complex,complex),hAPP(fun(complex,complex),fun(fun(complex,complex),fun(complex,complex)),combb(complex,complex,complex),uminus_uminus(complex)),D))),B),hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),C),hAPP(complex,complex,uminus_uminus(complex),E)))).  [resolve(5115,a,5103,a)].
19.00/18.98	5116 -real_normed_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),B),C),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),E),C),F)) | zero_zero(A) = hAPP(A,A,E,C) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),hAPP(fun(A,A),fun(A,A),hAPP(fun(A,fun(A,A)),fun(fun(A,A),fun(A,A)),combs(A,A,A),hAPP(fun(A,A),fun(A,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(A,A),fun(A,fun(A,A))),combb(A,fun(A,A),A),inverse_divide(A)),B)),E)),C),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),hAPP(A,A,E,C))),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,B,C)),F))),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,E,C)),hAPP(A,A,E,C))))) # label(fact_3811_DERIV__divide) # label(axiom).  [clausify(2019)].
19.00/18.98	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),A),B),C)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),D),B),E)) | zero_zero(real) = hAPP(real,real,D,B) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,real)),combs(real,real,real),hAPP(fun(real,real),fun(real,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,fun(real,real))),combb(real,fun(real,real),real),inverse_divide(real)),A)),D)),B),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),hAPP(real,real,D,B))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,A,B)),E))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,D,B)),hAPP(real,real,D,B))))).  [resolve(5116,a,5076,a)].
19.00/18.98	Derived: -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),A),B),C)) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),D),B),E)) | zero_zero(complex) = hAPP(complex,complex,D,B) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),hAPP(fun(complex,complex),fun(complex,complex),hAPP(fun(complex,fun(complex,complex)),fun(fun(complex,complex),fun(complex,complex)),combs(complex,complex,complex),hAPP(fun(complex,complex),fun(complex,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(complex,complex),fun(complex,fun(complex,complex))),combb(complex,fun(complex,complex),complex),inverse_divide(complex)),A)),D)),B),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),C),hAPP(complex,complex,D,B))),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,A,B)),E))),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,D,B)),hAPP(complex,complex,D,B))))).  [resolve(5116,a,5103,a)].
19.00/18.99	5117 -real_normed_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),B),C),D)) | hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(A,A,B,E)),hAPP(A,A,B,C)) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,f337(A,B,C,D),E)),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),E),C)) # label(fact_4882_CARAT__DERIV) # label(axiom).  [clausify(2026)].
19.00/18.99	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),A),B),C)) | hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,A,D)),hAPP(real,real,A,B)) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,f337(real,A,B,C),D)),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),D),B)).  [resolve(5117,a,5076,a)].
19.00/18.99	Derived: -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),A),B),C)) | hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),hAPP(complex,complex,A,D)),hAPP(complex,complex,A,B)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,f337(complex,A,B,C),D)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),D),B)).  [resolve(5117,a,5103,a)].
19.00/18.99	5118 -real_normed_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),B),C),D)) | hAPP(A,A,f337(A,B,C,D),C) = ti(A,D) # label(fact_4882_CARAT__DERIV) # label(axiom).  [clausify(2026)].
19.00/18.99	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),A),B),C)) | hAPP(real,real,f337(real,A,B,C),B) = ti(real,C).  [resolve(5118,a,5076,a)].
19.00/18.99	Derived: -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),A),B),C)) | hAPP(complex,complex,f337(complex,A,B,C),B) = ti(complex,C).  [resolve(5118,a,5103,a)].
19.00/18.99	5119 -real_normed_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),B),C),D)) | hBOOL(hAPP(A,bool,hAPP(fun(A,A),fun(A,bool),isCont(A,A),f337(A,B,C,D)),C)) # label(fact_4882_CARAT__DERIV) # label(axiom).  [clausify(2026)].
19.00/18.99	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),A),B),C)) | hBOOL(hAPP(real,bool,hAPP(fun(real,real),fun(real,bool),isCont(real,real),f337(real,A,B,C)),B)).  [resolve(5119,a,5076,a)].
19.00/18.99	Derived: -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),A),B),C)) | hBOOL(hAPP(complex,bool,hAPP(fun(complex,complex),fun(complex,bool),isCont(complex,complex),f337(complex,A,B,C)),B)).  [resolve(5119,a,5103,a)].
19.00/18.99	5120 -real_normed_field(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),B),C),D)) | hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(A,A,B,f338(A,B,C,D,E))),hAPP(A,A,B,C)) != hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,E,f338(A,B,C,D,E))),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),f338(A,B,C,D,E)),C)) | hAPP(A,A,E,C) != ti(A,D) | -hBOOL(hAPP(A,bool,hAPP(fun(A,A),fun(A,bool),isCont(A,A),E),C)) # label(fact_4882_CARAT__DERIV) # label(axiom).  [clausify(2026)].
19.06/19.01	Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),A),B),C)) | hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,A,f338(real,A,B,C,D))),hAPP(real,real,A,B)) != hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,D,f338(real,A,B,C,D))),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),f338(real,A,B,C,D)),B)) | hAPP(real,real,D,B) != ti(real,C) | -hBOOL(hAPP(real,bool,hAPP(fun(real,real),fun(real,bool),isCont(real,real),D),B)).  [resolve(5120,a,5076,a)].
19.06/19.01	Derived: hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),A),B),C)) | hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),hAPP(complex,complex,A,f338(complex,A,B,C,D))),hAPP(complex,complex,A,B)) != hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,D,f338(complex,A,B,C,D))),hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),f338(complex,A,B,C,D)),B)) | hAPP(complex,complex,D,B) != ti(complex,C) | -hBOOL(hAPP(complex,bool,hAPP(fun(complex,complex),fun(complex,bool),isCont(complex,complex),D),B)).  [resolve(5120,a,5103,a)].
19.06/19.01	5121 -real_normed_field(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f342(B,A,D,E,F,C)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),hAPP(fun(B,bool),fun(A,A),hAPP(fun(A,fun(fun(B,bool),A)),fun(fun(B,bool),fun(A,A)),combc(A,fun(B,bool),A),hAPP(fun(A,fun(B,A)),fun(A,fun(fun(B,bool),A)),hAPP(fun(fun(B,A),fun(fun(B,bool),A)),fun(fun(A,fun(B,A)),fun(A,fun(fun(B,bool),A))),combb(fun(B,A),fun(fun(B,bool),A),A),big_co1399186613setsum(B,A)),D)),C)),E),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),hAPP(A,fun(B,A),F,E)),C))) # label(fact_4304_DERIV__setsum) # label(axiom).  [clausify(2076)].
19.06/19.01	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f342(A,real,C,D,E,B)),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(fun(A,bool),fun(real,real),hAPP(fun(real,fun(fun(A,bool),real)),fun(fun(A,bool),fun(real,real)),combc(real,fun(A,bool),real),hAPP(fun(real,fun(A,real)),fun(real,fun(fun(A,bool),real)),hAPP(fun(fun(A,real),fun(fun(A,bool),real)),fun(fun(real,fun(A,real)),fun(real,fun(fun(A,bool),real))),combb(fun(A,real),fun(fun(A,bool),real),real),big_co1399186613setsum(A,real)),C)),B)),D),hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),hAPP(real,fun(A,real),E,D)),B))).  [resolve(5121,a,5076,a)].
19.06/19.01	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f342(A,complex,C,D,E,B)),B)) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),hAPP(fun(A,bool),fun(complex,complex),hAPP(fun(complex,fun(fun(A,bool),complex)),fun(fun(A,bool),fun(complex,complex)),combc(complex,fun(A,bool),complex),hAPP(fun(complex,fun(A,complex)),fun(complex,fun(fun(A,bool),complex)),hAPP(fun(fun(A,complex),fun(fun(A,bool),complex)),fun(fun(complex,fun(A,complex)),fun(complex,fun(fun(A,bool),complex))),combb(fun(A,complex),fun(fun(A,bool),complex),complex),big_co1399186613setsum(A,complex)),C)),B)),D),hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),hAPP(complex,fun(A,complex),E,D)),B))).  [resolve(5121,a,5103,a)].
19.06/19.01	5122 -real_normed_field(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),hAPP(B,fun(A,A),hAPP(fun(A,fun(B,A)),fun(B,fun(A,A)),combc(A,B,A),D),f342(B,A,D,E,F,C))),E),hAPP(B,A,hAPP(A,fun(B,A),F,E),f342(B,A,D,E,F,C)))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),hAPP(fun(B,bool),fun(A,A),hAPP(fun(A,fun(fun(B,bool),A)),fun(fun(B,bool),fun(A,A)),combc(A,fun(B,bool),A),hAPP(fun(A,fun(B,A)),fun(A,fun(fun(B,bool),A)),hAPP(fun(fun(B,A),fun(fun(B,bool),A)),fun(fun(A,fun(B,A)),fun(A,fun(fun(B,bool),A))),combb(fun(B,A),fun(fun(B,bool),A),A),big_co1399186613setsum(B,A)),D)),C)),E),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),hAPP(A,fun(B,A),F,E)),C))) # label(fact_4304_DERIV__setsum) # label(axiom).  [clausify(2076)].
19.06/19.04	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(A,fun(real,real),hAPP(fun(real,fun(A,real)),fun(A,fun(real,real)),combc(real,A,real),C),f342(A,real,C,D,E,B))),D),hAPP(A,real,hAPP(real,fun(A,real),E,D),f342(A,real,C,D,E,B)))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(fun(A,bool),fun(real,real),hAPP(fun(real,fun(fun(A,bool),real)),fun(fun(A,bool),fun(real,real)),combc(real,fun(A,bool),real),hAPP(fun(real,fun(A,real)),fun(real,fun(fun(A,bool),real)),hAPP(fun(fun(A,real),fun(fun(A,bool),real)),fun(fun(real,fun(A,real)),fun(real,fun(fun(A,bool),real))),combb(fun(A,real),fun(fun(A,bool),real),real),big_co1399186613setsum(A,real)),C)),B)),D),hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),hAPP(real,fun(A,real),E,D)),B))).  [resolve(5122,a,5076,a)].
19.06/19.04	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),hAPP(A,fun(complex,complex),hAPP(fun(complex,fun(A,complex)),fun(A,fun(complex,complex)),combc(complex,A,complex),C),f342(A,complex,C,D,E,B))),D),hAPP(A,complex,hAPP(complex,fun(A,complex),E,D),f342(A,complex,C,D,E,B)))) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),hAPP(fun(A,bool),fun(complex,complex),hAPP(fun(complex,fun(fun(A,bool),complex)),fun(fun(A,bool),fun(complex,complex)),combc(complex,fun(A,bool),complex),hAPP(fun(complex,fun(A,complex)),fun(complex,fun(fun(A,bool),complex)),hAPP(fun(fun(A,complex),fun(fun(A,bool),complex)),fun(fun(complex,fun(A,complex)),fun(complex,fun(fun(A,bool),complex))),combb(fun(A,complex),fun(fun(A,bool),complex),complex),big_co1399186613setsum(A,complex)),C)),B)),D),hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),hAPP(complex,fun(A,complex),E,D)),B))).  [resolve(5122,a,5103,a)].
19.06/19.04	5123 -real_normed_field(A) | zero_zero(A) = ti(A,B) | hAPP(A,real,norm_norm(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),B)) = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(A,real,norm_norm(A),C)),hAPP(A,real,norm_norm(A),B)) # label(fact_1790_nonzero__norm__divide) # label(axiom).  [clausify(2097)].
19.06/19.04	Derived: zero_zero(real) = ti(real,A) | hAPP(real,real,norm_norm(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),B),A)) = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,norm_norm(real),B)),hAPP(real,real,norm_norm(real),A)).  [resolve(5123,a,5076,a)].
19.06/19.04	Derived: zero_zero(complex) = ti(complex,A) | hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),B),A)) = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(complex,real,norm_norm(complex),B)),hAPP(complex,real,norm_norm(complex),A)).  [resolve(5123,a,5103,a)].
19.06/19.04	5124 -real_normed_field(A) | -hBOOL(hAPP(fun(nat,A),bool,summable(A),B)) | -hBOOL(hAPP(fun(nat,A),bool,summable(A),C)) | hBOOL(hAPP(fun(nat,A),bool,summable(A),hAPP(fun(nat,A),fun(nat,A),hAPP(fun(nat,fun(A,A)),fun(fun(nat,A),fun(nat,A)),combs(nat,A,A),hAPP(fun(nat,A),fun(nat,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(nat,A),fun(nat,fun(A,A))),combb(A,fun(A,A),nat),plus_plus(A)),B)),C))) # label(fact_4011_summable__add) # label(axiom).  [clausify(2159)].
19.06/19.04	Derived: -hBOOL(hAPP(fun(nat,real),bool,summable(real),A)) | -hBOOL(hAPP(fun(nat,real),bool,summable(real),B)) | hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),plus_plus(real)),A)),B))).  [resolve(5124,a,5076,a)].
19.06/19.04	Derived: -hBOOL(hAPP(fun(nat,complex),bool,summable(complex),A)) | -hBOOL(hAPP(fun(nat,complex),bool,summable(complex),B)) | hBOOL(hAPP(fun(nat,complex),bool,summable(complex),hAPP(fun(nat,complex),fun(nat,complex),hAPP(fun(nat,fun(complex,complex)),fun(fun(nat,complex),fun(nat,complex)),combs(nat,complex,complex),hAPP(fun(nat,complex),fun(nat,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(nat,complex),fun(nat,fun(complex,complex))),combb(complex,fun(complex,complex),nat),plus_plus(complex)),A)),B))).  [resolve(5124,a,5103,a)].
19.06/19.04	5125 -real_normed_field(A) | zero_zero(A) = ti(A,B) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(A,real,norm_norm(A),C)),D)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(A,real,norm_norm(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),B))),D)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(A,real,norm_norm(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),B)),E)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),C),E))),B)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(nat,A,semiring_1_of_nat(A),E)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),C),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),E),hAPP(nat,nat,suc,zero_zero(nat)))))))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,semiring_1_of_nat(real),E)),hAPP(nat,real,semiring_1_of_nat(real),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),E),hAPP(nat,nat,suc,zero_zero(nat)))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),D),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),E),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))),hAPP(A,real,norm_norm(A),B)))) # label(fact_1773_lemma__termdiff3) # label(axiom).  [clausify(2160)].
19.06/19.04	Derived: zero_zero(real) = ti(real,A) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,norm_norm(real),B)),C)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,norm_norm(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),B),A))),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,norm_norm(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),B),A)),D)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),B),D))),A)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,semiring_1_of_nat(real),D)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),D),hAPP(nat,nat,suc,zero_zero(nat)))))))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,semiring_1_of_nat(real),D)),hAPP(nat,real,semiring_1_of_nat(real),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),D),hAPP(nat,nat,suc,zero_zero(nat)))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),C),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),D),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))),hAPP(real,real,norm_norm(real),A)))).  [resolve(5125,a,5076,a)].
19.06/19.05	Derived: zero_zero(complex) = ti(complex,A) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(complex,real,norm_norm(complex),B)),C)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),B),A))),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),B),A)),D)),hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),B),D))),A)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(nat,complex,semiring_1_of_nat(complex),D)),hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),D),hAPP(nat,nat,suc,zero_zero(nat)))))))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,semiring_1_of_nat(real),D)),hAPP(nat,real,semiring_1_of_nat(real),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),D),hAPP(nat,nat,suc,zero_zero(nat)))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),C),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),D),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))),hAPP(complex,real,norm_norm(complex),A)))).  [resolve(5125,a,5103,a)].
19.06/19.05	5126 -real_normed_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),B),C),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),hAPP(nat,fun(A,A),hAPP(fun(A,fun(nat,A)),fun(nat,fun(A,A)),combc(A,nat,A),hAPP(fun(A,A),fun(A,fun(nat,A)),hAPP(fun(A,fun(nat,A)),fun(fun(A,A),fun(A,fun(nat,A))),combb(A,fun(nat,A),A),power_power(A)),B)),hAPP(nat,nat,suc,E))),C),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),one_one(A)),hAPP(nat,A,semiring_1_of_nat(A),E))),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),hAPP(A,A,B,C)),E))))) # label(fact_3887_DERIV__power__Suc) # label(axiom).  [clausify(2176)].
19.06/19.05	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),A),B),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(nat,fun(real,real),hAPP(fun(real,fun(nat,real)),fun(nat,fun(real,real)),combc(real,nat,real),hAPP(fun(real,real),fun(real,fun(nat,real)),hAPP(fun(real,fun(nat,real)),fun(fun(real,real),fun(real,fun(nat,real))),combb(real,fun(nat,real),real),power_power(real)),A)),hAPP(nat,nat,suc,D))),B),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),one_one(real)),hAPP(nat,real,semiring_1_of_nat(real),D))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,A,B)),D))))).  [resolve(5126,a,5076,a)].
19.06/19.05	Derived: -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),A),B),C)) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),hAPP(nat,fun(complex,complex),hAPP(fun(complex,fun(nat,complex)),fun(nat,fun(complex,complex)),combc(complex,nat,complex),hAPP(fun(complex,complex),fun(complex,fun(nat,complex)),hAPP(fun(complex,fun(nat,complex)),fun(fun(complex,complex),fun(complex,fun(nat,complex))),combb(complex,fun(nat,complex),complex),power_power(complex)),A)),hAPP(nat,nat,suc,D))),B),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),one_one(complex)),hAPP(nat,complex,semiring_1_of_nat(complex),D))),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),C),hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),hAPP(complex,complex,A,B)),D))))).  [resolve(5126,a,5103,a)].
19.06/19.07	5127 -real_normed_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),B),C),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),E),hAPP(A,A,B,C)),F)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),hAPP(fun(A,A),fun(A,A),hAPP(fun(A,A),fun(fun(A,A),fun(A,A)),combb(A,A,A),E),B)),C),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),F),D))) # label(fact_3862_DERIV__chain_H) # label(axiom).  [clausify(2199)].
19.06/19.07	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),A),B),C)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),D),hAPP(real,real,A,B)),E)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,real),fun(fun(real,real),fun(real,real)),combb(real,real,real),D),A)),B),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),E),C))).  [resolve(5127,a,5076,a)].
19.06/19.07	Derived: -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),A),B),C)) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),D),hAPP(complex,complex,A,B)),E)) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),hAPP(fun(complex,complex),fun(complex,complex),hAPP(fun(complex,complex),fun(fun(complex,complex),fun(complex,complex)),combb(complex,complex,complex),D),A)),B),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),E),C))).  [resolve(5127,a,5103,a)].
19.06/19.07	5128 -real_normed_field(A) | -hBOOL(hAPP(fun(nat,A),bool,summable(A),B)) | hBOOL(hAPP(fun(nat,A),bool,summable(A),hAPP(A,fun(nat,A),hAPP(fun(nat,fun(A,A)),fun(A,fun(nat,A)),combc(nat,A,A),hAPP(fun(nat,A),fun(nat,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(nat,A),fun(nat,fun(A,A))),combb(A,fun(A,A),nat),inverse_divide(A)),B)),C))) # label(fact_4008_divide_Osummable) # label(axiom).  [clausify(2208)].
19.06/19.07	Derived: -hBOOL(hAPP(fun(nat,real),bool,summable(real),A)) | hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(real,fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(real,fun(nat,real)),combc(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),inverse_divide(real)),A)),B))).  [resolve(5128,a,5076,a)].
19.06/19.07	Derived: -hBOOL(hAPP(fun(nat,complex),bool,summable(complex),A)) | hBOOL(hAPP(fun(nat,complex),bool,summable(complex),hAPP(complex,fun(nat,complex),hAPP(fun(nat,fun(complex,complex)),fun(complex,fun(nat,complex)),combc(nat,complex,complex),hAPP(fun(nat,complex),fun(nat,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(nat,complex),fun(nat,fun(complex,complex))),combb(complex,fun(complex,complex),nat),inverse_divide(complex)),A)),B))).  [resolve(5128,a,5103,a)].
19.06/19.07	5129 -real_normed_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),B),C),D)) | hBOOL(hAPP(filter(A),bool,hAPP(A,fun(filter(A),bool),hAPP(fun(A,A),fun(A,fun(filter(A),bool)),tendsto(A,A),hAPP(fun(A,A),fun(A,A),hAPP(fun(A,fun(A,A)),fun(fun(A,A),fun(A,A)),combs(A,A,A),hAPP(fun(A,A),fun(A,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(A,A),fun(A,fun(A,A))),combb(A,fun(A,A),A),inverse_divide(A)),hAPP(A,fun(A,A),hAPP(fun(A,fun(A,A)),fun(A,fun(A,A)),combc(A,A,A),hAPP(fun(A,A),fun(A,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(A,A),fun(A,fun(A,A))),combb(A,fun(A,A),A),minus_minus(A)),hAPP(fun(A,A),fun(A,A),hAPP(fun(A,A),fun(fun(A,A),fun(A,A)),combb(A,A,A),B),hAPP(A,fun(A,A),plus_plus(A),C)))),hAPP(A,A,B,C)))),combi(A))),D),hAPP(A,filter(A),at(A),zero_zero(A)))) # label(fact_4619_DERIV__iff) # label(axiom).  [clausify(2226)].
19.06/19.08	5130 -real_normed_field(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),B),C),D)) | -hBOOL(hAPP(filter(A),bool,hAPP(A,fun(filter(A),bool),hAPP(fun(A,A),fun(A,fun(filter(A),bool)),tendsto(A,A),hAPP(fun(A,A),fun(A,A),hAPP(fun(A,fun(A,A)),fun(fun(A,A),fun(A,A)),combs(A,A,A),hAPP(fun(A,A),fun(A,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(A,A),fun(A,fun(A,A))),combb(A,fun(A,A),A),inverse_divide(A)),hAPP(A,fun(A,A),hAPP(fun(A,fun(A,A)),fun(A,fun(A,A)),combc(A,A,A),hAPP(fun(A,A),fun(A,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(A,A),fun(A,fun(A,A))),combb(A,fun(A,A),A),minus_minus(A)),hAPP(fun(A,A),fun(A,A),hAPP(fun(A,A),fun(fun(A,A),fun(A,A)),combb(A,A,A),B),hAPP(A,fun(A,A),plus_plus(A),C)))),hAPP(A,A,B,C)))),combi(A))),D),hAPP(A,filter(A),at(A),zero_zero(A)))) # label(fact_4619_DERIV__iff) # label(axiom).  [clausify(2226)].
19.06/19.08	Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),A),B),C)) | -hBOOL(hAPP(filter(real),bool,hAPP(real,fun(filter(real),bool),hAPP(fun(real,real),fun(real,fun(filter(real),bool)),tendsto(real,real),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,real)),combs(real,real,real),hAPP(fun(real,real),fun(real,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,fun(real,real))),combb(real,fun(real,real),real),inverse_divide(real)),hAPP(real,fun(real,real),hAPP(fun(real,fun(real,real)),fun(real,fun(real,real)),combc(real,real,real),hAPP(fun(real,real),fun(real,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,fun(real,real))),combb(real,fun(real,real),real),minus_minus(real)),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,real),fun(fun(real,real),fun(real,real)),combb(real,real,real),A),hAPP(real,fun(real,real),plus_plus(real),B)))),hAPP(real,real,A,B)))),combi(real))),C),hAPP(real,filter(real),at(real),zero_zero(real)))).  [resolve(5130,a,5076,a)].
19.06/19.08	Derived: hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),A),B),C)) | -hBOOL(hAPP(filter(complex),bool,hAPP(complex,fun(filter(complex),bool),hAPP(fun(complex,complex),fun(complex,fun(filter(complex),bool)),tendsto(complex,complex),hAPP(fun(complex,complex),fun(complex,complex),hAPP(fun(complex,fun(complex,complex)),fun(fun(complex,complex),fun(complex,complex)),combs(complex,complex,complex),hAPP(fun(complex,complex),fun(complex,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(complex,complex),fun(complex,fun(complex,complex))),combb(complex,fun(complex,complex),complex),inverse_divide(complex)),hAPP(complex,fun(complex,complex),hAPP(fun(complex,fun(complex,complex)),fun(complex,fun(complex,complex)),combc(complex,complex,complex),hAPP(fun(complex,complex),fun(complex,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(complex,complex),fun(complex,fun(complex,complex))),combb(complex,fun(complex,complex),complex),minus_minus(complex)),hAPP(fun(complex,complex),fun(complex,complex),hAPP(fun(complex,complex),fun(fun(complex,complex),fun(complex,complex)),combb(complex,complex,complex),A),hAPP(complex,fun(complex,complex),plus_plus(complex),B)))),hAPP(complex,complex,A,B)))),combi(complex))),C),hAPP(complex,filter(complex),at(complex),zero_zero(complex)))).  [resolve(5130,a,5103,a)].
19.06/19.08	5131 -real_normed_field(A) | -hBOOL(hAPP(A,bool,hAPP(fun(nat,A),fun(A,bool),sums(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(fun(nat,A),fun(A,bool),sums(A),hAPP(fun(nat,A),fun(nat,A),hAPP(fun(A,A),fun(fun(nat,A),fun(nat,A)),combb(A,A,nat),uminus_uminus(A)),B)),hAPP(A,A,uminus_uminus(A),C))) # label(fact_4083_sums__minus) # label(axiom).  [clausify(2229)].
19.21/19.23	Derived: -hBOOL(hAPP(real,bool,hAPP(fun(nat,real),fun(real,bool),sums(real),A),B)) | hBOOL(hAPP(real,bool,hAPP(fun(nat,real),fun(real,bool),sums(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),uminus_uminus(real)),A)),hAPP(real,real,uminus_uminus(real),B))).  [resolve(5131,a,5076,a)].
19.21/19.23	Derived: -hBOOL(hAPP(complex,bool,hAPP(fun(nat,complex),fun(complex,bool),sums(complex),A),B)) | hBOOL(hAPP(complex,bool,hAPP(fun(nat,complex),fun(complex,bool),sums(complex),hAPP(fun(nat,complex),fun(nat,complex),hAPP(fun(complex,complex),fun(fun(nat,complex),fun(nat,complex)),combb(complex,complex,nat),uminus_uminus(complex)),A)),hAPP(complex,complex,uminus_uminus(complex),B))).  [resolve(5131,a,5103,a)].
19.21/19.23	5132 -field_inverse_zero(A) | -real_normed_field(A) | hAPP(A,real,norm_norm(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)) = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(A,real,norm_norm(A),B)),hAPP(A,real,norm_norm(A),C)) # label(fact_1783_norm__divide) # label(axiom).  [clausify(2282)].
19.21/19.23	Derived: -field_inverse_zero(real) | hAPP(real,real,norm_norm(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B)) = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,norm_norm(real),A)),hAPP(real,real,norm_norm(real),B)).  [resolve(5132,b,5076,a)].
19.21/19.23	Derived: -field_inverse_zero(complex) | hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),A),B)) = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(complex,real,norm_norm(complex),A)),hAPP(complex,real,norm_norm(complex),B)).  [resolve(5132,b,5103,a)].
19.21/19.23	5133 -banach(A) | -real_normed_field(A) | hBOOL(hAPP(A,bool,hAPP(fun(nat,A),fun(A,bool),sums(A),hAPP(fun(nat,A),fun(nat,A),hAPP(fun(nat,fun(A,A)),fun(fun(nat,A),fun(nat,A)),combs(nat,A,A),hAPP(fun(nat,real),fun(nat,fun(A,A)),hAPP(fun(real,fun(A,A)),fun(fun(nat,real),fun(nat,fun(A,A))),combb(real,fun(A,A),nat),scaleR_scaleR(A)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),inverse_inverse(real)),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),fact_fact(nat))))),hAPP(A,fun(nat,A),power_power(A),B))),hAPP(A,A,exp(A),B))) # label(fact_4752_exp__converges) # label(axiom).  [clausify(2352)].
19.21/19.23	Derived: -banach(real) | hBOOL(hAPP(real,bool,hAPP(fun(nat,real),fun(real,bool),sums(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),scaleR_scaleR(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),inverse_inverse(real)),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),fact_fact(nat))))),hAPP(real,fun(nat,real),power_power(real),A))),hAPP(real,real,exp(real),A))).  [resolve(5133,b,5076,a)].
19.21/19.23	Derived: -banach(complex) | hBOOL(hAPP(complex,bool,hAPP(fun(nat,complex),fun(complex,bool),sums(complex),hAPP(fun(nat,complex),fun(nat,complex),hAPP(fun(nat,fun(complex,complex)),fun(fun(nat,complex),fun(nat,complex)),combs(nat,complex,complex),hAPP(fun(nat,real),fun(nat,fun(complex,complex)),hAPP(fun(real,fun(complex,complex)),fun(fun(nat,real),fun(nat,fun(complex,complex))),combb(real,fun(complex,complex),nat),scaleR_scaleR(complex)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),inverse_inverse(real)),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),fact_fact(nat))))),hAPP(complex,fun(nat,complex),power_power(complex),A))),hAPP(complex,complex,exp(complex),A))).  [resolve(5133,b,5103,a)].
19.43/19.38	5134 -real_normed_field(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),combi(A)),B),one_one(A))) # label(fact_3839_DERIV__ident) # label(axiom).  [clausify(2367)].
19.43/19.38	Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),combi(real)),A),one_one(real))).  [resolve(5134,a,5076,a)].
19.43/19.38	Derived: hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),combi(complex)),A),one_one(complex))).  [resolve(5134,a,5103,a)].
19.43/19.38	5135 -real_normed_field(A) | -hBOOL(hAPP(fun(nat,A),bool,summable(A),B)) | hBOOL(hAPP(fun(nat,A),bool,summable(A),hAPP(A,fun(nat,A),hAPP(fun(nat,fun(A,A)),fun(A,fun(nat,A)),combc(nat,A,A),hAPP(fun(nat,A),fun(nat,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(nat,A),fun(nat,fun(A,A))),combb(A,fun(A,A),nat),inverse_divide(A)),B)),C))) # label(fact_4009_summable__divide) # label(axiom).  [clausify(2450)].
19.43/19.38	5136 -real_normed_field(A) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),hAPP(A,fun(B,A),hAPP(fun(B,fun(A,A)),fun(A,fun(B,A)),combc(B,A,A),hAPP(fun(B,A),fun(B,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(B,A),fun(B,fun(A,A))),combb(A,fun(A,A),B),inverse_divide(A)),C)),D)),E) = hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),C),E)),D) # label(fact_4184_divide_Osetsum) # label(axiom).  [clausify(2517)].
19.43/19.38	Derived: hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),hAPP(real,fun(A,real),hAPP(fun(A,fun(real,real)),fun(real,fun(A,real)),combc(A,real,real),hAPP(fun(A,real),fun(A,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(A,real),fun(A,fun(real,real))),combb(real,fun(real,real),A),inverse_divide(real)),B)),C)),D) = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),B),D)),C).  [resolve(5136,a,5076,a)].
19.43/19.38	Derived: hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),hAPP(complex,fun(A,complex),hAPP(fun(A,fun(complex,complex)),fun(complex,fun(A,complex)),combc(A,complex,complex),hAPP(fun(A,complex),fun(A,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(A,complex),fun(A,fun(complex,complex))),combb(complex,fun(complex,complex),A),inverse_divide(complex)),B)),C)),D) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),B),D)),C).  [resolve(5136,a,5103,a)].
19.43/19.38	5137 -real_normed_field(A) | -hBOOL(hAPP(fun(nat,A),bool,cauchy(A),B)) | hBOOL(hAPP(fun(nat,A),bool,cauchy(A),hAPP(A,fun(nat,A),hAPP(fun(nat,fun(A,A)),fun(A,fun(nat,A)),combc(nat,A,A),hAPP(fun(nat,A),fun(nat,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(nat,A),fun(nat,fun(A,A))),combb(A,fun(A,A),nat),inverse_divide(A)),B)),C))) # label(fact_4102_divide_OCauchy) # label(axiom).  [clausify(2609)].
19.43/19.38	Derived: -hBOOL(hAPP(fun(nat,real),bool,cauchy(real),A)) | hBOOL(hAPP(fun(nat,real),bool,cauchy(real),hAPP(real,fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(real,fun(nat,real)),combc(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),inverse_divide(real)),A)),B))).  [resolve(5137,a,5076,a)].
19.43/19.38	Derived: -hBOOL(hAPP(fun(nat,complex),bool,cauchy(complex),A)) | hBOOL(hAPP(fun(nat,complex),bool,cauchy(complex),hAPP(complex,fun(nat,complex),hAPP(fun(nat,fun(complex,complex)),fun(complex,fun(nat,complex)),combc(nat,complex,complex),hAPP(fun(nat,complex),fun(nat,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(nat,complex),fun(nat,fun(complex,complex))),combb(complex,fun(complex,complex),nat),inverse_divide(complex)),A)),B))).  [resolve(5137,a,5103,a)].
19.43/19.38	5138 -banach(A) | -real_normed_field(A) | hAPP(A,A,exp(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,exp(A),B)),hAPP(A,A,exp(A),C)) # label(fact_2585_exp__add) # label(axiom).  [clausify(2622)].
19.52/19.54	Derived: -banach(real) | hAPP(real,real,exp(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),B)) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,exp(real),A)),hAPP(real,real,exp(real),B)).  [resolve(5138,b,5076,a)].
19.52/19.54	Derived: -banach(complex) | hAPP(complex,complex,exp(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),A),B)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,exp(complex),A)),hAPP(complex,complex,exp(complex),B)).  [resolve(5138,b,5103,a)].
19.52/19.54	5139 -real_normed_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),B),hAPP(A,A,C,D)),E)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),C),D),F)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),hAPP(fun(A,A),fun(A,A),hAPP(fun(A,A),fun(fun(A,A),fun(A,A)),combb(A,A,A),B),C)),D),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),E),F))) # label(fact_3861_DERIV__chain2) # label(axiom).  [clausify(2648)].
19.52/19.54	5140 -real_normed_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),B),C),D)) | hBOOL(hAPP(A,bool,hAPP(fun(A,A),fun(A,bool),isCont(A,A),B),C)) # label(fact_4886_DERIV__isCont) # label(axiom).  [clausify(2658)].
19.52/19.54	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),A),B),C)) | hBOOL(hAPP(real,bool,hAPP(fun(real,real),fun(real,bool),isCont(real,real),A),B)).  [resolve(5140,a,5076,a)].
19.52/19.54	Derived: -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),A),B),C)) | hBOOL(hAPP(complex,bool,hAPP(fun(complex,complex),fun(complex,bool),isCont(complex,complex),A),B)).  [resolve(5140,a,5103,a)].
19.52/19.54	5141 -real_normed_field(A) | -banach(A) | hBOOL(hAPP(A,bool,hAPP(fun(A,A),fun(A,bool),isCont(A,A),exp(A)),B)) # label(fact_4891_isCont__exp) # label(axiom).  [clausify(2784)].
19.52/19.54	Derived: -banach(real) | hBOOL(hAPP(real,bool,hAPP(fun(real,real),fun(real,bool),isCont(real,real),exp(real)),A)).  [resolve(5141,a,5076,a)].
19.52/19.54	Derived: -banach(complex) | hBOOL(hAPP(complex,bool,hAPP(fun(complex,complex),fun(complex,bool),isCont(complex,complex),exp(complex)),A)).  [resolve(5141,a,5103,a)].
19.52/19.54	5142 -real_normed_field(A) | -hBOOL(hAPP(filter(B),bool,hAPP(A,fun(filter(B),bool),hAPP(fun(B,A),fun(A,fun(filter(B),bool)),tendsto(B,A),C),D),E)) | -hBOOL(hAPP(filter(B),bool,hAPP(A,fun(filter(B),bool),hAPP(fun(B,A),fun(A,fun(filter(B),bool)),tendsto(B,A),F),V6),E)) | zero_zero(A) = ti(A,V6) | hBOOL(hAPP(filter(B),bool,hAPP(A,fun(filter(B),bool),hAPP(fun(B,A),fun(A,fun(filter(B),bool)),tendsto(B,A),hAPP(fun(B,A),fun(B,A),hAPP(fun(B,fun(A,A)),fun(fun(B,A),fun(B,A)),combs(B,A,A),hAPP(fun(B,A),fun(B,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(B,A),fun(B,fun(A,A))),combb(A,fun(A,A),B),inverse_divide(A)),C)),F)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),V6)),E)) # label(fact_4452_tendsto__divide) # label(axiom).  [clausify(2904)].
19.52/19.54	Derived: -hBOOL(hAPP(filter(A),bool,hAPP(real,fun(filter(A),bool),hAPP(fun(A,real),fun(real,fun(filter(A),bool)),tendsto(A,real),B),C),D)) | -hBOOL(hAPP(filter(A),bool,hAPP(real,fun(filter(A),bool),hAPP(fun(A,real),fun(real,fun(filter(A),bool)),tendsto(A,real),E),F),D)) | zero_zero(real) = ti(real,F) | hBOOL(hAPP(filter(A),bool,hAPP(real,fun(filter(A),bool),hAPP(fun(A,real),fun(real,fun(filter(A),bool)),tendsto(A,real),hAPP(fun(A,real),fun(A,real),hAPP(fun(A,fun(real,real)),fun(fun(A,real),fun(A,real)),combs(A,real,real),hAPP(fun(A,real),fun(A,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(A,real),fun(A,fun(real,real))),combb(real,fun(real,real),A),inverse_divide(real)),B)),E)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),C),F)),D)).  [resolve(5142,a,5076,a)].
19.52/19.54	Derived: -hBOOL(hAPP(filter(A),bool,hAPP(complex,fun(filter(A),bool),hAPP(fun(A,complex),fun(complex,fun(filter(A),bool)),tendsto(A,complex),B),C),D)) | -hBOOL(hAPP(filter(A),bool,hAPP(complex,fun(filter(A),bool),hAPP(fun(A,complex),fun(complex,fun(filter(A),bool)),tendsto(A,complex),E),F),D)) | zero_zero(complex) = ti(complex,F) | hBOOL(hAPP(filter(A),bool,hAPP(complex,fun(filter(A),bool),hAPP(fun(A,complex),fun(complex,fun(filter(A),bool)),tendsto(A,complex),hAPP(fun(A,complex),fun(A,complex),hAPP(fun(A,fun(complex,complex)),fun(fun(A,complex),fun(A,complex)),combs(A,complex,complex),hAPP(fun(A,complex),fun(A,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(A,complex),fun(A,fun(complex,complex))),combb(complex,fun(complex,complex),A),inverse_divide(complex)),B)),E)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),C),F)),D)).  [resolve(5142,a,5103,a)].
19.67/19.68	5143 -banach(A) | -real_normed_field(A) | hAPP(A,A,exp(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,exp(A),B)),hAPP(A,A,exp(A),C)) # label(fact_2586_mult__exp__exp) # label(axiom).  [clausify(3087)].
19.67/19.68	5144 -real_normed_field(A) | zero_zero(A) = ti(A,B) | zero_zero(A) = ti(A,C) | hAPP(A,A,uminus_uminus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,inverse_inverse(A),B)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C)),D))),hAPP(A,A,inverse_inverse(A),C))) = hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(A,A,inverse_inverse(A),B)),hAPP(A,A,inverse_inverse(A),C))),D) # label(fact_2620_DERIV__inverse__lemma) # label(axiom).  [clausify(3105)].
19.67/19.68	Derived: zero_zero(real) = ti(real,A) | zero_zero(real) = ti(real,B) | hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,inverse_inverse(real),A)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),B)),C))),hAPP(real,real,inverse_inverse(real),B))) = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,inverse_inverse(real),A)),hAPP(real,real,inverse_inverse(real),B))),C).  [resolve(5144,a,5076,a)].
19.67/19.68	Derived: zero_zero(complex) = ti(complex,A) | zero_zero(complex) = ti(complex,B) | hAPP(complex,complex,uminus_uminus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,inverse_inverse(complex),A)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),A),B)),C))),hAPP(complex,complex,inverse_inverse(complex),B))) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),hAPP(complex,complex,inverse_inverse(complex),A)),hAPP(complex,complex,inverse_inverse(complex),B))),C).  [resolve(5144,a,5103,a)].
19.67/19.68	5145 -banach(A) | -real_normed_field(A) | -hBOOL(hAPP(fun(nat,A),bool,summable(A),hAPP(fun(nat,A),fun(nat,A),hAPP(fun(nat,fun(A,A)),fun(fun(nat,A),fun(nat,A)),combs(nat,A,A),hAPP(fun(nat,A),fun(nat,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(nat,A),fun(nat,fun(A,A))),combb(A,fun(A,A),nat),times_times(A)),hAPP(fun(nat,A),fun(nat,A),diffs(A),hAPP(fun(nat,A),fun(nat,A),diffs(A),B)))),hAPP(A,fun(nat,A),power_power(A),C)))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(A,real,norm_norm(A),D)),hAPP(A,real,norm_norm(A),C))) | hBOOL(hAPP(filter(A),bool,hAPP(A,fun(filter(A),bool),hAPP(fun(A,A),fun(A,fun(filter(A),bool)),tendsto(A,A),hAPP(fun(A,fun(nat,A)),fun(A,A),hAPP(fun(fun(nat,A),A),fun(fun(A,fun(nat,A)),fun(A,A)),combb(fun(nat,A),A,A),suminf(A)),hAPP(fun(A,fun(nat,A)),fun(A,fun(nat,A)),hAPP(fun(fun(nat,A),fun(nat,A)),fun(fun(A,fun(nat,A)),fun(A,fun(nat,A))),combb(fun(nat,A),fun(nat,A),A),hAPP(fun(nat,fun(A,A)),fun(fun(nat,A),fun(nat,A)),combs(nat,A,A),hAPP(fun(nat,A),fun(nat,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(nat,A),fun(nat,fun(A,A))),combb(A,fun(A,A),nat),times_times(A)),B))),hAPP(fun(nat,A),fun(A,fun(nat,A)),hAPP(fun(A,fun(fun(nat,A),fun(nat,A))),fun(fun(nat,A),fun(A,fun(nat,A))),combc(A,fun(nat,A),fun(nat,A)),hAPP(fun(A,fun(nat,fun(A,A))),fun(A,fun(fun(nat,A),fun(nat,A))),hAPP(fun(fun(nat,fun(A,A)),fun(fun(nat,A),fun(nat,A))),fun(fun(A,fun(nat,fun(A,A))),fun(A,fun(fun(nat,A),fun(nat,A)))),combb(fun(nat,fun(A,A)),fun(fun(nat,A),fun(nat,A)),A),combs(nat,A,A)),hAPP(fun(A,fun(nat,A)),fun(A,fun(nat,fun(A,A))),hAPP(fun(fun(nat,A),fun(nat,fun(A,A))),fun(fun(A,fun(nat,A)),fun(A,fun(nat,fun(A,A)))),combb(fun(nat,A),fun(nat,fun(A,A)),A),hAPP(fun(A,fun(A,A)),fun(fun(nat,A),fun(nat,fun(A,A))),combb(A,fun(A,A),nat),minus_minus(A))),hAPP(fun(A,A),fun(A,fun(nat,A)),hAPP(fun(A,fun(A,fun(nat,A))),fun(fun(A,A),fun(A,fun(nat,A))),combs(A,A,fun(nat,A)),hAPP(fun(A,fun(nat,fun(A,A))),fun(A,fun(A,fun(nat,A))),hAPP(fun(fun(nat,fun(A,A)),fun(A,fun(nat,A))),fun(fun(A,fun(nat,fun(A,A))),fun(A,fun(A,fun(nat,A)))),combb(fun(nat,fun(A,A)),fun(A,fun(nat,A)),A),combc(nat,A,A)),hAPP(fun(A,fun(nat,A)),fun(A,fun(nat,fun(A,A))),hAPP(fun(fun(nat,A),fun(nat,fun(A,A))),fun(fun(A,fun(nat,A)),fun(A,fun(nat,fun(A,A)))),combb(fun(nat,A),fun(nat,fun(A,A)),A),hAPP(fun(A,fun(A,A)),fun(fun(nat,A),fun(nat,fun(A,A))),combb(A,fun(A,A),nat),inverse_divide(A))),hAPP(fun(nat,A),fun(A,fun(nat,A)),hAPP(fun(A,fun(fun(nat,A),fun(nat,A))),fun(fun(nat,A),fun(A,fun(nat,A))),combc(A,fun(nat,A),fun(nat,A)),hAPP(fun(A,fun(nat,fun(A,A))),fun(A,fun(fun(nat,A),fun(nat,A))),hAPP(fun(fun(nat,fun(A,A)),fun(fun(nat,A),fun(nat,A))),fun(fun(A,fun(nat,fun(A,A))),fun(A,fun(fun(nat,A),fun(nat,A)))),combb(fun(nat,fun(A,A)),fun(fun(nat,A),fun(nat,A)),A),combs(nat,A,A)),hAPP(fun(A,fun(nat,A)),fun(A,fun(nat,fun(A,A))),hAPP(fun(fun(nat,A),fun(nat,fun(A,A))),fun(fun(A,fun(nat,A)),fun(A,fun(nat,fun(A,A)))),combb(fun(nat,A),fun(nat,fun(A,A)),A),hAPP(fun(A,fun(A,A)),fun(fun(nat,A),fun(nat,fun(A,A))),combb(A,fun(A,A),nat),minus_minus(A))),hAPP(fun(A,A),fun(A,fun(nat,A)),hAPP(fun(A,fun(nat,A)),fun(fun(A,A),fun(A,fun(nat,A))),combb(A,fun(nat,A),A),power_power(A)),hAPP(A,fun(A,A),plus_plus(A),D))))),hAPP(A,fun(nat,A),power_power(A),D))))),combi(A))))),hAPP(fun(nat,A),fun(nat,A),hAPP(fun(nat,fun(A,A)),fun(fun(nat,A),fun(nat,A)),combs(nat,A,A),hAPP(fun(nat,A),fun(nat,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(nat,A),fun(nat,fun(A,A))),combb(A,fun(A,A),nat),times_times(A)),semiring_1_of_nat(A))),hAPP(fun(nat,nat),fun(nat,A),hAPP(fun(nat,A),fun(fun(nat,nat),fun(nat,A)),combb(nat,A,nat),hAPP(A,fun(nat,A),power_power(A),D)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),minus_minus(nat)),hAPP(nat,nat,suc,zero_zero(nat))))))))),zero_zero(A)),hAPP(A,filter(A),at(A),zero_zero(A)))) # label(fact_4532_termdiffs__aux) # label(axiom).  [clausify(3140)].
19.67/19.68	Derived: -banach(real) | -hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(fun(nat,real),fun(nat,real),diffs(real),hAPP(fun(nat,real),fun(nat,real),diffs(real),A)))),hAPP(real,fun(nat,real),power_power(real),B)))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,norm_norm(real),C)),hAPP(real,real,norm_norm(real),B))) | hBOOL(hAPP(filter(real),bool,hAPP(real,fun(filter(real),bool),hAPP(fun(real,real),fun(real,fun(filter(real),bool)),tendsto(real,real),hAPP(fun(real,fun(nat,real)),fun(real,real),hAPP(fun(fun(nat,real),real),fun(fun(real,fun(nat,real)),fun(real,real)),combb(fun(nat,real),real,real),suminf(real)),hAPP(fun(real,fun(nat,real)),fun(real,fun(nat,real)),hAPP(fun(fun(nat,real),fun(nat,real)),fun(fun(real,fun(nat,real)),fun(real,fun(nat,real))),combb(fun(nat,real),fun(nat,real),real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),A))),hAPP(fun(nat,real),fun(real,fun(nat,real)),hAPP(fun(real,fun(fun(nat,real),fun(nat,real))),fun(fun(nat,real),fun(real,fun(nat,real))),combc(real,fun(nat,real),fun(nat,real)),hAPP(fun(real,fun(nat,fun(real,real))),fun(real,fun(fun(nat,real),fun(nat,real))),hAPP(fun(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real))),fun(fun(real,fun(nat,fun(real,real))),fun(real,fun(fun(nat,real),fun(nat,real)))),combb(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),real),combs(nat,real,real)),hAPP(fun(real,fun(nat,real)),fun(real,fun(nat,fun(real,real))),hAPP(fun(fun(nat,real),fun(nat,fun(real,real))),fun(fun(real,fun(nat,real)),fun(real,fun(nat,fun(real,real)))),combb(fun(nat,real),fun(nat,fun(real,real)),real),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),minus_minus(real))),hAPP(fun(real,real),fun(real,fun(nat,real)),hAPP(fun(real,fun(real,fun(nat,real))),fun(fun(real,real),fun(real,fun(nat,real))),combs(real,real,fun(nat,real)),hAPP(fun(real,fun(nat,fun(real,real))),fun(real,fun(real,fun(nat,real))),hAPP(fun(fun(nat,fun(real,real)),fun(real,fun(nat,real))),fun(fun(real,fun(nat,fun(real,real))),fun(real,fun(real,fun(nat,real)))),combb(fun(nat,fun(real,real)),fun(real,fun(nat,real)),real),combc(nat,real,real)),hAPP(fun(real,fun(nat,real)),fun(real,fun(nat,fun(real,real))),hAPP(fun(fun(nat,real),fun(nat,fun(real,real))),fun(fun(real,fun(nat,real)),fun(real,fun(nat,fun(real,real)))),combb(fun(nat,real),fun(nat,fun(real,real)),real),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),inverse_divide(real))),hAPP(fun(nat,real),fun(real,fun(nat,real)),hAPP(fun(real,fun(fun(nat,real),fun(nat,real))),fun(fun(nat,real),fun(real,fun(nat,real))),combc(real,fun(nat,real),fun(nat,real)),hAPP(fun(real,fun(nat,fun(real,real))),fun(real,fun(fun(nat,real),fun(nat,real))),hAPP(fun(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real))),fun(fun(real,fun(nat,fun(real,real))),fun(real,fun(fun(nat,real),fun(nat,real)))),combb(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),real),combs(nat,real,real)),hAPP(fun(real,fun(nat,real)),fun(real,fun(nat,fun(real,real))),hAPP(fun(fun(nat,real),fun(nat,fun(real,real))),fun(fun(real,fun(nat,real)),fun(real,fun(nat,fun(real,real)))),combb(fun(nat,real),fun(nat,fun(real,real)),real),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),minus_minus(real))),hAPP(fun(real,real),fun(real,fun(nat,real)),hAPP(fun(real,fun(nat,real)),fun(fun(real,real),fun(real,fun(nat,real))),combb(real,fun(nat,real),real),power_power(real)),hAPP(real,fun(real,real),plus_plus(real),C))))),hAPP(real,fun(nat,real),power_power(real),C))))),combi(real))))),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),semiring_1_of_nat(real))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),hAPP(real,fun(nat,real),power_power(real),C)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),minus_minus(nat)),hAPP(nat,nat,suc,zero_zero(nat))))))))),zero_zero(real)),hAPP(real,filter(real),at(real),zero_zero(real)))).  [resolve(5145,b,5076,a)].
19.67/19.68	Derived: -banach(complex) | -hBOOL(hAPP(fun(nat,complex),bool,summable(complex),hAPP(fun(nat,complex),fun(nat,complex),hAPP(fun(nat,fun(complex,complex)),fun(fun(nat,complex),fun(nat,complex)),combs(nat,complex,complex),hAPP(fun(nat,complex),fun(nat,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(nat,complex),fun(nat,fun(complex,complex))),combb(complex,fun(complex,complex),nat),times_times(complex)),hAPP(fun(nat,complex),fun(nat,complex),diffs(complex),hAPP(fun(nat,complex),fun(nat,complex),diffs(complex),A)))),hAPP(complex,fun(nat,complex),power_power(complex),B)))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(complex,real,norm_norm(complex),C)),hAPP(complex,real,norm_norm(complex),B))) | hBOOL(hAPP(filter(complex),bool,hAPP(complex,fun(filter(complex),bool),hAPP(fun(complex,complex),fun(complex,fun(filter(complex),bool)),tendsto(complex,complex),hAPP(fun(complex,fun(nat,complex)),fun(complex,complex),hAPP(fun(fun(nat,complex),complex),fun(fun(complex,fun(nat,complex)),fun(complex,complex)),combb(fun(nat,complex),complex,complex),suminf(complex)),hAPP(fun(complex,fun(nat,complex)),fun(complex,fun(nat,complex)),hAPP(fun(fun(nat,complex),fun(nat,complex)),fun(fun(complex,fun(nat,complex)),fun(complex,fun(nat,complex))),combb(fun(nat,complex),fun(nat,complex),complex),hAPP(fun(nat,fun(complex,complex)),fun(fun(nat,complex),fun(nat,complex)),combs(nat,complex,complex),hAPP(fun(nat,complex),fun(nat,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(nat,complex),fun(nat,fun(complex,complex))),combb(complex,fun(complex,complex),nat),times_times(complex)),A))),hAPP(fun(nat,complex),fun(complex,fun(nat,complex)),hAPP(fun(complex,fun(fun(nat,complex),fun(nat,complex))),fun(fun(nat,complex),fun(complex,fun(nat,complex))),combc(complex,fun(nat,complex),fun(nat,complex)),hAPP(fun(complex,fun(nat,fun(complex,complex))),fun(complex,fun(fun(nat,complex),fun(nat,complex))),hAPP(fun(fun(nat,fun(complex,complex)),fun(fun(nat,complex),fun(nat,complex))),fun(fun(complex,fun(nat,fun(complex,complex))),fun(complex,fun(fun(nat,complex),fun(nat,complex)))),combb(fun(nat,fun(complex,complex)),fun(fun(nat,complex),fun(nat,complex)),complex),combs(nat,complex,complex)),hAPP(fun(complex,fun(nat,complex)),fun(complex,fun(nat,fun(complex,complex))),hAPP(fun(fun(nat,complex),fun(nat,fun(complex,complex))),fun(fun(complex,fun(nat,complex)),fun(complex,fun(nat,fun(complex,complex)))),combb(fun(nat,complex),fun(nat,fun(complex,complex)),complex),hAPP(fun(complex,fun(complex,complex)),fun(fun(nat,complex),fun(nat,fun(complex,complex))),combb(complex,fun(complex,complex),nat),minus_minus(complex))),hAPP(fun(complex,complex),fun(complex,fun(nat,complex)),hAPP(fun(complex,fun(complex,fun(nat,complex))),fun(fun(complex,complex),fun(complex,fun(nat,complex))),combs(complex,complex,fun(nat,complex)),hAPP(fun(complex,fun(nat,fun(complex,complex))),fun(complex,fun(complex,fun(nat,complex))),hAPP(fun(fun(nat,fun(complex,complex)),fun(complex,fun(nat,complex))),fun(fun(complex,fun(nat,fun(complex,complex))),fun(complex,fun(complex,fun(nat,complex)))),combb(fun(nat,fun(complex,complex)),fun(complex,fun(nat,complex)),complex),combc(nat,complex,complex)),hAPP(fun(complex,fun(nat,complex)),fun(complex,fun(nat,fun(complex,complex))),hAPP(fun(fun(nat,complex),fun(nat,fun(complex,complex))),fun(fun(complex,fun(nat,complex)),fun(complex,fun(nat,fun(complex,complex)))),combb(fun(nat,complex),fun(nat,fun(complex,complex)),complex),hAPP(fun(complex,fun(complex,complex)),fun(fun(nat,complex),fun(nat,fun(complex,complex))),combb(complex,fun(complex,complex),nat),inverse_divide(complex))),hAPP(fun(nat,complex),fun(complex,fun(nat,complex)),hAPP(fun(complex,fun(fun(nat,complex),fun(nat,complex))),fun(fun(nat,complex),fun(complex,fun(nat,complex))),combc(complex,fun(nat,complex),fun(nat,complex)),hAPP(fun(complex,fun(nat,fun(complex,complex))),fun(complex,fun(fun(nat,complex),fun(nat,complex))),hAPP(fun(fun(nat,fun(complex,complex)),fun(fun(nat,complex),fun(nat,complex))),fun(fun(complex,fun(nat,fun(complex,complex))),fun(complex,fun(fun(nat,complex),fun(nat,complex)))),combb(fun(nat,fun(complex,complex)),fun(fun(nat,complex),fun(nat,complex)),complex),combs(nat,complex,complex)),hAPP(fun(complex,fun(nat,complex)),fun(complex,fun(nat,fun(complex,complex))),hAPP(fun(fun(nat,complex),fun(nat,fun(complex,complex))),fun(fun(complex,fun(nat,complex)),fun(complex,fun(nat,fun(complex,complex)))),combb(fun(nat,complex),fun(nat,fun(complex,complex)),complex),hAPP(fun(complex,fun(complex,complex)),fun(fun(nat,complex),fun(nat,fun(complex,complex))),combb(complex,fun(complex,complex),nat),minus_minus(complex))),hAPP(fun(complex,complex),fun(complex,fun(nat,complex)),hAPP(fun(complex,fun(nat,complex)),fun(fun(complex,complex),fun(complex,fun(nat,complex))),combb(complex,fun(nat,complex),complex),power_power(complex)),hAPP(complex,fun(complex,complex),plus_plus(complex),C))))),hAPP(complex,fun(nat,complex),power_power(complex),C))))),combi(complex))))),hAPP(fun(nat,complex),fun(nat,complex),hAPP(fun(nat,fun(complex,complex)),fun(fun(nat,complex),fun(nat,complex)),combs(nat,complex,complex),hAPP(fun(nat,complex),fun(nat,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(nat,complex),fun(nat,fun(complex,complex))),combb(complex,fun(complex,complex),nat),times_times(complex)),semiring_1_of_nat(complex))),hAPP(fun(nat,nat),fun(nat,complex),hAPP(fun(nat,complex),fun(fun(nat,nat),fun(nat,complex)),combb(nat,complex,nat),hAPP(complex,fun(nat,complex),power_power(complex),C)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),minus_minus(nat)),hAPP(nat,nat,suc,zero_zero(nat))))))))),zero_zero(complex)),hAPP(complex,filter(complex),at(complex),zero_zero(complex)))).  [resolve(5145,b,5103,a)].
19.82/19.79	5146 -real_normed_field(A) | -banach(A) | zero_zero(A) != hAPP(A,A,exp(A),B) # label(fact_2537_exp__not__eq__zero) # label(axiom).  [clausify(3149)].
19.82/19.79	Derived: -banach(real) | zero_zero(real) != hAPP(real,real,exp(real),A).  [resolve(5146,a,5076,a)].
19.82/19.79	Derived: -banach(complex) | zero_zero(complex) != hAPP(complex,complex,exp(complex),A).  [resolve(5146,a,5103,a)].
19.82/19.79	5147 -real_normed_field(A) | -banach(B) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),C)) | -hBOOL(hAPP(fun(nat,real),bool,summable(real),D)) | zero_zero(A) != ti(A,f577(B,A,E,D,C)) | hBOOL(hAPP(filter(A),bool,hAPP(B,fun(filter(A),bool),hAPP(fun(A,B),fun(B,fun(filter(A),bool)),tendsto(A,B),hAPP(fun(A,fun(nat,B)),fun(A,B),hAPP(fun(fun(nat,B),B),fun(fun(A,fun(nat,B)),fun(A,B)),combb(fun(nat,B),B,A),suminf(B)),E)),zero_zero(B)),hAPP(A,filter(A),at(A),zero_zero(A)))) # label(fact_4625_lemma__termdiff5) # label(axiom).  [clausify(3310)].
19.82/19.79	Derived: -banach(A) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B)) | -hBOOL(hAPP(fun(nat,real),bool,summable(real),C)) | zero_zero(real) != ti(real,f577(A,real,D,C,B)) | hBOOL(hAPP(filter(real),bool,hAPP(A,fun(filter(real),bool),hAPP(fun(real,A),fun(A,fun(filter(real),bool)),tendsto(real,A),hAPP(fun(real,fun(nat,A)),fun(real,A),hAPP(fun(fun(nat,A),A),fun(fun(real,fun(nat,A)),fun(real,A)),combb(fun(nat,A),A,real),suminf(A)),D)),zero_zero(A)),hAPP(real,filter(real),at(real),zero_zero(real)))).  [resolve(5147,a,5076,a)].
19.82/19.79	Derived: -banach(A) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B)) | -hBOOL(hAPP(fun(nat,real),bool,summable(real),C)) | zero_zero(complex) != ti(complex,f577(A,complex,D,C,B)) | hBOOL(hAPP(filter(complex),bool,hAPP(A,fun(filter(complex),bool),hAPP(fun(complex,A),fun(A,fun(filter(complex),bool)),tendsto(complex,A),hAPP(fun(complex,fun(nat,A)),fun(complex,A),hAPP(fun(fun(nat,A),A),fun(fun(complex,fun(nat,A)),fun(complex,A)),combb(fun(nat,A),A,complex),suminf(A)),D)),zero_zero(A)),hAPP(complex,filter(complex),at(complex),zero_zero(complex)))).  [resolve(5147,a,5103,a)].
19.82/19.79	5148 -real_normed_field(A) | -banach(B) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),C)) | -hBOOL(hAPP(fun(nat,real),bool,summable(real),D)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(A,real,norm_norm(A),f577(B,A,E,D,C))),C)) | hBOOL(hAPP(filter(A),bool,hAPP(B,fun(filter(A),bool),hAPP(fun(A,B),fun(B,fun(filter(A),bool)),tendsto(A,B),hAPP(fun(A,fun(nat,B)),fun(A,B),hAPP(fun(fun(nat,B),B),fun(fun(A,fun(nat,B)),fun(A,B)),combb(fun(nat,B),B,A),suminf(B)),E)),zero_zero(B)),hAPP(A,filter(A),at(A),zero_zero(A)))) # label(fact_4625_lemma__termdiff5) # label(axiom).  [clausify(3310)].
19.92/19.85	Derived: -banach(A) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B)) | -hBOOL(hAPP(fun(nat,real),bool,summable(real),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,norm_norm(real),f577(A,real,D,C,B))),B)) | hBOOL(hAPP(filter(real),bool,hAPP(A,fun(filter(real),bool),hAPP(fun(real,A),fun(A,fun(filter(real),bool)),tendsto(real,A),hAPP(fun(real,fun(nat,A)),fun(real,A),hAPP(fun(fun(nat,A),A),fun(fun(real,fun(nat,A)),fun(real,A)),combb(fun(nat,A),A,real),suminf(A)),D)),zero_zero(A)),hAPP(real,filter(real),at(real),zero_zero(real)))).  [resolve(5148,a,5076,a)].
19.92/19.85	Derived: -banach(A) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B)) | -hBOOL(hAPP(fun(nat,real),bool,summable(real),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(complex,real,norm_norm(complex),f577(A,complex,D,C,B))),B)) | hBOOL(hAPP(filter(complex),bool,hAPP(A,fun(filter(complex),bool),hAPP(fun(complex,A),fun(A,fun(filter(complex),bool)),tendsto(complex,A),hAPP(fun(complex,fun(nat,A)),fun(complex,A),hAPP(fun(fun(nat,A),A),fun(fun(complex,fun(nat,A)),fun(complex,A)),combb(fun(nat,A),A,complex),suminf(A)),D)),zero_zero(A)),hAPP(complex,filter(complex),at(complex),zero_zero(complex)))).  [resolve(5148,a,5103,a)].
19.92/19.85	5149 -real_normed_field(A) | -banach(B) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),C)) | -hBOOL(hAPP(fun(nat,real),bool,summable(real),D)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(B,real,norm_norm(B),hAPP(nat,B,hAPP(A,fun(nat,B),E,f577(B,A,E,D,C)),f578(B,A,E,D,C)))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,D,f578(B,A,E,D,C))),hAPP(A,real,norm_norm(A),f577(B,A,E,D,C))))) | hBOOL(hAPP(filter(A),bool,hAPP(B,fun(filter(A),bool),hAPP(fun(A,B),fun(B,fun(filter(A),bool)),tendsto(A,B),hAPP(fun(A,fun(nat,B)),fun(A,B),hAPP(fun(fun(nat,B),B),fun(fun(A,fun(nat,B)),fun(A,B)),combb(fun(nat,B),B,A),suminf(B)),E)),zero_zero(B)),hAPP(A,filter(A),at(A),zero_zero(A)))) # label(fact_4625_lemma__termdiff5) # label(axiom).  [clausify(3310)].
19.92/19.85	Derived: -banach(A) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B)) | -hBOOL(hAPP(fun(nat,real),bool,summable(real),C)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(A,real,norm_norm(A),hAPP(nat,A,hAPP(real,fun(nat,A),D,f577(A,real,D,C,B)),f578(A,real,D,C,B)))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,C,f578(A,real,D,C,B))),hAPP(real,real,norm_norm(real),f577(A,real,D,C,B))))) | hBOOL(hAPP(filter(real),bool,hAPP(A,fun(filter(real),bool),hAPP(fun(real,A),fun(A,fun(filter(real),bool)),tendsto(real,A),hAPP(fun(real,fun(nat,A)),fun(real,A),hAPP(fun(fun(nat,A),A),fun(fun(real,fun(nat,A)),fun(real,A)),combb(fun(nat,A),A,real),suminf(A)),D)),zero_zero(A)),hAPP(real,filter(real),at(real),zero_zero(real)))).  [resolve(5149,a,5076,a)].
19.92/19.85	Derived: -banach(A) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B)) | -hBOOL(hAPP(fun(nat,real),bool,summable(real),C)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(A,real,norm_norm(A),hAPP(nat,A,hAPP(complex,fun(nat,A),D,f577(A,complex,D,C,B)),f578(A,complex,D,C,B)))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,C,f578(A,complex,D,C,B))),hAPP(complex,real,norm_norm(complex),f577(A,complex,D,C,B))))) | hBOOL(hAPP(filter(complex),bool,hAPP(A,fun(filter(complex),bool),hAPP(fun(complex,A),fun(A,fun(filter(complex),bool)),tendsto(complex,A),hAPP(fun(complex,fun(nat,A)),fun(complex,A),hAPP(fun(fun(nat,A),A),fun(fun(complex,fun(nat,A)),fun(complex,A)),combb(fun(nat,A),A,complex),suminf(A)),D)),zero_zero(A)),hAPP(complex,filter(complex),at(complex),zero_zero(complex)))).  [resolve(5149,a,5103,a)].
19.92/19.85	5150 -real_normed_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),B),C),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),E),C),F)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),hAPP(fun(A,A),fun(A,A),hAPP(fun(A,fun(A,A)),fun(fun(A,A),fun(A,A)),combs(A,A,A),hAPP(fun(A,A),fun(A,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(A,A),fun(A,fun(A,A))),combb(A,fun(A,A),A),times_times(A)),B)),E)),C),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,B,C)),F)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),hAPP(A,A,E,C))))) # label(fact_3818_DERIV__mult_H) # label(axiom).  [clausify(3390)].
19.92/19.88	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),A),B),C)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),D),B),E)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,real)),combs(real,real,real),hAPP(fun(real,real),fun(real,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,fun(real,real))),combb(real,fun(real,real),real),times_times(real)),A)),D)),B),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,A,B)),E)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),hAPP(real,real,D,B))))).  [resolve(5150,a,5076,a)].
19.92/19.88	Derived: -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),A),B),C)) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),D),B),E)) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),hAPP(fun(complex,complex),fun(complex,complex),hAPP(fun(complex,fun(complex,complex)),fun(fun(complex,complex),fun(complex,complex)),combs(complex,complex,complex),hAPP(fun(complex,complex),fun(complex,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(complex,complex),fun(complex,fun(complex,complex))),combb(complex,fun(complex,complex),complex),times_times(complex)),A)),D)),B),hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,A,B)),E)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),C),hAPP(complex,complex,D,B))))).  [resolve(5150,a,5103,a)].
19.92/19.88	5151 -real_normed_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),B),C),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),hAPP(A,fun(A,A),hAPP(fun(A,fun(A,A)),fun(A,fun(A,A)),combc(A,A,A),hAPP(fun(A,A),fun(A,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(A,A),fun(A,fun(A,A))),combb(A,fun(A,A),A),inverse_divide(A)),B)),E)),C),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),E))) # label(fact_3836_DERIV__cdivide) # label(axiom).  [clausify(3433)].
19.92/19.88	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),A),B),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(real,fun(real,real),hAPP(fun(real,fun(real,real)),fun(real,fun(real,real)),combc(real,real,real),hAPP(fun(real,real),fun(real,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,fun(real,real))),combb(real,fun(real,real),real),inverse_divide(real)),A)),D)),B),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),C),D))).  [resolve(5151,a,5076,a)].
19.92/19.88	Derived: -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),A),B),C)) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),hAPP(complex,fun(complex,complex),hAPP(fun(complex,fun(complex,complex)),fun(complex,fun(complex,complex)),combc(complex,complex,complex),hAPP(fun(complex,complex),fun(complex,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(complex,complex),fun(complex,fun(complex,complex))),combb(complex,fun(complex,complex),complex),inverse_divide(complex)),A)),D)),B),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),C),D))).  [resolve(5151,a,5103,a)].
20.02/20.01	5152 -banach(A) | -real_normed_field(A) | exp(A) = ti(fun(A,A),exp(A)) # label(tsy_c_Transcendental_Oexp_res) # label(axiom).  [clausify(3494)].
20.02/20.01	Derived: -banach(real) | exp(real) = ti(fun(real,real),exp(real)).  [resolve(5152,b,5076,a)].
20.02/20.01	Derived: -banach(complex) | exp(complex) = ti(fun(complex,complex),exp(complex)).  [resolve(5152,b,5103,a)].
20.02/20.01	5153 -real_normed_field(A) | -real_normed_vector(B) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),C)) | zero_zero(A) != ti(A,f638(B,A,D,E,C)) | hBOOL(hAPP(filter(A),bool,hAPP(B,fun(filter(A),bool),hAPP(fun(A,B),fun(B,fun(filter(A),bool)),tendsto(A,B),D),zero_zero(B)),hAPP(A,filter(A),at(A),zero_zero(A)))) # label(fact_4626_lemma__termdiff4) # label(axiom).  [clausify(3624)].
20.02/20.01	Derived: -real_normed_vector(A) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B)) | zero_zero(real) != ti(real,f638(A,real,C,D,B)) | hBOOL(hAPP(filter(real),bool,hAPP(A,fun(filter(real),bool),hAPP(fun(real,A),fun(A,fun(filter(real),bool)),tendsto(real,A),C),zero_zero(A)),hAPP(real,filter(real),at(real),zero_zero(real)))).  [resolve(5153,a,5076,a)].
20.02/20.01	Derived: -real_normed_vector(A) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B)) | zero_zero(complex) != ti(complex,f638(A,complex,C,D,B)) | hBOOL(hAPP(filter(complex),bool,hAPP(A,fun(filter(complex),bool),hAPP(fun(complex,A),fun(A,fun(filter(complex),bool)),tendsto(complex,A),C),zero_zero(A)),hAPP(complex,filter(complex),at(complex),zero_zero(complex)))).  [resolve(5153,a,5103,a)].
20.02/20.01	5154 -real_normed_field(A) | -real_normed_vector(B) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(A,real,norm_norm(A),f638(B,A,D,E,C))),C)) | hBOOL(hAPP(filter(A),bool,hAPP(B,fun(filter(A),bool),hAPP(fun(A,B),fun(B,fun(filter(A),bool)),tendsto(A,B),D),zero_zero(B)),hAPP(A,filter(A),at(A),zero_zero(A)))) # label(fact_4626_lemma__termdiff4) # label(axiom).  [clausify(3624)].
20.02/20.01	Derived: -real_normed_vector(A) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,norm_norm(real),f638(A,real,C,D,B))),B)) | hBOOL(hAPP(filter(real),bool,hAPP(A,fun(filter(real),bool),hAPP(fun(real,A),fun(A,fun(filter(real),bool)),tendsto(real,A),C),zero_zero(A)),hAPP(real,filter(real),at(real),zero_zero(real)))).  [resolve(5154,a,5076,a)].
20.02/20.01	Derived: -real_normed_vector(A) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(complex,real,norm_norm(complex),f638(A,complex,C,D,B))),B)) | hBOOL(hAPP(filter(complex),bool,hAPP(A,fun(filter(complex),bool),hAPP(fun(complex,A),fun(A,fun(filter(complex),bool)),tendsto(complex,A),C),zero_zero(A)),hAPP(complex,filter(complex),at(complex),zero_zero(complex)))).  [resolve(5154,a,5103,a)].
20.02/20.01	5155 -real_normed_field(A) | -real_normed_vector(B) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),C)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(B,real,norm_norm(B),hAPP(A,B,D,f638(B,A,D,E,C)))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),E),hAPP(A,real,norm_norm(A),f638(B,A,D,E,C))))) | hBOOL(hAPP(filter(A),bool,hAPP(B,fun(filter(A),bool),hAPP(fun(A,B),fun(B,fun(filter(A),bool)),tendsto(A,B),D),zero_zero(B)),hAPP(A,filter(A),at(A),zero_zero(A)))) # label(fact_4626_lemma__termdiff4) # label(axiom).  [clausify(3624)].
20.02/20.01	Derived: -real_normed_vector(A) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(A,real,norm_norm(A),hAPP(real,A,C,f638(A,real,C,D,B)))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),D),hAPP(real,real,norm_norm(real),f638(A,real,C,D,B))))) | hBOOL(hAPP(filter(real),bool,hAPP(A,fun(filter(real),bool),hAPP(fun(real,A),fun(A,fun(filter(real),bool)),tendsto(real,A),C),zero_zero(A)),hAPP(real,filter(real),at(real),zero_zero(real)))).  [resolve(5155,a,5076,a)].
20.17/20.13	Derived: -real_normed_vector(A) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(A,real,norm_norm(A),hAPP(complex,A,C,f638(A,complex,C,D,B)))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),D),hAPP(complex,real,norm_norm(complex),f638(A,complex,C,D,B))))) | hBOOL(hAPP(filter(complex),bool,hAPP(A,fun(filter(complex),bool),hAPP(fun(complex,A),fun(A,fun(filter(complex),bool)),tendsto(complex,A),C),zero_zero(A)),hAPP(complex,filter(complex),at(complex),zero_zero(complex)))).  [resolve(5155,a,5103,a)].
20.17/20.13	5156 -real_normed_field(A) | -banach(A) | hAPP(A,A,exp(A),hAPP(real,A,of_real(A),B)) = hAPP(real,A,of_real(A),hAPP(real,real,exp(real),B)) # label(fact_2799_exp__of__real) # label(axiom).  [clausify(3672)].
20.17/20.13	Derived: -banach(real) | hAPP(real,real,exp(real),hAPP(real,real,of_real(real),A)) = hAPP(real,real,of_real(real),hAPP(real,real,exp(real),A)).  [resolve(5156,a,5076,a)].
20.17/20.13	Derived: -banach(complex) | hAPP(complex,complex,exp(complex),hAPP(real,complex,of_real(complex),A)) = hAPP(real,complex,of_real(complex),hAPP(real,real,exp(real),A)).  [resolve(5156,a,5103,a)].
20.17/20.13	5157 -real_normed_field(A) | -hBOOL(hAPP(filter(A),bool,hAPP(A,fun(filter(A),bool),hAPP(fun(A,A),fun(A,fun(filter(A),bool)),tendsto(A,A),hAPP(fun(A,A),fun(A,A),hAPP(fun(A,fun(A,A)),fun(fun(A,A),fun(A,A)),combs(A,A,A),hAPP(fun(A,A),fun(A,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(A,A),fun(A,fun(A,A))),combb(A,fun(A,A),A),inverse_divide(A)),hAPP(A,fun(A,A),hAPP(fun(A,fun(A,A)),fun(A,fun(A,A)),combc(A,A,A),hAPP(fun(A,A),fun(A,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(A,A),fun(A,fun(A,A))),combb(A,fun(A,A),A),minus_minus(A)),B)),hAPP(A,A,B,C)))),hAPP(A,fun(A,A),hAPP(fun(A,fun(A,A)),fun(A,fun(A,A)),combc(A,A,A),minus_minus(A)),C))),D),hAPP(A,filter(A),at(A),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),B),C),D)) # label(fact_4601_DERIV__iff2) # label(axiom).  [clausify(3771)].
20.17/20.13	Derived: -hBOOL(hAPP(filter(real),bool,hAPP(real,fun(filter(real),bool),hAPP(fun(real,real),fun(real,fun(filter(real),bool)),tendsto(real,real),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,real)),combs(real,real,real),hAPP(fun(real,real),fun(real,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,fun(real,real))),combb(real,fun(real,real),real),inverse_divide(real)),hAPP(real,fun(real,real),hAPP(fun(real,fun(real,real)),fun(real,fun(real,real)),combc(real,real,real),hAPP(fun(real,real),fun(real,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,fun(real,real))),combb(real,fun(real,real),real),minus_minus(real)),A)),hAPP(real,real,A,B)))),hAPP(real,fun(real,real),hAPP(fun(real,fun(real,real)),fun(real,fun(real,real)),combc(real,real,real),minus_minus(real)),B))),C),hAPP(real,filter(real),at(real),B))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),A),B),C)).  [resolve(5157,a,5076,a)].
20.17/20.13	Derived: -hBOOL(hAPP(filter(complex),bool,hAPP(complex,fun(filter(complex),bool),hAPP(fun(complex,complex),fun(complex,fun(filter(complex),bool)),tendsto(complex,complex),hAPP(fun(complex,complex),fun(complex,complex),hAPP(fun(complex,fun(complex,complex)),fun(fun(complex,complex),fun(complex,complex)),combs(complex,complex,complex),hAPP(fun(complex,complex),fun(complex,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(complex,complex),fun(complex,fun(complex,complex))),combb(complex,fun(complex,complex),complex),inverse_divide(complex)),hAPP(complex,fun(complex,complex),hAPP(fun(complex,fun(complex,complex)),fun(complex,fun(complex,complex)),combc(complex,complex,complex),hAPP(fun(complex,complex),fun(complex,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(complex,complex),fun(complex,fun(complex,complex))),combb(complex,fun(complex,complex),complex),minus_minus(complex)),A)),hAPP(complex,complex,A,B)))),hAPP(complex,fun(complex,complex),hAPP(fun(complex,fun(complex,complex)),fun(complex,fun(complex,complex)),combc(complex,complex,complex),minus_minus(complex)),B))),C),hAPP(complex,filter(complex),at(complex),B))) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),A),B),C)).  [resolve(5157,a,5103,a)].
20.17/20.13	5158 -real_normed_field(A) | hBOOL(hAPP(filter(A),bool,hAPP(A,fun(filter(A),bool),hAPP(fun(A,A),fun(A,fun(filter(A),bool)),tendsto(A,A),hAPP(fun(A,A),fun(A,A),hAPP(fun(A,fun(A,A)),fun(fun(A,A),fun(A,A)),combs(A,A,A),hAPP(fun(A,A),fun(A,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(A,A),fun(A,fun(A,A))),combb(A,fun(A,A),A),inverse_divide(A)),hAPP(A,fun(A,A),hAPP(fun(A,fun(A,A)),fun(A,fun(A,A)),combc(A,A,A),hAPP(fun(A,A),fun(A,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(A,A),fun(A,fun(A,A))),combb(A,fun(A,A),A),minus_minus(A)),B)),hAPP(A,A,B,C)))),hAPP(A,fun(A,A),hAPP(fun(A,fun(A,A)),fun(A,fun(A,A)),combc(A,A,A),minus_minus(A)),C))),D),hAPP(A,filter(A),at(A),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),B),C),D)) # label(fact_4601_DERIV__iff2) # label(axiom).  [clausify(3771)].
20.17/20.13	Derived: hBOOL(hAPP(filter(real),bool,hAPP(real,fun(filter(real),bool),hAPP(fun(real,real),fun(real,fun(filter(real),bool)),tendsto(real,real),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,real)),combs(real,real,real),hAPP(fun(real,real),fun(real,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,fun(real,real))),combb(real,fun(real,real),real),inverse_divide(real)),hAPP(real,fun(real,real),hAPP(fun(real,fun(real,real)),fun(real,fun(real,real)),combc(real,real,real),hAPP(fun(real,real),fun(real,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,fun(real,real))),combb(real,fun(real,real),real),minus_minus(real)),A)),hAPP(real,real,A,B)))),hAPP(real,fun(real,real),hAPP(fun(real,fun(real,real)),fun(real,fun(real,real)),combc(real,real,real),minus_minus(real)),B))),C),hAPP(real,filter(real),at(real),B))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),A),B),C)).  [resolve(5158,a,5076,a)].
20.17/20.13	Derived: hBOOL(hAPP(filter(complex),bool,hAPP(complex,fun(filter(complex),bool),hAPP(fun(complex,complex),fun(complex,fun(filter(complex),bool)),tendsto(complex,complex),hAPP(fun(complex,complex),fun(complex,complex),hAPP(fun(complex,fun(complex,complex)),fun(fun(complex,complex),fun(complex,complex)),combs(complex,complex,complex),hAPP(fun(complex,complex),fun(complex,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(complex,complex),fun(complex,fun(complex,complex))),combb(complex,fun(complex,complex),complex),inverse_divide(complex)),hAPP(complex,fun(complex,complex),hAPP(fun(complex,fun(complex,complex)),fun(complex,fun(complex,complex)),combc(complex,complex,complex),hAPP(fun(complex,complex),fun(complex,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(complex,complex),fun(complex,fun(complex,complex))),combb(complex,fun(complex,complex),complex),minus_minus(complex)),A)),hAPP(complex,complex,A,B)))),hAPP(complex,fun(complex,complex),hAPP(fun(complex,fun(complex,complex)),fun(complex,fun(complex,complex)),combc(complex,complex,complex),minus_minus(complex)),B))),C),hAPP(complex,filter(complex),at(complex),B))) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),A),B),C)).  [resolve(5158,a,5103,a)].
20.17/20.13	5159 -real_normed_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),B),C),D)) | zero_zero(A) = hAPP(A,A,B,C) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),hAPP(fun(A,A),fun(A,A),hAPP(fun(A,A),fun(fun(A,A),fun(A,A)),combb(A,A,A),inverse_inverse(A)),B)),C),hAPP(A,A,uminus_uminus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,inverse_inverse(A),hAPP(A,A,B,C))),D)),hAPP(A,A,inverse_inverse(A),hAPP(A,A,B,C)))))) # label(fact_3877_DERIV__inverse_H) # label(axiom).  [clausify(3781)].
20.22/20.16	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),A),B),C)) | zero_zero(real) = hAPP(real,real,A,B) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,real),fun(fun(real,real),fun(real,real)),combb(real,real,real),inverse_inverse(real)),A)),B),hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,inverse_inverse(real),hAPP(real,real,A,B))),C)),hAPP(real,real,inverse_inverse(real),hAPP(real,real,A,B)))))).  [resolve(5159,a,5076,a)].
20.22/20.16	Derived: -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),A),B),C)) | zero_zero(complex) = hAPP(complex,complex,A,B) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),hAPP(fun(complex,complex),fun(complex,complex),hAPP(fun(complex,complex),fun(fun(complex,complex),fun(complex,complex)),combb(complex,complex,complex),inverse_inverse(complex)),A)),B),hAPP(complex,complex,uminus_uminus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,inverse_inverse(complex),hAPP(complex,complex,A,B))),C)),hAPP(complex,complex,inverse_inverse(complex),hAPP(complex,complex,A,B)))))).  [resolve(5159,a,5103,a)].
20.22/20.16	5160 -real_normed_field(A) | -banach(A) | hAPP(fun(nat,A),A,suminf(A),hAPP(fun(nat,A),fun(nat,A),hAPP(fun(nat,fun(A,A)),fun(fun(nat,A),fun(nat,A)),combs(nat,A,A),hAPP(fun(nat,real),fun(nat,fun(A,A)),hAPP(fun(real,fun(A,A)),fun(fun(nat,real),fun(nat,fun(A,A))),combb(real,fun(A,A),nat),scaleR_scaleR(A)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),inverse_inverse(real)),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),fact_fact(nat))))),hAPP(A,fun(nat,A),power_power(A),B))) = hAPP(A,A,exp(A),B) # label(fact_4750_lemma__exp__ext) # label(axiom).  [clausify(3801)].
20.22/20.16	5161 -real_normed_field(A) | -hBOOL(hAPP(fun(nat,A),bool,summable(A),B)) | -hBOOL(hAPP(fun(nat,A),bool,summable(A),C)) | hAPP(fun(nat,A),A,suminf(A),hAPP(fun(nat,A),fun(nat,A),hAPP(fun(nat,fun(A,A)),fun(fun(nat,A),fun(nat,A)),combs(nat,A,A),hAPP(fun(nat,A),fun(nat,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(nat,A),fun(nat,fun(A,A))),combb(A,fun(A,A),nat),minus_minus(A)),B)),C)) = hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(fun(nat,A),A,suminf(A),B)),hAPP(fun(nat,A),A,suminf(A),C)) # label(fact_3982_suminf__diff) # label(axiom).  [clausify(3809)].
20.22/20.16	Derived: -hBOOL(hAPP(fun(nat,real),bool,summable(real),A)) | -hBOOL(hAPP(fun(nat,real),bool,summable(real),B)) | hAPP(fun(nat,real),real,suminf(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),minus_minus(real)),A)),B)) = hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(fun(nat,real),real,suminf(real),A)),hAPP(fun(nat,real),real,suminf(real),B)).  [resolve(5161,a,5076,a)].
20.22/20.16	Derived: -hBOOL(hAPP(fun(nat,complex),bool,summable(complex),A)) | -hBOOL(hAPP(fun(nat,complex),bool,summable(complex),B)) | hAPP(fun(nat,complex),complex,suminf(complex),hAPP(fun(nat,complex),fun(nat,complex),hAPP(fun(nat,fun(complex,complex)),fun(fun(nat,complex),fun(nat,complex)),combs(nat,complex,complex),hAPP(fun(nat,complex),fun(nat,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(nat,complex),fun(nat,fun(complex,complex))),combb(complex,fun(complex,complex),nat),minus_minus(complex)),A)),B)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),hAPP(fun(nat,complex),complex,suminf(complex),A)),hAPP(fun(nat,complex),complex,suminf(complex),B)).  [resolve(5161,a,5103,a)].
20.45/20.44	5162 -real_normed_field(A) | -hBOOL(hAPP(fun(nat,A),bool,summable(A),B)) | hAPP(fun(nat,A),A,suminf(A),hAPP(A,fun(nat,A),hAPP(fun(nat,fun(A,A)),fun(A,fun(nat,A)),combc(nat,A,A),hAPP(fun(nat,A),fun(nat,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(nat,A),fun(nat,fun(A,A))),combb(A,fun(A,A),nat),inverse_divide(A)),B)),C)) = hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),hAPP(fun(nat,A),A,suminf(A),B)),C) # label(fact_3984_suminf__divide) # label(axiom).  [clausify(3818)].
20.45/20.44	5163 -real_normed_field(A) | -hBOOL(hAPP(filter(nat),bool,hAPP(A,fun(filter(nat),bool),hAPP(fun(nat,A),fun(A,fun(filter(nat),bool)),tendsto(nat,A),B),C),sequentially)) | hBOOL(hAPP(filter(nat),bool,hAPP(A,fun(filter(nat),bool),hAPP(fun(nat,A),fun(A,fun(filter(nat),bool)),tendsto(nat,A),hAPP(A,fun(nat,A),hAPP(fun(nat,fun(A,A)),fun(A,fun(nat,A)),combc(nat,A,A),hAPP(fun(nat,A),fun(nat,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(nat,A),fun(nat,fun(A,A))),combb(A,fun(A,A),nat),inverse_divide(A)),B)),D)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),D)),sequentially)) # label(fact_4449_divide_OLIMSEQ) # label(axiom).  [clausify(3912)].
20.45/20.44	Derived: -hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),A),B),sequentially)) | hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),hAPP(real,fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(real,fun(nat,real)),combc(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),inverse_divide(real)),A)),C)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),B),C)),sequentially)).  [resolve(5163,a,5076,a)].
20.45/20.44	Derived: -hBOOL(hAPP(filter(nat),bool,hAPP(complex,fun(filter(nat),bool),hAPP(fun(nat,complex),fun(complex,fun(filter(nat),bool)),tendsto(nat,complex),A),B),sequentially)) | hBOOL(hAPP(filter(nat),bool,hAPP(complex,fun(filter(nat),bool),hAPP(fun(nat,complex),fun(complex,fun(filter(nat),bool)),tendsto(nat,complex),hAPP(complex,fun(nat,complex),hAPP(fun(nat,fun(complex,complex)),fun(complex,fun(nat,complex)),combc(nat,complex,complex),hAPP(fun(nat,complex),fun(nat,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(nat,complex),fun(nat,fun(complex,complex))),combb(complex,fun(complex,complex),nat),inverse_divide(complex)),A)),C)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),B),C)),sequentially)).  [resolve(5163,a,5103,a)].
20.45/20.44	5164 -real_normed_field(A) | -hBOOL(hAPP(fun(nat,A),bool,summable(A),B)) | -hBOOL(hAPP(fun(nat,A),bool,summable(A),C)) | hBOOL(hAPP(fun(nat,A),bool,summable(A),hAPP(fun(nat,A),fun(nat,A),hAPP(fun(nat,fun(A,A)),fun(fun(nat,A),fun(nat,A)),combs(nat,A,A),hAPP(fun(nat,A),fun(nat,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(nat,A),fun(nat,fun(A,A))),combb(A,fun(A,A),nat),minus_minus(A)),B)),C))) # label(fact_4012_summable__diff) # label(axiom).  [clausify(4008)].
20.45/20.44	Derived: -hBOOL(hAPP(fun(nat,real),bool,summable(real),A)) | -hBOOL(hAPP(fun(nat,real),bool,summable(real),B)) | hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),minus_minus(real)),A)),B))).  [resolve(5164,a,5076,a)].
20.45/20.44	Derived: -hBOOL(hAPP(fun(nat,complex),bool,summable(complex),A)) | -hBOOL(hAPP(fun(nat,complex),bool,summable(complex),B)) | hBOOL(hAPP(fun(nat,complex),bool,summable(complex),hAPP(fun(nat,complex),fun(nat,complex),hAPP(fun(nat,fun(complex,complex)),fun(fun(nat,complex),fun(nat,complex)),combs(nat,complex,complex),hAPP(fun(nat,complex),fun(nat,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(nat,complex),fun(nat,fun(complex,complex))),combb(complex,fun(complex,complex),nat),minus_minus(complex)),A)),B))).  [resolve(5164,a,5103,a)].
20.63/20.55	5165 -real_normed_field(A) | -hBOOL(hAPP(A,bool,hAPP(fun(nat,A),fun(A,bool),sums(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(fun(nat,A),fun(A,bool),sums(A),hAPP(A,fun(nat,A),hAPP(fun(nat,fun(A,A)),fun(A,fun(nat,A)),combc(nat,A,A),hAPP(fun(nat,A),fun(nat,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(nat,A),fun(nat,fun(A,A))),combb(A,fun(A,A),nat),inverse_divide(A)),B)),D)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),D))) # label(fact_4085_divide_Osums) # label(axiom).  [clausify(4068)].
20.63/20.55	Derived: -hBOOL(hAPP(real,bool,hAPP(fun(nat,real),fun(real,bool),sums(real),A),B)) | hBOOL(hAPP(real,bool,hAPP(fun(nat,real),fun(real,bool),sums(real),hAPP(real,fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(real,fun(nat,real)),combc(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),inverse_divide(real)),A)),C)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),B),C))).  [resolve(5165,a,5076,a)].
20.63/20.55	Derived: -hBOOL(hAPP(complex,bool,hAPP(fun(nat,complex),fun(complex,bool),sums(complex),A),B)) | hBOOL(hAPP(complex,bool,hAPP(fun(nat,complex),fun(complex,bool),sums(complex),hAPP(complex,fun(nat,complex),hAPP(fun(nat,fun(complex,complex)),fun(complex,fun(nat,complex)),combc(nat,complex,complex),hAPP(fun(nat,complex),fun(nat,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(nat,complex),fun(nat,fun(complex,complex))),combb(complex,fun(complex,complex),nat),inverse_divide(complex)),A)),C)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),B),C))).  [resolve(5165,a,5103,a)].
20.63/20.55	5166 -real_normed_field(A) | -banach(A) | hAPP(A,A,exp(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C)) = hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),hAPP(A,A,exp(A),B)),hAPP(A,A,exp(A),C)) # label(fact_2589_exp__diff) # label(axiom).  [clausify(4096)].
20.63/20.55	Derived: -banach(real) | hAPP(real,real,exp(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),B)) = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,exp(real),A)),hAPP(real,real,exp(real),B)).  [resolve(5166,a,5076,a)].
20.63/20.55	Derived: -banach(complex) | hAPP(complex,complex,exp(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),A),B)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),hAPP(complex,complex,exp(complex),A)),hAPP(complex,complex,exp(complex),B)).  [resolve(5166,a,5103,a)].
20.63/20.55	5167 -topological_space(A) | -real_normed_field(B) | -hBOOL(hAPP(filter(A),bool,hAPP(B,fun(filter(A),bool),hAPP(fun(A,B),fun(B,fun(filter(A),bool)),tendsto(A,B),C),D),hAPP(A,filter(A),at(A),E))) | hBOOL(hAPP(filter(A),bool,hAPP(B,fun(filter(A),bool),hAPP(fun(A,B),fun(B,fun(filter(A),bool)),tendsto(A,B),hAPP(B,fun(A,B),hAPP(fun(A,fun(B,B)),fun(B,fun(A,B)),combc(A,B,B),hAPP(fun(A,B),fun(A,fun(B,B)),hAPP(fun(B,fun(B,B)),fun(fun(A,B),fun(A,fun(B,B))),combb(B,fun(B,B),A),inverse_divide(B)),C)),F)),hAPP(B,B,hAPP(B,fun(B,B),inverse_divide(B),D),F)),hAPP(A,filter(A),at(A),E))) # label(fact_4563_divide_OLIM) # label(axiom).  [clausify(4148)].
20.63/20.55	Derived: -topological_space(A) | -hBOOL(hAPP(filter(A),bool,hAPP(real,fun(filter(A),bool),hAPP(fun(A,real),fun(real,fun(filter(A),bool)),tendsto(A,real),B),C),hAPP(A,filter(A),at(A),D))) | hBOOL(hAPP(filter(A),bool,hAPP(real,fun(filter(A),bool),hAPP(fun(A,real),fun(real,fun(filter(A),bool)),tendsto(A,real),hAPP(real,fun(A,real),hAPP(fun(A,fun(real,real)),fun(real,fun(A,real)),combc(A,real,real),hAPP(fun(A,real),fun(A,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(A,real),fun(A,fun(real,real))),combb(real,fun(real,real),A),inverse_divide(real)),B)),E)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),C),E)),hAPP(A,filter(A),at(A),D))).  [resolve(5167,b,5076,a)].
20.69/20.63	Derived: -topological_space(A) | -hBOOL(hAPP(filter(A),bool,hAPP(complex,fun(filter(A),bool),hAPP(fun(A,complex),fun(complex,fun(filter(A),bool)),tendsto(A,complex),B),C),hAPP(A,filter(A),at(A),D))) | hBOOL(hAPP(filter(A),bool,hAPP(complex,fun(filter(A),bool),hAPP(fun(A,complex),fun(complex,fun(filter(A),bool)),tendsto(A,complex),hAPP(complex,fun(A,complex),hAPP(fun(A,fun(complex,complex)),fun(complex,fun(A,complex)),combc(A,complex,complex),hAPP(fun(A,complex),fun(A,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(A,complex),fun(A,fun(complex,complex))),combb(complex,fun(complex,complex),A),inverse_divide(complex)),B)),E)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),C),E)),hAPP(A,filter(A),at(A),D))).  [resolve(5167,b,5103,a)].
20.69/20.63	5168 -real_normed_field(A) | hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),D) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),D)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),D)) # label(fact_1661_divide_Oadd) # label(axiom).  [clausify(4162)].
20.69/20.63	Derived: hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),B)),C) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),C)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),B),C)).  [resolve(5168,a,5076,a)].
20.69/20.63	Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),A),B)),C) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),A),C)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),B),C)).  [resolve(5168,a,5103,a)].
20.69/20.63	5169 -banach(A) | -real_normed_field(A) | -hBOOL(hAPP(fun(nat,A),bool,summable(A),hAPP(fun(nat,A),fun(nat,A),hAPP(fun(nat,fun(A,A)),fun(fun(nat,A),fun(nat,A)),combs(nat,A,A),hAPP(fun(nat,A),fun(nat,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(nat,A),fun(nat,fun(A,A))),combb(A,fun(A,A),nat),times_times(A)),B)),hAPP(A,fun(nat,A),power_power(A),C)))) | -hBOOL(hAPP(fun(nat,A),bool,summable(A),hAPP(fun(nat,A),fun(nat,A),hAPP(fun(nat,fun(A,A)),fun(fun(nat,A),fun(nat,A)),combs(nat,A,A),hAPP(fun(nat,A),fun(nat,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(nat,A),fun(nat,fun(A,A))),combb(A,fun(A,A),nat),times_times(A)),hAPP(fun(nat,A),fun(nat,A),diffs(A),B))),hAPP(A,fun(nat,A),power_power(A),C)))) | -hBOOL(hAPP(fun(nat,A),bool,summable(A),hAPP(fun(nat,A),fun(nat,A),hAPP(fun(nat,fun(A,A)),fun(fun(nat,A),fun(nat,A)),combs(nat,A,A),hAPP(fun(nat,A),fun(nat,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(nat,A),fun(nat,fun(A,A))),combb(A,fun(A,A),nat),times_times(A)),hAPP(fun(nat,A),fun(nat,A),diffs(A),hAPP(fun(nat,A),fun(nat,A),diffs(A),B)))),hAPP(A,fun(nat,A),power_power(A),C)))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(A,real,norm_norm(A),D)),hAPP(A,real,norm_norm(A),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),hAPP(fun(A,fun(nat,A)),fun(A,A),hAPP(fun(fun(nat,A),A),fun(fun(A,fun(nat,A)),fun(A,A)),combb(fun(nat,A),A,A),suminf(A)),hAPP(fun(A,fun(nat,A)),fun(A,fun(nat,A)),hAPP(fun(fun(nat,A),fun(nat,A)),fun(fun(A,fun(nat,A)),fun(A,fun(nat,A))),combb(fun(nat,A),fun(nat,A),A),hAPP(fun(nat,fun(A,A)),fun(fun(nat,A),fun(nat,A)),combs(nat,A,A),hAPP(fun(nat,A),fun(nat,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(nat,A),fun(nat,fun(A,A))),combb(A,fun(A,A),nat),times_times(A)),B))),power_power(A)))),D),hAPP(fun(nat,A),A,suminf(A),hAPP(fun(nat,A),fun(nat,A),hAPP(fun(nat,fun(A,A)),fun(fun(nat,A),fun(nat,A)),combs(nat,A,A),hAPP(fun(nat,A),fun(nat,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(nat,A),fun(nat,fun(A,A))),combb(A,fun(A,A),nat),times_times(A)),hAPP(fun(nat,A),fun(nat,A),diffs(A),B))),hAPP(A,fun(nat,A),power_power(A),D))))) # label(fact_4124_termdiffs) # label(axiom).  [clausify(4225)].
20.69/20.63	Derived: -banach(real) | -hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),A)),hAPP(real,fun(nat,real),power_power(real),B)))) | -hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(fun(nat,real),fun(nat,real),diffs(real),A))),hAPP(real,fun(nat,real),power_power(real),B)))) | -hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(fun(nat,real),fun(nat,real),diffs(real),hAPP(fun(nat,real),fun(nat,real),diffs(real),A)))),hAPP(real,fun(nat,real),power_power(real),B)))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,norm_norm(real),C)),hAPP(real,real,norm_norm(real),B))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(fun(real,fun(nat,real)),fun(real,real),hAPP(fun(fun(nat,real),real),fun(fun(real,fun(nat,real)),fun(real,real)),combb(fun(nat,real),real,real),suminf(real)),hAPP(fun(real,fun(nat,real)),fun(real,fun(nat,real)),hAPP(fun(fun(nat,real),fun(nat,real)),fun(fun(real,fun(nat,real)),fun(real,fun(nat,real))),combb(fun(nat,real),fun(nat,real),real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),A))),power_power(real)))),C),hAPP(fun(nat,real),real,suminf(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(fun(nat,real),fun(nat,real),diffs(real),A))),hAPP(real,fun(nat,real),power_power(real),C))))).  [resolve(5169,b,5076,a)].
20.69/20.63	Derived: -banach(complex) | -hBOOL(hAPP(fun(nat,complex),bool,summable(complex),hAPP(fun(nat,complex),fun(nat,complex),hAPP(fun(nat,fun(complex,complex)),fun(fun(nat,complex),fun(nat,complex)),combs(nat,complex,complex),hAPP(fun(nat,complex),fun(nat,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(nat,complex),fun(nat,fun(complex,complex))),combb(complex,fun(complex,complex),nat),times_times(complex)),A)),hAPP(complex,fun(nat,complex),power_power(complex),B)))) | -hBOOL(hAPP(fun(nat,complex),bool,summable(complex),hAPP(fun(nat,complex),fun(nat,complex),hAPP(fun(nat,fun(complex,complex)),fun(fun(nat,complex),fun(nat,complex)),combs(nat,complex,complex),hAPP(fun(nat,complex),fun(nat,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(nat,complex),fun(nat,fun(complex,complex))),combb(complex,fun(complex,complex),nat),times_times(complex)),hAPP(fun(nat,complex),fun(nat,complex),diffs(complex),A))),hAPP(complex,fun(nat,complex),power_power(complex),B)))) | -hBOOL(hAPP(fun(nat,complex),bool,summable(complex),hAPP(fun(nat,complex),fun(nat,complex),hAPP(fun(nat,fun(complex,complex)),fun(fun(nat,complex),fun(nat,complex)),combs(nat,complex,complex),hAPP(fun(nat,complex),fun(nat,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(nat,complex),fun(nat,fun(complex,complex))),combb(complex,fun(complex,complex),nat),times_times(complex)),hAPP(fun(nat,complex),fun(nat,complex),diffs(complex),hAPP(fun(nat,complex),fun(nat,complex),diffs(complex),A)))),hAPP(complex,fun(nat,complex),power_power(complex),B)))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(complex,real,norm_norm(complex),C)),hAPP(complex,real,norm_norm(complex),B))) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),hAPP(fun(complex,fun(nat,complex)),fun(complex,complex),hAPP(fun(fun(nat,complex),complex),fun(fun(complex,fun(nat,complex)),fun(complex,complex)),combb(fun(nat,complex),complex,complex),suminf(complex)),hAPP(fun(complex,fun(nat,complex)),fun(complex,fun(nat,complex)),hAPP(fun(fun(nat,complex),fun(nat,complex)),fun(fun(complex,fun(nat,complex)),fun(complex,fun(nat,complex))),combb(fun(nat,complex),fun(nat,complex),complex),hAPP(fun(nat,fun(complex,complex)),fun(fun(nat,complex),fun(nat,complex)),combs(nat,complex,complex),hAPP(fun(nat,complex),fun(nat,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(nat,complex),fun(nat,fun(complex,complex))),combb(complex,fun(complex,complex),nat),times_times(complex)),A))),power_power(complex)))),C),hAPP(fun(nat,complex),complex,suminf(complex),hAPP(fun(nat,complex),fun(nat,complex),hAPP(fun(nat,fun(complex,complex)),fun(fun(nat,complex),fun(nat,complex)),combs(nat,complex,complex),hAPP(fun(nat,complex),fun(nat,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(nat,complex),fun(nat,fun(complex,complex))),combb(complex,fun(complex,complex),nat),times_times(complex)),hAPP(fun(nat,complex),fun(nat,complex),diffs(complex),A))),hAPP(complex,fun(nat,complex),power_power(complex),C))))).  [resolve(5169,b,5103,a)].
20.74/20.70	5170 -real_normed_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),B),C),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),B),C),E)) | ti(A,D) = ti(A,E) # label(fact_2633_DERIV__unique) # label(axiom).  [clausify(4291)].
20.74/20.70	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),A),B),C)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),A),B),D)) | ti(real,C) = ti(real,D).  [resolve(5170,a,5076,a)].
20.74/20.70	Derived: -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),A),B),C)) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),A),B),D)) | ti(complex,C) = ti(complex,D).  [resolve(5170,a,5103,a)].
20.74/20.70	5171 -real_normed_field(A) | -hBOOL(hAPP(filter(B),bool,hAPP(A,fun(filter(B),bool),hAPP(fun(B,A),fun(A,fun(filter(B),bool)),tendsto(B,A),C),D),E)) | hBOOL(hAPP(filter(B),bool,hAPP(A,fun(filter(B),bool),hAPP(fun(B,A),fun(A,fun(filter(B),bool)),tendsto(B,A),hAPP(A,fun(B,A),hAPP(fun(B,fun(A,A)),fun(A,fun(B,A)),combc(B,A,A),hAPP(fun(B,A),fun(B,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(B,A),fun(B,fun(A,A))),combb(A,fun(A,A),B),inverse_divide(A)),C)),F)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),F)),E)) # label(fact_4456_divide_Otendsto) # label(axiom).  [clausify(4306)].
20.74/20.70	Derived: -hBOOL(hAPP(filter(A),bool,hAPP(real,fun(filter(A),bool),hAPP(fun(A,real),fun(real,fun(filter(A),bool)),tendsto(A,real),B),C),D)) | hBOOL(hAPP(filter(A),bool,hAPP(real,fun(filter(A),bool),hAPP(fun(A,real),fun(real,fun(filter(A),bool)),tendsto(A,real),hAPP(real,fun(A,real),hAPP(fun(A,fun(real,real)),fun(real,fun(A,real)),combc(A,real,real),hAPP(fun(A,real),fun(A,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(A,real),fun(A,fun(real,real))),combb(real,fun(real,real),A),inverse_divide(real)),B)),E)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),C),E)),D)).  [resolve(5171,a,5076,a)].
20.74/20.70	Derived: -hBOOL(hAPP(filter(A),bool,hAPP(complex,fun(filter(A),bool),hAPP(fun(A,complex),fun(complex,fun(filter(A),bool)),tendsto(A,complex),B),C),D)) | hBOOL(hAPP(filter(A),bool,hAPP(complex,fun(filter(A),bool),hAPP(fun(A,complex),fun(complex,fun(filter(A),bool)),tendsto(A,complex),hAPP(complex,fun(A,complex),hAPP(fun(A,fun(complex,complex)),fun(complex,fun(A,complex)),combc(A,complex,complex),hAPP(fun(A,complex),fun(A,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(A,complex),fun(A,fun(complex,complex))),combb(complex,fun(complex,complex),A),inverse_divide(complex)),B)),E)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),C),E)),D)).  [resolve(5171,a,5103,a)].
20.74/20.71	5172 -real_normed_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),B),C),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),E),C),F)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),hAPP(fun(A,A),fun(A,A),hAPP(fun(A,fun(A,A)),fun(fun(A,A),fun(A,A)),combs(A,A,A),hAPP(fun(A,A),fun(A,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(A,A),fun(A,fun(A,A))),combb(A,fun(A,A),A),times_times(A)),B)),E)),C),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),hAPP(A,A,E,C))),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),F),hAPP(A,A,B,C))))) # label(fact_3817_DERIV__mult) # label(axiom).  [clausify(4312)].
20.74/20.71	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),A),B),C)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),D),B),E)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,real)),combs(real,real,real),hAPP(fun(real,real),fun(real,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,fun(real,real))),combb(real,fun(real,real),real),times_times(real)),A)),D)),B),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),hAPP(real,real,D,B))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),E),hAPP(real,real,A,B))))).  [resolve(5172,a,5076,a)].
20.74/20.71	Derived: -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),A),B),C)) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),D),B),E)) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),hAPP(fun(complex,complex),fun(complex,complex),hAPP(fun(complex,fun(complex,complex)),fun(fun(complex,complex),fun(complex,complex)),combs(complex,complex,complex),hAPP(fun(complex,complex),fun(complex,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(complex,complex),fun(complex,fun(complex,complex))),combb(complex,fun(complex,complex),complex),times_times(complex)),A)),D)),B),hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),C),hAPP(complex,complex,D,B))),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),E),hAPP(complex,complex,A,B))))).  [resolve(5172,a,5103,a)].
20.74/20.71	5173 -real_normed_field(A) | -hBOOL(hAPP(fun(nat,A),bool,summable(A),B)) | hAPP(fun(nat,A),A,suminf(A),hAPP(fun(nat,A),fun(nat,A),hAPP(fun(A,A),fun(fun(nat,A),fun(nat,A)),combb(A,A,nat),uminus_uminus(A)),B)) = hAPP(A,A,uminus_uminus(A),hAPP(fun(nat,A),A,suminf(A),B)) # label(fact_3986_suminf__minus) # label(axiom).  [clausify(4323)].
20.74/20.71	Derived: -hBOOL(hAPP(fun(nat,real),bool,summable(real),A)) | hAPP(fun(nat,real),real,suminf(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),uminus_uminus(real)),A)) = hAPP(real,real,uminus_uminus(real),hAPP(fun(nat,real),real,suminf(real),A)).  [resolve(5173,a,5076,a)].
20.74/20.71	Derived: -hBOOL(hAPP(fun(nat,complex),bool,summable(complex),A)) | hAPP(fun(nat,complex),complex,suminf(complex),hAPP(fun(nat,complex),fun(nat,complex),hAPP(fun(complex,complex),fun(fun(nat,complex),fun(nat,complex)),combb(complex,complex,nat),uminus_uminus(complex)),A)) = hAPP(complex,complex,uminus_uminus(complex),hAPP(fun(nat,complex),complex,suminf(complex),A)).  [resolve(5173,a,5103,a)].
21.06/21.09	5174 -real_normed_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),B),C),D)) | ti(A,E) != ti(A,D) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),B),C),E)) # label(fact_2634_DERIV__cong) # label(axiom).  [clausify(4440)].
21.06/21.09	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),A),B),C)) | ti(real,D) != ti(real,C) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),A),B),D)).  [resolve(5174,a,5076,a)].
21.06/21.09	Derived: -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),A),B),C)) | ti(complex,D) != ti(complex,C) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),A),B),D)).  [resolve(5174,a,5103,a)].
21.06/21.09	5175 -real_normed_field(A) | -banach(A) | hAPP(A,A,exp(A),hAPP(A,A,uminus_uminus(A),B)) = hAPP(A,A,inverse_inverse(A),hAPP(A,A,exp(A),B)) # label(fact_2535_exp__minus) # label(axiom).  [clausify(4505)].
21.06/21.09	Derived: -banach(real) | hAPP(real,real,exp(real),hAPP(real,real,uminus_uminus(real),A)) = hAPP(real,real,inverse_inverse(real),hAPP(real,real,exp(real),A)).  [resolve(5175,a,5076,a)].
21.06/21.09	Derived: -banach(complex) | hAPP(complex,complex,exp(complex),hAPP(complex,complex,uminus_uminus(complex),A)) = hAPP(complex,complex,inverse_inverse(complex),hAPP(complex,complex,exp(complex),A)).  [resolve(5175,a,5103,a)].
21.06/21.09	5176 -real_normed_field(A) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(A,real,norm_norm(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(A,real,norm_norm(A),B)),f814(A,C)))) # label(fact_1810_divide_Obounded) # label(axiom).  [clausify(4588)].
21.06/21.09	Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,norm_norm(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,norm_norm(real),A)),f814(real,B)))).  [resolve(5176,a,5076,a)].
21.06/21.09	Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),A),B))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(complex,real,norm_norm(complex),A)),f814(complex,B)))).  [resolve(5176,a,5103,a)].
21.06/21.09	5177 -real_normed_field(A) | hBOOL(hAPP(filter(A),bool,hAPP(A,fun(filter(A),bool),hAPP(fun(A,A),fun(A,fun(filter(A),bool)),tendsto(A,A),hAPP(A,fun(A,A),hAPP(fun(A,fun(A,A)),fun(A,fun(A,A)),combc(A,A,A),inverse_divide(A)),B)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),B)),hAPP(A,filter(A),at(A),C))) # label(fact_4564_divide_Ocont) # label(axiom).  [clausify(4771)].
21.06/21.09	Derived: hBOOL(hAPP(filter(real),bool,hAPP(real,fun(filter(real),bool),hAPP(fun(real,real),fun(real,fun(filter(real),bool)),tendsto(real,real),hAPP(real,fun(real,real),hAPP(fun(real,fun(real,real)),fun(real,fun(real,real)),combc(real,real,real),inverse_divide(real)),A)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),B),A)),hAPP(real,filter(real),at(real),B))).  [resolve(5177,a,5076,a)].
21.06/21.09	Derived: hBOOL(hAPP(filter(complex),bool,hAPP(complex,fun(filter(complex),bool),hAPP(fun(complex,complex),fun(complex,fun(filter(complex),bool)),tendsto(complex,complex),hAPP(complex,fun(complex,complex),hAPP(fun(complex,fun(complex,complex)),fun(complex,fun(complex,complex)),combc(complex,complex,complex),inverse_divide(complex)),A)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),B),A)),hAPP(complex,filter(complex),at(complex),B))).  [resolve(5177,a,5103,a)].
21.30/21.22	5178 -real_normed_field(A) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(A,real,norm_norm(A),B)),one_one(real))) | hBOOL(hAPP(A,bool,hAPP(fun(nat,A),fun(A,bool),sums(A),hAPP(A,fun(nat,A),power_power(A),B)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),one_one(A)),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),one_one(A)),B)))) # label(fact_4098_geometric__sums) # label(axiom).  [clausify(4815)].
21.30/21.22	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,norm_norm(real),A)),one_one(real))) | hBOOL(hAPP(real,bool,hAPP(fun(nat,real),fun(real,bool),sums(real),hAPP(real,fun(nat,real),power_power(real),A)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),one_one(real)),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),one_one(real)),A)))).  [resolve(5178,a,5076,a)].
21.30/21.22	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(complex,real,norm_norm(complex),A)),one_one(real))) | hBOOL(hAPP(complex,bool,hAPP(fun(nat,complex),fun(complex,bool),sums(complex),hAPP(complex,fun(nat,complex),power_power(complex),A)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),one_one(complex)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),one_one(complex)),A)))).  [resolve(5178,a,5103,a)].
21.30/21.22	5179 -real_normed_field(A) | -hBOOL(hAPP(A,bool,hAPP(fun(nat,A),fun(A,bool),sums(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(fun(nat,A),fun(A,bool),sums(A),hAPP(A,fun(nat,A),hAPP(fun(nat,fun(A,A)),fun(A,fun(nat,A)),combc(nat,A,A),hAPP(fun(nat,A),fun(nat,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(nat,A),fun(nat,fun(A,A))),combb(A,fun(A,A),nat),inverse_divide(A)),B)),D)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),D))) # label(fact_4086_sums__divide) # label(axiom).  [clausify(4819)].
21.30/21.22	5180 -real_normed_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),B),C),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),E),C),F)) | zero_zero(A) = hAPP(A,A,E,C) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),hAPP(fun(A,A),fun(A,A),hAPP(fun(A,fun(A,A)),fun(fun(A,A),fun(A,A)),combs(A,A,A),hAPP(fun(A,A),fun(A,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(A,A),fun(A,fun(A,A))),combb(A,fun(A,A),A),inverse_divide(A)),B)),E)),C),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),hAPP(A,A,E,C))),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),F),hAPP(A,A,B,C)))),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),hAPP(A,A,E,C)),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat))))))) # label(fact_3899_DERIV__quotient) # label(axiom).  [clausify(4927)].
21.30/21.22	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),A),B),C)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),D),B),E)) | zero_zero(real) = hAPP(real,real,D,B) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,real)),combs(real,real,real),hAPP(fun(real,real),fun(real,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,fun(real,real))),combb(real,fun(real,real),real),inverse_divide(real)),A)),D)),B),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),hAPP(real,real,D,B))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),E),hAPP(real,real,A,B)))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,D,B)),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat))))))).  [resolve(5180,a,5076,a)].
21.30/21.22	Derived: -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),A),B),C)) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),D),B),E)) | zero_zero(complex) = hAPP(complex,complex,D,B) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),hAPP(fun(complex,complex),fun(complex,complex),hAPP(fun(complex,fun(complex,complex)),fun(fun(complex,complex),fun(complex,complex)),combs(complex,complex,complex),hAPP(fun(complex,complex),fun(complex,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(complex,complex),fun(complex,fun(complex,complex))),combb(complex,fun(complex,complex),complex),inverse_divide(complex)),A)),D)),B),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),C),hAPP(complex,complex,D,B))),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),E),hAPP(complex,complex,A,B)))),hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),hAPP(complex,complex,D,B)),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat))))))).  [resolve(5180,a,5103,a)].
22.15/22.09	5181 -semiring_div(A) | zero_zero(A) = hAPP(A,A,hAPP(A,fun(A,A),div_div(A),zero_zero(A)),B) # label(fact_965_div__0) # label(axiom).  [clausify(102)].
22.15/22.09	5182 semiring_div(nat) # label(arity_Nat_Onat___Divides_Osemiring__div) # label(axiom).  [assumption].
22.15/22.09	Derived: zero_zero(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),zero_zero(nat)),A).  [resolve(5181,a,5182,a)].
22.15/22.09	5183 -semiring_div(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),div_div(A),B),C)),C)),hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),B),C)) = ti(A,B) # label(fact_915_mod__div__equality) # label(axiom).  [clausify(239)].
22.15/22.09	Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),A),B)),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),A),B)) = ti(nat,A).  [resolve(5183,a,5182,a)].
22.15/22.09	5184 -semiring_div(A) | hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),B),C)),D)),C) = hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D)),C) # label(fact_929_mod__mult__left__eq) # label(axiom).  [clausify(259)].
22.15/22.09	Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),A),B)),C)),B) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),C)),B).  [resolve(5184,a,5182,a)].
22.15/22.09	5185 -semiring_div(A) | zero_zero(A) = hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),B),B) # label(fact_924_mod__self) # label(axiom).  [clausify(299)].
22.15/22.09	Derived: zero_zero(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),A),A).  [resolve(5185,a,5182,a)].
22.15/22.09	5186 -semiring_div(A) | hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),B),C)),D)),C) = hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),D)),C) # label(fact_939_mod__add__left__eq) # label(axiom).  [clausify(308)].
22.15/22.09	Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),A),B)),C)),B) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),C)),B).  [resolve(5186,a,5182,a)].
22.15/22.09	5187 -semiring_div(A) | hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),B),C) != hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),D),C) | hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),E),C) != hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),F),C) | hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),E)),C) = hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),F)),C) # label(fact_934_mod__mult__cong) # label(axiom).  [clausify(332)].
22.15/22.09	Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),A),B) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),C),B) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),D),B) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),E),B) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),D)),B) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),C),E)),B).  [resolve(5187,a,5182,a)].
22.19/22.11	5188 -semiring_div(A) | zero_zero(A) != ti(A,B) | zero_zero(A) = hAPP(A,A,hAPP(A,fun(A,A),div_div(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D)) # label(fact_998_div__mult__mult1__if) # label(axiom).  [clausify(339)].
22.19/22.11	Derived: zero_zero(nat) != ti(nat,A) | zero_zero(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),C)).  [resolve(5188,a,5182,a)].
22.19/22.11	5189 -semiring_div(A) | zero_zero(A) = ti(A,B) | hAPP(A,A,hAPP(A,fun(A,A),div_div(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D)) = hAPP(A,A,hAPP(A,fun(A,A),div_div(A),C),D) # label(fact_998_div__mult__mult1__if) # label(axiom).  [clausify(339)].
22.19/22.11	Derived: zero_zero(nat) = ti(nat,A) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),C)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),B),C).  [resolve(5189,a,5182,a)].
22.19/22.11	5190 -semiring_div(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),C),D))) # label(fact_949_dvd__mod) # label(axiom).  [clausify(405)].
22.19/22.11	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A),C)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),B),C))).  [resolve(5190,a,5182,a)].
22.19/22.11	5191 semiring_div(code_code_numeral) # label(arity_Code__Numeral_Ocode__numeral___Divides_Osemiring__div) # label(axiom).  [assumption].
22.19/22.11	Derived: zero_zero(code_code_numeral) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),zero_zero(code_code_numeral)),A).  [resolve(5191,a,5181,a)].
22.19/22.11	Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),A),B)),B)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),A),B)) = ti(code_code_numeral,A).  [resolve(5191,a,5183,a)].
22.19/22.11	Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),A),B)),C)),B) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),C)),B).  [resolve(5191,a,5184,a)].
22.19/22.11	Derived: zero_zero(code_code_numeral) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),A),A).  [resolve(5191,a,5185,a)].
22.19/22.11	Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),A),B)),C)),B) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),A),C)),B).  [resolve(5191,a,5186,a)].
22.19/22.12	Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),A),B) != hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),C),B) | hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),D),B) != hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),E),B) | hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),D)),B) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),C),E)),B).  [resolve(5191,a,5187,a)].
22.19/22.12	Derived: zero_zero(code_code_numeral) != ti(code_code_numeral,A) | zero_zero(code_code_numeral) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),B)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),C)).  [resolve(5191,a,5188,a)].
22.19/22.12	Derived: zero_zero(code_code_numeral) = ti(code_code_numeral,A) | hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),B)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),C)) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),B),C).  [resolve(5191,a,5189,a)].
22.19/22.12	Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),A),B)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),A),C)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),A),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),B),C))).  [resolve(5191,a,5190,a)].
22.19/22.12	5192 -semiring_div(A) | zero_zero(A) = ti(A,B) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),C)) | hAPP(A,A,hAPP(A,fun(A,A),div_div(A),C),B) != ti(A,D) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),B) = ti(A,C) # label(fact_1044_dvd__div__eq__mult) # label(axiom).  [clausify(482)].
22.19/22.12	Derived: zero_zero(nat) = ti(nat,A) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A),B)) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),B),A) != ti(nat,C) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),C),A) = ti(nat,B).  [resolve(5192,a,5182,a)].
22.23/22.14	Derived: zero_zero(code_code_numeral) = ti(code_code_numeral,A) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),A),B)) | hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),B),A) != ti(code_code_numeral,C) | hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),C),A) = ti(code_code_numeral,B).  [resolve(5192,a,5191,a)].
22.23/22.14	5193 -semiring_div(A) | zero_zero(A) = ti(A,B) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),C)) | hAPP(A,A,hAPP(A,fun(A,A),div_div(A),C),B) = ti(A,D) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),B) != ti(A,C) # label(fact_1044_dvd__div__eq__mult) # label(axiom).  [clausify(482)].
22.23/22.14	Derived: zero_zero(nat) = ti(nat,A) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A),B)) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),B),A) = ti(nat,C) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),C),A) != ti(nat,B).  [resolve(5193,a,5182,a)].
22.23/22.14	Derived: zero_zero(code_code_numeral) = ti(code_code_numeral,A) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),A),B)) | hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),B),A) = ti(code_code_numeral,C) | hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),C),A) != ti(code_code_numeral,B).  [resolve(5193,a,5191,a)].
22.23/22.14	5194 -semiring_div(A) | hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),B),C)),D)),C) = hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D)),C) # label(fact_933_zmod__simps_I4_J) # label(axiom).  [clausify(491)].
22.23/22.14	5195 -semiring_div(A) | hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),B),C) != hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),D),C) | hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),E),C) != hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),F),C) | hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),E)),C) = hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),D),F)),C) # label(fact_935_mod__add__cong) # label(axiom).  [clausify(572)].
22.23/22.14	Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),A),B) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),C),B) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),D),B) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),E),B) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),D)),B) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),C),E)),B).  [resolve(5195,a,5182,a)].
22.23/22.14	Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),A),B) != hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),C),B) | hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),D),B) != hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),E),B) | hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),A),D)),B) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),C),E)),B).  [resolve(5195,a,5191,a)].
22.23/22.14	5196 -semiring_div(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),C)) | zero_zero(A) = hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),C),B) # label(fact_979_dvd__imp__mod__0) # label(axiom).  [clausify(578)].
22.23/22.20	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A),B)) | zero_zero(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),B),A).  [resolve(5196,a,5182,a)].
22.23/22.20	Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),A),B)) | zero_zero(code_code_numeral) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),B),A).  [resolve(5196,a,5191,a)].
22.23/22.20	5197 -semiring_div(A) | zero_zero(A) = hAPP(A,A,hAPP(A,fun(A,A),div_div(A),hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),B),C)),C) # label(fact_909_mod__div__trivial) # label(axiom).  [clausify(693)].
22.23/22.20	Derived: zero_zero(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),A),B)),B).  [resolve(5197,a,5182,a)].
22.23/22.20	Derived: zero_zero(code_code_numeral) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),A),B)),B).  [resolve(5197,a,5191,a)].
22.23/22.20	5198 -semiring_div(A) | zero_zero(A) = hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),C) # label(fact_974_mod__mult__self2__is__0) # label(axiom).  [clausify(771)].
22.23/22.20	Derived: zero_zero(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),B)),B).  [resolve(5198,a,5182,a)].
22.23/22.20	Derived: zero_zero(code_code_numeral) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),B)),B).  [resolve(5198,a,5191,a)].
22.23/22.20	5199 -semiring_div(A) | zero_zero(A) = ti(A,B) | hAPP(A,A,hAPP(A,fun(A,A),div_div(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),B) = ti(A,C) # label(fact_996_div__mult__self1__is__id) # label(axiom).  [clausify(886)].
22.23/22.20	Derived: zero_zero(nat) = ti(nat,A) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),B)),A) = ti(nat,B).  [resolve(5199,a,5182,a)].
22.23/22.20	Derived: zero_zero(code_code_numeral) = ti(code_code_numeral,A) | hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),B)),A) = ti(code_code_numeral,B).  [resolve(5199,a,5191,a)].
22.23/22.20	5200 -semiring_div(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),C)) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),div_div(A),C),B)),B) = ti(A,C) # label(fact_1002_dvd__div__mult__self) # label(axiom).  [clausify(931)].
22.23/22.20	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A),B)) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),B),A)),A) = ti(nat,B).  [resolve(5200,a,5182,a)].
22.23/22.20	Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),A),B)) | hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),B),A)),A) = ti(code_code_numeral,B).  [resolve(5200,a,5191,a)].
22.23/22.20	5201 -semiring_div(A) | div_mod(A) = ti(fun(A,fun(A,A)),div_mod(A)) # label(tsy_c_Divides_Odiv__class_Omod_res) # label(axiom).  [clausify(967)].
22.23/22.20	Derived: div_mod(nat) = ti(fun(nat,fun(nat,nat)),div_mod(nat)).  [resolve(5201,a,5182,a)].
22.23/22.20	Derived: div_mod(code_code_numeral) = ti(fun(code_code_numeral,fun(code_code_numeral,code_code_numeral)),div_mod(code_code_numeral)).  [resolve(5201,a,5191,a)].
22.33/22.24	5202 -semiring_div(A) | zero_zero(A) = ti(A,B) | hAPP(A,A,hAPP(A,fun(A,A),div_div(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),B)),B) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),div_div(A),C),B)),one_one(A)) # label(fact_1042_div__add__self2) # label(axiom).  [clausify(1018)].
22.33/22.24	Derived: zero_zero(nat) = ti(nat,A) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),A)),A) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),B),A)),one_one(nat)).  [resolve(5202,a,5182,a)].
22.33/22.24	Derived: zero_zero(code_code_numeral) = ti(code_code_numeral,A) | hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),B),A)),A) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),B),A)),one_one(code_code_numeral)).  [resolve(5202,a,5191,a)].
22.33/22.24	5203 -semiring_div(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),hAPP(A,A,hAPP(A,fun(A,A),div_div(A),C),B)),hAPP(A,A,hAPP(A,fun(A,A),div_div(A),D),B))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),C),D)) # label(fact_967_div__dvd__div) # label(axiom).  [clausify(1126)].
22.33/22.24	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A),C)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),B),A)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),C),A))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),B),C)).  [resolve(5203,a,5182,a)].
22.33/22.24	Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),A),B)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),A),C)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),B),A)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),C),A))) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),B),C)).  [resolve(5203,a,5191,a)].
22.33/22.24	5204 -semiring_div(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),hAPP(A,A,hAPP(A,fun(A,A),div_div(A),C),B)),hAPP(A,A,hAPP(A,fun(A,A),div_div(A),D),B))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),C),D)) # label(fact_967_div__dvd__div) # label(axiom).  [clausify(1126)].
22.33/22.24	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A),C)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),B),A)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),C),A))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),B),C)).  [resolve(5204,a,5182,a)].
22.33/22.24	Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),A),B)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),A),C)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),B),A)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),C),A))) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),B),C)).  [resolve(5204,a,5191,a)].
22.33/22.26	5205 semiring_div(int) # label(arity_Int_Oint___Divides_Osemiring__div) # label(axiom).  [assumption].
22.33/22.26	Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A),B)),B)),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A),B)) = ti(int,A).  [resolve(5205,a,5183,a)].
22.33/22.26	Derived: hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A),B)),C)),B) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),C)),B).  [resolve(5205,a,5184,a)].
22.33/22.26	Derived: hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A),B)),C)),B) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),C)),B).  [resolve(5205,a,5186,a)].
22.33/22.26	Derived: hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A),B) != hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),C),B) | hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),D),B) != hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),E),B) | hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),D)),B) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),E)),B).  [resolve(5205,a,5187,a)].
22.33/22.26	Derived: zero_zero(int) != ti(int,A) | zero_zero(int) = hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),C)).  [resolve(5205,a,5188,a)].
22.33/22.26	Derived: zero_zero(int) = ti(int,A) | hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),C)) = hAPP(int,int,hAPP(int,fun(int,int),div_div(int),B),C).  [resolve(5205,a,5189,a)].
22.33/22.26	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),B),C))).  [resolve(5205,a,5190,a)].
22.33/22.26	Derived: zero_zero(int) = ti(int,A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),B)) | hAPP(int,int,hAPP(int,fun(int,int),div_div(int),B),A) != ti(int,C) | hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),A) = ti(int,B).  [resolve(5205,a,5192,a)].
22.33/22.26	Derived: zero_zero(int) = ti(int,A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),B)) | hAPP(int,int,hAPP(int,fun(int,int),div_div(int),B),A) = ti(int,C) | hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),A) != ti(int,B).  [resolve(5205,a,5193,a)].
22.33/22.26	Derived: hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A),B) != hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),C),B) | hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),D),B) != hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),E),B) | hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),D)),B) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),C),E)),B).  [resolve(5205,a,5195,a)].
22.33/22.26	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),B)) | zero_zero(int) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),B),A).  [resolve(5205,a,5196,a)].
22.33/22.26	Derived: zero_zero(int) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),B).  [resolve(5205,a,5198,a)].
22.33/22.29	Derived: zero_zero(int) = ti(int,A) | hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),A) = ti(int,B).  [resolve(5205,a,5199,a)].
22.33/22.29	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),B)) | hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),B),A)),A) = ti(int,B).  [resolve(5205,a,5200,a)].
22.33/22.29	Derived: div_mod(int) = ti(fun(int,fun(int,int)),div_mod(int)).  [resolve(5205,a,5201,a)].
22.33/22.29	Derived: zero_zero(int) = ti(int,A) | hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),B),A)),A) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),B),A)),one_one(int)).  [resolve(5205,a,5202,a)].
22.33/22.29	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),C)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),B),A)),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),C),A))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),B),C)).  [resolve(5205,a,5203,a)].
22.33/22.29	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),B),A)),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),C),A))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),B),C)).  [resolve(5205,a,5204,a)].
22.33/22.29	5206 -semiring_div(A) | zero_zero(A) = ti(A,B) | hAPP(A,A,hAPP(A,fun(A,A),div_div(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),B))),B) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),D),hAPP(A,A,hAPP(A,fun(A,A),div_div(A),C),B)) # label(fact_1039_div__mult__self1) # label(axiom).  [clausify(1210)].
22.33/22.29	Derived: zero_zero(nat) = ti(nat,A) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),C),A))),A) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),C),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),B),A)).  [resolve(5206,a,5182,a)].
22.33/22.29	Derived: zero_zero(code_code_numeral) = ti(code_code_numeral,A) | hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),B),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),C),A))),A) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),C),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),B),A)).  [resolve(5206,a,5191,a)].
22.33/22.29	Derived: zero_zero(int) = ti(int,A) | hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),B),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),A))),A) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),C),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),B),A)).  [resolve(5206,a,5205,a)].
22.33/22.29	5207 -semiring_div(A) | hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),D),C))),C) = hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),D)),C) # label(fact_938_mod__add__eq) # label(axiom).  [clausify(1235)].
22.33/22.29	Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),A),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),C),B))),B) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),C)),B).  [resolve(5207,a,5182,a)].
22.50/22.41	Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),A),B)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),C),B))),B) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),A),C)),B).  [resolve(5207,a,5191,a)].
22.50/22.41	Derived: hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),C),B))),B) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),C)),B).  [resolve(5207,a,5205,a)].
22.50/22.41	5208 -semiring_div(A) | hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),B),C)),C) = hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),B),C) # label(fact_906_mod__mod__trivial) # label(axiom).  [clausify(1578)].
22.50/22.41	Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),A),B)),B) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),A),B).  [resolve(5208,a,5182,a)].
22.50/22.41	Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),A),B)),B) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),A),B).  [resolve(5208,a,5191,a)].
22.50/22.41	Derived: hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A),B)),B) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A),B).  [resolve(5208,a,5205,a)].
22.50/22.41	5209 -semiring_div(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),C)) | hAPP(A,A,hAPP(A,fun(A,A),div_div(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),C)),B) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),hAPP(A,A,hAPP(A,fun(A,A),div_div(A),C),B)) # label(fact_1003_div__mult__swap) # label(axiom).  [clausify(1652)].
22.50/22.41	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A),B)) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),C),B)),A) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),C),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),B),A)).  [resolve(5209,a,5182,a)].
22.50/22.41	Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),A),B)) | hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),C),B)),A) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),C),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),B),A)).  [resolve(5209,a,5191,a)].
22.50/22.41	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),B)) | hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),B)),A) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),B),A)).  [resolve(5209,a,5205,a)].
22.50/22.41	5210 -semiring_div(A) | hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),C)) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),B),D)),C) # label(fact_932_mod__mult__mult2) # label(axiom).  [clausify(1653)].
22.54/22.51	Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),B)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),C),B)) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),A),C)),B).  [resolve(5210,a,5191,a)].
22.54/22.51	Derived: hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),B)) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A),C)),B).  [resolve(5210,a,5205,a)].
22.54/22.51	5211 -semiring_div(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),C),D))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),C)) # label(fact_950_dvd__mod__imp__dvd) # label(axiom).  [clausify(1848)].
22.54/22.51	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),B),C))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A),C)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A),B)).  [resolve(5211,a,5182,a)].
22.54/22.51	Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),A),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),B),C))) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),A),C)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),A),B)).  [resolve(5211,a,5191,a)].
22.54/22.51	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),B),C))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),B)).  [resolve(5211,a,5205,a)].
22.54/22.51	5212 -semiring_div(A) | hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),C),D))),D) = hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),D) # label(fact_937_zmod__simps_I2_J) # label(axiom).  [clausify(1876)].
22.54/22.51	Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),B),C))),C) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B)),C).  [resolve(5212,a,5182,a)].
22.54/22.51	Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),A),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),B),C))),C) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),A),B)),C).  [resolve(5212,a,5191,a)].
22.54/22.51	Derived: hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),B),C))),C) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B)),C).  [resolve(5212,a,5205,a)].
22.68/22.63	5213 -semiring_div(A) | -number(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),hAPP(int,A,number_number_of(A),B)),hAPP(int,A,number_number_of(A),C))) | zero_zero(A) = hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),hAPP(int,A,number_number_of(A),C)),hAPP(int,A,number_number_of(A),B)) # label(fact_1009_dvd__eq__mod__eq__0__number__of) # label(axiom).  [clausify(1987)].
22.68/22.63	5214 -semiring_div(A) | -number(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),hAPP(int,A,number_number_of(A),B)),hAPP(int,A,number_number_of(A),C))) | zero_zero(A) != hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),hAPP(int,A,number_number_of(A),C)),hAPP(int,A,number_number_of(A),B)) # label(fact_1009_dvd__eq__mod__eq__0__number__of) # label(axiom).  [clausify(1987)].
22.68/22.63	Derived: -number(nat) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(int,nat,number_number_of(nat),A)),hAPP(int,nat,number_number_of(nat),B))) | zero_zero(nat) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(int,nat,number_number_of(nat),B)),hAPP(int,nat,number_number_of(nat),A)).  [resolve(5214,a,5182,a)].
22.68/22.63	Derived: -number(code_code_numeral) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),A)),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),B))) | zero_zero(code_code_numeral) != hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),B)),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),A)).  [resolve(5214,a,5191,a)].
22.68/22.63	Derived: -number(int) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(int,int,number_number_of(int),A)),hAPP(int,int,number_number_of(int),B))) | zero_zero(int) != hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,number_number_of(int),B)),hAPP(int,int,number_number_of(int),A)).  [resolve(5214,a,5205,a)].
22.68/22.63	5215 -semiring_div(A) | div_div(A) = ti(fun(A,fun(A,A)),div_div(A)) # label(tsy_c_Divides_Odiv__class_Odiv_res) # label(axiom).  [clausify(2163)].
22.68/22.63	Derived: div_div(nat) = ti(fun(nat,fun(nat,nat)),div_div(nat)).  [resolve(5215,a,5182,a)].
22.68/22.63	Derived: div_div(code_code_numeral) = ti(fun(code_code_numeral,fun(code_code_numeral,code_code_numeral)),div_div(code_code_numeral)).  [resolve(5215,a,5191,a)].
22.68/22.63	Derived: div_div(int) = ti(fun(int,fun(int,int)),div_div(int)).  [resolve(5215,a,5205,a)].
22.68/22.63	5216 -semiring_div(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(A,A,hAPP(A,fun(A,A),div_div(A),C),B))),hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),C),B))),D) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),D) # label(fact_916_div__mod__equality2) # label(axiom).  [clausify(2178)].
22.68/22.63	Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),B),A))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),B),A))),C) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),C).  [resolve(5216,a,5182,a)].
22.68/22.63	Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),B),A))),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),B),A))),C) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),B),C).  [resolve(5216,a,5191,a)].
22.98/22.94	5217 -semiring_div(A) | zero_zero(A) = hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),B),one_one(A)) # label(fact_975_mod__by__1) # label(axiom).  [clausify(2202)].
22.98/22.94	Derived: zero_zero(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),A),one_one(nat)).  [resolve(5217,a,5182,a)].
22.98/22.94	Derived: zero_zero(code_code_numeral) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),A),one_one(code_code_numeral)).  [resolve(5217,a,5191,a)].
22.98/22.94	Derived: zero_zero(int) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A),one_one(int)).  [resolve(5217,a,5205,a)].
22.98/22.94	5218 -semiring_div(A) | hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),C) = hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),B),C) # label(fact_942_mod__add__self2) # label(axiom).  [clausify(2374)].
22.98/22.94	Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B)),B) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),A),B).  [resolve(5218,a,5182,a)].
22.98/22.94	Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),A),B)),B) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),A),B).  [resolve(5218,a,5191,a)].
22.98/22.94	Derived: hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B)),B) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A),B).  [resolve(5218,a,5205,a)].
22.98/22.94	5219 -semiring_div(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),C)) | hAPP(A,A,hAPP(A,fun(A,A),div_div(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),D)),B) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),div_div(A),C),B)),D) # label(fact_1001_dvd__div__mult) # label(axiom).  [clausify(2407)].
22.98/22.94	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A),B)) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),C)),A) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),B),A)),C).  [resolve(5219,a,5182,a)].
22.98/22.94	Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),A),B)) | hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),B),C)),A) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),B),A)),C).  [resolve(5219,a,5191,a)].
22.98/22.94	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),B)) | hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),C)),A) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),B),A)),C).  [resolve(5219,a,5205,a)].
22.98/22.94	5220 -semiring_div(A) | hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),D))),C) = hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),B),C) # label(fact_978_mod__mult__self2) # label(axiom).  [clausify(2574)].
22.98/22.94	Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),C))),B) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),A),B).  [resolve(5220,a,5182,a)].
23.10/23.01	Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),A),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),B),C))),B) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),A),B).  [resolve(5220,a,5191,a)].
23.10/23.01	Derived: hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),C))),B) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A),B).  [resolve(5220,a,5205,a)].
23.10/23.01	5221 -semiring_div(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),D)) | hAPP(A,A,hAPP(A,fun(A,A),div_div(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),D)),B) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),div_div(A),C),B)),hAPP(A,A,hAPP(A,fun(A,A),div_div(A),D),B)) # label(fact_1005_div__add) # label(axiom).  [clausify(2643)].
23.10/23.01	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A),C)) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),C)),A) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),B),A)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),C),A)).  [resolve(5221,a,5182,a)].
23.10/23.01	Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),A),B)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),A),C)) | hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),B),C)),A) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),B),A)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),C),A)).  [resolve(5221,a,5191,a)].
23.10/23.01	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),C)) | hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),B),C)),A) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),B),A)),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),C),A)).  [resolve(5221,a,5205,a)].
23.10/23.01	5222 -semiring_div(A) | zero_zero(A) = hAPP(A,A,hAPP(A,fun(A,A),div_div(A),B),zero_zero(A)) # label(fact_964_div__by__0) # label(axiom).  [clausify(2649)].
23.10/23.01	Derived: zero_zero(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),A),zero_zero(nat)).  [resolve(5222,a,5182,a)].
23.10/23.01	Derived: zero_zero(code_code_numeral) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),A),zero_zero(code_code_numeral)).  [resolve(5222,a,5191,a)].
23.10/23.01	Derived: zero_zero(int) = hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A),zero_zero(int)).  [resolve(5222,a,5205,a)].
23.10/23.01	5223 -semiring_div(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),C)) | hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),D),C)),B) = hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),D),B) # label(fact_948_mod__mod__cancel) # label(axiom).  [clausify(2668)].
23.14/23.14	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A),B)) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),C),B)),A) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),C),A).  [resolve(5223,a,5182,a)].
23.14/23.14	Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),A),B)) | hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),C),B)),A) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),C),A).  [resolve(5223,a,5191,a)].
23.14/23.14	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),B)) | hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),C),B)),A) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),C),A).  [resolve(5223,a,5205,a)].
23.14/23.14	5224 -semiring_div(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(A,A,hAPP(A,fun(A,A),div_div(A),C),B))),hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),C),B)) = ti(A,C) # label(fact_914_mod__div__equality2) # label(axiom).  [clausify(2724)].
23.14/23.14	Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),B),A))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),B),A)) = ti(nat,B).  [resolve(5224,a,5182,a)].
23.14/23.14	Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),B),A))),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),B),A)) = ti(code_code_numeral,B).  [resolve(5224,a,5191,a)].
23.14/23.14	5225 -semiring_div(A) | hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),B),C)),D)),C) = hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),D)),C) # label(fact_936_zmod__simps_I1_J) # label(axiom).  [clausify(2744)].
23.14/23.14	5226 -semiring_div(A) | hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),B),zero_zero(A)) = ti(A,B) # label(fact_925_mod__by__0) # label(axiom).  [clausify(2841)].
23.14/23.14	Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),A),zero_zero(nat)) = ti(nat,A).  [resolve(5226,a,5182,a)].
23.14/23.14	Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),A),zero_zero(code_code_numeral)) = ti(code_code_numeral,A).  [resolve(5226,a,5191,a)].
23.14/23.14	Derived: hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A),zero_zero(int)) = ti(int,A).  [resolve(5226,a,5205,a)].
23.14/23.14	5227 -semiring_div(A) | hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D)) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),C),D)) # label(fact_931_mod__mult__mult1) # label(axiom).  [clausify(2869)].
23.14/23.14	Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),C)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),B),C)).  [resolve(5227,a,5182,a)].
23.14/23.14	Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),B)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),C)) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),B),C)).  [resolve(5227,a,5191,a)].
23.40/23.33	Derived: hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),C)) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),B),C)).  [resolve(5227,a,5205,a)].
23.40/23.33	5228 -semiring_div(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),div_div(A),B),C)),C)) = ti(A,B) # label(fact_913_semiring__div__class_Omod__div__equality_H) # label(axiom).  [clausify(2898)].
23.40/23.33	Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),A),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),A),B)),B)) = ti(nat,A).  [resolve(5228,a,5182,a)].
23.40/23.33	Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),A),B)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),A),B)),B)) = ti(code_code_numeral,A).  [resolve(5228,a,5191,a)].
23.40/23.33	Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A),B)),B)) = ti(int,A).  [resolve(5228,a,5205,a)].
23.40/23.33	5229 -semiring_div(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),D),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),D)) # label(fact_947_dvd__mod__iff) # label(axiom).  [clausify(3100)].
23.40/23.33	5230 -semiring_div(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),D),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),D)) # label(fact_947_dvd__mod__iff) # label(axiom).  [clausify(3100)].
23.40/23.33	5231 -semiring_div(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),div_div(A),B),C)),C)),hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),B),C))),D) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),D) # label(fact_917_div__mod__equality) # label(axiom).  [clausify(3134)].
23.40/23.33	Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),A),B)),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),A),B))),C) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),C).  [resolve(5231,a,5182,a)].
23.40/23.33	Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),A),B)),B)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),A),B))),C) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),A),C).  [resolve(5231,a,5191,a)].
23.58/23.53	Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A),B)),B)),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A),B))),C) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),C).  [resolve(5231,a,5205,a)].
23.58/23.53	5232 -semiring_div(A) | zero_zero(A) = ti(A,B) | hAPP(A,A,hAPP(A,fun(A,A),div_div(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),B)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),B)) = hAPP(A,A,hAPP(A,fun(A,A),div_div(A),C),D) # label(fact_995_div__mult__mult2) # label(axiom).  [clausify(3229)].
23.58/23.53	Derived: zero_zero(nat) = ti(nat,A) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),A)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),C),A)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),B),C).  [resolve(5232,a,5182,a)].
23.58/23.53	Derived: zero_zero(code_code_numeral) = ti(code_code_numeral,A) | hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),B),A)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),C),A)) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),B),C).  [resolve(5232,a,5191,a)].
23.58/23.53	Derived: zero_zero(int) = ti(int,A) | hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),A)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),A)) = hAPP(int,int,hAPP(int,fun(int,int),div_div(int),B),C).  [resolve(5232,a,5205,a)].
23.58/23.53	5233 -semiring_div(A) | hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),D))),D) = hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),B),D) # label(fact_977_mod__mult__self1) # label(axiom).  [clausify(3329)].
23.58/23.53	Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),C))),C) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),A),C).  [resolve(5233,a,5182,a)].
23.58/23.53	Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),A),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),B),C))),C) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),A),C).  [resolve(5233,a,5191,a)].
23.58/23.53	Derived: hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),C))),C) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A),C).  [resolve(5233,a,5205,a)].
23.58/23.53	5234 -semiring_div(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),div_div(A),B),C)),C)),hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),B),C)) = ti(A,B) # label(fact_1074_mod__div__decomp) # label(axiom).  [clausify(3385)].
23.58/23.53	5235 -semiring_div(A) | zero_zero(A) = ti(A,B) | one_one(A) = hAPP(A,A,hAPP(A,fun(A,A),div_div(A),B),B) # label(fact_999_div__self) # label(axiom).  [clausify(3394)].
23.58/23.53	Derived: zero_zero(nat) = ti(nat,A) | one_one(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),A),A).  [resolve(5235,a,5182,a)].
23.84/23.80	Derived: zero_zero(code_code_numeral) = ti(code_code_numeral,A) | one_one(code_code_numeral) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),A),A).  [resolve(5235,a,5191,a)].
23.84/23.80	Derived: zero_zero(int) = ti(int,A) | one_one(int) = hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A),A).  [resolve(5235,a,5205,a)].
23.84/23.80	5236 -semiring_div(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),D),E)) | hAPP(A,A,hAPP(A,fun(A,A),div_div(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),E)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D)) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),div_div(A),C),B)),hAPP(A,A,hAPP(A,fun(A,A),div_div(A),E),D)) # label(fact_1000_div__mult__div__if__dvd) # label(axiom).  [clausify(3642)].
23.84/23.80	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),C),D)) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),D)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),C)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),B),A)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),D),C)).  [resolve(5236,a,5182,a)].
23.84/23.80	Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),A),B)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),C),D)) | hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),B),D)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),C)) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),B),A)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),D),C)).  [resolve(5236,a,5191,a)].
23.84/23.80	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),C),D)) | hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),D)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),C)) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),B),A)),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),D),C)).  [resolve(5236,a,5205,a)].
23.84/23.80	5237 -semiring_div(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),C)) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(A,A,hAPP(A,fun(A,A),div_div(A),C),B)) = ti(A,C) # label(fact_1004_dvd__mult__div__cancel) # label(axiom).  [clausify(3735)].
23.84/23.80	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A),B)) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),B),A)) = ti(nat,B).  [resolve(5237,a,5182,a)].
23.84/23.80	Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),A),B)) | hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),B),A)) = ti(code_code_numeral,B).  [resolve(5237,a,5191,a)].
23.84/23.80	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),B)) | hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),B),A)) = ti(int,B).  [resolve(5237,a,5205,a)].
24.28/24.21	5238 -semiring_div(A) | hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),C),D))),D) = hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),D) # label(fact_940_mod__add__right__eq) # label(axiom).  [clausify(3823)].
24.28/24.21	5239 -semiring_div(A) | hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),D),C))),C) = hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D)),C) # label(fact_930_mod__mult__eq) # label(axiom).  [clausify(3998)].
24.28/24.21	Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),A),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),C),B))),B) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),C)),B).  [resolve(5239,a,5182,a)].
24.28/24.21	Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),A),B)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),C),B))),B) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),C)),B).  [resolve(5239,a,5191,a)].
24.28/24.21	Derived: hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),C),B))),B) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),C)),B).  [resolve(5239,a,5205,a)].
24.28/24.21	5240 -semiring_div(A) | zero_zero(A) = ti(A,B) | zero_zero(A) = ti(A,C) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),C),E)) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),E) != hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),C) | hAPP(A,A,hAPP(A,fun(A,A),div_div(A),E),C) = hAPP(A,A,hAPP(A,fun(A,A),div_div(A),D),B) # label(fact_1043_dvd__div__div__eq__mult) # label(axiom).  [clausify(4025)].
24.28/24.21	Derived: zero_zero(nat) = ti(nat,A) | zero_zero(nat) = ti(nat,B) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A),C)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),B),D)) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),D) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),C),B) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),D),B) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),C),A).  [resolve(5240,a,5182,a)].
24.28/24.21	Derived: zero_zero(code_code_numeral) = ti(code_code_numeral,A) | zero_zero(code_code_numeral) = ti(code_code_numeral,B) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),A),C)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),B),D)) | hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),D) != hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),C),B) | hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),D),B) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),C),A).  [resolve(5240,a,5191,a)].
24.40/24.31	Derived: zero_zero(int) = ti(int,A) | zero_zero(int) = ti(int,B) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),C)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),B),D)) | hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),D) != hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),B) | hAPP(int,int,hAPP(int,fun(int,int),div_div(int),D),B) = hAPP(int,int,hAPP(int,fun(int,int),div_div(int),C),A).  [resolve(5240,a,5205,a)].
24.40/24.31	5241 -semiring_div(A) | zero_zero(A) = ti(A,B) | zero_zero(A) = ti(A,C) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),C),E)) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),E) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),C) | hAPP(A,A,hAPP(A,fun(A,A),div_div(A),E),C) != hAPP(A,A,hAPP(A,fun(A,A),div_div(A),D),B) # label(fact_1043_dvd__div__div__eq__mult) # label(axiom).  [clausify(4025)].
24.40/24.31	Derived: zero_zero(nat) = ti(nat,A) | zero_zero(nat) = ti(nat,B) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A),C)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),B),D)) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),D) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),C),B) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),D),B) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),C),A).  [resolve(5241,a,5182,a)].
24.40/24.31	Derived: zero_zero(code_code_numeral) = ti(code_code_numeral,A) | zero_zero(code_code_numeral) = ti(code_code_numeral,B) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),A),C)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),B),D)) | hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),D) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),C),B) | hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),D),B) != hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),C),A).  [resolve(5241,a,5191,a)].
24.40/24.31	Derived: zero_zero(int) = ti(int,A) | zero_zero(int) = ti(int,B) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),C)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),B),D)) | hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),D) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),B) | hAPP(int,int,hAPP(int,fun(int,int),div_div(int),D),B) != hAPP(int,int,hAPP(int,fun(int,int),div_div(int),C),A).  [resolve(5241,a,5205,a)].
24.40/24.31	5242 -semiring_div(A) | hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),B) = hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),C),B) # label(fact_941_mod__add__self1) # label(axiom).  [clausify(4107)].
24.40/24.31	Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B)),A) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),B),A).  [resolve(5242,a,5182,a)].
24.40/24.31	Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),A),B)),A) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),B),A).  [resolve(5242,a,5191,a)].
24.40/24.31	Derived: hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B)),A) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),B),A).  [resolve(5242,a,5205,a)].
24.40/24.31	5243 -semiring_div(A) | zero_zero(A) = hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),zero_zero(A)),B) # label(fact_926_mod__0) # label(axiom).  [clausify(4137)].
24.64/24.56	Derived: zero_zero(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),zero_zero(nat)),A).  [resolve(5243,a,5182,a)].
24.64/24.56	Derived: zero_zero(code_code_numeral) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),zero_zero(code_code_numeral)),A).  [resolve(5243,a,5191,a)].
24.64/24.56	Derived: zero_zero(int) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),zero_zero(int)),A).  [resolve(5243,a,5205,a)].
24.64/24.56	5244 -semiring_div(A) | zero_zero(A) = ti(A,B) | hAPP(A,A,hAPP(A,fun(A,A),div_div(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),B)),B) = ti(A,C) # label(fact_997_div__mult__self2__is__id) # label(axiom).  [clausify(4226)].
24.64/24.56	Derived: zero_zero(nat) = ti(nat,A) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),A)),A) = ti(nat,B).  [resolve(5244,a,5182,a)].
24.64/24.56	Derived: zero_zero(code_code_numeral) = ti(code_code_numeral,A) | hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),B),A)),A) = ti(code_code_numeral,B).  [resolve(5244,a,5191,a)].
24.64/24.56	Derived: zero_zero(int) = ti(int,A) | hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),A)),A) = ti(int,B).  [resolve(5244,a,5205,a)].
24.64/24.56	5245 -semiring_div(A) | zero_zero(A) = hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),B) # label(fact_973_mod__mult__self1__is__0) # label(axiom).  [clausify(4315)].
24.64/24.56	Derived: zero_zero(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),B)),A).  [resolve(5245,a,5182,a)].
24.64/24.56	Derived: zero_zero(code_code_numeral) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),B)),A).  [resolve(5245,a,5191,a)].
24.64/24.56	Derived: zero_zero(int) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),A).  [resolve(5245,a,5205,a)].
24.64/24.56	5246 -semiring_div(A) | hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),C),D))),D) = hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),D) # label(fact_928_mod__mult__right__eq) # label(axiom).  [clausify(4356)].
24.64/24.56	Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),B),C))),C) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),B)),C).  [resolve(5246,a,5182,a)].
24.64/24.56	Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),B),C))),C) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),B)),C).  [resolve(5246,a,5191,a)].
24.64/24.56	5247 -semiring_div(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),C)) | hAPP(A,A,hAPP(A,fun(A,A),div_div(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),C),D)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),D)) = hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),hAPP(A,A,hAPP(A,fun(A,A),div_div(A),C),B)),D) # label(fact_1006_div__power) # label(axiom).  [clausify(4368)].
24.88/24.82	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A),B)) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),B),C)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),C)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),B),A)),C).  [resolve(5247,a,5182,a)].
24.88/24.82	Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),A),B)) | hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),B),C)),hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A),C)) = hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),B),A)),C).  [resolve(5247,a,5191,a)].
24.88/24.82	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),B)) | hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),B),C)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),C)) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),B),A)),C).  [resolve(5247,a,5205,a)].
24.88/24.82	5248 -semiring_div(A) | zero_zero(A) = ti(A,B) | hAPP(A,A,hAPP(A,fun(A,A),div_div(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D))),B) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),D),hAPP(A,A,hAPP(A,fun(A,A),div_div(A),C),B)) # label(fact_1040_div__mult__self2) # label(axiom).  [clausify(4384)].
24.88/24.82	Derived: zero_zero(nat) = ti(nat,A) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),C))),A) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),C),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),B),A)).  [resolve(5248,a,5182,a)].
24.88/24.82	Derived: zero_zero(code_code_numeral) = ti(code_code_numeral,A) | hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),B),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),C))),A) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),C),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),B),A)).  [resolve(5248,a,5191,a)].
24.88/24.82	Derived: zero_zero(int) = ti(int,A) | hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),B),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),C))),A) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),C),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),B),A)).  [resolve(5248,a,5205,a)].
24.88/24.82	5249 -semiring_div(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),C)) | zero_zero(A) = hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),C),B) # label(fact_980_dvd__eq__mod__eq__0) # label(axiom).  [clausify(4617)].
24.88/24.82	5250 -semiring_div(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),C)) | zero_zero(A) != hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),C),B) # label(fact_980_dvd__eq__mod__eq__0) # label(axiom).  [clausify(4617)].
24.88/24.82	Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A),B)) | zero_zero(nat) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),B),A).  [resolve(5250,a,5182,a)].
24.88/24.82	Derived: hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),A),B)) | zero_zero(code_code_numeral) != hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),B),A).  [resolve(5250,a,5191,a)].
25.05/24.98	Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),B)) | zero_zero(int) != hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),B),A).  [resolve(5250,a,5205,a)].
25.05/24.98	5251 -semiring_div(A) | zero_zero(A) = ti(A,B) | hAPP(A,A,hAPP(A,fun(A,A),div_div(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D)) = hAPP(A,A,hAPP(A,fun(A,A),div_div(A),C),D) # label(fact_994_div__mult__mult1) # label(axiom).  [clausify(4684)].
25.05/24.98	5252 semiring_div(quickcheck_code_int) # label(arity_Quickcheck__Narrowing_Ocode__int___Divides_Osemiring__div) # label(axiom).  [assumption].
25.05/24.98	Derived: zero_zero(quickcheck_code_int) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),zero_zero(quickcheck_code_int)),A).  [resolve(5252,a,5181,a)].
25.05/24.98	Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),A),B)),B)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),A),B)) = ti(quickcheck_code_int,A).  [resolve(5252,a,5183,a)].
25.05/24.98	Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),A),B)),C)),B) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),C)),B).  [resolve(5252,a,5184,a)].
25.05/24.98	Derived: zero_zero(quickcheck_code_int) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),A),A).  [resolve(5252,a,5185,a)].
25.05/24.98	Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),A),B)),C)),B) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),A),C)),B).  [resolve(5252,a,5186,a)].
25.05/24.98	Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),A),B) != hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),C),B) | hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),D),B) != hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),E),B) | hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),D)),B) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),C),E)),B).  [resolve(5252,a,5187,a)].
25.05/24.98	Derived: zero_zero(quickcheck_code_int) != ti(quickcheck_code_int,A) | zero_zero(quickcheck_code_int) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),B)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),C)).  [resolve(5252,a,5188,a)].
25.05/24.98	Derived: zero_zero(quickcheck_code_int) = ti(quickcheck_code_int,A) | hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),B)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),C)) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),B),C).  [resolve(5252,a,5189,a)].
25.05/24.98	Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),A),B)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),A),C)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),A),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),B),C))).  [resolve(5252,a,5190,a)].
25.05/24.98	Derived: zero_zero(quickcheck_code_int) = ti(quickcheck_code_int,A) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),A),B)) | hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),B),A) != ti(quickcheck_code_int,C) | hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),C),A) = ti(quickcheck_code_int,B).  [resolve(5252,a,5192,a)].
25.05/24.98	Derived: zero_zero(quickcheck_code_int) = ti(quickcheck_code_int,A) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),A),B)) | hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),B),A) = ti(quickcheck_code_int,C) | hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),C),A) != ti(quickcheck_code_int,B).  [resolve(5252,a,5193,a)].
25.05/24.98	Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),A),B) != hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),C),B) | hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),D),B) != hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),E),B) | hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),A),D)),B) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),C),E)),B).  [resolve(5252,a,5195,a)].
25.05/24.98	Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),A),B)) | zero_zero(quickcheck_code_int) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),B),A).  [resolve(5252,a,5196,a)].
25.05/24.98	Derived: zero_zero(quickcheck_code_int) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),A),B)),B).  [resolve(5252,a,5197,a)].
25.05/24.98	Derived: zero_zero(quickcheck_code_int) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),B)),B).  [resolve(5252,a,5198,a)].
25.05/24.98	Derived: zero_zero(quickcheck_code_int) = ti(quickcheck_code_int,A) | hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),B)),A) = ti(quickcheck_code_int,B).  [resolve(5252,a,5199,a)].
25.05/24.98	Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),A),B)) | hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),B),A)),A) = ti(quickcheck_code_int,B).  [resolve(5252,a,5200,a)].
25.05/24.98	Derived: div_mod(quickcheck_code_int) = ti(fun(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int)),div_mod(quickcheck_code_int)).  [resolve(5252,a,5201,a)].
25.05/24.98	Derived: zero_zero(quickcheck_code_int) = ti(quickcheck_code_int,A) | hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),B),A)),A) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),B),A)),one_one(quickcheck_code_int)).  [resolve(5252,a,5202,a)].
25.05/24.98	Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),A),B)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),A),C)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),B),A)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),C),A))) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),B),C)).  [resolve(5252,a,5203,a)].
25.05/24.98	Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),A),B)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),A),C)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),B),A)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),C),A))) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),B),C)).  [resolve(5252,a,5204,a)].
25.05/24.98	Derived: zero_zero(quickcheck_code_int) = ti(quickcheck_code_int,A) | hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),B),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),C),A))),A) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),C),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),B),A)).  [resolve(5252,a,5206,a)].
25.05/24.98	Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),A),B)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),C),B))),B) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),A),C)),B).  [resolve(5252,a,5207,a)].
25.05/24.98	Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),A),B)),B) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),A),B).  [resolve(5252,a,5208,a)].
25.05/24.98	Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),A),B)) | hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),C),B)),A) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),C),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),B),A)).  [resolve(5252,a,5209,a)].
25.05/24.98	Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),B)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),C),B)) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),A),C)),B).  [resolve(5252,a,5210,a)].
25.05/24.98	Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),A),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),B),C))) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),A),C)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),A),B)).  [resolve(5252,a,5211,a)].
25.05/24.98	Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),A),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),B),C))),C) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),A),B)),C).  [resolve(5252,a,5212,a)].
25.05/24.98	Derived: -number(quickcheck_code_int) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),A)),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),B))) | zero_zero(quickcheck_code_int) != hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),B)),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),A)).  [resolve(5252,a,5214,a)].
25.05/24.98	Derived: div_div(quickcheck_code_int) = ti(fun(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int)),div_div(quickcheck_code_int)).  [resolve(5252,a,5215,a)].
25.05/24.98	Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),B),A))),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),B),A))),C) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),B),C).  [resolve(5252,a,5216,a)].
25.05/24.98	Derived: zero_zero(quickcheck_code_int) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),A),one_one(quickcheck_code_int)).  [resolve(5252,a,5217,a)].
25.05/24.98	Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),A),B)),B) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),A),B).  [resolve(5252,a,5218,a)].
25.05/24.98	Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),A),B)) | hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),B),C)),A) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),B),A)),C).  [resolve(5252,a,5219,a)].
25.05/24.98	Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),A),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),B),C))),B) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),A),B).  [resolve(5252,a,5220,a)].
25.05/24.98	Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),A),B)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),A),C)) | hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),B),C)),A) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),B),A)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),C),A)).  [resolve(5252,a,5221,a)].
25.05/24.98	Derived: zero_zero(quickcheck_code_int) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),A),zero_zero(quickcheck_code_int)).  [resolve(5252,a,5222,a)].
25.05/24.98	Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),A),B)) | hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),C),B)),A) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),C),A).  [resolve(5252,a,5223,a)].
25.05/24.99	Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),B),A))),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),B),A)) = ti(quickcheck_code_int,B).  [resolve(5252,a,5224,a)].
25.05/24.99	Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),A),zero_zero(quickcheck_code_int)) = ti(quickcheck_code_int,A).  [resolve(5252,a,5226,a)].
25.05/24.99	Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),B)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),C)) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),B),C)).  [resolve(5252,a,5227,a)].
25.05/24.99	Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),A),B)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),A),B)),B)) = ti(quickcheck_code_int,A).  [resolve(5252,a,5228,a)].
25.05/24.99	Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),A),B)),B)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),A),B))),C) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),A),C).  [resolve(5252,a,5231,a)].
25.05/24.99	Derived: zero_zero(quickcheck_code_int) = ti(quickcheck_code_int,A) | hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),B),A)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),C),A)) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),B),C).  [resolve(5252,a,5232,a)].
25.05/24.99	Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),A),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),B),C))),C) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),A),C).  [resolve(5252,a,5233,a)].
25.05/24.99	Derived: zero_zero(quickcheck_code_int) = ti(quickcheck_code_int,A) | one_one(quickcheck_code_int) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),A),A).  [resolve(5252,a,5235,a)].
25.05/24.99	Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),A),B)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),C),D)) | hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),B),D)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),C)) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),B),A)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),D),C)).  [resolve(5252,a,5236,a)].
25.05/24.99	Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),A),B)) | hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),B),A)) = ti(quickcheck_code_int,B).  [resolve(5252,a,5237,a)].
25.05/24.99	Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),A),B)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),C),B))),B) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),C)),B).  [resolve(5252,a,5239,a)].
25.05/24.99	Derived: zero_zero(quickcheck_code_int) = ti(quickcheck_code_int,A) | zero_zero(quickcheck_code_int) = ti(quickcheck_code_int,B) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),A),C)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),B),D)) | hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),D) != hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),C),B) | hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),D),B) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),C),A).  [resolve(5252,a,5240,a)].
25.05/24.99	Derived: zero_zero(quickcheck_code_int) = ti(quickcheck_code_int,A) | zero_zero(quickcheck_code_int) = ti(quickcheck_code_int,B) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),A),C)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),B),D)) | hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),D) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),C),B) | hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),D),B) != hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),C),A).  [resolve(5252,a,5241,a)].
25.05/24.99	Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),A),B)),A) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),B),A).  [resolve(5252,a,5242,a)].
25.05/24.99	Derived: zero_zero(quickcheck_code_int) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),zero_zero(quickcheck_code_int)),A).  [resolve(5252,a,5243,a)].
25.05/24.99	Derived: zero_zero(quickcheck_code_int) = ti(quickcheck_code_int,A) | hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),B),A)),A) = ti(quickcheck_code_int,B).  [resolve(5252,a,5244,a)].
25.05/24.99	Derived: zero_zero(quickcheck_code_int) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),B)),A).  [resolve(5252,a,5245,a)].
25.05/24.99	Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),B),C))),C) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),B)),C).  [resolve(5252,a,5246,a)].
25.05/24.99	Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),A),B)) | hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),B),C)),hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A),C)) = hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),B),A)),C).  [resolve(5252,a,5247,a)].
25.15/25.08	Derived: zero_zero(quickcheck_code_int) = ti(quickcheck_code_int,A) | hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),B),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),C))),A) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),C),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),B),A)).  [resolve(5252,a,5248,a)].
25.15/25.08	Derived: hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),A),B)) | zero_zero(quickcheck_code_int) != hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),B),A).  [resolve(5252,a,5250,a)].
25.15/25.08	5253 -semiring_div(A) | zero_zero(A) = ti(A,B) | hAPP(A,A,hAPP(A,fun(A,A),div_div(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),B) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),div_div(A),C),B)),one_one(A)) # label(fact_1041_div__add__self1) # label(axiom).  [clausify(4873)].
25.15/25.08	Derived: zero_zero(nat) = ti(nat,A) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B)),A) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),B),A)),one_one(nat)).  [resolve(5253,a,5182,a)].
25.15/25.08	Derived: zero_zero(code_code_numeral) = ti(code_code_numeral,A) | hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),A),B)),A) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),B),A)),one_one(code_code_numeral)).  [resolve(5253,a,5191,a)].
25.15/25.08	Derived: zero_zero(int) = ti(int,A) | hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B)),A) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),B),A)),one_one(int)).  [resolve(5253,a,5205,a)].
25.15/25.08	Derived: zero_zero(quickcheck_code_int) = ti(quickcheck_code_int,A) | hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),A),B)),A) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),B),A)),one_one(quickcheck_code_int)).  [resolve(5253,a,5252,a)].
26.10/26.04	5254 -semiring_div(A) | hAPP(A,A,hAPP(A,fun(A,A),div_div(A),B),one_one(A)) = ti(A,B) # label(fact_966_div__by__1) # label(axiom).  [clausify(4885)].
26.10/26.04	Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),A),one_one(nat)) = ti(nat,A).  [resolve(5254,a,5182,a)].
26.10/26.04	Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),A),one_one(code_code_numeral)) = ti(code_code_numeral,A).  [resolve(5254,a,5191,a)].
26.10/26.04	Derived: hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A),one_one(int)) = ti(int,A).  [resolve(5254,a,5205,a)].
26.10/26.04	Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),A),one_one(quickcheck_code_int)) = ti(quickcheck_code_int,A).  [resolve(5254,a,5252,a)].
26.10/26.04	5255 linord1117847801e_zero(real) # label(arity_RealDef_Oreal___Fields_Olinordered__field__inverse__zero) # label(axiom).  [assumption].
26.10/26.04	5256 -number(A) | -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),C)),B)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(int,A,number_number_of(A),C)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),B))) # label(fact_1753_le__divide__eq__number__of) # label(axiom).  [clausify(10)].
26.10/26.04	5257 -number(A) | -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(int,A,number_number_of(A),C)),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(int,A,number_number_of(A),C)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),B))) # label(fact_1753_le__divide__eq__number__of) # label(axiom).  [clausify(10)].
26.10/26.04	5258 -number(A) | -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(int,A,number_number_of(A),C)),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),C)),B)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(int,A,number_number_of(A),C)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),B))) # label(fact_1753_le__divide__eq__number__of) # label(axiom).  [clausify(10)].
26.10/26.04	5259 -number(A) | -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),C)),D))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(int,A,number_number_of(A),C)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),D))) # label(fact_1753_le__divide__eq__number__of) # label(axiom).  [clausify(10)].
26.10/26.04	5260 -number(A) | -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),C)),D))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),C)),D)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(int,A,number_number_of(A),C)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),D))) # label(fact_1753_le__divide__eq__number__of) # label(axiom).  [clausify(10)].
26.10/26.04	5261 -number(A) | -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),C)),D))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(int,A,number_number_of(A),C)),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(int,A,number_number_of(A),C)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),D))) # label(fact_1753_le__divide__eq__number__of) # label(axiom).  [clausify(10)].
26.10/26.04	5262 -number(A) | -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),C)),D))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(int,A,number_number_of(A),C)),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),C)),D)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(int,A,number_number_of(A),C)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),D))) # label(fact_1753_le__divide__eq__number__of) # label(axiom).  [clausify(10)].
26.10/26.04	5263 -number(A) | -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),D)),B))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(int,A,number_number_of(A),D)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),B))) # label(fact_1753_le__divide__eq__number__of) # label(axiom).  [clausify(10)].
26.10/26.04	5264 -number(A) | -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(int,A,number_number_of(A),C)),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(int,A,number_number_of(A),C)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),B))) # label(fact_1753_le__divide__eq__number__of) # label(axiom).  [clausify(10)].
26.10/26.04	5265 -number(A) | -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),C)),B)),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(int,A,number_number_of(A),C)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),B))) # label(fact_1753_le__divide__eq__number__of) # label(axiom).  [clausify(10)].
26.10/26.04	5266 -linord1117847801e_zero(A) | hAPP(A,A,abs_abs(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)) = hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),hAPP(A,A,abs_abs(A),B)),hAPP(A,A,abs_abs(A),C)) # label(fact_1848_abs__divide) # label(axiom).  [clausify(16)].
26.10/26.04	5267 -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),B)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),B))) # label(fact_1735_le__divide__eq) # label(axiom).  [clausify(65)].
26.10/26.04	5268 -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),B))) # label(fact_1735_le__divide__eq) # label(axiom).  [clausify(65)].
26.10/26.04	5269 -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_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)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),B))) # label(fact_1735_le__divide__eq) # label(axiom).  [clausify(65)].
26.10/26.04	5270 -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),D))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),D))) # label(fact_1735_le__divide__eq) # label(axiom).  [clausify(65)].
26.10/26.04	5271 -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),D))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),D)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),D))) # label(fact_1735_le__divide__eq) # label(axiom).  [clausify(65)].
26.10/26.04	5272 -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),D))) | -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),zero_zero(A)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),D))) # label(fact_1735_le__divide__eq) # label(axiom).  [clausify(65)].
26.10/26.04	5273 -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),D))) | -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),D)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),D))) # label(fact_1735_le__divide__eq) # label(axiom).  [clausify(65)].
26.10/26.04	5274 -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),B))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),D),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),B))) # label(fact_1735_le__divide__eq) # label(axiom).  [clausify(65)].
26.10/26.04	5275 -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | 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),C),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),B))) # label(fact_1735_le__divide__eq) # label(axiom).  [clausify(65)].
26.10/26.04	5276 -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),B)),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),B))) # label(fact_1735_le__divide__eq) # label(axiom).  [clausify(65)].
26.10/26.04	5277 -linord1117847801e_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))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)),zero_zero(A))) # label(fact_1674_divide__le__0__iff) # label(axiom).  [clausify(173)].
26.10/26.04	5278 -linord1117847801e_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))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),B)),zero_zero(A))) # label(fact_1674_divide__le__0__iff) # label(axiom).  [clausify(173)].
26.10/26.04	5279 -linord1117847801e_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)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)),zero_zero(A))) # label(fact_1674_divide__le__0__iff) # label(axiom).  [clausify(173)].
26.10/26.04	5280 -linord1117847801e_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))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)),zero_zero(A))) # label(fact_1674_divide__le__0__iff) # label(axiom).  [clausify(173)].
26.10/26.04	5281 -linord1117847801e_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)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),B)),zero_zero(A))) # label(fact_1674_divide__le__0__iff) # label(axiom).  [clausify(173)].
26.10/26.04	5282 -linord1117847801e_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),C),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),B)),zero_zero(A))) # label(fact_1674_divide__le__0__iff) # label(axiom).  [clausify(173)].
26.10/26.04	5283 -number(A) | -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),hAPP(int,A,number_number_of(A),D)))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(int,A,number_number_of(A),D))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),D)),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),zero_zero(A))) # label(fact_1752_le__divide__eq__number__of1) # label(axiom).  [clausify(438)].
26.10/26.04	5284 -number(A) | -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),hAPP(int,A,number_number_of(A),D)))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(int,A,number_number_of(A),D))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),D)),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(int,A,number_number_of(A),D)))) # label(fact_1752_le__divide__eq__number__of1) # label(axiom).  [clausify(438)].
26.10/26.04	5285 -number(A) | -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),hAPP(int,A,number_number_of(A),D)))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(int,A,number_number_of(A),D))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(int,A,number_number_of(A),D))),C)) # label(fact_1752_le__divide__eq__number__of1) # label(axiom).  [clausify(438)].
26.10/26.04	5286 -number(A) | -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),hAPP(int,A,number_number_of(A),D)))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(int,A,number_number_of(A),D))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(int,A,number_number_of(A),D))),C)) # label(fact_1752_le__divide__eq__number__of1) # label(axiom).  [clausify(438)].
26.10/26.04	5287 -number(A) | -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),hAPP(int,A,number_number_of(A),D)))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),D)),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(int,A,number_number_of(A),D)))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(int,A,number_number_of(A),D))) # label(fact_1752_le__divide__eq__number__of1) # label(axiom).  [clausify(438)].
26.10/26.04	5288 -number(A) | -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),hAPP(int,A,number_number_of(A),D)))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),D)),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(int,A,number_number_of(A),D)))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(int,A,number_number_of(A),D))),C)) # label(fact_1752_le__divide__eq__number__of1) # label(axiom).  [clausify(438)].
26.10/26.04	5289 -number(A) | -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),hAPP(int,A,number_number_of(A),D)))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),D)),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(int,A,number_number_of(A),D))) # label(fact_1752_le__divide__eq__number__of1) # label(axiom).  [clausify(438)].
26.10/26.04	5290 -number(A) | -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),hAPP(int,A,number_number_of(A),D)))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),D)),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(int,A,number_number_of(A),D))),C)) # label(fact_1752_le__divide__eq__number__of1) # label(axiom).  [clausify(438)].
26.10/26.04	5291 -number(A) | -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),hAPP(int,A,number_number_of(A),D)))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(int,A,number_number_of(A),D)))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(int,A,number_number_of(A),D))) # label(fact_1752_le__divide__eq__number__of1) # label(axiom).  [clausify(438)].
26.10/26.04	5292 -number(A) | -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),hAPP(int,A,number_number_of(A),D)))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(int,A,number_number_of(A),D)))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(int,A,number_number_of(A),D))),C)) # label(fact_1752_le__divide__eq__number__of1) # label(axiom).  [clausify(438)].
26.10/26.04	5293 -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),hAPP(A,A,inverse_inverse(A),B))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) # label(fact_2575_one__less__inverse__iff) # label(axiom).  [clausify(481)].
26.10/26.04	5294 -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),hAPP(A,A,inverse_inverse(A),B))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),one_one(A))) # label(fact_2575_one__less__inverse__iff) # label(axiom).  [clausify(481)].
26.10/26.04	5295 -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),hAPP(A,A,inverse_inverse(A),B))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),one_one(A))) # label(fact_2575_one__less__inverse__iff) # label(axiom).  [clausify(481)].
26.10/26.04	5296 -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,inverse_inverse(A),B)),hAPP(A,A,inverse_inverse(A),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B)) # label(fact_2606_inverse__less__iff) # label(axiom).  [clausify(592)].
26.10/26.04	5297 -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,inverse_inverse(A),B)),hAPP(A,A,inverse_inverse(A),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) # label(fact_2606_inverse__less__iff) # label(axiom).  [clausify(592)].
26.14/26.05	5298 -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,inverse_inverse(A),B)),hAPP(A,A,inverse_inverse(A),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),zero_zero(A))) # label(fact_2606_inverse__less__iff) # label(axiom).  [clausify(592)].
26.14/26.05	5299 -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,inverse_inverse(A),B)),hAPP(A,A,inverse_inverse(A),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) # label(fact_2606_inverse__less__iff) # label(axiom).  [clausify(592)].
26.14/26.05	5300 -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,inverse_inverse(A),B)),hAPP(A,A,inverse_inverse(A),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),zero_zero(A))) # label(fact_2606_inverse__less__iff) # label(axiom).  [clausify(592)].
26.14/26.05	5301 -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,inverse_inverse(A),B)),hAPP(A,A,inverse_inverse(A),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) # label(fact_2606_inverse__less__iff) # label(axiom).  [clausify(592)].
26.14/26.05	5302 -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,inverse_inverse(A),B))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) # label(fact_2541_inverse__positive__iff__positive) # label(axiom).  [clausify(611)].
26.14/26.05	5303 -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,inverse_inverse(A),B))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) # label(fact_2541_inverse__positive__iff__positive) # label(axiom).  [clausify(611)].
26.14/26.05	Derived: -number(real) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),B)),A)),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,number_number_of(real),B)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),C),A))).  [resolve(5255,a,5256,b)].
26.14/26.05	Derived: -number(real) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,number_number_of(real),B)),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,number_number_of(real),B)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),C),A))).  [resolve(5255,a,5257,b)].
26.14/26.05	Derived: -number(real) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,number_number_of(real),B)),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),B)),A)),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,number_number_of(real),B)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),C),A))).  [resolve(5255,a,5258,b)].
26.14/26.05	Derived: -number(real) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),B)),C))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),C),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,number_number_of(real),B)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),C))).  [resolve(5255,a,5259,b)].
26.14/26.06	Derived: -number(real) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),B)),C))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),C),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),B)),C)),A)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,number_number_of(real),B)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),C))).  [resolve(5255,a,5260,b)].
26.14/26.06	Derived: -number(real) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),B)),C))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,number_number_of(real),B)),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,number_number_of(real),B)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),C))).  [resolve(5255,a,5261,b)].
26.14/26.06	Derived: -number(real) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),B)),C))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,number_number_of(real),B)),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),B)),C)),A)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,number_number_of(real),B)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),C))).  [resolve(5255,a,5262,b)].
26.14/26.06	Derived: -number(real) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),C)),A))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,number_number_of(real),C)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),B),A))).  [resolve(5255,a,5263,b)].
26.14/26.06	Derived: -number(real) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,number_number_of(real),B)),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,number_number_of(real),B)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),C),A))).  [resolve(5255,a,5264,b)].
26.14/26.06	Derived: -number(real) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),B)),A)),C)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,number_number_of(real),B)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),C),A))).  [resolve(5255,a,5265,b)].
26.14/26.06	Derived: hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B)) = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,abs_abs(real),A)),hAPP(real,real,abs_abs(real),B)).  [resolve(5255,a,5266,a)].
26.14/26.07	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),A)),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),C),A))).  [resolve(5255,a,5267,a)].
26.14/26.07	Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),C),A))).  [resolve(5255,a,5268,a)].
26.14/26.07	Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),A)),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),C),A))).  [resolve(5255,a,5269,a)].
26.14/26.07	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),C))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),C),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),C))).  [resolve(5255,a,5270,a)].
26.14/26.07	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),C))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),C),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),C)),A)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),C))).  [resolve(5255,a,5271,a)].
26.14/26.07	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),C))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),C))).  [resolve(5255,a,5272,a)].
26.14/26.07	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),C))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),C)),A)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),C))).  [resolve(5255,a,5273,a)].
26.14/26.07	Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),A))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),C),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),B),A))).  [resolve(5255,a,5274,a)].
26.14/26.07	Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),C),A))).  [resolve(5255,a,5275,a)].
26.14/26.10	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),A)),C)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),C),A))).  [resolve(5255,a,5276,a)].
26.14/26.10	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B)),zero_zero(real))).  [resolve(5255,a,5277,a)].
26.14/26.10	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),B),A)),zero_zero(real))).  [resolve(5255,a,5278,a)].
26.14/26.10	Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B)),zero_zero(real))).  [resolve(5255,a,5279,a)].
26.14/26.10	Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),B),A)),zero_zero(real))).  [resolve(5255,a,5282,a)].
26.14/26.10	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),hAPP(real,real,inverse_inverse(real),A))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)).  [resolve(5255,a,5293,a)].
26.14/26.10	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),hAPP(real,real,inverse_inverse(real),A))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),one_one(real))).  [resolve(5255,a,5294,a)].
26.14/26.10	Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),hAPP(real,real,inverse_inverse(real),A))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),one_one(real))).  [resolve(5255,a,5295,a)].
26.14/26.10	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,inverse_inverse(real),A)),hAPP(real,real,inverse_inverse(real),B))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),A)).  [resolve(5255,a,5296,a)].
26.14/26.10	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,inverse_inverse(real),A)),hAPP(real,real,inverse_inverse(real),B))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)).  [resolve(5255,a,5297,a)].
26.14/26.10	Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,inverse_inverse(real),A)),hAPP(real,real,inverse_inverse(real),B))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),zero_zero(real))).  [resolve(5255,a,5298,a)].
26.24/26.16	Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,inverse_inverse(real),A)),hAPP(real,real,inverse_inverse(real),B))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)).  [resolve(5255,a,5299,a)].
26.24/26.16	Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,inverse_inverse(real),A)),hAPP(real,real,inverse_inverse(real),B))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),A)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),zero_zero(real))).  [resolve(5255,a,5300,a)].
26.24/26.16	Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,inverse_inverse(real),A)),hAPP(real,real,inverse_inverse(real),B))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)).  [resolve(5255,a,5301,a)].
26.24/26.16	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,inverse_inverse(real),A))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)).  [resolve(5255,a,5302,a)].
26.24/26.16	Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,inverse_inverse(real),A))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)).  [resolve(5255,a,5303,a)].
26.24/26.16	5304 linord1117847801e_zero(rat) # label(arity_Rat_Orat___Fields_Olinordered__field__inverse__zero) # label(axiom).  [assumption].
26.24/26.16	Derived: -number(rat) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(int,rat,number_number_of(rat),B)),A)),C)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(int,rat,number_number_of(rat),B)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),C),A))).  [resolve(5304,a,5256,b)].
26.24/26.16	Derived: -number(rat) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(int,rat,number_number_of(rat),B)),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(int,rat,number_number_of(rat),B)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),C),A))).  [resolve(5304,a,5257,b)].
26.24/26.16	Derived: -number(rat) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(int,rat,number_number_of(rat),B)),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(int,rat,number_number_of(rat),B)),A)),C)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(int,rat,number_number_of(rat),B)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),C),A))).  [resolve(5304,a,5258,b)].
26.24/26.16	Derived: -number(rat) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(int,rat,number_number_of(rat),B)),C))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),C),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),C)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(int,rat,number_number_of(rat),B)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),C))).  [resolve(5304,a,5259,b)].
26.24/26.16	Derived: -number(rat) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(int,rat,number_number_of(rat),B)),C))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),C),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(int,rat,number_number_of(rat),B)),C)),A)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(int,rat,number_number_of(rat),B)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),C))).  [resolve(5304,a,5260,b)].
26.24/26.17	Derived: -number(rat) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(int,rat,number_number_of(rat),B)),C))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(int,rat,number_number_of(rat),B)),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),C)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(int,rat,number_number_of(rat),B)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),C))).  [resolve(5304,a,5261,b)].
26.24/26.17	Derived: -number(rat) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(int,rat,number_number_of(rat),B)),C))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(int,rat,number_number_of(rat),B)),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(int,rat,number_number_of(rat),B)),C)),A)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(int,rat,number_number_of(rat),B)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),C))).  [resolve(5304,a,5262,b)].
26.24/26.17	Derived: -number(rat) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),B),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(int,rat,number_number_of(rat),C)),A))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(int,rat,number_number_of(rat),C)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),B),A))).  [resolve(5304,a,5263,b)].
26.24/26.17	Derived: -number(rat) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(int,rat,number_number_of(rat),B)),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(int,rat,number_number_of(rat),B)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),C),A))).  [resolve(5304,a,5264,b)].
26.24/26.17	Derived: -number(rat) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(int,rat,number_number_of(rat),B)),A)),C)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(int,rat,number_number_of(rat),B)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),C),A))).  [resolve(5304,a,5265,b)].
26.24/26.17	Derived: hAPP(rat,rat,abs_abs(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),B)) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),hAPP(rat,rat,abs_abs(rat),A)),hAPP(rat,rat,abs_abs(rat),B)).  [resolve(5304,a,5266,a)].
26.24/26.17	Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),B),A)),C)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),B),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),C),A))).  [resolve(5304,a,5267,a)].
26.24/26.17	Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),B),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),B),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),C),A))).  [resolve(5304,a,5268,a)].
26.30/26.19	Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),B),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),B),A)),C)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),B),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),C),A))).  [resolve(5304,a,5269,a)].
26.30/26.19	Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),B),C))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),C),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),C)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),B),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),C))).  [resolve(5304,a,5270,a)].
26.30/26.19	Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),B),C))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),C),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),B),C)),A)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),B),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),C))).  [resolve(5304,a,5271,a)].
26.30/26.19	Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),B),C))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),B),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),C)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),B),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),C))).  [resolve(5304,a,5272,a)].
26.30/26.19	Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),B),C))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),B),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),B),C)),A)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),B),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),C))).  [resolve(5304,a,5273,a)].
26.30/26.19	Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),B),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),C),A))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),C),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),B),A))).  [resolve(5304,a,5274,a)].
26.30/26.19	Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),B),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),B),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),C),A))).  [resolve(5304,a,5275,a)].
26.30/26.19	Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),B),A)),C)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),B),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),C),A))).  [resolve(5304,a,5276,a)].
26.30/26.19	Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),B),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),B)),zero_zero(rat))).  [resolve(5304,a,5277,a)].
26.30/26.19	Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),B),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),B),A)),zero_zero(rat))).  [resolve(5304,a,5278,a)].
26.30/26.22	Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),A)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),B)),zero_zero(rat))).  [resolve(5304,a,5279,a)].
26.30/26.22	Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),A)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),B)),zero_zero(rat))).  [resolve(5304,a,5280,a)].
26.30/26.22	Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),B),A)),zero_zero(rat))).  [resolve(5304,a,5281,a)].
26.30/26.22	Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),B),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),B),A)),zero_zero(rat))).  [resolve(5304,a,5282,a)].
26.30/26.22	Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),one_one(rat)),hAPP(rat,rat,inverse_inverse(rat),A))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)).  [resolve(5304,a,5293,a)].
26.30/26.22	Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),one_one(rat)),hAPP(rat,rat,inverse_inverse(rat),A))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),one_one(rat))).  [resolve(5304,a,5294,a)].
26.30/26.22	Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),one_one(rat)),hAPP(rat,rat,inverse_inverse(rat),A))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),one_one(rat))).  [resolve(5304,a,5295,a)].
26.30/26.22	Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,inverse_inverse(rat),A)),hAPP(rat,rat,inverse_inverse(rat),B))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),A)).  [resolve(5304,a,5296,a)].
26.30/26.22	Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,inverse_inverse(rat),A)),hAPP(rat,rat,inverse_inverse(rat),B))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B)),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),B)).  [resolve(5304,a,5297,a)].
26.30/26.22	Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,inverse_inverse(rat),A)),hAPP(rat,rat,inverse_inverse(rat),B))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B)),zero_zero(rat))).  [resolve(5304,a,5298,a)].
26.30/26.22	Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,inverse_inverse(rat),A)),hAPP(rat,rat,inverse_inverse(rat),B))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),B)).  [resolve(5304,a,5299,a)].
26.30/26.22	Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,inverse_inverse(rat),A)),hAPP(rat,rat,inverse_inverse(rat),B))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),A)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B)),zero_zero(rat))).  [resolve(5304,a,5300,a)].
26.42/26.34	Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,inverse_inverse(rat),A)),hAPP(rat,rat,inverse_inverse(rat),B))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),B)).  [resolve(5304,a,5301,a)].
26.42/26.34	Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(rat,rat,inverse_inverse(rat),A))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)).  [resolve(5304,a,5302,a)].
26.42/26.34	Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(rat,rat,inverse_inverse(rat),A))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)).  [resolve(5304,a,5303,a)].
26.42/26.34	5305 -linord1117847801e_zero(A) | -number(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),hAPP(int,A,number_number_of(A),C)),B)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),C)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),B))) # label(fact_1746_less__divide__eq__number__of) # label(axiom).  [clausify(1580)].
26.42/26.34	Derived: -number(real) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),B)),A)),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,number_number_of(real),B)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),C),A))).  [resolve(5305,a,5255,a)].
26.42/26.34	Derived: -number(rat) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(int,rat,number_number_of(rat),B)),A)),C)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(int,rat,number_number_of(rat),B)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),C),A))).  [resolve(5305,a,5304,a)].
26.42/26.34	5306 -linord1117847801e_zero(A) | -number(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(int,A,number_number_of(A),C)),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),C)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),B))) # label(fact_1746_less__divide__eq__number__of) # label(axiom).  [clausify(1580)].
26.42/26.34	Derived: -number(real) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,number_number_of(real),B)),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,number_number_of(real),B)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),C),A))).  [resolve(5306,a,5255,a)].
26.42/26.34	Derived: -number(rat) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(int,rat,number_number_of(rat),B)),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(int,rat,number_number_of(rat),B)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),C),A))).  [resolve(5306,a,5304,a)].
26.42/26.34	5307 -linord1117847801e_zero(A) | -number(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(int,A,number_number_of(A),C)),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),C)),B)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),C)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),B))) # label(fact_1746_less__divide__eq__number__of) # label(axiom).  [clausify(1580)].
26.46/26.35	Derived: -number(real) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,number_number_of(real),B)),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),B)),A)),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,number_number_of(real),B)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),C),A))).  [resolve(5307,a,5255,a)].
26.46/26.35	Derived: -number(rat) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(int,rat,number_number_of(rat),B)),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(int,rat,number_number_of(rat),B)),A)),C)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(int,rat,number_number_of(rat),B)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),C),A))).  [resolve(5307,a,5304,a)].
26.46/26.35	5308 -linord1117847801e_zero(A) | -number(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),C)),D))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),C)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),D))) # label(fact_1746_less__divide__eq__number__of) # label(axiom).  [clausify(1580)].
26.46/26.35	Derived: -number(real) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),B)),C))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),C),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,number_number_of(real),B)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),C))).  [resolve(5308,a,5255,a)].
26.46/26.35	Derived: -number(rat) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(int,rat,number_number_of(rat),B)),C))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),C),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),C)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(int,rat,number_number_of(rat),B)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),C))).  [resolve(5308,a,5304,a)].
26.46/26.35	5309 -linord1117847801e_zero(A) | -number(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),C)),D))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),C)),D)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),C)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),D))) # label(fact_1746_less__divide__eq__number__of) # label(axiom).  [clausify(1580)].
26.46/26.35	Derived: -number(real) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),B)),C))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),C),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),B)),C)),A)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,number_number_of(real),B)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),C))).  [resolve(5309,a,5255,a)].
26.46/26.35	Derived: -number(rat) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(int,rat,number_number_of(rat),B)),C))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),C),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(int,rat,number_number_of(rat),B)),C)),A)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(int,rat,number_number_of(rat),B)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),C))).  [resolve(5309,a,5304,a)].
26.46/26.35	5310 -linord1117847801e_zero(A) | -number(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),C)),D))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),C)),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),C)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),D))) # label(fact_1746_less__divide__eq__number__of) # label(axiom).  [clausify(1580)].
26.46/26.35	Derived: -number(real) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),B)),C))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,number_number_of(real),B)),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,number_number_of(real),B)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),C))).  [resolve(5310,a,5255,a)].
26.46/26.35	Derived: -number(rat) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(int,rat,number_number_of(rat),B)),C))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(int,rat,number_number_of(rat),B)),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),C)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(int,rat,number_number_of(rat),B)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),C))).  [resolve(5310,a,5304,a)].
26.46/26.35	5311 -linord1117847801e_zero(A) | -number(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),C)),D))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),C)),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),C)),D)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),C)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),D))) # label(fact_1746_less__divide__eq__number__of) # label(axiom).  [clausify(1580)].
26.46/26.35	Derived: -number(real) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),B)),C))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,number_number_of(real),B)),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),B)),C)),A)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,number_number_of(real),B)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),C))).  [resolve(5311,a,5255,a)].
26.46/26.35	Derived: -number(rat) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(int,rat,number_number_of(rat),B)),C))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(int,rat,number_number_of(rat),B)),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(int,rat,number_number_of(rat),B)),C)),A)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(int,rat,number_number_of(rat),B)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),C))).  [resolve(5311,a,5304,a)].
26.46/26.36	5312 -linord1117847801e_zero(A) | -number(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),D)),B))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),D)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),B))) # label(fact_1746_less__divide__eq__number__of) # label(axiom).  [clausify(1580)].
26.46/26.36	Derived: -number(real) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),C)),A))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,number_number_of(real),C)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),B),A))).  [resolve(5312,a,5255,a)].
26.46/26.36	Derived: -number(rat) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(int,rat,number_number_of(rat),C)),A))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(int,rat,number_number_of(rat),C)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),B),A))).  [resolve(5312,a,5304,a)].
26.46/26.36	5313 -linord1117847801e_zero(A) | -number(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),C)),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),C)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),B))) # label(fact_1746_less__divide__eq__number__of) # label(axiom).  [clausify(1580)].
26.46/26.36	Derived: -number(real) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,number_number_of(real),B)),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,number_number_of(real),B)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),C),A))).  [resolve(5313,a,5255,a)].
26.46/26.36	Derived: -number(rat) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(int,rat,number_number_of(rat),B)),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(int,rat,number_number_of(rat),B)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),C),A))).  [resolve(5313,a,5304,a)].
26.46/26.36	5314 -linord1117847801e_zero(A) | -number(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),hAPP(int,A,number_number_of(A),C)),B)),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),C)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),B))) # label(fact_1746_less__divide__eq__number__of) # label(axiom).  [clausify(1580)].
26.46/26.43	Derived: -number(real) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),B)),A)),C)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,number_number_of(real),B)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),C),A))).  [resolve(5314,a,5255,a)].
26.46/26.43	Derived: -number(rat) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(int,rat,number_number_of(rat),B)),A)),C)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(int,rat,number_number_of(rat),B)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),C),A))).  [resolve(5314,a,5304,a)].
26.46/26.43	5315 -linord1117847801e_zero(A) | -number(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)),hAPP(int,A,number_number_of(A),D))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(int,A,number_number_of(A),D))) # label(fact_1754_divide__le__eq__number__of) # label(axiom).  [clausify(1793)].
26.46/26.43	Derived: -number(real) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B)),hAPP(int,real,number_number_of(real),C))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(int,real,number_number_of(real),C))).  [resolve(5315,a,5255,a)].
26.46/26.43	Derived: -number(rat) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),B)),hAPP(int,rat,number_number_of(rat),C))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),hAPP(int,rat,number_number_of(rat),C))).  [resolve(5315,a,5304,a)].
26.46/26.43	5316 -linord1117847801e_zero(A) | -number(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)),hAPP(int,A,number_number_of(A),D))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),D)),C)),B)) # label(fact_1754_divide__le__eq__number__of) # label(axiom).  [clausify(1793)].
26.46/26.43	Derived: -number(real) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B)),hAPP(int,real,number_number_of(real),C))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),C)),B)),A)).  [resolve(5316,a,5255,a)].
26.46/26.43	Derived: -number(rat) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),B)),hAPP(int,rat,number_number_of(rat),C))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(int,rat,number_number_of(rat),C)),B)),A)).  [resolve(5316,a,5304,a)].
26.55/26.44	5317 -linord1117847801e_zero(A) | -number(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)),hAPP(int,A,number_number_of(A),D))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),D)),C))) # label(fact_1754_divide__le__eq__number__of) # label(axiom).  [clausify(1793)].
26.55/26.44	Derived: -number(real) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B)),hAPP(int,real,number_number_of(real),C))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),C)),B))).  [resolve(5317,a,5255,a)].
26.55/26.44	Derived: -number(rat) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),B)),hAPP(int,rat,number_number_of(rat),C))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(int,rat,number_number_of(rat),C)),B))).  [resolve(5317,a,5304,a)].
26.55/26.44	5318 -linord1117847801e_zero(A) | -number(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)),hAPP(int,A,number_number_of(A),D))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),D)),C))) # label(fact_1754_divide__le__eq__number__of) # label(axiom).  [clausify(1793)].
26.55/26.44	Derived: -number(real) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B)),hAPP(int,real,number_number_of(real),C))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),C)),B))).  [resolve(5318,a,5255,a)].
26.55/26.44	Derived: -number(rat) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),B)),hAPP(int,rat,number_number_of(rat),C))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(int,rat,number_number_of(rat),C)),B))).  [resolve(5318,a,5304,a)].
26.55/26.44	5319 -linord1117847801e_zero(A) | -number(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)),hAPP(int,A,number_number_of(A),D))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),D)),C)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),C)) # label(fact_1754_divide__le__eq__number__of) # label(axiom).  [clausify(1793)].
26.55/26.44	Derived: -number(real) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B)),hAPP(int,real,number_number_of(real),C))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),C)),B)),A)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B)).  [resolve(5319,a,5255,a)].
26.55/26.44	Derived: -number(rat) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),B)),hAPP(int,rat,number_number_of(rat),C))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(int,rat,number_number_of(rat),C)),B)),A)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),B)).  [resolve(5319,a,5304,a)].
26.55/26.45	5320 -linord1117847801e_zero(A) | -number(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)),hAPP(int,A,number_number_of(A),D))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),D)),C)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),D)),C))) # label(fact_1754_divide__le__eq__number__of) # label(axiom).  [clausify(1793)].
26.55/26.45	Derived: -number(real) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B)),hAPP(int,real,number_number_of(real),C))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),C)),B)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),C)),B))).  [resolve(5320,a,5255,a)].
26.55/26.45	Derived: -number(rat) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),B)),hAPP(int,rat,number_number_of(rat),C))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(int,rat,number_number_of(rat),C)),B)),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(int,rat,number_number_of(rat),C)),B))).  [resolve(5320,a,5304,a)].
26.55/26.45	5321 -linord1117847801e_zero(A) | -number(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)),hAPP(int,A,number_number_of(A),D))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(int,A,number_number_of(A),D))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),C)) # label(fact_1754_divide__le__eq__number__of) # label(axiom).  [clausify(1793)].
26.55/26.45	Derived: -number(real) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B)),hAPP(int,real,number_number_of(real),C))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(int,real,number_number_of(real),C))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B)).  [resolve(5321,a,5255,a)].
26.55/26.45	Derived: -number(rat) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),B)),hAPP(int,rat,number_number_of(rat),C))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),hAPP(int,rat,number_number_of(rat),C))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),B)).  [resolve(5321,a,5304,a)].
26.55/26.45	5322 -linord1117847801e_zero(A) | -number(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)),hAPP(int,A,number_number_of(A),D))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(int,A,number_number_of(A),D))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),D)),C))) # label(fact_1754_divide__le__eq__number__of) # label(axiom).  [clausify(1793)].
26.55/26.45	Derived: -number(real) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B)),hAPP(int,real,number_number_of(real),C))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(int,real,number_number_of(real),C))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),C)),B))).  [resolve(5322,a,5255,a)].
26.55/26.45	Derived: -number(rat) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),B)),hAPP(int,rat,number_number_of(rat),C))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),hAPP(int,rat,number_number_of(rat),C))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(int,rat,number_number_of(rat),C)),B))).  [resolve(5322,a,5304,a)].
26.55/26.45	5323 -linord1117847801e_zero(A) | -number(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)),hAPP(int,A,number_number_of(A),D))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(int,A,number_number_of(A),D))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),D)),C)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),C)) # label(fact_1754_divide__le__eq__number__of) # label(axiom).  [clausify(1793)].
26.55/26.45	Derived: -number(real) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B)),hAPP(int,real,number_number_of(real),C))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(int,real,number_number_of(real),C))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),C)),B)),A)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B)).  [resolve(5323,a,5255,a)].
26.55/26.45	Derived: -number(rat) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),B)),hAPP(int,rat,number_number_of(rat),C))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),hAPP(int,rat,number_number_of(rat),C))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(int,rat,number_number_of(rat),C)),B)),A)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),B)).  [resolve(5323,a,5304,a)].
26.55/26.45	5324 -linord1117847801e_zero(A) | -number(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)),hAPP(int,A,number_number_of(A),D))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(int,A,number_number_of(A),D))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),D)),C)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),D)),C))) # label(fact_1754_divide__le__eq__number__of) # label(axiom).  [clausify(1793)].
26.55/26.45	Derived: -number(real) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B)),hAPP(int,real,number_number_of(real),C))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(int,real,number_number_of(real),C))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),C)),B)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),C)),B))).  [resolve(5324,a,5255,a)].
26.60/26.51	Derived: -number(rat) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),B)),hAPP(int,rat,number_number_of(rat),C))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),hAPP(int,rat,number_number_of(rat),C))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(int,rat,number_number_of(rat),C)),B)),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(int,rat,number_number_of(rat),C)),B))).  [resolve(5324,a,5304,a)].
26.60/26.51	5325 -linord1117847801e_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),hAPP(A,A,inverse_inverse(A),B)),zero_zero(A))) # label(fact_2539_inverse__nonpositive__iff__nonpositive) # label(axiom).  [clausify(1832)].
26.60/26.51	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,inverse_inverse(real),A)),zero_zero(real))).  [resolve(5325,a,5255,a)].
26.60/26.51	Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,inverse_inverse(rat),A)),zero_zero(rat))).  [resolve(5325,a,5304,a)].
26.60/26.51	5326 -linord1117847801e_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),hAPP(A,A,inverse_inverse(A),B)),zero_zero(A))) # label(fact_2539_inverse__nonpositive__iff__nonpositive) # label(axiom).  [clausify(1832)].
26.60/26.51	Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,inverse_inverse(real),A)),zero_zero(real))).  [resolve(5326,a,5255,a)].
26.60/26.51	Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,inverse_inverse(rat),A)),zero_zero(rat))).  [resolve(5326,a,5304,a)].
26.60/26.51	5327 -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),D)) # label(fact_1700_divide__le__cancel) # label(axiom).  [clausify(1946)].
26.60/26.51	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),C),B))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),C)).  [resolve(5327,a,5255,a)].
26.60/26.51	Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),B)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),C),B))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),C)).  [resolve(5327,a,5304,a)].
26.60/26.51	5328 -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),D),B)) # label(fact_1700_divide__le__cancel) # label(axiom).  [clausify(1946)].
26.60/26.52	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),C),B))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),C),A)).  [resolve(5328,a,5255,a)].
26.60/26.52	Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),B)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),C),B))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),C),A)).  [resolve(5328,a,5304,a)].
26.60/26.52	5329 -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),zero_zero(A))) # label(fact_1700_divide__le__cancel) # label(axiom).  [clausify(1946)].
26.60/26.52	Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),C),B))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),zero_zero(real))).  [resolve(5329,a,5255,a)].
26.60/26.52	Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),B)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),C),B))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),zero_zero(rat))).  [resolve(5329,a,5304,a)].
26.60/26.52	5330 -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),D),B)) # label(fact_1700_divide__le__cancel) # label(axiom).  [clausify(1946)].
26.60/26.52	Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),C),B))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),C),A)).  [resolve(5330,a,5255,a)].
26.60/26.52	Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),B)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),C),B))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),C),A)).  [resolve(5330,a,5304,a)].
26.60/26.52	5331 -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),zero_zero(A))) # label(fact_1700_divide__le__cancel) # label(axiom).  [clausify(1946)].
26.60/26.52	Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),C),B))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),zero_zero(real))).  [resolve(5331,a,5255,a)].
26.72/26.61	Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),B)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),C),B))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),C)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),zero_zero(rat))).  [resolve(5331,a,5304,a)].
26.72/26.61	5332 -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),D),B)) # label(fact_1700_divide__le__cancel) # label(axiom).  [clausify(1946)].
26.72/26.61	Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),C),B))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),C)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),C),A)).  [resolve(5332,a,5255,a)].
26.72/26.61	Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),B)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),C),B))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),C)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),C),A)).  [resolve(5332,a,5304,a)].
26.72/26.61	5333 -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),D),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),D)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),D))) # label(fact_1672_divide__right__mono__neg) # label(axiom).  [clausify(1959)].
26.72/26.61	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),C),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),B),C)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),C))).  [resolve(5333,a,5255,a)].
26.72/26.61	Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),C),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),B),C)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),C))).  [resolve(5333,a,5304,a)].
26.72/26.61	5334 -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),D),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),B)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),C))) # label(fact_1744_divide__left__mono__neg) # label(axiom).  [clausify(2189)].
26.72/26.61	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),C),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),C),A)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),C),B))).  [resolve(5334,a,5255,a)].
26.72/26.61	Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),C),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),C),A)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),C),B))).  [resolve(5334,a,5304,a)].
26.86/26.78	5335 -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),C))) | zero_zero(A) != ti(A,C) # label(fact_1678_divide__less__cancel) # label(axiom).  [clausify(2369)].
26.86/26.78	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),C),B))) | zero_zero(real) != ti(real,B).  [resolve(5335,a,5255,a)].
26.86/26.78	Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),B)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),C),B))) | zero_zero(rat) != ti(rat,B).  [resolve(5335,a,5304,a)].
26.86/26.78	5336 -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),B)) # label(fact_1678_divide__less__cancel) # label(axiom).  [clausify(2369)].
26.86/26.78	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),C),B))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),C),A)).  [resolve(5336,a,5255,a)].
26.86/26.78	Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),B)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),C),B))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),C),A)).  [resolve(5336,a,5304,a)].
26.86/26.78	5337 -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),D)) # label(fact_1678_divide__less__cancel) # label(axiom).  [clausify(2369)].
26.86/26.78	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),C),B))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),C)).  [resolve(5337,a,5255,a)].
26.86/26.78	Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),B)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),C),B))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),C)).  [resolve(5337,a,5304,a)].
26.86/26.78	5338 -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),C))) | zero_zero(A) = ti(A,C) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),C)) # label(fact_1678_divide__less__cancel) # label(axiom).  [clausify(2369)].
26.86/26.78	Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),C),B))) | zero_zero(real) = ti(real,B) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B)).  [resolve(5338,a,5255,a)].
26.90/26.81	Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),B)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),C),B))) | zero_zero(rat) = ti(rat,B) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),B)).  [resolve(5338,a,5304,a)].
26.90/26.81	5339 -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),C))) | zero_zero(A) = ti(A,C) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),D)) # label(fact_1678_divide__less__cancel) # label(axiom).  [clausify(2369)].
26.90/26.81	Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),C),B))) | zero_zero(real) = ti(real,B) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),C)).  [resolve(5339,a,5255,a)].
26.90/26.81	Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),B)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),C),B))) | zero_zero(rat) = ti(rat,B) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),C)).  [resolve(5339,a,5304,a)].
26.90/26.81	5340 -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),C))) | zero_zero(A) = ti(A,C) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),C)) # label(fact_1678_divide__less__cancel) # label(axiom).  [clausify(2369)].
26.90/26.81	Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),C),B))) | zero_zero(real) = ti(real,B) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),C),A)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B)).  [resolve(5340,a,5255,a)].
26.90/26.81	Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),B)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),C),B))) | zero_zero(rat) = ti(rat,B) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),C),A)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),B)).  [resolve(5340,a,5304,a)].
26.90/26.81	5341 -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),C))) | zero_zero(A) = ti(A,C) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),D)) # label(fact_1678_divide__less__cancel) # label(axiom).  [clausify(2369)].
26.90/26.81	Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),C),B))) | zero_zero(real) = ti(real,B) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),C),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),C)).  [resolve(5341,a,5255,a)].
26.90/26.81	Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),B)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),C),B))) | zero_zero(rat) = ti(rat,B) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),C),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),C)).  [resolve(5341,a,5304,a)].
26.90/26.81	5342 -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),one_one(A)),hAPP(A,A,inverse_inverse(A),B))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),one_one(A))) # label(fact_2608_one__le__inverse__iff) # label(axiom).  [clausify(2420)].
26.90/26.83	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),one_one(real)),hAPP(real,real,inverse_inverse(real),A))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),one_one(real))).  [resolve(5342,a,5255,a)].
26.90/26.83	Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),one_one(rat)),hAPP(rat,rat,inverse_inverse(rat),A))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),one_one(rat))).  [resolve(5342,a,5304,a)].
26.90/26.83	5343 -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),one_one(A)),hAPP(A,A,inverse_inverse(A),B))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) # label(fact_2608_one__le__inverse__iff) # label(axiom).  [clausify(2420)].
26.90/26.83	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),one_one(real)),hAPP(real,real,inverse_inverse(real),A))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)).  [resolve(5343,a,5255,a)].
26.90/26.83	Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),one_one(rat)),hAPP(rat,rat,inverse_inverse(rat),A))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)).  [resolve(5343,a,5304,a)].
26.90/26.83	5344 -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),one_one(A)),hAPP(A,A,inverse_inverse(A),B))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),one_one(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) # label(fact_2608_one__le__inverse__iff) # label(axiom).  [clausify(2420)].
26.90/26.83	Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),one_one(real)),hAPP(real,real,inverse_inverse(real),A))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),one_one(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)).  [resolve(5344,a,5255,a)].
26.90/26.83	Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),one_one(rat)),hAPP(rat,rat,inverse_inverse(rat),A))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),one_one(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)).  [resolve(5344,a,5304,a)].
26.90/26.83	5345 -linord1117847801e_zero(A) | -number_ring(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),hAPP(int,A,number_number_of(A),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) # label(fact_1757_half__gt__zero) # label(axiom).  [clausify(2453)].
26.90/26.83	Derived: -number_ring(real) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))).  [resolve(5345,a,5255,a)].
26.90/26.83	Derived: -number_ring(rat) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),hAPP(int,rat,number_number_of(rat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))).  [resolve(5345,a,5304,a)].
26.90/26.83	5346 -number_ring(A) | -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),one_one(A)),hAPP(int,A,number_number_of(A),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) # label(fact_1768_half) # label(axiom).  [clausify(2460)].
26.90/26.83	Derived: -number_ring(real) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),one_one(real)),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))).  [resolve(5346,b,5255,a)].
26.96/26.85	Derived: -number_ring(rat) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),one_one(rat)),hAPP(int,rat,number_number_of(rat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))).  [resolve(5346,b,5304,a)].
26.96/26.85	5347 -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),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))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,inverse_inverse(A),B)),hAPP(A,A,inverse_inverse(A),C))) # label(fact_2607_inverse__le__iff) # label(axiom).  [clausify(2475)].
26.96/26.85	Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,inverse_inverse(real),A)),hAPP(real,real,inverse_inverse(real),B))).  [resolve(5347,a,5255,a)].
26.96/26.85	Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B)),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,inverse_inverse(rat),A)),hAPP(rat,rat,inverse_inverse(rat),B))).  [resolve(5347,a,5304,a)].
26.96/26.85	5348 -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,inverse_inverse(A),B)),hAPP(A,A,inverse_inverse(A),C))) # label(fact_2607_inverse__le__iff) # label(axiom).  [clausify(2475)].
26.96/26.85	Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),A)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,inverse_inverse(real),A)),hAPP(real,real,inverse_inverse(real),B))).  [resolve(5348,a,5255,a)].
26.96/26.85	Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B)),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),B),A)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,inverse_inverse(rat),A)),hAPP(rat,rat,inverse_inverse(rat),B))).  [resolve(5348,a,5304,a)].
26.96/26.85	5349 -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,inverse_inverse(A),B)),hAPP(A,A,inverse_inverse(A),C))) # label(fact_2607_inverse__le__iff) # label(axiom).  [clausify(2475)].
26.96/26.85	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,inverse_inverse(real),A)),hAPP(real,real,inverse_inverse(real),B))).  [resolve(5349,a,5255,a)].
26.96/26.85	Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,inverse_inverse(rat),A)),hAPP(rat,rat,inverse_inverse(rat),B))).  [resolve(5349,a,5304,a)].
26.96/26.88	5350 -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,inverse_inverse(A),B)),hAPP(A,A,inverse_inverse(A),C))) # label(fact_2607_inverse__le__iff) # label(axiom).  [clausify(2475)].
26.96/26.88	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),A)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,inverse_inverse(real),A)),hAPP(real,real,inverse_inverse(real),B))).  [resolve(5350,a,5255,a)].
26.96/26.88	Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),B),A)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,inverse_inverse(rat),A)),hAPP(rat,rat,inverse_inverse(rat),B))).  [resolve(5350,a,5304,a)].
26.96/26.88	5351 -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,inverse_inverse(A),B)),hAPP(A,A,inverse_inverse(A),C))) # label(fact_2607_inverse__le__iff) # label(axiom).  [clausify(2475)].
26.96/26.88	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,inverse_inverse(real),A)),hAPP(real,real,inverse_inverse(real),B))).  [resolve(5351,a,5255,a)].
26.96/26.88	Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B)),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,inverse_inverse(rat),A)),hAPP(rat,rat,inverse_inverse(rat),B))).  [resolve(5351,a,5304,a)].
26.96/26.88	5352 -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,inverse_inverse(A),B)),hAPP(A,A,inverse_inverse(A),C))) # label(fact_2607_inverse__le__iff) # label(axiom).  [clausify(2475)].
26.96/26.88	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,inverse_inverse(real),A)),hAPP(real,real,inverse_inverse(real),B))).  [resolve(5352,a,5255,a)].
26.96/26.88	Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),B),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,inverse_inverse(rat),A)),hAPP(rat,rat,inverse_inverse(rat),B))).  [resolve(5352,a,5304,a)].
26.96/26.88	5353 -number(A) | -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),D)),B))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),B)),hAPP(int,A,number_number_of(A),D))) # label(fact_1747_divide__less__eq__number__of) # label(axiom).  [clausify(2525)].
26.96/26.88	Derived: -number(real) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),C)),A))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),B),A)),hAPP(int,real,number_number_of(real),C))).  [resolve(5353,b,5255,a)].
26.96/26.89	Derived: -number(rat) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(int,rat,number_number_of(rat),C)),A))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),B),A)),hAPP(int,rat,number_number_of(rat),C))).  [resolve(5353,b,5304,a)].
26.96/26.89	5354 -number(A) | -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(int,A,number_number_of(A),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),B)),hAPP(int,A,number_number_of(A),C))) # label(fact_1747_divide__less__eq__number__of) # label(axiom).  [clausify(2525)].
26.96/26.89	Derived: -number(real) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(int,real,number_number_of(real),B))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),C),A)),hAPP(int,real,number_number_of(real),B))).  [resolve(5354,b,5255,a)].
26.96/26.89	Derived: -number(rat) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(int,rat,number_number_of(rat),B))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),C),A)),hAPP(int,rat,number_number_of(rat),B))).  [resolve(5354,b,5304,a)].
26.96/26.89	5355 -number(A) | -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(int,A,number_number_of(A),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),C)),B))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),B)),hAPP(int,A,number_number_of(A),C))) # label(fact_1747_divide__less__eq__number__of) # label(axiom).  [clausify(2525)].
26.96/26.89	Derived: -number(real) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(int,real,number_number_of(real),B))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),C),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),B)),A))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),C),A)),hAPP(int,real,number_number_of(real),B))).  [resolve(5355,b,5255,a)].
26.96/26.89	Derived: -number(rat) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(int,rat,number_number_of(rat),B))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),C),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(int,rat,number_number_of(rat),B)),A))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),C),A)),hAPP(int,rat,number_number_of(rat),B))).  [resolve(5355,b,5304,a)].
26.96/26.89	5356 -number(A) | -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),B)),C)),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),C)),hAPP(int,A,number_number_of(A),B))) # label(fact_1747_divide__less__eq__number__of) # label(axiom).  [clausify(2525)].
26.96/26.89	Derived: -number(real) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),A)),B)),C)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),C),B)),hAPP(int,real,number_number_of(real),A))).  [resolve(5356,b,5255,a)].
26.96/26.89	Derived: -number(rat) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(int,rat,number_number_of(rat),A)),B)),C)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),C),B)),hAPP(int,rat,number_number_of(rat),A))).  [resolve(5356,b,5304,a)].
26.96/26.89	5357 -number(A) | -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),B)),C)),D)) | -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),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),B)),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),C)),hAPP(int,A,number_number_of(A),B))) # label(fact_1747_divide__less__eq__number__of) # label(axiom).  [clausify(2525)].
26.96/26.89	Derived: -number(real) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),A)),B)),C)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),C),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),A)),B))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),C),B)),hAPP(int,real,number_number_of(real),A))).  [resolve(5357,b,5255,a)].
26.96/26.89	Derived: -number(rat) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(int,rat,number_number_of(rat),A)),B)),C)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),C),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(int,rat,number_number_of(rat),A)),B))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),C),B)),hAPP(int,rat,number_number_of(rat),A))).  [resolve(5357,b,5304,a)].
26.96/26.89	5358 -number(A) | -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),B)),C)),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(int,A,number_number_of(A),B))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),C)),hAPP(int,A,number_number_of(A),B))) # label(fact_1747_divide__less__eq__number__of) # label(axiom).  [clausify(2525)].
26.96/26.89	Derived: -number(real) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),A)),B)),C)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(int,real,number_number_of(real),A))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),C),B)),hAPP(int,real,number_number_of(real),A))).  [resolve(5358,b,5255,a)].
26.96/26.90	Derived: -number(rat) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(int,rat,number_number_of(rat),A)),B)),C)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(int,rat,number_number_of(rat),A))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),C),B)),hAPP(int,rat,number_number_of(rat),A))).  [resolve(5358,b,5304,a)].
26.96/26.90	5359 -number(A) | -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),B)),C)),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(int,A,number_number_of(A),B))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),B)),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),C)),hAPP(int,A,number_number_of(A),B))) # label(fact_1747_divide__less__eq__number__of) # label(axiom).  [clausify(2525)].
26.96/26.90	Derived: -number(real) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),A)),B)),C)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(int,real,number_number_of(real),A))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),C),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),A)),B))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),C),B)),hAPP(int,real,number_number_of(real),A))).  [resolve(5359,b,5255,a)].
26.96/26.90	Derived: -number(rat) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(int,rat,number_number_of(rat),A)),B)),C)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(int,rat,number_number_of(rat),A))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),C),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(int,rat,number_number_of(rat),A)),B))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),C),B)),hAPP(int,rat,number_number_of(rat),A))).  [resolve(5359,b,5304,a)].
26.96/26.90	5360 -number(A) | -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),C)),B)),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),B)),hAPP(int,A,number_number_of(A),C))) # label(fact_1747_divide__less__eq__number__of) # label(axiom).  [clausify(2525)].
26.96/26.90	Derived: -number(real) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),B)),A)),C)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),C),A)),hAPP(int,real,number_number_of(real),B))).  [resolve(5360,b,5255,a)].
26.96/26.90	Derived: -number(rat) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(int,rat,number_number_of(rat),B)),A)),C)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),C),A)),hAPP(int,rat,number_number_of(rat),B))).  [resolve(5360,b,5304,a)].
27.07/27.00	5361 -number(A) | -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(int,A,number_number_of(A),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),B)),hAPP(int,A,number_number_of(A),C))) # label(fact_1747_divide__less__eq__number__of) # label(axiom).  [clausify(2525)].
27.07/27.00	Derived: -number(real) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(int,real,number_number_of(real),B))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),C),A)),hAPP(int,real,number_number_of(real),B))).  [resolve(5361,b,5255,a)].
27.07/27.00	Derived: -number(rat) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(int,rat,number_number_of(rat),B))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),C),A)),hAPP(int,rat,number_number_of(rat),B))).  [resolve(5361,b,5304,a)].
27.07/27.00	5362 -number(A) | -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),D)),B))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),B)),hAPP(int,A,number_number_of(A),D))) # label(fact_1747_divide__less__eq__number__of) # label(axiom).  [clausify(2525)].
27.07/27.00	Derived: -number(real) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),C)),A))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),B),A)),hAPP(int,real,number_number_of(real),C))).  [resolve(5362,b,5255,a)].
27.07/27.00	Derived: -number(rat) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(int,rat,number_number_of(rat),C)),A))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),B),A)),hAPP(int,rat,number_number_of(rat),C))).  [resolve(5362,b,5304,a)].
27.07/27.00	5363 -linord1117847801e_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)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),B))) # label(fact_1675_zero__le__divide__iff) # label(axiom).  [clausify(2708)].
27.07/27.00	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),B),A))).  [resolve(5363,a,5255,a)].
27.07/27.01	Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),B),A))).  [resolve(5363,a,5304,a)].
27.07/27.01	5364 -linord1117847801e_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),C),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),B))) # label(fact_1675_zero__le__divide__iff) # label(axiom).  [clausify(2708)].
27.07/27.01	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),B),A))).  [resolve(5364,a,5255,a)].
27.07/27.01	Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),B),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),B),A))).  [resolve(5364,a,5304,a)].
27.07/27.01	5365 -linord1117847801e_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))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),B))) # label(fact_1675_zero__le__divide__iff) # label(axiom).  [clausify(2708)].
27.07/27.01	Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),B),A))).  [resolve(5365,a,5255,a)].
27.07/27.01	Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),A)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),B),A))).  [resolve(5365,a,5304,a)].
27.07/27.01	5366 -linord1117847801e_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))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),B))) # label(fact_1675_zero__le__divide__iff) # label(axiom).  [clausify(2708)].
27.07/27.01	Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),B),A))).  [resolve(5366,a,5255,a)].
27.07/27.01	Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),A)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),B),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),B),A))).  [resolve(5366,a,5304,a)].
27.07/27.01	5367 -linord1117847801e_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))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C))) # label(fact_1675_zero__le__divide__iff) # label(axiom).  [clausify(2708)].
27.07/27.01	Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B))).  [resolve(5367,a,5255,a)].
27.46/27.36	Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),A)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),B),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),B))).  [resolve(5367,a,5304,a)].
27.46/27.36	5368 -linord1117847801e_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))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C))) # label(fact_1675_zero__le__divide__iff) # label(axiom).  [clausify(2708)].
27.46/27.36	Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B))).  [resolve(5368,a,5255,a)].
27.46/27.36	Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),A)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),B))).  [resolve(5368,a,5304,a)].
27.46/27.36	5369 -linord1117847801e_zero(A) | -number_ring(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),hAPP(int,A,number_number_of(A),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) # label(fact_1756_half__gt__zero__iff) # label(axiom).  [clausify(2952)].
27.46/27.36	5370 -linord1117847801e_zero(A) | -number_ring(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),hAPP(int,A,number_number_of(A),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) # label(fact_1756_half__gt__zero__iff) # label(axiom).  [clausify(2952)].
27.46/27.36	Derived: -number_ring(real) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))).  [resolve(5370,a,5255,a)].
27.46/27.36	Derived: -number_ring(rat) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),hAPP(int,rat,number_number_of(rat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))).  [resolve(5370,a,5304,a)].
27.46/27.36	5371 -linord1117847801e_zero(A) | hAPP(A,A,abs_abs(A),hAPP(A,A,inverse_inverse(A),B)) = hAPP(A,A,inverse_inverse(A),hAPP(A,A,abs_abs(A),B)) # label(fact_2534_abs__inverse) # label(axiom).  [clausify(3262)].
27.46/27.36	Derived: hAPP(real,real,abs_abs(real),hAPP(real,real,inverse_inverse(real),A)) = hAPP(real,real,inverse_inverse(real),hAPP(real,real,abs_abs(real),A)).  [resolve(5371,a,5255,a)].
27.46/27.36	Derived: hAPP(rat,rat,abs_abs(rat),hAPP(rat,rat,inverse_inverse(rat),A)) = hAPP(rat,rat,inverse_inverse(rat),hAPP(rat,rat,abs_abs(rat),A)).  [resolve(5371,a,5304,a)].
27.46/27.36	5372 -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),B))) # label(fact_1708_less__divide__eq) # label(axiom).  [clausify(3315)].
27.46/27.37	Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),C),A))).  [resolve(5372,a,5255,a)].
27.46/27.37	Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),C),A))).  [resolve(5372,a,5304,a)].
27.46/27.37	5373 -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),B))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),B))) # label(fact_1708_less__divide__eq) # label(axiom).  [clausify(3315)].
27.46/27.37	Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),A))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),C),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),B),A))).  [resolve(5373,a,5255,a)].
27.46/27.37	Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),C),A))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),C),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),B),A))).  [resolve(5373,a,5304,a)].
27.46/27.37	5374 -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),B))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),B))) # label(fact_1708_less__divide__eq) # label(axiom).  [clausify(3315)].
27.46/27.37	Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),A))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),C),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),C),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),B),A))).  [resolve(5374,a,5255,a)].
27.46/27.37	Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),C),A))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),C),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),C),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),B),A))).  [resolve(5374,a,5304,a)].
27.46/27.37	5375 -linord1117847801e_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)),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),C))) # label(fact_1708_less__divide__eq) # label(axiom).  [clausify(3315)].
27.46/27.37	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),C)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),C),B))).  [resolve(5375,a,5255,a)].
27.46/27.37	Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B)),C)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),C),B))).  [resolve(5375,a,5304,a)].
27.46/27.37	5376 -linord1117847801e_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)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),C))) # label(fact_1708_less__divide__eq) # label(axiom).  [clausify(3315)].
27.46/27.37	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),C),B))).  [resolve(5376,a,5255,a)].
27.46/27.37	Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B)),C)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),C),B))).  [resolve(5376,a,5304,a)].
27.46/27.37	5377 -linord1117847801e_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)),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),C))) # label(fact_1708_less__divide__eq) # label(axiom).  [clausify(3315)].
27.46/27.37	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),C)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),C),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),C),B))).  [resolve(5377,a,5255,a)].
27.46/27.37	Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B)),C)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),C),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),C),B))).  [resolve(5377,a,5304,a)].
27.46/27.37	5378 -linord1117847801e_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)),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),C))) # label(fact_1708_less__divide__eq) # label(axiom).  [clausify(3315)].
27.46/27.37	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),C)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),C),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),C),B))).  [resolve(5378,a,5255,a)].
27.46/27.38	Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B)),C)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),C),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),C),B))).  [resolve(5378,a,5304,a)].
27.46/27.38	5379 -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),B)),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),B))) # label(fact_1708_less__divide__eq) # label(axiom).  [clausify(3315)].
27.46/27.38	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),A)),C)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),C),A))).  [resolve(5379,a,5255,a)].
27.46/27.38	Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),B),A)),C)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),C),A))).  [resolve(5379,a,5304,a)].
27.46/27.38	5380 -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),B))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),B))) # label(fact_1708_less__divide__eq) # label(axiom).  [clausify(3315)].
27.46/27.38	Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),A))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),C),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),B),A))).  [resolve(5380,a,5255,a)].
27.46/27.38	Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),C),A))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),C),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),B),A))).  [resolve(5380,a,5304,a)].
27.46/27.38	5381 -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),B))) # label(fact_1708_less__divide__eq) # label(axiom).  [clausify(3315)].
27.46/27.38	Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),C),A))).  [resolve(5381,a,5255,a)].
27.46/27.42	Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),C),A))).  [resolve(5381,a,5304,a)].
27.46/27.42	5382 -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),D)) # label(fact_1736_divide__le__eq) # label(axiom).  [clausify(3372)].
27.46/27.42	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B)),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),C)).  [resolve(5382,a,5255,a)].
27.46/27.42	Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),B)),C)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),C)).  [resolve(5382,a,5304,a)].
27.46/27.42	5383 -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),C)),B)) # label(fact_1736_divide__le__eq) # label(axiom).  [clausify(3372)].
27.46/27.42	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B)),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),B)),A)).  [resolve(5383,a,5255,a)].
27.46/27.42	Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),B)),C)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),C),B)),A)).  [resolve(5383,a,5304,a)].
27.46/27.42	5384 -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),C))) # label(fact_1736_divide__le__eq) # label(axiom).  [clausify(3372)].
27.46/27.42	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B)),C)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),B))).  [resolve(5384,a,5255,a)].
27.46/27.42	Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),B)),C)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),C),B))).  [resolve(5384,a,5304,a)].
27.46/27.43	5385 -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),C))) # label(fact_1736_divide__le__eq) # label(axiom).  [clausify(3372)].
27.46/27.43	Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B)),C)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),B))).  [resolve(5385,a,5255,a)].
27.46/27.43	Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),B)),C)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),C),B))).  [resolve(5385,a,5304,a)].
27.46/27.43	5386 -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),C)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),C)) # label(fact_1736_divide__le__eq) # label(axiom).  [clausify(3372)].
27.46/27.43	Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B)),C)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),B)),A)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B)).  [resolve(5386,a,5255,a)].
27.46/27.43	Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),B)),C)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),C),B)),A)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),B)).  [resolve(5386,a,5304,a)].
27.46/27.43	5387 -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),C)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),C))) # label(fact_1736_divide__le__eq) # label(axiom).  [clausify(3372)].
27.46/27.43	Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B)),C)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),B)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),B))).  [resolve(5387,a,5255,a)].
27.46/27.43	Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),B)),C)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),C),B)),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),C),B))).  [resolve(5387,a,5304,a)].
27.46/27.43	5388 -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),C)) # label(fact_1736_divide__le__eq) # label(axiom).  [clausify(3372)].
27.46/27.43	Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B)),C)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B)).  [resolve(5388,a,5255,a)].
27.46/27.43	Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),B)),C)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),C)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),B)).  [resolve(5388,a,5304,a)].
27.46/27.43	5389 -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),C))) # label(fact_1736_divide__le__eq) # label(axiom).  [clausify(3372)].
27.46/27.43	Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B)),C)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),B))).  [resolve(5389,a,5255,a)].
27.46/27.43	Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),B)),C)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),C)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),C),B))).  [resolve(5389,a,5304,a)].
27.46/27.43	5390 -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),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),C)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),C)) # label(fact_1736_divide__le__eq) # label(axiom).  [clausify(3372)].
27.46/27.43	Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B)),C)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),C)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),B)),A)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B)).  [resolve(5390,a,5255,a)].
27.46/27.43	Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),B)),C)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),C)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),C),B)),A)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),B)).  [resolve(5390,a,5304,a)].
27.67/27.56	5391 -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),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),C)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),C))) # label(fact_1736_divide__le__eq) # label(axiom).  [clausify(3372)].
27.67/27.56	Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B)),C)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),C)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),B)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),B))).  [resolve(5391,a,5255,a)].
27.67/27.56	Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),B)),C)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),C)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),C),B)),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),C),B))).  [resolve(5391,a,5304,a)].
27.67/27.56	5392 -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),D)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),D))) # label(fact_1673_divide__right__mono) # label(axiom).  [clausify(3527)].
27.67/27.56	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),C)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),B),C))).  [resolve(5392,a,5255,a)].
27.67/27.56	Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),C)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),C)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),B),C))).  [resolve(5392,a,5304,a)].
27.67/27.56	5393 -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,inverse_inverse(A),B)),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) # label(fact_2542_inverse__negative__iff__negative) # label(axiom).  [clausify(3556)].
27.67/27.56	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,inverse_inverse(real),A)),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))).  [resolve(5393,a,5255,a)].
27.67/27.56	Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,inverse_inverse(rat),A)),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),zero_zero(rat))).  [resolve(5393,a,5304,a)].
27.67/27.56	5394 -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,inverse_inverse(A),B)),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) # label(fact_2542_inverse__negative__iff__negative) # label(axiom).  [clausify(3556)].
27.67/27.56	Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,inverse_inverse(real),A)),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))).  [resolve(5394,a,5255,a)].
27.67/27.56	Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,inverse_inverse(rat),A)),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),zero_zero(rat))).  [resolve(5394,a,5304,a)].
27.71/27.69	5395 -linord1117847801e_zero(A) | -number(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(int,A,number_number_of(A),B))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),hAPP(int,A,number_number_of(A),B))),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),hAPP(int,A,number_number_of(A),B)))) # label(fact_1745_less__divide__eq__number__of1) # label(axiom).  [clausify(3740)].
27.71/27.69	5396 -linord1117847801e_zero(A) | -number(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),B)),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),hAPP(int,A,number_number_of(A),B)))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(int,A,number_number_of(A),B))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),hAPP(int,A,number_number_of(A),B)))) # label(fact_1745_less__divide__eq__number__of1) # label(axiom).  [clausify(3740)].
27.71/27.69	5397 -linord1117847801e_zero(A) | -number(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),B)),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),hAPP(int,A,number_number_of(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),D),hAPP(int,A,number_number_of(A),B))),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),hAPP(int,A,number_number_of(A),B)))) # label(fact_1745_less__divide__eq__number__of1) # label(axiom).  [clausify(3740)].
27.71/27.69	5398 -linord1117847801e_zero(A) | -number(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(int,A,number_number_of(A),C)),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(int,A,number_number_of(A),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),hAPP(int,A,number_number_of(A),C)))) # label(fact_1745_less__divide__eq__number__of1) # label(axiom).  [clausify(3740)].
27.71/27.69	5399 -linord1117847801e_zero(A) | -number(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(int,A,number_number_of(A),C)),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(int,A,number_number_of(A),C))),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),hAPP(int,A,number_number_of(A),C)))) # label(fact_1745_less__divide__eq__number__of1) # label(axiom).  [clausify(3740)].
27.71/27.69	5400 -linord1117847801e_zero(A) | -number(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(int,A,number_number_of(A),D)))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(int,A,number_number_of(A),D))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),hAPP(int,A,number_number_of(A),D)))) # label(fact_1745_less__divide__eq__number__of1) # label(axiom).  [clausify(3740)].
27.71/27.69	5401 -linord1117847801e_zero(A) | -number(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(int,A,number_number_of(A),D)))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(int,A,number_number_of(A),D))),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),hAPP(int,A,number_number_of(A),D)))) # label(fact_1745_less__divide__eq__number__of1) # label(axiom).  [clausify(3740)].
27.77/27.73	5402 -linord1117847801e_zero(A) | -number(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(int,A,number_number_of(A),B))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(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),C),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),hAPP(int,A,number_number_of(A),B)))) # label(fact_1745_less__divide__eq__number__of1) # label(axiom).  [clausify(3740)].
27.77/27.73	5403 -linord1117847801e_zero(A) | -number(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(int,A,number_number_of(A),B))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),B)),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),hAPP(int,A,number_number_of(A),B)))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),hAPP(int,A,number_number_of(A),B)))) # label(fact_1745_less__divide__eq__number__of1) # label(axiom).  [clausify(3740)].
27.77/27.73	5404 -linord1117847801e_zero(A) | -number(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(int,A,number_number_of(A),B))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),hAPP(int,A,number_number_of(A),B))),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),hAPP(int,A,number_number_of(A),B)))) # label(fact_1745_less__divide__eq__number__of1) # label(axiom).  [clausify(3740)].
27.77/27.73	5405 -number(A) | -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(int,A,number_number_of(A),B))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),B)),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),hAPP(int,A,number_number_of(A),B))),C)) # label(fact_1748_divide__less__eq__number__of1) # label(axiom).  [clausify(3782)].
27.77/27.73	Derived: -number(real) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(int,real,number_number_of(real),A))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,number_number_of(real),A)),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),C),hAPP(int,real,number_number_of(real),A))),B)).  [resolve(5405,b,5255,a)].
27.77/27.73	Derived: -number(rat) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(int,rat,number_number_of(rat),A))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(int,rat,number_number_of(rat),A)),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),C),hAPP(int,rat,number_number_of(rat),A))),B)).  [resolve(5405,b,5304,a)].
27.77/27.73	5406 -number(A) | -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(int,A,number_number_of(A),B))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),hAPP(int,A,number_number_of(A),B))),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),B)),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),hAPP(int,A,number_number_of(A),B))),C)) # label(fact_1748_divide__less__eq__number__of1) # label(axiom).  [clausify(3782)].
27.77/27.73	Derived: -number(real) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(int,real,number_number_of(real),A))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),hAPP(int,real,number_number_of(real),A))),C)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,number_number_of(real),A)),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),C),hAPP(int,real,number_number_of(real),A))),B)).  [resolve(5406,b,5255,a)].
27.77/27.73	Derived: -number(rat) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(int,rat,number_number_of(rat),A))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),B),hAPP(int,rat,number_number_of(rat),A))),C)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(int,rat,number_number_of(rat),A)),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),C),hAPP(int,rat,number_number_of(rat),A))),B)).  [resolve(5406,b,5304,a)].
27.77/27.73	5407 -number(A) | -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(int,A,number_number_of(A),B))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),hAPP(int,A,number_number_of(A),B))),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),hAPP(int,A,number_number_of(A),B))),C)) # label(fact_1748_divide__less__eq__number__of1) # label(axiom).  [clausify(3782)].
27.77/27.73	Derived: -number(real) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(int,real,number_number_of(real),A))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),hAPP(int,real,number_number_of(real),A))),C)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),C),hAPP(int,real,number_number_of(real),A))),B)).  [resolve(5407,b,5255,a)].
27.77/27.73	Derived: -number(rat) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(int,rat,number_number_of(rat),A))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),B),hAPP(int,rat,number_number_of(rat),A))),C)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),C),hAPP(int,rat,number_number_of(rat),A))),B)).  [resolve(5407,b,5304,a)].
27.77/27.73	5408 -number(A) | -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),hAPP(int,A,number_number_of(A),D)))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(int,A,number_number_of(A),D))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),hAPP(int,A,number_number_of(A),D))),C)) # label(fact_1748_divide__less__eq__number__of1) # label(axiom).  [clausify(3782)].
27.77/27.73	Derived: -number(real) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),hAPP(int,real,number_number_of(real),C)))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(int,real,number_number_of(real),C))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),hAPP(int,real,number_number_of(real),C))),B)).  [resolve(5408,b,5255,a)].
27.77/27.73	Derived: -number(rat) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),B),hAPP(int,rat,number_number_of(rat),C)))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(int,rat,number_number_of(rat),C))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),hAPP(int,rat,number_number_of(rat),C))),B)).  [resolve(5408,b,5304,a)].
27.77/27.74	5409 -number(A) | -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),hAPP(int,A,number_number_of(A),D)))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),D)),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),hAPP(int,A,number_number_of(A),D))),C)) # label(fact_1748_divide__less__eq__number__of1) # label(axiom).  [clausify(3782)].
27.77/27.74	Derived: -number(real) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),hAPP(int,real,number_number_of(real),C)))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,number_number_of(real),C)),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),hAPP(int,real,number_number_of(real),C))),B)).  [resolve(5409,b,5255,a)].
27.77/27.74	Derived: -number(rat) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),B),hAPP(int,rat,number_number_of(rat),C)))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(int,rat,number_number_of(rat),C)),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),hAPP(int,rat,number_number_of(rat),C))),B)).  [resolve(5409,b,5304,a)].
27.77/27.74	5410 -number(A) | -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),hAPP(int,A,number_number_of(A),D)))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),hAPP(int,A,number_number_of(A),D))),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),D)),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),hAPP(int,A,number_number_of(A),D))),C)) # label(fact_1748_divide__less__eq__number__of1) # label(axiom).  [clausify(3782)].
27.77/27.74	Derived: -number(real) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),hAPP(int,real,number_number_of(real),C)))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),hAPP(int,real,number_number_of(real),C))),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,number_number_of(real),C)),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),hAPP(int,real,number_number_of(real),C))),B)).  [resolve(5410,b,5255,a)].
27.77/27.74	Derived: -number(rat) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),B),hAPP(int,rat,number_number_of(rat),C)))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),B),hAPP(int,rat,number_number_of(rat),C))),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(int,rat,number_number_of(rat),C)),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),hAPP(int,rat,number_number_of(rat),C))),B)).  [resolve(5410,b,5304,a)].
27.77/27.74	5411 -number(A) | -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),hAPP(int,A,number_number_of(A),D)))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),hAPP(int,A,number_number_of(A),D))),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),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),hAPP(int,A,number_number_of(A),D))),C)) # label(fact_1748_divide__less__eq__number__of1) # label(axiom).  [clausify(3782)].
27.77/27.74	Derived: -number(real) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),hAPP(int,real,number_number_of(real),C)))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),hAPP(int,real,number_number_of(real),C))),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),hAPP(int,real,number_number_of(real),C))),B)).  [resolve(5411,b,5255,a)].
27.77/27.74	Derived: -number(rat) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),B),hAPP(int,rat,number_number_of(rat),C)))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),B),hAPP(int,rat,number_number_of(rat),C))),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),hAPP(int,rat,number_number_of(rat),C))),B)).  [resolve(5411,b,5304,a)].
27.77/27.74	5412 -number(A) | -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(int,A,number_number_of(A),B))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),hAPP(int,A,number_number_of(A),B)))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),hAPP(int,A,number_number_of(A),B))),D)) # label(fact_1748_divide__less__eq__number__of1) # label(axiom).  [clausify(3782)].
27.77/27.74	Derived: -number(real) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(int,real,number_number_of(real),A))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),hAPP(int,real,number_number_of(real),A)))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),B),hAPP(int,real,number_number_of(real),A))),C)).  [resolve(5412,b,5255,a)].
27.77/27.74	Derived: -number(rat) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(int,rat,number_number_of(rat),A))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),C),hAPP(int,rat,number_number_of(rat),A)))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),B),hAPP(int,rat,number_number_of(rat),A))),C)).  [resolve(5412,b,5304,a)].
27.77/27.74	5413 -number(A) | -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(int,A,number_number_of(A),B))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(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),C),hAPP(int,A,number_number_of(A),B))),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),hAPP(int,A,number_number_of(A),B))),C)) # label(fact_1748_divide__less__eq__number__of1) # label(axiom).  [clausify(3782)].
27.77/27.74	Derived: -number(real) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(int,real,number_number_of(real),A))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,number_number_of(real),A)),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),hAPP(int,real,number_number_of(real),A))),C)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),C),hAPP(int,real,number_number_of(real),A))),B)).  [resolve(5413,b,5255,a)].
28.08/28.00	Derived: -number(rat) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(int,rat,number_number_of(rat),A))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(int,rat,number_number_of(rat),A)),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),B),hAPP(int,rat,number_number_of(rat),A))),C)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),C),hAPP(int,rat,number_number_of(rat),A))),B)).  [resolve(5413,b,5304,a)].
28.08/28.00	5414 -number(A) | -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(int,A,number_number_of(A),B))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),B)),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),hAPP(int,A,number_number_of(A),B))),C)) # label(fact_1748_divide__less__eq__number__of1) # label(axiom).  [clausify(3782)].
28.08/28.00	Derived: -number(real) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(int,real,number_number_of(real),A))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,number_number_of(real),A)),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),C),hAPP(int,real,number_number_of(real),A))),B)).  [resolve(5414,b,5255,a)].
28.08/28.00	Derived: -number(rat) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(int,rat,number_number_of(rat),A))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(int,rat,number_number_of(rat),A)),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),C),hAPP(int,rat,number_number_of(rat),A))),B)).  [resolve(5414,b,5304,a)].
28.08/28.00	5415 -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),f712(A,B,C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) # label(fact_1523_field__le__mult__one__interval) # label(axiom).  [clausify(3963)].
28.08/28.00	Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),f712(real,A,B))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),B)).  [resolve(5415,a,5255,a)].
28.08/28.00	Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),f712(rat,A,B))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),B)).  [resolve(5415,a,5304,a)].
28.08/28.00	5416 -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),f712(A,B,C)),one_one(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) # label(fact_1523_field__le__mult__one__interval) # label(axiom).  [clausify(3963)].
28.08/28.00	Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),f712(real,A,B)),one_one(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),B)).  [resolve(5416,a,5255,a)].
28.08/28.00	Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),f712(rat,A,B)),one_one(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),B)).  [resolve(5416,a,5304,a)].
28.08/28.00	5417 -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),f712(A,B,C)),B)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) # label(fact_1523_field__le__mult__one__interval) # label(axiom).  [clausify(3963)].
28.26/28.15	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),f712(real,A,B)),A)),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),B)).  [resolve(5417,a,5255,a)].
28.26/28.15	Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),f712(rat,A,B)),A)),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),B)).  [resolve(5417,a,5304,a)].
28.26/28.15	5418 -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(A,A,inverse_inverse(A),B))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) # label(fact_2540_inverse__nonnegative__iff__nonnegative) # label(axiom).  [clausify(4085)].
28.26/28.15	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(real,real,inverse_inverse(real),A))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A)).  [resolve(5418,a,5255,a)].
28.26/28.15	Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),hAPP(rat,rat,inverse_inverse(rat),A))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),A)).  [resolve(5418,a,5304,a)].
28.26/28.15	5419 -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(A,A,inverse_inverse(A),B))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) # label(fact_2540_inverse__nonnegative__iff__nonnegative) # label(axiom).  [clausify(4085)].
28.26/28.15	Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(real,real,inverse_inverse(real),A))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A)).  [resolve(5419,a,5255,a)].
28.26/28.15	Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),hAPP(rat,rat,inverse_inverse(rat),A))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),A)).  [resolve(5419,a,5304,a)].
28.26/28.15	5420 -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),D)) # label(fact_1709_divide__less__eq) # label(axiom).  [clausify(4158)].
28.26/28.15	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B)),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),C)).  [resolve(5420,a,5255,a)].
28.26/28.15	Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),B)),C)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),C)).  [resolve(5420,a,5304,a)].
28.26/28.15	5421 -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),C)),B)) # label(fact_1709_divide__less__eq) # label(axiom).  [clausify(4158)].
28.26/28.15	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B)),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),B)),A)).  [resolve(5421,a,5255,a)].
28.27/28.15	Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),B)),C)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),C),B)),A)).  [resolve(5421,a,5304,a)].
28.27/28.15	5422 -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),C))) # label(fact_1709_divide__less__eq) # label(axiom).  [clausify(4158)].
28.27/28.15	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B)),C)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),B))).  [resolve(5422,a,5255,a)].
28.27/28.15	Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),B)),C)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),C),B))).  [resolve(5422,a,5304,a)].
28.27/28.15	5423 -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),C))) # label(fact_1709_divide__less__eq) # label(axiom).  [clausify(4158)].
28.27/28.15	Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B)),C)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),B))).  [resolve(5423,a,5255,a)].
28.27/28.15	Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),B)),C)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),C),B))).  [resolve(5423,a,5304,a)].
28.27/28.15	5424 -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),C)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),C)) # label(fact_1709_divide__less__eq) # label(axiom).  [clausify(4158)].
28.27/28.15	Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B)),C)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),B)),A)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B)).  [resolve(5424,a,5255,a)].
28.27/28.15	Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),B)),C)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),C),B)),A)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),B)).  [resolve(5424,a,5304,a)].
28.27/28.16	5425 -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),C)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),C))) # label(fact_1709_divide__less__eq) # label(axiom).  [clausify(4158)].
28.27/28.16	Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B)),C)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),B)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),B))).  [resolve(5425,a,5255,a)].
28.27/28.16	Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),B)),C)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),C),B)),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),C),B))).  [resolve(5425,a,5304,a)].
28.27/28.16	5426 -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),C)) # label(fact_1709_divide__less__eq) # label(axiom).  [clausify(4158)].
28.27/28.16	Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B)),C)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B)).  [resolve(5426,a,5255,a)].
28.27/28.16	Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),B)),C)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),C)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),B)).  [resolve(5426,a,5304,a)].
28.27/28.16	5427 -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),C))) # label(fact_1709_divide__less__eq) # label(axiom).  [clausify(4158)].
28.27/28.16	Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B)),C)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),B))).  [resolve(5427,a,5255,a)].
28.27/28.16	Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),B)),C)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),C)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),C),B))).  [resolve(5427,a,5304,a)].
28.33/28.24	5428 -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),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),C)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),C)) # label(fact_1709_divide__less__eq) # label(axiom).  [clausify(4158)].
28.33/28.24	Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B)),C)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),C)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),B)),A)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B)).  [resolve(5428,a,5255,a)].
28.33/28.24	Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),B)),C)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),C)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),C),B)),A)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),B)).  [resolve(5428,a,5304,a)].
28.33/28.24	5429 -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),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),C)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),C))) # label(fact_1709_divide__less__eq) # label(axiom).  [clausify(4158)].
28.33/28.24	Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B)),C)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),C)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),B)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),B))).  [resolve(5429,a,5255,a)].
28.33/28.24	Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),B)),C)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),C)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),C),B)),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),C),B))).  [resolve(5429,a,5304,a)].
28.33/28.24	5430 -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),B)),zero_zero(A))) # label(fact_1677_divide__less__0__iff) # label(axiom).  [clausify(4247)].
28.33/28.24	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),B),A)),zero_zero(real))).  [resolve(5430,a,5255,a)].
28.33/28.24	Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),B),A)),zero_zero(rat))).  [resolve(5430,a,5304,a)].
28.33/28.25	5431 -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)),zero_zero(A))) # label(fact_1677_divide__less__0__iff) # label(axiom).  [clausify(4247)].
28.33/28.25	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B)),zero_zero(real))).  [resolve(5431,a,5255,a)].
28.33/28.25	Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),B)),zero_zero(rat))).  [resolve(5431,a,5304,a)].
28.33/28.25	5432 -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),B)),zero_zero(A))) # label(fact_1677_divide__less__0__iff) # label(axiom).  [clausify(4247)].
28.33/28.25	Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),B),A)),zero_zero(real))).  [resolve(5432,a,5255,a)].
28.33/28.25	Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),B),A)),zero_zero(rat))).  [resolve(5432,a,5304,a)].
28.33/28.25	5433 -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),B)),zero_zero(A))) # label(fact_1677_divide__less__0__iff) # label(axiom).  [clausify(4247)].
28.33/28.25	Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),B),A)),zero_zero(real))).  [resolve(5433,a,5255,a)].
28.33/28.25	Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),B),A)),zero_zero(rat))).  [resolve(5433,a,5304,a)].
28.33/28.25	5434 -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)),zero_zero(A))) # label(fact_1677_divide__less__0__iff) # label(axiom).  [clausify(4247)].
28.33/28.25	Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B)),zero_zero(real))).  [resolve(5434,a,5255,a)].
28.33/28.25	Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),B)),zero_zero(rat))).  [resolve(5434,a,5304,a)].
28.39/28.34	5435 -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)),zero_zero(A))) # label(fact_1677_divide__less__0__iff) # label(axiom).  [clausify(4247)].
28.39/28.34	Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B)),zero_zero(real))).  [resolve(5435,a,5255,a)].
28.39/28.34	Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),B)),zero_zero(rat))).  [resolve(5435,a,5304,a)].
28.39/28.34	5436 -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | hAPP(A,A,abs_abs(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),B)) = hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),hAPP(A,A,abs_abs(A),C)),B) # label(fact_1884_abs__div__pos) # label(axiom).  [clausify(4347)].
28.39/28.34	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),B),A)) = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,abs_abs(real),B)),A).  [resolve(5436,a,5255,a)].
28.39/28.34	Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)) | hAPP(rat,rat,abs_abs(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),B),A)) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),hAPP(rat,rat,abs_abs(rat),B)),A).  [resolve(5436,a,5304,a)].
28.39/28.34	5437 -linord1117847801e_zero(A) | -number(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),hAPP(int,A,number_number_of(A),C))),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(int,A,number_number_of(A),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),C)),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),D)) # label(fact_1755_divide__le__eq__number__of1) # label(axiom).  [clausify(4361)].
28.39/28.34	5438 -linord1117847801e_zero(A) | -number(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),hAPP(int,A,number_number_of(A),C))),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(int,A,number_number_of(A),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),C)),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),hAPP(int,A,number_number_of(A),C))),B)) # label(fact_1755_divide__le__eq__number__of1) # label(axiom).  [clausify(4361)].
28.39/28.34	5439 -linord1117847801e_zero(A) | -number(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),hAPP(int,A,number_number_of(A),C))),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(int,A,number_number_of(A),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),hAPP(int,A,number_number_of(A),C)))) # label(fact_1755_divide__le__eq__number__of1) # label(axiom).  [clausify(4361)].
28.39/28.34	5440 -linord1117847801e_zero(A) | -number(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),hAPP(int,A,number_number_of(A),C))),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(int,A,number_number_of(A),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),hAPP(int,A,number_number_of(A),C)))) # label(fact_1755_divide__le__eq__number__of1) # label(axiom).  [clausify(4361)].
28.51/28.40	5441 -linord1117847801e_zero(A) | -number(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),hAPP(int,A,number_number_of(A),C))),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),C)),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),hAPP(int,A,number_number_of(A),C))),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(int,A,number_number_of(A),C))) # label(fact_1755_divide__le__eq__number__of1) # label(axiom).  [clausify(4361)].
28.51/28.40	5442 -linord1117847801e_zero(A) | -number(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),hAPP(int,A,number_number_of(A),C))),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),C)),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),hAPP(int,A,number_number_of(A),C))),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),hAPP(int,A,number_number_of(A),C)))) # label(fact_1755_divide__le__eq__number__of1) # label(axiom).  [clausify(4361)].
28.51/28.40	5443 -linord1117847801e_zero(A) | -number(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),hAPP(int,A,number_number_of(A),C))),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),C)),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(int,A,number_number_of(A),C))) # label(fact_1755_divide__le__eq__number__of1) # label(axiom).  [clausify(4361)].
28.51/28.40	5444 -linord1117847801e_zero(A) | -number(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),hAPP(int,A,number_number_of(A),C))),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),C)),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),hAPP(int,A,number_number_of(A),C)))) # label(fact_1755_divide__le__eq__number__of1) # label(axiom).  [clausify(4361)].
28.51/28.40	5445 -linord1117847801e_zero(A) | -number(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),hAPP(int,A,number_number_of(A),C))),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),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),hAPP(int,A,number_number_of(A),C))),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(int,A,number_number_of(A),C))) # label(fact_1755_divide__le__eq__number__of1) # label(axiom).  [clausify(4361)].
28.51/28.40	5446 -linord1117847801e_zero(A) | -number(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),hAPP(int,A,number_number_of(A),C))),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),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),hAPP(int,A,number_number_of(A),C))),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),hAPP(int,A,number_number_of(A),C)))) # label(fact_1755_divide__le__eq__number__of1) # label(axiom).  [clausify(4361)].
28.51/28.40	5447 -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),B))) # label(fact_1676_zero__less__divide__iff) # label(axiom).  [clausify(4414)].
28.51/28.40	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),B),A))).  [resolve(5447,a,5255,a)].
28.51/28.40	Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),B),A))).  [resolve(5447,a,5304,a)].
28.51/28.40	5448 -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C))) # label(fact_1676_zero__less__divide__iff) # label(axiom).  [clausify(4414)].
28.51/28.40	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B))).  [resolve(5448,a,5255,a)].
28.51/28.40	Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),B))).  [resolve(5448,a,5304,a)].
28.51/28.40	5449 -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),B))) # label(fact_1676_zero__less__divide__iff) # label(axiom).  [clausify(4414)].
28.51/28.40	Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),B),A))).  [resolve(5449,a,5255,a)].
28.51/28.40	Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),B),A))).  [resolve(5449,a,5304,a)].
28.51/28.40	5450 -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),B))) # label(fact_1676_zero__less__divide__iff) # label(axiom).  [clausify(4414)].
28.51/28.40	Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),B),A))).  [resolve(5450,a,5255,a)].
28.51/28.40	Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),B),A))).  [resolve(5450,a,5304,a)].
28.51/28.40	5451 -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C))) # label(fact_1676_zero__less__divide__iff) # label(axiom).  [clausify(4414)].
28.63/28.53	Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B))).  [resolve(5451,a,5255,a)].
28.63/28.53	Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),B))).  [resolve(5451,a,5304,a)].
28.63/28.53	5452 -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C))) # label(fact_1676_zero__less__divide__iff) # label(axiom).  [clausify(4414)].
28.63/28.53	Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B))).  [resolve(5452,a,5255,a)].
28.63/28.53	Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),B))).  [resolve(5452,a,5304,a)].
28.63/28.53	5453 -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,inverse_inverse(A),B)),one_one(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),zero_zero(A))) # label(fact_2609_inverse__less__1__iff) # label(axiom).  [clausify(4564)].
28.63/28.53	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,inverse_inverse(real),A)),one_one(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),A)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),zero_zero(real))).  [resolve(5453,a,5255,a)].
28.63/28.53	Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,inverse_inverse(rat),A)),one_one(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),one_one(rat)),A)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),zero_zero(rat))).  [resolve(5453,a,5304,a)].
28.63/28.53	5454 -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,inverse_inverse(A),B)),one_one(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),B)) # label(fact_2609_inverse__less__1__iff) # label(axiom).  [clausify(4564)].
28.63/28.53	Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,inverse_inverse(real),A)),one_one(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),A)).  [resolve(5454,a,5255,a)].
28.63/28.53	Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,inverse_inverse(rat),A)),one_one(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),one_one(rat)),A)).  [resolve(5454,a,5304,a)].
28.63/28.53	5455 -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,inverse_inverse(A),B)),one_one(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),zero_zero(A))) # label(fact_2609_inverse__less__1__iff) # label(axiom).  [clausify(4564)].
28.63/28.53	Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,inverse_inverse(real),A)),one_one(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),zero_zero(real))).  [resolve(5455,a,5255,a)].
28.63/28.53	Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,inverse_inverse(rat),A)),one_one(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),zero_zero(rat))).  [resolve(5455,a,5304,a)].
30.41/30.29	5456 -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,inverse_inverse(A),B)),one_one(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),one_one(A)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),zero_zero(A))) # label(fact_2574_inverse__le__1__iff) # label(axiom).  [clausify(4710)].
30.41/30.29	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,inverse_inverse(real),A)),one_one(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),one_one(real)),A)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),zero_zero(real))).  [resolve(5456,a,5255,a)].
30.41/30.29	Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,inverse_inverse(rat),A)),one_one(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),one_one(rat)),A)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),zero_zero(rat))).  [resolve(5456,a,5304,a)].
30.41/30.29	5457 -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,inverse_inverse(A),B)),one_one(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),one_one(A)),B)) # label(fact_2574_inverse__le__1__iff) # label(axiom).  [clausify(4710)].
30.41/30.29	Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,inverse_inverse(real),A)),one_one(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),one_one(real)),A)).  [resolve(5457,a,5255,a)].
30.41/30.29	Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,inverse_inverse(rat),A)),one_one(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),one_one(rat)),A)).  [resolve(5457,a,5304,a)].
30.41/30.29	5458 -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,inverse_inverse(A),B)),one_one(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),zero_zero(A))) # label(fact_2574_inverse__le__1__iff) # label(axiom).  [clausify(4710)].
30.41/30.29	Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,inverse_inverse(real),A)),one_one(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),zero_zero(real))).  [resolve(5458,a,5255,a)].
30.41/30.29	Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,inverse_inverse(rat),A)),one_one(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),zero_zero(rat))).  [resolve(5458,a,5304,a)].
30.41/30.29	5459 -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_757_add__pos__nonneg) # label(axiom).  [clausify(31)].
30.41/30.29	5460 ordere216010020id_add(real) # label(arity_RealDef_Oreal___Groups_Oordered__comm__monoid__add) # label(axiom).  [assumption].
30.41/30.29	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),B))).  [resolve(5459,a,5460,a)].
30.41/30.29	5461 -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_812_add__nonpos__nonpos) # label(axiom).  [clausify(1345)].
30.41/30.29	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),B)),zero_zero(real))).  [resolve(5461,a,5460,a)].
30.90/30.80	5462 -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_762_add__nonpos__neg) # label(axiom).  [clausify(1584)].
30.90/30.80	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),B)),zero_zero(real))).  [resolve(5462,a,5460,a)].
30.90/30.80	5463 ordere216010020id_add(code_code_numeral) # label(arity_Code__Numeral_Ocode__numeral___Groups_Oordered__comm__monoid__add) # label(axiom).  [assumption].
30.90/30.80	Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),zero_zero(code_code_numeral)),A)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),zero_zero(code_code_numeral)),B)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),zero_zero(code_code_numeral)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),A),B))).  [resolve(5463,a,5459,a)].
30.90/30.80	Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),A),zero_zero(code_code_numeral))) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),B),zero_zero(code_code_numeral))) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),A),B)),zero_zero(code_code_numeral))).  [resolve(5463,a,5461,a)].
30.90/30.80	Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),A),zero_zero(code_code_numeral))) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),B),zero_zero(code_code_numeral))) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),A),B)),zero_zero(code_code_numeral))).  [resolve(5463,a,5462,a)].
30.90/30.80	5464 -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_819_add__neg__neg) # label(axiom).  [clausify(2373)].
30.90/30.80	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),B)),zero_zero(real))).  [resolve(5464,a,5460,a)].
30.90/30.80	Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),A),zero_zero(code_code_numeral))) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),B),zero_zero(code_code_numeral))) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),A),B)),zero_zero(code_code_numeral))).  [resolve(5464,a,5463,a)].
31.06/30.98	5465 -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_820_add__pos__pos) # label(axiom).  [clausify(2423)].
31.06/30.98	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),B))).  [resolve(5465,a,5460,a)].
31.06/30.98	Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),zero_zero(code_code_numeral)),A)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),zero_zero(code_code_numeral)),B)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),zero_zero(code_code_numeral)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),A),B))).  [resolve(5465,a,5463,a)].
31.06/30.98	5466 ordere216010020id_add(nat) # label(arity_Nat_Onat___Groups_Oordered__comm__monoid__add) # label(axiom).  [assumption].
31.06/30.98	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(5466,a,5461,a)].
31.06/30.98	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(5466,a,5462,a)].
31.06/30.98	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(5466,a,5464,a)].
31.06/30.98	5467 ordere216010020id_add(rat) # label(arity_Rat_Orat___Groups_Oordered__comm__monoid__add) # label(axiom).  [assumption].
31.06/30.98	Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),B))).  [resolve(5467,a,5459,a)].
31.06/30.98	Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),B),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),B)),zero_zero(rat))).  [resolve(5467,a,5461,a)].
31.06/30.98	Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),B)),zero_zero(rat))).  [resolve(5467,a,5462,a)].
31.06/30.98	Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),B)),zero_zero(rat))).  [resolve(5467,a,5464,a)].
31.06/30.98	Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),B))).  [resolve(5467,a,5465,a)].
31.42/31.31	5468 -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_814_add__increasing) # label(axiom).  [clausify(2941)].
31.42/31.31	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),C))).  [resolve(5468,a,5460,a)].
31.42/31.31	Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),zero_zero(code_code_numeral)),A)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),B),C)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),B),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),A),C))).  [resolve(5468,a,5463,a)].
31.42/31.31	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(5468,a,5466,a)].
31.42/31.31	Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),B),C)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),B),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),C))).  [resolve(5468,a,5467,a)].
31.42/31.31	5469 -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_758_add__nonneg__pos) # label(axiom).  [clausify(3158)].
31.42/31.31	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),B))).  [resolve(5469,a,5460,a)].
31.42/31.31	Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),zero_zero(code_code_numeral)),A)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),zero_zero(code_code_numeral)),B)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),zero_zero(code_code_numeral)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),A),B))).  [resolve(5469,a,5463,a)].
31.42/31.31	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(5469,a,5466,a)].
31.42/31.31	Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),B))).  [resolve(5469,a,5467,a)].
31.50/31.39	5470 ordere216010020id_add(quickcheck_code_int) # label(arity_Quickcheck__Narrowing_Ocode__int___Groups_Oordered__comm__monoid__add) # label(axiom).  [assumption].
31.50/31.39	Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),zero_zero(quickcheck_code_int)),A)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),zero_zero(quickcheck_code_int)),B)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),zero_zero(quickcheck_code_int)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),A),B))).  [resolve(5470,a,5459,a)].
31.50/31.39	Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),A),zero_zero(quickcheck_code_int))) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),B),zero_zero(quickcheck_code_int))) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),A),B)),zero_zero(quickcheck_code_int))).  [resolve(5470,a,5461,a)].
31.50/31.39	Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),A),zero_zero(quickcheck_code_int))) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),B),zero_zero(quickcheck_code_int))) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),A),B)),zero_zero(quickcheck_code_int))).  [resolve(5470,a,5462,a)].
31.50/31.39	Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),A),zero_zero(quickcheck_code_int))) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),B),zero_zero(quickcheck_code_int))) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),A),B)),zero_zero(quickcheck_code_int))).  [resolve(5470,a,5464,a)].
31.50/31.39	Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),zero_zero(quickcheck_code_int)),A)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),zero_zero(quickcheck_code_int)),B)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),zero_zero(quickcheck_code_int)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),A),B))).  [resolve(5470,a,5465,a)].
31.50/31.39	Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),zero_zero(quickcheck_code_int)),A)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),B),C)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),B),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),A),C))).  [resolve(5470,a,5468,a)].
31.52/31.40	Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),zero_zero(quickcheck_code_int)),A)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),zero_zero(quickcheck_code_int)),B)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),zero_zero(quickcheck_code_int)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),A),B))).  [resolve(5470,a,5469,a)].
31.52/31.40	5471 -ordere216010020id_add(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | -hBOOL(hAPP(fun(B,bool),bool,hAPP(fun(B,bool),fun(fun(B,bool),bool),ord_less_eq(fun(B,bool)),D),C)) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f562(B,A,E,D,C)),hAPP(fun(B,bool),fun(B,bool),hAPP(fun(B,bool),fun(fun(B,bool),fun(B,bool)),minus_minus(fun(B,bool)),C),D))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),E),D)),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),E),C))) # label(fact_4293_setsum__mono2) # label(axiom).  [clausify(3257)].
31.52/31.40	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f562(A,real,D,C,B)),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),B),C))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),D),C)),hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),D),B))).  [resolve(5471,a,5460,a)].
31.52/31.40	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f562(A,code_code_numeral,D,C,B)),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),B),C))) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),D),C)),hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),D),B))).  [resolve(5471,a,5463,a)].
31.52/31.40	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f562(A,nat,D,C,B)),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),B),C))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),D),C)),hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),D),B))).  [resolve(5471,a,5466,a)].
31.52/31.40	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f562(A,rat,D,C,B)),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),B),C))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),D),C)),hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),D),B))).  [resolve(5471,a,5467,a)].
31.52/31.40	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f562(A,quickcheck_code_int,D,C,B)),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),B),C))) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),D),C)),hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),D),B))).  [resolve(5471,a,5470,a)].
31.52/31.40	5472 -ordere216010020id_add(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | -hBOOL(hAPP(fun(B,bool),bool,hAPP(fun(B,bool),fun(fun(B,bool),bool),ord_less_eq(fun(B,bool)),D),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(B,A,E,f562(B,A,E,D,C)))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),E),D)),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),E),C))) # label(fact_4293_setsum__mono2) # label(axiom).  [clausify(3257)].
31.52/31.40	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(A,real,D,f562(A,real,D,C,B)))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),D),C)),hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),D),B))).  [resolve(5472,a,5460,a)].
31.52/31.40	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),zero_zero(code_code_numeral)),hAPP(A,code_code_numeral,D,f562(A,code_code_numeral,D,C,B)))) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),D),C)),hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),D),B))).  [resolve(5472,a,5463,a)].
31.52/31.40	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),hAPP(A,nat,D,f562(A,nat,D,C,B)))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),D),C)),hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),D),B))).  [resolve(5472,a,5466,a)].
31.52/31.40	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),hAPP(A,rat,D,f562(A,rat,D,C,B)))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),D),C)),hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),D),B))).  [resolve(5472,a,5467,a)].
31.52/31.40	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),zero_zero(quickcheck_code_int)),hAPP(A,quickcheck_code_int,D,f562(A,quickcheck_code_int,D,C,B)))) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),D),C)),hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),D),B))).  [resolve(5472,a,5470,a)].
31.94/31.82	5473 -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)) | zero_zero(A) != ti(A,B) | zero_zero(A) != ti(A,C) | zero_zero(A) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C) # label(fact_815_add__nonneg__eq__0__iff) # label(axiom).  [clausify(3819)].
31.94/31.82	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),B)) | zero_zero(real) != ti(real,A) | zero_zero(real) != ti(real,B) | zero_zero(real) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),B).  [resolve(5473,a,5460,a)].
31.94/31.82	Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),zero_zero(code_code_numeral)),A)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),zero_zero(code_code_numeral)),B)) | zero_zero(code_code_numeral) != ti(code_code_numeral,A) | zero_zero(code_code_numeral) != ti(code_code_numeral,B) | zero_zero(code_code_numeral) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),A),B).  [resolve(5473,a,5463,a)].
31.94/31.82	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)) | zero_zero(nat) != ti(nat,A) | zero_zero(nat) != ti(nat,B) | zero_zero(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B).  [resolve(5473,a,5466,a)].
31.94/31.82	Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),B)) | zero_zero(rat) != ti(rat,A) | zero_zero(rat) != ti(rat,B) | zero_zero(rat) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),B).  [resolve(5473,a,5467,a)].
31.94/31.82	Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),zero_zero(quickcheck_code_int)),A)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),zero_zero(quickcheck_code_int)),B)) | zero_zero(quickcheck_code_int) != ti(quickcheck_code_int,A) | zero_zero(quickcheck_code_int) != ti(quickcheck_code_int,B) | zero_zero(quickcheck_code_int) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),A),B).  [resolve(5473,a,5470,a)].
31.94/31.82	5474 -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)) | zero_zero(A) = ti(A,B) | zero_zero(A) != hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C) # label(fact_815_add__nonneg__eq__0__iff) # label(axiom).  [clausify(3819)].
31.94/31.82	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),B)) | zero_zero(real) = ti(real,A) | zero_zero(real) != hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),B).  [resolve(5474,a,5460,a)].
31.94/31.83	Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),zero_zero(code_code_numeral)),A)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),zero_zero(code_code_numeral)),B)) | zero_zero(code_code_numeral) = ti(code_code_numeral,A) | zero_zero(code_code_numeral) != hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),A),B).  [resolve(5474,a,5463,a)].
31.94/31.83	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)) | zero_zero(nat) = ti(nat,A) | zero_zero(nat) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B).  [resolve(5474,a,5466,a)].
31.94/31.83	Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),B)) | zero_zero(rat) = ti(rat,A) | zero_zero(rat) != hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),B).  [resolve(5474,a,5467,a)].
31.94/31.83	Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),zero_zero(quickcheck_code_int)),A)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),zero_zero(quickcheck_code_int)),B)) | zero_zero(quickcheck_code_int) = ti(quickcheck_code_int,A) | zero_zero(quickcheck_code_int) != hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),A),B).  [resolve(5474,a,5470,a)].
31.94/31.83	5475 -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)) | zero_zero(A) = ti(A,C) | zero_zero(A) != hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C) # label(fact_815_add__nonneg__eq__0__iff) # label(axiom).  [clausify(3819)].
31.94/31.83	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),B)) | zero_zero(real) = ti(real,B) | zero_zero(real) != hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),B).  [resolve(5475,a,5460,a)].
31.94/31.83	Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),zero_zero(code_code_numeral)),A)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),zero_zero(code_code_numeral)),B)) | zero_zero(code_code_numeral) = ti(code_code_numeral,B) | zero_zero(code_code_numeral) != hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),A),B).  [resolve(5475,a,5463,a)].
31.94/31.83	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)) | zero_zero(nat) = ti(nat,B) | zero_zero(nat) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B).  [resolve(5475,a,5466,a)].
31.94/31.83	Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),B)) | zero_zero(rat) = ti(rat,B) | zero_zero(rat) != hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),B).  [resolve(5475,a,5467,a)].
31.94/31.83	Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),zero_zero(quickcheck_code_int)),A)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),zero_zero(quickcheck_code_int)),B)) | zero_zero(quickcheck_code_int) = ti(quickcheck_code_int,B) | zero_zero(quickcheck_code_int) != hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),A),B).  [resolve(5475,a,5470,a)].
32.29/32.21	5476 -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_816_add__nonneg__nonneg) # label(axiom).  [clausify(4074)].
32.29/32.21	5477 ordere216010020id_add(int) # label(arity_Int_Oint___Groups_Oordered__comm__monoid__add) # label(axiom).  [assumption].
32.29/32.21	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(5477,a,5459,a)].
32.29/32.21	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(5477,a,5461,a)].
32.29/32.21	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(5477,a,5462,a)].
32.29/32.21	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(5477,a,5464,a)].
32.29/32.21	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B))).  [resolve(5477,a,5465,a)].
32.29/32.21	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(5477,a,5468,a)].
32.29/32.21	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(5477,a,5469,a)].
32.29/32.21	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f562(A,int,D,C,B)),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),B),C))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),D),C)),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),D),B))).  [resolve(5477,a,5471,a)].
32.29/32.21	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(A,int,D,f562(A,int,D,C,B)))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),D),C)),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),D),B))).  [resolve(5477,a,5472,a)].
32.63/32.53	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),B)) | zero_zero(int) != ti(int,A) | zero_zero(int) != ti(int,B) | zero_zero(int) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B).  [resolve(5477,a,5473,a)].
32.63/32.53	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),B)) | zero_zero(int) = ti(int,A) | zero_zero(int) != hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B).  [resolve(5477,a,5474,a)].
32.63/32.53	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),B)) | zero_zero(int) = ti(int,B) | zero_zero(int) != hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B).  [resolve(5477,a,5475,a)].
32.63/32.53	5478 -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_813_add__increasing2) # label(axiom).  [clausify(4202)].
32.63/32.53	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),C),A))).  [resolve(5478,a,5460,a)].
32.63/32.53	Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),zero_zero(code_code_numeral)),A)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),B),C)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),B),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),C),A))).  [resolve(5478,a,5463,a)].
32.63/32.53	Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),B),C)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),B),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),C),A))).  [resolve(5478,a,5467,a)].
32.63/32.53	Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),zero_zero(quickcheck_code_int)),A)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),B),C)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),B),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),C),A))).  [resolve(5478,a,5470,a)].
32.63/32.53	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),C),A))).  [resolve(5478,a,5477,a)].
32.63/32.53	5479 -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_761_add__neg__nonpos) # label(axiom).  [clausify(4443)].
32.63/32.53	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),B)),zero_zero(real))).  [resolve(5479,a,5460,a)].
32.66/32.60	Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),A),zero_zero(code_code_numeral))) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),B),zero_zero(code_code_numeral))) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),A),B)),zero_zero(code_code_numeral))).  [resolve(5479,a,5463,a)].
32.66/32.60	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(5479,a,5466,a)].
32.66/32.60	Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),B),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),B)),zero_zero(rat))).  [resolve(5479,a,5467,a)].
32.66/32.60	Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),A),zero_zero(quickcheck_code_int))) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),B),zero_zero(quickcheck_code_int))) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),A),B)),zero_zero(quickcheck_code_int))).  [resolve(5479,a,5470,a)].
32.66/32.60	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(5479,a,5477,a)].
32.66/32.60	5480 -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_760_add__strict__increasing2) # label(axiom).  [clausify(4515)].
32.66/32.60	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),C))).  [resolve(5480,a,5460,a)].
32.66/32.60	Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),zero_zero(code_code_numeral)),A)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),B),C)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),B),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),A),C))).  [resolve(5480,a,5463,a)].
32.66/32.60	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(5480,a,5466,a)].
32.66/32.60	Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),C)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),C))).  [resolve(5480,a,5467,a)].
34.42/34.30	Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),zero_zero(quickcheck_code_int)),A)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),B),C)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),B),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),A),C))).  [resolve(5480,a,5470,a)].
34.42/34.30	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(5480,a,5477,a)].
34.42/34.30	5481 -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_759_add__strict__increasing) # label(axiom).  [clausify(4525)].
34.42/34.30	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),C))).  [resolve(5481,a,5460,a)].
34.42/34.30	Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),zero_zero(code_code_numeral)),A)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),B),C)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),B),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),A),C))).  [resolve(5481,a,5463,a)].
34.42/34.30	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(5481,a,5466,a)].
34.42/34.30	Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),B),C)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),C))).  [resolve(5481,a,5467,a)].
34.42/34.30	Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),zero_zero(quickcheck_code_int)),A)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),B),C)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),B),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),A),C))).  [resolve(5481,a,5470,a)].
34.42/34.30	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),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(5481,a,5477,a)].
34.42/34.30	5482 real_vector(complex) # label(arity_Complex_Ocomplex___RealVector_Oreal__vector) # label(axiom).  [assumption].
34.42/34.30	5483 -real_vector(A) | hAPP(A,A,uminus_uminus(A),hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),B),C)) = hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),hAPP(real,real,uminus_uminus(real),B)),C) # label(fact_4687_scaleR__left_Ominus) # label(axiom).  [clausify(11)].
34.42/34.31	5484 -real_vector(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),B),C)),hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),D),C)) = hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),B),D)),C) # label(fact_4713_scaleR__left_Oadd) # label(axiom).  [clausify(82)].
34.42/34.31	5485 -real_vector(A) | hAPP(A,A,uminus_uminus(A),hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),B),C)) = hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),hAPP(real,real,uminus_uminus(real),B)),C) # label(fact_4686_scaleR__minus__left) # label(axiom).  [clausify(513)].
34.42/34.31	5486 -real_vector(A) | hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),B),C) != hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),B),D) | zero_zero(real) = B | ti(A,C) = ti(A,D) # label(fact_4700_scaleR__cancel__left) # label(axiom).  [clausify(553)].
34.42/34.31	5487 -real_vector(A) | hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),B),C) = hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),B),D) | zero_zero(real) != B # label(fact_4700_scaleR__cancel__left) # label(axiom).  [clausify(553)].
34.42/34.31	5488 -real_vector(A) | hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),B),C) = hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),B),D) | ti(A,C) != ti(A,D) # label(fact_4700_scaleR__cancel__left) # label(axiom).  [clausify(553)].
34.42/34.31	5489 -real_vector(A) | hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),B),C) != hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),D),C) | B = D | zero_zero(A) = ti(A,C) # label(fact_4704_scaleR__cancel__right) # label(axiom).  [clausify(631)].
34.42/34.31	5490 -real_vector(A) | hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),B),C) = hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),D),C) | B != D # label(fact_4704_scaleR__cancel__right) # label(axiom).  [clausify(631)].
34.42/34.31	5491 -real_vector(A) | hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),B),C) = hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),D),C) | zero_zero(A) != ti(A,C) # label(fact_4704_scaleR__cancel__right) # label(axiom).  [clausify(631)].
34.42/34.31	5492 -real_vector(A) | hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),one_one(real)),B) = ti(A,B) # label(fact_4706_real__vector_Oscale__one) # label(axiom).  [clausify(641)].
34.42/34.31	5493 -real_vector(A) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),hAPP(A,fun(B,A),hAPP(fun(B,fun(A,A)),fun(A,fun(B,A)),combc(B,A,A),hAPP(fun(B,real),fun(B,fun(A,A)),hAPP(fun(real,fun(A,A)),fun(fun(B,real),fun(B,fun(A,A))),combb(real,fun(A,A),B),scaleR_scaleR(A)),C)),D)),E) = hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),hAPP(fun(B,bool),real,hAPP(fun(B,real),fun(fun(B,bool),real),big_co1399186613setsum(B,real),C),E)),D) # label(fact_4731_scaleR__left_Osetsum) # label(axiom).  [clausify(1041)].
34.42/34.31	5494 -real_vector(A) | hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),B),hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),C),D)) = hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),C),hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),B),D)) # label(fact_4694_scaleR__left__commute) # label(axiom).  [clausify(1096)].
34.42/34.31	5495 -real_vector(A) | zero_zero(A) != hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),B),C) | zero_zero(real) = B | zero_zero(A) = ti(A,C) # label(fact_4708_scaleR__eq__0__iff) # label(axiom).  [clausify(1202)].
34.42/34.31	5496 -real_vector(A) | zero_zero(A) = hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),B),C) | zero_zero(real) != B # label(fact_4708_scaleR__eq__0__iff) # label(axiom).  [clausify(1202)].
34.42/34.31	5497 -real_vector(A) | zero_zero(A) = hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),B),C) | zero_zero(A) != ti(A,C) # label(fact_4708_scaleR__eq__0__iff) # label(axiom).  [clausify(1202)].
34.42/34.31	Derived: hAPP(complex,complex,uminus_uminus(complex),hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),A),B)) = hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),hAPP(real,real,uminus_uminus(real),A)),B).  [resolve(5482,a,5483,a)].
34.42/34.31	Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),A),B)),hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),C),B)) = hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),C)),B).  [resolve(5482,a,5484,a)].
34.42/34.33	Derived: hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),A),B) != hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),A),C) | zero_zero(real) = A | ti(complex,B) = ti(complex,C).  [resolve(5482,a,5486,a)].
34.42/34.33	Derived: hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),A),B) = hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),A),C) | zero_zero(real) != A.  [resolve(5482,a,5487,a)].
34.42/34.33	Derived: hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),A),B) = hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),A),C) | ti(complex,B) != ti(complex,C).  [resolve(5482,a,5488,a)].
34.42/34.33	Derived: hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),A),B) != hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),C),B) | A = C | zero_zero(complex) = ti(complex,B).  [resolve(5482,a,5489,a)].
34.42/34.33	Derived: hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),A),B) = hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),C),B) | A != C.  [resolve(5482,a,5490,a)].
34.42/34.33	Derived: hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),A),B) = hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),C),B) | zero_zero(complex) != ti(complex,B).  [resolve(5482,a,5491,a)].
34.42/34.33	Derived: hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),one_one(real)),A) = ti(complex,A).  [resolve(5482,a,5492,a)].
34.42/34.33	Derived: hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),hAPP(complex,fun(A,complex),hAPP(fun(A,fun(complex,complex)),fun(complex,fun(A,complex)),combc(A,complex,complex),hAPP(fun(A,real),fun(A,fun(complex,complex)),hAPP(fun(real,fun(complex,complex)),fun(fun(A,real),fun(A,fun(complex,complex))),combb(real,fun(complex,complex),A),scaleR_scaleR(complex)),B)),C)),D) = hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),B),D)),C).  [resolve(5482,a,5493,a)].
34.42/34.33	Derived: hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),A),hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),B),C)) = hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),B),hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),A),C)).  [resolve(5482,a,5494,a)].
34.42/34.33	Derived: zero_zero(complex) != hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),A),B) | zero_zero(real) = A | zero_zero(complex) = ti(complex,B).  [resolve(5482,a,5495,a)].
34.42/34.33	Derived: zero_zero(complex) = hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),A),B) | zero_zero(real) != A.  [resolve(5482,a,5496,a)].
34.42/34.33	Derived: zero_zero(complex) = hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),A),B) | zero_zero(complex) != ti(complex,B).  [resolve(5482,a,5497,a)].
34.42/34.33	5498 -real_vector(A) | hAPP(A,A,uminus_uminus(A),hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),B),C)) = hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),B),hAPP(A,A,uminus_uminus(A),C)) # label(fact_4688_scaleR__minus__right) # label(axiom).  [clausify(1479)].
34.42/34.33	Derived: hAPP(complex,complex,uminus_uminus(complex),hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),A),B)) = hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),A),hAPP(complex,complex,uminus_uminus(complex),B)).  [resolve(5498,a,5482,a)].
34.42/34.33	5499 -real_vector(A) | hAPP(A,A,uminus_uminus(A),B) = hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),hAPP(int,real,number_number_of(real),min_1)),B) # label(fact_4724_scaleR__minus1__left) # label(axiom).  [clausify(1492)].
35.02/34.97	Derived: hAPP(complex,complex,uminus_uminus(complex),A) = hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),hAPP(int,real,number_number_of(real),min_1)),A).  [resolve(5499,a,5482,a)].
35.02/34.97	5500 -real_vector(A) | zero_zero(A) = hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),B),zero_zero(A)) # label(fact_4702_scaleR__right_Ozero) # label(axiom).  [clausify(1936)].
35.02/34.97	Derived: zero_zero(complex) = hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),A),zero_zero(complex)).  [resolve(5500,a,5482,a)].
35.02/34.97	5501 -real_vector(A) | hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),B),C)),hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),D),C)) = hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),B),D)),C) # label(fact_4714_scaleR__left__diff__distrib) # label(axiom).  [clausify(2346)].
35.02/34.97	Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),A),B)),hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),C),B)) = hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),C)),B).  [resolve(5501,a,5482,a)].
35.02/34.97	5502 -real_vector(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),B),C)),hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),B),D)) = hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),B),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),D)) # label(fact_4718_scaleR__right_Oadd) # label(axiom).  [clausify(2414)].
35.02/34.97	Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),A),B)),hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),A),C)) = hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),A),hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),B),C)).  [resolve(5502,a,5482,a)].
35.02/34.97	5503 -real_vector(A) | scaleR_scaleR(A) = ti(fun(real,fun(A,A)),scaleR_scaleR(A)) # label(tsy_c_RealVector_OscaleR__class_OscaleR_1_res) # label(axiom).  [clausify(2672)].
35.02/34.97	Derived: scaleR_scaleR(complex) = ti(fun(real,fun(complex,complex)),scaleR_scaleR(complex)).  [resolve(5503,a,5482,a)].
35.02/34.97	5504 -real_vector(A) | hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),B),C)),hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),D),C)) = hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),B),D)),C) # label(fact_4716_scaleR__left_Odiff) # label(axiom).  [clausify(2702)].
35.02/34.97	5505 real_vector(real) # label(arity_RealDef_Oreal___RealVector_Oreal__vector) # label(axiom).  [assumption].
35.02/34.97	Derived: hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),A),B)) = hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),hAPP(real,real,uminus_uminus(real),A)),B).  [resolve(5505,a,5483,a)].
35.02/34.97	Derived: hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),C),B)) = hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),C)),B).  [resolve(5505,a,5484,a)].
35.02/34.97	Derived: hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),A),B) != hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),A),C) | zero_zero(real) = A | ti(real,B) = ti(real,C).  [resolve(5505,a,5486,a)].
35.02/34.97	Derived: hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),A),B) = hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),A),C) | zero_zero(real) != A.  [resolve(5505,a,5487,a)].
35.02/34.97	Derived: hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),A),B) = hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),A),C) | ti(real,B) != ti(real,C).  [resolve(5505,a,5488,a)].
35.02/34.97	Derived: hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),A),B) != hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),C),B) | A = C | zero_zero(real) = ti(real,B).  [resolve(5505,a,5489,a)].
35.13/35.07	Derived: hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),A),B) = hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),C),B) | A != C.  [resolve(5505,a,5490,a)].
35.13/35.07	Derived: hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),A),B) = hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),C),B) | zero_zero(real) != ti(real,B).  [resolve(5505,a,5491,a)].
35.13/35.07	Derived: hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),one_one(real)),A) = ti(real,A).  [resolve(5505,a,5492,a)].
35.13/35.07	Derived: hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),hAPP(real,fun(A,real),hAPP(fun(A,fun(real,real)),fun(real,fun(A,real)),combc(A,real,real),hAPP(fun(A,real),fun(A,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(A,real),fun(A,fun(real,real))),combb(real,fun(real,real),A),scaleR_scaleR(real)),B)),C)),D) = hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),B),D)),C).  [resolve(5505,a,5493,a)].
35.13/35.07	Derived: hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),A),hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),B),C)) = hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),B),hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),A),C)).  [resolve(5505,a,5494,a)].
35.13/35.07	Derived: zero_zero(real) != hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),A),B) | zero_zero(real) = A | zero_zero(real) = ti(real,B).  [resolve(5505,a,5495,a)].
35.13/35.07	Derived: zero_zero(real) = hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),A),B) | zero_zero(real) != A.  [resolve(5505,a,5496,a)].
35.13/35.07	Derived: zero_zero(real) = hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),A),B) | zero_zero(real) != ti(real,B).  [resolve(5505,a,5497,a)].
35.13/35.07	Derived: hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),A),B)) = hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),A),hAPP(real,real,uminus_uminus(real),B)).  [resolve(5505,a,5498,a)].
35.13/35.07	Derived: hAPP(real,real,uminus_uminus(real),A) = hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),hAPP(int,real,number_number_of(real),min_1)),A).  [resolve(5505,a,5499,a)].
35.13/35.07	Derived: zero_zero(real) = hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),A),zero_zero(real)).  [resolve(5505,a,5500,a)].
35.13/35.07	Derived: hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),C),B)) = hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),C)),B).  [resolve(5505,a,5501,a)].
35.13/35.07	Derived: hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),A),C)) = hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),A),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),B),C)).  [resolve(5505,a,5502,a)].
35.13/35.07	Derived: scaleR_scaleR(real) = ti(fun(real,fun(real,real)),scaleR_scaleR(real)).  [resolve(5505,a,5503,a)].
35.13/35.07	5506 -real_vector(A) | zero_zero(real) = B | hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),B),C) != hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),B),D) | ti(A,C) = ti(A,D) # label(fact_4701_scaleR__left__imp__eq) # label(axiom).  [clausify(2984)].
35.13/35.07	5507 -real_vector(A) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),hAPP(fun(B,A),fun(B,A),hAPP(fun(A,A),fun(fun(B,A),fun(B,A)),combb(A,A,B),hAPP(real,fun(A,A),scaleR_scaleR(A),C)),D)),E) = hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),C),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),D),E)) # label(fact_4730_scaleR__right_Osetsum) # label(axiom).  [clausify(3099)].
36.48/36.37	Derived: hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),hAPP(fun(A,complex),fun(A,complex),hAPP(fun(complex,complex),fun(fun(A,complex),fun(A,complex)),combb(complex,complex,A),hAPP(real,fun(complex,complex),scaleR_scaleR(complex),B)),C)),D) = hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),B),hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),C),D)).  [resolve(5507,a,5482,a)].
36.48/36.37	Derived: hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),hAPP(fun(A,real),fun(A,real),hAPP(fun(real,real),fun(fun(A,real),fun(A,real)),combb(real,real,A),hAPP(real,fun(real,real),scaleR_scaleR(real),B)),C)),D) = hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),B),hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),C),D)).  [resolve(5507,a,5505,a)].
36.48/36.37	5508 -real_vector(A) | zero_zero(A) = ti(A,B) | hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),C),B) != hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),D),B) | C = D # label(fact_4705_scaleR__right__imp__eq) # label(axiom).  [clausify(3173)].
36.48/36.37	5509 -real_vector(A) | hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),B),C)),hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),B),D)) = hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),B),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),C),D)) # label(fact_4720_scaleR__right_Odiff) # label(axiom).  [clausify(3639)].
36.48/36.37	Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),A),B)),hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),A),C)) = hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),A),hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),B),C)).  [resolve(5509,a,5482,a)].
36.48/36.37	Derived: hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),A),C)) = hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),A),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),B),C)).  [resolve(5509,a,5505,a)].
36.48/36.37	5510 -real_vector(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),B),C)),hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),D),C)) = hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),B),D)),C) # label(fact_4711_real__vector_Oscale__left__distrib) # label(axiom).  [clausify(3859)].
36.48/36.37	5511 -real_vector(A) | hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),C)),D) = hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),B),hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),C),D)) # label(fact_4672_real__vector_Oscale__scale) # label(axiom).  [clausify(4672)].
36.48/36.37	Derived: hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),C) = hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),A),hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),B),C)).  [resolve(5511,a,5482,a)].
36.48/36.37	Derived: hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),C) = hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),A),hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),B),C)).  [resolve(5511,a,5505,a)].
36.48/36.37	5512 -real_vector(A) | zero_zero(A) = hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),zero_zero(real)),B) # label(fact_4709_scaleR__left_Ozero) # label(axiom).  [clausify(4850)].
36.48/36.37	Derived: zero_zero(complex) = hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),zero_zero(real)),A).  [resolve(5512,a,5482,a)].
36.48/36.37	Derived: zero_zero(real) = hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),zero_zero(real)),A).  [resolve(5512,a,5505,a)].
37.78/37.67	5513 comm_monoid_add(real) # label(arity_RealDef_Oreal___Groups_Ocomm__monoid__add) # label(axiom).  [assumption].
37.78/37.67	5514 -comm_monoid_add(A) | zero_zero(A) = hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),hAPP(A,fun(B,A),combk(A,B),zero_zero(A))),C) # label(fact_4217_setsum__0) # label(axiom).  [clausify(13)].
37.78/37.67	5515 -comm_monoid_add(A) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f2(B,A,C,D)),D)) | zero_zero(A) = hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),C),D) # label(fact_4775_setsum__0_H) # label(axiom).  [clausify(15)].
37.78/37.67	5516 -comm_monoid_add(A) | zero_zero(A) != hAPP(B,A,C,f2(B,A,C,D)) | zero_zero(A) = hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),C),D) # label(fact_4775_setsum__0_H) # label(axiom).  [clausify(15)].
37.78/37.67	5517 -comm_monoid_add(A) | -topological_space(A) | -hBOOL(hAPP(A,bool,hAPP(fun(nat,A),fun(A,bool),sums(A),B),C)) | hBOOL(hAPP(filter(nat),bool,hAPP(A,fun(filter(nat),bool),hAPP(fun(nat,A),fun(A,fun(filter(nat),bool)),tendsto(nat,A),hAPP(fun(nat,fun(nat,bool)),fun(nat,A),hAPP(fun(fun(nat,bool),A),fun(fun(nat,fun(nat,bool)),fun(nat,A)),combb(fun(nat,bool),A,nat),hAPP(fun(nat,A),fun(fun(nat,bool),A),big_co1399186613setsum(nat,A),B)),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)))),C),sequentially)) # label(fact_4496_sums__def) # label(axiom).  [clausify(44)].
37.78/37.67	5518 -comm_monoid_add(A) | -topological_space(A) | hBOOL(hAPP(A,bool,hAPP(fun(nat,A),fun(A,bool),sums(A),B),C)) | -hBOOL(hAPP(filter(nat),bool,hAPP(A,fun(filter(nat),bool),hAPP(fun(nat,A),fun(A,fun(filter(nat),bool)),tendsto(nat,A),hAPP(fun(nat,fun(nat,bool)),fun(nat,A),hAPP(fun(fun(nat,bool),A),fun(fun(nat,fun(nat,bool)),fun(nat,A)),combb(fun(nat,bool),A,nat),hAPP(fun(nat,A),fun(fun(nat,bool),A),big_co1399186613setsum(nat,A),B)),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)))),C),sequentially)) # label(fact_4496_sums__def) # label(axiom).  [clausify(44)].
37.78/37.67	5519 -ordere779506340up_add(A) | -comm_monoid_add(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | -hBOOL(hAPP(fun(B,bool),bool,hAPP(fun(B,bool),fun(fun(B,bool),bool),ord_less_eq(fun(B,bool)),D),C)) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f20(B,A,E,D,C)),hAPP(fun(B,bool),fun(B,bool),hAPP(fun(B,bool),fun(fun(B,bool),fun(B,bool)),minus_minus(fun(B,bool)),C),D))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),E),D)),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),E),C))) # label(fact_4292_setsum__mono3) # label(axiom).  [clausify(97)].
37.78/37.67	5520 -ordere779506340up_add(A) | -comm_monoid_add(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | -hBOOL(hAPP(fun(B,bool),bool,hAPP(fun(B,bool),fun(fun(B,bool),bool),ord_less_eq(fun(B,bool)),D),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(B,A,E,f20(B,A,E,D,C)))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),E),D)),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),E),C))) # label(fact_4292_setsum__mono3) # label(axiom).  [clausify(97)].
37.78/37.67	5521 -comm_monoid_add(A) | -topological_space(A) | sums(A) = ti(fun(fun(nat,A),fun(A,bool)),sums(A)) # label(tsy_c_Series_Osums_res) # label(axiom).  [clausify(210)].
37.78/37.67	Derived: zero_zero(real) = hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),hAPP(real,fun(A,real),combk(real,A),zero_zero(real))),B).  [resolve(5513,a,5514,a)].
37.78/37.67	Derived: hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f2(A,real,B,C)),C)) | zero_zero(real) = hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),B),C).  [resolve(5513,a,5515,a)].
37.78/37.67	Derived: zero_zero(real) != hAPP(A,real,B,f2(A,real,B,C)) | zero_zero(real) = hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),B),C).  [resolve(5513,a,5516,a)].
37.78/37.69	Derived: -topological_space(real) | -hBOOL(hAPP(real,bool,hAPP(fun(nat,real),fun(real,bool),sums(real),A),B)) | hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),hAPP(fun(nat,fun(nat,bool)),fun(nat,real),hAPP(fun(fun(nat,bool),real),fun(fun(nat,fun(nat,bool)),fun(nat,real)),combb(fun(nat,bool),real,nat),hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),A)),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)))),B),sequentially)).  [resolve(5513,a,5517,a)].
37.78/37.69	Derived: -topological_space(real) | hBOOL(hAPP(real,bool,hAPP(fun(nat,real),fun(real,bool),sums(real),A),B)) | -hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),hAPP(fun(nat,fun(nat,bool)),fun(nat,real),hAPP(fun(fun(nat,bool),real),fun(fun(nat,fun(nat,bool)),fun(nat,real)),combb(fun(nat,bool),real,nat),hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),A)),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)))),B),sequentially)).  [resolve(5513,a,5518,a)].
37.78/37.69	Derived: -ordere779506340up_add(real) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f20(A,real,D,C,B)),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),B),C))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),D),C)),hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),D),B))).  [resolve(5513,a,5519,b)].
37.78/37.69	Derived: -ordere779506340up_add(real) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(A,real,D,f20(A,real,D,C,B)))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),D),C)),hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),D),B))).  [resolve(5513,a,5520,b)].
37.78/37.69	Derived: -topological_space(real) | sums(real) = ti(fun(fun(nat,real),fun(real,bool)),sums(real)).  [resolve(5513,a,5521,a)].
37.78/37.69	5522 -comm_monoid_add(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | -hBOOL(hAPP(fun(B,bool),bool,hAPP(fun(B,bool),fun(fun(B,bool),bool),ord_less_eq(fun(B,bool)),D),C)) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f56(B,A,E,D,C)),hAPP(fun(B,bool),fun(B,bool),hAPP(fun(B,bool),fun(fun(B,bool),fun(B,bool)),minus_minus(fun(B,bool)),C),D))) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),E),C) = hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),E),D) # label(fact_4294_setsum__mono__zero__right) # label(axiom).  [clausify(341)].
37.78/37.69	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f56(A,real,D,C,B)),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),B),C))) | hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),D),B) = hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),D),C).  [resolve(5522,a,5513,a)].
37.78/37.69	5523 -comm_monoid_add(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | -hBOOL(hAPP(fun(B,bool),bool,hAPP(fun(B,bool),fun(fun(B,bool),bool),ord_less_eq(fun(B,bool)),D),C)) | zero_zero(A) != hAPP(B,A,E,f56(B,A,E,D,C)) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),E),C) = hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),E),D) # label(fact_4294_setsum__mono__zero__right) # label(axiom).  [clausify(341)].
37.83/37.71	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | zero_zero(real) != hAPP(A,real,D,f56(A,real,D,C,B)) | hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),D),B) = hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),D),C).  [resolve(5523,a,5513,a)].
37.83/37.71	5524 comm_monoid_add(int) # label(arity_Int_Oint___Groups_Ocomm__monoid__add) # label(axiom).  [assumption].
37.83/37.71	Derived: zero_zero(int) = hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),hAPP(int,fun(A,int),combk(int,A),zero_zero(int))),B).  [resolve(5524,a,5514,a)].
37.83/37.71	Derived: hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f2(A,int,B,C)),C)) | zero_zero(int) = hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),B),C).  [resolve(5524,a,5515,a)].
37.83/37.71	Derived: zero_zero(int) != hAPP(A,int,B,f2(A,int,B,C)) | zero_zero(int) = hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),B),C).  [resolve(5524,a,5516,a)].
37.83/37.71	Derived: -topological_space(int) | -hBOOL(hAPP(int,bool,hAPP(fun(nat,int),fun(int,bool),sums(int),A),B)) | hBOOL(hAPP(filter(nat),bool,hAPP(int,fun(filter(nat),bool),hAPP(fun(nat,int),fun(int,fun(filter(nat),bool)),tendsto(nat,int),hAPP(fun(nat,fun(nat,bool)),fun(nat,int),hAPP(fun(fun(nat,bool),int),fun(fun(nat,fun(nat,bool)),fun(nat,int)),combb(fun(nat,bool),int,nat),hAPP(fun(nat,int),fun(fun(nat,bool),int),big_co1399186613setsum(nat,int),A)),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)))),B),sequentially)).  [resolve(5524,a,5517,a)].
37.83/37.71	Derived: -topological_space(int) | hBOOL(hAPP(int,bool,hAPP(fun(nat,int),fun(int,bool),sums(int),A),B)) | -hBOOL(hAPP(filter(nat),bool,hAPP(int,fun(filter(nat),bool),hAPP(fun(nat,int),fun(int,fun(filter(nat),bool)),tendsto(nat,int),hAPP(fun(nat,fun(nat,bool)),fun(nat,int),hAPP(fun(fun(nat,bool),int),fun(fun(nat,fun(nat,bool)),fun(nat,int)),combb(fun(nat,bool),int,nat),hAPP(fun(nat,int),fun(fun(nat,bool),int),big_co1399186613setsum(nat,int),A)),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)))),B),sequentially)).  [resolve(5524,a,5518,a)].
37.83/37.71	Derived: -ordere779506340up_add(int) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f20(A,int,D,C,B)),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),B),C))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),D),C)),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),D),B))).  [resolve(5524,a,5519,b)].
37.83/37.71	Derived: -ordere779506340up_add(int) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(A,int,D,f20(A,int,D,C,B)))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),D),C)),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),D),B))).  [resolve(5524,a,5520,b)].
37.83/37.71	Derived: -topological_space(int) | sums(int) = ti(fun(fun(nat,int),fun(int,bool)),sums(int)).  [resolve(5524,a,5521,a)].
37.83/37.71	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f56(A,int,D,C,B)),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),B),C))) | hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),D),B) = hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),D),C).  [resolve(5524,a,5522,a)].
37.83/37.73	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | zero_zero(int) != hAPP(A,int,D,f56(A,int,D,C,B)) | hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),D),B) = hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),D),C).  [resolve(5524,a,5523,a)].
37.83/37.73	5525 -comm_monoid_add(A) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),C),one_one(nat)))) | hAPP(fun(nat,bool),A,hAPP(fun(nat,A),fun(fun(nat,bool),A),big_co1399186613setsum(nat,A),D),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),C),E))) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(fun(nat,bool),A,hAPP(fun(nat,A),fun(fun(nat,bool),A),big_co1399186613setsum(nat,A),D),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),B),C))),hAPP(fun(nat,bool),A,hAPP(fun(nat,A),fun(fun(nat,bool),A),big_co1399186613setsum(nat,A),D),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),C),one_one(nat))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),C),E)))) # label(fact_4604_setsum__ub__add__nat) # label(axiom).  [clausify(581)].
37.83/37.73	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),one_one(nat)))) | hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),C),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),D))) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),C),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),A),B))),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),C),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),one_one(nat))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),D)))).  [resolve(5525,a,5513,a)].
37.83/37.73	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),one_one(nat)))) | hAPP(fun(nat,bool),int,hAPP(fun(nat,int),fun(fun(nat,bool),int),big_co1399186613setsum(nat,int),C),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),D))) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(fun(nat,bool),int,hAPP(fun(nat,int),fun(fun(nat,bool),int),big_co1399186613setsum(nat,int),C),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),A),B))),hAPP(fun(nat,bool),int,hAPP(fun(nat,int),fun(fun(nat,bool),int),big_co1399186613setsum(nat,int),C),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),one_one(nat))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),D)))).  [resolve(5525,a,5524,a)].
37.83/37.73	5526 -comm_monoid_add(A) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),C)) | hAPP(fun(nat,bool),A,hAPP(fun(nat,A),fun(fun(nat,bool),A),big_co1399186613setsum(nat,A),D),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),B),C)) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(nat,A,D,B)),hAPP(fun(nat,bool),A,hAPP(fun(nat,A),fun(fun(nat,bool),A),big_co1399186613setsum(nat,A),D),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,suc,B)),C))) # label(fact_4598_setsum__head__Suc) # label(axiom).  [clausify(618)].
37.87/37.74	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),C),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),A),B)) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,C,A)),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),C),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,suc,A)),B))).  [resolve(5526,a,5513,a)].
37.87/37.74	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | hAPP(fun(nat,bool),int,hAPP(fun(nat,int),fun(fun(nat,bool),int),big_co1399186613setsum(nat,int),C),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),A),B)) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,C,A)),hAPP(fun(nat,bool),int,hAPP(fun(nat,int),fun(fun(nat,bool),int),big_co1399186613setsum(nat,int),C),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,suc,A)),B))).  [resolve(5526,a,5524,a)].
37.87/37.74	5527 -comm_monoid_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),B,zero_zero(A)),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),B,f102(C,A,D,E,F,B)),f104(C,A,D,E,F,B))) | -hBOOL(hAPP(fun(C,bool),bool,finite_finite_1(C),F)) | hBOOL(hAPP(fun(C,bool),bool,hAPP(C,fun(fun(C,bool),bool),member(C),f106(C,A,D,E,F,B)),F)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),B,hAPP(fun(C,bool),A,hAPP(fun(C,A),fun(fun(C,bool),A),big_co1399186613setsum(C,A),D),F)),hAPP(fun(C,bool),A,hAPP(fun(C,A),fun(fun(C,bool),A),big_co1399186613setsum(C,A),E),F))) # label(fact_4795_setsum_Orelated) # label(axiom).  [clausify(638)].
37.87/37.74	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),A,zero_zero(real)),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),A,f102(B,real,C,D,E,A)),f104(B,real,C,D,E,A))) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),E)) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f106(B,real,C,D,E,A)),E)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),A,hAPP(fun(B,bool),real,hAPP(fun(B,real),fun(fun(B,bool),real),big_co1399186613setsum(B,real),C),E)),hAPP(fun(B,bool),real,hAPP(fun(B,real),fun(fun(B,bool),real),big_co1399186613setsum(B,real),D),E))).  [resolve(5527,a,5513,a)].
37.87/37.74	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),A,zero_zero(int)),zero_zero(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),A,f102(B,int,C,D,E,A)),f104(B,int,C,D,E,A))) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),E)) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f106(B,int,C,D,E,A)),E)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),A,hAPP(fun(B,bool),int,hAPP(fun(B,int),fun(fun(B,bool),int),big_co1399186613setsum(B,int),C),E)),hAPP(fun(B,bool),int,hAPP(fun(B,int),fun(fun(B,bool),int),big_co1399186613setsum(B,int),D),E))).  [resolve(5527,a,5524,a)].
37.87/37.74	5528 -comm_monoid_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),B,zero_zero(A)),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),B,f102(C,A,D,E,F,B)),f104(C,A,D,E,F,B))) | -hBOOL(hAPP(fun(C,bool),bool,finite_finite_1(C),F)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),B,hAPP(C,A,D,f106(C,A,D,E,F,B))),hAPP(C,A,E,f106(C,A,D,E,F,B)))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),B,hAPP(fun(C,bool),A,hAPP(fun(C,A),fun(fun(C,bool),A),big_co1399186613setsum(C,A),D),F)),hAPP(fun(C,bool),A,hAPP(fun(C,A),fun(fun(C,bool),A),big_co1399186613setsum(C,A),E),F))) # label(fact_4795_setsum_Orelated) # label(axiom).  [clausify(638)].
37.87/37.74	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),A,zero_zero(real)),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),A,f102(B,real,C,D,E,A)),f104(B,real,C,D,E,A))) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),E)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),A,hAPP(B,real,C,f106(B,real,C,D,E,A))),hAPP(B,real,D,f106(B,real,C,D,E,A)))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),A,hAPP(fun(B,bool),real,hAPP(fun(B,real),fun(fun(B,bool),real),big_co1399186613setsum(B,real),C),E)),hAPP(fun(B,bool),real,hAPP(fun(B,real),fun(fun(B,bool),real),big_co1399186613setsum(B,real),D),E))).  [resolve(5528,a,5513,a)].
37.87/37.75	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),A,zero_zero(int)),zero_zero(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),A,f102(B,int,C,D,E,A)),f104(B,int,C,D,E,A))) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),E)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),A,hAPP(B,int,C,f106(B,int,C,D,E,A))),hAPP(B,int,D,f106(B,int,C,D,E,A)))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),A,hAPP(fun(B,bool),int,hAPP(fun(B,int),fun(fun(B,bool),int),big_co1399186613setsum(B,int),C),E)),hAPP(fun(B,bool),int,hAPP(fun(B,int),fun(fun(B,bool),int),big_co1399186613setsum(B,int),D),E))).  [resolve(5528,a,5524,a)].
37.87/37.75	5529 -comm_monoid_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),B,zero_zero(A)),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),B,f103(C,A,D,E,F,B)),f105(C,A,D,E,F,B))) | -hBOOL(hAPP(fun(C,bool),bool,finite_finite_1(C),F)) | hBOOL(hAPP(fun(C,bool),bool,hAPP(C,fun(fun(C,bool),bool),member(C),f106(C,A,D,E,F,B)),F)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),B,hAPP(fun(C,bool),A,hAPP(fun(C,A),fun(fun(C,bool),A),big_co1399186613setsum(C,A),D),F)),hAPP(fun(C,bool),A,hAPP(fun(C,A),fun(fun(C,bool),A),big_co1399186613setsum(C,A),E),F))) # label(fact_4795_setsum_Orelated) # label(axiom).  [clausify(638)].
37.87/37.75	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),A,zero_zero(real)),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),A,f103(B,real,C,D,E,A)),f105(B,real,C,D,E,A))) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),E)) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f106(B,real,C,D,E,A)),E)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),A,hAPP(fun(B,bool),real,hAPP(fun(B,real),fun(fun(B,bool),real),big_co1399186613setsum(B,real),C),E)),hAPP(fun(B,bool),real,hAPP(fun(B,real),fun(fun(B,bool),real),big_co1399186613setsum(B,real),D),E))).  [resolve(5529,a,5513,a)].
37.87/37.75	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),A,zero_zero(int)),zero_zero(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),A,f103(B,int,C,D,E,A)),f105(B,int,C,D,E,A))) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),E)) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f106(B,int,C,D,E,A)),E)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),A,hAPP(fun(B,bool),int,hAPP(fun(B,int),fun(fun(B,bool),int),big_co1399186613setsum(B,int),C),E)),hAPP(fun(B,bool),int,hAPP(fun(B,int),fun(fun(B,bool),int),big_co1399186613setsum(B,int),D),E))).  [resolve(5529,a,5524,a)].
37.87/37.75	5530 -comm_monoid_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),B,zero_zero(A)),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),B,f103(C,A,D,E,F,B)),f105(C,A,D,E,F,B))) | -hBOOL(hAPP(fun(C,bool),bool,finite_finite_1(C),F)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),B,hAPP(C,A,D,f106(C,A,D,E,F,B))),hAPP(C,A,E,f106(C,A,D,E,F,B)))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),B,hAPP(fun(C,bool),A,hAPP(fun(C,A),fun(fun(C,bool),A),big_co1399186613setsum(C,A),D),F)),hAPP(fun(C,bool),A,hAPP(fun(C,A),fun(fun(C,bool),A),big_co1399186613setsum(C,A),E),F))) # label(fact_4795_setsum_Orelated) # label(axiom).  [clausify(638)].
37.87/37.75	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),A,zero_zero(real)),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),A,f103(B,real,C,D,E,A)),f105(B,real,C,D,E,A))) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),E)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),A,hAPP(B,real,C,f106(B,real,C,D,E,A))),hAPP(B,real,D,f106(B,real,C,D,E,A)))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),A,hAPP(fun(B,bool),real,hAPP(fun(B,real),fun(fun(B,bool),real),big_co1399186613setsum(B,real),C),E)),hAPP(fun(B,bool),real,hAPP(fun(B,real),fun(fun(B,bool),real),big_co1399186613setsum(B,real),D),E))).  [resolve(5530,a,5513,a)].
37.87/37.76	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),A,zero_zero(int)),zero_zero(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),A,f103(B,int,C,D,E,A)),f105(B,int,C,D,E,A))) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),E)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),A,hAPP(B,int,C,f106(B,int,C,D,E,A))),hAPP(B,int,D,f106(B,int,C,D,E,A)))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),A,hAPP(fun(B,bool),int,hAPP(fun(B,int),fun(fun(B,bool),int),big_co1399186613setsum(B,int),C),E)),hAPP(fun(B,bool),int,hAPP(fun(B,int),fun(fun(B,bool),int),big_co1399186613setsum(B,int),D),E))).  [resolve(5530,a,5524,a)].
37.87/37.76	5531 -comm_monoid_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),B,zero_zero(A)),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),B,hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),f102(C,A,D,E,F,B)),f103(C,A,D,E,F,B))),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),f104(C,A,D,E,F,B)),f105(C,A,D,E,F,B)))) | -hBOOL(hAPP(fun(C,bool),bool,finite_finite_1(C),F)) | hBOOL(hAPP(fun(C,bool),bool,hAPP(C,fun(fun(C,bool),bool),member(C),f106(C,A,D,E,F,B)),F)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),B,hAPP(fun(C,bool),A,hAPP(fun(C,A),fun(fun(C,bool),A),big_co1399186613setsum(C,A),D),F)),hAPP(fun(C,bool),A,hAPP(fun(C,A),fun(fun(C,bool),A),big_co1399186613setsum(C,A),E),F))) # label(fact_4795_setsum_Orelated) # label(axiom).  [clausify(638)].
37.87/37.76	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),A,zero_zero(real)),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),A,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),f102(B,real,C,D,E,A)),f103(B,real,C,D,E,A))),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),f104(B,real,C,D,E,A)),f105(B,real,C,D,E,A)))) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),E)) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f106(B,real,C,D,E,A)),E)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),A,hAPP(fun(B,bool),real,hAPP(fun(B,real),fun(fun(B,bool),real),big_co1399186613setsum(B,real),C),E)),hAPP(fun(B,bool),real,hAPP(fun(B,real),fun(fun(B,bool),real),big_co1399186613setsum(B,real),D),E))).  [resolve(5531,a,5513,a)].
37.87/37.76	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),A,zero_zero(int)),zero_zero(int))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),A,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),f102(B,int,C,D,E,A)),f103(B,int,C,D,E,A))),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),f104(B,int,C,D,E,A)),f105(B,int,C,D,E,A)))) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),E)) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f106(B,int,C,D,E,A)),E)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),A,hAPP(fun(B,bool),int,hAPP(fun(B,int),fun(fun(B,bool),int),big_co1399186613setsum(B,int),C),E)),hAPP(fun(B,bool),int,hAPP(fun(B,int),fun(fun(B,bool),int),big_co1399186613setsum(B,int),D),E))).  [resolve(5531,a,5524,a)].
37.87/37.76	5532 -comm_monoid_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),B,zero_zero(A)),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),B,hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),f102(C,A,D,E,F,B)),f103(C,A,D,E,F,B))),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),f104(C,A,D,E,F,B)),f105(C,A,D,E,F,B)))) | -hBOOL(hAPP(fun(C,bool),bool,finite_finite_1(C),F)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),B,hAPP(C,A,D,f106(C,A,D,E,F,B))),hAPP(C,A,E,f106(C,A,D,E,F,B)))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),B,hAPP(fun(C,bool),A,hAPP(fun(C,A),fun(fun(C,bool),A),big_co1399186613setsum(C,A),D),F)),hAPP(fun(C,bool),A,hAPP(fun(C,A),fun(fun(C,bool),A),big_co1399186613setsum(C,A),E),F))) # label(fact_4795_setsum_Orelated) # label(axiom).  [clausify(638)].
37.87/37.76	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),A,zero_zero(real)),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),A,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),f102(B,real,C,D,E,A)),f103(B,real,C,D,E,A))),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),f104(B,real,C,D,E,A)),f105(B,real,C,D,E,A)))) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),E)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),A,hAPP(B,real,C,f106(B,real,C,D,E,A))),hAPP(B,real,D,f106(B,real,C,D,E,A)))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),A,hAPP(fun(B,bool),real,hAPP(fun(B,real),fun(fun(B,bool),real),big_co1399186613setsum(B,real),C),E)),hAPP(fun(B,bool),real,hAPP(fun(B,real),fun(fun(B,bool),real),big_co1399186613setsum(B,real),D),E))).  [resolve(5532,a,5513,a)].
37.87/37.80	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),A,zero_zero(int)),zero_zero(int))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),A,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),f102(B,int,C,D,E,A)),f103(B,int,C,D,E,A))),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),f104(B,int,C,D,E,A)),f105(B,int,C,D,E,A)))) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),E)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),A,hAPP(B,int,C,f106(B,int,C,D,E,A))),hAPP(B,int,D,f106(B,int,C,D,E,A)))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),A,hAPP(fun(B,bool),int,hAPP(fun(B,int),fun(fun(B,bool),int),big_co1399186613setsum(B,int),C),E)),hAPP(fun(B,bool),int,hAPP(fun(B,int),fun(fun(B,bool),int),big_co1399186613setsum(B,int),D),E))).  [resolve(5532,a,5524,a)].
37.87/37.80	5533 -t2_space(A) | -comm_monoid_add(A) | zero_zero(A) = hAPP(fun(nat,A),A,suminf(A),hAPP(A,fun(nat,A),combk(A,nat),zero_zero(A))) # label(fact_3968_suminf__zero) # label(axiom).  [clausify(679)].
37.87/37.80	Derived: -t2_space(real) | zero_zero(real) = hAPP(fun(nat,real),real,suminf(real),hAPP(real,fun(nat,real),combk(real,nat),zero_zero(real))).  [resolve(5533,b,5513,a)].
37.87/37.80	Derived: -t2_space(int) | zero_zero(int) = hAPP(fun(nat,int),int,suminf(int),hAPP(int,fun(nat,int),combk(int,nat),zero_zero(int))).  [resolve(5533,b,5524,a)].
37.87/37.80	5534 -comm_monoid_add(A) | -topological_space(A) | zero_zero(A) != hAPP(nat,A,B,zero_zero(nat)) | -hBOOL(hAPP(A,bool,hAPP(fun(nat,A),fun(A,bool),sums(A),hAPP(fun(nat,nat),fun(nat,A),hAPP(fun(nat,A),fun(fun(nat,nat),fun(nat,A)),combb(nat,A,nat),B),suc)),C)) | hBOOL(hAPP(A,bool,hAPP(fun(nat,A),fun(A,bool),sums(A),B),C)) # label(fact_4094_sums__Suc__imp) # label(axiom).  [clausify(767)].
37.87/37.80	Derived: -topological_space(real) | zero_zero(real) != hAPP(nat,real,A,zero_zero(nat)) | -hBOOL(hAPP(real,bool,hAPP(fun(nat,real),fun(real,bool),sums(real),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),A),suc)),B)) | hBOOL(hAPP(real,bool,hAPP(fun(nat,real),fun(real,bool),sums(real),A),B)).  [resolve(5534,a,5513,a)].
37.87/37.80	Derived: -topological_space(int) | zero_zero(int) != hAPP(nat,int,A,zero_zero(nat)) | -hBOOL(hAPP(int,bool,hAPP(fun(nat,int),fun(int,bool),sums(int),hAPP(fun(nat,nat),fun(nat,int),hAPP(fun(nat,int),fun(fun(nat,nat),fun(nat,int)),combb(nat,int,nat),A),suc)),B)) | hBOOL(hAPP(int,bool,hAPP(fun(nat,int),fun(int,bool),sums(int),A),B)).  [resolve(5534,a,5524,a)].
37.87/37.80	5535 -comm_monoid_add(A) | -topological_space(A) | the(A) = ti(fun(fun(A,bool),A),the(A)) # label(tsy_c_HOL_OThe_3_res) # label(axiom).  [clausify(856)].
37.87/37.80	Derived: -topological_space(real) | the(real) = ti(fun(fun(real,bool),real),the(real)).  [resolve(5535,a,5513,a)].
37.87/37.80	Derived: -topological_space(int) | the(int) = ti(fun(fun(int,bool),int),the(int)).  [resolve(5535,a,5524,a)].
37.87/37.80	5536 -ordere779506340up_add(A) | -comm_monoid_add(A) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f137(B,A,C,D)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),C),D)),zero_zero(A))) # label(fact_4308_setsum__nonpos) # label(axiom).  [clausify(921)].
37.87/37.80	Derived: -ordere779506340up_add(real) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f137(A,real,B,C)),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),B),C)),zero_zero(real))).  [resolve(5536,b,5513,a)].
37.87/37.80	Derived: -ordere779506340up_add(int) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f137(A,int,B,C)),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),B),C)),zero_zero(int))).  [resolve(5536,b,5524,a)].
37.97/37.84	5537 -ordere779506340up_add(A) | -comm_monoid_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(B,A,C,f137(B,A,C,D))),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),C),D)),zero_zero(A))) # label(fact_4308_setsum__nonpos) # label(axiom).  [clausify(921)].
37.97/37.84	Derived: -ordere779506340up_add(real) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(A,real,B,f137(A,real,B,C))),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),B),C)),zero_zero(real))).  [resolve(5537,b,5513,a)].
37.97/37.84	Derived: -ordere779506340up_add(int) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(A,int,B,f137(A,int,B,C))),zero_zero(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),B),C)),zero_zero(int))).  [resolve(5537,b,5524,a)].
37.97/37.84	5538 -t2_space(A) | -comm_monoid_add(A) | -hBOOL(hAPP(fun(nat,A),bool,summable(A),B)) | hBOOL(hAPP(A,bool,hAPP(fun(nat,A),fun(A,bool),sums(A),B),hAPP(fun(nat,A),A,suminf(A),B))) # label(fact_4092_summable__sums) # label(axiom).  [clausify(954)].
37.97/37.84	Derived: -t2_space(real) | -hBOOL(hAPP(fun(nat,real),bool,summable(real),A)) | hBOOL(hAPP(real,bool,hAPP(fun(nat,real),fun(real,bool),sums(real),A),hAPP(fun(nat,real),real,suminf(real),A))).  [resolve(5538,b,5513,a)].
37.97/37.84	Derived: -t2_space(int) | -hBOOL(hAPP(fun(nat,int),bool,summable(int),A)) | hBOOL(hAPP(int,bool,hAPP(fun(nat,int),fun(int,bool),sums(int),A),hAPP(fun(nat,int),int,suminf(int),A))).  [resolve(5538,b,5524,a)].
37.97/37.84	5539 comm_monoid_add(code_code_numeral) # label(arity_Code__Numeral_Ocode__numeral___Groups_Ocomm__monoid__add) # label(axiom).  [assumption].
37.97/37.84	Derived: zero_zero(code_code_numeral) = hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),hAPP(code_code_numeral,fun(A,code_code_numeral),combk(code_code_numeral,A),zero_zero(code_code_numeral))),B).  [resolve(5539,a,5514,a)].
37.97/37.84	Derived: hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f2(A,code_code_numeral,B,C)),C)) | zero_zero(code_code_numeral) = hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),B),C).  [resolve(5539,a,5515,a)].
37.97/37.84	Derived: zero_zero(code_code_numeral) != hAPP(A,code_code_numeral,B,f2(A,code_code_numeral,B,C)) | zero_zero(code_code_numeral) = hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),B),C).  [resolve(5539,a,5516,a)].
37.97/37.84	Derived: -topological_space(code_code_numeral) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(fun(nat,code_code_numeral),fun(code_code_numeral,bool),sums(code_code_numeral),A),B)) | hBOOL(hAPP(filter(nat),bool,hAPP(code_code_numeral,fun(filter(nat),bool),hAPP(fun(nat,code_code_numeral),fun(code_code_numeral,fun(filter(nat),bool)),tendsto(nat,code_code_numeral),hAPP(fun(nat,fun(nat,bool)),fun(nat,code_code_numeral),hAPP(fun(fun(nat,bool),code_code_numeral),fun(fun(nat,fun(nat,bool)),fun(nat,code_code_numeral)),combb(fun(nat,bool),code_code_numeral,nat),hAPP(fun(nat,code_code_numeral),fun(fun(nat,bool),code_code_numeral),big_co1399186613setsum(nat,code_code_numeral),A)),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)))),B),sequentially)).  [resolve(5539,a,5517,a)].
37.97/37.84	Derived: -topological_space(code_code_numeral) | hBOOL(hAPP(code_code_numeral,bool,hAPP(fun(nat,code_code_numeral),fun(code_code_numeral,bool),sums(code_code_numeral),A),B)) | -hBOOL(hAPP(filter(nat),bool,hAPP(code_code_numeral,fun(filter(nat),bool),hAPP(fun(nat,code_code_numeral),fun(code_code_numeral,fun(filter(nat),bool)),tendsto(nat,code_code_numeral),hAPP(fun(nat,fun(nat,bool)),fun(nat,code_code_numeral),hAPP(fun(fun(nat,bool),code_code_numeral),fun(fun(nat,fun(nat,bool)),fun(nat,code_code_numeral)),combb(fun(nat,bool),code_code_numeral,nat),hAPP(fun(nat,code_code_numeral),fun(fun(nat,bool),code_code_numeral),big_co1399186613setsum(nat,code_code_numeral),A)),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)))),B),sequentially)).  [resolve(5539,a,5518,a)].
37.97/37.85	Derived: -ordere779506340up_add(code_code_numeral) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f20(A,code_code_numeral,D,C,B)),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),B),C))) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),D),C)),hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),D),B))).  [resolve(5539,a,5519,b)].
37.97/37.85	Derived: -ordere779506340up_add(code_code_numeral) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),zero_zero(code_code_numeral)),hAPP(A,code_code_numeral,D,f20(A,code_code_numeral,D,C,B)))) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),D),C)),hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),D),B))).  [resolve(5539,a,5520,b)].
37.97/37.85	Derived: -topological_space(code_code_numeral) | sums(code_code_numeral) = ti(fun(fun(nat,code_code_numeral),fun(code_code_numeral,bool)),sums(code_code_numeral)).  [resolve(5539,a,5521,a)].
37.97/37.85	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f56(A,code_code_numeral,D,C,B)),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),B),C))) | hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),D),B) = hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),D),C).  [resolve(5539,a,5522,a)].
37.97/37.85	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | zero_zero(code_code_numeral) != hAPP(A,code_code_numeral,D,f56(A,code_code_numeral,D,C,B)) | hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),D),B) = hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),D),C).  [resolve(5539,a,5523,a)].
37.97/37.85	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),one_one(nat)))) | hAPP(fun(nat,bool),code_code_numeral,hAPP(fun(nat,code_code_numeral),fun(fun(nat,bool),code_code_numeral),big_co1399186613setsum(nat,code_code_numeral),C),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),D))) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),hAPP(fun(nat,bool),code_code_numeral,hAPP(fun(nat,code_code_numeral),fun(fun(nat,bool),code_code_numeral),big_co1399186613setsum(nat,code_code_numeral),C),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),A),B))),hAPP(fun(nat,bool),code_code_numeral,hAPP(fun(nat,code_code_numeral),fun(fun(nat,bool),code_code_numeral),big_co1399186613setsum(nat,code_code_numeral),C),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),one_one(nat))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),D)))).  [resolve(5539,a,5525,a)].
37.97/37.85	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | hAPP(fun(nat,bool),code_code_numeral,hAPP(fun(nat,code_code_numeral),fun(fun(nat,bool),code_code_numeral),big_co1399186613setsum(nat,code_code_numeral),C),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),A),B)) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),hAPP(nat,code_code_numeral,C,A)),hAPP(fun(nat,bool),code_code_numeral,hAPP(fun(nat,code_code_numeral),fun(fun(nat,bool),code_code_numeral),big_co1399186613setsum(nat,code_code_numeral),C),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,suc,A)),B))).  [resolve(5539,a,5526,a)].
37.97/37.85	Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),A,zero_zero(code_code_numeral)),zero_zero(code_code_numeral))) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),A,f102(B,code_code_numeral,C,D,E,A)),f104(B,code_code_numeral,C,D,E,A))) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),E)) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f106(B,code_code_numeral,C,D,E,A)),E)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),A,hAPP(fun(B,bool),code_code_numeral,hAPP(fun(B,code_code_numeral),fun(fun(B,bool),code_code_numeral),big_co1399186613setsum(B,code_code_numeral),C),E)),hAPP(fun(B,bool),code_code_numeral,hAPP(fun(B,code_code_numeral),fun(fun(B,bool),code_code_numeral),big_co1399186613setsum(B,code_code_numeral),D),E))).  [resolve(5539,a,5527,a)].
37.97/37.85	Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),A,zero_zero(code_code_numeral)),zero_zero(code_code_numeral))) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),A,f102(B,code_code_numeral,C,D,E,A)),f104(B,code_code_numeral,C,D,E,A))) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),E)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),A,hAPP(B,code_code_numeral,C,f106(B,code_code_numeral,C,D,E,A))),hAPP(B,code_code_numeral,D,f106(B,code_code_numeral,C,D,E,A)))) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),A,hAPP(fun(B,bool),code_code_numeral,hAPP(fun(B,code_code_numeral),fun(fun(B,bool),code_code_numeral),big_co1399186613setsum(B,code_code_numeral),C),E)),hAPP(fun(B,bool),code_code_numeral,hAPP(fun(B,code_code_numeral),fun(fun(B,bool),code_code_numeral),big_co1399186613setsum(B,code_code_numeral),D),E))).  [resolve(5539,a,5528,a)].
37.97/37.85	Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),A,zero_zero(code_code_numeral)),zero_zero(code_code_numeral))) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),A,f103(B,code_code_numeral,C,D,E,A)),f105(B,code_code_numeral,C,D,E,A))) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),E)) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f106(B,code_code_numeral,C,D,E,A)),E)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),A,hAPP(fun(B,bool),code_code_numeral,hAPP(fun(B,code_code_numeral),fun(fun(B,bool),code_code_numeral),big_co1399186613setsum(B,code_code_numeral),C),E)),hAPP(fun(B,bool),code_code_numeral,hAPP(fun(B,code_code_numeral),fun(fun(B,bool),code_code_numeral),big_co1399186613setsum(B,code_code_numeral),D),E))).  [resolve(5539,a,5529,a)].
37.97/37.86	Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),A,zero_zero(code_code_numeral)),zero_zero(code_code_numeral))) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),A,f103(B,code_code_numeral,C,D,E,A)),f105(B,code_code_numeral,C,D,E,A))) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),E)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),A,hAPP(B,code_code_numeral,C,f106(B,code_code_numeral,C,D,E,A))),hAPP(B,code_code_numeral,D,f106(B,code_code_numeral,C,D,E,A)))) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),A,hAPP(fun(B,bool),code_code_numeral,hAPP(fun(B,code_code_numeral),fun(fun(B,bool),code_code_numeral),big_co1399186613setsum(B,code_code_numeral),C),E)),hAPP(fun(B,bool),code_code_numeral,hAPP(fun(B,code_code_numeral),fun(fun(B,bool),code_code_numeral),big_co1399186613setsum(B,code_code_numeral),D),E))).  [resolve(5539,a,5530,a)].
37.97/37.86	Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),A,zero_zero(code_code_numeral)),zero_zero(code_code_numeral))) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),A,hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),f102(B,code_code_numeral,C,D,E,A)),f103(B,code_code_numeral,C,D,E,A))),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),f104(B,code_code_numeral,C,D,E,A)),f105(B,code_code_numeral,C,D,E,A)))) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),E)) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f106(B,code_code_numeral,C,D,E,A)),E)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),A,hAPP(fun(B,bool),code_code_numeral,hAPP(fun(B,code_code_numeral),fun(fun(B,bool),code_code_numeral),big_co1399186613setsum(B,code_code_numeral),C),E)),hAPP(fun(B,bool),code_code_numeral,hAPP(fun(B,code_code_numeral),fun(fun(B,bool),code_code_numeral),big_co1399186613setsum(B,code_code_numeral),D),E))).  [resolve(5539,a,5531,a)].
37.97/37.86	Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),A,zero_zero(code_code_numeral)),zero_zero(code_code_numeral))) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),A,hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),f102(B,code_code_numeral,C,D,E,A)),f103(B,code_code_numeral,C,D,E,A))),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),f104(B,code_code_numeral,C,D,E,A)),f105(B,code_code_numeral,C,D,E,A)))) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),E)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),A,hAPP(B,code_code_numeral,C,f106(B,code_code_numeral,C,D,E,A))),hAPP(B,code_code_numeral,D,f106(B,code_code_numeral,C,D,E,A)))) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),A,hAPP(fun(B,bool),code_code_numeral,hAPP(fun(B,code_code_numeral),fun(fun(B,bool),code_code_numeral),big_co1399186613setsum(B,code_code_numeral),C),E)),hAPP(fun(B,bool),code_code_numeral,hAPP(fun(B,code_code_numeral),fun(fun(B,bool),code_code_numeral),big_co1399186613setsum(B,code_code_numeral),D),E))).  [resolve(5539,a,5532,a)].
37.97/37.86	Derived: -t2_space(code_code_numeral) | zero_zero(code_code_numeral) = hAPP(fun(nat,code_code_numeral),code_code_numeral,suminf(code_code_numeral),hAPP(code_code_numeral,fun(nat,code_code_numeral),combk(code_code_numeral,nat),zero_zero(code_code_numeral))).  [resolve(5539,a,5533,b)].
37.97/37.86	Derived: -topological_space(code_code_numeral) | zero_zero(code_code_numeral) != hAPP(nat,code_code_numeral,A,zero_zero(nat)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(fun(nat,code_code_numeral),fun(code_code_numeral,bool),sums(code_code_numeral),hAPP(fun(nat,nat),fun(nat,code_code_numeral),hAPP(fun(nat,code_code_numeral),fun(fun(nat,nat),fun(nat,code_code_numeral)),combb(nat,code_code_numeral,nat),A),suc)),B)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(fun(nat,code_code_numeral),fun(code_code_numeral,bool),sums(code_code_numeral),A),B)).  [resolve(5539,a,5534,a)].
38.09/37.96	Derived: -topological_space(code_code_numeral) | the(code_code_numeral) = ti(fun(fun(code_code_numeral,bool),code_code_numeral),the(code_code_numeral)).  [resolve(5539,a,5535,a)].
38.09/37.96	Derived: -ordere779506340up_add(code_code_numeral) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f137(A,code_code_numeral,B,C)),C)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),B),C)),zero_zero(code_code_numeral))).  [resolve(5539,a,5536,b)].
38.09/37.96	Derived: -ordere779506340up_add(code_code_numeral) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),hAPP(A,code_code_numeral,B,f137(A,code_code_numeral,B,C))),zero_zero(code_code_numeral))) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),B),C)),zero_zero(code_code_numeral))).  [resolve(5539,a,5537,b)].
38.09/37.96	Derived: -t2_space(code_code_numeral) | -hBOOL(hAPP(fun(nat,code_code_numeral),bool,summable(code_code_numeral),A)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(fun(nat,code_code_numeral),fun(code_code_numeral,bool),sums(code_code_numeral),A),hAPP(fun(nat,code_code_numeral),code_code_numeral,suminf(code_code_numeral),A))).  [resolve(5539,a,5538,b)].
38.09/37.96	5540 -comm_monoid_add(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),zero_zero(A)),B) = ti(A,B) # label(fact_777_add__0) # label(axiom).  [clausify(1100)].
38.09/37.96	Derived: hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),zero_zero(real)),A) = ti(real,A).  [resolve(5540,a,5513,a)].
38.09/37.96	Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),zero_zero(code_code_numeral)),A) = ti(code_code_numeral,A).  [resolve(5540,a,5539,a)].
38.09/37.96	5541 -comm_monoid_add(A) | -topological_space(A) | hBOOL(hAPP(A,bool,hAPP(fun(nat,A),fun(A,bool),sums(A),hAPP(A,fun(nat,A),combk(A,nat),zero_zero(A))),zero_zero(A))) # label(fact_4078_sums__zero) # label(axiom).  [clausify(1266)].
38.09/37.96	Derived: -topological_space(real) | hBOOL(hAPP(real,bool,hAPP(fun(nat,real),fun(real,bool),sums(real),hAPP(real,fun(nat,real),combk(real,nat),zero_zero(real))),zero_zero(real))).  [resolve(5541,a,5513,a)].
38.09/37.96	Derived: -topological_space(int) | hBOOL(hAPP(int,bool,hAPP(fun(nat,int),fun(int,bool),sums(int),hAPP(int,fun(nat,int),combk(int,nat),zero_zero(int))),zero_zero(int))).  [resolve(5541,a,5524,a)].
38.09/37.96	Derived: -topological_space(code_code_numeral) | hBOOL(hAPP(code_code_numeral,bool,hAPP(fun(nat,code_code_numeral),fun(code_code_numeral,bool),sums(code_code_numeral),hAPP(code_code_numeral,fun(nat,code_code_numeral),combk(code_code_numeral,nat),zero_zero(code_code_numeral))),zero_zero(code_code_numeral))).  [resolve(5541,a,5539,a)].
38.09/37.96	5542 -topological_space(A) | -comm_monoid_add(A) | suminf(A) = ti(fun(fun(nat,A),A),suminf(A)) # label(tsy_c_Series_Osuminf_res) # label(axiom).  [clausify(1448)].
38.09/37.96	Derived: -topological_space(real) | suminf(real) = ti(fun(fun(nat,real),real),suminf(real)).  [resolve(5542,b,5513,a)].
38.09/37.96	Derived: -topological_space(int) | suminf(int) = ti(fun(fun(nat,int),int),suminf(int)).  [resolve(5542,b,5524,a)].
38.09/37.96	Derived: -topological_space(code_code_numeral) | suminf(code_code_numeral) = ti(fun(fun(nat,code_code_numeral),code_code_numeral),suminf(code_code_numeral)).  [resolve(5542,b,5539,a)].
38.13/38.03	5543 -comm_monoid_add(A) | hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | zero_zero(A) = hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),D),C) # label(fact_4207_setsum_Oinfinite) # label(axiom).  [clausify(1456)].
38.13/38.03	Derived: hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | zero_zero(real) = hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),C),B).  [resolve(5543,a,5513,a)].
38.13/38.03	Derived: hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | zero_zero(int) = hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),C),B).  [resolve(5543,a,5524,a)].
38.13/38.03	Derived: hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | zero_zero(code_code_numeral) = hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),C),B).  [resolve(5543,a,5539,a)].
38.13/38.03	5544 -t2_space(A) | -comm_monoid_add(A) | -hBOOL(hAPP(A,bool,hAPP(fun(nat,A),fun(A,bool),sums(A),B),C)) | hAPP(fun(nat,A),A,suminf(A),B) = ti(A,C) # label(fact_4089_sums__unique) # label(axiom).  [clausify(1655)].
38.13/38.03	Derived: -t2_space(real) | -hBOOL(hAPP(real,bool,hAPP(fun(nat,real),fun(real,bool),sums(real),A),B)) | hAPP(fun(nat,real),real,suminf(real),A) = ti(real,B).  [resolve(5544,b,5513,a)].
38.13/38.03	Derived: -t2_space(int) | -hBOOL(hAPP(int,bool,hAPP(fun(nat,int),fun(int,bool),sums(int),A),B)) | hAPP(fun(nat,int),int,suminf(int),A) = ti(int,B).  [resolve(5544,b,5524,a)].
38.13/38.03	Derived: -t2_space(code_code_numeral) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(fun(nat,code_code_numeral),fun(code_code_numeral,bool),sums(code_code_numeral),A),B)) | hAPP(fun(nat,code_code_numeral),code_code_numeral,suminf(code_code_numeral),A) = ti(code_code_numeral,B).  [resolve(5544,b,5539,a)].
38.13/38.03	5545 -comm_monoid_add(A) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),hAPP(fun(C,bool),fun(B,A),hAPP(fun(B,fun(fun(C,bool),A)),fun(fun(C,bool),fun(B,A)),combc(B,fun(C,bool),A),hAPP(fun(B,fun(C,A)),fun(B,fun(fun(C,bool),A)),hAPP(fun(fun(C,A),fun(fun(C,bool),A)),fun(fun(B,fun(C,A)),fun(B,fun(fun(C,bool),A))),combb(fun(C,A),fun(fun(C,bool),A),B),big_co1399186613setsum(C,A)),hAPP(fun(C,fun(B,A)),fun(B,fun(C,A)),combc(C,B,A),D))),E)),F) = hAPP(fun(C,bool),A,hAPP(fun(C,A),fun(fun(C,bool),A),big_co1399186613setsum(C,A),hAPP(fun(B,bool),fun(C,A),hAPP(fun(C,fun(fun(B,bool),A)),fun(fun(B,bool),fun(C,A)),combc(C,fun(B,bool),A),hAPP(fun(C,fun(B,A)),fun(C,fun(fun(B,bool),A)),hAPP(fun(fun(B,A),fun(fun(B,bool),A)),fun(fun(C,fun(B,A)),fun(C,fun(fun(B,bool),A))),combb(fun(B,A),fun(fun(B,bool),A),C),big_co1399186613setsum(B,A)),D)),F)),E) # label(fact_4214_setsum__commute) # label(axiom).  [clausify(1700)].
38.13/38.03	Derived: hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),hAPP(fun(B,bool),fun(A,real),hAPP(fun(A,fun(fun(B,bool),real)),fun(fun(B,bool),fun(A,real)),combc(A,fun(B,bool),real),hAPP(fun(A,fun(B,real)),fun(A,fun(fun(B,bool),real)),hAPP(fun(fun(B,real),fun(fun(B,bool),real)),fun(fun(A,fun(B,real)),fun(A,fun(fun(B,bool),real))),combb(fun(B,real),fun(fun(B,bool),real),A),big_co1399186613setsum(B,real)),hAPP(fun(B,fun(A,real)),fun(A,fun(B,real)),combc(B,A,real),C))),D)),E) = hAPP(fun(B,bool),real,hAPP(fun(B,real),fun(fun(B,bool),real),big_co1399186613setsum(B,real),hAPP(fun(A,bool),fun(B,real),hAPP(fun(B,fun(fun(A,bool),real)),fun(fun(A,bool),fun(B,real)),combc(B,fun(A,bool),real),hAPP(fun(B,fun(A,real)),fun(B,fun(fun(A,bool),real)),hAPP(fun(fun(A,real),fun(fun(A,bool),real)),fun(fun(B,fun(A,real)),fun(B,fun(fun(A,bool),real))),combb(fun(A,real),fun(fun(A,bool),real),B),big_co1399186613setsum(A,real)),C)),E)),D).  [resolve(5545,a,5513,a)].
38.13/38.03	Derived: hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),hAPP(fun(B,bool),fun(A,int),hAPP(fun(A,fun(fun(B,bool),int)),fun(fun(B,bool),fun(A,int)),combc(A,fun(B,bool),int),hAPP(fun(A,fun(B,int)),fun(A,fun(fun(B,bool),int)),hAPP(fun(fun(B,int),fun(fun(B,bool),int)),fun(fun(A,fun(B,int)),fun(A,fun(fun(B,bool),int))),combb(fun(B,int),fun(fun(B,bool),int),A),big_co1399186613setsum(B,int)),hAPP(fun(B,fun(A,int)),fun(A,fun(B,int)),combc(B,A,int),C))),D)),E) = hAPP(fun(B,bool),int,hAPP(fun(B,int),fun(fun(B,bool),int),big_co1399186613setsum(B,int),hAPP(fun(A,bool),fun(B,int),hAPP(fun(B,fun(fun(A,bool),int)),fun(fun(A,bool),fun(B,int)),combc(B,fun(A,bool),int),hAPP(fun(B,fun(A,int)),fun(B,fun(fun(A,bool),int)),hAPP(fun(fun(A,int),fun(fun(A,bool),int)),fun(fun(B,fun(A,int)),fun(B,fun(fun(A,bool),int))),combb(fun(A,int),fun(fun(A,bool),int),B),big_co1399186613setsum(A,int)),C)),E)),D).  [resolve(5545,a,5524,a)].
38.17/38.06	Derived: hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),hAPP(fun(B,bool),fun(A,code_code_numeral),hAPP(fun(A,fun(fun(B,bool),code_code_numeral)),fun(fun(B,bool),fun(A,code_code_numeral)),combc(A,fun(B,bool),code_code_numeral),hAPP(fun(A,fun(B,code_code_numeral)),fun(A,fun(fun(B,bool),code_code_numeral)),hAPP(fun(fun(B,code_code_numeral),fun(fun(B,bool),code_code_numeral)),fun(fun(A,fun(B,code_code_numeral)),fun(A,fun(fun(B,bool),code_code_numeral))),combb(fun(B,code_code_numeral),fun(fun(B,bool),code_code_numeral),A),big_co1399186613setsum(B,code_code_numeral)),hAPP(fun(B,fun(A,code_code_numeral)),fun(A,fun(B,code_code_numeral)),combc(B,A,code_code_numeral),C))),D)),E) = hAPP(fun(B,bool),code_code_numeral,hAPP(fun(B,code_code_numeral),fun(fun(B,bool),code_code_numeral),big_co1399186613setsum(B,code_code_numeral),hAPP(fun(A,bool),fun(B,code_code_numeral),hAPP(fun(B,fun(fun(A,bool),code_code_numeral)),fun(fun(A,bool),fun(B,code_code_numeral)),combc(B,fun(A,bool),code_code_numeral),hAPP(fun(B,fun(A,code_code_numeral)),fun(B,fun(fun(A,bool),code_code_numeral)),hAPP(fun(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral)),fun(fun(B,fun(A,code_code_numeral)),fun(B,fun(fun(A,bool),code_code_numeral))),combb(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),B),big_co1399186613setsum(A,code_code_numeral)),C)),E)),D).  [resolve(5545,a,5539,a)].
38.17/38.06	5546 -comm_monoid_add(A) | hAPP(fun(nat,bool),A,hAPP(fun(nat,A),fun(fun(nat,bool),A),big_co1399186613setsum(nat,A),hAPP(fun(nat,fun(nat,bool)),fun(nat,A),hAPP(fun(fun(nat,bool),A),fun(fun(nat,fun(nat,bool)),fun(nat,A)),combb(fun(nat,bool),A,nat),hAPP(fun(nat,A),fun(fun(nat,bool),A),big_co1399186613setsum(nat,A),B)),hAPP(fun(nat,nat),fun(nat,fun(nat,bool)),hAPP(fun(nat,fun(nat,fun(nat,bool))),fun(fun(nat,nat),fun(nat,fun(nat,bool))),combs(nat,nat,fun(nat,bool)),hAPP(fun(nat,nat),fun(nat,fun(nat,fun(nat,bool))),hAPP(fun(nat,fun(nat,fun(nat,bool))),fun(fun(nat,nat),fun(nat,fun(nat,fun(nat,bool)))),combb(nat,fun(nat,fun(nat,bool)),nat),ord_atLeastLessThan(nat)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),times_times(nat)),C))),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),hAPP(fun(nat,nat),fun(nat,fun(nat,nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,nat),fun(nat,fun(nat,nat))),combb(nat,fun(nat,nat),nat),plus_plus(nat)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),times_times(nat)),C))),C)))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),D)) = hAPP(fun(nat,bool),A,hAPP(fun(nat,A),fun(fun(nat,bool),A),big_co1399186613setsum(nat,A),B),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),D),C))) # label(fact_4173_sumr__group) # label(axiom).  [clausify(1778)].
38.17/38.06	Derived: hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,fun(nat,bool)),fun(nat,real),hAPP(fun(fun(nat,bool),real),fun(fun(nat,fun(nat,bool)),fun(nat,real)),combb(fun(nat,bool),real,nat),hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),A)),hAPP(fun(nat,nat),fun(nat,fun(nat,bool)),hAPP(fun(nat,fun(nat,fun(nat,bool))),fun(fun(nat,nat),fun(nat,fun(nat,bool))),combs(nat,nat,fun(nat,bool)),hAPP(fun(nat,nat),fun(nat,fun(nat,fun(nat,bool))),hAPP(fun(nat,fun(nat,fun(nat,bool))),fun(fun(nat,nat),fun(nat,fun(nat,fun(nat,bool)))),combb(nat,fun(nat,fun(nat,bool)),nat),ord_atLeastLessThan(nat)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),times_times(nat)),B))),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),hAPP(fun(nat,nat),fun(nat,fun(nat,nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,nat),fun(nat,fun(nat,nat))),combb(nat,fun(nat,nat),nat),plus_plus(nat)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),times_times(nat)),B))),B)))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),C)) = hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),A),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),C),B))).  [resolve(5546,a,5513,a)].
38.17/38.06	Derived: hAPP(fun(nat,bool),int,hAPP(fun(nat,int),fun(fun(nat,bool),int),big_co1399186613setsum(nat,int),hAPP(fun(nat,fun(nat,bool)),fun(nat,int),hAPP(fun(fun(nat,bool),int),fun(fun(nat,fun(nat,bool)),fun(nat,int)),combb(fun(nat,bool),int,nat),hAPP(fun(nat,int),fun(fun(nat,bool),int),big_co1399186613setsum(nat,int),A)),hAPP(fun(nat,nat),fun(nat,fun(nat,bool)),hAPP(fun(nat,fun(nat,fun(nat,bool))),fun(fun(nat,nat),fun(nat,fun(nat,bool))),combs(nat,nat,fun(nat,bool)),hAPP(fun(nat,nat),fun(nat,fun(nat,fun(nat,bool))),hAPP(fun(nat,fun(nat,fun(nat,bool))),fun(fun(nat,nat),fun(nat,fun(nat,fun(nat,bool)))),combb(nat,fun(nat,fun(nat,bool)),nat),ord_atLeastLessThan(nat)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),times_times(nat)),B))),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),hAPP(fun(nat,nat),fun(nat,fun(nat,nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,nat),fun(nat,fun(nat,nat))),combb(nat,fun(nat,nat),nat),plus_plus(nat)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),times_times(nat)),B))),B)))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),C)) = hAPP(fun(nat,bool),int,hAPP(fun(nat,int),fun(fun(nat,bool),int),big_co1399186613setsum(nat,int),A),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),C),B))).  [resolve(5546,a,5524,a)].
38.17/38.06	Derived: hAPP(fun(nat,bool),code_code_numeral,hAPP(fun(nat,code_code_numeral),fun(fun(nat,bool),code_code_numeral),big_co1399186613setsum(nat,code_code_numeral),hAPP(fun(nat,fun(nat,bool)),fun(nat,code_code_numeral),hAPP(fun(fun(nat,bool),code_code_numeral),fun(fun(nat,fun(nat,bool)),fun(nat,code_code_numeral)),combb(fun(nat,bool),code_code_numeral,nat),hAPP(fun(nat,code_code_numeral),fun(fun(nat,bool),code_code_numeral),big_co1399186613setsum(nat,code_code_numeral),A)),hAPP(fun(nat,nat),fun(nat,fun(nat,bool)),hAPP(fun(nat,fun(nat,fun(nat,bool))),fun(fun(nat,nat),fun(nat,fun(nat,bool))),combs(nat,nat,fun(nat,bool)),hAPP(fun(nat,nat),fun(nat,fun(nat,fun(nat,bool))),hAPP(fun(nat,fun(nat,fun(nat,bool))),fun(fun(nat,nat),fun(nat,fun(nat,fun(nat,bool)))),combb(nat,fun(nat,fun(nat,bool)),nat),ord_atLeastLessThan(nat)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),times_times(nat)),B))),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),hAPP(fun(nat,nat),fun(nat,fun(nat,nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,nat),fun(nat,fun(nat,nat))),combb(nat,fun(nat,nat),nat),plus_plus(nat)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),times_times(nat)),B))),B)))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),C)) = hAPP(fun(nat,bool),code_code_numeral,hAPP(fun(nat,code_code_numeral),fun(fun(nat,bool),code_code_numeral),big_co1399186613setsum(nat,code_code_numeral),A),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),C),B))).  [resolve(5546,a,5539,a)].
38.17/38.07	5547 -comm_monoid_add(A) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),C)) | zero_zero(A) = hAPP(fun(nat,bool),A,hAPP(fun(nat,A),fun(fun(nat,bool),A),big_co1399186613setsum(nat,A),D),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),C),hAPP(nat,nat,suc,B))) # label(fact_4204_setsum__op__ivl__Suc) # label(axiom).  [clausify(1781)].
38.17/38.07	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | zero_zero(real) = hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),C),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),B),hAPP(nat,nat,suc,A))).  [resolve(5547,a,5513,a)].
38.17/38.07	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | zero_zero(int) = hAPP(fun(nat,bool),int,hAPP(fun(nat,int),fun(fun(nat,bool),int),big_co1399186613setsum(nat,int),C),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),B),hAPP(nat,nat,suc,A))).  [resolve(5547,a,5524,a)].
38.17/38.07	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | zero_zero(code_code_numeral) = hAPP(fun(nat,bool),code_code_numeral,hAPP(fun(nat,code_code_numeral),fun(fun(nat,bool),code_code_numeral),big_co1399186613setsum(nat,code_code_numeral),C),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),B),hAPP(nat,nat,suc,A))).  [resolve(5547,a,5539,a)].
38.17/38.07	5548 -comm_monoid_add(A) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),C)) | hAPP(fun(nat,bool),A,hAPP(fun(nat,A),fun(fun(nat,bool),A),big_co1399186613setsum(nat,A),D),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),C),hAPP(nat,nat,suc,B))) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(fun(nat,bool),A,hAPP(fun(nat,A),fun(fun(nat,bool),A),big_co1399186613setsum(nat,A),D),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),C),B))),hAPP(nat,A,D,B)) # label(fact_4204_setsum__op__ivl__Suc) # label(axiom).  [clausify(1781)].
38.17/38.07	Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),C),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),B),hAPP(nat,nat,suc,A))) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),C),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),B),A))),hAPP(nat,real,C,A)).  [resolve(5548,a,5513,a)].
38.17/38.07	Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | hAPP(fun(nat,bool),int,hAPP(fun(nat,int),fun(fun(nat,bool),int),big_co1399186613setsum(nat,int),C),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),B),hAPP(nat,nat,suc,A))) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(fun(nat,bool),int,hAPP(fun(nat,int),fun(fun(nat,bool),int),big_co1399186613setsum(nat,int),C),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),B),A))),hAPP(nat,int,C,A)).  [resolve(5548,a,5524,a)].
38.17/38.07	Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | hAPP(fun(nat,bool),code_code_numeral,hAPP(fun(nat,code_code_numeral),fun(fun(nat,bool),code_code_numeral),big_co1399186613setsum(nat,code_code_numeral),C),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),B),hAPP(nat,nat,suc,A))) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),hAPP(fun(nat,bool),code_code_numeral,hAPP(fun(nat,code_code_numeral),fun(fun(nat,bool),code_code_numeral),big_co1399186613setsum(nat,code_code_numeral),C),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),B),A))),hAPP(nat,code_code_numeral,C,A)).  [resolve(5548,a,5539,a)].
38.17/38.11	5549 -comm_monoid_add(A) | -ordere779506340up_add(A) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f306(B,A,C,D)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),C),D))) # label(fact_4309_setsum__nonneg) # label(axiom).  [clausify(1801)].
38.17/38.11	Derived: -ordere779506340up_add(real) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f306(A,real,B,C)),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),B),C))).  [resolve(5549,a,5513,a)].
38.17/38.11	Derived: -ordere779506340up_add(int) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f306(A,int,B,C)),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),B),C))).  [resolve(5549,a,5524,a)].
38.17/38.11	Derived: -ordere779506340up_add(code_code_numeral) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f306(A,code_code_numeral,B,C)),C)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),zero_zero(code_code_numeral)),hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),B),C))).  [resolve(5549,a,5539,a)].
38.17/38.11	5550 -comm_monoid_add(A) | -ordere779506340up_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(B,A,C,f306(B,A,C,D)))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),C),D))) # label(fact_4309_setsum__nonneg) # label(axiom).  [clausify(1801)].
38.17/38.11	Derived: -ordere779506340up_add(real) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(A,real,B,f306(A,real,B,C)))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),B),C))).  [resolve(5550,a,5513,a)].
38.17/38.11	Derived: -ordere779506340up_add(int) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(A,int,B,f306(A,int,B,C)))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),B),C))).  [resolve(5550,a,5524,a)].
38.17/38.11	Derived: -ordere779506340up_add(code_code_numeral) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),zero_zero(code_code_numeral)),hAPP(A,code_code_numeral,B,f306(A,code_code_numeral,B,C)))) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),zero_zero(code_code_numeral)),hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),B),C))).  [resolve(5550,a,5539,a)].
38.17/38.11	5551 -comm_monoid_add(A) | hAPP(fun(nat,bool),A,hAPP(fun(nat,A),fun(fun(nat,bool),A),big_co1399186613setsum(nat,A),B),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),C),D))) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(fun(nat,bool),A,hAPP(fun(nat,A),fun(fun(nat,bool),A),big_co1399186613setsum(nat,A),hAPP(fun(nat,nat),fun(nat,A),hAPP(fun(nat,A),fun(fun(nat,nat),fun(nat,A)),combb(nat,A,nat),B),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),D))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),C))),hAPP(fun(nat,bool),A,hAPP(fun(nat,A),fun(fun(nat,bool),A),big_co1399186613setsum(nat,A),B),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),D))) # label(fact_4182_sumr__offset3) # label(axiom).  [clausify(1868)].
38.28/38.16	Derived: hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),A),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),C))) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),A),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),C))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),B))),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),A),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),C))).  [resolve(5551,a,5513,a)].
38.28/38.16	Derived: hAPP(fun(nat,bool),int,hAPP(fun(nat,int),fun(fun(nat,bool),int),big_co1399186613setsum(nat,int),A),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),C))) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(fun(nat,bool),int,hAPP(fun(nat,int),fun(fun(nat,bool),int),big_co1399186613setsum(nat,int),hAPP(fun(nat,nat),fun(nat,int),hAPP(fun(nat,int),fun(fun(nat,nat),fun(nat,int)),combb(nat,int,nat),A),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),C))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),B))),hAPP(fun(nat,bool),int,hAPP(fun(nat,int),fun(fun(nat,bool),int),big_co1399186613setsum(nat,int),A),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),C))).  [resolve(5551,a,5524,a)].
38.28/38.16	Derived: hAPP(fun(nat,bool),code_code_numeral,hAPP(fun(nat,code_code_numeral),fun(fun(nat,bool),code_code_numeral),big_co1399186613setsum(nat,code_code_numeral),A),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),C))) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),hAPP(fun(nat,bool),code_code_numeral,hAPP(fun(nat,code_code_numeral),fun(fun(nat,bool),code_code_numeral),big_co1399186613setsum(nat,code_code_numeral),hAPP(fun(nat,nat),fun(nat,code_code_numeral),hAPP(fun(nat,code_code_numeral),fun(fun(nat,nat),fun(nat,code_code_numeral)),combb(nat,code_code_numeral,nat),A),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),C))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),B))),hAPP(fun(nat,bool),code_code_numeral,hAPP(fun(nat,code_code_numeral),fun(fun(nat,bool),code_code_numeral),big_co1399186613setsum(nat,code_code_numeral),A),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),C))).  [resolve(5551,a,5539,a)].
38.28/38.16	5552 -comm_monoid_mult(A) | -comm_monoid_add(A) | B != C | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),f335(A,D,E,C,B))) | hAPP(fun(int,bool),A,hAPP(fun(int,A),fun(fun(int,bool),A),big_co1399186613setsum(int,A),E),B) = hAPP(fun(int,bool),A,hAPP(fun(int,A),fun(fun(int,bool),A),big_co1399186613setsum(int,A),D),C) # label(fact_4297_transfer__nat__int__sum__prod__cong_I1_J) # label(axiom).  [clausify(2020)].
38.28/38.16	Derived: -comm_monoid_mult(real) | A != B | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),f335(real,C,D,B,A))) | hAPP(fun(int,bool),real,hAPP(fun(int,real),fun(fun(int,bool),real),big_co1399186613setsum(int,real),D),A) = hAPP(fun(int,bool),real,hAPP(fun(int,real),fun(fun(int,bool),real),big_co1399186613setsum(int,real),C),B).  [resolve(5552,b,5513,a)].
38.28/38.17	Derived: -comm_monoid_mult(int) | A != B | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),f335(int,C,D,B,A))) | hAPP(fun(int,bool),int,hAPP(fun(int,int),fun(fun(int,bool),int),big_co1399186613setsum(int,int),D),A) = hAPP(fun(int,bool),int,hAPP(fun(int,int),fun(fun(int,bool),int),big_co1399186613setsum(int,int),C),B).  [resolve(5552,b,5524,a)].
38.28/38.17	Derived: -comm_monoid_mult(code_code_numeral) | A != B | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),f335(code_code_numeral,C,D,B,A))) | hAPP(fun(int,bool),code_code_numeral,hAPP(fun(int,code_code_numeral),fun(fun(int,bool),code_code_numeral),big_co1399186613setsum(int,code_code_numeral),D),A) = hAPP(fun(int,bool),code_code_numeral,hAPP(fun(int,code_code_numeral),fun(fun(int,bool),code_code_numeral),big_co1399186613setsum(int,code_code_numeral),C),B).  [resolve(5552,b,5539,a)].
38.28/38.17	5553 -comm_monoid_mult(A) | -comm_monoid_add(A) | B != C | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,B)) | hAPP(int,A,D,f335(A,E,D,C,B)) != hAPP(int,A,E,f335(A,E,D,C,B)) | hAPP(fun(int,bool),A,hAPP(fun(int,A),fun(fun(int,bool),A),big_co1399186613setsum(int,A),D),B) = hAPP(fun(int,bool),A,hAPP(fun(int,A),fun(fun(int,bool),A),big_co1399186613setsum(int,A),E),C) # label(fact_4297_transfer__nat__int__sum__prod__cong_I1_J) # label(axiom).  [clausify(2020)].
38.28/38.17	Derived: -comm_monoid_mult(real) | A != B | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A)) | hAPP(int,real,C,f335(real,D,C,B,A)) != hAPP(int,real,D,f335(real,D,C,B,A)) | hAPP(fun(int,bool),real,hAPP(fun(int,real),fun(fun(int,bool),real),big_co1399186613setsum(int,real),C),A) = hAPP(fun(int,bool),real,hAPP(fun(int,real),fun(fun(int,bool),real),big_co1399186613setsum(int,real),D),B).  [resolve(5553,b,5513,a)].
38.28/38.17	Derived: -comm_monoid_mult(int) | A != B | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A)) | hAPP(int,int,C,f335(int,D,C,B,A)) != hAPP(int,int,D,f335(int,D,C,B,A)) | hAPP(fun(int,bool),int,hAPP(fun(int,int),fun(fun(int,bool),int),big_co1399186613setsum(int,int),C),A) = hAPP(fun(int,bool),int,hAPP(fun(int,int),fun(fun(int,bool),int),big_co1399186613setsum(int,int),D),B).  [resolve(5553,b,5524,a)].
38.28/38.17	Derived: -comm_monoid_mult(code_code_numeral) | A != B | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A)) | hAPP(int,code_code_numeral,C,f335(code_code_numeral,D,C,B,A)) != hAPP(int,code_code_numeral,D,f335(code_code_numeral,D,C,B,A)) | hAPP(fun(int,bool),code_code_numeral,hAPP(fun(int,code_code_numeral),fun(fun(int,bool),code_code_numeral),big_co1399186613setsum(int,code_code_numeral),C),A) = hAPP(fun(int,bool),code_code_numeral,hAPP(fun(int,code_code_numeral),fun(fun(int,bool),code_code_numeral),big_co1399186613setsum(int,code_code_numeral),D),B).  [resolve(5553,b,5539,a)].
38.28/38.17	5554 -comm_monoid_add(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),D),C)) | zero_zero(A) = hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),hAPP(A,fun(B,A),hAPP(fun(B,fun(A,A)),fun(A,fun(B,A)),combc(B,A,A),hAPP(fun(B,A),fun(B,fun(A,A)),hAPP(fun(B,fun(A,fun(A,A))),fun(fun(B,A),fun(B,fun(A,A))),combs(B,A,fun(A,A)),hAPP(fun(B,bool),fun(B,fun(A,fun(A,A))),hAPP(fun(bool,fun(A,fun(A,A))),fun(fun(B,bool),fun(B,fun(A,fun(A,A)))),combb(bool,fun(A,fun(A,A)),B),if(A)),hAPP(B,fun(B,bool),hAPP(fun(B,fun(B,bool)),fun(B,fun(B,bool)),combc(B,B,bool),fequal(B)),D))),E)),zero_zero(A))),C) # label(fact_4215_setsum__delta) # label(axiom).  [clausify(2037)].
38.28/38.17	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | zero_zero(real) = hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),hAPP(real,fun(A,real),hAPP(fun(A,fun(real,real)),fun(real,fun(A,real)),combc(A,real,real),hAPP(fun(A,real),fun(A,fun(real,real)),hAPP(fun(A,fun(real,fun(real,real))),fun(fun(A,real),fun(A,fun(real,real))),combs(A,real,fun(real,real)),hAPP(fun(A,bool),fun(A,fun(real,fun(real,real))),hAPP(fun(bool,fun(real,fun(real,real))),fun(fun(A,bool),fun(A,fun(real,fun(real,real)))),combb(bool,fun(real,fun(real,real)),A),if(real)),hAPP(A,fun(A,bool),hAPP(fun(A,fun(A,bool)),fun(A,fun(A,bool)),combc(A,A,bool),fequal(A)),C))),D)),zero_zero(real))),B).  [resolve(5554,a,5513,a)].
38.28/38.17	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | zero_zero(int) = hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),hAPP(int,fun(A,int),hAPP(fun(A,fun(int,int)),fun(int,fun(A,int)),combc(A,int,int),hAPP(fun(A,int),fun(A,fun(int,int)),hAPP(fun(A,fun(int,fun(int,int))),fun(fun(A,int),fun(A,fun(int,int))),combs(A,int,fun(int,int)),hAPP(fun(A,bool),fun(A,fun(int,fun(int,int))),hAPP(fun(bool,fun(int,fun(int,int))),fun(fun(A,bool),fun(A,fun(int,fun(int,int)))),combb(bool,fun(int,fun(int,int)),A),if(int)),hAPP(A,fun(A,bool),hAPP(fun(A,fun(A,bool)),fun(A,fun(A,bool)),combc(A,A,bool),fequal(A)),C))),D)),zero_zero(int))),B).  [resolve(5554,a,5524,a)].
38.28/38.17	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | zero_zero(code_code_numeral) = hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),hAPP(code_code_numeral,fun(A,code_code_numeral),hAPP(fun(A,fun(code_code_numeral,code_code_numeral)),fun(code_code_numeral,fun(A,code_code_numeral)),combc(A,code_code_numeral,code_code_numeral),hAPP(fun(A,code_code_numeral),fun(A,fun(code_code_numeral,code_code_numeral)),hAPP(fun(A,fun(code_code_numeral,fun(code_code_numeral,code_code_numeral))),fun(fun(A,code_code_numeral),fun(A,fun(code_code_numeral,code_code_numeral))),combs(A,code_code_numeral,fun(code_code_numeral,code_code_numeral)),hAPP(fun(A,bool),fun(A,fun(code_code_numeral,fun(code_code_numeral,code_code_numeral))),hAPP(fun(bool,fun(code_code_numeral,fun(code_code_numeral,code_code_numeral))),fun(fun(A,bool),fun(A,fun(code_code_numeral,fun(code_code_numeral,code_code_numeral)))),combb(bool,fun(code_code_numeral,fun(code_code_numeral,code_code_numeral)),A),if(code_code_numeral)),hAPP(A,fun(A,bool),hAPP(fun(A,fun(A,bool)),fun(A,fun(A,bool)),combc(A,A,bool),fequal(A)),C))),D)),zero_zero(code_code_numeral))),B).  [resolve(5554,a,5539,a)].
38.28/38.17	5555 -comm_monoid_add(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | -hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),D),C)) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),hAPP(A,fun(B,A),hAPP(fun(B,fun(A,A)),fun(A,fun(B,A)),combc(B,A,A),hAPP(fun(B,A),fun(B,fun(A,A)),hAPP(fun(B,fun(A,fun(A,A))),fun(fun(B,A),fun(B,fun(A,A))),combs(B,A,fun(A,A)),hAPP(fun(B,bool),fun(B,fun(A,fun(A,A))),hAPP(fun(bool,fun(A,fun(A,A))),fun(fun(B,bool),fun(B,fun(A,fun(A,A)))),combb(bool,fun(A,fun(A,A)),B),if(A)),hAPP(B,fun(B,bool),hAPP(fun(B,fun(B,bool)),fun(B,fun(B,bool)),combc(B,B,bool),fequal(B)),D))),E)),zero_zero(A))),C) = hAPP(B,A,E,D) # label(fact_4215_setsum__delta) # label(axiom).  [clausify(2037)].
38.28/38.17	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),hAPP(real,fun(A,real),hAPP(fun(A,fun(real,real)),fun(real,fun(A,real)),combc(A,real,real),hAPP(fun(A,real),fun(A,fun(real,real)),hAPP(fun(A,fun(real,fun(real,real))),fun(fun(A,real),fun(A,fun(real,real))),combs(A,real,fun(real,real)),hAPP(fun(A,bool),fun(A,fun(real,fun(real,real))),hAPP(fun(bool,fun(real,fun(real,real))),fun(fun(A,bool),fun(A,fun(real,fun(real,real)))),combb(bool,fun(real,fun(real,real)),A),if(real)),hAPP(A,fun(A,bool),hAPP(fun(A,fun(A,bool)),fun(A,fun(A,bool)),combc(A,A,bool),fequal(A)),C))),D)),zero_zero(real))),B) = hAPP(A,real,D,C).  [resolve(5555,a,5513,a)].
38.28/38.20	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),hAPP(int,fun(A,int),hAPP(fun(A,fun(int,int)),fun(int,fun(A,int)),combc(A,int,int),hAPP(fun(A,int),fun(A,fun(int,int)),hAPP(fun(A,fun(int,fun(int,int))),fun(fun(A,int),fun(A,fun(int,int))),combs(A,int,fun(int,int)),hAPP(fun(A,bool),fun(A,fun(int,fun(int,int))),hAPP(fun(bool,fun(int,fun(int,int))),fun(fun(A,bool),fun(A,fun(int,fun(int,int)))),combb(bool,fun(int,fun(int,int)),A),if(int)),hAPP(A,fun(A,bool),hAPP(fun(A,fun(A,bool)),fun(A,fun(A,bool)),combc(A,A,bool),fequal(A)),C))),D)),zero_zero(int))),B) = hAPP(A,int,D,C).  [resolve(5555,a,5524,a)].
38.28/38.20	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),hAPP(code_code_numeral,fun(A,code_code_numeral),hAPP(fun(A,fun(code_code_numeral,code_code_numeral)),fun(code_code_numeral,fun(A,code_code_numeral)),combc(A,code_code_numeral,code_code_numeral),hAPP(fun(A,code_code_numeral),fun(A,fun(code_code_numeral,code_code_numeral)),hAPP(fun(A,fun(code_code_numeral,fun(code_code_numeral,code_code_numeral))),fun(fun(A,code_code_numeral),fun(A,fun(code_code_numeral,code_code_numeral))),combs(A,code_code_numeral,fun(code_code_numeral,code_code_numeral)),hAPP(fun(A,bool),fun(A,fun(code_code_numeral,fun(code_code_numeral,code_code_numeral))),hAPP(fun(bool,fun(code_code_numeral,fun(code_code_numeral,code_code_numeral))),fun(fun(A,bool),fun(A,fun(code_code_numeral,fun(code_code_numeral,code_code_numeral)))),combb(bool,fun(code_code_numeral,fun(code_code_numeral,code_code_numeral)),A),if(code_code_numeral)),hAPP(A,fun(A,bool),hAPP(fun(A,fun(A,bool)),fun(A,fun(A,bool)),combc(A,A,bool),fequal(A)),C))),D)),zero_zero(code_code_numeral))),B) = hAPP(A,code_code_numeral,D,C).  [resolve(5555,a,5539,a)].
38.28/38.20	5556 -metric_space(A) | -comm_monoid_add(A) | hAPP(fun(nat,A),A,lim(A),hAPP(fun(nat,fun(nat,bool)),fun(nat,A),hAPP(fun(fun(nat,bool),A),fun(fun(nat,fun(nat,bool)),fun(nat,A)),combb(fun(nat,bool),A,nat),hAPP(fun(nat,A),fun(fun(nat,bool),A),big_co1399186613setsum(nat,A),B)),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)))) = hAPP(fun(nat,A),A,suminf(A),B) # label(fact_4328_suminf__eq__lim) # label(axiom).  [clausify(2089)].
38.28/38.20	Derived: -metric_space(real) | hAPP(fun(nat,real),real,lim(real),hAPP(fun(nat,fun(nat,bool)),fun(nat,real),hAPP(fun(fun(nat,bool),real),fun(fun(nat,fun(nat,bool)),fun(nat,real)),combb(fun(nat,bool),real,nat),hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),A)),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)))) = hAPP(fun(nat,real),real,suminf(real),A).  [resolve(5556,b,5513,a)].
38.28/38.20	Derived: -metric_space(int) | hAPP(fun(nat,int),int,lim(int),hAPP(fun(nat,fun(nat,bool)),fun(nat,int),hAPP(fun(fun(nat,bool),int),fun(fun(nat,fun(nat,bool)),fun(nat,int)),combb(fun(nat,bool),int,nat),hAPP(fun(nat,int),fun(fun(nat,bool),int),big_co1399186613setsum(nat,int),A)),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)))) = hAPP(fun(nat,int),int,suminf(int),A).  [resolve(5556,b,5524,a)].
38.28/38.20	Derived: -metric_space(code_code_numeral) | hAPP(fun(nat,code_code_numeral),code_code_numeral,lim(code_code_numeral),hAPP(fun(nat,fun(nat,bool)),fun(nat,code_code_numeral),hAPP(fun(fun(nat,bool),code_code_numeral),fun(fun(nat,fun(nat,bool)),fun(nat,code_code_numeral)),combb(fun(nat,bool),code_code_numeral,nat),hAPP(fun(nat,code_code_numeral),fun(fun(nat,bool),code_code_numeral),big_co1399186613setsum(nat,code_code_numeral),A)),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)))) = hAPP(fun(nat,code_code_numeral),code_code_numeral,suminf(code_code_numeral),A).  [resolve(5556,b,5539,a)].
38.35/38.24	5557 -comm_monoid_add(A) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,B)),C)) | zero_zero(A) = hAPP(fun(nat,bool),A,hAPP(fun(nat,A),fun(fun(nat,bool),A),big_co1399186613setsum(nat,A),D),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),C),hAPP(nat,nat,suc,B))) # label(fact_4606_setsum__cl__ivl__Suc2) # label(axiom).  [clausify(2221)].
38.35/38.24	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,A)),B)) | zero_zero(real) = hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),C),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),B),hAPP(nat,nat,suc,A))).  [resolve(5557,a,5513,a)].
38.35/38.24	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,A)),B)) | zero_zero(int) = hAPP(fun(nat,bool),int,hAPP(fun(nat,int),fun(fun(nat,bool),int),big_co1399186613setsum(nat,int),C),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),B),hAPP(nat,nat,suc,A))).  [resolve(5557,a,5524,a)].
38.35/38.24	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,A)),B)) | zero_zero(code_code_numeral) = hAPP(fun(nat,bool),code_code_numeral,hAPP(fun(nat,code_code_numeral),fun(fun(nat,bool),code_code_numeral),big_co1399186613setsum(nat,code_code_numeral),C),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),B),hAPP(nat,nat,suc,A))).  [resolve(5557,a,5539,a)].
38.35/38.24	5558 -comm_monoid_add(A) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,B)),C)) | hAPP(fun(nat,bool),A,hAPP(fun(nat,A),fun(fun(nat,bool),A),big_co1399186613setsum(nat,A),D),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),C),hAPP(nat,nat,suc,B))) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(nat,A,D,C)),hAPP(fun(nat,bool),A,hAPP(fun(nat,A),fun(fun(nat,bool),A),big_co1399186613setsum(nat,A),hAPP(fun(nat,nat),fun(nat,A),hAPP(fun(nat,A),fun(fun(nat,nat),fun(nat,A)),combb(nat,A,nat),D),suc)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),C),B))) # label(fact_4606_setsum__cl__ivl__Suc2) # label(axiom).  [clausify(2221)].
38.35/38.24	Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,A)),B)) | hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),C),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),B),hAPP(nat,nat,suc,A))) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,C,B)),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),C),suc)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),B),A))).  [resolve(5558,a,5513,a)].
38.35/38.24	Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,A)),B)) | hAPP(fun(nat,bool),int,hAPP(fun(nat,int),fun(fun(nat,bool),int),big_co1399186613setsum(nat,int),C),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),B),hAPP(nat,nat,suc,A))) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,C,B)),hAPP(fun(nat,bool),int,hAPP(fun(nat,int),fun(fun(nat,bool),int),big_co1399186613setsum(nat,int),hAPP(fun(nat,nat),fun(nat,int),hAPP(fun(nat,int),fun(fun(nat,nat),fun(nat,int)),combb(nat,int,nat),C),suc)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),B),A))).  [resolve(5558,a,5524,a)].
38.35/38.24	Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,A)),B)) | hAPP(fun(nat,bool),code_code_numeral,hAPP(fun(nat,code_code_numeral),fun(fun(nat,bool),code_code_numeral),big_co1399186613setsum(nat,code_code_numeral),C),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),B),hAPP(nat,nat,suc,A))) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),hAPP(nat,code_code_numeral,C,B)),hAPP(fun(nat,bool),code_code_numeral,hAPP(fun(nat,code_code_numeral),fun(fun(nat,bool),code_code_numeral),big_co1399186613setsum(nat,code_code_numeral),hAPP(fun(nat,nat),fun(nat,code_code_numeral),hAPP(fun(nat,code_code_numeral),fun(fun(nat,nat),fun(nat,code_code_numeral)),combb(nat,code_code_numeral,nat),C),suc)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),B),A))).  [resolve(5558,a,5539,a)].
38.55/38.41	5559 -comm_monoid_add(A) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),hAPP(fun(B,A),fun(B,A),hAPP(fun(B,fun(A,A)),fun(fun(B,A),fun(B,A)),combs(B,A,A),hAPP(fun(B,A),fun(B,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(B,A),fun(B,fun(A,A))),combb(A,fun(A,A),B),plus_plus(A)),C)),D)),E) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),C),E)),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),D),E)) # label(fact_4220_setsum__addf) # label(axiom).  [clausify(2283)].
38.55/38.41	Derived: hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),hAPP(fun(A,real),fun(A,real),hAPP(fun(A,fun(real,real)),fun(fun(A,real),fun(A,real)),combs(A,real,real),hAPP(fun(A,real),fun(A,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(A,real),fun(A,fun(real,real))),combb(real,fun(real,real),A),plus_plus(real)),B)),C)),D) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),B),D)),hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),C),D)).  [resolve(5559,a,5513,a)].
38.55/38.41	Derived: hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),hAPP(fun(A,int),fun(A,int),hAPP(fun(A,fun(int,int)),fun(fun(A,int),fun(A,int)),combs(A,int,int),hAPP(fun(A,int),fun(A,fun(int,int)),hAPP(fun(int,fun(int,int)),fun(fun(A,int),fun(A,fun(int,int))),combb(int,fun(int,int),A),plus_plus(int)),B)),C)),D) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),B),D)),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),C),D)).  [resolve(5559,a,5524,a)].
38.55/38.41	Derived: hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),hAPP(fun(A,code_code_numeral),fun(A,code_code_numeral),hAPP(fun(A,fun(code_code_numeral,code_code_numeral)),fun(fun(A,code_code_numeral),fun(A,code_code_numeral)),combs(A,code_code_numeral,code_code_numeral),hAPP(fun(A,code_code_numeral),fun(A,fun(code_code_numeral,code_code_numeral)),hAPP(fun(code_code_numeral,fun(code_code_numeral,code_code_numeral)),fun(fun(A,code_code_numeral),fun(A,fun(code_code_numeral,code_code_numeral))),combb(code_code_numeral,fun(code_code_numeral,code_code_numeral),A),plus_plus(code_code_numeral)),B)),C)),D) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),B),D)),hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),C),D)).  [resolve(5559,a,5539,a)].
38.55/38.41	5560 -comm_monoid_mult(A) | -comm_monoid_add(A) | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,B)) | hAPP(fun(nat,bool),A,hAPP(fun(nat,A),fun(fun(nat,bool),A),big_co1399186613setsum(nat,A),hAPP(fun(nat,int),fun(nat,A),hAPP(fun(int,A),fun(fun(nat,int),fun(nat,A)),combb(int,A,nat),C),semiring_1_of_nat(int))),hAPP(fun(int,bool),fun(nat,bool),hAPP(fun(int,nat),fun(fun(int,bool),fun(nat,bool)),image(int,nat),nat_1),B)) = hAPP(fun(int,bool),A,hAPP(fun(int,A),fun(fun(int,bool),A),big_co1399186613setsum(int,A),C),B) # label(fact_4266_transfer__int__nat__sum__prod_I1_J) # label(axiom).  [clausify(2430)].
38.55/38.43	Derived: -comm_monoid_mult(real) | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A)) | hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,int),fun(nat,real),hAPP(fun(int,real),fun(fun(nat,int),fun(nat,real)),combb(int,real,nat),B),semiring_1_of_nat(int))),hAPP(fun(int,bool),fun(nat,bool),hAPP(fun(int,nat),fun(fun(int,bool),fun(nat,bool)),image(int,nat),nat_1),A)) = hAPP(fun(int,bool),real,hAPP(fun(int,real),fun(fun(int,bool),real),big_co1399186613setsum(int,real),B),A).  [resolve(5560,b,5513,a)].
38.55/38.43	Derived: -comm_monoid_mult(int) | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A)) | hAPP(fun(nat,bool),int,hAPP(fun(nat,int),fun(fun(nat,bool),int),big_co1399186613setsum(nat,int),hAPP(fun(nat,int),fun(nat,int),hAPP(fun(int,int),fun(fun(nat,int),fun(nat,int)),combb(int,int,nat),B),semiring_1_of_nat(int))),hAPP(fun(int,bool),fun(nat,bool),hAPP(fun(int,nat),fun(fun(int,bool),fun(nat,bool)),image(int,nat),nat_1),A)) = hAPP(fun(int,bool),int,hAPP(fun(int,int),fun(fun(int,bool),int),big_co1399186613setsum(int,int),B),A).  [resolve(5560,b,5524,a)].
38.55/38.43	Derived: -comm_monoid_mult(code_code_numeral) | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A)) | hAPP(fun(nat,bool),code_code_numeral,hAPP(fun(nat,code_code_numeral),fun(fun(nat,bool),code_code_numeral),big_co1399186613setsum(nat,code_code_numeral),hAPP(fun(nat,int),fun(nat,code_code_numeral),hAPP(fun(int,code_code_numeral),fun(fun(nat,int),fun(nat,code_code_numeral)),combb(int,code_code_numeral,nat),B),semiring_1_of_nat(int))),hAPP(fun(int,bool),fun(nat,bool),hAPP(fun(int,nat),fun(fun(int,bool),fun(nat,bool)),image(int,nat),nat_1),A)) = hAPP(fun(int,bool),code_code_numeral,hAPP(fun(int,code_code_numeral),fun(fun(int,bool),code_code_numeral),big_co1399186613setsum(int,code_code_numeral),B),A).  [resolve(5560,b,5539,a)].
38.55/38.43	5561 comm_monoid_add(rat) # label(arity_Rat_Orat___Groups_Ocomm__monoid__add) # label(axiom).  [assumption].
38.55/38.43	Derived: zero_zero(rat) = hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),hAPP(rat,fun(A,rat),combk(rat,A),zero_zero(rat))),B).  [resolve(5561,a,5514,a)].
38.55/38.43	Derived: hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f2(A,rat,B,C)),C)) | zero_zero(rat) = hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),B),C).  [resolve(5561,a,5515,a)].
38.55/38.43	Derived: zero_zero(rat) != hAPP(A,rat,B,f2(A,rat,B,C)) | zero_zero(rat) = hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),B),C).  [resolve(5561,a,5516,a)].
38.55/38.43	Derived: -topological_space(rat) | -hBOOL(hAPP(rat,bool,hAPP(fun(nat,rat),fun(rat,bool),sums(rat),A),B)) | hBOOL(hAPP(filter(nat),bool,hAPP(rat,fun(filter(nat),bool),hAPP(fun(nat,rat),fun(rat,fun(filter(nat),bool)),tendsto(nat,rat),hAPP(fun(nat,fun(nat,bool)),fun(nat,rat),hAPP(fun(fun(nat,bool),rat),fun(fun(nat,fun(nat,bool)),fun(nat,rat)),combb(fun(nat,bool),rat,nat),hAPP(fun(nat,rat),fun(fun(nat,bool),rat),big_co1399186613setsum(nat,rat),A)),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)))),B),sequentially)).  [resolve(5561,a,5517,a)].
38.55/38.43	Derived: -topological_space(rat) | hBOOL(hAPP(rat,bool,hAPP(fun(nat,rat),fun(rat,bool),sums(rat),A),B)) | -hBOOL(hAPP(filter(nat),bool,hAPP(rat,fun(filter(nat),bool),hAPP(fun(nat,rat),fun(rat,fun(filter(nat),bool)),tendsto(nat,rat),hAPP(fun(nat,fun(nat,bool)),fun(nat,rat),hAPP(fun(fun(nat,bool),rat),fun(fun(nat,fun(nat,bool)),fun(nat,rat)),combb(fun(nat,bool),rat,nat),hAPP(fun(nat,rat),fun(fun(nat,bool),rat),big_co1399186613setsum(nat,rat),A)),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)))),B),sequentially)).  [resolve(5561,a,5518,a)].
38.55/38.43	Derived: -ordere779506340up_add(rat) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f20(A,rat,D,C,B)),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),B),C))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),D),C)),hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),D),B))).  [resolve(5561,a,5519,b)].
38.55/38.43	Derived: -ordere779506340up_add(rat) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),hAPP(A,rat,D,f20(A,rat,D,C,B)))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),D),C)),hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),D),B))).  [resolve(5561,a,5520,b)].
38.55/38.43	Derived: -topological_space(rat) | sums(rat) = ti(fun(fun(nat,rat),fun(rat,bool)),sums(rat)).  [resolve(5561,a,5521,a)].
38.55/38.43	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f56(A,rat,D,C,B)),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),B),C))) | hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),D),B) = hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),D),C).  [resolve(5561,a,5522,a)].
38.55/38.43	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | zero_zero(rat) != hAPP(A,rat,D,f56(A,rat,D,C,B)) | hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),D),B) = hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),D),C).  [resolve(5561,a,5523,a)].
38.55/38.43	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),one_one(nat)))) | hAPP(fun(nat,bool),rat,hAPP(fun(nat,rat),fun(fun(nat,bool),rat),big_co1399186613setsum(nat,rat),C),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),D))) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(fun(nat,bool),rat,hAPP(fun(nat,rat),fun(fun(nat,bool),rat),big_co1399186613setsum(nat,rat),C),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),A),B))),hAPP(fun(nat,bool),rat,hAPP(fun(nat,rat),fun(fun(nat,bool),rat),big_co1399186613setsum(nat,rat),C),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),one_one(nat))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),D)))).  [resolve(5561,a,5525,a)].
38.55/38.43	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | hAPP(fun(nat,bool),rat,hAPP(fun(nat,rat),fun(fun(nat,bool),rat),big_co1399186613setsum(nat,rat),C),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),A),B)) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(nat,rat,C,A)),hAPP(fun(nat,bool),rat,hAPP(fun(nat,rat),fun(fun(nat,bool),rat),big_co1399186613setsum(nat,rat),C),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,suc,A)),B))).  [resolve(5561,a,5526,a)].
38.55/38.43	Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),A,zero_zero(rat)),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),A,f102(B,rat,C,D,E,A)),f104(B,rat,C,D,E,A))) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),E)) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f106(B,rat,C,D,E,A)),E)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),A,hAPP(fun(B,bool),rat,hAPP(fun(B,rat),fun(fun(B,bool),rat),big_co1399186613setsum(B,rat),C),E)),hAPP(fun(B,bool),rat,hAPP(fun(B,rat),fun(fun(B,bool),rat),big_co1399186613setsum(B,rat),D),E))).  [resolve(5561,a,5527,a)].
38.55/38.44	Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),A,zero_zero(rat)),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),A,f102(B,rat,C,D,E,A)),f104(B,rat,C,D,E,A))) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),E)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),A,hAPP(B,rat,C,f106(B,rat,C,D,E,A))),hAPP(B,rat,D,f106(B,rat,C,D,E,A)))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),A,hAPP(fun(B,bool),rat,hAPP(fun(B,rat),fun(fun(B,bool),rat),big_co1399186613setsum(B,rat),C),E)),hAPP(fun(B,bool),rat,hAPP(fun(B,rat),fun(fun(B,bool),rat),big_co1399186613setsum(B,rat),D),E))).  [resolve(5561,a,5528,a)].
38.55/38.44	Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),A,zero_zero(rat)),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),A,f103(B,rat,C,D,E,A)),f105(B,rat,C,D,E,A))) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),E)) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f106(B,rat,C,D,E,A)),E)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),A,hAPP(fun(B,bool),rat,hAPP(fun(B,rat),fun(fun(B,bool),rat),big_co1399186613setsum(B,rat),C),E)),hAPP(fun(B,bool),rat,hAPP(fun(B,rat),fun(fun(B,bool),rat),big_co1399186613setsum(B,rat),D),E))).  [resolve(5561,a,5529,a)].
38.55/38.44	Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),A,zero_zero(rat)),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),A,f103(B,rat,C,D,E,A)),f105(B,rat,C,D,E,A))) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),E)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),A,hAPP(B,rat,C,f106(B,rat,C,D,E,A))),hAPP(B,rat,D,f106(B,rat,C,D,E,A)))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),A,hAPP(fun(B,bool),rat,hAPP(fun(B,rat),fun(fun(B,bool),rat),big_co1399186613setsum(B,rat),C),E)),hAPP(fun(B,bool),rat,hAPP(fun(B,rat),fun(fun(B,bool),rat),big_co1399186613setsum(B,rat),D),E))).  [resolve(5561,a,5530,a)].
38.55/38.44	Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),A,zero_zero(rat)),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),A,hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),f102(B,rat,C,D,E,A)),f103(B,rat,C,D,E,A))),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),f104(B,rat,C,D,E,A)),f105(B,rat,C,D,E,A)))) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),E)) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f106(B,rat,C,D,E,A)),E)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),A,hAPP(fun(B,bool),rat,hAPP(fun(B,rat),fun(fun(B,bool),rat),big_co1399186613setsum(B,rat),C),E)),hAPP(fun(B,bool),rat,hAPP(fun(B,rat),fun(fun(B,bool),rat),big_co1399186613setsum(B,rat),D),E))).  [resolve(5561,a,5531,a)].
38.55/38.44	Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),A,zero_zero(rat)),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),A,hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),f102(B,rat,C,D,E,A)),f103(B,rat,C,D,E,A))),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),f104(B,rat,C,D,E,A)),f105(B,rat,C,D,E,A)))) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),E)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),A,hAPP(B,rat,C,f106(B,rat,C,D,E,A))),hAPP(B,rat,D,f106(B,rat,C,D,E,A)))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),A,hAPP(fun(B,bool),rat,hAPP(fun(B,rat),fun(fun(B,bool),rat),big_co1399186613setsum(B,rat),C),E)),hAPP(fun(B,bool),rat,hAPP(fun(B,rat),fun(fun(B,bool),rat),big_co1399186613setsum(B,rat),D),E))).  [resolve(5561,a,5532,a)].
38.55/38.44	Derived: -t2_space(rat) | zero_zero(rat) = hAPP(fun(nat,rat),rat,suminf(rat),hAPP(rat,fun(nat,rat),combk(rat,nat),zero_zero(rat))).  [resolve(5561,a,5533,b)].
38.55/38.44	Derived: -topological_space(rat) | zero_zero(rat) != hAPP(nat,rat,A,zero_zero(nat)) | -hBOOL(hAPP(rat,bool,hAPP(fun(nat,rat),fun(rat,bool),sums(rat),hAPP(fun(nat,nat),fun(nat,rat),hAPP(fun(nat,rat),fun(fun(nat,nat),fun(nat,rat)),combb(nat,rat,nat),A),suc)),B)) | hBOOL(hAPP(rat,bool,hAPP(fun(nat,rat),fun(rat,bool),sums(rat),A),B)).  [resolve(5561,a,5534,a)].
38.55/38.44	Derived: -topological_space(rat) | the(rat) = ti(fun(fun(rat,bool),rat),the(rat)).  [resolve(5561,a,5535,a)].
38.55/38.44	Derived: -ordere779506340up_add(rat) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f137(A,rat,B,C)),C)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),B),C)),zero_zero(rat))).  [resolve(5561,a,5536,b)].
38.55/38.45	Derived: -ordere779506340up_add(rat) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(A,rat,B,f137(A,rat,B,C))),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),B),C)),zero_zero(rat))).  [resolve(5561,a,5537,b)].
38.55/38.45	Derived: -t2_space(rat) | -hBOOL(hAPP(fun(nat,rat),bool,summable(rat),A)) | hBOOL(hAPP(rat,bool,hAPP(fun(nat,rat),fun(rat,bool),sums(rat),A),hAPP(fun(nat,rat),rat,suminf(rat),A))).  [resolve(5561,a,5538,b)].
38.55/38.45	Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),zero_zero(rat)),A) = ti(rat,A).  [resolve(5561,a,5540,a)].
38.55/38.45	Derived: -topological_space(rat) | hBOOL(hAPP(rat,bool,hAPP(fun(nat,rat),fun(rat,bool),sums(rat),hAPP(rat,fun(nat,rat),combk(rat,nat),zero_zero(rat))),zero_zero(rat))).  [resolve(5561,a,5541,a)].
38.55/38.45	Derived: -topological_space(rat) | suminf(rat) = ti(fun(fun(nat,rat),rat),suminf(rat)).  [resolve(5561,a,5542,b)].
38.55/38.45	Derived: hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | zero_zero(rat) = hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),C),B).  [resolve(5561,a,5543,a)].
38.55/38.45	Derived: -t2_space(rat) | -hBOOL(hAPP(rat,bool,hAPP(fun(nat,rat),fun(rat,bool),sums(rat),A),B)) | hAPP(fun(nat,rat),rat,suminf(rat),A) = ti(rat,B).  [resolve(5561,a,5544,b)].
38.55/38.45	Derived: hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),hAPP(fun(B,bool),fun(A,rat),hAPP(fun(A,fun(fun(B,bool),rat)),fun(fun(B,bool),fun(A,rat)),combc(A,fun(B,bool),rat),hAPP(fun(A,fun(B,rat)),fun(A,fun(fun(B,bool),rat)),hAPP(fun(fun(B,rat),fun(fun(B,bool),rat)),fun(fun(A,fun(B,rat)),fun(A,fun(fun(B,bool),rat))),combb(fun(B,rat),fun(fun(B,bool),rat),A),big_co1399186613setsum(B,rat)),hAPP(fun(B,fun(A,rat)),fun(A,fun(B,rat)),combc(B,A,rat),C))),D)),E) = hAPP(fun(B,bool),rat,hAPP(fun(B,rat),fun(fun(B,bool),rat),big_co1399186613setsum(B,rat),hAPP(fun(A,bool),fun(B,rat),hAPP(fun(B,fun(fun(A,bool),rat)),fun(fun(A,bool),fun(B,rat)),combc(B,fun(A,bool),rat),hAPP(fun(B,fun(A,rat)),fun(B,fun(fun(A,bool),rat)),hAPP(fun(fun(A,rat),fun(fun(A,bool),rat)),fun(fun(B,fun(A,rat)),fun(B,fun(fun(A,bool),rat))),combb(fun(A,rat),fun(fun(A,bool),rat),B),big_co1399186613setsum(A,rat)),C)),E)),D).  [resolve(5561,a,5545,a)].
38.55/38.45	Derived: hAPP(fun(nat,bool),rat,hAPP(fun(nat,rat),fun(fun(nat,bool),rat),big_co1399186613setsum(nat,rat),hAPP(fun(nat,fun(nat,bool)),fun(nat,rat),hAPP(fun(fun(nat,bool),rat),fun(fun(nat,fun(nat,bool)),fun(nat,rat)),combb(fun(nat,bool),rat,nat),hAPP(fun(nat,rat),fun(fun(nat,bool),rat),big_co1399186613setsum(nat,rat),A)),hAPP(fun(nat,nat),fun(nat,fun(nat,bool)),hAPP(fun(nat,fun(nat,fun(nat,bool))),fun(fun(nat,nat),fun(nat,fun(nat,bool))),combs(nat,nat,fun(nat,bool)),hAPP(fun(nat,nat),fun(nat,fun(nat,fun(nat,bool))),hAPP(fun(nat,fun(nat,fun(nat,bool))),fun(fun(nat,nat),fun(nat,fun(nat,fun(nat,bool)))),combb(nat,fun(nat,fun(nat,bool)),nat),ord_atLeastLessThan(nat)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),times_times(nat)),B))),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),hAPP(fun(nat,nat),fun(nat,fun(nat,nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,nat),fun(nat,fun(nat,nat))),combb(nat,fun(nat,nat),nat),plus_plus(nat)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),times_times(nat)),B))),B)))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),C)) = hAPP(fun(nat,bool),rat,hAPP(fun(nat,rat),fun(fun(nat,bool),rat),big_co1399186613setsum(nat,rat),A),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),C),B))).  [resolve(5561,a,5546,a)].
38.55/38.46	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | zero_zero(rat) = hAPP(fun(nat,bool),rat,hAPP(fun(nat,rat),fun(fun(nat,bool),rat),big_co1399186613setsum(nat,rat),C),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),B),hAPP(nat,nat,suc,A))).  [resolve(5561,a,5547,a)].
38.55/38.46	Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | hAPP(fun(nat,bool),rat,hAPP(fun(nat,rat),fun(fun(nat,bool),rat),big_co1399186613setsum(nat,rat),C),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),B),hAPP(nat,nat,suc,A))) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(fun(nat,bool),rat,hAPP(fun(nat,rat),fun(fun(nat,bool),rat),big_co1399186613setsum(nat,rat),C),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),B),A))),hAPP(nat,rat,C,A)).  [resolve(5561,a,5548,a)].
38.55/38.46	Derived: -ordere779506340up_add(rat) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f306(A,rat,B,C)),C)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),B),C))).  [resolve(5561,a,5549,a)].
38.55/38.46	Derived: -ordere779506340up_add(rat) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),hAPP(A,rat,B,f306(A,rat,B,C)))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),B),C))).  [resolve(5561,a,5550,a)].
38.55/38.46	Derived: hAPP(fun(nat,bool),rat,hAPP(fun(nat,rat),fun(fun(nat,bool),rat),big_co1399186613setsum(nat,rat),A),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),C))) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(fun(nat,bool),rat,hAPP(fun(nat,rat),fun(fun(nat,bool),rat),big_co1399186613setsum(nat,rat),hAPP(fun(nat,nat),fun(nat,rat),hAPP(fun(nat,rat),fun(fun(nat,nat),fun(nat,rat)),combb(nat,rat,nat),A),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),C))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),B))),hAPP(fun(nat,bool),rat,hAPP(fun(nat,rat),fun(fun(nat,bool),rat),big_co1399186613setsum(nat,rat),A),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),C))).  [resolve(5561,a,5551,a)].
38.55/38.46	Derived: -comm_monoid_mult(rat) | A != B | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),f335(rat,C,D,B,A))) | hAPP(fun(int,bool),rat,hAPP(fun(int,rat),fun(fun(int,bool),rat),big_co1399186613setsum(int,rat),D),A) = hAPP(fun(int,bool),rat,hAPP(fun(int,rat),fun(fun(int,bool),rat),big_co1399186613setsum(int,rat),C),B).  [resolve(5561,a,5552,b)].
38.55/38.46	Derived: -comm_monoid_mult(rat) | A != B | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A)) | hAPP(int,rat,C,f335(rat,D,C,B,A)) != hAPP(int,rat,D,f335(rat,D,C,B,A)) | hAPP(fun(int,bool),rat,hAPP(fun(int,rat),fun(fun(int,bool),rat),big_co1399186613setsum(int,rat),C),A) = hAPP(fun(int,bool),rat,hAPP(fun(int,rat),fun(fun(int,bool),rat),big_co1399186613setsum(int,rat),D),B).  [resolve(5561,a,5553,b)].
38.55/38.46	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | zero_zero(rat) = hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),hAPP(rat,fun(A,rat),hAPP(fun(A,fun(rat,rat)),fun(rat,fun(A,rat)),combc(A,rat,rat),hAPP(fun(A,rat),fun(A,fun(rat,rat)),hAPP(fun(A,fun(rat,fun(rat,rat))),fun(fun(A,rat),fun(A,fun(rat,rat))),combs(A,rat,fun(rat,rat)),hAPP(fun(A,bool),fun(A,fun(rat,fun(rat,rat))),hAPP(fun(bool,fun(rat,fun(rat,rat))),fun(fun(A,bool),fun(A,fun(rat,fun(rat,rat)))),combb(bool,fun(rat,fun(rat,rat)),A),if(rat)),hAPP(A,fun(A,bool),hAPP(fun(A,fun(A,bool)),fun(A,fun(A,bool)),combc(A,A,bool),fequal(A)),C))),D)),zero_zero(rat))),B).  [resolve(5561,a,5554,a)].
38.55/38.48	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),hAPP(rat,fun(A,rat),hAPP(fun(A,fun(rat,rat)),fun(rat,fun(A,rat)),combc(A,rat,rat),hAPP(fun(A,rat),fun(A,fun(rat,rat)),hAPP(fun(A,fun(rat,fun(rat,rat))),fun(fun(A,rat),fun(A,fun(rat,rat))),combs(A,rat,fun(rat,rat)),hAPP(fun(A,bool),fun(A,fun(rat,fun(rat,rat))),hAPP(fun(bool,fun(rat,fun(rat,rat))),fun(fun(A,bool),fun(A,fun(rat,fun(rat,rat)))),combb(bool,fun(rat,fun(rat,rat)),A),if(rat)),hAPP(A,fun(A,bool),hAPP(fun(A,fun(A,bool)),fun(A,fun(A,bool)),combc(A,A,bool),fequal(A)),C))),D)),zero_zero(rat))),B) = hAPP(A,rat,D,C).  [resolve(5561,a,5555,a)].
38.55/38.48	Derived: -metric_space(rat) | hAPP(fun(nat,rat),rat,lim(rat),hAPP(fun(nat,fun(nat,bool)),fun(nat,rat),hAPP(fun(fun(nat,bool),rat),fun(fun(nat,fun(nat,bool)),fun(nat,rat)),combb(fun(nat,bool),rat,nat),hAPP(fun(nat,rat),fun(fun(nat,bool),rat),big_co1399186613setsum(nat,rat),A)),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)))) = hAPP(fun(nat,rat),rat,suminf(rat),A).  [resolve(5561,a,5556,b)].
38.55/38.48	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,A)),B)) | zero_zero(rat) = hAPP(fun(nat,bool),rat,hAPP(fun(nat,rat),fun(fun(nat,bool),rat),big_co1399186613setsum(nat,rat),C),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),B),hAPP(nat,nat,suc,A))).  [resolve(5561,a,5557,a)].
38.55/38.48	Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,A)),B)) | hAPP(fun(nat,bool),rat,hAPP(fun(nat,rat),fun(fun(nat,bool),rat),big_co1399186613setsum(nat,rat),C),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),B),hAPP(nat,nat,suc,A))) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(nat,rat,C,B)),hAPP(fun(nat,bool),rat,hAPP(fun(nat,rat),fun(fun(nat,bool),rat),big_co1399186613setsum(nat,rat),hAPP(fun(nat,nat),fun(nat,rat),hAPP(fun(nat,rat),fun(fun(nat,nat),fun(nat,rat)),combb(nat,rat,nat),C),suc)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),B),A))).  [resolve(5561,a,5558,a)].
38.55/38.48	Derived: hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),hAPP(fun(A,rat),fun(A,rat),hAPP(fun(A,fun(rat,rat)),fun(fun(A,rat),fun(A,rat)),combs(A,rat,rat),hAPP(fun(A,rat),fun(A,fun(rat,rat)),hAPP(fun(rat,fun(rat,rat)),fun(fun(A,rat),fun(A,fun(rat,rat))),combb(rat,fun(rat,rat),A),plus_plus(rat)),B)),C)),D) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),B),D)),hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),C),D)).  [resolve(5561,a,5559,a)].
38.55/38.48	Derived: -comm_monoid_mult(rat) | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A)) | hAPP(fun(nat,bool),rat,hAPP(fun(nat,rat),fun(fun(nat,bool),rat),big_co1399186613setsum(nat,rat),hAPP(fun(nat,int),fun(nat,rat),hAPP(fun(int,rat),fun(fun(nat,int),fun(nat,rat)),combb(int,rat,nat),B),semiring_1_of_nat(int))),hAPP(fun(int,bool),fun(nat,bool),hAPP(fun(int,nat),fun(fun(int,bool),fun(nat,bool)),image(int,nat),nat_1),A)) = hAPP(fun(int,bool),rat,hAPP(fun(int,rat),fun(fun(int,bool),rat),big_co1399186613setsum(int,rat),B),A).  [resolve(5561,a,5560,b)].
38.55/38.48	5562 -comm_monoid_add(A) | big_co1399186613setsum(B,A) = ti(fun(fun(B,A),fun(fun(B,bool),A)),big_co1399186613setsum(B,A)) # label(tsy_c_Big__Operators_Ocomm__monoid__add__class_Osetsum_res) # label(axiom).  [clausify(2472)].
38.55/38.48	Derived: big_co1399186613setsum(A,real) = ti(fun(fun(A,real),fun(fun(A,bool),real)),big_co1399186613setsum(A,real)).  [resolve(5562,a,5513,a)].
38.55/38.48	Derived: big_co1399186613setsum(A,int) = ti(fun(fun(A,int),fun(fun(A,bool),int)),big_co1399186613setsum(A,int)).  [resolve(5562,a,5524,a)].
38.55/38.48	Derived: big_co1399186613setsum(A,code_code_numeral) = ti(fun(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral)),big_co1399186613setsum(A,code_code_numeral)).  [resolve(5562,a,5539,a)].
38.63/38.51	Derived: big_co1399186613setsum(A,rat) = ti(fun(fun(A,rat),fun(fun(A,bool),rat)),big_co1399186613setsum(A,rat)).  [resolve(5562,a,5561,a)].
38.63/38.51	5563 -topological_space(A) | -comm_monoid_add(A) | hAPP(fun(A,bool),A,the(A),hAPP(fun(nat,A),fun(A,bool),sums(A),B)) = hAPP(fun(nat,A),A,suminf(A),B) # label(fact_4135_suminf__def) # label(axiom).  [clausify(2476)].
38.63/38.51	Derived: -topological_space(real) | hAPP(fun(real,bool),real,the(real),hAPP(fun(nat,real),fun(real,bool),sums(real),A)) = hAPP(fun(nat,real),real,suminf(real),A).  [resolve(5563,b,5513,a)].
38.63/38.51	Derived: -topological_space(int) | hAPP(fun(int,bool),int,the(int),hAPP(fun(nat,int),fun(int,bool),sums(int),A)) = hAPP(fun(nat,int),int,suminf(int),A).  [resolve(5563,b,5524,a)].
38.63/38.51	Derived: -topological_space(code_code_numeral) | hAPP(fun(code_code_numeral,bool),code_code_numeral,the(code_code_numeral),hAPP(fun(nat,code_code_numeral),fun(code_code_numeral,bool),sums(code_code_numeral),A)) = hAPP(fun(nat,code_code_numeral),code_code_numeral,suminf(code_code_numeral),A).  [resolve(5563,b,5539,a)].
38.63/38.51	Derived: -topological_space(rat) | hAPP(fun(rat,bool),rat,the(rat),hAPP(fun(nat,rat),fun(rat,bool),sums(rat),A)) = hAPP(fun(nat,rat),rat,suminf(rat),A).  [resolve(5563,b,5561,a)].
38.63/38.51	5564 -comm_monoid_add(A) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),C)) | hAPP(fun(nat,bool),A,hAPP(fun(nat,A),fun(fun(nat,bool),A),big_co1399186613setsum(nat,A),D),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),B),C)) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(nat,A,D,B)),hAPP(fun(nat,bool),A,hAPP(fun(nat,A),fun(fun(nat,bool),A),big_co1399186613setsum(nat,A),D),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),hAPP(nat,nat,suc,B)),C))) # label(fact_4203_setsum__head__upt__Suc) # label(axiom).  [clausify(2514)].
38.63/38.51	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),C),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),A),B)) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,C,A)),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),C),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),hAPP(nat,nat,suc,A)),B))).  [resolve(5564,a,5513,a)].
38.63/38.51	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | hAPP(fun(nat,bool),int,hAPP(fun(nat,int),fun(fun(nat,bool),int),big_co1399186613setsum(nat,int),C),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),A),B)) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,C,A)),hAPP(fun(nat,bool),int,hAPP(fun(nat,int),fun(fun(nat,bool),int),big_co1399186613setsum(nat,int),C),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),hAPP(nat,nat,suc,A)),B))).  [resolve(5564,a,5524,a)].
38.63/38.51	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | hAPP(fun(nat,bool),code_code_numeral,hAPP(fun(nat,code_code_numeral),fun(fun(nat,bool),code_code_numeral),big_co1399186613setsum(nat,code_code_numeral),C),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),A),B)) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),hAPP(nat,code_code_numeral,C,A)),hAPP(fun(nat,bool),code_code_numeral,hAPP(fun(nat,code_code_numeral),fun(fun(nat,bool),code_code_numeral),big_co1399186613setsum(nat,code_code_numeral),C),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),hAPP(nat,nat,suc,A)),B))).  [resolve(5564,a,5539,a)].
38.63/38.51	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | hAPP(fun(nat,bool),rat,hAPP(fun(nat,rat),fun(fun(nat,bool),rat),big_co1399186613setsum(nat,rat),C),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),A),B)) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(nat,rat,C,A)),hAPP(fun(nat,bool),rat,hAPP(fun(nat,rat),fun(fun(nat,bool),rat),big_co1399186613setsum(nat,rat),C),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),hAPP(nat,nat,suc,A)),B))).  [resolve(5564,a,5561,a)].
38.63/38.55	5565 -comm_monoid_add(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | -hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),D),C)) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),hAPP(A,fun(B,A),hAPP(fun(B,fun(A,A)),fun(A,fun(B,A)),combc(B,A,A),hAPP(fun(B,A),fun(B,fun(A,A)),hAPP(fun(B,fun(A,fun(A,A))),fun(fun(B,A),fun(B,fun(A,A))),combs(B,A,fun(A,A)),hAPP(fun(B,bool),fun(B,fun(A,fun(A,A))),hAPP(fun(bool,fun(A,fun(A,A))),fun(fun(B,bool),fun(B,fun(A,fun(A,A)))),combb(bool,fun(A,fun(A,A)),B),if(A)),hAPP(B,fun(B,bool),fequal(B),D))),E)),zero_zero(A))),C) = hAPP(B,A,E,D) # label(fact_4216_setsum__delta_H) # label(axiom).  [clausify(2577)].
38.63/38.55	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),hAPP(real,fun(A,real),hAPP(fun(A,fun(real,real)),fun(real,fun(A,real)),combc(A,real,real),hAPP(fun(A,real),fun(A,fun(real,real)),hAPP(fun(A,fun(real,fun(real,real))),fun(fun(A,real),fun(A,fun(real,real))),combs(A,real,fun(real,real)),hAPP(fun(A,bool),fun(A,fun(real,fun(real,real))),hAPP(fun(bool,fun(real,fun(real,real))),fun(fun(A,bool),fun(A,fun(real,fun(real,real)))),combb(bool,fun(real,fun(real,real)),A),if(real)),hAPP(A,fun(A,bool),fequal(A),C))),D)),zero_zero(real))),B) = hAPP(A,real,D,C).  [resolve(5565,a,5513,a)].
38.63/38.55	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),hAPP(int,fun(A,int),hAPP(fun(A,fun(int,int)),fun(int,fun(A,int)),combc(A,int,int),hAPP(fun(A,int),fun(A,fun(int,int)),hAPP(fun(A,fun(int,fun(int,int))),fun(fun(A,int),fun(A,fun(int,int))),combs(A,int,fun(int,int)),hAPP(fun(A,bool),fun(A,fun(int,fun(int,int))),hAPP(fun(bool,fun(int,fun(int,int))),fun(fun(A,bool),fun(A,fun(int,fun(int,int)))),combb(bool,fun(int,fun(int,int)),A),if(int)),hAPP(A,fun(A,bool),fequal(A),C))),D)),zero_zero(int))),B) = hAPP(A,int,D,C).  [resolve(5565,a,5524,a)].
38.63/38.55	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),hAPP(code_code_numeral,fun(A,code_code_numeral),hAPP(fun(A,fun(code_code_numeral,code_code_numeral)),fun(code_code_numeral,fun(A,code_code_numeral)),combc(A,code_code_numeral,code_code_numeral),hAPP(fun(A,code_code_numeral),fun(A,fun(code_code_numeral,code_code_numeral)),hAPP(fun(A,fun(code_code_numeral,fun(code_code_numeral,code_code_numeral))),fun(fun(A,code_code_numeral),fun(A,fun(code_code_numeral,code_code_numeral))),combs(A,code_code_numeral,fun(code_code_numeral,code_code_numeral)),hAPP(fun(A,bool),fun(A,fun(code_code_numeral,fun(code_code_numeral,code_code_numeral))),hAPP(fun(bool,fun(code_code_numeral,fun(code_code_numeral,code_code_numeral))),fun(fun(A,bool),fun(A,fun(code_code_numeral,fun(code_code_numeral,code_code_numeral)))),combb(bool,fun(code_code_numeral,fun(code_code_numeral,code_code_numeral)),A),if(code_code_numeral)),hAPP(A,fun(A,bool),fequal(A),C))),D)),zero_zero(code_code_numeral))),B) = hAPP(A,code_code_numeral,D,C).  [resolve(5565,a,5539,a)].
38.63/38.55	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),hAPP(rat,fun(A,rat),hAPP(fun(A,fun(rat,rat)),fun(rat,fun(A,rat)),combc(A,rat,rat),hAPP(fun(A,rat),fun(A,fun(rat,rat)),hAPP(fun(A,fun(rat,fun(rat,rat))),fun(fun(A,rat),fun(A,fun(rat,rat))),combs(A,rat,fun(rat,rat)),hAPP(fun(A,bool),fun(A,fun(rat,fun(rat,rat))),hAPP(fun(bool,fun(rat,fun(rat,rat))),fun(fun(A,bool),fun(A,fun(rat,fun(rat,rat)))),combb(bool,fun(rat,fun(rat,rat)),A),if(rat)),hAPP(A,fun(A,bool),fequal(A),C))),D)),zero_zero(rat))),B) = hAPP(A,rat,D,C).  [resolve(5565,a,5561,a)].
38.63/38.55	5566 -comm_monoid_add(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),D),C)) | zero_zero(A) = hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),hAPP(A,fun(B,A),hAPP(fun(B,fun(A,A)),fun(A,fun(B,A)),combc(B,A,A),hAPP(fun(B,A),fun(B,fun(A,A)),hAPP(fun(B,fun(A,fun(A,A))),fun(fun(B,A),fun(B,fun(A,A))),combs(B,A,fun(A,A)),hAPP(fun(B,bool),fun(B,fun(A,fun(A,A))),hAPP(fun(bool,fun(A,fun(A,A))),fun(fun(B,bool),fun(B,fun(A,fun(A,A)))),combb(bool,fun(A,fun(A,A)),B),if(A)),hAPP(B,fun(B,bool),fequal(B),D))),E)),zero_zero(A))),C) # label(fact_4216_setsum__delta_H) # label(axiom).  [clausify(2577)].
38.63/38.55	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | zero_zero(real) = hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),hAPP(real,fun(A,real),hAPP(fun(A,fun(real,real)),fun(real,fun(A,real)),combc(A,real,real),hAPP(fun(A,real),fun(A,fun(real,real)),hAPP(fun(A,fun(real,fun(real,real))),fun(fun(A,real),fun(A,fun(real,real))),combs(A,real,fun(real,real)),hAPP(fun(A,bool),fun(A,fun(real,fun(real,real))),hAPP(fun(bool,fun(real,fun(real,real))),fun(fun(A,bool),fun(A,fun(real,fun(real,real)))),combb(bool,fun(real,fun(real,real)),A),if(real)),hAPP(A,fun(A,bool),fequal(A),C))),D)),zero_zero(real))),B).  [resolve(5566,a,5513,a)].
38.63/38.55	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | zero_zero(int) = hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),hAPP(int,fun(A,int),hAPP(fun(A,fun(int,int)),fun(int,fun(A,int)),combc(A,int,int),hAPP(fun(A,int),fun(A,fun(int,int)),hAPP(fun(A,fun(int,fun(int,int))),fun(fun(A,int),fun(A,fun(int,int))),combs(A,int,fun(int,int)),hAPP(fun(A,bool),fun(A,fun(int,fun(int,int))),hAPP(fun(bool,fun(int,fun(int,int))),fun(fun(A,bool),fun(A,fun(int,fun(int,int)))),combb(bool,fun(int,fun(int,int)),A),if(int)),hAPP(A,fun(A,bool),fequal(A),C))),D)),zero_zero(int))),B).  [resolve(5566,a,5524,a)].
38.63/38.55	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | zero_zero(code_code_numeral) = hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),hAPP(code_code_numeral,fun(A,code_code_numeral),hAPP(fun(A,fun(code_code_numeral,code_code_numeral)),fun(code_code_numeral,fun(A,code_code_numeral)),combc(A,code_code_numeral,code_code_numeral),hAPP(fun(A,code_code_numeral),fun(A,fun(code_code_numeral,code_code_numeral)),hAPP(fun(A,fun(code_code_numeral,fun(code_code_numeral,code_code_numeral))),fun(fun(A,code_code_numeral),fun(A,fun(code_code_numeral,code_code_numeral))),combs(A,code_code_numeral,fun(code_code_numeral,code_code_numeral)),hAPP(fun(A,bool),fun(A,fun(code_code_numeral,fun(code_code_numeral,code_code_numeral))),hAPP(fun(bool,fun(code_code_numeral,fun(code_code_numeral,code_code_numeral))),fun(fun(A,bool),fun(A,fun(code_code_numeral,fun(code_code_numeral,code_code_numeral)))),combb(bool,fun(code_code_numeral,fun(code_code_numeral,code_code_numeral)),A),if(code_code_numeral)),hAPP(A,fun(A,bool),fequal(A),C))),D)),zero_zero(code_code_numeral))),B).  [resolve(5566,a,5539,a)].
38.63/38.55	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | zero_zero(rat) = hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),hAPP(rat,fun(A,rat),hAPP(fun(A,fun(rat,rat)),fun(rat,fun(A,rat)),combc(A,rat,rat),hAPP(fun(A,rat),fun(A,fun(rat,rat)),hAPP(fun(A,fun(rat,fun(rat,rat))),fun(fun(A,rat),fun(A,fun(rat,rat))),combs(A,rat,fun(rat,rat)),hAPP(fun(A,bool),fun(A,fun(rat,fun(rat,rat))),hAPP(fun(bool,fun(rat,fun(rat,rat))),fun(fun(A,bool),fun(A,fun(rat,fun(rat,rat)))),combb(bool,fun(rat,fun(rat,rat)),A),if(rat)),hAPP(A,fun(A,bool),fequal(A),C))),D)),zero_zero(rat))),B).  [resolve(5566,a,5561,a)].
38.63/38.57	5567 -comm_monoid_add(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),hAPP(A,fun(B,A),hAPP(fun(B,fun(A,A)),fun(A,fun(B,A)),combc(B,A,A),hAPP(fun(B,A),fun(B,fun(A,A)),hAPP(fun(B,fun(A,fun(A,A))),fun(fun(B,A),fun(B,fun(A,A))),combs(B,A,fun(A,A)),hAPP(fun(B,bool),fun(B,fun(A,fun(A,A))),hAPP(fun(bool,fun(A,fun(A,A))),fun(fun(B,bool),fun(B,fun(A,fun(A,A)))),combb(bool,fun(A,fun(A,A)),B),if(A)),hAPP(fun(B,bool),fun(B,bool),hAPP(fun(B,fun(fun(B,bool),bool)),fun(fun(B,bool),fun(B,bool)),combc(B,fun(B,bool),bool),member(B)),D))),E)),zero_zero(A))),C) = hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),E),hAPP(fun(B,bool),fun(B,bool),collect(B),hAPP(fun(B,bool),fun(B,bool),hAPP(fun(B,fun(bool,bool)),fun(fun(B,bool),fun(B,bool)),combs(B,bool,bool),hAPP(fun(B,bool),fun(B,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(B,bool),fun(B,fun(bool,bool))),combb(bool,fun(bool,bool),B),fconj),hAPP(fun(B,bool),fun(B,bool),hAPP(fun(B,fun(fun(B,bool),bool)),fun(fun(B,bool),fun(B,bool)),combc(B,fun(B,bool),bool),member(B)),C))),hAPP(fun(B,bool),fun(B,bool),hAPP(fun(B,fun(fun(B,bool),bool)),fun(fun(B,bool),fun(B,bool)),combc(B,fun(B,bool),bool),member(B)),D)))) # label(fact_4185_setsum__restrict__set_H) # label(axiom).  [clausify(2605)].
38.63/38.57	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),hAPP(real,fun(A,real),hAPP(fun(A,fun(real,real)),fun(real,fun(A,real)),combc(A,real,real),hAPP(fun(A,real),fun(A,fun(real,real)),hAPP(fun(A,fun(real,fun(real,real))),fun(fun(A,real),fun(A,fun(real,real))),combs(A,real,fun(real,real)),hAPP(fun(A,bool),fun(A,fun(real,fun(real,real))),hAPP(fun(bool,fun(real,fun(real,real))),fun(fun(A,bool),fun(A,fun(real,fun(real,real)))),combb(bool,fun(real,fun(real,real)),A),if(real)),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,fun(fun(A,bool),bool)),fun(fun(A,bool),fun(A,bool)),combc(A,fun(A,bool),bool),member(A)),C))),D)),zero_zero(real))),B) = hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),D),hAPP(fun(A,bool),fun(A,bool),collect(A),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,fun(bool,bool)),fun(fun(A,bool),fun(A,bool)),combs(A,bool,bool),hAPP(fun(A,bool),fun(A,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(A,bool),fun(A,fun(bool,bool))),combb(bool,fun(bool,bool),A),fconj),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,fun(fun(A,bool),bool)),fun(fun(A,bool),fun(A,bool)),combc(A,fun(A,bool),bool),member(A)),B))),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,fun(fun(A,bool),bool)),fun(fun(A,bool),fun(A,bool)),combc(A,fun(A,bool),bool),member(A)),C)))).  [resolve(5567,a,5513,a)].
38.63/38.57	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),hAPP(int,fun(A,int),hAPP(fun(A,fun(int,int)),fun(int,fun(A,int)),combc(A,int,int),hAPP(fun(A,int),fun(A,fun(int,int)),hAPP(fun(A,fun(int,fun(int,int))),fun(fun(A,int),fun(A,fun(int,int))),combs(A,int,fun(int,int)),hAPP(fun(A,bool),fun(A,fun(int,fun(int,int))),hAPP(fun(bool,fun(int,fun(int,int))),fun(fun(A,bool),fun(A,fun(int,fun(int,int)))),combb(bool,fun(int,fun(int,int)),A),if(int)),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,fun(fun(A,bool),bool)),fun(fun(A,bool),fun(A,bool)),combc(A,fun(A,bool),bool),member(A)),C))),D)),zero_zero(int))),B) = hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),D),hAPP(fun(A,bool),fun(A,bool),collect(A),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,fun(bool,bool)),fun(fun(A,bool),fun(A,bool)),combs(A,bool,bool),hAPP(fun(A,bool),fun(A,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(A,bool),fun(A,fun(bool,bool))),combb(bool,fun(bool,bool),A),fconj),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,fun(fun(A,bool),bool)),fun(fun(A,bool),fun(A,bool)),combc(A,fun(A,bool),bool),member(A)),B))),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,fun(fun(A,bool),bool)),fun(fun(A,bool),fun(A,bool)),combc(A,fun(A,bool),bool),member(A)),C)))).  [resolve(5567,a,5524,a)].
38.63/38.57	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),hAPP(code_code_numeral,fun(A,code_code_numeral),hAPP(fun(A,fun(code_code_numeral,code_code_numeral)),fun(code_code_numeral,fun(A,code_code_numeral)),combc(A,code_code_numeral,code_code_numeral),hAPP(fun(A,code_code_numeral),fun(A,fun(code_code_numeral,code_code_numeral)),hAPP(fun(A,fun(code_code_numeral,fun(code_code_numeral,code_code_numeral))),fun(fun(A,code_code_numeral),fun(A,fun(code_code_numeral,code_code_numeral))),combs(A,code_code_numeral,fun(code_code_numeral,code_code_numeral)),hAPP(fun(A,bool),fun(A,fun(code_code_numeral,fun(code_code_numeral,code_code_numeral))),hAPP(fun(bool,fun(code_code_numeral,fun(code_code_numeral,code_code_numeral))),fun(fun(A,bool),fun(A,fun(code_code_numeral,fun(code_code_numeral,code_code_numeral)))),combb(bool,fun(code_code_numeral,fun(code_code_numeral,code_code_numeral)),A),if(code_code_numeral)),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,fun(fun(A,bool),bool)),fun(fun(A,bool),fun(A,bool)),combc(A,fun(A,bool),bool),member(A)),C))),D)),zero_zero(code_code_numeral))),B) = hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),D),hAPP(fun(A,bool),fun(A,bool),collect(A),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,fun(bool,bool)),fun(fun(A,bool),fun(A,bool)),combs(A,bool,bool),hAPP(fun(A,bool),fun(A,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(A,bool),fun(A,fun(bool,bool))),combb(bool,fun(bool,bool),A),fconj),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,fun(fun(A,bool),bool)),fun(fun(A,bool),fun(A,bool)),combc(A,fun(A,bool),bool),member(A)),B))),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,fun(fun(A,bool),bool)),fun(fun(A,bool),fun(A,bool)),combc(A,fun(A,bool),bool),member(A)),C)))).  [resolve(5567,a,5539,a)].
38.63/38.57	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),hAPP(rat,fun(A,rat),hAPP(fun(A,fun(rat,rat)),fun(rat,fun(A,rat)),combc(A,rat,rat),hAPP(fun(A,rat),fun(A,fun(rat,rat)),hAPP(fun(A,fun(rat,fun(rat,rat))),fun(fun(A,rat),fun(A,fun(rat,rat))),combs(A,rat,fun(rat,rat)),hAPP(fun(A,bool),fun(A,fun(rat,fun(rat,rat))),hAPP(fun(bool,fun(rat,fun(rat,rat))),fun(fun(A,bool),fun(A,fun(rat,fun(rat,rat)))),combb(bool,fun(rat,fun(rat,rat)),A),if(rat)),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,fun(fun(A,bool),bool)),fun(fun(A,bool),fun(A,bool)),combc(A,fun(A,bool),bool),member(A)),C))),D)),zero_zero(rat))),B) = hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),D),hAPP(fun(A,bool),fun(A,bool),collect(A),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,fun(bool,bool)),fun(fun(A,bool),fun(A,bool)),combs(A,bool,bool),hAPP(fun(A,bool),fun(A,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(A,bool),fun(A,fun(bool,bool))),combb(bool,fun(bool,bool),A),fconj),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,fun(fun(A,bool),bool)),fun(fun(A,bool),fun(A,bool)),combc(A,fun(A,bool),bool),member(A)),B))),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,fun(fun(A,bool),bool)),fun(fun(A,bool),fun(A,bool)),combc(A,fun(A,bool),bool),member(A)),C)))).  [resolve(5567,a,5561,a)].
38.63/38.57	5568 -comm_monoid_add(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | -hBOOL(hAPP(fun(B,bool),bool,hAPP(fun(B,bool),fun(fun(B,bool),bool),ord_less_eq(fun(B,bool)),D),C)) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f457(B,A,E,F,D,C)),hAPP(fun(B,bool),fun(B,bool),hAPP(fun(B,bool),fun(fun(B,bool),fun(B,bool)),minus_minus(fun(B,bool)),C),D))) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f458(B,A,E,F,D,C)),D)) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),E),D) = hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),F),C) # label(fact_4417_setsum__mono__zero__cong__right) # label(axiom).  [clausify(2611)].
38.72/38.58	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f457(A,real,D,E,C,B)),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),B),C))) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f458(A,real,D,E,C,B)),C)) | hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),D),C) = hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),E),B).  [resolve(5568,a,5513,a)].
38.72/38.58	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f457(A,int,D,E,C,B)),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),B),C))) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f458(A,int,D,E,C,B)),C)) | hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),D),C) = hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),E),B).  [resolve(5568,a,5524,a)].
38.72/38.58	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f457(A,code_code_numeral,D,E,C,B)),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),B),C))) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f458(A,code_code_numeral,D,E,C,B)),C)) | hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),D),C) = hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),E),B).  [resolve(5568,a,5539,a)].
38.72/38.58	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f457(A,rat,D,E,C,B)),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),B),C))) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f458(A,rat,D,E,C,B)),C)) | hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),D),C) = hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),E),B).  [resolve(5568,a,5561,a)].
38.72/38.58	5569 -comm_monoid_add(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | -hBOOL(hAPP(fun(B,bool),bool,hAPP(fun(B,bool),fun(fun(B,bool),bool),ord_less_eq(fun(B,bool)),D),C)) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f457(B,A,E,F,D,C)),hAPP(fun(B,bool),fun(B,bool),hAPP(fun(B,bool),fun(fun(B,bool),fun(B,bool)),minus_minus(fun(B,bool)),C),D))) | hAPP(B,A,E,f458(B,A,E,F,D,C)) != hAPP(B,A,F,f458(B,A,E,F,D,C)) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),E),D) = hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),F),C) # label(fact_4417_setsum__mono__zero__cong__right) # label(axiom).  [clausify(2611)].
38.72/38.58	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f457(A,real,D,E,C,B)),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),B),C))) | hAPP(A,real,D,f458(A,real,D,E,C,B)) != hAPP(A,real,E,f458(A,real,D,E,C,B)) | hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),D),C) = hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),E),B).  [resolve(5569,a,5513,a)].
38.72/38.59	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f457(A,int,D,E,C,B)),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),B),C))) | hAPP(A,int,D,f458(A,int,D,E,C,B)) != hAPP(A,int,E,f458(A,int,D,E,C,B)) | hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),D),C) = hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),E),B).  [resolve(5569,a,5524,a)].
38.72/38.59	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f457(A,code_code_numeral,D,E,C,B)),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),B),C))) | hAPP(A,code_code_numeral,D,f458(A,code_code_numeral,D,E,C,B)) != hAPP(A,code_code_numeral,E,f458(A,code_code_numeral,D,E,C,B)) | hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),D),C) = hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),E),B).  [resolve(5569,a,5539,a)].
38.72/38.59	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f457(A,rat,D,E,C,B)),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),B),C))) | hAPP(A,rat,D,f458(A,rat,D,E,C,B)) != hAPP(A,rat,E,f458(A,rat,D,E,C,B)) | hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),D),C) = hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),E),B).  [resolve(5569,a,5561,a)].
38.72/38.59	5570 -comm_monoid_add(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | -hBOOL(hAPP(fun(B,bool),bool,hAPP(fun(B,bool),fun(fun(B,bool),bool),ord_less_eq(fun(B,bool)),D),C)) | zero_zero(A) != hAPP(B,A,E,f457(B,A,F,E,D,C)) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f458(B,A,F,E,D,C)),D)) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),F),D) = hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),E),C) # label(fact_4417_setsum__mono__zero__cong__right) # label(axiom).  [clausify(2611)].
38.72/38.59	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | zero_zero(real) != hAPP(A,real,D,f457(A,real,E,D,C,B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f458(A,real,E,D,C,B)),C)) | hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),E),C) = hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),D),B).  [resolve(5570,a,5513,a)].
38.72/38.59	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | zero_zero(int) != hAPP(A,int,D,f457(A,int,E,D,C,B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f458(A,int,E,D,C,B)),C)) | hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),E),C) = hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),D),B).  [resolve(5570,a,5524,a)].
38.73/38.60	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | zero_zero(code_code_numeral) != hAPP(A,code_code_numeral,D,f457(A,code_code_numeral,E,D,C,B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f458(A,code_code_numeral,E,D,C,B)),C)) | hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),E),C) = hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),D),B).  [resolve(5570,a,5539,a)].
38.73/38.60	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | zero_zero(rat) != hAPP(A,rat,D,f457(A,rat,E,D,C,B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f458(A,rat,E,D,C,B)),C)) | hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),E),C) = hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),D),B).  [resolve(5570,a,5561,a)].
38.73/38.60	5571 -comm_monoid_add(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | -hBOOL(hAPP(fun(B,bool),bool,hAPP(fun(B,bool),fun(fun(B,bool),bool),ord_less_eq(fun(B,bool)),D),C)) | zero_zero(A) != hAPP(B,A,E,f457(B,A,F,E,D,C)) | hAPP(B,A,F,f458(B,A,F,E,D,C)) != hAPP(B,A,E,f458(B,A,F,E,D,C)) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),F),D) = hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),E),C) # label(fact_4417_setsum__mono__zero__cong__right) # label(axiom).  [clausify(2611)].
38.73/38.60	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | zero_zero(real) != hAPP(A,real,D,f457(A,real,E,D,C,B)) | hAPP(A,real,E,f458(A,real,E,D,C,B)) != hAPP(A,real,D,f458(A,real,E,D,C,B)) | hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),E),C) = hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),D),B).  [resolve(5571,a,5513,a)].
38.73/38.60	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | zero_zero(int) != hAPP(A,int,D,f457(A,int,E,D,C,B)) | hAPP(A,int,E,f458(A,int,E,D,C,B)) != hAPP(A,int,D,f458(A,int,E,D,C,B)) | hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),E),C) = hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),D),B).  [resolve(5571,a,5524,a)].
38.73/38.60	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | zero_zero(code_code_numeral) != hAPP(A,code_code_numeral,D,f457(A,code_code_numeral,E,D,C,B)) | hAPP(A,code_code_numeral,E,f458(A,code_code_numeral,E,D,C,B)) != hAPP(A,code_code_numeral,D,f458(A,code_code_numeral,E,D,C,B)) | hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),E),C) = hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),D),B).  [resolve(5571,a,5539,a)].
38.73/38.60	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | zero_zero(rat) != hAPP(A,rat,D,f457(A,rat,E,D,C,B)) | hAPP(A,rat,E,f458(A,rat,E,D,C,B)) != hAPP(A,rat,D,f458(A,rat,E,D,C,B)) | hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),E),C) = hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),D),B).  [resolve(5571,a,5561,a)].
38.84/38.71	5572 -comm_monoid_add(A) | hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | zero_zero(A) = hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),D),C) # label(fact_4208_setsum__infinite) # label(axiom).  [clausify(2698)].
38.84/38.71	5573 -topological_space(A) | -comm_monoid_add(A) | summable(A) = ti(fun(fun(nat,A),bool),summable(A)) # label(tsy_c_Series_Osummable_res) # label(axiom).  [clausify(2726)].
38.84/38.71	Derived: -topological_space(real) | summable(real) = ti(fun(fun(nat,real),bool),summable(real)).  [resolve(5573,b,5513,a)].
38.84/38.71	Derived: -topological_space(int) | summable(int) = ti(fun(fun(nat,int),bool),summable(int)).  [resolve(5573,b,5524,a)].
38.84/38.71	Derived: -topological_space(code_code_numeral) | summable(code_code_numeral) = ti(fun(fun(nat,code_code_numeral),bool),summable(code_code_numeral)).  [resolve(5573,b,5539,a)].
38.84/38.71	Derived: -topological_space(rat) | summable(rat) = ti(fun(fun(nat,rat),bool),summable(rat)).  [resolve(5573,b,5561,a)].
38.84/38.71	5574 -t2_space(A) | -comm_monoid_add(A) | -hBOOL(hAPP(A,bool,hAPP(fun(nat,A),fun(A,bool),sums(A),B),C)) | hAPP(fun(nat,A),A,suminf(A),B) = ti(A,C) # label(fact_4093_sums__iff) # label(axiom).  [clausify(2751)].
38.84/38.71	5575 -t2_space(A) | -comm_monoid_add(A) | -hBOOL(hAPP(A,bool,hAPP(fun(nat,A),fun(A,bool),sums(A),B),C)) | hBOOL(hAPP(fun(nat,A),bool,summable(A),B)) # label(fact_4093_sums__iff) # label(axiom).  [clausify(2751)].
38.84/38.71	Derived: -t2_space(real) | -hBOOL(hAPP(real,bool,hAPP(fun(nat,real),fun(real,bool),sums(real),A),B)) | hBOOL(hAPP(fun(nat,real),bool,summable(real),A)).  [resolve(5575,b,5513,a)].
38.84/38.71	Derived: -t2_space(int) | -hBOOL(hAPP(int,bool,hAPP(fun(nat,int),fun(int,bool),sums(int),A),B)) | hBOOL(hAPP(fun(nat,int),bool,summable(int),A)).  [resolve(5575,b,5524,a)].
38.84/38.71	Derived: -t2_space(code_code_numeral) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(fun(nat,code_code_numeral),fun(code_code_numeral,bool),sums(code_code_numeral),A),B)) | hBOOL(hAPP(fun(nat,code_code_numeral),bool,summable(code_code_numeral),A)).  [resolve(5575,b,5539,a)].
38.84/38.71	Derived: -t2_space(rat) | -hBOOL(hAPP(rat,bool,hAPP(fun(nat,rat),fun(rat,bool),sums(rat),A),B)) | hBOOL(hAPP(fun(nat,rat),bool,summable(rat),A)).  [resolve(5575,b,5561,a)].
38.84/38.71	5576 -t2_space(A) | -comm_monoid_add(A) | hBOOL(hAPP(A,bool,hAPP(fun(nat,A),fun(A,bool),sums(A),B),C)) | hAPP(fun(nat,A),A,suminf(A),B) != ti(A,C) | -hBOOL(hAPP(fun(nat,A),bool,summable(A),B)) # label(fact_4093_sums__iff) # label(axiom).  [clausify(2751)].
38.84/38.71	Derived: -t2_space(real) | hBOOL(hAPP(real,bool,hAPP(fun(nat,real),fun(real,bool),sums(real),A),B)) | hAPP(fun(nat,real),real,suminf(real),A) != ti(real,B) | -hBOOL(hAPP(fun(nat,real),bool,summable(real),A)).  [resolve(5576,b,5513,a)].
38.84/38.71	Derived: -t2_space(int) | hBOOL(hAPP(int,bool,hAPP(fun(nat,int),fun(int,bool),sums(int),A),B)) | hAPP(fun(nat,int),int,suminf(int),A) != ti(int,B) | -hBOOL(hAPP(fun(nat,int),bool,summable(int),A)).  [resolve(5576,b,5524,a)].
38.84/38.71	Derived: -t2_space(code_code_numeral) | hBOOL(hAPP(code_code_numeral,bool,hAPP(fun(nat,code_code_numeral),fun(code_code_numeral,bool),sums(code_code_numeral),A),B)) | hAPP(fun(nat,code_code_numeral),code_code_numeral,suminf(code_code_numeral),A) != ti(code_code_numeral,B) | -hBOOL(hAPP(fun(nat,code_code_numeral),bool,summable(code_code_numeral),A)).  [resolve(5576,b,5539,a)].
38.84/38.71	Derived: -t2_space(rat) | hBOOL(hAPP(rat,bool,hAPP(fun(nat,rat),fun(rat,bool),sums(rat),A),B)) | hAPP(fun(nat,rat),rat,suminf(rat),A) != ti(rat,B) | -hBOOL(hAPP(fun(nat,rat),bool,summable(rat),A)).  [resolve(5576,b,5561,a)].
38.84/38.71	5577 -comm_monoid_add(A) | zero_zero(A) != hAPP(nat,A,B,zero_zero(nat)) | hAPP(fun(nat,bool),A,hAPP(fun(nat,A),fun(fun(nat,bool),A),big_co1399186613setsum(nat,A),B),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),C)) = hAPP(fun(nat,bool),A,hAPP(fun(nat,A),fun(fun(nat,bool),A),big_co1399186613setsum(nat,A),B),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),hAPP(nat,nat,suc,zero_zero(nat))),C)) # label(fact_4198_setsum__shift__lb__Suc0__0__upt) # label(axiom).  [clausify(2825)].
38.84/38.78	Derived: zero_zero(real) != hAPP(nat,real,A,zero_zero(nat)) | hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),A),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),B)) = hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),A),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),hAPP(nat,nat,suc,zero_zero(nat))),B)).  [resolve(5577,a,5513,a)].
38.84/38.78	Derived: zero_zero(int) != hAPP(nat,int,A,zero_zero(nat)) | hAPP(fun(nat,bool),int,hAPP(fun(nat,int),fun(fun(nat,bool),int),big_co1399186613setsum(nat,int),A),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),B)) = hAPP(fun(nat,bool),int,hAPP(fun(nat,int),fun(fun(nat,bool),int),big_co1399186613setsum(nat,int),A),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),hAPP(nat,nat,suc,zero_zero(nat))),B)).  [resolve(5577,a,5524,a)].
38.84/38.78	Derived: zero_zero(code_code_numeral) != hAPP(nat,code_code_numeral,A,zero_zero(nat)) | hAPP(fun(nat,bool),code_code_numeral,hAPP(fun(nat,code_code_numeral),fun(fun(nat,bool),code_code_numeral),big_co1399186613setsum(nat,code_code_numeral),A),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),B)) = hAPP(fun(nat,bool),code_code_numeral,hAPP(fun(nat,code_code_numeral),fun(fun(nat,bool),code_code_numeral),big_co1399186613setsum(nat,code_code_numeral),A),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),hAPP(nat,nat,suc,zero_zero(nat))),B)).  [resolve(5577,a,5539,a)].
38.84/38.78	Derived: zero_zero(rat) != hAPP(nat,rat,A,zero_zero(nat)) | hAPP(fun(nat,bool),rat,hAPP(fun(nat,rat),fun(fun(nat,bool),rat),big_co1399186613setsum(nat,rat),A),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),B)) = hAPP(fun(nat,bool),rat,hAPP(fun(nat,rat),fun(fun(nat,bool),rat),big_co1399186613setsum(nat,rat),A),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),hAPP(nat,nat,suc,zero_zero(nat))),B)).  [resolve(5577,a,5561,a)].
38.84/38.78	5578 -comm_monoid_add(A) | -topological_space(A) | -hBOOL(hAPP(A,bool,hAPP(fun(nat,A),fun(A,bool),sums(A),B),C)) | hBOOL(hAPP(fun(nat,A),bool,summable(A),B)) # label(fact_4091_sums__summable) # label(axiom).  [clausify(2920)].
38.84/38.78	Derived: -topological_space(real) | -hBOOL(hAPP(real,bool,hAPP(fun(nat,real),fun(real,bool),sums(real),A),B)) | hBOOL(hAPP(fun(nat,real),bool,summable(real),A)).  [resolve(5578,a,5513,a)].
38.84/38.78	Derived: -topological_space(int) | -hBOOL(hAPP(int,bool,hAPP(fun(nat,int),fun(int,bool),sums(int),A),B)) | hBOOL(hAPP(fun(nat,int),bool,summable(int),A)).  [resolve(5578,a,5524,a)].
38.84/38.78	Derived: -topological_space(code_code_numeral) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(fun(nat,code_code_numeral),fun(code_code_numeral,bool),sums(code_code_numeral),A),B)) | hBOOL(hAPP(fun(nat,code_code_numeral),bool,summable(code_code_numeral),A)).  [resolve(5578,a,5539,a)].
38.84/38.78	Derived: -topological_space(rat) | -hBOOL(hAPP(rat,bool,hAPP(fun(nat,rat),fun(rat,bool),sums(rat),A),B)) | hBOOL(hAPP(fun(nat,rat),bool,summable(rat),A)).  [resolve(5578,a,5561,a)].
38.84/38.78	5579 -t2_space(A) | -comm_monoid_add(A) | -hBOOL(hAPP(fun(nat,A),bool,summable(A),B)) | hBOOL(hAPP(filter(nat),bool,hAPP(A,fun(filter(nat),bool),hAPP(fun(nat,A),fun(A,fun(filter(nat),bool)),tendsto(nat,A),hAPP(fun(nat,fun(nat,bool)),fun(nat,A),hAPP(fun(fun(nat,bool),A),fun(fun(nat,fun(nat,bool)),fun(nat,A)),combb(fun(nat,bool),A,nat),hAPP(fun(nat,A),fun(fun(nat,bool),A),big_co1399186613setsum(nat,A),B)),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)))),hAPP(fun(nat,A),A,suminf(A),B)),sequentially)) # label(fact_4497_summable__sumr__LIMSEQ__suminf) # label(axiom).  [clausify(2922)].
38.84/38.78	Derived: -t2_space(real) | -hBOOL(hAPP(fun(nat,real),bool,summable(real),A)) | hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),hAPP(fun(nat,fun(nat,bool)),fun(nat,real),hAPP(fun(fun(nat,bool),real),fun(fun(nat,fun(nat,bool)),fun(nat,real)),combb(fun(nat,bool),real,nat),hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),A)),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)))),hAPP(fun(nat,real),real,suminf(real),A)),sequentially)).  [resolve(5579,b,5513,a)].
38.93/38.87	Derived: -t2_space(int) | -hBOOL(hAPP(fun(nat,int),bool,summable(int),A)) | hBOOL(hAPP(filter(nat),bool,hAPP(int,fun(filter(nat),bool),hAPP(fun(nat,int),fun(int,fun(filter(nat),bool)),tendsto(nat,int),hAPP(fun(nat,fun(nat,bool)),fun(nat,int),hAPP(fun(fun(nat,bool),int),fun(fun(nat,fun(nat,bool)),fun(nat,int)),combb(fun(nat,bool),int,nat),hAPP(fun(nat,int),fun(fun(nat,bool),int),big_co1399186613setsum(nat,int),A)),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)))),hAPP(fun(nat,int),int,suminf(int),A)),sequentially)).  [resolve(5579,b,5524,a)].
38.93/38.87	Derived: -t2_space(code_code_numeral) | -hBOOL(hAPP(fun(nat,code_code_numeral),bool,summable(code_code_numeral),A)) | hBOOL(hAPP(filter(nat),bool,hAPP(code_code_numeral,fun(filter(nat),bool),hAPP(fun(nat,code_code_numeral),fun(code_code_numeral,fun(filter(nat),bool)),tendsto(nat,code_code_numeral),hAPP(fun(nat,fun(nat,bool)),fun(nat,code_code_numeral),hAPP(fun(fun(nat,bool),code_code_numeral),fun(fun(nat,fun(nat,bool)),fun(nat,code_code_numeral)),combb(fun(nat,bool),code_code_numeral,nat),hAPP(fun(nat,code_code_numeral),fun(fun(nat,bool),code_code_numeral),big_co1399186613setsum(nat,code_code_numeral),A)),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)))),hAPP(fun(nat,code_code_numeral),code_code_numeral,suminf(code_code_numeral),A)),sequentially)).  [resolve(5579,b,5539,a)].
38.93/38.87	Derived: -t2_space(rat) | -hBOOL(hAPP(fun(nat,rat),bool,summable(rat),A)) | hBOOL(hAPP(filter(nat),bool,hAPP(rat,fun(filter(nat),bool),hAPP(fun(nat,rat),fun(rat,fun(filter(nat),bool)),tendsto(nat,rat),hAPP(fun(nat,fun(nat,bool)),fun(nat,rat),hAPP(fun(fun(nat,bool),rat),fun(fun(nat,fun(nat,bool)),fun(nat,rat)),combb(fun(nat,bool),rat,nat),hAPP(fun(nat,rat),fun(fun(nat,bool),rat),big_co1399186613setsum(nat,rat),A)),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)))),hAPP(fun(nat,rat),rat,suminf(rat),A)),sequentially)).  [resolve(5579,b,5561,a)].
38.93/38.87	5580 -comm_monoid_add(A) | -topological_space(A) | hBOOL(hAPP(fun(nat,A),bool,summable(A),hAPP(A,fun(nat,A),combk(A,nat),zero_zero(A)))) # label(fact_3980_summable__zero) # label(axiom).  [clausify(2971)].
38.93/38.87	Derived: -topological_space(real) | hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(real,fun(nat,real),combk(real,nat),zero_zero(real)))).  [resolve(5580,a,5513,a)].
38.93/38.87	Derived: -topological_space(int) | hBOOL(hAPP(fun(nat,int),bool,summable(int),hAPP(int,fun(nat,int),combk(int,nat),zero_zero(int)))).  [resolve(5580,a,5524,a)].
38.93/38.87	Derived: -topological_space(code_code_numeral) | hBOOL(hAPP(fun(nat,code_code_numeral),bool,summable(code_code_numeral),hAPP(code_code_numeral,fun(nat,code_code_numeral),combk(code_code_numeral,nat),zero_zero(code_code_numeral)))).  [resolve(5580,a,5539,a)].
38.93/38.87	Derived: -topological_space(rat) | hBOOL(hAPP(fun(nat,rat),bool,summable(rat),hAPP(rat,fun(nat,rat),combk(rat,nat),zero_zero(rat)))).  [resolve(5580,a,5561,a)].
38.93/38.87	5581 -comm_monoid_add(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | -hBOOL(hAPP(fun(B,bool),bool,hAPP(fun(B,bool),fun(fun(B,bool),bool),ord_less_eq(fun(B,bool)),D),C)) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f538(B,A,E,F,D,C)),hAPP(fun(B,bool),fun(B,bool),hAPP(fun(B,bool),fun(fun(B,bool),fun(B,bool)),minus_minus(fun(B,bool)),C),D))) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f539(B,A,E,F,D,C)),D)) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),F),C) = hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),E),D) # label(fact_4416_setsum__mono__zero__cong__left) # label(axiom).  [clausify(3083)].
38.93/38.88	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f538(A,real,D,E,C,B)),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),B),C))) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f539(A,real,D,E,C,B)),C)) | hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),E),B) = hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),D),C).  [resolve(5581,a,5513,a)].
38.93/38.88	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f538(A,int,D,E,C,B)),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),B),C))) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f539(A,int,D,E,C,B)),C)) | hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),E),B) = hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),D),C).  [resolve(5581,a,5524,a)].
38.93/38.88	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f538(A,code_code_numeral,D,E,C,B)),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),B),C))) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f539(A,code_code_numeral,D,E,C,B)),C)) | hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),E),B) = hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),D),C).  [resolve(5581,a,5539,a)].
38.93/38.88	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f538(A,rat,D,E,C,B)),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),B),C))) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f539(A,rat,D,E,C,B)),C)) | hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),E),B) = hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),D),C).  [resolve(5581,a,5561,a)].
38.93/38.88	5582 -comm_monoid_add(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | -hBOOL(hAPP(fun(B,bool),bool,hAPP(fun(B,bool),fun(fun(B,bool),bool),ord_less_eq(fun(B,bool)),D),C)) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f538(B,A,E,F,D,C)),hAPP(fun(B,bool),fun(B,bool),hAPP(fun(B,bool),fun(fun(B,bool),fun(B,bool)),minus_minus(fun(B,bool)),C),D))) | hAPP(B,A,F,f539(B,A,E,F,D,C)) != hAPP(B,A,E,f539(B,A,E,F,D,C)) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),F),C) = hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),E),D) # label(fact_4416_setsum__mono__zero__cong__left) # label(axiom).  [clausify(3083)].
38.93/38.88	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f538(A,real,D,E,C,B)),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),B),C))) | hAPP(A,real,E,f539(A,real,D,E,C,B)) != hAPP(A,real,D,f539(A,real,D,E,C,B)) | hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),E),B) = hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),D),C).  [resolve(5582,a,5513,a)].
38.93/38.89	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f538(A,int,D,E,C,B)),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),B),C))) | hAPP(A,int,E,f539(A,int,D,E,C,B)) != hAPP(A,int,D,f539(A,int,D,E,C,B)) | hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),E),B) = hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),D),C).  [resolve(5582,a,5524,a)].
38.93/38.89	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f538(A,code_code_numeral,D,E,C,B)),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),B),C))) | hAPP(A,code_code_numeral,E,f539(A,code_code_numeral,D,E,C,B)) != hAPP(A,code_code_numeral,D,f539(A,code_code_numeral,D,E,C,B)) | hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),E),B) = hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),D),C).  [resolve(5582,a,5539,a)].
38.93/38.89	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f538(A,rat,D,E,C,B)),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),B),C))) | hAPP(A,rat,E,f539(A,rat,D,E,C,B)) != hAPP(A,rat,D,f539(A,rat,D,E,C,B)) | hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),E),B) = hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),D),C).  [resolve(5582,a,5561,a)].
38.93/38.89	5583 -comm_monoid_add(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | -hBOOL(hAPP(fun(B,bool),bool,hAPP(fun(B,bool),fun(fun(B,bool),bool),ord_less_eq(fun(B,bool)),D),C)) | zero_zero(A) != hAPP(B,A,E,f538(B,A,F,E,D,C)) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f539(B,A,F,E,D,C)),D)) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),E),C) = hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),F),D) # label(fact_4416_setsum__mono__zero__cong__left) # label(axiom).  [clausify(3083)].
38.93/38.89	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | zero_zero(real) != hAPP(A,real,D,f538(A,real,E,D,C,B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f539(A,real,E,D,C,B)),C)) | hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),D),B) = hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),E),C).  [resolve(5583,a,5513,a)].
38.93/38.89	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | zero_zero(int) != hAPP(A,int,D,f538(A,int,E,D,C,B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f539(A,int,E,D,C,B)),C)) | hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),D),B) = hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),E),C).  [resolve(5583,a,5524,a)].
38.93/38.89	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | zero_zero(code_code_numeral) != hAPP(A,code_code_numeral,D,f538(A,code_code_numeral,E,D,C,B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f539(A,code_code_numeral,E,D,C,B)),C)) | hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),D),B) = hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),E),C).  [resolve(5583,a,5539,a)].
38.93/38.90	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | zero_zero(rat) != hAPP(A,rat,D,f538(A,rat,E,D,C,B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f539(A,rat,E,D,C,B)),C)) | hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),D),B) = hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),E),C).  [resolve(5583,a,5561,a)].
38.93/38.90	5584 -comm_monoid_add(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | -hBOOL(hAPP(fun(B,bool),bool,hAPP(fun(B,bool),fun(fun(B,bool),bool),ord_less_eq(fun(B,bool)),D),C)) | zero_zero(A) != hAPP(B,A,E,f538(B,A,F,E,D,C)) | hAPP(B,A,E,f539(B,A,F,E,D,C)) != hAPP(B,A,F,f539(B,A,F,E,D,C)) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),E),C) = hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),F),D) # label(fact_4416_setsum__mono__zero__cong__left) # label(axiom).  [clausify(3083)].
38.93/38.90	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | zero_zero(real) != hAPP(A,real,D,f538(A,real,E,D,C,B)) | hAPP(A,real,D,f539(A,real,E,D,C,B)) != hAPP(A,real,E,f539(A,real,E,D,C,B)) | hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),D),B) = hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),E),C).  [resolve(5584,a,5513,a)].
38.93/38.90	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | zero_zero(int) != hAPP(A,int,D,f538(A,int,E,D,C,B)) | hAPP(A,int,D,f539(A,int,E,D,C,B)) != hAPP(A,int,E,f539(A,int,E,D,C,B)) | hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),D),B) = hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),E),C).  [resolve(5584,a,5524,a)].
38.93/38.90	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | zero_zero(code_code_numeral) != hAPP(A,code_code_numeral,D,f538(A,code_code_numeral,E,D,C,B)) | hAPP(A,code_code_numeral,D,f539(A,code_code_numeral,E,D,C,B)) != hAPP(A,code_code_numeral,E,f539(A,code_code_numeral,E,D,C,B)) | hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),D),B) = hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),E),C).  [resolve(5584,a,5539,a)].
38.93/38.90	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | zero_zero(rat) != hAPP(A,rat,D,f538(A,rat,E,D,C,B)) | hAPP(A,rat,D,f539(A,rat,E,D,C,B)) != hAPP(A,rat,E,f539(A,rat,E,D,C,B)) | hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),D),B) = hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),E),C).  [resolve(5584,a,5561,a)].
38.93/38.90	5585 -comm_monoid_add(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f543(B,A,D,E,C)),C)) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),E),C) = hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),D),C) # label(fact_4774_setsum_Ocong) # label(axiom).  [clausify(3106)].
38.93/38.92	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f543(A,real,C,D,B)),B)) | hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),D),B) = hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),C),B).  [resolve(5585,a,5513,a)].
38.93/38.92	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f543(A,int,C,D,B)),B)) | hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),D),B) = hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),C),B).  [resolve(5585,a,5524,a)].
38.93/38.92	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f543(A,code_code_numeral,C,D,B)),B)) | hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),D),B) = hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),C),B).  [resolve(5585,a,5539,a)].
38.93/38.92	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f543(A,rat,C,D,B)),B)) | hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),D),B) = hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),C),B).  [resolve(5585,a,5561,a)].
38.93/38.92	5586 -comm_monoid_add(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | hAPP(B,A,D,f543(B,A,E,D,C)) != hAPP(B,A,E,f543(B,A,E,D,C)) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),D),C) = hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),E),C) # label(fact_4774_setsum_Ocong) # label(axiom).  [clausify(3106)].
38.93/38.92	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(A,real,C,f543(A,real,D,C,B)) != hAPP(A,real,D,f543(A,real,D,C,B)) | hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),C),B) = hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),D),B).  [resolve(5586,a,5513,a)].
38.93/38.92	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(A,int,C,f543(A,int,D,C,B)) != hAPP(A,int,D,f543(A,int,D,C,B)) | hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),C),B) = hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),D),B).  [resolve(5586,a,5524,a)].
38.93/38.92	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(A,code_code_numeral,C,f543(A,code_code_numeral,D,C,B)) != hAPP(A,code_code_numeral,D,f543(A,code_code_numeral,D,C,B)) | hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),C),B) = hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),D),B).  [resolve(5586,a,5539,a)].
38.93/38.92	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(A,rat,C,f543(A,rat,D,C,B)) != hAPP(A,rat,D,f543(A,rat,D,C,B)) | hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),C),B) = hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),D),B).  [resolve(5586,a,5561,a)].
38.93/38.92	5587 -comm_monoid_add(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f545(B,A,D,C)),C)) | zero_zero(A) = hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),D),C) # label(fact_4307_setsum_Oneutral) # label(axiom).  [clausify(3121)].
39.08/38.94	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f545(A,real,C,B)),B)) | zero_zero(real) = hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),C),B).  [resolve(5587,a,5513,a)].
39.08/38.94	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f545(A,int,C,B)),B)) | zero_zero(int) = hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),C),B).  [resolve(5587,a,5524,a)].
39.08/38.94	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f545(A,code_code_numeral,C,B)),B)) | zero_zero(code_code_numeral) = hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),C),B).  [resolve(5587,a,5539,a)].
39.08/38.94	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f545(A,rat,C,B)),B)) | zero_zero(rat) = hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),C),B).  [resolve(5587,a,5561,a)].
39.08/38.94	5588 -comm_monoid_add(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | zero_zero(A) != hAPP(B,A,D,f545(B,A,D,C)) | zero_zero(A) = hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),D),C) # label(fact_4307_setsum_Oneutral) # label(axiom).  [clausify(3121)].
39.08/38.94	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | zero_zero(real) != hAPP(A,real,C,f545(A,real,C,B)) | zero_zero(real) = hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),C),B).  [resolve(5588,a,5513,a)].
39.08/38.94	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | zero_zero(int) != hAPP(A,int,C,f545(A,int,C,B)) | zero_zero(int) = hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),C),B).  [resolve(5588,a,5524,a)].
39.08/38.94	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | zero_zero(code_code_numeral) != hAPP(A,code_code_numeral,C,f545(A,code_code_numeral,C,B)) | zero_zero(code_code_numeral) = hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),C),B).  [resolve(5588,a,5539,a)].
39.08/38.94	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | zero_zero(rat) != hAPP(A,rat,C,f545(A,rat,C,B)) | zero_zero(rat) = hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),C),B).  [resolve(5588,a,5561,a)].
39.08/38.94	5589 -comm_monoid_add(A) | -ord(B) | ti(B,C) != ti(B,D) | ti(B,E) != ti(B,F) | hBOOL(hAPP(B,bool,hAPP(B,fun(B,bool),ord_less_eq(B),C),f547(A,B,V6,V7,F,E,D,C))) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),V7),hAPP(B,fun(B,bool),hAPP(B,fun(B,fun(B,bool)),ord_atLeastLessThan(B),C),E)) = hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),V6),hAPP(B,fun(B,bool),hAPP(B,fun(B,fun(B,bool)),ord_atLeastLessThan(B),D),F)) # label(fact_4302_setsum__ivl__cong) # label(axiom).  [clausify(3150)].
39.08/38.94	Derived: -ord(A) | ti(A,B) != ti(A,C) | ti(A,D) != ti(A,E) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),f547(real,A,F,V6,E,D,C,B))) | hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),V6),hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_atLeastLessThan(A),B),D)) = hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),F),hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_atLeastLessThan(A),C),E)).  [resolve(5589,a,5513,a)].
39.08/38.94	Derived: -ord(A) | ti(A,B) != ti(A,C) | ti(A,D) != ti(A,E) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),f547(int,A,F,V6,E,D,C,B))) | hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),V6),hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_atLeastLessThan(A),B),D)) = hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),F),hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_atLeastLessThan(A),C),E)).  [resolve(5589,a,5524,a)].
39.08/38.95	Derived: -ord(A) | ti(A,B) != ti(A,C) | ti(A,D) != ti(A,E) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),f547(code_code_numeral,A,F,V6,E,D,C,B))) | hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),V6),hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_atLeastLessThan(A),B),D)) = hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),F),hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_atLeastLessThan(A),C),E)).  [resolve(5589,a,5539,a)].
39.08/38.95	Derived: -ord(A) | ti(A,B) != ti(A,C) | ti(A,D) != ti(A,E) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),f547(rat,A,F,V6,E,D,C,B))) | hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),V6),hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_atLeastLessThan(A),B),D)) = hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),F),hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_atLeastLessThan(A),C),E)).  [resolve(5589,a,5561,a)].
39.08/38.95	5590 -comm_monoid_add(A) | -ord(B) | ti(B,C) != ti(B,D) | ti(B,E) != ti(B,F) | hBOOL(hAPP(B,bool,hAPP(B,fun(B,bool),ord_less(B),f547(A,B,V6,V7,F,E,D,C)),E)) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),V7),hAPP(B,fun(B,bool),hAPP(B,fun(B,fun(B,bool)),ord_atLeastLessThan(B),C),E)) = hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),V6),hAPP(B,fun(B,bool),hAPP(B,fun(B,fun(B,bool)),ord_atLeastLessThan(B),D),F)) # label(fact_4302_setsum__ivl__cong) # label(axiom).  [clausify(3150)].
39.08/38.95	Derived: -ord(A) | ti(A,B) != ti(A,C) | ti(A,D) != ti(A,E) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),f547(real,A,F,V6,E,D,C,B)),D)) | hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),V6),hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_atLeastLessThan(A),B),D)) = hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),F),hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_atLeastLessThan(A),C),E)).  [resolve(5590,a,5513,a)].
39.08/38.95	Derived: -ord(A) | ti(A,B) != ti(A,C) | ti(A,D) != ti(A,E) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),f547(int,A,F,V6,E,D,C,B)),D)) | hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),V6),hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_atLeastLessThan(A),B),D)) = hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),F),hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_atLeastLessThan(A),C),E)).  [resolve(5590,a,5524,a)].
39.08/38.95	Derived: -ord(A) | ti(A,B) != ti(A,C) | ti(A,D) != ti(A,E) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),f547(code_code_numeral,A,F,V6,E,D,C,B)),D)) | hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),V6),hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_atLeastLessThan(A),B),D)) = hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),F),hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_atLeastLessThan(A),C),E)).  [resolve(5590,a,5539,a)].
39.08/38.95	Derived: -ord(A) | ti(A,B) != ti(A,C) | ti(A,D) != ti(A,E) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),f547(rat,A,F,V6,E,D,C,B)),D)) | hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),V6),hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_atLeastLessThan(A),B),D)) = hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),F),hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_atLeastLessThan(A),C),E)).  [resolve(5590,a,5561,a)].
39.09/39.01	5591 -comm_monoid_add(A) | -ord(B) | ti(B,C) != ti(B,D) | ti(B,E) != ti(B,F) | hAPP(B,A,V6,f547(A,B,V7,V6,F,E,D,C)) != hAPP(B,A,V7,f547(A,B,V7,V6,F,E,D,C)) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),V6),hAPP(B,fun(B,bool),hAPP(B,fun(B,fun(B,bool)),ord_atLeastLessThan(B),C),E)) = hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),V7),hAPP(B,fun(B,bool),hAPP(B,fun(B,fun(B,bool)),ord_atLeastLessThan(B),D),F)) # label(fact_4302_setsum__ivl__cong) # label(axiom).  [clausify(3150)].
39.09/39.01	Derived: -ord(A) | ti(A,B) != ti(A,C) | ti(A,D) != ti(A,E) | hAPP(A,real,F,f547(real,A,V6,F,E,D,C,B)) != hAPP(A,real,V6,f547(real,A,V6,F,E,D,C,B)) | hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),F),hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_atLeastLessThan(A),B),D)) = hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),V6),hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_atLeastLessThan(A),C),E)).  [resolve(5591,a,5513,a)].
39.09/39.01	Derived: -ord(A) | ti(A,B) != ti(A,C) | ti(A,D) != ti(A,E) | hAPP(A,int,F,f547(int,A,V6,F,E,D,C,B)) != hAPP(A,int,V6,f547(int,A,V6,F,E,D,C,B)) | hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),F),hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_atLeastLessThan(A),B),D)) = hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),V6),hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_atLeastLessThan(A),C),E)).  [resolve(5591,a,5524,a)].
39.09/39.01	Derived: -ord(A) | ti(A,B) != ti(A,C) | ti(A,D) != ti(A,E) | hAPP(A,code_code_numeral,F,f547(code_code_numeral,A,V6,F,E,D,C,B)) != hAPP(A,code_code_numeral,V6,f547(code_code_numeral,A,V6,F,E,D,C,B)) | hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),F),hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_atLeastLessThan(A),B),D)) = hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),V6),hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_atLeastLessThan(A),C),E)).  [resolve(5591,a,5539,a)].
39.09/39.01	Derived: -ord(A) | ti(A,B) != ti(A,C) | ti(A,D) != ti(A,E) | hAPP(A,rat,F,f547(rat,A,V6,F,E,D,C,B)) != hAPP(A,rat,V6,f547(rat,A,V6,F,E,D,C,B)) | hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),F),hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_atLeastLessThan(A),B),D)) = hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),V6),hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_atLeastLessThan(A),C),E)).  [resolve(5591,a,5561,a)].
39.09/39.01	5592 -comm_monoid_add(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),hAPP(A,fun(B,A),hAPP(fun(B,fun(A,A)),fun(A,fun(B,A)),combc(B,A,A),hAPP(fun(B,A),fun(B,fun(A,A)),hAPP(fun(B,fun(A,fun(A,A))),fun(fun(B,A),fun(B,fun(A,A))),combs(B,A,fun(A,A)),hAPP(fun(B,bool),fun(B,fun(A,fun(A,A))),hAPP(fun(bool,fun(A,fun(A,A))),fun(fun(B,bool),fun(B,fun(A,fun(A,A)))),combb(bool,fun(A,fun(A,A)),B),if(A)),D)),E)),zero_zero(A))),C) = hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),E),hAPP(fun(B,bool),fun(B,bool),collect(B),hAPP(fun(B,bool),fun(B,bool),hAPP(fun(B,fun(bool,bool)),fun(fun(B,bool),fun(B,bool)),combs(B,bool,bool),hAPP(fun(B,bool),fun(B,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(B,bool),fun(B,fun(bool,bool))),combb(bool,fun(bool,bool),B),fconj),hAPP(fun(B,bool),fun(B,bool),hAPP(fun(B,fun(fun(B,bool),bool)),fun(fun(B,bool),fun(B,bool)),combc(B,fun(B,bool),bool),member(B)),C))),D))) # label(fact_4186_setsum__restrict__set_H_H) # label(axiom).  [clausify(3236)].
39.09/39.01	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),hAPP(real,fun(A,real),hAPP(fun(A,fun(real,real)),fun(real,fun(A,real)),combc(A,real,real),hAPP(fun(A,real),fun(A,fun(real,real)),hAPP(fun(A,fun(real,fun(real,real))),fun(fun(A,real),fun(A,fun(real,real))),combs(A,real,fun(real,real)),hAPP(fun(A,bool),fun(A,fun(real,fun(real,real))),hAPP(fun(bool,fun(real,fun(real,real))),fun(fun(A,bool),fun(A,fun(real,fun(real,real)))),combb(bool,fun(real,fun(real,real)),A),if(real)),C)),D)),zero_zero(real))),B) = hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),D),hAPP(fun(A,bool),fun(A,bool),collect(A),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,fun(bool,bool)),fun(fun(A,bool),fun(A,bool)),combs(A,bool,bool),hAPP(fun(A,bool),fun(A,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(A,bool),fun(A,fun(bool,bool))),combb(bool,fun(bool,bool),A),fconj),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,fun(fun(A,bool),bool)),fun(fun(A,bool),fun(A,bool)),combc(A,fun(A,bool),bool),member(A)),B))),C))).  [resolve(5592,a,5513,a)].
39.09/39.01	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),hAPP(int,fun(A,int),hAPP(fun(A,fun(int,int)),fun(int,fun(A,int)),combc(A,int,int),hAPP(fun(A,int),fun(A,fun(int,int)),hAPP(fun(A,fun(int,fun(int,int))),fun(fun(A,int),fun(A,fun(int,int))),combs(A,int,fun(int,int)),hAPP(fun(A,bool),fun(A,fun(int,fun(int,int))),hAPP(fun(bool,fun(int,fun(int,int))),fun(fun(A,bool),fun(A,fun(int,fun(int,int)))),combb(bool,fun(int,fun(int,int)),A),if(int)),C)),D)),zero_zero(int))),B) = hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),D),hAPP(fun(A,bool),fun(A,bool),collect(A),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,fun(bool,bool)),fun(fun(A,bool),fun(A,bool)),combs(A,bool,bool),hAPP(fun(A,bool),fun(A,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(A,bool),fun(A,fun(bool,bool))),combb(bool,fun(bool,bool),A),fconj),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,fun(fun(A,bool),bool)),fun(fun(A,bool),fun(A,bool)),combc(A,fun(A,bool),bool),member(A)),B))),C))).  [resolve(5592,a,5524,a)].
39.09/39.01	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),hAPP(code_code_numeral,fun(A,code_code_numeral),hAPP(fun(A,fun(code_code_numeral,code_code_numeral)),fun(code_code_numeral,fun(A,code_code_numeral)),combc(A,code_code_numeral,code_code_numeral),hAPP(fun(A,code_code_numeral),fun(A,fun(code_code_numeral,code_code_numeral)),hAPP(fun(A,fun(code_code_numeral,fun(code_code_numeral,code_code_numeral))),fun(fun(A,code_code_numeral),fun(A,fun(code_code_numeral,code_code_numeral))),combs(A,code_code_numeral,fun(code_code_numeral,code_code_numeral)),hAPP(fun(A,bool),fun(A,fun(code_code_numeral,fun(code_code_numeral,code_code_numeral))),hAPP(fun(bool,fun(code_code_numeral,fun(code_code_numeral,code_code_numeral))),fun(fun(A,bool),fun(A,fun(code_code_numeral,fun(code_code_numeral,code_code_numeral)))),combb(bool,fun(code_code_numeral,fun(code_code_numeral,code_code_numeral)),A),if(code_code_numeral)),C)),D)),zero_zero(code_code_numeral))),B) = hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),D),hAPP(fun(A,bool),fun(A,bool),collect(A),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,fun(bool,bool)),fun(fun(A,bool),fun(A,bool)),combs(A,bool,bool),hAPP(fun(A,bool),fun(A,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(A,bool),fun(A,fun(bool,bool))),combb(bool,fun(bool,bool),A),fconj),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,fun(fun(A,bool),bool)),fun(fun(A,bool),fun(A,bool)),combc(A,fun(A,bool),bool),member(A)),B))),C))).  [resolve(5592,a,5539,a)].
39.09/39.01	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),hAPP(rat,fun(A,rat),hAPP(fun(A,fun(rat,rat)),fun(rat,fun(A,rat)),combc(A,rat,rat),hAPP(fun(A,rat),fun(A,fun(rat,rat)),hAPP(fun(A,fun(rat,fun(rat,rat))),fun(fun(A,rat),fun(A,fun(rat,rat))),combs(A,rat,fun(rat,rat)),hAPP(fun(A,bool),fun(A,fun(rat,fun(rat,rat))),hAPP(fun(bool,fun(rat,fun(rat,rat))),fun(fun(A,bool),fun(A,fun(rat,fun(rat,rat)))),combb(bool,fun(rat,fun(rat,rat)),A),if(rat)),C)),D)),zero_zero(rat))),B) = hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),D),hAPP(fun(A,bool),fun(A,bool),collect(A),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,fun(bool,bool)),fun(fun(A,bool),fun(A,bool)),combs(A,bool,bool),hAPP(fun(A,bool),fun(A,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(A,bool),fun(A,fun(bool,bool))),combb(bool,fun(bool,bool),A),fconj),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,fun(fun(A,bool),bool)),fun(fun(A,bool),fun(A,bool)),combc(A,fun(A,bool),bool),member(A)),B))),C))).  [resolve(5592,a,5561,a)].
39.20/39.06	5593 -comm_monoid_add(A) | -comm_monoid_mult(A) | hAPP(fun(nat,bool),A,hAPP(fun(nat,A),fun(fun(nat,bool),A),big_co302546470etprod(nat,A),B),C) = hAPP(fun(int,bool),A,hAPP(fun(int,A),fun(fun(int,bool),A),big_co302546470etprod(int,A),hAPP(fun(int,nat),fun(int,A),hAPP(fun(nat,A),fun(fun(int,nat),fun(int,A)),combb(nat,A,int),B),nat_1)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),C)) # label(fact_3944_transfer__nat__int__sum__prod_I2_J) # label(axiom).  [clausify(3313)].
39.20/39.06	Derived: -comm_monoid_mult(real) | hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co302546470etprod(nat,real),A),B) = hAPP(fun(int,bool),real,hAPP(fun(int,real),fun(fun(int,bool),real),big_co302546470etprod(int,real),hAPP(fun(int,nat),fun(int,real),hAPP(fun(nat,real),fun(fun(int,nat),fun(int,real)),combb(nat,real,int),A),nat_1)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),B)).  [resolve(5593,a,5513,a)].
39.20/39.06	Derived: -comm_monoid_mult(int) | hAPP(fun(nat,bool),int,hAPP(fun(nat,int),fun(fun(nat,bool),int),big_co302546470etprod(nat,int),A),B) = hAPP(fun(int,bool),int,hAPP(fun(int,int),fun(fun(int,bool),int),big_co302546470etprod(int,int),hAPP(fun(int,nat),fun(int,int),hAPP(fun(nat,int),fun(fun(int,nat),fun(int,int)),combb(nat,int,int),A),nat_1)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),B)).  [resolve(5593,a,5524,a)].
39.20/39.06	Derived: -comm_monoid_mult(code_code_numeral) | hAPP(fun(nat,bool),code_code_numeral,hAPP(fun(nat,code_code_numeral),fun(fun(nat,bool),code_code_numeral),big_co302546470etprod(nat,code_code_numeral),A),B) = hAPP(fun(int,bool),code_code_numeral,hAPP(fun(int,code_code_numeral),fun(fun(int,bool),code_code_numeral),big_co302546470etprod(int,code_code_numeral),hAPP(fun(int,nat),fun(int,code_code_numeral),hAPP(fun(nat,code_code_numeral),fun(fun(int,nat),fun(int,code_code_numeral)),combb(nat,code_code_numeral,int),A),nat_1)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),B)).  [resolve(5593,a,5539,a)].
39.20/39.06	Derived: -comm_monoid_mult(rat) | hAPP(fun(nat,bool),rat,hAPP(fun(nat,rat),fun(fun(nat,bool),rat),big_co302546470etprod(nat,rat),A),B) = hAPP(fun(int,bool),rat,hAPP(fun(int,rat),fun(fun(int,bool),rat),big_co302546470etprod(int,rat),hAPP(fun(int,nat),fun(int,rat),hAPP(fun(nat,rat),fun(fun(int,nat),fun(int,rat)),combb(nat,rat,int),A),nat_1)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),B)).  [resolve(5593,a,5561,a)].
39.20/39.06	5594 -comm_monoid_add(A) | hAPP(fun(product_prod(nat,nat),bool),A,hAPP(fun(product_prod(nat,nat),A),fun(fun(product_prod(nat,nat),bool),A),big_co1399186613setsum(product_prod(nat,nat),A),hAPP(fun(nat,fun(nat,A)),fun(product_prod(nat,nat),A),product_prod_case(nat,nat,A),B)),hAPP(fun(product_prod(nat,nat),bool),fun(product_prod(nat,nat),bool),collect(product_prod(nat,nat)),hAPP(fun(nat,fun(nat,bool)),fun(product_prod(nat,nat),bool),product_prod_case(nat,nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),hAPP(fun(nat,fun(nat,fun(nat,bool))),fun(nat,fun(nat,fun(nat,bool))),combc(nat,nat,fun(nat,bool)),hAPP(fun(nat,fun(nat,fun(nat,bool))),fun(nat,fun(nat,fun(nat,bool))),hAPP(fun(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool))),fun(fun(nat,fun(nat,fun(nat,bool))),fun(nat,fun(nat,fun(nat,bool)))),combb(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),nat),combc(nat,nat,bool)),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,fun(nat,bool))),hAPP(fun(fun(nat,nat),fun(nat,fun(nat,bool))),fun(fun(nat,fun(nat,nat)),fun(nat,fun(nat,fun(nat,bool)))),combb(fun(nat,nat),fun(nat,fun(nat,bool)),nat),hAPP(fun(nat,fun(nat,bool)),fun(fun(nat,nat),fun(nat,fun(nat,bool))),combb(nat,fun(nat,bool),nat),ord_less(nat))),plus_plus(nat)))),C)))) = hAPP(fun(nat,bool),A,hAPP(fun(nat,A),fun(fun(nat,bool),A),big_co1399186613setsum(nat,A),hAPP(fun(nat,fun(nat,bool)),fun(nat,A),hAPP(fun(nat,fun(fun(nat,bool),A)),fun(fun(nat,fun(nat,bool)),fun(nat,A)),combs(nat,fun(nat,bool),A),hAPP(fun(nat,fun(nat,A)),fun(nat,fun(fun(nat,bool),A)),hAPP(fun(fun(nat,A),fun(fun(nat,bool),A)),fun(fun(nat,fun(nat,A)),fun(nat,fun(fun(nat,bool),A))),combb(fun(nat,A),fun(fun(nat,bool),A),nat),big_co1399186613setsum(nat,A)),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,A)),hAPP(fun(fun(nat,nat),fun(nat,A)),fun(fun(nat,fun(nat,nat)),fun(nat,fun(nat,A))),combb(fun(nat,nat),fun(nat,A),nat),hAPP(fun(nat,fun(nat,A)),fun(fun(nat,nat),fun(nat,A)),combs(nat,nat,A),B)),minus_minus(nat)))),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),zero_zero(nat)))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),C)) # label(fact_4622_setsum__triangle__reindex) # label(axiom).  [clausify(3318)].
39.20/39.07	Derived: hAPP(fun(product_prod(nat,nat),bool),real,hAPP(fun(product_prod(nat,nat),real),fun(fun(product_prod(nat,nat),bool),real),big_co1399186613setsum(product_prod(nat,nat),real),hAPP(fun(nat,fun(nat,real)),fun(product_prod(nat,nat),real),product_prod_case(nat,nat,real),A)),hAPP(fun(product_prod(nat,nat),bool),fun(product_prod(nat,nat),bool),collect(product_prod(nat,nat)),hAPP(fun(nat,fun(nat,bool)),fun(product_prod(nat,nat),bool),product_prod_case(nat,nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),hAPP(fun(nat,fun(nat,fun(nat,bool))),fun(nat,fun(nat,fun(nat,bool))),combc(nat,nat,fun(nat,bool)),hAPP(fun(nat,fun(nat,fun(nat,bool))),fun(nat,fun(nat,fun(nat,bool))),hAPP(fun(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool))),fun(fun(nat,fun(nat,fun(nat,bool))),fun(nat,fun(nat,fun(nat,bool)))),combb(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),nat),combc(nat,nat,bool)),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,fun(nat,bool))),hAPP(fun(fun(nat,nat),fun(nat,fun(nat,bool))),fun(fun(nat,fun(nat,nat)),fun(nat,fun(nat,fun(nat,bool)))),combb(fun(nat,nat),fun(nat,fun(nat,bool)),nat),hAPP(fun(nat,fun(nat,bool)),fun(fun(nat,nat),fun(nat,fun(nat,bool))),combb(nat,fun(nat,bool),nat),ord_less(nat))),plus_plus(nat)))),B)))) = hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,fun(nat,bool)),fun(nat,real),hAPP(fun(nat,fun(fun(nat,bool),real)),fun(fun(nat,fun(nat,bool)),fun(nat,real)),combs(nat,fun(nat,bool),real),hAPP(fun(nat,fun(nat,real)),fun(nat,fun(fun(nat,bool),real)),hAPP(fun(fun(nat,real),fun(fun(nat,bool),real)),fun(fun(nat,fun(nat,real)),fun(nat,fun(fun(nat,bool),real))),combb(fun(nat,real),fun(fun(nat,bool),real),nat),big_co1399186613setsum(nat,real)),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,real)),hAPP(fun(fun(nat,nat),fun(nat,real)),fun(fun(nat,fun(nat,nat)),fun(nat,fun(nat,real))),combb(fun(nat,nat),fun(nat,real),nat),hAPP(fun(nat,fun(nat,real)),fun(fun(nat,nat),fun(nat,real)),combs(nat,nat,real),A)),minus_minus(nat)))),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),zero_zero(nat)))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),B)).  [resolve(5594,a,5513,a)].
39.20/39.07	Derived: hAPP(fun(product_prod(nat,nat),bool),int,hAPP(fun(product_prod(nat,nat),int),fun(fun(product_prod(nat,nat),bool),int),big_co1399186613setsum(product_prod(nat,nat),int),hAPP(fun(nat,fun(nat,int)),fun(product_prod(nat,nat),int),product_prod_case(nat,nat,int),A)),hAPP(fun(product_prod(nat,nat),bool),fun(product_prod(nat,nat),bool),collect(product_prod(nat,nat)),hAPP(fun(nat,fun(nat,bool)),fun(product_prod(nat,nat),bool),product_prod_case(nat,nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),hAPP(fun(nat,fun(nat,fun(nat,bool))),fun(nat,fun(nat,fun(nat,bool))),combc(nat,nat,fun(nat,bool)),hAPP(fun(nat,fun(nat,fun(nat,bool))),fun(nat,fun(nat,fun(nat,bool))),hAPP(fun(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool))),fun(fun(nat,fun(nat,fun(nat,bool))),fun(nat,fun(nat,fun(nat,bool)))),combb(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),nat),combc(nat,nat,bool)),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,fun(nat,bool))),hAPP(fun(fun(nat,nat),fun(nat,fun(nat,bool))),fun(fun(nat,fun(nat,nat)),fun(nat,fun(nat,fun(nat,bool)))),combb(fun(nat,nat),fun(nat,fun(nat,bool)),nat),hAPP(fun(nat,fun(nat,bool)),fun(fun(nat,nat),fun(nat,fun(nat,bool))),combb(nat,fun(nat,bool),nat),ord_less(nat))),plus_plus(nat)))),B)))) = hAPP(fun(nat,bool),int,hAPP(fun(nat,int),fun(fun(nat,bool),int),big_co1399186613setsum(nat,int),hAPP(fun(nat,fun(nat,bool)),fun(nat,int),hAPP(fun(nat,fun(fun(nat,bool),int)),fun(fun(nat,fun(nat,bool)),fun(nat,int)),combs(nat,fun(nat,bool),int),hAPP(fun(nat,fun(nat,int)),fun(nat,fun(fun(nat,bool),int)),hAPP(fun(fun(nat,int),fun(fun(nat,bool),int)),fun(fun(nat,fun(nat,int)),fun(nat,fun(fun(nat,bool),int))),combb(fun(nat,int),fun(fun(nat,bool),int),nat),big_co1399186613setsum(nat,int)),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,int)),hAPP(fun(fun(nat,nat),fun(nat,int)),fun(fun(nat,fun(nat,nat)),fun(nat,fun(nat,int))),combb(fun(nat,nat),fun(nat,int),nat),hAPP(fun(nat,fun(nat,int)),fun(fun(nat,nat),fun(nat,int)),combs(nat,nat,int),A)),minus_minus(nat)))),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),zero_zero(nat)))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),B)).  [resolve(5594,a,5524,a)].
39.20/39.07	Derived: hAPP(fun(product_prod(nat,nat),bool),code_code_numeral,hAPP(fun(product_prod(nat,nat),code_code_numeral),fun(fun(product_prod(nat,nat),bool),code_code_numeral),big_co1399186613setsum(product_prod(nat,nat),code_code_numeral),hAPP(fun(nat,fun(nat,code_code_numeral)),fun(product_prod(nat,nat),code_code_numeral),product_prod_case(nat,nat,code_code_numeral),A)),hAPP(fun(product_prod(nat,nat),bool),fun(product_prod(nat,nat),bool),collect(product_prod(nat,nat)),hAPP(fun(nat,fun(nat,bool)),fun(product_prod(nat,nat),bool),product_prod_case(nat,nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),hAPP(fun(nat,fun(nat,fun(nat,bool))),fun(nat,fun(nat,fun(nat,bool))),combc(nat,nat,fun(nat,bool)),hAPP(fun(nat,fun(nat,fun(nat,bool))),fun(nat,fun(nat,fun(nat,bool))),hAPP(fun(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool))),fun(fun(nat,fun(nat,fun(nat,bool))),fun(nat,fun(nat,fun(nat,bool)))),combb(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),nat),combc(nat,nat,bool)),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,fun(nat,bool))),hAPP(fun(fun(nat,nat),fun(nat,fun(nat,bool))),fun(fun(nat,fun(nat,nat)),fun(nat,fun(nat,fun(nat,bool)))),combb(fun(nat,nat),fun(nat,fun(nat,bool)),nat),hAPP(fun(nat,fun(nat,bool)),fun(fun(nat,nat),fun(nat,fun(nat,bool))),combb(nat,fun(nat,bool),nat),ord_less(nat))),plus_plus(nat)))),B)))) = hAPP(fun(nat,bool),code_code_numeral,hAPP(fun(nat,code_code_numeral),fun(fun(nat,bool),code_code_numeral),big_co1399186613setsum(nat,code_code_numeral),hAPP(fun(nat,fun(nat,bool)),fun(nat,code_code_numeral),hAPP(fun(nat,fun(fun(nat,bool),code_code_numeral)),fun(fun(nat,fun(nat,bool)),fun(nat,code_code_numeral)),combs(nat,fun(nat,bool),code_code_numeral),hAPP(fun(nat,fun(nat,code_code_numeral)),fun(nat,fun(fun(nat,bool),code_code_numeral)),hAPP(fun(fun(nat,code_code_numeral),fun(fun(nat,bool),code_code_numeral)),fun(fun(nat,fun(nat,code_code_numeral)),fun(nat,fun(fun(nat,bool),code_code_numeral))),combb(fun(nat,code_code_numeral),fun(fun(nat,bool),code_code_numeral),nat),big_co1399186613setsum(nat,code_code_numeral)),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,code_code_numeral)),hAPP(fun(fun(nat,nat),fun(nat,code_code_numeral)),fun(fun(nat,fun(nat,nat)),fun(nat,fun(nat,code_code_numeral))),combb(fun(nat,nat),fun(nat,code_code_numeral),nat),hAPP(fun(nat,fun(nat,code_code_numeral)),fun(fun(nat,nat),fun(nat,code_code_numeral)),combs(nat,nat,code_code_numeral),A)),minus_minus(nat)))),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),zero_zero(nat)))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),B)).  [resolve(5594,a,5539,a)].
39.20/39.07	Derived: hAPP(fun(product_prod(nat,nat),bool),rat,hAPP(fun(product_prod(nat,nat),rat),fun(fun(product_prod(nat,nat),bool),rat),big_co1399186613setsum(product_prod(nat,nat),rat),hAPP(fun(nat,fun(nat,rat)),fun(product_prod(nat,nat),rat),product_prod_case(nat,nat,rat),A)),hAPP(fun(product_prod(nat,nat),bool),fun(product_prod(nat,nat),bool),collect(product_prod(nat,nat)),hAPP(fun(nat,fun(nat,bool)),fun(product_prod(nat,nat),bool),product_prod_case(nat,nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),hAPP(fun(nat,fun(nat,fun(nat,bool))),fun(nat,fun(nat,fun(nat,bool))),combc(nat,nat,fun(nat,bool)),hAPP(fun(nat,fun(nat,fun(nat,bool))),fun(nat,fun(nat,fun(nat,bool))),hAPP(fun(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool))),fun(fun(nat,fun(nat,fun(nat,bool))),fun(nat,fun(nat,fun(nat,bool)))),combb(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),nat),combc(nat,nat,bool)),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,fun(nat,bool))),hAPP(fun(fun(nat,nat),fun(nat,fun(nat,bool))),fun(fun(nat,fun(nat,nat)),fun(nat,fun(nat,fun(nat,bool)))),combb(fun(nat,nat),fun(nat,fun(nat,bool)),nat),hAPP(fun(nat,fun(nat,bool)),fun(fun(nat,nat),fun(nat,fun(nat,bool))),combb(nat,fun(nat,bool),nat),ord_less(nat))),plus_plus(nat)))),B)))) = hAPP(fun(nat,bool),rat,hAPP(fun(nat,rat),fun(fun(nat,bool),rat),big_co1399186613setsum(nat,rat),hAPP(fun(nat,fun(nat,bool)),fun(nat,rat),hAPP(fun(nat,fun(fun(nat,bool),rat)),fun(fun(nat,fun(nat,bool)),fun(nat,rat)),combs(nat,fun(nat,bool),rat),hAPP(fun(nat,fun(nat,rat)),fun(nat,fun(fun(nat,bool),rat)),hAPP(fun(fun(nat,rat),fun(fun(nat,bool),rat)),fun(fun(nat,fun(nat,rat)),fun(nat,fun(fun(nat,bool),rat))),combb(fun(nat,rat),fun(fun(nat,bool),rat),nat),big_co1399186613setsum(nat,rat)),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,rat)),hAPP(fun(fun(nat,nat),fun(nat,rat)),fun(fun(nat,fun(nat,nat)),fun(nat,fun(nat,rat))),combb(fun(nat,nat),fun(nat,rat),nat),hAPP(fun(nat,fun(nat,rat)),fun(fun(nat,nat),fun(nat,rat)),combs(nat,nat,rat),A)),minus_minus(nat)))),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),zero_zero(nat)))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),B)).  [resolve(5594,a,5561,a)].
39.20/39.07	5595 -t2_space(A) | -comm_monoid_add(A) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),f585(A,C,B))) | hBOOL(hAPP(A,bool,hAPP(fun(nat,A),fun(A,bool),sums(A),C),hAPP(fun(nat,bool),A,hAPP(fun(nat,A),fun(fun(nat,bool),A),big_co1399186613setsum(nat,A),C),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),B)))) # label(fact_4291_series__zero) # label(axiom).  [clausify(3320)].
39.20/39.07	Derived: -t2_space(real) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),f585(real,B,A))) | hBOOL(hAPP(real,bool,hAPP(fun(nat,real),fun(real,bool),sums(real),B),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),B),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),A)))).  [resolve(5595,b,5513,a)].
39.20/39.07	Derived: -t2_space(int) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),f585(int,B,A))) | hBOOL(hAPP(int,bool,hAPP(fun(nat,int),fun(int,bool),sums(int),B),hAPP(fun(nat,bool),int,hAPP(fun(nat,int),fun(fun(nat,bool),int),big_co1399186613setsum(nat,int),B),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),A)))).  [resolve(5595,b,5524,a)].
39.20/39.07	Derived: -t2_space(code_code_numeral) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),f585(code_code_numeral,B,A))) | hBOOL(hAPP(code_code_numeral,bool,hAPP(fun(nat,code_code_numeral),fun(code_code_numeral,bool),sums(code_code_numeral),B),hAPP(fun(nat,bool),code_code_numeral,hAPP(fun(nat,code_code_numeral),fun(fun(nat,bool),code_code_numeral),big_co1399186613setsum(nat,code_code_numeral),B),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),A)))).  [resolve(5595,b,5539,a)].
39.20/39.09	Derived: -t2_space(rat) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),f585(rat,B,A))) | hBOOL(hAPP(rat,bool,hAPP(fun(nat,rat),fun(rat,bool),sums(rat),B),hAPP(fun(nat,bool),rat,hAPP(fun(nat,rat),fun(fun(nat,bool),rat),big_co1399186613setsum(nat,rat),B),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),A)))).  [resolve(5595,b,5561,a)].
39.20/39.09	5596 -t2_space(A) | -comm_monoid_add(A) | zero_zero(A) != hAPP(nat,A,B,f585(A,B,C)) | hBOOL(hAPP(A,bool,hAPP(fun(nat,A),fun(A,bool),sums(A),B),hAPP(fun(nat,bool),A,hAPP(fun(nat,A),fun(fun(nat,bool),A),big_co1399186613setsum(nat,A),B),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),C)))) # label(fact_4291_series__zero) # label(axiom).  [clausify(3320)].
39.20/39.09	Derived: -t2_space(real) | zero_zero(real) != hAPP(nat,real,A,f585(real,A,B)) | hBOOL(hAPP(real,bool,hAPP(fun(nat,real),fun(real,bool),sums(real),A),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),A),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),B)))).  [resolve(5596,b,5513,a)].
39.20/39.09	Derived: -t2_space(int) | zero_zero(int) != hAPP(nat,int,A,f585(int,A,B)) | hBOOL(hAPP(int,bool,hAPP(fun(nat,int),fun(int,bool),sums(int),A),hAPP(fun(nat,bool),int,hAPP(fun(nat,int),fun(fun(nat,bool),int),big_co1399186613setsum(nat,int),A),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),B)))).  [resolve(5596,b,5524,a)].
39.20/39.09	Derived: -t2_space(code_code_numeral) | zero_zero(code_code_numeral) != hAPP(nat,code_code_numeral,A,f585(code_code_numeral,A,B)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(fun(nat,code_code_numeral),fun(code_code_numeral,bool),sums(code_code_numeral),A),hAPP(fun(nat,bool),code_code_numeral,hAPP(fun(nat,code_code_numeral),fun(fun(nat,bool),code_code_numeral),big_co1399186613setsum(nat,code_code_numeral),A),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),B)))).  [resolve(5596,b,5539,a)].
39.20/39.09	Derived: -t2_space(rat) | zero_zero(rat) != hAPP(nat,rat,A,f585(rat,A,B)) | hBOOL(hAPP(rat,bool,hAPP(fun(nat,rat),fun(rat,bool),sums(rat),A),hAPP(fun(nat,bool),rat,hAPP(fun(nat,rat),fun(fun(nat,bool),rat),big_co1399186613setsum(nat,rat),A),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),B)))).  [resolve(5596,b,5561,a)].
39.20/39.09	5597 -comm_monoid_add(A) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,B)),C)) | zero_zero(A) = hAPP(fun(nat,bool),A,hAPP(fun(nat,A),fun(fun(nat,bool),A),big_co1399186613setsum(nat,A),D),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),C),hAPP(nat,nat,suc,B))) # label(fact_4603_setsum__cl__ivl__Suc) # label(axiom).  [clausify(3342)].
39.20/39.09	5598 -comm_monoid_add(A) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,B)),C)) | hAPP(fun(nat,bool),A,hAPP(fun(nat,A),fun(fun(nat,bool),A),big_co1399186613setsum(nat,A),D),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),C),hAPP(nat,nat,suc,B))) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(fun(nat,bool),A,hAPP(fun(nat,A),fun(fun(nat,bool),A),big_co1399186613setsum(nat,A),D),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),C),B))),hAPP(nat,A,D,hAPP(nat,nat,suc,B))) # label(fact_4603_setsum__cl__ivl__Suc) # label(axiom).  [clausify(3342)].
39.20/39.09	Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,A)),B)) | hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),C),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),B),hAPP(nat,nat,suc,A))) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),C),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),B),A))),hAPP(nat,real,C,hAPP(nat,nat,suc,A))).  [resolve(5598,a,5513,a)].
39.32/39.19	Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,A)),B)) | hAPP(fun(nat,bool),int,hAPP(fun(nat,int),fun(fun(nat,bool),int),big_co1399186613setsum(nat,int),C),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),B),hAPP(nat,nat,suc,A))) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(fun(nat,bool),int,hAPP(fun(nat,int),fun(fun(nat,bool),int),big_co1399186613setsum(nat,int),C),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),B),A))),hAPP(nat,int,C,hAPP(nat,nat,suc,A))).  [resolve(5598,a,5524,a)].
39.32/39.19	Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,A)),B)) | hAPP(fun(nat,bool),code_code_numeral,hAPP(fun(nat,code_code_numeral),fun(fun(nat,bool),code_code_numeral),big_co1399186613setsum(nat,code_code_numeral),C),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),B),hAPP(nat,nat,suc,A))) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),hAPP(fun(nat,bool),code_code_numeral,hAPP(fun(nat,code_code_numeral),fun(fun(nat,bool),code_code_numeral),big_co1399186613setsum(nat,code_code_numeral),C),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),B),A))),hAPP(nat,code_code_numeral,C,hAPP(nat,nat,suc,A))).  [resolve(5598,a,5539,a)].
39.32/39.19	Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,A)),B)) | hAPP(fun(nat,bool),rat,hAPP(fun(nat,rat),fun(fun(nat,bool),rat),big_co1399186613setsum(nat,rat),C),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),B),hAPP(nat,nat,suc,A))) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(fun(nat,bool),rat,hAPP(fun(nat,rat),fun(fun(nat,bool),rat),big_co1399186613setsum(nat,rat),C),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),B),A))),hAPP(nat,rat,C,hAPP(nat,nat,suc,A))).  [resolve(5598,a,5561,a)].
39.32/39.19	5599 -comm_monoid_add(A) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),C)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),C),D)) | hAPP(fun(nat,bool),A,hAPP(fun(nat,A),fun(fun(nat,bool),A),big_co1399186613setsum(nat,A),E),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),B),D)) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(fun(nat,bool),A,hAPP(fun(nat,A),fun(fun(nat,bool),A),big_co1399186613setsum(nat,A),E),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),B),C))),hAPP(fun(nat,bool),A,hAPP(fun(nat,A),fun(fun(nat,bool),A),big_co1399186613setsum(nat,A),E),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),C),D))) # label(fact_4201_setsum__add__nat__ivl) # label(axiom).  [clausify(3495)].
39.32/39.19	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),C)) | hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),D),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),A),C)) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),D),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),A),B))),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),D),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),B),C))).  [resolve(5599,a,5513,a)].
39.32/39.19	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),C)) | hAPP(fun(nat,bool),int,hAPP(fun(nat,int),fun(fun(nat,bool),int),big_co1399186613setsum(nat,int),D),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),A),C)) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(fun(nat,bool),int,hAPP(fun(nat,int),fun(fun(nat,bool),int),big_co1399186613setsum(nat,int),D),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),A),B))),hAPP(fun(nat,bool),int,hAPP(fun(nat,int),fun(fun(nat,bool),int),big_co1399186613setsum(nat,int),D),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),B),C))).  [resolve(5599,a,5524,a)].
39.39/39.27	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),C)) | hAPP(fun(nat,bool),code_code_numeral,hAPP(fun(nat,code_code_numeral),fun(fun(nat,bool),code_code_numeral),big_co1399186613setsum(nat,code_code_numeral),D),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),A),C)) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),hAPP(fun(nat,bool),code_code_numeral,hAPP(fun(nat,code_code_numeral),fun(fun(nat,bool),code_code_numeral),big_co1399186613setsum(nat,code_code_numeral),D),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),A),B))),hAPP(fun(nat,bool),code_code_numeral,hAPP(fun(nat,code_code_numeral),fun(fun(nat,bool),code_code_numeral),big_co1399186613setsum(nat,code_code_numeral),D),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),B),C))).  [resolve(5599,a,5539,a)].
39.39/39.27	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),C)) | hAPP(fun(nat,bool),rat,hAPP(fun(nat,rat),fun(fun(nat,bool),rat),big_co1399186613setsum(nat,rat),D),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),A),C)) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(fun(nat,bool),rat,hAPP(fun(nat,rat),fun(fun(nat,bool),rat),big_co1399186613setsum(nat,rat),D),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),A),B))),hAPP(fun(nat,bool),rat,hAPP(fun(nat,rat),fun(fun(nat,bool),rat),big_co1399186613setsum(nat,rat),D),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),B),C))).  [resolve(5599,a,5561,a)].
39.39/39.27	5600 -comm_monoid_add(A) | hAPP(fun(nat,bool),A,hAPP(fun(nat,A),fun(fun(nat,bool),A),big_co1399186613setsum(nat,A),hAPP(fun(nat,nat),fun(nat,A),hAPP(fun(nat,A),fun(fun(nat,nat),fun(nat,A)),combb(nat,A,nat),B),suc)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),C),D)) = hAPP(fun(nat,bool),A,hAPP(fun(nat,A),fun(fun(nat,bool),A),big_co1399186613setsum(nat,A),B),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,suc,C)),hAPP(nat,nat,suc,D))) # label(fact_4544_setsum__shift__bounds__cl__Suc__ivl) # label(axiom).  [clausify(3621)].
39.39/39.27	Derived: hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),A),suc)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),B),C)) = hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),A),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,suc,B)),hAPP(nat,nat,suc,C))).  [resolve(5600,a,5513,a)].
39.39/39.27	Derived: hAPP(fun(nat,bool),int,hAPP(fun(nat,int),fun(fun(nat,bool),int),big_co1399186613setsum(nat,int),hAPP(fun(nat,nat),fun(nat,int),hAPP(fun(nat,int),fun(fun(nat,nat),fun(nat,int)),combb(nat,int,nat),A),suc)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),B),C)) = hAPP(fun(nat,bool),int,hAPP(fun(nat,int),fun(fun(nat,bool),int),big_co1399186613setsum(nat,int),A),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,suc,B)),hAPP(nat,nat,suc,C))).  [resolve(5600,a,5524,a)].
39.39/39.30	Derived: hAPP(fun(nat,bool),code_code_numeral,hAPP(fun(nat,code_code_numeral),fun(fun(nat,bool),code_code_numeral),big_co1399186613setsum(nat,code_code_numeral),hAPP(fun(nat,nat),fun(nat,code_code_numeral),hAPP(fun(nat,code_code_numeral),fun(fun(nat,nat),fun(nat,code_code_numeral)),combb(nat,code_code_numeral,nat),A),suc)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),B),C)) = hAPP(fun(nat,bool),code_code_numeral,hAPP(fun(nat,code_code_numeral),fun(fun(nat,bool),code_code_numeral),big_co1399186613setsum(nat,code_code_numeral),A),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,suc,B)),hAPP(nat,nat,suc,C))).  [resolve(5600,a,5539,a)].
39.39/39.30	Derived: hAPP(fun(nat,bool),rat,hAPP(fun(nat,rat),fun(fun(nat,bool),rat),big_co1399186613setsum(nat,rat),hAPP(fun(nat,nat),fun(nat,rat),hAPP(fun(nat,rat),fun(fun(nat,nat),fun(nat,rat)),combb(nat,rat,nat),A),suc)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),B),C)) = hAPP(fun(nat,bool),rat,hAPP(fun(nat,rat),fun(fun(nat,bool),rat),big_co1399186613setsum(nat,rat),A),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,suc,B)),hAPP(nat,nat,suc,C))).  [resolve(5600,a,5561,a)].
39.39/39.30	5601 -comm_monoid_add(A) | -hBOOL(hAPP(fun(fun(B,bool),bool),bool,finite_finite_1(fun(B,bool)),C)) | hBOOL(hAPP(fun(fun(B,bool),bool),bool,hAPP(fun(B,bool),fun(fun(fun(B,bool),bool),bool),member(fun(B,bool)),f646(B,A,D,C)),C)) | hBOOL(hAPP(fun(fun(B,bool),bool),bool,hAPP(fun(B,bool),fun(fun(fun(B,bool),bool),bool),member(fun(B,bool)),f647(B,A,D,C)),C)) | hAPP(fun(fun(B,bool),bool),A,hAPP(fun(fun(B,bool),A),fun(fun(fun(B,bool),bool),A),big_co1399186613setsum(fun(B,bool),A),hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),D)),C) = hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),D),hAPP(fun(fun(B,bool),bool),fun(B,bool),complete_Sup_Sup(fun(B,bool)),C)) # label(fact_4310_setsum__UNION__zero) # label(axiom).  [clausify(3649)].
39.39/39.30	Derived: -hBOOL(hAPP(fun(fun(A,bool),bool),bool,finite_finite_1(fun(A,bool)),B)) | hBOOL(hAPP(fun(fun(A,bool),bool),bool,hAPP(fun(A,bool),fun(fun(fun(A,bool),bool),bool),member(fun(A,bool)),f646(A,real,C,B)),B)) | hBOOL(hAPP(fun(fun(A,bool),bool),bool,hAPP(fun(A,bool),fun(fun(fun(A,bool),bool),bool),member(fun(A,bool)),f647(A,real,C,B)),B)) | hAPP(fun(fun(A,bool),bool),real,hAPP(fun(fun(A,bool),real),fun(fun(fun(A,bool),bool),real),big_co1399186613setsum(fun(A,bool),real),hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),C)),B) = hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),C),hAPP(fun(fun(A,bool),bool),fun(A,bool),complete_Sup_Sup(fun(A,bool)),B)).  [resolve(5601,a,5513,a)].
39.39/39.30	Derived: -hBOOL(hAPP(fun(fun(A,bool),bool),bool,finite_finite_1(fun(A,bool)),B)) | hBOOL(hAPP(fun(fun(A,bool),bool),bool,hAPP(fun(A,bool),fun(fun(fun(A,bool),bool),bool),member(fun(A,bool)),f646(A,int,C,B)),B)) | hBOOL(hAPP(fun(fun(A,bool),bool),bool,hAPP(fun(A,bool),fun(fun(fun(A,bool),bool),bool),member(fun(A,bool)),f647(A,int,C,B)),B)) | hAPP(fun(fun(A,bool),bool),int,hAPP(fun(fun(A,bool),int),fun(fun(fun(A,bool),bool),int),big_co1399186613setsum(fun(A,bool),int),hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),C)),B) = hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),C),hAPP(fun(fun(A,bool),bool),fun(A,bool),complete_Sup_Sup(fun(A,bool)),B)).  [resolve(5601,a,5524,a)].
39.39/39.30	Derived: -hBOOL(hAPP(fun(fun(A,bool),bool),bool,finite_finite_1(fun(A,bool)),B)) | hBOOL(hAPP(fun(fun(A,bool),bool),bool,hAPP(fun(A,bool),fun(fun(fun(A,bool),bool),bool),member(fun(A,bool)),f646(A,code_code_numeral,C,B)),B)) | hBOOL(hAPP(fun(fun(A,bool),bool),bool,hAPP(fun(A,bool),fun(fun(fun(A,bool),bool),bool),member(fun(A,bool)),f647(A,code_code_numeral,C,B)),B)) | hAPP(fun(fun(A,bool),bool),code_code_numeral,hAPP(fun(fun(A,bool),code_code_numeral),fun(fun(fun(A,bool),bool),code_code_numeral),big_co1399186613setsum(fun(A,bool),code_code_numeral),hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),C)),B) = hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),C),hAPP(fun(fun(A,bool),bool),fun(A,bool),complete_Sup_Sup(fun(A,bool)),B)).  [resolve(5601,a,5539,a)].
39.39/39.30	Derived: -hBOOL(hAPP(fun(fun(A,bool),bool),bool,finite_finite_1(fun(A,bool)),B)) | hBOOL(hAPP(fun(fun(A,bool),bool),bool,hAPP(fun(A,bool),fun(fun(fun(A,bool),bool),bool),member(fun(A,bool)),f646(A,rat,C,B)),B)) | hBOOL(hAPP(fun(fun(A,bool),bool),bool,hAPP(fun(A,bool),fun(fun(fun(A,bool),bool),bool),member(fun(A,bool)),f647(A,rat,C,B)),B)) | hAPP(fun(fun(A,bool),bool),rat,hAPP(fun(fun(A,bool),rat),fun(fun(fun(A,bool),bool),rat),big_co1399186613setsum(fun(A,bool),rat),hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),C)),B) = hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),C),hAPP(fun(fun(A,bool),bool),fun(A,bool),complete_Sup_Sup(fun(A,bool)),B)).  [resolve(5601,a,5561,a)].
39.39/39.30	5602 -comm_monoid_add(A) | -hBOOL(hAPP(fun(fun(B,bool),bool),bool,finite_finite_1(fun(B,bool)),C)) | hBOOL(hAPP(fun(fun(B,bool),bool),bool,hAPP(fun(B,bool),fun(fun(fun(B,bool),bool),bool),member(fun(B,bool)),f646(B,A,D,C)),C)) | hBOOL(hAPP(fun(fun(B,bool),bool),bool,hAPP(fun(B,bool),fun(fun(fun(B,bool),bool),bool),member(fun(B,bool)),f648(B,A,D,C)),C)) | hAPP(fun(fun(B,bool),bool),A,hAPP(fun(fun(B,bool),A),fun(fun(fun(B,bool),bool),A),big_co1399186613setsum(fun(B,bool),A),hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),D)),C) = hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),D),hAPP(fun(fun(B,bool),bool),fun(B,bool),complete_Sup_Sup(fun(B,bool)),C)) # label(fact_4310_setsum__UNION__zero) # label(axiom).  [clausify(3649)].
39.39/39.30	Derived: -hBOOL(hAPP(fun(fun(A,bool),bool),bool,finite_finite_1(fun(A,bool)),B)) | hBOOL(hAPP(fun(fun(A,bool),bool),bool,hAPP(fun(A,bool),fun(fun(fun(A,bool),bool),bool),member(fun(A,bool)),f646(A,real,C,B)),B)) | hBOOL(hAPP(fun(fun(A,bool),bool),bool,hAPP(fun(A,bool),fun(fun(fun(A,bool),bool),bool),member(fun(A,bool)),f648(A,real,C,B)),B)) | hAPP(fun(fun(A,bool),bool),real,hAPP(fun(fun(A,bool),real),fun(fun(fun(A,bool),bool),real),big_co1399186613setsum(fun(A,bool),real),hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),C)),B) = hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),C),hAPP(fun(fun(A,bool),bool),fun(A,bool),complete_Sup_Sup(fun(A,bool)),B)).  [resolve(5602,a,5513,a)].
39.39/39.30	Derived: -hBOOL(hAPP(fun(fun(A,bool),bool),bool,finite_finite_1(fun(A,bool)),B)) | hBOOL(hAPP(fun(fun(A,bool),bool),bool,hAPP(fun(A,bool),fun(fun(fun(A,bool),bool),bool),member(fun(A,bool)),f646(A,int,C,B)),B)) | hBOOL(hAPP(fun(fun(A,bool),bool),bool,hAPP(fun(A,bool),fun(fun(fun(A,bool),bool),bool),member(fun(A,bool)),f648(A,int,C,B)),B)) | hAPP(fun(fun(A,bool),bool),int,hAPP(fun(fun(A,bool),int),fun(fun(fun(A,bool),bool),int),big_co1399186613setsum(fun(A,bool),int),hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),C)),B) = hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),C),hAPP(fun(fun(A,bool),bool),fun(A,bool),complete_Sup_Sup(fun(A,bool)),B)).  [resolve(5602,a,5524,a)].
39.39/39.30	Derived: -hBOOL(hAPP(fun(fun(A,bool),bool),bool,finite_finite_1(fun(A,bool)),B)) | hBOOL(hAPP(fun(fun(A,bool),bool),bool,hAPP(fun(A,bool),fun(fun(fun(A,bool),bool),bool),member(fun(A,bool)),f646(A,code_code_numeral,C,B)),B)) | hBOOL(hAPP(fun(fun(A,bool),bool),bool,hAPP(fun(A,bool),fun(fun(fun(A,bool),bool),bool),member(fun(A,bool)),f648(A,code_code_numeral,C,B)),B)) | hAPP(fun(fun(A,bool),bool),code_code_numeral,hAPP(fun(fun(A,bool),code_code_numeral),fun(fun(fun(A,bool),bool),code_code_numeral),big_co1399186613setsum(fun(A,bool),code_code_numeral),hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),C)),B) = hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),C),hAPP(fun(fun(A,bool),bool),fun(A,bool),complete_Sup_Sup(fun(A,bool)),B)).  [resolve(5602,a,5539,a)].
39.39/39.31	Derived: -hBOOL(hAPP(fun(fun(A,bool),bool),bool,finite_finite_1(fun(A,bool)),B)) | hBOOL(hAPP(fun(fun(A,bool),bool),bool,hAPP(fun(A,bool),fun(fun(fun(A,bool),bool),bool),member(fun(A,bool)),f646(A,rat,C,B)),B)) | hBOOL(hAPP(fun(fun(A,bool),bool),bool,hAPP(fun(A,bool),fun(fun(fun(A,bool),bool),bool),member(fun(A,bool)),f648(A,rat,C,B)),B)) | hAPP(fun(fun(A,bool),bool),rat,hAPP(fun(fun(A,bool),rat),fun(fun(fun(A,bool),bool),rat),big_co1399186613setsum(fun(A,bool),rat),hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),C)),B) = hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),C),hAPP(fun(fun(A,bool),bool),fun(A,bool),complete_Sup_Sup(fun(A,bool)),B)).  [resolve(5602,a,5561,a)].
39.39/39.31	5603 -comm_monoid_add(A) | -hBOOL(hAPP(fun(fun(B,bool),bool),bool,finite_finite_1(fun(B,bool)),C)) | hBOOL(hAPP(fun(fun(B,bool),bool),bool,hAPP(fun(B,bool),fun(fun(fun(B,bool),bool),bool),member(fun(B,bool)),f646(B,A,D,C)),C)) | ti(fun(B,bool),f648(B,A,D,C)) != ti(fun(B,bool),f647(B,A,D,C)) | hAPP(fun(fun(B,bool),bool),A,hAPP(fun(fun(B,bool),A),fun(fun(fun(B,bool),bool),A),big_co1399186613setsum(fun(B,bool),A),hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),D)),C) = hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),D),hAPP(fun(fun(B,bool),bool),fun(B,bool),complete_Sup_Sup(fun(B,bool)),C)) # label(fact_4310_setsum__UNION__zero) # label(axiom).  [clausify(3649)].
39.39/39.31	Derived: -hBOOL(hAPP(fun(fun(A,bool),bool),bool,finite_finite_1(fun(A,bool)),B)) | hBOOL(hAPP(fun(fun(A,bool),bool),bool,hAPP(fun(A,bool),fun(fun(fun(A,bool),bool),bool),member(fun(A,bool)),f646(A,real,C,B)),B)) | ti(fun(A,bool),f648(A,real,C,B)) != ti(fun(A,bool),f647(A,real,C,B)) | hAPP(fun(fun(A,bool),bool),real,hAPP(fun(fun(A,bool),real),fun(fun(fun(A,bool),bool),real),big_co1399186613setsum(fun(A,bool),real),hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),C)),B) = hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),C),hAPP(fun(fun(A,bool),bool),fun(A,bool),complete_Sup_Sup(fun(A,bool)),B)).  [resolve(5603,a,5513,a)].
39.39/39.31	Derived: -hBOOL(hAPP(fun(fun(A,bool),bool),bool,finite_finite_1(fun(A,bool)),B)) | hBOOL(hAPP(fun(fun(A,bool),bool),bool,hAPP(fun(A,bool),fun(fun(fun(A,bool),bool),bool),member(fun(A,bool)),f646(A,int,C,B)),B)) | ti(fun(A,bool),f648(A,int,C,B)) != ti(fun(A,bool),f647(A,int,C,B)) | hAPP(fun(fun(A,bool),bool),int,hAPP(fun(fun(A,bool),int),fun(fun(fun(A,bool),bool),int),big_co1399186613setsum(fun(A,bool),int),hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),C)),B) = hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),C),hAPP(fun(fun(A,bool),bool),fun(A,bool),complete_Sup_Sup(fun(A,bool)),B)).  [resolve(5603,a,5524,a)].
39.39/39.31	Derived: -hBOOL(hAPP(fun(fun(A,bool),bool),bool,finite_finite_1(fun(A,bool)),B)) | hBOOL(hAPP(fun(fun(A,bool),bool),bool,hAPP(fun(A,bool),fun(fun(fun(A,bool),bool),bool),member(fun(A,bool)),f646(A,code_code_numeral,C,B)),B)) | ti(fun(A,bool),f648(A,code_code_numeral,C,B)) != ti(fun(A,bool),f647(A,code_code_numeral,C,B)) | hAPP(fun(fun(A,bool),bool),code_code_numeral,hAPP(fun(fun(A,bool),code_code_numeral),fun(fun(fun(A,bool),bool),code_code_numeral),big_co1399186613setsum(fun(A,bool),code_code_numeral),hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),C)),B) = hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),C),hAPP(fun(fun(A,bool),bool),fun(A,bool),complete_Sup_Sup(fun(A,bool)),B)).  [resolve(5603,a,5539,a)].
39.39/39.31	Derived: -hBOOL(hAPP(fun(fun(A,bool),bool),bool,finite_finite_1(fun(A,bool)),B)) | hBOOL(hAPP(fun(fun(A,bool),bool),bool,hAPP(fun(A,bool),fun(fun(fun(A,bool),bool),bool),member(fun(A,bool)),f646(A,rat,C,B)),B)) | ti(fun(A,bool),f648(A,rat,C,B)) != ti(fun(A,bool),f647(A,rat,C,B)) | hAPP(fun(fun(A,bool),bool),rat,hAPP(fun(fun(A,bool),rat),fun(fun(fun(A,bool),bool),rat),big_co1399186613setsum(fun(A,bool),rat),hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),C)),B) = hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),C),hAPP(fun(fun(A,bool),bool),fun(A,bool),complete_Sup_Sup(fun(A,bool)),B)).  [resolve(5603,a,5561,a)].
39.39/39.31	5604 -comm_monoid_add(A) | -hBOOL(hAPP(fun(fun(B,bool),bool),bool,finite_finite_1(fun(B,bool)),C)) | hBOOL(hAPP(fun(fun(B,bool),bool),bool,hAPP(fun(B,bool),fun(fun(fun(B,bool),bool),bool),member(fun(B,bool)),f646(B,A,D,C)),C)) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f649(B,A,D,C)),f647(B,A,D,C))) | hAPP(fun(fun(B,bool),bool),A,hAPP(fun(fun(B,bool),A),fun(fun(fun(B,bool),bool),A),big_co1399186613setsum(fun(B,bool),A),hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),D)),C) = hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),D),hAPP(fun(fun(B,bool),bool),fun(B,bool),complete_Sup_Sup(fun(B,bool)),C)) # label(fact_4310_setsum__UNION__zero) # label(axiom).  [clausify(3649)].
39.39/39.31	Derived: -hBOOL(hAPP(fun(fun(A,bool),bool),bool,finite_finite_1(fun(A,bool)),B)) | hBOOL(hAPP(fun(fun(A,bool),bool),bool,hAPP(fun(A,bool),fun(fun(fun(A,bool),bool),bool),member(fun(A,bool)),f646(A,real,C,B)),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f649(A,real,C,B)),f647(A,real,C,B))) | hAPP(fun(fun(A,bool),bool),real,hAPP(fun(fun(A,bool),real),fun(fun(fun(A,bool),bool),real),big_co1399186613setsum(fun(A,bool),real),hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),C)),B) = hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),C),hAPP(fun(fun(A,bool),bool),fun(A,bool),complete_Sup_Sup(fun(A,bool)),B)).  [resolve(5604,a,5513,a)].
39.39/39.31	Derived: -hBOOL(hAPP(fun(fun(A,bool),bool),bool,finite_finite_1(fun(A,bool)),B)) | hBOOL(hAPP(fun(fun(A,bool),bool),bool,hAPP(fun(A,bool),fun(fun(fun(A,bool),bool),bool),member(fun(A,bool)),f646(A,int,C,B)),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f649(A,int,C,B)),f647(A,int,C,B))) | hAPP(fun(fun(A,bool),bool),int,hAPP(fun(fun(A,bool),int),fun(fun(fun(A,bool),bool),int),big_co1399186613setsum(fun(A,bool),int),hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),C)),B) = hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),C),hAPP(fun(fun(A,bool),bool),fun(A,bool),complete_Sup_Sup(fun(A,bool)),B)).  [resolve(5604,a,5524,a)].
39.39/39.31	Derived: -hBOOL(hAPP(fun(fun(A,bool),bool),bool,finite_finite_1(fun(A,bool)),B)) | hBOOL(hAPP(fun(fun(A,bool),bool),bool,hAPP(fun(A,bool),fun(fun(fun(A,bool),bool),bool),member(fun(A,bool)),f646(A,code_code_numeral,C,B)),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f649(A,code_code_numeral,C,B)),f647(A,code_code_numeral,C,B))) | hAPP(fun(fun(A,bool),bool),code_code_numeral,hAPP(fun(fun(A,bool),code_code_numeral),fun(fun(fun(A,bool),bool),code_code_numeral),big_co1399186613setsum(fun(A,bool),code_code_numeral),hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),C)),B) = hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),C),hAPP(fun(fun(A,bool),bool),fun(A,bool),complete_Sup_Sup(fun(A,bool)),B)).  [resolve(5604,a,5539,a)].
39.39/39.31	Derived: -hBOOL(hAPP(fun(fun(A,bool),bool),bool,finite_finite_1(fun(A,bool)),B)) | hBOOL(hAPP(fun(fun(A,bool),bool),bool,hAPP(fun(A,bool),fun(fun(fun(A,bool),bool),bool),member(fun(A,bool)),f646(A,rat,C,B)),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f649(A,rat,C,B)),f647(A,rat,C,B))) | hAPP(fun(fun(A,bool),bool),rat,hAPP(fun(fun(A,bool),rat),fun(fun(fun(A,bool),bool),rat),big_co1399186613setsum(fun(A,bool),rat),hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),C)),B) = hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),C),hAPP(fun(fun(A,bool),bool),fun(A,bool),complete_Sup_Sup(fun(A,bool)),B)).  [resolve(5604,a,5561,a)].
39.46/39.31	5605 -comm_monoid_add(A) | -hBOOL(hAPP(fun(fun(B,bool),bool),bool,finite_finite_1(fun(B,bool)),C)) | hBOOL(hAPP(fun(fun(B,bool),bool),bool,hAPP(fun(B,bool),fun(fun(fun(B,bool),bool),bool),member(fun(B,bool)),f646(B,A,D,C)),C)) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f649(B,A,D,C)),f648(B,A,D,C))) | hAPP(fun(fun(B,bool),bool),A,hAPP(fun(fun(B,bool),A),fun(fun(fun(B,bool),bool),A),big_co1399186613setsum(fun(B,bool),A),hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),D)),C) = hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),D),hAPP(fun(fun(B,bool),bool),fun(B,bool),complete_Sup_Sup(fun(B,bool)),C)) # label(fact_4310_setsum__UNION__zero) # label(axiom).  [clausify(3649)].
39.46/39.31	Derived: -hBOOL(hAPP(fun(fun(A,bool),bool),bool,finite_finite_1(fun(A,bool)),B)) | hBOOL(hAPP(fun(fun(A,bool),bool),bool,hAPP(fun(A,bool),fun(fun(fun(A,bool),bool),bool),member(fun(A,bool)),f646(A,real,C,B)),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f649(A,real,C,B)),f648(A,real,C,B))) | hAPP(fun(fun(A,bool),bool),real,hAPP(fun(fun(A,bool),real),fun(fun(fun(A,bool),bool),real),big_co1399186613setsum(fun(A,bool),real),hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),C)),B) = hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),C),hAPP(fun(fun(A,bool),bool),fun(A,bool),complete_Sup_Sup(fun(A,bool)),B)).  [resolve(5605,a,5513,a)].
39.46/39.31	Derived: -hBOOL(hAPP(fun(fun(A,bool),bool),bool,finite_finite_1(fun(A,bool)),B)) | hBOOL(hAPP(fun(fun(A,bool),bool),bool,hAPP(fun(A,bool),fun(fun(fun(A,bool),bool),bool),member(fun(A,bool)),f646(A,int,C,B)),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f649(A,int,C,B)),f648(A,int,C,B))) | hAPP(fun(fun(A,bool),bool),int,hAPP(fun(fun(A,bool),int),fun(fun(fun(A,bool),bool),int),big_co1399186613setsum(fun(A,bool),int),hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),C)),B) = hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),C),hAPP(fun(fun(A,bool),bool),fun(A,bool),complete_Sup_Sup(fun(A,bool)),B)).  [resolve(5605,a,5524,a)].
39.46/39.31	Derived: -hBOOL(hAPP(fun(fun(A,bool),bool),bool,finite_finite_1(fun(A,bool)),B)) | hBOOL(hAPP(fun(fun(A,bool),bool),bool,hAPP(fun(A,bool),fun(fun(fun(A,bool),bool),bool),member(fun(A,bool)),f646(A,code_code_numeral,C,B)),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f649(A,code_code_numeral,C,B)),f648(A,code_code_numeral,C,B))) | hAPP(fun(fun(A,bool),bool),code_code_numeral,hAPP(fun(fun(A,bool),code_code_numeral),fun(fun(fun(A,bool),bool),code_code_numeral),big_co1399186613setsum(fun(A,bool),code_code_numeral),hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),C)),B) = hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),C),hAPP(fun(fun(A,bool),bool),fun(A,bool),complete_Sup_Sup(fun(A,bool)),B)).  [resolve(5605,a,5539,a)].
39.46/39.31	Derived: -hBOOL(hAPP(fun(fun(A,bool),bool),bool,finite_finite_1(fun(A,bool)),B)) | hBOOL(hAPP(fun(fun(A,bool),bool),bool,hAPP(fun(A,bool),fun(fun(fun(A,bool),bool),bool),member(fun(A,bool)),f646(A,rat,C,B)),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f649(A,rat,C,B)),f648(A,rat,C,B))) | hAPP(fun(fun(A,bool),bool),rat,hAPP(fun(fun(A,bool),rat),fun(fun(fun(A,bool),bool),rat),big_co1399186613setsum(fun(A,bool),rat),hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),C)),B) = hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),C),hAPP(fun(fun(A,bool),bool),fun(A,bool),complete_Sup_Sup(fun(A,bool)),B)).  [resolve(5605,a,5561,a)].
39.46/39.31	5606 -comm_monoid_add(A) | -hBOOL(hAPP(fun(fun(B,bool),bool),bool,finite_finite_1(fun(B,bool)),C)) | hBOOL(hAPP(fun(fun(B,bool),bool),bool,hAPP(fun(B,bool),fun(fun(fun(B,bool),bool),bool),member(fun(B,bool)),f646(B,A,D,C)),C)) | zero_zero(A) != hAPP(B,A,D,f649(B,A,D,C)) | hAPP(fun(fun(B,bool),bool),A,hAPP(fun(fun(B,bool),A),fun(fun(fun(B,bool),bool),A),big_co1399186613setsum(fun(B,bool),A),hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),D)),C) = hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),D),hAPP(fun(fun(B,bool),bool),fun(B,bool),complete_Sup_Sup(fun(B,bool)),C)) # label(fact_4310_setsum__UNION__zero) # label(axiom).  [clausify(3649)].
39.46/39.32	Derived: -hBOOL(hAPP(fun(fun(A,bool),bool),bool,finite_finite_1(fun(A,bool)),B)) | hBOOL(hAPP(fun(fun(A,bool),bool),bool,hAPP(fun(A,bool),fun(fun(fun(A,bool),bool),bool),member(fun(A,bool)),f646(A,real,C,B)),B)) | zero_zero(real) != hAPP(A,real,C,f649(A,real,C,B)) | hAPP(fun(fun(A,bool),bool),real,hAPP(fun(fun(A,bool),real),fun(fun(fun(A,bool),bool),real),big_co1399186613setsum(fun(A,bool),real),hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),C)),B) = hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),C),hAPP(fun(fun(A,bool),bool),fun(A,bool),complete_Sup_Sup(fun(A,bool)),B)).  [resolve(5606,a,5513,a)].
39.46/39.32	Derived: -hBOOL(hAPP(fun(fun(A,bool),bool),bool,finite_finite_1(fun(A,bool)),B)) | hBOOL(hAPP(fun(fun(A,bool),bool),bool,hAPP(fun(A,bool),fun(fun(fun(A,bool),bool),bool),member(fun(A,bool)),f646(A,int,C,B)),B)) | zero_zero(int) != hAPP(A,int,C,f649(A,int,C,B)) | hAPP(fun(fun(A,bool),bool),int,hAPP(fun(fun(A,bool),int),fun(fun(fun(A,bool),bool),int),big_co1399186613setsum(fun(A,bool),int),hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),C)),B) = hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),C),hAPP(fun(fun(A,bool),bool),fun(A,bool),complete_Sup_Sup(fun(A,bool)),B)).  [resolve(5606,a,5524,a)].
39.46/39.32	Derived: -hBOOL(hAPP(fun(fun(A,bool),bool),bool,finite_finite_1(fun(A,bool)),B)) | hBOOL(hAPP(fun(fun(A,bool),bool),bool,hAPP(fun(A,bool),fun(fun(fun(A,bool),bool),bool),member(fun(A,bool)),f646(A,code_code_numeral,C,B)),B)) | zero_zero(code_code_numeral) != hAPP(A,code_code_numeral,C,f649(A,code_code_numeral,C,B)) | hAPP(fun(fun(A,bool),bool),code_code_numeral,hAPP(fun(fun(A,bool),code_code_numeral),fun(fun(fun(A,bool),bool),code_code_numeral),big_co1399186613setsum(fun(A,bool),code_code_numeral),hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),C)),B) = hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),C),hAPP(fun(fun(A,bool),bool),fun(A,bool),complete_Sup_Sup(fun(A,bool)),B)).  [resolve(5606,a,5539,a)].
39.46/39.32	Derived: -hBOOL(hAPP(fun(fun(A,bool),bool),bool,finite_finite_1(fun(A,bool)),B)) | hBOOL(hAPP(fun(fun(A,bool),bool),bool,hAPP(fun(A,bool),fun(fun(fun(A,bool),bool),bool),member(fun(A,bool)),f646(A,rat,C,B)),B)) | zero_zero(rat) != hAPP(A,rat,C,f649(A,rat,C,B)) | hAPP(fun(fun(A,bool),bool),rat,hAPP(fun(fun(A,bool),rat),fun(fun(fun(A,bool),bool),rat),big_co1399186613setsum(fun(A,bool),rat),hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),C)),B) = hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),C),hAPP(fun(fun(A,bool),bool),fun(A,bool),complete_Sup_Sup(fun(A,bool)),B)).  [resolve(5606,a,5561,a)].
39.46/39.32	5607 -comm_monoid_add(A) | -hBOOL(hAPP(fun(fun(B,bool),bool),bool,finite_finite_1(fun(B,bool)),C)) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),f646(B,A,D,C))) | hBOOL(hAPP(fun(fun(B,bool),bool),bool,hAPP(fun(B,bool),fun(fun(fun(B,bool),bool),bool),member(fun(B,bool)),f647(B,A,D,C)),C)) | hAPP(fun(fun(B,bool),bool),A,hAPP(fun(fun(B,bool),A),fun(fun(fun(B,bool),bool),A),big_co1399186613setsum(fun(B,bool),A),hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),D)),C) = hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),D),hAPP(fun(fun(B,bool),bool),fun(B,bool),complete_Sup_Sup(fun(B,bool)),C)) # label(fact_4310_setsum__UNION__zero) # label(axiom).  [clausify(3649)].
39.46/39.32	Derived: -hBOOL(hAPP(fun(fun(A,bool),bool),bool,finite_finite_1(fun(A,bool)),B)) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),f646(A,real,C,B))) | hBOOL(hAPP(fun(fun(A,bool),bool),bool,hAPP(fun(A,bool),fun(fun(fun(A,bool),bool),bool),member(fun(A,bool)),f647(A,real,C,B)),B)) | hAPP(fun(fun(A,bool),bool),real,hAPP(fun(fun(A,bool),real),fun(fun(fun(A,bool),bool),real),big_co1399186613setsum(fun(A,bool),real),hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),C)),B) = hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),C),hAPP(fun(fun(A,bool),bool),fun(A,bool),complete_Sup_Sup(fun(A,bool)),B)).  [resolve(5607,a,5513,a)].
39.46/39.32	Derived: -hBOOL(hAPP(fun(fun(A,bool),bool),bool,finite_finite_1(fun(A,bool)),B)) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),f646(A,int,C,B))) | hBOOL(hAPP(fun(fun(A,bool),bool),bool,hAPP(fun(A,bool),fun(fun(fun(A,bool),bool),bool),member(fun(A,bool)),f647(A,int,C,B)),B)) | hAPP(fun(fun(A,bool),bool),int,hAPP(fun(fun(A,bool),int),fun(fun(fun(A,bool),bool),int),big_co1399186613setsum(fun(A,bool),int),hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),C)),B) = hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),C),hAPP(fun(fun(A,bool),bool),fun(A,bool),complete_Sup_Sup(fun(A,bool)),B)).  [resolve(5607,a,5524,a)].
39.46/39.32	Derived: -hBOOL(hAPP(fun(fun(A,bool),bool),bool,finite_finite_1(fun(A,bool)),B)) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),f646(A,code_code_numeral,C,B))) | hBOOL(hAPP(fun(fun(A,bool),bool),bool,hAPP(fun(A,bool),fun(fun(fun(A,bool),bool),bool),member(fun(A,bool)),f647(A,code_code_numeral,C,B)),B)) | hAPP(fun(fun(A,bool),bool),code_code_numeral,hAPP(fun(fun(A,bool),code_code_numeral),fun(fun(fun(A,bool),bool),code_code_numeral),big_co1399186613setsum(fun(A,bool),code_code_numeral),hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),C)),B) = hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),C),hAPP(fun(fun(A,bool),bool),fun(A,bool),complete_Sup_Sup(fun(A,bool)),B)).  [resolve(5607,a,5539,a)].
39.46/39.32	Derived: -hBOOL(hAPP(fun(fun(A,bool),bool),bool,finite_finite_1(fun(A,bool)),B)) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),f646(A,rat,C,B))) | hBOOL(hAPP(fun(fun(A,bool),bool),bool,hAPP(fun(A,bool),fun(fun(fun(A,bool),bool),bool),member(fun(A,bool)),f647(A,rat,C,B)),B)) | hAPP(fun(fun(A,bool),bool),rat,hAPP(fun(fun(A,bool),rat),fun(fun(fun(A,bool),bool),rat),big_co1399186613setsum(fun(A,bool),rat),hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),C)),B) = hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),C),hAPP(fun(fun(A,bool),bool),fun(A,bool),complete_Sup_Sup(fun(A,bool)),B)).  [resolve(5607,a,5561,a)].
39.46/39.32	5608 -comm_monoid_add(A) | -hBOOL(hAPP(fun(fun(B,bool),bool),bool,finite_finite_1(fun(B,bool)),C)) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),f646(B,A,D,C))) | hBOOL(hAPP(fun(fun(B,bool),bool),bool,hAPP(fun(B,bool),fun(fun(fun(B,bool),bool),bool),member(fun(B,bool)),f648(B,A,D,C)),C)) | hAPP(fun(fun(B,bool),bool),A,hAPP(fun(fun(B,bool),A),fun(fun(fun(B,bool),bool),A),big_co1399186613setsum(fun(B,bool),A),hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),D)),C) = hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),D),hAPP(fun(fun(B,bool),bool),fun(B,bool),complete_Sup_Sup(fun(B,bool)),C)) # label(fact_4310_setsum__UNION__zero) # label(axiom).  [clausify(3649)].
39.46/39.32	Derived: -hBOOL(hAPP(fun(fun(A,bool),bool),bool,finite_finite_1(fun(A,bool)),B)) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),f646(A,real,C,B))) | hBOOL(hAPP(fun(fun(A,bool),bool),bool,hAPP(fun(A,bool),fun(fun(fun(A,bool),bool),bool),member(fun(A,bool)),f648(A,real,C,B)),B)) | hAPP(fun(fun(A,bool),bool),real,hAPP(fun(fun(A,bool),real),fun(fun(fun(A,bool),bool),real),big_co1399186613setsum(fun(A,bool),real),hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),C)),B) = hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),C),hAPP(fun(fun(A,bool),bool),fun(A,bool),complete_Sup_Sup(fun(A,bool)),B)).  [resolve(5608,a,5513,a)].
39.46/39.33	Derived: -hBOOL(hAPP(fun(fun(A,bool),bool),bool,finite_finite_1(fun(A,bool)),B)) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),f646(A,int,C,B))) | hBOOL(hAPP(fun(fun(A,bool),bool),bool,hAPP(fun(A,bool),fun(fun(fun(A,bool),bool),bool),member(fun(A,bool)),f648(A,int,C,B)),B)) | hAPP(fun(fun(A,bool),bool),int,hAPP(fun(fun(A,bool),int),fun(fun(fun(A,bool),bool),int),big_co1399186613setsum(fun(A,bool),int),hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),C)),B) = hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),C),hAPP(fun(fun(A,bool),bool),fun(A,bool),complete_Sup_Sup(fun(A,bool)),B)).  [resolve(5608,a,5524,a)].
39.46/39.33	Derived: -hBOOL(hAPP(fun(fun(A,bool),bool),bool,finite_finite_1(fun(A,bool)),B)) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),f646(A,code_code_numeral,C,B))) | hBOOL(hAPP(fun(fun(A,bool),bool),bool,hAPP(fun(A,bool),fun(fun(fun(A,bool),bool),bool),member(fun(A,bool)),f648(A,code_code_numeral,C,B)),B)) | hAPP(fun(fun(A,bool),bool),code_code_numeral,hAPP(fun(fun(A,bool),code_code_numeral),fun(fun(fun(A,bool),bool),code_code_numeral),big_co1399186613setsum(fun(A,bool),code_code_numeral),hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),C)),B) = hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),C),hAPP(fun(fun(A,bool),bool),fun(A,bool),complete_Sup_Sup(fun(A,bool)),B)).  [resolve(5608,a,5539,a)].
39.46/39.33	Derived: -hBOOL(hAPP(fun(fun(A,bool),bool),bool,finite_finite_1(fun(A,bool)),B)) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),f646(A,rat,C,B))) | hBOOL(hAPP(fun(fun(A,bool),bool),bool,hAPP(fun(A,bool),fun(fun(fun(A,bool),bool),bool),member(fun(A,bool)),f648(A,rat,C,B)),B)) | hAPP(fun(fun(A,bool),bool),rat,hAPP(fun(fun(A,bool),rat),fun(fun(fun(A,bool),bool),rat),big_co1399186613setsum(fun(A,bool),rat),hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),C)),B) = hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),C),hAPP(fun(fun(A,bool),bool),fun(A,bool),complete_Sup_Sup(fun(A,bool)),B)).  [resolve(5608,a,5561,a)].
39.46/39.33	5609 -comm_monoid_add(A) | -hBOOL(hAPP(fun(fun(B,bool),bool),bool,finite_finite_1(fun(B,bool)),C)) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),f646(B,A,D,C))) | ti(fun(B,bool),f648(B,A,D,C)) != ti(fun(B,bool),f647(B,A,D,C)) | hAPP(fun(fun(B,bool),bool),A,hAPP(fun(fun(B,bool),A),fun(fun(fun(B,bool),bool),A),big_co1399186613setsum(fun(B,bool),A),hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),D)),C) = hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),D),hAPP(fun(fun(B,bool),bool),fun(B,bool),complete_Sup_Sup(fun(B,bool)),C)) # label(fact_4310_setsum__UNION__zero) # label(axiom).  [clausify(3649)].
39.46/39.33	Derived: -hBOOL(hAPP(fun(fun(A,bool),bool),bool,finite_finite_1(fun(A,bool)),B)) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),f646(A,real,C,B))) | ti(fun(A,bool),f648(A,real,C,B)) != ti(fun(A,bool),f647(A,real,C,B)) | hAPP(fun(fun(A,bool),bool),real,hAPP(fun(fun(A,bool),real),fun(fun(fun(A,bool),bool),real),big_co1399186613setsum(fun(A,bool),real),hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),C)),B) = hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),C),hAPP(fun(fun(A,bool),bool),fun(A,bool),complete_Sup_Sup(fun(A,bool)),B)).  [resolve(5609,a,5513,a)].
39.46/39.33	Derived: -hBOOL(hAPP(fun(fun(A,bool),bool),bool,finite_finite_1(fun(A,bool)),B)) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),f646(A,int,C,B))) | ti(fun(A,bool),f648(A,int,C,B)) != ti(fun(A,bool),f647(A,int,C,B)) | hAPP(fun(fun(A,bool),bool),int,hAPP(fun(fun(A,bool),int),fun(fun(fun(A,bool),bool),int),big_co1399186613setsum(fun(A,bool),int),hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),C)),B) = hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),C),hAPP(fun(fun(A,bool),bool),fun(A,bool),complete_Sup_Sup(fun(A,bool)),B)).  [resolve(5609,a,5524,a)].
39.46/39.33	Derived: -hBOOL(hAPP(fun(fun(A,bool),bool),bool,finite_finite_1(fun(A,bool)),B)) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),f646(A,code_code_numeral,C,B))) | ti(fun(A,bool),f648(A,code_code_numeral,C,B)) != ti(fun(A,bool),f647(A,code_code_numeral,C,B)) | hAPP(fun(fun(A,bool),bool),code_code_numeral,hAPP(fun(fun(A,bool),code_code_numeral),fun(fun(fun(A,bool),bool),code_code_numeral),big_co1399186613setsum(fun(A,bool),code_code_numeral),hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),C)),B) = hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),C),hAPP(fun(fun(A,bool),bool),fun(A,bool),complete_Sup_Sup(fun(A,bool)),B)).  [resolve(5609,a,5539,a)].
39.46/39.33	Derived: -hBOOL(hAPP(fun(fun(A,bool),bool),bool,finite_finite_1(fun(A,bool)),B)) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),f646(A,rat,C,B))) | ti(fun(A,bool),f648(A,rat,C,B)) != ti(fun(A,bool),f647(A,rat,C,B)) | hAPP(fun(fun(A,bool),bool),rat,hAPP(fun(fun(A,bool),rat),fun(fun(fun(A,bool),bool),rat),big_co1399186613setsum(fun(A,bool),rat),hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),C)),B) = hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),C),hAPP(fun(fun(A,bool),bool),fun(A,bool),complete_Sup_Sup(fun(A,bool)),B)).  [resolve(5609,a,5561,a)].
39.46/39.33	5610 -comm_monoid_add(A) | -hBOOL(hAPP(fun(fun(B,bool),bool),bool,finite_finite_1(fun(B,bool)),C)) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),f646(B,A,D,C))) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f649(B,A,D,C)),f647(B,A,D,C))) | hAPP(fun(fun(B,bool),bool),A,hAPP(fun(fun(B,bool),A),fun(fun(fun(B,bool),bool),A),big_co1399186613setsum(fun(B,bool),A),hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),D)),C) = hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),D),hAPP(fun(fun(B,bool),bool),fun(B,bool),complete_Sup_Sup(fun(B,bool)),C)) # label(fact_4310_setsum__UNION__zero) # label(axiom).  [clausify(3649)].
39.46/39.33	Derived: -hBOOL(hAPP(fun(fun(A,bool),bool),bool,finite_finite_1(fun(A,bool)),B)) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),f646(A,real,C,B))) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f649(A,real,C,B)),f647(A,real,C,B))) | hAPP(fun(fun(A,bool),bool),real,hAPP(fun(fun(A,bool),real),fun(fun(fun(A,bool),bool),real),big_co1399186613setsum(fun(A,bool),real),hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),C)),B) = hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),C),hAPP(fun(fun(A,bool),bool),fun(A,bool),complete_Sup_Sup(fun(A,bool)),B)).  [resolve(5610,a,5513,a)].
39.46/39.33	Derived: -hBOOL(hAPP(fun(fun(A,bool),bool),bool,finite_finite_1(fun(A,bool)),B)) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),f646(A,int,C,B))) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f649(A,int,C,B)),f647(A,int,C,B))) | hAPP(fun(fun(A,bool),bool),int,hAPP(fun(fun(A,bool),int),fun(fun(fun(A,bool),bool),int),big_co1399186613setsum(fun(A,bool),int),hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),C)),B) = hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),C),hAPP(fun(fun(A,bool),bool),fun(A,bool),complete_Sup_Sup(fun(A,bool)),B)).  [resolve(5610,a,5524,a)].
39.46/39.33	Derived: -hBOOL(hAPP(fun(fun(A,bool),bool),bool,finite_finite_1(fun(A,bool)),B)) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),f646(A,code_code_numeral,C,B))) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f649(A,code_code_numeral,C,B)),f647(A,code_code_numeral,C,B))) | hAPP(fun(fun(A,bool),bool),code_code_numeral,hAPP(fun(fun(A,bool),code_code_numeral),fun(fun(fun(A,bool),bool),code_code_numeral),big_co1399186613setsum(fun(A,bool),code_code_numeral),hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),C)),B) = hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),C),hAPP(fun(fun(A,bool),bool),fun(A,bool),complete_Sup_Sup(fun(A,bool)),B)).  [resolve(5610,a,5539,a)].
39.46/39.34	Derived: -hBOOL(hAPP(fun(fun(A,bool),bool),bool,finite_finite_1(fun(A,bool)),B)) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),f646(A,rat,C,B))) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f649(A,rat,C,B)),f647(A,rat,C,B))) | hAPP(fun(fun(A,bool),bool),rat,hAPP(fun(fun(A,bool),rat),fun(fun(fun(A,bool),bool),rat),big_co1399186613setsum(fun(A,bool),rat),hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),C)),B) = hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),C),hAPP(fun(fun(A,bool),bool),fun(A,bool),complete_Sup_Sup(fun(A,bool)),B)).  [resolve(5610,a,5561,a)].
39.46/39.34	5611 -comm_monoid_add(A) | -hBOOL(hAPP(fun(fun(B,bool),bool),bool,finite_finite_1(fun(B,bool)),C)) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),f646(B,A,D,C))) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f649(B,A,D,C)),f648(B,A,D,C))) | hAPP(fun(fun(B,bool),bool),A,hAPP(fun(fun(B,bool),A),fun(fun(fun(B,bool),bool),A),big_co1399186613setsum(fun(B,bool),A),hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),D)),C) = hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),D),hAPP(fun(fun(B,bool),bool),fun(B,bool),complete_Sup_Sup(fun(B,bool)),C)) # label(fact_4310_setsum__UNION__zero) # label(axiom).  [clausify(3649)].
39.46/39.34	Derived: -hBOOL(hAPP(fun(fun(A,bool),bool),bool,finite_finite_1(fun(A,bool)),B)) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),f646(A,real,C,B))) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f649(A,real,C,B)),f648(A,real,C,B))) | hAPP(fun(fun(A,bool),bool),real,hAPP(fun(fun(A,bool),real),fun(fun(fun(A,bool),bool),real),big_co1399186613setsum(fun(A,bool),real),hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),C)),B) = hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),C),hAPP(fun(fun(A,bool),bool),fun(A,bool),complete_Sup_Sup(fun(A,bool)),B)).  [resolve(5611,a,5513,a)].
39.46/39.34	Derived: -hBOOL(hAPP(fun(fun(A,bool),bool),bool,finite_finite_1(fun(A,bool)),B)) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),f646(A,int,C,B))) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f649(A,int,C,B)),f648(A,int,C,B))) | hAPP(fun(fun(A,bool),bool),int,hAPP(fun(fun(A,bool),int),fun(fun(fun(A,bool),bool),int),big_co1399186613setsum(fun(A,bool),int),hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),C)),B) = hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),C),hAPP(fun(fun(A,bool),bool),fun(A,bool),complete_Sup_Sup(fun(A,bool)),B)).  [resolve(5611,a,5524,a)].
39.46/39.34	Derived: -hBOOL(hAPP(fun(fun(A,bool),bool),bool,finite_finite_1(fun(A,bool)),B)) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),f646(A,code_code_numeral,C,B))) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f649(A,code_code_numeral,C,B)),f648(A,code_code_numeral,C,B))) | hAPP(fun(fun(A,bool),bool),code_code_numeral,hAPP(fun(fun(A,bool),code_code_numeral),fun(fun(fun(A,bool),bool),code_code_numeral),big_co1399186613setsum(fun(A,bool),code_code_numeral),hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),C)),B) = hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),C),hAPP(fun(fun(A,bool),bool),fun(A,bool),complete_Sup_Sup(fun(A,bool)),B)).  [resolve(5611,a,5539,a)].
39.46/39.34	Derived: -hBOOL(hAPP(fun(fun(A,bool),bool),bool,finite_finite_1(fun(A,bool)),B)) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),f646(A,rat,C,B))) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f649(A,rat,C,B)),f648(A,rat,C,B))) | hAPP(fun(fun(A,bool),bool),rat,hAPP(fun(fun(A,bool),rat),fun(fun(fun(A,bool),bool),rat),big_co1399186613setsum(fun(A,bool),rat),hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),C)),B) = hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),C),hAPP(fun(fun(A,bool),bool),fun(A,bool),complete_Sup_Sup(fun(A,bool)),B)).  [resolve(5611,a,5561,a)].
39.46/39.35	5612 -comm_monoid_add(A) | -hBOOL(hAPP(fun(fun(B,bool),bool),bool,finite_finite_1(fun(B,bool)),C)) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),f646(B,A,D,C))) | zero_zero(A) != hAPP(B,A,D,f649(B,A,D,C)) | hAPP(fun(fun(B,bool),bool),A,hAPP(fun(fun(B,bool),A),fun(fun(fun(B,bool),bool),A),big_co1399186613setsum(fun(B,bool),A),hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),D)),C) = hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),D),hAPP(fun(fun(B,bool),bool),fun(B,bool),complete_Sup_Sup(fun(B,bool)),C)) # label(fact_4310_setsum__UNION__zero) # label(axiom).  [clausify(3649)].
39.46/39.35	Derived: -hBOOL(hAPP(fun(fun(A,bool),bool),bool,finite_finite_1(fun(A,bool)),B)) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),f646(A,real,C,B))) | zero_zero(real) != hAPP(A,real,C,f649(A,real,C,B)) | hAPP(fun(fun(A,bool),bool),real,hAPP(fun(fun(A,bool),real),fun(fun(fun(A,bool),bool),real),big_co1399186613setsum(fun(A,bool),real),hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),C)),B) = hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),C),hAPP(fun(fun(A,bool),bool),fun(A,bool),complete_Sup_Sup(fun(A,bool)),B)).  [resolve(5612,a,5513,a)].
39.46/39.35	Derived: -hBOOL(hAPP(fun(fun(A,bool),bool),bool,finite_finite_1(fun(A,bool)),B)) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),f646(A,int,C,B))) | zero_zero(int) != hAPP(A,int,C,f649(A,int,C,B)) | hAPP(fun(fun(A,bool),bool),int,hAPP(fun(fun(A,bool),int),fun(fun(fun(A,bool),bool),int),big_co1399186613setsum(fun(A,bool),int),hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),C)),B) = hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),C),hAPP(fun(fun(A,bool),bool),fun(A,bool),complete_Sup_Sup(fun(A,bool)),B)).  [resolve(5612,a,5524,a)].
39.46/39.35	Derived: -hBOOL(hAPP(fun(fun(A,bool),bool),bool,finite_finite_1(fun(A,bool)),B)) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),f646(A,code_code_numeral,C,B))) | zero_zero(code_code_numeral) != hAPP(A,code_code_numeral,C,f649(A,code_code_numeral,C,B)) | hAPP(fun(fun(A,bool),bool),code_code_numeral,hAPP(fun(fun(A,bool),code_code_numeral),fun(fun(fun(A,bool),bool),code_code_numeral),big_co1399186613setsum(fun(A,bool),code_code_numeral),hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),C)),B) = hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),C),hAPP(fun(fun(A,bool),bool),fun(A,bool),complete_Sup_Sup(fun(A,bool)),B)).  [resolve(5612,a,5539,a)].
39.46/39.35	Derived: -hBOOL(hAPP(fun(fun(A,bool),bool),bool,finite_finite_1(fun(A,bool)),B)) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),f646(A,rat,C,B))) | zero_zero(rat) != hAPP(A,rat,C,f649(A,rat,C,B)) | hAPP(fun(fun(A,bool),bool),rat,hAPP(fun(fun(A,bool),rat),fun(fun(fun(A,bool),bool),rat),big_co1399186613setsum(fun(A,bool),rat),hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),C)),B) = hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),C),hAPP(fun(fun(A,bool),bool),fun(A,bool),complete_Sup_Sup(fun(A,bool)),B)).  [resolve(5612,a,5561,a)].
39.46/39.35	5613 -comm_monoid_add(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),hAPP(fun(B,A),fun(B,A),hAPP(fun(B,fun(A,A)),fun(fun(B,A),fun(B,A)),combs(B,A,A),hAPP(fun(B,A),fun(B,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(B,A),fun(B,fun(A,A))),combb(A,fun(A,A),B),plus_plus(A)),D)),E)),C) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),D),C)),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),E),C)) # label(fact_4219_setsum_Odistrib) # label(axiom).  [clausify(3666)].
39.51/39.41	5614 -ordere779506340up_add(A) | -comm_monoid_add(A) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f657(B,A,C,D,E)),E)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),C),E)),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),D),E))) # label(fact_4343_setsum__mono) # label(axiom).  [clausify(3744)].
39.51/39.41	Derived: -ordere779506340up_add(real) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f657(A,real,B,C,D)),D)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),B),D)),hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),C),D))).  [resolve(5614,b,5513,a)].
39.51/39.41	Derived: -ordere779506340up_add(int) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f657(A,int,B,C,D)),D)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),B),D)),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),C),D))).  [resolve(5614,b,5524,a)].
39.51/39.41	Derived: -ordere779506340up_add(code_code_numeral) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f657(A,code_code_numeral,B,C,D)),D)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),B),D)),hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),C),D))).  [resolve(5614,b,5539,a)].
39.51/39.41	Derived: -ordere779506340up_add(rat) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f657(A,rat,B,C,D)),D)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),B),D)),hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),C),D))).  [resolve(5614,b,5561,a)].
39.51/39.41	5615 -ordere779506340up_add(A) | -comm_monoid_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(B,A,C,f657(B,A,C,D,E))),hAPP(B,A,D,f657(B,A,C,D,E)))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),C),E)),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),D),E))) # label(fact_4343_setsum__mono) # label(axiom).  [clausify(3744)].
39.51/39.41	Derived: -ordere779506340up_add(real) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(A,real,B,f657(A,real,B,C,D))),hAPP(A,real,C,f657(A,real,B,C,D)))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),B),D)),hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),C),D))).  [resolve(5615,b,5513,a)].
39.51/39.41	Derived: -ordere779506340up_add(int) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(A,int,B,f657(A,int,B,C,D))),hAPP(A,int,C,f657(A,int,B,C,D)))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),B),D)),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),C),D))).  [resolve(5615,b,5524,a)].
39.51/39.41	Derived: -ordere779506340up_add(code_code_numeral) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),hAPP(A,code_code_numeral,B,f657(A,code_code_numeral,B,C,D))),hAPP(A,code_code_numeral,C,f657(A,code_code_numeral,B,C,D)))) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),B),D)),hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),C),D))).  [resolve(5615,b,5539,a)].
39.61/39.51	Derived: -ordere779506340up_add(rat) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(A,rat,B,f657(A,rat,B,C,D))),hAPP(A,rat,C,f657(A,rat,B,C,D)))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),B),D)),hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),C),D))).  [resolve(5615,b,5561,a)].
39.61/39.51	5616 -comm_monoid_add(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | hAPP(fun(D,bool),A,hAPP(fun(D,A),fun(fun(D,bool),A),big_co1399186613setsum(D,A),hAPP(fun(D,fun(B,bool)),fun(D,A),hAPP(fun(fun(B,bool),A),fun(fun(D,fun(B,bool)),fun(D,A)),combb(fun(B,bool),A,D),hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),E)),hAPP(fun(D,fun(B,bool)),fun(D,fun(B,bool)),hAPP(fun(fun(B,bool),fun(B,bool)),fun(fun(D,fun(B,bool)),fun(D,fun(B,bool))),combb(fun(B,bool),fun(B,bool),D),collect(B)),hAPP(fun(D,fun(B,bool)),fun(D,fun(B,bool)),hAPP(fun(fun(B,bool),fun(B,bool)),fun(fun(D,fun(B,bool)),fun(D,fun(B,bool))),combb(fun(B,bool),fun(B,bool),D),hAPP(fun(B,fun(bool,bool)),fun(fun(B,bool),fun(B,bool)),combs(B,bool,bool),hAPP(fun(B,bool),fun(B,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(B,bool),fun(B,fun(bool,bool))),combb(bool,fun(bool,bool),B),fconj),hAPP(fun(B,bool),fun(B,bool),hAPP(fun(B,fun(fun(B,bool),bool)),fun(fun(B,bool),fun(B,bool)),combc(B,fun(B,bool),bool),member(B)),C)))),hAPP(fun(B,fun(D,bool)),fun(D,fun(B,bool)),combc(B,D,bool),hAPP(fun(B,D),fun(B,fun(D,bool)),hAPP(fun(D,fun(D,bool)),fun(fun(B,D),fun(B,fun(D,bool))),combb(D,fun(D,bool),B),fequal(D)),F)))))),hAPP(fun(B,bool),fun(D,bool),hAPP(fun(B,D),fun(fun(B,bool),fun(D,bool)),image(B,D),F),C)) = hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),E),C) # label(fact_4224_setsum__image__gen) # label(axiom).  [clausify(3889)].
39.61/39.51	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(fun(C,bool),real,hAPP(fun(C,real),fun(fun(C,bool),real),big_co1399186613setsum(C,real),hAPP(fun(C,fun(A,bool)),fun(C,real),hAPP(fun(fun(A,bool),real),fun(fun(C,fun(A,bool)),fun(C,real)),combb(fun(A,bool),real,C),hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),D)),hAPP(fun(C,fun(A,bool)),fun(C,fun(A,bool)),hAPP(fun(fun(A,bool),fun(A,bool)),fun(fun(C,fun(A,bool)),fun(C,fun(A,bool))),combb(fun(A,bool),fun(A,bool),C),collect(A)),hAPP(fun(C,fun(A,bool)),fun(C,fun(A,bool)),hAPP(fun(fun(A,bool),fun(A,bool)),fun(fun(C,fun(A,bool)),fun(C,fun(A,bool))),combb(fun(A,bool),fun(A,bool),C),hAPP(fun(A,fun(bool,bool)),fun(fun(A,bool),fun(A,bool)),combs(A,bool,bool),hAPP(fun(A,bool),fun(A,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(A,bool),fun(A,fun(bool,bool))),combb(bool,fun(bool,bool),A),fconj),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,fun(fun(A,bool),bool)),fun(fun(A,bool),fun(A,bool)),combc(A,fun(A,bool),bool),member(A)),B)))),hAPP(fun(A,fun(C,bool)),fun(C,fun(A,bool)),combc(A,C,bool),hAPP(fun(A,C),fun(A,fun(C,bool)),hAPP(fun(C,fun(C,bool)),fun(fun(A,C),fun(A,fun(C,bool))),combb(C,fun(C,bool),A),fequal(C)),E)))))),hAPP(fun(A,bool),fun(C,bool),hAPP(fun(A,C),fun(fun(A,bool),fun(C,bool)),image(A,C),E),B)) = hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),D),B).  [resolve(5616,a,5513,a)].
39.61/39.51	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(fun(C,bool),int,hAPP(fun(C,int),fun(fun(C,bool),int),big_co1399186613setsum(C,int),hAPP(fun(C,fun(A,bool)),fun(C,int),hAPP(fun(fun(A,bool),int),fun(fun(C,fun(A,bool)),fun(C,int)),combb(fun(A,bool),int,C),hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),D)),hAPP(fun(C,fun(A,bool)),fun(C,fun(A,bool)),hAPP(fun(fun(A,bool),fun(A,bool)),fun(fun(C,fun(A,bool)),fun(C,fun(A,bool))),combb(fun(A,bool),fun(A,bool),C),collect(A)),hAPP(fun(C,fun(A,bool)),fun(C,fun(A,bool)),hAPP(fun(fun(A,bool),fun(A,bool)),fun(fun(C,fun(A,bool)),fun(C,fun(A,bool))),combb(fun(A,bool),fun(A,bool),C),hAPP(fun(A,fun(bool,bool)),fun(fun(A,bool),fun(A,bool)),combs(A,bool,bool),hAPP(fun(A,bool),fun(A,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(A,bool),fun(A,fun(bool,bool))),combb(bool,fun(bool,bool),A),fconj),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,fun(fun(A,bool),bool)),fun(fun(A,bool),fun(A,bool)),combc(A,fun(A,bool),bool),member(A)),B)))),hAPP(fun(A,fun(C,bool)),fun(C,fun(A,bool)),combc(A,C,bool),hAPP(fun(A,C),fun(A,fun(C,bool)),hAPP(fun(C,fun(C,bool)),fun(fun(A,C),fun(A,fun(C,bool))),combb(C,fun(C,bool),A),fequal(C)),E)))))),hAPP(fun(A,bool),fun(C,bool),hAPP(fun(A,C),fun(fun(A,bool),fun(C,bool)),image(A,C),E),B)) = hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),D),B).  [resolve(5616,a,5524,a)].
39.61/39.51	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(fun(C,bool),code_code_numeral,hAPP(fun(C,code_code_numeral),fun(fun(C,bool),code_code_numeral),big_co1399186613setsum(C,code_code_numeral),hAPP(fun(C,fun(A,bool)),fun(C,code_code_numeral),hAPP(fun(fun(A,bool),code_code_numeral),fun(fun(C,fun(A,bool)),fun(C,code_code_numeral)),combb(fun(A,bool),code_code_numeral,C),hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),D)),hAPP(fun(C,fun(A,bool)),fun(C,fun(A,bool)),hAPP(fun(fun(A,bool),fun(A,bool)),fun(fun(C,fun(A,bool)),fun(C,fun(A,bool))),combb(fun(A,bool),fun(A,bool),C),collect(A)),hAPP(fun(C,fun(A,bool)),fun(C,fun(A,bool)),hAPP(fun(fun(A,bool),fun(A,bool)),fun(fun(C,fun(A,bool)),fun(C,fun(A,bool))),combb(fun(A,bool),fun(A,bool),C),hAPP(fun(A,fun(bool,bool)),fun(fun(A,bool),fun(A,bool)),combs(A,bool,bool),hAPP(fun(A,bool),fun(A,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(A,bool),fun(A,fun(bool,bool))),combb(bool,fun(bool,bool),A),fconj),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,fun(fun(A,bool),bool)),fun(fun(A,bool),fun(A,bool)),combc(A,fun(A,bool),bool),member(A)),B)))),hAPP(fun(A,fun(C,bool)),fun(C,fun(A,bool)),combc(A,C,bool),hAPP(fun(A,C),fun(A,fun(C,bool)),hAPP(fun(C,fun(C,bool)),fun(fun(A,C),fun(A,fun(C,bool))),combb(C,fun(C,bool),A),fequal(C)),E)))))),hAPP(fun(A,bool),fun(C,bool),hAPP(fun(A,C),fun(fun(A,bool),fun(C,bool)),image(A,C),E),B)) = hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),D),B).  [resolve(5616,a,5539,a)].
39.61/39.51	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(fun(C,bool),rat,hAPP(fun(C,rat),fun(fun(C,bool),rat),big_co1399186613setsum(C,rat),hAPP(fun(C,fun(A,bool)),fun(C,rat),hAPP(fun(fun(A,bool),rat),fun(fun(C,fun(A,bool)),fun(C,rat)),combb(fun(A,bool),rat,C),hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),D)),hAPP(fun(C,fun(A,bool)),fun(C,fun(A,bool)),hAPP(fun(fun(A,bool),fun(A,bool)),fun(fun(C,fun(A,bool)),fun(C,fun(A,bool))),combb(fun(A,bool),fun(A,bool),C),collect(A)),hAPP(fun(C,fun(A,bool)),fun(C,fun(A,bool)),hAPP(fun(fun(A,bool),fun(A,bool)),fun(fun(C,fun(A,bool)),fun(C,fun(A,bool))),combb(fun(A,bool),fun(A,bool),C),hAPP(fun(A,fun(bool,bool)),fun(fun(A,bool),fun(A,bool)),combs(A,bool,bool),hAPP(fun(A,bool),fun(A,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(A,bool),fun(A,fun(bool,bool))),combb(bool,fun(bool,bool),A),fconj),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,fun(fun(A,bool),bool)),fun(fun(A,bool),fun(A,bool)),combc(A,fun(A,bool),bool),member(A)),B)))),hAPP(fun(A,fun(C,bool)),fun(C,fun(A,bool)),combc(A,C,bool),hAPP(fun(A,C),fun(A,fun(C,bool)),hAPP(fun(C,fun(C,bool)),fun(fun(A,C),fun(A,fun(C,bool))),combb(C,fun(C,bool),A),fequal(C)),E)))))),hAPP(fun(A,bool),fun(C,bool),hAPP(fun(A,C),fun(fun(A,bool),fun(C,bool)),image(A,C),E),B)) = hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),D),B).  [resolve(5616,a,5561,a)].
39.68/39.53	5617 -comm_monoid_add(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | -hBOOL(hAPP(fun(B,bool),bool,hAPP(fun(B,bool),fun(fun(B,bool),bool),ord_less_eq(fun(B,bool)),D),C)) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f694(B,A,E,D,C)),hAPP(fun(B,bool),fun(B,bool),hAPP(fun(B,bool),fun(fun(B,bool),fun(B,bool)),minus_minus(fun(B,bool)),C),D))) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),E),C) = hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),E),D) # label(fact_4295_setsum__mono__zero__left) # label(axiom).  [clausify(3909)].
39.68/39.53	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f694(A,real,D,C,B)),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),B),C))) | hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),D),B) = hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),D),C).  [resolve(5617,a,5513,a)].
39.68/39.53	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f694(A,int,D,C,B)),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),B),C))) | hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),D),B) = hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),D),C).  [resolve(5617,a,5524,a)].
39.68/39.53	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f694(A,code_code_numeral,D,C,B)),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),B),C))) | hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),D),B) = hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),D),C).  [resolve(5617,a,5539,a)].
39.68/39.53	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f694(A,rat,D,C,B)),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),B),C))) | hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),D),B) = hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),D),C).  [resolve(5617,a,5561,a)].
39.68/39.53	5618 -comm_monoid_add(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | -hBOOL(hAPP(fun(B,bool),bool,hAPP(fun(B,bool),fun(fun(B,bool),bool),ord_less_eq(fun(B,bool)),D),C)) | zero_zero(A) != hAPP(B,A,E,f694(B,A,E,D,C)) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),E),C) = hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),E),D) # label(fact_4295_setsum__mono__zero__left) # label(axiom).  [clausify(3909)].
39.68/39.53	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | zero_zero(real) != hAPP(A,real,D,f694(A,real,D,C,B)) | hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),D),B) = hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),D),C).  [resolve(5618,a,5513,a)].
39.68/39.54	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | zero_zero(int) != hAPP(A,int,D,f694(A,int,D,C,B)) | hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),D),B) = hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),D),C).  [resolve(5618,a,5524,a)].
39.68/39.54	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | zero_zero(code_code_numeral) != hAPP(A,code_code_numeral,D,f694(A,code_code_numeral,D,C,B)) | hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),D),B) = hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),D),C).  [resolve(5618,a,5539,a)].
39.68/39.54	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | zero_zero(rat) != hAPP(A,rat,D,f694(A,rat,D,C,B)) | hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),D),B) = hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),D),C).  [resolve(5618,a,5561,a)].
39.68/39.54	5619 -comm_monoid_add(A) | hAPP(fun(nat,bool),A,hAPP(fun(nat,A),fun(fun(nat,bool),A),big_co1399186613setsum(nat,A),hAPP(fun(nat,nat),fun(nat,A),hAPP(fun(nat,A),fun(fun(nat,nat),fun(nat,A)),combb(nat,A,nat),B),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),C))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),D),E)) = hAPP(fun(nat,bool),A,hAPP(fun(nat,A),fun(fun(nat,bool),A),big_co1399186613setsum(nat,A),B),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),D),C)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),E),C))) # label(fact_4178_setsum__shift__bounds__nat__ivl) # label(axiom).  [clausify(3918)].
39.68/39.54	Derived: hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),A),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),B))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),C),D)) = hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),A),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),C),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),D),B))).  [resolve(5619,a,5513,a)].
39.68/39.54	Derived: hAPP(fun(nat,bool),int,hAPP(fun(nat,int),fun(fun(nat,bool),int),big_co1399186613setsum(nat,int),hAPP(fun(nat,nat),fun(nat,int),hAPP(fun(nat,int),fun(fun(nat,nat),fun(nat,int)),combb(nat,int,nat),A),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),B))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),C),D)) = hAPP(fun(nat,bool),int,hAPP(fun(nat,int),fun(fun(nat,bool),int),big_co1399186613setsum(nat,int),A),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),C),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),D),B))).  [resolve(5619,a,5524,a)].
39.68/39.54	Derived: hAPP(fun(nat,bool),code_code_numeral,hAPP(fun(nat,code_code_numeral),fun(fun(nat,bool),code_code_numeral),big_co1399186613setsum(nat,code_code_numeral),hAPP(fun(nat,nat),fun(nat,code_code_numeral),hAPP(fun(nat,code_code_numeral),fun(fun(nat,nat),fun(nat,code_code_numeral)),combb(nat,code_code_numeral,nat),A),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),B))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),C),D)) = hAPP(fun(nat,bool),code_code_numeral,hAPP(fun(nat,code_code_numeral),fun(fun(nat,bool),code_code_numeral),big_co1399186613setsum(nat,code_code_numeral),A),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),C),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),D),B))).  [resolve(5619,a,5539,a)].
39.82/39.70	Derived: hAPP(fun(nat,bool),rat,hAPP(fun(nat,rat),fun(fun(nat,bool),rat),big_co1399186613setsum(nat,rat),hAPP(fun(nat,nat),fun(nat,rat),hAPP(fun(nat,rat),fun(fun(nat,nat),fun(nat,rat)),combb(nat,rat,nat),A),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),B))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),C),D)) = hAPP(fun(nat,bool),rat,hAPP(fun(nat,rat),fun(fun(nat,bool),rat),big_co1399186613setsum(nat,rat),A),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),C),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),D),B))).  [resolve(5619,a,5561,a)].
39.82/39.70	5620 comm_monoid_add(quickcheck_code_int) # label(arity_Quickcheck__Narrowing_Ocode__int___Groups_Ocomm__monoid__add) # label(axiom).  [assumption].
39.82/39.70	Derived: zero_zero(quickcheck_code_int) = hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),hAPP(quickcheck_code_int,fun(A,quickcheck_code_int),combk(quickcheck_code_int,A),zero_zero(quickcheck_code_int))),B).  [resolve(5620,a,5514,a)].
39.82/39.70	Derived: hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f2(A,quickcheck_code_int,B,C)),C)) | zero_zero(quickcheck_code_int) = hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),B),C).  [resolve(5620,a,5515,a)].
39.82/39.70	Derived: zero_zero(quickcheck_code_int) != hAPP(A,quickcheck_code_int,B,f2(A,quickcheck_code_int,B,C)) | zero_zero(quickcheck_code_int) = hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),B),C).  [resolve(5620,a,5516,a)].
39.82/39.70	Derived: -topological_space(quickcheck_code_int) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(fun(nat,quickcheck_code_int),fun(quickcheck_code_int,bool),sums(quickcheck_code_int),A),B)) | hBOOL(hAPP(filter(nat),bool,hAPP(quickcheck_code_int,fun(filter(nat),bool),hAPP(fun(nat,quickcheck_code_int),fun(quickcheck_code_int,fun(filter(nat),bool)),tendsto(nat,quickcheck_code_int),hAPP(fun(nat,fun(nat,bool)),fun(nat,quickcheck_code_int),hAPP(fun(fun(nat,bool),quickcheck_code_int),fun(fun(nat,fun(nat,bool)),fun(nat,quickcheck_code_int)),combb(fun(nat,bool),quickcheck_code_int,nat),hAPP(fun(nat,quickcheck_code_int),fun(fun(nat,bool),quickcheck_code_int),big_co1399186613setsum(nat,quickcheck_code_int),A)),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)))),B),sequentially)).  [resolve(5620,a,5517,a)].
39.82/39.70	Derived: -topological_space(quickcheck_code_int) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(fun(nat,quickcheck_code_int),fun(quickcheck_code_int,bool),sums(quickcheck_code_int),A),B)) | -hBOOL(hAPP(filter(nat),bool,hAPP(quickcheck_code_int,fun(filter(nat),bool),hAPP(fun(nat,quickcheck_code_int),fun(quickcheck_code_int,fun(filter(nat),bool)),tendsto(nat,quickcheck_code_int),hAPP(fun(nat,fun(nat,bool)),fun(nat,quickcheck_code_int),hAPP(fun(fun(nat,bool),quickcheck_code_int),fun(fun(nat,fun(nat,bool)),fun(nat,quickcheck_code_int)),combb(fun(nat,bool),quickcheck_code_int,nat),hAPP(fun(nat,quickcheck_code_int),fun(fun(nat,bool),quickcheck_code_int),big_co1399186613setsum(nat,quickcheck_code_int),A)),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)))),B),sequentially)).  [resolve(5620,a,5518,a)].
39.82/39.71	Derived: -ordere779506340up_add(quickcheck_code_int) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f20(A,quickcheck_code_int,D,C,B)),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),B),C))) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),D),C)),hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),D),B))).  [resolve(5620,a,5519,b)].
39.82/39.71	Derived: -ordere779506340up_add(quickcheck_code_int) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),zero_zero(quickcheck_code_int)),hAPP(A,quickcheck_code_int,D,f20(A,quickcheck_code_int,D,C,B)))) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),D),C)),hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),D),B))).  [resolve(5620,a,5520,b)].
39.82/39.71	Derived: -topological_space(quickcheck_code_int) | sums(quickcheck_code_int) = ti(fun(fun(nat,quickcheck_code_int),fun(quickcheck_code_int,bool)),sums(quickcheck_code_int)).  [resolve(5620,a,5521,a)].
39.82/39.71	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f56(A,quickcheck_code_int,D,C,B)),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),B),C))) | hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),D),B) = hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),D),C).  [resolve(5620,a,5522,a)].
39.82/39.71	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | zero_zero(quickcheck_code_int) != hAPP(A,quickcheck_code_int,D,f56(A,quickcheck_code_int,D,C,B)) | hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),D),B) = hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),D),C).  [resolve(5620,a,5523,a)].
39.82/39.71	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),one_one(nat)))) | hAPP(fun(nat,bool),quickcheck_code_int,hAPP(fun(nat,quickcheck_code_int),fun(fun(nat,bool),quickcheck_code_int),big_co1399186613setsum(nat,quickcheck_code_int),C),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),D))) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),hAPP(fun(nat,bool),quickcheck_code_int,hAPP(fun(nat,quickcheck_code_int),fun(fun(nat,bool),quickcheck_code_int),big_co1399186613setsum(nat,quickcheck_code_int),C),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),A),B))),hAPP(fun(nat,bool),quickcheck_code_int,hAPP(fun(nat,quickcheck_code_int),fun(fun(nat,bool),quickcheck_code_int),big_co1399186613setsum(nat,quickcheck_code_int),C),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),one_one(nat))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),D)))).  [resolve(5620,a,5525,a)].
39.82/39.71	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | hAPP(fun(nat,bool),quickcheck_code_int,hAPP(fun(nat,quickcheck_code_int),fun(fun(nat,bool),quickcheck_code_int),big_co1399186613setsum(nat,quickcheck_code_int),C),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),A),B)) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),hAPP(nat,quickcheck_code_int,C,A)),hAPP(fun(nat,bool),quickcheck_code_int,hAPP(fun(nat,quickcheck_code_int),fun(fun(nat,bool),quickcheck_code_int),big_co1399186613setsum(nat,quickcheck_code_int),C),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,suc,A)),B))).  [resolve(5620,a,5526,a)].
39.82/39.71	Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),A,zero_zero(quickcheck_code_int)),zero_zero(quickcheck_code_int))) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),A,f102(B,quickcheck_code_int,C,D,E,A)),f104(B,quickcheck_code_int,C,D,E,A))) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),E)) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f106(B,quickcheck_code_int,C,D,E,A)),E)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),A,hAPP(fun(B,bool),quickcheck_code_int,hAPP(fun(B,quickcheck_code_int),fun(fun(B,bool),quickcheck_code_int),big_co1399186613setsum(B,quickcheck_code_int),C),E)),hAPP(fun(B,bool),quickcheck_code_int,hAPP(fun(B,quickcheck_code_int),fun(fun(B,bool),quickcheck_code_int),big_co1399186613setsum(B,quickcheck_code_int),D),E))).  [resolve(5620,a,5527,a)].
39.82/39.71	Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),A,zero_zero(quickcheck_code_int)),zero_zero(quickcheck_code_int))) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),A,f102(B,quickcheck_code_int,C,D,E,A)),f104(B,quickcheck_code_int,C,D,E,A))) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),E)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),A,hAPP(B,quickcheck_code_int,C,f106(B,quickcheck_code_int,C,D,E,A))),hAPP(B,quickcheck_code_int,D,f106(B,quickcheck_code_int,C,D,E,A)))) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),A,hAPP(fun(B,bool),quickcheck_code_int,hAPP(fun(B,quickcheck_code_int),fun(fun(B,bool),quickcheck_code_int),big_co1399186613setsum(B,quickcheck_code_int),C),E)),hAPP(fun(B,bool),quickcheck_code_int,hAPP(fun(B,quickcheck_code_int),fun(fun(B,bool),quickcheck_code_int),big_co1399186613setsum(B,quickcheck_code_int),D),E))).  [resolve(5620,a,5528,a)].
39.82/39.71	Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),A,zero_zero(quickcheck_code_int)),zero_zero(quickcheck_code_int))) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),A,f103(B,quickcheck_code_int,C,D,E,A)),f105(B,quickcheck_code_int,C,D,E,A))) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),E)) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f106(B,quickcheck_code_int,C,D,E,A)),E)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),A,hAPP(fun(B,bool),quickcheck_code_int,hAPP(fun(B,quickcheck_code_int),fun(fun(B,bool),quickcheck_code_int),big_co1399186613setsum(B,quickcheck_code_int),C),E)),hAPP(fun(B,bool),quickcheck_code_int,hAPP(fun(B,quickcheck_code_int),fun(fun(B,bool),quickcheck_code_int),big_co1399186613setsum(B,quickcheck_code_int),D),E))).  [resolve(5620,a,5529,a)].
39.82/39.71	Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),A,zero_zero(quickcheck_code_int)),zero_zero(quickcheck_code_int))) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),A,f103(B,quickcheck_code_int,C,D,E,A)),f105(B,quickcheck_code_int,C,D,E,A))) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),E)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),A,hAPP(B,quickcheck_code_int,C,f106(B,quickcheck_code_int,C,D,E,A))),hAPP(B,quickcheck_code_int,D,f106(B,quickcheck_code_int,C,D,E,A)))) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),A,hAPP(fun(B,bool),quickcheck_code_int,hAPP(fun(B,quickcheck_code_int),fun(fun(B,bool),quickcheck_code_int),big_co1399186613setsum(B,quickcheck_code_int),C),E)),hAPP(fun(B,bool),quickcheck_code_int,hAPP(fun(B,quickcheck_code_int),fun(fun(B,bool),quickcheck_code_int),big_co1399186613setsum(B,quickcheck_code_int),D),E))).  [resolve(5620,a,5530,a)].
39.82/39.71	Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),A,zero_zero(quickcheck_code_int)),zero_zero(quickcheck_code_int))) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),A,hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),f102(B,quickcheck_code_int,C,D,E,A)),f103(B,quickcheck_code_int,C,D,E,A))),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),f104(B,quickcheck_code_int,C,D,E,A)),f105(B,quickcheck_code_int,C,D,E,A)))) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),E)) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f106(B,quickcheck_code_int,C,D,E,A)),E)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),A,hAPP(fun(B,bool),quickcheck_code_int,hAPP(fun(B,quickcheck_code_int),fun(fun(B,bool),quickcheck_code_int),big_co1399186613setsum(B,quickcheck_code_int),C),E)),hAPP(fun(B,bool),quickcheck_code_int,hAPP(fun(B,quickcheck_code_int),fun(fun(B,bool),quickcheck_code_int),big_co1399186613setsum(B,quickcheck_code_int),D),E))).  [resolve(5620,a,5531,a)].
39.82/39.71	Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),A,zero_zero(quickcheck_code_int)),zero_zero(quickcheck_code_int))) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),A,hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),f102(B,quickcheck_code_int,C,D,E,A)),f103(B,quickcheck_code_int,C,D,E,A))),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),f104(B,quickcheck_code_int,C,D,E,A)),f105(B,quickcheck_code_int,C,D,E,A)))) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),E)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),A,hAPP(B,quickcheck_code_int,C,f106(B,quickcheck_code_int,C,D,E,A))),hAPP(B,quickcheck_code_int,D,f106(B,quickcheck_code_int,C,D,E,A)))) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),A,hAPP(fun(B,bool),quickcheck_code_int,hAPP(fun(B,quickcheck_code_int),fun(fun(B,bool),quickcheck_code_int),big_co1399186613setsum(B,quickcheck_code_int),C),E)),hAPP(fun(B,bool),quickcheck_code_int,hAPP(fun(B,quickcheck_code_int),fun(fun(B,bool),quickcheck_code_int),big_co1399186613setsum(B,quickcheck_code_int),D),E))).  [resolve(5620,a,5532,a)].
39.86/39.72	Derived: -t2_space(quickcheck_code_int) | zero_zero(quickcheck_code_int) = hAPP(fun(nat,quickcheck_code_int),quickcheck_code_int,suminf(quickcheck_code_int),hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),combk(quickcheck_code_int,nat),zero_zero(quickcheck_code_int))).  [resolve(5620,a,5533,b)].
39.86/39.72	Derived: -topological_space(quickcheck_code_int) | zero_zero(quickcheck_code_int) != hAPP(nat,quickcheck_code_int,A,zero_zero(nat)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(fun(nat,quickcheck_code_int),fun(quickcheck_code_int,bool),sums(quickcheck_code_int),hAPP(fun(nat,nat),fun(nat,quickcheck_code_int),hAPP(fun(nat,quickcheck_code_int),fun(fun(nat,nat),fun(nat,quickcheck_code_int)),combb(nat,quickcheck_code_int,nat),A),suc)),B)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(fun(nat,quickcheck_code_int),fun(quickcheck_code_int,bool),sums(quickcheck_code_int),A),B)).  [resolve(5620,a,5534,a)].
39.86/39.72	Derived: -topological_space(quickcheck_code_int) | the(quickcheck_code_int) = ti(fun(fun(quickcheck_code_int,bool),quickcheck_code_int),the(quickcheck_code_int)).  [resolve(5620,a,5535,a)].
39.86/39.72	Derived: -ordere779506340up_add(quickcheck_code_int) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f137(A,quickcheck_code_int,B,C)),C)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),B),C)),zero_zero(quickcheck_code_int))).  [resolve(5620,a,5536,b)].
39.86/39.72	Derived: -ordere779506340up_add(quickcheck_code_int) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),hAPP(A,quickcheck_code_int,B,f137(A,quickcheck_code_int,B,C))),zero_zero(quickcheck_code_int))) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),B),C)),zero_zero(quickcheck_code_int))).  [resolve(5620,a,5537,b)].
39.86/39.72	Derived: -t2_space(quickcheck_code_int) | -hBOOL(hAPP(fun(nat,quickcheck_code_int),bool,summable(quickcheck_code_int),A)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(fun(nat,quickcheck_code_int),fun(quickcheck_code_int,bool),sums(quickcheck_code_int),A),hAPP(fun(nat,quickcheck_code_int),quickcheck_code_int,suminf(quickcheck_code_int),A))).  [resolve(5620,a,5538,b)].
39.86/39.72	Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),zero_zero(quickcheck_code_int)),A) = ti(quickcheck_code_int,A).  [resolve(5620,a,5540,a)].
39.86/39.72	Derived: -topological_space(quickcheck_code_int) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(fun(nat,quickcheck_code_int),fun(quickcheck_code_int,bool),sums(quickcheck_code_int),hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),combk(quickcheck_code_int,nat),zero_zero(quickcheck_code_int))),zero_zero(quickcheck_code_int))).  [resolve(5620,a,5541,a)].
39.86/39.72	Derived: -topological_space(quickcheck_code_int) | suminf(quickcheck_code_int) = ti(fun(fun(nat,quickcheck_code_int),quickcheck_code_int),suminf(quickcheck_code_int)).  [resolve(5620,a,5542,b)].
39.86/39.72	Derived: hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | zero_zero(quickcheck_code_int) = hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),C),B).  [resolve(5620,a,5543,a)].
39.86/39.72	Derived: -t2_space(quickcheck_code_int) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(fun(nat,quickcheck_code_int),fun(quickcheck_code_int,bool),sums(quickcheck_code_int),A),B)) | hAPP(fun(nat,quickcheck_code_int),quickcheck_code_int,suminf(quickcheck_code_int),A) = ti(quickcheck_code_int,B).  [resolve(5620,a,5544,b)].
39.86/39.72	Derived: hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),hAPP(fun(B,bool),fun(A,quickcheck_code_int),hAPP(fun(A,fun(fun(B,bool),quickcheck_code_int)),fun(fun(B,bool),fun(A,quickcheck_code_int)),combc(A,fun(B,bool),quickcheck_code_int),hAPP(fun(A,fun(B,quickcheck_code_int)),fun(A,fun(fun(B,bool),quickcheck_code_int)),hAPP(fun(fun(B,quickcheck_code_int),fun(fun(B,bool),quickcheck_code_int)),fun(fun(A,fun(B,quickcheck_code_int)),fun(A,fun(fun(B,bool),quickcheck_code_int))),combb(fun(B,quickcheck_code_int),fun(fun(B,bool),quickcheck_code_int),A),big_co1399186613setsum(B,quickcheck_code_int)),hAPP(fun(B,fun(A,quickcheck_code_int)),fun(A,fun(B,quickcheck_code_int)),combc(B,A,quickcheck_code_int),C))),D)),E) = hAPP(fun(B,bool),quickcheck_code_int,hAPP(fun(B,quickcheck_code_int),fun(fun(B,bool),quickcheck_code_int),big_co1399186613setsum(B,quickcheck_code_int),hAPP(fun(A,bool),fun(B,quickcheck_code_int),hAPP(fun(B,fun(fun(A,bool),quickcheck_code_int)),fun(fun(A,bool),fun(B,quickcheck_code_int)),combc(B,fun(A,bool),quickcheck_code_int),hAPP(fun(B,fun(A,quickcheck_code_int)),fun(B,fun(fun(A,bool),quickcheck_code_int)),hAPP(fun(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int)),fun(fun(B,fun(A,quickcheck_code_int)),fun(B,fun(fun(A,bool),quickcheck_code_int))),combb(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),B),big_co1399186613setsum(A,quickcheck_code_int)),C)),E)),D).  [resolve(5620,a,5545,a)].
39.86/39.72	Derived: hAPP(fun(nat,bool),quickcheck_code_int,hAPP(fun(nat,quickcheck_code_int),fun(fun(nat,bool),quickcheck_code_int),big_co1399186613setsum(nat,quickcheck_code_int),hAPP(fun(nat,fun(nat,bool)),fun(nat,quickcheck_code_int),hAPP(fun(fun(nat,bool),quickcheck_code_int),fun(fun(nat,fun(nat,bool)),fun(nat,quickcheck_code_int)),combb(fun(nat,bool),quickcheck_code_int,nat),hAPP(fun(nat,quickcheck_code_int),fun(fun(nat,bool),quickcheck_code_int),big_co1399186613setsum(nat,quickcheck_code_int),A)),hAPP(fun(nat,nat),fun(nat,fun(nat,bool)),hAPP(fun(nat,fun(nat,fun(nat,bool))),fun(fun(nat,nat),fun(nat,fun(nat,bool))),combs(nat,nat,fun(nat,bool)),hAPP(fun(nat,nat),fun(nat,fun(nat,fun(nat,bool))),hAPP(fun(nat,fun(nat,fun(nat,bool))),fun(fun(nat,nat),fun(nat,fun(nat,fun(nat,bool)))),combb(nat,fun(nat,fun(nat,bool)),nat),ord_atLeastLessThan(nat)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),times_times(nat)),B))),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),hAPP(fun(nat,nat),fun(nat,fun(nat,nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,nat),fun(nat,fun(nat,nat))),combb(nat,fun(nat,nat),nat),plus_plus(nat)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),times_times(nat)),B))),B)))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),C)) = hAPP(fun(nat,bool),quickcheck_code_int,hAPP(fun(nat,quickcheck_code_int),fun(fun(nat,bool),quickcheck_code_int),big_co1399186613setsum(nat,quickcheck_code_int),A),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),C),B))).  [resolve(5620,a,5546,a)].
39.86/39.72	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | zero_zero(quickcheck_code_int) = hAPP(fun(nat,bool),quickcheck_code_int,hAPP(fun(nat,quickcheck_code_int),fun(fun(nat,bool),quickcheck_code_int),big_co1399186613setsum(nat,quickcheck_code_int),C),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),B),hAPP(nat,nat,suc,A))).  [resolve(5620,a,5547,a)].
39.86/39.72	Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | hAPP(fun(nat,bool),quickcheck_code_int,hAPP(fun(nat,quickcheck_code_int),fun(fun(nat,bool),quickcheck_code_int),big_co1399186613setsum(nat,quickcheck_code_int),C),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),B),hAPP(nat,nat,suc,A))) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),hAPP(fun(nat,bool),quickcheck_code_int,hAPP(fun(nat,quickcheck_code_int),fun(fun(nat,bool),quickcheck_code_int),big_co1399186613setsum(nat,quickcheck_code_int),C),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),B),A))),hAPP(nat,quickcheck_code_int,C,A)).  [resolve(5620,a,5548,a)].
39.86/39.72	Derived: -ordere779506340up_add(quickcheck_code_int) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f306(A,quickcheck_code_int,B,C)),C)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),zero_zero(quickcheck_code_int)),hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),B),C))).  [resolve(5620,a,5549,a)].
39.86/39.72	Derived: -ordere779506340up_add(quickcheck_code_int) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),zero_zero(quickcheck_code_int)),hAPP(A,quickcheck_code_int,B,f306(A,quickcheck_code_int,B,C)))) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),zero_zero(quickcheck_code_int)),hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),B),C))).  [resolve(5620,a,5550,a)].
39.86/39.72	Derived: hAPP(fun(nat,bool),quickcheck_code_int,hAPP(fun(nat,quickcheck_code_int),fun(fun(nat,bool),quickcheck_code_int),big_co1399186613setsum(nat,quickcheck_code_int),A),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),C))) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),hAPP(fun(nat,bool),quickcheck_code_int,hAPP(fun(nat,quickcheck_code_int),fun(fun(nat,bool),quickcheck_code_int),big_co1399186613setsum(nat,quickcheck_code_int),hAPP(fun(nat,nat),fun(nat,quickcheck_code_int),hAPP(fun(nat,quickcheck_code_int),fun(fun(nat,nat),fun(nat,quickcheck_code_int)),combb(nat,quickcheck_code_int,nat),A),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),C))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),B))),hAPP(fun(nat,bool),quickcheck_code_int,hAPP(fun(nat,quickcheck_code_int),fun(fun(nat,bool),quickcheck_code_int),big_co1399186613setsum(nat,quickcheck_code_int),A),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),C))).  [resolve(5620,a,5551,a)].
39.86/39.72	Derived: -comm_monoid_mult(quickcheck_code_int) | A != B | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),f335(quickcheck_code_int,C,D,B,A))) | hAPP(fun(int,bool),quickcheck_code_int,hAPP(fun(int,quickcheck_code_int),fun(fun(int,bool),quickcheck_code_int),big_co1399186613setsum(int,quickcheck_code_int),D),A) = hAPP(fun(int,bool),quickcheck_code_int,hAPP(fun(int,quickcheck_code_int),fun(fun(int,bool),quickcheck_code_int),big_co1399186613setsum(int,quickcheck_code_int),C),B).  [resolve(5620,a,5552,b)].
39.86/39.72	Derived: -comm_monoid_mult(quickcheck_code_int) | A != B | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A)) | hAPP(int,quickcheck_code_int,C,f335(quickcheck_code_int,D,C,B,A)) != hAPP(int,quickcheck_code_int,D,f335(quickcheck_code_int,D,C,B,A)) | hAPP(fun(int,bool),quickcheck_code_int,hAPP(fun(int,quickcheck_code_int),fun(fun(int,bool),quickcheck_code_int),big_co1399186613setsum(int,quickcheck_code_int),C),A) = hAPP(fun(int,bool),quickcheck_code_int,hAPP(fun(int,quickcheck_code_int),fun(fun(int,bool),quickcheck_code_int),big_co1399186613setsum(int,quickcheck_code_int),D),B).  [resolve(5620,a,5553,b)].
39.86/39.72	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | zero_zero(quickcheck_code_int) = hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),hAPP(quickcheck_code_int,fun(A,quickcheck_code_int),hAPP(fun(A,fun(quickcheck_code_int,quickcheck_code_int)),fun(quickcheck_code_int,fun(A,quickcheck_code_int)),combc(A,quickcheck_code_int,quickcheck_code_int),hAPP(fun(A,quickcheck_code_int),fun(A,fun(quickcheck_code_int,quickcheck_code_int)),hAPP(fun(A,fun(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int))),fun(fun(A,quickcheck_code_int),fun(A,fun(quickcheck_code_int,quickcheck_code_int))),combs(A,quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int)),hAPP(fun(A,bool),fun(A,fun(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int))),hAPP(fun(bool,fun(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int))),fun(fun(A,bool),fun(A,fun(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int)))),combb(bool,fun(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int)),A),if(quickcheck_code_int)),hAPP(A,fun(A,bool),hAPP(fun(A,fun(A,bool)),fun(A,fun(A,bool)),combc(A,A,bool),fequal(A)),C))),D)),zero_zero(quickcheck_code_int))),B).  [resolve(5620,a,5554,a)].
39.86/39.73	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),hAPP(quickcheck_code_int,fun(A,quickcheck_code_int),hAPP(fun(A,fun(quickcheck_code_int,quickcheck_code_int)),fun(quickcheck_code_int,fun(A,quickcheck_code_int)),combc(A,quickcheck_code_int,quickcheck_code_int),hAPP(fun(A,quickcheck_code_int),fun(A,fun(quickcheck_code_int,quickcheck_code_int)),hAPP(fun(A,fun(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int))),fun(fun(A,quickcheck_code_int),fun(A,fun(quickcheck_code_int,quickcheck_code_int))),combs(A,quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int)),hAPP(fun(A,bool),fun(A,fun(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int))),hAPP(fun(bool,fun(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int))),fun(fun(A,bool),fun(A,fun(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int)))),combb(bool,fun(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int)),A),if(quickcheck_code_int)),hAPP(A,fun(A,bool),hAPP(fun(A,fun(A,bool)),fun(A,fun(A,bool)),combc(A,A,bool),fequal(A)),C))),D)),zero_zero(quickcheck_code_int))),B) = hAPP(A,quickcheck_code_int,D,C).  [resolve(5620,a,5555,a)].
39.86/39.73	Derived: -metric_space(quickcheck_code_int) | hAPP(fun(nat,quickcheck_code_int),quickcheck_code_int,lim(quickcheck_code_int),hAPP(fun(nat,fun(nat,bool)),fun(nat,quickcheck_code_int),hAPP(fun(fun(nat,bool),quickcheck_code_int),fun(fun(nat,fun(nat,bool)),fun(nat,quickcheck_code_int)),combb(fun(nat,bool),quickcheck_code_int,nat),hAPP(fun(nat,quickcheck_code_int),fun(fun(nat,bool),quickcheck_code_int),big_co1399186613setsum(nat,quickcheck_code_int),A)),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)))) = hAPP(fun(nat,quickcheck_code_int),quickcheck_code_int,suminf(quickcheck_code_int),A).  [resolve(5620,a,5556,b)].
39.86/39.73	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,A)),B)) | zero_zero(quickcheck_code_int) = hAPP(fun(nat,bool),quickcheck_code_int,hAPP(fun(nat,quickcheck_code_int),fun(fun(nat,bool),quickcheck_code_int),big_co1399186613setsum(nat,quickcheck_code_int),C),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),B),hAPP(nat,nat,suc,A))).  [resolve(5620,a,5557,a)].
39.86/39.73	Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,A)),B)) | hAPP(fun(nat,bool),quickcheck_code_int,hAPP(fun(nat,quickcheck_code_int),fun(fun(nat,bool),quickcheck_code_int),big_co1399186613setsum(nat,quickcheck_code_int),C),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),B),hAPP(nat,nat,suc,A))) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),hAPP(nat,quickcheck_code_int,C,B)),hAPP(fun(nat,bool),quickcheck_code_int,hAPP(fun(nat,quickcheck_code_int),fun(fun(nat,bool),quickcheck_code_int),big_co1399186613setsum(nat,quickcheck_code_int),hAPP(fun(nat,nat),fun(nat,quickcheck_code_int),hAPP(fun(nat,quickcheck_code_int),fun(fun(nat,nat),fun(nat,quickcheck_code_int)),combb(nat,quickcheck_code_int,nat),C),suc)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),B),A))).  [resolve(5620,a,5558,a)].
39.86/39.73	Derived: hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),hAPP(fun(A,quickcheck_code_int),fun(A,quickcheck_code_int),hAPP(fun(A,fun(quickcheck_code_int,quickcheck_code_int)),fun(fun(A,quickcheck_code_int),fun(A,quickcheck_code_int)),combs(A,quickcheck_code_int,quickcheck_code_int),hAPP(fun(A,quickcheck_code_int),fun(A,fun(quickcheck_code_int,quickcheck_code_int)),hAPP(fun(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int)),fun(fun(A,quickcheck_code_int),fun(A,fun(quickcheck_code_int,quickcheck_code_int))),combb(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),A),plus_plus(quickcheck_code_int)),B)),C)),D) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),B),D)),hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),C),D)).  [resolve(5620,a,5559,a)].
39.86/39.73	Derived: -comm_monoid_mult(quickcheck_code_int) | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A)) | hAPP(fun(nat,bool),quickcheck_code_int,hAPP(fun(nat,quickcheck_code_int),fun(fun(nat,bool),quickcheck_code_int),big_co1399186613setsum(nat,quickcheck_code_int),hAPP(fun(nat,int),fun(nat,quickcheck_code_int),hAPP(fun(int,quickcheck_code_int),fun(fun(nat,int),fun(nat,quickcheck_code_int)),combb(int,quickcheck_code_int,nat),B),semiring_1_of_nat(int))),hAPP(fun(int,bool),fun(nat,bool),hAPP(fun(int,nat),fun(fun(int,bool),fun(nat,bool)),image(int,nat),nat_1),A)) = hAPP(fun(int,bool),quickcheck_code_int,hAPP(fun(int,quickcheck_code_int),fun(fun(int,bool),quickcheck_code_int),big_co1399186613setsum(int,quickcheck_code_int),B),A).  [resolve(5620,a,5560,b)].
39.86/39.73	Derived: big_co1399186613setsum(A,quickcheck_code_int) = ti(fun(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int)),big_co1399186613setsum(A,quickcheck_code_int)).  [resolve(5620,a,5562,a)].
39.86/39.73	Derived: -topological_space(quickcheck_code_int) | hAPP(fun(quickcheck_code_int,bool),quickcheck_code_int,the(quickcheck_code_int),hAPP(fun(nat,quickcheck_code_int),fun(quickcheck_code_int,bool),sums(quickcheck_code_int),A)) = hAPP(fun(nat,quickcheck_code_int),quickcheck_code_int,suminf(quickcheck_code_int),A).  [resolve(5620,a,5563,b)].
39.86/39.73	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | hAPP(fun(nat,bool),quickcheck_code_int,hAPP(fun(nat,quickcheck_code_int),fun(fun(nat,bool),quickcheck_code_int),big_co1399186613setsum(nat,quickcheck_code_int),C),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),A),B)) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),hAPP(nat,quickcheck_code_int,C,A)),hAPP(fun(nat,bool),quickcheck_code_int,hAPP(fun(nat,quickcheck_code_int),fun(fun(nat,bool),quickcheck_code_int),big_co1399186613setsum(nat,quickcheck_code_int),C),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),hAPP(nat,nat,suc,A)),B))).  [resolve(5620,a,5564,a)].
39.86/39.73	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),hAPP(quickcheck_code_int,fun(A,quickcheck_code_int),hAPP(fun(A,fun(quickcheck_code_int,quickcheck_code_int)),fun(quickcheck_code_int,fun(A,quickcheck_code_int)),combc(A,quickcheck_code_int,quickcheck_code_int),hAPP(fun(A,quickcheck_code_int),fun(A,fun(quickcheck_code_int,quickcheck_code_int)),hAPP(fun(A,fun(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int))),fun(fun(A,quickcheck_code_int),fun(A,fun(quickcheck_code_int,quickcheck_code_int))),combs(A,quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int)),hAPP(fun(A,bool),fun(A,fun(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int))),hAPP(fun(bool,fun(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int))),fun(fun(A,bool),fun(A,fun(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int)))),combb(bool,fun(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int)),A),if(quickcheck_code_int)),hAPP(A,fun(A,bool),fequal(A),C))),D)),zero_zero(quickcheck_code_int))),B) = hAPP(A,quickcheck_code_int,D,C).  [resolve(5620,a,5565,a)].
39.86/39.73	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | zero_zero(quickcheck_code_int) = hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),hAPP(quickcheck_code_int,fun(A,quickcheck_code_int),hAPP(fun(A,fun(quickcheck_code_int,quickcheck_code_int)),fun(quickcheck_code_int,fun(A,quickcheck_code_int)),combc(A,quickcheck_code_int,quickcheck_code_int),hAPP(fun(A,quickcheck_code_int),fun(A,fun(quickcheck_code_int,quickcheck_code_int)),hAPP(fun(A,fun(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int))),fun(fun(A,quickcheck_code_int),fun(A,fun(quickcheck_code_int,quickcheck_code_int))),combs(A,quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int)),hAPP(fun(A,bool),fun(A,fun(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int))),hAPP(fun(bool,fun(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int))),fun(fun(A,bool),fun(A,fun(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int)))),combb(bool,fun(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int)),A),if(quickcheck_code_int)),hAPP(A,fun(A,bool),fequal(A),C))),D)),zero_zero(quickcheck_code_int))),B).  [resolve(5620,a,5566,a)].
39.86/39.73	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),hAPP(quickcheck_code_int,fun(A,quickcheck_code_int),hAPP(fun(A,fun(quickcheck_code_int,quickcheck_code_int)),fun(quickcheck_code_int,fun(A,quickcheck_code_int)),combc(A,quickcheck_code_int,quickcheck_code_int),hAPP(fun(A,quickcheck_code_int),fun(A,fun(quickcheck_code_int,quickcheck_code_int)),hAPP(fun(A,fun(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int))),fun(fun(A,quickcheck_code_int),fun(A,fun(quickcheck_code_int,quickcheck_code_int))),combs(A,quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int)),hAPP(fun(A,bool),fun(A,fun(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int))),hAPP(fun(bool,fun(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int))),fun(fun(A,bool),fun(A,fun(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int)))),combb(bool,fun(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int)),A),if(quickcheck_code_int)),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,fun(fun(A,bool),bool)),fun(fun(A,bool),fun(A,bool)),combc(A,fun(A,bool),bool),member(A)),C))),D)),zero_zero(quickcheck_code_int))),B) = hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),D),hAPP(fun(A,bool),fun(A,bool),collect(A),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,fun(bool,bool)),fun(fun(A,bool),fun(A,bool)),combs(A,bool,bool),hAPP(fun(A,bool),fun(A,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(A,bool),fun(A,fun(bool,bool))),combb(bool,fun(bool,bool),A),fconj),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,fun(fun(A,bool),bool)),fun(fun(A,bool),fun(A,bool)),combc(A,fun(A,bool),bool),member(A)),B))),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,fun(fun(A,bool),bool)),fun(fun(A,bool),fun(A,bool)),combc(A,fun(A,bool),bool),member(A)),C)))).  [resolve(5620,a,5567,a)].
39.86/39.74	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f457(A,quickcheck_code_int,D,E,C,B)),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),B),C))) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f458(A,quickcheck_code_int,D,E,C,B)),C)) | hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),D),C) = hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),E),B).  [resolve(5620,a,5568,a)].
39.86/39.74	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f457(A,quickcheck_code_int,D,E,C,B)),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),B),C))) | hAPP(A,quickcheck_code_int,D,f458(A,quickcheck_code_int,D,E,C,B)) != hAPP(A,quickcheck_code_int,E,f458(A,quickcheck_code_int,D,E,C,B)) | hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),D),C) = hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),E),B).  [resolve(5620,a,5569,a)].
39.86/39.74	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | zero_zero(quickcheck_code_int) != hAPP(A,quickcheck_code_int,D,f457(A,quickcheck_code_int,E,D,C,B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f458(A,quickcheck_code_int,E,D,C,B)),C)) | hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),E),C) = hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),D),B).  [resolve(5620,a,5570,a)].
39.86/39.74	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | zero_zero(quickcheck_code_int) != hAPP(A,quickcheck_code_int,D,f457(A,quickcheck_code_int,E,D,C,B)) | hAPP(A,quickcheck_code_int,E,f458(A,quickcheck_code_int,E,D,C,B)) != hAPP(A,quickcheck_code_int,D,f458(A,quickcheck_code_int,E,D,C,B)) | hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),E),C) = hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),D),B).  [resolve(5620,a,5571,a)].
39.86/39.74	Derived: -topological_space(quickcheck_code_int) | summable(quickcheck_code_int) = ti(fun(fun(nat,quickcheck_code_int),bool),summable(quickcheck_code_int)).  [resolve(5620,a,5573,b)].
39.86/39.74	Derived: -t2_space(quickcheck_code_int) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(fun(nat,quickcheck_code_int),fun(quickcheck_code_int,bool),sums(quickcheck_code_int),A),B)) | hBOOL(hAPP(fun(nat,quickcheck_code_int),bool,summable(quickcheck_code_int),A)).  [resolve(5620,a,5575,b)].
39.89/39.74	Derived: -t2_space(quickcheck_code_int) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(fun(nat,quickcheck_code_int),fun(quickcheck_code_int,bool),sums(quickcheck_code_int),A),B)) | hAPP(fun(nat,quickcheck_code_int),quickcheck_code_int,suminf(quickcheck_code_int),A) != ti(quickcheck_code_int,B) | -hBOOL(hAPP(fun(nat,quickcheck_code_int),bool,summable(quickcheck_code_int),A)).  [resolve(5620,a,5576,b)].
39.89/39.74	Derived: zero_zero(quickcheck_code_int) != hAPP(nat,quickcheck_code_int,A,zero_zero(nat)) | hAPP(fun(nat,bool),quickcheck_code_int,hAPP(fun(nat,quickcheck_code_int),fun(fun(nat,bool),quickcheck_code_int),big_co1399186613setsum(nat,quickcheck_code_int),A),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),B)) = hAPP(fun(nat,bool),quickcheck_code_int,hAPP(fun(nat,quickcheck_code_int),fun(fun(nat,bool),quickcheck_code_int),big_co1399186613setsum(nat,quickcheck_code_int),A),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),hAPP(nat,nat,suc,zero_zero(nat))),B)).  [resolve(5620,a,5577,a)].
39.89/39.74	Derived: -topological_space(quickcheck_code_int) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(fun(nat,quickcheck_code_int),fun(quickcheck_code_int,bool),sums(quickcheck_code_int),A),B)) | hBOOL(hAPP(fun(nat,quickcheck_code_int),bool,summable(quickcheck_code_int),A)).  [resolve(5620,a,5578,a)].
39.89/39.74	Derived: -t2_space(quickcheck_code_int) | -hBOOL(hAPP(fun(nat,quickcheck_code_int),bool,summable(quickcheck_code_int),A)) | hBOOL(hAPP(filter(nat),bool,hAPP(quickcheck_code_int,fun(filter(nat),bool),hAPP(fun(nat,quickcheck_code_int),fun(quickcheck_code_int,fun(filter(nat),bool)),tendsto(nat,quickcheck_code_int),hAPP(fun(nat,fun(nat,bool)),fun(nat,quickcheck_code_int),hAPP(fun(fun(nat,bool),quickcheck_code_int),fun(fun(nat,fun(nat,bool)),fun(nat,quickcheck_code_int)),combb(fun(nat,bool),quickcheck_code_int,nat),hAPP(fun(nat,quickcheck_code_int),fun(fun(nat,bool),quickcheck_code_int),big_co1399186613setsum(nat,quickcheck_code_int),A)),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)))),hAPP(fun(nat,quickcheck_code_int),quickcheck_code_int,suminf(quickcheck_code_int),A)),sequentially)).  [resolve(5620,a,5579,b)].
39.89/39.74	Derived: -topological_space(quickcheck_code_int) | hBOOL(hAPP(fun(nat,quickcheck_code_int),bool,summable(quickcheck_code_int),hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),combk(quickcheck_code_int,nat),zero_zero(quickcheck_code_int)))).  [resolve(5620,a,5580,a)].
39.89/39.74	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f538(A,quickcheck_code_int,D,E,C,B)),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),B),C))) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f539(A,quickcheck_code_int,D,E,C,B)),C)) | hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),E),B) = hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),D),C).  [resolve(5620,a,5581,a)].
39.89/39.74	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f538(A,quickcheck_code_int,D,E,C,B)),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),B),C))) | hAPP(A,quickcheck_code_int,E,f539(A,quickcheck_code_int,D,E,C,B)) != hAPP(A,quickcheck_code_int,D,f539(A,quickcheck_code_int,D,E,C,B)) | hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),E),B) = hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),D),C).  [resolve(5620,a,5582,a)].
39.89/39.75	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | zero_zero(quickcheck_code_int) != hAPP(A,quickcheck_code_int,D,f538(A,quickcheck_code_int,E,D,C,B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f539(A,quickcheck_code_int,E,D,C,B)),C)) | hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),D),B) = hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),E),C).  [resolve(5620,a,5583,a)].
39.89/39.75	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | zero_zero(quickcheck_code_int) != hAPP(A,quickcheck_code_int,D,f538(A,quickcheck_code_int,E,D,C,B)) | hAPP(A,quickcheck_code_int,D,f539(A,quickcheck_code_int,E,D,C,B)) != hAPP(A,quickcheck_code_int,E,f539(A,quickcheck_code_int,E,D,C,B)) | hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),D),B) = hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),E),C).  [resolve(5620,a,5584,a)].
39.89/39.75	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f543(A,quickcheck_code_int,C,D,B)),B)) | hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),D),B) = hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),C),B).  [resolve(5620,a,5585,a)].
39.89/39.75	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(A,quickcheck_code_int,C,f543(A,quickcheck_code_int,D,C,B)) != hAPP(A,quickcheck_code_int,D,f543(A,quickcheck_code_int,D,C,B)) | hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),C),B) = hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),D),B).  [resolve(5620,a,5586,a)].
39.89/39.75	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f545(A,quickcheck_code_int,C,B)),B)) | zero_zero(quickcheck_code_int) = hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),C),B).  [resolve(5620,a,5587,a)].
39.89/39.75	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | zero_zero(quickcheck_code_int) != hAPP(A,quickcheck_code_int,C,f545(A,quickcheck_code_int,C,B)) | zero_zero(quickcheck_code_int) = hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),C),B).  [resolve(5620,a,5588,a)].
39.89/39.75	Derived: -ord(A) | ti(A,B) != ti(A,C) | ti(A,D) != ti(A,E) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),f547(quickcheck_code_int,A,F,V6,E,D,C,B))) | hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),V6),hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_atLeastLessThan(A),B),D)) = hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),F),hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_atLeastLessThan(A),C),E)).  [resolve(5620,a,5589,a)].
39.89/39.75	Derived: -ord(A) | ti(A,B) != ti(A,C) | ti(A,D) != ti(A,E) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),f547(quickcheck_code_int,A,F,V6,E,D,C,B)),D)) | hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),V6),hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_atLeastLessThan(A),B),D)) = hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),F),hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_atLeastLessThan(A),C),E)).  [resolve(5620,a,5590,a)].
39.89/39.75	Derived: -ord(A) | ti(A,B) != ti(A,C) | ti(A,D) != ti(A,E) | hAPP(A,quickcheck_code_int,F,f547(quickcheck_code_int,A,V6,F,E,D,C,B)) != hAPP(A,quickcheck_code_int,V6,f547(quickcheck_code_int,A,V6,F,E,D,C,B)) | hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),F),hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_atLeastLessThan(A),B),D)) = hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),V6),hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_atLeastLessThan(A),C),E)).  [resolve(5620,a,5591,a)].
39.89/39.75	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),hAPP(quickcheck_code_int,fun(A,quickcheck_code_int),hAPP(fun(A,fun(quickcheck_code_int,quickcheck_code_int)),fun(quickcheck_code_int,fun(A,quickcheck_code_int)),combc(A,quickcheck_code_int,quickcheck_code_int),hAPP(fun(A,quickcheck_code_int),fun(A,fun(quickcheck_code_int,quickcheck_code_int)),hAPP(fun(A,fun(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int))),fun(fun(A,quickcheck_code_int),fun(A,fun(quickcheck_code_int,quickcheck_code_int))),combs(A,quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int)),hAPP(fun(A,bool),fun(A,fun(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int))),hAPP(fun(bool,fun(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int))),fun(fun(A,bool),fun(A,fun(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int)))),combb(bool,fun(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int)),A),if(quickcheck_code_int)),C)),D)),zero_zero(quickcheck_code_int))),B) = hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),D),hAPP(fun(A,bool),fun(A,bool),collect(A),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,fun(bool,bool)),fun(fun(A,bool),fun(A,bool)),combs(A,bool,bool),hAPP(fun(A,bool),fun(A,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(A,bool),fun(A,fun(bool,bool))),combb(bool,fun(bool,bool),A),fconj),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,fun(fun(A,bool),bool)),fun(fun(A,bool),fun(A,bool)),combc(A,fun(A,bool),bool),member(A)),B))),C))).  [resolve(5620,a,5592,a)].
39.89/39.75	Derived: -comm_monoid_mult(quickcheck_code_int) | hAPP(fun(nat,bool),quickcheck_code_int,hAPP(fun(nat,quickcheck_code_int),fun(fun(nat,bool),quickcheck_code_int),big_co302546470etprod(nat,quickcheck_code_int),A),B) = hAPP(fun(int,bool),quickcheck_code_int,hAPP(fun(int,quickcheck_code_int),fun(fun(int,bool),quickcheck_code_int),big_co302546470etprod(int,quickcheck_code_int),hAPP(fun(int,nat),fun(int,quickcheck_code_int),hAPP(fun(nat,quickcheck_code_int),fun(fun(int,nat),fun(int,quickcheck_code_int)),combb(nat,quickcheck_code_int,int),A),nat_1)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),B)).  [resolve(5620,a,5593,a)].
39.89/39.75	Derived: hAPP(fun(product_prod(nat,nat),bool),quickcheck_code_int,hAPP(fun(product_prod(nat,nat),quickcheck_code_int),fun(fun(product_prod(nat,nat),bool),quickcheck_code_int),big_co1399186613setsum(product_prod(nat,nat),quickcheck_code_int),hAPP(fun(nat,fun(nat,quickcheck_code_int)),fun(product_prod(nat,nat),quickcheck_code_int),product_prod_case(nat,nat,quickcheck_code_int),A)),hAPP(fun(product_prod(nat,nat),bool),fun(product_prod(nat,nat),bool),collect(product_prod(nat,nat)),hAPP(fun(nat,fun(nat,bool)),fun(product_prod(nat,nat),bool),product_prod_case(nat,nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),hAPP(fun(nat,fun(nat,fun(nat,bool))),fun(nat,fun(nat,fun(nat,bool))),combc(nat,nat,fun(nat,bool)),hAPP(fun(nat,fun(nat,fun(nat,bool))),fun(nat,fun(nat,fun(nat,bool))),hAPP(fun(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool))),fun(fun(nat,fun(nat,fun(nat,bool))),fun(nat,fun(nat,fun(nat,bool)))),combb(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),nat),combc(nat,nat,bool)),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,fun(nat,bool))),hAPP(fun(fun(nat,nat),fun(nat,fun(nat,bool))),fun(fun(nat,fun(nat,nat)),fun(nat,fun(nat,fun(nat,bool)))),combb(fun(nat,nat),fun(nat,fun(nat,bool)),nat),hAPP(fun(nat,fun(nat,bool)),fun(fun(nat,nat),fun(nat,fun(nat,bool))),combb(nat,fun(nat,bool),nat),ord_less(nat))),plus_plus(nat)))),B)))) = hAPP(fun(nat,bool),quickcheck_code_int,hAPP(fun(nat,quickcheck_code_int),fun(fun(nat,bool),quickcheck_code_int),big_co1399186613setsum(nat,quickcheck_code_int),hAPP(fun(nat,fun(nat,bool)),fun(nat,quickcheck_code_int),hAPP(fun(nat,fun(fun(nat,bool),quickcheck_code_int)),fun(fun(nat,fun(nat,bool)),fun(nat,quickcheck_code_int)),combs(nat,fun(nat,bool),quickcheck_code_int),hAPP(fun(nat,fun(nat,quickcheck_code_int)),fun(nat,fun(fun(nat,bool),quickcheck_code_int)),hAPP(fun(fun(nat,quickcheck_code_int),fun(fun(nat,bool),quickcheck_code_int)),fun(fun(nat,fun(nat,quickcheck_code_int)),fun(nat,fun(fun(nat,bool),quickcheck_code_int))),combb(fun(nat,quickcheck_code_int),fun(fun(nat,bool),quickcheck_code_int),nat),big_co1399186613setsum(nat,quickcheck_code_int)),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,quickcheck_code_int)),hAPP(fun(fun(nat,nat),fun(nat,quickcheck_code_int)),fun(fun(nat,fun(nat,nat)),fun(nat,fun(nat,quickcheck_code_int))),combb(fun(nat,nat),fun(nat,quickcheck_code_int),nat),hAPP(fun(nat,fun(nat,quickcheck_code_int)),fun(fun(nat,nat),fun(nat,quickcheck_code_int)),combs(nat,nat,quickcheck_code_int),A)),minus_minus(nat)))),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),zero_zero(nat)))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),B)).  [resolve(5620,a,5594,a)].
39.89/39.75	Derived: -t2_space(quickcheck_code_int) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),f585(quickcheck_code_int,B,A))) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(fun(nat,quickcheck_code_int),fun(quickcheck_code_int,bool),sums(quickcheck_code_int),B),hAPP(fun(nat,bool),quickcheck_code_int,hAPP(fun(nat,quickcheck_code_int),fun(fun(nat,bool),quickcheck_code_int),big_co1399186613setsum(nat,quickcheck_code_int),B),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),A)))).  [resolve(5620,a,5595,b)].
39.89/39.75	Derived: -t2_space(quickcheck_code_int) | zero_zero(quickcheck_code_int) != hAPP(nat,quickcheck_code_int,A,f585(quickcheck_code_int,A,B)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(fun(nat,quickcheck_code_int),fun(quickcheck_code_int,bool),sums(quickcheck_code_int),A),hAPP(fun(nat,bool),quickcheck_code_int,hAPP(fun(nat,quickcheck_code_int),fun(fun(nat,bool),quickcheck_code_int),big_co1399186613setsum(nat,quickcheck_code_int),A),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),B)))).  [resolve(5620,a,5596,b)].
39.89/39.75	Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,A)),B)) | hAPP(fun(nat,bool),quickcheck_code_int,hAPP(fun(nat,quickcheck_code_int),fun(fun(nat,bool),quickcheck_code_int),big_co1399186613setsum(nat,quickcheck_code_int),C),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),B),hAPP(nat,nat,suc,A))) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),hAPP(fun(nat,bool),quickcheck_code_int,hAPP(fun(nat,quickcheck_code_int),fun(fun(nat,bool),quickcheck_code_int),big_co1399186613setsum(nat,quickcheck_code_int),C),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),B),A))),hAPP(nat,quickcheck_code_int,C,hAPP(nat,nat,suc,A))).  [resolve(5620,a,5598,a)].
39.89/39.76	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),C)) | hAPP(fun(nat,bool),quickcheck_code_int,hAPP(fun(nat,quickcheck_code_int),fun(fun(nat,bool),quickcheck_code_int),big_co1399186613setsum(nat,quickcheck_code_int),D),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),A),C)) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),hAPP(fun(nat,bool),quickcheck_code_int,hAPP(fun(nat,quickcheck_code_int),fun(fun(nat,bool),quickcheck_code_int),big_co1399186613setsum(nat,quickcheck_code_int),D),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),A),B))),hAPP(fun(nat,bool),quickcheck_code_int,hAPP(fun(nat,quickcheck_code_int),fun(fun(nat,bool),quickcheck_code_int),big_co1399186613setsum(nat,quickcheck_code_int),D),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),B),C))).  [resolve(5620,a,5599,a)].
39.89/39.76	Derived: hAPP(fun(nat,bool),quickcheck_code_int,hAPP(fun(nat,quickcheck_code_int),fun(fun(nat,bool),quickcheck_code_int),big_co1399186613setsum(nat,quickcheck_code_int),hAPP(fun(nat,nat),fun(nat,quickcheck_code_int),hAPP(fun(nat,quickcheck_code_int),fun(fun(nat,nat),fun(nat,quickcheck_code_int)),combb(nat,quickcheck_code_int,nat),A),suc)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),B),C)) = hAPP(fun(nat,bool),quickcheck_code_int,hAPP(fun(nat,quickcheck_code_int),fun(fun(nat,bool),quickcheck_code_int),big_co1399186613setsum(nat,quickcheck_code_int),A),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,suc,B)),hAPP(nat,nat,suc,C))).  [resolve(5620,a,5600,a)].
39.89/39.76	Derived: -hBOOL(hAPP(fun(fun(A,bool),bool),bool,finite_finite_1(fun(A,bool)),B)) | hBOOL(hAPP(fun(fun(A,bool),bool),bool,hAPP(fun(A,bool),fun(fun(fun(A,bool),bool),bool),member(fun(A,bool)),f646(A,quickcheck_code_int,C,B)),B)) | hBOOL(hAPP(fun(fun(A,bool),bool),bool,hAPP(fun(A,bool),fun(fun(fun(A,bool),bool),bool),member(fun(A,bool)),f647(A,quickcheck_code_int,C,B)),B)) | hAPP(fun(fun(A,bool),bool),quickcheck_code_int,hAPP(fun(fun(A,bool),quickcheck_code_int),fun(fun(fun(A,bool),bool),quickcheck_code_int),big_co1399186613setsum(fun(A,bool),quickcheck_code_int),hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),C)),B) = hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),C),hAPP(fun(fun(A,bool),bool),fun(A,bool),complete_Sup_Sup(fun(A,bool)),B)).  [resolve(5620,a,5601,a)].
39.89/39.76	Derived: -hBOOL(hAPP(fun(fun(A,bool),bool),bool,finite_finite_1(fun(A,bool)),B)) | hBOOL(hAPP(fun(fun(A,bool),bool),bool,hAPP(fun(A,bool),fun(fun(fun(A,bool),bool),bool),member(fun(A,bool)),f646(A,quickcheck_code_int,C,B)),B)) | hBOOL(hAPP(fun(fun(A,bool),bool),bool,hAPP(fun(A,bool),fun(fun(fun(A,bool),bool),bool),member(fun(A,bool)),f648(A,quickcheck_code_int,C,B)),B)) | hAPP(fun(fun(A,bool),bool),quickcheck_code_int,hAPP(fun(fun(A,bool),quickcheck_code_int),fun(fun(fun(A,bool),bool),quickcheck_code_int),big_co1399186613setsum(fun(A,bool),quickcheck_code_int),hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),C)),B) = hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),C),hAPP(fun(fun(A,bool),bool),fun(A,bool),complete_Sup_Sup(fun(A,bool)),B)).  [resolve(5620,a,5602,a)].
39.89/39.76	Derived: -hBOOL(hAPP(fun(fun(A,bool),bool),bool,finite_finite_1(fun(A,bool)),B)) | hBOOL(hAPP(fun(fun(A,bool),bool),bool,hAPP(fun(A,bool),fun(fun(fun(A,bool),bool),bool),member(fun(A,bool)),f646(A,quickcheck_code_int,C,B)),B)) | ti(fun(A,bool),f648(A,quickcheck_code_int,C,B)) != ti(fun(A,bool),f647(A,quickcheck_code_int,C,B)) | hAPP(fun(fun(A,bool),bool),quickcheck_code_int,hAPP(fun(fun(A,bool),quickcheck_code_int),fun(fun(fun(A,bool),bool),quickcheck_code_int),big_co1399186613setsum(fun(A,bool),quickcheck_code_int),hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),C)),B) = hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),C),hAPP(fun(fun(A,bool),bool),fun(A,bool),complete_Sup_Sup(fun(A,bool)),B)).  [resolve(5620,a,5603,a)].
39.89/39.76	Derived: -hBOOL(hAPP(fun(fun(A,bool),bool),bool,finite_finite_1(fun(A,bool)),B)) | hBOOL(hAPP(fun(fun(A,bool),bool),bool,hAPP(fun(A,bool),fun(fun(fun(A,bool),bool),bool),member(fun(A,bool)),f646(A,quickcheck_code_int,C,B)),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f649(A,quickcheck_code_int,C,B)),f647(A,quickcheck_code_int,C,B))) | hAPP(fun(fun(A,bool),bool),quickcheck_code_int,hAPP(fun(fun(A,bool),quickcheck_code_int),fun(fun(fun(A,bool),bool),quickcheck_code_int),big_co1399186613setsum(fun(A,bool),quickcheck_code_int),hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),C)),B) = hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),C),hAPP(fun(fun(A,bool),bool),fun(A,bool),complete_Sup_Sup(fun(A,bool)),B)).  [resolve(5620,a,5604,a)].
39.89/39.76	Derived: -hBOOL(hAPP(fun(fun(A,bool),bool),bool,finite_finite_1(fun(A,bool)),B)) | hBOOL(hAPP(fun(fun(A,bool),bool),bool,hAPP(fun(A,bool),fun(fun(fun(A,bool),bool),bool),member(fun(A,bool)),f646(A,quickcheck_code_int,C,B)),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f649(A,quickcheck_code_int,C,B)),f648(A,quickcheck_code_int,C,B))) | hAPP(fun(fun(A,bool),bool),quickcheck_code_int,hAPP(fun(fun(A,bool),quickcheck_code_int),fun(fun(fun(A,bool),bool),quickcheck_code_int),big_co1399186613setsum(fun(A,bool),quickcheck_code_int),hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),C)),B) = hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),C),hAPP(fun(fun(A,bool),bool),fun(A,bool),complete_Sup_Sup(fun(A,bool)),B)).  [resolve(5620,a,5605,a)].
39.89/39.76	Derived: -hBOOL(hAPP(fun(fun(A,bool),bool),bool,finite_finite_1(fun(A,bool)),B)) | hBOOL(hAPP(fun(fun(A,bool),bool),bool,hAPP(fun(A,bool),fun(fun(fun(A,bool),bool),bool),member(fun(A,bool)),f646(A,quickcheck_code_int,C,B)),B)) | zero_zero(quickcheck_code_int) != hAPP(A,quickcheck_code_int,C,f649(A,quickcheck_code_int,C,B)) | hAPP(fun(fun(A,bool),bool),quickcheck_code_int,hAPP(fun(fun(A,bool),quickcheck_code_int),fun(fun(fun(A,bool),bool),quickcheck_code_int),big_co1399186613setsum(fun(A,bool),quickcheck_code_int),hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),C)),B) = hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),C),hAPP(fun(fun(A,bool),bool),fun(A,bool),complete_Sup_Sup(fun(A,bool)),B)).  [resolve(5620,a,5606,a)].
39.89/39.76	Derived: -hBOOL(hAPP(fun(fun(A,bool),bool),bool,finite_finite_1(fun(A,bool)),B)) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),f646(A,quickcheck_code_int,C,B))) | hBOOL(hAPP(fun(fun(A,bool),bool),bool,hAPP(fun(A,bool),fun(fun(fun(A,bool),bool),bool),member(fun(A,bool)),f647(A,quickcheck_code_int,C,B)),B)) | hAPP(fun(fun(A,bool),bool),quickcheck_code_int,hAPP(fun(fun(A,bool),quickcheck_code_int),fun(fun(fun(A,bool),bool),quickcheck_code_int),big_co1399186613setsum(fun(A,bool),quickcheck_code_int),hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),C)),B) = hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),C),hAPP(fun(fun(A,bool),bool),fun(A,bool),complete_Sup_Sup(fun(A,bool)),B)).  [resolve(5620,a,5607,a)].
39.89/39.76	Derived: -hBOOL(hAPP(fun(fun(A,bool),bool),bool,finite_finite_1(fun(A,bool)),B)) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),f646(A,quickcheck_code_int,C,B))) | hBOOL(hAPP(fun(fun(A,bool),bool),bool,hAPP(fun(A,bool),fun(fun(fun(A,bool),bool),bool),member(fun(A,bool)),f648(A,quickcheck_code_int,C,B)),B)) | hAPP(fun(fun(A,bool),bool),quickcheck_code_int,hAPP(fun(fun(A,bool),quickcheck_code_int),fun(fun(fun(A,bool),bool),quickcheck_code_int),big_co1399186613setsum(fun(A,bool),quickcheck_code_int),hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),C)),B) = hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),C),hAPP(fun(fun(A,bool),bool),fun(A,bool),complete_Sup_Sup(fun(A,bool)),B)).  [resolve(5620,a,5608,a)].
39.89/39.76	Derived: -hBOOL(hAPP(fun(fun(A,bool),bool),bool,finite_finite_1(fun(A,bool)),B)) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),f646(A,quickcheck_code_int,C,B))) | ti(fun(A,bool),f648(A,quickcheck_code_int,C,B)) != ti(fun(A,bool),f647(A,quickcheck_code_int,C,B)) | hAPP(fun(fun(A,bool),bool),quickcheck_code_int,hAPP(fun(fun(A,bool),quickcheck_code_int),fun(fun(fun(A,bool),bool),quickcheck_code_int),big_co1399186613setsum(fun(A,bool),quickcheck_code_int),hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),C)),B) = hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),C),hAPP(fun(fun(A,bool),bool),fun(A,bool),complete_Sup_Sup(fun(A,bool)),B)).  [resolve(5620,a,5609,a)].
39.89/39.76	Derived: -hBOOL(hAPP(fun(fun(A,bool),bool),bool,finite_finite_1(fun(A,bool)),B)) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),f646(A,quickcheck_code_int,C,B))) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f649(A,quickcheck_code_int,C,B)),f647(A,quickcheck_code_int,C,B))) | hAPP(fun(fun(A,bool),bool),quickcheck_code_int,hAPP(fun(fun(A,bool),quickcheck_code_int),fun(fun(fun(A,bool),bool),quickcheck_code_int),big_co1399186613setsum(fun(A,bool),quickcheck_code_int),hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),C)),B) = hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),C),hAPP(fun(fun(A,bool),bool),fun(A,bool),complete_Sup_Sup(fun(A,bool)),B)).  [resolve(5620,a,5610,a)].
39.89/39.76	Derived: -hBOOL(hAPP(fun(fun(A,bool),bool),bool,finite_finite_1(fun(A,bool)),B)) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),f646(A,quickcheck_code_int,C,B))) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f649(A,quickcheck_code_int,C,B)),f648(A,quickcheck_code_int,C,B))) | hAPP(fun(fun(A,bool),bool),quickcheck_code_int,hAPP(fun(fun(A,bool),quickcheck_code_int),fun(fun(fun(A,bool),bool),quickcheck_code_int),big_co1399186613setsum(fun(A,bool),quickcheck_code_int),hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),C)),B) = hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),C),hAPP(fun(fun(A,bool),bool),fun(A,bool),complete_Sup_Sup(fun(A,bool)),B)).  [resolve(5620,a,5611,a)].
39.89/39.76	Derived: -hBOOL(hAPP(fun(fun(A,bool),bool),bool,finite_finite_1(fun(A,bool)),B)) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),f646(A,quickcheck_code_int,C,B))) | zero_zero(quickcheck_code_int) != hAPP(A,quickcheck_code_int,C,f649(A,quickcheck_code_int,C,B)) | hAPP(fun(fun(A,bool),bool),quickcheck_code_int,hAPP(fun(fun(A,bool),quickcheck_code_int),fun(fun(fun(A,bool),bool),quickcheck_code_int),big_co1399186613setsum(fun(A,bool),quickcheck_code_int),hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),C)),B) = hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),C),hAPP(fun(fun(A,bool),bool),fun(A,bool),complete_Sup_Sup(fun(A,bool)),B)).  [resolve(5620,a,5612,a)].
39.89/39.77	Derived: -ordere779506340up_add(quickcheck_code_int) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f657(A,quickcheck_code_int,B,C,D)),D)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),B),D)),hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),C),D))).  [resolve(5620,a,5614,b)].
39.89/39.77	Derived: -ordere779506340up_add(quickcheck_code_int) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),hAPP(A,quickcheck_code_int,B,f657(A,quickcheck_code_int,B,C,D))),hAPP(A,quickcheck_code_int,C,f657(A,quickcheck_code_int,B,C,D)))) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),B),D)),hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),C),D))).  [resolve(5620,a,5615,b)].
39.89/39.77	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(fun(C,bool),quickcheck_code_int,hAPP(fun(C,quickcheck_code_int),fun(fun(C,bool),quickcheck_code_int),big_co1399186613setsum(C,quickcheck_code_int),hAPP(fun(C,fun(A,bool)),fun(C,quickcheck_code_int),hAPP(fun(fun(A,bool),quickcheck_code_int),fun(fun(C,fun(A,bool)),fun(C,quickcheck_code_int)),combb(fun(A,bool),quickcheck_code_int,C),hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),D)),hAPP(fun(C,fun(A,bool)),fun(C,fun(A,bool)),hAPP(fun(fun(A,bool),fun(A,bool)),fun(fun(C,fun(A,bool)),fun(C,fun(A,bool))),combb(fun(A,bool),fun(A,bool),C),collect(A)),hAPP(fun(C,fun(A,bool)),fun(C,fun(A,bool)),hAPP(fun(fun(A,bool),fun(A,bool)),fun(fun(C,fun(A,bool)),fun(C,fun(A,bool))),combb(fun(A,bool),fun(A,bool),C),hAPP(fun(A,fun(bool,bool)),fun(fun(A,bool),fun(A,bool)),combs(A,bool,bool),hAPP(fun(A,bool),fun(A,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(A,bool),fun(A,fun(bool,bool))),combb(bool,fun(bool,bool),A),fconj),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,fun(fun(A,bool),bool)),fun(fun(A,bool),fun(A,bool)),combc(A,fun(A,bool),bool),member(A)),B)))),hAPP(fun(A,fun(C,bool)),fun(C,fun(A,bool)),combc(A,C,bool),hAPP(fun(A,C),fun(A,fun(C,bool)),hAPP(fun(C,fun(C,bool)),fun(fun(A,C),fun(A,fun(C,bool))),combb(C,fun(C,bool),A),fequal(C)),E)))))),hAPP(fun(A,bool),fun(C,bool),hAPP(fun(A,C),fun(fun(A,bool),fun(C,bool)),image(A,C),E),B)) = hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),D),B).  [resolve(5620,a,5616,a)].
39.89/39.77	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f694(A,quickcheck_code_int,D,C,B)),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),B),C))) | hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),D),B) = hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),D),C).  [resolve(5620,a,5617,a)].
40.04/39.91	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | zero_zero(quickcheck_code_int) != hAPP(A,quickcheck_code_int,D,f694(A,quickcheck_code_int,D,C,B)) | hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),D),B) = hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),D),C).  [resolve(5620,a,5618,a)].
40.04/39.91	Derived: hAPP(fun(nat,bool),quickcheck_code_int,hAPP(fun(nat,quickcheck_code_int),fun(fun(nat,bool),quickcheck_code_int),big_co1399186613setsum(nat,quickcheck_code_int),hAPP(fun(nat,nat),fun(nat,quickcheck_code_int),hAPP(fun(nat,quickcheck_code_int),fun(fun(nat,nat),fun(nat,quickcheck_code_int)),combb(nat,quickcheck_code_int,nat),A),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),B))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),C),D)) = hAPP(fun(nat,bool),quickcheck_code_int,hAPP(fun(nat,quickcheck_code_int),fun(fun(nat,bool),quickcheck_code_int),big_co1399186613setsum(nat,quickcheck_code_int),A),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),C),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),D),B))).  [resolve(5620,a,5619,a)].
40.04/39.91	5621 -topological_space(A) | -comm_monoid_add(A) | -hBOOL(hAPP(fun(nat,A),bool,summable(A),B)) | hBOOL(hAPP(A,bool,hAPP(fun(nat,A),fun(A,bool),sums(A),B),f737(A,B))) # label(fact_4090_summable__def) # label(axiom).  [clausify(4121)].
40.04/39.91	Derived: -topological_space(real) | -hBOOL(hAPP(fun(nat,real),bool,summable(real),A)) | hBOOL(hAPP(real,bool,hAPP(fun(nat,real),fun(real,bool),sums(real),A),f737(real,A))).  [resolve(5621,b,5513,a)].
40.04/39.91	Derived: -topological_space(int) | -hBOOL(hAPP(fun(nat,int),bool,summable(int),A)) | hBOOL(hAPP(int,bool,hAPP(fun(nat,int),fun(int,bool),sums(int),A),f737(int,A))).  [resolve(5621,b,5524,a)].
40.04/39.91	Derived: -topological_space(code_code_numeral) | -hBOOL(hAPP(fun(nat,code_code_numeral),bool,summable(code_code_numeral),A)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(fun(nat,code_code_numeral),fun(code_code_numeral,bool),sums(code_code_numeral),A),f737(code_code_numeral,A))).  [resolve(5621,b,5539,a)].
40.04/39.91	Derived: -topological_space(rat) | -hBOOL(hAPP(fun(nat,rat),bool,summable(rat),A)) | hBOOL(hAPP(rat,bool,hAPP(fun(nat,rat),fun(rat,bool),sums(rat),A),f737(rat,A))).  [resolve(5621,b,5561,a)].
40.04/39.91	Derived: -topological_space(quickcheck_code_int) | -hBOOL(hAPP(fun(nat,quickcheck_code_int),bool,summable(quickcheck_code_int),A)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(fun(nat,quickcheck_code_int),fun(quickcheck_code_int,bool),sums(quickcheck_code_int),A),f737(quickcheck_code_int,A))).  [resolve(5621,b,5620,a)].
40.04/39.91	5622 -topological_space(A) | -comm_monoid_add(A) | hBOOL(hAPP(fun(nat,A),bool,summable(A),B)) | -hBOOL(hAPP(A,bool,hAPP(fun(nat,A),fun(A,bool),sums(A),B),C)) # label(fact_4090_summable__def) # label(axiom).  [clausify(4121)].
40.04/39.91	5623 -power(A) | -comm_monoid_add(A) | hAPP(fun(nat,bool),A,hAPP(fun(nat,A),fun(fun(nat,bool),A),big_co1399186613setsum(nat,A),hAPP(fun(nat,A),fun(nat,A),hAPP(fun(nat,fun(A,A)),fun(fun(nat,A),fun(nat,A)),combs(nat,A,A),hAPP(fun(nat,A),fun(nat,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(nat,A),fun(nat,fun(A,A))),combb(A,fun(A,A),nat),times_times(A)),hAPP(fun(nat,nat),fun(nat,A),hAPP(fun(nat,A),fun(fun(nat,nat),fun(nat,A)),combb(nat,A,nat),hAPP(A,fun(nat,A),power_power(A),B)),hAPP(nat,fun(nat,nat),minus_minus(nat),C)))),hAPP(A,fun(nat,A),power_power(A),D))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,suc,C))) = hAPP(fun(nat,bool),A,hAPP(fun(nat,A),fun(fun(nat,bool),A),big_co1399186613setsum(nat,A),hAPP(fun(nat,A),fun(nat,A),hAPP(fun(nat,fun(A,A)),fun(fun(nat,A),fun(nat,A)),combs(nat,A,A),hAPP(fun(nat,A),fun(nat,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(nat,A),fun(nat,fun(A,A))),combb(A,fun(A,A),nat),times_times(A)),hAPP(A,fun(nat,A),power_power(A),B))),hAPP(fun(nat,nat),fun(nat,A),hAPP(fun(nat,A),fun(fun(nat,nat),fun(nat,A)),combb(nat,A,nat),hAPP(A,fun(nat,A),power_power(A),D)),hAPP(nat,fun(nat,nat),minus_minus(nat),C)))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,suc,C))) # label(fact_4175_lemma__realpow__rev__sumr) # label(axiom).  [clausify(4139)].
40.04/39.91	Derived: -power(real) | hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),hAPP(real,fun(nat,real),power_power(real),A)),hAPP(nat,fun(nat,nat),minus_minus(nat),B)))),hAPP(real,fun(nat,real),power_power(real),C))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,suc,B))) = hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(real,fun(nat,real),power_power(real),A))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),hAPP(real,fun(nat,real),power_power(real),C)),hAPP(nat,fun(nat,nat),minus_minus(nat),B)))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,suc,B))).  [resolve(5623,b,5513,a)].
40.04/39.91	Derived: -power(int) | hAPP(fun(nat,bool),int,hAPP(fun(nat,int),fun(fun(nat,bool),int),big_co1399186613setsum(nat,int),hAPP(fun(nat,int),fun(nat,int),hAPP(fun(nat,fun(int,int)),fun(fun(nat,int),fun(nat,int)),combs(nat,int,int),hAPP(fun(nat,int),fun(nat,fun(int,int)),hAPP(fun(int,fun(int,int)),fun(fun(nat,int),fun(nat,fun(int,int))),combb(int,fun(int,int),nat),times_times(int)),hAPP(fun(nat,nat),fun(nat,int),hAPP(fun(nat,int),fun(fun(nat,nat),fun(nat,int)),combb(nat,int,nat),hAPP(int,fun(nat,int),power_power(int),A)),hAPP(nat,fun(nat,nat),minus_minus(nat),B)))),hAPP(int,fun(nat,int),power_power(int),C))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,suc,B))) = hAPP(fun(nat,bool),int,hAPP(fun(nat,int),fun(fun(nat,bool),int),big_co1399186613setsum(nat,int),hAPP(fun(nat,int),fun(nat,int),hAPP(fun(nat,fun(int,int)),fun(fun(nat,int),fun(nat,int)),combs(nat,int,int),hAPP(fun(nat,int),fun(nat,fun(int,int)),hAPP(fun(int,fun(int,int)),fun(fun(nat,int),fun(nat,fun(int,int))),combb(int,fun(int,int),nat),times_times(int)),hAPP(int,fun(nat,int),power_power(int),A))),hAPP(fun(nat,nat),fun(nat,int),hAPP(fun(nat,int),fun(fun(nat,nat),fun(nat,int)),combb(nat,int,nat),hAPP(int,fun(nat,int),power_power(int),C)),hAPP(nat,fun(nat,nat),minus_minus(nat),B)))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,suc,B))).  [resolve(5623,b,5524,a)].
40.04/39.91	Derived: -power(code_code_numeral) | hAPP(fun(nat,bool),code_code_numeral,hAPP(fun(nat,code_code_numeral),fun(fun(nat,bool),code_code_numeral),big_co1399186613setsum(nat,code_code_numeral),hAPP(fun(nat,code_code_numeral),fun(nat,code_code_numeral),hAPP(fun(nat,fun(code_code_numeral,code_code_numeral)),fun(fun(nat,code_code_numeral),fun(nat,code_code_numeral)),combs(nat,code_code_numeral,code_code_numeral),hAPP(fun(nat,code_code_numeral),fun(nat,fun(code_code_numeral,code_code_numeral)),hAPP(fun(code_code_numeral,fun(code_code_numeral,code_code_numeral)),fun(fun(nat,code_code_numeral),fun(nat,fun(code_code_numeral,code_code_numeral))),combb(code_code_numeral,fun(code_code_numeral,code_code_numeral),nat),times_times(code_code_numeral)),hAPP(fun(nat,nat),fun(nat,code_code_numeral),hAPP(fun(nat,code_code_numeral),fun(fun(nat,nat),fun(nat,code_code_numeral)),combb(nat,code_code_numeral,nat),hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A)),hAPP(nat,fun(nat,nat),minus_minus(nat),B)))),hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),C))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,suc,B))) = hAPP(fun(nat,bool),code_code_numeral,hAPP(fun(nat,code_code_numeral),fun(fun(nat,bool),code_code_numeral),big_co1399186613setsum(nat,code_code_numeral),hAPP(fun(nat,code_code_numeral),fun(nat,code_code_numeral),hAPP(fun(nat,fun(code_code_numeral,code_code_numeral)),fun(fun(nat,code_code_numeral),fun(nat,code_code_numeral)),combs(nat,code_code_numeral,code_code_numeral),hAPP(fun(nat,code_code_numeral),fun(nat,fun(code_code_numeral,code_code_numeral)),hAPP(fun(code_code_numeral,fun(code_code_numeral,code_code_numeral)),fun(fun(nat,code_code_numeral),fun(nat,fun(code_code_numeral,code_code_numeral))),combb(code_code_numeral,fun(code_code_numeral,code_code_numeral),nat),times_times(code_code_numeral)),hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A))),hAPP(fun(nat,nat),fun(nat,code_code_numeral),hAPP(fun(nat,code_code_numeral),fun(fun(nat,nat),fun(nat,code_code_numeral)),combb(nat,code_code_numeral,nat),hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),C)),hAPP(nat,fun(nat,nat),minus_minus(nat),B)))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,suc,B))).  [resolve(5623,b,5539,a)].
40.04/39.92	Derived: -power(rat) | hAPP(fun(nat,bool),rat,hAPP(fun(nat,rat),fun(fun(nat,bool),rat),big_co1399186613setsum(nat,rat),hAPP(fun(nat,rat),fun(nat,rat),hAPP(fun(nat,fun(rat,rat)),fun(fun(nat,rat),fun(nat,rat)),combs(nat,rat,rat),hAPP(fun(nat,rat),fun(nat,fun(rat,rat)),hAPP(fun(rat,fun(rat,rat)),fun(fun(nat,rat),fun(nat,fun(rat,rat))),combb(rat,fun(rat,rat),nat),times_times(rat)),hAPP(fun(nat,nat),fun(nat,rat),hAPP(fun(nat,rat),fun(fun(nat,nat),fun(nat,rat)),combb(nat,rat,nat),hAPP(rat,fun(nat,rat),power_power(rat),A)),hAPP(nat,fun(nat,nat),minus_minus(nat),B)))),hAPP(rat,fun(nat,rat),power_power(rat),C))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,suc,B))) = hAPP(fun(nat,bool),rat,hAPP(fun(nat,rat),fun(fun(nat,bool),rat),big_co1399186613setsum(nat,rat),hAPP(fun(nat,rat),fun(nat,rat),hAPP(fun(nat,fun(rat,rat)),fun(fun(nat,rat),fun(nat,rat)),combs(nat,rat,rat),hAPP(fun(nat,rat),fun(nat,fun(rat,rat)),hAPP(fun(rat,fun(rat,rat)),fun(fun(nat,rat),fun(nat,fun(rat,rat))),combb(rat,fun(rat,rat),nat),times_times(rat)),hAPP(rat,fun(nat,rat),power_power(rat),A))),hAPP(fun(nat,nat),fun(nat,rat),hAPP(fun(nat,rat),fun(fun(nat,nat),fun(nat,rat)),combb(nat,rat,nat),hAPP(rat,fun(nat,rat),power_power(rat),C)),hAPP(nat,fun(nat,nat),minus_minus(nat),B)))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,suc,B))).  [resolve(5623,b,5561,a)].
40.04/39.92	Derived: -power(quickcheck_code_int) | hAPP(fun(nat,bool),quickcheck_code_int,hAPP(fun(nat,quickcheck_code_int),fun(fun(nat,bool),quickcheck_code_int),big_co1399186613setsum(nat,quickcheck_code_int),hAPP(fun(nat,quickcheck_code_int),fun(nat,quickcheck_code_int),hAPP(fun(nat,fun(quickcheck_code_int,quickcheck_code_int)),fun(fun(nat,quickcheck_code_int),fun(nat,quickcheck_code_int)),combs(nat,quickcheck_code_int,quickcheck_code_int),hAPP(fun(nat,quickcheck_code_int),fun(nat,fun(quickcheck_code_int,quickcheck_code_int)),hAPP(fun(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int)),fun(fun(nat,quickcheck_code_int),fun(nat,fun(quickcheck_code_int,quickcheck_code_int))),combb(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),nat),times_times(quickcheck_code_int)),hAPP(fun(nat,nat),fun(nat,quickcheck_code_int),hAPP(fun(nat,quickcheck_code_int),fun(fun(nat,nat),fun(nat,quickcheck_code_int)),combb(nat,quickcheck_code_int,nat),hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A)),hAPP(nat,fun(nat,nat),minus_minus(nat),B)))),hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),C))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,suc,B))) = hAPP(fun(nat,bool),quickcheck_code_int,hAPP(fun(nat,quickcheck_code_int),fun(fun(nat,bool),quickcheck_code_int),big_co1399186613setsum(nat,quickcheck_code_int),hAPP(fun(nat,quickcheck_code_int),fun(nat,quickcheck_code_int),hAPP(fun(nat,fun(quickcheck_code_int,quickcheck_code_int)),fun(fun(nat,quickcheck_code_int),fun(nat,quickcheck_code_int)),combs(nat,quickcheck_code_int,quickcheck_code_int),hAPP(fun(nat,quickcheck_code_int),fun(nat,fun(quickcheck_code_int,quickcheck_code_int)),hAPP(fun(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int)),fun(fun(nat,quickcheck_code_int),fun(nat,fun(quickcheck_code_int,quickcheck_code_int))),combb(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),nat),times_times(quickcheck_code_int)),hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A))),hAPP(fun(nat,nat),fun(nat,quickcheck_code_int),hAPP(fun(nat,quickcheck_code_int),fun(fun(nat,nat),fun(nat,quickcheck_code_int)),combb(nat,quickcheck_code_int,nat),hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),C)),hAPP(nat,fun(nat,nat),minus_minus(nat),B)))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,suc,B))).  [resolve(5623,b,5620,a)].
40.11/39.96	5624 -comm_monoid_add(A) | hAPP(fun(nat,bool),A,hAPP(fun(nat,A),fun(fun(nat,bool),A),big_co1399186613setsum(nat,A),B),hAPP(nat,fun(nat,bool),ord_lessThan(nat),hAPP(nat,nat,suc,C))) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(fun(nat,bool),A,hAPP(fun(nat,A),fun(fun(nat,bool),A),big_co1399186613setsum(nat,A),B),hAPP(nat,fun(nat,bool),ord_lessThan(nat),C))),hAPP(nat,A,B,C)) # label(fact_4321_setsum__lessThan__Suc) # label(axiom).  [clausify(4180)].
40.11/39.96	Derived: hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),A),hAPP(nat,fun(nat,bool),ord_lessThan(nat),hAPP(nat,nat,suc,B))) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),A),hAPP(nat,fun(nat,bool),ord_lessThan(nat),B))),hAPP(nat,real,A,B)).  [resolve(5624,a,5513,a)].
40.11/39.96	Derived: hAPP(fun(nat,bool),int,hAPP(fun(nat,int),fun(fun(nat,bool),int),big_co1399186613setsum(nat,int),A),hAPP(nat,fun(nat,bool),ord_lessThan(nat),hAPP(nat,nat,suc,B))) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(fun(nat,bool),int,hAPP(fun(nat,int),fun(fun(nat,bool),int),big_co1399186613setsum(nat,int),A),hAPP(nat,fun(nat,bool),ord_lessThan(nat),B))),hAPP(nat,int,A,B)).  [resolve(5624,a,5524,a)].
40.11/39.96	Derived: hAPP(fun(nat,bool),code_code_numeral,hAPP(fun(nat,code_code_numeral),fun(fun(nat,bool),code_code_numeral),big_co1399186613setsum(nat,code_code_numeral),A),hAPP(nat,fun(nat,bool),ord_lessThan(nat),hAPP(nat,nat,suc,B))) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),hAPP(fun(nat,bool),code_code_numeral,hAPP(fun(nat,code_code_numeral),fun(fun(nat,bool),code_code_numeral),big_co1399186613setsum(nat,code_code_numeral),A),hAPP(nat,fun(nat,bool),ord_lessThan(nat),B))),hAPP(nat,code_code_numeral,A,B)).  [resolve(5624,a,5539,a)].
40.11/39.96	Derived: hAPP(fun(nat,bool),rat,hAPP(fun(nat,rat),fun(fun(nat,bool),rat),big_co1399186613setsum(nat,rat),A),hAPP(nat,fun(nat,bool),ord_lessThan(nat),hAPP(nat,nat,suc,B))) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(fun(nat,bool),rat,hAPP(fun(nat,rat),fun(fun(nat,bool),rat),big_co1399186613setsum(nat,rat),A),hAPP(nat,fun(nat,bool),ord_lessThan(nat),B))),hAPP(nat,rat,A,B)).  [resolve(5624,a,5561,a)].
40.25/40.16	Derived: hAPP(fun(nat,bool),quickcheck_code_int,hAPP(fun(nat,quickcheck_code_int),fun(fun(nat,bool),quickcheck_code_int),big_co1399186613setsum(nat,quickcheck_code_int),A),hAPP(nat,fun(nat,bool),ord_lessThan(nat),hAPP(nat,nat,suc,B))) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),hAPP(fun(nat,bool),quickcheck_code_int,hAPP(fun(nat,quickcheck_code_int),fun(fun(nat,bool),quickcheck_code_int),big_co1399186613setsum(nat,quickcheck_code_int),A),hAPP(nat,fun(nat,bool),ord_lessThan(nat),B))),hAPP(nat,quickcheck_code_int,A,B)).  [resolve(5624,a,5620,a)].
40.25/40.16	5625 -comm_monoid_add(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),zero_zero(A)) = ti(A,B) # label(fact_774_add_Ocomm__neutral) # label(axiom).  [clausify(4262)].
40.25/40.16	Derived: hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),zero_zero(real)) = ti(real,A).  [resolve(5625,a,5513,a)].
40.25/40.16	Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),zero_zero(int)) = ti(int,A).  [resolve(5625,a,5524,a)].
40.25/40.16	Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),A),zero_zero(code_code_numeral)) = ti(code_code_numeral,A).  [resolve(5625,a,5539,a)].
40.25/40.16	Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),zero_zero(rat)) = ti(rat,A).  [resolve(5625,a,5561,a)].
40.25/40.16	Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),A),zero_zero(quickcheck_code_int)) = ti(quickcheck_code_int,A).  [resolve(5625,a,5620,a)].
40.25/40.16	5626 -comm_monoid_add(A) | hAPP(fun(nat,bool),A,hAPP(fun(nat,A),fun(fun(nat,bool),A),big_co1399186613setsum(nat,A),hAPP(fun(nat,nat),fun(nat,A),hAPP(fun(nat,A),fun(fun(nat,nat),fun(nat,A)),combb(nat,A,nat),B),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),C))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),D),E)) = hAPP(fun(nat,bool),A,hAPP(fun(nat,A),fun(fun(nat,bool),A),big_co1399186613setsum(nat,A),B),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),D),C)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),E),C))) # label(fact_4543_setsum__shift__bounds__cl__nat__ivl) # label(axiom).  [clausify(4412)].
40.25/40.16	Derived: hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),A),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),B))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),C),D)) = hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),A),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),C),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),D),B))).  [resolve(5626,a,5513,a)].
40.25/40.16	Derived: hAPP(fun(nat,bool),int,hAPP(fun(nat,int),fun(fun(nat,bool),int),big_co1399186613setsum(nat,int),hAPP(fun(nat,nat),fun(nat,int),hAPP(fun(nat,int),fun(fun(nat,nat),fun(nat,int)),combb(nat,int,nat),A),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),B))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),C),D)) = hAPP(fun(nat,bool),int,hAPP(fun(nat,int),fun(fun(nat,bool),int),big_co1399186613setsum(nat,int),A),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),C),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),D),B))).  [resolve(5626,a,5524,a)].
40.25/40.17	Derived: hAPP(fun(nat,bool),code_code_numeral,hAPP(fun(nat,code_code_numeral),fun(fun(nat,bool),code_code_numeral),big_co1399186613setsum(nat,code_code_numeral),hAPP(fun(nat,nat),fun(nat,code_code_numeral),hAPP(fun(nat,code_code_numeral),fun(fun(nat,nat),fun(nat,code_code_numeral)),combb(nat,code_code_numeral,nat),A),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),B))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),C),D)) = hAPP(fun(nat,bool),code_code_numeral,hAPP(fun(nat,code_code_numeral),fun(fun(nat,bool),code_code_numeral),big_co1399186613setsum(nat,code_code_numeral),A),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),C),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),D),B))).  [resolve(5626,a,5539,a)].
40.25/40.17	Derived: hAPP(fun(nat,bool),rat,hAPP(fun(nat,rat),fun(fun(nat,bool),rat),big_co1399186613setsum(nat,rat),hAPP(fun(nat,nat),fun(nat,rat),hAPP(fun(nat,rat),fun(fun(nat,nat),fun(nat,rat)),combb(nat,rat,nat),A),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),B))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),C),D)) = hAPP(fun(nat,bool),rat,hAPP(fun(nat,rat),fun(fun(nat,bool),rat),big_co1399186613setsum(nat,rat),A),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),C),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),D),B))).  [resolve(5626,a,5561,a)].
40.25/40.17	Derived: hAPP(fun(nat,bool),quickcheck_code_int,hAPP(fun(nat,quickcheck_code_int),fun(fun(nat,bool),quickcheck_code_int),big_co1399186613setsum(nat,quickcheck_code_int),hAPP(fun(nat,nat),fun(nat,quickcheck_code_int),hAPP(fun(nat,quickcheck_code_int),fun(fun(nat,nat),fun(nat,quickcheck_code_int)),combb(nat,quickcheck_code_int,nat),A),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),B))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),C),D)) = hAPP(fun(nat,bool),quickcheck_code_int,hAPP(fun(nat,quickcheck_code_int),fun(fun(nat,bool),quickcheck_code_int),big_co1399186613setsum(nat,quickcheck_code_int),A),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),C),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),D),B))).  [resolve(5626,a,5620,a)].
40.25/40.17	5627 -comm_monoid_add(A) | hAPP(fun(nat,bool),A,hAPP(fun(nat,A),fun(fun(nat,bool),A),big_co1399186613setsum(nat,A),hAPP(fun(nat,nat),fun(nat,A),hAPP(fun(nat,A),fun(fun(nat,nat),fun(nat,A)),combb(nat,A,nat),B),suc)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),C),D)) = hAPP(fun(nat,bool),A,hAPP(fun(nat,A),fun(fun(nat,bool),A),big_co1399186613setsum(nat,A),B),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),hAPP(nat,nat,suc,C)),hAPP(nat,nat,suc,D))) # label(fact_4187_setsum__shift__bounds__Suc__ivl) # label(axiom).  [clausify(4421)].
40.25/40.17	Derived: hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),A),suc)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),B),C)) = hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),A),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),hAPP(nat,nat,suc,B)),hAPP(nat,nat,suc,C))).  [resolve(5627,a,5513,a)].
40.25/40.17	Derived: hAPP(fun(nat,bool),int,hAPP(fun(nat,int),fun(fun(nat,bool),int),big_co1399186613setsum(nat,int),hAPP(fun(nat,nat),fun(nat,int),hAPP(fun(nat,int),fun(fun(nat,nat),fun(nat,int)),combb(nat,int,nat),A),suc)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),B),C)) = hAPP(fun(nat,bool),int,hAPP(fun(nat,int),fun(fun(nat,bool),int),big_co1399186613setsum(nat,int),A),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),hAPP(nat,nat,suc,B)),hAPP(nat,nat,suc,C))).  [resolve(5627,a,5524,a)].
40.34/40.19	Derived: hAPP(fun(nat,bool),code_code_numeral,hAPP(fun(nat,code_code_numeral),fun(fun(nat,bool),code_code_numeral),big_co1399186613setsum(nat,code_code_numeral),hAPP(fun(nat,nat),fun(nat,code_code_numeral),hAPP(fun(nat,code_code_numeral),fun(fun(nat,nat),fun(nat,code_code_numeral)),combb(nat,code_code_numeral,nat),A),suc)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),B),C)) = hAPP(fun(nat,bool),code_code_numeral,hAPP(fun(nat,code_code_numeral),fun(fun(nat,bool),code_code_numeral),big_co1399186613setsum(nat,code_code_numeral),A),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),hAPP(nat,nat,suc,B)),hAPP(nat,nat,suc,C))).  [resolve(5627,a,5539,a)].
40.34/40.19	Derived: hAPP(fun(nat,bool),rat,hAPP(fun(nat,rat),fun(fun(nat,bool),rat),big_co1399186613setsum(nat,rat),hAPP(fun(nat,nat),fun(nat,rat),hAPP(fun(nat,rat),fun(fun(nat,nat),fun(nat,rat)),combb(nat,rat,nat),A),suc)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),B),C)) = hAPP(fun(nat,bool),rat,hAPP(fun(nat,rat),fun(fun(nat,bool),rat),big_co1399186613setsum(nat,rat),A),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),hAPP(nat,nat,suc,B)),hAPP(nat,nat,suc,C))).  [resolve(5627,a,5561,a)].
40.34/40.19	Derived: hAPP(fun(nat,bool),quickcheck_code_int,hAPP(fun(nat,quickcheck_code_int),fun(fun(nat,bool),quickcheck_code_int),big_co1399186613setsum(nat,quickcheck_code_int),hAPP(fun(nat,nat),fun(nat,quickcheck_code_int),hAPP(fun(nat,quickcheck_code_int),fun(fun(nat,nat),fun(nat,quickcheck_code_int)),combb(nat,quickcheck_code_int,nat),A),suc)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),B),C)) = hAPP(fun(nat,bool),quickcheck_code_int,hAPP(fun(nat,quickcheck_code_int),fun(fun(nat,bool),quickcheck_code_int),big_co1399186613setsum(nat,quickcheck_code_int),A),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),hAPP(nat,nat,suc,B)),hAPP(nat,nat,suc,C))).  [resolve(5627,a,5620,a)].
40.34/40.19	5628 -comm_monoid_add(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | -hBOOL(hAPP(fun(D,bool),bool,finite_finite_1(D),E)) | hAPP(fun(D,bool),A,hAPP(fun(D,A),fun(fun(D,bool),A),big_co1399186613setsum(D,A),hAPP(fun(D,fun(B,bool)),fun(D,A),hAPP(fun(D,fun(fun(B,bool),A)),fun(fun(D,fun(B,bool)),fun(D,A)),combs(D,fun(B,bool),A),hAPP(fun(D,fun(B,A)),fun(D,fun(fun(B,bool),A)),hAPP(fun(fun(B,A),fun(fun(B,bool),A)),fun(fun(D,fun(B,A)),fun(D,fun(fun(B,bool),A))),combb(fun(B,A),fun(fun(B,bool),A),D),big_co1399186613setsum(B,A)),hAPP(fun(B,fun(D,A)),fun(D,fun(B,A)),combc(B,D,A),F))),hAPP(fun(D,fun(B,bool)),fun(D,fun(B,bool)),hAPP(fun(fun(B,bool),fun(B,bool)),fun(fun(D,fun(B,bool)),fun(D,fun(B,bool))),combb(fun(B,bool),fun(B,bool),D),collect(B)),hAPP(fun(D,fun(B,bool)),fun(D,fun(B,bool)),hAPP(fun(fun(B,bool),fun(B,bool)),fun(fun(D,fun(B,bool)),fun(D,fun(B,bool))),combb(fun(B,bool),fun(B,bool),D),hAPP(fun(B,fun(bool,bool)),fun(fun(B,bool),fun(B,bool)),combs(B,bool,bool),hAPP(fun(B,bool),fun(B,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(B,bool),fun(B,fun(bool,bool))),combb(bool,fun(bool,bool),B),fconj),hAPP(fun(B,bool),fun(B,bool),hAPP(fun(B,fun(fun(B,bool),bool)),fun(fun(B,bool),fun(B,bool)),combc(B,fun(B,bool),bool),member(B)),C)))),hAPP(fun(B,fun(D,bool)),fun(D,fun(B,bool)),combc(B,D,bool),V6))))),E) = hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),hAPP(fun(B,fun(D,bool)),fun(B,A),hAPP(fun(B,fun(fun(D,bool),A)),fun(fun(B,fun(D,bool)),fun(B,A)),combs(B,fun(D,bool),A),hAPP(fun(B,fun(D,A)),fun(B,fun(fun(D,bool),A)),hAPP(fun(fun(D,A),fun(fun(D,bool),A)),fun(fun(B,fun(D,A)),fun(B,fun(fun(D,bool),A))),combb(fun(D,A),fun(fun(D,bool),A),B),big_co1399186613setsum(D,A)),F)),hAPP(fun(B,fun(D,bool)),fun(B,fun(D,bool)),hAPP(fun(fun(D,bool),fun(D,bool)),fun(fun(B,fun(D,bool)),fun(B,fun(D,bool))),combb(fun(D,bool),fun(D,bool),B),collect(D)),hAPP(fun(B,fun(D,bool)),fun(B,fun(D,bool)),hAPP(fun(fun(D,bool),fun(D,bool)),fun(fun(B,fun(D,bool)),fun(B,fun(D,bool))),combb(fun(D,bool),fun(D,bool),B),hAPP(fun(D,fun(bool,bool)),fun(fun(D,bool),fun(D,bool)),combs(D,bool,bool),hAPP(fun(D,bool),fun(D,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(D,bool),fun(D,fun(bool,bool))),combb(bool,fun(bool,bool),D),fconj),hAPP(fun(D,bool),fun(D,bool),hAPP(fun(D,fun(fun(D,bool),bool)),fun(fun(D,bool),fun(D,bool)),combc(D,fun(D,bool),bool),member(D)),E)))),V6)))),C) # label(fact_4188_setsum__setsum__restrict) # label(axiom).  [clausify(4438)].
40.34/40.19	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(C,bool),bool,finite_finite_1(C),D)) | hAPP(fun(C,bool),real,hAPP(fun(C,real),fun(fun(C,bool),real),big_co1399186613setsum(C,real),hAPP(fun(C,fun(A,bool)),fun(C,real),hAPP(fun(C,fun(fun(A,bool),real)),fun(fun(C,fun(A,bool)),fun(C,real)),combs(C,fun(A,bool),real),hAPP(fun(C,fun(A,real)),fun(C,fun(fun(A,bool),real)),hAPP(fun(fun(A,real),fun(fun(A,bool),real)),fun(fun(C,fun(A,real)),fun(C,fun(fun(A,bool),real))),combb(fun(A,real),fun(fun(A,bool),real),C),big_co1399186613setsum(A,real)),hAPP(fun(A,fun(C,real)),fun(C,fun(A,real)),combc(A,C,real),E))),hAPP(fun(C,fun(A,bool)),fun(C,fun(A,bool)),hAPP(fun(fun(A,bool),fun(A,bool)),fun(fun(C,fun(A,bool)),fun(C,fun(A,bool))),combb(fun(A,bool),fun(A,bool),C),collect(A)),hAPP(fun(C,fun(A,bool)),fun(C,fun(A,bool)),hAPP(fun(fun(A,bool),fun(A,bool)),fun(fun(C,fun(A,bool)),fun(C,fun(A,bool))),combb(fun(A,bool),fun(A,bool),C),hAPP(fun(A,fun(bool,bool)),fun(fun(A,bool),fun(A,bool)),combs(A,bool,bool),hAPP(fun(A,bool),fun(A,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(A,bool),fun(A,fun(bool,bool))),combb(bool,fun(bool,bool),A),fconj),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,fun(fun(A,bool),bool)),fun(fun(A,bool),fun(A,bool)),combc(A,fun(A,bool),bool),member(A)),B)))),hAPP(fun(A,fun(C,bool)),fun(C,fun(A,bool)),combc(A,C,bool),F))))),D) = hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),hAPP(fun(A,fun(C,bool)),fun(A,real),hAPP(fun(A,fun(fun(C,bool),real)),fun(fun(A,fun(C,bool)),fun(A,real)),combs(A,fun(C,bool),real),hAPP(fun(A,fun(C,real)),fun(A,fun(fun(C,bool),real)),hAPP(fun(fun(C,real),fun(fun(C,bool),real)),fun(fun(A,fun(C,real)),fun(A,fun(fun(C,bool),real))),combb(fun(C,real),fun(fun(C,bool),real),A),big_co1399186613setsum(C,real)),E)),hAPP(fun(A,fun(C,bool)),fun(A,fun(C,bool)),hAPP(fun(fun(C,bool),fun(C,bool)),fun(fun(A,fun(C,bool)),fun(A,fun(C,bool))),combb(fun(C,bool),fun(C,bool),A),collect(C)),hAPP(fun(A,fun(C,bool)),fun(A,fun(C,bool)),hAPP(fun(fun(C,bool),fun(C,bool)),fun(fun(A,fun(C,bool)),fun(A,fun(C,bool))),combb(fun(C,bool),fun(C,bool),A),hAPP(fun(C,fun(bool,bool)),fun(fun(C,bool),fun(C,bool)),combs(C,bool,bool),hAPP(fun(C,bool),fun(C,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(C,bool),fun(C,fun(bool,bool))),combb(bool,fun(bool,bool),C),fconj),hAPP(fun(C,bool),fun(C,bool),hAPP(fun(C,fun(fun(C,bool),bool)),fun(fun(C,bool),fun(C,bool)),combc(C,fun(C,bool),bool),member(C)),D)))),F)))),B).  [resolve(5628,a,5513,a)].
40.34/40.19	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(C,bool),bool,finite_finite_1(C),D)) | hAPP(fun(C,bool),int,hAPP(fun(C,int),fun(fun(C,bool),int),big_co1399186613setsum(C,int),hAPP(fun(C,fun(A,bool)),fun(C,int),hAPP(fun(C,fun(fun(A,bool),int)),fun(fun(C,fun(A,bool)),fun(C,int)),combs(C,fun(A,bool),int),hAPP(fun(C,fun(A,int)),fun(C,fun(fun(A,bool),int)),hAPP(fun(fun(A,int),fun(fun(A,bool),int)),fun(fun(C,fun(A,int)),fun(C,fun(fun(A,bool),int))),combb(fun(A,int),fun(fun(A,bool),int),C),big_co1399186613setsum(A,int)),hAPP(fun(A,fun(C,int)),fun(C,fun(A,int)),combc(A,C,int),E))),hAPP(fun(C,fun(A,bool)),fun(C,fun(A,bool)),hAPP(fun(fun(A,bool),fun(A,bool)),fun(fun(C,fun(A,bool)),fun(C,fun(A,bool))),combb(fun(A,bool),fun(A,bool),C),collect(A)),hAPP(fun(C,fun(A,bool)),fun(C,fun(A,bool)),hAPP(fun(fun(A,bool),fun(A,bool)),fun(fun(C,fun(A,bool)),fun(C,fun(A,bool))),combb(fun(A,bool),fun(A,bool),C),hAPP(fun(A,fun(bool,bool)),fun(fun(A,bool),fun(A,bool)),combs(A,bool,bool),hAPP(fun(A,bool),fun(A,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(A,bool),fun(A,fun(bool,bool))),combb(bool,fun(bool,bool),A),fconj),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,fun(fun(A,bool),bool)),fun(fun(A,bool),fun(A,bool)),combc(A,fun(A,bool),bool),member(A)),B)))),hAPP(fun(A,fun(C,bool)),fun(C,fun(A,bool)),combc(A,C,bool),F))))),D) = hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),hAPP(fun(A,fun(C,bool)),fun(A,int),hAPP(fun(A,fun(fun(C,bool),int)),fun(fun(A,fun(C,bool)),fun(A,int)),combs(A,fun(C,bool),int),hAPP(fun(A,fun(C,int)),fun(A,fun(fun(C,bool),int)),hAPP(fun(fun(C,int),fun(fun(C,bool),int)),fun(fun(A,fun(C,int)),fun(A,fun(fun(C,bool),int))),combb(fun(C,int),fun(fun(C,bool),int),A),big_co1399186613setsum(C,int)),E)),hAPP(fun(A,fun(C,bool)),fun(A,fun(C,bool)),hAPP(fun(fun(C,bool),fun(C,bool)),fun(fun(A,fun(C,bool)),fun(A,fun(C,bool))),combb(fun(C,bool),fun(C,bool),A),collect(C)),hAPP(fun(A,fun(C,bool)),fun(A,fun(C,bool)),hAPP(fun(fun(C,bool),fun(C,bool)),fun(fun(A,fun(C,bool)),fun(A,fun(C,bool))),combb(fun(C,bool),fun(C,bool),A),hAPP(fun(C,fun(bool,bool)),fun(fun(C,bool),fun(C,bool)),combs(C,bool,bool),hAPP(fun(C,bool),fun(C,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(C,bool),fun(C,fun(bool,bool))),combb(bool,fun(bool,bool),C),fconj),hAPP(fun(C,bool),fun(C,bool),hAPP(fun(C,fun(fun(C,bool),bool)),fun(fun(C,bool),fun(C,bool)),combc(C,fun(C,bool),bool),member(C)),D)))),F)))),B).  [resolve(5628,a,5524,a)].
40.34/40.19	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(C,bool),bool,finite_finite_1(C),D)) | hAPP(fun(C,bool),code_code_numeral,hAPP(fun(C,code_code_numeral),fun(fun(C,bool),code_code_numeral),big_co1399186613setsum(C,code_code_numeral),hAPP(fun(C,fun(A,bool)),fun(C,code_code_numeral),hAPP(fun(C,fun(fun(A,bool),code_code_numeral)),fun(fun(C,fun(A,bool)),fun(C,code_code_numeral)),combs(C,fun(A,bool),code_code_numeral),hAPP(fun(C,fun(A,code_code_numeral)),fun(C,fun(fun(A,bool),code_code_numeral)),hAPP(fun(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral)),fun(fun(C,fun(A,code_code_numeral)),fun(C,fun(fun(A,bool),code_code_numeral))),combb(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),C),big_co1399186613setsum(A,code_code_numeral)),hAPP(fun(A,fun(C,code_code_numeral)),fun(C,fun(A,code_code_numeral)),combc(A,C,code_code_numeral),E))),hAPP(fun(C,fun(A,bool)),fun(C,fun(A,bool)),hAPP(fun(fun(A,bool),fun(A,bool)),fun(fun(C,fun(A,bool)),fun(C,fun(A,bool))),combb(fun(A,bool),fun(A,bool),C),collect(A)),hAPP(fun(C,fun(A,bool)),fun(C,fun(A,bool)),hAPP(fun(fun(A,bool),fun(A,bool)),fun(fun(C,fun(A,bool)),fun(C,fun(A,bool))),combb(fun(A,bool),fun(A,bool),C),hAPP(fun(A,fun(bool,bool)),fun(fun(A,bool),fun(A,bool)),combs(A,bool,bool),hAPP(fun(A,bool),fun(A,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(A,bool),fun(A,fun(bool,bool))),combb(bool,fun(bool,bool),A),fconj),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,fun(fun(A,bool),bool)),fun(fun(A,bool),fun(A,bool)),combc(A,fun(A,bool),bool),member(A)),B)))),hAPP(fun(A,fun(C,bool)),fun(C,fun(A,bool)),combc(A,C,bool),F))))),D) = hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),hAPP(fun(A,fun(C,bool)),fun(A,code_code_numeral),hAPP(fun(A,fun(fun(C,bool),code_code_numeral)),fun(fun(A,fun(C,bool)),fun(A,code_code_numeral)),combs(A,fun(C,bool),code_code_numeral),hAPP(fun(A,fun(C,code_code_numeral)),fun(A,fun(fun(C,bool),code_code_numeral)),hAPP(fun(fun(C,code_code_numeral),fun(fun(C,bool),code_code_numeral)),fun(fun(A,fun(C,code_code_numeral)),fun(A,fun(fun(C,bool),code_code_numeral))),combb(fun(C,code_code_numeral),fun(fun(C,bool),code_code_numeral),A),big_co1399186613setsum(C,code_code_numeral)),E)),hAPP(fun(A,fun(C,bool)),fun(A,fun(C,bool)),hAPP(fun(fun(C,bool),fun(C,bool)),fun(fun(A,fun(C,bool)),fun(A,fun(C,bool))),combb(fun(C,bool),fun(C,bool),A),collect(C)),hAPP(fun(A,fun(C,bool)),fun(A,fun(C,bool)),hAPP(fun(fun(C,bool),fun(C,bool)),fun(fun(A,fun(C,bool)),fun(A,fun(C,bool))),combb(fun(C,bool),fun(C,bool),A),hAPP(fun(C,fun(bool,bool)),fun(fun(C,bool),fun(C,bool)),combs(C,bool,bool),hAPP(fun(C,bool),fun(C,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(C,bool),fun(C,fun(bool,bool))),combb(bool,fun(bool,bool),C),fconj),hAPP(fun(C,bool),fun(C,bool),hAPP(fun(C,fun(fun(C,bool),bool)),fun(fun(C,bool),fun(C,bool)),combc(C,fun(C,bool),bool),member(C)),D)))),F)))),B).  [resolve(5628,a,5539,a)].
40.34/40.19	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(C,bool),bool,finite_finite_1(C),D)) | hAPP(fun(C,bool),rat,hAPP(fun(C,rat),fun(fun(C,bool),rat),big_co1399186613setsum(C,rat),hAPP(fun(C,fun(A,bool)),fun(C,rat),hAPP(fun(C,fun(fun(A,bool),rat)),fun(fun(C,fun(A,bool)),fun(C,rat)),combs(C,fun(A,bool),rat),hAPP(fun(C,fun(A,rat)),fun(C,fun(fun(A,bool),rat)),hAPP(fun(fun(A,rat),fun(fun(A,bool),rat)),fun(fun(C,fun(A,rat)),fun(C,fun(fun(A,bool),rat))),combb(fun(A,rat),fun(fun(A,bool),rat),C),big_co1399186613setsum(A,rat)),hAPP(fun(A,fun(C,rat)),fun(C,fun(A,rat)),combc(A,C,rat),E))),hAPP(fun(C,fun(A,bool)),fun(C,fun(A,bool)),hAPP(fun(fun(A,bool),fun(A,bool)),fun(fun(C,fun(A,bool)),fun(C,fun(A,bool))),combb(fun(A,bool),fun(A,bool),C),collect(A)),hAPP(fun(C,fun(A,bool)),fun(C,fun(A,bool)),hAPP(fun(fun(A,bool),fun(A,bool)),fun(fun(C,fun(A,bool)),fun(C,fun(A,bool))),combb(fun(A,bool),fun(A,bool),C),hAPP(fun(A,fun(bool,bool)),fun(fun(A,bool),fun(A,bool)),combs(A,bool,bool),hAPP(fun(A,bool),fun(A,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(A,bool),fun(A,fun(bool,bool))),combb(bool,fun(bool,bool),A),fconj),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,fun(fun(A,bool),bool)),fun(fun(A,bool),fun(A,bool)),combc(A,fun(A,bool),bool),member(A)),B)))),hAPP(fun(A,fun(C,bool)),fun(C,fun(A,bool)),combc(A,C,bool),F))))),D) = hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),hAPP(fun(A,fun(C,bool)),fun(A,rat),hAPP(fun(A,fun(fun(C,bool),rat)),fun(fun(A,fun(C,bool)),fun(A,rat)),combs(A,fun(C,bool),rat),hAPP(fun(A,fun(C,rat)),fun(A,fun(fun(C,bool),rat)),hAPP(fun(fun(C,rat),fun(fun(C,bool),rat)),fun(fun(A,fun(C,rat)),fun(A,fun(fun(C,bool),rat))),combb(fun(C,rat),fun(fun(C,bool),rat),A),big_co1399186613setsum(C,rat)),E)),hAPP(fun(A,fun(C,bool)),fun(A,fun(C,bool)),hAPP(fun(fun(C,bool),fun(C,bool)),fun(fun(A,fun(C,bool)),fun(A,fun(C,bool))),combb(fun(C,bool),fun(C,bool),A),collect(C)),hAPP(fun(A,fun(C,bool)),fun(A,fun(C,bool)),hAPP(fun(fun(C,bool),fun(C,bool)),fun(fun(A,fun(C,bool)),fun(A,fun(C,bool))),combb(fun(C,bool),fun(C,bool),A),hAPP(fun(C,fun(bool,bool)),fun(fun(C,bool),fun(C,bool)),combs(C,bool,bool),hAPP(fun(C,bool),fun(C,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(C,bool),fun(C,fun(bool,bool))),combb(bool,fun(bool,bool),C),fconj),hAPP(fun(C,bool),fun(C,bool),hAPP(fun(C,fun(fun(C,bool),bool)),fun(fun(C,bool),fun(C,bool)),combc(C,fun(C,bool),bool),member(C)),D)))),F)))),B).  [resolve(5628,a,5561,a)].
40.34/40.19	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(C,bool),bool,finite_finite_1(C),D)) | hAPP(fun(C,bool),quickcheck_code_int,hAPP(fun(C,quickcheck_code_int),fun(fun(C,bool),quickcheck_code_int),big_co1399186613setsum(C,quickcheck_code_int),hAPP(fun(C,fun(A,bool)),fun(C,quickcheck_code_int),hAPP(fun(C,fun(fun(A,bool),quickcheck_code_int)),fun(fun(C,fun(A,bool)),fun(C,quickcheck_code_int)),combs(C,fun(A,bool),quickcheck_code_int),hAPP(fun(C,fun(A,quickcheck_code_int)),fun(C,fun(fun(A,bool),quickcheck_code_int)),hAPP(fun(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int)),fun(fun(C,fun(A,quickcheck_code_int)),fun(C,fun(fun(A,bool),quickcheck_code_int))),combb(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),C),big_co1399186613setsum(A,quickcheck_code_int)),hAPP(fun(A,fun(C,quickcheck_code_int)),fun(C,fun(A,quickcheck_code_int)),combc(A,C,quickcheck_code_int),E))),hAPP(fun(C,fun(A,bool)),fun(C,fun(A,bool)),hAPP(fun(fun(A,bool),fun(A,bool)),fun(fun(C,fun(A,bool)),fun(C,fun(A,bool))),combb(fun(A,bool),fun(A,bool),C),collect(A)),hAPP(fun(C,fun(A,bool)),fun(C,fun(A,bool)),hAPP(fun(fun(A,bool),fun(A,bool)),fun(fun(C,fun(A,bool)),fun(C,fun(A,bool))),combb(fun(A,bool),fun(A,bool),C),hAPP(fun(A,fun(bool,bool)),fun(fun(A,bool),fun(A,bool)),combs(A,bool,bool),hAPP(fun(A,bool),fun(A,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(A,bool),fun(A,fun(bool,bool))),combb(bool,fun(bool,bool),A),fconj),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,fun(fun(A,bool),bool)),fun(fun(A,bool),fun(A,bool)),combc(A,fun(A,bool),bool),member(A)),B)))),hAPP(fun(A,fun(C,bool)),fun(C,fun(A,bool)),combc(A,C,bool),F))))),D) = hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),hAPP(fun(A,fun(C,bool)),fun(A,quickcheck_code_int),hAPP(fun(A,fun(fun(C,bool),quickcheck_code_int)),fun(fun(A,fun(C,bool)),fun(A,quickcheck_code_int)),combs(A,fun(C,bool),quickcheck_code_int),hAPP(fun(A,fun(C,quickcheck_code_int)),fun(A,fun(fun(C,bool),quickcheck_code_int)),hAPP(fun(fun(C,quickcheck_code_int),fun(fun(C,bool),quickcheck_code_int)),fun(fun(A,fun(C,quickcheck_code_int)),fun(A,fun(fun(C,bool),quickcheck_code_int))),combb(fun(C,quickcheck_code_int),fun(fun(C,bool),quickcheck_code_int),A),big_co1399186613setsum(C,quickcheck_code_int)),E)),hAPP(fun(A,fun(C,bool)),fun(A,fun(C,bool)),hAPP(fun(fun(C,bool),fun(C,bool)),fun(fun(A,fun(C,bool)),fun(A,fun(C,bool))),combb(fun(C,bool),fun(C,bool),A),collect(C)),hAPP(fun(A,fun(C,bool)),fun(A,fun(C,bool)),hAPP(fun(fun(C,bool),fun(C,bool)),fun(fun(A,fun(C,bool)),fun(A,fun(C,bool))),combb(fun(C,bool),fun(C,bool),A),hAPP(fun(C,fun(bool,bool)),fun(fun(C,bool),fun(C,bool)),combs(C,bool,bool),hAPP(fun(C,bool),fun(C,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(C,bool),fun(C,fun(bool,bool))),combb(bool,fun(bool,bool),C),fconj),hAPP(fun(C,bool),fun(C,bool),hAPP(fun(C,fun(fun(C,bool),bool)),fun(fun(C,bool),fun(C,bool)),combc(C,fun(C,bool),bool),member(C)),D)))),F)))),B).  [resolve(5628,a,5620,a)].
40.37/40.22	5629 comm_monoid_add(nat) # label(arity_Nat_Onat___Groups_Ocomm__monoid__add) # label(axiom).  [assumption].
40.37/40.22	Derived: zero_zero(nat) = hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),hAPP(nat,fun(A,nat),combk(nat,A),zero_zero(nat))),B).  [resolve(5629,a,5514,a)].
40.37/40.22	Derived: hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f2(A,nat,B,C)),C)) | zero_zero(nat) = hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),B),C).  [resolve(5629,a,5515,a)].
40.37/40.22	Derived: zero_zero(nat) != hAPP(A,nat,B,f2(A,nat,B,C)) | zero_zero(nat) = hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),B),C).  [resolve(5629,a,5516,a)].
40.37/40.22	Derived: -topological_space(nat) | -hBOOL(hAPP(nat,bool,hAPP(fun(nat,nat),fun(nat,bool),sums(nat),A),B)) | hBOOL(hAPP(filter(nat),bool,hAPP(nat,fun(filter(nat),bool),hAPP(fun(nat,nat),fun(nat,fun(filter(nat),bool)),tendsto(nat,nat),hAPP(fun(nat,fun(nat,bool)),fun(nat,nat),hAPP(fun(fun(nat,bool),nat),fun(fun(nat,fun(nat,bool)),fun(nat,nat)),combb(fun(nat,bool),nat,nat),hAPP(fun(nat,nat),fun(fun(nat,bool),nat),big_co1399186613setsum(nat,nat),A)),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)))),B),sequentially)).  [resolve(5629,a,5517,a)].
40.37/40.22	Derived: -topological_space(nat) | hBOOL(hAPP(nat,bool,hAPP(fun(nat,nat),fun(nat,bool),sums(nat),A),B)) | -hBOOL(hAPP(filter(nat),bool,hAPP(nat,fun(filter(nat),bool),hAPP(fun(nat,nat),fun(nat,fun(filter(nat),bool)),tendsto(nat,nat),hAPP(fun(nat,fun(nat,bool)),fun(nat,nat),hAPP(fun(fun(nat,bool),nat),fun(fun(nat,fun(nat,bool)),fun(nat,nat)),combb(fun(nat,bool),nat,nat),hAPP(fun(nat,nat),fun(fun(nat,bool),nat),big_co1399186613setsum(nat,nat),A)),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)))),B),sequentially)).  [resolve(5629,a,5518,a)].
40.37/40.22	Derived: -ordere779506340up_add(nat) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f20(A,nat,D,C,B)),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),B),C))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),D),C)),hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),D),B))).  [resolve(5629,a,5519,b)].
40.38/40.22	Derived: -ordere779506340up_add(nat) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),hAPP(A,nat,D,f20(A,nat,D,C,B)))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),D),C)),hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),D),B))).  [resolve(5629,a,5520,b)].
40.38/40.22	Derived: -topological_space(nat) | sums(nat) = ti(fun(fun(nat,nat),fun(nat,bool)),sums(nat)).  [resolve(5629,a,5521,a)].
40.38/40.22	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f56(A,nat,D,C,B)),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),B),C))) | hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),D),B) = hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),D),C).  [resolve(5629,a,5522,a)].
40.38/40.22	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | zero_zero(nat) != hAPP(A,nat,D,f56(A,nat,D,C,B)) | hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),D),B) = hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),D),C).  [resolve(5629,a,5523,a)].
40.38/40.22	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),one_one(nat)))) | hAPP(fun(nat,bool),nat,hAPP(fun(nat,nat),fun(fun(nat,bool),nat),big_co1399186613setsum(nat,nat),C),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),D))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(fun(nat,bool),nat,hAPP(fun(nat,nat),fun(fun(nat,bool),nat),big_co1399186613setsum(nat,nat),C),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),A),B))),hAPP(fun(nat,bool),nat,hAPP(fun(nat,nat),fun(fun(nat,bool),nat),big_co1399186613setsum(nat,nat),C),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),one_one(nat))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),D)))).  [resolve(5629,a,5525,a)].
40.38/40.22	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | hAPP(fun(nat,bool),nat,hAPP(fun(nat,nat),fun(fun(nat,bool),nat),big_co1399186613setsum(nat,nat),C),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),A),B)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,C,A)),hAPP(fun(nat,bool),nat,hAPP(fun(nat,nat),fun(fun(nat,bool),nat),big_co1399186613setsum(nat,nat),C),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,suc,A)),B))).  [resolve(5629,a,5526,a)].
40.38/40.22	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),A,zero_zero(nat)),zero_zero(nat))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),A,f102(B,nat,C,D,E,A)),f104(B,nat,C,D,E,A))) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),E)) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f106(B,nat,C,D,E,A)),E)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),A,hAPP(fun(B,bool),nat,hAPP(fun(B,nat),fun(fun(B,bool),nat),big_co1399186613setsum(B,nat),C),E)),hAPP(fun(B,bool),nat,hAPP(fun(B,nat),fun(fun(B,bool),nat),big_co1399186613setsum(B,nat),D),E))).  [resolve(5629,a,5527,a)].
40.38/40.23	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),A,zero_zero(nat)),zero_zero(nat))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),A,f102(B,nat,C,D,E,A)),f104(B,nat,C,D,E,A))) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),E)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),A,hAPP(B,nat,C,f106(B,nat,C,D,E,A))),hAPP(B,nat,D,f106(B,nat,C,D,E,A)))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),A,hAPP(fun(B,bool),nat,hAPP(fun(B,nat),fun(fun(B,bool),nat),big_co1399186613setsum(B,nat),C),E)),hAPP(fun(B,bool),nat,hAPP(fun(B,nat),fun(fun(B,bool),nat),big_co1399186613setsum(B,nat),D),E))).  [resolve(5629,a,5528,a)].
40.38/40.23	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),A,zero_zero(nat)),zero_zero(nat))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),A,f103(B,nat,C,D,E,A)),f105(B,nat,C,D,E,A))) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),E)) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f106(B,nat,C,D,E,A)),E)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),A,hAPP(fun(B,bool),nat,hAPP(fun(B,nat),fun(fun(B,bool),nat),big_co1399186613setsum(B,nat),C),E)),hAPP(fun(B,bool),nat,hAPP(fun(B,nat),fun(fun(B,bool),nat),big_co1399186613setsum(B,nat),D),E))).  [resolve(5629,a,5529,a)].
40.38/40.23	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),A,zero_zero(nat)),zero_zero(nat))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),A,f103(B,nat,C,D,E,A)),f105(B,nat,C,D,E,A))) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),E)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),A,hAPP(B,nat,C,f106(B,nat,C,D,E,A))),hAPP(B,nat,D,f106(B,nat,C,D,E,A)))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),A,hAPP(fun(B,bool),nat,hAPP(fun(B,nat),fun(fun(B,bool),nat),big_co1399186613setsum(B,nat),C),E)),hAPP(fun(B,bool),nat,hAPP(fun(B,nat),fun(fun(B,bool),nat),big_co1399186613setsum(B,nat),D),E))).  [resolve(5629,a,5530,a)].
40.38/40.23	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),A,zero_zero(nat)),zero_zero(nat))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),A,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),f102(B,nat,C,D,E,A)),f103(B,nat,C,D,E,A))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),f104(B,nat,C,D,E,A)),f105(B,nat,C,D,E,A)))) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),E)) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f106(B,nat,C,D,E,A)),E)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),A,hAPP(fun(B,bool),nat,hAPP(fun(B,nat),fun(fun(B,bool),nat),big_co1399186613setsum(B,nat),C),E)),hAPP(fun(B,bool),nat,hAPP(fun(B,nat),fun(fun(B,bool),nat),big_co1399186613setsum(B,nat),D),E))).  [resolve(5629,a,5531,a)].
40.38/40.23	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),A,zero_zero(nat)),zero_zero(nat))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),A,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),f102(B,nat,C,D,E,A)),f103(B,nat,C,D,E,A))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),f104(B,nat,C,D,E,A)),f105(B,nat,C,D,E,A)))) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),E)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),A,hAPP(B,nat,C,f106(B,nat,C,D,E,A))),hAPP(B,nat,D,f106(B,nat,C,D,E,A)))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),A,hAPP(fun(B,bool),nat,hAPP(fun(B,nat),fun(fun(B,bool),nat),big_co1399186613setsum(B,nat),C),E)),hAPP(fun(B,bool),nat,hAPP(fun(B,nat),fun(fun(B,bool),nat),big_co1399186613setsum(B,nat),D),E))).  [resolve(5629,a,5532,a)].
40.38/40.23	Derived: -t2_space(nat) | zero_zero(nat) = hAPP(fun(nat,nat),nat,suminf(nat),hAPP(nat,fun(nat,nat),combk(nat,nat),zero_zero(nat))).  [resolve(5629,a,5533,b)].
40.38/40.23	Derived: -topological_space(nat) | zero_zero(nat) != hAPP(nat,nat,A,zero_zero(nat)) | -hBOOL(hAPP(nat,bool,hAPP(fun(nat,nat),fun(nat,bool),sums(nat),hAPP(fun(nat,nat),fun(nat,nat),hAPP(fun(nat,nat),fun(fun(nat,nat),fun(nat,nat)),combb(nat,nat,nat),A),suc)),B)) | hBOOL(hAPP(nat,bool,hAPP(fun(nat,nat),fun(nat,bool),sums(nat),A),B)).  [resolve(5629,a,5534,a)].
40.38/40.23	Derived: -topological_space(nat) | the(nat) = ti(fun(fun(nat,bool),nat),the(nat)).  [resolve(5629,a,5535,a)].
40.38/40.23	Derived: -ordere779506340up_add(nat) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f137(A,nat,B,C)),C)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),B),C)),zero_zero(nat))).  [resolve(5629,a,5536,b)].
40.38/40.23	Derived: -ordere779506340up_add(nat) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(A,nat,B,f137(A,nat,B,C))),zero_zero(nat))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),B),C)),zero_zero(nat))).  [resolve(5629,a,5537,b)].
40.38/40.23	Derived: -t2_space(nat) | -hBOOL(hAPP(fun(nat,nat),bool,summable(nat),A)) | hBOOL(hAPP(nat,bool,hAPP(fun(nat,nat),fun(nat,bool),sums(nat),A),hAPP(fun(nat,nat),nat,suminf(nat),A))).  [resolve(5629,a,5538,b)].
40.38/40.23	Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),zero_zero(nat)),A) = ti(nat,A).  [resolve(5629,a,5540,a)].
40.38/40.23	Derived: -topological_space(nat) | hBOOL(hAPP(nat,bool,hAPP(fun(nat,nat),fun(nat,bool),sums(nat),hAPP(nat,fun(nat,nat),combk(nat,nat),zero_zero(nat))),zero_zero(nat))).  [resolve(5629,a,5541,a)].
40.38/40.23	Derived: -topological_space(nat) | suminf(nat) = ti(fun(fun(nat,nat),nat),suminf(nat)).  [resolve(5629,a,5542,b)].
40.38/40.23	Derived: hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | zero_zero(nat) = hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),C),B).  [resolve(5629,a,5543,a)].
40.38/40.23	Derived: -t2_space(nat) | -hBOOL(hAPP(nat,bool,hAPP(fun(nat,nat),fun(nat,bool),sums(nat),A),B)) | hAPP(fun(nat,nat),nat,suminf(nat),A) = ti(nat,B).  [resolve(5629,a,5544,b)].
40.38/40.23	Derived: hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),hAPP(fun(B,bool),fun(A,nat),hAPP(fun(A,fun(fun(B,bool),nat)),fun(fun(B,bool),fun(A,nat)),combc(A,fun(B,bool),nat),hAPP(fun(A,fun(B,nat)),fun(A,fun(fun(B,bool),nat)),hAPP(fun(fun(B,nat),fun(fun(B,bool),nat)),fun(fun(A,fun(B,nat)),fun(A,fun(fun(B,bool),nat))),combb(fun(B,nat),fun(fun(B,bool),nat),A),big_co1399186613setsum(B,nat)),hAPP(fun(B,fun(A,nat)),fun(A,fun(B,nat)),combc(B,A,nat),C))),D)),E) = hAPP(fun(B,bool),nat,hAPP(fun(B,nat),fun(fun(B,bool),nat),big_co1399186613setsum(B,nat),hAPP(fun(A,bool),fun(B,nat),hAPP(fun(B,fun(fun(A,bool),nat)),fun(fun(A,bool),fun(B,nat)),combc(B,fun(A,bool),nat),hAPP(fun(B,fun(A,nat)),fun(B,fun(fun(A,bool),nat)),hAPP(fun(fun(A,nat),fun(fun(A,bool),nat)),fun(fun(B,fun(A,nat)),fun(B,fun(fun(A,bool),nat))),combb(fun(A,nat),fun(fun(A,bool),nat),B),big_co1399186613setsum(A,nat)),C)),E)),D).  [resolve(5629,a,5545,a)].
40.38/40.23	Derived: hAPP(fun(nat,bool),nat,hAPP(fun(nat,nat),fun(fun(nat,bool),nat),big_co1399186613setsum(nat,nat),hAPP(fun(nat,fun(nat,bool)),fun(nat,nat),hAPP(fun(fun(nat,bool),nat),fun(fun(nat,fun(nat,bool)),fun(nat,nat)),combb(fun(nat,bool),nat,nat),hAPP(fun(nat,nat),fun(fun(nat,bool),nat),big_co1399186613setsum(nat,nat),A)),hAPP(fun(nat,nat),fun(nat,fun(nat,bool)),hAPP(fun(nat,fun(nat,fun(nat,bool))),fun(fun(nat,nat),fun(nat,fun(nat,bool))),combs(nat,nat,fun(nat,bool)),hAPP(fun(nat,nat),fun(nat,fun(nat,fun(nat,bool))),hAPP(fun(nat,fun(nat,fun(nat,bool))),fun(fun(nat,nat),fun(nat,fun(nat,fun(nat,bool)))),combb(nat,fun(nat,fun(nat,bool)),nat),ord_atLeastLessThan(nat)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),times_times(nat)),B))),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),hAPP(fun(nat,nat),fun(nat,fun(nat,nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,nat),fun(nat,fun(nat,nat))),combb(nat,fun(nat,nat),nat),plus_plus(nat)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),times_times(nat)),B))),B)))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),C)) = hAPP(fun(nat,bool),nat,hAPP(fun(nat,nat),fun(fun(nat,bool),nat),big_co1399186613setsum(nat,nat),A),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),C),B))).  [resolve(5629,a,5546,a)].
40.38/40.23	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | zero_zero(nat) = hAPP(fun(nat,bool),nat,hAPP(fun(nat,nat),fun(fun(nat,bool),nat),big_co1399186613setsum(nat,nat),C),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),B),hAPP(nat,nat,suc,A))).  [resolve(5629,a,5547,a)].
40.38/40.23	Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | hAPP(fun(nat,bool),nat,hAPP(fun(nat,nat),fun(fun(nat,bool),nat),big_co1399186613setsum(nat,nat),C),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),B),hAPP(nat,nat,suc,A))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(fun(nat,bool),nat,hAPP(fun(nat,nat),fun(fun(nat,bool),nat),big_co1399186613setsum(nat,nat),C),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),B),A))),hAPP(nat,nat,C,A)).  [resolve(5629,a,5548,a)].
40.38/40.24	Derived: hAPP(fun(nat,bool),nat,hAPP(fun(nat,nat),fun(fun(nat,bool),nat),big_co1399186613setsum(nat,nat),A),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),C))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(fun(nat,bool),nat,hAPP(fun(nat,nat),fun(fun(nat,bool),nat),big_co1399186613setsum(nat,nat),hAPP(fun(nat,nat),fun(nat,nat),hAPP(fun(nat,nat),fun(fun(nat,nat),fun(nat,nat)),combb(nat,nat,nat),A),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),C))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),B))),hAPP(fun(nat,bool),nat,hAPP(fun(nat,nat),fun(fun(nat,bool),nat),big_co1399186613setsum(nat,nat),A),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),C))).  [resolve(5629,a,5551,a)].
40.38/40.24	Derived: -comm_monoid_mult(nat) | A != B | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),f335(nat,C,D,B,A))) | hAPP(fun(int,bool),nat,hAPP(fun(int,nat),fun(fun(int,bool),nat),big_co1399186613setsum(int,nat),D),A) = hAPP(fun(int,bool),nat,hAPP(fun(int,nat),fun(fun(int,bool),nat),big_co1399186613setsum(int,nat),C),B).  [resolve(5629,a,5552,b)].
40.38/40.24	Derived: -comm_monoid_mult(nat) | A != B | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A)) | hAPP(int,nat,C,f335(nat,D,C,B,A)) != hAPP(int,nat,D,f335(nat,D,C,B,A)) | hAPP(fun(int,bool),nat,hAPP(fun(int,nat),fun(fun(int,bool),nat),big_co1399186613setsum(int,nat),C),A) = hAPP(fun(int,bool),nat,hAPP(fun(int,nat),fun(fun(int,bool),nat),big_co1399186613setsum(int,nat),D),B).  [resolve(5629,a,5553,b)].
40.38/40.24	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | zero_zero(nat) = hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),hAPP(nat,fun(A,nat),hAPP(fun(A,fun(nat,nat)),fun(nat,fun(A,nat)),combc(A,nat,nat),hAPP(fun(A,nat),fun(A,fun(nat,nat)),hAPP(fun(A,fun(nat,fun(nat,nat))),fun(fun(A,nat),fun(A,fun(nat,nat))),combs(A,nat,fun(nat,nat)),hAPP(fun(A,bool),fun(A,fun(nat,fun(nat,nat))),hAPP(fun(bool,fun(nat,fun(nat,nat))),fun(fun(A,bool),fun(A,fun(nat,fun(nat,nat)))),combb(bool,fun(nat,fun(nat,nat)),A),if(nat)),hAPP(A,fun(A,bool),hAPP(fun(A,fun(A,bool)),fun(A,fun(A,bool)),combc(A,A,bool),fequal(A)),C))),D)),zero_zero(nat))),B).  [resolve(5629,a,5554,a)].
40.38/40.24	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),hAPP(nat,fun(A,nat),hAPP(fun(A,fun(nat,nat)),fun(nat,fun(A,nat)),combc(A,nat,nat),hAPP(fun(A,nat),fun(A,fun(nat,nat)),hAPP(fun(A,fun(nat,fun(nat,nat))),fun(fun(A,nat),fun(A,fun(nat,nat))),combs(A,nat,fun(nat,nat)),hAPP(fun(A,bool),fun(A,fun(nat,fun(nat,nat))),hAPP(fun(bool,fun(nat,fun(nat,nat))),fun(fun(A,bool),fun(A,fun(nat,fun(nat,nat)))),combb(bool,fun(nat,fun(nat,nat)),A),if(nat)),hAPP(A,fun(A,bool),hAPP(fun(A,fun(A,bool)),fun(A,fun(A,bool)),combc(A,A,bool),fequal(A)),C))),D)),zero_zero(nat))),B) = hAPP(A,nat,D,C).  [resolve(5629,a,5555,a)].
40.38/40.24	Derived: -metric_space(nat) | hAPP(fun(nat,nat),nat,lim(nat),hAPP(fun(nat,fun(nat,bool)),fun(nat,nat),hAPP(fun(fun(nat,bool),nat),fun(fun(nat,fun(nat,bool)),fun(nat,nat)),combb(fun(nat,bool),nat,nat),hAPP(fun(nat,nat),fun(fun(nat,bool),nat),big_co1399186613setsum(nat,nat),A)),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)))) = hAPP(fun(nat,nat),nat,suminf(nat),A).  [resolve(5629,a,5556,b)].
40.38/40.24	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,A)),B)) | zero_zero(nat) = hAPP(fun(nat,bool),nat,hAPP(fun(nat,nat),fun(fun(nat,bool),nat),big_co1399186613setsum(nat,nat),C),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),B),hAPP(nat,nat,suc,A))).  [resolve(5629,a,5557,a)].
40.38/40.24	Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,A)),B)) | hAPP(fun(nat,bool),nat,hAPP(fun(nat,nat),fun(fun(nat,bool),nat),big_co1399186613setsum(nat,nat),C),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),B),hAPP(nat,nat,suc,A))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,C,B)),hAPP(fun(nat,bool),nat,hAPP(fun(nat,nat),fun(fun(nat,bool),nat),big_co1399186613setsum(nat,nat),hAPP(fun(nat,nat),fun(nat,nat),hAPP(fun(nat,nat),fun(fun(nat,nat),fun(nat,nat)),combb(nat,nat,nat),C),suc)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),B),A))).  [resolve(5629,a,5558,a)].
40.38/40.24	Derived: hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),hAPP(fun(A,nat),fun(A,nat),hAPP(fun(A,fun(nat,nat)),fun(fun(A,nat),fun(A,nat)),combs(A,nat,nat),hAPP(fun(A,nat),fun(A,fun(nat,nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(A,nat),fun(A,fun(nat,nat))),combb(nat,fun(nat,nat),A),plus_plus(nat)),B)),C)),D) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),B),D)),hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),C),D)).  [resolve(5629,a,5559,a)].
40.38/40.24	Derived: -comm_monoid_mult(nat) | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A)) | hAPP(fun(nat,bool),nat,hAPP(fun(nat,nat),fun(fun(nat,bool),nat),big_co1399186613setsum(nat,nat),hAPP(fun(nat,int),fun(nat,nat),hAPP(fun(int,nat),fun(fun(nat,int),fun(nat,nat)),combb(int,nat,nat),B),semiring_1_of_nat(int))),hAPP(fun(int,bool),fun(nat,bool),hAPP(fun(int,nat),fun(fun(int,bool),fun(nat,bool)),image(int,nat),nat_1),A)) = hAPP(fun(int,bool),nat,hAPP(fun(int,nat),fun(fun(int,bool),nat),big_co1399186613setsum(int,nat),B),A).  [resolve(5629,a,5560,b)].
40.38/40.24	Derived: big_co1399186613setsum(A,nat) = ti(fun(fun(A,nat),fun(fun(A,bool),nat)),big_co1399186613setsum(A,nat)).  [resolve(5629,a,5562,a)].
40.38/40.24	Derived: -topological_space(nat) | hAPP(fun(nat,bool),nat,the(nat),hAPP(fun(nat,nat),fun(nat,bool),sums(nat),A)) = hAPP(fun(nat,nat),nat,suminf(nat),A).  [resolve(5629,a,5563,b)].
40.38/40.24	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | hAPP(fun(nat,bool),nat,hAPP(fun(nat,nat),fun(fun(nat,bool),nat),big_co1399186613setsum(nat,nat),C),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),A),B)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,C,A)),hAPP(fun(nat,bool),nat,hAPP(fun(nat,nat),fun(fun(nat,bool),nat),big_co1399186613setsum(nat,nat),C),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),hAPP(nat,nat,suc,A)),B))).  [resolve(5629,a,5564,a)].
40.38/40.24	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),hAPP(nat,fun(A,nat),hAPP(fun(A,fun(nat,nat)),fun(nat,fun(A,nat)),combc(A,nat,nat),hAPP(fun(A,nat),fun(A,fun(nat,nat)),hAPP(fun(A,fun(nat,fun(nat,nat))),fun(fun(A,nat),fun(A,fun(nat,nat))),combs(A,nat,fun(nat,nat)),hAPP(fun(A,bool),fun(A,fun(nat,fun(nat,nat))),hAPP(fun(bool,fun(nat,fun(nat,nat))),fun(fun(A,bool),fun(A,fun(nat,fun(nat,nat)))),combb(bool,fun(nat,fun(nat,nat)),A),if(nat)),hAPP(A,fun(A,bool),fequal(A),C))),D)),zero_zero(nat))),B) = hAPP(A,nat,D,C).  [resolve(5629,a,5565,a)].
40.38/40.24	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | zero_zero(nat) = hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),hAPP(nat,fun(A,nat),hAPP(fun(A,fun(nat,nat)),fun(nat,fun(A,nat)),combc(A,nat,nat),hAPP(fun(A,nat),fun(A,fun(nat,nat)),hAPP(fun(A,fun(nat,fun(nat,nat))),fun(fun(A,nat),fun(A,fun(nat,nat))),combs(A,nat,fun(nat,nat)),hAPP(fun(A,bool),fun(A,fun(nat,fun(nat,nat))),hAPP(fun(bool,fun(nat,fun(nat,nat))),fun(fun(A,bool),fun(A,fun(nat,fun(nat,nat)))),combb(bool,fun(nat,fun(nat,nat)),A),if(nat)),hAPP(A,fun(A,bool),fequal(A),C))),D)),zero_zero(nat))),B).  [resolve(5629,a,5566,a)].
40.38/40.24	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),hAPP(nat,fun(A,nat),hAPP(fun(A,fun(nat,nat)),fun(nat,fun(A,nat)),combc(A,nat,nat),hAPP(fun(A,nat),fun(A,fun(nat,nat)),hAPP(fun(A,fun(nat,fun(nat,nat))),fun(fun(A,nat),fun(A,fun(nat,nat))),combs(A,nat,fun(nat,nat)),hAPP(fun(A,bool),fun(A,fun(nat,fun(nat,nat))),hAPP(fun(bool,fun(nat,fun(nat,nat))),fun(fun(A,bool),fun(A,fun(nat,fun(nat,nat)))),combb(bool,fun(nat,fun(nat,nat)),A),if(nat)),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,fun(fun(A,bool),bool)),fun(fun(A,bool),fun(A,bool)),combc(A,fun(A,bool),bool),member(A)),C))),D)),zero_zero(nat))),B) = hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),D),hAPP(fun(A,bool),fun(A,bool),collect(A),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,fun(bool,bool)),fun(fun(A,bool),fun(A,bool)),combs(A,bool,bool),hAPP(fun(A,bool),fun(A,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(A,bool),fun(A,fun(bool,bool))),combb(bool,fun(bool,bool),A),fconj),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,fun(fun(A,bool),bool)),fun(fun(A,bool),fun(A,bool)),combc(A,fun(A,bool),bool),member(A)),B))),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,fun(fun(A,bool),bool)),fun(fun(A,bool),fun(A,bool)),combc(A,fun(A,bool),bool),member(A)),C)))).  [resolve(5629,a,5567,a)].
40.38/40.24	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f457(A,nat,D,E,C,B)),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),B),C))) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f458(A,nat,D,E,C,B)),C)) | hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),D),C) = hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),E),B).  [resolve(5629,a,5568,a)].
40.38/40.24	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f457(A,nat,D,E,C,B)),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),B),C))) | hAPP(A,nat,D,f458(A,nat,D,E,C,B)) != hAPP(A,nat,E,f458(A,nat,D,E,C,B)) | hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),D),C) = hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),E),B).  [resolve(5629,a,5569,a)].
40.38/40.24	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | zero_zero(nat) != hAPP(A,nat,D,f457(A,nat,E,D,C,B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f458(A,nat,E,D,C,B)),C)) | hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),E),C) = hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),D),B).  [resolve(5629,a,5570,a)].
40.38/40.25	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | zero_zero(nat) != hAPP(A,nat,D,f457(A,nat,E,D,C,B)) | hAPP(A,nat,E,f458(A,nat,E,D,C,B)) != hAPP(A,nat,D,f458(A,nat,E,D,C,B)) | hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),E),C) = hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),D),B).  [resolve(5629,a,5571,a)].
40.38/40.25	Derived: -topological_space(nat) | summable(nat) = ti(fun(fun(nat,nat),bool),summable(nat)).  [resolve(5629,a,5573,b)].
40.38/40.25	Derived: -t2_space(nat) | -hBOOL(hAPP(nat,bool,hAPP(fun(nat,nat),fun(nat,bool),sums(nat),A),B)) | hBOOL(hAPP(fun(nat,nat),bool,summable(nat),A)).  [resolve(5629,a,5575,b)].
40.38/40.25	Derived: -t2_space(nat) | hBOOL(hAPP(nat,bool,hAPP(fun(nat,nat),fun(nat,bool),sums(nat),A),B)) | hAPP(fun(nat,nat),nat,suminf(nat),A) != ti(nat,B) | -hBOOL(hAPP(fun(nat,nat),bool,summable(nat),A)).  [resolve(5629,a,5576,b)].
40.38/40.25	Derived: zero_zero(nat) != hAPP(nat,nat,A,zero_zero(nat)) | hAPP(fun(nat,bool),nat,hAPP(fun(nat,nat),fun(fun(nat,bool),nat),big_co1399186613setsum(nat,nat),A),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),B)) = hAPP(fun(nat,bool),nat,hAPP(fun(nat,nat),fun(fun(nat,bool),nat),big_co1399186613setsum(nat,nat),A),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),hAPP(nat,nat,suc,zero_zero(nat))),B)).  [resolve(5629,a,5577,a)].
40.38/40.25	Derived: -topological_space(nat) | -hBOOL(hAPP(nat,bool,hAPP(fun(nat,nat),fun(nat,bool),sums(nat),A),B)) | hBOOL(hAPP(fun(nat,nat),bool,summable(nat),A)).  [resolve(5629,a,5578,a)].
40.38/40.25	Derived: -t2_space(nat) | -hBOOL(hAPP(fun(nat,nat),bool,summable(nat),A)) | hBOOL(hAPP(filter(nat),bool,hAPP(nat,fun(filter(nat),bool),hAPP(fun(nat,nat),fun(nat,fun(filter(nat),bool)),tendsto(nat,nat),hAPP(fun(nat,fun(nat,bool)),fun(nat,nat),hAPP(fun(fun(nat,bool),nat),fun(fun(nat,fun(nat,bool)),fun(nat,nat)),combb(fun(nat,bool),nat,nat),hAPP(fun(nat,nat),fun(fun(nat,bool),nat),big_co1399186613setsum(nat,nat),A)),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)))),hAPP(fun(nat,nat),nat,suminf(nat),A)),sequentially)).  [resolve(5629,a,5579,b)].
40.38/40.25	Derived: -topological_space(nat) | hBOOL(hAPP(fun(nat,nat),bool,summable(nat),hAPP(nat,fun(nat,nat),combk(nat,nat),zero_zero(nat)))).  [resolve(5629,a,5580,a)].
40.38/40.25	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f538(A,nat,D,E,C,B)),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),B),C))) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f539(A,nat,D,E,C,B)),C)) | hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),E),B) = hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),D),C).  [resolve(5629,a,5581,a)].
40.38/40.25	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f538(A,nat,D,E,C,B)),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),B),C))) | hAPP(A,nat,E,f539(A,nat,D,E,C,B)) != hAPP(A,nat,D,f539(A,nat,D,E,C,B)) | hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),E),B) = hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),D),C).  [resolve(5629,a,5582,a)].
40.38/40.25	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | zero_zero(nat) != hAPP(A,nat,D,f538(A,nat,E,D,C,B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f539(A,nat,E,D,C,B)),C)) | hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),D),B) = hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),E),C).  [resolve(5629,a,5583,a)].
40.38/40.25	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | zero_zero(nat) != hAPP(A,nat,D,f538(A,nat,E,D,C,B)) | hAPP(A,nat,D,f539(A,nat,E,D,C,B)) != hAPP(A,nat,E,f539(A,nat,E,D,C,B)) | hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),D),B) = hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),E),C).  [resolve(5629,a,5584,a)].
40.38/40.25	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f543(A,nat,C,D,B)),B)) | hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),D),B) = hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),C),B).  [resolve(5629,a,5585,a)].
40.38/40.25	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(A,nat,C,f543(A,nat,D,C,B)) != hAPP(A,nat,D,f543(A,nat,D,C,B)) | hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),C),B) = hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),D),B).  [resolve(5629,a,5586,a)].
40.38/40.25	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f545(A,nat,C,B)),B)) | zero_zero(nat) = hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),C),B).  [resolve(5629,a,5587,a)].
40.38/40.25	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | zero_zero(nat) != hAPP(A,nat,C,f545(A,nat,C,B)) | zero_zero(nat) = hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),C),B).  [resolve(5629,a,5588,a)].
40.38/40.25	Derived: -ord(A) | ti(A,B) != ti(A,C) | ti(A,D) != ti(A,E) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),f547(nat,A,F,V6,E,D,C,B))) | hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),V6),hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_atLeastLessThan(A),B),D)) = hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),F),hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_atLeastLessThan(A),C),E)).  [resolve(5629,a,5589,a)].
40.38/40.25	Derived: -ord(A) | ti(A,B) != ti(A,C) | ti(A,D) != ti(A,E) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),f547(nat,A,F,V6,E,D,C,B)),D)) | hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),V6),hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_atLeastLessThan(A),B),D)) = hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),F),hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_atLeastLessThan(A),C),E)).  [resolve(5629,a,5590,a)].
40.38/40.25	Derived: -ord(A) | ti(A,B) != ti(A,C) | ti(A,D) != ti(A,E) | hAPP(A,nat,F,f547(nat,A,V6,F,E,D,C,B)) != hAPP(A,nat,V6,f547(nat,A,V6,F,E,D,C,B)) | hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),F),hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_atLeastLessThan(A),B),D)) = hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),V6),hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_atLeastLessThan(A),C),E)).  [resolve(5629,a,5591,a)].
40.38/40.25	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),hAPP(nat,fun(A,nat),hAPP(fun(A,fun(nat,nat)),fun(nat,fun(A,nat)),combc(A,nat,nat),hAPP(fun(A,nat),fun(A,fun(nat,nat)),hAPP(fun(A,fun(nat,fun(nat,nat))),fun(fun(A,nat),fun(A,fun(nat,nat))),combs(A,nat,fun(nat,nat)),hAPP(fun(A,bool),fun(A,fun(nat,fun(nat,nat))),hAPP(fun(bool,fun(nat,fun(nat,nat))),fun(fun(A,bool),fun(A,fun(nat,fun(nat,nat)))),combb(bool,fun(nat,fun(nat,nat)),A),if(nat)),C)),D)),zero_zero(nat))),B) = hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),D),hAPP(fun(A,bool),fun(A,bool),collect(A),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,fun(bool,bool)),fun(fun(A,bool),fun(A,bool)),combs(A,bool,bool),hAPP(fun(A,bool),fun(A,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(A,bool),fun(A,fun(bool,bool))),combb(bool,fun(bool,bool),A),fconj),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,fun(fun(A,bool),bool)),fun(fun(A,bool),fun(A,bool)),combc(A,fun(A,bool),bool),member(A)),B))),C))).  [resolve(5629,a,5592,a)].
40.38/40.26	Derived: -comm_monoid_mult(nat) | hAPP(fun(nat,bool),nat,hAPP(fun(nat,nat),fun(fun(nat,bool),nat),big_co302546470etprod(nat,nat),A),B) = hAPP(fun(int,bool),nat,hAPP(fun(int,nat),fun(fun(int,bool),nat),big_co302546470etprod(int,nat),hAPP(fun(int,nat),fun(int,nat),hAPP(fun(nat,nat),fun(fun(int,nat),fun(int,nat)),combb(nat,nat,int),A),nat_1)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),B)).  [resolve(5629,a,5593,a)].
40.38/40.26	Derived: hAPP(fun(product_prod(nat,nat),bool),nat,hAPP(fun(product_prod(nat,nat),nat),fun(fun(product_prod(nat,nat),bool),nat),big_co1399186613setsum(product_prod(nat,nat),nat),hAPP(fun(nat,fun(nat,nat)),fun(product_prod(nat,nat),nat),product_prod_case(nat,nat,nat),A)),hAPP(fun(product_prod(nat,nat),bool),fun(product_prod(nat,nat),bool),collect(product_prod(nat,nat)),hAPP(fun(nat,fun(nat,bool)),fun(product_prod(nat,nat),bool),product_prod_case(nat,nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),hAPP(fun(nat,fun(nat,fun(nat,bool))),fun(nat,fun(nat,fun(nat,bool))),combc(nat,nat,fun(nat,bool)),hAPP(fun(nat,fun(nat,fun(nat,bool))),fun(nat,fun(nat,fun(nat,bool))),hAPP(fun(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool))),fun(fun(nat,fun(nat,fun(nat,bool))),fun(nat,fun(nat,fun(nat,bool)))),combb(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),nat),combc(nat,nat,bool)),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,fun(nat,bool))),hAPP(fun(fun(nat,nat),fun(nat,fun(nat,bool))),fun(fun(nat,fun(nat,nat)),fun(nat,fun(nat,fun(nat,bool)))),combb(fun(nat,nat),fun(nat,fun(nat,bool)),nat),hAPP(fun(nat,fun(nat,bool)),fun(fun(nat,nat),fun(nat,fun(nat,bool))),combb(nat,fun(nat,bool),nat),ord_less(nat))),plus_plus(nat)))),B)))) = hAPP(fun(nat,bool),nat,hAPP(fun(nat,nat),fun(fun(nat,bool),nat),big_co1399186613setsum(nat,nat),hAPP(fun(nat,fun(nat,bool)),fun(nat,nat),hAPP(fun(nat,fun(fun(nat,bool),nat)),fun(fun(nat,fun(nat,bool)),fun(nat,nat)),combs(nat,fun(nat,bool),nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(fun(nat,bool),nat)),hAPP(fun(fun(nat,nat),fun(fun(nat,bool),nat)),fun(fun(nat,fun(nat,nat)),fun(nat,fun(fun(nat,bool),nat))),combb(fun(nat,nat),fun(fun(nat,bool),nat),nat),big_co1399186613setsum(nat,nat)),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),hAPP(fun(fun(nat,nat),fun(nat,nat)),fun(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat))),combb(fun(nat,nat),fun(nat,nat),nat),hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,nat),fun(nat,nat)),combs(nat,nat,nat),A)),minus_minus(nat)))),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),zero_zero(nat)))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),B)).  [resolve(5629,a,5594,a)].
40.38/40.26	Derived: -t2_space(nat) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),f585(nat,B,A))) | hBOOL(hAPP(nat,bool,hAPP(fun(nat,nat),fun(nat,bool),sums(nat),B),hAPP(fun(nat,bool),nat,hAPP(fun(nat,nat),fun(fun(nat,bool),nat),big_co1399186613setsum(nat,nat),B),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),A)))).  [resolve(5629,a,5595,b)].
40.38/40.26	Derived: -t2_space(nat) | zero_zero(nat) != hAPP(nat,nat,A,f585(nat,A,B)) | hBOOL(hAPP(nat,bool,hAPP(fun(nat,nat),fun(nat,bool),sums(nat),A),hAPP(fun(nat,bool),nat,hAPP(fun(nat,nat),fun(fun(nat,bool),nat),big_co1399186613setsum(nat,nat),A),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),B)))).  [resolve(5629,a,5596,b)].
40.38/40.26	Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,A)),B)) | hAPP(fun(nat,bool),nat,hAPP(fun(nat,nat),fun(fun(nat,bool),nat),big_co1399186613setsum(nat,nat),C),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),B),hAPP(nat,nat,suc,A))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(fun(nat,bool),nat,hAPP(fun(nat,nat),fun(fun(nat,bool),nat),big_co1399186613setsum(nat,nat),C),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),B),A))),hAPP(nat,nat,C,hAPP(nat,nat,suc,A))).  [resolve(5629,a,5598,a)].
40.38/40.26	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),C)) | hAPP(fun(nat,bool),nat,hAPP(fun(nat,nat),fun(fun(nat,bool),nat),big_co1399186613setsum(nat,nat),D),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),A),C)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(fun(nat,bool),nat,hAPP(fun(nat,nat),fun(fun(nat,bool),nat),big_co1399186613setsum(nat,nat),D),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),A),B))),hAPP(fun(nat,bool),nat,hAPP(fun(nat,nat),fun(fun(nat,bool),nat),big_co1399186613setsum(nat,nat),D),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),B),C))).  [resolve(5629,a,5599,a)].
40.38/40.26	Derived: hAPP(fun(nat,bool),nat,hAPP(fun(nat,nat),fun(fun(nat,bool),nat),big_co1399186613setsum(nat,nat),hAPP(fun(nat,nat),fun(nat,nat),hAPP(fun(nat,nat),fun(fun(nat,nat),fun(nat,nat)),combb(nat,nat,nat),A),suc)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),B),C)) = hAPP(fun(nat,bool),nat,hAPP(fun(nat,nat),fun(fun(nat,bool),nat),big_co1399186613setsum(nat,nat),A),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,suc,B)),hAPP(nat,nat,suc,C))).  [resolve(5629,a,5600,a)].
40.38/40.26	Derived: -hBOOL(hAPP(fun(fun(A,bool),bool),bool,finite_finite_1(fun(A,bool)),B)) | hBOOL(hAPP(fun(fun(A,bool),bool),bool,hAPP(fun(A,bool),fun(fun(fun(A,bool),bool),bool),member(fun(A,bool)),f646(A,nat,C,B)),B)) | hBOOL(hAPP(fun(fun(A,bool),bool),bool,hAPP(fun(A,bool),fun(fun(fun(A,bool),bool),bool),member(fun(A,bool)),f647(A,nat,C,B)),B)) | hAPP(fun(fun(A,bool),bool),nat,hAPP(fun(fun(A,bool),nat),fun(fun(fun(A,bool),bool),nat),big_co1399186613setsum(fun(A,bool),nat),hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),C)),B) = hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),C),hAPP(fun(fun(A,bool),bool),fun(A,bool),complete_Sup_Sup(fun(A,bool)),B)).  [resolve(5629,a,5601,a)].
40.38/40.26	Derived: -hBOOL(hAPP(fun(fun(A,bool),bool),bool,finite_finite_1(fun(A,bool)),B)) | hBOOL(hAPP(fun(fun(A,bool),bool),bool,hAPP(fun(A,bool),fun(fun(fun(A,bool),bool),bool),member(fun(A,bool)),f646(A,nat,C,B)),B)) | hBOOL(hAPP(fun(fun(A,bool),bool),bool,hAPP(fun(A,bool),fun(fun(fun(A,bool),bool),bool),member(fun(A,bool)),f648(A,nat,C,B)),B)) | hAPP(fun(fun(A,bool),bool),nat,hAPP(fun(fun(A,bool),nat),fun(fun(fun(A,bool),bool),nat),big_co1399186613setsum(fun(A,bool),nat),hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),C)),B) = hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),C),hAPP(fun(fun(A,bool),bool),fun(A,bool),complete_Sup_Sup(fun(A,bool)),B)).  [resolve(5629,a,5602,a)].
40.38/40.26	Derived: -hBOOL(hAPP(fun(fun(A,bool),bool),bool,finite_finite_1(fun(A,bool)),B)) | hBOOL(hAPP(fun(fun(A,bool),bool),bool,hAPP(fun(A,bool),fun(fun(fun(A,bool),bool),bool),member(fun(A,bool)),f646(A,nat,C,B)),B)) | ti(fun(A,bool),f648(A,nat,C,B)) != ti(fun(A,bool),f647(A,nat,C,B)) | hAPP(fun(fun(A,bool),bool),nat,hAPP(fun(fun(A,bool),nat),fun(fun(fun(A,bool),bool),nat),big_co1399186613setsum(fun(A,bool),nat),hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),C)),B) = hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),C),hAPP(fun(fun(A,bool),bool),fun(A,bool),complete_Sup_Sup(fun(A,bool)),B)).  [resolve(5629,a,5603,a)].
40.38/40.26	Derived: -hBOOL(hAPP(fun(fun(A,bool),bool),bool,finite_finite_1(fun(A,bool)),B)) | hBOOL(hAPP(fun(fun(A,bool),bool),bool,hAPP(fun(A,bool),fun(fun(fun(A,bool),bool),bool),member(fun(A,bool)),f646(A,nat,C,B)),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f649(A,nat,C,B)),f647(A,nat,C,B))) | hAPP(fun(fun(A,bool),bool),nat,hAPP(fun(fun(A,bool),nat),fun(fun(fun(A,bool),bool),nat),big_co1399186613setsum(fun(A,bool),nat),hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),C)),B) = hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),C),hAPP(fun(fun(A,bool),bool),fun(A,bool),complete_Sup_Sup(fun(A,bool)),B)).  [resolve(5629,a,5604,a)].
40.38/40.26	Derived: -hBOOL(hAPP(fun(fun(A,bool),bool),bool,finite_finite_1(fun(A,bool)),B)) | hBOOL(hAPP(fun(fun(A,bool),bool),bool,hAPP(fun(A,bool),fun(fun(fun(A,bool),bool),bool),member(fun(A,bool)),f646(A,nat,C,B)),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f649(A,nat,C,B)),f648(A,nat,C,B))) | hAPP(fun(fun(A,bool),bool),nat,hAPP(fun(fun(A,bool),nat),fun(fun(fun(A,bool),bool),nat),big_co1399186613setsum(fun(A,bool),nat),hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),C)),B) = hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),C),hAPP(fun(fun(A,bool),bool),fun(A,bool),complete_Sup_Sup(fun(A,bool)),B)).  [resolve(5629,a,5605,a)].
40.38/40.26	Derived: -hBOOL(hAPP(fun(fun(A,bool),bool),bool,finite_finite_1(fun(A,bool)),B)) | hBOOL(hAPP(fun(fun(A,bool),bool),bool,hAPP(fun(A,bool),fun(fun(fun(A,bool),bool),bool),member(fun(A,bool)),f646(A,nat,C,B)),B)) | zero_zero(nat) != hAPP(A,nat,C,f649(A,nat,C,B)) | hAPP(fun(fun(A,bool),bool),nat,hAPP(fun(fun(A,bool),nat),fun(fun(fun(A,bool),bool),nat),big_co1399186613setsum(fun(A,bool),nat),hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),C)),B) = hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),C),hAPP(fun(fun(A,bool),bool),fun(A,bool),complete_Sup_Sup(fun(A,bool)),B)).  [resolve(5629,a,5606,a)].
40.38/40.26	Derived: -hBOOL(hAPP(fun(fun(A,bool),bool),bool,finite_finite_1(fun(A,bool)),B)) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),f646(A,nat,C,B))) | hBOOL(hAPP(fun(fun(A,bool),bool),bool,hAPP(fun(A,bool),fun(fun(fun(A,bool),bool),bool),member(fun(A,bool)),f647(A,nat,C,B)),B)) | hAPP(fun(fun(A,bool),bool),nat,hAPP(fun(fun(A,bool),nat),fun(fun(fun(A,bool),bool),nat),big_co1399186613setsum(fun(A,bool),nat),hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),C)),B) = hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),C),hAPP(fun(fun(A,bool),bool),fun(A,bool),complete_Sup_Sup(fun(A,bool)),B)).  [resolve(5629,a,5607,a)].
40.38/40.26	Derived: -hBOOL(hAPP(fun(fun(A,bool),bool),bool,finite_finite_1(fun(A,bool)),B)) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),f646(A,nat,C,B))) | hBOOL(hAPP(fun(fun(A,bool),bool),bool,hAPP(fun(A,bool),fun(fun(fun(A,bool),bool),bool),member(fun(A,bool)),f648(A,nat,C,B)),B)) | hAPP(fun(fun(A,bool),bool),nat,hAPP(fun(fun(A,bool),nat),fun(fun(fun(A,bool),bool),nat),big_co1399186613setsum(fun(A,bool),nat),hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),C)),B) = hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),C),hAPP(fun(fun(A,bool),bool),fun(A,bool),complete_Sup_Sup(fun(A,bool)),B)).  [resolve(5629,a,5608,a)].
40.38/40.26	Derived: -hBOOL(hAPP(fun(fun(A,bool),bool),bool,finite_finite_1(fun(A,bool)),B)) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),f646(A,nat,C,B))) | ti(fun(A,bool),f648(A,nat,C,B)) != ti(fun(A,bool),f647(A,nat,C,B)) | hAPP(fun(fun(A,bool),bool),nat,hAPP(fun(fun(A,bool),nat),fun(fun(fun(A,bool),bool),nat),big_co1399186613setsum(fun(A,bool),nat),hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),C)),B) = hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),C),hAPP(fun(fun(A,bool),bool),fun(A,bool),complete_Sup_Sup(fun(A,bool)),B)).  [resolve(5629,a,5609,a)].
40.38/40.27	Derived: -hBOOL(hAPP(fun(fun(A,bool),bool),bool,finite_finite_1(fun(A,bool)),B)) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),f646(A,nat,C,B))) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f649(A,nat,C,B)),f647(A,nat,C,B))) | hAPP(fun(fun(A,bool),bool),nat,hAPP(fun(fun(A,bool),nat),fun(fun(fun(A,bool),bool),nat),big_co1399186613setsum(fun(A,bool),nat),hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),C)),B) = hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),C),hAPP(fun(fun(A,bool),bool),fun(A,bool),complete_Sup_Sup(fun(A,bool)),B)).  [resolve(5629,a,5610,a)].
40.38/40.27	Derived: -hBOOL(hAPP(fun(fun(A,bool),bool),bool,finite_finite_1(fun(A,bool)),B)) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),f646(A,nat,C,B))) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f649(A,nat,C,B)),f648(A,nat,C,B))) | hAPP(fun(fun(A,bool),bool),nat,hAPP(fun(fun(A,bool),nat),fun(fun(fun(A,bool),bool),nat),big_co1399186613setsum(fun(A,bool),nat),hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),C)),B) = hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),C),hAPP(fun(fun(A,bool),bool),fun(A,bool),complete_Sup_Sup(fun(A,bool)),B)).  [resolve(5629,a,5611,a)].
40.38/40.27	Derived: -hBOOL(hAPP(fun(fun(A,bool),bool),bool,finite_finite_1(fun(A,bool)),B)) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),f646(A,nat,C,B))) | zero_zero(nat) != hAPP(A,nat,C,f649(A,nat,C,B)) | hAPP(fun(fun(A,bool),bool),nat,hAPP(fun(fun(A,bool),nat),fun(fun(fun(A,bool),bool),nat),big_co1399186613setsum(fun(A,bool),nat),hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),C)),B) = hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),C),hAPP(fun(fun(A,bool),bool),fun(A,bool),complete_Sup_Sup(fun(A,bool)),B)).  [resolve(5629,a,5612,a)].
40.38/40.27	Derived: -ordere779506340up_add(nat) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f657(A,nat,B,C,D)),D)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),B),D)),hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),C),D))).  [resolve(5629,a,5614,b)].
40.38/40.27	Derived: -ordere779506340up_add(nat) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(A,nat,B,f657(A,nat,B,C,D))),hAPP(A,nat,C,f657(A,nat,B,C,D)))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),B),D)),hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),C),D))).  [resolve(5629,a,5615,b)].
40.38/40.27	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(fun(C,bool),nat,hAPP(fun(C,nat),fun(fun(C,bool),nat),big_co1399186613setsum(C,nat),hAPP(fun(C,fun(A,bool)),fun(C,nat),hAPP(fun(fun(A,bool),nat),fun(fun(C,fun(A,bool)),fun(C,nat)),combb(fun(A,bool),nat,C),hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),D)),hAPP(fun(C,fun(A,bool)),fun(C,fun(A,bool)),hAPP(fun(fun(A,bool),fun(A,bool)),fun(fun(C,fun(A,bool)),fun(C,fun(A,bool))),combb(fun(A,bool),fun(A,bool),C),collect(A)),hAPP(fun(C,fun(A,bool)),fun(C,fun(A,bool)),hAPP(fun(fun(A,bool),fun(A,bool)),fun(fun(C,fun(A,bool)),fun(C,fun(A,bool))),combb(fun(A,bool),fun(A,bool),C),hAPP(fun(A,fun(bool,bool)),fun(fun(A,bool),fun(A,bool)),combs(A,bool,bool),hAPP(fun(A,bool),fun(A,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(A,bool),fun(A,fun(bool,bool))),combb(bool,fun(bool,bool),A),fconj),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,fun(fun(A,bool),bool)),fun(fun(A,bool),fun(A,bool)),combc(A,fun(A,bool),bool),member(A)),B)))),hAPP(fun(A,fun(C,bool)),fun(C,fun(A,bool)),combc(A,C,bool),hAPP(fun(A,C),fun(A,fun(C,bool)),hAPP(fun(C,fun(C,bool)),fun(fun(A,C),fun(A,fun(C,bool))),combb(C,fun(C,bool),A),fequal(C)),E)))))),hAPP(fun(A,bool),fun(C,bool),hAPP(fun(A,C),fun(fun(A,bool),fun(C,bool)),image(A,C),E),B)) = hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),D),B).  [resolve(5629,a,5616,a)].
40.38/40.27	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f694(A,nat,D,C,B)),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),B),C))) | hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),D),B) = hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),D),C).  [resolve(5629,a,5617,a)].
40.38/40.27	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | zero_zero(nat) != hAPP(A,nat,D,f694(A,nat,D,C,B)) | hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),D),B) = hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),D),C).  [resolve(5629,a,5618,a)].
40.38/40.27	Derived: hAPP(fun(nat,bool),nat,hAPP(fun(nat,nat),fun(fun(nat,bool),nat),big_co1399186613setsum(nat,nat),hAPP(fun(nat,nat),fun(nat,nat),hAPP(fun(nat,nat),fun(fun(nat,nat),fun(nat,nat)),combb(nat,nat,nat),A),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),B))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),C),D)) = hAPP(fun(nat,bool),nat,hAPP(fun(nat,nat),fun(fun(nat,bool),nat),big_co1399186613setsum(nat,nat),A),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),C),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),D),B))).  [resolve(5629,a,5619,a)].
40.38/40.27	Derived: -topological_space(nat) | -hBOOL(hAPP(fun(nat,nat),bool,summable(nat),A)) | hBOOL(hAPP(nat,bool,hAPP(fun(nat,nat),fun(nat,bool),sums(nat),A),f737(nat,A))).  [resolve(5629,a,5621,b)].
40.38/40.27	Derived: -power(nat) | hAPP(fun(nat,bool),nat,hAPP(fun(nat,nat),fun(fun(nat,bool),nat),big_co1399186613setsum(nat,nat),hAPP(fun(nat,nat),fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,nat),fun(nat,nat)),combs(nat,nat,nat),hAPP(fun(nat,nat),fun(nat,fun(nat,nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,nat),fun(nat,fun(nat,nat))),combb(nat,fun(nat,nat),nat),times_times(nat)),hAPP(fun(nat,nat),fun(nat,nat),hAPP(fun(nat,nat),fun(fun(nat,nat),fun(nat,nat)),combb(nat,nat,nat),hAPP(nat,fun(nat,nat),power_power(nat),A)),hAPP(nat,fun(nat,nat),minus_minus(nat),B)))),hAPP(nat,fun(nat,nat),power_power(nat),C))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,suc,B))) = hAPP(fun(nat,bool),nat,hAPP(fun(nat,nat),fun(fun(nat,bool),nat),big_co1399186613setsum(nat,nat),hAPP(fun(nat,nat),fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,nat),fun(nat,nat)),combs(nat,nat,nat),hAPP(fun(nat,nat),fun(nat,fun(nat,nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,nat),fun(nat,fun(nat,nat))),combb(nat,fun(nat,nat),nat),times_times(nat)),hAPP(nat,fun(nat,nat),power_power(nat),A))),hAPP(fun(nat,nat),fun(nat,nat),hAPP(fun(nat,nat),fun(fun(nat,nat),fun(nat,nat)),combb(nat,nat,nat),hAPP(nat,fun(nat,nat),power_power(nat),C)),hAPP(nat,fun(nat,nat),minus_minus(nat),B)))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,suc,B))).  [resolve(5629,a,5623,b)].
40.38/40.27	Derived: hAPP(fun(nat,bool),nat,hAPP(fun(nat,nat),fun(fun(nat,bool),nat),big_co1399186613setsum(nat,nat),A),hAPP(nat,fun(nat,bool),ord_lessThan(nat),hAPP(nat,nat,suc,B))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(fun(nat,bool),nat,hAPP(fun(nat,nat),fun(fun(nat,bool),nat),big_co1399186613setsum(nat,nat),A),hAPP(nat,fun(nat,bool),ord_lessThan(nat),B))),hAPP(nat,nat,A,B)).  [resolve(5629,a,5624,a)].
40.38/40.27	Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),zero_zero(nat)) = ti(nat,A).  [resolve(5629,a,5625,a)].
40.56/40.41	Derived: hAPP(fun(nat,bool),nat,hAPP(fun(nat,nat),fun(fun(nat,bool),nat),big_co1399186613setsum(nat,nat),hAPP(fun(nat,nat),fun(nat,nat),hAPP(fun(nat,nat),fun(fun(nat,nat),fun(nat,nat)),combb(nat,nat,nat),A),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),B))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),C),D)) = hAPP(fun(nat,bool),nat,hAPP(fun(nat,nat),fun(fun(nat,bool),nat),big_co1399186613setsum(nat,nat),A),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),C),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),D),B))).  [resolve(5629,a,5626,a)].
40.56/40.41	Derived: hAPP(fun(nat,bool),nat,hAPP(fun(nat,nat),fun(fun(nat,bool),nat),big_co1399186613setsum(nat,nat),hAPP(fun(nat,nat),fun(nat,nat),hAPP(fun(nat,nat),fun(fun(nat,nat),fun(nat,nat)),combb(nat,nat,nat),A),suc)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),B),C)) = hAPP(fun(nat,bool),nat,hAPP(fun(nat,nat),fun(fun(nat,bool),nat),big_co1399186613setsum(nat,nat),A),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),hAPP(nat,nat,suc,B)),hAPP(nat,nat,suc,C))).  [resolve(5629,a,5627,a)].
40.56/40.41	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(C,bool),bool,finite_finite_1(C),D)) | hAPP(fun(C,bool),nat,hAPP(fun(C,nat),fun(fun(C,bool),nat),big_co1399186613setsum(C,nat),hAPP(fun(C,fun(A,bool)),fun(C,nat),hAPP(fun(C,fun(fun(A,bool),nat)),fun(fun(C,fun(A,bool)),fun(C,nat)),combs(C,fun(A,bool),nat),hAPP(fun(C,fun(A,nat)),fun(C,fun(fun(A,bool),nat)),hAPP(fun(fun(A,nat),fun(fun(A,bool),nat)),fun(fun(C,fun(A,nat)),fun(C,fun(fun(A,bool),nat))),combb(fun(A,nat),fun(fun(A,bool),nat),C),big_co1399186613setsum(A,nat)),hAPP(fun(A,fun(C,nat)),fun(C,fun(A,nat)),combc(A,C,nat),E))),hAPP(fun(C,fun(A,bool)),fun(C,fun(A,bool)),hAPP(fun(fun(A,bool),fun(A,bool)),fun(fun(C,fun(A,bool)),fun(C,fun(A,bool))),combb(fun(A,bool),fun(A,bool),C),collect(A)),hAPP(fun(C,fun(A,bool)),fun(C,fun(A,bool)),hAPP(fun(fun(A,bool),fun(A,bool)),fun(fun(C,fun(A,bool)),fun(C,fun(A,bool))),combb(fun(A,bool),fun(A,bool),C),hAPP(fun(A,fun(bool,bool)),fun(fun(A,bool),fun(A,bool)),combs(A,bool,bool),hAPP(fun(A,bool),fun(A,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(A,bool),fun(A,fun(bool,bool))),combb(bool,fun(bool,bool),A),fconj),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,fun(fun(A,bool),bool)),fun(fun(A,bool),fun(A,bool)),combc(A,fun(A,bool),bool),member(A)),B)))),hAPP(fun(A,fun(C,bool)),fun(C,fun(A,bool)),combc(A,C,bool),F))))),D) = hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),hAPP(fun(A,fun(C,bool)),fun(A,nat),hAPP(fun(A,fun(fun(C,bool),nat)),fun(fun(A,fun(C,bool)),fun(A,nat)),combs(A,fun(C,bool),nat),hAPP(fun(A,fun(C,nat)),fun(A,fun(fun(C,bool),nat)),hAPP(fun(fun(C,nat),fun(fun(C,bool),nat)),fun(fun(A,fun(C,nat)),fun(A,fun(fun(C,bool),nat))),combb(fun(C,nat),fun(fun(C,bool),nat),A),big_co1399186613setsum(C,nat)),E)),hAPP(fun(A,fun(C,bool)),fun(A,fun(C,bool)),hAPP(fun(fun(C,bool),fun(C,bool)),fun(fun(A,fun(C,bool)),fun(A,fun(C,bool))),combb(fun(C,bool),fun(C,bool),A),collect(C)),hAPP(fun(A,fun(C,bool)),fun(A,fun(C,bool)),hAPP(fun(fun(C,bool),fun(C,bool)),fun(fun(A,fun(C,bool)),fun(A,fun(C,bool))),combb(fun(C,bool),fun(C,bool),A),hAPP(fun(C,fun(bool,bool)),fun(fun(C,bool),fun(C,bool)),combs(C,bool,bool),hAPP(fun(C,bool),fun(C,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(C,bool),fun(C,fun(bool,bool))),combb(bool,fun(bool,bool),C),fconj),hAPP(fun(C,bool),fun(C,bool),hAPP(fun(C,fun(fun(C,bool),bool)),fun(fun(C,bool),fun(C,bool)),combc(C,fun(C,bool),bool),member(C)),D)))),F)))),B).  [resolve(5629,a,5628,a)].
40.56/40.41	5630 -comm_monoid_mult(A) | -comm_monoid_add(A) | B != C | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),f817(A,D,E,C,B))) | hAPP(fun(int,bool),A,hAPP(fun(int,A),fun(fun(int,bool),A),big_co302546470etprod(int,A),E),B) = hAPP(fun(int,bool),A,hAPP(fun(int,A),fun(fun(int,bool),A),big_co302546470etprod(int,A),D),C) # label(fact_3962_transfer__nat__int__sum__prod__cong_I2_J) # label(axiom).  [clausify(4637)].
40.56/40.42	Derived: -comm_monoid_mult(real) | A != B | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),f817(real,C,D,B,A))) | hAPP(fun(int,bool),real,hAPP(fun(int,real),fun(fun(int,bool),real),big_co302546470etprod(int,real),D),A) = hAPP(fun(int,bool),real,hAPP(fun(int,real),fun(fun(int,bool),real),big_co302546470etprod(int,real),C),B).  [resolve(5630,b,5513,a)].
40.56/40.42	Derived: -comm_monoid_mult(int) | A != B | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),f817(int,C,D,B,A))) | hAPP(fun(int,bool),int,hAPP(fun(int,int),fun(fun(int,bool),int),big_co302546470etprod(int,int),D),A) = hAPP(fun(int,bool),int,hAPP(fun(int,int),fun(fun(int,bool),int),big_co302546470etprod(int,int),C),B).  [resolve(5630,b,5524,a)].
40.56/40.42	Derived: -comm_monoid_mult(code_code_numeral) | A != B | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),f817(code_code_numeral,C,D,B,A))) | hAPP(fun(int,bool),code_code_numeral,hAPP(fun(int,code_code_numeral),fun(fun(int,bool),code_code_numeral),big_co302546470etprod(int,code_code_numeral),D),A) = hAPP(fun(int,bool),code_code_numeral,hAPP(fun(int,code_code_numeral),fun(fun(int,bool),code_code_numeral),big_co302546470etprod(int,code_code_numeral),C),B).  [resolve(5630,b,5539,a)].
40.56/40.42	Derived: -comm_monoid_mult(rat) | A != B | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),f817(rat,C,D,B,A))) | hAPP(fun(int,bool),rat,hAPP(fun(int,rat),fun(fun(int,bool),rat),big_co302546470etprod(int,rat),D),A) = hAPP(fun(int,bool),rat,hAPP(fun(int,rat),fun(fun(int,bool),rat),big_co302546470etprod(int,rat),C),B).  [resolve(5630,b,5561,a)].
40.56/40.42	Derived: -comm_monoid_mult(quickcheck_code_int) | A != B | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),f817(quickcheck_code_int,C,D,B,A))) | hAPP(fun(int,bool),quickcheck_code_int,hAPP(fun(int,quickcheck_code_int),fun(fun(int,bool),quickcheck_code_int),big_co302546470etprod(int,quickcheck_code_int),D),A) = hAPP(fun(int,bool),quickcheck_code_int,hAPP(fun(int,quickcheck_code_int),fun(fun(int,bool),quickcheck_code_int),big_co302546470etprod(int,quickcheck_code_int),C),B).  [resolve(5630,b,5620,a)].
40.56/40.42	Derived: -comm_monoid_mult(nat) | A != B | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),f817(nat,C,D,B,A))) | hAPP(fun(int,bool),nat,hAPP(fun(int,nat),fun(fun(int,bool),nat),big_co302546470etprod(int,nat),D),A) = hAPP(fun(int,bool),nat,hAPP(fun(int,nat),fun(fun(int,bool),nat),big_co302546470etprod(int,nat),C),B).  [resolve(5630,b,5629,a)].
40.56/40.42	5631 -comm_monoid_mult(A) | -comm_monoid_add(A) | B != C | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,B)) | hAPP(int,A,D,f817(A,E,D,C,B)) != hAPP(int,A,E,f817(A,E,D,C,B)) | hAPP(fun(int,bool),A,hAPP(fun(int,A),fun(fun(int,bool),A),big_co302546470etprod(int,A),D),B) = hAPP(fun(int,bool),A,hAPP(fun(int,A),fun(fun(int,bool),A),big_co302546470etprod(int,A),E),C) # label(fact_3962_transfer__nat__int__sum__prod__cong_I2_J) # label(axiom).  [clausify(4637)].
40.56/40.42	Derived: -comm_monoid_mult(real) | A != B | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A)) | hAPP(int,real,C,f817(real,D,C,B,A)) != hAPP(int,real,D,f817(real,D,C,B,A)) | hAPP(fun(int,bool),real,hAPP(fun(int,real),fun(fun(int,bool),real),big_co302546470etprod(int,real),C),A) = hAPP(fun(int,bool),real,hAPP(fun(int,real),fun(fun(int,bool),real),big_co302546470etprod(int,real),D),B).  [resolve(5631,b,5513,a)].
40.56/40.42	Derived: -comm_monoid_mult(int) | A != B | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A)) | hAPP(int,int,C,f817(int,D,C,B,A)) != hAPP(int,int,D,f817(int,D,C,B,A)) | hAPP(fun(int,bool),int,hAPP(fun(int,int),fun(fun(int,bool),int),big_co302546470etprod(int,int),C),A) = hAPP(fun(int,bool),int,hAPP(fun(int,int),fun(fun(int,bool),int),big_co302546470etprod(int,int),D),B).  [resolve(5631,b,5524,a)].
40.65/40.48	Derived: -comm_monoid_mult(code_code_numeral) | A != B | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A)) | hAPP(int,code_code_numeral,C,f817(code_code_numeral,D,C,B,A)) != hAPP(int,code_code_numeral,D,f817(code_code_numeral,D,C,B,A)) | hAPP(fun(int,bool),code_code_numeral,hAPP(fun(int,code_code_numeral),fun(fun(int,bool),code_code_numeral),big_co302546470etprod(int,code_code_numeral),C),A) = hAPP(fun(int,bool),code_code_numeral,hAPP(fun(int,code_code_numeral),fun(fun(int,bool),code_code_numeral),big_co302546470etprod(int,code_code_numeral),D),B).  [resolve(5631,b,5539,a)].
40.65/40.48	Derived: -comm_monoid_mult(rat) | A != B | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A)) | hAPP(int,rat,C,f817(rat,D,C,B,A)) != hAPP(int,rat,D,f817(rat,D,C,B,A)) | hAPP(fun(int,bool),rat,hAPP(fun(int,rat),fun(fun(int,bool),rat),big_co302546470etprod(int,rat),C),A) = hAPP(fun(int,bool),rat,hAPP(fun(int,rat),fun(fun(int,bool),rat),big_co302546470etprod(int,rat),D),B).  [resolve(5631,b,5561,a)].
40.65/40.48	Derived: -comm_monoid_mult(quickcheck_code_int) | A != B | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A)) | hAPP(int,quickcheck_code_int,C,f817(quickcheck_code_int,D,C,B,A)) != hAPP(int,quickcheck_code_int,D,f817(quickcheck_code_int,D,C,B,A)) | hAPP(fun(int,bool),quickcheck_code_int,hAPP(fun(int,quickcheck_code_int),fun(fun(int,bool),quickcheck_code_int),big_co302546470etprod(int,quickcheck_code_int),C),A) = hAPP(fun(int,bool),quickcheck_code_int,hAPP(fun(int,quickcheck_code_int),fun(fun(int,bool),quickcheck_code_int),big_co302546470etprod(int,quickcheck_code_int),D),B).  [resolve(5631,b,5620,a)].
40.65/40.48	Derived: -comm_monoid_mult(nat) | A != B | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A)) | hAPP(int,nat,C,f817(nat,D,C,B,A)) != hAPP(int,nat,D,f817(nat,D,C,B,A)) | hAPP(fun(int,bool),nat,hAPP(fun(int,nat),fun(fun(int,bool),nat),big_co302546470etprod(int,nat),C),A) = hAPP(fun(int,bool),nat,hAPP(fun(int,nat),fun(fun(int,bool),nat),big_co302546470etprod(int,nat),D),B).  [resolve(5631,b,5629,a)].
40.65/40.48	5632 comm_monoid_add(complex) # label(arity_Complex_Ocomplex___Groups_Ocomm__monoid__add) # label(axiom).  [assumption].
40.65/40.48	Derived: zero_zero(complex) = hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),hAPP(complex,fun(A,complex),combk(complex,A),zero_zero(complex))),B).  [resolve(5632,a,5514,a)].
40.65/40.48	Derived: hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f2(A,complex,B,C)),C)) | zero_zero(complex) = hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),B),C).  [resolve(5632,a,5515,a)].
40.65/40.48	Derived: zero_zero(complex) != hAPP(A,complex,B,f2(A,complex,B,C)) | zero_zero(complex) = hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),B),C).  [resolve(5632,a,5516,a)].
40.65/40.48	Derived: -topological_space(complex) | -hBOOL(hAPP(complex,bool,hAPP(fun(nat,complex),fun(complex,bool),sums(complex),A),B)) | hBOOL(hAPP(filter(nat),bool,hAPP(complex,fun(filter(nat),bool),hAPP(fun(nat,complex),fun(complex,fun(filter(nat),bool)),tendsto(nat,complex),hAPP(fun(nat,fun(nat,bool)),fun(nat,complex),hAPP(fun(fun(nat,bool),complex),fun(fun(nat,fun(nat,bool)),fun(nat,complex)),combb(fun(nat,bool),complex,nat),hAPP(fun(nat,complex),fun(fun(nat,bool),complex),big_co1399186613setsum(nat,complex),A)),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)))),B),sequentially)).  [resolve(5632,a,5517,a)].
40.65/40.48	Derived: -topological_space(complex) | hBOOL(hAPP(complex,bool,hAPP(fun(nat,complex),fun(complex,bool),sums(complex),A),B)) | -hBOOL(hAPP(filter(nat),bool,hAPP(complex,fun(filter(nat),bool),hAPP(fun(nat,complex),fun(complex,fun(filter(nat),bool)),tendsto(nat,complex),hAPP(fun(nat,fun(nat,bool)),fun(nat,complex),hAPP(fun(fun(nat,bool),complex),fun(fun(nat,fun(nat,bool)),fun(nat,complex)),combb(fun(nat,bool),complex,nat),hAPP(fun(nat,complex),fun(fun(nat,bool),complex),big_co1399186613setsum(nat,complex),A)),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)))),B),sequentially)).  [resolve(5632,a,5518,a)].
40.65/40.49	Derived: -ordere779506340up_add(complex) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f20(A,complex,D,C,B)),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),B),C))) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less_eq(complex),hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),D),C)),hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),D),B))).  [resolve(5632,a,5519,b)].
40.65/40.49	Derived: -ordere779506340up_add(complex) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less_eq(complex),zero_zero(complex)),hAPP(A,complex,D,f20(A,complex,D,C,B)))) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less_eq(complex),hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),D),C)),hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),D),B))).  [resolve(5632,a,5520,b)].
40.65/40.49	Derived: -topological_space(complex) | sums(complex) = ti(fun(fun(nat,complex),fun(complex,bool)),sums(complex)).  [resolve(5632,a,5521,a)].
40.65/40.49	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f56(A,complex,D,C,B)),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),B),C))) | hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),D),B) = hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),D),C).  [resolve(5632,a,5522,a)].
40.65/40.49	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | zero_zero(complex) != hAPP(A,complex,D,f56(A,complex,D,C,B)) | hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),D),B) = hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),D),C).  [resolve(5632,a,5523,a)].
40.65/40.49	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),one_one(nat)))) | hAPP(fun(nat,bool),complex,hAPP(fun(nat,complex),fun(fun(nat,bool),complex),big_co1399186613setsum(nat,complex),C),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),D))) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(fun(nat,bool),complex,hAPP(fun(nat,complex),fun(fun(nat,bool),complex),big_co1399186613setsum(nat,complex),C),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),A),B))),hAPP(fun(nat,bool),complex,hAPP(fun(nat,complex),fun(fun(nat,bool),complex),big_co1399186613setsum(nat,complex),C),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),one_one(nat))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),D)))).  [resolve(5632,a,5525,a)].
40.65/40.49	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | hAPP(fun(nat,bool),complex,hAPP(fun(nat,complex),fun(fun(nat,bool),complex),big_co1399186613setsum(nat,complex),C),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),A),B)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(nat,complex,C,A)),hAPP(fun(nat,bool),complex,hAPP(fun(nat,complex),fun(fun(nat,bool),complex),big_co1399186613setsum(nat,complex),C),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,suc,A)),B))).  [resolve(5632,a,5526,a)].
40.65/40.49	Derived: -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),A,zero_zero(complex)),zero_zero(complex))) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),A,f102(B,complex,C,D,E,A)),f104(B,complex,C,D,E,A))) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),E)) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f106(B,complex,C,D,E,A)),E)) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),A,hAPP(fun(B,bool),complex,hAPP(fun(B,complex),fun(fun(B,bool),complex),big_co1399186613setsum(B,complex),C),E)),hAPP(fun(B,bool),complex,hAPP(fun(B,complex),fun(fun(B,bool),complex),big_co1399186613setsum(B,complex),D),E))).  [resolve(5632,a,5527,a)].
40.65/40.49	Derived: -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),A,zero_zero(complex)),zero_zero(complex))) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),A,f102(B,complex,C,D,E,A)),f104(B,complex,C,D,E,A))) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),E)) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),A,hAPP(B,complex,C,f106(B,complex,C,D,E,A))),hAPP(B,complex,D,f106(B,complex,C,D,E,A)))) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),A,hAPP(fun(B,bool),complex,hAPP(fun(B,complex),fun(fun(B,bool),complex),big_co1399186613setsum(B,complex),C),E)),hAPP(fun(B,bool),complex,hAPP(fun(B,complex),fun(fun(B,bool),complex),big_co1399186613setsum(B,complex),D),E))).  [resolve(5632,a,5528,a)].
40.65/40.49	Derived: -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),A,zero_zero(complex)),zero_zero(complex))) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),A,f103(B,complex,C,D,E,A)),f105(B,complex,C,D,E,A))) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),E)) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f106(B,complex,C,D,E,A)),E)) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),A,hAPP(fun(B,bool),complex,hAPP(fun(B,complex),fun(fun(B,bool),complex),big_co1399186613setsum(B,complex),C),E)),hAPP(fun(B,bool),complex,hAPP(fun(B,complex),fun(fun(B,bool),complex),big_co1399186613setsum(B,complex),D),E))).  [resolve(5632,a,5529,a)].
40.65/40.49	Derived: -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),A,zero_zero(complex)),zero_zero(complex))) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),A,f103(B,complex,C,D,E,A)),f105(B,complex,C,D,E,A))) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),E)) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),A,hAPP(B,complex,C,f106(B,complex,C,D,E,A))),hAPP(B,complex,D,f106(B,complex,C,D,E,A)))) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),A,hAPP(fun(B,bool),complex,hAPP(fun(B,complex),fun(fun(B,bool),complex),big_co1399186613setsum(B,complex),C),E)),hAPP(fun(B,bool),complex,hAPP(fun(B,complex),fun(fun(B,bool),complex),big_co1399186613setsum(B,complex),D),E))).  [resolve(5632,a,5530,a)].
40.65/40.49	Derived: -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),A,zero_zero(complex)),zero_zero(complex))) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),A,hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),f102(B,complex,C,D,E,A)),f103(B,complex,C,D,E,A))),hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),f104(B,complex,C,D,E,A)),f105(B,complex,C,D,E,A)))) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),E)) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f106(B,complex,C,D,E,A)),E)) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),A,hAPP(fun(B,bool),complex,hAPP(fun(B,complex),fun(fun(B,bool),complex),big_co1399186613setsum(B,complex),C),E)),hAPP(fun(B,bool),complex,hAPP(fun(B,complex),fun(fun(B,bool),complex),big_co1399186613setsum(B,complex),D),E))).  [resolve(5632,a,5531,a)].
40.65/40.49	Derived: -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),A,zero_zero(complex)),zero_zero(complex))) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),A,hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),f102(B,complex,C,D,E,A)),f103(B,complex,C,D,E,A))),hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),f104(B,complex,C,D,E,A)),f105(B,complex,C,D,E,A)))) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),E)) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),A,hAPP(B,complex,C,f106(B,complex,C,D,E,A))),hAPP(B,complex,D,f106(B,complex,C,D,E,A)))) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),A,hAPP(fun(B,bool),complex,hAPP(fun(B,complex),fun(fun(B,bool),complex),big_co1399186613setsum(B,complex),C),E)),hAPP(fun(B,bool),complex,hAPP(fun(B,complex),fun(fun(B,bool),complex),big_co1399186613setsum(B,complex),D),E))).  [resolve(5632,a,5532,a)].
40.65/40.50	Derived: -t2_space(complex) | zero_zero(complex) = hAPP(fun(nat,complex),complex,suminf(complex),hAPP(complex,fun(nat,complex),combk(complex,nat),zero_zero(complex))).  [resolve(5632,a,5533,b)].
40.65/40.50	Derived: -topological_space(complex) | zero_zero(complex) != hAPP(nat,complex,A,zero_zero(nat)) | -hBOOL(hAPP(complex,bool,hAPP(fun(nat,complex),fun(complex,bool),sums(complex),hAPP(fun(nat,nat),fun(nat,complex),hAPP(fun(nat,complex),fun(fun(nat,nat),fun(nat,complex)),combb(nat,complex,nat),A),suc)),B)) | hBOOL(hAPP(complex,bool,hAPP(fun(nat,complex),fun(complex,bool),sums(complex),A),B)).  [resolve(5632,a,5534,a)].
40.65/40.50	Derived: -topological_space(complex) | the(complex) = ti(fun(fun(complex,bool),complex),the(complex)).  [resolve(5632,a,5535,a)].
40.65/40.50	Derived: -ordere779506340up_add(complex) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f137(A,complex,B,C)),C)) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less_eq(complex),hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),B),C)),zero_zero(complex))).  [resolve(5632,a,5536,b)].
40.65/40.50	Derived: -ordere779506340up_add(complex) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less_eq(complex),hAPP(A,complex,B,f137(A,complex,B,C))),zero_zero(complex))) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less_eq(complex),hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),B),C)),zero_zero(complex))).  [resolve(5632,a,5537,b)].
40.65/40.50	Derived: -t2_space(complex) | -hBOOL(hAPP(fun(nat,complex),bool,summable(complex),A)) | hBOOL(hAPP(complex,bool,hAPP(fun(nat,complex),fun(complex,bool),sums(complex),A),hAPP(fun(nat,complex),complex,suminf(complex),A))).  [resolve(5632,a,5538,b)].
40.65/40.50	Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),zero_zero(complex)),A) = ti(complex,A).  [resolve(5632,a,5540,a)].
40.65/40.50	Derived: -topological_space(complex) | hBOOL(hAPP(complex,bool,hAPP(fun(nat,complex),fun(complex,bool),sums(complex),hAPP(complex,fun(nat,complex),combk(complex,nat),zero_zero(complex))),zero_zero(complex))).  [resolve(5632,a,5541,a)].
40.65/40.50	Derived: -topological_space(complex) | suminf(complex) = ti(fun(fun(nat,complex),complex),suminf(complex)).  [resolve(5632,a,5542,b)].
40.65/40.50	Derived: hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | zero_zero(complex) = hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),C),B).  [resolve(5632,a,5543,a)].
40.65/40.50	Derived: -t2_space(complex) | -hBOOL(hAPP(complex,bool,hAPP(fun(nat,complex),fun(complex,bool),sums(complex),A),B)) | hAPP(fun(nat,complex),complex,suminf(complex),A) = ti(complex,B).  [resolve(5632,a,5544,b)].
40.65/40.50	Derived: hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),hAPP(fun(B,bool),fun(A,complex),hAPP(fun(A,fun(fun(B,bool),complex)),fun(fun(B,bool),fun(A,complex)),combc(A,fun(B,bool),complex),hAPP(fun(A,fun(B,complex)),fun(A,fun(fun(B,bool),complex)),hAPP(fun(fun(B,complex),fun(fun(B,bool),complex)),fun(fun(A,fun(B,complex)),fun(A,fun(fun(B,bool),complex))),combb(fun(B,complex),fun(fun(B,bool),complex),A),big_co1399186613setsum(B,complex)),hAPP(fun(B,fun(A,complex)),fun(A,fun(B,complex)),combc(B,A,complex),C))),D)),E) = hAPP(fun(B,bool),complex,hAPP(fun(B,complex),fun(fun(B,bool),complex),big_co1399186613setsum(B,complex),hAPP(fun(A,bool),fun(B,complex),hAPP(fun(B,fun(fun(A,bool),complex)),fun(fun(A,bool),fun(B,complex)),combc(B,fun(A,bool),complex),hAPP(fun(B,fun(A,complex)),fun(B,fun(fun(A,bool),complex)),hAPP(fun(fun(A,complex),fun(fun(A,bool),complex)),fun(fun(B,fun(A,complex)),fun(B,fun(fun(A,bool),complex))),combb(fun(A,complex),fun(fun(A,bool),complex),B),big_co1399186613setsum(A,complex)),C)),E)),D).  [resolve(5632,a,5545,a)].
40.65/40.50	Derived: hAPP(fun(nat,bool),complex,hAPP(fun(nat,complex),fun(fun(nat,bool),complex),big_co1399186613setsum(nat,complex),hAPP(fun(nat,fun(nat,bool)),fun(nat,complex),hAPP(fun(fun(nat,bool),complex),fun(fun(nat,fun(nat,bool)),fun(nat,complex)),combb(fun(nat,bool),complex,nat),hAPP(fun(nat,complex),fun(fun(nat,bool),complex),big_co1399186613setsum(nat,complex),A)),hAPP(fun(nat,nat),fun(nat,fun(nat,bool)),hAPP(fun(nat,fun(nat,fun(nat,bool))),fun(fun(nat,nat),fun(nat,fun(nat,bool))),combs(nat,nat,fun(nat,bool)),hAPP(fun(nat,nat),fun(nat,fun(nat,fun(nat,bool))),hAPP(fun(nat,fun(nat,fun(nat,bool))),fun(fun(nat,nat),fun(nat,fun(nat,fun(nat,bool)))),combb(nat,fun(nat,fun(nat,bool)),nat),ord_atLeastLessThan(nat)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),times_times(nat)),B))),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),hAPP(fun(nat,nat),fun(nat,fun(nat,nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,nat),fun(nat,fun(nat,nat))),combb(nat,fun(nat,nat),nat),plus_plus(nat)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),times_times(nat)),B))),B)))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),C)) = hAPP(fun(nat,bool),complex,hAPP(fun(nat,complex),fun(fun(nat,bool),complex),big_co1399186613setsum(nat,complex),A),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),C),B))).  [resolve(5632,a,5546,a)].
40.65/40.50	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | zero_zero(complex) = hAPP(fun(nat,bool),complex,hAPP(fun(nat,complex),fun(fun(nat,bool),complex),big_co1399186613setsum(nat,complex),C),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),B),hAPP(nat,nat,suc,A))).  [resolve(5632,a,5547,a)].
40.65/40.50	Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | hAPP(fun(nat,bool),complex,hAPP(fun(nat,complex),fun(fun(nat,bool),complex),big_co1399186613setsum(nat,complex),C),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),B),hAPP(nat,nat,suc,A))) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(fun(nat,bool),complex,hAPP(fun(nat,complex),fun(fun(nat,bool),complex),big_co1399186613setsum(nat,complex),C),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),B),A))),hAPP(nat,complex,C,A)).  [resolve(5632,a,5548,a)].
40.65/40.50	Derived: -ordere779506340up_add(complex) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f306(A,complex,B,C)),C)) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less_eq(complex),zero_zero(complex)),hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),B),C))).  [resolve(5632,a,5549,a)].
40.65/40.50	Derived: -ordere779506340up_add(complex) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less_eq(complex),zero_zero(complex)),hAPP(A,complex,B,f306(A,complex,B,C)))) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less_eq(complex),zero_zero(complex)),hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),B),C))).  [resolve(5632,a,5550,a)].
40.65/40.50	Derived: hAPP(fun(nat,bool),complex,hAPP(fun(nat,complex),fun(fun(nat,bool),complex),big_co1399186613setsum(nat,complex),A),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),C))) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(fun(nat,bool),complex,hAPP(fun(nat,complex),fun(fun(nat,bool),complex),big_co1399186613setsum(nat,complex),hAPP(fun(nat,nat),fun(nat,complex),hAPP(fun(nat,complex),fun(fun(nat,nat),fun(nat,complex)),combb(nat,complex,nat),A),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),C))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),B))),hAPP(fun(nat,bool),complex,hAPP(fun(nat,complex),fun(fun(nat,bool),complex),big_co1399186613setsum(nat,complex),A),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),C))).  [resolve(5632,a,5551,a)].
40.65/40.50	Derived: -comm_monoid_mult(complex) | A != B | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),f335(complex,C,D,B,A))) | hAPP(fun(int,bool),complex,hAPP(fun(int,complex),fun(fun(int,bool),complex),big_co1399186613setsum(int,complex),D),A) = hAPP(fun(int,bool),complex,hAPP(fun(int,complex),fun(fun(int,bool),complex),big_co1399186613setsum(int,complex),C),B).  [resolve(5632,a,5552,b)].
40.65/40.50	Derived: -comm_monoid_mult(complex) | A != B | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A)) | hAPP(int,complex,C,f335(complex,D,C,B,A)) != hAPP(int,complex,D,f335(complex,D,C,B,A)) | hAPP(fun(int,bool),complex,hAPP(fun(int,complex),fun(fun(int,bool),complex),big_co1399186613setsum(int,complex),C),A) = hAPP(fun(int,bool),complex,hAPP(fun(int,complex),fun(fun(int,bool),complex),big_co1399186613setsum(int,complex),D),B).  [resolve(5632,a,5553,b)].
40.65/40.50	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | zero_zero(complex) = hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),hAPP(complex,fun(A,complex),hAPP(fun(A,fun(complex,complex)),fun(complex,fun(A,complex)),combc(A,complex,complex),hAPP(fun(A,complex),fun(A,fun(complex,complex)),hAPP(fun(A,fun(complex,fun(complex,complex))),fun(fun(A,complex),fun(A,fun(complex,complex))),combs(A,complex,fun(complex,complex)),hAPP(fun(A,bool),fun(A,fun(complex,fun(complex,complex))),hAPP(fun(bool,fun(complex,fun(complex,complex))),fun(fun(A,bool),fun(A,fun(complex,fun(complex,complex)))),combb(bool,fun(complex,fun(complex,complex)),A),if(complex)),hAPP(A,fun(A,bool),hAPP(fun(A,fun(A,bool)),fun(A,fun(A,bool)),combc(A,A,bool),fequal(A)),C))),D)),zero_zero(complex))),B).  [resolve(5632,a,5554,a)].
40.65/40.50	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),hAPP(complex,fun(A,complex),hAPP(fun(A,fun(complex,complex)),fun(complex,fun(A,complex)),combc(A,complex,complex),hAPP(fun(A,complex),fun(A,fun(complex,complex)),hAPP(fun(A,fun(complex,fun(complex,complex))),fun(fun(A,complex),fun(A,fun(complex,complex))),combs(A,complex,fun(complex,complex)),hAPP(fun(A,bool),fun(A,fun(complex,fun(complex,complex))),hAPP(fun(bool,fun(complex,fun(complex,complex))),fun(fun(A,bool),fun(A,fun(complex,fun(complex,complex)))),combb(bool,fun(complex,fun(complex,complex)),A),if(complex)),hAPP(A,fun(A,bool),hAPP(fun(A,fun(A,bool)),fun(A,fun(A,bool)),combc(A,A,bool),fequal(A)),C))),D)),zero_zero(complex))),B) = hAPP(A,complex,D,C).  [resolve(5632,a,5555,a)].
40.65/40.50	Derived: -metric_space(complex) | hAPP(fun(nat,complex),complex,lim(complex),hAPP(fun(nat,fun(nat,bool)),fun(nat,complex),hAPP(fun(fun(nat,bool),complex),fun(fun(nat,fun(nat,bool)),fun(nat,complex)),combb(fun(nat,bool),complex,nat),hAPP(fun(nat,complex),fun(fun(nat,bool),complex),big_co1399186613setsum(nat,complex),A)),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)))) = hAPP(fun(nat,complex),complex,suminf(complex),A).  [resolve(5632,a,5556,b)].
40.65/40.50	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,A)),B)) | zero_zero(complex) = hAPP(fun(nat,bool),complex,hAPP(fun(nat,complex),fun(fun(nat,bool),complex),big_co1399186613setsum(nat,complex),C),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),B),hAPP(nat,nat,suc,A))).  [resolve(5632,a,5557,a)].
40.65/40.50	Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,A)),B)) | hAPP(fun(nat,bool),complex,hAPP(fun(nat,complex),fun(fun(nat,bool),complex),big_co1399186613setsum(nat,complex),C),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),B),hAPP(nat,nat,suc,A))) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(nat,complex,C,B)),hAPP(fun(nat,bool),complex,hAPP(fun(nat,complex),fun(fun(nat,bool),complex),big_co1399186613setsum(nat,complex),hAPP(fun(nat,nat),fun(nat,complex),hAPP(fun(nat,complex),fun(fun(nat,nat),fun(nat,complex)),combb(nat,complex,nat),C),suc)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),B),A))).  [resolve(5632,a,5558,a)].
40.65/40.50	Derived: hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),hAPP(fun(A,complex),fun(A,complex),hAPP(fun(A,fun(complex,complex)),fun(fun(A,complex),fun(A,complex)),combs(A,complex,complex),hAPP(fun(A,complex),fun(A,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(A,complex),fun(A,fun(complex,complex))),combb(complex,fun(complex,complex),A),plus_plus(complex)),B)),C)),D) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),B),D)),hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),C),D)).  [resolve(5632,a,5559,a)].
40.65/40.50	Derived: -comm_monoid_mult(complex) | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A)) | hAPP(fun(nat,bool),complex,hAPP(fun(nat,complex),fun(fun(nat,bool),complex),big_co1399186613setsum(nat,complex),hAPP(fun(nat,int),fun(nat,complex),hAPP(fun(int,complex),fun(fun(nat,int),fun(nat,complex)),combb(int,complex,nat),B),semiring_1_of_nat(int))),hAPP(fun(int,bool),fun(nat,bool),hAPP(fun(int,nat),fun(fun(int,bool),fun(nat,bool)),image(int,nat),nat_1),A)) = hAPP(fun(int,bool),complex,hAPP(fun(int,complex),fun(fun(int,bool),complex),big_co1399186613setsum(int,complex),B),A).  [resolve(5632,a,5560,b)].
40.65/40.50	Derived: big_co1399186613setsum(A,complex) = ti(fun(fun(A,complex),fun(fun(A,bool),complex)),big_co1399186613setsum(A,complex)).  [resolve(5632,a,5562,a)].
40.65/40.50	Derived: -topological_space(complex) | hAPP(fun(complex,bool),complex,the(complex),hAPP(fun(nat,complex),fun(complex,bool),sums(complex),A)) = hAPP(fun(nat,complex),complex,suminf(complex),A).  [resolve(5632,a,5563,b)].
40.65/40.50	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | hAPP(fun(nat,bool),complex,hAPP(fun(nat,complex),fun(fun(nat,bool),complex),big_co1399186613setsum(nat,complex),C),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),A),B)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(nat,complex,C,A)),hAPP(fun(nat,bool),complex,hAPP(fun(nat,complex),fun(fun(nat,bool),complex),big_co1399186613setsum(nat,complex),C),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),hAPP(nat,nat,suc,A)),B))).  [resolve(5632,a,5564,a)].
40.65/40.50	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),hAPP(complex,fun(A,complex),hAPP(fun(A,fun(complex,complex)),fun(complex,fun(A,complex)),combc(A,complex,complex),hAPP(fun(A,complex),fun(A,fun(complex,complex)),hAPP(fun(A,fun(complex,fun(complex,complex))),fun(fun(A,complex),fun(A,fun(complex,complex))),combs(A,complex,fun(complex,complex)),hAPP(fun(A,bool),fun(A,fun(complex,fun(complex,complex))),hAPP(fun(bool,fun(complex,fun(complex,complex))),fun(fun(A,bool),fun(A,fun(complex,fun(complex,complex)))),combb(bool,fun(complex,fun(complex,complex)),A),if(complex)),hAPP(A,fun(A,bool),fequal(A),C))),D)),zero_zero(complex))),B) = hAPP(A,complex,D,C).  [resolve(5632,a,5565,a)].
40.68/40.51	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | zero_zero(complex) = hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),hAPP(complex,fun(A,complex),hAPP(fun(A,fun(complex,complex)),fun(complex,fun(A,complex)),combc(A,complex,complex),hAPP(fun(A,complex),fun(A,fun(complex,complex)),hAPP(fun(A,fun(complex,fun(complex,complex))),fun(fun(A,complex),fun(A,fun(complex,complex))),combs(A,complex,fun(complex,complex)),hAPP(fun(A,bool),fun(A,fun(complex,fun(complex,complex))),hAPP(fun(bool,fun(complex,fun(complex,complex))),fun(fun(A,bool),fun(A,fun(complex,fun(complex,complex)))),combb(bool,fun(complex,fun(complex,complex)),A),if(complex)),hAPP(A,fun(A,bool),fequal(A),C))),D)),zero_zero(complex))),B).  [resolve(5632,a,5566,a)].
40.68/40.51	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),hAPP(complex,fun(A,complex),hAPP(fun(A,fun(complex,complex)),fun(complex,fun(A,complex)),combc(A,complex,complex),hAPP(fun(A,complex),fun(A,fun(complex,complex)),hAPP(fun(A,fun(complex,fun(complex,complex))),fun(fun(A,complex),fun(A,fun(complex,complex))),combs(A,complex,fun(complex,complex)),hAPP(fun(A,bool),fun(A,fun(complex,fun(complex,complex))),hAPP(fun(bool,fun(complex,fun(complex,complex))),fun(fun(A,bool),fun(A,fun(complex,fun(complex,complex)))),combb(bool,fun(complex,fun(complex,complex)),A),if(complex)),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,fun(fun(A,bool),bool)),fun(fun(A,bool),fun(A,bool)),combc(A,fun(A,bool),bool),member(A)),C))),D)),zero_zero(complex))),B) = hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),D),hAPP(fun(A,bool),fun(A,bool),collect(A),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,fun(bool,bool)),fun(fun(A,bool),fun(A,bool)),combs(A,bool,bool),hAPP(fun(A,bool),fun(A,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(A,bool),fun(A,fun(bool,bool))),combb(bool,fun(bool,bool),A),fconj),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,fun(fun(A,bool),bool)),fun(fun(A,bool),fun(A,bool)),combc(A,fun(A,bool),bool),member(A)),B))),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,fun(fun(A,bool),bool)),fun(fun(A,bool),fun(A,bool)),combc(A,fun(A,bool),bool),member(A)),C)))).  [resolve(5632,a,5567,a)].
40.68/40.51	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f457(A,complex,D,E,C,B)),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),B),C))) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f458(A,complex,D,E,C,B)),C)) | hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),D),C) = hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),E),B).  [resolve(5632,a,5568,a)].
40.68/40.51	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f457(A,complex,D,E,C,B)),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),B),C))) | hAPP(A,complex,D,f458(A,complex,D,E,C,B)) != hAPP(A,complex,E,f458(A,complex,D,E,C,B)) | hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),D),C) = hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),E),B).  [resolve(5632,a,5569,a)].
40.68/40.51	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | zero_zero(complex) != hAPP(A,complex,D,f457(A,complex,E,D,C,B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f458(A,complex,E,D,C,B)),C)) | hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),E),C) = hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),D),B).  [resolve(5632,a,5570,a)].
40.68/40.51	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | zero_zero(complex) != hAPP(A,complex,D,f457(A,complex,E,D,C,B)) | hAPP(A,complex,E,f458(A,complex,E,D,C,B)) != hAPP(A,complex,D,f458(A,complex,E,D,C,B)) | hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),E),C) = hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),D),B).  [resolve(5632,a,5571,a)].
40.68/40.51	Derived: -topological_space(complex) | summable(complex) = ti(fun(fun(nat,complex),bool),summable(complex)).  [resolve(5632,a,5573,b)].
40.68/40.51	Derived: -t2_space(complex) | -hBOOL(hAPP(complex,bool,hAPP(fun(nat,complex),fun(complex,bool),sums(complex),A),B)) | hBOOL(hAPP(fun(nat,complex),bool,summable(complex),A)).  [resolve(5632,a,5575,b)].
40.68/40.51	Derived: -t2_space(complex) | hBOOL(hAPP(complex,bool,hAPP(fun(nat,complex),fun(complex,bool),sums(complex),A),B)) | hAPP(fun(nat,complex),complex,suminf(complex),A) != ti(complex,B) | -hBOOL(hAPP(fun(nat,complex),bool,summable(complex),A)).  [resolve(5632,a,5576,b)].
40.68/40.51	Derived: zero_zero(complex) != hAPP(nat,complex,A,zero_zero(nat)) | hAPP(fun(nat,bool),complex,hAPP(fun(nat,complex),fun(fun(nat,bool),complex),big_co1399186613setsum(nat,complex),A),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),B)) = hAPP(fun(nat,bool),complex,hAPP(fun(nat,complex),fun(fun(nat,bool),complex),big_co1399186613setsum(nat,complex),A),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),hAPP(nat,nat,suc,zero_zero(nat))),B)).  [resolve(5632,a,5577,a)].
40.68/40.51	Derived: -topological_space(complex) | -hBOOL(hAPP(complex,bool,hAPP(fun(nat,complex),fun(complex,bool),sums(complex),A),B)) | hBOOL(hAPP(fun(nat,complex),bool,summable(complex),A)).  [resolve(5632,a,5578,a)].
40.68/40.51	Derived: -t2_space(complex) | -hBOOL(hAPP(fun(nat,complex),bool,summable(complex),A)) | hBOOL(hAPP(filter(nat),bool,hAPP(complex,fun(filter(nat),bool),hAPP(fun(nat,complex),fun(complex,fun(filter(nat),bool)),tendsto(nat,complex),hAPP(fun(nat,fun(nat,bool)),fun(nat,complex),hAPP(fun(fun(nat,bool),complex),fun(fun(nat,fun(nat,bool)),fun(nat,complex)),combb(fun(nat,bool),complex,nat),hAPP(fun(nat,complex),fun(fun(nat,bool),complex),big_co1399186613setsum(nat,complex),A)),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)))),hAPP(fun(nat,complex),complex,suminf(complex),A)),sequentially)).  [resolve(5632,a,5579,b)].
40.68/40.51	Derived: -topological_space(complex) | hBOOL(hAPP(fun(nat,complex),bool,summable(complex),hAPP(complex,fun(nat,complex),combk(complex,nat),zero_zero(complex)))).  [resolve(5632,a,5580,a)].
40.68/40.51	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f538(A,complex,D,E,C,B)),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),B),C))) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f539(A,complex,D,E,C,B)),C)) | hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),E),B) = hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),D),C).  [resolve(5632,a,5581,a)].
40.68/40.52	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f538(A,complex,D,E,C,B)),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),B),C))) | hAPP(A,complex,E,f539(A,complex,D,E,C,B)) != hAPP(A,complex,D,f539(A,complex,D,E,C,B)) | hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),E),B) = hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),D),C).  [resolve(5632,a,5582,a)].
40.68/40.52	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | zero_zero(complex) != hAPP(A,complex,D,f538(A,complex,E,D,C,B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f539(A,complex,E,D,C,B)),C)) | hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),D),B) = hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),E),C).  [resolve(5632,a,5583,a)].
40.68/40.52	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | zero_zero(complex) != hAPP(A,complex,D,f538(A,complex,E,D,C,B)) | hAPP(A,complex,D,f539(A,complex,E,D,C,B)) != hAPP(A,complex,E,f539(A,complex,E,D,C,B)) | hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),D),B) = hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),E),C).  [resolve(5632,a,5584,a)].
40.68/40.52	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f543(A,complex,C,D,B)),B)) | hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),D),B) = hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),C),B).  [resolve(5632,a,5585,a)].
40.68/40.52	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(A,complex,C,f543(A,complex,D,C,B)) != hAPP(A,complex,D,f543(A,complex,D,C,B)) | hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),C),B) = hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),D),B).  [resolve(5632,a,5586,a)].
40.68/40.52	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f545(A,complex,C,B)),B)) | zero_zero(complex) = hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),C),B).  [resolve(5632,a,5587,a)].
40.68/40.52	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | zero_zero(complex) != hAPP(A,complex,C,f545(A,complex,C,B)) | zero_zero(complex) = hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),C),B).  [resolve(5632,a,5588,a)].
40.68/40.52	Derived: -ord(A) | ti(A,B) != ti(A,C) | ti(A,D) != ti(A,E) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),f547(complex,A,F,V6,E,D,C,B))) | hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),V6),hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_atLeastLessThan(A),B),D)) = hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),F),hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_atLeastLessThan(A),C),E)).  [resolve(5632,a,5589,a)].
40.68/40.52	Derived: -ord(A) | ti(A,B) != ti(A,C) | ti(A,D) != ti(A,E) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),f547(complex,A,F,V6,E,D,C,B)),D)) | hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),V6),hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_atLeastLessThan(A),B),D)) = hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),F),hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_atLeastLessThan(A),C),E)).  [resolve(5632,a,5590,a)].
40.68/40.52	Derived: -ord(A) | ti(A,B) != ti(A,C) | ti(A,D) != ti(A,E) | hAPP(A,complex,F,f547(complex,A,V6,F,E,D,C,B)) != hAPP(A,complex,V6,f547(complex,A,V6,F,E,D,C,B)) | hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),F),hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_atLeastLessThan(A),B),D)) = hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),V6),hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_atLeastLessThan(A),C),E)).  [resolve(5632,a,5591,a)].
40.68/40.52	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),hAPP(complex,fun(A,complex),hAPP(fun(A,fun(complex,complex)),fun(complex,fun(A,complex)),combc(A,complex,complex),hAPP(fun(A,complex),fun(A,fun(complex,complex)),hAPP(fun(A,fun(complex,fun(complex,complex))),fun(fun(A,complex),fun(A,fun(complex,complex))),combs(A,complex,fun(complex,complex)),hAPP(fun(A,bool),fun(A,fun(complex,fun(complex,complex))),hAPP(fun(bool,fun(complex,fun(complex,complex))),fun(fun(A,bool),fun(A,fun(complex,fun(complex,complex)))),combb(bool,fun(complex,fun(complex,complex)),A),if(complex)),C)),D)),zero_zero(complex))),B) = hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),D),hAPP(fun(A,bool),fun(A,bool),collect(A),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,fun(bool,bool)),fun(fun(A,bool),fun(A,bool)),combs(A,bool,bool),hAPP(fun(A,bool),fun(A,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(A,bool),fun(A,fun(bool,bool))),combb(bool,fun(bool,bool),A),fconj),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,fun(fun(A,bool),bool)),fun(fun(A,bool),fun(A,bool)),combc(A,fun(A,bool),bool),member(A)),B))),C))).  [resolve(5632,a,5592,a)].
40.68/40.52	Derived: -comm_monoid_mult(complex) | hAPP(fun(nat,bool),complex,hAPP(fun(nat,complex),fun(fun(nat,bool),complex),big_co302546470etprod(nat,complex),A),B) = hAPP(fun(int,bool),complex,hAPP(fun(int,complex),fun(fun(int,bool),complex),big_co302546470etprod(int,complex),hAPP(fun(int,nat),fun(int,complex),hAPP(fun(nat,complex),fun(fun(int,nat),fun(int,complex)),combb(nat,complex,int),A),nat_1)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),B)).  [resolve(5632,a,5593,a)].
40.68/40.52	Derived: hAPP(fun(product_prod(nat,nat),bool),complex,hAPP(fun(product_prod(nat,nat),complex),fun(fun(product_prod(nat,nat),bool),complex),big_co1399186613setsum(product_prod(nat,nat),complex),hAPP(fun(nat,fun(nat,complex)),fun(product_prod(nat,nat),complex),product_prod_case(nat,nat,complex),A)),hAPP(fun(product_prod(nat,nat),bool),fun(product_prod(nat,nat),bool),collect(product_prod(nat,nat)),hAPP(fun(nat,fun(nat,bool)),fun(product_prod(nat,nat),bool),product_prod_case(nat,nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),hAPP(fun(nat,fun(nat,fun(nat,bool))),fun(nat,fun(nat,fun(nat,bool))),combc(nat,nat,fun(nat,bool)),hAPP(fun(nat,fun(nat,fun(nat,bool))),fun(nat,fun(nat,fun(nat,bool))),hAPP(fun(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool))),fun(fun(nat,fun(nat,fun(nat,bool))),fun(nat,fun(nat,fun(nat,bool)))),combb(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),nat),combc(nat,nat,bool)),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,fun(nat,bool))),hAPP(fun(fun(nat,nat),fun(nat,fun(nat,bool))),fun(fun(nat,fun(nat,nat)),fun(nat,fun(nat,fun(nat,bool)))),combb(fun(nat,nat),fun(nat,fun(nat,bool)),nat),hAPP(fun(nat,fun(nat,bool)),fun(fun(nat,nat),fun(nat,fun(nat,bool))),combb(nat,fun(nat,bool),nat),ord_less(nat))),plus_plus(nat)))),B)))) = hAPP(fun(nat,bool),complex,hAPP(fun(nat,complex),fun(fun(nat,bool),complex),big_co1399186613setsum(nat,complex),hAPP(fun(nat,fun(nat,bool)),fun(nat,complex),hAPP(fun(nat,fun(fun(nat,bool),complex)),fun(fun(nat,fun(nat,bool)),fun(nat,complex)),combs(nat,fun(nat,bool),complex),hAPP(fun(nat,fun(nat,complex)),fun(nat,fun(fun(nat,bool),complex)),hAPP(fun(fun(nat,complex),fun(fun(nat,bool),complex)),fun(fun(nat,fun(nat,complex)),fun(nat,fun(fun(nat,bool),complex))),combb(fun(nat,complex),fun(fun(nat,bool),complex),nat),big_co1399186613setsum(nat,complex)),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,complex)),hAPP(fun(fun(nat,nat),fun(nat,complex)),fun(fun(nat,fun(nat,nat)),fun(nat,fun(nat,complex))),combb(fun(nat,nat),fun(nat,complex),nat),hAPP(fun(nat,fun(nat,complex)),fun(fun(nat,nat),fun(nat,complex)),combs(nat,nat,complex),A)),minus_minus(nat)))),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),zero_zero(nat)))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),B)).  [resolve(5632,a,5594,a)].
40.68/40.52	Derived: -t2_space(complex) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),f585(complex,B,A))) | hBOOL(hAPP(complex,bool,hAPP(fun(nat,complex),fun(complex,bool),sums(complex),B),hAPP(fun(nat,bool),complex,hAPP(fun(nat,complex),fun(fun(nat,bool),complex),big_co1399186613setsum(nat,complex),B),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),A)))).  [resolve(5632,a,5595,b)].
40.68/40.52	Derived: -t2_space(complex) | zero_zero(complex) != hAPP(nat,complex,A,f585(complex,A,B)) | hBOOL(hAPP(complex,bool,hAPP(fun(nat,complex),fun(complex,bool),sums(complex),A),hAPP(fun(nat,bool),complex,hAPP(fun(nat,complex),fun(fun(nat,bool),complex),big_co1399186613setsum(nat,complex),A),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),B)))).  [resolve(5632,a,5596,b)].
40.68/40.52	Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,A)),B)) | hAPP(fun(nat,bool),complex,hAPP(fun(nat,complex),fun(fun(nat,bool),complex),big_co1399186613setsum(nat,complex),C),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),B),hAPP(nat,nat,suc,A))) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(fun(nat,bool),complex,hAPP(fun(nat,complex),fun(fun(nat,bool),complex),big_co1399186613setsum(nat,complex),C),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),B),A))),hAPP(nat,complex,C,hAPP(nat,nat,suc,A))).  [resolve(5632,a,5598,a)].
40.68/40.52	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),C)) | hAPP(fun(nat,bool),complex,hAPP(fun(nat,complex),fun(fun(nat,bool),complex),big_co1399186613setsum(nat,complex),D),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),A),C)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(fun(nat,bool),complex,hAPP(fun(nat,complex),fun(fun(nat,bool),complex),big_co1399186613setsum(nat,complex),D),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),A),B))),hAPP(fun(nat,bool),complex,hAPP(fun(nat,complex),fun(fun(nat,bool),complex),big_co1399186613setsum(nat,complex),D),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),B),C))).  [resolve(5632,a,5599,a)].
40.68/40.52	Derived: hAPP(fun(nat,bool),complex,hAPP(fun(nat,complex),fun(fun(nat,bool),complex),big_co1399186613setsum(nat,complex),hAPP(fun(nat,nat),fun(nat,complex),hAPP(fun(nat,complex),fun(fun(nat,nat),fun(nat,complex)),combb(nat,complex,nat),A),suc)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),B),C)) = hAPP(fun(nat,bool),complex,hAPP(fun(nat,complex),fun(fun(nat,bool),complex),big_co1399186613setsum(nat,complex),A),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,suc,B)),hAPP(nat,nat,suc,C))).  [resolve(5632,a,5600,a)].
40.68/40.52	Derived: -hBOOL(hAPP(fun(fun(A,bool),bool),bool,finite_finite_1(fun(A,bool)),B)) | hBOOL(hAPP(fun(fun(A,bool),bool),bool,hAPP(fun(A,bool),fun(fun(fun(A,bool),bool),bool),member(fun(A,bool)),f646(A,complex,C,B)),B)) | hBOOL(hAPP(fun(fun(A,bool),bool),bool,hAPP(fun(A,bool),fun(fun(fun(A,bool),bool),bool),member(fun(A,bool)),f647(A,complex,C,B)),B)) | hAPP(fun(fun(A,bool),bool),complex,hAPP(fun(fun(A,bool),complex),fun(fun(fun(A,bool),bool),complex),big_co1399186613setsum(fun(A,bool),complex),hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),C)),B) = hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),C),hAPP(fun(fun(A,bool),bool),fun(A,bool),complete_Sup_Sup(fun(A,bool)),B)).  [resolve(5632,a,5601,a)].
40.68/40.53	Derived: -hBOOL(hAPP(fun(fun(A,bool),bool),bool,finite_finite_1(fun(A,bool)),B)) | hBOOL(hAPP(fun(fun(A,bool),bool),bool,hAPP(fun(A,bool),fun(fun(fun(A,bool),bool),bool),member(fun(A,bool)),f646(A,complex,C,B)),B)) | hBOOL(hAPP(fun(fun(A,bool),bool),bool,hAPP(fun(A,bool),fun(fun(fun(A,bool),bool),bool),member(fun(A,bool)),f648(A,complex,C,B)),B)) | hAPP(fun(fun(A,bool),bool),complex,hAPP(fun(fun(A,bool),complex),fun(fun(fun(A,bool),bool),complex),big_co1399186613setsum(fun(A,bool),complex),hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),C)),B) = hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),C),hAPP(fun(fun(A,bool),bool),fun(A,bool),complete_Sup_Sup(fun(A,bool)),B)).  [resolve(5632,a,5602,a)].
40.68/40.53	Derived: -hBOOL(hAPP(fun(fun(A,bool),bool),bool,finite_finite_1(fun(A,bool)),B)) | hBOOL(hAPP(fun(fun(A,bool),bool),bool,hAPP(fun(A,bool),fun(fun(fun(A,bool),bool),bool),member(fun(A,bool)),f646(A,complex,C,B)),B)) | ti(fun(A,bool),f648(A,complex,C,B)) != ti(fun(A,bool),f647(A,complex,C,B)) | hAPP(fun(fun(A,bool),bool),complex,hAPP(fun(fun(A,bool),complex),fun(fun(fun(A,bool),bool),complex),big_co1399186613setsum(fun(A,bool),complex),hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),C)),B) = hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),C),hAPP(fun(fun(A,bool),bool),fun(A,bool),complete_Sup_Sup(fun(A,bool)),B)).  [resolve(5632,a,5603,a)].
40.68/40.53	Derived: -hBOOL(hAPP(fun(fun(A,bool),bool),bool,finite_finite_1(fun(A,bool)),B)) | hBOOL(hAPP(fun(fun(A,bool),bool),bool,hAPP(fun(A,bool),fun(fun(fun(A,bool),bool),bool),member(fun(A,bool)),f646(A,complex,C,B)),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f649(A,complex,C,B)),f647(A,complex,C,B))) | hAPP(fun(fun(A,bool),bool),complex,hAPP(fun(fun(A,bool),complex),fun(fun(fun(A,bool),bool),complex),big_co1399186613setsum(fun(A,bool),complex),hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),C)),B) = hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),C),hAPP(fun(fun(A,bool),bool),fun(A,bool),complete_Sup_Sup(fun(A,bool)),B)).  [resolve(5632,a,5604,a)].
40.68/40.53	Derived: -hBOOL(hAPP(fun(fun(A,bool),bool),bool,finite_finite_1(fun(A,bool)),B)) | hBOOL(hAPP(fun(fun(A,bool),bool),bool,hAPP(fun(A,bool),fun(fun(fun(A,bool),bool),bool),member(fun(A,bool)),f646(A,complex,C,B)),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f649(A,complex,C,B)),f648(A,complex,C,B))) | hAPP(fun(fun(A,bool),bool),complex,hAPP(fun(fun(A,bool),complex),fun(fun(fun(A,bool),bool),complex),big_co1399186613setsum(fun(A,bool),complex),hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),C)),B) = hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),C),hAPP(fun(fun(A,bool),bool),fun(A,bool),complete_Sup_Sup(fun(A,bool)),B)).  [resolve(5632,a,5605,a)].
40.68/40.53	Derived: -hBOOL(hAPP(fun(fun(A,bool),bool),bool,finite_finite_1(fun(A,bool)),B)) | hBOOL(hAPP(fun(fun(A,bool),bool),bool,hAPP(fun(A,bool),fun(fun(fun(A,bool),bool),bool),member(fun(A,bool)),f646(A,complex,C,B)),B)) | zero_zero(complex) != hAPP(A,complex,C,f649(A,complex,C,B)) | hAPP(fun(fun(A,bool),bool),complex,hAPP(fun(fun(A,bool),complex),fun(fun(fun(A,bool),bool),complex),big_co1399186613setsum(fun(A,bool),complex),hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),C)),B) = hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),C),hAPP(fun(fun(A,bool),bool),fun(A,bool),complete_Sup_Sup(fun(A,bool)),B)).  [resolve(5632,a,5606,a)].
40.68/40.53	Derived: -hBOOL(hAPP(fun(fun(A,bool),bool),bool,finite_finite_1(fun(A,bool)),B)) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),f646(A,complex,C,B))) | hBOOL(hAPP(fun(fun(A,bool),bool),bool,hAPP(fun(A,bool),fun(fun(fun(A,bool),bool),bool),member(fun(A,bool)),f647(A,complex,C,B)),B)) | hAPP(fun(fun(A,bool),bool),complex,hAPP(fun(fun(A,bool),complex),fun(fun(fun(A,bool),bool),complex),big_co1399186613setsum(fun(A,bool),complex),hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),C)),B) = hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),C),hAPP(fun(fun(A,bool),bool),fun(A,bool),complete_Sup_Sup(fun(A,bool)),B)).  [resolve(5632,a,5607,a)].
40.68/40.53	Derived: -hBOOL(hAPP(fun(fun(A,bool),bool),bool,finite_finite_1(fun(A,bool)),B)) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),f646(A,complex,C,B))) | hBOOL(hAPP(fun(fun(A,bool),bool),bool,hAPP(fun(A,bool),fun(fun(fun(A,bool),bool),bool),member(fun(A,bool)),f648(A,complex,C,B)),B)) | hAPP(fun(fun(A,bool),bool),complex,hAPP(fun(fun(A,bool),complex),fun(fun(fun(A,bool),bool),complex),big_co1399186613setsum(fun(A,bool),complex),hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),C)),B) = hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),C),hAPP(fun(fun(A,bool),bool),fun(A,bool),complete_Sup_Sup(fun(A,bool)),B)).  [resolve(5632,a,5608,a)].
40.68/40.53	Derived: -hBOOL(hAPP(fun(fun(A,bool),bool),bool,finite_finite_1(fun(A,bool)),B)) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),f646(A,complex,C,B))) | ti(fun(A,bool),f648(A,complex,C,B)) != ti(fun(A,bool),f647(A,complex,C,B)) | hAPP(fun(fun(A,bool),bool),complex,hAPP(fun(fun(A,bool),complex),fun(fun(fun(A,bool),bool),complex),big_co1399186613setsum(fun(A,bool),complex),hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),C)),B) = hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),C),hAPP(fun(fun(A,bool),bool),fun(A,bool),complete_Sup_Sup(fun(A,bool)),B)).  [resolve(5632,a,5609,a)].
40.68/40.53	Derived: -hBOOL(hAPP(fun(fun(A,bool),bool),bool,finite_finite_1(fun(A,bool)),B)) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),f646(A,complex,C,B))) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f649(A,complex,C,B)),f647(A,complex,C,B))) | hAPP(fun(fun(A,bool),bool),complex,hAPP(fun(fun(A,bool),complex),fun(fun(fun(A,bool),bool),complex),big_co1399186613setsum(fun(A,bool),complex),hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),C)),B) = hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),C),hAPP(fun(fun(A,bool),bool),fun(A,bool),complete_Sup_Sup(fun(A,bool)),B)).  [resolve(5632,a,5610,a)].
40.68/40.53	Derived: -hBOOL(hAPP(fun(fun(A,bool),bool),bool,finite_finite_1(fun(A,bool)),B)) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),f646(A,complex,C,B))) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f649(A,complex,C,B)),f648(A,complex,C,B))) | hAPP(fun(fun(A,bool),bool),complex,hAPP(fun(fun(A,bool),complex),fun(fun(fun(A,bool),bool),complex),big_co1399186613setsum(fun(A,bool),complex),hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),C)),B) = hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),C),hAPP(fun(fun(A,bool),bool),fun(A,bool),complete_Sup_Sup(fun(A,bool)),B)).  [resolve(5632,a,5611,a)].
40.68/40.53	Derived: -hBOOL(hAPP(fun(fun(A,bool),bool),bool,finite_finite_1(fun(A,bool)),B)) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),f646(A,complex,C,B))) | zero_zero(complex) != hAPP(A,complex,C,f649(A,complex,C,B)) | hAPP(fun(fun(A,bool),bool),complex,hAPP(fun(fun(A,bool),complex),fun(fun(fun(A,bool),bool),complex),big_co1399186613setsum(fun(A,bool),complex),hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),C)),B) = hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),C),hAPP(fun(fun(A,bool),bool),fun(A,bool),complete_Sup_Sup(fun(A,bool)),B)).  [resolve(5632,a,5612,a)].
40.68/40.53	Derived: -ordere779506340up_add(complex) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f657(A,complex,B,C,D)),D)) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less_eq(complex),hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),B),D)),hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),C),D))).  [resolve(5632,a,5614,b)].
40.68/40.53	Derived: -ordere779506340up_add(complex) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less_eq(complex),hAPP(A,complex,B,f657(A,complex,B,C,D))),hAPP(A,complex,C,f657(A,complex,B,C,D)))) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less_eq(complex),hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),B),D)),hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),C),D))).  [resolve(5632,a,5615,b)].
40.68/40.53	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(fun(C,bool),complex,hAPP(fun(C,complex),fun(fun(C,bool),complex),big_co1399186613setsum(C,complex),hAPP(fun(C,fun(A,bool)),fun(C,complex),hAPP(fun(fun(A,bool),complex),fun(fun(C,fun(A,bool)),fun(C,complex)),combb(fun(A,bool),complex,C),hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),D)),hAPP(fun(C,fun(A,bool)),fun(C,fun(A,bool)),hAPP(fun(fun(A,bool),fun(A,bool)),fun(fun(C,fun(A,bool)),fun(C,fun(A,bool))),combb(fun(A,bool),fun(A,bool),C),collect(A)),hAPP(fun(C,fun(A,bool)),fun(C,fun(A,bool)),hAPP(fun(fun(A,bool),fun(A,bool)),fun(fun(C,fun(A,bool)),fun(C,fun(A,bool))),combb(fun(A,bool),fun(A,bool),C),hAPP(fun(A,fun(bool,bool)),fun(fun(A,bool),fun(A,bool)),combs(A,bool,bool),hAPP(fun(A,bool),fun(A,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(A,bool),fun(A,fun(bool,bool))),combb(bool,fun(bool,bool),A),fconj),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,fun(fun(A,bool),bool)),fun(fun(A,bool),fun(A,bool)),combc(A,fun(A,bool),bool),member(A)),B)))),hAPP(fun(A,fun(C,bool)),fun(C,fun(A,bool)),combc(A,C,bool),hAPP(fun(A,C),fun(A,fun(C,bool)),hAPP(fun(C,fun(C,bool)),fun(fun(A,C),fun(A,fun(C,bool))),combb(C,fun(C,bool),A),fequal(C)),E)))))),hAPP(fun(A,bool),fun(C,bool),hAPP(fun(A,C),fun(fun(A,bool),fun(C,bool)),image(A,C),E),B)) = hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),D),B).  [resolve(5632,a,5616,a)].
40.68/40.53	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f694(A,complex,D,C,B)),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),B),C))) | hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),D),B) = hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),D),C).  [resolve(5632,a,5617,a)].
40.68/40.53	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | zero_zero(complex) != hAPP(A,complex,D,f694(A,complex,D,C,B)) | hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),D),B) = hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),D),C).  [resolve(5632,a,5618,a)].
40.68/40.53	Derived: hAPP(fun(nat,bool),complex,hAPP(fun(nat,complex),fun(fun(nat,bool),complex),big_co1399186613setsum(nat,complex),hAPP(fun(nat,nat),fun(nat,complex),hAPP(fun(nat,complex),fun(fun(nat,nat),fun(nat,complex)),combb(nat,complex,nat),A),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),B))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),C),D)) = hAPP(fun(nat,bool),complex,hAPP(fun(nat,complex),fun(fun(nat,bool),complex),big_co1399186613setsum(nat,complex),A),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),C),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),D),B))).  [resolve(5632,a,5619,a)].
40.68/40.54	Derived: -topological_space(complex) | -hBOOL(hAPP(fun(nat,complex),bool,summable(complex),A)) | hBOOL(hAPP(complex,bool,hAPP(fun(nat,complex),fun(complex,bool),sums(complex),A),f737(complex,A))).  [resolve(5632,a,5621,b)].
40.68/40.54	Derived: -power(complex) | hAPP(fun(nat,bool),complex,hAPP(fun(nat,complex),fun(fun(nat,bool),complex),big_co1399186613setsum(nat,complex),hAPP(fun(nat,complex),fun(nat,complex),hAPP(fun(nat,fun(complex,complex)),fun(fun(nat,complex),fun(nat,complex)),combs(nat,complex,complex),hAPP(fun(nat,complex),fun(nat,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(nat,complex),fun(nat,fun(complex,complex))),combb(complex,fun(complex,complex),nat),times_times(complex)),hAPP(fun(nat,nat),fun(nat,complex),hAPP(fun(nat,complex),fun(fun(nat,nat),fun(nat,complex)),combb(nat,complex,nat),hAPP(complex,fun(nat,complex),power_power(complex),A)),hAPP(nat,fun(nat,nat),minus_minus(nat),B)))),hAPP(complex,fun(nat,complex),power_power(complex),C))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,suc,B))) = hAPP(fun(nat,bool),complex,hAPP(fun(nat,complex),fun(fun(nat,bool),complex),big_co1399186613setsum(nat,complex),hAPP(fun(nat,complex),fun(nat,complex),hAPP(fun(nat,fun(complex,complex)),fun(fun(nat,complex),fun(nat,complex)),combs(nat,complex,complex),hAPP(fun(nat,complex),fun(nat,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(nat,complex),fun(nat,fun(complex,complex))),combb(complex,fun(complex,complex),nat),times_times(complex)),hAPP(complex,fun(nat,complex),power_power(complex),A))),hAPP(fun(nat,nat),fun(nat,complex),hAPP(fun(nat,complex),fun(fun(nat,nat),fun(nat,complex)),combb(nat,complex,nat),hAPP(complex,fun(nat,complex),power_power(complex),C)),hAPP(nat,fun(nat,nat),minus_minus(nat),B)))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,suc,B))).  [resolve(5632,a,5623,b)].
40.68/40.54	Derived: hAPP(fun(nat,bool),complex,hAPP(fun(nat,complex),fun(fun(nat,bool),complex),big_co1399186613setsum(nat,complex),A),hAPP(nat,fun(nat,bool),ord_lessThan(nat),hAPP(nat,nat,suc,B))) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(fun(nat,bool),complex,hAPP(fun(nat,complex),fun(fun(nat,bool),complex),big_co1399186613setsum(nat,complex),A),hAPP(nat,fun(nat,bool),ord_lessThan(nat),B))),hAPP(nat,complex,A,B)).  [resolve(5632,a,5624,a)].
40.68/40.54	Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),A),zero_zero(complex)) = ti(complex,A).  [resolve(5632,a,5625,a)].
40.68/40.54	Derived: hAPP(fun(nat,bool),complex,hAPP(fun(nat,complex),fun(fun(nat,bool),complex),big_co1399186613setsum(nat,complex),hAPP(fun(nat,nat),fun(nat,complex),hAPP(fun(nat,complex),fun(fun(nat,nat),fun(nat,complex)),combb(nat,complex,nat),A),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),B))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),C),D)) = hAPP(fun(nat,bool),complex,hAPP(fun(nat,complex),fun(fun(nat,bool),complex),big_co1399186613setsum(nat,complex),A),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),C),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),D),B))).  [resolve(5632,a,5626,a)].
40.68/40.54	Derived: hAPP(fun(nat,bool),complex,hAPP(fun(nat,complex),fun(fun(nat,bool),complex),big_co1399186613setsum(nat,complex),hAPP(fun(nat,nat),fun(nat,complex),hAPP(fun(nat,complex),fun(fun(nat,nat),fun(nat,complex)),combb(nat,complex,nat),A),suc)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),B),C)) = hAPP(fun(nat,bool),complex,hAPP(fun(nat,complex),fun(fun(nat,bool),complex),big_co1399186613setsum(nat,complex),A),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),hAPP(nat,nat,suc,B)),hAPP(nat,nat,suc,C))).  [resolve(5632,a,5627,a)].
40.83/40.67	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(C,bool),bool,finite_finite_1(C),D)) | hAPP(fun(C,bool),complex,hAPP(fun(C,complex),fun(fun(C,bool),complex),big_co1399186613setsum(C,complex),hAPP(fun(C,fun(A,bool)),fun(C,complex),hAPP(fun(C,fun(fun(A,bool),complex)),fun(fun(C,fun(A,bool)),fun(C,complex)),combs(C,fun(A,bool),complex),hAPP(fun(C,fun(A,complex)),fun(C,fun(fun(A,bool),complex)),hAPP(fun(fun(A,complex),fun(fun(A,bool),complex)),fun(fun(C,fun(A,complex)),fun(C,fun(fun(A,bool),complex))),combb(fun(A,complex),fun(fun(A,bool),complex),C),big_co1399186613setsum(A,complex)),hAPP(fun(A,fun(C,complex)),fun(C,fun(A,complex)),combc(A,C,complex),E))),hAPP(fun(C,fun(A,bool)),fun(C,fun(A,bool)),hAPP(fun(fun(A,bool),fun(A,bool)),fun(fun(C,fun(A,bool)),fun(C,fun(A,bool))),combb(fun(A,bool),fun(A,bool),C),collect(A)),hAPP(fun(C,fun(A,bool)),fun(C,fun(A,bool)),hAPP(fun(fun(A,bool),fun(A,bool)),fun(fun(C,fun(A,bool)),fun(C,fun(A,bool))),combb(fun(A,bool),fun(A,bool),C),hAPP(fun(A,fun(bool,bool)),fun(fun(A,bool),fun(A,bool)),combs(A,bool,bool),hAPP(fun(A,bool),fun(A,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(A,bool),fun(A,fun(bool,bool))),combb(bool,fun(bool,bool),A),fconj),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,fun(fun(A,bool),bool)),fun(fun(A,bool),fun(A,bool)),combc(A,fun(A,bool),bool),member(A)),B)))),hAPP(fun(A,fun(C,bool)),fun(C,fun(A,bool)),combc(A,C,bool),F))))),D) = hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),hAPP(fun(A,fun(C,bool)),fun(A,complex),hAPP(fun(A,fun(fun(C,bool),complex)),fun(fun(A,fun(C,bool)),fun(A,complex)),combs(A,fun(C,bool),complex),hAPP(fun(A,fun(C,complex)),fun(A,fun(fun(C,bool),complex)),hAPP(fun(fun(C,complex),fun(fun(C,bool),complex)),fun(fun(A,fun(C,complex)),fun(A,fun(fun(C,bool),complex))),combb(fun(C,complex),fun(fun(C,bool),complex),A),big_co1399186613setsum(C,complex)),E)),hAPP(fun(A,fun(C,bool)),fun(A,fun(C,bool)),hAPP(fun(fun(C,bool),fun(C,bool)),fun(fun(A,fun(C,bool)),fun(A,fun(C,bool))),combb(fun(C,bool),fun(C,bool),A),collect(C)),hAPP(fun(A,fun(C,bool)),fun(A,fun(C,bool)),hAPP(fun(fun(C,bool),fun(C,bool)),fun(fun(A,fun(C,bool)),fun(A,fun(C,bool))),combb(fun(C,bool),fun(C,bool),A),hAPP(fun(C,fun(bool,bool)),fun(fun(C,bool),fun(C,bool)),combs(C,bool,bool),hAPP(fun(C,bool),fun(C,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(C,bool),fun(C,fun(bool,bool))),combb(bool,fun(bool,bool),C),fconj),hAPP(fun(C,bool),fun(C,bool),hAPP(fun(C,fun(fun(C,bool),bool)),fun(fun(C,bool),fun(C,bool)),combc(C,fun(C,bool),bool),member(C)),D)))),F)))),B).  [resolve(5632,a,5628,a)].
40.83/40.67	Derived: -comm_monoid_mult(complex) | A != B | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),f817(complex,C,D,B,A))) | hAPP(fun(int,bool),complex,hAPP(fun(int,complex),fun(fun(int,bool),complex),big_co302546470etprod(int,complex),D),A) = hAPP(fun(int,bool),complex,hAPP(fun(int,complex),fun(fun(int,bool),complex),big_co302546470etprod(int,complex),C),B).  [resolve(5632,a,5630,b)].
40.83/40.67	Derived: -comm_monoid_mult(complex) | A != B | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A)) | hAPP(int,complex,C,f817(complex,D,C,B,A)) != hAPP(int,complex,D,f817(complex,D,C,B,A)) | hAPP(fun(int,bool),complex,hAPP(fun(int,complex),fun(fun(int,bool),complex),big_co302546470etprod(int,complex),C),A) = hAPP(fun(int,bool),complex,hAPP(fun(int,complex),fun(fun(int,bool),complex),big_co302546470etprod(int,complex),D),B).  [resolve(5632,a,5631,b)].
40.83/40.67	5633 -comm_monoid_mult(A) | -comm_monoid_add(A) | hAPP(fun(nat,bool),A,hAPP(fun(nat,A),fun(fun(nat,bool),A),big_co1399186613setsum(nat,A),B),C) = hAPP(fun(int,bool),A,hAPP(fun(int,A),fun(fun(int,bool),A),big_co1399186613setsum(int,A),hAPP(fun(int,nat),fun(int,A),hAPP(fun(nat,A),fun(fun(int,nat),fun(int,A)),combb(nat,A,int),B),nat_1)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),C)) # label(fact_4264_transfer__nat__int__sum__prod_I1_J) # label(axiom).  [clausify(4865)].
40.83/40.67	Derived: -comm_monoid_mult(real) | hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),A),B) = hAPP(fun(int,bool),real,hAPP(fun(int,real),fun(fun(int,bool),real),big_co1399186613setsum(int,real),hAPP(fun(int,nat),fun(int,real),hAPP(fun(nat,real),fun(fun(int,nat),fun(int,real)),combb(nat,real,int),A),nat_1)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),B)).  [resolve(5633,b,5513,a)].
40.83/40.67	Derived: -comm_monoid_mult(int) | hAPP(fun(nat,bool),int,hAPP(fun(nat,int),fun(fun(nat,bool),int),big_co1399186613setsum(nat,int),A),B) = hAPP(fun(int,bool),int,hAPP(fun(int,int),fun(fun(int,bool),int),big_co1399186613setsum(int,int),hAPP(fun(int,nat),fun(int,int),hAPP(fun(nat,int),fun(fun(int,nat),fun(int,int)),combb(nat,int,int),A),nat_1)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),B)).  [resolve(5633,b,5524,a)].
40.83/40.67	Derived: -comm_monoid_mult(code_code_numeral) | hAPP(fun(nat,bool),code_code_numeral,hAPP(fun(nat,code_code_numeral),fun(fun(nat,bool),code_code_numeral),big_co1399186613setsum(nat,code_code_numeral),A),B) = hAPP(fun(int,bool),code_code_numeral,hAPP(fun(int,code_code_numeral),fun(fun(int,bool),code_code_numeral),big_co1399186613setsum(int,code_code_numeral),hAPP(fun(int,nat),fun(int,code_code_numeral),hAPP(fun(nat,code_code_numeral),fun(fun(int,nat),fun(int,code_code_numeral)),combb(nat,code_code_numeral,int),A),nat_1)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),B)).  [resolve(5633,b,5539,a)].
40.83/40.67	Derived: -comm_monoid_mult(rat) | hAPP(fun(nat,bool),rat,hAPP(fun(nat,rat),fun(fun(nat,bool),rat),big_co1399186613setsum(nat,rat),A),B) = hAPP(fun(int,bool),rat,hAPP(fun(int,rat),fun(fun(int,bool),rat),big_co1399186613setsum(int,rat),hAPP(fun(int,nat),fun(int,rat),hAPP(fun(nat,rat),fun(fun(int,nat),fun(int,rat)),combb(nat,rat,int),A),nat_1)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),B)).  [resolve(5633,b,5561,a)].
40.83/40.67	Derived: -comm_monoid_mult(quickcheck_code_int) | hAPP(fun(nat,bool),quickcheck_code_int,hAPP(fun(nat,quickcheck_code_int),fun(fun(nat,bool),quickcheck_code_int),big_co1399186613setsum(nat,quickcheck_code_int),A),B) = hAPP(fun(int,bool),quickcheck_code_int,hAPP(fun(int,quickcheck_code_int),fun(fun(int,bool),quickcheck_code_int),big_co1399186613setsum(int,quickcheck_code_int),hAPP(fun(int,nat),fun(int,quickcheck_code_int),hAPP(fun(nat,quickcheck_code_int),fun(fun(int,nat),fun(int,quickcheck_code_int)),combb(nat,quickcheck_code_int,int),A),nat_1)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),B)).  [resolve(5633,b,5620,a)].
40.83/40.67	Derived: -comm_monoid_mult(nat) | hAPP(fun(nat,bool),nat,hAPP(fun(nat,nat),fun(fun(nat,bool),nat),big_co1399186613setsum(nat,nat),A),B) = hAPP(fun(int,bool),nat,hAPP(fun(int,nat),fun(fun(int,bool),nat),big_co1399186613setsum(int,nat),hAPP(fun(int,nat),fun(int,nat),hAPP(fun(nat,nat),fun(fun(int,nat),fun(int,nat)),combb(nat,nat,int),A),nat_1)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),B)).  [resolve(5633,b,5629,a)].
40.83/40.67	Derived: -comm_monoid_mult(complex) | hAPP(fun(nat,bool),complex,hAPP(fun(nat,complex),fun(fun(nat,bool),complex),big_co1399186613setsum(nat,complex),A),B) = hAPP(fun(int,bool),complex,hAPP(fun(int,complex),fun(fun(int,bool),complex),big_co1399186613setsum(int,complex),hAPP(fun(int,nat),fun(int,complex),hAPP(fun(nat,complex),fun(fun(int,nat),fun(int,complex)),combb(nat,complex,int),A),nat_1)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),B)).  [resolve(5633,b,5632,a)].
40.83/40.69	5634 -comm_monoid_mult(A) | -comm_monoid_add(A) | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,B)) | hAPP(fun(nat,bool),A,hAPP(fun(nat,A),fun(fun(nat,bool),A),big_co302546470etprod(nat,A),hAPP(fun(nat,int),fun(nat,A),hAPP(fun(int,A),fun(fun(nat,int),fun(nat,A)),combb(int,A,nat),C),semiring_1_of_nat(int))),hAPP(fun(int,bool),fun(nat,bool),hAPP(fun(int,nat),fun(fun(int,bool),fun(nat,bool)),image(int,nat),nat_1),B)) = hAPP(fun(int,bool),A,hAPP(fun(int,A),fun(fun(int,bool),A),big_co302546470etprod(int,A),C),B) # label(fact_3945_transfer__int__nat__sum__prod_I2_J) # label(axiom).  [clausify(4881)].
40.83/40.69	Derived: -comm_monoid_mult(real) | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A)) | hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co302546470etprod(nat,real),hAPP(fun(nat,int),fun(nat,real),hAPP(fun(int,real),fun(fun(nat,int),fun(nat,real)),combb(int,real,nat),B),semiring_1_of_nat(int))),hAPP(fun(int,bool),fun(nat,bool),hAPP(fun(int,nat),fun(fun(int,bool),fun(nat,bool)),image(int,nat),nat_1),A)) = hAPP(fun(int,bool),real,hAPP(fun(int,real),fun(fun(int,bool),real),big_co302546470etprod(int,real),B),A).  [resolve(5634,b,5513,a)].
40.83/40.69	Derived: -comm_monoid_mult(int) | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A)) | hAPP(fun(nat,bool),int,hAPP(fun(nat,int),fun(fun(nat,bool),int),big_co302546470etprod(nat,int),hAPP(fun(nat,int),fun(nat,int),hAPP(fun(int,int),fun(fun(nat,int),fun(nat,int)),combb(int,int,nat),B),semiring_1_of_nat(int))),hAPP(fun(int,bool),fun(nat,bool),hAPP(fun(int,nat),fun(fun(int,bool),fun(nat,bool)),image(int,nat),nat_1),A)) = hAPP(fun(int,bool),int,hAPP(fun(int,int),fun(fun(int,bool),int),big_co302546470etprod(int,int),B),A).  [resolve(5634,b,5524,a)].
40.83/40.69	Derived: -comm_monoid_mult(code_code_numeral) | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A)) | hAPP(fun(nat,bool),code_code_numeral,hAPP(fun(nat,code_code_numeral),fun(fun(nat,bool),code_code_numeral),big_co302546470etprod(nat,code_code_numeral),hAPP(fun(nat,int),fun(nat,code_code_numeral),hAPP(fun(int,code_code_numeral),fun(fun(nat,int),fun(nat,code_code_numeral)),combb(int,code_code_numeral,nat),B),semiring_1_of_nat(int))),hAPP(fun(int,bool),fun(nat,bool),hAPP(fun(int,nat),fun(fun(int,bool),fun(nat,bool)),image(int,nat),nat_1),A)) = hAPP(fun(int,bool),code_code_numeral,hAPP(fun(int,code_code_numeral),fun(fun(int,bool),code_code_numeral),big_co302546470etprod(int,code_code_numeral),B),A).  [resolve(5634,b,5539,a)].
40.83/40.69	Derived: -comm_monoid_mult(rat) | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A)) | hAPP(fun(nat,bool),rat,hAPP(fun(nat,rat),fun(fun(nat,bool),rat),big_co302546470etprod(nat,rat),hAPP(fun(nat,int),fun(nat,rat),hAPP(fun(int,rat),fun(fun(nat,int),fun(nat,rat)),combb(int,rat,nat),B),semiring_1_of_nat(int))),hAPP(fun(int,bool),fun(nat,bool),hAPP(fun(int,nat),fun(fun(int,bool),fun(nat,bool)),image(int,nat),nat_1),A)) = hAPP(fun(int,bool),rat,hAPP(fun(int,rat),fun(fun(int,bool),rat),big_co302546470etprod(int,rat),B),A).  [resolve(5634,b,5561,a)].
40.83/40.69	Derived: -comm_monoid_mult(quickcheck_code_int) | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A)) | hAPP(fun(nat,bool),quickcheck_code_int,hAPP(fun(nat,quickcheck_code_int),fun(fun(nat,bool),quickcheck_code_int),big_co302546470etprod(nat,quickcheck_code_int),hAPP(fun(nat,int),fun(nat,quickcheck_code_int),hAPP(fun(int,quickcheck_code_int),fun(fun(nat,int),fun(nat,quickcheck_code_int)),combb(int,quickcheck_code_int,nat),B),semiring_1_of_nat(int))),hAPP(fun(int,bool),fun(nat,bool),hAPP(fun(int,nat),fun(fun(int,bool),fun(nat,bool)),image(int,nat),nat_1),A)) = hAPP(fun(int,bool),quickcheck_code_int,hAPP(fun(int,quickcheck_code_int),fun(fun(int,bool),quickcheck_code_int),big_co302546470etprod(int,quickcheck_code_int),B),A).  [resolve(5634,b,5620,a)].
43.51/43.34	Derived: -comm_monoid_mult(nat) | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A)) | hAPP(fun(nat,bool),nat,hAPP(fun(nat,nat),fun(fun(nat,bool),nat),big_co302546470etprod(nat,nat),hAPP(fun(nat,int),fun(nat,nat),hAPP(fun(int,nat),fun(fun(nat,int),fun(nat,nat)),combb(int,nat,nat),B),semiring_1_of_nat(int))),hAPP(fun(int,bool),fun(nat,bool),hAPP(fun(int,nat),fun(fun(int,bool),fun(nat,bool)),image(int,nat),nat_1),A)) = hAPP(fun(int,bool),nat,hAPP(fun(int,nat),fun(fun(int,bool),nat),big_co302546470etprod(int,nat),B),A).  [resolve(5634,b,5629,a)].
43.51/43.34	Derived: -comm_monoid_mult(complex) | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A)) | hAPP(fun(nat,bool),complex,hAPP(fun(nat,complex),fun(fun(nat,bool),complex),big_co302546470etprod(nat,complex),hAPP(fun(nat,int),fun(nat,complex),hAPP(fun(int,complex),fun(fun(nat,int),fun(nat,complex)),combb(int,complex,nat),B),semiring_1_of_nat(int))),hAPP(fun(int,bool),fun(nat,bool),hAPP(fun(int,nat),fun(fun(int,bool),fun(nat,bool)),image(int,nat),nat_1),A)) = hAPP(fun(int,bool),complex,hAPP(fun(int,complex),fun(fun(int,bool),complex),big_co302546470etprod(int,complex),B),A).  [resolve(5634,b,5632,a)].
43.51/43.34	5635 real_n1866405975lgebra(complex) # label(arity_Complex_Ocomplex___RealVector_Oreal__normed__div__algebra) # label(axiom).  [assumption].
43.51/43.34	5636 -real_n1866405975lgebra(A) | -divisi14063676e_zero(A) | hAPP(A,real,norm_norm(A),hAPP(A,A,inverse_inverse(A),B)) = hAPP(real,real,inverse_inverse(real),hAPP(A,real,norm_norm(A),B)) # label(fact_2510_norm__inverse) # label(axiom).  [clausify(21)].
43.51/43.34	5637 -real_n1866405975lgebra(A) | -hBOOL(hAPP(filter(nat),bool,hAPP(A,fun(filter(nat),bool),hAPP(fun(nat,A),fun(A,fun(filter(nat),bool)),tendsto(nat,A),B),C),sequentially)) | zero_zero(A) = ti(A,C) | hBOOL(hAPP(filter(nat),bool,hAPP(A,fun(filter(nat),bool),hAPP(fun(nat,A),fun(A,fun(filter(nat),bool)),tendsto(nat,A),hAPP(fun(nat,A),fun(nat,A),hAPP(fun(A,A),fun(fun(nat,A),fun(nat,A)),combb(A,A,nat),inverse_inverse(A)),B)),hAPP(A,A,inverse_inverse(A),C)),sequentially)) # label(fact_4483_LIMSEQ__inverse) # label(axiom).  [clausify(188)].
43.51/43.34	5638 -real_n1866405975lgebra(A) | -hBOOL(hAPP(filter(B),bool,hAPP(A,fun(filter(B),bool),hAPP(fun(B,A),fun(A,fun(filter(B),bool)),tendsto(B,A),C),D),E)) | zero_zero(A) = ti(A,D) | hBOOL(hAPP(filter(B),bool,hAPP(A,fun(filter(B),bool),hAPP(fun(B,A),fun(A,fun(filter(B),bool)),tendsto(B,A),hAPP(fun(B,A),fun(B,A),hAPP(fun(A,A),fun(fun(B,A),fun(B,A)),combb(A,A,B),inverse_inverse(A)),C)),hAPP(A,A,inverse_inverse(A),D)),E)) # label(fact_4481_tendsto__inverse) # label(axiom).  [clausify(522)].
43.51/43.34	5639 -real_n1866405975lgebra(A) | hAPP(A,real,norm_norm(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(A,real,norm_norm(A),B)),hAPP(A,real,norm_norm(A),C)) # label(fact_1778_norm__mult) # label(axiom).  [clausify(1301)].
43.51/43.34	5640 -real_n1866405975lgebra(A) | hAPP(A,real,norm_norm(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C)) = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(A,real,norm_norm(A),B)),C) # label(fact_1782_norm__power) # label(axiom).  [clausify(1309)].
43.51/43.34	5641 -real_n1866405975lgebra(A) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),hAPP(A,real,norm_norm(A),C))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(A,real,norm_norm(A),hAPP(A,A,inverse_inverse(A),C))),hAPP(real,real,inverse_inverse(real),B))) # label(fact_2538_Bseq__inverse__lemma) # label(axiom).  [clausify(1472)].
43.51/43.34	5642 -real_n1866405975lgebra(A) | zero_zero(A) = ti(A,B) | hAPP(A,real,norm_norm(A),hAPP(A,A,inverse_inverse(A),B)) = hAPP(real,real,inverse_inverse(real),hAPP(A,real,norm_norm(A),B)) # label(fact_2511_nonzero__norm__inverse) # label(axiom).  [clausify(1686)].
43.51/43.34	5643 -topological_space(A) | -real_n1866405975lgebra(B) | -hBOOL(hAPP(A,bool,hAPP(fun(A,B),fun(A,bool),isCont(A,B),C),D)) | zero_zero(B) = hAPP(A,B,C,D) | hBOOL(hAPP(A,bool,hAPP(fun(A,B),fun(A,bool),isCont(A,B),hAPP(fun(A,B),fun(A,B),hAPP(fun(B,B),fun(fun(A,B),fun(A,B)),combb(B,B,A),inverse_inverse(B)),C)),D)) # label(fact_4912_isCont__inverse) # label(axiom).  [clausify(2862)].
43.65/43.52	Derived: -divisi14063676e_zero(complex) | hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,inverse_inverse(complex),A)) = hAPP(real,real,inverse_inverse(real),hAPP(complex,real,norm_norm(complex),A)).  [resolve(5635,a,5636,a)].
43.65/43.52	Derived: -hBOOL(hAPP(filter(nat),bool,hAPP(complex,fun(filter(nat),bool),hAPP(fun(nat,complex),fun(complex,fun(filter(nat),bool)),tendsto(nat,complex),A),B),sequentially)) | zero_zero(complex) = ti(complex,B) | hBOOL(hAPP(filter(nat),bool,hAPP(complex,fun(filter(nat),bool),hAPP(fun(nat,complex),fun(complex,fun(filter(nat),bool)),tendsto(nat,complex),hAPP(fun(nat,complex),fun(nat,complex),hAPP(fun(complex,complex),fun(fun(nat,complex),fun(nat,complex)),combb(complex,complex,nat),inverse_inverse(complex)),A)),hAPP(complex,complex,inverse_inverse(complex),B)),sequentially)).  [resolve(5635,a,5637,a)].
43.65/43.52	Derived: -hBOOL(hAPP(filter(A),bool,hAPP(complex,fun(filter(A),bool),hAPP(fun(A,complex),fun(complex,fun(filter(A),bool)),tendsto(A,complex),B),C),D)) | zero_zero(complex) = ti(complex,C) | hBOOL(hAPP(filter(A),bool,hAPP(complex,fun(filter(A),bool),hAPP(fun(A,complex),fun(complex,fun(filter(A),bool)),tendsto(A,complex),hAPP(fun(A,complex),fun(A,complex),hAPP(fun(complex,complex),fun(fun(A,complex),fun(A,complex)),combb(complex,complex,A),inverse_inverse(complex)),B)),hAPP(complex,complex,inverse_inverse(complex),C)),D)).  [resolve(5635,a,5638,a)].
43.65/43.52	Derived: hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),B)) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(complex,real,norm_norm(complex),A)),hAPP(complex,real,norm_norm(complex),B)).  [resolve(5635,a,5639,a)].
43.65/43.52	Derived: hAPP(complex,real,norm_norm(complex),hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),A),B)) = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(complex,real,norm_norm(complex),A)),B).  [resolve(5635,a,5640,a)].
43.65/43.52	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),hAPP(complex,real,norm_norm(complex),B))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,inverse_inverse(complex),B))),hAPP(real,real,inverse_inverse(real),A))).  [resolve(5635,a,5641,a)].
43.65/43.52	Derived: zero_zero(complex) = ti(complex,A) | hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,inverse_inverse(complex),A)) = hAPP(real,real,inverse_inverse(real),hAPP(complex,real,norm_norm(complex),A)).  [resolve(5635,a,5642,a)].
43.65/43.52	Derived: -topological_space(A) | -hBOOL(hAPP(A,bool,hAPP(fun(A,complex),fun(A,bool),isCont(A,complex),B),C)) | zero_zero(complex) = hAPP(A,complex,B,C) | hBOOL(hAPP(A,bool,hAPP(fun(A,complex),fun(A,bool),isCont(A,complex),hAPP(fun(A,complex),fun(A,complex),hAPP(fun(complex,complex),fun(fun(A,complex),fun(A,complex)),combb(complex,complex,A),inverse_inverse(complex)),B)),C)).  [resolve(5635,a,5643,b)].
43.65/43.52	5644 -real_n1866405975lgebra(A) | hAPP(A,A,sgn_sgn(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),hAPP(A,A,sgn_sgn(A),B)),hAPP(A,A,sgn_sgn(A),C)) # label(fact_2204_sgn__mult) # label(axiom).  [clausify(2950)].
43.65/43.52	Derived: hAPP(complex,complex,sgn_sgn(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),B)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,sgn_sgn(complex),A)),hAPP(complex,complex,sgn_sgn(complex),B)).  [resolve(5644,a,5635,a)].
43.65/43.52	5645 real_n1866405975lgebra(real) # label(arity_RealDef_Oreal___RealVector_Oreal__normed__div__algebra) # label(axiom).  [assumption].
43.65/43.52	Derived: -divisi14063676e_zero(real) | hAPP(real,real,norm_norm(real),hAPP(real,real,inverse_inverse(real),A)) = hAPP(real,real,inverse_inverse(real),hAPP(real,real,norm_norm(real),A)).  [resolve(5645,a,5636,a)].
44.73/44.56	Derived: -hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),A),B),sequentially)) | zero_zero(real) = ti(real,B) | hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),inverse_inverse(real)),A)),hAPP(real,real,inverse_inverse(real),B)),sequentially)).  [resolve(5645,a,5637,a)].
44.73/44.56	Derived: -hBOOL(hAPP(filter(A),bool,hAPP(real,fun(filter(A),bool),hAPP(fun(A,real),fun(real,fun(filter(A),bool)),tendsto(A,real),B),C),D)) | zero_zero(real) = ti(real,C) | hBOOL(hAPP(filter(A),bool,hAPP(real,fun(filter(A),bool),hAPP(fun(A,real),fun(real,fun(filter(A),bool)),tendsto(A,real),hAPP(fun(A,real),fun(A,real),hAPP(fun(real,real),fun(fun(A,real),fun(A,real)),combb(real,real,A),inverse_inverse(real)),B)),hAPP(real,real,inverse_inverse(real),C)),D)).  [resolve(5645,a,5638,a)].
44.73/44.56	Derived: hAPP(real,real,norm_norm(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,norm_norm(real),A)),hAPP(real,real,norm_norm(real),B)).  [resolve(5645,a,5639,a)].
44.73/44.56	Derived: hAPP(real,real,norm_norm(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),B)) = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,norm_norm(real),A)),B).  [resolve(5645,a,5640,a)].
44.73/44.56	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),hAPP(real,real,norm_norm(real),B))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,norm_norm(real),hAPP(real,real,inverse_inverse(real),B))),hAPP(real,real,inverse_inverse(real),A))).  [resolve(5645,a,5641,a)].
44.73/44.56	Derived: zero_zero(real) = ti(real,A) | hAPP(real,real,norm_norm(real),hAPP(real,real,inverse_inverse(real),A)) = hAPP(real,real,inverse_inverse(real),hAPP(real,real,norm_norm(real),A)).  [resolve(5645,a,5642,a)].
44.73/44.56	Derived: -topological_space(A) | -hBOOL(hAPP(A,bool,hAPP(fun(A,real),fun(A,bool),isCont(A,real),B),C)) | zero_zero(real) = hAPP(A,real,B,C) | hBOOL(hAPP(A,bool,hAPP(fun(A,real),fun(A,bool),isCont(A,real),hAPP(fun(A,real),fun(A,real),hAPP(fun(real,real),fun(fun(A,real),fun(A,real)),combb(real,real,A),inverse_inverse(real)),B)),C)).  [resolve(5645,a,5643,b)].
44.73/44.56	Derived: hAPP(real,real,sgn_sgn(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,sgn_sgn(real),A)),hAPP(real,real,sgn_sgn(real),B)).  [resolve(5645,a,5644,a)].
44.73/44.56	5646 -real_n1866405975lgebra(A) | -topological_space(B) | -hBOOL(hAPP(filter(B),bool,hAPP(A,fun(filter(B),bool),hAPP(fun(B,A),fun(A,fun(filter(B),bool)),tendsto(B,A),C),D),hAPP(B,filter(B),at(B),E))) | zero_zero(A) = ti(A,D) | hBOOL(hAPP(filter(B),bool,hAPP(A,fun(filter(B),bool),hAPP(fun(B,A),fun(A,fun(filter(B),bool)),tendsto(B,A),hAPP(fun(B,A),fun(B,A),hAPP(fun(A,A),fun(fun(B,A),fun(B,A)),combb(A,A,B),inverse_inverse(A)),C)),hAPP(A,A,inverse_inverse(A),D)),hAPP(B,filter(B),at(B),E))) # label(fact_4588_LIM__inverse) # label(axiom).  [clausify(4485)].
44.73/44.56	5647 -real_n1866405975lgebra(A) | zero_zero(A) = ti(A,B) | hBOOL(hAPP(filter(A),bool,hAPP(A,fun(filter(A),bool),hAPP(fun(A,A),fun(A,fun(filter(A),bool)),tendsto(A,A),inverse_inverse(A)),hAPP(A,A,inverse_inverse(A),B)),hAPP(A,filter(A),at(A),B))) # label(fact_4547_LIM__inverse__fun) # label(axiom).  [clausify(4671)].
44.73/44.56	Derived: zero_zero(complex) = ti(complex,A) | hBOOL(hAPP(filter(complex),bool,hAPP(complex,fun(filter(complex),bool),hAPP(fun(complex,complex),fun(complex,fun(filter(complex),bool)),tendsto(complex,complex),inverse_inverse(complex)),hAPP(complex,complex,inverse_inverse(complex),A)),hAPP(complex,filter(complex),at(complex),A))).  [resolve(5647,a,5635,a)].
44.73/44.56	Derived: zero_zero(real) = ti(real,A) | hBOOL(hAPP(filter(real),bool,hAPP(real,fun(filter(real),bool),hAPP(fun(real,real),fun(real,fun(filter(real),bool)),tendsto(real,real),inverse_inverse(real)),hAPP(real,real,inverse_inverse(real),A)),hAPP(real,filter(real),at(real),A))).  [resolve(5647,a,5645,a)].
46.94/46.80	5648 -real_n1866405975lgebra(A) | -hBOOL(hAPP(filter(nat),bool,hAPP(A,fun(filter(nat),bool),hAPP(fun(nat,A),fun(A,fun(filter(nat),bool)),tendsto(nat,A),B),C),sequentially)) | zero_zero(A) = ti(A,C) | hBOOL(hAPP(fun(nat,A),bool,bseq(A),hAPP(fun(nat,A),fun(nat,A),hAPP(fun(A,A),fun(fun(nat,A),fun(nat,A)),combb(A,A,nat),inverse_inverse(A)),B))) # label(fact_4489_Bseq__inverse) # label(axiom).  [clausify(4833)].
46.94/46.80	Derived: -hBOOL(hAPP(filter(nat),bool,hAPP(complex,fun(filter(nat),bool),hAPP(fun(nat,complex),fun(complex,fun(filter(nat),bool)),tendsto(nat,complex),A),B),sequentially)) | zero_zero(complex) = ti(complex,B) | hBOOL(hAPP(fun(nat,complex),bool,bseq(complex),hAPP(fun(nat,complex),fun(nat,complex),hAPP(fun(complex,complex),fun(fun(nat,complex),fun(nat,complex)),combb(complex,complex,nat),inverse_inverse(complex)),A))).  [resolve(5648,a,5635,a)].
46.94/46.81	Derived: -hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),A),B),sequentially)) | zero_zero(real) = ti(real,B) | hBOOL(hAPP(fun(nat,real),bool,bseq(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),inverse_inverse(real)),A))).  [resolve(5648,a,5645,a)].
46.94/46.81	5649 -ordered_ab_group_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),zero_zero(A)),hAPP(A,A,uminus_uminus(A),B))) # label(fact_2061_neg__0__less__iff__less) # label(axiom).  [clausify(237)].
46.94/46.81	5650 ordered_ab_group_add(rat) # label(arity_Rat_Orat___Groups_Oordered__ab__group__add) # label(axiom).  [assumption].
46.94/46.81	Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(rat,rat,uminus_uminus(rat),A))).  [resolve(5649,a,5650,a)].
46.94/46.81	5651 -ordered_ab_group_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),zero_zero(A)),hAPP(A,A,uminus_uminus(A),B))) # label(fact_2061_neg__0__less__iff__less) # label(axiom).  [clausify(237)].
46.94/46.81	Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(rat,rat,uminus_uminus(rat),A))).  [resolve(5651,a,5650,a)].
46.94/46.81	5652 -ordered_ab_group_add(A) | hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,A),fun(fun(A,bool),fun(A,bool)),image(A,A),uminus_uminus(A)),hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_gr676655987ssThan(A),B),C)) = hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_gr676655987ssThan(A),hAPP(A,A,uminus_uminus(A),C)),hAPP(A,A,uminus_uminus(A),B)) # label(fact_3678_image__uminus__greaterThanLessThan) # label(axiom).  [clausify(454)].
46.94/46.81	Derived: hAPP(fun(rat,bool),fun(rat,bool),hAPP(fun(rat,rat),fun(fun(rat,bool),fun(rat,bool)),image(rat,rat),uminus_uminus(rat)),hAPP(rat,fun(rat,bool),hAPP(rat,fun(rat,fun(rat,bool)),ord_gr676655987ssThan(rat),A),B)) = hAPP(rat,fun(rat,bool),hAPP(rat,fun(rat,fun(rat,bool)),ord_gr676655987ssThan(rat),hAPP(rat,rat,uminus_uminus(rat),B)),hAPP(rat,rat,uminus_uminus(rat),A)).  [resolve(5652,a,5650,a)].
46.94/46.81	5653 -ordered_ab_group_add(A) | -hBOOL(hAPP(fun(nat,A),bool,monoseq(A),B)) | hBOOL(hAPP(fun(nat,A),bool,monoseq(A),hAPP(fun(nat,A),fun(nat,A),hAPP(fun(A,A),fun(fun(nat,A),fun(nat,A)),combb(A,A,nat),uminus_uminus(A)),B))) # label(fact_3921_monoseq__minus) # label(axiom).  [clausify(671)].
46.94/46.81	Derived: -hBOOL(hAPP(fun(nat,rat),bool,monoseq(rat),A)) | hBOOL(hAPP(fun(nat,rat),bool,monoseq(rat),hAPP(fun(nat,rat),fun(nat,rat),hAPP(fun(rat,rat),fun(fun(nat,rat),fun(nat,rat)),combb(rat,rat,nat),uminus_uminus(rat)),A))).  [resolve(5653,a,5650,a)].
46.94/46.81	5654 -ordered_ab_group_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,uminus_uminus(A),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),hAPP(A,A,uminus_uminus(A),B))) # label(fact_2026_le__minus__iff) # label(axiom).  [clausify(991)].
47.04/46.92	Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),hAPP(rat,rat,uminus_uminus(rat),B))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),B),hAPP(rat,rat,uminus_uminus(rat),A))).  [resolve(5654,a,5650,a)].
47.04/46.92	5655 -ordered_ab_group_add(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,uminus_uminus(A),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),hAPP(A,A,uminus_uminus(A),B))) # label(fact_2026_le__minus__iff) # label(axiom).  [clausify(991)].
47.04/46.92	5656 -ordered_ab_group_add(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f163(B,A,D,E,F,C)),C)) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),F),C) != E | -hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),D),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(B,A,F,D)),E)) # label(fact_4299_setsum__nonneg__leq__bound) # label(axiom).  [clausify(1026)].
47.04/46.92	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f163(A,rat,C,D,E,B)),B)) | hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),E),B) != D | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(A,rat,E,C)),D)).  [resolve(5656,a,5650,a)].
47.04/46.92	5657 -ordered_ab_group_add(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(B,A,D,f163(B,A,E,F,D,C)))) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),D),C) != F | -hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),E),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(B,A,D,E)),F)) # label(fact_4299_setsum__nonneg__leq__bound) # label(axiom).  [clausify(1026)].
47.04/46.92	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),hAPP(A,rat,C,f163(A,rat,D,E,C,B)))) | hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),C),B) != E | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),D),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(A,rat,C,D)),E)).  [resolve(5657,a,5650,a)].
47.04/46.92	5658 -ordered_ab_group_add(A) | -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))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) # label(fact_826_less__iff__diff__less__0) # label(axiom).  [clausify(1379)].
47.04/46.92	Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),A),B)),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),B)).  [resolve(5658,a,5650,a)].
47.09/46.92	5659 -ordered_ab_group_add(A) | 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))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) # label(fact_826_less__iff__diff__less__0) # label(axiom).  [clausify(1379)].
47.09/46.92	Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),A),B)),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),B)).  [resolve(5659,a,5650,a)].
47.09/46.92	5660 -ordered_ab_group_add(A) | ord_gr676655987ssThan(A) = ti(fun(A,fun(A,fun(A,bool))),ord_gr676655987ssThan(A)) # label(tsy_c_SetInterval_Oord__class_OgreaterThanLessThan_2_res) # label(axiom).  [clausify(1421)].
47.09/46.92	Derived: ord_gr676655987ssThan(rat) = ti(fun(rat,fun(rat,fun(rat,bool))),ord_gr676655987ssThan(rat)).  [resolve(5660,a,5650,a)].
47.09/46.92	5661 -ordered_ab_group_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,uminus_uminus(A),B)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,uminus_uminus(A),C)),B)) # label(fact_2015_minus__less__iff) # label(axiom).  [clausify(1439)].
47.46/47.32	Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,uminus_uminus(rat),A)),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,uminus_uminus(rat),B)),A)).  [resolve(5661,a,5650,a)].
47.46/47.32	5662 -ordered_ab_group_add(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,uminus_uminus(A),B)),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,uminus_uminus(A),C)),B)) # label(fact_2015_minus__less__iff) # label(axiom).  [clausify(1439)].
47.46/47.32	5663 -ordered_ab_group_add(A) | hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C) != hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),D),E) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),E)) # label(fact_798_diff__eq__diff__less) # label(axiom).  [clausify(1965)].
47.46/47.32	Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),A),B) != hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),C),D) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),C),D)).  [resolve(5663,a,5650,a)].
47.46/47.32	5664 -ordered_ab_group_add(A) | hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C) != hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),D),E) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),E)) # label(fact_798_diff__eq__diff__less) # label(axiom).  [clausify(1965)].
47.46/47.32	Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),A),B) != hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),C),D) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),C),D)).  [resolve(5664,a,5650,a)].
47.46/47.32	5665 -ordered_ab_group_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),zero_zero(A)),hAPP(A,A,uminus_uminus(A),B))) # label(fact_2059_neg__0__le__iff__le) # label(axiom).  [clausify(2183)].
47.46/47.32	Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),hAPP(rat,rat,uminus_uminus(rat),A))).  [resolve(5665,a,5650,a)].
47.46/47.32	5666 -ordered_ab_group_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),zero_zero(A)),hAPP(A,A,uminus_uminus(A),B))) # label(fact_2059_neg__0__le__iff__le) # label(axiom).  [clausify(2183)].
47.46/47.32	Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),hAPP(rat,rat,uminus_uminus(rat),A))).  [resolve(5666,a,5650,a)].
47.46/47.32	5667 -ordered_ab_group_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(A,A,uminus_uminus(A),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),hAPP(A,A,uminus_uminus(A),B))) # label(fact_2014_less__minus__iff) # label(axiom).  [clausify(2253)].
47.46/47.32	Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),hAPP(rat,rat,uminus_uminus(rat),B))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),hAPP(rat,rat,uminus_uminus(rat),A))).  [resolve(5667,a,5650,a)].
47.46/47.32	5668 -ordered_ab_group_add(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(A,A,uminus_uminus(A),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),hAPP(A,A,uminus_uminus(A),B))) # label(fact_2014_less__minus__iff) # label(axiom).  [clausify(2253)].
47.46/47.32	5669 -ordered_ab_group_add(A) | hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,A),fun(fun(A,bool),fun(A,bool)),image(A,A),uminus_uminus(A)),hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_atLeastAtMost(A),B),C)) = hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_atLeastAtMost(A),hAPP(A,A,uminus_uminus(A),C)),hAPP(A,A,uminus_uminus(A),B)) # label(fact_4526_image__uminus__atLeastAtMost) # label(axiom).  [clausify(2308)].
47.46/47.32	Derived: hAPP(fun(rat,bool),fun(rat,bool),hAPP(fun(rat,rat),fun(fun(rat,bool),fun(rat,bool)),image(rat,rat),uminus_uminus(rat)),hAPP(rat,fun(rat,bool),hAPP(rat,fun(rat,fun(rat,bool)),ord_atLeastAtMost(rat),A),B)) = hAPP(rat,fun(rat,bool),hAPP(rat,fun(rat,fun(rat,bool)),ord_atLeastAtMost(rat),hAPP(rat,rat,uminus_uminus(rat),B)),hAPP(rat,rat,uminus_uminus(rat),A)).  [resolve(5669,a,5650,a)].
47.88/47.73	5670 -ordered_ab_group_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,uminus_uminus(A),B)),hAPP(A,A,uminus_uminus(A),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B)) # label(fact_2016_neg__less__iff__less) # label(axiom).  [clausify(2379)].
47.88/47.73	Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,uminus_uminus(rat),A)),hAPP(rat,rat,uminus_uminus(rat),B))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),A)).  [resolve(5670,a,5650,a)].
47.88/47.73	5671 -ordered_ab_group_add(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,uminus_uminus(A),B)),hAPP(A,A,uminus_uminus(A),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B)) # label(fact_2016_neg__less__iff__less) # label(axiom).  [clausify(2379)].
47.88/47.73	Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,uminus_uminus(rat),A)),hAPP(rat,rat,uminus_uminus(rat),B))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),A)).  [resolve(5671,a,5650,a)].
47.88/47.73	5672 -ordered_ab_group_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,uminus_uminus(A),B)),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) # label(fact_2062_neg__less__0__iff__less) # label(axiom).  [clausify(2765)].
47.88/47.73	Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,uminus_uminus(rat),A)),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)).  [resolve(5672,a,5650,a)].
47.88/47.73	5673 -ordered_ab_group_add(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,uminus_uminus(A),B)),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) # label(fact_2062_neg__less__0__iff__less) # label(axiom).  [clausify(2765)].
47.88/47.73	Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,uminus_uminus(rat),A)),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)).  [resolve(5673,a,5650,a)].
47.88/47.73	5674 -ordered_ab_group_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),hAPP(A,A,uminus_uminus(A),B)),zero_zero(A))) # label(fact_2057_neg__le__0__iff__le) # label(axiom).  [clausify(2885)].
47.88/47.73	Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),A)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,uminus_uminus(rat),A)),zero_zero(rat))).  [resolve(5674,a,5650,a)].
47.88/47.73	5675 -ordered_ab_group_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),hAPP(A,A,uminus_uminus(A),B)),zero_zero(A))) # label(fact_2057_neg__le__0__iff__le) # label(axiom).  [clausify(2885)].
47.88/47.73	Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,uminus_uminus(rat),A)),zero_zero(rat))).  [resolve(5675,a,5650,a)].
47.88/47.73	5676 -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_825_le__iff__diff__le__0) # label(axiom).  [clausify(3009)].
47.88/47.73	Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),A),B)),zero_zero(rat))).  [resolve(5676,a,5650,a)].
47.88/47.73	5677 -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_825_le__iff__diff__le__0) # label(axiom).  [clausify(3009)].
47.91/47.80	Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),A),B)),zero_zero(rat))).  [resolve(5677,a,5650,a)].
47.91/47.80	5678 ordered_ab_group_add(int) # label(arity_Int_Oint___Groups_Oordered__ab__group__add) # label(axiom).  [assumption].
47.91/47.80	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),zero_zero(int)),hAPP(int,int,uminus_uminus(int),A))).  [resolve(5678,a,5649,a)].
47.91/47.80	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),zero_zero(int)),hAPP(int,int,uminus_uminus(int),A))).  [resolve(5678,a,5651,a)].
47.91/47.80	Derived: hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,int),fun(fun(int,bool),fun(int,bool)),image(int,int),uminus_uminus(int)),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_gr676655987ssThan(int),A),B)) = hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_gr676655987ssThan(int),hAPP(int,int,uminus_uminus(int),B)),hAPP(int,int,uminus_uminus(int),A)).  [resolve(5678,a,5652,a)].
47.91/47.80	Derived: -hBOOL(hAPP(fun(nat,int),bool,monoseq(int),A)) | hBOOL(hAPP(fun(nat,int),bool,monoseq(int),hAPP(fun(nat,int),fun(nat,int),hAPP(fun(int,int),fun(fun(nat,int),fun(nat,int)),combb(int,int,nat),uminus_uminus(int)),A))).  [resolve(5678,a,5653,a)].
47.91/47.80	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),hAPP(int,int,uminus_uminus(int),B))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),hAPP(int,int,uminus_uminus(int),A))).  [resolve(5678,a,5654,a)].
47.91/47.80	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f163(A,int,C,D,E,B)),B)) | hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),E),B) != D | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(A,int,E,C)),D)).  [resolve(5678,a,5656,a)].
47.91/47.80	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(A,int,C,f163(A,int,D,E,C,B)))) | hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),C),B) != E | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),D),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(A,int,C,D)),E)).  [resolve(5678,a,5657,a)].
47.91/47.80	Derived: -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))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)).  [resolve(5678,a,5658,a)].
47.91/47.80	Derived: 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))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)).  [resolve(5678,a,5659,a)].
47.91/47.80	Derived: ord_gr676655987ssThan(int) = ti(fun(int,fun(int,fun(int,bool))),ord_gr676655987ssThan(int)).  [resolve(5678,a,5660,a)].
47.91/47.80	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,uminus_uminus(int),A)),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,uminus_uminus(int),B)),A)).  [resolve(5678,a,5661,a)].
47.91/47.80	Derived: hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),B) != hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),C),D) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),C),D)).  [resolve(5678,a,5663,a)].
47.91/47.80	Derived: hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),B) != hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),C),D) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),C),D)).  [resolve(5678,a,5664,a)].
48.20/48.04	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)),hAPP(int,int,uminus_uminus(int),A))).  [resolve(5678,a,5665,a)].
48.20/48.04	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)),hAPP(int,int,uminus_uminus(int),A))).  [resolve(5678,a,5666,a)].
48.20/48.04	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),hAPP(int,int,uminus_uminus(int),B))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),hAPP(int,int,uminus_uminus(int),A))).  [resolve(5678,a,5667,a)].
48.20/48.04	Derived: hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,int),fun(fun(int,bool),fun(int,bool)),image(int,int),uminus_uminus(int)),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastAtMost(int),A),B)) = hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastAtMost(int),hAPP(int,int,uminus_uminus(int),B)),hAPP(int,int,uminus_uminus(int),A)).  [resolve(5678,a,5669,a)].
48.20/48.04	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,uminus_uminus(int),A)),hAPP(int,int,uminus_uminus(int),B))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),A)).  [resolve(5678,a,5670,a)].
48.20/48.04	Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,uminus_uminus(int),A)),hAPP(int,int,uminus_uminus(int),B))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),A)).  [resolve(5678,a,5671,a)].
48.20/48.04	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,uminus_uminus(int),A)),zero_zero(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A)).  [resolve(5678,a,5672,a)].
48.20/48.04	Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,uminus_uminus(int),A)),zero_zero(int))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A)).  [resolve(5678,a,5673,a)].
48.20/48.04	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),hAPP(int,int,uminus_uminus(int),A)),zero_zero(int))).  [resolve(5678,a,5674,a)].
48.20/48.04	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),hAPP(int,int,uminus_uminus(int),A)),zero_zero(int))).  [resolve(5678,a,5675,a)].
48.20/48.04	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(5678,a,5676,a)].
48.20/48.04	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(5678,a,5677,a)].
48.20/48.04	5679 -ordered_ab_group_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,uminus_uminus(A),B)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,uminus_uminus(A),C)),B)) # label(fact_2027_minus__le__iff) # label(axiom).  [clausify(3308)].
48.20/48.04	Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,uminus_uminus(rat),A)),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,uminus_uminus(rat),B)),A)).  [resolve(5679,a,5650,a)].
48.20/48.04	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,uminus_uminus(int),A)),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,uminus_uminus(int),B)),A)).  [resolve(5679,a,5678,a)].
48.20/48.04	5680 -ordered_ab_group_add(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,uminus_uminus(A),B)),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,uminus_uminus(A),C)),B)) # label(fact_2027_minus__le__iff) # label(axiom).  [clausify(3308)].
48.20/48.04	5681 -ordered_ab_group_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,uminus_uminus(A),C)),hAPP(A,A,uminus_uminus(A),B))) # label(fact_2028_neg__le__iff__le) # label(axiom).  [clausify(3466)].
48.23/48.09	Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,uminus_uminus(rat),B)),hAPP(rat,rat,uminus_uminus(rat),A))).  [resolve(5681,a,5650,a)].
48.23/48.09	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,uminus_uminus(int),B)),hAPP(int,int,uminus_uminus(int),A))).  [resolve(5681,a,5678,a)].
48.23/48.09	5682 -ordered_ab_group_add(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,uminus_uminus(A),C)),hAPP(A,A,uminus_uminus(A),B))) # label(fact_2028_neg__le__iff__le) # label(axiom).  [clausify(3466)].
48.23/48.09	Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,uminus_uminus(rat),B)),hAPP(rat,rat,uminus_uminus(rat),A))).  [resolve(5682,a,5650,a)].
48.23/48.09	Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,uminus_uminus(int),B)),hAPP(int,int,uminus_uminus(int),A))).  [resolve(5682,a,5678,a)].
48.23/48.09	5683 ordered_ab_group_add(real) # label(arity_RealDef_Oreal___Groups_Oordered__ab__group__add) # label(axiom).  [assumption].
48.23/48.09	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,uminus_uminus(real),A))).  [resolve(5683,a,5649,a)].
48.23/48.09	Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,uminus_uminus(real),A))).  [resolve(5683,a,5651,a)].
48.23/48.09	Derived: hAPP(fun(real,bool),fun(real,bool),hAPP(fun(real,real),fun(fun(real,bool),fun(real,bool)),image(real,real),uminus_uminus(real)),hAPP(real,fun(real,bool),hAPP(real,fun(real,fun(real,bool)),ord_gr676655987ssThan(real),A),B)) = hAPP(real,fun(real,bool),hAPP(real,fun(real,fun(real,bool)),ord_gr676655987ssThan(real),hAPP(real,real,uminus_uminus(real),B)),hAPP(real,real,uminus_uminus(real),A)).  [resolve(5683,a,5652,a)].
48.23/48.09	Derived: -hBOOL(hAPP(fun(nat,real),bool,monoseq(real),A)) | hBOOL(hAPP(fun(nat,real),bool,monoseq(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),uminus_uminus(real)),A))).  [resolve(5683,a,5653,a)].
48.23/48.09	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),hAPP(real,real,uminus_uminus(real),B))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),hAPP(real,real,uminus_uminus(real),A))).  [resolve(5683,a,5654,a)].
48.23/48.09	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f163(A,real,C,D,E,B)),B)) | hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),E),B) != D | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(A,real,E,C)),D)).  [resolve(5683,a,5656,a)].
48.23/48.09	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(A,real,C,f163(A,real,D,E,C,B)))) | hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),C),B) != E | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),D),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(A,real,C,D)),E)).  [resolve(5683,a,5657,a)].
48.23/48.09	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),B)),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)).  [resolve(5683,a,5658,a)].
48.23/48.10	Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),B)),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)).  [resolve(5683,a,5659,a)].
48.23/48.10	Derived: ord_gr676655987ssThan(real) = ti(fun(real,fun(real,fun(real,bool))),ord_gr676655987ssThan(real)).  [resolve(5683,a,5660,a)].
48.23/48.10	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,uminus_uminus(real),A)),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,uminus_uminus(real),B)),A)).  [resolve(5683,a,5661,a)].
48.23/48.10	Derived: hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),B) != hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),C),D) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),C),D)).  [resolve(5683,a,5663,a)].
48.23/48.10	Derived: hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),B) != hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),C),D) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),C),D)).  [resolve(5683,a,5664,a)].
48.23/48.10	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(real,real,uminus_uminus(real),A))).  [resolve(5683,a,5665,a)].
48.23/48.10	Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(real,real,uminus_uminus(real),A))).  [resolve(5683,a,5666,a)].
48.23/48.10	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),hAPP(real,real,uminus_uminus(real),B))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),hAPP(real,real,uminus_uminus(real),A))).  [resolve(5683,a,5667,a)].
48.23/48.10	Derived: hAPP(fun(real,bool),fun(real,bool),hAPP(fun(real,real),fun(fun(real,bool),fun(real,bool)),image(real,real),uminus_uminus(real)),hAPP(real,fun(real,bool),hAPP(real,fun(real,fun(real,bool)),ord_atLeastAtMost(real),A),B)) = hAPP(real,fun(real,bool),hAPP(real,fun(real,fun(real,bool)),ord_atLeastAtMost(real),hAPP(real,real,uminus_uminus(real),B)),hAPP(real,real,uminus_uminus(real),A)).  [resolve(5683,a,5669,a)].
48.23/48.10	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,uminus_uminus(real),A)),hAPP(real,real,uminus_uminus(real),B))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),A)).  [resolve(5683,a,5670,a)].
48.23/48.10	Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,uminus_uminus(real),A)),hAPP(real,real,uminus_uminus(real),B))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),A)).  [resolve(5683,a,5671,a)].
48.23/48.10	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,uminus_uminus(real),A)),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)).  [resolve(5683,a,5672,a)].
48.23/48.10	Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,uminus_uminus(real),A)),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)).  [resolve(5683,a,5673,a)].
48.23/48.10	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,uminus_uminus(real),A)),zero_zero(real))).  [resolve(5683,a,5674,a)].
48.23/48.10	Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,uminus_uminus(real),A)),zero_zero(real))).  [resolve(5683,a,5675,a)].
48.23/48.10	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,uminus_uminus(real),A)),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,uminus_uminus(real),B)),A)).  [resolve(5683,a,5679,a)].
48.86/48.74	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,uminus_uminus(real),B)),hAPP(real,real,uminus_uminus(real),A))).  [resolve(5683,a,5681,a)].
48.86/48.74	Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,uminus_uminus(real),B)),hAPP(real,real,uminus_uminus(real),A))).  [resolve(5683,a,5682,a)].
48.86/48.74	5684 -ordered_ab_group_add(A) | hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),D),C)) = hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),D)),C) # label(fact_4958_max__diff__distrib__left) # label(axiom).  [clausify(3562)].
48.86/48.74	Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_max(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),A),B)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),C),B)) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_max(rat),A),C)),B).  [resolve(5684,a,5650,a)].
48.86/48.74	Derived: hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),C),B)) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),A),C)),B).  [resolve(5684,a,5678,a)].
48.86/48.74	Derived: hAPP(real,real,hAPP(real,fun(real,real),ord_max(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),C),B)) = hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,hAPP(real,fun(real,real),ord_max(real),A),C)),B).  [resolve(5684,a,5683,a)].
48.86/48.74	5685 -ordered_ab_group_add(A) | hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C) != hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),D),E) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),D),E)) # label(fact_797_diff__eq__diff__less__eq) # label(axiom).  [clausify(4156)].
48.86/48.74	Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),A),B) != hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),C),D) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),C),D)).  [resolve(5685,a,5650,a)].
48.86/48.74	Derived: hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),B) != hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),C),D) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),C),D)).  [resolve(5685,a,5678,a)].
48.86/48.74	Derived: hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),B) != hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),C),D) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),C),D)).  [resolve(5685,a,5683,a)].
48.86/48.74	5686 -ordered_ab_group_add(A) | hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C) != hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),D),E) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),D),E)) # label(fact_797_diff__eq__diff__less__eq) # label(axiom).  [clausify(4156)].
48.86/48.74	Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),A),B) != hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),C),D) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),C),D)).  [resolve(5686,a,5650,a)].
48.86/48.74	Derived: hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),B) != hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),C),D) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),C),D)).  [resolve(5686,a,5678,a)].
48.86/48.74	Derived: hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),B) != hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),C),D) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),C),D)).  [resolve(5686,a,5683,a)].
49.01/48.91	5687 -ordered_ab_group_add(A) | hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),D),C)) = hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),D)),C) # label(fact_4803_min__diff__distrib__left) # label(axiom).  [clausify(4172)].
49.01/48.91	Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_min(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),A),B)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),C),B)) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_min(rat),A),C)),B).  [resolve(5687,a,5650,a)].
49.01/48.91	Derived: hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),C),B)) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),A),C)),B).  [resolve(5687,a,5678,a)].
49.01/48.91	Derived: hAPP(real,real,hAPP(real,fun(real,real),ord_min(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),C),B)) = hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,hAPP(real,fun(real,real),ord_min(real),A),C)),B).  [resolve(5687,a,5683,a)].
49.01/48.91	5688 -ordered_ab_group_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,uminus_uminus(A),C)),hAPP(A,A,uminus_uminus(A),B))) # label(fact_2029_le__imp__neg__le) # label(axiom).  [clausify(4283)].
49.01/48.91	5689 -ordered_ab_group_add(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f773(B,A,D,E,C)),C)) | zero_zero(A) != hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),E),C) | -hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),D),C)) | zero_zero(A) = hAPP(B,A,E,D) # label(fact_4300_setsum__nonneg__0) # label(axiom).  [clausify(4357)].
49.01/48.91	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f773(A,rat,C,D,B)),B)) | zero_zero(rat) != hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),D),B) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | zero_zero(rat) = hAPP(A,rat,D,C).  [resolve(5689,a,5650,a)].
49.01/48.91	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f773(A,int,C,D,B)),B)) | zero_zero(int) != hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),D),B) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | zero_zero(int) = hAPP(A,int,D,C).  [resolve(5689,a,5678,a)].
49.01/48.91	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f773(A,real,C,D,B)),B)) | zero_zero(real) != hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),D),B) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | zero_zero(real) = hAPP(A,real,D,C).  [resolve(5689,a,5683,a)].
49.01/48.91	5690 -ordered_ab_group_add(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(B,A,D,f773(B,A,E,D,C)))) | zero_zero(A) != hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),D),C) | -hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),E),C)) | zero_zero(A) = hAPP(B,A,D,E) # label(fact_4300_setsum__nonneg__0) # label(axiom).  [clausify(4357)].
49.01/48.91	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),hAPP(A,rat,C,f773(A,rat,D,C,B)))) | zero_zero(rat) != hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),C),B) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),D),B)) | zero_zero(rat) = hAPP(A,rat,C,D).  [resolve(5690,a,5650,a)].
52.61/52.52	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(A,int,C,f773(A,int,D,C,B)))) | zero_zero(int) != hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),C),B) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),D),B)) | zero_zero(int) = hAPP(A,int,C,D).  [resolve(5690,a,5678,a)].
52.61/52.52	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(A,real,C,f773(A,real,D,C,B)))) | zero_zero(real) != hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),C),B) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),D),B)) | zero_zero(real) = hAPP(A,real,C,D).  [resolve(5690,a,5683,a)].
52.61/52.52	5691 linordered_field(rat) # label(arity_Rat_Orat___Fields_Olinordered__field) # label(axiom).  [assumption].
52.61/52.52	5692 -linordered_field(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),f8(A,B,C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) # label(fact_1540_field__le__epsilon) # label(axiom).  [clausify(27)].
52.61/52.52	5693 -linordered_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),f8(A,B,C)))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) # label(fact_1540_field__le__epsilon) # label(axiom).  [clausify(27)].
52.61/52.52	5694 -linordered_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),B)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),B))) # label(fact_1740_mult__imp__le__div__pos) # label(axiom).  [clausify(75)].
52.61/52.52	5695 -linordered_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,inverse_inverse(A),C)),hAPP(A,A,inverse_inverse(A),B))) # label(fact_2571_le__imp__inverse__le__neg) # label(axiom).  [clausify(249)].
52.61/52.52	5696 -linordered_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),D)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),D))) # label(fact_1683_divide__strict__right__mono) # label(axiom).  [clausify(253)].
52.61/52.52	5697 -linordered_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),B)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),B)),C)) # label(fact_1742_neg__divide__le__eq) # label(axiom).  [clausify(526)].
52.61/52.52	5698 -linordered_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),B)),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),B)),C)) # label(fact_1742_neg__divide__le__eq) # label(axiom).  [clausify(526)].
52.61/52.52	5699 -linordered_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)),zero_zero(A))) # label(fact_1706_divide__nonpos__pos) # label(axiom).  [clausify(613)].
52.61/52.52	5700 -linordered_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),B))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),B)),D)) # label(fact_1711_pos__divide__less__eq) # label(axiom).  [clausify(617)].
52.61/52.52	5701 -linordered_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),B))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),B)),D)) # label(fact_1711_pos__divide__less__eq) # label(axiom).  [clausify(617)].
52.61/52.52	5702 -linordered_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),D),E)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),E)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),D))) # label(fact_1704_frac__less) # label(axiom).  [clausify(621)].
52.61/52.52	5703 -linordered_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,inverse_inverse(A),C)),hAPP(A,A,inverse_inverse(A),B))) # label(fact_2570_le__imp__inverse__le) # label(axiom).  [clausify(680)].
52.61/52.52	5704 -linordered_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,inverse_inverse(A),C)),hAPP(A,A,inverse_inverse(A),B))) # label(fact_2547_less__imp__inverse__less__neg) # label(axiom).  [clausify(828)].
52.61/52.52	5705 -linordered_field(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,inverse_inverse(A),hAPP(nat,A,semiring_1_of_nat(A),hAPP(nat,nat,fact_fact(nat),B))))) # label(fact_2613_inv__of__nat__fact__gt__zero) # label(axiom).  [clausify(885)].
52.61/52.52	5706 -linordered_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)),zero_zero(A))) # label(fact_1680_divide__pos__neg) # label(axiom).  [clausify(903)].
52.61/52.52	5707 -linordered_field(A) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),hAPP(fun(B,A),fun(B,A),hAPP(fun(A,A),fun(fun(B,A),fun(B,A)),combb(A,A,B),abs_abs(A)),C)),D) = hAPP(A,A,abs_abs(A),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),C),D)) # label(fact_3948_abs__setprod) # label(axiom).  [clausify(1357)].
52.61/52.52	5708 -linordered_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),one_one(A)),one_one(A)))),C)) # label(fact_1731_gt__half__sum) # label(axiom).  [clausify(1382)].
52.61/52.52	5709 -linordered_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,inverse_inverse(A),B)),hAPP(A,A,inverse_inverse(A),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B)) # label(fact_2550_inverse__less__imp__less__neg) # label(axiom).  [clausify(1489)].
52.61/52.52	5710 -linordered_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),B))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),B)),D)) # label(fact_1712_mult__imp__div__pos__less) # label(axiom).  [clausify(1518)].
52.61/52.52	5711 -linordered_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,inverse_inverse(A),C)),hAPP(A,A,inverse_inverse(A),B))) # label(fact_2546_less__imp__inverse__less) # label(axiom).  [clausify(1576)].
52.61/52.52	5712 -linordered_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),B))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),B)),D)) # label(fact_1739_mult__imp__div__pos__le) # label(axiom).  [clausify(1680)].
52.61/52.52	5713 -linordered_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,inverse_inverse(A),B))) | zero_zero(A) = ti(A,B) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) # label(fact_2544_inverse__positive__imp__positive) # label(axiom).  [clausify(1743)].
52.61/52.52	5714 -linordered_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),B))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),B))) # label(fact_1714_neg__less__divide__eq) # label(axiom).  [clausify(1750)].
52.61/52.52	5715 -linordered_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),B))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),B))) # label(fact_1714_neg__less__divide__eq) # label(axiom).  [clausify(1750)].
52.61/52.52	5716 -linordered_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C))) # label(fact_1682_divide__neg__neg) # label(axiom).  [clausify(1823)].
52.61/52.52	5717 -linordered_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C))) # label(fact_1707_divide__nonpos__neg) # label(axiom).  [clausify(1842)].
52.61/52.52	5718 -linordered_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),B)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),C))) # label(fact_1717_divide__strict__left__mono__neg) # label(axiom).  [clausify(1948)].
52.61/52.52	5719 -linordered_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),E)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),E)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),D))) # label(fact_1703_frac__less2) # label(axiom).  [clausify(2043)].
52.61/52.52	5720 -linordered_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)),zero_zero(A))) # label(fact_1681_divide__neg__pos) # label(axiom).  [clausify(2053)].
52.61/52.52	5721 -linordered_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,inverse_inverse(A),B))) # label(fact_2543_positive__imp__inverse__positive) # label(axiom).  [clausify(2055)].
52.61/52.52	5722 -linordered_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),B))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),C)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),B))) # label(fact_1743_divide__left__mono) # label(axiom).  [clausify(2057)].
52.61/52.52	5723 -linordered_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,inverse_inverse(A),B)),zero_zero(A))) | zero_zero(A) = ti(A,B) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) # label(fact_2548_inverse__negative__imp__negative) # label(axiom).  [clausify(2215)].
52.61/52.52	5724 -linordered_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),B))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),C)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),B))) # label(fact_1716_divide__strict__left__mono) # label(axiom).  [clausify(2216)].
52.61/52.52	5725 -linordered_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),B))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),D),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),B))) # label(fact_1741_neg__le__divide__eq) # label(axiom).  [clausify(2359)].
52.61/52.52	5726 -linordered_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),B))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),D),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),B))) # label(fact_1741_neg__le__divide__eq) # label(axiom).  [clausify(2359)].
52.61/52.52	5727 -linordered_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),B)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),B)),C)) # label(fact_1715_neg__divide__less__eq) # label(axiom).  [clausify(2470)].
52.61/52.52	5728 -linordered_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),B)),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),B)),C)) # label(fact_1715_neg__divide__less__eq) # label(axiom).  [clausify(2470)].
52.61/52.52	5729 -linordered_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)),zero_zero(A))) # label(fact_1702_divide__nonneg__neg) # label(axiom).  [clausify(2655)].
52.61/52.52	5730 -linordered_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C))) # label(fact_1701_divide__nonneg__pos) # label(axiom).  [clausify(2848)].
52.61/52.52	5731 -linordered_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),D)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),D))) # label(fact_1684_divide__strict__right__mono__neg) # label(axiom).  [clausify(2895)].
52.61/52.52	5732 -linordered_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),B)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),B))) # label(fact_1737_pos__le__divide__eq) # label(axiom).  [clausify(2915)].
52.61/52.52	5733 -linordered_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),B)),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),B))) # label(fact_1737_pos__le__divide__eq) # label(axiom).  [clausify(2915)].
52.61/52.52	5734 -linordered_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,inverse_inverse(A),B)),hAPP(A,A,inverse_inverse(A),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B)) # label(fact_2549_inverse__less__imp__less) # label(axiom).  [clausify(2938)].
52.61/52.52	5735 -linordered_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,inverse_inverse(A),B)),hAPP(A,A,inverse_inverse(A),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),B)) # label(fact_2573_inverse__le__imp__le__neg) # label(axiom).  [clausify(3405)].
52.61/52.52	5736 -linordered_field(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(A,A,inverse_inverse(A),hAPP(nat,A,semiring_1_of_nat(A),hAPP(nat,nat,fact_fact(nat),B))))) # label(fact_2612_inv__of__nat__fact__ge__zero) # label(axiom).  [clausify(3442)].
52.61/52.52	5737 -linordered_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),one_one(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),hAPP(A,A,inverse_inverse(A),B))) # label(fact_2576_one__less__inverse) # label(axiom).  [clausify(3491)].
52.61/52.52	5738 -linordered_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),B)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),B))) # label(fact_1713_mult__imp__less__div__pos) # label(axiom).  [clausify(3539)].
52.61/52.52	5739 -linordered_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,inverse_inverse(A),B)),zero_zero(A))) # label(fact_2545_negative__imp__inverse__negative) # label(axiom).  [clausify(3759)].
52.61/52.52	5740 -linordered_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),one_one(A)),one_one(A))))) # label(fact_1730_less__half__sum) # label(axiom).  [clausify(3770)].
52.61/52.52	Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),f8(rat,A,B))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),B)).  [resolve(5691,a,5692,a)].
52.61/52.52	Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),B),f8(rat,A,B)))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),B)).  [resolve(5691,a,5693,a)].
52.61/52.52	Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,inverse_inverse(rat),B)),hAPP(rat,rat,inverse_inverse(rat),A))).  [resolve(5691,a,5695,a)].
52.61/52.52	Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),C)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),C)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),B),C))).  [resolve(5691,a,5696,a)].
52.70/52.53	Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),B),A)),C)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),C),A)),B)).  [resolve(5691,a,5697,a)].
52.70/52.53	Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),B),A)),C)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),C),A)),B)).  [resolve(5691,a,5698,a)].
52.70/52.53	Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),B)),zero_zero(rat))).  [resolve(5691,a,5699,a)].
52.70/52.53	Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),C)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),C),D)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),D)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),B),C))).  [resolve(5691,a,5702,a)].
52.70/52.53	Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,inverse_inverse(rat),B)),hAPP(rat,rat,inverse_inverse(rat),A))).  [resolve(5691,a,5703,a)].
52.70/52.53	Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,inverse_inverse(rat),B)),hAPP(rat,rat,inverse_inverse(rat),A))).  [resolve(5691,a,5704,a)].
52.70/52.53	Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(rat,rat,inverse_inverse(rat),hAPP(nat,rat,semiring_1_of_nat(rat),hAPP(nat,nat,fact_fact(nat),A))))).  [resolve(5691,a,5705,a)].
52.70/52.53	Derived: hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co302546470etprod(A,rat),hAPP(fun(A,rat),fun(A,rat),hAPP(fun(rat,rat),fun(fun(A,rat),fun(A,rat)),combb(rat,rat,A),abs_abs(rat)),B)),C) = hAPP(rat,rat,abs_abs(rat),hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co302546470etprod(A,rat),B),C)).  [resolve(5691,a,5707,a)].
52.70/52.53	Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),B)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),one_one(rat)),one_one(rat)))),B)).  [resolve(5691,a,5708,a)].
52.70/52.53	Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,inverse_inverse(rat),A)),hAPP(rat,rat,inverse_inverse(rat),B))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),A)).  [resolve(5691,a,5709,a)].
52.70/52.53	Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,inverse_inverse(rat),B)),hAPP(rat,rat,inverse_inverse(rat),A))).  [resolve(5691,a,5711,a)].
52.70/52.53	Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),C),A))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),C),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),B),A))).  [resolve(5691,a,5714,a)].
52.70/52.54	Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),C),A))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),C),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),B),A))).  [resolve(5691,a,5715,a)].
52.70/52.54	Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),B))).  [resolve(5691,a,5717,a)].
52.70/52.54	Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),C),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),C),A)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),C),B))).  [resolve(5691,a,5718,a)].
52.70/52.54	Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),C)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),C),D)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),D)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),B),C))).  [resolve(5691,a,5719,a)].
52.70/52.54	Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),C)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),B),A))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),C),B)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),C),A))).  [resolve(5691,a,5722,a)].
52.70/52.54	Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),C)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),B),A))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),C),B)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),C),A))).  [resolve(5691,a,5724,a)].
52.70/52.54	Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),B),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),C),A))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),C),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),B),A))).  [resolve(5691,a,5725,a)].
52.70/52.54	Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),B),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),C),A))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),C),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),B),A))).  [resolve(5691,a,5726,a)].
52.70/52.54	Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),B),A)),C)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),C),A)),B)).  [resolve(5691,a,5727,a)].
52.70/52.54	Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),B),A)),C)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),C),A)),B)).  [resolve(5691,a,5728,a)].
53.07/52.89	Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),B)),zero_zero(rat))).  [resolve(5691,a,5729,a)].
53.07/52.89	Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),B))).  [resolve(5691,a,5730,a)].
53.07/52.89	Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),C),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),B),C)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),C))).  [resolve(5691,a,5731,a)].
53.07/52.89	Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,inverse_inverse(rat),A)),hAPP(rat,rat,inverse_inverse(rat),B))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),A)).  [resolve(5691,a,5734,a)].
53.07/52.89	Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,inverse_inverse(rat),A)),hAPP(rat,rat,inverse_inverse(rat),B))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),B),A)).  [resolve(5691,a,5735,a)].
53.07/52.89	Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),hAPP(rat,rat,inverse_inverse(rat),hAPP(nat,rat,semiring_1_of_nat(rat),hAPP(nat,nat,fact_fact(nat),A))))).  [resolve(5691,a,5736,a)].
53.07/52.89	Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),B)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),one_one(rat)),one_one(rat))))).  [resolve(5691,a,5740,a)].
53.07/52.89	5741 -linordered_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C))) # label(fact_1679_divide__pos__pos) # label(axiom).  [clausify(4042)].
53.07/52.89	5742 -linordered_field(A) | zero_zero(A) = ti(A,B) | hAPP(A,A,abs_abs(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),B)) = hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),hAPP(A,A,abs_abs(A),C)),hAPP(A,A,abs_abs(A),B)) # label(fact_1871_nonzero__abs__divide) # label(axiom).  [clausify(4050)].
53.07/52.89	5743 -linordered_field(A) | zero_zero(A) = ti(A,B) | hAPP(A,A,abs_abs(A),hAPP(A,A,inverse_inverse(A),B)) = hAPP(A,A,inverse_inverse(A),hAPP(A,A,abs_abs(A),B)) # label(fact_2559_nonzero__abs__inverse) # label(axiom).  [clausify(4144)].
53.07/52.89	5744 -linordered_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),B)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),B))) # label(fact_1738_pos__divide__le__eq) # label(axiom).  [clausify(4205)].
53.07/52.89	5745 -linordered_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),B)),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),B))) # label(fact_1738_pos__divide__le__eq) # label(axiom).  [clausify(4205)].
53.17/52.99	5746 linordered_field(real) # label(arity_RealDef_Oreal___Fields_Olinordered__field) # label(axiom).  [assumption].
53.17/52.99	Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),f8(real,A,B))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),B)).  [resolve(5746,a,5692,a)].
53.17/52.99	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),B),f8(real,A,B)))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),B)).  [resolve(5746,a,5693,a)].
53.17/52.99	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,inverse_inverse(real),B)),hAPP(real,real,inverse_inverse(real),A))).  [resolve(5746,a,5695,a)].
53.17/52.99	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),C)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),B),C))).  [resolve(5746,a,5696,a)].
53.17/52.99	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),B),A)),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),A)),B)).  [resolve(5746,a,5697,a)].
53.17/52.99	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),B),A)),C)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),A)),B)).  [resolve(5746,a,5698,a)].
53.17/52.99	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B)),zero_zero(real))).  [resolve(5746,a,5699,a)].
53.17/52.99	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),C)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),C),D)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),D)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),B),C))).  [resolve(5746,a,5702,a)].
53.17/52.99	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,inverse_inverse(real),B)),hAPP(real,real,inverse_inverse(real),A))).  [resolve(5746,a,5703,a)].
53.17/52.99	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,inverse_inverse(real),B)),hAPP(real,real,inverse_inverse(real),A))).  [resolve(5746,a,5704,a)].
53.17/52.99	Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,inverse_inverse(real),hAPP(nat,real,semiring_1_of_nat(real),hAPP(nat,nat,fact_fact(nat),A))))).  [resolve(5746,a,5705,a)].
53.17/52.99	Derived: hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co302546470etprod(A,real),hAPP(fun(A,real),fun(A,real),hAPP(fun(real,real),fun(fun(A,real),fun(A,real)),combb(real,real,A),abs_abs(real)),B)),C) = hAPP(real,real,abs_abs(real),hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co302546470etprod(A,real),B),C)).  [resolve(5746,a,5707,a)].
53.17/53.00	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),one_one(real)),one_one(real)))),B)).  [resolve(5746,a,5708,a)].
53.17/53.00	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,inverse_inverse(real),A)),hAPP(real,real,inverse_inverse(real),B))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),A)).  [resolve(5746,a,5709,a)].
53.17/53.00	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,inverse_inverse(real),B)),hAPP(real,real,inverse_inverse(real),A))).  [resolve(5746,a,5711,a)].
53.17/53.00	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),A))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),C),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),B),A))).  [resolve(5746,a,5714,a)].
53.17/53.00	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),A))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),C),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),B),A))).  [resolve(5746,a,5715,a)].
53.17/53.00	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B))).  [resolve(5746,a,5717,a)].
53.17/53.00	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),C),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),C),A)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),C),B))).  [resolve(5746,a,5718,a)].
53.17/53.00	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),C)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),C),D)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),D)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),B),C))).  [resolve(5746,a,5719,a)].
53.17/53.00	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),C)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),A))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),C),B)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),C),A))).  [resolve(5746,a,5722,a)].
53.17/53.00	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),C)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),A))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),C),B)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),C),A))).  [resolve(5746,a,5724,a)].
53.18/53.01	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),C),A))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),C),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),A))).  [resolve(5746,a,5725,a)].
53.18/53.01	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),C),A))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),C),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),A))).  [resolve(5746,a,5726,a)].
53.18/53.01	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),A)),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),C),A)),B)).  [resolve(5746,a,5727,a)].
53.18/53.01	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),A)),C)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),C),A)),B)).  [resolve(5746,a,5728,a)].
53.18/53.01	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B)),zero_zero(real))).  [resolve(5746,a,5729,a)].
53.18/53.01	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B))).  [resolve(5746,a,5730,a)].
53.18/53.01	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),C),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),B),C)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),C))).  [resolve(5746,a,5731,a)].
53.18/53.01	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,inverse_inverse(real),A)),hAPP(real,real,inverse_inverse(real),B))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),A)).  [resolve(5746,a,5734,a)].
53.18/53.01	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,inverse_inverse(real),A)),hAPP(real,real,inverse_inverse(real),B))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),A)).  [resolve(5746,a,5735,a)].
53.18/53.01	Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(real,real,inverse_inverse(real),hAPP(nat,real,semiring_1_of_nat(real),hAPP(nat,nat,fact_fact(nat),A))))).  [resolve(5746,a,5736,a)].
53.18/53.01	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),one_one(real)),one_one(real))))).  [resolve(5746,a,5740,a)].
55.44/55.31	5747 -linordered_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),B)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),B))) # label(fact_1710_pos__less__divide__eq) # label(axiom).  [clausify(4521)].
55.44/55.31	5748 -linordered_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),B)),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),B))) # label(fact_1710_pos__less__divide__eq) # label(axiom).  [clausify(4521)].
55.44/55.31	5749 -linordered_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),D),E)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),E)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),D))) # label(fact_1705_frac__le) # label(axiom).  [clausify(4560)].
55.44/55.31	Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),C)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),C),D)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),D)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),B),C))).  [resolve(5749,a,5691,a)].
55.44/55.31	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),C)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),C),D)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),D)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),B),C))).  [resolve(5749,a,5746,a)].
55.44/55.31	5750 -linordered_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,inverse_inverse(A),B)),hAPP(A,A,inverse_inverse(A),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),B)) # label(fact_2572_inverse__le__imp__le) # label(axiom).  [clausify(4718)].
55.44/55.31	Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,inverse_inverse(rat),A)),hAPP(rat,rat,inverse_inverse(rat),B))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),B),A)).  [resolve(5750,a,5691,a)].
55.44/55.31	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,inverse_inverse(real),A)),hAPP(real,real,inverse_inverse(real),B))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),A)).  [resolve(5750,a,5746,a)].
55.44/55.31	5751 -linordered_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),one_one(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),one_one(A)),hAPP(A,A,inverse_inverse(A),B))) # label(fact_2610_one__le__inverse) # label(axiom).  [clausify(4721)].
55.44/55.31	5752 monoid_mult(nat) # label(arity_Nat_Onat___Groups_Omonoid__mult) # label(axiom).  [assumption].
55.54/55.40	5753 -monoid_mult(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C)),B) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C)) # label(fact_331_power__commutes) # label(axiom).  [clausify(30)].
55.54/55.40	5754 -linordered_ring(A) | -monoid_mult(A) | -hBOOL(hAPP(nat,bool,even_odd_even(nat),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),C),B))) # label(fact_2433_zero__le__even__power) # label(axiom).  [clausify(529)].
55.54/55.40	5755 monoid_mult(code_code_numeral) # label(arity_Code__Numeral_Ocode__numeral___Groups_Omonoid__mult) # label(axiom).  [assumption].
55.54/55.40	Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A),B)),A) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A),B)).  [resolve(5755,a,5753,a)].
55.54/55.40	Derived: -linordered_ring(code_code_numeral) | -hBOOL(hAPP(nat,bool,even_odd_even(nat),A)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),zero_zero(code_code_numeral)),hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),B),A))).  [resolve(5755,a,5754,b)].
55.54/55.40	5756 -monoid_mult(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),D)) = hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),C),D)) # label(fact_416_power__add) # label(axiom).  [clausify(785)].
55.54/55.40	Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),C)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),C)).  [resolve(5756,a,5752,a)].
55.54/55.40	Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A),B)),hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A),C)) = hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),C)).  [resolve(5756,a,5755,a)].
55.54/55.40	5757 monoid_mult(real) # label(arity_RealDef_Oreal___Groups_Omonoid__mult) # label(axiom).  [assumption].
55.54/55.40	Derived: -linordered_ring(real) | -hBOOL(hAPP(nat,bool,even_odd_even(nat),A)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),B),A))).  [resolve(5757,a,5754,b)].
55.54/55.40	Derived: hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),B)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),C)) = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),C)).  [resolve(5757,a,5756,a)].
55.54/55.40	5758 -monoid_mult(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),B) = hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) # label(fact_143_power2__eq__square) # label(axiom).  [clausify(1130)].
55.54/55.40	Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),A) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))).  [resolve(5758,a,5752,a)].
55.61/55.45	Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),A) = hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))).  [resolve(5758,a,5755,a)].
55.61/55.45	Derived: hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),A) = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))).  [resolve(5758,a,5757,a)].
55.61/55.45	5759 -monoid_mult(A) | -comm_ring(A) | hAPP(fun(nat,bool),A,hAPP(fun(nat,A),fun(fun(nat,bool),A),big_co1399186613setsum(nat,A),hAPP(fun(nat,A),fun(nat,A),hAPP(fun(nat,fun(A,A)),fun(fun(nat,A),fun(nat,A)),combs(nat,A,A),hAPP(fun(nat,A),fun(nat,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(nat,A),fun(nat,fun(A,A))),combb(A,fun(A,A),nat),times_times(A)),hAPP(A,fun(nat,A),power_power(A),B))),hAPP(fun(nat,A),fun(nat,A),hAPP(fun(nat,fun(A,A)),fun(fun(nat,A),fun(nat,A)),combs(nat,A,A),hAPP(fun(nat,A),fun(nat,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(nat,A),fun(nat,fun(A,A))),combb(A,fun(A,A),nat),minus_minus(A)),hAPP(fun(nat,nat),fun(nat,A),hAPP(fun(nat,A),fun(fun(nat,nat),fun(nat,A)),combb(nat,A,nat),hAPP(A,fun(nat,A),power_power(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C))),hAPP(nat,fun(nat,nat),minus_minus(nat),D)))),hAPP(fun(nat,nat),fun(nat,A),hAPP(fun(nat,A),fun(fun(nat,nat),fun(nat,A)),combb(nat,A,nat),hAPP(A,fun(nat,A),power_power(A),B)),hAPP(nat,fun(nat,nat),minus_minus(nat),D))))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),D)) = hAPP(fun(nat,bool),A,hAPP(fun(nat,A),fun(fun(nat,bool),A),big_co1399186613setsum(nat,A),hAPP(A,fun(nat,A),hAPP(fun(nat,fun(A,A)),fun(A,fun(nat,A)),combc(nat,A,A),hAPP(fun(nat,A),fun(nat,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(nat,A),fun(nat,fun(A,A))),combb(A,fun(A,A),nat),minus_minus(A)),hAPP(fun(nat,A),fun(nat,A),hAPP(fun(nat,fun(A,A)),fun(fun(nat,A),fun(nat,A)),combs(nat,A,A),hAPP(fun(nat,A),fun(nat,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(nat,A),fun(nat,fun(A,A))),combb(A,fun(A,A),nat),times_times(A)),hAPP(fun(nat,nat),fun(nat,A),hAPP(fun(nat,A),fun(fun(nat,nat),fun(nat,A)),combb(nat,A,nat),hAPP(A,fun(nat,A),power_power(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C))),hAPP(nat,fun(nat,nat),minus_minus(nat),D)))),hAPP(A,fun(nat,A),power_power(A),B)))),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),D))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),D)) # label(fact_4226_lemma__termdiff1) # label(axiom).  [clausify(1354)].
55.61/55.45	Derived: -comm_ring(nat) | hAPP(fun(nat,bool),nat,hAPP(fun(nat,nat),fun(fun(nat,bool),nat),big_co1399186613setsum(nat,nat),hAPP(fun(nat,nat),fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,nat),fun(nat,nat)),combs(nat,nat,nat),hAPP(fun(nat,nat),fun(nat,fun(nat,nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,nat),fun(nat,fun(nat,nat))),combb(nat,fun(nat,nat),nat),times_times(nat)),hAPP(nat,fun(nat,nat),power_power(nat),A))),hAPP(fun(nat,nat),fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,nat),fun(nat,nat)),combs(nat,nat,nat),hAPP(fun(nat,nat),fun(nat,fun(nat,nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,nat),fun(nat,fun(nat,nat))),combb(nat,fun(nat,nat),nat),minus_minus(nat)),hAPP(fun(nat,nat),fun(nat,nat),hAPP(fun(nat,nat),fun(fun(nat,nat),fun(nat,nat)),combb(nat,nat,nat),hAPP(nat,fun(nat,nat),power_power(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B))),hAPP(nat,fun(nat,nat),minus_minus(nat),C)))),hAPP(fun(nat,nat),fun(nat,nat),hAPP(fun(nat,nat),fun(fun(nat,nat),fun(nat,nat)),combb(nat,nat,nat),hAPP(nat,fun(nat,nat),power_power(nat),A)),hAPP(nat,fun(nat,nat),minus_minus(nat),C))))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),C)) = hAPP(fun(nat,bool),nat,hAPP(fun(nat,nat),fun(fun(nat,bool),nat),big_co1399186613setsum(nat,nat),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),hAPP(fun(nat,nat),fun(nat,fun(nat,nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,nat),fun(nat,fun(nat,nat))),combb(nat,fun(nat,nat),nat),minus_minus(nat)),hAPP(fun(nat,nat),fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,nat),fun(nat,nat)),combs(nat,nat,nat),hAPP(fun(nat,nat),fun(nat,fun(nat,nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,nat),fun(nat,fun(nat,nat))),combb(nat,fun(nat,nat),nat),times_times(nat)),hAPP(fun(nat,nat),fun(nat,nat),hAPP(fun(nat,nat),fun(fun(nat,nat),fun(nat,nat)),combb(nat,nat,nat),hAPP(nat,fun(nat,nat),power_power(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B))),hAPP(nat,fun(nat,nat),minus_minus(nat),C)))),hAPP(nat,fun(nat,nat),power_power(nat),A)))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),C))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),C)).  [resolve(5759,a,5752,a)].
55.61/55.45	Derived: -comm_ring(code_code_numeral) | hAPP(fun(nat,bool),code_code_numeral,hAPP(fun(nat,code_code_numeral),fun(fun(nat,bool),code_code_numeral),big_co1399186613setsum(nat,code_code_numeral),hAPP(fun(nat,code_code_numeral),fun(nat,code_code_numeral),hAPP(fun(nat,fun(code_code_numeral,code_code_numeral)),fun(fun(nat,code_code_numeral),fun(nat,code_code_numeral)),combs(nat,code_code_numeral,code_code_numeral),hAPP(fun(nat,code_code_numeral),fun(nat,fun(code_code_numeral,code_code_numeral)),hAPP(fun(code_code_numeral,fun(code_code_numeral,code_code_numeral)),fun(fun(nat,code_code_numeral),fun(nat,fun(code_code_numeral,code_code_numeral))),combb(code_code_numeral,fun(code_code_numeral,code_code_numeral),nat),times_times(code_code_numeral)),hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A))),hAPP(fun(nat,code_code_numeral),fun(nat,code_code_numeral),hAPP(fun(nat,fun(code_code_numeral,code_code_numeral)),fun(fun(nat,code_code_numeral),fun(nat,code_code_numeral)),combs(nat,code_code_numeral,code_code_numeral),hAPP(fun(nat,code_code_numeral),fun(nat,fun(code_code_numeral,code_code_numeral)),hAPP(fun(code_code_numeral,fun(code_code_numeral,code_code_numeral)),fun(fun(nat,code_code_numeral),fun(nat,fun(code_code_numeral,code_code_numeral))),combb(code_code_numeral,fun(code_code_numeral,code_code_numeral),nat),minus_minus(code_code_numeral)),hAPP(fun(nat,nat),fun(nat,code_code_numeral),hAPP(fun(nat,code_code_numeral),fun(fun(nat,nat),fun(nat,code_code_numeral)),combb(nat,code_code_numeral,nat),hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),A),B))),hAPP(nat,fun(nat,nat),minus_minus(nat),C)))),hAPP(fun(nat,nat),fun(nat,code_code_numeral),hAPP(fun(nat,code_code_numeral),fun(fun(nat,nat),fun(nat,code_code_numeral)),combb(nat,code_code_numeral,nat),hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A)),hAPP(nat,fun(nat,nat),minus_minus(nat),C))))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),C)) = hAPP(fun(nat,bool),code_code_numeral,hAPP(fun(nat,code_code_numeral),fun(fun(nat,bool),code_code_numeral),big_co1399186613setsum(nat,code_code_numeral),hAPP(code_code_numeral,fun(nat,code_code_numeral),hAPP(fun(nat,fun(code_code_numeral,code_code_numeral)),fun(code_code_numeral,fun(nat,code_code_numeral)),combc(nat,code_code_numeral,code_code_numeral),hAPP(fun(nat,code_code_numeral),fun(nat,fun(code_code_numeral,code_code_numeral)),hAPP(fun(code_code_numeral,fun(code_code_numeral,code_code_numeral)),fun(fun(nat,code_code_numeral),fun(nat,fun(code_code_numeral,code_code_numeral))),combb(code_code_numeral,fun(code_code_numeral,code_code_numeral),nat),minus_minus(code_code_numeral)),hAPP(fun(nat,code_code_numeral),fun(nat,code_code_numeral),hAPP(fun(nat,fun(code_code_numeral,code_code_numeral)),fun(fun(nat,code_code_numeral),fun(nat,code_code_numeral)),combs(nat,code_code_numeral,code_code_numeral),hAPP(fun(nat,code_code_numeral),fun(nat,fun(code_code_numeral,code_code_numeral)),hAPP(fun(code_code_numeral,fun(code_code_numeral,code_code_numeral)),fun(fun(nat,code_code_numeral),fun(nat,fun(code_code_numeral,code_code_numeral))),combb(code_code_numeral,fun(code_code_numeral,code_code_numeral),nat),times_times(code_code_numeral)),hAPP(fun(nat,nat),fun(nat,code_code_numeral),hAPP(fun(nat,code_code_numeral),fun(fun(nat,nat),fun(nat,code_code_numeral)),combb(nat,code_code_numeral,nat),hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),A),B))),hAPP(nat,fun(nat,nat),minus_minus(nat),C)))),hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A)))),hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A),C))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),C)).  [resolve(5759,a,5755,a)].
55.65/55.52	Derived: -comm_ring(real) | hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(real,fun(nat,real),power_power(real),A))),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),minus_minus(real)),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),B))),hAPP(nat,fun(nat,nat),minus_minus(nat),C)))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),hAPP(real,fun(nat,real),power_power(real),A)),hAPP(nat,fun(nat,nat),minus_minus(nat),C))))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),C)) = hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(real,fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(real,fun(nat,real)),combc(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),minus_minus(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),B))),hAPP(nat,fun(nat,nat),minus_minus(nat),C)))),hAPP(real,fun(nat,real),power_power(real),A)))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),C))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),C)).  [resolve(5759,a,5757,a)].
55.65/55.52	5760 -monoid_mult(A) | -number(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),hAPP(int,A,number_number_of(A),B)),hAPP(int,nat,number_number_of(nat),C))),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),hAPP(int,A,number_number_of(A),B)),hAPP(int,nat,number_number_of(nat),C))) = hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),hAPP(int,A,number_number_of(A),B)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,C))) # label(fact_3872_power__number__of__even__number__of) # label(axiom).  [clausify(1643)].
55.65/55.52	Derived: -number(nat) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),hAPP(int,nat,number_number_of(nat),A)),hAPP(int,nat,number_number_of(nat),B))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),hAPP(int,nat,number_number_of(nat),A)),hAPP(int,nat,number_number_of(nat),B))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),hAPP(int,nat,number_number_of(nat),A)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,B))).  [resolve(5760,a,5752,a)].
55.92/55.81	Derived: -number(code_code_numeral) | hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),A)),hAPP(int,nat,number_number_of(nat),B))),hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),A)),hAPP(int,nat,number_number_of(nat),B))) = hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),A)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,B))).  [resolve(5760,a,5755,a)].
55.92/55.81	Derived: -number(real) | hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),A)),hAPP(int,nat,number_number_of(nat),B))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),A)),hAPP(int,nat,number_number_of(nat),B))) = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),A)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,B))).  [resolve(5760,a,5757,a)].
55.92/55.81	5761 -monoid_mult(A) | -comm_semiring_0(A) | hAPP(fun(nat,bool),A,hAPP(fun(nat,A),fun(fun(nat,bool),A),big_co1399186613setsum(nat,A),hAPP(fun(nat,A),fun(nat,A),hAPP(fun(nat,fun(A,A)),fun(fun(nat,A),fun(nat,A)),combs(nat,A,A),hAPP(fun(nat,A),fun(nat,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(nat,A),fun(nat,fun(A,A))),combb(A,fun(A,A),nat),times_times(A)),hAPP(A,fun(nat,A),power_power(A),B))),hAPP(fun(nat,nat),fun(nat,A),hAPP(fun(nat,A),fun(fun(nat,nat),fun(nat,A)),combb(nat,A,nat),hAPP(A,fun(nat,A),power_power(A),C)),hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,D))))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,suc,D))) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),hAPP(fun(nat,bool),A,hAPP(fun(nat,A),fun(fun(nat,bool),A),big_co1399186613setsum(nat,A),hAPP(fun(nat,A),fun(nat,A),hAPP(fun(nat,fun(A,A)),fun(fun(nat,A),fun(nat,A)),combs(nat,A,A),hAPP(fun(nat,A),fun(nat,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(nat,A),fun(nat,fun(A,A))),combb(A,fun(A,A),nat),times_times(A)),hAPP(A,fun(nat,A),power_power(A),B))),hAPP(fun(nat,nat),fun(nat,A),hAPP(fun(nat,A),fun(fun(nat,nat),fun(nat,A)),combb(nat,A,nat),hAPP(A,fun(nat,A),power_power(A),C)),hAPP(nat,fun(nat,nat),minus_minus(nat),D)))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,suc,D)))) # label(fact_4174_lemma__realpow__diff__sumr) # label(axiom).  [clausify(2377)].
55.92/55.81	Derived: -comm_semiring_0(nat) | hAPP(fun(nat,bool),nat,hAPP(fun(nat,nat),fun(fun(nat,bool),nat),big_co1399186613setsum(nat,nat),hAPP(fun(nat,nat),fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,nat),fun(nat,nat)),combs(nat,nat,nat),hAPP(fun(nat,nat),fun(nat,fun(nat,nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,nat),fun(nat,fun(nat,nat))),combb(nat,fun(nat,nat),nat),times_times(nat)),hAPP(nat,fun(nat,nat),power_power(nat),A))),hAPP(fun(nat,nat),fun(nat,nat),hAPP(fun(nat,nat),fun(fun(nat,nat),fun(nat,nat)),combb(nat,nat,nat),hAPP(nat,fun(nat,nat),power_power(nat),B)),hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,C))))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,suc,C))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),hAPP(fun(nat,bool),nat,hAPP(fun(nat,nat),fun(fun(nat,bool),nat),big_co1399186613setsum(nat,nat),hAPP(fun(nat,nat),fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,nat),fun(nat,nat)),combs(nat,nat,nat),hAPP(fun(nat,nat),fun(nat,fun(nat,nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,nat),fun(nat,fun(nat,nat))),combb(nat,fun(nat,nat),nat),times_times(nat)),hAPP(nat,fun(nat,nat),power_power(nat),A))),hAPP(fun(nat,nat),fun(nat,nat),hAPP(fun(nat,nat),fun(fun(nat,nat),fun(nat,nat)),combb(nat,nat,nat),hAPP(nat,fun(nat,nat),power_power(nat),B)),hAPP(nat,fun(nat,nat),minus_minus(nat),C)))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,suc,C)))).  [resolve(5761,a,5752,a)].
55.92/55.82	Derived: -comm_semiring_0(code_code_numeral) | hAPP(fun(nat,bool),code_code_numeral,hAPP(fun(nat,code_code_numeral),fun(fun(nat,bool),code_code_numeral),big_co1399186613setsum(nat,code_code_numeral),hAPP(fun(nat,code_code_numeral),fun(nat,code_code_numeral),hAPP(fun(nat,fun(code_code_numeral,code_code_numeral)),fun(fun(nat,code_code_numeral),fun(nat,code_code_numeral)),combs(nat,code_code_numeral,code_code_numeral),hAPP(fun(nat,code_code_numeral),fun(nat,fun(code_code_numeral,code_code_numeral)),hAPP(fun(code_code_numeral,fun(code_code_numeral,code_code_numeral)),fun(fun(nat,code_code_numeral),fun(nat,fun(code_code_numeral,code_code_numeral))),combb(code_code_numeral,fun(code_code_numeral,code_code_numeral),nat),times_times(code_code_numeral)),hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A))),hAPP(fun(nat,nat),fun(nat,code_code_numeral),hAPP(fun(nat,code_code_numeral),fun(fun(nat,nat),fun(nat,code_code_numeral)),combb(nat,code_code_numeral,nat),hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),B)),hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,C))))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,suc,C))) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),B),hAPP(fun(nat,bool),code_code_numeral,hAPP(fun(nat,code_code_numeral),fun(fun(nat,bool),code_code_numeral),big_co1399186613setsum(nat,code_code_numeral),hAPP(fun(nat,code_code_numeral),fun(nat,code_code_numeral),hAPP(fun(nat,fun(code_code_numeral,code_code_numeral)),fun(fun(nat,code_code_numeral),fun(nat,code_code_numeral)),combs(nat,code_code_numeral,code_code_numeral),hAPP(fun(nat,code_code_numeral),fun(nat,fun(code_code_numeral,code_code_numeral)),hAPP(fun(code_code_numeral,fun(code_code_numeral,code_code_numeral)),fun(fun(nat,code_code_numeral),fun(nat,fun(code_code_numeral,code_code_numeral))),combb(code_code_numeral,fun(code_code_numeral,code_code_numeral),nat),times_times(code_code_numeral)),hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A))),hAPP(fun(nat,nat),fun(nat,code_code_numeral),hAPP(fun(nat,code_code_numeral),fun(fun(nat,nat),fun(nat,code_code_numeral)),combb(nat,code_code_numeral,nat),hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),B)),hAPP(nat,fun(nat,nat),minus_minus(nat),C)))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,suc,C)))).  [resolve(5761,a,5755,a)].
55.92/55.82	Derived: -comm_semiring_0(real) | hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(real,fun(nat,real),power_power(real),A))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),hAPP(real,fun(nat,real),power_power(real),B)),hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,C))))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,suc,C))) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(real,fun(nat,real),power_power(real),A))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),hAPP(real,fun(nat,real),power_power(real),B)),hAPP(nat,fun(nat,nat),minus_minus(nat),C)))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,suc,C)))).  [resolve(5761,a,5757,a)].
56.07/55.93	5762 -monoid_mult(A) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),B)) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),C),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),B),one_one(nat)))),C) = hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),C),B) # label(fact_717_realpow__minus__mult) # label(axiom).  [clausify(2448)].
56.07/55.93	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A)) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),A),one_one(nat)))),B) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),B),A).  [resolve(5762,a,5752,a)].
56.07/55.93	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A)) | hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),A),one_one(nat)))),B) = hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),B),A).  [resolve(5762,a,5755,a)].
56.07/55.93	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A)) | hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),A),one_one(nat)))),B) = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),B),A).  [resolve(5762,a,5757,a)].
56.07/55.93	5763 -monoid_mult(A) | hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),C)) # label(fact_233_power__even__eq) # label(axiom).  [clausify(2634)].
56.07/55.93	Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),B)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),B)).  [resolve(5763,a,5752,a)].
56.07/55.93	Derived: hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A),B)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),B)).  [resolve(5763,a,5755,a)].
56.07/55.93	Derived: hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),B)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),B)).  [resolve(5763,a,5757,a)].
56.22/56.08	5764 monoid_mult(rat) # label(arity_Rat_Orat___Groups_Omonoid__mult) # label(axiom).  [assumption].
56.22/56.08	Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),B)),A) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),B)).  [resolve(5764,a,5753,a)].
56.22/56.08	Derived: -linordered_ring(rat) | -hBOOL(hAPP(nat,bool,even_odd_even(nat),A)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),B),A))).  [resolve(5764,a,5754,b)].
56.22/56.08	Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),B)),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),C)) = hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),C)).  [resolve(5764,a,5756,a)].
56.22/56.08	Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),A) = hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))).  [resolve(5764,a,5758,a)].
56.22/56.08	Derived: -comm_ring(rat) | hAPP(fun(nat,bool),rat,hAPP(fun(nat,rat),fun(fun(nat,bool),rat),big_co1399186613setsum(nat,rat),hAPP(fun(nat,rat),fun(nat,rat),hAPP(fun(nat,fun(rat,rat)),fun(fun(nat,rat),fun(nat,rat)),combs(nat,rat,rat),hAPP(fun(nat,rat),fun(nat,fun(rat,rat)),hAPP(fun(rat,fun(rat,rat)),fun(fun(nat,rat),fun(nat,fun(rat,rat))),combb(rat,fun(rat,rat),nat),times_times(rat)),hAPP(rat,fun(nat,rat),power_power(rat),A))),hAPP(fun(nat,rat),fun(nat,rat),hAPP(fun(nat,fun(rat,rat)),fun(fun(nat,rat),fun(nat,rat)),combs(nat,rat,rat),hAPP(fun(nat,rat),fun(nat,fun(rat,rat)),hAPP(fun(rat,fun(rat,rat)),fun(fun(nat,rat),fun(nat,fun(rat,rat))),combb(rat,fun(rat,rat),nat),minus_minus(rat)),hAPP(fun(nat,nat),fun(nat,rat),hAPP(fun(nat,rat),fun(fun(nat,nat),fun(nat,rat)),combb(nat,rat,nat),hAPP(rat,fun(nat,rat),power_power(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),B))),hAPP(nat,fun(nat,nat),minus_minus(nat),C)))),hAPP(fun(nat,nat),fun(nat,rat),hAPP(fun(nat,rat),fun(fun(nat,nat),fun(nat,rat)),combb(nat,rat,nat),hAPP(rat,fun(nat,rat),power_power(rat),A)),hAPP(nat,fun(nat,nat),minus_minus(nat),C))))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),C)) = hAPP(fun(nat,bool),rat,hAPP(fun(nat,rat),fun(fun(nat,bool),rat),big_co1399186613setsum(nat,rat),hAPP(rat,fun(nat,rat),hAPP(fun(nat,fun(rat,rat)),fun(rat,fun(nat,rat)),combc(nat,rat,rat),hAPP(fun(nat,rat),fun(nat,fun(rat,rat)),hAPP(fun(rat,fun(rat,rat)),fun(fun(nat,rat),fun(nat,fun(rat,rat))),combb(rat,fun(rat,rat),nat),minus_minus(rat)),hAPP(fun(nat,rat),fun(nat,rat),hAPP(fun(nat,fun(rat,rat)),fun(fun(nat,rat),fun(nat,rat)),combs(nat,rat,rat),hAPP(fun(nat,rat),fun(nat,fun(rat,rat)),hAPP(fun(rat,fun(rat,rat)),fun(fun(nat,rat),fun(nat,fun(rat,rat))),combb(rat,fun(rat,rat),nat),times_times(rat)),hAPP(fun(nat,nat),fun(nat,rat),hAPP(fun(nat,rat),fun(fun(nat,nat),fun(nat,rat)),combb(nat,rat,nat),hAPP(rat,fun(nat,rat),power_power(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),B))),hAPP(nat,fun(nat,nat),minus_minus(nat),C)))),hAPP(rat,fun(nat,rat),power_power(rat),A)))),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),C))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),C)).  [resolve(5764,a,5759,a)].
56.22/56.08	Derived: -number(rat) | hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),hAPP(int,rat,number_number_of(rat),A)),hAPP(int,nat,number_number_of(nat),B))),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),hAPP(int,rat,number_number_of(rat),A)),hAPP(int,nat,number_number_of(nat),B))) = hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),hAPP(int,rat,number_number_of(rat),A)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,B))).  [resolve(5764,a,5760,a)].
56.31/56.13	Derived: -comm_semiring_0(rat) | hAPP(fun(nat,bool),rat,hAPP(fun(nat,rat),fun(fun(nat,bool),rat),big_co1399186613setsum(nat,rat),hAPP(fun(nat,rat),fun(nat,rat),hAPP(fun(nat,fun(rat,rat)),fun(fun(nat,rat),fun(nat,rat)),combs(nat,rat,rat),hAPP(fun(nat,rat),fun(nat,fun(rat,rat)),hAPP(fun(rat,fun(rat,rat)),fun(fun(nat,rat),fun(nat,fun(rat,rat))),combb(rat,fun(rat,rat),nat),times_times(rat)),hAPP(rat,fun(nat,rat),power_power(rat),A))),hAPP(fun(nat,nat),fun(nat,rat),hAPP(fun(nat,rat),fun(fun(nat,nat),fun(nat,rat)),combb(nat,rat,nat),hAPP(rat,fun(nat,rat),power_power(rat),B)),hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,C))))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,suc,C))) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),B),hAPP(fun(nat,bool),rat,hAPP(fun(nat,rat),fun(fun(nat,bool),rat),big_co1399186613setsum(nat,rat),hAPP(fun(nat,rat),fun(nat,rat),hAPP(fun(nat,fun(rat,rat)),fun(fun(nat,rat),fun(nat,rat)),combs(nat,rat,rat),hAPP(fun(nat,rat),fun(nat,fun(rat,rat)),hAPP(fun(rat,fun(rat,rat)),fun(fun(nat,rat),fun(nat,fun(rat,rat))),combb(rat,fun(rat,rat),nat),times_times(rat)),hAPP(rat,fun(nat,rat),power_power(rat),A))),hAPP(fun(nat,nat),fun(nat,rat),hAPP(fun(nat,rat),fun(fun(nat,nat),fun(nat,rat)),combb(nat,rat,nat),hAPP(rat,fun(nat,rat),power_power(rat),B)),hAPP(nat,fun(nat,nat),minus_minus(nat),C)))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,suc,C)))).  [resolve(5764,a,5761,a)].
56.31/56.13	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A)) | hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),A),one_one(nat)))),B) = hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),B),A).  [resolve(5764,a,5762,a)].
56.31/56.13	Derived: hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),B)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),B)).  [resolve(5764,a,5763,a)].
56.31/56.13	5765 -comm_ring(A) | -monoid_mult(A) | hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(nat,nat,suc,C))),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),D),hAPP(nat,nat,suc,C))) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),D)),hAPP(fun(nat,bool),A,hAPP(fun(nat,A),fun(fun(nat,bool),A),big_co1399186613setsum(nat,A),hAPP(fun(nat,A),fun(nat,A),hAPP(fun(nat,fun(A,A)),fun(fun(nat,A),fun(nat,A)),combs(nat,A,A),hAPP(fun(nat,A),fun(nat,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(nat,A),fun(nat,fun(A,A))),combb(A,fun(A,A),nat),times_times(A)),hAPP(A,fun(nat,A),power_power(A),B))),hAPP(fun(nat,nat),fun(nat,A),hAPP(fun(nat,A),fun(fun(nat,nat),fun(nat,A)),combb(nat,A,nat),hAPP(A,fun(nat,A),power_power(A),D)),hAPP(nat,fun(nat,nat),minus_minus(nat),C)))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,suc,C)))) # label(fact_4227_lemma__realpow__diff__sumr2) # label(axiom).  [clausify(3034)].
56.31/56.13	Derived: -comm_ring(nat) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),hAPP(nat,nat,suc,B))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),C),hAPP(nat,nat,suc,B))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),A),C)),hAPP(fun(nat,bool),nat,hAPP(fun(nat,nat),fun(fun(nat,bool),nat),big_co1399186613setsum(nat,nat),hAPP(fun(nat,nat),fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,nat),fun(nat,nat)),combs(nat,nat,nat),hAPP(fun(nat,nat),fun(nat,fun(nat,nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,nat),fun(nat,fun(nat,nat))),combb(nat,fun(nat,nat),nat),times_times(nat)),hAPP(nat,fun(nat,nat),power_power(nat),A))),hAPP(fun(nat,nat),fun(nat,nat),hAPP(fun(nat,nat),fun(fun(nat,nat),fun(nat,nat)),combb(nat,nat,nat),hAPP(nat,fun(nat,nat),power_power(nat),C)),hAPP(nat,fun(nat,nat),minus_minus(nat),B)))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,suc,B)))).  [resolve(5765,b,5752,a)].
56.31/56.14	Derived: -comm_ring(code_code_numeral) | hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),minus_minus(code_code_numeral),hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A),hAPP(nat,nat,suc,B))),hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),C),hAPP(nat,nat,suc,B))) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),minus_minus(code_code_numeral),A),C)),hAPP(fun(nat,bool),code_code_numeral,hAPP(fun(nat,code_code_numeral),fun(fun(nat,bool),code_code_numeral),big_co1399186613setsum(nat,code_code_numeral),hAPP(fun(nat,code_code_numeral),fun(nat,code_code_numeral),hAPP(fun(nat,fun(code_code_numeral,code_code_numeral)),fun(fun(nat,code_code_numeral),fun(nat,code_code_numeral)),combs(nat,code_code_numeral,code_code_numeral),hAPP(fun(nat,code_code_numeral),fun(nat,fun(code_code_numeral,code_code_numeral)),hAPP(fun(code_code_numeral,fun(code_code_numeral,code_code_numeral)),fun(fun(nat,code_code_numeral),fun(nat,fun(code_code_numeral,code_code_numeral))),combb(code_code_numeral,fun(code_code_numeral,code_code_numeral),nat),times_times(code_code_numeral)),hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A))),hAPP(fun(nat,nat),fun(nat,code_code_numeral),hAPP(fun(nat,code_code_numeral),fun(fun(nat,nat),fun(nat,code_code_numeral)),combb(nat,code_code_numeral,nat),hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),C)),hAPP(nat,fun(nat,nat),minus_minus(nat),B)))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,suc,B)))).  [resolve(5765,b,5755,a)].
56.31/56.14	Derived: -comm_ring(real) | hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),hAPP(nat,nat,suc,B))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),C),hAPP(nat,nat,suc,B))) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),C)),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(real,fun(nat,real),power_power(real),A))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),hAPP(real,fun(nat,real),power_power(real),C)),hAPP(nat,fun(nat,nat),minus_minus(nat),B)))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,suc,B)))).  [resolve(5765,b,5757,a)].
56.31/56.14	Derived: -comm_ring(rat) | hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),hAPP(nat,nat,suc,B))),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),C),hAPP(nat,nat,suc,B))) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),A),C)),hAPP(fun(nat,bool),rat,hAPP(fun(nat,rat),fun(fun(nat,bool),rat),big_co1399186613setsum(nat,rat),hAPP(fun(nat,rat),fun(nat,rat),hAPP(fun(nat,fun(rat,rat)),fun(fun(nat,rat),fun(nat,rat)),combs(nat,rat,rat),hAPP(fun(nat,rat),fun(nat,fun(rat,rat)),hAPP(fun(rat,fun(rat,rat)),fun(fun(nat,rat),fun(nat,fun(rat,rat))),combb(rat,fun(rat,rat),nat),times_times(rat)),hAPP(rat,fun(nat,rat),power_power(rat),A))),hAPP(fun(nat,nat),fun(nat,rat),hAPP(fun(nat,rat),fun(fun(nat,nat),fun(nat,rat)),combb(nat,rat,nat),hAPP(rat,fun(nat,rat),power_power(rat),C)),hAPP(nat,fun(nat,nat),minus_minus(nat),B)))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,suc,B)))).  [resolve(5765,b,5764,a)].
56.39/56.23	5766 -monoid_mult(A) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),B))) | one_one(A) = hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),C),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,B))) # label(fact_3898_power__number__of__odd) # label(axiom).  [clausify(3226)].
56.39/56.23	Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),A))) | one_one(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,A))).  [resolve(5766,a,5752,a)].
56.39/56.23	Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),A))) | one_one(code_code_numeral) = hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,A))).  [resolve(5766,a,5755,a)].
56.39/56.23	Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),A))) | one_one(real) = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,A))).  [resolve(5766,a,5757,a)].
56.39/56.23	Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),A))) | one_one(rat) = hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,A))).  [resolve(5766,a,5764,a)].
56.39/56.23	5767 -monoid_mult(A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),B))) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),C),hAPP(int,nat,number_number_of(nat),B)))),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),C),hAPP(int,nat,number_number_of(nat),B))) = hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),C),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,B))) # label(fact_3898_power__number__of__odd) # label(axiom).  [clausify(3226)].
56.39/56.23	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),A))) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),B),hAPP(int,nat,number_number_of(nat),A)))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),B),hAPP(int,nat,number_number_of(nat),A))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,A))).  [resolve(5767,a,5752,a)].
56.39/56.23	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),A))) | hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),B),hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),B),hAPP(int,nat,number_number_of(nat),A)))),hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),B),hAPP(int,nat,number_number_of(nat),A))) = hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,A))).  [resolve(5767,a,5755,a)].
56.68/56.49	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),A))) | hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),B),hAPP(int,nat,number_number_of(nat),A)))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),B),hAPP(int,nat,number_number_of(nat),A))) = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,A))).  [resolve(5767,a,5757,a)].
56.68/56.49	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),A))) | hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),B),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),B),hAPP(int,nat,number_number_of(nat),A)))),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),B),hAPP(int,nat,number_number_of(nat),A))) = hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,A))).  [resolve(5767,a,5764,a)].
56.68/56.49	5768 -monoid_mult(A) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),C)) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),D),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),C),B))),D) = hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),D),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,C)),B)) # label(fact_1412_lemma__realpow__diff) # label(axiom).  [clausify(3615)].
56.68/56.49	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),C),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),B),A))),C) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),C),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,B)),A)).  [resolve(5768,a,5752,a)].
56.68/56.49	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),C),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),B),A))),C) = hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),C),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,B)),A)).  [resolve(5768,a,5755,a)].
56.68/56.49	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),C),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),B),A))),C) = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),C),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,B)),A)).  [resolve(5768,a,5757,a)].
56.68/56.49	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),C),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),B),A))),C) = hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),C),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,B)),A)).  [resolve(5768,a,5764,a)].
56.68/56.49	5769 -monoid_mult(A) | one_one(A) = hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),one_one(A)),B) # label(fact_341_power__one) # label(axiom).  [clausify(3670)].
56.68/56.49	Derived: one_one(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),one_one(nat)),A).  [resolve(5769,a,5752,a)].
56.68/56.49	Derived: one_one(code_code_numeral) = hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),one_one(code_code_numeral)),A).  [resolve(5769,a,5755,a)].
56.98/56.79	Derived: one_one(real) = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),one_one(real)),A).  [resolve(5769,a,5757,a)].
56.98/56.79	Derived: one_one(rat) = hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),one_one(rat)),A).  [resolve(5769,a,5764,a)].
56.98/56.79	5770 -monoid_mult(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),one_one(A)) = ti(A,B) # label(fact_800_mult__1__right) # label(axiom).  [clausify(3687)].
56.98/56.79	Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),one_one(nat)) = ti(nat,A).  [resolve(5770,a,5752,a)].
56.98/56.79	Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),one_one(code_code_numeral)) = ti(code_code_numeral,A).  [resolve(5770,a,5755,a)].
56.98/56.79	Derived: hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),one_one(real)) = ti(real,A).  [resolve(5770,a,5757,a)].
56.98/56.79	Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),one_one(rat)) = ti(rat,A).  [resolve(5770,a,5764,a)].
56.98/56.79	5771 -monoid_mult(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C)),B) = hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(nat,nat,suc,C)) # label(fact_1307_power__Suc2) # label(axiom).  [clausify(3795)].
56.98/56.79	Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),B)),A) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),hAPP(nat,nat,suc,B)).  [resolve(5771,a,5752,a)].
56.98/56.79	Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A),B)),A) = hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A),hAPP(nat,nat,suc,B)).  [resolve(5771,a,5755,a)].
56.98/56.79	Derived: hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),B)),A) = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),hAPP(nat,nat,suc,B)).  [resolve(5771,a,5757,a)].
56.98/56.79	Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),B)),A) = hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),hAPP(nat,nat,suc,B)).  [resolve(5771,a,5764,a)].
56.98/56.79	5772 -monoid_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),B)),B) = hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,hAPP(int,int,bit1,pls)))) # label(fact_138_power3__eq__cube) # label(axiom).  [clausify(3871)].
56.98/56.79	Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),A)),A) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,hAPP(int,int,bit1,pls)))).  [resolve(5772,a,5752,a)].
56.98/56.79	Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),A)),A) = hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,hAPP(int,int,bit1,pls)))).  [resolve(5772,a,5755,a)].
56.98/56.79	Derived: hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),A)),A) = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,hAPP(int,int,bit1,pls)))).  [resolve(5772,a,5757,a)].
56.98/56.79	Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),A)),A) = hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,hAPP(int,int,bit1,pls)))).  [resolve(5772,a,5764,a)].
56.98/56.79	5773 monoid_mult(int) # label(arity_Int_Oint___Groups_Omonoid__mult) # label(axiom).  [assumption].
56.98/56.79	Derived: hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),B)),A) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),B)).  [resolve(5773,a,5753,a)].
56.98/56.79	Derived: -linordered_ring(int) | -hBOOL(hAPP(nat,bool,even_odd_even(nat),A)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),B),A))).  [resolve(5773,a,5754,b)].
56.98/56.79	Derived: hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),B)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),C)) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),C)).  [resolve(5773,a,5756,a)].
56.98/56.79	Derived: hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),A) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))).  [resolve(5773,a,5758,a)].
56.98/56.79	Derived: -comm_ring(int) | hAPP(fun(nat,bool),int,hAPP(fun(nat,int),fun(fun(nat,bool),int),big_co1399186613setsum(nat,int),hAPP(fun(nat,int),fun(nat,int),hAPP(fun(nat,fun(int,int)),fun(fun(nat,int),fun(nat,int)),combs(nat,int,int),hAPP(fun(nat,int),fun(nat,fun(int,int)),hAPP(fun(int,fun(int,int)),fun(fun(nat,int),fun(nat,fun(int,int))),combb(int,fun(int,int),nat),times_times(int)),hAPP(int,fun(nat,int),power_power(int),A))),hAPP(fun(nat,int),fun(nat,int),hAPP(fun(nat,fun(int,int)),fun(fun(nat,int),fun(nat,int)),combs(nat,int,int),hAPP(fun(nat,int),fun(nat,fun(int,int)),hAPP(fun(int,fun(int,int)),fun(fun(nat,int),fun(nat,fun(int,int))),combb(int,fun(int,int),nat),minus_minus(int)),hAPP(fun(nat,nat),fun(nat,int),hAPP(fun(nat,int),fun(fun(nat,nat),fun(nat,int)),combb(nat,int,nat),hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B))),hAPP(nat,fun(nat,nat),minus_minus(nat),C)))),hAPP(fun(nat,nat),fun(nat,int),hAPP(fun(nat,int),fun(fun(nat,nat),fun(nat,int)),combb(nat,int,nat),hAPP(int,fun(nat,int),power_power(int),A)),hAPP(nat,fun(nat,nat),minus_minus(nat),C))))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),C)) = hAPP(fun(nat,bool),int,hAPP(fun(nat,int),fun(fun(nat,bool),int),big_co1399186613setsum(nat,int),hAPP(int,fun(nat,int),hAPP(fun(nat,fun(int,int)),fun(int,fun(nat,int)),combc(nat,int,int),hAPP(fun(nat,int),fun(nat,fun(int,int)),hAPP(fun(int,fun(int,int)),fun(fun(nat,int),fun(nat,fun(int,int))),combb(int,fun(int,int),nat),minus_minus(int)),hAPP(fun(nat,int),fun(nat,int),hAPP(fun(nat,fun(int,int)),fun(fun(nat,int),fun(nat,int)),combs(nat,int,int),hAPP(fun(nat,int),fun(nat,fun(int,int)),hAPP(fun(int,fun(int,int)),fun(fun(nat,int),fun(nat,fun(int,int))),combb(int,fun(int,int),nat),times_times(int)),hAPP(fun(nat,nat),fun(nat,int),hAPP(fun(nat,int),fun(fun(nat,nat),fun(nat,int)),combb(nat,int,nat),hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B))),hAPP(nat,fun(nat,nat),minus_minus(nat),C)))),hAPP(int,fun(nat,int),power_power(int),A)))),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),C))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),C)).  [resolve(5773,a,5759,a)].
56.98/56.79	Derived: -number(int) | hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,number_number_of(int),A)),hAPP(int,nat,number_number_of(nat),B))),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,number_number_of(int),A)),hAPP(int,nat,number_number_of(nat),B))) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,number_number_of(int),A)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,B))).  [resolve(5773,a,5760,a)].
56.98/56.79	Derived: -comm_semiring_0(int) | hAPP(fun(nat,bool),int,hAPP(fun(nat,int),fun(fun(nat,bool),int),big_co1399186613setsum(nat,int),hAPP(fun(nat,int),fun(nat,int),hAPP(fun(nat,fun(int,int)),fun(fun(nat,int),fun(nat,int)),combs(nat,int,int),hAPP(fun(nat,int),fun(nat,fun(int,int)),hAPP(fun(int,fun(int,int)),fun(fun(nat,int),fun(nat,fun(int,int))),combb(int,fun(int,int),nat),times_times(int)),hAPP(int,fun(nat,int),power_power(int),A))),hAPP(fun(nat,nat),fun(nat,int),hAPP(fun(nat,int),fun(fun(nat,nat),fun(nat,int)),combb(nat,int,nat),hAPP(int,fun(nat,int),power_power(int),B)),hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,C))))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,suc,C))) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),hAPP(fun(nat,bool),int,hAPP(fun(nat,int),fun(fun(nat,bool),int),big_co1399186613setsum(nat,int),hAPP(fun(nat,int),fun(nat,int),hAPP(fun(nat,fun(int,int)),fun(fun(nat,int),fun(nat,int)),combs(nat,int,int),hAPP(fun(nat,int),fun(nat,fun(int,int)),hAPP(fun(int,fun(int,int)),fun(fun(nat,int),fun(nat,fun(int,int))),combb(int,fun(int,int),nat),times_times(int)),hAPP(int,fun(nat,int),power_power(int),A))),hAPP(fun(nat,nat),fun(nat,int),hAPP(fun(nat,int),fun(fun(nat,nat),fun(nat,int)),combb(nat,int,nat),hAPP(int,fun(nat,int),power_power(int),B)),hAPP(nat,fun(nat,nat),minus_minus(nat),C)))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,suc,C)))).  [resolve(5773,a,5761,a)].
56.98/56.80	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A)) | hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),A),one_one(nat)))),B) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),B),A).  [resolve(5773,a,5762,a)].
56.98/56.80	Derived: hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),B)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),B)).  [resolve(5773,a,5763,a)].
56.98/56.80	Derived: -comm_ring(int) | hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),hAPP(nat,nat,suc,B))),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),C),hAPP(nat,nat,suc,B))) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),C)),hAPP(fun(nat,bool),int,hAPP(fun(nat,int),fun(fun(nat,bool),int),big_co1399186613setsum(nat,int),hAPP(fun(nat,int),fun(nat,int),hAPP(fun(nat,fun(int,int)),fun(fun(nat,int),fun(nat,int)),combs(nat,int,int),hAPP(fun(nat,int),fun(nat,fun(int,int)),hAPP(fun(int,fun(int,int)),fun(fun(nat,int),fun(nat,fun(int,int))),combb(int,fun(int,int),nat),times_times(int)),hAPP(int,fun(nat,int),power_power(int),A))),hAPP(fun(nat,nat),fun(nat,int),hAPP(fun(nat,int),fun(fun(nat,nat),fun(nat,int)),combb(nat,int,nat),hAPP(int,fun(nat,int),power_power(int),C)),hAPP(nat,fun(nat,nat),minus_minus(nat),B)))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,suc,B)))).  [resolve(5773,a,5765,b)].
56.98/56.80	Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),A))) | one_one(int) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,A))).  [resolve(5773,a,5766,a)].
56.98/56.80	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),A))) | hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),B),hAPP(int,nat,number_number_of(nat),A)))),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),B),hAPP(int,nat,number_number_of(nat),A))) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,A))).  [resolve(5773,a,5767,a)].
56.98/56.81	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),C),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),B),A))),C) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),C),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,B)),A)).  [resolve(5773,a,5768,a)].
56.98/56.81	Derived: one_one(int) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),one_one(int)),A).  [resolve(5773,a,5769,a)].
56.98/56.81	Derived: hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),one_one(int)) = ti(int,A).  [resolve(5773,a,5770,a)].
56.98/56.81	Derived: hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),B)),A) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),hAPP(nat,nat,suc,B)).  [resolve(5773,a,5771,a)].
56.98/56.81	Derived: hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),A)),A) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,hAPP(int,int,bit1,pls)))).  [resolve(5773,a,5772,a)].
56.98/56.81	5774 -monoid_mult(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) = hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),C))) # label(fact_1456_power__odd__eq) # label(axiom).  [clausify(3955)].
56.98/56.81	Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),B)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),B))).  [resolve(5774,a,5752,a)].
56.98/56.81	Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A),B)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) = hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),B))).  [resolve(5774,a,5755,a)].
56.98/56.81	Derived: hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),B)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),B))).  [resolve(5774,a,5757,a)].
56.98/56.81	Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),B)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) = hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),B))).  [resolve(5774,a,5764,a)].
56.98/56.81	Derived: hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),B)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),B))).  [resolve(5774,a,5773,a)].
57.25/57.08	5775 -monoid_mult(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(int,nat,number_number_of(nat),C))),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(int,nat,number_number_of(nat),C))) = hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,C))) # label(fact_3871_power__number__of__even) # label(axiom).  [clausify(4046)].
57.25/57.08	Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),hAPP(int,nat,number_number_of(nat),B))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),hAPP(int,nat,number_number_of(nat),B))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,B))).  [resolve(5775,a,5752,a)].
57.25/57.08	Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A),hAPP(int,nat,number_number_of(nat),B))),hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A),hAPP(int,nat,number_number_of(nat),B))) = hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,B))).  [resolve(5775,a,5755,a)].
57.25/57.08	Derived: hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),hAPP(int,nat,number_number_of(nat),B))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),hAPP(int,nat,number_number_of(nat),B))) = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,B))).  [resolve(5775,a,5757,a)].
57.25/57.08	Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),hAPP(int,nat,number_number_of(nat),B))),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),hAPP(int,nat,number_number_of(nat),B))) = hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,B))).  [resolve(5775,a,5764,a)].
57.25/57.08	Derived: hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),hAPP(int,nat,number_number_of(nat),B))),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),hAPP(int,nat,number_number_of(nat),B))) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,B))).  [resolve(5775,a,5773,a)].
57.25/57.08	5776 -number(A) | -monoid_mult(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),B)),hAPP(int,A,number_number_of(A),B)) = hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),hAPP(int,A,number_number_of(A),B)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) # label(fact_168_power2__eq__square__number__of) # label(axiom).  [clausify(4244)].
57.25/57.08	5777 -monoid_mult(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),one_one(A)),B) = ti(A,B) # label(fact_802_mult__1__left) # label(axiom).  [clausify(4305)].
57.25/57.08	Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),one_one(nat)),A) = ti(nat,A).  [resolve(5777,a,5752,a)].
57.25/57.08	Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),one_one(code_code_numeral)),A) = ti(code_code_numeral,A).  [resolve(5777,a,5755,a)].
57.25/57.08	Derived: hAPP(real,real,hAPP(real,fun(real,real),times_times(real),one_one(real)),A) = ti(real,A).  [resolve(5777,a,5757,a)].
57.25/57.08	Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),one_one(rat)),A) = ti(rat,A).  [resolve(5777,a,5764,a)].
57.44/57.28	Derived: hAPP(int,int,hAPP(int,fun(int,int),times_times(int),one_one(int)),A) = ti(int,A).  [resolve(5777,a,5773,a)].
57.44/57.28	5778 -monoid_mult(A) | hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),one_one(nat)) = ti(A,B) # label(fact_351_power__one__right) # label(axiom).  [clausify(4378)].
57.44/57.28	Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),one_one(nat)) = ti(nat,A).  [resolve(5778,a,5752,a)].
57.44/57.28	Derived: hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A),one_one(nat)) = ti(code_code_numeral,A).  [resolve(5778,a,5755,a)].
57.44/57.28	Derived: hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),one_one(nat)) = ti(real,A).  [resolve(5778,a,5757,a)].
57.44/57.28	Derived: hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),one_one(nat)) = ti(rat,A).  [resolve(5778,a,5764,a)].
57.44/57.28	Derived: hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),one_one(nat)) = ti(int,A).  [resolve(5778,a,5773,a)].
57.44/57.28	5779 -monoid_mult(A) | -number(A) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),B))) | one_one(A) = hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),hAPP(int,A,number_number_of(A),C)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,B))) # label(fact_3905_power__number__of__odd__number__of) # label(axiom).  [clausify(4380)].
57.44/57.28	5780 -monoid_mult(A) | -number(A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),B))) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),C)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),hAPP(int,A,number_number_of(A),C)),hAPP(int,nat,number_number_of(nat),B)))),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),hAPP(int,A,number_number_of(A),C)),hAPP(int,nat,number_number_of(nat),B))) = hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),hAPP(int,A,number_number_of(A),C)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,B))) # label(fact_3905_power__number__of__odd__number__of) # label(axiom).  [clausify(4380)].
57.44/57.28	5781 -monoid_mult(A) | hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C)),D) = hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),C),D)) # label(fact_349_power__mult) # label(axiom).  [clausify(4419)].
57.44/57.28	Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),B)),C) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),C)).  [resolve(5781,a,5752,a)].
57.44/57.28	Derived: hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A),B)),C) = hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),C)).  [resolve(5781,a,5755,a)].
57.44/57.28	Derived: hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),B)),C) = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),C)).  [resolve(5781,a,5757,a)].
57.44/57.28	Derived: hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),B)),C) = hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),C)).  [resolve(5781,a,5764,a)].
57.44/57.28	Derived: hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),B)),C) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),C)).  [resolve(5781,a,5773,a)].
57.44/57.28	5782 monoid_mult(complex) # label(arity_Complex_Ocomplex___Groups_Omonoid__mult) # label(axiom).  [assumption].
57.44/57.28	Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),A),B)),A) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),A),B)).  [resolve(5782,a,5753,a)].
57.44/57.29	Derived: -linordered_ring(complex) | -hBOOL(hAPP(nat,bool,even_odd_even(nat),A)) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less_eq(complex),zero_zero(complex)),hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),B),A))).  [resolve(5782,a,5754,b)].
57.44/57.29	Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),A),B)),hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),A),C)) = hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),C)).  [resolve(5782,a,5756,a)].
57.44/57.29	Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),A) = hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))).  [resolve(5782,a,5758,a)].
57.44/57.29	Derived: -comm_ring(complex) | hAPP(fun(nat,bool),complex,hAPP(fun(nat,complex),fun(fun(nat,bool),complex),big_co1399186613setsum(nat,complex),hAPP(fun(nat,complex),fun(nat,complex),hAPP(fun(nat,fun(complex,complex)),fun(fun(nat,complex),fun(nat,complex)),combs(nat,complex,complex),hAPP(fun(nat,complex),fun(nat,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(nat,complex),fun(nat,fun(complex,complex))),combb(complex,fun(complex,complex),nat),times_times(complex)),hAPP(complex,fun(nat,complex),power_power(complex),A))),hAPP(fun(nat,complex),fun(nat,complex),hAPP(fun(nat,fun(complex,complex)),fun(fun(nat,complex),fun(nat,complex)),combs(nat,complex,complex),hAPP(fun(nat,complex),fun(nat,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(nat,complex),fun(nat,fun(complex,complex))),combb(complex,fun(complex,complex),nat),minus_minus(complex)),hAPP(fun(nat,nat),fun(nat,complex),hAPP(fun(nat,complex),fun(fun(nat,nat),fun(nat,complex)),combb(nat,complex,nat),hAPP(complex,fun(nat,complex),power_power(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),A),B))),hAPP(nat,fun(nat,nat),minus_minus(nat),C)))),hAPP(fun(nat,nat),fun(nat,complex),hAPP(fun(nat,complex),fun(fun(nat,nat),fun(nat,complex)),combb(nat,complex,nat),hAPP(complex,fun(nat,complex),power_power(complex),A)),hAPP(nat,fun(nat,nat),minus_minus(nat),C))))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),C)) = hAPP(fun(nat,bool),complex,hAPP(fun(nat,complex),fun(fun(nat,bool),complex),big_co1399186613setsum(nat,complex),hAPP(complex,fun(nat,complex),hAPP(fun(nat,fun(complex,complex)),fun(complex,fun(nat,complex)),combc(nat,complex,complex),hAPP(fun(nat,complex),fun(nat,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(nat,complex),fun(nat,fun(complex,complex))),combb(complex,fun(complex,complex),nat),minus_minus(complex)),hAPP(fun(nat,complex),fun(nat,complex),hAPP(fun(nat,fun(complex,complex)),fun(fun(nat,complex),fun(nat,complex)),combs(nat,complex,complex),hAPP(fun(nat,complex),fun(nat,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(nat,complex),fun(nat,fun(complex,complex))),combb(complex,fun(complex,complex),nat),times_times(complex)),hAPP(fun(nat,nat),fun(nat,complex),hAPP(fun(nat,complex),fun(fun(nat,nat),fun(nat,complex)),combb(nat,complex,nat),hAPP(complex,fun(nat,complex),power_power(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),A),B))),hAPP(nat,fun(nat,nat),minus_minus(nat),C)))),hAPP(complex,fun(nat,complex),power_power(complex),A)))),hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),A),C))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),C)).  [resolve(5782,a,5759,a)].
57.44/57.29	Derived: -number(complex) | hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),hAPP(int,complex,number_number_of(complex),A)),hAPP(int,nat,number_number_of(nat),B))),hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),hAPP(int,complex,number_number_of(complex),A)),hAPP(int,nat,number_number_of(nat),B))) = hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),hAPP(int,complex,number_number_of(complex),A)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,B))).  [resolve(5782,a,5760,a)].
57.44/57.29	Derived: -comm_semiring_0(complex) | hAPP(fun(nat,bool),complex,hAPP(fun(nat,complex),fun(fun(nat,bool),complex),big_co1399186613setsum(nat,complex),hAPP(fun(nat,complex),fun(nat,complex),hAPP(fun(nat,fun(complex,complex)),fun(fun(nat,complex),fun(nat,complex)),combs(nat,complex,complex),hAPP(fun(nat,complex),fun(nat,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(nat,complex),fun(nat,fun(complex,complex))),combb(complex,fun(complex,complex),nat),times_times(complex)),hAPP(complex,fun(nat,complex),power_power(complex),A))),hAPP(fun(nat,nat),fun(nat,complex),hAPP(fun(nat,complex),fun(fun(nat,nat),fun(nat,complex)),combb(nat,complex,nat),hAPP(complex,fun(nat,complex),power_power(complex),B)),hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,C))))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,suc,C))) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),B),hAPP(fun(nat,bool),complex,hAPP(fun(nat,complex),fun(fun(nat,bool),complex),big_co1399186613setsum(nat,complex),hAPP(fun(nat,complex),fun(nat,complex),hAPP(fun(nat,fun(complex,complex)),fun(fun(nat,complex),fun(nat,complex)),combs(nat,complex,complex),hAPP(fun(nat,complex),fun(nat,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(nat,complex),fun(nat,fun(complex,complex))),combb(complex,fun(complex,complex),nat),times_times(complex)),hAPP(complex,fun(nat,complex),power_power(complex),A))),hAPP(fun(nat,nat),fun(nat,complex),hAPP(fun(nat,complex),fun(fun(nat,nat),fun(nat,complex)),combb(nat,complex,nat),hAPP(complex,fun(nat,complex),power_power(complex),B)),hAPP(nat,fun(nat,nat),minus_minus(nat),C)))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,suc,C)))).  [resolve(5782,a,5761,a)].
57.44/57.29	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A)) | hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),A),one_one(nat)))),B) = hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),B),A).  [resolve(5782,a,5762,a)].
57.44/57.29	Derived: hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),A),B)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),B)).  [resolve(5782,a,5763,a)].
57.44/57.29	Derived: -comm_ring(complex) | hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),A),hAPP(nat,nat,suc,B))),hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),C),hAPP(nat,nat,suc,B))) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),A),C)),hAPP(fun(nat,bool),complex,hAPP(fun(nat,complex),fun(fun(nat,bool),complex),big_co1399186613setsum(nat,complex),hAPP(fun(nat,complex),fun(nat,complex),hAPP(fun(nat,fun(complex,complex)),fun(fun(nat,complex),fun(nat,complex)),combs(nat,complex,complex),hAPP(fun(nat,complex),fun(nat,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(nat,complex),fun(nat,fun(complex,complex))),combb(complex,fun(complex,complex),nat),times_times(complex)),hAPP(complex,fun(nat,complex),power_power(complex),A))),hAPP(fun(nat,nat),fun(nat,complex),hAPP(fun(nat,complex),fun(fun(nat,nat),fun(nat,complex)),combb(nat,complex,nat),hAPP(complex,fun(nat,complex),power_power(complex),C)),hAPP(nat,fun(nat,nat),minus_minus(nat),B)))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,suc,B)))).  [resolve(5782,a,5765,b)].
57.44/57.29	Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),A))) | one_one(complex) = hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,A))).  [resolve(5782,a,5766,a)].
57.44/57.29	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),A))) | hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),B),hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),B),hAPP(int,nat,number_number_of(nat),A)))),hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),B),hAPP(int,nat,number_number_of(nat),A))) = hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,A))).  [resolve(5782,a,5767,a)].
57.44/57.29	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),C),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),B),A))),C) = hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),C),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,B)),A)).  [resolve(5782,a,5768,a)].
57.44/57.29	Derived: one_one(complex) = hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),one_one(complex)),A).  [resolve(5782,a,5769,a)].
57.44/57.29	Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),one_one(complex)) = ti(complex,A).  [resolve(5782,a,5770,a)].
57.44/57.29	Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),A),B)),A) = hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),A),hAPP(nat,nat,suc,B)).  [resolve(5782,a,5771,a)].
57.44/57.29	Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),A)),A) = hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,hAPP(int,int,bit1,pls)))).  [resolve(5782,a,5772,a)].
57.44/57.29	Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),A),B)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) = hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),A),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),B))).  [resolve(5782,a,5774,a)].
57.44/57.29	Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),A),hAPP(int,nat,number_number_of(nat),B))),hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),A),hAPP(int,nat,number_number_of(nat),B))) = hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,B))).  [resolve(5782,a,5775,a)].
57.44/57.29	Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),one_one(complex)),A) = ti(complex,A).  [resolve(5782,a,5777,a)].
57.65/57.49	Derived: hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),A),one_one(nat)) = ti(complex,A).  [resolve(5782,a,5778,a)].
57.65/57.49	Derived: hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),A),B)),C) = hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),C)).  [resolve(5782,a,5781,a)].
57.65/57.49	5783 monoid_mult(quickcheck_code_int) # label(arity_Quickcheck__Narrowing_Ocode__int___Groups_Omonoid__mult) # label(axiom).  [assumption].
57.65/57.49	Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A),B)),A) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A),B)).  [resolve(5783,a,5753,a)].
57.65/57.49	Derived: -linordered_ring(quickcheck_code_int) | -hBOOL(hAPP(nat,bool,even_odd_even(nat),A)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),zero_zero(quickcheck_code_int)),hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),B),A))).  [resolve(5783,a,5754,b)].
57.65/57.49	Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A),B)),hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A),C)) = hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),C)).  [resolve(5783,a,5756,a)].
57.65/57.49	Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),A) = hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))).  [resolve(5783,a,5758,a)].
57.65/57.49	Derived: -comm_ring(quickcheck_code_int) | hAPP(fun(nat,bool),quickcheck_code_int,hAPP(fun(nat,quickcheck_code_int),fun(fun(nat,bool),quickcheck_code_int),big_co1399186613setsum(nat,quickcheck_code_int),hAPP(fun(nat,quickcheck_code_int),fun(nat,quickcheck_code_int),hAPP(fun(nat,fun(quickcheck_code_int,quickcheck_code_int)),fun(fun(nat,quickcheck_code_int),fun(nat,quickcheck_code_int)),combs(nat,quickcheck_code_int,quickcheck_code_int),hAPP(fun(nat,quickcheck_code_int),fun(nat,fun(quickcheck_code_int,quickcheck_code_int)),hAPP(fun(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int)),fun(fun(nat,quickcheck_code_int),fun(nat,fun(quickcheck_code_int,quickcheck_code_int))),combb(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),nat),times_times(quickcheck_code_int)),hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A))),hAPP(fun(nat,quickcheck_code_int),fun(nat,quickcheck_code_int),hAPP(fun(nat,fun(quickcheck_code_int,quickcheck_code_int)),fun(fun(nat,quickcheck_code_int),fun(nat,quickcheck_code_int)),combs(nat,quickcheck_code_int,quickcheck_code_int),hAPP(fun(nat,quickcheck_code_int),fun(nat,fun(quickcheck_code_int,quickcheck_code_int)),hAPP(fun(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int)),fun(fun(nat,quickcheck_code_int),fun(nat,fun(quickcheck_code_int,quickcheck_code_int))),combb(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),nat),minus_minus(quickcheck_code_int)),hAPP(fun(nat,nat),fun(nat,quickcheck_code_int),hAPP(fun(nat,quickcheck_code_int),fun(fun(nat,nat),fun(nat,quickcheck_code_int)),combb(nat,quickcheck_code_int,nat),hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),A),B))),hAPP(nat,fun(nat,nat),minus_minus(nat),C)))),hAPP(fun(nat,nat),fun(nat,quickcheck_code_int),hAPP(fun(nat,quickcheck_code_int),fun(fun(nat,nat),fun(nat,quickcheck_code_int)),combb(nat,quickcheck_code_int,nat),hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A)),hAPP(nat,fun(nat,nat),minus_minus(nat),C))))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),C)) = hAPP(fun(nat,bool),quickcheck_code_int,hAPP(fun(nat,quickcheck_code_int),fun(fun(nat,bool),quickcheck_code_int),big_co1399186613setsum(nat,quickcheck_code_int),hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),hAPP(fun(nat,fun(quickcheck_code_int,quickcheck_code_int)),fun(quickcheck_code_int,fun(nat,quickcheck_code_int)),combc(nat,quickcheck_code_int,quickcheck_code_int),hAPP(fun(nat,quickcheck_code_int),fun(nat,fun(quickcheck_code_int,quickcheck_code_int)),hAPP(fun(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int)),fun(fun(nat,quickcheck_code_int),fun(nat,fun(quickcheck_code_int,quickcheck_code_int))),combb(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),nat),minus_minus(quickcheck_code_int)),hAPP(fun(nat,quickcheck_code_int),fun(nat,quickcheck_code_int),hAPP(fun(nat,fun(quickcheck_code_int,quickcheck_code_int)),fun(fun(nat,quickcheck_code_int),fun(nat,quickcheck_code_int)),combs(nat,quickcheck_code_int,quickcheck_code_int),hAPP(fun(nat,quickcheck_code_int),fun(nat,fun(quickcheck_code_int,quickcheck_code_int)),hAPP(fun(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int)),fun(fun(nat,quickcheck_code_int),fun(nat,fun(quickcheck_code_int,quickcheck_code_int))),combb(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),nat),times_times(quickcheck_code_int)),hAPP(fun(nat,nat),fun(nat,quickcheck_code_int),hAPP(fun(nat,quickcheck_code_int),fun(fun(nat,nat),fun(nat,quickcheck_code_int)),combb(nat,quickcheck_code_int,nat),hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),A),B))),hAPP(nat,fun(nat,nat),minus_minus(nat),C)))),hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A)))),hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A),C))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),C)).  [resolve(5783,a,5759,a)].
57.65/57.49	Derived: -number(quickcheck_code_int) | hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),A)),hAPP(int,nat,number_number_of(nat),B))),hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),A)),hAPP(int,nat,number_number_of(nat),B))) = hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),A)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,B))).  [resolve(5783,a,5760,a)].
57.65/57.49	Derived: -comm_semiring_0(quickcheck_code_int) | hAPP(fun(nat,bool),quickcheck_code_int,hAPP(fun(nat,quickcheck_code_int),fun(fun(nat,bool),quickcheck_code_int),big_co1399186613setsum(nat,quickcheck_code_int),hAPP(fun(nat,quickcheck_code_int),fun(nat,quickcheck_code_int),hAPP(fun(nat,fun(quickcheck_code_int,quickcheck_code_int)),fun(fun(nat,quickcheck_code_int),fun(nat,quickcheck_code_int)),combs(nat,quickcheck_code_int,quickcheck_code_int),hAPP(fun(nat,quickcheck_code_int),fun(nat,fun(quickcheck_code_int,quickcheck_code_int)),hAPP(fun(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int)),fun(fun(nat,quickcheck_code_int),fun(nat,fun(quickcheck_code_int,quickcheck_code_int))),combb(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),nat),times_times(quickcheck_code_int)),hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A))),hAPP(fun(nat,nat),fun(nat,quickcheck_code_int),hAPP(fun(nat,quickcheck_code_int),fun(fun(nat,nat),fun(nat,quickcheck_code_int)),combb(nat,quickcheck_code_int,nat),hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),B)),hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,C))))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,suc,C))) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),B),hAPP(fun(nat,bool),quickcheck_code_int,hAPP(fun(nat,quickcheck_code_int),fun(fun(nat,bool),quickcheck_code_int),big_co1399186613setsum(nat,quickcheck_code_int),hAPP(fun(nat,quickcheck_code_int),fun(nat,quickcheck_code_int),hAPP(fun(nat,fun(quickcheck_code_int,quickcheck_code_int)),fun(fun(nat,quickcheck_code_int),fun(nat,quickcheck_code_int)),combs(nat,quickcheck_code_int,quickcheck_code_int),hAPP(fun(nat,quickcheck_code_int),fun(nat,fun(quickcheck_code_int,quickcheck_code_int)),hAPP(fun(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int)),fun(fun(nat,quickcheck_code_int),fun(nat,fun(quickcheck_code_int,quickcheck_code_int))),combb(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),nat),times_times(quickcheck_code_int)),hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A))),hAPP(fun(nat,nat),fun(nat,quickcheck_code_int),hAPP(fun(nat,quickcheck_code_int),fun(fun(nat,nat),fun(nat,quickcheck_code_int)),combb(nat,quickcheck_code_int,nat),hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),B)),hAPP(nat,fun(nat,nat),minus_minus(nat),C)))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,suc,C)))).  [resolve(5783,a,5761,a)].
57.65/57.49	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A)) | hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),A),one_one(nat)))),B) = hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),B),A).  [resolve(5783,a,5762,a)].
57.65/57.49	Derived: hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A),B)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),B)).  [resolve(5783,a,5763,a)].
57.65/57.49	Derived: -comm_ring(quickcheck_code_int) | hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),minus_minus(quickcheck_code_int),hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A),hAPP(nat,nat,suc,B))),hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),C),hAPP(nat,nat,suc,B))) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),minus_minus(quickcheck_code_int),A),C)),hAPP(fun(nat,bool),quickcheck_code_int,hAPP(fun(nat,quickcheck_code_int),fun(fun(nat,bool),quickcheck_code_int),big_co1399186613setsum(nat,quickcheck_code_int),hAPP(fun(nat,quickcheck_code_int),fun(nat,quickcheck_code_int),hAPP(fun(nat,fun(quickcheck_code_int,quickcheck_code_int)),fun(fun(nat,quickcheck_code_int),fun(nat,quickcheck_code_int)),combs(nat,quickcheck_code_int,quickcheck_code_int),hAPP(fun(nat,quickcheck_code_int),fun(nat,fun(quickcheck_code_int,quickcheck_code_int)),hAPP(fun(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int)),fun(fun(nat,quickcheck_code_int),fun(nat,fun(quickcheck_code_int,quickcheck_code_int))),combb(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),nat),times_times(quickcheck_code_int)),hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A))),hAPP(fun(nat,nat),fun(nat,quickcheck_code_int),hAPP(fun(nat,quickcheck_code_int),fun(fun(nat,nat),fun(nat,quickcheck_code_int)),combb(nat,quickcheck_code_int,nat),hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),C)),hAPP(nat,fun(nat,nat),minus_minus(nat),B)))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,suc,B)))).  [resolve(5783,a,5765,b)].
57.65/57.50	Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),A))) | one_one(quickcheck_code_int) = hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,A))).  [resolve(5783,a,5766,a)].
57.65/57.50	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),A))) | hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),B),hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),B),hAPP(int,nat,number_number_of(nat),A)))),hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),B),hAPP(int,nat,number_number_of(nat),A))) = hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,A))).  [resolve(5783,a,5767,a)].
57.65/57.50	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),C),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),B),A))),C) = hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),C),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,B)),A)).  [resolve(5783,a,5768,a)].
57.65/57.50	Derived: one_one(quickcheck_code_int) = hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),one_one(quickcheck_code_int)),A).  [resolve(5783,a,5769,a)].
57.65/57.50	Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),one_one(quickcheck_code_int)) = ti(quickcheck_code_int,A).  [resolve(5783,a,5770,a)].
61.77/61.63	Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A),B)),A) = hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A),hAPP(nat,nat,suc,B)).  [resolve(5783,a,5771,a)].
61.77/61.63	Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),A)),A) = hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,hAPP(int,int,bit1,pls)))).  [resolve(5783,a,5772,a)].
61.77/61.63	Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A),B)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) = hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),B))).  [resolve(5783,a,5774,a)].
61.77/61.63	Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A),hAPP(int,nat,number_number_of(nat),B))),hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A),hAPP(int,nat,number_number_of(nat),B))) = hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,B))).  [resolve(5783,a,5775,a)].
61.77/61.63	Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),one_one(quickcheck_code_int)),A) = ti(quickcheck_code_int,A).  [resolve(5783,a,5777,a)].
61.77/61.63	Derived: hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A),one_one(nat)) = ti(quickcheck_code_int,A).  [resolve(5783,a,5778,a)].
61.77/61.63	Derived: hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A),B)),C) = hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),C)).  [resolve(5783,a,5781,a)].
61.77/61.63	5784 sgn_div_norm(real) # label(arity_RealDef_Oreal___RealVector_Osgn__div__norm) # label(axiom).  [assumption].
61.77/61.63	5785 -sgn_div_norm(A) | sgn_sgn(A) = ti(fun(A,A),sgn_sgn(A)) # label(tsy_c_Groups_Osgn__class_Osgn_0_res) # label(axiom).  [clausify(33)].
61.77/61.63	5786 -sgn_div_norm(A) | norm_norm(A) = ti(fun(A,real),norm_norm(A)) # label(tsy_c_RealVector_Onorm__class_Onorm_0_res) # label(axiom).  [clausify(604)].
61.77/61.63	5787 -sgn_div_norm(A) | hAPP(A,A,sgn_sgn(A),B) = hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),hAPP(real,real,inverse_inverse(real),hAPP(A,real,norm_norm(A),B))),B) # label(fact_4725_sgn__div__norm) # label(axiom).  [clausify(2725)].
61.77/61.63	5788 -sgn_div_norm(A) | scaleR_scaleR(A) = ti(fun(real,fun(A,A)),scaleR_scaleR(A)) # label(tsy_c_RealVector_OscaleR__class_OscaleR_0_res) # label(axiom).  [clausify(3325)].
65.10/64.93	Derived: sgn_sgn(real) = ti(fun(real,real),sgn_sgn(real)).  [resolve(5784,a,5785,a)].
65.10/64.93	Derived: norm_norm(real) = ti(fun(real,real),norm_norm(real)).  [resolve(5784,a,5786,a)].
65.10/64.93	Derived: hAPP(real,real,sgn_sgn(real),A) = hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),hAPP(real,real,inverse_inverse(real),hAPP(real,real,norm_norm(real),A))),A).  [resolve(5784,a,5787,a)].
65.10/64.93	5789 sgn_div_norm(complex) # label(arity_Complex_Ocomplex___RealVector_Osgn__div__norm) # label(axiom).  [assumption].
65.10/64.93	Derived: sgn_sgn(complex) = ti(fun(complex,complex),sgn_sgn(complex)).  [resolve(5789,a,5785,a)].
65.10/64.93	Derived: norm_norm(complex) = ti(fun(complex,real),norm_norm(complex)).  [resolve(5789,a,5786,a)].
65.10/64.93	Derived: hAPP(complex,complex,sgn_sgn(complex),A) = hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),hAPP(real,real,inverse_inverse(real),hAPP(complex,real,norm_norm(complex),A))),A).  [resolve(5789,a,5787,a)].
65.10/64.93	5790 -linordered_idom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),C),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),zero_zero(A))) | zero_zero(A) = ti(A,C) # label(fact_106_sum__power2__le__zero__iff) # label(axiom).  [clausify(50)].
65.10/64.93	5791 linordered_idom(real) # label(arity_RealDef_Oreal___Rings_Olinordered__idom) # label(axiom).  [assumption].
65.10/64.93	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),zero_zero(real))) | zero_zero(real) = ti(real,B).  [resolve(5790,a,5791,a)].
65.10/64.93	5792 -linordered_idom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),C),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),zero_zero(A))) | zero_zero(A) = ti(A,B) # label(fact_106_sum__power2__le__zero__iff) # label(axiom).  [clausify(50)].
65.10/64.93	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),zero_zero(real))) | zero_zero(real) = ti(real,A).  [resolve(5792,a,5791,a)].
65.10/64.93	5793 -linordered_idom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),C),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),zero_zero(A))) | zero_zero(A) != ti(A,C) | zero_zero(A) != ti(A,B) # label(fact_106_sum__power2__le__zero__iff) # label(axiom).  [clausify(50)].
65.10/64.93	Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),zero_zero(real))) | zero_zero(real) != ti(real,B) | zero_zero(real) != ti(real,A).  [resolve(5793,a,5791,a)].
65.12/64.96	5794 -linordered_idom(A) | hAPP(A,A,abs_abs(A),B) != hAPP(A,A,abs_abs(A),C) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),C),B)) # label(fact_1847_dvd__if__abs__eq) # label(axiom).  [clausify(100)].
65.12/64.96	Derived: hAPP(real,real,abs_abs(real),A) != hAPP(real,real,abs_abs(real),B) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),dvd_dvd(real),B),A)).  [resolve(5794,a,5791,a)].
65.12/64.96	5795 -linordered_idom(A) | hAPP(A,A,abs_abs(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C)) = hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),hAPP(A,A,abs_abs(A),B)),C) # label(fact_1844_power__abs) # label(axiom).  [clausify(179)].
65.12/64.96	Derived: hAPP(real,real,abs_abs(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),B)) = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,abs_abs(real),A)),B).  [resolve(5795,a,5791,a)].
65.12/64.96	5796 -linordered_idom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),C))))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) # label(fact_1470_odd__0__le__power__imp__0__le) # label(axiom).  [clausify(258)].
65.12/64.96	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),B))))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A)).  [resolve(5796,a,5791,a)].
65.12/64.96	5797 -linordered_idom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C))) | hBOOL(hAPP(nat,bool,even_odd_even(nat),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) # label(fact_2434_zero__le__power__iff) # label(axiom).  [clausify(297)].
65.12/64.96	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),B))) | hBOOL(hAPP(nat,bool,even_odd_even(nat),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A)).  [resolve(5797,a,5791,a)].
65.12/64.96	5798 -linordered_idom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C))) | -hBOOL(hAPP(nat,bool,even_odd_even(nat),C)) # label(fact_2434_zero__le__power__iff) # label(axiom).  [clausify(297)].
65.12/64.96	Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),B))) | -hBOOL(hAPP(nat,bool,even_odd_even(nat),B)).  [resolve(5798,a,5791,a)].
65.12/64.96	5799 -linordered_idom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) # label(fact_2434_zero__le__power__iff) # label(axiom).  [clausify(297)].
65.12/64.96	Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),B))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A)).  [resolve(5799,a,5791,a)].
65.12/64.96	5800 -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_1866_abs__mult__less) # label(axiom).  [clausify(348)].
65.12/64.96	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,abs_abs(real),A)),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,abs_abs(real),C)),D)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,abs_abs(real),A)),hAPP(real,real,abs_abs(real),C))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),D))).  [resolve(5800,a,5791,a)].
65.12/65.00	5801 linordered_idom(rat) # label(arity_Rat_Orat___Rings_Olinordered__idom) # label(axiom).  [assumption].
65.12/65.00	Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),zero_zero(rat))) | zero_zero(rat) = ti(rat,B).  [resolve(5801,a,5790,a)].
65.12/65.00	Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),zero_zero(rat))) | zero_zero(rat) = ti(rat,A).  [resolve(5801,a,5792,a)].
65.12/65.00	Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),zero_zero(rat))) | zero_zero(rat) != ti(rat,B) | zero_zero(rat) != ti(rat,A).  [resolve(5801,a,5793,a)].
65.12/65.00	Derived: hAPP(rat,rat,abs_abs(rat),A) != hAPP(rat,rat,abs_abs(rat),B) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),dvd_dvd(rat),B),A)).  [resolve(5801,a,5794,a)].
65.12/65.00	Derived: hAPP(rat,rat,abs_abs(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),B)) = hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),hAPP(rat,rat,abs_abs(rat),A)),B).  [resolve(5801,a,5795,a)].
65.12/65.00	Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),B))))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),A)).  [resolve(5801,a,5796,a)].
65.12/65.00	Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),B))) | hBOOL(hAPP(nat,bool,even_odd_even(nat),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),A)).  [resolve(5801,a,5797,a)].
65.12/65.00	Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),B))) | -hBOOL(hAPP(nat,bool,even_odd_even(nat),B)).  [resolve(5801,a,5798,a)].
65.12/65.00	Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),B))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),A)).  [resolve(5801,a,5799,a)].
65.12/65.00	Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,abs_abs(rat),A)),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,abs_abs(rat),C)),D)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(rat,rat,abs_abs(rat),A)),hAPP(rat,rat,abs_abs(rat),C))),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),B),D))).  [resolve(5801,a,5800,a)].
65.12/65.00	5802 -linordered_idom(A) | -number_ring(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(nat,A,semiring_1_of_nat(A),B)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),hAPP(int,A,number_number_of(A),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),B))) # label(fact_1445_of__nat__less__two__power) # label(axiom).  [clausify(493)].
65.20/65.07	Derived: -number_ring(real) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(nat,real,semiring_1_of_nat(real),A)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),A))).  [resolve(5802,a,5791,a)].
65.20/65.07	Derived: -number_ring(rat) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(nat,rat,semiring_1_of_nat(rat),A)),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),hAPP(int,rat,number_number_of(rat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),A))).  [resolve(5802,a,5801,a)].
65.20/65.07	5803 -number_ring(A) | -linordered_idom(A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(int,A,number_number_of(A),B))) # label(fact_48_le__special_I1_J) # label(axiom).  [clausify(580)].
65.20/65.07	Derived: -number_ring(real) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),A)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(int,real,number_number_of(real),A))).  [resolve(5803,b,5791,a)].
65.20/65.07	Derived: -number_ring(rat) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),A)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),hAPP(int,rat,number_number_of(rat),A))).  [resolve(5803,b,5801,a)].
65.20/65.07	5804 -number_ring(A) | -linordered_idom(A) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(int,A,number_number_of(A),B))) # label(fact_48_le__special_I1_J) # label(axiom).  [clausify(580)].
65.20/65.07	Derived: -number_ring(real) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(int,real,number_number_of(real),A))).  [resolve(5804,b,5791,a)].
65.20/65.07	Derived: -number_ring(rat) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),hAPP(int,rat,number_number_of(rat),A))).  [resolve(5804,b,5801,a)].
65.20/65.07	5805 -linordered_idom(A) | -number_ring(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_27_le__number__of) # label(axiom).  [clausify(699)].
65.20/65.07	Derived: -number_ring(real) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,number_number_of(real),A)),hAPP(int,real,number_number_of(real),B))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)).  [resolve(5805,a,5791,a)].
65.20/65.07	Derived: -number_ring(rat) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(int,rat,number_number_of(rat),A)),hAPP(int,rat,number_number_of(rat),B))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)).  [resolve(5805,a,5801,a)].
65.20/65.07	5806 -linordered_idom(A) | -number_ring(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_27_le__number__of) # label(axiom).  [clausify(699)].
65.20/65.07	Derived: -number_ring(real) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,number_number_of(real),A)),hAPP(int,real,number_number_of(real),B))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)).  [resolve(5806,a,5791,a)].
65.20/65.07	Derived: -number_ring(rat) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(int,rat,number_number_of(rat),A)),hAPP(int,rat,number_number_of(rat),B))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)).  [resolve(5806,a,5801,a)].
65.20/65.07	5807 -linordered_idom(A) | hBOOL(hAPP(nat,bool,even_odd_even(nat),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),C),B)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),D),B))) # label(fact_2421_power__mono__odd) # label(axiom).  [clausify(800)].
65.26/65.12	Derived: hBOOL(hAPP(nat,bool,even_odd_even(nat),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),B),A)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),C),A))).  [resolve(5807,a,5791,a)].
65.26/65.12	Derived: hBOOL(hAPP(nat,bool,even_odd_even(nat),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),B),C)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),B),A)),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),C),A))).  [resolve(5807,a,5801,a)].
65.26/65.12	5808 -linordered_idom(A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),zero_zero(int))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(int,A,ring_1_of_int(A),B)),zero_zero(A))) # label(fact_3603_of__int__le__0__iff) # label(axiom).  [clausify(823)].
65.26/65.12	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),zero_zero(int))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,ring_1_of_int(real),A)),zero_zero(real))).  [resolve(5808,a,5791,a)].
65.26/65.12	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),zero_zero(int))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(int,rat,ring_1_of_int(rat),A)),zero_zero(rat))).  [resolve(5808,a,5801,a)].
65.26/65.12	5809 -linordered_idom(A) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),zero_zero(int))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(int,A,ring_1_of_int(A),B)),zero_zero(A))) # label(fact_3603_of__int__le__0__iff) # label(axiom).  [clausify(823)].
65.26/65.12	Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),zero_zero(int))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,ring_1_of_int(real),A)),zero_zero(real))).  [resolve(5809,a,5791,a)].
65.26/65.12	Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),zero_zero(int))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(int,rat,ring_1_of_int(rat),A)),zero_zero(rat))).  [resolve(5809,a,5801,a)].
65.26/65.12	5810 -linordered_idom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),C),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),zero_zero(A))) # label(fact_7_not__sum__power2__lt__zero) # label(axiom).  [clausify(847)].
65.26/65.12	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),zero_zero(real))).  [resolve(5810,a,5791,a)].
65.26/65.12	Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),zero_zero(rat))).  [resolve(5810,a,5801,a)].
65.26/65.12	5811 -linordered_idom(A) | one_one(A) = hAPP(A,A,abs_abs(A),one_one(A)) # label(fact_1853_abs__one) # label(axiom).  [clausify(905)].
65.26/65.12	Derived: one_one(real) = hAPP(real,real,abs_abs(real),one_one(real)).  [resolve(5811,a,5791,a)].
65.26/65.12	Derived: one_one(rat) = hAPP(rat,rat,abs_abs(rat),one_one(rat)).  [resolve(5811,a,5801,a)].
65.36/65.23	5812 -linordered_idom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,ring_1_of_int(A),B)),zero_zero(A))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),zero_zero(int))) # label(fact_3601_of__int__less__0__iff) # label(axiom).  [clausify(960)].
65.36/65.23	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,ring_1_of_int(real),A)),zero_zero(real))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),zero_zero(int))).  [resolve(5812,a,5791,a)].
65.36/65.23	Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(int,rat,ring_1_of_int(rat),A)),zero_zero(rat))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),zero_zero(int))).  [resolve(5812,a,5801,a)].
65.36/65.23	5813 -linordered_idom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,ring_1_of_int(A),B)),zero_zero(A))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),zero_zero(int))) # label(fact_3601_of__int__less__0__iff) # label(axiom).  [clausify(960)].
65.36/65.23	Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,ring_1_of_int(real),A)),zero_zero(real))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),zero_zero(int))).  [resolve(5813,a,5791,a)].
65.36/65.23	Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(int,rat,ring_1_of_int(rat),A)),zero_zero(rat))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),zero_zero(int))).  [resolve(5813,a,5801,a)].
65.36/65.23	5814 -linordered_idom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),zero_zero(A))) # label(fact_10_power2__less__0) # label(axiom).  [clausify(1160)].
65.36/65.23	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),zero_zero(real))).  [resolve(5814,a,5791,a)].
65.36/65.23	Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),zero_zero(rat))).  [resolve(5814,a,5801,a)].
65.36/65.23	5815 -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_437_mult__left__le__one__le) # label(axiom).  [clausify(1242)].
65.36/65.23	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),one_one(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),A)),A)).  [resolve(5815,a,5791,a)].
65.36/65.23	Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),B),one_one(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),B),A)),A)).  [resolve(5815,a,5801,a)].
65.36/65.23	5816 -linordered_idom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(int,nat,number_number_of(nat),C)))) | zero_zero(nat) = hAPP(int,nat,number_number_of(nat),C) | zero_zero(A) != ti(A,B) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) # label(fact_2464_zero__less__power__eq__number__of) # label(axiom).  [clausify(1274)].
65.36/65.23	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),hAPP(int,nat,number_number_of(nat),B)))) | zero_zero(nat) = hAPP(int,nat,number_number_of(nat),B) | zero_zero(real) != ti(real,A) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)).  [resolve(5816,a,5791,a)].
65.36/65.25	Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),hAPP(int,nat,number_number_of(nat),B)))) | zero_zero(nat) = hAPP(int,nat,number_number_of(nat),B) | zero_zero(rat) != ti(rat,A) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)).  [resolve(5816,a,5801,a)].
65.36/65.25	5817 -linordered_idom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(int,nat,number_number_of(nat),C)))) | zero_zero(nat) = hAPP(int,nat,number_number_of(nat),C) | zero_zero(A) != ti(A,B) | -hBOOL(hAPP(nat,bool,even_odd_even(nat),hAPP(int,nat,number_number_of(nat),C))) # label(fact_2464_zero__less__power__eq__number__of) # label(axiom).  [clausify(1274)].
65.36/65.25	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),hAPP(int,nat,number_number_of(nat),B)))) | zero_zero(nat) = hAPP(int,nat,number_number_of(nat),B) | zero_zero(real) != ti(real,A) | -hBOOL(hAPP(nat,bool,even_odd_even(nat),hAPP(int,nat,number_number_of(nat),B))).  [resolve(5817,a,5791,a)].
65.36/65.25	Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),hAPP(int,nat,number_number_of(nat),B)))) | zero_zero(nat) = hAPP(int,nat,number_number_of(nat),B) | zero_zero(rat) != ti(rat,A) | -hBOOL(hAPP(nat,bool,even_odd_even(nat),hAPP(int,nat,number_number_of(nat),B))).  [resolve(5817,a,5801,a)].
65.36/65.25	5818 -linordered_idom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(int,nat,number_number_of(nat),C)))) | zero_zero(nat) = hAPP(int,nat,number_number_of(nat),C) | hBOOL(hAPP(nat,bool,even_odd_even(nat),hAPP(int,nat,number_number_of(nat),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) # label(fact_2464_zero__less__power__eq__number__of) # label(axiom).  [clausify(1274)].
65.36/65.25	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),hAPP(int,nat,number_number_of(nat),B)))) | zero_zero(nat) = hAPP(int,nat,number_number_of(nat),B) | hBOOL(hAPP(nat,bool,even_odd_even(nat),hAPP(int,nat,number_number_of(nat),B))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)).  [resolve(5818,a,5791,a)].
65.36/65.25	Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),hAPP(int,nat,number_number_of(nat),B)))) | zero_zero(nat) = hAPP(int,nat,number_number_of(nat),B) | hBOOL(hAPP(nat,bool,even_odd_even(nat),hAPP(int,nat,number_number_of(nat),B))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)).  [resolve(5818,a,5801,a)].
65.36/65.25	5819 -linordered_idom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(int,nat,number_number_of(nat),C)))) | zero_zero(nat) != hAPP(int,nat,number_number_of(nat),C) # label(fact_2464_zero__less__power__eq__number__of) # label(axiom).  [clausify(1274)].
65.36/65.25	Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),hAPP(int,nat,number_number_of(nat),B)))) | zero_zero(nat) != hAPP(int,nat,number_number_of(nat),B).  [resolve(5819,a,5791,a)].
65.36/65.25	Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),hAPP(int,nat,number_number_of(nat),B)))) | zero_zero(nat) != hAPP(int,nat,number_number_of(nat),B).  [resolve(5819,a,5801,a)].
65.36/65.25	5820 -linordered_idom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(int,nat,number_number_of(nat),C)))) | zero_zero(A) = ti(A,B) | -hBOOL(hAPP(nat,bool,even_odd_even(nat),hAPP(int,nat,number_number_of(nat),C))) # label(fact_2464_zero__less__power__eq__number__of) # label(axiom).  [clausify(1274)].
65.46/65.31	Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),hAPP(int,nat,number_number_of(nat),B)))) | zero_zero(real) = ti(real,A) | -hBOOL(hAPP(nat,bool,even_odd_even(nat),hAPP(int,nat,number_number_of(nat),B))).  [resolve(5820,a,5791,a)].
65.46/65.31	Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),hAPP(int,nat,number_number_of(nat),B)))) | zero_zero(rat) = ti(rat,A) | -hBOOL(hAPP(nat,bool,even_odd_even(nat),hAPP(int,nat,number_number_of(nat),B))).  [resolve(5820,a,5801,a)].
65.46/65.31	5821 -linordered_idom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(int,nat,number_number_of(nat),C)))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | hBOOL(hAPP(nat,bool,even_odd_even(nat),hAPP(int,nat,number_number_of(nat),C))) # label(fact_2464_zero__less__power__eq__number__of) # label(axiom).  [clausify(1274)].
65.46/65.31	Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),hAPP(int,nat,number_number_of(nat),B)))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | hBOOL(hAPP(nat,bool,even_odd_even(nat),hAPP(int,nat,number_number_of(nat),B))).  [resolve(5821,a,5791,a)].
65.46/65.31	Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),hAPP(int,nat,number_number_of(nat),B)))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)) | hBOOL(hAPP(nat,bool,even_odd_even(nat),hAPP(int,nat,number_number_of(nat),B))).  [resolve(5821,a,5801,a)].
65.46/65.31	5822 -linordered_idom(A) | -hBOOL(hAPP(nat,bool,even_odd_even(nat),hAPP(int,nat,number_number_of(nat),B))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),C),hAPP(int,nat,number_number_of(nat),B)))) # label(fact_2455_zero__le__power__eq__number__of) # label(axiom).  [clausify(1313)].
65.46/65.31	5823 -linordered_idom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) | hBOOL(hAPP(nat,bool,even_odd_even(nat),hAPP(int,nat,number_number_of(nat),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(int,nat,number_number_of(nat),C)))) # label(fact_2455_zero__le__power__eq__number__of) # label(axiom).  [clausify(1313)].
65.46/65.31	5824 -linordered_idom(A) | hBOOL(hAPP(nat,bool,even_odd_even(nat),hAPP(int,nat,number_number_of(nat),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(nat,A,hAPP(A,fun(nat,A),power_power(A),C),hAPP(int,nat,number_number_of(nat),B)))) # label(fact_2455_zero__le__power__eq__number__of) # label(axiom).  [clausify(1313)].
65.46/65.31	5825 -linordered_idom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,abs_abs(A),B)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) # label(fact_2083_abs__less__iff) # label(axiom).  [clausify(1340)].
65.46/65.31	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,abs_abs(real),A)),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)).  [resolve(5825,a,5791,a)].
65.46/65.31	Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,abs_abs(rat),A)),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),B)).  [resolve(5825,a,5801,a)].
65.46/65.31	5826 -linordered_idom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,abs_abs(A),B)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,uminus_uminus(A),B)),C)) # label(fact_2083_abs__less__iff) # label(axiom).  [clausify(1340)].
65.60/65.43	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,abs_abs(real),A)),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,uminus_uminus(real),A)),B)).  [resolve(5826,a,5791,a)].
65.60/65.43	Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,abs_abs(rat),A)),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,uminus_uminus(rat),A)),B)).  [resolve(5826,a,5801,a)].
65.60/65.43	5827 -linordered_idom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,abs_abs(A),B)),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,uminus_uminus(A),B)),C)) # label(fact_2083_abs__less__iff) # label(axiom).  [clausify(1340)].
65.60/65.43	Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,abs_abs(real),A)),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,uminus_uminus(real),A)),B)).  [resolve(5827,a,5791,a)].
65.60/65.43	Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,abs_abs(rat),A)),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,uminus_uminus(rat),A)),B)).  [resolve(5827,a,5801,a)].
65.60/65.43	5828 -linordered_idom(A) | -number_ring(A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,pls)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),one_one(A)),hAPP(int,A,number_number_of(A),B))) # label(fact_60_le__special_I2_J) # label(axiom).  [clausify(1411)].
65.60/65.43	Derived: -number_ring(real) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,pls)),A)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),one_one(real)),hAPP(int,real,number_number_of(real),A))).  [resolve(5828,a,5791,a)].
65.60/65.43	Derived: -number_ring(rat) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,pls)),A)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),one_one(rat)),hAPP(int,rat,number_number_of(rat),A))).  [resolve(5828,a,5801,a)].
65.60/65.43	5829 -linordered_idom(A) | -number_ring(A) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,pls)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),one_one(A)),hAPP(int,A,number_number_of(A),B))) # label(fact_60_le__special_I2_J) # label(axiom).  [clausify(1411)].
65.60/65.43	Derived: -number_ring(real) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,pls)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),one_one(real)),hAPP(int,real,number_number_of(real),A))).  [resolve(5829,a,5791,a)].
65.60/65.43	Derived: -number_ring(rat) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,pls)),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),one_one(rat)),hAPP(int,rat,number_number_of(rat),A))).  [resolve(5829,a,5801,a)].
65.60/65.43	5830 -linordered_idom(A) | hAPP(A,A,abs_abs(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),hAPP(A,A,abs_abs(A),B)),hAPP(A,A,abs_abs(A),C)) # label(fact_1854_abs__mult) # label(axiom).  [clausify(1449)].
65.60/65.43	Derived: hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,abs_abs(real),A)),hAPP(real,real,abs_abs(real),B)).  [resolve(5830,a,5791,a)].
65.60/65.43	Derived: hAPP(rat,rat,abs_abs(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B)) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(rat,rat,abs_abs(rat),A)),hAPP(rat,rat,abs_abs(rat),B)).  [resolve(5830,a,5801,a)].
65.60/65.43	5831 -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_310_linorder__neqE__linordered__idom) # label(axiom).  [clausify(1585)].
65.70/65.52	Derived: ti(real,A) = ti(real,B) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),A)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)).  [resolve(5831,a,5791,a)].
65.70/65.52	Derived: ti(rat,A) = ti(rat,B) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),A)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),B)).  [resolve(5831,a,5801,a)].
65.70/65.52	5832 -linordered_idom(A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,ring_1_of_int(A),B)),hAPP(int,A,ring_1_of_int(A),C))) # label(fact_3569_of__int__less__iff) # label(axiom).  [clausify(1708)].
65.70/65.52	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,ring_1_of_int(real),A)),hAPP(int,real,ring_1_of_int(real),B))).  [resolve(5832,a,5791,a)].
65.70/65.52	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(int,rat,ring_1_of_int(rat),A)),hAPP(int,rat,ring_1_of_int(rat),B))).  [resolve(5832,a,5801,a)].
65.70/65.52	5833 -linordered_idom(A) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,ring_1_of_int(A),B)),hAPP(int,A,ring_1_of_int(A),C))) # label(fact_3569_of__int__less__iff) # label(axiom).  [clausify(1708)].
65.70/65.52	Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,ring_1_of_int(real),A)),hAPP(int,real,ring_1_of_int(real),B))).  [resolve(5833,a,5791,a)].
65.70/65.52	Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(int,rat,ring_1_of_int(rat),A)),hAPP(int,rat,ring_1_of_int(rat),B))).  [resolve(5833,a,5801,a)].
65.70/65.52	5834 -linordered_idom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | one_one(A) = hAPP(A,A,sgn_sgn(A),B) # label(fact_2223_sgn__pos) # label(axiom).  [clausify(1726)].
65.70/65.52	Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)) | one_one(rat) = hAPP(rat,rat,sgn_sgn(rat),A).  [resolve(5834,a,5801,a)].
65.70/65.52	5835 -linordered_idom(A) | zero_zero(A) != ti(A,B) | zero_zero(A) != ti(A,C) | zero_zero(A) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),C),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) # label(fact_9_sum__power2__eq__zero__iff) # label(axiom).  [clausify(1744)].
65.70/65.52	Derived: zero_zero(real) != ti(real,A) | zero_zero(real) != ti(real,B) | zero_zero(real) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))).  [resolve(5835,a,5791,a)].
65.70/65.52	Derived: zero_zero(rat) != ti(rat,A) | zero_zero(rat) != ti(rat,B) | zero_zero(rat) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))).  [resolve(5835,a,5801,a)].
65.70/65.52	5836 -linordered_idom(A) | zero_zero(A) = ti(A,B) | zero_zero(A) != hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),C),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) # label(fact_9_sum__power2__eq__zero__iff) # label(axiom).  [clausify(1744)].
65.76/65.62	Derived: zero_zero(real) = ti(real,A) | zero_zero(real) != hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))).  [resolve(5836,a,5791,a)].
65.76/65.62	Derived: zero_zero(rat) = ti(rat,A) | zero_zero(rat) != hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))).  [resolve(5836,a,5801,a)].
65.76/65.62	5837 -linordered_idom(A) | zero_zero(A) = ti(A,B) | zero_zero(A) != hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),C),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) # label(fact_9_sum__power2__eq__zero__iff) # label(axiom).  [clausify(1744)].
65.76/65.62	Derived: zero_zero(real) = ti(real,A) | zero_zero(real) != hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))).  [resolve(5837,a,5791,a)].
65.76/65.62	Derived: zero_zero(rat) = ti(rat,A) | zero_zero(rat) != hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))).  [resolve(5837,a,5801,a)].
65.76/65.62	5838 -linordered_idom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),C))),zero_zero(A))) | zero_zero(A) = ti(A,B) # label(fact_234_even__power__le__0__imp__0) # label(axiom).  [clausify(1757)].
65.76/65.62	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),B))),zero_zero(real))) | zero_zero(real) = ti(real,A).  [resolve(5838,a,5791,a)].
65.76/65.62	Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),B))),zero_zero(rat))) | zero_zero(rat) = ti(rat,A).  [resolve(5838,a,5801,a)].
65.76/65.62	5839 -linordered_idom(A) | zero_zero(A) != hAPP(A,A,sgn_sgn(A),B) | zero_zero(A) = ti(A,B) # label(fact_2202_sgn__0__0) # label(axiom).  [clausify(1825)].
65.76/65.62	Derived: zero_zero(real) != hAPP(real,real,sgn_sgn(real),A) | zero_zero(real) = ti(real,A).  [resolve(5839,a,5791,a)].
65.76/65.62	Derived: zero_zero(rat) != hAPP(rat,rat,sgn_sgn(rat),A) | zero_zero(rat) = ti(rat,A).  [resolve(5839,a,5801,a)].
65.76/65.62	5840 -linordered_idom(A) | zero_zero(A) = hAPP(A,A,sgn_sgn(A),B) | zero_zero(A) != ti(A,B) # label(fact_2202_sgn__0__0) # label(axiom).  [clausify(1825)].
65.76/65.62	Derived: zero_zero(real) = hAPP(real,real,sgn_sgn(real),A) | zero_zero(real) != ti(real,A).  [resolve(5840,a,5791,a)].
65.76/65.62	Derived: zero_zero(rat) = hAPP(rat,rat,sgn_sgn(rat),A) | zero_zero(rat) != ti(rat,A).  [resolve(5840,a,5801,a)].
65.76/65.62	5841 linordered_idom(int) # label(arity_Int_Oint___Rings_Olinordered__idom) # label(axiom).  [assumption].
65.76/65.62	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),zero_zero(int))) | zero_zero(int) = ti(int,B).  [resolve(5841,a,5790,a)].
65.76/65.65	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),zero_zero(int))) | zero_zero(int) = ti(int,A).  [resolve(5841,a,5792,a)].
65.76/65.65	Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),zero_zero(int))) | zero_zero(int) != ti(int,B) | zero_zero(int) != ti(int,A).  [resolve(5841,a,5793,a)].
65.76/65.65	Derived: hAPP(int,int,abs_abs(int),A) != hAPP(int,int,abs_abs(int),B) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),B),A)).  [resolve(5841,a,5794,a)].
65.76/65.65	Derived: hAPP(int,int,abs_abs(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),B)) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,abs_abs(int),A)),B).  [resolve(5841,a,5795,a)].
65.76/65.65	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),B))))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A)).  [resolve(5841,a,5796,a)].
65.76/65.65	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),B))) | hBOOL(hAPP(nat,bool,even_odd_even(nat),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A)).  [resolve(5841,a,5797,a)].
65.76/65.65	Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),B))) | -hBOOL(hAPP(nat,bool,even_odd_even(nat),B)).  [resolve(5841,a,5798,a)].
65.76/65.65	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(5841,a,5800,a)].
65.76/65.65	Derived: -number_ring(int) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,semiring_1_of_nat(int),A)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),A))).  [resolve(5841,a,5802,a)].
65.76/65.65	Derived: -number_ring(int) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),A)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),A))).  [resolve(5841,a,5803,b)].
65.76/65.65	Derived: -number_ring(int) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),A))).  [resolve(5841,a,5804,b)].
65.76/65.65	Derived: hBOOL(hAPP(nat,bool,even_odd_even(nat),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),B),A)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),C),A))).  [resolve(5841,a,5807,a)].
65.86/65.68	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),hAPP(int,int,ring_1_of_int(int),A)),zero_zero(int))).  [resolve(5841,a,5808,a)].
65.86/65.68	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),hAPP(int,int,ring_1_of_int(int),A)),zero_zero(int))).  [resolve(5841,a,5809,a)].
65.86/65.68	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),zero_zero(int))).  [resolve(5841,a,5810,a)].
65.86/65.68	Derived: one_one(int) = hAPP(int,int,abs_abs(int),one_one(int)).  [resolve(5841,a,5811,a)].
65.86/65.68	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,ring_1_of_int(int),A)),zero_zero(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),zero_zero(int))).  [resolve(5841,a,5812,a)].
65.86/65.68	Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,ring_1_of_int(int),A)),zero_zero(int))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),zero_zero(int))).  [resolve(5841,a,5813,a)].
65.86/65.68	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),zero_zero(int))).  [resolve(5841,a,5814,a)].
65.86/65.68	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(5841,a,5815,a)].
65.86/65.68	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),hAPP(int,nat,number_number_of(nat),B)))) | zero_zero(nat) = hAPP(int,nat,number_number_of(nat),B) | zero_zero(int) != ti(int,A) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A)).  [resolve(5841,a,5816,a)].
65.86/65.68	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),hAPP(int,nat,number_number_of(nat),B)))) | zero_zero(nat) = hAPP(int,nat,number_number_of(nat),B) | zero_zero(int) != ti(int,A) | -hBOOL(hAPP(nat,bool,even_odd_even(nat),hAPP(int,nat,number_number_of(nat),B))).  [resolve(5841,a,5817,a)].
65.86/65.68	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),hAPP(int,nat,number_number_of(nat),B)))) | zero_zero(nat) = hAPP(int,nat,number_number_of(nat),B) | hBOOL(hAPP(nat,bool,even_odd_even(nat),hAPP(int,nat,number_number_of(nat),B))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A)).  [resolve(5841,a,5818,a)].
65.86/65.68	Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),hAPP(int,nat,number_number_of(nat),B)))) | zero_zero(nat) != hAPP(int,nat,number_number_of(nat),B).  [resolve(5841,a,5819,a)].
65.86/65.68	Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),hAPP(int,nat,number_number_of(nat),B)))) | zero_zero(int) = ti(int,A) | -hBOOL(hAPP(nat,bool,even_odd_even(nat),hAPP(int,nat,number_number_of(nat),B))).  [resolve(5841,a,5820,a)].
65.86/65.68	Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),hAPP(int,nat,number_number_of(nat),B)))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A)) | hBOOL(hAPP(nat,bool,even_odd_even(nat),hAPP(int,nat,number_number_of(nat),B))).  [resolve(5841,a,5821,a)].
65.89/65.72	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,abs_abs(int),A)),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)).  [resolve(5841,a,5825,a)].
65.89/65.72	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,abs_abs(int),A)),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,uminus_uminus(int),A)),B)).  [resolve(5841,a,5826,a)].
65.89/65.72	Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,abs_abs(int),A)),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,uminus_uminus(int),A)),B)).  [resolve(5841,a,5827,a)].
65.89/65.72	Derived: -number_ring(int) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,pls)),A)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),hAPP(int,int,number_number_of(int),A))).  [resolve(5841,a,5828,a)].
65.89/65.72	Derived: -number_ring(int) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,pls)),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),hAPP(int,int,number_number_of(int),A))).  [resolve(5841,a,5829,a)].
65.89/65.72	Derived: hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,abs_abs(int),A)),hAPP(int,int,abs_abs(int),B)).  [resolve(5841,a,5830,a)].
65.89/65.72	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,ring_1_of_int(int),A)),hAPP(int,int,ring_1_of_int(int),B))).  [resolve(5841,a,5832,a)].
65.89/65.72	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,ring_1_of_int(int),A)),hAPP(int,int,ring_1_of_int(int),B))).  [resolve(5841,a,5833,a)].
65.89/65.72	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A)) | one_one(int) = hAPP(int,int,sgn_sgn(int),A).  [resolve(5841,a,5834,a)].
65.89/65.72	Derived: zero_zero(int) != ti(int,A) | zero_zero(int) != ti(int,B) | zero_zero(int) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))).  [resolve(5841,a,5835,a)].
65.89/65.72	Derived: zero_zero(int) = ti(int,A) | zero_zero(int) != hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))).  [resolve(5841,a,5836,a)].
65.89/65.72	Derived: zero_zero(int) = ti(int,A) | zero_zero(int) != hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))).  [resolve(5841,a,5837,a)].
65.89/65.72	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),B))),zero_zero(int))) | zero_zero(int) = ti(int,A).  [resolve(5841,a,5838,a)].
65.89/65.72	Derived: zero_zero(int) != hAPP(int,int,sgn_sgn(int),A) | zero_zero(int) = ti(int,A).  [resolve(5841,a,5839,a)].
65.89/65.72	Derived: zero_zero(int) = hAPP(int,int,sgn_sgn(int),A) | zero_zero(int) != ti(int,A).  [resolve(5841,a,5840,a)].
65.93/65.82	5842 -linordered_idom(A) | -hBOOL(hAPP(nat,bool,even_odd_even(nat),hAPP(int,nat,number_number_of(nat),B))) | hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),hAPP(A,A,abs_abs(A),C)),hAPP(int,nat,number_number_of(nat),B)) = hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),C),hAPP(int,nat,number_number_of(nat),B)) # label(fact_2444_power__even__abs__number__of) # label(axiom).  [clausify(2011)].
65.93/65.82	Derived: -hBOOL(hAPP(nat,bool,even_odd_even(nat),hAPP(int,nat,number_number_of(nat),A))) | hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,abs_abs(real),B)),hAPP(int,nat,number_number_of(nat),A)) = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),B),hAPP(int,nat,number_number_of(nat),A)).  [resolve(5842,a,5791,a)].
65.93/65.82	Derived: -hBOOL(hAPP(nat,bool,even_odd_even(nat),hAPP(int,nat,number_number_of(nat),A))) | hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),hAPP(rat,rat,abs_abs(rat),B)),hAPP(int,nat,number_number_of(nat),A)) = hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),B),hAPP(int,nat,number_number_of(nat),A)).  [resolve(5842,a,5801,a)].
65.93/65.82	Derived: -hBOOL(hAPP(nat,bool,even_odd_even(nat),hAPP(int,nat,number_number_of(nat),A))) | hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,abs_abs(int),B)),hAPP(int,nat,number_number_of(nat),A)) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),B),hAPP(int,nat,number_number_of(nat),A)).  [resolve(5842,a,5841,a)].
65.93/65.82	5843 -linordered_idom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),hAPP(A,A,abs_abs(A),B)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),C)) # label(fact_1846_abs__dvd__iff) # label(axiom).  [clausify(2024)].
65.93/65.82	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),dvd_dvd(real),hAPP(real,real,abs_abs(real),A)),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),dvd_dvd(real),A),B)).  [resolve(5843,a,5791,a)].
65.93/65.82	Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),dvd_dvd(rat),hAPP(rat,rat,abs_abs(rat),A)),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),dvd_dvd(rat),A),B)).  [resolve(5843,a,5801,a)].
65.93/65.82	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(int,int,abs_abs(int),A)),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),B)).  [resolve(5843,a,5841,a)].
65.93/65.82	5844 -linordered_idom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),hAPP(A,A,abs_abs(A),B)),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),C)) # label(fact_1846_abs__dvd__iff) # label(axiom).  [clausify(2024)].
65.93/65.82	Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),dvd_dvd(real),hAPP(real,real,abs_abs(real),A)),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),dvd_dvd(real),A),B)).  [resolve(5844,a,5791,a)].
65.93/65.82	Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),dvd_dvd(rat),hAPP(rat,rat,abs_abs(rat),A)),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),dvd_dvd(rat),A),B)).  [resolve(5844,a,5801,a)].
65.93/65.82	Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(int,int,abs_abs(int),A)),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),B)).  [resolve(5844,a,5841,a)].
65.93/65.82	5845 -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_438_mult__right__le__one__le) # label(axiom).  [clausify(2047)].
65.93/65.82	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),one_one(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),A)).  [resolve(5845,a,5791,a)].
65.93/65.82	Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),B),one_one(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B)),A)).  [resolve(5845,a,5801,a)].
66.04/65.91	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(5845,a,5841,a)].
66.04/65.91	5846 -linordered_idom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(int,A,ring_1_of_int(A),B)),hAPP(int,A,ring_1_of_int(A),C))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),C)) # label(fact_3570_of__int__le__iff) # label(axiom).  [clausify(2071)].
66.04/65.91	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,ring_1_of_int(real),A)),hAPP(int,real,ring_1_of_int(real),B))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)).  [resolve(5846,a,5791,a)].
66.04/65.91	Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(int,rat,ring_1_of_int(rat),A)),hAPP(int,rat,ring_1_of_int(rat),B))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)).  [resolve(5846,a,5801,a)].
66.04/65.91	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,ring_1_of_int(int),A)),hAPP(int,int,ring_1_of_int(int),B))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)).  [resolve(5846,a,5841,a)].
66.04/65.91	5847 -linordered_idom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(int,A,ring_1_of_int(A),B)),hAPP(int,A,ring_1_of_int(A),C))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),C)) # label(fact_3570_of__int__le__iff) # label(axiom).  [clausify(2071)].
66.04/65.91	Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,ring_1_of_int(real),A)),hAPP(int,real,ring_1_of_int(real),B))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)).  [resolve(5847,a,5791,a)].
66.04/65.91	Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(int,rat,ring_1_of_int(rat),A)),hAPP(int,rat,ring_1_of_int(rat),B))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)).  [resolve(5847,a,5801,a)].
66.04/65.91	Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,ring_1_of_int(int),A)),hAPP(int,int,ring_1_of_int(int),B))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)).  [resolve(5847,a,5841,a)].
66.04/65.91	5848 -linordered_idom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(int,A,ring_1_of_int(A),B))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B)) # label(fact_3600_of__int__0__less__iff) # label(axiom).  [clausify(2195)].
66.04/65.91	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(int,real,ring_1_of_int(real),A))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A)).  [resolve(5848,a,5791,a)].
66.04/65.91	Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(int,rat,ring_1_of_int(rat),A))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A)).  [resolve(5848,a,5801,a)].
66.04/65.91	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,ring_1_of_int(int),A))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A)).  [resolve(5848,a,5841,a)].
66.04/65.91	5849 -linordered_idom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(int,A,ring_1_of_int(A),B))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B)) # label(fact_3600_of__int__0__less__iff) # label(axiom).  [clausify(2195)].
66.04/65.91	Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(int,real,ring_1_of_int(real),A))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A)).  [resolve(5849,a,5791,a)].
66.34/66.22	Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(int,rat,ring_1_of_int(rat),A))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A)).  [resolve(5849,a,5801,a)].
66.34/66.22	Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,ring_1_of_int(int),A))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A)).  [resolve(5849,a,5841,a)].
66.34/66.22	5850 -linordered_idom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),C),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))) # label(fact_107_sum__power2__ge__zero) # label(axiom).  [clausify(2252)].
66.34/66.22	Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))).  [resolve(5850,a,5791,a)].
66.34/66.22	Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))).  [resolve(5850,a,5801,a)].
66.34/66.22	Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))).  [resolve(5850,a,5841,a)].
66.34/66.22	5851 -linordered_idom(A) | hBOOL(hAPP(nat,bool,even_odd_even(nat),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),C),B))) # label(fact_2435_zero__le__power__eq) # label(axiom).  [clausify(2392)].
66.34/66.22	5852 -linordered_idom(A) | -hBOOL(hAPP(nat,bool,even_odd_even(nat),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),C),B))) # label(fact_2435_zero__le__power__eq) # label(axiom).  [clausify(2392)].
66.34/66.22	5853 -linordered_idom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) | hBOOL(hAPP(nat,bool,even_odd_even(nat),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C))) # label(fact_2435_zero__le__power__eq) # label(axiom).  [clausify(2392)].
66.34/66.22	5854 -linordered_idom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,abs_abs(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C))),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),D))) # label(fact_1883_abs__diff__less__iff) # label(axiom).  [clausify(2454)].
66.34/66.22	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),B))),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),B),C))).  [resolve(5854,a,5791,a)].
66.34/66.22	Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,abs_abs(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),A),B))),C)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),B),C))).  [resolve(5854,a,5801,a)].
66.52/66.39	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),B))),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),B),C))).  [resolve(5854,a,5841,a)].
66.52/66.39	5855 -linordered_idom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,abs_abs(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C))),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),C),D)),B)) # label(fact_1883_abs__diff__less__iff) # label(axiom).  [clausify(2454)].
66.52/66.39	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),B))),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),B),C)),A)).  [resolve(5855,a,5791,a)].
66.52/66.39	Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,abs_abs(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),A),B))),C)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),B),C)),A)).  [resolve(5855,a,5801,a)].
66.52/66.39	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),B))),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),B),C)),A)).  [resolve(5855,a,5841,a)].
66.52/66.39	5856 -linordered_idom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,abs_abs(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C))),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),D))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),C),D)),B)) # label(fact_1883_abs__diff__less__iff) # label(axiom).  [clausify(2454)].
66.52/66.39	Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),B))),C)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),B),C))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),B),C)),A)).  [resolve(5856,a,5791,a)].
66.52/66.39	Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,abs_abs(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),A),B))),C)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),B),C))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),B),C)),A)).  [resolve(5856,a,5801,a)].
66.52/66.39	Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),B))),C)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),B),C))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),B),C)),A)).  [resolve(5856,a,5841,a)].
66.52/66.39	5857 -number_ring(A) | -linordered_idom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(int,A,number_number_of(A),B)),zero_zero(A))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),pls)) # label(fact_47_le__special_I3_J) # label(axiom).  [clausify(2667)].
66.52/66.39	Derived: -number_ring(real) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,number_number_of(real),A)),zero_zero(real))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),pls)).  [resolve(5857,b,5791,a)].
66.52/66.39	Derived: -number_ring(rat) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(int,rat,number_number_of(rat),A)),zero_zero(rat))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),pls)).  [resolve(5857,b,5801,a)].
66.68/66.51	Derived: -number_ring(int) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),A)),zero_zero(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),pls)).  [resolve(5857,b,5841,a)].
66.68/66.51	5858 -number_ring(A) | -linordered_idom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(int,A,number_number_of(A),B)),zero_zero(A))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),pls)) # label(fact_47_le__special_I3_J) # label(axiom).  [clausify(2667)].
66.68/66.51	Derived: -number_ring(real) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,number_number_of(real),A)),zero_zero(real))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),pls)).  [resolve(5858,b,5791,a)].
66.68/66.51	Derived: -number_ring(rat) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(int,rat,number_number_of(rat),A)),zero_zero(rat))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),pls)).  [resolve(5858,b,5801,a)].
66.68/66.51	Derived: -number_ring(int) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),A)),zero_zero(int))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),pls)).  [resolve(5858,b,5841,a)].
66.68/66.51	5859 -linordered_idom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) # label(fact_104_zero__le__power2) # label(axiom).  [clausify(2693)].
66.68/66.51	Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))).  [resolve(5859,a,5791,a)].
66.68/66.51	Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))).  [resolve(5859,a,5801,a)].
66.68/66.51	Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))).  [resolve(5859,a,5841,a)].
66.68/66.51	5860 -linordered_idom(A) | hAPP(A,A,abs_abs(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) = hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) # label(fact_1900_abs__power2) # label(axiom).  [clausify(2778)].
66.68/66.51	Derived: hAPP(real,real,abs_abs(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))).  [resolve(5860,a,5791,a)].
66.68/66.51	Derived: hAPP(rat,rat,abs_abs(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) = hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))).  [resolve(5860,a,5801,a)].
66.68/66.51	Derived: hAPP(int,int,abs_abs(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))).  [resolve(5860,a,5841,a)].
66.68/66.51	5861 -linordered_idom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(A,A,uminus_uminus(A),B))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) # label(fact_2060_less__minus__self__iff) # label(axiom).  [clausify(2805)].
66.70/66.56	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),hAPP(real,real,uminus_uminus(real),A))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))).  [resolve(5861,a,5791,a)].
66.70/66.56	Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),hAPP(rat,rat,uminus_uminus(rat),A))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),zero_zero(rat))).  [resolve(5861,a,5801,a)].
66.70/66.56	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),hAPP(int,int,uminus_uminus(int),A))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),zero_zero(int))).  [resolve(5861,a,5841,a)].
66.70/66.56	5862 -linordered_idom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(A,A,uminus_uminus(A),B))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) # label(fact_2060_less__minus__self__iff) # label(axiom).  [clausify(2805)].
66.70/66.56	Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),hAPP(real,real,uminus_uminus(real),A))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))).  [resolve(5862,a,5791,a)].
66.70/66.56	Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),hAPP(rat,rat,uminus_uminus(rat),A))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),zero_zero(rat))).  [resolve(5862,a,5801,a)].
66.70/66.56	Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),hAPP(int,int,uminus_uminus(int),A))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),zero_zero(int))).  [resolve(5862,a,5841,a)].
66.70/66.56	5863 -number_ring(A) | -linordered_idom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(int,A,number_number_of(A),B))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),B)) # label(fact_177_less__special_I1_J) # label(axiom).  [clausify(2816)].
66.70/66.56	Derived: -number_ring(real) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(int,real,number_number_of(real),A))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),A)).  [resolve(5863,b,5791,a)].
66.70/66.56	Derived: -number_ring(rat) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(int,rat,number_number_of(rat),A))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),A)).  [resolve(5863,b,5801,a)].
66.70/66.56	Derived: -number_ring(int) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,number_number_of(int),A))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),A)).  [resolve(5863,b,5841,a)].
66.70/66.56	5864 -number_ring(A) | -linordered_idom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(int,A,number_number_of(A),B))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),B)) # label(fact_177_less__special_I1_J) # label(axiom).  [clausify(2816)].
66.70/66.56	Derived: -number_ring(real) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(int,real,number_number_of(real),A))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),A)).  [resolve(5864,b,5791,a)].
66.70/66.56	Derived: -number_ring(rat) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(int,rat,number_number_of(rat),A))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),A)).  [resolve(5864,b,5801,a)].
66.70/66.56	Derived: -number_ring(int) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,number_number_of(int),A))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),A)).  [resolve(5864,b,5841,a)].
66.70/66.56	5865 -linordered_idom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C)),zero_zero(A))) | zero_zero(nat) != C # label(fact_2453_power__le__zero__eq) # label(axiom).  [clausify(2827)].
66.70/66.56	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),B)),zero_zero(real))) | zero_zero(nat) != B.  [resolve(5865,a,5791,a)].
66.70/66.56	Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),B)),zero_zero(rat))) | zero_zero(nat) != B.  [resolve(5865,a,5801,a)].
66.70/66.58	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),B)),zero_zero(int))) | zero_zero(nat) != B.  [resolve(5865,a,5841,a)].
66.70/66.58	5866 -linordered_idom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C)),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),zero_zero(A))) | zero_zero(A) = ti(A,B) # label(fact_2453_power__le__zero__eq) # label(axiom).  [clausify(2827)].
66.70/66.58	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),B)),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),zero_zero(real))) | zero_zero(real) = ti(real,A).  [resolve(5866,a,5791,a)].
66.70/66.58	Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),B)),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),zero_zero(rat))) | zero_zero(rat) = ti(rat,A).  [resolve(5866,a,5801,a)].
66.70/66.58	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),B)),zero_zero(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),zero_zero(int))) | zero_zero(int) = ti(int,A).  [resolve(5866,a,5841,a)].
66.70/66.58	5867 -linordered_idom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C)),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),zero_zero(A))) | hBOOL(hAPP(nat,bool,even_odd_even(nat),C)) # label(fact_2453_power__le__zero__eq) # label(axiom).  [clausify(2827)].
66.70/66.58	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),B)),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),zero_zero(real))) | hBOOL(hAPP(nat,bool,even_odd_even(nat),B)).  [resolve(5867,a,5791,a)].
66.70/66.58	Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),B)),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),zero_zero(rat))) | hBOOL(hAPP(nat,bool,even_odd_even(nat),B)).  [resolve(5867,a,5801,a)].
66.70/66.58	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),B)),zero_zero(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),zero_zero(int))) | hBOOL(hAPP(nat,bool,even_odd_even(nat),B)).  [resolve(5867,a,5841,a)].
66.70/66.58	5868 -linordered_idom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C)),zero_zero(A))) | -hBOOL(hAPP(nat,bool,even_odd_even(nat),C)) | zero_zero(A) = ti(A,B) # label(fact_2453_power__le__zero__eq) # label(axiom).  [clausify(2827)].
66.70/66.58	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),B)),zero_zero(real))) | -hBOOL(hAPP(nat,bool,even_odd_even(nat),B)) | zero_zero(real) = ti(real,A).  [resolve(5868,a,5791,a)].
66.70/66.58	Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),B)),zero_zero(rat))) | -hBOOL(hAPP(nat,bool,even_odd_even(nat),B)) | zero_zero(rat) = ti(rat,A).  [resolve(5868,a,5801,a)].
66.70/66.58	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),B)),zero_zero(int))) | -hBOOL(hAPP(nat,bool,even_odd_even(nat),B)) | zero_zero(int) = ti(int,A).  [resolve(5868,a,5841,a)].
66.70/66.58	5869 -linordered_idom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C)),zero_zero(A))) | zero_zero(nat) = C | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),zero_zero(A))) | hBOOL(hAPP(nat,bool,even_odd_even(nat),C)) # label(fact_2453_power__le__zero__eq) # label(axiom).  [clausify(2827)].
66.80/66.64	Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),B)),zero_zero(real))) | zero_zero(nat) = B | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),zero_zero(real))) | hBOOL(hAPP(nat,bool,even_odd_even(nat),B)).  [resolve(5869,a,5791,a)].
66.80/66.64	Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),B)),zero_zero(rat))) | zero_zero(nat) = B | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),zero_zero(rat))) | hBOOL(hAPP(nat,bool,even_odd_even(nat),B)).  [resolve(5869,a,5801,a)].
66.80/66.64	Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),B)),zero_zero(int))) | zero_zero(nat) = B | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),zero_zero(int))) | hBOOL(hAPP(nat,bool,even_odd_even(nat),B)).  [resolve(5869,a,5841,a)].
66.80/66.64	5870 -linordered_idom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C)),zero_zero(A))) | zero_zero(nat) = C | zero_zero(A) != ti(A,B) | -hBOOL(hAPP(nat,bool,even_odd_even(nat),C)) # label(fact_2453_power__le__zero__eq) # label(axiom).  [clausify(2827)].
66.80/66.64	Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),B)),zero_zero(real))) | zero_zero(nat) = B | zero_zero(real) != ti(real,A) | -hBOOL(hAPP(nat,bool,even_odd_even(nat),B)).  [resolve(5870,a,5791,a)].
66.80/66.64	Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),B)),zero_zero(rat))) | zero_zero(nat) = B | zero_zero(rat) != ti(rat,A) | -hBOOL(hAPP(nat,bool,even_odd_even(nat),B)).  [resolve(5870,a,5801,a)].
66.80/66.64	Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),B)),zero_zero(int))) | zero_zero(nat) = B | zero_zero(int) != ti(int,A) | -hBOOL(hAPP(nat,bool,even_odd_even(nat),B)).  [resolve(5870,a,5841,a)].
66.80/66.64	5871 -number_ring(A) | -linordered_idom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),hAPP(int,A,number_number_of(A),B))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,pls)),B)) # label(fact_181_less__special_I2_J) # label(axiom).  [clausify(2878)].
66.80/66.64	Derived: -number_ring(real) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),hAPP(int,real,number_number_of(real),A))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,pls)),A)).  [resolve(5871,b,5791,a)].
66.80/66.64	Derived: -number_ring(rat) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),one_one(rat)),hAPP(int,rat,number_number_of(rat),A))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,pls)),A)).  [resolve(5871,b,5801,a)].
66.80/66.64	Derived: -number_ring(int) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),hAPP(int,int,number_number_of(int),A))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,pls)),A)).  [resolve(5871,b,5841,a)].
66.80/66.64	5872 -number_ring(A) | -linordered_idom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),hAPP(int,A,number_number_of(A),B))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,pls)),B)) # label(fact_181_less__special_I2_J) # label(axiom).  [clausify(2878)].
66.80/66.64	Derived: -number_ring(real) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),hAPP(int,real,number_number_of(real),A))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,pls)),A)).  [resolve(5872,b,5791,a)].
66.80/66.64	Derived: -number_ring(rat) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),one_one(rat)),hAPP(int,rat,number_number_of(rat),A))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,pls)),A)).  [resolve(5872,b,5801,a)].
67.00/66.87	Derived: -number_ring(int) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),hAPP(int,int,number_number_of(int),A))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,pls)),A)).  [resolve(5872,b,5841,a)].
67.00/66.87	5873 -linordered_idom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),C)))),zero_zero(A))) # label(fact_1471_odd__power__less__zero) # label(axiom).  [clausify(2892)].
67.00/66.87	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),B)))),zero_zero(real))).  [resolve(5873,a,5791,a)].
67.00/66.87	Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),B)))),zero_zero(rat))).  [resolve(5873,a,5801,a)].
67.00/66.87	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),zero_zero(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),B)))),zero_zero(int))).  [resolve(5873,a,5841,a)].
67.00/66.87	5874 -linordered_idom(A) | hBOOL(hAPP(nat,bool,even_odd_even(nat),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),C),B))) # label(fact_2432_zero__le__odd__power) # label(axiom).  [clausify(2910)].
67.00/66.87	5875 -linordered_idom(A) | hBOOL(hAPP(nat,bool,even_odd_even(nat),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),C),B))) # label(fact_2432_zero__le__odd__power) # label(axiom).  [clausify(2910)].
67.00/66.87	5876 -linordered_idom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | hAPP(A,A,sgn_sgn(A),B) = hAPP(A,A,uminus_uminus(A),one_one(A)) # label(fact_2231_sgn__neg) # label(axiom).  [clausify(3012)].
67.00/66.87	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))) | hAPP(real,real,sgn_sgn(real),A) = hAPP(real,real,uminus_uminus(real),one_one(real)).  [resolve(5876,a,5791,a)].
67.00/66.87	Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),zero_zero(rat))) | hAPP(rat,rat,sgn_sgn(rat),A) = hAPP(rat,rat,uminus_uminus(rat),one_one(rat)).  [resolve(5876,a,5801,a)].
67.00/66.87	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),zero_zero(int))) | hAPP(int,int,sgn_sgn(int),A) = hAPP(int,int,uminus_uminus(int),one_one(int)).  [resolve(5876,a,5841,a)].
67.00/66.87	5877 -number_ring(A) | -linordered_idom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(int,A,number_number_of(A),B)),one_one(A))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),hAPP(int,int,bit1,pls))) # label(fact_59_le__special_I4_J) # label(axiom).  [clausify(3110)].
67.00/66.87	Derived: -number_ring(real) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,number_number_of(real),A)),one_one(real))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),hAPP(int,int,bit1,pls))).  [resolve(5877,b,5791,a)].
67.00/66.87	Derived: -number_ring(rat) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(int,rat,number_number_of(rat),A)),one_one(rat))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),hAPP(int,int,bit1,pls))).  [resolve(5877,b,5801,a)].
67.10/66.96	Derived: -number_ring(int) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),A)),one_one(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),hAPP(int,int,bit1,pls))).  [resolve(5877,b,5841,a)].
67.10/66.96	5878 -number_ring(A) | -linordered_idom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(int,A,number_number_of(A),B)),one_one(A))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),hAPP(int,int,bit1,pls))) # label(fact_59_le__special_I4_J) # label(axiom).  [clausify(3110)].
67.10/66.96	Derived: -number_ring(real) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,number_number_of(real),A)),one_one(real))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),hAPP(int,int,bit1,pls))).  [resolve(5878,b,5791,a)].
67.10/66.96	Derived: -number_ring(rat) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(int,rat,number_number_of(rat),A)),one_one(rat))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),hAPP(int,int,bit1,pls))).  [resolve(5878,b,5801,a)].
67.10/66.96	Derived: -number_ring(int) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),A)),one_one(int))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),hAPP(int,int,bit1,pls))).  [resolve(5878,b,5841,a)].
67.10/66.96	5879 -linordered_idom(A) | -hBOOL(hAPP(nat,bool,even_odd_even(nat),B)) | hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),hAPP(A,A,abs_abs(A),C)),B) = hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),C),B) # label(fact_2426_power__even__abs) # label(axiom).  [clausify(3131)].
67.10/66.96	Derived: -hBOOL(hAPP(nat,bool,even_odd_even(nat),A)) | hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,abs_abs(real),B)),A) = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),B),A).  [resolve(5879,a,5791,a)].
67.10/66.96	Derived: -hBOOL(hAPP(nat,bool,even_odd_even(nat),A)) | hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),hAPP(rat,rat,abs_abs(rat),B)),A) = hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),B),A).  [resolve(5879,a,5801,a)].
67.10/66.96	Derived: -hBOOL(hAPP(nat,bool,even_odd_even(nat),A)) | hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,abs_abs(int),B)),A) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),B),A).  [resolve(5879,a,5841,a)].
67.10/66.96	5880 -linordered_idom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,sgn_sgn(A),B))) # label(fact_2211_sgn__greater) # label(axiom).  [clausify(3197)].
67.10/66.96	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,sgn_sgn(real),A))).  [resolve(5880,a,5791,a)].
67.10/66.96	Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(rat,rat,sgn_sgn(rat),A))).  [resolve(5880,a,5801,a)].
67.10/66.96	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,sgn_sgn(int),A))).  [resolve(5880,a,5841,a)].
67.10/66.96	5881 -linordered_idom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,sgn_sgn(A),B))) # label(fact_2211_sgn__greater) # label(axiom).  [clausify(3197)].
67.10/66.96	Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,sgn_sgn(real),A))).  [resolve(5881,a,5791,a)].
67.10/66.96	Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(rat,rat,sgn_sgn(rat),A))).  [resolve(5881,a,5801,a)].
67.29/67.16	Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,sgn_sgn(int),A))).  [resolve(5881,a,5841,a)].
67.29/67.16	5882 -linordered_idom(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,sgn_sgn(A),B)),hAPP(A,A,abs_abs(A),B)) = ti(A,B) # label(fact_2215_mult__sgn__abs) # label(axiom).  [clausify(3290)].
67.29/67.16	Derived: hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,sgn_sgn(real),A)),hAPP(real,real,abs_abs(real),A)) = ti(real,A).  [resolve(5882,a,5791,a)].
67.29/67.16	Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(rat,rat,sgn_sgn(rat),A)),hAPP(rat,rat,abs_abs(rat),A)) = ti(rat,A).  [resolve(5882,a,5801,a)].
67.29/67.16	Derived: hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,sgn_sgn(int),A)),hAPP(int,int,abs_abs(int),A)) = ti(int,A).  [resolve(5882,a,5841,a)].
67.29/67.16	5883 -linordered_idom(A) | hAPP(A,A,sgn_sgn(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),hAPP(A,A,sgn_sgn(A),B)),hAPP(A,A,sgn_sgn(A),C)) # label(fact_2205_sgn__times) # label(axiom).  [clausify(3371)].
67.29/67.16	Derived: hAPP(rat,rat,sgn_sgn(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B)) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(rat,rat,sgn_sgn(rat),A)),hAPP(rat,rat,sgn_sgn(rat),B)).  [resolve(5883,a,5801,a)].
67.29/67.16	Derived: hAPP(int,int,sgn_sgn(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,sgn_sgn(int),A)),hAPP(int,int,sgn_sgn(int),B)).  [resolve(5883,a,5841,a)].
67.29/67.16	5884 -linordered_idom(A) | -number_ring(A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),hAPP(int,int,bit1,pls))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),B)),one_one(A))) # label(fact_180_less__special_I4_J) # label(axiom).  [clausify(3383)].
67.29/67.16	Derived: -number_ring(real) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),hAPP(int,int,bit1,pls))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,number_number_of(real),A)),one_one(real))).  [resolve(5884,a,5791,a)].
67.29/67.16	Derived: -number_ring(rat) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),hAPP(int,int,bit1,pls))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(int,rat,number_number_of(rat),A)),one_one(rat))).  [resolve(5884,a,5801,a)].
67.29/67.16	Derived: -number_ring(int) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),hAPP(int,int,bit1,pls))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),A)),one_one(int))).  [resolve(5884,a,5841,a)].
67.29/67.16	5885 -linordered_idom(A) | -number_ring(A) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),hAPP(int,int,bit1,pls))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),B)),one_one(A))) # label(fact_180_less__special_I4_J) # label(axiom).  [clausify(3383)].
67.29/67.16	Derived: -number_ring(real) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),hAPP(int,int,bit1,pls))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,number_number_of(real),A)),one_one(real))).  [resolve(5885,a,5791,a)].
67.29/67.16	Derived: -number_ring(rat) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),hAPP(int,int,bit1,pls))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(int,rat,number_number_of(rat),A)),one_one(rat))).  [resolve(5885,a,5801,a)].
67.29/67.16	Derived: -number_ring(int) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),hAPP(int,int,bit1,pls))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),A)),one_one(int))).  [resolve(5885,a,5841,a)].
67.29/67.16	5886 -linordered_idom(A) | -number_ring(A) | one_one(A) = hAPP(A,A,abs_abs(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),hAPP(int,A,number_number_of(A),min_1)),B)) # label(fact_1896_abs__power__minus__one) # label(axiom).  [clausify(3400)].
67.29/67.16	Derived: -number_ring(real) | one_one(real) = hAPP(real,real,abs_abs(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),min_1)),A)).  [resolve(5886,a,5791,a)].
67.38/67.21	Derived: -number_ring(rat) | one_one(rat) = hAPP(rat,rat,abs_abs(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),hAPP(int,rat,number_number_of(rat),min_1)),A)).  [resolve(5886,a,5801,a)].
67.38/67.21	Derived: -number_ring(int) | one_one(int) = hAPP(int,int,abs_abs(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,number_number_of(int),min_1)),A)).  [resolve(5886,a,5841,a)].
67.38/67.21	5887 -linordered_idom(A) | zero_zero(A) = ti(A,B) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) # label(fact_11_zero__less__power2) # label(axiom).  [clausify(3410)].
67.38/67.21	Derived: zero_zero(real) = ti(real,A) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))).  [resolve(5887,a,5791,a)].
67.38/67.21	Derived: zero_zero(rat) = ti(rat,A) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))).  [resolve(5887,a,5801,a)].
67.38/67.21	Derived: zero_zero(int) = ti(int,A) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))).  [resolve(5887,a,5841,a)].
67.38/67.21	5888 -linordered_idom(A) | zero_zero(A) != ti(A,B) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) # label(fact_11_zero__less__power2) # label(axiom).  [clausify(3410)].
67.38/67.21	Derived: zero_zero(real) != ti(real,A) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))).  [resolve(5888,a,5791,a)].
67.38/67.21	Derived: zero_zero(rat) != ti(rat,A) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))).  [resolve(5888,a,5801,a)].
67.38/67.21	Derived: zero_zero(int) != ti(int,A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))).  [resolve(5888,a,5841,a)].
67.38/67.21	5889 -linordered_idom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,sgn_sgn(A),B)),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) # label(fact_2212_sgn__less) # label(axiom).  [clausify(3429)].
67.38/67.21	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,sgn_sgn(real),A)),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))).  [resolve(5889,a,5791,a)].
67.38/67.21	Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,sgn_sgn(rat),A)),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),zero_zero(rat))).  [resolve(5889,a,5801,a)].
67.38/67.21	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,sgn_sgn(int),A)),zero_zero(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),zero_zero(int))).  [resolve(5889,a,5841,a)].
67.38/67.21	5890 -linordered_idom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,sgn_sgn(A),B)),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) # label(fact_2212_sgn__less) # label(axiom).  [clausify(3429)].
67.38/67.21	Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,sgn_sgn(real),A)),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))).  [resolve(5890,a,5791,a)].
67.46/67.30	Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,sgn_sgn(rat),A)),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),zero_zero(rat))).  [resolve(5890,a,5801,a)].
67.46/67.30	Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,sgn_sgn(int),A)),zero_zero(int))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),zero_zero(int))).  [resolve(5890,a,5841,a)].
67.46/67.30	5891 -linordered_idom(A) | zero_zero(nat) = hAPP(int,nat,number_number_of(nat),B) | zero_zero(A) != ti(A,C) | -hBOOL(hAPP(nat,bool,even_odd_even(nat),hAPP(int,nat,number_number_of(nat),B))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),C),hAPP(int,nat,number_number_of(nat),B))),zero_zero(A))) # label(fact_2463_power__le__zero__eq__number__of) # label(axiom).  [clausify(3431)].
67.46/67.30	5892 -linordered_idom(A) | zero_zero(nat) = hAPP(int,nat,number_number_of(nat),B) | hBOOL(hAPP(nat,bool,even_odd_even(nat),hAPP(int,nat,number_number_of(nat),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(nat,A,hAPP(A,fun(nat,A),power_power(A),C),hAPP(int,nat,number_number_of(nat),B))),zero_zero(A))) # label(fact_2463_power__le__zero__eq__number__of) # label(axiom).  [clausify(3431)].
67.46/67.30	5893 -linordered_idom(A) | zero_zero(nat) != hAPP(int,nat,number_number_of(nat),B) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),C),hAPP(int,nat,number_number_of(nat),B))),zero_zero(A))) # label(fact_2463_power__le__zero__eq__number__of) # label(axiom).  [clausify(3431)].
67.46/67.30	5894 -linordered_idom(A) | zero_zero(A) = ti(A,B) | -hBOOL(hAPP(nat,bool,even_odd_even(nat),hAPP(int,nat,number_number_of(nat),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(int,nat,number_number_of(nat),C))),zero_zero(A))) # label(fact_2463_power__le__zero__eq__number__of) # label(axiom).  [clausify(3431)].
67.46/67.30	5895 -linordered_idom(A) | zero_zero(A) = ti(A,B) | 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),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(int,nat,number_number_of(nat),C))),zero_zero(A))) # label(fact_2463_power__le__zero__eq__number__of) # label(axiom).  [clausify(3431)].
67.46/67.30	5896 -linordered_idom(A) | hBOOL(hAPP(nat,bool,even_odd_even(nat),hAPP(int,nat,number_number_of(nat),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(nat,A,hAPP(A,fun(nat,A),power_power(A),C),hAPP(int,nat,number_number_of(nat),B))),zero_zero(A))) # label(fact_2463_power__le__zero__eq__number__of) # label(axiom).  [clausify(3431)].
67.46/67.30	5897 -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_144_even__less__0__iff) # label(axiom).  [clausify(3480)].
67.46/67.30	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),A)),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))).  [resolve(5897,a,5791,a)].
67.46/67.30	Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),A)),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),zero_zero(rat))).  [resolve(5897,a,5801,a)].
67.46/67.30	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(5897,a,5841,a)].
67.46/67.30	5898 -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_144_even__less__0__iff) # label(axiom).  [clausify(3480)].
67.46/67.37	5899 -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_3799_Ints__odd__less__0) # label(axiom).  [clausify(3516)].
67.46/67.37	Derived: -hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),A),ring_1_Ints(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),one_one(real)),A)),A)),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))).  [resolve(5899,a,5791,a)].
67.46/67.37	Derived: -hBOOL(hAPP(fun(rat,bool),bool,hAPP(rat,fun(fun(rat,bool),bool),member(rat),A),ring_1_Ints(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),one_one(rat)),A)),A)),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),zero_zero(rat))).  [resolve(5899,a,5801,a)].
67.46/67.37	5900 -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_3799_Ints__odd__less__0) # label(axiom).  [clausify(3516)].
67.46/67.37	Derived: -hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),A),ring_1_Ints(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),one_one(real)),A)),A)),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))).  [resolve(5900,a,5791,a)].
67.46/67.37	Derived: -hBOOL(hAPP(fun(rat,bool),bool,hAPP(rat,fun(fun(rat,bool),bool),member(rat),A),ring_1_Ints(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),one_one(rat)),A)),A)),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),zero_zero(rat))).  [resolve(5900,a,5801,a)].
67.46/67.37	5901 -number_ring(A) | -linordered_idom(A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),C)) | 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))) # label(fact_150_less__number__of) # label(axiom).  [clausify(3522)].
67.46/67.37	Derived: -number_ring(real) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,number_number_of(real),A)),hAPP(int,real,number_number_of(real),B))).  [resolve(5901,b,5791,a)].
67.46/67.37	Derived: -number_ring(rat) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(int,rat,number_number_of(rat),A)),hAPP(int,rat,number_number_of(rat),B))).  [resolve(5901,b,5801,a)].
67.46/67.37	Derived: -number_ring(int) | -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,number_number_of(int),A)),hAPP(int,int,number_number_of(int),B))).  [resolve(5901,b,5841,a)].
67.46/67.37	5902 -number_ring(A) | -linordered_idom(A) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),C)) | -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))) # label(fact_150_less__number__of) # label(axiom).  [clausify(3522)].
67.68/67.58	Derived: -number_ring(real) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,number_number_of(real),A)),hAPP(int,real,number_number_of(real),B))).  [resolve(5902,b,5791,a)].
67.68/67.58	Derived: -number_ring(rat) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(int,rat,number_number_of(rat),A)),hAPP(int,rat,number_number_of(rat),B))).  [resolve(5902,b,5801,a)].
67.68/67.58	Derived: -number_ring(int) | 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,number_number_of(int),A)),hAPP(int,int,number_number_of(int),B))).  [resolve(5902,b,5841,a)].
67.68/67.58	5903 -linordered_idom(A) | hAPP(A,A,abs_abs(A),B) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(A,A,sgn_sgn(A),B)) # label(fact_2214_abs__sgn) # label(axiom).  [clausify(3616)].
67.68/67.58	Derived: hAPP(real,real,abs_abs(real),A) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),hAPP(real,real,sgn_sgn(real),A)).  [resolve(5903,a,5791,a)].
67.68/67.58	Derived: hAPP(rat,rat,abs_abs(rat),A) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),hAPP(rat,rat,sgn_sgn(rat),A)).  [resolve(5903,a,5801,a)].
67.68/67.58	Derived: hAPP(int,int,abs_abs(int),A) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),hAPP(int,int,sgn_sgn(int),A)).  [resolve(5903,a,5841,a)].
67.68/67.58	5904 -linordered_idom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(int,A,ring_1_of_int(A),B))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),B)) # label(fact_3602_of__int__0__le__iff) # label(axiom).  [clausify(3695)].
67.68/67.58	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(int,real,ring_1_of_int(real),A))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A)).  [resolve(5904,a,5791,a)].
67.68/67.58	Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),hAPP(int,rat,ring_1_of_int(rat),A))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A)).  [resolve(5904,a,5801,a)].
67.68/67.58	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,ring_1_of_int(int),A))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A)).  [resolve(5904,a,5841,a)].
67.68/67.58	5905 -linordered_idom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(int,A,ring_1_of_int(A),B))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),B)) # label(fact_3602_of__int__0__le__iff) # label(axiom).  [clausify(3695)].
67.68/67.58	Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(int,real,ring_1_of_int(real),A))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A)).  [resolve(5905,a,5791,a)].
67.68/67.58	Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),hAPP(int,rat,ring_1_of_int(rat),A))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A)).  [resolve(5905,a,5801,a)].
67.68/67.58	Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,ring_1_of_int(int),A))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A)).  [resolve(5905,a,5841,a)].
67.68/67.58	5906 -linordered_idom(A) | hAPP(A,A,sgn_sgn(A),hAPP(A,A,sgn_sgn(A),B)) = hAPP(A,A,sgn_sgn(A),B) # label(fact_2199_sgn__sgn) # label(axiom).  [clausify(3705)].
67.68/67.58	Derived: hAPP(real,real,sgn_sgn(real),hAPP(real,real,sgn_sgn(real),A)) = hAPP(real,real,sgn_sgn(real),A).  [resolve(5906,a,5791,a)].
67.68/67.58	Derived: hAPP(rat,rat,sgn_sgn(rat),hAPP(rat,rat,sgn_sgn(rat),A)) = hAPP(rat,rat,sgn_sgn(rat),A).  [resolve(5906,a,5801,a)].
67.68/67.58	Derived: hAPP(int,int,sgn_sgn(int),hAPP(int,int,sgn_sgn(int),A)) = hAPP(int,int,sgn_sgn(int),A).  [resolve(5906,a,5841,a)].
67.68/67.58	5907 -number_ring(A) | -linordered_idom(A) | one_one(A) = hAPP(A,A,abs_abs(A),hAPP(int,A,number_number_of(A),min_1)) # label(fact_1885_abs__minus__one) # label(axiom).  [clausify(3725)].
67.76/67.65	Derived: -number_ring(real) | one_one(real) = hAPP(real,real,abs_abs(real),hAPP(int,real,number_number_of(real),min_1)).  [resolve(5907,b,5791,a)].
67.76/67.65	Derived: -number_ring(rat) | one_one(rat) = hAPP(rat,rat,abs_abs(rat),hAPP(int,rat,number_number_of(rat),min_1)).  [resolve(5907,b,5801,a)].
67.76/67.65	Derived: -number_ring(int) | one_one(int) = hAPP(int,int,abs_abs(int),hAPP(int,int,number_number_of(int),min_1)).  [resolve(5907,b,5841,a)].
67.76/67.65	5908 -linordered_idom(A) | -number_ring(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),B)),zero_zero(A))) | hAPP(A,A,abs_abs(A),hAPP(int,A,number_number_of(A),B)) = hAPP(A,A,uminus_uminus(A),hAPP(int,A,number_number_of(A),B)) # label(fact_2113_abs__number__of) # label(axiom).  [clausify(3778)].
67.76/67.65	Derived: -number_ring(real) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,number_number_of(real),A)),zero_zero(real))) | hAPP(real,real,abs_abs(real),hAPP(int,real,number_number_of(real),A)) = hAPP(real,real,uminus_uminus(real),hAPP(int,real,number_number_of(real),A)).  [resolve(5908,a,5791,a)].
67.76/67.65	Derived: -number_ring(rat) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(int,rat,number_number_of(rat),A)),zero_zero(rat))) | hAPP(rat,rat,abs_abs(rat),hAPP(int,rat,number_number_of(rat),A)) = hAPP(rat,rat,uminus_uminus(rat),hAPP(int,rat,number_number_of(rat),A)).  [resolve(5908,a,5801,a)].
67.76/67.65	Derived: -number_ring(int) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),A)),zero_zero(int))) | hAPP(int,int,abs_abs(int),hAPP(int,int,number_number_of(int),A)) = hAPP(int,int,uminus_uminus(int),hAPP(int,int,number_number_of(int),A)).  [resolve(5908,a,5841,a)].
67.76/67.65	5909 -linordered_idom(A) | -number_ring(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),B)),zero_zero(A))) | hAPP(A,A,abs_abs(A),hAPP(int,A,number_number_of(A),B)) = hAPP(int,A,number_number_of(A),B) # label(fact_2113_abs__number__of) # label(axiom).  [clausify(3778)].
67.76/67.65	Derived: -number_ring(real) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,number_number_of(real),A)),zero_zero(real))) | hAPP(real,real,abs_abs(real),hAPP(int,real,number_number_of(real),A)) = hAPP(int,real,number_number_of(real),A).  [resolve(5909,a,5791,a)].
67.76/67.65	Derived: -number_ring(rat) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(int,rat,number_number_of(rat),A)),zero_zero(rat))) | hAPP(rat,rat,abs_abs(rat),hAPP(int,rat,number_number_of(rat),A)) = hAPP(int,rat,number_number_of(rat),A).  [resolve(5909,a,5801,a)].
67.76/67.65	Derived: -number_ring(int) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),A)),zero_zero(int))) | hAPP(int,int,abs_abs(int),hAPP(int,int,number_number_of(int),A)) = hAPP(int,int,number_number_of(int),A).  [resolve(5909,a,5841,a)].
67.76/67.65	5910 -number_ring(A) | -linordered_idom(A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),pls)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),B)),zero_zero(A))) # label(fact_176_less__special_I3_J) # label(axiom).  [clausify(3779)].
67.76/67.65	Derived: -number_ring(real) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),pls)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,number_number_of(real),A)),zero_zero(real))).  [resolve(5910,b,5791,a)].
67.76/67.65	Derived: -number_ring(rat) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),pls)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(int,rat,number_number_of(rat),A)),zero_zero(rat))).  [resolve(5910,b,5801,a)].
67.76/67.65	Derived: -number_ring(int) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),pls)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),A)),zero_zero(int))).  [resolve(5910,b,5841,a)].
67.76/67.65	5911 -number_ring(A) | -linordered_idom(A) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),pls)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),B)),zero_zero(A))) # label(fact_176_less__special_I3_J) # label(axiom).  [clausify(3779)].
68.23/68.08	Derived: -number_ring(real) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),pls)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,number_number_of(real),A)),zero_zero(real))).  [resolve(5911,b,5791,a)].
68.23/68.08	Derived: -number_ring(rat) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),pls)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(int,rat,number_number_of(rat),A)),zero_zero(rat))).  [resolve(5911,b,5801,a)].
68.23/68.08	Derived: -number_ring(int) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),pls)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),A)),zero_zero(int))).  [resolve(5911,b,5841,a)].
68.23/68.08	5912 -linordered_idom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),C)))) # label(fact_251_zero__le__even__power_H) # label(axiom).  [clausify(3943)].
68.23/68.08	Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),B)))).  [resolve(5912,a,5791,a)].
68.23/68.08	Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),B)))).  [resolve(5912,a,5801,a)].
68.23/68.08	Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),B)))).  [resolve(5912,a,5841,a)].
68.23/68.08	5913 -linordered_idom(A) | hAPP(A,A,abs_abs(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),hAPP(A,A,uminus_uminus(A),B)),C)) = hAPP(A,A,abs_abs(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C)) # label(fact_2084_abs__power__minus) # label(axiom).  [clausify(3960)].
68.23/68.08	Derived: hAPP(real,real,abs_abs(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,uminus_uminus(real),A)),B)) = hAPP(real,real,abs_abs(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),B)).  [resolve(5913,a,5791,a)].
68.23/68.08	Derived: hAPP(rat,rat,abs_abs(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),hAPP(rat,rat,uminus_uminus(rat),A)),B)) = hAPP(rat,rat,abs_abs(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),B)).  [resolve(5913,a,5801,a)].
68.23/68.08	Derived: hAPP(int,int,abs_abs(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,uminus_uminus(int),A)),B)) = hAPP(int,int,abs_abs(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),B)).  [resolve(5913,a,5841,a)].
68.23/68.08	5914 -linordered_idom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),hAPP(A,A,abs_abs(A),C))) # label(fact_1845_dvd__abs__iff) # label(axiom).  [clausify(3993)].
68.23/68.08	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),dvd_dvd(real),A),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),dvd_dvd(real),A),hAPP(real,real,abs_abs(real),B))).  [resolve(5914,a,5791,a)].
68.23/68.08	Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),dvd_dvd(rat),A),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),dvd_dvd(rat),A),hAPP(rat,rat,abs_abs(rat),B))).  [resolve(5914,a,5801,a)].
68.23/68.08	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),hAPP(int,int,abs_abs(int),B))).  [resolve(5914,a,5841,a)].
68.23/68.08	5915 -linordered_idom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),hAPP(A,A,abs_abs(A),C))) # label(fact_1845_dvd__abs__iff) # label(axiom).  [clausify(3993)].
68.34/68.27	Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),dvd_dvd(real),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),dvd_dvd(real),A),hAPP(real,real,abs_abs(real),B))).  [resolve(5915,a,5791,a)].
68.34/68.27	Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),dvd_dvd(rat),A),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),dvd_dvd(rat),A),hAPP(rat,rat,abs_abs(rat),B))).  [resolve(5915,a,5801,a)].
68.34/68.27	Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),hAPP(int,int,abs_abs(int),B))).  [resolve(5915,a,5841,a)].
68.34/68.27	5916 -linordered_idom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | one_one(A) = hAPP(A,A,sgn_sgn(A),B) # label(fact_2222_sgn__1__pos) # label(axiom).  [clausify(4014)].
68.34/68.27	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | one_one(real) = hAPP(real,real,sgn_sgn(real),A).  [resolve(5916,a,5791,a)].
68.34/68.27	5917 -linordered_idom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | one_one(A) != hAPP(A,A,sgn_sgn(A),B) # label(fact_2222_sgn__1__pos) # label(axiom).  [clausify(4014)].
68.34/68.27	Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | one_one(real) != hAPP(real,real,sgn_sgn(real),A).  [resolve(5917,a,5791,a)].
68.34/68.27	Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)) | one_one(rat) != hAPP(rat,rat,sgn_sgn(rat),A).  [resolve(5917,a,5801,a)].
68.34/68.27	Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A)) | one_one(int) != hAPP(int,int,sgn_sgn(int),A).  [resolve(5917,a,5841,a)].
68.34/68.27	5918 -linordered_idom(A) | hAPP(A,A,abs_abs(A),hAPP(nat,A,semiring_1_of_nat(A),B)) = hAPP(nat,A,semiring_1_of_nat(A),B) # label(fact_1849_abs__of__nat) # label(axiom).  [clausify(4028)].
68.34/68.27	Derived: hAPP(real,real,abs_abs(real),hAPP(nat,real,semiring_1_of_nat(real),A)) = hAPP(nat,real,semiring_1_of_nat(real),A).  [resolve(5918,a,5791,a)].
68.34/68.27	Derived: hAPP(rat,rat,abs_abs(rat),hAPP(nat,rat,semiring_1_of_nat(rat),A)) = hAPP(nat,rat,semiring_1_of_nat(rat),A).  [resolve(5918,a,5801,a)].
68.34/68.27	Derived: hAPP(int,int,abs_abs(int),hAPP(nat,int,semiring_1_of_nat(int),A)) = hAPP(nat,int,semiring_1_of_nat(int),A).  [resolve(5918,a,5841,a)].
68.34/68.27	5919 -linordered_idom(A) | -hBOOL(hAPP(nat,bool,even_odd_even(nat),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,abs_abs(A),C)),hAPP(A,A,abs_abs(A),D))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),C),B)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),D),B))) # label(fact_2440_power__mono__even) # label(axiom).  [clausify(4131)].
68.34/68.27	Derived: -hBOOL(hAPP(nat,bool,even_odd_even(nat),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),B)),hAPP(real,real,abs_abs(real),C))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),B),A)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),C),A))).  [resolve(5919,a,5791,a)].
68.34/68.27	Derived: -hBOOL(hAPP(nat,bool,even_odd_even(nat),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,abs_abs(rat),B)),hAPP(rat,rat,abs_abs(rat),C))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),B),A)),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),C),A))).  [resolve(5919,a,5801,a)].
68.34/68.27	Derived: -hBOOL(hAPP(nat,bool,even_odd_even(nat),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,abs_abs(int),B)),hAPP(int,int,abs_abs(int),C))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),B),A)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),C),A))).  [resolve(5919,a,5841,a)].
68.34/68.27	5920 -linordered_idom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C)),zero_zero(A))) | -hBOOL(hAPP(nat,bool,even_odd_even(nat),C)) # label(fact_2436_power__less__zero__eq) # label(axiom).  [clausify(4147)].
68.70/68.51	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),B)),zero_zero(real))) | -hBOOL(hAPP(nat,bool,even_odd_even(nat),B)).  [resolve(5920,a,5791,a)].
68.70/68.51	Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),B)),zero_zero(rat))) | -hBOOL(hAPP(nat,bool,even_odd_even(nat),B)).  [resolve(5920,a,5801,a)].
68.70/68.51	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),B)),zero_zero(int))) | -hBOOL(hAPP(nat,bool,even_odd_even(nat),B)).  [resolve(5920,a,5841,a)].
68.70/68.51	5921 -linordered_idom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C)),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) # label(fact_2436_power__less__zero__eq) # label(axiom).  [clausify(4147)].
68.70/68.51	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),B)),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))).  [resolve(5921,a,5791,a)].
68.70/68.51	Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),B)),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),zero_zero(rat))).  [resolve(5921,a,5801,a)].
68.70/68.51	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),B)),zero_zero(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),zero_zero(int))).  [resolve(5921,a,5841,a)].
68.70/68.51	5922 -linordered_idom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C)),zero_zero(A))) | hBOOL(hAPP(nat,bool,even_odd_even(nat),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) # label(fact_2436_power__less__zero__eq) # label(axiom).  [clausify(4147)].
68.70/68.51	Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),B)),zero_zero(real))) | hBOOL(hAPP(nat,bool,even_odd_even(nat),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))).  [resolve(5922,a,5791,a)].
68.70/68.51	Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),B)),zero_zero(rat))) | hBOOL(hAPP(nat,bool,even_odd_even(nat),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),zero_zero(rat))).  [resolve(5922,a,5801,a)].
68.70/68.51	Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),B)),zero_zero(int))) | hBOOL(hAPP(nat,bool,even_odd_even(nat),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),zero_zero(int))).  [resolve(5922,a,5841,a)].
68.70/68.51	5923 -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_1855_abs__mult__self) # label(axiom).  [clausify(4217)].
68.70/68.51	Derived: hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,abs_abs(real),A)),hAPP(real,real,abs_abs(real),A)) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),A).  [resolve(5923,a,5791,a)].
68.70/68.51	Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(rat,rat,abs_abs(rat),A)),hAPP(rat,rat,abs_abs(rat),A)) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),A).  [resolve(5923,a,5801,a)].
68.70/68.51	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(5923,a,5841,a)].
68.70/68.51	5924 -linordered_idom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(int,nat,number_number_of(nat),C))),zero_zero(A))) | -hBOOL(hAPP(nat,bool,even_odd_even(nat),hAPP(int,nat,number_number_of(nat),C))) # label(fact_2456_power__less__zero__eq__number__of) # label(axiom).  [clausify(4337)].
68.96/68.79	5925 -linordered_idom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(int,nat,number_number_of(nat),C))),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) # label(fact_2456_power__less__zero__eq__number__of) # label(axiom).  [clausify(4337)].
68.96/68.79	5926 -linordered_idom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(int,nat,number_number_of(nat),C))),zero_zero(A))) | hBOOL(hAPP(nat,bool,even_odd_even(nat),hAPP(int,nat,number_number_of(nat),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) # label(fact_2456_power__less__zero__eq__number__of) # label(axiom).  [clausify(4337)].
68.96/68.79	5927 -linordered_idom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) | hAPP(A,A,abs_abs(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),B)) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,abs_abs(A),C)),B) # label(fact_1879_abs__mult__pos) # label(axiom).  [clausify(4542)].
68.96/68.79	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A)) | hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),A)) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,abs_abs(real),B)),A).  [resolve(5927,a,5791,a)].
68.96/68.79	Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),A)) | hAPP(rat,rat,abs_abs(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),B),A)) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(rat,rat,abs_abs(rat),B)),A).  [resolve(5927,a,5801,a)].
68.96/68.79	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A)) | hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),A)) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,abs_abs(int),B)),A).  [resolve(5927,a,5841,a)].
68.96/68.79	5928 -linordered_idom(A) | zero_zero(A) = ti(A,B) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),C),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))) # label(fact_8_sum__power2__gt__zero__iff) # label(axiom).  [clausify(4553)].
68.96/68.79	Derived: zero_zero(real) = ti(real,A) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))).  [resolve(5928,a,5791,a)].
68.96/68.79	Derived: zero_zero(rat) = ti(rat,A) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))).  [resolve(5928,a,5801,a)].
68.96/68.79	Derived: zero_zero(int) = ti(int,A) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))).  [resolve(5928,a,5841,a)].
69.07/68.95	5929 -linordered_idom(A) | zero_zero(A) = ti(A,B) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),C),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))) # label(fact_8_sum__power2__gt__zero__iff) # label(axiom).  [clausify(4553)].
69.07/68.95	Derived: zero_zero(real) = ti(real,A) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))).  [resolve(5929,a,5791,a)].
69.07/68.95	Derived: zero_zero(rat) = ti(rat,A) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))).  [resolve(5929,a,5801,a)].
69.07/68.95	Derived: zero_zero(int) = ti(int,A) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))).  [resolve(5929,a,5841,a)].
69.07/68.95	5930 -linordered_idom(A) | zero_zero(A) != ti(A,B) | zero_zero(A) != ti(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),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),C),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))) # label(fact_8_sum__power2__gt__zero__iff) # label(axiom).  [clausify(4553)].
69.07/68.95	Derived: zero_zero(real) != ti(real,A) | zero_zero(real) != ti(real,B) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))).  [resolve(5930,a,5791,a)].
69.07/68.95	Derived: zero_zero(rat) != ti(rat,A) | zero_zero(rat) != ti(rat,B) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))).  [resolve(5930,a,5801,a)].
69.07/68.95	Derived: zero_zero(int) != ti(int,A) | zero_zero(int) != ti(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),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))).  [resolve(5930,a,5841,a)].
69.07/68.95	5931 -linordered_idom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | hAPP(A,A,sgn_sgn(A),B) = hAPP(A,A,uminus_uminus(A),one_one(A)) # label(fact_2230_sgn__1__neg) # label(axiom).  [clausify(4696)].
69.21/69.06	5932 -linordered_idom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | hAPP(A,A,sgn_sgn(A),B) != hAPP(A,A,uminus_uminus(A),one_one(A)) # label(fact_2230_sgn__1__neg) # label(axiom).  [clausify(4696)].
69.21/69.06	Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))) | hAPP(real,real,sgn_sgn(real),A) != hAPP(real,real,uminus_uminus(real),one_one(real)).  [resolve(5932,a,5791,a)].
69.21/69.06	Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),zero_zero(rat))) | hAPP(rat,rat,sgn_sgn(rat),A) != hAPP(rat,rat,uminus_uminus(rat),one_one(rat)).  [resolve(5932,a,5801,a)].
69.21/69.06	Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),zero_zero(int))) | hAPP(int,int,sgn_sgn(int),A) != hAPP(int,int,uminus_uminus(int),one_one(int)).  [resolve(5932,a,5841,a)].
69.21/69.06	5933 -linordered_idom(A) | zero_zero(nat) != B | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),C),B))) # label(fact_2454_zero__less__power__eq) # label(axiom).  [clausify(4776)].
69.21/69.06	Derived: zero_zero(nat) != A | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),B),A))).  [resolve(5933,a,5791,a)].
69.21/69.06	Derived: zero_zero(nat) != A | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),B),A))).  [resolve(5933,a,5801,a)].
69.21/69.06	Derived: zero_zero(nat) != A | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),B),A))).  [resolve(5933,a,5841,a)].
69.21/69.06	5934 -linordered_idom(A) | -hBOOL(hAPP(nat,bool,even_odd_even(nat),B)) | zero_zero(A) = ti(A,C) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),C),B))) # label(fact_2454_zero__less__power__eq) # label(axiom).  [clausify(4776)].
69.21/69.06	Derived: -hBOOL(hAPP(nat,bool,even_odd_even(nat),A)) | zero_zero(real) = ti(real,B) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),B),A))).  [resolve(5934,a,5791,a)].
69.21/69.06	Derived: -hBOOL(hAPP(nat,bool,even_odd_even(nat),A)) | zero_zero(rat) = ti(rat,B) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),B),A))).  [resolve(5934,a,5801,a)].
69.21/69.06	Derived: -hBOOL(hAPP(nat,bool,even_odd_even(nat),A)) | zero_zero(int) = ti(int,B) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),B),A))).  [resolve(5934,a,5841,a)].
69.21/69.06	5935 -linordered_idom(A) | hBOOL(hAPP(nat,bool,even_odd_even(nat),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(nat,A,hAPP(A,fun(nat,A),power_power(A),C),B))) # label(fact_2454_zero__less__power__eq) # label(axiom).  [clausify(4776)].
69.21/69.06	Derived: hBOOL(hAPP(nat,bool,even_odd_even(nat),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),B),A))).  [resolve(5935,a,5791,a)].
69.21/69.06	Derived: hBOOL(hAPP(nat,bool,even_odd_even(nat),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),B),A))).  [resolve(5935,a,5801,a)].
69.21/69.06	Derived: hBOOL(hAPP(nat,bool,even_odd_even(nat),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(nat,int,hAPP(int,fun(nat,int),power_power(int),B),A))).  [resolve(5935,a,5841,a)].
69.21/69.06	5936 -linordered_idom(A) | zero_zero(nat) = B | hBOOL(hAPP(nat,bool,even_odd_even(nat),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(nat,A,hAPP(A,fun(nat,A),power_power(A),C),B))) # label(fact_2454_zero__less__power__eq) # label(axiom).  [clausify(4776)].
69.21/69.09	Derived: zero_zero(nat) = A | hBOOL(hAPP(nat,bool,even_odd_even(nat),A)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),B),A))).  [resolve(5936,a,5791,a)].
69.21/69.09	Derived: zero_zero(nat) = A | hBOOL(hAPP(nat,bool,even_odd_even(nat),A)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),B),A))).  [resolve(5936,a,5801,a)].
69.21/69.09	Derived: zero_zero(nat) = A | hBOOL(hAPP(nat,bool,even_odd_even(nat),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(nat,int,hAPP(int,fun(nat,int),power_power(int),B),A))).  [resolve(5936,a,5841,a)].
69.21/69.09	5937 -linordered_idom(A) | zero_zero(nat) = B | zero_zero(A) != ti(A,C) | -hBOOL(hAPP(nat,bool,even_odd_even(nat),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),C),B))) # label(fact_2454_zero__less__power__eq) # label(axiom).  [clausify(4776)].
69.21/69.09	Derived: zero_zero(nat) = A | zero_zero(real) != ti(real,B) | -hBOOL(hAPP(nat,bool,even_odd_even(nat),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),B),A))).  [resolve(5937,a,5791,a)].
69.21/69.09	Derived: zero_zero(nat) = A | zero_zero(rat) != ti(rat,B) | -hBOOL(hAPP(nat,bool,even_odd_even(nat),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),B),A))).  [resolve(5937,a,5801,a)].
69.21/69.09	Derived: zero_zero(nat) = A | zero_zero(int) != ti(int,B) | -hBOOL(hAPP(nat,bool,even_odd_even(nat),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),B),A))).  [resolve(5937,a,5841,a)].
69.21/69.09	5938 -linordered_idom(A) | zero_zero(nat) = B | zero_zero(A) != ti(A,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)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),C),B))) # label(fact_2454_zero__less__power__eq) # label(axiom).  [clausify(4776)].
69.21/69.09	Derived: zero_zero(nat) = A | zero_zero(real) != ti(real,B) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),B),A))).  [resolve(5938,a,5791,a)].
69.21/69.09	Derived: zero_zero(nat) = A | zero_zero(rat) != ti(rat,B) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),B),A))).  [resolve(5938,a,5801,a)].
69.21/69.09	Derived: zero_zero(nat) = A | zero_zero(int) != ti(int,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)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),B),A))).  [resolve(5938,a,5841,a)].
69.21/69.09	5939 -linordered_idom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),hAPP(A,A,abs_abs(A),B)),C))) # label(fact_1880_zero__le__power__abs) # label(axiom).  [clausify(4781)].
69.21/69.09	Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,abs_abs(real),A)),B))).  [resolve(5939,a,5791,a)].
69.21/69.09	Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),hAPP(rat,rat,abs_abs(rat),A)),B))).  [resolve(5939,a,5801,a)].
72.97/72.80	Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,abs_abs(int),A)),B))).  [resolve(5939,a,5841,a)].
72.97/72.80	5940 -linordered_idom(A) | hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),hAPP(A,A,abs_abs(A),B)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) # label(fact_1901_power2__abs) # label(axiom).  [clausify(4846)].
72.97/72.80	Derived: hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,abs_abs(real),A)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))).  [resolve(5940,a,5791,a)].
72.97/72.80	Derived: hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),hAPP(rat,rat,abs_abs(rat),A)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))).  [resolve(5940,a,5801,a)].
72.97/72.80	Derived: hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,abs_abs(int),A)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))).  [resolve(5940,a,5841,a)].
72.97/72.80	5941 ordere453448008miring(nat) # label(arity_Nat_Onat___Rings_Oordered__cancel__semiring) # label(axiom).  [assumption].
72.97/72.80	5942 -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_377_mult__nonneg__nonpos) # label(axiom).  [clausify(41)].
72.97/72.80	5943 -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_376_mult__nonneg__nonpos2) # label(axiom).  [clausify(180)].
72.97/72.80	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(5941,a,5942,a)].
72.97/72.80	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),zero_zero(nat))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),A)),zero_zero(nat))).  [resolve(5941,a,5943,a)].
72.97/72.80	5944 -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_378_mult__nonneg__nonneg) # label(axiom).  [clausify(1093)].
72.97/72.80	5945 ordere453448008miring(rat) # label(arity_Rat_Orat___Rings_Oordered__cancel__semiring) # label(axiom).  [assumption].
72.97/72.80	Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),B),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B)),zero_zero(rat))).  [resolve(5945,a,5942,a)].
72.97/72.80	Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),B),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),B),A)),zero_zero(rat))).  [resolve(5945,a,5943,a)].
73.89/73.73	Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B))).  [resolve(5945,a,5944,a)].
73.89/73.73	5946 ordere453448008miring(quickcheck_code_int) # label(arity_Quickcheck__Narrowing_Ocode__int___Rings_Oordered__cancel__semiring) # label(axiom).  [assumption].
73.89/73.73	Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),zero_zero(quickcheck_code_int)),A)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),B),zero_zero(quickcheck_code_int))) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),B)),zero_zero(quickcheck_code_int))).  [resolve(5946,a,5942,a)].
73.89/73.73	Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),zero_zero(quickcheck_code_int)),A)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),B),zero_zero(quickcheck_code_int))) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),B),A)),zero_zero(quickcheck_code_int))).  [resolve(5946,a,5943,a)].
73.89/73.73	Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),zero_zero(quickcheck_code_int)),A)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),zero_zero(quickcheck_code_int)),B)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),zero_zero(quickcheck_code_int)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),B))).  [resolve(5946,a,5944,a)].
73.89/73.73	5947 ordere453448008miring(real) # label(arity_RealDef_Oreal___Rings_Oordered__cancel__semiring) # label(axiom).  [assumption].
73.89/73.73	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),zero_zero(real))).  [resolve(5947,a,5942,a)].
73.89/73.73	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),A)),zero_zero(real))).  [resolve(5947,a,5943,a)].
73.89/73.73	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B))).  [resolve(5947,a,5944,a)].
73.89/73.73	5948 -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_375_mult__nonpos__nonneg) # label(axiom).  [clausify(2926)].
75.61/75.47	5949 ordere453448008miring(int) # label(arity_Int_Oint___Rings_Oordered__cancel__semiring) # label(axiom).  [assumption].
75.61/75.47	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(5949,a,5942,a)].
75.61/75.47	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),B),A)),zero_zero(int))).  [resolve(5949,a,5943,a)].
75.61/75.47	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(5949,a,5944,a)].
75.61/75.47	5950 ordere453448008miring(code_code_numeral) # label(arity_Code__Numeral_Ocode__numeral___Rings_Oordered__cancel__semiring) # label(axiom).  [assumption].
75.61/75.47	Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),zero_zero(code_code_numeral)),A)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),B),zero_zero(code_code_numeral))) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),B)),zero_zero(code_code_numeral))).  [resolve(5950,a,5942,a)].
75.61/75.47	Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),zero_zero(code_code_numeral)),A)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),B),zero_zero(code_code_numeral))) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),B),A)),zero_zero(code_code_numeral))).  [resolve(5950,a,5943,a)].
75.61/75.47	Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),zero_zero(code_code_numeral)),A)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),zero_zero(code_code_numeral)),B)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),zero_zero(code_code_numeral)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),B))).  [resolve(5950,a,5944,a)].
75.61/75.47	5951 -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_365_split__mult__neg__le) # label(axiom).  [clausify(4828)].
75.61/75.47	5952 -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_365_split__mult__neg__le) # label(axiom).  [clausify(4828)].
79.97/79.86	5953 division_ring(complex) # label(arity_Complex_Ocomplex___Fields_Odivision__ring) # label(axiom).  [assumption].
79.97/79.86	5954 -division_ring(A) | zero_zero(A) = ti(A,B) | hAPP(A,A,inverse_inverse(A),B) = hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),one_one(A)),B) # label(fact_2584_nonzero__inverse__eq__divide) # label(axiom).  [clausify(45)].
79.97/79.86	5955 -division_ring(A) | zero_zero(A) = ti(A,B) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),B) != ti(A,D) | hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),B) = ti(A,C) # label(fact_1693_eq__divide__imp) # label(axiom).  [clausify(67)].
79.97/79.86	5956 -division_ring(A) | zero_zero(A) = ti(A,B) | one_one(A) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(A,A,inverse_inverse(A),B)) # label(fact_2579_right__inverse) # label(axiom).  [clausify(197)].
79.97/79.86	5957 -division_ring(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),D)) = hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),D) # label(fact_1659_times__divide__eq__right) # label(axiom).  [clausify(582)].
79.97/79.86	5958 -division_ring(A) | zero_zero(A) = ti(A,B) | hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),hAPP(A,A,uminus_uminus(A),C)),hAPP(A,A,uminus_uminus(A),B)) = hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),B) # label(fact_2078_nonzero__minus__divide__divide) # label(axiom).  [clausify(586)].
79.97/79.86	5959 -division_ring(A) | zero_zero(A) = ti(A,B) | ti(A,C) != ti(A,B) | one_one(A) = hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),B) # label(fact_1696_right__inverse__eq) # label(axiom).  [clausify(632)].
79.97/79.86	5960 -division_ring(A) | zero_zero(A) = ti(A,B) | ti(A,C) = ti(A,B) | one_one(A) != hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),B) # label(fact_1696_right__inverse__eq) # label(axiom).  [clausify(632)].
79.97/79.86	5961 -division_ring(A) | hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),one_one(A)) = ti(A,B) # label(fact_1663_divide__1) # label(axiom).  [clausify(652)].
79.97/79.86	5962 -division_ring(A) | zero_zero(A) != hAPP(A,A,inverse_inverse(A),B) | zero_zero(A) = ti(A,B) # label(fact_2530_inverse__zero__imp__zero) # label(axiom).  [clausify(718)].
79.97/79.86	5963 -division_ring(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(A,A,inverse_inverse(A),C)) = hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C) # label(fact_2557_divide__inverse) # label(axiom).  [clausify(723)].
79.97/79.86	5964 -division_ring(A) | zero_zero(A) = ti(A,B) | zero_zero(A) = ti(A,C) | hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(A,A,inverse_inverse(A),B)),hAPP(A,A,inverse_inverse(A),C)) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,inverse_inverse(A),B)),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),C),B))),hAPP(A,A,inverse_inverse(A),C)) # label(fact_2582_division__ring__inverse__diff) # label(axiom).  [clausify(998)].
79.97/79.86	5965 -division_ring(A) | inverse_divide(A) = ti(fun(A,fun(A,A)),inverse_divide(A)) # label(tsy_c_Fields_Oinverse__class_Odivide_1_res) # label(axiom).  [clausify(1068)].
79.97/79.86	5966 -division_ring(A) | zero_zero(A) = ti(A,B) | zero_zero(A) = ti(A,C) | hAPP(A,A,uminus_uminus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,inverse_inverse(A),B)),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C))),hAPP(A,A,inverse_inverse(A),C))) = hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(A,A,inverse_inverse(A),B)),hAPP(A,A,inverse_inverse(A),C)) # label(fact_2611_inverse__diff__inverse) # label(axiom).  [clausify(1171)].
79.97/79.86	5967 -division_ring(A) | zero_zero(A) = ti(A,B) | hAPP(A,A,uminus_uminus(A),hAPP(A,A,inverse_inverse(A),B)) = hAPP(A,A,inverse_inverse(A),hAPP(A,A,uminus_uminus(A),B)) # label(fact_2556_nonzero__inverse__minus__eq) # label(axiom).  [clausify(1275)].
79.97/79.86	5968 -division_ring(A) | hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),D) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),D)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),D)) # label(fact_1662_add__divide__distrib) # label(axiom).  [clausify(1277)].
79.97/79.88	5969 -division_ring(A) | zero_zero(A) = ti(A,B) | zero_zero(A) = ti(A,C) | hAPP(A,A,inverse_inverse(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),hAPP(A,A,inverse_inverse(A),C)),hAPP(A,A,inverse_inverse(A),B)) # label(fact_2551_nonzero__inverse__mult__distrib) # label(axiom).  [clausify(1284)].
79.97/79.88	5970 -division_ring(A) | hAPP(A,A,uminus_uminus(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)) = hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),hAPP(A,A,uminus_uminus(A),B)),C) # label(fact_2019_minus__divide__left) # label(axiom).  [clausify(1856)].
79.97/79.88	5971 -division_ring(A) | zero_zero(A) = ti(A,B) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),B) != ti(A,D) | hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),B) = ti(A,C) # label(fact_1687_nonzero__eq__divide__eq) # label(axiom).  [clausify(2052)].
79.97/79.88	5972 -division_ring(A) | zero_zero(A) = ti(A,B) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),B) = ti(A,D) | hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),B) != ti(A,C) # label(fact_1687_nonzero__eq__divide__eq) # label(axiom).  [clausify(2052)].
79.97/79.88	5973 -division_ring(A) | one_one(A) = hAPP(A,A,inverse_inverse(A),one_one(A)) # label(fact_2516_inverse__1) # label(axiom).  [clausify(2389)].
79.97/79.88	5974 -division_ring(A) | hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),C)) = hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),D)),C) # label(fact_1665_diff__divide__distrib) # label(axiom).  [clausify(2837)].
79.97/79.88	Derived: zero_zero(complex) = ti(complex,A) | hAPP(complex,complex,inverse_inverse(complex),A) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),one_one(complex)),A).  [resolve(5953,a,5954,a)].
79.97/79.88	Derived: zero_zero(complex) = ti(complex,A) | hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),B),A) != ti(complex,C) | hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),C),A) = ti(complex,B).  [resolve(5953,a,5955,a)].
79.97/79.88	Derived: zero_zero(complex) = ti(complex,A) | one_one(complex) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),hAPP(complex,complex,inverse_inverse(complex),A)).  [resolve(5953,a,5956,a)].
79.97/79.88	Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),B),C)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),B)),C).  [resolve(5953,a,5957,a)].
79.97/79.88	Derived: zero_zero(complex) = ti(complex,A) | hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),hAPP(complex,complex,uminus_uminus(complex),B)),hAPP(complex,complex,uminus_uminus(complex),A)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),B),A).  [resolve(5953,a,5958,a)].
79.97/79.88	Derived: zero_zero(complex) = ti(complex,A) | ti(complex,B) != ti(complex,A) | one_one(complex) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),B),A).  [resolve(5953,a,5959,a)].
79.97/79.88	Derived: zero_zero(complex) = ti(complex,A) | ti(complex,B) = ti(complex,A) | one_one(complex) != hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),B),A).  [resolve(5953,a,5960,a)].
79.97/79.88	Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),A),one_one(complex)) = ti(complex,A).  [resolve(5953,a,5961,a)].
79.97/79.88	Derived: zero_zero(complex) != hAPP(complex,complex,inverse_inverse(complex),A) | zero_zero(complex) = ti(complex,A).  [resolve(5953,a,5962,a)].
79.97/79.88	Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),hAPP(complex,complex,inverse_inverse(complex),B)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),A),B).  [resolve(5953,a,5963,a)].
79.97/79.88	Derived: zero_zero(complex) = ti(complex,A) | zero_zero(complex) = ti(complex,B) | hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),hAPP(complex,complex,inverse_inverse(complex),A)),hAPP(complex,complex,inverse_inverse(complex),B)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,inverse_inverse(complex),A)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),B),A))),hAPP(complex,complex,inverse_inverse(complex),B)).  [resolve(5953,a,5964,a)].
80.20/80.06	Derived: inverse_divide(complex) = ti(fun(complex,fun(complex,complex)),inverse_divide(complex)).  [resolve(5953,a,5965,a)].
80.20/80.06	Derived: zero_zero(complex) = ti(complex,A) | zero_zero(complex) = ti(complex,B) | hAPP(complex,complex,uminus_uminus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,inverse_inverse(complex),A)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),A),B))),hAPP(complex,complex,inverse_inverse(complex),B))) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),hAPP(complex,complex,inverse_inverse(complex),A)),hAPP(complex,complex,inverse_inverse(complex),B)).  [resolve(5953,a,5966,a)].
80.20/80.06	Derived: zero_zero(complex) = ti(complex,A) | hAPP(complex,complex,uminus_uminus(complex),hAPP(complex,complex,inverse_inverse(complex),A)) = hAPP(complex,complex,inverse_inverse(complex),hAPP(complex,complex,uminus_uminus(complex),A)).  [resolve(5953,a,5967,a)].
80.20/80.06	Derived: zero_zero(complex) = ti(complex,A) | zero_zero(complex) = ti(complex,B) | hAPP(complex,complex,inverse_inverse(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),B)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,inverse_inverse(complex),B)),hAPP(complex,complex,inverse_inverse(complex),A)).  [resolve(5953,a,5969,a)].
80.20/80.06	Derived: zero_zero(complex) = ti(complex,A) | hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),B),A) = ti(complex,C) | hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),C),A) != ti(complex,B).  [resolve(5953,a,5972,a)].
80.20/80.06	Derived: one_one(complex) = hAPP(complex,complex,inverse_inverse(complex),one_one(complex)).  [resolve(5953,a,5973,a)].
80.20/80.06	5975 -number(A) | -division_ring(A) | hAPP(A,A,inverse_inverse(A),hAPP(int,A,number_number_of(A),B)) = hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),one_one(A)),hAPP(int,A,number_number_of(A),B)) # label(fact_2588_inverse__eq__divide__number__of) # label(axiom).  [clausify(2946)].
80.20/80.06	Derived: -number(complex) | hAPP(complex,complex,inverse_inverse(complex),hAPP(int,complex,number_number_of(complex),A)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),one_one(complex)),hAPP(int,complex,number_number_of(complex),A)).  [resolve(5975,b,5953,a)].
80.20/80.06	5976 -division_ring(A) | zero_zero(A) = ti(A,B) | hAPP(A,A,uminus_uminus(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),B)) = hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),hAPP(A,A,uminus_uminus(A),B)) # label(fact_2077_nonzero__minus__divide__right) # label(axiom).  [clausify(3114)].
80.20/80.06	Derived: zero_zero(complex) = ti(complex,A) | hAPP(complex,complex,uminus_uminus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),B),A)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),B),hAPP(complex,complex,uminus_uminus(complex),A)).  [resolve(5976,a,5953,a)].
80.20/80.06	5977 -division_ring(A) | zero_zero(A) = ti(A,B) | hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),B) != ti(A,D) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),B) = ti(A,C) # label(fact_1688_nonzero__divide__eq__eq) # label(axiom).  [clausify(3174)].
80.20/80.06	5978 -division_ring(A) | zero_zero(A) = ti(A,B) | hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),B) = ti(A,D) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),B) != ti(A,C) # label(fact_1688_nonzero__divide__eq__eq) # label(axiom).  [clausify(3174)].
80.47/80.40	5979 -division_ring(A) | zero_zero(A) = ti(A,B) | zero_zero(A) = ti(A,C) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,inverse_inverse(A),B)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C))),hAPP(A,A,inverse_inverse(A),C)) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,inverse_inverse(A),B)),hAPP(A,A,inverse_inverse(A),C)) # label(fact_2577_division__ring__inverse__add) # label(axiom).  [clausify(3449)].
80.47/80.40	Derived: zero_zero(complex) = ti(complex,A) | zero_zero(complex) = ti(complex,B) | hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,inverse_inverse(complex),A)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),A),B))),hAPP(complex,complex,inverse_inverse(complex),B)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(complex,complex,inverse_inverse(complex),A)),hAPP(complex,complex,inverse_inverse(complex),B)).  [resolve(5979,a,5953,a)].
80.47/80.40	5980 -division_ring(A) | one_one(A) != hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C) | hAPP(A,A,inverse_inverse(A),B) = ti(A,C) # label(fact_2552_inverse__unique) # label(axiom).  [clausify(3548)].
80.47/80.40	Derived: one_one(complex) != hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),B) | hAPP(complex,complex,inverse_inverse(complex),A) = ti(complex,B).  [resolve(5980,a,5953,a)].
80.47/80.40	5981 division_ring(rat) # label(arity_Rat_Orat___Fields_Odivision__ring) # label(axiom).  [assumption].
80.47/80.40	Derived: zero_zero(rat) = ti(rat,A) | hAPP(rat,rat,inverse_inverse(rat),A) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),one_one(rat)),A).  [resolve(5981,a,5954,a)].
80.47/80.40	Derived: zero_zero(rat) = ti(rat,A) | hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),B),A) != ti(rat,C) | hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),C),A) = ti(rat,B).  [resolve(5981,a,5955,a)].
80.47/80.40	Derived: zero_zero(rat) = ti(rat,A) | one_one(rat) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),hAPP(rat,rat,inverse_inverse(rat),A)).  [resolve(5981,a,5956,a)].
80.47/80.40	Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),B),C)) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B)),C).  [resolve(5981,a,5957,a)].
80.47/80.40	Derived: zero_zero(rat) = ti(rat,A) | hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),hAPP(rat,rat,uminus_uminus(rat),B)),hAPP(rat,rat,uminus_uminus(rat),A)) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),B),A).  [resolve(5981,a,5958,a)].
80.47/80.40	Derived: zero_zero(rat) = ti(rat,A) | ti(rat,B) != ti(rat,A) | one_one(rat) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),B),A).  [resolve(5981,a,5959,a)].
80.47/80.40	Derived: zero_zero(rat) = ti(rat,A) | ti(rat,B) = ti(rat,A) | one_one(rat) != hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),B),A).  [resolve(5981,a,5960,a)].
80.47/80.40	Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),one_one(rat)) = ti(rat,A).  [resolve(5981,a,5961,a)].
80.47/80.40	Derived: zero_zero(rat) != hAPP(rat,rat,inverse_inverse(rat),A) | zero_zero(rat) = ti(rat,A).  [resolve(5981,a,5962,a)].
80.47/80.40	Derived: zero_zero(rat) = ti(rat,A) | zero_zero(rat) = ti(rat,B) | hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),hAPP(rat,rat,inverse_inverse(rat),A)),hAPP(rat,rat,inverse_inverse(rat),B)) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(rat,rat,inverse_inverse(rat),A)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),B),A))),hAPP(rat,rat,inverse_inverse(rat),B)).  [resolve(5981,a,5964,a)].
80.47/80.40	Derived: inverse_divide(rat) = ti(fun(rat,fun(rat,rat)),inverse_divide(rat)).  [resolve(5981,a,5965,a)].
80.47/80.40	Derived: zero_zero(rat) = ti(rat,A) | zero_zero(rat) = ti(rat,B) | hAPP(rat,rat,uminus_uminus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(rat,rat,inverse_inverse(rat),A)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),A),B))),hAPP(rat,rat,inverse_inverse(rat),B))) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),hAPP(rat,rat,inverse_inverse(rat),A)),hAPP(rat,rat,inverse_inverse(rat),B)).  [resolve(5981,a,5966,a)].
80.99/80.92	Derived: zero_zero(rat) = ti(rat,A) | hAPP(rat,rat,uminus_uminus(rat),hAPP(rat,rat,inverse_inverse(rat),A)) = hAPP(rat,rat,inverse_inverse(rat),hAPP(rat,rat,uminus_uminus(rat),A)).  [resolve(5981,a,5967,a)].
80.99/80.92	Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),B)),C) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),C)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),B),C)).  [resolve(5981,a,5968,a)].
80.99/80.92	Derived: zero_zero(rat) = ti(rat,A) | zero_zero(rat) = ti(rat,B) | hAPP(rat,rat,inverse_inverse(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B)) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(rat,rat,inverse_inverse(rat),B)),hAPP(rat,rat,inverse_inverse(rat),A)).  [resolve(5981,a,5969,a)].
80.99/80.92	Derived: hAPP(rat,rat,uminus_uminus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),B)) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),hAPP(rat,rat,uminus_uminus(rat),A)),B).  [resolve(5981,a,5970,a)].
80.99/80.92	Derived: zero_zero(rat) = ti(rat,A) | hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),B),A) = ti(rat,C) | hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),C),A) != ti(rat,B).  [resolve(5981,a,5972,a)].
80.99/80.92	Derived: one_one(rat) = hAPP(rat,rat,inverse_inverse(rat),one_one(rat)).  [resolve(5981,a,5973,a)].
80.99/80.92	Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),B)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),C),B)) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),A),C)),B).  [resolve(5981,a,5974,a)].
80.99/80.92	Derived: -number(rat) | hAPP(rat,rat,inverse_inverse(rat),hAPP(int,rat,number_number_of(rat),A)) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),one_one(rat)),hAPP(int,rat,number_number_of(rat),A)).  [resolve(5981,a,5975,b)].
80.99/80.92	Derived: zero_zero(rat) = ti(rat,A) | hAPP(rat,rat,uminus_uminus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),B),A)) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),B),hAPP(rat,rat,uminus_uminus(rat),A)).  [resolve(5981,a,5976,a)].
80.99/80.92	Derived: zero_zero(rat) = ti(rat,A) | zero_zero(rat) = ti(rat,B) | hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(rat,rat,inverse_inverse(rat),A)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),B))),hAPP(rat,rat,inverse_inverse(rat),B)) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(rat,rat,inverse_inverse(rat),A)),hAPP(rat,rat,inverse_inverse(rat),B)).  [resolve(5981,a,5979,a)].
80.99/80.92	Derived: one_one(rat) != hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B) | hAPP(rat,rat,inverse_inverse(rat),A) = ti(rat,B).  [resolve(5981,a,5980,a)].
80.99/80.92	5982 division_ring(real) # label(arity_RealDef_Oreal___Fields_Odivision__ring) # label(axiom).  [assumption].
80.99/80.92	Derived: zero_zero(real) = ti(real,A) | hAPP(real,real,inverse_inverse(real),A) = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),one_one(real)),A).  [resolve(5982,a,5954,a)].
80.99/80.92	Derived: zero_zero(real) = ti(real,A) | hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),A) != ti(real,C) | hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),C),A) = ti(real,B).  [resolve(5982,a,5955,a)].
80.99/80.92	Derived: zero_zero(real) = ti(real,A) | one_one(real) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),hAPP(real,real,inverse_inverse(real),A)).  [resolve(5982,a,5956,a)].
80.99/80.92	Derived: hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),B),C)) = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),C).  [resolve(5982,a,5957,a)].
80.99/80.92	Derived: zero_zero(real) = ti(real,A) | hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,uminus_uminus(real),B)),hAPP(real,real,uminus_uminus(real),A)) = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),B),A).  [resolve(5982,a,5958,a)].
81.04/80.94	Derived: zero_zero(real) = ti(real,A) | ti(real,B) != ti(real,A) | one_one(real) = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),B),A).  [resolve(5982,a,5959,a)].
81.04/80.94	Derived: zero_zero(real) = ti(real,A) | ti(real,B) = ti(real,A) | one_one(real) != hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),B),A).  [resolve(5982,a,5960,a)].
81.04/80.94	Derived: hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),one_one(real)) = ti(real,A).  [resolve(5982,a,5961,a)].
81.04/80.94	Derived: zero_zero(real) != hAPP(real,real,inverse_inverse(real),A) | zero_zero(real) = ti(real,A).  [resolve(5982,a,5962,a)].
81.04/80.94	Derived: zero_zero(real) = ti(real,A) | zero_zero(real) = ti(real,B) | hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,inverse_inverse(real),A)),hAPP(real,real,inverse_inverse(real),B)) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,inverse_inverse(real),A)),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),B),A))),hAPP(real,real,inverse_inverse(real),B)).  [resolve(5982,a,5964,a)].
81.04/80.94	Derived: inverse_divide(real) = ti(fun(real,fun(real,real)),inverse_divide(real)).  [resolve(5982,a,5965,a)].
81.04/80.94	Derived: zero_zero(real) = ti(real,A) | zero_zero(real) = ti(real,B) | hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,inverse_inverse(real),A)),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),B))),hAPP(real,real,inverse_inverse(real),B))) = hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,inverse_inverse(real),A)),hAPP(real,real,inverse_inverse(real),B)).  [resolve(5982,a,5966,a)].
81.04/80.94	Derived: zero_zero(real) = ti(real,A) | hAPP(real,real,uminus_uminus(real),hAPP(real,real,inverse_inverse(real),A)) = hAPP(real,real,inverse_inverse(real),hAPP(real,real,uminus_uminus(real),A)).  [resolve(5982,a,5967,a)].
81.04/80.94	Derived: zero_zero(real) = ti(real,A) | zero_zero(real) = ti(real,B) | hAPP(real,real,inverse_inverse(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,inverse_inverse(real),B)),hAPP(real,real,inverse_inverse(real),A)).  [resolve(5982,a,5969,a)].
81.04/80.94	Derived: zero_zero(real) = ti(real,A) | hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),A) = ti(real,C) | hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),C),A) != ti(real,B).  [resolve(5982,a,5972,a)].
81.04/80.94	Derived: one_one(real) = hAPP(real,real,inverse_inverse(real),one_one(real)).  [resolve(5982,a,5973,a)].
81.04/80.94	Derived: -number(real) | hAPP(real,real,inverse_inverse(real),hAPP(int,real,number_number_of(real),A)) = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),one_one(real)),hAPP(int,real,number_number_of(real),A)).  [resolve(5982,a,5975,b)].
81.04/80.94	Derived: zero_zero(real) = ti(real,A) | hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),B),A)) = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),B),hAPP(real,real,uminus_uminus(real),A)).  [resolve(5982,a,5976,a)].
81.04/80.94	Derived: zero_zero(real) = ti(real,A) | zero_zero(real) = ti(real,B) | hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,inverse_inverse(real),A)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),B))),hAPP(real,real,inverse_inverse(real),B)) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,inverse_inverse(real),A)),hAPP(real,real,inverse_inverse(real),B)).  [resolve(5982,a,5979,a)].
81.04/80.94	Derived: one_one(real) != hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B) | hAPP(real,real,inverse_inverse(real),A) = ti(real,B).  [resolve(5982,a,5980,a)].
81.56/81.48	5983 -division_ring(A) | zero_zero(A) = hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),zero_zero(A)),B) # label(fact_1658_divide__zero__left) # label(axiom).  [clausify(4243)].
81.56/81.48	Derived: zero_zero(rat) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),zero_zero(rat)),A).  [resolve(5983,a,5981,a)].
81.56/81.48	5984 -division_ring(A) | zero_zero(A) = ti(A,B) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),B) != ti(A,D) | hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),B) = ti(A,C) # label(fact_1692_divide__eq__imp) # label(axiom).  [clausify(4268)].
81.56/81.48	5985 -division_ring(A) | inverse_inverse(A) = ti(fun(A,A),inverse_inverse(A)) # label(tsy_c_Fields_Oinverse__class_Oinverse_res) # label(axiom).  [clausify(4284)].
81.56/81.48	Derived: inverse_inverse(complex) = ti(fun(complex,complex),inverse_inverse(complex)).  [resolve(5985,a,5953,a)].
81.56/81.48	Derived: inverse_inverse(rat) = ti(fun(rat,rat),inverse_inverse(rat)).  [resolve(5985,a,5981,a)].
81.56/81.48	Derived: inverse_inverse(real) = ti(fun(real,real),inverse_inverse(real)).  [resolve(5985,a,5982,a)].
81.56/81.48	5986 -division_ring(A) | zero_zero(A) = ti(A,B) | hAPP(A,A,inverse_inverse(A),hAPP(A,A,inverse_inverse(A),B)) = ti(A,B) # label(fact_2529_nonzero__inverse__inverse__eq) # label(axiom).  [clausify(4324)].
81.56/81.48	Derived: zero_zero(complex) = ti(complex,A) | hAPP(complex,complex,inverse_inverse(complex),hAPP(complex,complex,inverse_inverse(complex),A)) = ti(complex,A).  [resolve(5986,a,5953,a)].
81.56/81.48	Derived: zero_zero(rat) = ti(rat,A) | hAPP(rat,rat,inverse_inverse(rat),hAPP(rat,rat,inverse_inverse(rat),A)) = ti(rat,A).  [resolve(5986,a,5981,a)].
81.56/81.48	Derived: zero_zero(real) = ti(real,A) | hAPP(real,real,inverse_inverse(real),hAPP(real,real,inverse_inverse(real),A)) = ti(real,A).  [resolve(5986,a,5982,a)].
81.56/81.48	5987 -division_ring(A) | hAPP(A,A,inverse_inverse(A),B) = hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),one_one(A)),B) # label(fact_2560_inverse__eq__divide) # label(axiom).  [clausify(4335)].
81.56/81.48	Derived: hAPP(complex,complex,inverse_inverse(complex),A) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),one_one(complex)),A).  [resolve(5987,a,5953,a)].
81.56/81.48	Derived: hAPP(rat,rat,inverse_inverse(rat),A) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),one_one(rat)),A).  [resolve(5987,a,5981,a)].
81.56/81.48	Derived: hAPP(real,real,inverse_inverse(real),A) = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),one_one(real)),A).  [resolve(5987,a,5982,a)].
81.56/81.48	5988 -division_ring(A) | hAPP(A,A,inverse_inverse(A),B) != hAPP(A,A,inverse_inverse(A),C) | zero_zero(A) = ti(A,C) | zero_zero(A) = ti(A,B) | ti(A,B) = ti(A,C) # label(fact_2531_nonzero__inverse__eq__imp__eq) # label(axiom).  [clausify(4437)].
81.56/81.48	Derived: hAPP(complex,complex,inverse_inverse(complex),A) != hAPP(complex,complex,inverse_inverse(complex),B) | zero_zero(complex) = ti(complex,B) | zero_zero(complex) = ti(complex,A) | ti(complex,A) = ti(complex,B).  [resolve(5988,a,5953,a)].
81.56/81.48	Derived: hAPP(rat,rat,inverse_inverse(rat),A) != hAPP(rat,rat,inverse_inverse(rat),B) | zero_zero(rat) = ti(rat,B) | zero_zero(rat) = ti(rat,A) | ti(rat,A) = ti(rat,B).  [resolve(5988,a,5981,a)].
81.56/81.48	Derived: hAPP(real,real,inverse_inverse(real),A) != hAPP(real,real,inverse_inverse(real),B) | zero_zero(real) = ti(real,B) | zero_zero(real) = ti(real,A) | ti(real,A) = ti(real,B).  [resolve(5988,a,5982,a)].
81.56/81.48	5989 -division_ring(A) | zero_zero(A) = ti(A,B) | one_one(A) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,inverse_inverse(A),B)),B) # label(fact_2581_left__inverse) # label(axiom).  [clausify(4454)].
81.56/81.48	Derived: zero_zero(complex) = ti(complex,A) | one_one(complex) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,inverse_inverse(complex),A)),A).  [resolve(5989,a,5953,a)].
81.56/81.48	Derived: zero_zero(rat) = ti(rat,A) | one_one(rat) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(rat,rat,inverse_inverse(rat),A)),A).  [resolve(5989,a,5981,a)].
81.56/81.48	Derived: zero_zero(real) = ti(real,A) | one_one(real) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,inverse_inverse(real),A)),A).  [resolve(5989,a,5982,a)].
85.56/85.47	5990 -division_ring(A) | zero_zero(A) = ti(A,B) | hAPP(A,A,inverse_inverse(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C)) = hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),hAPP(A,A,inverse_inverse(A),B)),C) # label(fact_2553_nonzero__power__inverse) # label(axiom).  [clausify(4489)].
85.56/85.47	Derived: zero_zero(complex) = ti(complex,A) | hAPP(complex,complex,inverse_inverse(complex),hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),A),B)) = hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),hAPP(complex,complex,inverse_inverse(complex),A)),B).  [resolve(5990,a,5953,a)].
85.56/85.47	Derived: zero_zero(rat) = ti(rat,A) | hAPP(rat,rat,inverse_inverse(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),B)) = hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),hAPP(rat,rat,inverse_inverse(rat),A)),B).  [resolve(5990,a,5981,a)].
85.56/85.47	Derived: zero_zero(real) = ti(real,A) | hAPP(real,real,inverse_inverse(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),B)) = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,inverse_inverse(real),A)),B).  [resolve(5990,a,5982,a)].
85.56/85.47	5991 -division_ring(A) | zero_zero(A) = ti(A,B) | one_one(A) = hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),B) # label(fact_1695_divide__self) # label(axiom).  [clausify(4498)].
85.56/85.47	Derived: zero_zero(complex) = ti(complex,A) | one_one(complex) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),A),A).  [resolve(5991,a,5953,a)].
85.56/85.47	Derived: zero_zero(rat) = ti(rat,A) | one_one(rat) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),A).  [resolve(5991,a,5981,a)].
85.56/85.47	Derived: zero_zero(real) = ti(real,A) | one_one(real) = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),A).  [resolve(5991,a,5982,a)].
85.56/85.47	5992 -division_ring(A) | zero_zero(A) = ti(A,B) | zero_zero(A) != hAPP(A,A,inverse_inverse(A),B) # label(fact_2528_nonzero__imp__inverse__nonzero) # label(axiom).  [clausify(4627)].
85.56/85.47	5993 ring_1(complex) # label(arity_Complex_Ocomplex___Rings_Oring__1) # label(axiom).  [assumption].
85.56/85.47	5994 -ring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),hAPP(A,A,uminus_uminus(A),one_one(A))),B)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),C),B)) = hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),hAPP(A,A,uminus_uminus(A),C)),B) # label(fact_2097_power__minus) # label(axiom).  [clausify(55)].
85.56/85.47	Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),hAPP(complex,complex,uminus_uminus(complex),one_one(complex))),A)),hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),B),A)) = hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),hAPP(complex,complex,uminus_uminus(complex),B)),A).  [resolve(5993,a,5994,a)].
85.56/85.47	5995 -ring_1(A) | hAPP(A,A,uminus_uminus(A),hAPP(int,A,ring_1_of_int(A),B)) = hAPP(int,A,ring_1_of_int(A),hAPP(int,int,uminus_uminus(int),B)) # label(fact_3568_of__int__minus) # label(axiom).  [clausify(403)].
85.56/85.47	Derived: hAPP(complex,complex,uminus_uminus(complex),hAPP(int,complex,ring_1_of_int(complex),A)) = hAPP(int,complex,ring_1_of_int(complex),hAPP(int,int,uminus_uminus(int),A)).  [resolve(5995,a,5993,a)].
85.56/85.47	5996 -ring_1(A) | hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),hAPP(A,A,uminus_uminus(A),B)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) # label(fact_2115_power2__minus) # label(axiom).  [clausify(678)].
85.56/85.47	Derived: hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),hAPP(complex,complex,uminus_uminus(complex),A)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))).  [resolve(5996,a,5993,a)].
85.56/85.47	5997 -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_3805_Ints__of__nat) # label(axiom).  [clausify(692)].
85.56/85.48	Derived: hBOOL(hAPP(fun(complex,bool),bool,hAPP(complex,fun(fun(complex,bool),bool),member(complex),hAPP(nat,complex,semiring_1_of_nat(complex),A)),ring_1_Ints(complex))).  [resolve(5997,a,5993,a)].
85.56/85.48	5998 -ring_1(A) | -real_normed_vector(A) | -hBOOL(hAPP(fun(nat,A),bool,summable(A),hAPP(fun(nat,A),fun(nat,A),hAPP(fun(nat,fun(A,A)),fun(fun(nat,A),fun(nat,A)),combs(nat,A,A),hAPP(fun(nat,A),fun(nat,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(nat,A),fun(nat,fun(A,A))),combb(A,fun(A,A),nat),times_times(A)),hAPP(fun(nat,A),fun(nat,A),diffs(A),B))),hAPP(A,fun(nat,A),power_power(A),C)))) | hBOOL(hAPP(A,bool,hAPP(fun(nat,A),fun(A,bool),sums(A),hAPP(fun(nat,A),fun(nat,A),hAPP(fun(nat,fun(A,A)),fun(fun(nat,A),fun(nat,A)),combs(nat,A,A),hAPP(fun(nat,A),fun(nat,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(nat,A),fun(nat,fun(A,A))),combb(A,fun(A,A),nat),times_times(A)),hAPP(fun(nat,A),fun(nat,A),hAPP(fun(nat,fun(A,A)),fun(fun(nat,A),fun(nat,A)),combs(nat,A,A),hAPP(fun(nat,A),fun(nat,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(nat,A),fun(nat,fun(A,A))),combb(A,fun(A,A),nat),times_times(A)),semiring_1_of_nat(A))),B))),hAPP(fun(nat,nat),fun(nat,A),hAPP(fun(nat,A),fun(fun(nat,nat),fun(nat,A)),combb(nat,A,nat),hAPP(A,fun(nat,A),power_power(A),C)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),minus_minus(nat)),hAPP(nat,nat,suc,zero_zero(nat)))))),hAPP(fun(nat,A),A,suminf(A),hAPP(fun(nat,A),fun(nat,A),hAPP(fun(nat,fun(A,A)),fun(fun(nat,A),fun(nat,A)),combs(nat,A,A),hAPP(fun(nat,A),fun(nat,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(nat,A),fun(nat,fun(A,A))),combb(A,fun(A,A),nat),times_times(A)),hAPP(fun(nat,A),fun(nat,A),diffs(A),B))),hAPP(A,fun(nat,A),power_power(A),C))))) # label(fact_4107_diffs__equiv) # label(axiom).  [clausify(706)].
85.56/85.48	Derived: -real_normed_vector(complex) | -hBOOL(hAPP(fun(nat,complex),bool,summable(complex),hAPP(fun(nat,complex),fun(nat,complex),hAPP(fun(nat,fun(complex,complex)),fun(fun(nat,complex),fun(nat,complex)),combs(nat,complex,complex),hAPP(fun(nat,complex),fun(nat,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(nat,complex),fun(nat,fun(complex,complex))),combb(complex,fun(complex,complex),nat),times_times(complex)),hAPP(fun(nat,complex),fun(nat,complex),diffs(complex),A))),hAPP(complex,fun(nat,complex),power_power(complex),B)))) | hBOOL(hAPP(complex,bool,hAPP(fun(nat,complex),fun(complex,bool),sums(complex),hAPP(fun(nat,complex),fun(nat,complex),hAPP(fun(nat,fun(complex,complex)),fun(fun(nat,complex),fun(nat,complex)),combs(nat,complex,complex),hAPP(fun(nat,complex),fun(nat,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(nat,complex),fun(nat,fun(complex,complex))),combb(complex,fun(complex,complex),nat),times_times(complex)),hAPP(fun(nat,complex),fun(nat,complex),hAPP(fun(nat,fun(complex,complex)),fun(fun(nat,complex),fun(nat,complex)),combs(nat,complex,complex),hAPP(fun(nat,complex),fun(nat,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(nat,complex),fun(nat,fun(complex,complex))),combb(complex,fun(complex,complex),nat),times_times(complex)),semiring_1_of_nat(complex))),A))),hAPP(fun(nat,nat),fun(nat,complex),hAPP(fun(nat,complex),fun(fun(nat,nat),fun(nat,complex)),combb(nat,complex,nat),hAPP(complex,fun(nat,complex),power_power(complex),B)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),minus_minus(nat)),hAPP(nat,nat,suc,zero_zero(nat)))))),hAPP(fun(nat,complex),complex,suminf(complex),hAPP(fun(nat,complex),fun(nat,complex),hAPP(fun(nat,fun(complex,complex)),fun(fun(nat,complex),fun(nat,complex)),combs(nat,complex,complex),hAPP(fun(nat,complex),fun(nat,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(nat,complex),fun(nat,fun(complex,complex))),combb(complex,fun(complex,complex),nat),times_times(complex)),hAPP(fun(nat,complex),fun(nat,complex),diffs(complex),A))),hAPP(complex,fun(nat,complex),power_power(complex),B))))).  [resolve(5998,a,5993,a)].
85.71/85.63	5999 -ring_1(A) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),B),ring_1_Ints(A))) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),hAPP(A,A,uminus_uminus(A),B)),ring_1_Ints(A))) # label(fact_3858_Ints__minus) # label(axiom).  [clausify(716)].
85.71/85.63	Derived: -hBOOL(hAPP(fun(complex,bool),bool,hAPP(complex,fun(fun(complex,bool),bool),member(complex),A),ring_1_Ints(complex))) | hBOOL(hAPP(fun(complex,bool),bool,hAPP(complex,fun(fun(complex,bool),bool),member(complex),hAPP(complex,complex,uminus_uminus(complex),A)),ring_1_Ints(complex))).  [resolve(5999,a,5993,a)].
85.71/85.63	6000 -ring_1(A) | zero_zero(A) = hAPP(int,A,ring_1_of_int(A),zero_zero(int)) # label(fact_3580_of__int__0) # label(axiom).  [clausify(978)].
85.71/85.63	Derived: zero_zero(complex) = hAPP(int,complex,ring_1_of_int(complex),zero_zero(int)).  [resolve(6000,a,5993,a)].
85.71/85.63	6001 -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_3824_Ints__add) # label(axiom).  [clausify(1027)].
85.71/85.63	Derived: -hBOOL(hAPP(fun(complex,bool),bool,hAPP(complex,fun(fun(complex,bool),bool),member(complex),A),ring_1_Ints(complex))) | -hBOOL(hAPP(fun(complex,bool),bool,hAPP(complex,fun(fun(complex,bool),bool),member(complex),B),ring_1_Ints(complex))) | hBOOL(hAPP(fun(complex,bool),bool,hAPP(complex,fun(fun(complex,bool),bool),member(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),A),B)),ring_1_Ints(complex))).  [resolve(6001,a,5993,a)].
85.71/85.63	6002 ring_1(real) # label(arity_RealDef_Oreal___Rings_Oring__1) # label(axiom).  [assumption].
85.71/85.63	Derived: hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,uminus_uminus(real),one_one(real))),A)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),B),A)) = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,uminus_uminus(real),B)),A).  [resolve(6002,a,5994,a)].
85.71/85.63	Derived: hAPP(real,real,uminus_uminus(real),hAPP(int,real,ring_1_of_int(real),A)) = hAPP(int,real,ring_1_of_int(real),hAPP(int,int,uminus_uminus(int),A)).  [resolve(6002,a,5995,a)].
85.71/85.63	Derived: hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,uminus_uminus(real),A)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))).  [resolve(6002,a,5996,a)].
85.71/85.63	Derived: hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),hAPP(nat,real,semiring_1_of_nat(real),A)),ring_1_Ints(real))).  [resolve(6002,a,5997,a)].
85.71/85.63	Derived: -real_normed_vector(real) | -hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(fun(nat,real),fun(nat,real),diffs(real),A))),hAPP(real,fun(nat,real),power_power(real),B)))) | hBOOL(hAPP(real,bool,hAPP(fun(nat,real),fun(real,bool),sums(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),semiring_1_of_nat(real))),A))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),hAPP(real,fun(nat,real),power_power(real),B)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),minus_minus(nat)),hAPP(nat,nat,suc,zero_zero(nat)))))),hAPP(fun(nat,real),real,suminf(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(fun(nat,real),fun(nat,real),diffs(real),A))),hAPP(real,fun(nat,real),power_power(real),B))))).  [resolve(6002,a,5998,a)].
85.96/85.85	Derived: -hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),A),ring_1_Ints(real))) | hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),hAPP(real,real,uminus_uminus(real),A)),ring_1_Ints(real))).  [resolve(6002,a,5999,a)].
85.96/85.85	Derived: zero_zero(real) = hAPP(int,real,ring_1_of_int(real),zero_zero(int)).  [resolve(6002,a,6000,a)].
85.96/85.85	Derived: -hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),A),ring_1_Ints(real))) | -hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),B),ring_1_Ints(real))) | hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),B)),ring_1_Ints(real))).  [resolve(6002,a,6001,a)].
85.96/85.85	6003 -ring_1(A) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),C)) | 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)) = hAPP(nat,A,semiring_1_of_nat(A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),C),B)) # label(fact_1371_of__nat__diff) # label(axiom).  [clausify(1453)].
85.96/85.85	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),B)),hAPP(nat,complex,semiring_1_of_nat(complex),A)) = hAPP(nat,complex,semiring_1_of_nat(complex),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),B),A)).  [resolve(6003,a,5993,a)].
85.96/85.85	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(nat,real,semiring_1_of_nat(real),B)),hAPP(nat,real,semiring_1_of_nat(real),A)) = hAPP(nat,real,semiring_1_of_nat(real),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),B),A)).  [resolve(6003,a,6002,a)].
85.96/85.85	6004 -ring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(nat,A,semiring_1_of_nat(A),hAPP(nat,nat,suc,B))),hAPP(nat,A,C,hAPP(nat,nat,suc,B))) = hAPP(nat,A,hAPP(fun(nat,A),fun(nat,A),diffs(A),C),B) # label(fact_4118_diffs__def) # label(axiom).  [clausify(1554)].
85.96/85.85	Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(nat,complex,semiring_1_of_nat(complex),hAPP(nat,nat,suc,A))),hAPP(nat,complex,B,hAPP(nat,nat,suc,A))) = hAPP(nat,complex,hAPP(fun(nat,complex),fun(nat,complex),diffs(complex),B),A).  [resolve(6004,a,5993,a)].
85.96/85.85	Derived: hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,semiring_1_of_nat(real),hAPP(nat,nat,suc,A))),hAPP(nat,real,B,hAPP(nat,nat,suc,A))) = hAPP(nat,real,hAPP(fun(nat,real),fun(nat,real),diffs(real),B),A).  [resolve(6004,a,6002,a)].
85.96/85.85	6005 -ring_1(A) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),hAPP(int,A,ring_1_of_int(A),B)),ring_1_Ints(A))) # label(fact_3804_Ints__of__int) # label(axiom).  [clausify(1637)].
85.96/85.85	Derived: hBOOL(hAPP(fun(complex,bool),bool,hAPP(complex,fun(fun(complex,bool),bool),member(complex),hAPP(int,complex,ring_1_of_int(complex),A)),ring_1_Ints(complex))).  [resolve(6005,a,5993,a)].
85.96/85.85	Derived: hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),hAPP(int,real,ring_1_of_int(real),A)),ring_1_Ints(real))).  [resolve(6005,a,6002,a)].
85.96/85.85	6006 -ring_1(A) | one_one(A) = hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),hAPP(A,A,uminus_uminus(A),one_one(A))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),B)) # label(fact_2121_power__minus1__even) # label(axiom).  [clausify(1855)].
86.04/85.95	Derived: one_one(complex) = hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),hAPP(complex,complex,uminus_uminus(complex),one_one(complex))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),A)).  [resolve(6006,a,5993,a)].
86.04/85.95	Derived: one_one(real) = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,uminus_uminus(real),one_one(real))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),A)).  [resolve(6006,a,6002,a)].
86.04/85.95	6007 -ring_1(A) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),hAPP(fun(B,int),fun(B,A),hAPP(fun(int,A),fun(fun(B,int),fun(B,A)),combb(int,A,B),ring_1_of_int(A)),C)),D) = hAPP(int,A,ring_1_of_int(A),hAPP(fun(B,bool),int,hAPP(fun(B,int),fun(fun(B,bool),int),big_co1399186613setsum(B,int),C),D)) # label(fact_4170_of__int__setsum) # label(axiom).  [clausify(1895)].
86.04/85.95	Derived: hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),hAPP(fun(A,int),fun(A,complex),hAPP(fun(int,complex),fun(fun(A,int),fun(A,complex)),combb(int,complex,A),ring_1_of_int(complex)),B)),C) = hAPP(int,complex,ring_1_of_int(complex),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),B),C)).  [resolve(6007,a,5993,a)].
86.04/85.95	Derived: hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),hAPP(fun(A,int),fun(A,real),hAPP(fun(int,real),fun(fun(A,int),fun(A,real)),combb(int,real,A),ring_1_of_int(real)),B)),C) = hAPP(int,real,ring_1_of_int(real),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),B),C)).  [resolve(6007,a,6002,a)].
86.04/85.95	6008 -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_3837_Ints__1) # label(axiom).  [clausify(1969)].
86.04/85.95	Derived: hBOOL(hAPP(fun(complex,bool),bool,hAPP(complex,fun(fun(complex,bool),bool),member(complex),one_one(complex)),ring_1_Ints(complex))).  [resolve(6008,a,5993,a)].
86.04/85.95	Derived: hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),one_one(real)),ring_1_Ints(real))).  [resolve(6008,a,6002,a)].
86.04/85.95	6009 -ring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,ring_1_of_int(A),B)),hAPP(int,A,ring_1_of_int(A),C)) = hAPP(int,A,ring_1_of_int(A),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),C)) # label(fact_3588_of__int__mult) # label(axiom).  [clausify(2021)].
86.04/85.95	Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(int,complex,ring_1_of_int(complex),A)),hAPP(int,complex,ring_1_of_int(complex),B)) = hAPP(int,complex,ring_1_of_int(complex),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)).  [resolve(6009,a,5993,a)].
86.04/85.95	Derived: hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,ring_1_of_int(real),A)),hAPP(int,real,ring_1_of_int(real),B)) = hAPP(int,real,ring_1_of_int(real),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)).  [resolve(6009,a,6002,a)].
86.04/85.95	6010 -ring_1(A) | hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),hAPP(A,A,uminus_uminus(A),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),C)) = hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),C)) # label(fact_2117_ring__1__class_Opower__minus__even) # label(axiom).  [clausify(2083)].
86.04/85.95	Derived: hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),hAPP(complex,complex,uminus_uminus(complex),A)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),B)) = hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),B)).  [resolve(6010,a,5993,a)].
86.10/86.02	Derived: hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,uminus_uminus(real),A)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),B)) = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),B)).  [resolve(6010,a,6002,a)].
86.10/86.02	6011 -ring_1(A) | hAPP(fun(nat,bool),A,hAPP(fun(nat,A),fun(fun(nat,bool),A),big_co1399186613setsum(nat,A),hAPP(A,fun(nat,A),hAPP(fun(nat,fun(A,A)),fun(A,fun(nat,A)),combc(nat,A,A),hAPP(fun(nat,A),fun(nat,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(nat,A),fun(nat,fun(A,A))),combb(A,fun(A,A),nat),minus_minus(A)),B)),C)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),D)) = hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(fun(nat,bool),A,hAPP(fun(nat,A),fun(fun(nat,bool),A),big_co1399186613setsum(nat,A),B),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),D))),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(nat,A,semiring_1_of_nat(A),D)),C)) # label(fact_4172_sumr__diff__mult__const2) # label(axiom).  [clausify(2162)].
86.10/86.02	Derived: hAPP(fun(nat,bool),complex,hAPP(fun(nat,complex),fun(fun(nat,bool),complex),big_co1399186613setsum(nat,complex),hAPP(complex,fun(nat,complex),hAPP(fun(nat,fun(complex,complex)),fun(complex,fun(nat,complex)),combc(nat,complex,complex),hAPP(fun(nat,complex),fun(nat,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(nat,complex),fun(nat,fun(complex,complex))),combb(complex,fun(complex,complex),nat),minus_minus(complex)),A)),B)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),C)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),hAPP(fun(nat,bool),complex,hAPP(fun(nat,complex),fun(fun(nat,bool),complex),big_co1399186613setsum(nat,complex),A),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),C))),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(nat,complex,semiring_1_of_nat(complex),C)),B)).  [resolve(6011,a,5993,a)].
86.10/86.02	Derived: hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(real,fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(real,fun(nat,real)),combc(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),minus_minus(real)),A)),B)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),C)) = hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),A),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),C))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,semiring_1_of_nat(real),C)),B)).  [resolve(6011,a,6002,a)].
86.10/86.02	6012 -comm_monoid_mult(A) | -ring_1(A) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),hAPP(fun(B,int),fun(B,A),hAPP(fun(int,A),fun(fun(B,int),fun(B,A)),combb(int,A,B),ring_1_of_int(A)),C)),D) = hAPP(int,A,ring_1_of_int(A),hAPP(fun(B,bool),int,hAPP(fun(B,int),fun(fun(B,bool),int),big_co302546470etprod(B,int),C),D)) # label(fact_3929_of__int__setprod) # label(axiom).  [clausify(2203)].
86.10/86.02	Derived: -comm_monoid_mult(complex) | hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co302546470etprod(A,complex),hAPP(fun(A,int),fun(A,complex),hAPP(fun(int,complex),fun(fun(A,int),fun(A,complex)),combb(int,complex,A),ring_1_of_int(complex)),B)),C) = hAPP(int,complex,ring_1_of_int(complex),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),B),C)).  [resolve(6012,b,5993,a)].
86.20/86.08	Derived: -comm_monoid_mult(real) | hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co302546470etprod(A,real),hAPP(fun(A,int),fun(A,real),hAPP(fun(int,real),fun(fun(A,int),fun(A,real)),combb(int,real,A),ring_1_of_int(real)),B)),C) = hAPP(int,real,ring_1_of_int(real),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),B),C)).  [resolve(6012,b,6002,a)].
86.20/86.08	6013 -ring_1(A) | hAPP(A,A,uminus_uminus(A),hAPP(nat,A,hAPP(fun(nat,A),fun(nat,A),diffs(A),B),C)) = hAPP(nat,A,hAPP(fun(nat,A),fun(nat,A),diffs(A),hAPP(fun(nat,A),fun(nat,A),hAPP(fun(A,A),fun(fun(nat,A),fun(nat,A)),combb(A,A,nat),uminus_uminus(A)),B)),C) # label(fact_4113_diffs__minus) # label(axiom).  [clausify(2246)].
86.20/86.08	Derived: hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,hAPP(fun(nat,complex),fun(nat,complex),diffs(complex),A),B)) = hAPP(nat,complex,hAPP(fun(nat,complex),fun(nat,complex),diffs(complex),hAPP(fun(nat,complex),fun(nat,complex),hAPP(fun(complex,complex),fun(fun(nat,complex),fun(nat,complex)),combb(complex,complex,nat),uminus_uminus(complex)),A)),B).  [resolve(6013,a,5993,a)].
86.20/86.08	Derived: hAPP(real,real,uminus_uminus(real),hAPP(nat,real,hAPP(fun(nat,real),fun(nat,real),diffs(real),A),B)) = hAPP(nat,real,hAPP(fun(nat,real),fun(nat,real),diffs(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),uminus_uminus(real)),A)),B).  [resolve(6013,a,6002,a)].
86.20/86.08	6014 -ring_1(A) | zero_zero(int) != ti(int,B) | zero_zero(A) = hAPP(int,A,ring_1_of_int(A),B) # label(fact_3978_of__int__num) # label(axiom).  [clausify(2277)].
86.20/86.08	Derived: zero_zero(int) != ti(int,A) | zero_zero(complex) = hAPP(int,complex,ring_1_of_int(complex),A).  [resolve(6014,a,5993,a)].
86.20/86.08	Derived: zero_zero(int) != ti(int,A) | zero_zero(real) = hAPP(int,real,ring_1_of_int(real),A).  [resolve(6014,a,6002,a)].
86.20/86.08	6015 -ring_1(A) | zero_zero(int) = ti(int,B) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),zero_zero(int))) | hAPP(A,A,uminus_uminus(A),hAPP(int,A,ring_1_of_int(A),hAPP(int,int,uminus_uminus(int),B))) = hAPP(int,A,ring_1_of_int(A),B) # label(fact_3978_of__int__num) # label(axiom).  [clausify(2277)].
86.20/86.08	Derived: zero_zero(int) = ti(int,A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),zero_zero(int))) | hAPP(complex,complex,uminus_uminus(complex),hAPP(int,complex,ring_1_of_int(complex),hAPP(int,int,uminus_uminus(int),A))) = hAPP(int,complex,ring_1_of_int(complex),A).  [resolve(6015,a,5993,a)].
86.20/86.08	Derived: zero_zero(int) = ti(int,A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),zero_zero(int))) | hAPP(real,real,uminus_uminus(real),hAPP(int,real,ring_1_of_int(real),hAPP(int,int,uminus_uminus(int),A))) = hAPP(int,real,ring_1_of_int(real),A).  [resolve(6015,a,6002,a)].
86.20/86.08	6016 -ring_1(A) | zero_zero(int) = ti(int,B) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),zero_zero(int))) | hAPP(product_prod(int,int),A,hAPP(fun(int,fun(int,A)),fun(product_prod(int,int),A),product_prod_case(int,int,A),hAPP(fun(int,A),fun(int,fun(int,A)),hAPP(fun(int,fun(A,fun(int,A))),fun(fun(int,A),fun(int,fun(int,A))),combs(int,A,fun(int,A)),hAPP(fun(int,fun(int,fun(A,A))),fun(int,fun(A,fun(int,A))),hAPP(fun(fun(int,fun(A,A)),fun(A,fun(int,A))),fun(fun(int,fun(int,fun(A,A))),fun(int,fun(A,fun(int,A)))),combb(fun(int,fun(A,A)),fun(A,fun(int,A)),int),combc(int,A,A)),hAPP(fun(int,A),fun(int,fun(int,fun(A,A))),hAPP(fun(A,fun(int,fun(A,A))),fun(fun(int,A),fun(int,fun(int,fun(A,A)))),combb(A,fun(int,fun(A,A)),int),hAPP(fun(int,fun(A,fun(A,A))),fun(A,fun(int,fun(A,A))),combc(int,A,fun(A,A)),hAPP(fun(int,bool),fun(int,fun(A,fun(A,A))),hAPP(fun(bool,fun(A,fun(A,A))),fun(fun(int,bool),fun(int,fun(A,fun(A,A)))),combb(bool,fun(A,fun(A,A)),int),if(A)),hAPP(int,fun(int,bool),hAPP(fun(int,fun(int,bool)),fun(int,fun(int,bool)),combc(int,int,bool),fequal(int)),zero_zero(int))))),hAPP(fun(int,A),fun(int,A),hAPP(fun(int,fun(A,A)),fun(fun(int,A),fun(int,A)),combs(int,A,A),hAPP(fun(int,A),fun(int,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(int,A),fun(int,fun(A,A))),combb(A,fun(A,A),int),plus_plus(A)),ring_1_of_int(A))),ring_1_of_int(A))))),hAPP(A,fun(int,A),hAPP(fun(int,fun(A,A)),fun(A,fun(int,A)),combc(int,A,A),hAPP(fun(int,A),fun(int,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(int,A),fun(int,fun(A,A))),combb(A,fun(A,A),int),plus_plus(A)),hAPP(fun(int,A),fun(int,A),hAPP(fun(int,fun(A,A)),fun(fun(int,A),fun(int,A)),combs(int,A,A),hAPP(fun(int,A),fun(int,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(int,A),fun(int,fun(A,A))),combb(A,fun(A,A),int),plus_plus(A)),ring_1_of_int(A))),ring_1_of_int(A)))),one_one(A)))),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),divmod_int,B),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) = hAPP(int,A,ring_1_of_int(A),B) # label(fact_3978_of__int__num) # label(axiom).  [clausify(2277)].
86.20/86.09	Derived: zero_zero(int) = ti(int,A) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),zero_zero(int))) | hAPP(product_prod(int,int),complex,hAPP(fun(int,fun(int,complex)),fun(product_prod(int,int),complex),product_prod_case(int,int,complex),hAPP(fun(int,complex),fun(int,fun(int,complex)),hAPP(fun(int,fun(complex,fun(int,complex))),fun(fun(int,complex),fun(int,fun(int,complex))),combs(int,complex,fun(int,complex)),hAPP(fun(int,fun(int,fun(complex,complex))),fun(int,fun(complex,fun(int,complex))),hAPP(fun(fun(int,fun(complex,complex)),fun(complex,fun(int,complex))),fun(fun(int,fun(int,fun(complex,complex))),fun(int,fun(complex,fun(int,complex)))),combb(fun(int,fun(complex,complex)),fun(complex,fun(int,complex)),int),combc(int,complex,complex)),hAPP(fun(int,complex),fun(int,fun(int,fun(complex,complex))),hAPP(fun(complex,fun(int,fun(complex,complex))),fun(fun(int,complex),fun(int,fun(int,fun(complex,complex)))),combb(complex,fun(int,fun(complex,complex)),int),hAPP(fun(int,fun(complex,fun(complex,complex))),fun(complex,fun(int,fun(complex,complex))),combc(int,complex,fun(complex,complex)),hAPP(fun(int,bool),fun(int,fun(complex,fun(complex,complex))),hAPP(fun(bool,fun(complex,fun(complex,complex))),fun(fun(int,bool),fun(int,fun(complex,fun(complex,complex)))),combb(bool,fun(complex,fun(complex,complex)),int),if(complex)),hAPP(int,fun(int,bool),hAPP(fun(int,fun(int,bool)),fun(int,fun(int,bool)),combc(int,int,bool),fequal(int)),zero_zero(int))))),hAPP(fun(int,complex),fun(int,complex),hAPP(fun(int,fun(complex,complex)),fun(fun(int,complex),fun(int,complex)),combs(int,complex,complex),hAPP(fun(int,complex),fun(int,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(int,complex),fun(int,fun(complex,complex))),combb(complex,fun(complex,complex),int),plus_plus(complex)),ring_1_of_int(complex))),ring_1_of_int(complex))))),hAPP(complex,fun(int,complex),hAPP(fun(int,fun(complex,complex)),fun(complex,fun(int,complex)),combc(int,complex,complex),hAPP(fun(int,complex),fun(int,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(int,complex),fun(int,fun(complex,complex))),combb(complex,fun(complex,complex),int),plus_plus(complex)),hAPP(fun(int,complex),fun(int,complex),hAPP(fun(int,fun(complex,complex)),fun(fun(int,complex),fun(int,complex)),combs(int,complex,complex),hAPP(fun(int,complex),fun(int,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(int,complex),fun(int,fun(complex,complex))),combb(complex,fun(complex,complex),int),plus_plus(complex)),ring_1_of_int(complex))),ring_1_of_int(complex)))),one_one(complex)))),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),divmod_int,A),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) = hAPP(int,complex,ring_1_of_int(complex),A).  [resolve(6016,a,5993,a)].
86.20/86.09	Derived: zero_zero(int) = ti(int,A) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),zero_zero(int))) | hAPP(product_prod(int,int),real,hAPP(fun(int,fun(int,real)),fun(product_prod(int,int),real),product_prod_case(int,int,real),hAPP(fun(int,real),fun(int,fun(int,real)),hAPP(fun(int,fun(real,fun(int,real))),fun(fun(int,real),fun(int,fun(int,real))),combs(int,real,fun(int,real)),hAPP(fun(int,fun(int,fun(real,real))),fun(int,fun(real,fun(int,real))),hAPP(fun(fun(int,fun(real,real)),fun(real,fun(int,real))),fun(fun(int,fun(int,fun(real,real))),fun(int,fun(real,fun(int,real)))),combb(fun(int,fun(real,real)),fun(real,fun(int,real)),int),combc(int,real,real)),hAPP(fun(int,real),fun(int,fun(int,fun(real,real))),hAPP(fun(real,fun(int,fun(real,real))),fun(fun(int,real),fun(int,fun(int,fun(real,real)))),combb(real,fun(int,fun(real,real)),int),hAPP(fun(int,fun(real,fun(real,real))),fun(real,fun(int,fun(real,real))),combc(int,real,fun(real,real)),hAPP(fun(int,bool),fun(int,fun(real,fun(real,real))),hAPP(fun(bool,fun(real,fun(real,real))),fun(fun(int,bool),fun(int,fun(real,fun(real,real)))),combb(bool,fun(real,fun(real,real)),int),if(real)),hAPP(int,fun(int,bool),hAPP(fun(int,fun(int,bool)),fun(int,fun(int,bool)),combc(int,int,bool),fequal(int)),zero_zero(int))))),hAPP(fun(int,real),fun(int,real),hAPP(fun(int,fun(real,real)),fun(fun(int,real),fun(int,real)),combs(int,real,real),hAPP(fun(int,real),fun(int,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(int,real),fun(int,fun(real,real))),combb(real,fun(real,real),int),plus_plus(real)),ring_1_of_int(real))),ring_1_of_int(real))))),hAPP(real,fun(int,real),hAPP(fun(int,fun(real,real)),fun(real,fun(int,real)),combc(int,real,real),hAPP(fun(int,real),fun(int,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(int,real),fun(int,fun(real,real))),combb(real,fun(real,real),int),plus_plus(real)),hAPP(fun(int,real),fun(int,real),hAPP(fun(int,fun(real,real)),fun(fun(int,real),fun(int,real)),combs(int,real,real),hAPP(fun(int,real),fun(int,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(int,real),fun(int,fun(real,real))),combb(real,fun(real,real),int),plus_plus(real)),ring_1_of_int(real))),ring_1_of_int(real)))),one_one(real)))),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),divmod_int,A),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) = hAPP(int,real,ring_1_of_int(real),A).  [resolve(6016,a,6002,a)].
86.26/86.23	6017 -ring_1(A) | hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),hAPP(int,A,ring_1_of_int(A),B)),C) = hAPP(int,A,ring_1_of_int(A),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),B),C)) # label(fact_3566_of__int__power) # label(axiom).  [clausify(2296)].
86.26/86.23	Derived: hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),hAPP(int,complex,ring_1_of_int(complex),A)),B) = hAPP(int,complex,ring_1_of_int(complex),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),B)).  [resolve(6017,a,5993,a)].
86.26/86.23	Derived: hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,ring_1_of_int(real),A)),B) = hAPP(int,real,ring_1_of_int(real),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),B)).  [resolve(6017,a,6002,a)].
86.26/86.23	6018 ring_1(int) # label(arity_Int_Oint___Rings_Oring__1) # label(axiom).  [assumption].
86.26/86.23	Derived: hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,uminus_uminus(int),one_one(int))),A)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),B),A)) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,uminus_uminus(int),B)),A).  [resolve(6018,a,5994,a)].
86.26/86.23	Derived: hAPP(int,int,uminus_uminus(int),hAPP(int,int,ring_1_of_int(int),A)) = hAPP(int,int,ring_1_of_int(int),hAPP(int,int,uminus_uminus(int),A)).  [resolve(6018,a,5995,a)].
86.26/86.23	Derived: hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,uminus_uminus(int),A)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))).  [resolve(6018,a,5996,a)].
86.26/86.23	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(6018,a,5997,a)].
86.26/86.23	Derived: -real_normed_vector(int) | -hBOOL(hAPP(fun(nat,int),bool,summable(int),hAPP(fun(nat,int),fun(nat,int),hAPP(fun(nat,fun(int,int)),fun(fun(nat,int),fun(nat,int)),combs(nat,int,int),hAPP(fun(nat,int),fun(nat,fun(int,int)),hAPP(fun(int,fun(int,int)),fun(fun(nat,int),fun(nat,fun(int,int))),combb(int,fun(int,int),nat),times_times(int)),hAPP(fun(nat,int),fun(nat,int),diffs(int),A))),hAPP(int,fun(nat,int),power_power(int),B)))) | hBOOL(hAPP(int,bool,hAPP(fun(nat,int),fun(int,bool),sums(int),hAPP(fun(nat,int),fun(nat,int),hAPP(fun(nat,fun(int,int)),fun(fun(nat,int),fun(nat,int)),combs(nat,int,int),hAPP(fun(nat,int),fun(nat,fun(int,int)),hAPP(fun(int,fun(int,int)),fun(fun(nat,int),fun(nat,fun(int,int))),combb(int,fun(int,int),nat),times_times(int)),hAPP(fun(nat,int),fun(nat,int),hAPP(fun(nat,fun(int,int)),fun(fun(nat,int),fun(nat,int)),combs(nat,int,int),hAPP(fun(nat,int),fun(nat,fun(int,int)),hAPP(fun(int,fun(int,int)),fun(fun(nat,int),fun(nat,fun(int,int))),combb(int,fun(int,int),nat),times_times(int)),semiring_1_of_nat(int))),A))),hAPP(fun(nat,nat),fun(nat,int),hAPP(fun(nat,int),fun(fun(nat,nat),fun(nat,int)),combb(nat,int,nat),hAPP(int,fun(nat,int),power_power(int),B)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),minus_minus(nat)),hAPP(nat,nat,suc,zero_zero(nat)))))),hAPP(fun(nat,int),int,suminf(int),hAPP(fun(nat,int),fun(nat,int),hAPP(fun(nat,fun(int,int)),fun(fun(nat,int),fun(nat,int)),combs(nat,int,int),hAPP(fun(nat,int),fun(nat,fun(int,int)),hAPP(fun(int,fun(int,int)),fun(fun(nat,int),fun(nat,fun(int,int))),combb(int,fun(int,int),nat),times_times(int)),hAPP(fun(nat,int),fun(nat,int),diffs(int),A))),hAPP(int,fun(nat,int),power_power(int),B))))).  [resolve(6018,a,5998,a)].
86.26/86.25	Derived: -hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),A),ring_1_Ints(int))) | hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),hAPP(int,int,uminus_uminus(int),A)),ring_1_Ints(int))).  [resolve(6018,a,5999,a)].
86.26/86.25	Derived: zero_zero(int) = hAPP(int,int,ring_1_of_int(int),zero_zero(int)).  [resolve(6018,a,6000,a)].
86.26/86.25	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(6018,a,6001,a)].
86.26/86.25	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | 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)) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),B),A)).  [resolve(6018,a,6003,a)].
86.26/86.25	Derived: hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,A))),hAPP(nat,int,B,hAPP(nat,nat,suc,A))) = hAPP(nat,int,hAPP(fun(nat,int),fun(nat,int),diffs(int),B),A).  [resolve(6018,a,6004,a)].
86.26/86.25	Derived: hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),hAPP(int,int,ring_1_of_int(int),A)),ring_1_Ints(int))).  [resolve(6018,a,6005,a)].
86.26/86.25	Derived: one_one(int) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,uminus_uminus(int),one_one(int))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),A)).  [resolve(6018,a,6006,a)].
86.26/86.25	Derived: hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),hAPP(fun(A,int),fun(A,int),hAPP(fun(int,int),fun(fun(A,int),fun(A,int)),combb(int,int,A),ring_1_of_int(int)),B)),C) = hAPP(int,int,ring_1_of_int(int),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),B),C)).  [resolve(6018,a,6007,a)].
86.26/86.25	Derived: hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),one_one(int)),ring_1_Ints(int))).  [resolve(6018,a,6008,a)].
86.26/86.25	Derived: hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,ring_1_of_int(int),A)),hAPP(int,int,ring_1_of_int(int),B)) = hAPP(int,int,ring_1_of_int(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)).  [resolve(6018,a,6009,a)].
86.36/86.27	Derived: hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,uminus_uminus(int),A)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),B)) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),B)).  [resolve(6018,a,6010,a)].
86.36/86.27	Derived: hAPP(fun(nat,bool),int,hAPP(fun(nat,int),fun(fun(nat,bool),int),big_co1399186613setsum(nat,int),hAPP(int,fun(nat,int),hAPP(fun(nat,fun(int,int)),fun(int,fun(nat,int)),combc(nat,int,int),hAPP(fun(nat,int),fun(nat,fun(int,int)),hAPP(fun(int,fun(int,int)),fun(fun(nat,int),fun(nat,fun(int,int))),combb(int,fun(int,int),nat),minus_minus(int)),A)),B)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),C)) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(fun(nat,bool),int,hAPP(fun(nat,int),fun(fun(nat,bool),int),big_co1399186613setsum(nat,int),A),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),C))),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(nat,int,semiring_1_of_nat(int),C)),B)).  [resolve(6018,a,6011,a)].
86.36/86.27	Derived: -comm_monoid_mult(int) | hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),hAPP(fun(A,int),fun(A,int),hAPP(fun(int,int),fun(fun(A,int),fun(A,int)),combb(int,int,A),ring_1_of_int(int)),B)),C) = hAPP(int,int,ring_1_of_int(int),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),B),C)).  [resolve(6018,a,6012,b)].
86.36/86.27	Derived: hAPP(int,int,uminus_uminus(int),hAPP(nat,int,hAPP(fun(nat,int),fun(nat,int),diffs(int),A),B)) = hAPP(nat,int,hAPP(fun(nat,int),fun(nat,int),diffs(int),hAPP(fun(nat,int),fun(nat,int),hAPP(fun(int,int),fun(fun(nat,int),fun(nat,int)),combb(int,int,nat),uminus_uminus(int)),A)),B).  [resolve(6018,a,6013,a)].
86.36/86.27	Derived: zero_zero(int) != ti(int,A) | zero_zero(int) = hAPP(int,int,ring_1_of_int(int),A).  [resolve(6018,a,6014,a)].
86.36/86.27	Derived: zero_zero(int) = ti(int,A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),zero_zero(int))) | hAPP(int,int,uminus_uminus(int),hAPP(int,int,ring_1_of_int(int),hAPP(int,int,uminus_uminus(int),A))) = hAPP(int,int,ring_1_of_int(int),A).  [resolve(6018,a,6015,a)].
86.36/86.27	Derived: zero_zero(int) = ti(int,A) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),zero_zero(int))) | hAPP(product_prod(int,int),int,hAPP(fun(int,fun(int,int)),fun(product_prod(int,int),int),product_prod_case(int,int,int),hAPP(fun(int,int),fun(int,fun(int,int)),hAPP(fun(int,fun(int,fun(int,int))),fun(fun(int,int),fun(int,fun(int,int))),combs(int,int,fun(int,int)),hAPP(fun(int,fun(int,fun(int,int))),fun(int,fun(int,fun(int,int))),hAPP(fun(fun(int,fun(int,int)),fun(int,fun(int,int))),fun(fun(int,fun(int,fun(int,int))),fun(int,fun(int,fun(int,int)))),combb(fun(int,fun(int,int)),fun(int,fun(int,int)),int),combc(int,int,int)),hAPP(fun(int,int),fun(int,fun(int,fun(int,int))),hAPP(fun(int,fun(int,fun(int,int))),fun(fun(int,int),fun(int,fun(int,fun(int,int)))),combb(int,fun(int,fun(int,int)),int),hAPP(fun(int,fun(int,fun(int,int))),fun(int,fun(int,fun(int,int))),combc(int,int,fun(int,int)),hAPP(fun(int,bool),fun(int,fun(int,fun(int,int))),hAPP(fun(bool,fun(int,fun(int,int))),fun(fun(int,bool),fun(int,fun(int,fun(int,int)))),combb(bool,fun(int,fun(int,int)),int),if(int)),hAPP(int,fun(int,bool),hAPP(fun(int,fun(int,bool)),fun(int,fun(int,bool)),combc(int,int,bool),fequal(int)),zero_zero(int))))),hAPP(fun(int,int),fun(int,int),hAPP(fun(int,fun(int,int)),fun(fun(int,int),fun(int,int)),combs(int,int,int),hAPP(fun(int,int),fun(int,fun(int,int)),hAPP(fun(int,fun(int,int)),fun(fun(int,int),fun(int,fun(int,int))),combb(int,fun(int,int),int),plus_plus(int)),ring_1_of_int(int))),ring_1_of_int(int))))),hAPP(int,fun(int,int),hAPP(fun(int,fun(int,int)),fun(int,fun(int,int)),combc(int,int,int),hAPP(fun(int,int),fun(int,fun(int,int)),hAPP(fun(int,fun(int,int)),fun(fun(int,int),fun(int,fun(int,int))),combb(int,fun(int,int),int),plus_plus(int)),hAPP(fun(int,int),fun(int,int),hAPP(fun(int,fun(int,int)),fun(fun(int,int),fun(int,int)),combs(int,int,int),hAPP(fun(int,int),fun(int,fun(int,int)),hAPP(fun(int,fun(int,int)),fun(fun(int,int),fun(int,fun(int,int))),combb(int,fun(int,int),int),plus_plus(int)),ring_1_of_int(int))),ring_1_of_int(int)))),one_one(int)))),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),divmod_int,A),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) = hAPP(int,int,ring_1_of_int(int),A).  [resolve(6018,a,6016,a)].
86.75/86.69	Derived: hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,ring_1_of_int(int),A)),B) = hAPP(int,int,ring_1_of_int(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),B)).  [resolve(6018,a,6017,a)].
86.75/86.69	6019 -ring_1(A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),B)) | hAPP(nat,A,semiring_1_of_nat(A),hAPP(int,nat,nat_1,B)) = hAPP(int,A,ring_1_of_int(A),B) # label(fact_3604_of__nat__nat) # label(axiom).  [clausify(2353)].
86.75/86.69	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A)) | hAPP(nat,complex,semiring_1_of_nat(complex),hAPP(int,nat,nat_1,A)) = hAPP(int,complex,ring_1_of_int(complex),A).  [resolve(6019,a,5993,a)].
86.75/86.69	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A)) | hAPP(nat,real,semiring_1_of_nat(real),hAPP(int,nat,nat_1,A)) = hAPP(int,real,ring_1_of_int(real),A).  [resolve(6019,a,6002,a)].
86.75/86.69	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A)) | hAPP(nat,int,semiring_1_of_nat(int),hAPP(int,nat,nat_1,A)) = hAPP(int,int,ring_1_of_int(int),A).  [resolve(6019,a,6018,a)].
86.75/86.69	6020 -ring_1(A) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),B),ring_1_Ints(A))) | hAPP(int,A,ring_1_of_int(A),f475(A,B)) = ti(A,B) # label(fact_4345_Ints__cases) # label(axiom).  [clausify(2694)].
86.75/86.69	Derived: -hBOOL(hAPP(fun(complex,bool),bool,hAPP(complex,fun(fun(complex,bool),bool),member(complex),A),ring_1_Ints(complex))) | hAPP(int,complex,ring_1_of_int(complex),f475(complex,A)) = ti(complex,A).  [resolve(6020,a,5993,a)].
86.75/86.69	Derived: -hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),A),ring_1_Ints(real))) | hAPP(int,real,ring_1_of_int(real),f475(real,A)) = ti(real,A).  [resolve(6020,a,6002,a)].
86.75/86.69	Derived: -hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),A),ring_1_Ints(int))) | hAPP(int,int,ring_1_of_int(int),f475(int,A)) = ti(int,A).  [resolve(6020,a,6018,a)].
86.75/86.69	6021 -ring_1(A) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),B),ring_1_Ints(A))) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C)),ring_1_Ints(A))) # label(fact_3851_Ints__power) # label(axiom).  [clausify(2780)].
86.75/86.69	Derived: -hBOOL(hAPP(fun(complex,bool),bool,hAPP(complex,fun(fun(complex,bool),bool),member(complex),A),ring_1_Ints(complex))) | hBOOL(hAPP(fun(complex,bool),bool,hAPP(complex,fun(fun(complex,bool),bool),member(complex),hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),A),B)),ring_1_Ints(complex))).  [resolve(6021,a,5993,a)].
86.75/86.69	Derived: -hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),A),ring_1_Ints(real))) | hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),B)),ring_1_Ints(real))).  [resolve(6021,a,6002,a)].
86.75/86.69	Derived: -hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),A),ring_1_Ints(int))) | hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),B)),ring_1_Ints(int))).  [resolve(6021,a,6018,a)].
86.75/86.69	6022 -ring_1(A) | hAPP(nat,A,semiring_1_of_nat(A),B) = hAPP(int,A,ring_1_of_int(A),hAPP(nat,int,semiring_1_of_nat(int),B)) # label(fact_3587_of__int__of__nat__eq) # label(axiom).  [clausify(2989)].
86.91/86.79	Derived: hAPP(nat,complex,semiring_1_of_nat(complex),A) = hAPP(int,complex,ring_1_of_int(complex),hAPP(nat,int,semiring_1_of_nat(int),A)).  [resolve(6022,a,5993,a)].
86.91/86.79	Derived: hAPP(nat,real,semiring_1_of_nat(real),A) = hAPP(int,real,ring_1_of_int(real),hAPP(nat,int,semiring_1_of_nat(int),A)).  [resolve(6022,a,6002,a)].
86.91/86.79	6023 ring_1(rat) # label(arity_Rat_Orat___Rings_Oring__1) # label(axiom).  [assumption].
86.91/86.79	Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),hAPP(rat,rat,uminus_uminus(rat),one_one(rat))),A)),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),B),A)) = hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),hAPP(rat,rat,uminus_uminus(rat),B)),A).  [resolve(6023,a,5994,a)].
86.91/86.79	Derived: hAPP(rat,rat,uminus_uminus(rat),hAPP(int,rat,ring_1_of_int(rat),A)) = hAPP(int,rat,ring_1_of_int(rat),hAPP(int,int,uminus_uminus(int),A)).  [resolve(6023,a,5995,a)].
86.91/86.79	Derived: hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),hAPP(rat,rat,uminus_uminus(rat),A)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))).  [resolve(6023,a,5996,a)].
86.91/86.79	Derived: hBOOL(hAPP(fun(rat,bool),bool,hAPP(rat,fun(fun(rat,bool),bool),member(rat),hAPP(nat,rat,semiring_1_of_nat(rat),A)),ring_1_Ints(rat))).  [resolve(6023,a,5997,a)].
86.91/86.79	Derived: -real_normed_vector(rat) | -hBOOL(hAPP(fun(nat,rat),bool,summable(rat),hAPP(fun(nat,rat),fun(nat,rat),hAPP(fun(nat,fun(rat,rat)),fun(fun(nat,rat),fun(nat,rat)),combs(nat,rat,rat),hAPP(fun(nat,rat),fun(nat,fun(rat,rat)),hAPP(fun(rat,fun(rat,rat)),fun(fun(nat,rat),fun(nat,fun(rat,rat))),combb(rat,fun(rat,rat),nat),times_times(rat)),hAPP(fun(nat,rat),fun(nat,rat),diffs(rat),A))),hAPP(rat,fun(nat,rat),power_power(rat),B)))) | hBOOL(hAPP(rat,bool,hAPP(fun(nat,rat),fun(rat,bool),sums(rat),hAPP(fun(nat,rat),fun(nat,rat),hAPP(fun(nat,fun(rat,rat)),fun(fun(nat,rat),fun(nat,rat)),combs(nat,rat,rat),hAPP(fun(nat,rat),fun(nat,fun(rat,rat)),hAPP(fun(rat,fun(rat,rat)),fun(fun(nat,rat),fun(nat,fun(rat,rat))),combb(rat,fun(rat,rat),nat),times_times(rat)),hAPP(fun(nat,rat),fun(nat,rat),hAPP(fun(nat,fun(rat,rat)),fun(fun(nat,rat),fun(nat,rat)),combs(nat,rat,rat),hAPP(fun(nat,rat),fun(nat,fun(rat,rat)),hAPP(fun(rat,fun(rat,rat)),fun(fun(nat,rat),fun(nat,fun(rat,rat))),combb(rat,fun(rat,rat),nat),times_times(rat)),semiring_1_of_nat(rat))),A))),hAPP(fun(nat,nat),fun(nat,rat),hAPP(fun(nat,rat),fun(fun(nat,nat),fun(nat,rat)),combb(nat,rat,nat),hAPP(rat,fun(nat,rat),power_power(rat),B)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),minus_minus(nat)),hAPP(nat,nat,suc,zero_zero(nat)))))),hAPP(fun(nat,rat),rat,suminf(rat),hAPP(fun(nat,rat),fun(nat,rat),hAPP(fun(nat,fun(rat,rat)),fun(fun(nat,rat),fun(nat,rat)),combs(nat,rat,rat),hAPP(fun(nat,rat),fun(nat,fun(rat,rat)),hAPP(fun(rat,fun(rat,rat)),fun(fun(nat,rat),fun(nat,fun(rat,rat))),combb(rat,fun(rat,rat),nat),times_times(rat)),hAPP(fun(nat,rat),fun(nat,rat),diffs(rat),A))),hAPP(rat,fun(nat,rat),power_power(rat),B))))).  [resolve(6023,a,5998,a)].
86.91/86.79	Derived: -hBOOL(hAPP(fun(rat,bool),bool,hAPP(rat,fun(fun(rat,bool),bool),member(rat),A),ring_1_Ints(rat))) | hBOOL(hAPP(fun(rat,bool),bool,hAPP(rat,fun(fun(rat,bool),bool),member(rat),hAPP(rat,rat,uminus_uminus(rat),A)),ring_1_Ints(rat))).  [resolve(6023,a,5999,a)].
86.91/86.79	Derived: zero_zero(rat) = hAPP(int,rat,ring_1_of_int(rat),zero_zero(int)).  [resolve(6023,a,6000,a)].
86.91/86.79	Derived: -hBOOL(hAPP(fun(rat,bool),bool,hAPP(rat,fun(fun(rat,bool),bool),member(rat),A),ring_1_Ints(rat))) | -hBOOL(hAPP(fun(rat,bool),bool,hAPP(rat,fun(fun(rat,bool),bool),member(rat),B),ring_1_Ints(rat))) | hBOOL(hAPP(fun(rat,bool),bool,hAPP(rat,fun(fun(rat,bool),bool),member(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),B)),ring_1_Ints(rat))).  [resolve(6023,a,6001,a)].
86.91/86.79	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),hAPP(nat,rat,semiring_1_of_nat(rat),B)),hAPP(nat,rat,semiring_1_of_nat(rat),A)) = hAPP(nat,rat,semiring_1_of_nat(rat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),B),A)).  [resolve(6023,a,6003,a)].
86.91/86.81	Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(nat,rat,semiring_1_of_nat(rat),hAPP(nat,nat,suc,A))),hAPP(nat,rat,B,hAPP(nat,nat,suc,A))) = hAPP(nat,rat,hAPP(fun(nat,rat),fun(nat,rat),diffs(rat),B),A).  [resolve(6023,a,6004,a)].
86.91/86.81	Derived: hBOOL(hAPP(fun(rat,bool),bool,hAPP(rat,fun(fun(rat,bool),bool),member(rat),hAPP(int,rat,ring_1_of_int(rat),A)),ring_1_Ints(rat))).  [resolve(6023,a,6005,a)].
86.91/86.81	Derived: one_one(rat) = hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),hAPP(rat,rat,uminus_uminus(rat),one_one(rat))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),A)).  [resolve(6023,a,6006,a)].
86.91/86.81	Derived: hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),hAPP(fun(A,int),fun(A,rat),hAPP(fun(int,rat),fun(fun(A,int),fun(A,rat)),combb(int,rat,A),ring_1_of_int(rat)),B)),C) = hAPP(int,rat,ring_1_of_int(rat),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),B),C)).  [resolve(6023,a,6007,a)].
86.91/86.81	Derived: hBOOL(hAPP(fun(rat,bool),bool,hAPP(rat,fun(fun(rat,bool),bool),member(rat),one_one(rat)),ring_1_Ints(rat))).  [resolve(6023,a,6008,a)].
86.91/86.81	Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(int,rat,ring_1_of_int(rat),A)),hAPP(int,rat,ring_1_of_int(rat),B)) = hAPP(int,rat,ring_1_of_int(rat),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)).  [resolve(6023,a,6009,a)].
86.91/86.81	Derived: hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),hAPP(rat,rat,uminus_uminus(rat),A)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),B)) = hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),B)).  [resolve(6023,a,6010,a)].
86.91/86.81	Derived: hAPP(fun(nat,bool),rat,hAPP(fun(nat,rat),fun(fun(nat,bool),rat),big_co1399186613setsum(nat,rat),hAPP(rat,fun(nat,rat),hAPP(fun(nat,fun(rat,rat)),fun(rat,fun(nat,rat)),combc(nat,rat,rat),hAPP(fun(nat,rat),fun(nat,fun(rat,rat)),hAPP(fun(rat,fun(rat,rat)),fun(fun(nat,rat),fun(nat,fun(rat,rat))),combb(rat,fun(rat,rat),nat),minus_minus(rat)),A)),B)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),C)) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),hAPP(fun(nat,bool),rat,hAPP(fun(nat,rat),fun(fun(nat,bool),rat),big_co1399186613setsum(nat,rat),A),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),C))),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(nat,rat,semiring_1_of_nat(rat),C)),B)).  [resolve(6023,a,6011,a)].
86.91/86.81	Derived: -comm_monoid_mult(rat) | hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co302546470etprod(A,rat),hAPP(fun(A,int),fun(A,rat),hAPP(fun(int,rat),fun(fun(A,int),fun(A,rat)),combb(int,rat,A),ring_1_of_int(rat)),B)),C) = hAPP(int,rat,ring_1_of_int(rat),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),B),C)).  [resolve(6023,a,6012,b)].
86.91/86.81	Derived: hAPP(rat,rat,uminus_uminus(rat),hAPP(nat,rat,hAPP(fun(nat,rat),fun(nat,rat),diffs(rat),A),B)) = hAPP(nat,rat,hAPP(fun(nat,rat),fun(nat,rat),diffs(rat),hAPP(fun(nat,rat),fun(nat,rat),hAPP(fun(rat,rat),fun(fun(nat,rat),fun(nat,rat)),combb(rat,rat,nat),uminus_uminus(rat)),A)),B).  [resolve(6023,a,6013,a)].
86.91/86.81	Derived: zero_zero(int) != ti(int,A) | zero_zero(rat) = hAPP(int,rat,ring_1_of_int(rat),A).  [resolve(6023,a,6014,a)].
86.91/86.81	Derived: zero_zero(int) = ti(int,A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),zero_zero(int))) | hAPP(rat,rat,uminus_uminus(rat),hAPP(int,rat,ring_1_of_int(rat),hAPP(int,int,uminus_uminus(int),A))) = hAPP(int,rat,ring_1_of_int(rat),A).  [resolve(6023,a,6015,a)].
87.00/86.93	Derived: zero_zero(int) = ti(int,A) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),zero_zero(int))) | hAPP(product_prod(int,int),rat,hAPP(fun(int,fun(int,rat)),fun(product_prod(int,int),rat),product_prod_case(int,int,rat),hAPP(fun(int,rat),fun(int,fun(int,rat)),hAPP(fun(int,fun(rat,fun(int,rat))),fun(fun(int,rat),fun(int,fun(int,rat))),combs(int,rat,fun(int,rat)),hAPP(fun(int,fun(int,fun(rat,rat))),fun(int,fun(rat,fun(int,rat))),hAPP(fun(fun(int,fun(rat,rat)),fun(rat,fun(int,rat))),fun(fun(int,fun(int,fun(rat,rat))),fun(int,fun(rat,fun(int,rat)))),combb(fun(int,fun(rat,rat)),fun(rat,fun(int,rat)),int),combc(int,rat,rat)),hAPP(fun(int,rat),fun(int,fun(int,fun(rat,rat))),hAPP(fun(rat,fun(int,fun(rat,rat))),fun(fun(int,rat),fun(int,fun(int,fun(rat,rat)))),combb(rat,fun(int,fun(rat,rat)),int),hAPP(fun(int,fun(rat,fun(rat,rat))),fun(rat,fun(int,fun(rat,rat))),combc(int,rat,fun(rat,rat)),hAPP(fun(int,bool),fun(int,fun(rat,fun(rat,rat))),hAPP(fun(bool,fun(rat,fun(rat,rat))),fun(fun(int,bool),fun(int,fun(rat,fun(rat,rat)))),combb(bool,fun(rat,fun(rat,rat)),int),if(rat)),hAPP(int,fun(int,bool),hAPP(fun(int,fun(int,bool)),fun(int,fun(int,bool)),combc(int,int,bool),fequal(int)),zero_zero(int))))),hAPP(fun(int,rat),fun(int,rat),hAPP(fun(int,fun(rat,rat)),fun(fun(int,rat),fun(int,rat)),combs(int,rat,rat),hAPP(fun(int,rat),fun(int,fun(rat,rat)),hAPP(fun(rat,fun(rat,rat)),fun(fun(int,rat),fun(int,fun(rat,rat))),combb(rat,fun(rat,rat),int),plus_plus(rat)),ring_1_of_int(rat))),ring_1_of_int(rat))))),hAPP(rat,fun(int,rat),hAPP(fun(int,fun(rat,rat)),fun(rat,fun(int,rat)),combc(int,rat,rat),hAPP(fun(int,rat),fun(int,fun(rat,rat)),hAPP(fun(rat,fun(rat,rat)),fun(fun(int,rat),fun(int,fun(rat,rat))),combb(rat,fun(rat,rat),int),plus_plus(rat)),hAPP(fun(int,rat),fun(int,rat),hAPP(fun(int,fun(rat,rat)),fun(fun(int,rat),fun(int,rat)),combs(int,rat,rat),hAPP(fun(int,rat),fun(int,fun(rat,rat)),hAPP(fun(rat,fun(rat,rat)),fun(fun(int,rat),fun(int,fun(rat,rat))),combb(rat,fun(rat,rat),int),plus_plus(rat)),ring_1_of_int(rat))),ring_1_of_int(rat)))),one_one(rat)))),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),divmod_int,A),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) = hAPP(int,rat,ring_1_of_int(rat),A).  [resolve(6023,a,6016,a)].
87.00/86.93	Derived: hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),hAPP(int,rat,ring_1_of_int(rat),A)),B) = hAPP(int,rat,ring_1_of_int(rat),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),B)).  [resolve(6023,a,6017,a)].
87.00/86.93	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A)) | hAPP(nat,rat,semiring_1_of_nat(rat),hAPP(int,nat,nat_1,A)) = hAPP(int,rat,ring_1_of_int(rat),A).  [resolve(6023,a,6019,a)].
87.00/86.93	Derived: -hBOOL(hAPP(fun(rat,bool),bool,hAPP(rat,fun(fun(rat,bool),bool),member(rat),A),ring_1_Ints(rat))) | hAPP(int,rat,ring_1_of_int(rat),f475(rat,A)) = ti(rat,A).  [resolve(6023,a,6020,a)].
87.00/86.93	Derived: -hBOOL(hAPP(fun(rat,bool),bool,hAPP(rat,fun(fun(rat,bool),bool),member(rat),A),ring_1_Ints(rat))) | hBOOL(hAPP(fun(rat,bool),bool,hAPP(rat,fun(fun(rat,bool),bool),member(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),B)),ring_1_Ints(rat))).  [resolve(6023,a,6021,a)].
87.00/86.93	Derived: hAPP(nat,rat,semiring_1_of_nat(rat),A) = hAPP(int,rat,ring_1_of_int(rat),hAPP(nat,int,semiring_1_of_nat(int),A)).  [resolve(6023,a,6022,a)].
87.00/86.93	6024 -ring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(int,A,ring_1_of_int(A),B)),hAPP(int,A,ring_1_of_int(A),C)) = hAPP(int,A,ring_1_of_int(A),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),B),C)) # label(fact_3589_of__int__diff) # label(axiom).  [clausify(3272)].
87.00/86.93	Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),hAPP(int,complex,ring_1_of_int(complex),A)),hAPP(int,complex,ring_1_of_int(complex),B)) = hAPP(int,complex,ring_1_of_int(complex),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),B)).  [resolve(6024,a,5993,a)].
87.00/86.93	Derived: hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(int,real,ring_1_of_int(real),A)),hAPP(int,real,ring_1_of_int(real),B)) = hAPP(int,real,ring_1_of_int(real),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),B)).  [resolve(6024,a,6002,a)].
87.26/87.15	Derived: hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,ring_1_of_int(int),A)),hAPP(int,int,ring_1_of_int(int),B)) = hAPP(int,int,ring_1_of_int(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),B)).  [resolve(6024,a,6018,a)].
87.26/87.15	Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),hAPP(int,rat,ring_1_of_int(rat),A)),hAPP(int,rat,ring_1_of_int(rat),B)) = hAPP(int,rat,ring_1_of_int(rat),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),B)).  [resolve(6024,a,6023,a)].
87.26/87.15	6025 -ring_1(A) | ring_1_of_int(A) = ti(fun(int,A),ring_1_of_int(A)) # label(tsy_c_Int_Oring__1__class_Oof__int_res) # label(axiom).  [clausify(3496)].
87.26/87.15	Derived: ring_1_of_int(complex) = ti(fun(int,complex),ring_1_of_int(complex)).  [resolve(6025,a,5993,a)].
87.26/87.15	Derived: ring_1_of_int(real) = ti(fun(int,real),ring_1_of_int(real)).  [resolve(6025,a,6002,a)].
87.26/87.15	Derived: ring_1_of_int(int) = ti(fun(int,int),ring_1_of_int(int)).  [resolve(6025,a,6018,a)].
87.26/87.15	Derived: ring_1_of_int(rat) = ti(fun(int,rat),ring_1_of_int(rat)).  [resolve(6025,a,6023,a)].
87.26/87.15	6026 -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_3838_Ints__0) # label(axiom).  [clausify(3532)].
87.26/87.15	Derived: hBOOL(hAPP(fun(complex,bool),bool,hAPP(complex,fun(fun(complex,bool),bool),member(complex),zero_zero(complex)),ring_1_Ints(complex))).  [resolve(6026,a,5993,a)].
87.26/87.15	Derived: hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),zero_zero(real)),ring_1_Ints(real))).  [resolve(6026,a,6002,a)].
87.26/87.15	Derived: hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),zero_zero(int)),ring_1_Ints(int))).  [resolve(6026,a,6018,a)].
87.26/87.15	Derived: hBOOL(hAPP(fun(rat,bool),bool,hAPP(rat,fun(fun(rat,bool),bool),member(rat),zero_zero(rat)),ring_1_Ints(rat))).  [resolve(6026,a,6023,a)].
87.26/87.15	6027 -ring_1(A) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),zero_zero(int))) | hAPP(nat,A,semiring_1_of_nat(A),hAPP(int,nat,nat_1,B)) = hAPP(int,A,ring_1_of_int(A),B) # label(fact_3559_of__int__of__nat) # label(axiom).  [clausify(3536)].
87.26/87.15	Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),zero_zero(int))) | hAPP(nat,complex,semiring_1_of_nat(complex),hAPP(int,nat,nat_1,A)) = hAPP(int,complex,ring_1_of_int(complex),A).  [resolve(6027,a,5993,a)].
87.26/87.15	Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),zero_zero(int))) | hAPP(nat,real,semiring_1_of_nat(real),hAPP(int,nat,nat_1,A)) = hAPP(int,real,ring_1_of_int(real),A).  [resolve(6027,a,6002,a)].
87.26/87.15	Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),zero_zero(int))) | hAPP(nat,int,semiring_1_of_nat(int),hAPP(int,nat,nat_1,A)) = hAPP(int,int,ring_1_of_int(int),A).  [resolve(6027,a,6018,a)].
87.26/87.15	Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),zero_zero(int))) | hAPP(nat,rat,semiring_1_of_nat(rat),hAPP(int,nat,nat_1,A)) = hAPP(int,rat,ring_1_of_int(rat),A).  [resolve(6027,a,6023,a)].
87.26/87.15	6028 -ring_1(A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),zero_zero(int))) | hAPP(A,A,uminus_uminus(A),hAPP(nat,A,semiring_1_of_nat(A),hAPP(int,nat,nat_1,hAPP(int,int,uminus_uminus(int),B)))) = hAPP(int,A,ring_1_of_int(A),B) # label(fact_3559_of__int__of__nat) # label(axiom).  [clausify(3536)].
87.26/87.15	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),zero_zero(int))) | hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),hAPP(int,nat,nat_1,hAPP(int,int,uminus_uminus(int),A)))) = hAPP(int,complex,ring_1_of_int(complex),A).  [resolve(6028,a,5993,a)].
87.26/87.15	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),zero_zero(int))) | hAPP(real,real,uminus_uminus(real),hAPP(nat,real,semiring_1_of_nat(real),hAPP(int,nat,nat_1,hAPP(int,int,uminus_uminus(int),A)))) = hAPP(int,real,ring_1_of_int(real),A).  [resolve(6028,a,6002,a)].
87.26/87.15	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),zero_zero(int))) | hAPP(int,int,uminus_uminus(int),hAPP(nat,int,semiring_1_of_nat(int),hAPP(int,nat,nat_1,hAPP(int,int,uminus_uminus(int),A)))) = hAPP(int,int,ring_1_of_int(int),A).  [resolve(6028,a,6018,a)].
87.46/87.40	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),zero_zero(int))) | hAPP(rat,rat,uminus_uminus(rat),hAPP(nat,rat,semiring_1_of_nat(rat),hAPP(int,nat,nat_1,hAPP(int,int,uminus_uminus(int),A)))) = hAPP(int,rat,ring_1_of_int(rat),A).  [resolve(6028,a,6023,a)].
87.46/87.40	6029 -ring_1(A) | hAPP(A,A,uminus_uminus(A),one_one(A)) = hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),hAPP(A,A,uminus_uminus(A),one_one(A))),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),B))) # label(fact_2123_power__minus1__odd) # label(axiom).  [clausify(3700)].
87.46/87.40	Derived: hAPP(complex,complex,uminus_uminus(complex),one_one(complex)) = hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),hAPP(complex,complex,uminus_uminus(complex),one_one(complex))),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),A))).  [resolve(6029,a,5993,a)].
87.46/87.40	Derived: hAPP(real,real,uminus_uminus(real),one_one(real)) = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,uminus_uminus(real),one_one(real))),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),A))).  [resolve(6029,a,6002,a)].
87.46/87.40	Derived: hAPP(int,int,uminus_uminus(int),one_one(int)) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,uminus_uminus(int),one_one(int))),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),A))).  [resolve(6029,a,6018,a)].
87.46/87.40	Derived: hAPP(rat,rat,uminus_uminus(rat),one_one(rat)) = hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),hAPP(rat,rat,uminus_uminus(rat),one_one(rat))),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),A))).  [resolve(6029,a,6023,a)].
87.46/87.40	6030 -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(3748)].
87.46/87.40	Derived: ring_1_Ints(complex) = ti(fun(complex,bool),ring_1_Ints(complex)).  [resolve(6030,a,5993,a)].
87.46/87.40	Derived: ring_1_Ints(real) = ti(fun(real,bool),ring_1_Ints(real)).  [resolve(6030,a,6002,a)].
87.46/87.40	Derived: ring_1_Ints(int) = ti(fun(int,bool),ring_1_Ints(int)).  [resolve(6030,a,6018,a)].
87.46/87.40	Derived: ring_1_Ints(rat) = ti(fun(rat,bool),ring_1_Ints(rat)).  [resolve(6030,a,6023,a)].
87.46/87.40	6031 -ring_1(A) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),B),ring_1_Ints(A))) | -hBOOL(hAPP(A,bool,C,hAPP(int,A,ring_1_of_int(A),f680(A,C,B)))) | hBOOL(hAPP(A,bool,C,B)) # label(fact_4415_Ints__induct) # label(axiom).  [clausify(3845)].
87.46/87.40	Derived: -hBOOL(hAPP(fun(complex,bool),bool,hAPP(complex,fun(fun(complex,bool),bool),member(complex),A),ring_1_Ints(complex))) | -hBOOL(hAPP(complex,bool,B,hAPP(int,complex,ring_1_of_int(complex),f680(complex,B,A)))) | hBOOL(hAPP(complex,bool,B,A)).  [resolve(6031,a,5993,a)].
87.46/87.40	Derived: -hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),A),ring_1_Ints(real))) | -hBOOL(hAPP(real,bool,B,hAPP(int,real,ring_1_of_int(real),f680(real,B,A)))) | hBOOL(hAPP(real,bool,B,A)).  [resolve(6031,a,6002,a)].
87.46/87.40	Derived: -hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),A),ring_1_Ints(int))) | -hBOOL(hAPP(int,bool,B,hAPP(int,int,ring_1_of_int(int),f680(int,B,A)))) | hBOOL(hAPP(int,bool,B,A)).  [resolve(6031,a,6018,a)].
87.46/87.40	Derived: -hBOOL(hAPP(fun(rat,bool),bool,hAPP(rat,fun(fun(rat,bool),bool),member(rat),A),ring_1_Ints(rat))) | -hBOOL(hAPP(rat,bool,B,hAPP(int,rat,ring_1_of_int(rat),f680(rat,B,A)))) | hBOOL(hAPP(rat,bool,B,A)).  [resolve(6031,a,6023,a)].
88.18/88.08	6032 -ring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(int,A,ring_1_of_int(A),B)),hAPP(int,A,ring_1_of_int(A),C)) = hAPP(int,A,ring_1_of_int(A),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),B),C)) # label(fact_3590_of__int__add) # label(axiom).  [clausify(3865)].
88.18/88.08	Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(int,complex,ring_1_of_int(complex),A)),hAPP(int,complex,ring_1_of_int(complex),B)) = hAPP(int,complex,ring_1_of_int(complex),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B)).  [resolve(6032,a,5993,a)].
88.18/88.08	Derived: hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(int,real,ring_1_of_int(real),A)),hAPP(int,real,ring_1_of_int(real),B)) = hAPP(int,real,ring_1_of_int(real),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B)).  [resolve(6032,a,6002,a)].
88.18/88.08	Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,ring_1_of_int(int),A)),hAPP(int,int,ring_1_of_int(int),B)) = hAPP(int,int,ring_1_of_int(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B)).  [resolve(6032,a,6018,a)].
88.18/88.08	Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(int,rat,ring_1_of_int(rat),A)),hAPP(int,rat,ring_1_of_int(rat),B)) = hAPP(int,rat,ring_1_of_int(rat),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B)).  [resolve(6032,a,6023,a)].
88.18/88.08	6033 -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_3860_Ints__mult) # label(axiom).  [clausify(4301)].
88.18/88.08	Derived: -hBOOL(hAPP(fun(complex,bool),bool,hAPP(complex,fun(fun(complex,bool),bool),member(complex),A),ring_1_Ints(complex))) | -hBOOL(hAPP(fun(complex,bool),bool,hAPP(complex,fun(fun(complex,bool),bool),member(complex),B),ring_1_Ints(complex))) | hBOOL(hAPP(fun(complex,bool),bool,hAPP(complex,fun(fun(complex,bool),bool),member(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),B)),ring_1_Ints(complex))).  [resolve(6033,a,5993,a)].
88.18/88.08	Derived: -hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),A),ring_1_Ints(real))) | -hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),B),ring_1_Ints(real))) | hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),ring_1_Ints(real))).  [resolve(6033,a,6002,a)].
88.18/88.08	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(6033,a,6018,a)].
88.18/88.08	Derived: -hBOOL(hAPP(fun(rat,bool),bool,hAPP(rat,fun(fun(rat,bool),bool),member(rat),A),ring_1_Ints(rat))) | -hBOOL(hAPP(fun(rat,bool),bool,hAPP(rat,fun(fun(rat,bool),bool),member(rat),B),ring_1_Ints(rat))) | hBOOL(hAPP(fun(rat,bool),bool,hAPP(rat,fun(fun(rat,bool),bool),member(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B)),ring_1_Ints(rat))).  [resolve(6033,a,6023,a)].
88.18/88.08	6034 -ring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),B)),one_one(A)) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),one_one(A))),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),one_one(A))) # label(fact_731_real__squared__diff__one__factored) # label(axiom).  [clausify(4417)].
88.18/88.08	Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),A)),one_one(complex)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),A),one_one(complex))),hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),A),one_one(complex))).  [resolve(6034,a,5993,a)].
88.59/88.47	Derived: hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),A)),one_one(real)) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),one_one(real))),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),one_one(real))).  [resolve(6034,a,6002,a)].
88.59/88.47	Derived: hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),A)),one_one(int)) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),one_one(int))),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),one_one(int))).  [resolve(6034,a,6018,a)].
88.59/88.47	Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),A)),one_one(rat)) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),one_one(rat))),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),A),one_one(rat))).  [resolve(6034,a,6023,a)].
88.59/88.47	6035 -ring_1(A) | one_one(A) = hAPP(int,A,ring_1_of_int(A),one_one(int)) # label(fact_3585_of__int__1) # label(axiom).  [clausify(4422)].
88.59/88.47	Derived: one_one(complex) = hAPP(int,complex,ring_1_of_int(complex),one_one(int)).  [resolve(6035,a,5993,a)].
88.59/88.47	Derived: one_one(real) = hAPP(int,real,ring_1_of_int(real),one_one(int)).  [resolve(6035,a,6002,a)].
88.59/88.47	Derived: one_one(int) = hAPP(int,int,ring_1_of_int(int),one_one(int)).  [resolve(6035,a,6018,a)].
88.59/88.47	Derived: one_one(rat) = hAPP(int,rat,ring_1_of_int(rat),one_one(int)).  [resolve(6035,a,6023,a)].
88.59/88.47	6036 -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_3821_Ints__diff) # label(axiom).  [clausify(4539)].
88.59/88.47	Derived: -hBOOL(hAPP(fun(complex,bool),bool,hAPP(complex,fun(fun(complex,bool),bool),member(complex),A),ring_1_Ints(complex))) | -hBOOL(hAPP(fun(complex,bool),bool,hAPP(complex,fun(fun(complex,bool),bool),member(complex),B),ring_1_Ints(complex))) | hBOOL(hAPP(fun(complex,bool),bool,hAPP(complex,fun(fun(complex,bool),bool),member(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),A),B)),ring_1_Ints(complex))).  [resolve(6036,a,5993,a)].
88.59/88.47	Derived: -hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),A),ring_1_Ints(real))) | -hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),B),ring_1_Ints(real))) | hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),B)),ring_1_Ints(real))).  [resolve(6036,a,6002,a)].
88.59/88.47	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(6036,a,6018,a)].
88.59/88.47	Derived: -hBOOL(hAPP(fun(rat,bool),bool,hAPP(rat,fun(fun(rat,bool),bool),member(rat),A),ring_1_Ints(rat))) | -hBOOL(hAPP(fun(rat,bool),bool,hAPP(rat,fun(fun(rat,bool),bool),member(rat),B),ring_1_Ints(rat))) | hBOOL(hAPP(fun(rat,bool),bool,hAPP(rat,fun(fun(rat,bool),bool),member(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),A),B)),ring_1_Ints(rat))).  [resolve(6036,a,6023,a)].
88.59/88.47	6037 -ring_1(A) | diffs(A) = ti(fun(fun(nat,A),fun(nat,A)),diffs(A)) # label(tsy_c_Transcendental_Odiffs_res) # label(axiom).  [clausify(4834)].
88.59/88.47	Derived: diffs(complex) = ti(fun(fun(nat,complex),fun(nat,complex)),diffs(complex)).  [resolve(6037,a,5993,a)].
92.45/92.33	Derived: diffs(real) = ti(fun(fun(nat,real),fun(nat,real)),diffs(real)).  [resolve(6037,a,6002,a)].
92.45/92.33	Derived: diffs(int) = ti(fun(fun(nat,int),fun(nat,int)),diffs(int)).  [resolve(6037,a,6018,a)].
92.45/92.33	Derived: diffs(rat) = ti(fun(fun(nat,rat),fun(nat,rat)),diffs(rat)).  [resolve(6037,a,6023,a)].
92.45/92.33	6038 dense_linorder(rat) # label(arity_Rat_Orat___Orderings_Odense__linorder) # label(axiom).  [assumption].
92.45/92.33	6039 -dense_linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_atLeastLessThan(A),B),C)),hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_atLeastAtMost(A),D),E))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),E)) # label(fact_4528_atLeastLessThan__subseteq__atLeastAtMost__iff) # label(axiom).  [clausify(60)].
92.45/92.33	6040 -dense_linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_atLeastLessThan(A),B),C)),hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_atLeastAtMost(A),D),E))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),D),B)) # label(fact_4528_atLeastLessThan__subseteq__atLeastAtMost__iff) # label(axiom).  [clausify(60)].
92.45/92.33	6041 -dense_linorder(A) | hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_atLeastLessThan(A),B),C)),hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_atLeastAtMost(A),D),E))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) # label(fact_4528_atLeastLessThan__subseteq__atLeastAtMost__iff) # label(axiom).  [clausify(60)].
92.45/92.33	6042 -dense_linorder(A) | hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_atLeastLessThan(A),B),C)),hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_atLeastAtMost(A),D),E))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),E)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),D),B)) # label(fact_4528_atLeastLessThan__subseteq__atLeastAtMost__iff) # label(axiom).  [clausify(60)].
92.45/92.33	Derived: -hBOOL(hAPP(fun(rat,bool),bool,hAPP(fun(rat,bool),fun(fun(rat,bool),bool),ord_less_eq(fun(rat,bool)),hAPP(rat,fun(rat,bool),hAPP(rat,fun(rat,fun(rat,bool)),ord_atLeastLessThan(rat),A),B)),hAPP(rat,fun(rat,bool),hAPP(rat,fun(rat,fun(rat,bool)),ord_atLeastAtMost(rat),C),D))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),B),D)).  [resolve(6038,a,6039,a)].
92.45/92.33	Derived: -hBOOL(hAPP(fun(rat,bool),bool,hAPP(fun(rat,bool),fun(fun(rat,bool),bool),ord_less_eq(fun(rat,bool)),hAPP(rat,fun(rat,bool),hAPP(rat,fun(rat,fun(rat,bool)),ord_atLeastLessThan(rat),A),B)),hAPP(rat,fun(rat,bool),hAPP(rat,fun(rat,fun(rat,bool)),ord_atLeastAtMost(rat),C),D))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),C),A)).  [resolve(6038,a,6040,a)].
92.45/92.33	Derived: hBOOL(hAPP(fun(rat,bool),bool,hAPP(fun(rat,bool),fun(fun(rat,bool),bool),ord_less_eq(fun(rat,bool)),hAPP(rat,fun(rat,bool),hAPP(rat,fun(rat,fun(rat,bool)),ord_atLeastLessThan(rat),A),B)),hAPP(rat,fun(rat,bool),hAPP(rat,fun(rat,fun(rat,bool)),ord_atLeastAtMost(rat),C),D))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),B)).  [resolve(6038,a,6041,a)].
92.45/92.33	Derived: hBOOL(hAPP(fun(rat,bool),bool,hAPP(fun(rat,bool),fun(fun(rat,bool),bool),ord_less_eq(fun(rat,bool)),hAPP(rat,fun(rat,bool),hAPP(rat,fun(rat,fun(rat,bool)),ord_atLeastLessThan(rat),A),B)),hAPP(rat,fun(rat,bool),hAPP(rat,fun(rat,fun(rat,bool)),ord_atLeastAtMost(rat),C),D))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),B),D)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),C),A)).  [resolve(6038,a,6042,a)].
92.45/92.33	6043 -dense_linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),f167(A,B,C)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),B)) # label(fact_2825_dense__le) # label(axiom).  [clausify(1077)].
93.56/93.51	Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),f167(rat,A,B)),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),B),A)).  [resolve(6043,a,6038,a)].
93.56/93.51	6044 -dense_linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),f167(A,B,C)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),B)) # label(fact_2825_dense__le) # label(axiom).  [clausify(1077)].
93.56/93.51	Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),f167(rat,A,B)),A)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),B),A)).  [resolve(6044,a,6038,a)].
93.56/93.51	6045 dense_linorder(real) # label(arity_RealDef_Oreal___Orderings_Odense__linorder) # label(axiom).  [assumption].
93.56/93.51	Derived: -hBOOL(hAPP(fun(real,bool),bool,hAPP(fun(real,bool),fun(fun(real,bool),bool),ord_less_eq(fun(real,bool)),hAPP(real,fun(real,bool),hAPP(real,fun(real,fun(real,bool)),ord_atLeastLessThan(real),A),B)),hAPP(real,fun(real,bool),hAPP(real,fun(real,fun(real,bool)),ord_atLeastAtMost(real),C),D))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),D)).  [resolve(6045,a,6039,a)].
93.56/93.51	Derived: -hBOOL(hAPP(fun(real,bool),bool,hAPP(fun(real,bool),fun(fun(real,bool),bool),ord_less_eq(fun(real,bool)),hAPP(real,fun(real,bool),hAPP(real,fun(real,fun(real,bool)),ord_atLeastLessThan(real),A),B)),hAPP(real,fun(real,bool),hAPP(real,fun(real,fun(real,bool)),ord_atLeastAtMost(real),C),D))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),C),A)).  [resolve(6045,a,6040,a)].
93.56/93.51	Derived: hBOOL(hAPP(fun(real,bool),bool,hAPP(fun(real,bool),fun(fun(real,bool),bool),ord_less_eq(fun(real,bool)),hAPP(real,fun(real,bool),hAPP(real,fun(real,fun(real,bool)),ord_atLeastLessThan(real),A),B)),hAPP(real,fun(real,bool),hAPP(real,fun(real,fun(real,bool)),ord_atLeastAtMost(real),C),D))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)).  [resolve(6045,a,6041,a)].
93.56/93.51	Derived: hBOOL(hAPP(fun(real,bool),bool,hAPP(fun(real,bool),fun(fun(real,bool),bool),ord_less_eq(fun(real,bool)),hAPP(real,fun(real,bool),hAPP(real,fun(real,fun(real,bool)),ord_atLeastLessThan(real),A),B)),hAPP(real,fun(real,bool),hAPP(real,fun(real,fun(real,bool)),ord_atLeastAtMost(real),C),D))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),D)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),C),A)).  [resolve(6045,a,6042,a)].
93.56/93.51	Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),f167(real,A,B)),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),A)).  [resolve(6045,a,6043,a)].
93.56/93.51	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),f167(real,A,B)),A)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),A)).  [resolve(6045,a,6044,a)].
93.56/93.51	6046 -dense_linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_gr676655987ssThan(A),B),C)),hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_atLeastLessThan(A),D),E))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),E)) # label(fact_4234_greaterThanLessThan__subseteq__atLeastLessThan__iff) # label(axiom).  [clausify(3001)].
93.56/93.51	Derived: -hBOOL(hAPP(fun(rat,bool),bool,hAPP(fun(rat,bool),fun(fun(rat,bool),bool),ord_less_eq(fun(rat,bool)),hAPP(rat,fun(rat,bool),hAPP(rat,fun(rat,fun(rat,bool)),ord_gr676655987ssThan(rat),A),B)),hAPP(rat,fun(rat,bool),hAPP(rat,fun(rat,fun(rat,bool)),ord_atLeastLessThan(rat),C),D))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),B),D)).  [resolve(6046,a,6038,a)].
93.56/93.51	Derived: -hBOOL(hAPP(fun(real,bool),bool,hAPP(fun(real,bool),fun(fun(real,bool),bool),ord_less_eq(fun(real,bool)),hAPP(real,fun(real,bool),hAPP(real,fun(real,fun(real,bool)),ord_gr676655987ssThan(real),A),B)),hAPP(real,fun(real,bool),hAPP(real,fun(real,fun(real,bool)),ord_atLeastLessThan(real),C),D))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),D)).  [resolve(6046,a,6045,a)].
93.56/93.53	6047 -dense_linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_gr676655987ssThan(A),B),C)),hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_atLeastLessThan(A),D),E))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),D),B)) # label(fact_4234_greaterThanLessThan__subseteq__atLeastLessThan__iff) # label(axiom).  [clausify(3001)].
93.56/93.53	Derived: -hBOOL(hAPP(fun(rat,bool),bool,hAPP(fun(rat,bool),fun(fun(rat,bool),bool),ord_less_eq(fun(rat,bool)),hAPP(rat,fun(rat,bool),hAPP(rat,fun(rat,fun(rat,bool)),ord_gr676655987ssThan(rat),A),B)),hAPP(rat,fun(rat,bool),hAPP(rat,fun(rat,fun(rat,bool)),ord_atLeastLessThan(rat),C),D))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),C),A)).  [resolve(6047,a,6038,a)].
93.56/93.53	Derived: -hBOOL(hAPP(fun(real,bool),bool,hAPP(fun(real,bool),fun(fun(real,bool),bool),ord_less_eq(fun(real,bool)),hAPP(real,fun(real,bool),hAPP(real,fun(real,fun(real,bool)),ord_gr676655987ssThan(real),A),B)),hAPP(real,fun(real,bool),hAPP(real,fun(real,fun(real,bool)),ord_atLeastLessThan(real),C),D))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),C),A)).  [resolve(6047,a,6045,a)].
93.56/93.53	6048 -dense_linorder(A) | hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_gr676655987ssThan(A),B),C)),hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_atLeastLessThan(A),D),E))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) # label(fact_4234_greaterThanLessThan__subseteq__atLeastLessThan__iff) # label(axiom).  [clausify(3001)].
93.56/93.53	Derived: hBOOL(hAPP(fun(rat,bool),bool,hAPP(fun(rat,bool),fun(fun(rat,bool),bool),ord_less_eq(fun(rat,bool)),hAPP(rat,fun(rat,bool),hAPP(rat,fun(rat,fun(rat,bool)),ord_gr676655987ssThan(rat),A),B)),hAPP(rat,fun(rat,bool),hAPP(rat,fun(rat,fun(rat,bool)),ord_atLeastLessThan(rat),C),D))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),B)).  [resolve(6048,a,6038,a)].
93.56/93.53	Derived: hBOOL(hAPP(fun(real,bool),bool,hAPP(fun(real,bool),fun(fun(real,bool),bool),ord_less_eq(fun(real,bool)),hAPP(real,fun(real,bool),hAPP(real,fun(real,fun(real,bool)),ord_gr676655987ssThan(real),A),B)),hAPP(real,fun(real,bool),hAPP(real,fun(real,fun(real,bool)),ord_atLeastLessThan(real),C),D))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)).  [resolve(6048,a,6045,a)].
93.56/93.53	6049 -dense_linorder(A) | hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_gr676655987ssThan(A),B),C)),hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_atLeastLessThan(A),D),E))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),E)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),D),B)) # label(fact_4234_greaterThanLessThan__subseteq__atLeastLessThan__iff) # label(axiom).  [clausify(3001)].
93.56/93.53	Derived: hBOOL(hAPP(fun(rat,bool),bool,hAPP(fun(rat,bool),fun(fun(rat,bool),bool),ord_less_eq(fun(rat,bool)),hAPP(rat,fun(rat,bool),hAPP(rat,fun(rat,fun(rat,bool)),ord_gr676655987ssThan(rat),A),B)),hAPP(rat,fun(rat,bool),hAPP(rat,fun(rat,fun(rat,bool)),ord_atLeastLessThan(rat),C),D))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),B),D)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),C),A)).  [resolve(6049,a,6038,a)].
93.56/93.53	Derived: hBOOL(hAPP(fun(real,bool),bool,hAPP(fun(real,bool),fun(fun(real,bool),bool),ord_less_eq(fun(real,bool)),hAPP(real,fun(real,bool),hAPP(real,fun(real,fun(real,bool)),ord_gr676655987ssThan(real),A),B)),hAPP(real,fun(real,bool),hAPP(real,fun(real,fun(real,bool)),ord_atLeastLessThan(real),C),D))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),D)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),C),A)).  [resolve(6049,a,6045,a)].
94.84/94.75	6050 -dense_linorder(A) | ord_gr676655987ssThan(A) = ti(fun(A,fun(A,fun(A,bool))),ord_gr676655987ssThan(A)) # label(tsy_c_SetInterval_Oord__class_OgreaterThanLessThan_0_res) # label(axiom).  [clausify(3678)].
94.84/94.75	6051 -dense_linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_gr676655987ssThan(A),B),C)),hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_atLeastAtMost(A),D),E))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),E)) # label(fact_4530_greaterThanLessThan__subseteq__atLeastAtMost__iff) # label(axiom).  [clausify(4127)].
94.84/94.75	Derived: -hBOOL(hAPP(fun(rat,bool),bool,hAPP(fun(rat,bool),fun(fun(rat,bool),bool),ord_less_eq(fun(rat,bool)),hAPP(rat,fun(rat,bool),hAPP(rat,fun(rat,fun(rat,bool)),ord_gr676655987ssThan(rat),A),B)),hAPP(rat,fun(rat,bool),hAPP(rat,fun(rat,fun(rat,bool)),ord_atLeastAtMost(rat),C),D))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),B),D)).  [resolve(6051,a,6038,a)].
94.84/94.75	Derived: -hBOOL(hAPP(fun(real,bool),bool,hAPP(fun(real,bool),fun(fun(real,bool),bool),ord_less_eq(fun(real,bool)),hAPP(real,fun(real,bool),hAPP(real,fun(real,fun(real,bool)),ord_gr676655987ssThan(real),A),B)),hAPP(real,fun(real,bool),hAPP(real,fun(real,fun(real,bool)),ord_atLeastAtMost(real),C),D))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),D)).  [resolve(6051,a,6045,a)].
94.84/94.75	6052 -dense_linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_gr676655987ssThan(A),B),C)),hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_atLeastAtMost(A),D),E))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),D),B)) # label(fact_4530_greaterThanLessThan__subseteq__atLeastAtMost__iff) # label(axiom).  [clausify(4127)].
94.84/94.75	Derived: -hBOOL(hAPP(fun(rat,bool),bool,hAPP(fun(rat,bool),fun(fun(rat,bool),bool),ord_less_eq(fun(rat,bool)),hAPP(rat,fun(rat,bool),hAPP(rat,fun(rat,fun(rat,bool)),ord_gr676655987ssThan(rat),A),B)),hAPP(rat,fun(rat,bool),hAPP(rat,fun(rat,fun(rat,bool)),ord_atLeastAtMost(rat),C),D))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),C),A)).  [resolve(6052,a,6038,a)].
94.84/94.75	Derived: -hBOOL(hAPP(fun(real,bool),bool,hAPP(fun(real,bool),fun(fun(real,bool),bool),ord_less_eq(fun(real,bool)),hAPP(real,fun(real,bool),hAPP(real,fun(real,fun(real,bool)),ord_gr676655987ssThan(real),A),B)),hAPP(real,fun(real,bool),hAPP(real,fun(real,fun(real,bool)),ord_atLeastAtMost(real),C),D))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),C),A)).  [resolve(6052,a,6045,a)].
94.84/94.75	6053 -dense_linorder(A) | hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_gr676655987ssThan(A),B),C)),hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_atLeastAtMost(A),D),E))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) # label(fact_4530_greaterThanLessThan__subseteq__atLeastAtMost__iff) # label(axiom).  [clausify(4127)].
94.84/94.75	Derived: hBOOL(hAPP(fun(rat,bool),bool,hAPP(fun(rat,bool),fun(fun(rat,bool),bool),ord_less_eq(fun(rat,bool)),hAPP(rat,fun(rat,bool),hAPP(rat,fun(rat,fun(rat,bool)),ord_gr676655987ssThan(rat),A),B)),hAPP(rat,fun(rat,bool),hAPP(rat,fun(rat,fun(rat,bool)),ord_atLeastAtMost(rat),C),D))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),B)).  [resolve(6053,a,6038,a)].
94.93/94.85	Derived: hBOOL(hAPP(fun(real,bool),bool,hAPP(fun(real,bool),fun(fun(real,bool),bool),ord_less_eq(fun(real,bool)),hAPP(real,fun(real,bool),hAPP(real,fun(real,fun(real,bool)),ord_gr676655987ssThan(real),A),B)),hAPP(real,fun(real,bool),hAPP(real,fun(real,fun(real,bool)),ord_atLeastAtMost(real),C),D))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)).  [resolve(6053,a,6045,a)].
94.93/94.85	6054 -dense_linorder(A) | hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_gr676655987ssThan(A),B),C)),hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_atLeastAtMost(A),D),E))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),E)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),D),B)) # label(fact_4530_greaterThanLessThan__subseteq__atLeastAtMost__iff) # label(axiom).  [clausify(4127)].
94.93/94.85	Derived: hBOOL(hAPP(fun(rat,bool),bool,hAPP(fun(rat,bool),fun(fun(rat,bool),bool),ord_less_eq(fun(rat,bool)),hAPP(rat,fun(rat,bool),hAPP(rat,fun(rat,fun(rat,bool)),ord_gr676655987ssThan(rat),A),B)),hAPP(rat,fun(rat,bool),hAPP(rat,fun(rat,fun(rat,bool)),ord_atLeastAtMost(rat),C),D))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),B),D)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),C),A)).  [resolve(6054,a,6038,a)].
94.93/94.85	Derived: hBOOL(hAPP(fun(real,bool),bool,hAPP(fun(real,bool),fun(fun(real,bool),bool),ord_less_eq(fun(real,bool)),hAPP(real,fun(real,bool),hAPP(real,fun(real,fun(real,bool)),ord_gr676655987ssThan(real),A),B)),hAPP(real,fun(real,bool),hAPP(real,fun(real,fun(real,bool)),ord_atLeastAtMost(real),C),D))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),D)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),C),A)).  [resolve(6054,a,6045,a)].
94.93/94.85	6055 -dense_linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),f748(A,D,B,C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),D)) # label(fact_2826_dense__le__bounded) # label(axiom).  [clausify(4193)].
94.93/94.85	Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),f748(rat,C,A,B))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),B),C)).  [resolve(6055,a,6038,a)].
94.93/94.85	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),f748(real,C,A,B))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),C)).  [resolve(6055,a,6045,a)].
94.93/94.85	6056 -dense_linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),f748(A,D,B,C)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),D)) # label(fact_2826_dense__le__bounded) # label(axiom).  [clausify(4193)].
94.93/94.85	Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),f748(rat,C,A,B)),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),B),C)).  [resolve(6056,a,6038,a)].
94.93/94.85	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),f748(real,C,A,B)),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),C)).  [resolve(6056,a,6045,a)].
94.93/94.85	6057 -dense_linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),f748(A,D,B,C)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),D)) # label(fact_2826_dense__le__bounded) # label(axiom).  [clausify(4193)].
94.93/94.85	Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),f748(rat,C,A,B)),C)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),B),C)).  [resolve(6057,a,6038,a)].
94.93/94.85	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),f748(real,C,A,B)),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),C)).  [resolve(6057,a,6045,a)].
95.00/94.91	6058 -dense_linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_atLeastAtMost(A),B),C)),hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_atLeastLessThan(A),D),E))) # label(fact_4529_atLeastAtMost__subseteq__atLeastLessThan__iff) # label(axiom).  [clausify(4241)].
95.00/94.91	Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),B)) | hBOOL(hAPP(fun(rat,bool),bool,hAPP(fun(rat,bool),fun(fun(rat,bool),bool),ord_less_eq(fun(rat,bool)),hAPP(rat,fun(rat,bool),hAPP(rat,fun(rat,fun(rat,bool)),ord_atLeastAtMost(rat),A),B)),hAPP(rat,fun(rat,bool),hAPP(rat,fun(rat,fun(rat,bool)),ord_atLeastLessThan(rat),C),D))).  [resolve(6058,a,6038,a)].
95.00/94.91	Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),B)) | hBOOL(hAPP(fun(real,bool),bool,hAPP(fun(real,bool),fun(fun(real,bool),bool),ord_less_eq(fun(real,bool)),hAPP(real,fun(real,bool),hAPP(real,fun(real,fun(real,bool)),ord_atLeastAtMost(real),A),B)),hAPP(real,fun(real,bool),hAPP(real,fun(real,fun(real,bool)),ord_atLeastLessThan(real),C),D))).  [resolve(6058,a,6045,a)].
95.00/94.91	6059 -dense_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),D),E)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_atLeastAtMost(A),C),D)),hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_atLeastLessThan(A),B),E))) # label(fact_4529_atLeastAtMost__subseteq__atLeastLessThan__iff) # label(axiom).  [clausify(4241)].
95.00/94.91	Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),C),D)) | hBOOL(hAPP(fun(rat,bool),bool,hAPP(fun(rat,bool),fun(fun(rat,bool),bool),ord_less_eq(fun(rat,bool)),hAPP(rat,fun(rat,bool),hAPP(rat,fun(rat,fun(rat,bool)),ord_atLeastAtMost(rat),B),C)),hAPP(rat,fun(rat,bool),hAPP(rat,fun(rat,fun(rat,bool)),ord_atLeastLessThan(rat),A),D))).  [resolve(6059,a,6038,a)].
95.00/94.91	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),C),D)) | hBOOL(hAPP(fun(real,bool),bool,hAPP(fun(real,bool),fun(fun(real,bool),bool),ord_less_eq(fun(real,bool)),hAPP(real,fun(real,bool),hAPP(real,fun(real,fun(real,bool)),ord_atLeastAtMost(real),B),C)),hAPP(real,fun(real,bool),hAPP(real,fun(real,fun(real,bool)),ord_atLeastLessThan(real),A),D))).  [resolve(6059,a,6045,a)].
95.00/94.91	6060 -dense_linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),D),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_atLeastAtMost(A),B),C)),hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_atLeastLessThan(A),D),E))) # label(fact_4529_atLeastAtMost__subseteq__atLeastLessThan__iff) # label(axiom).  [clausify(4241)].
95.00/94.91	Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),C),A)) | -hBOOL(hAPP(fun(rat,bool),bool,hAPP(fun(rat,bool),fun(fun(rat,bool),bool),ord_less_eq(fun(rat,bool)),hAPP(rat,fun(rat,bool),hAPP(rat,fun(rat,fun(rat,bool)),ord_atLeastAtMost(rat),A),B)),hAPP(rat,fun(rat,bool),hAPP(rat,fun(rat,fun(rat,bool)),ord_atLeastLessThan(rat),C),D))).  [resolve(6060,a,6038,a)].
95.00/94.91	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),C),A)) | -hBOOL(hAPP(fun(real,bool),bool,hAPP(fun(real,bool),fun(fun(real,bool),bool),ord_less_eq(fun(real,bool)),hAPP(real,fun(real,bool),hAPP(real,fun(real,fun(real,bool)),ord_atLeastAtMost(real),A),B)),hAPP(real,fun(real,bool),hAPP(real,fun(real,fun(real,bool)),ord_atLeastLessThan(real),C),D))).  [resolve(6060,a,6045,a)].
100.51/100.47	6061 -dense_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),D)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_atLeastAtMost(A),B),C)),hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_atLeastLessThan(A),E),D))) # label(fact_4529_atLeastAtMost__subseteq__atLeastLessThan__iff) # label(axiom).  [clausify(4241)].
100.51/100.47	Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),C)) | -hBOOL(hAPP(fun(rat,bool),bool,hAPP(fun(rat,bool),fun(fun(rat,bool),bool),ord_less_eq(fun(rat,bool)),hAPP(rat,fun(rat,bool),hAPP(rat,fun(rat,fun(rat,bool)),ord_atLeastAtMost(rat),A),B)),hAPP(rat,fun(rat,bool),hAPP(rat,fun(rat,fun(rat,bool)),ord_atLeastLessThan(rat),D),C))).  [resolve(6061,a,6038,a)].
100.51/100.47	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),C)) | -hBOOL(hAPP(fun(real,bool),bool,hAPP(fun(real,bool),fun(fun(real,bool),bool),ord_less_eq(fun(real,bool)),hAPP(real,fun(real,bool),hAPP(real,fun(real,fun(real,bool)),ord_atLeastAtMost(real),A),B)),hAPP(real,fun(real,bool),hAPP(real,fun(real,fun(real,bool)),ord_atLeastLessThan(real),D),C))).  [resolve(6061,a,6045,a)].
100.51/100.47	6062 real_normed_algebra(real) # label(arity_RealDef_Oreal___RealVector_Oreal__normed__algebra) # label(axiom).  [assumption].
100.51/100.47	6063 -topological_space(A) | -real_normed_algebra(B) | -hBOOL(hAPP(A,bool,hAPP(fun(A,B),fun(A,bool),isCont(A,B),C),D)) | -hBOOL(hAPP(A,bool,hAPP(fun(A,B),fun(A,bool),isCont(A,B),E),D)) | hBOOL(hAPP(A,bool,hAPP(fun(A,B),fun(A,bool),isCont(A,B),hAPP(fun(A,B),fun(A,B),hAPP(fun(A,fun(B,B)),fun(fun(A,B),fun(A,B)),combs(A,B,B),hAPP(fun(A,B),fun(A,fun(B,B)),hAPP(fun(B,fun(B,B)),fun(fun(A,B),fun(A,fun(B,B))),combb(B,fun(B,B),A),times_times(B)),C)),E)),D)) # label(fact_4910_mult_OisCont) # label(axiom).  [clausify(89)].
100.51/100.47	6064 -real_normed_algebra(A) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),f24(A,B))) # label(fact_1808_mult__right_Ononneg__bounded) # label(axiom).  [clausify(109)].
100.51/100.47	6065 -real_normed_algebra(A) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(A,real,norm_norm(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(A,real,norm_norm(A),C)),f24(A,B)))) # label(fact_1808_mult__right_Ononneg__bounded) # label(axiom).  [clausify(109)].
100.51/100.47	6066 -real_normed_algebra(A) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),hAPP(A,fun(B,A),hAPP(fun(B,fun(A,A)),fun(A,fun(B,A)),combc(B,A,A),hAPP(fun(B,A),fun(B,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(B,A),fun(B,fun(A,A))),combb(A,fun(A,A),B),times_times(A)),C)),D)),E) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),C),E)),D) # label(fact_4190_mult__left_Osetsum) # label(axiom).  [clausify(120)].
100.51/100.47	6067 -real_normed_algebra(A) | -hBOOL(hAPP(A,bool,hAPP(fun(nat,A),fun(A,bool),sums(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(fun(nat,A),fun(A,bool),sums(A),hAPP(A,fun(nat,A),hAPP(fun(nat,fun(A,A)),fun(A,fun(nat,A)),combc(nat,A,A),hAPP(fun(nat,A),fun(nat,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(nat,A),fun(nat,fun(A,A))),combb(A,fun(A,A),nat),times_times(A)),B)),D)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),D))) # label(fact_4080_sums__mult2) # label(axiom).  [clausify(195)].
100.51/100.47	6068 -real_normed_algebra(A) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(A,real,norm_norm(A),B)),C)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(A,real,norm_norm(A),D)),E)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(A,real,norm_norm(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),E))) # label(fact_1789_norm__mult__less) # label(axiom).  [clausify(269)].
100.51/100.47	6069 -real_normed_algebra(A) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),hAPP(fun(B,A),fun(B,A),hAPP(fun(A,A),fun(fun(B,A),fun(B,A)),combb(A,A,B),hAPP(A,fun(A,A),times_times(A),C)),D)),E) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),D),E)) # label(fact_4191_mult__right_Osetsum) # label(axiom).  [clausify(285)].
100.51/100.47	6070 -real_normed_algebra(A) | -hBOOL(hAPP(fun(nat,A),bool,cauchy(A),B)) | hBOOL(hAPP(fun(nat,A),bool,cauchy(A),hAPP(fun(nat,A),fun(nat,A),hAPP(fun(A,A),fun(fun(nat,A),fun(nat,A)),combb(A,A,nat),hAPP(A,fun(A,A),times_times(A),C)),B))) # label(fact_4100_mult__right_OCauchy) # label(axiom).  [clausify(370)].
100.51/100.47	6071 -banach(A) | -real_normed_algebra(A) | -hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,A),fun(nat,real),hAPP(fun(A,real),fun(fun(nat,A),fun(nat,real)),combb(A,real,nat),norm_norm(A)),B))) | -hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,A),fun(nat,real),hAPP(fun(A,real),fun(fun(nat,A),fun(nat,real)),combb(A,real,nat),norm_norm(A)),C))) | hBOOL(hAPP(A,bool,hAPP(fun(nat,A),fun(A,bool),sums(A),hAPP(fun(nat,fun(nat,bool)),fun(nat,A),hAPP(fun(nat,fun(fun(nat,bool),A)),fun(fun(nat,fun(nat,bool)),fun(nat,A)),combs(nat,fun(nat,bool),A),hAPP(fun(nat,fun(nat,A)),fun(nat,fun(fun(nat,bool),A)),hAPP(fun(fun(nat,A),fun(fun(nat,bool),A)),fun(fun(nat,fun(nat,A)),fun(nat,fun(fun(nat,bool),A))),combb(fun(nat,A),fun(fun(nat,bool),A),nat),big_co1399186613setsum(nat,A)),hAPP(fun(nat,fun(nat,A)),fun(nat,fun(nat,A)),hAPP(fun(fun(nat,A),fun(nat,A)),fun(fun(nat,fun(nat,A)),fun(nat,fun(nat,A))),combb(fun(nat,A),fun(nat,A),nat),hAPP(fun(nat,fun(A,A)),fun(fun(nat,A),fun(nat,A)),combs(nat,A,A),hAPP(fun(nat,A),fun(nat,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(nat,A),fun(nat,fun(A,A))),combb(A,fun(A,A),nat),times_times(A)),B))),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,A)),hAPP(fun(fun(nat,nat),fun(nat,A)),fun(fun(nat,fun(nat,nat)),fun(nat,fun(nat,A))),combb(fun(nat,nat),fun(nat,A),nat),hAPP(fun(nat,A),fun(fun(nat,nat),fun(nat,A)),combb(nat,A,nat),C)),minus_minus(nat))))),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),zero_zero(nat)))),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(fun(nat,A),A,suminf(A),B)),hAPP(fun(nat,A),A,suminf(A),C)))) # label(fact_4623_Cauchy__product__sums) # label(axiom).  [clausify(387)].
100.51/100.47	6072 -real_normed_algebra(A) | -hBOOL(hAPP(fun(nat,A),bool,summable(A),B)) | hBOOL(hAPP(fun(nat,A),bool,summable(A),hAPP(A,fun(nat,A),hAPP(fun(nat,fun(A,A)),fun(A,fun(nat,A)),combc(nat,A,A),hAPP(fun(nat,A),fun(nat,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(nat,A),fun(nat,fun(A,A))),combb(A,fun(A,A),nat),times_times(A)),B)),C))) # label(fact_4000_mult__left_Osummable) # label(axiom).  [clausify(432)].
100.51/100.47	6073 -real_normed_algebra(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),D)) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D)) # label(fact_881_mult__right_Oadd) # label(axiom).  [clausify(446)].
100.51/100.47	6074 -real_normed_algebra(A) | hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),C)) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),D)),C) # label(fact_884_mult__left_Odiff) # label(axiom).  [clausify(518)].
100.51/100.47	6075 -real_normed_algebra(A) | hBOOL(hAPP(A,bool,hAPP(fun(A,A),fun(A,bool),isCont(A,A),hAPP(A,fun(A,A),hAPP(fun(A,fun(A,A)),fun(A,fun(A,A)),combc(A,A,A),times_times(A)),B)),C)) # label(fact_4908_mult__left_OisCont) # label(axiom).  [clausify(569)].
100.51/100.47	6076 -real_normed_algebra(A) | -hBOOL(hAPP(fun(nat,A),bool,summable(A),B)) | hBOOL(hAPP(fun(nat,A),bool,summable(A),hAPP(A,fun(nat,A),hAPP(fun(nat,fun(A,A)),fun(A,fun(nat,A)),combc(nat,A,A),hAPP(fun(nat,A),fun(nat,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(nat,A),fun(nat,fun(A,A))),combb(A,fun(A,A),nat),times_times(A)),B)),C))) # label(fact_3998_summable__mult2) # label(axiom).  [clausify(623)].
100.51/100.47	6077 -real_normed_algebra(A) | -hBOOL(hAPP(A,bool,hAPP(fun(nat,A),fun(A,bool),sums(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(fun(nat,A),fun(A,bool),sums(A),hAPP(fun(nat,A),fun(nat,A),hAPP(fun(A,A),fun(fun(nat,A),fun(nat,A)),combb(A,A,nat),hAPP(A,fun(A,A),times_times(A),D)),B)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),C))) # label(fact_4081_mult__right_Osums) # label(axiom).  [clausify(677)].
100.51/100.47	6078 -real_normed_algebra(A) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(A,real,norm_norm(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(A,real,norm_norm(A),C)),f108(A,B)))) # label(fact_1804_mult__right_Opos__bounded) # label(axiom).  [clausify(684)].
100.51/100.47	6079 -real_normed_algebra(A) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),f108(A,B))) # label(fact_1804_mult__right_Opos__bounded) # label(axiom).  [clausify(684)].
100.51/100.48	6080 -real_normed_algebra(A) | -hBOOL(hAPP(fun(nat,A),bool,summable(A),B)) | hAPP(fun(nat,A),A,suminf(A),hAPP(fun(nat,A),fun(nat,A),hAPP(fun(A,A),fun(fun(nat,A),fun(nat,A)),combb(A,A,nat),hAPP(A,fun(A,A),times_times(A),C)),B)) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),hAPP(fun(nat,A),A,suminf(A),B)) # label(fact_3990_suminf__mult) # label(axiom).  [clausify(757)].
100.51/100.48	6081 -real_normed_algebra(A) | zero_zero(A) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),zero_zero(A)),B) # label(fact_876_mult_Ozero__left) # label(axiom).  [clausify(860)].
100.51/100.48	6082 -real_normed_algebra(A) | hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D)) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),C),D)) # label(fact_887_mult_Odiff__right) # label(axiom).  [clausify(925)].
100.51/100.48	6083 -real_normed_algebra(A) | hAPP(A,A,uminus_uminus(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),hAPP(A,A,uminus_uminus(A),B)),C) # label(fact_2035_mult__left_Ominus) # label(axiom).  [clausify(948)].
100.51/100.48	6084 -real_normed_algebra(A) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(A,real,norm_norm(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(A,real,norm_norm(A),B)),hAPP(A,real,norm_norm(A),C)))) # label(fact_1788_norm__mult__ineq) # label(axiom).  [clausify(1025)].
100.51/100.48	6085 -banach(A) | -real_normed_algebra(A) | -hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,A),fun(nat,real),hAPP(fun(A,real),fun(fun(nat,A),fun(nat,real)),combb(A,real,nat),norm_norm(A)),B))) | -hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,A),fun(nat,real),hAPP(fun(A,real),fun(fun(nat,A),fun(nat,real)),combb(A,real,nat),norm_norm(A)),C))) | hAPP(fun(nat,A),A,suminf(A),hAPP(fun(nat,fun(nat,bool)),fun(nat,A),hAPP(fun(nat,fun(fun(nat,bool),A)),fun(fun(nat,fun(nat,bool)),fun(nat,A)),combs(nat,fun(nat,bool),A),hAPP(fun(nat,fun(nat,A)),fun(nat,fun(fun(nat,bool),A)),hAPP(fun(fun(nat,A),fun(fun(nat,bool),A)),fun(fun(nat,fun(nat,A)),fun(nat,fun(fun(nat,bool),A))),combb(fun(nat,A),fun(fun(nat,bool),A),nat),big_co1399186613setsum(nat,A)),hAPP(fun(nat,fun(nat,A)),fun(nat,fun(nat,A)),hAPP(fun(fun(nat,A),fun(nat,A)),fun(fun(nat,fun(nat,A)),fun(nat,fun(nat,A))),combb(fun(nat,A),fun(nat,A),nat),hAPP(fun(nat,fun(A,A)),fun(fun(nat,A),fun(nat,A)),combs(nat,A,A),hAPP(fun(nat,A),fun(nat,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(nat,A),fun(nat,fun(A,A))),combb(A,fun(A,A),nat),times_times(A)),B))),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,A)),hAPP(fun(fun(nat,nat),fun(nat,A)),fun(fun(nat,fun(nat,nat)),fun(nat,fun(nat,A))),combb(fun(nat,nat),fun(nat,A),nat),hAPP(fun(nat,A),fun(fun(nat,nat),fun(nat,A)),combb(nat,A,nat),C)),minus_minus(nat))))),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),zero_zero(nat)))) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(fun(nat,A),A,suminf(A),B)),hAPP(fun(nat,A),A,suminf(A),C)) # label(fact_4621_Cauchy__product) # label(axiom).  [clausify(1048)].
100.51/100.48	6086 -metric_space(A) | -real_normed_algebra(B) | -hBOOL(hAPP(filter(A),bool,hAPP(B,fun(filter(A),bool),hAPP(fun(A,B),fun(B,fun(filter(A),bool)),tendsto(A,B),C),zero_zero(B)),hAPP(A,filter(A),at(A),D))) | -hBOOL(hAPP(filter(A),bool,hAPP(B,fun(filter(A),bool),hAPP(fun(A,B),fun(B,fun(filter(A),bool)),tendsto(A,B),E),zero_zero(B)),hAPP(A,filter(A),at(A),D))) | hBOOL(hAPP(filter(A),bool,hAPP(B,fun(filter(A),bool),hAPP(fun(A,B),fun(B,fun(filter(A),bool)),tendsto(A,B),hAPP(fun(A,B),fun(A,B),hAPP(fun(A,fun(B,B)),fun(fun(A,B),fun(A,B)),combs(A,B,B),hAPP(fun(A,B),fun(A,fun(B,B)),hAPP(fun(B,fun(B,B)),fun(fun(A,B),fun(A,fun(B,B))),combb(B,fun(B,B),A),times_times(B)),C)),E)),zero_zero(B)),hAPP(A,filter(A),at(A),D))) # label(fact_4577_LIM__mult__zero) # label(axiom).  [clausify(1066)].
100.51/100.48	6087 -real_normed_algebra(A) | -power(A) | -hBOOL(hAPP(filter(nat),bool,hAPP(A,fun(filter(nat),bool),hAPP(fun(nat,A),fun(A,fun(filter(nat),bool)),tendsto(nat,A),B),C),sequentially)) | hBOOL(hAPP(filter(nat),bool,hAPP(A,fun(filter(nat),bool),hAPP(fun(nat,A),fun(A,fun(filter(nat),bool)),tendsto(nat,A),hAPP(nat,fun(nat,A),hAPP(fun(nat,fun(nat,A)),fun(nat,fun(nat,A)),combc(nat,nat,A),hAPP(fun(nat,A),fun(nat,fun(nat,A)),hAPP(fun(A,fun(nat,A)),fun(fun(nat,A),fun(nat,fun(nat,A))),combb(A,fun(nat,A),nat),power_power(A)),B)),D)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),C),D)),sequentially)) # label(fact_4467_LIMSEQ__pow) # label(axiom).  [clausify(1080)].
100.51/100.48	6088 -real_normed_algebra(A) | -topological_space(B) | -hBOOL(hAPP(filter(B),bool,hAPP(A,fun(filter(B),bool),hAPP(fun(B,A),fun(A,fun(filter(B),bool)),tendsto(B,A),C),D),hAPP(B,filter(B),at(B),E))) | hBOOL(hAPP(filter(B),bool,hAPP(A,fun(filter(B),bool),hAPP(fun(B,A),fun(A,fun(filter(B),bool)),tendsto(B,A),hAPP(A,fun(B,A),hAPP(fun(B,fun(A,A)),fun(A,fun(B,A)),combc(B,A,A),hAPP(fun(B,A),fun(B,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(B,A),fun(B,fun(A,A))),combb(A,fun(A,A),B),times_times(A)),C)),F)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),F)),hAPP(B,filter(B),at(B),E))) # label(fact_4549_mult__left_OLIM) # label(axiom).  [clausify(1111)].
100.51/100.48	6089 -real_normed_algebra(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),C),D)) = hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),C),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D)) # label(fact_4676_mult__right_OscaleR) # label(axiom).  [clausify(1166)].
100.51/100.48	6090 -real_normed_algebra(A) | zero_zero(A) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),zero_zero(A)),B) # label(fact_877_mult__left_Ozero) # label(axiom).  [clausify(1173)].
100.51/100.48	6091 -real_normed_algebra(A) | -power(A) | -topological_space(B) | -hBOOL(hAPP(B,bool,hAPP(fun(B,A),fun(B,bool),isCont(B,A),C),D)) | hBOOL(hAPP(B,bool,hAPP(fun(B,A),fun(B,bool),isCont(B,A),hAPP(nat,fun(B,A),hAPP(fun(B,fun(nat,A)),fun(nat,fun(B,A)),combc(B,nat,A),hAPP(fun(B,A),fun(B,fun(nat,A)),hAPP(fun(A,fun(nat,A)),fun(fun(B,A),fun(B,fun(nat,A))),combb(A,fun(nat,A),B),power_power(A)),C)),E)),D)) # label(fact_4902_isCont__power) # label(axiom).  [clausify(1413)].
100.51/100.48	6092 -real_normed_algebra(A) | -hBOOL(hAPP(filter(B),bool,hAPP(A,fun(filter(B),bool),hAPP(fun(B,A),fun(A,fun(filter(B),bool)),tendsto(B,A),C),D),E)) | -hBOOL(hAPP(filter(B),bool,hAPP(A,fun(filter(B),bool),hAPP(fun(B,A),fun(A,fun(filter(B),bool)),tendsto(B,A),F),V6),E)) | hBOOL(hAPP(filter(B),bool,hAPP(A,fun(filter(B),bool),hAPP(fun(B,A),fun(A,fun(filter(B),bool)),tendsto(B,A),hAPP(fun(B,A),fun(B,A),hAPP(fun(B,fun(A,A)),fun(fun(B,A),fun(B,A)),combs(B,A,A),hAPP(fun(B,A),fun(B,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(B,A),fun(B,fun(A,A))),combb(A,fun(A,A),B),times_times(A)),C)),F)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),V6)),E)) # label(fact_4474_mult_Otendsto) # label(axiom).  [clausify(1482)].
100.51/100.48	6093 -real_normed_algebra(A) | -hBOOL(hAPP(fun(nat,A),bool,cauchy(A),B)) | hBOOL(hAPP(fun(nat,A),bool,cauchy(A),hAPP(A,fun(nat,A),hAPP(fun(nat,fun(A,A)),fun(A,fun(nat,A)),combc(nat,A,A),hAPP(fun(nat,A),fun(nat,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(nat,A),fun(nat,fun(A,A))),combb(A,fun(A,A),nat),times_times(A)),B)),C))) # label(fact_4101_mult__left_OCauchy) # label(axiom).  [clausify(1539)].
100.51/100.48	6094 -topological_space(A) | -real_normed_algebra(B) | -hBOOL(hAPP(A,bool,hAPP(fun(A,B),fun(A,bool),isCont(A,B),C),D)) | -hBOOL(hAPP(A,bool,hAPP(fun(A,B),fun(A,bool),isCont(A,B),E),D)) | hBOOL(hAPP(A,bool,hAPP(fun(A,B),fun(A,bool),isCont(A,B),hAPP(fun(A,B),fun(A,B),hAPP(fun(A,fun(B,B)),fun(fun(A,B),fun(A,B)),combs(A,B,B),hAPP(fun(A,B),fun(A,fun(B,B)),hAPP(fun(B,fun(B,B)),fun(fun(A,B),fun(A,fun(B,B))),combb(B,fun(B,B),A),times_times(B)),C)),E)),D)) # label(fact_4909_isCont__mult) # label(axiom).  [clausify(1599)].
100.51/100.48	6095 -real_normed_algebra(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),D) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),D)) # label(fact_882_mult_Oadd__left) # label(axiom).  [clausify(1632)].
100.51/100.48	6096 -real_normed_algebra(A) | hBOOL(hAPP(filter(A),bool,hAPP(A,fun(filter(A),bool),hAPP(fun(A,A),fun(A,fun(filter(A),bool)),tendsto(A,A),hAPP(A,fun(A,A),times_times(A),B)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),hAPP(A,filter(A),at(A),C))) # label(fact_4552_mult__right_Ocont) # label(axiom).  [clausify(1814)].
100.51/100.48	6097 -topological_space(A) | -real_normed_algebra(B) | -hBOOL(hAPP(filter(A),bool,hAPP(B,fun(filter(A),bool),hAPP(fun(A,B),fun(B,fun(filter(A),bool)),tendsto(A,B),C),zero_zero(B)),hAPP(A,filter(A),at(A),D))) | hBOOL(hAPP(filter(A),bool,hAPP(B,fun(filter(A),bool),hAPP(fun(A,B),fun(B,fun(filter(A),bool)),tendsto(A,B),hAPP(B,fun(A,B),hAPP(fun(A,fun(B,B)),fun(B,fun(A,B)),combc(A,B,B),hAPP(fun(A,B),fun(A,fun(B,B)),hAPP(fun(B,fun(B,B)),fun(fun(A,B),fun(A,fun(B,B))),combb(B,fun(B,B),A),times_times(B)),C)),E)),zero_zero(B)),hAPP(A,filter(A),at(A),D))) # label(fact_4575_LIM__mult__left__zero) # label(axiom).  [clausify(1952)].
100.51/100.48	6098 -real_normed_algebra(A) | -hBOOL(hAPP(filter(B),bool,hAPP(A,fun(filter(B),bool),hAPP(fun(B,A),fun(A,fun(filter(B),bool)),tendsto(B,A),C),D),E)) | hBOOL(hAPP(filter(B),bool,hAPP(A,fun(filter(B),bool),hAPP(fun(B,A),fun(A,fun(filter(B),bool)),tendsto(B,A),hAPP(fun(B,A),fun(B,A),hAPP(fun(A,A),fun(fun(B,A),fun(B,A)),combb(A,A,B),hAPP(A,fun(A,A),times_times(A),F)),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),F),D)),E)) # label(fact_4476_mult__right_Otendsto) # label(axiom).  [clausify(1986)].
100.51/100.48	6099 -real_normed_algebra(A) | hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),E)) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),D)),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),C),E))),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),D)),E))),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),C),E))) # label(fact_875_mult_Oprod__diff__prod) # label(axiom).  [clausify(2085)].
100.51/100.48	6100 -real_normed_algebra(A) | hAPP(A,A,uminus_uminus(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),hAPP(A,A,uminus_uminus(A),C)) # label(fact_2038_mult_Ominus__right) # label(axiom).  [clausify(2118)].
100.51/100.48	6101 -real_normed_algebra(A) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(A,real,norm_norm(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(A,real,norm_norm(A),B)),hAPP(A,real,norm_norm(A),C))),f365(A)))) # label(fact_1807_mult_Ononneg__bounded) # label(axiom).  [clausify(2204)].
100.51/100.48	6102 -real_normed_algebra(A) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),f365(A))) # label(fact_1807_mult_Ononneg__bounded) # label(axiom).  [clausify(2204)].
100.51/100.48	6103 -real_normed_algebra(A) | -hBOOL(hAPP(filter(nat),bool,hAPP(A,fun(filter(nat),bool),hAPP(fun(nat,A),fun(A,fun(filter(nat),bool)),tendsto(nat,A),B),C),sequentially)) | hBOOL(hAPP(filter(nat),bool,hAPP(A,fun(filter(nat),bool),hAPP(fun(nat,A),fun(A,fun(filter(nat),bool)),tendsto(nat,A),hAPP(A,fun(nat,A),hAPP(fun(nat,fun(A,A)),fun(A,fun(nat,A)),combc(nat,A,A),hAPP(fun(nat,A),fun(nat,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(nat,A),fun(nat,fun(A,A))),combb(A,fun(A,A),nat),times_times(A)),B)),D)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),D)),sequentially)) # label(fact_4478_mult__left_OLIMSEQ) # label(axiom).  [clausify(2207)].
100.51/100.48	6104 -real_normed_algebra(A) | -hBOOL(hAPP(filter(nat),bool,hAPP(A,fun(filter(nat),bool),hAPP(fun(nat,A),fun(A,fun(filter(nat),bool)),tendsto(nat,A),B),C),sequentially)) | -hBOOL(hAPP(filter(nat),bool,hAPP(A,fun(filter(nat),bool),hAPP(fun(nat,A),fun(A,fun(filter(nat),bool)),tendsto(nat,A),D),E),sequentially)) | hBOOL(hAPP(filter(nat),bool,hAPP(A,fun(filter(nat),bool),hAPP(fun(nat,A),fun(A,fun(filter(nat),bool)),tendsto(nat,A),hAPP(fun(nat,A),fun(nat,A),hAPP(fun(nat,fun(A,A)),fun(fun(nat,A),fun(nat,A)),combs(nat,A,A),hAPP(fun(nat,A),fun(nat,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(nat,A),fun(nat,fun(A,A))),combb(A,fun(A,A),nat),times_times(A)),B)),D)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),E)),sequentially)) # label(fact_4477_LIMSEQ__mult) # label(axiom).  [clausify(2333)].
100.51/100.48	6105 -real_normed_algebra(A) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(A,real,norm_norm(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(A,real,norm_norm(A),B)),hAPP(A,real,norm_norm(A),C))),f408(A)))) # label(fact_1811_mult_Obounded) # label(axiom).  [clausify(2366)].
100.51/100.48	6106 -real_normed_algebra(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),C),D)) = hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),C),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D)) # label(fact_4674_mult_OscaleR__right) # label(axiom).  [clausify(2370)].
100.51/100.48	6107 -real_normed_algebra(A) | zero_zero(A) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),zero_zero(A)) # label(fact_878_mult_Ozero__right) # label(axiom).  [clausify(2421)].
100.51/100.48	6108 -real_normed_algebra(A) | -comm_ring_1(A) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f440(B,A,C,D,E)),E)) | hBOOL(hAPP(filter(nat),bool,hAPP(A,fun(filter(nat),bool),hAPP(fun(nat,A),fun(A,fun(filter(nat),bool)),tendsto(nat,A),hAPP(fun(B,bool),fun(nat,A),hAPP(fun(nat,fun(fun(B,bool),A)),fun(fun(B,bool),fun(nat,A)),combc(nat,fun(B,bool),A),hAPP(fun(nat,fun(B,A)),fun(nat,fun(fun(B,bool),A)),hAPP(fun(fun(B,A),fun(fun(B,bool),A)),fun(fun(nat,fun(B,A)),fun(nat,fun(fun(B,bool),A))),combb(fun(B,A),fun(fun(B,bool),A),nat),big_co302546470etprod(B,A)),hAPP(fun(B,fun(nat,A)),fun(nat,fun(B,A)),combc(B,nat,A),C))),E)),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),D),E)),sequentially)) # label(fact_4657_LIMSEQ__setprod) # label(axiom).  [clausify(2539)].
100.51/100.48	6109 -real_normed_algebra(A) | -comm_ring_1(A) | -hBOOL(hAPP(filter(nat),bool,hAPP(A,fun(filter(nat),bool),hAPP(fun(nat,A),fun(A,fun(filter(nat),bool)),tendsto(nat,A),hAPP(B,fun(nat,A),C,f440(B,A,C,D,E))),hAPP(B,A,D,f440(B,A,C,D,E))),sequentially)) | hBOOL(hAPP(filter(nat),bool,hAPP(A,fun(filter(nat),bool),hAPP(fun(nat,A),fun(A,fun(filter(nat),bool)),tendsto(nat,A),hAPP(fun(B,bool),fun(nat,A),hAPP(fun(nat,fun(fun(B,bool),A)),fun(fun(B,bool),fun(nat,A)),combc(nat,fun(B,bool),A),hAPP(fun(nat,fun(B,A)),fun(nat,fun(fun(B,bool),A)),hAPP(fun(fun(B,A),fun(fun(B,bool),A)),fun(fun(nat,fun(B,A)),fun(nat,fun(fun(B,bool),A))),combb(fun(B,A),fun(fun(B,bool),A),nat),big_co302546470etprod(B,A)),hAPP(fun(B,fun(nat,A)),fun(nat,fun(B,A)),combc(B,nat,A),C))),E)),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),D),E)),sequentially)) # label(fact_4657_LIMSEQ__setprod) # label(axiom).  [clausify(2539)].
100.51/100.48	6110 -real_normed_algebra(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),D)) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D)) # label(fact_880_mult_Oadd__right) # label(axiom).  [clausify(2619)].
100.59/100.49	6111 -real_normed_algebra(A) | -hBOOL(hAPP(fun(nat,A),bool,summable(A),B)) | hBOOL(hAPP(fun(nat,A),bool,summable(A),hAPP(fun(nat,A),fun(nat,A),hAPP(fun(A,A),fun(fun(nat,A),fun(nat,A)),combb(A,A,nat),hAPP(A,fun(A,A),times_times(A),C)),B))) # label(fact_3999_mult__right_Osummable) # label(axiom).  [clausify(2828)].
100.59/100.49	6112 -real_normed_algebra(A) | hBOOL(hAPP(filter(A),bool,hAPP(A,fun(filter(A),bool),hAPP(fun(A,A),fun(A,fun(filter(A),bool)),tendsto(A,A),hAPP(A,fun(A,A),hAPP(fun(A,fun(A,A)),fun(A,fun(A,A)),combc(A,A,A),times_times(A)),B)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),B)),hAPP(A,filter(A),at(A),C))) # label(fact_4551_mult__left_Ocont) # label(axiom).  [clausify(2834)].
100.59/100.49	6113 -real_normed_algebra(A) | zero_zero(A) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),zero_zero(A)) # label(fact_879_mult__right_Ozero) # label(axiom).  [clausify(2966)].
100.59/100.49	6114 -real_normed_algebra(A) | -hBOOL(hAPP(filter(nat),bool,hAPP(A,fun(filter(nat),bool),hAPP(fun(nat,A),fun(A,fun(filter(nat),bool)),tendsto(nat,A),B),C),sequentially)) | hBOOL(hAPP(filter(nat),bool,hAPP(A,fun(filter(nat),bool),hAPP(fun(nat,A),fun(A,fun(filter(nat),bool)),tendsto(nat,A),hAPP(fun(nat,A),fun(nat,A),hAPP(fun(A,A),fun(fun(nat,A),fun(nat,A)),combb(A,A,nat),hAPP(A,fun(A,A),times_times(A),D)),B)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),C)),sequentially)) # label(fact_4479_mult__right_OLIMSEQ) # label(axiom).  [clausify(3109)].
100.59/100.49	6115 -real_normed_algebra(A) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(A,real,norm_norm(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(A,real,norm_norm(A),B)),hAPP(A,real,norm_norm(A),C))),f556(A)))) # label(fact_1805_mult_Opos__bounded) # label(axiom).  [clausify(3200)].
100.59/100.49	6116 -real_normed_algebra(A) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),f556(A))) # label(fact_1805_mult_Opos__bounded) # label(axiom).  [clausify(3200)].
100.59/100.49	Derived: -topological_space(A) | -hBOOL(hAPP(A,bool,hAPP(fun(A,real),fun(A,bool),isCont(A,real),B),C)) | -hBOOL(hAPP(A,bool,hAPP(fun(A,real),fun(A,bool),isCont(A,real),D),C)) | hBOOL(hAPP(A,bool,hAPP(fun(A,real),fun(A,bool),isCont(A,real),hAPP(fun(A,real),fun(A,real),hAPP(fun(A,fun(real,real)),fun(fun(A,real),fun(A,real)),combs(A,real,real),hAPP(fun(A,real),fun(A,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(A,real),fun(A,fun(real,real))),combb(real,fun(real,real),A),times_times(real)),B)),D)),C)).  [resolve(6062,a,6063,b)].
100.59/100.49	Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),f24(real,A))).  [resolve(6062,a,6064,a)].
100.59/100.49	Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,norm_norm(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,norm_norm(real),B)),f24(real,A)))).  [resolve(6062,a,6065,a)].
100.59/100.49	Derived: hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),hAPP(real,fun(A,real),hAPP(fun(A,fun(real,real)),fun(real,fun(A,real)),combc(A,real,real),hAPP(fun(A,real),fun(A,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(A,real),fun(A,fun(real,real))),combb(real,fun(real,real),A),times_times(real)),B)),C)),D) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),B),D)),C).  [resolve(6062,a,6066,a)].
100.59/100.49	Derived: -hBOOL(hAPP(real,bool,hAPP(fun(nat,real),fun(real,bool),sums(real),A),B)) | hBOOL(hAPP(real,bool,hAPP(fun(nat,real),fun(real,bool),sums(real),hAPP(real,fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(real,fun(nat,real)),combc(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),A)),C)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),C))).  [resolve(6062,a,6067,a)].
100.59/100.50	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,norm_norm(real),A)),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,norm_norm(real),C)),D)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,norm_norm(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),C))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),D))).  [resolve(6062,a,6068,a)].
100.59/100.50	Derived: hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),hAPP(fun(A,real),fun(A,real),hAPP(fun(real,real),fun(fun(A,real),fun(A,real)),combb(real,real,A),hAPP(real,fun(real,real),times_times(real),B)),C)),D) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),C),D)).  [resolve(6062,a,6069,a)].
100.59/100.50	Derived: -hBOOL(hAPP(fun(nat,real),bool,cauchy(real),A)) | hBOOL(hAPP(fun(nat,real),bool,cauchy(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),hAPP(real,fun(real,real),times_times(real),B)),A))).  [resolve(6062,a,6070,a)].
100.59/100.50	Derived: -banach(real) | -hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),norm_norm(real)),A))) | -hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),norm_norm(real)),B))) | hBOOL(hAPP(real,bool,hAPP(fun(nat,real),fun(real,bool),sums(real),hAPP(fun(nat,fun(nat,bool)),fun(nat,real),hAPP(fun(nat,fun(fun(nat,bool),real)),fun(fun(nat,fun(nat,bool)),fun(nat,real)),combs(nat,fun(nat,bool),real),hAPP(fun(nat,fun(nat,real)),fun(nat,fun(fun(nat,bool),real)),hAPP(fun(fun(nat,real),fun(fun(nat,bool),real)),fun(fun(nat,fun(nat,real)),fun(nat,fun(fun(nat,bool),real))),combb(fun(nat,real),fun(fun(nat,bool),real),nat),big_co1399186613setsum(nat,real)),hAPP(fun(nat,fun(nat,real)),fun(nat,fun(nat,real)),hAPP(fun(fun(nat,real),fun(nat,real)),fun(fun(nat,fun(nat,real)),fun(nat,fun(nat,real))),combb(fun(nat,real),fun(nat,real),nat),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),A))),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,real)),hAPP(fun(fun(nat,nat),fun(nat,real)),fun(fun(nat,fun(nat,nat)),fun(nat,fun(nat,real))),combb(fun(nat,nat),fun(nat,real),nat),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),B)),minus_minus(nat))))),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),zero_zero(nat)))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(fun(nat,real),real,suminf(real),A)),hAPP(fun(nat,real),real,suminf(real),B)))).  [resolve(6062,a,6071,b)].
100.59/100.50	Derived: -hBOOL(hAPP(fun(nat,real),bool,summable(real),A)) | hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(real,fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(real,fun(nat,real)),combc(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),A)),B))).  [resolve(6062,a,6072,a)].
100.59/100.50	Derived: hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),B),C)) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),C)).  [resolve(6062,a,6073,a)].
100.59/100.50	Derived: hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),B)) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),C)),B).  [resolve(6062,a,6074,a)].
100.59/100.52	Derived: hBOOL(hAPP(real,bool,hAPP(fun(real,real),fun(real,bool),isCont(real,real),hAPP(real,fun(real,real),hAPP(fun(real,fun(real,real)),fun(real,fun(real,real)),combc(real,real,real),times_times(real)),A)),B)).  [resolve(6062,a,6075,a)].
100.59/100.52	Derived: -hBOOL(hAPP(real,bool,hAPP(fun(nat,real),fun(real,bool),sums(real),A),B)) | hBOOL(hAPP(real,bool,hAPP(fun(nat,real),fun(real,bool),sums(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),hAPP(real,fun(real,real),times_times(real),C)),A)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),B))).  [resolve(6062,a,6077,a)].
100.59/100.52	Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,norm_norm(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,norm_norm(real),B)),f108(real,A)))).  [resolve(6062,a,6078,a)].
100.59/100.52	Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),f108(real,A))).  [resolve(6062,a,6079,a)].
100.59/100.52	Derived: -hBOOL(hAPP(fun(nat,real),bool,summable(real),A)) | hAPP(fun(nat,real),real,suminf(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),hAPP(real,fun(real,real),times_times(real),B)),A)) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),hAPP(fun(nat,real),real,suminf(real),A)).  [resolve(6062,a,6080,a)].
100.59/100.52	Derived: zero_zero(real) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),zero_zero(real)),A).  [resolve(6062,a,6081,a)].
100.59/100.52	Derived: hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),C)) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),B),C)).  [resolve(6062,a,6082,a)].
100.59/100.52	Derived: hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,uminus_uminus(real),A)),B).  [resolve(6062,a,6083,a)].
100.59/100.52	Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,norm_norm(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,norm_norm(real),A)),hAPP(real,real,norm_norm(real),B)))).  [resolve(6062,a,6084,a)].
100.59/100.52	Derived: -banach(real) | -hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),norm_norm(real)),A))) | -hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),norm_norm(real)),B))) | hAPP(fun(nat,real),real,suminf(real),hAPP(fun(nat,fun(nat,bool)),fun(nat,real),hAPP(fun(nat,fun(fun(nat,bool),real)),fun(fun(nat,fun(nat,bool)),fun(nat,real)),combs(nat,fun(nat,bool),real),hAPP(fun(nat,fun(nat,real)),fun(nat,fun(fun(nat,bool),real)),hAPP(fun(fun(nat,real),fun(fun(nat,bool),real)),fun(fun(nat,fun(nat,real)),fun(nat,fun(fun(nat,bool),real))),combb(fun(nat,real),fun(fun(nat,bool),real),nat),big_co1399186613setsum(nat,real)),hAPP(fun(nat,fun(nat,real)),fun(nat,fun(nat,real)),hAPP(fun(fun(nat,real),fun(nat,real)),fun(fun(nat,fun(nat,real)),fun(nat,fun(nat,real))),combb(fun(nat,real),fun(nat,real),nat),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),A))),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,real)),hAPP(fun(fun(nat,nat),fun(nat,real)),fun(fun(nat,fun(nat,nat)),fun(nat,fun(nat,real))),combb(fun(nat,nat),fun(nat,real),nat),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),B)),minus_minus(nat))))),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),zero_zero(nat)))) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(fun(nat,real),real,suminf(real),A)),hAPP(fun(nat,real),real,suminf(real),B)).  [resolve(6062,a,6085,b)].
100.59/100.54	Derived: -metric_space(A) | -hBOOL(hAPP(filter(A),bool,hAPP(real,fun(filter(A),bool),hAPP(fun(A,real),fun(real,fun(filter(A),bool)),tendsto(A,real),B),zero_zero(real)),hAPP(A,filter(A),at(A),C))) | -hBOOL(hAPP(filter(A),bool,hAPP(real,fun(filter(A),bool),hAPP(fun(A,real),fun(real,fun(filter(A),bool)),tendsto(A,real),D),zero_zero(real)),hAPP(A,filter(A),at(A),C))) | hBOOL(hAPP(filter(A),bool,hAPP(real,fun(filter(A),bool),hAPP(fun(A,real),fun(real,fun(filter(A),bool)),tendsto(A,real),hAPP(fun(A,real),fun(A,real),hAPP(fun(A,fun(real,real)),fun(fun(A,real),fun(A,real)),combs(A,real,real),hAPP(fun(A,real),fun(A,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(A,real),fun(A,fun(real,real))),combb(real,fun(real,real),A),times_times(real)),B)),D)),zero_zero(real)),hAPP(A,filter(A),at(A),C))).  [resolve(6062,a,6086,b)].
100.59/100.54	Derived: -power(real) | -hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),A),B),sequentially)) | hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),hAPP(nat,fun(nat,real),hAPP(fun(nat,fun(nat,real)),fun(nat,fun(nat,real)),combc(nat,nat,real),hAPP(fun(nat,real),fun(nat,fun(nat,real)),hAPP(fun(real,fun(nat,real)),fun(fun(nat,real),fun(nat,fun(nat,real))),combb(real,fun(nat,real),nat),power_power(real)),A)),C)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),B),C)),sequentially)).  [resolve(6062,a,6087,a)].
100.59/100.54	Derived: -topological_space(A) | -hBOOL(hAPP(filter(A),bool,hAPP(real,fun(filter(A),bool),hAPP(fun(A,real),fun(real,fun(filter(A),bool)),tendsto(A,real),B),C),hAPP(A,filter(A),at(A),D))) | hBOOL(hAPP(filter(A),bool,hAPP(real,fun(filter(A),bool),hAPP(fun(A,real),fun(real,fun(filter(A),bool)),tendsto(A,real),hAPP(real,fun(A,real),hAPP(fun(A,fun(real,real)),fun(real,fun(A,real)),combc(A,real,real),hAPP(fun(A,real),fun(A,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(A,real),fun(A,fun(real,real))),combb(real,fun(real,real),A),times_times(real)),B)),E)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),E)),hAPP(A,filter(A),at(A),D))).  [resolve(6062,a,6088,a)].
100.59/100.54	Derived: hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),B),C)) = hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),B),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),C)).  [resolve(6062,a,6089,a)].
100.59/100.54	Derived: -power(real) | -topological_space(A) | -hBOOL(hAPP(A,bool,hAPP(fun(A,real),fun(A,bool),isCont(A,real),B),C)) | hBOOL(hAPP(A,bool,hAPP(fun(A,real),fun(A,bool),isCont(A,real),hAPP(nat,fun(A,real),hAPP(fun(A,fun(nat,real)),fun(nat,fun(A,real)),combc(A,nat,real),hAPP(fun(A,real),fun(A,fun(nat,real)),hAPP(fun(real,fun(nat,real)),fun(fun(A,real),fun(A,fun(nat,real))),combb(real,fun(nat,real),A),power_power(real)),B)),D)),C)).  [resolve(6062,a,6091,a)].
100.59/100.54	Derived: -hBOOL(hAPP(filter(A),bool,hAPP(real,fun(filter(A),bool),hAPP(fun(A,real),fun(real,fun(filter(A),bool)),tendsto(A,real),B),C),D)) | -hBOOL(hAPP(filter(A),bool,hAPP(real,fun(filter(A),bool),hAPP(fun(A,real),fun(real,fun(filter(A),bool)),tendsto(A,real),E),F),D)) | hBOOL(hAPP(filter(A),bool,hAPP(real,fun(filter(A),bool),hAPP(fun(A,real),fun(real,fun(filter(A),bool)),tendsto(A,real),hAPP(fun(A,real),fun(A,real),hAPP(fun(A,fun(real,real)),fun(fun(A,real),fun(A,real)),combs(A,real,real),hAPP(fun(A,real),fun(A,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(A,real),fun(A,fun(real,real))),combb(real,fun(real,real),A),times_times(real)),B)),E)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),F)),D)).  [resolve(6062,a,6092,a)].
100.59/100.54	Derived: -hBOOL(hAPP(fun(nat,real),bool,cauchy(real),A)) | hBOOL(hAPP(fun(nat,real),bool,cauchy(real),hAPP(real,fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(real,fun(nat,real)),combc(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),A)),B))).  [resolve(6062,a,6093,a)].
100.59/100.56	Derived: hBOOL(hAPP(filter(real),bool,hAPP(real,fun(filter(real),bool),hAPP(fun(real,real),fun(real,fun(filter(real),bool)),tendsto(real,real),hAPP(real,fun(real,real),times_times(real),A)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),hAPP(real,filter(real),at(real),B))).  [resolve(6062,a,6096,a)].
100.59/100.56	Derived: -topological_space(A) | -hBOOL(hAPP(filter(A),bool,hAPP(real,fun(filter(A),bool),hAPP(fun(A,real),fun(real,fun(filter(A),bool)),tendsto(A,real),B),zero_zero(real)),hAPP(A,filter(A),at(A),C))) | hBOOL(hAPP(filter(A),bool,hAPP(real,fun(filter(A),bool),hAPP(fun(A,real),fun(real,fun(filter(A),bool)),tendsto(A,real),hAPP(real,fun(A,real),hAPP(fun(A,fun(real,real)),fun(real,fun(A,real)),combc(A,real,real),hAPP(fun(A,real),fun(A,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(A,real),fun(A,fun(real,real))),combb(real,fun(real,real),A),times_times(real)),B)),D)),zero_zero(real)),hAPP(A,filter(A),at(A),C))).  [resolve(6062,a,6097,b)].
100.59/100.56	Derived: -hBOOL(hAPP(filter(A),bool,hAPP(real,fun(filter(A),bool),hAPP(fun(A,real),fun(real,fun(filter(A),bool)),tendsto(A,real),B),C),D)) | hBOOL(hAPP(filter(A),bool,hAPP(real,fun(filter(A),bool),hAPP(fun(A,real),fun(real,fun(filter(A),bool)),tendsto(A,real),hAPP(fun(A,real),fun(A,real),hAPP(fun(real,real),fun(fun(A,real),fun(A,real)),combb(real,real,A),hAPP(real,fun(real,real),times_times(real),E)),B)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),E),C)),D)).  [resolve(6062,a,6098,a)].
100.59/100.56	Derived: hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),D)) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),C)),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),B),D))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),C)),D))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),B),D))).  [resolve(6062,a,6099,a)].
100.59/100.56	Derived: hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),hAPP(real,real,uminus_uminus(real),B)).  [resolve(6062,a,6100,a)].
100.59/100.56	Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,norm_norm(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,norm_norm(real),A)),hAPP(real,real,norm_norm(real),B))),f365(real)))).  [resolve(6062,a,6101,a)].
100.59/100.56	Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),f365(real))).  [resolve(6062,a,6102,a)].
100.59/100.56	Derived: -hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),A),B),sequentially)) | hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),hAPP(real,fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(real,fun(nat,real)),combc(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),A)),C)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),C)),sequentially)).  [resolve(6062,a,6103,a)].
100.59/100.56	Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,norm_norm(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,norm_norm(real),A)),hAPP(real,real,norm_norm(real),B))),f408(real)))).  [resolve(6062,a,6105,a)].
100.72/100.68	Derived: zero_zero(real) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),zero_zero(real)).  [resolve(6062,a,6107,a)].
100.72/100.68	Derived: -comm_ring_1(real) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f440(A,real,B,C,D)),D)) | hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),hAPP(fun(A,bool),fun(nat,real),hAPP(fun(nat,fun(fun(A,bool),real)),fun(fun(A,bool),fun(nat,real)),combc(nat,fun(A,bool),real),hAPP(fun(nat,fun(A,real)),fun(nat,fun(fun(A,bool),real)),hAPP(fun(fun(A,real),fun(fun(A,bool),real)),fun(fun(nat,fun(A,real)),fun(nat,fun(fun(A,bool),real))),combb(fun(A,real),fun(fun(A,bool),real),nat),big_co302546470etprod(A,real)),hAPP(fun(A,fun(nat,real)),fun(nat,fun(A,real)),combc(A,nat,real),B))),D)),hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co302546470etprod(A,real),C),D)),sequentially)).  [resolve(6062,a,6108,a)].
100.72/100.68	Derived: -comm_ring_1(real) | -hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),hAPP(A,fun(nat,real),B,f440(A,real,B,C,D))),hAPP(A,real,C,f440(A,real,B,C,D))),sequentially)) | hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),hAPP(fun(A,bool),fun(nat,real),hAPP(fun(nat,fun(fun(A,bool),real)),fun(fun(A,bool),fun(nat,real)),combc(nat,fun(A,bool),real),hAPP(fun(nat,fun(A,real)),fun(nat,fun(fun(A,bool),real)),hAPP(fun(fun(A,real),fun(fun(A,bool),real)),fun(fun(nat,fun(A,real)),fun(nat,fun(fun(A,bool),real))),combb(fun(A,real),fun(fun(A,bool),real),nat),big_co302546470etprod(A,real)),hAPP(fun(A,fun(nat,real)),fun(nat,fun(A,real)),combc(A,nat,real),B))),D)),hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co302546470etprod(A,real),C),D)),sequentially)).  [resolve(6062,a,6109,a)].
100.72/100.68	Derived: -hBOOL(hAPP(fun(nat,real),bool,summable(real),A)) | hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),hAPP(real,fun(real,real),times_times(real),B)),A))).  [resolve(6062,a,6111,a)].
100.72/100.68	Derived: hBOOL(hAPP(filter(real),bool,hAPP(real,fun(filter(real),bool),hAPP(fun(real,real),fun(real,fun(filter(real),bool)),tendsto(real,real),hAPP(real,fun(real,real),hAPP(fun(real,fun(real,real)),fun(real,fun(real,real)),combc(real,real,real),times_times(real)),A)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),A)),hAPP(real,filter(real),at(real),B))).  [resolve(6062,a,6112,a)].
100.72/100.68	Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,norm_norm(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,norm_norm(real),A)),hAPP(real,real,norm_norm(real),B))),f556(real)))).  [resolve(6062,a,6115,a)].
100.72/100.68	Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),f556(real))).  [resolve(6062,a,6116,a)].
100.72/100.68	6117 -real_normed_algebra(A) | -hBOOL(hAPP(A,bool,hAPP(fun(nat,A),fun(A,bool),sums(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(fun(nat,A),fun(A,bool),sums(A),hAPP(fun(nat,A),fun(nat,A),hAPP(fun(A,A),fun(fun(nat,A),fun(nat,A)),combb(A,A,nat),hAPP(A,fun(A,A),times_times(A),D)),B)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),C))) # label(fact_4079_sums__mult) # label(axiom).  [clausify(3297)].
100.72/100.68	6118 -topological_space(A) | -real_normed_algebra(B) | -power(B) | -hBOOL(hAPP(filter(A),bool,hAPP(B,fun(filter(A),bool),hAPP(fun(A,B),fun(B,fun(filter(A),bool)),tendsto(A,B),C),D),hAPP(A,filter(A),at(A),E))) | hBOOL(hAPP(filter(A),bool,hAPP(B,fun(filter(A),bool),hAPP(fun(A,B),fun(B,fun(filter(A),bool)),tendsto(A,B),hAPP(nat,fun(A,B),hAPP(fun(A,fun(nat,B)),fun(nat,fun(A,B)),combc(A,nat,B),hAPP(fun(A,B),fun(A,fun(nat,B)),hAPP(fun(B,fun(nat,B)),fun(fun(A,B),fun(A,fun(nat,B))),combb(B,fun(nat,B),A),power_power(B)),C)),F)),hAPP(nat,B,hAPP(B,fun(nat,B),power_power(B),D),F)),hAPP(A,filter(A),at(A),E))) # label(fact_4556_LIM__power) # label(axiom).  [clausify(3358)].
100.94/100.86	Derived: -topological_space(A) | -power(real) | -hBOOL(hAPP(filter(A),bool,hAPP(real,fun(filter(A),bool),hAPP(fun(A,real),fun(real,fun(filter(A),bool)),tendsto(A,real),B),C),hAPP(A,filter(A),at(A),D))) | hBOOL(hAPP(filter(A),bool,hAPP(real,fun(filter(A),bool),hAPP(fun(A,real),fun(real,fun(filter(A),bool)),tendsto(A,real),hAPP(nat,fun(A,real),hAPP(fun(A,fun(nat,real)),fun(nat,fun(A,real)),combc(A,nat,real),hAPP(fun(A,real),fun(A,fun(nat,real)),hAPP(fun(real,fun(nat,real)),fun(fun(A,real),fun(A,fun(nat,real))),combb(real,fun(nat,real),A),power_power(real)),B)),E)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),C),E)),hAPP(A,filter(A),at(A),D))).  [resolve(6118,b,6062,a)].
100.94/100.86	6119 -real_normed_algebra(A) | hAPP(A,A,uminus_uminus(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),hAPP(A,A,uminus_uminus(A),B)),C) # label(fact_2036_mult_Ominus__left) # label(axiom).  [clausify(3417)].
100.94/100.86	6120 -topological_space(A) | -real_normed_algebra(B) | -hBOOL(hAPP(filter(A),bool,hAPP(B,fun(filter(A),bool),hAPP(fun(A,B),fun(B,fun(filter(A),bool)),tendsto(A,B),C),zero_zero(B)),hAPP(A,filter(A),at(A),D))) | hBOOL(hAPP(filter(A),bool,hAPP(B,fun(filter(A),bool),hAPP(fun(A,B),fun(B,fun(filter(A),bool)),tendsto(A,B),hAPP(fun(A,B),fun(A,B),hAPP(fun(B,B),fun(fun(A,B),fun(A,B)),combb(B,B,A),hAPP(B,fun(B,B),times_times(B),E)),C)),zero_zero(B)),hAPP(A,filter(A),at(A),D))) # label(fact_4573_LIM__mult__right__zero) # label(axiom).  [clausify(3452)].
100.94/100.86	Derived: -topological_space(A) | -hBOOL(hAPP(filter(A),bool,hAPP(real,fun(filter(A),bool),hAPP(fun(A,real),fun(real,fun(filter(A),bool)),tendsto(A,real),B),zero_zero(real)),hAPP(A,filter(A),at(A),C))) | hBOOL(hAPP(filter(A),bool,hAPP(real,fun(filter(A),bool),hAPP(fun(A,real),fun(real,fun(filter(A),bool)),tendsto(A,real),hAPP(fun(A,real),fun(A,real),hAPP(fun(real,real),fun(fun(A,real),fun(A,real)),combb(real,real,A),hAPP(real,fun(real,real),times_times(real),D)),B)),zero_zero(real)),hAPP(A,filter(A),at(A),C))).  [resolve(6120,b,6062,a)].
100.94/100.86	6121 -real_normed_algebra(A) | -topological_space(B) | -hBOOL(hAPP(filter(B),bool,hAPP(A,fun(filter(B),bool),hAPP(fun(B,A),fun(A,fun(filter(B),bool)),tendsto(B,A),C),D),hAPP(B,filter(B),at(B),E))) | -hBOOL(hAPP(filter(B),bool,hAPP(A,fun(filter(B),bool),hAPP(fun(B,A),fun(A,fun(filter(B),bool)),tendsto(B,A),F),V6),hAPP(B,filter(B),at(B),E))) | hBOOL(hAPP(filter(B),bool,hAPP(A,fun(filter(B),bool),hAPP(fun(B,A),fun(A,fun(filter(B),bool)),tendsto(B,A),hAPP(fun(B,A),fun(B,A),hAPP(fun(B,fun(A,A)),fun(fun(B,A),fun(B,A)),combs(B,A,A),hAPP(fun(B,A),fun(B,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(B,A),fun(B,fun(A,A))),combb(A,fun(A,A),B),times_times(A)),C)),F)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),V6)),hAPP(B,filter(B),at(B),E))) # label(fact_4548_LIM__mult) # label(axiom).  [clausify(3592)].
100.94/100.86	6122 -real_normed_algebra(A) | -hBOOL(hAPP(fun(nat,A),bool,summable(A),B)) | hAPP(fun(nat,A),A,suminf(A),hAPP(A,fun(nat,A),hAPP(fun(nat,fun(A,A)),fun(A,fun(nat,A)),combc(nat,A,A),hAPP(fun(nat,A),fun(nat,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(nat,A),fun(nat,fun(A,A))),combb(A,fun(A,A),nat),times_times(A)),B)),C)) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(fun(nat,A),A,suminf(A),B)),C) # label(fact_3987_mult__left_Osuminf) # label(axiom).  [clausify(3605)].
100.94/100.86	Derived: -hBOOL(hAPP(fun(nat,real),bool,summable(real),A)) | hAPP(fun(nat,real),real,suminf(real),hAPP(real,fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(real,fun(nat,real)),combc(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),A)),B)) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(fun(nat,real),real,suminf(real),A)),B).  [resolve(6122,a,6062,a)].
101.39/101.33	6123 -real_normed_algebra(A) | -hBOOL(hAPP(fun(nat,A),bool,summable(A),B)) | hAPP(fun(nat,A),A,suminf(A),hAPP(A,fun(nat,A),hAPP(fun(nat,fun(A,A)),fun(A,fun(nat,A)),combc(nat,A,A),hAPP(fun(nat,A),fun(nat,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(nat,A),fun(nat,fun(A,A))),combb(A,fun(A,A),nat),times_times(A)),B)),C)) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(fun(nat,A),A,suminf(A),B)),C) # label(fact_3989_suminf__mult2) # label(axiom).  [clausify(3607)].
101.39/101.33	6124 -real_normed_algebra(A) | -topological_space(B) | -hBOOL(hAPP(filter(B),bool,hAPP(A,fun(filter(B),bool),hAPP(fun(B,A),fun(A,fun(filter(B),bool)),tendsto(B,A),C),D),hAPP(B,filter(B),at(B),E))) | hBOOL(hAPP(filter(B),bool,hAPP(A,fun(filter(B),bool),hAPP(fun(B,A),fun(A,fun(filter(B),bool)),tendsto(B,A),hAPP(fun(B,A),fun(B,A),hAPP(fun(A,A),fun(fun(B,A),fun(B,A)),combb(A,A,B),hAPP(A,fun(A,A),times_times(A),F)),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),F),D)),hAPP(B,filter(B),at(B),E))) # label(fact_4550_mult__right_OLIM) # label(axiom).  [clausify(3628)].
101.39/101.33	6125 -real_normed_algebra(A) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(A,real,norm_norm(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(A,real,norm_norm(A),B)),f650(A,C)))) # label(fact_1812_mult__left_Obounded) # label(axiom).  [clausify(3684)].
101.39/101.33	Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,norm_norm(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,norm_norm(real),A)),f650(real,B)))).  [resolve(6125,a,6062,a)].
101.39/101.33	6126 -real_normed_algebra(A) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(A,real,norm_norm(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(A,real,norm_norm(A),B)),f676(A,C)))) # label(fact_1809_mult__left_Ononneg__bounded) # label(axiom).  [clausify(3824)].
101.39/101.33	Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,norm_norm(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,norm_norm(real),A)),f676(real,B)))).  [resolve(6126,a,6062,a)].
101.39/101.33	6127 -real_normed_algebra(A) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),f676(A,B))) # label(fact_1809_mult__left_Ononneg__bounded) # label(axiom).  [clausify(3824)].
101.39/101.33	Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),f676(real,A))).  [resolve(6127,a,6062,a)].
101.39/101.33	6128 -real_normed_algebra(A) | -hBOOL(hAPP(fun(nat,A),bool,summable(A),B)) | hAPP(fun(nat,A),A,suminf(A),hAPP(fun(nat,A),fun(nat,A),hAPP(fun(A,A),fun(fun(nat,A),fun(nat,A)),combb(A,A,nat),hAPP(A,fun(A,A),times_times(A),C)),B)) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),hAPP(fun(nat,A),A,suminf(A),B)) # label(fact_3988_mult__right_Osuminf) # label(axiom).  [clausify(3880)].
101.39/101.33	6129 -real_normed_algebra(A) | -topological_space(B) | -hBOOL(hAPP(filter(B),bool,hAPP(A,fun(filter(B),bool),hAPP(fun(B,A),fun(A,fun(filter(B),bool)),tendsto(B,A),C),zero_zero(A)),hAPP(B,filter(B),at(B),D))) | hBOOL(hAPP(filter(B),bool,hAPP(A,fun(filter(B),bool),hAPP(fun(B,A),fun(A,fun(filter(B),bool)),tendsto(B,A),hAPP(A,fun(B,A),hAPP(fun(B,fun(A,A)),fun(A,fun(B,A)),combc(B,A,A),hAPP(fun(B,A),fun(B,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(B,A),fun(B,fun(A,A))),combb(A,fun(A,A),B),times_times(A)),C)),E)),zero_zero(A)),hAPP(B,filter(B),at(B),D))) # label(fact_4576_mult__left_OLIM__zero) # label(axiom).  [clausify(3988)].
101.39/101.33	6130 -real_normed_algebra(A) | -hBOOL(hAPP(A,bool,hAPP(fun(nat,A),fun(A,bool),sums(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(fun(nat,A),fun(A,bool),sums(A),hAPP(A,fun(nat,A),hAPP(fun(nat,fun(A,A)),fun(A,fun(nat,A)),combc(nat,A,A),hAPP(fun(nat,A),fun(nat,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(nat,A),fun(nat,fun(A,A))),combb(A,fun(A,A),nat),times_times(A)),B)),D)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),D))) # label(fact_4082_mult__left_Osums) # label(axiom).  [clausify(4005)].
101.56/101.47	6131 -real_normed_algebra(A) | hAPP(A,A,uminus_uminus(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),hAPP(A,A,uminus_uminus(A),C)) # label(fact_2037_mult__right_Ominus) # label(axiom).  [clausify(4026)].
101.56/101.47	6132 -real_normed_algebra(A) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(A,real,norm_norm(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(A,real,norm_norm(A),C)),f735(A,B)))) # label(fact_1813_mult__right_Obounded) # label(axiom).  [clausify(4112)].
101.56/101.47	Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,norm_norm(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,norm_norm(real),B)),f735(real,A)))).  [resolve(6132,a,6062,a)].
101.56/101.47	6133 real_normed_algebra(complex) # label(arity_Complex_Ocomplex___RealVector_Oreal__normed__algebra) # label(axiom).  [assumption].
101.56/101.47	Derived: -topological_space(A) | -hBOOL(hAPP(A,bool,hAPP(fun(A,complex),fun(A,bool),isCont(A,complex),B),C)) | -hBOOL(hAPP(A,bool,hAPP(fun(A,complex),fun(A,bool),isCont(A,complex),D),C)) | hBOOL(hAPP(A,bool,hAPP(fun(A,complex),fun(A,bool),isCont(A,complex),hAPP(fun(A,complex),fun(A,complex),hAPP(fun(A,fun(complex,complex)),fun(fun(A,complex),fun(A,complex)),combs(A,complex,complex),hAPP(fun(A,complex),fun(A,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(A,complex),fun(A,fun(complex,complex))),combb(complex,fun(complex,complex),A),times_times(complex)),B)),D)),C)).  [resolve(6133,a,6063,b)].
101.56/101.47	Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),f24(complex,A))).  [resolve(6133,a,6064,a)].
101.56/101.47	Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),B))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(complex,real,norm_norm(complex),B)),f24(complex,A)))).  [resolve(6133,a,6065,a)].
101.56/101.47	Derived: hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),hAPP(complex,fun(A,complex),hAPP(fun(A,fun(complex,complex)),fun(complex,fun(A,complex)),combc(A,complex,complex),hAPP(fun(A,complex),fun(A,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(A,complex),fun(A,fun(complex,complex))),combb(complex,fun(complex,complex),A),times_times(complex)),B)),C)),D) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),B),D)),C).  [resolve(6133,a,6066,a)].
101.56/101.47	Derived: -hBOOL(hAPP(complex,bool,hAPP(fun(nat,complex),fun(complex,bool),sums(complex),A),B)) | hBOOL(hAPP(complex,bool,hAPP(fun(nat,complex),fun(complex,bool),sums(complex),hAPP(complex,fun(nat,complex),hAPP(fun(nat,fun(complex,complex)),fun(complex,fun(nat,complex)),combc(nat,complex,complex),hAPP(fun(nat,complex),fun(nat,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(nat,complex),fun(nat,fun(complex,complex))),combb(complex,fun(complex,complex),nat),times_times(complex)),A)),C)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),B),C))).  [resolve(6133,a,6067,a)].
101.56/101.47	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(complex,real,norm_norm(complex),A)),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(complex,real,norm_norm(complex),C)),D)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),C))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),D))).  [resolve(6133,a,6068,a)].
101.56/101.47	Derived: hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),hAPP(fun(A,complex),fun(A,complex),hAPP(fun(complex,complex),fun(fun(A,complex),fun(A,complex)),combb(complex,complex,A),hAPP(complex,fun(complex,complex),times_times(complex),B)),C)),D) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),B),hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),C),D)).  [resolve(6133,a,6069,a)].
101.56/101.47	Derived: -hBOOL(hAPP(fun(nat,complex),bool,cauchy(complex),A)) | hBOOL(hAPP(fun(nat,complex),bool,cauchy(complex),hAPP(fun(nat,complex),fun(nat,complex),hAPP(fun(complex,complex),fun(fun(nat,complex),fun(nat,complex)),combb(complex,complex,nat),hAPP(complex,fun(complex,complex),times_times(complex),B)),A))).  [resolve(6133,a,6070,a)].
101.56/101.47	Derived: -banach(complex) | -hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,complex),fun(nat,real),hAPP(fun(complex,real),fun(fun(nat,complex),fun(nat,real)),combb(complex,real,nat),norm_norm(complex)),A))) | -hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,complex),fun(nat,real),hAPP(fun(complex,real),fun(fun(nat,complex),fun(nat,real)),combb(complex,real,nat),norm_norm(complex)),B))) | hBOOL(hAPP(complex,bool,hAPP(fun(nat,complex),fun(complex,bool),sums(complex),hAPP(fun(nat,fun(nat,bool)),fun(nat,complex),hAPP(fun(nat,fun(fun(nat,bool),complex)),fun(fun(nat,fun(nat,bool)),fun(nat,complex)),combs(nat,fun(nat,bool),complex),hAPP(fun(nat,fun(nat,complex)),fun(nat,fun(fun(nat,bool),complex)),hAPP(fun(fun(nat,complex),fun(fun(nat,bool),complex)),fun(fun(nat,fun(nat,complex)),fun(nat,fun(fun(nat,bool),complex))),combb(fun(nat,complex),fun(fun(nat,bool),complex),nat),big_co1399186613setsum(nat,complex)),hAPP(fun(nat,fun(nat,complex)),fun(nat,fun(nat,complex)),hAPP(fun(fun(nat,complex),fun(nat,complex)),fun(fun(nat,fun(nat,complex)),fun(nat,fun(nat,complex))),combb(fun(nat,complex),fun(nat,complex),nat),hAPP(fun(nat,fun(complex,complex)),fun(fun(nat,complex),fun(nat,complex)),combs(nat,complex,complex),hAPP(fun(nat,complex),fun(nat,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(nat,complex),fun(nat,fun(complex,complex))),combb(complex,fun(complex,complex),nat),times_times(complex)),A))),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,complex)),hAPP(fun(fun(nat,nat),fun(nat,complex)),fun(fun(nat,fun(nat,nat)),fun(nat,fun(nat,complex))),combb(fun(nat,nat),fun(nat,complex),nat),hAPP(fun(nat,complex),fun(fun(nat,nat),fun(nat,complex)),combb(nat,complex,nat),B)),minus_minus(nat))))),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),zero_zero(nat)))),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(fun(nat,complex),complex,suminf(complex),A)),hAPP(fun(nat,complex),complex,suminf(complex),B)))).  [resolve(6133,a,6071,b)].
101.56/101.47	Derived: -hBOOL(hAPP(fun(nat,complex),bool,summable(complex),A)) | hBOOL(hAPP(fun(nat,complex),bool,summable(complex),hAPP(complex,fun(nat,complex),hAPP(fun(nat,fun(complex,complex)),fun(complex,fun(nat,complex)),combc(nat,complex,complex),hAPP(fun(nat,complex),fun(nat,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(nat,complex),fun(nat,fun(complex,complex))),combb(complex,fun(complex,complex),nat),times_times(complex)),A)),B))).  [resolve(6133,a,6072,a)].
101.56/101.47	Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),B),C)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),B)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),C)).  [resolve(6133,a,6073,a)].
101.56/101.47	Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),B)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),C),B)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),A),C)),B).  [resolve(6133,a,6074,a)].
101.58/101.49	Derived: hBOOL(hAPP(complex,bool,hAPP(fun(complex,complex),fun(complex,bool),isCont(complex,complex),hAPP(complex,fun(complex,complex),hAPP(fun(complex,fun(complex,complex)),fun(complex,fun(complex,complex)),combc(complex,complex,complex),times_times(complex)),A)),B)).  [resolve(6133,a,6075,a)].
101.58/101.49	Derived: -hBOOL(hAPP(complex,bool,hAPP(fun(nat,complex),fun(complex,bool),sums(complex),A),B)) | hBOOL(hAPP(complex,bool,hAPP(fun(nat,complex),fun(complex,bool),sums(complex),hAPP(fun(nat,complex),fun(nat,complex),hAPP(fun(complex,complex),fun(fun(nat,complex),fun(nat,complex)),combb(complex,complex,nat),hAPP(complex,fun(complex,complex),times_times(complex),C)),A)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),C),B))).  [resolve(6133,a,6077,a)].
101.58/101.49	Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),B))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(complex,real,norm_norm(complex),B)),f108(complex,A)))).  [resolve(6133,a,6078,a)].
101.58/101.49	Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),f108(complex,A))).  [resolve(6133,a,6079,a)].
101.58/101.49	Derived: -hBOOL(hAPP(fun(nat,complex),bool,summable(complex),A)) | hAPP(fun(nat,complex),complex,suminf(complex),hAPP(fun(nat,complex),fun(nat,complex),hAPP(fun(complex,complex),fun(fun(nat,complex),fun(nat,complex)),combb(complex,complex,nat),hAPP(complex,fun(complex,complex),times_times(complex),B)),A)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),B),hAPP(fun(nat,complex),complex,suminf(complex),A)).  [resolve(6133,a,6080,a)].
101.58/101.49	Derived: zero_zero(complex) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),zero_zero(complex)),A).  [resolve(6133,a,6081,a)].
101.58/101.49	Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),B)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),C)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),B),C)).  [resolve(6133,a,6082,a)].
101.58/101.49	Derived: hAPP(complex,complex,uminus_uminus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),B)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,uminus_uminus(complex),A)),B).  [resolve(6133,a,6083,a)].
101.58/101.49	Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),B))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(complex,real,norm_norm(complex),A)),hAPP(complex,real,norm_norm(complex),B)))).  [resolve(6133,a,6084,a)].
101.58/101.49	Derived: -banach(complex) | -hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,complex),fun(nat,real),hAPP(fun(complex,real),fun(fun(nat,complex),fun(nat,real)),combb(complex,real,nat),norm_norm(complex)),A))) | -hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,complex),fun(nat,real),hAPP(fun(complex,real),fun(fun(nat,complex),fun(nat,real)),combb(complex,real,nat),norm_norm(complex)),B))) | hAPP(fun(nat,complex),complex,suminf(complex),hAPP(fun(nat,fun(nat,bool)),fun(nat,complex),hAPP(fun(nat,fun(fun(nat,bool),complex)),fun(fun(nat,fun(nat,bool)),fun(nat,complex)),combs(nat,fun(nat,bool),complex),hAPP(fun(nat,fun(nat,complex)),fun(nat,fun(fun(nat,bool),complex)),hAPP(fun(fun(nat,complex),fun(fun(nat,bool),complex)),fun(fun(nat,fun(nat,complex)),fun(nat,fun(fun(nat,bool),complex))),combb(fun(nat,complex),fun(fun(nat,bool),complex),nat),big_co1399186613setsum(nat,complex)),hAPP(fun(nat,fun(nat,complex)),fun(nat,fun(nat,complex)),hAPP(fun(fun(nat,complex),fun(nat,complex)),fun(fun(nat,fun(nat,complex)),fun(nat,fun(nat,complex))),combb(fun(nat,complex),fun(nat,complex),nat),hAPP(fun(nat,fun(complex,complex)),fun(fun(nat,complex),fun(nat,complex)),combs(nat,complex,complex),hAPP(fun(nat,complex),fun(nat,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(nat,complex),fun(nat,fun(complex,complex))),combb(complex,fun(complex,complex),nat),times_times(complex)),A))),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,complex)),hAPP(fun(fun(nat,nat),fun(nat,complex)),fun(fun(nat,fun(nat,nat)),fun(nat,fun(nat,complex))),combb(fun(nat,nat),fun(nat,complex),nat),hAPP(fun(nat,complex),fun(fun(nat,nat),fun(nat,complex)),combb(nat,complex,nat),B)),minus_minus(nat))))),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),zero_zero(nat)))) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(fun(nat,complex),complex,suminf(complex),A)),hAPP(fun(nat,complex),complex,suminf(complex),B)).  [resolve(6133,a,6085,b)].
101.58/101.49	Derived: -metric_space(A) | -hBOOL(hAPP(filter(A),bool,hAPP(complex,fun(filter(A),bool),hAPP(fun(A,complex),fun(complex,fun(filter(A),bool)),tendsto(A,complex),B),zero_zero(complex)),hAPP(A,filter(A),at(A),C))) | -hBOOL(hAPP(filter(A),bool,hAPP(complex,fun(filter(A),bool),hAPP(fun(A,complex),fun(complex,fun(filter(A),bool)),tendsto(A,complex),D),zero_zero(complex)),hAPP(A,filter(A),at(A),C))) | hBOOL(hAPP(filter(A),bool,hAPP(complex,fun(filter(A),bool),hAPP(fun(A,complex),fun(complex,fun(filter(A),bool)),tendsto(A,complex),hAPP(fun(A,complex),fun(A,complex),hAPP(fun(A,fun(complex,complex)),fun(fun(A,complex),fun(A,complex)),combs(A,complex,complex),hAPP(fun(A,complex),fun(A,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(A,complex),fun(A,fun(complex,complex))),combb(complex,fun(complex,complex),A),times_times(complex)),B)),D)),zero_zero(complex)),hAPP(A,filter(A),at(A),C))).  [resolve(6133,a,6086,b)].
101.58/101.49	Derived: -power(complex) | -hBOOL(hAPP(filter(nat),bool,hAPP(complex,fun(filter(nat),bool),hAPP(fun(nat,complex),fun(complex,fun(filter(nat),bool)),tendsto(nat,complex),A),B),sequentially)) | hBOOL(hAPP(filter(nat),bool,hAPP(complex,fun(filter(nat),bool),hAPP(fun(nat,complex),fun(complex,fun(filter(nat),bool)),tendsto(nat,complex),hAPP(nat,fun(nat,complex),hAPP(fun(nat,fun(nat,complex)),fun(nat,fun(nat,complex)),combc(nat,nat,complex),hAPP(fun(nat,complex),fun(nat,fun(nat,complex)),hAPP(fun(complex,fun(nat,complex)),fun(fun(nat,complex),fun(nat,fun(nat,complex))),combb(complex,fun(nat,complex),nat),power_power(complex)),A)),C)),hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),B),C)),sequentially)).  [resolve(6133,a,6087,a)].
101.58/101.49	Derived: -topological_space(A) | -hBOOL(hAPP(filter(A),bool,hAPP(complex,fun(filter(A),bool),hAPP(fun(A,complex),fun(complex,fun(filter(A),bool)),tendsto(A,complex),B),C),hAPP(A,filter(A),at(A),D))) | hBOOL(hAPP(filter(A),bool,hAPP(complex,fun(filter(A),bool),hAPP(fun(A,complex),fun(complex,fun(filter(A),bool)),tendsto(A,complex),hAPP(complex,fun(A,complex),hAPP(fun(A,fun(complex,complex)),fun(complex,fun(A,complex)),combc(A,complex,complex),hAPP(fun(A,complex),fun(A,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(A,complex),fun(A,fun(complex,complex))),combb(complex,fun(complex,complex),A),times_times(complex)),B)),E)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),C),E)),hAPP(A,filter(A),at(A),D))).  [resolve(6133,a,6088,a)].
101.58/101.49	Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),B),C)) = hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),B),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),C)).  [resolve(6133,a,6089,a)].
101.58/101.49	Derived: -power(complex) | -topological_space(A) | -hBOOL(hAPP(A,bool,hAPP(fun(A,complex),fun(A,bool),isCont(A,complex),B),C)) | hBOOL(hAPP(A,bool,hAPP(fun(A,complex),fun(A,bool),isCont(A,complex),hAPP(nat,fun(A,complex),hAPP(fun(A,fun(nat,complex)),fun(nat,fun(A,complex)),combc(A,nat,complex),hAPP(fun(A,complex),fun(A,fun(nat,complex)),hAPP(fun(complex,fun(nat,complex)),fun(fun(A,complex),fun(A,fun(nat,complex))),combb(complex,fun(nat,complex),A),power_power(complex)),B)),D)),C)).  [resolve(6133,a,6091,a)].
101.58/101.50	Derived: -hBOOL(hAPP(filter(A),bool,hAPP(complex,fun(filter(A),bool),hAPP(fun(A,complex),fun(complex,fun(filter(A),bool)),tendsto(A,complex),B),C),D)) | -hBOOL(hAPP(filter(A),bool,hAPP(complex,fun(filter(A),bool),hAPP(fun(A,complex),fun(complex,fun(filter(A),bool)),tendsto(A,complex),E),F),D)) | hBOOL(hAPP(filter(A),bool,hAPP(complex,fun(filter(A),bool),hAPP(fun(A,complex),fun(complex,fun(filter(A),bool)),tendsto(A,complex),hAPP(fun(A,complex),fun(A,complex),hAPP(fun(A,fun(complex,complex)),fun(fun(A,complex),fun(A,complex)),combs(A,complex,complex),hAPP(fun(A,complex),fun(A,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(A,complex),fun(A,fun(complex,complex))),combb(complex,fun(complex,complex),A),times_times(complex)),B)),E)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),C),F)),D)).  [resolve(6133,a,6092,a)].
101.58/101.50	Derived: -hBOOL(hAPP(fun(nat,complex),bool,cauchy(complex),A)) | hBOOL(hAPP(fun(nat,complex),bool,cauchy(complex),hAPP(complex,fun(nat,complex),hAPP(fun(nat,fun(complex,complex)),fun(complex,fun(nat,complex)),combc(nat,complex,complex),hAPP(fun(nat,complex),fun(nat,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(nat,complex),fun(nat,fun(complex,complex))),combb(complex,fun(complex,complex),nat),times_times(complex)),A)),B))).  [resolve(6133,a,6093,a)].
101.58/101.50	Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),A),B)),C) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),C)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),B),C)).  [resolve(6133,a,6095,a)].
101.58/101.50	Derived: hBOOL(hAPP(filter(complex),bool,hAPP(complex,fun(filter(complex),bool),hAPP(fun(complex,complex),fun(complex,fun(filter(complex),bool)),tendsto(complex,complex),hAPP(complex,fun(complex,complex),times_times(complex),A)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),B)),hAPP(complex,filter(complex),at(complex),B))).  [resolve(6133,a,6096,a)].
101.58/101.50	Derived: -topological_space(A) | -hBOOL(hAPP(filter(A),bool,hAPP(complex,fun(filter(A),bool),hAPP(fun(A,complex),fun(complex,fun(filter(A),bool)),tendsto(A,complex),B),zero_zero(complex)),hAPP(A,filter(A),at(A),C))) | hBOOL(hAPP(filter(A),bool,hAPP(complex,fun(filter(A),bool),hAPP(fun(A,complex),fun(complex,fun(filter(A),bool)),tendsto(A,complex),hAPP(complex,fun(A,complex),hAPP(fun(A,fun(complex,complex)),fun(complex,fun(A,complex)),combc(A,complex,complex),hAPP(fun(A,complex),fun(A,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(A,complex),fun(A,fun(complex,complex))),combb(complex,fun(complex,complex),A),times_times(complex)),B)),D)),zero_zero(complex)),hAPP(A,filter(A),at(A),C))).  [resolve(6133,a,6097,b)].
101.58/101.50	Derived: -hBOOL(hAPP(filter(A),bool,hAPP(complex,fun(filter(A),bool),hAPP(fun(A,complex),fun(complex,fun(filter(A),bool)),tendsto(A,complex),B),C),D)) | hBOOL(hAPP(filter(A),bool,hAPP(complex,fun(filter(A),bool),hAPP(fun(A,complex),fun(complex,fun(filter(A),bool)),tendsto(A,complex),hAPP(fun(A,complex),fun(A,complex),hAPP(fun(complex,complex),fun(fun(A,complex),fun(A,complex)),combb(complex,complex,A),hAPP(complex,fun(complex,complex),times_times(complex),E)),B)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),E),C)),D)).  [resolve(6133,a,6098,a)].
101.58/101.50	Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),B)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),C),D)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),A),C)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),B),D))),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),A),C)),D))),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),C),hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),B),D))).  [resolve(6133,a,6099,a)].
101.58/101.51	Derived: hAPP(complex,complex,uminus_uminus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),B)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),hAPP(complex,complex,uminus_uminus(complex),B)).  [resolve(6133,a,6100,a)].
101.58/101.51	Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),B))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(complex,real,norm_norm(complex),A)),hAPP(complex,real,norm_norm(complex),B))),f365(complex)))).  [resolve(6133,a,6101,a)].
101.58/101.51	Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),f365(complex))).  [resolve(6133,a,6102,a)].
101.58/101.51	Derived: -hBOOL(hAPP(filter(nat),bool,hAPP(complex,fun(filter(nat),bool),hAPP(fun(nat,complex),fun(complex,fun(filter(nat),bool)),tendsto(nat,complex),A),B),sequentially)) | hBOOL(hAPP(filter(nat),bool,hAPP(complex,fun(filter(nat),bool),hAPP(fun(nat,complex),fun(complex,fun(filter(nat),bool)),tendsto(nat,complex),hAPP(complex,fun(nat,complex),hAPP(fun(nat,fun(complex,complex)),fun(complex,fun(nat,complex)),combc(nat,complex,complex),hAPP(fun(nat,complex),fun(nat,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(nat,complex),fun(nat,fun(complex,complex))),combb(complex,fun(complex,complex),nat),times_times(complex)),A)),C)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),B),C)),sequentially)).  [resolve(6133,a,6103,a)].
101.58/101.51	Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),B))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(complex,real,norm_norm(complex),A)),hAPP(complex,real,norm_norm(complex),B))),f408(complex)))).  [resolve(6133,a,6105,a)].
101.58/101.51	Derived: zero_zero(complex) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),zero_zero(complex)).  [resolve(6133,a,6107,a)].
101.58/101.51	Derived: -comm_ring_1(complex) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f440(A,complex,B,C,D)),D)) | hBOOL(hAPP(filter(nat),bool,hAPP(complex,fun(filter(nat),bool),hAPP(fun(nat,complex),fun(complex,fun(filter(nat),bool)),tendsto(nat,complex),hAPP(fun(A,bool),fun(nat,complex),hAPP(fun(nat,fun(fun(A,bool),complex)),fun(fun(A,bool),fun(nat,complex)),combc(nat,fun(A,bool),complex),hAPP(fun(nat,fun(A,complex)),fun(nat,fun(fun(A,bool),complex)),hAPP(fun(fun(A,complex),fun(fun(A,bool),complex)),fun(fun(nat,fun(A,complex)),fun(nat,fun(fun(A,bool),complex))),combb(fun(A,complex),fun(fun(A,bool),complex),nat),big_co302546470etprod(A,complex)),hAPP(fun(A,fun(nat,complex)),fun(nat,fun(A,complex)),combc(A,nat,complex),B))),D)),hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co302546470etprod(A,complex),C),D)),sequentially)).  [resolve(6133,a,6108,a)].
101.58/101.51	Derived: -comm_ring_1(complex) | -hBOOL(hAPP(filter(nat),bool,hAPP(complex,fun(filter(nat),bool),hAPP(fun(nat,complex),fun(complex,fun(filter(nat),bool)),tendsto(nat,complex),hAPP(A,fun(nat,complex),B,f440(A,complex,B,C,D))),hAPP(A,complex,C,f440(A,complex,B,C,D))),sequentially)) | hBOOL(hAPP(filter(nat),bool,hAPP(complex,fun(filter(nat),bool),hAPP(fun(nat,complex),fun(complex,fun(filter(nat),bool)),tendsto(nat,complex),hAPP(fun(A,bool),fun(nat,complex),hAPP(fun(nat,fun(fun(A,bool),complex)),fun(fun(A,bool),fun(nat,complex)),combc(nat,fun(A,bool),complex),hAPP(fun(nat,fun(A,complex)),fun(nat,fun(fun(A,bool),complex)),hAPP(fun(fun(A,complex),fun(fun(A,bool),complex)),fun(fun(nat,fun(A,complex)),fun(nat,fun(fun(A,bool),complex))),combb(fun(A,complex),fun(fun(A,bool),complex),nat),big_co302546470etprod(A,complex)),hAPP(fun(A,fun(nat,complex)),fun(nat,fun(A,complex)),combc(A,nat,complex),B))),D)),hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co302546470etprod(A,complex),C),D)),sequentially)).  [resolve(6133,a,6109,a)].
101.63/101.53	Derived: -hBOOL(hAPP(fun(nat,complex),bool,summable(complex),A)) | hBOOL(hAPP(fun(nat,complex),bool,summable(complex),hAPP(fun(nat,complex),fun(nat,complex),hAPP(fun(complex,complex),fun(fun(nat,complex),fun(nat,complex)),combb(complex,complex,nat),hAPP(complex,fun(complex,complex),times_times(complex),B)),A))).  [resolve(6133,a,6111,a)].
101.63/101.53	Derived: hBOOL(hAPP(filter(complex),bool,hAPP(complex,fun(filter(complex),bool),hAPP(fun(complex,complex),fun(complex,fun(filter(complex),bool)),tendsto(complex,complex),hAPP(complex,fun(complex,complex),hAPP(fun(complex,fun(complex,complex)),fun(complex,fun(complex,complex)),combc(complex,complex,complex),times_times(complex)),A)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),B),A)),hAPP(complex,filter(complex),at(complex),B))).  [resolve(6133,a,6112,a)].
101.63/101.53	Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),B))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(complex,real,norm_norm(complex),A)),hAPP(complex,real,norm_norm(complex),B))),f556(complex)))).  [resolve(6133,a,6115,a)].
101.63/101.53	Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),f556(complex))).  [resolve(6133,a,6116,a)].
101.63/101.53	Derived: -topological_space(A) | -power(complex) | -hBOOL(hAPP(filter(A),bool,hAPP(complex,fun(filter(A),bool),hAPP(fun(A,complex),fun(complex,fun(filter(A),bool)),tendsto(A,complex),B),C),hAPP(A,filter(A),at(A),D))) | hBOOL(hAPP(filter(A),bool,hAPP(complex,fun(filter(A),bool),hAPP(fun(A,complex),fun(complex,fun(filter(A),bool)),tendsto(A,complex),hAPP(nat,fun(A,complex),hAPP(fun(A,fun(nat,complex)),fun(nat,fun(A,complex)),combc(A,nat,complex),hAPP(fun(A,complex),fun(A,fun(nat,complex)),hAPP(fun(complex,fun(nat,complex)),fun(fun(A,complex),fun(A,fun(nat,complex))),combb(complex,fun(nat,complex),A),power_power(complex)),B)),E)),hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),C),E)),hAPP(A,filter(A),at(A),D))).  [resolve(6133,a,6118,b)].
101.63/101.53	Derived: -topological_space(A) | -hBOOL(hAPP(filter(A),bool,hAPP(complex,fun(filter(A),bool),hAPP(fun(A,complex),fun(complex,fun(filter(A),bool)),tendsto(A,complex),B),zero_zero(complex)),hAPP(A,filter(A),at(A),C))) | hBOOL(hAPP(filter(A),bool,hAPP(complex,fun(filter(A),bool),hAPP(fun(A,complex),fun(complex,fun(filter(A),bool)),tendsto(A,complex),hAPP(fun(A,complex),fun(A,complex),hAPP(fun(complex,complex),fun(fun(A,complex),fun(A,complex)),combb(complex,complex,A),hAPP(complex,fun(complex,complex),times_times(complex),D)),B)),zero_zero(complex)),hAPP(A,filter(A),at(A),C))).  [resolve(6133,a,6120,b)].
101.63/101.53	Derived: -hBOOL(hAPP(fun(nat,complex),bool,summable(complex),A)) | hAPP(fun(nat,complex),complex,suminf(complex),hAPP(complex,fun(nat,complex),hAPP(fun(nat,fun(complex,complex)),fun(complex,fun(nat,complex)),combc(nat,complex,complex),hAPP(fun(nat,complex),fun(nat,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(nat,complex),fun(nat,fun(complex,complex))),combb(complex,fun(complex,complex),nat),times_times(complex)),A)),B)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(fun(nat,complex),complex,suminf(complex),A)),B).  [resolve(6133,a,6122,a)].
101.63/101.53	Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),B))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(complex,real,norm_norm(complex),A)),f650(complex,B)))).  [resolve(6133,a,6125,a)].
101.95/101.89	Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),B))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(complex,real,norm_norm(complex),A)),f676(complex,B)))).  [resolve(6133,a,6126,a)].
101.95/101.89	Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),f676(complex,A))).  [resolve(6133,a,6127,a)].
101.95/101.89	Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),B))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(complex,real,norm_norm(complex),B)),f735(complex,A)))).  [resolve(6133,a,6132,a)].
101.95/101.89	6134 -real_normed_algebra(A) | hBOOL(hAPP(A,bool,hAPP(fun(A,A),fun(A,bool),isCont(A,A),hAPP(A,fun(A,A),times_times(A),B)),C)) # label(fact_4907_mult__right_OisCont) # label(axiom).  [clausify(4177)].
101.95/101.89	Derived: hBOOL(hAPP(real,bool,hAPP(fun(real,real),fun(real,bool),isCont(real,real),hAPP(real,fun(real,real),times_times(real),A)),B)).  [resolve(6134,a,6062,a)].
101.95/101.89	Derived: hBOOL(hAPP(complex,bool,hAPP(fun(complex,complex),fun(complex,bool),isCont(complex,complex),hAPP(complex,fun(complex,complex),times_times(complex),A)),B)).  [resolve(6134,a,6133,a)].
101.95/101.89	6135 -real_normed_algebra(A) | hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),C)) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),D)),C) # label(fact_885_mult_Odiff__left) # label(axiom).  [clausify(4232)].
101.95/101.89	6136 -topological_space(A) | -real_normed_algebra(B) | -hBOOL(hAPP(filter(A),bool,hAPP(B,fun(filter(A),bool),hAPP(fun(A,B),fun(B,fun(filter(A),bool)),tendsto(A,B),C),zero_zero(B)),hAPP(A,filter(A),at(A),D))) | hBOOL(hAPP(filter(A),bool,hAPP(B,fun(filter(A),bool),hAPP(fun(A,B),fun(B,fun(filter(A),bool)),tendsto(A,B),hAPP(fun(A,B),fun(A,B),hAPP(fun(B,B),fun(fun(A,B),fun(A,B)),combb(B,B,A),hAPP(B,fun(B,B),times_times(B),E)),C)),zero_zero(B)),hAPP(A,filter(A),at(A),D))) # label(fact_4574_mult__right_OLIM__zero) # label(axiom).  [clausify(4282)].
101.95/101.89	6137 -real_normed_algebra(A) | -hBOOL(hAPP(filter(B),bool,hAPP(A,fun(filter(B),bool),hAPP(fun(B,A),fun(A,fun(filter(B),bool)),tendsto(B,A),C),D),E)) | hBOOL(hAPP(filter(B),bool,hAPP(A,fun(filter(B),bool),hAPP(fun(B,A),fun(A,fun(filter(B),bool)),tendsto(B,A),hAPP(A,fun(B,A),hAPP(fun(B,fun(A,A)),fun(A,fun(B,A)),combc(B,A,A),hAPP(fun(B,A),fun(B,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(B,A),fun(B,fun(A,A))),combb(A,fun(A,A),B),times_times(A)),C)),F)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),F)),E)) # label(fact_4475_mult__left_Otendsto) # label(axiom).  [clausify(4529)].
101.95/101.89	Derived: -hBOOL(hAPP(filter(A),bool,hAPP(real,fun(filter(A),bool),hAPP(fun(A,real),fun(real,fun(filter(A),bool)),tendsto(A,real),B),C),D)) | hBOOL(hAPP(filter(A),bool,hAPP(real,fun(filter(A),bool),hAPP(fun(A,real),fun(real,fun(filter(A),bool)),tendsto(A,real),hAPP(real,fun(A,real),hAPP(fun(A,fun(real,real)),fun(real,fun(A,real)),combc(A,real,real),hAPP(fun(A,real),fun(A,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(A,real),fun(A,fun(real,real))),combb(real,fun(real,real),A),times_times(real)),B)),E)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),E)),D)).  [resolve(6137,a,6062,a)].
101.95/101.89	Derived: -hBOOL(hAPP(filter(A),bool,hAPP(complex,fun(filter(A),bool),hAPP(fun(A,complex),fun(complex,fun(filter(A),bool)),tendsto(A,complex),B),C),D)) | hBOOL(hAPP(filter(A),bool,hAPP(complex,fun(filter(A),bool),hAPP(fun(A,complex),fun(complex,fun(filter(A),bool)),tendsto(A,complex),hAPP(complex,fun(A,complex),hAPP(fun(A,fun(complex,complex)),fun(complex,fun(A,complex)),combc(A,complex,complex),hAPP(fun(A,complex),fun(A,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(A,complex),fun(A,fun(complex,complex))),combb(complex,fun(complex,complex),A),times_times(complex)),B)),E)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),C),E)),D)).  [resolve(6137,a,6133,a)].
102.28/102.25	6138 -real_normed_algebra(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),B),C)),D) = hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),B),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),D)) # label(fact_4679_mult__left_OscaleR) # label(axiom).  [clausify(4545)].
102.28/102.25	Derived: hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),A),B)),C) = hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),A),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),C)).  [resolve(6138,a,6062,a)].
102.28/102.25	Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),A),B)),C) = hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),A),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),B),C)).  [resolve(6138,a,6133,a)].
102.28/102.25	6139 -real_normed_algebra(A) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),f813(A,B))) # label(fact_1803_mult__left_Opos__bounded) # label(axiom).  [clausify(4568)].
102.28/102.25	Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),f813(real,A))).  [resolve(6139,a,6062,a)].
102.28/102.25	Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),f813(complex,A))).  [resolve(6139,a,6133,a)].
102.28/102.25	6140 -real_normed_algebra(A) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(A,real,norm_norm(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(A,real,norm_norm(A),B)),f813(A,C)))) # label(fact_1803_mult__left_Opos__bounded) # label(axiom).  [clausify(4568)].
102.28/102.25	Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,norm_norm(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,norm_norm(real),A)),f813(real,B)))).  [resolve(6140,a,6062,a)].
102.28/102.25	Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),B))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(complex,real,norm_norm(complex),A)),f813(complex,B)))).  [resolve(6140,a,6133,a)].
102.28/102.25	6141 -real_normed_algebra(A) | -hBOOL(hAPP(fun(nat,A),bool,summable(A),B)) | hBOOL(hAPP(fun(nat,A),bool,summable(A),hAPP(fun(nat,A),fun(nat,A),hAPP(fun(A,A),fun(fun(nat,A),fun(nat,A)),combb(A,A,nat),hAPP(A,fun(A,A),times_times(A),C)),B))) # label(fact_3997_summable__mult) # label(axiom).  [clausify(4711)].
102.28/102.25	6142 -real_normed_algebra(A) | hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D)) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),C),D)) # label(fact_886_mult__right_Odiff) # label(axiom).  [clausify(4772)].
102.28/102.25	6143 -real_normed_algebra(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),D) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),D)) # label(fact_883_mult__left_Oadd) # label(axiom).  [clausify(4856)].
102.28/102.25	Derived: hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),B)),C) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),C)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),C)).  [resolve(6143,a,6062,a)].
102.28/102.25	6144 -real_normed_algebra(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),B),C)),D) = hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),B),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),D)) # label(fact_4678_mult_OscaleR__left) # label(axiom).  [clausify(4915)].
105.86/105.85	6145 ab_group_add(rat) # label(arity_Rat_Orat___Groups_Oab__group__add) # label(axiom).  [assumption].
105.86/105.85	6146 -ab_group_add(A) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),hAPP(fun(B,A),fun(B,A),hAPP(fun(A,A),fun(fun(B,A),fun(B,A)),combb(A,A,B),uminus_uminus(A)),C)),D) = hAPP(A,A,uminus_uminus(A),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),C),D)) # label(fact_4213_setsum__negf) # label(axiom).  [clausify(94)].
105.86/105.85	6147 -ab_group_add(A) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),C)) | hAPP(fun(nat,bool),A,hAPP(fun(nat,A),fun(fun(nat,bool),A),big_co1399186613setsum(nat,A),hAPP(fun(nat,A),fun(nat,A),hAPP(fun(nat,fun(A,A)),fun(fun(nat,A),fun(nat,A)),combs(nat,A,A),hAPP(fun(nat,A),fun(nat,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(nat,A),fun(nat,fun(A,A))),combb(A,fun(A,A),nat),minus_minus(A)),D)),hAPP(fun(nat,nat),fun(nat,A),hAPP(fun(nat,A),fun(fun(nat,nat),fun(nat,A)),combb(nat,A,nat),D),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),one_one(nat))))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),B),C)) = hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(nat,A,D,B)),hAPP(nat,A,D,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),C),one_one(nat)))) # label(fact_4618_setsum__natinterval__difff) # label(axiom).  [clausify(227)].
105.86/105.85	6148 -ab_group_add(A) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),C)) | zero_zero(A) = hAPP(fun(nat,bool),A,hAPP(fun(nat,A),fun(fun(nat,bool),A),big_co1399186613setsum(nat,A),hAPP(fun(nat,A),fun(nat,A),hAPP(fun(nat,fun(A,A)),fun(fun(nat,A),fun(nat,A)),combs(nat,A,A),hAPP(fun(nat,A),fun(nat,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(nat,A),fun(nat,fun(A,A))),combb(A,fun(A,A),nat),minus_minus(A)),D)),hAPP(fun(nat,nat),fun(nat,A),hAPP(fun(nat,A),fun(fun(nat,nat),fun(nat,A)),combb(nat,A,nat),D),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),one_one(nat))))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),B),C)) # label(fact_4618_setsum__natinterval__difff) # label(axiom).  [clausify(227)].
105.86/105.85	6149 -ab_group_add(A) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),hAPP(fun(B,A),fun(B,A),hAPP(fun(B,fun(A,A)),fun(fun(B,A),fun(B,A)),combs(B,A,A),hAPP(fun(B,A),fun(B,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(B,A),fun(B,fun(A,A))),combb(A,fun(A,A),B),minus_minus(A)),C)),D)),E) = hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),C),E)),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),D),E)) # label(fact_4221_setsum__subtractf) # label(axiom).  [clausify(306)].
105.86/105.85	Derived: hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),hAPP(fun(A,rat),fun(A,rat),hAPP(fun(rat,rat),fun(fun(A,rat),fun(A,rat)),combb(rat,rat,A),uminus_uminus(rat)),B)),C) = hAPP(rat,rat,uminus_uminus(rat),hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),B),C)).  [resolve(6145,a,6146,a)].
105.86/105.85	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | hAPP(fun(nat,bool),rat,hAPP(fun(nat,rat),fun(fun(nat,bool),rat),big_co1399186613setsum(nat,rat),hAPP(fun(nat,rat),fun(nat,rat),hAPP(fun(nat,fun(rat,rat)),fun(fun(nat,rat),fun(nat,rat)),combs(nat,rat,rat),hAPP(fun(nat,rat),fun(nat,fun(rat,rat)),hAPP(fun(rat,fun(rat,rat)),fun(fun(nat,rat),fun(nat,fun(rat,rat))),combb(rat,fun(rat,rat),nat),minus_minus(rat)),C)),hAPP(fun(nat,nat),fun(nat,rat),hAPP(fun(nat,rat),fun(fun(nat,nat),fun(nat,rat)),combb(nat,rat,nat),C),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),one_one(nat))))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),A),B)) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),hAPP(nat,rat,C,A)),hAPP(nat,rat,C,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),one_one(nat)))).  [resolve(6145,a,6147,a)].
106.26/106.23	Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | zero_zero(rat) = hAPP(fun(nat,bool),rat,hAPP(fun(nat,rat),fun(fun(nat,bool),rat),big_co1399186613setsum(nat,rat),hAPP(fun(nat,rat),fun(nat,rat),hAPP(fun(nat,fun(rat,rat)),fun(fun(nat,rat),fun(nat,rat)),combs(nat,rat,rat),hAPP(fun(nat,rat),fun(nat,fun(rat,rat)),hAPP(fun(rat,fun(rat,rat)),fun(fun(nat,rat),fun(nat,fun(rat,rat))),combb(rat,fun(rat,rat),nat),minus_minus(rat)),C)),hAPP(fun(nat,nat),fun(nat,rat),hAPP(fun(nat,rat),fun(fun(nat,nat),fun(nat,rat)),combb(nat,rat,nat),C),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),one_one(nat))))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),A),B)).  [resolve(6145,a,6148,a)].
106.26/106.23	Derived: hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),hAPP(fun(A,rat),fun(A,rat),hAPP(fun(A,fun(rat,rat)),fun(fun(A,rat),fun(A,rat)),combs(A,rat,rat),hAPP(fun(A,rat),fun(A,fun(rat,rat)),hAPP(fun(rat,fun(rat,rat)),fun(fun(A,rat),fun(A,fun(rat,rat))),combb(rat,fun(rat,rat),A),minus_minus(rat)),B)),C)),D) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),B),D)),hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),C),D)).  [resolve(6145,a,6149,a)].
106.26/106.23	6150 -ab_group_add(A) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),C)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),C),D)) | hAPP(fun(nat,bool),A,hAPP(fun(nat,A),fun(fun(nat,bool),A),big_co1399186613setsum(nat,A),E),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),C),D)) = hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(fun(nat,bool),A,hAPP(fun(nat,A),fun(fun(nat,bool),A),big_co1399186613setsum(nat,A),E),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),B),D))),hAPP(fun(nat,bool),A,hAPP(fun(nat,A),fun(fun(nat,bool),A),big_co1399186613setsum(nat,A),E),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),B),C))) # label(fact_4200_setsum__diff__nat__ivl) # label(axiom).  [clausify(1387)].
106.26/106.23	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),C)) | hAPP(fun(nat,bool),rat,hAPP(fun(nat,rat),fun(fun(nat,bool),rat),big_co1399186613setsum(nat,rat),D),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),B),C)) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),hAPP(fun(nat,bool),rat,hAPP(fun(nat,rat),fun(fun(nat,bool),rat),big_co1399186613setsum(nat,rat),D),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),A),C))),hAPP(fun(nat,bool),rat,hAPP(fun(nat,rat),fun(fun(nat,bool),rat),big_co1399186613setsum(nat,rat),D),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),A),B))).  [resolve(6150,a,6145,a)].
106.26/106.23	6151 -ab_group_add(A) | hAPP(A,A,uminus_uminus(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),hAPP(A,A,uminus_uminus(A),B)),hAPP(A,A,uminus_uminus(A),C)) # label(fact_2052_minus__diff__minus) # label(axiom).  [clausify(1884)].
106.26/106.23	Derived: hAPP(rat,rat,uminus_uminus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),A),B)) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),hAPP(rat,rat,uminus_uminus(rat),A)),hAPP(rat,rat,uminus_uminus(rat),B)).  [resolve(6151,a,6145,a)].
106.26/106.23	6152 -ab_group_add(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | -hBOOL(hAPP(fun(B,bool),bool,hAPP(fun(B,bool),fun(fun(B,bool),bool),ord_less_eq(fun(B,bool)),D),C)) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),E),hAPP(fun(B,bool),fun(B,bool),hAPP(fun(B,bool),fun(fun(B,bool),fun(B,bool)),minus_minus(fun(B,bool)),C),D)) = hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),E),C)),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),E),D)) # label(fact_4233_setsum__diff) # label(axiom).  [clausify(2109)].
106.68/106.59	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),D),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),B),C)) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),D),B)),hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),D),C)).  [resolve(6152,a,6145,a)].
106.68/106.59	6153 -ab_group_add(A) | hAPP(fun(nat,bool),A,hAPP(fun(nat,A),fun(fun(nat,bool),A),big_co1399186613setsum(nat,A),hAPP(fun(nat,nat),fun(nat,A),hAPP(fun(nat,A),fun(fun(nat,nat),fun(nat,A)),combb(nat,A,nat),B),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),C))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),D)) = hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(fun(nat,bool),A,hAPP(fun(nat,A),fun(fun(nat,bool),A),big_co1399186613setsum(nat,A),B),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),D),C)))),hAPP(fun(nat,bool),A,hAPP(fun(nat,A),fun(fun(nat,bool),A),big_co1399186613setsum(nat,A),B),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),C))) # label(fact_4180_sumr__offset) # label(axiom).  [clausify(2409)].
106.68/106.59	Derived: hAPP(fun(nat,bool),rat,hAPP(fun(nat,rat),fun(fun(nat,bool),rat),big_co1399186613setsum(nat,rat),hAPP(fun(nat,nat),fun(nat,rat),hAPP(fun(nat,rat),fun(fun(nat,nat),fun(nat,rat)),combb(nat,rat,nat),A),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),B))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),C)) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),hAPP(fun(nat,bool),rat,hAPP(fun(nat,rat),fun(fun(nat,bool),rat),big_co1399186613setsum(nat,rat),A),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),C),B)))),hAPP(fun(nat,bool),rat,hAPP(fun(nat,rat),fun(fun(nat,bool),rat),big_co1399186613setsum(nat,rat),A),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),B))).  [resolve(6153,a,6145,a)].
106.68/106.59	6154 ab_group_add(complex) # label(arity_Complex_Ocomplex___Groups_Oab__group__add) # label(axiom).  [assumption].
106.68/106.59	Derived: hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),hAPP(fun(A,complex),fun(A,complex),hAPP(fun(complex,complex),fun(fun(A,complex),fun(A,complex)),combb(complex,complex,A),uminus_uminus(complex)),B)),C) = hAPP(complex,complex,uminus_uminus(complex),hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),B),C)).  [resolve(6154,a,6146,a)].
106.68/106.59	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | hAPP(fun(nat,bool),complex,hAPP(fun(nat,complex),fun(fun(nat,bool),complex),big_co1399186613setsum(nat,complex),hAPP(fun(nat,complex),fun(nat,complex),hAPP(fun(nat,fun(complex,complex)),fun(fun(nat,complex),fun(nat,complex)),combs(nat,complex,complex),hAPP(fun(nat,complex),fun(nat,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(nat,complex),fun(nat,fun(complex,complex))),combb(complex,fun(complex,complex),nat),minus_minus(complex)),C)),hAPP(fun(nat,nat),fun(nat,complex),hAPP(fun(nat,complex),fun(fun(nat,nat),fun(nat,complex)),combb(nat,complex,nat),C),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),one_one(nat))))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),A),B)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),hAPP(nat,complex,C,A)),hAPP(nat,complex,C,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),one_one(nat)))).  [resolve(6154,a,6147,a)].
106.68/106.60	Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | zero_zero(complex) = hAPP(fun(nat,bool),complex,hAPP(fun(nat,complex),fun(fun(nat,bool),complex),big_co1399186613setsum(nat,complex),hAPP(fun(nat,complex),fun(nat,complex),hAPP(fun(nat,fun(complex,complex)),fun(fun(nat,complex),fun(nat,complex)),combs(nat,complex,complex),hAPP(fun(nat,complex),fun(nat,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(nat,complex),fun(nat,fun(complex,complex))),combb(complex,fun(complex,complex),nat),minus_minus(complex)),C)),hAPP(fun(nat,nat),fun(nat,complex),hAPP(fun(nat,complex),fun(fun(nat,nat),fun(nat,complex)),combb(nat,complex,nat),C),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),one_one(nat))))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),A),B)).  [resolve(6154,a,6148,a)].
106.68/106.60	Derived: hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),hAPP(fun(A,complex),fun(A,complex),hAPP(fun(A,fun(complex,complex)),fun(fun(A,complex),fun(A,complex)),combs(A,complex,complex),hAPP(fun(A,complex),fun(A,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(A,complex),fun(A,fun(complex,complex))),combb(complex,fun(complex,complex),A),minus_minus(complex)),B)),C)),D) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),B),D)),hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),C),D)).  [resolve(6154,a,6149,a)].
106.68/106.60	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),C)) | hAPP(fun(nat,bool),complex,hAPP(fun(nat,complex),fun(fun(nat,bool),complex),big_co1399186613setsum(nat,complex),D),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),B),C)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),hAPP(fun(nat,bool),complex,hAPP(fun(nat,complex),fun(fun(nat,bool),complex),big_co1399186613setsum(nat,complex),D),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),A),C))),hAPP(fun(nat,bool),complex,hAPP(fun(nat,complex),fun(fun(nat,bool),complex),big_co1399186613setsum(nat,complex),D),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),A),B))).  [resolve(6154,a,6150,a)].
106.68/106.60	Derived: hAPP(complex,complex,uminus_uminus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),A),B)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),hAPP(complex,complex,uminus_uminus(complex),A)),hAPP(complex,complex,uminus_uminus(complex),B)).  [resolve(6154,a,6151,a)].
106.68/106.60	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),D),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),B),C)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),D),B)),hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),D),C)).  [resolve(6154,a,6152,a)].
106.68/106.60	Derived: hAPP(fun(nat,bool),complex,hAPP(fun(nat,complex),fun(fun(nat,bool),complex),big_co1399186613setsum(nat,complex),hAPP(fun(nat,nat),fun(nat,complex),hAPP(fun(nat,complex),fun(fun(nat,nat),fun(nat,complex)),combb(nat,complex,nat),A),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),B))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),C)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),hAPP(fun(nat,bool),complex,hAPP(fun(nat,complex),fun(fun(nat,bool),complex),big_co1399186613setsum(nat,complex),A),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),C),B)))),hAPP(fun(nat,bool),complex,hAPP(fun(nat,complex),fun(fun(nat,bool),complex),big_co1399186613setsum(nat,complex),A),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),B))).  [resolve(6154,a,6153,a)].
107.50/107.44	6155 -ab_group_add(A) | zero_zero(A) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,uminus_uminus(A),B)),B) # label(fact_2068_ab__left__minus) # label(axiom).  [clausify(2756)].
107.50/107.44	Derived: zero_zero(rat) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(rat,rat,uminus_uminus(rat),A)),A).  [resolve(6155,a,6145,a)].
107.50/107.44	Derived: zero_zero(complex) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(complex,complex,uminus_uminus(complex),A)),A).  [resolve(6155,a,6154,a)].
107.50/107.44	6156 -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),plus_plus(A),B),hAPP(A,A,uminus_uminus(A),C)) # label(fact_2075_ab__diff__minus) # label(axiom).  [clausify(2783)].
107.50/107.44	Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),A),B) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),A),hAPP(complex,complex,uminus_uminus(complex),B)).  [resolve(6156,a,6154,a)].
107.50/107.44	6157 -ab_group_add(A) | hAPP(A,A,uminus_uminus(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),C),B) # label(fact_2053_minus__diff__eq) # label(axiom).  [clausify(2811)].
107.50/107.44	Derived: hAPP(rat,rat,uminus_uminus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),A),B)) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),B),A).  [resolve(6157,a,6145,a)].
107.50/107.44	Derived: hAPP(complex,complex,uminus_uminus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),A),B)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),B),A).  [resolve(6157,a,6154,a)].
107.50/107.44	6158 -ab_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)),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),minus_minus(A),B),D)),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),C),E)) # label(fact_722_add__diff__add) # label(axiom).  [clausify(3569)].
107.50/107.44	Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),B)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),C),D)) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),A),C)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),B),D)).  [resolve(6158,a,6145,a)].
107.50/107.44	Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),A),B)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),C),D)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),A),C)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),B),D)).  [resolve(6158,a,6154,a)].
107.50/107.44	6159 -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,B) != ti(A,C) | ti(A,D) = ti(A,E) # label(fact_773_diff__eq__diff__eq) # label(axiom).  [clausify(3849)].
108.18/108.16	Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),A),B) != hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),C),D) | ti(rat,A) != ti(rat,B) | ti(rat,C) = ti(rat,D).  [resolve(6159,a,6145,a)].
108.18/108.16	Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),A),B) != hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),C),D) | ti(complex,A) != ti(complex,B) | ti(complex,C) = ti(complex,D).  [resolve(6159,a,6154,a)].
108.18/108.16	6160 -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,B) = ti(A,C) | ti(A,D) != ti(A,E) # label(fact_773_diff__eq__diff__eq) # label(axiom).  [clausify(3849)].
108.18/108.16	Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),A),B) != hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),C),D) | ti(rat,A) = ti(rat,B) | ti(rat,C) != ti(rat,D).  [resolve(6160,a,6145,a)].
108.18/108.16	Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),A),B) != hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),C),D) | ti(complex,A) = ti(complex,B) | ti(complex,C) != ti(complex,D).  [resolve(6160,a,6154,a)].
108.18/108.16	6161 -ab_group_add(A) | hAPP(A,A,uminus_uminus(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,uminus_uminus(A),B)),hAPP(A,A,uminus_uminus(A),C)) # label(fact_2051_minus__add__distrib) # label(axiom).  [clausify(4285)].
108.18/108.16	Derived: hAPP(rat,rat,uminus_uminus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),B)) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(rat,rat,uminus_uminus(rat),A)),hAPP(rat,rat,uminus_uminus(rat),B)).  [resolve(6161,a,6145,a)].
108.18/108.16	Derived: hAPP(complex,complex,uminus_uminus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),A),B)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(complex,complex,uminus_uminus(complex),A)),hAPP(complex,complex,uminus_uminus(complex),B)).  [resolve(6161,a,6154,a)].
108.18/108.16	6162 ab_group_add(int) # label(arity_Int_Oint___Groups_Oab__group__add) # label(axiom).  [assumption].
108.18/108.16	Derived: hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),hAPP(fun(A,int),fun(A,int),hAPP(fun(int,int),fun(fun(A,int),fun(A,int)),combb(int,int,A),uminus_uminus(int)),B)),C) = hAPP(int,int,uminus_uminus(int),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),B),C)).  [resolve(6162,a,6146,a)].
108.18/108.16	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | hAPP(fun(nat,bool),int,hAPP(fun(nat,int),fun(fun(nat,bool),int),big_co1399186613setsum(nat,int),hAPP(fun(nat,int),fun(nat,int),hAPP(fun(nat,fun(int,int)),fun(fun(nat,int),fun(nat,int)),combs(nat,int,int),hAPP(fun(nat,int),fun(nat,fun(int,int)),hAPP(fun(int,fun(int,int)),fun(fun(nat,int),fun(nat,fun(int,int))),combb(int,fun(int,int),nat),minus_minus(int)),C)),hAPP(fun(nat,nat),fun(nat,int),hAPP(fun(nat,int),fun(fun(nat,nat),fun(nat,int)),combb(nat,int,nat),C),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),one_one(nat))))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),A),B)) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(nat,int,C,A)),hAPP(nat,int,C,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),one_one(nat)))).  [resolve(6162,a,6147,a)].
108.18/108.16	Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | zero_zero(int) = hAPP(fun(nat,bool),int,hAPP(fun(nat,int),fun(fun(nat,bool),int),big_co1399186613setsum(nat,int),hAPP(fun(nat,int),fun(nat,int),hAPP(fun(nat,fun(int,int)),fun(fun(nat,int),fun(nat,int)),combs(nat,int,int),hAPP(fun(nat,int),fun(nat,fun(int,int)),hAPP(fun(int,fun(int,int)),fun(fun(nat,int),fun(nat,fun(int,int))),combb(int,fun(int,int),nat),minus_minus(int)),C)),hAPP(fun(nat,nat),fun(nat,int),hAPP(fun(nat,int),fun(fun(nat,nat),fun(nat,int)),combb(nat,int,nat),C),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),one_one(nat))))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),A),B)).  [resolve(6162,a,6148,a)].
108.18/108.17	Derived: hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),hAPP(fun(A,int),fun(A,int),hAPP(fun(A,fun(int,int)),fun(fun(A,int),fun(A,int)),combs(A,int,int),hAPP(fun(A,int),fun(A,fun(int,int)),hAPP(fun(int,fun(int,int)),fun(fun(A,int),fun(A,fun(int,int))),combb(int,fun(int,int),A),minus_minus(int)),B)),C)),D) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),B),D)),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),C),D)).  [resolve(6162,a,6149,a)].
108.18/108.17	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),C)) | hAPP(fun(nat,bool),int,hAPP(fun(nat,int),fun(fun(nat,bool),int),big_co1399186613setsum(nat,int),D),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),B),C)) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(fun(nat,bool),int,hAPP(fun(nat,int),fun(fun(nat,bool),int),big_co1399186613setsum(nat,int),D),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),A),C))),hAPP(fun(nat,bool),int,hAPP(fun(nat,int),fun(fun(nat,bool),int),big_co1399186613setsum(nat,int),D),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),A),B))).  [resolve(6162,a,6150,a)].
108.18/108.17	Derived: hAPP(int,int,uminus_uminus(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),B)) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,uminus_uminus(int),A)),hAPP(int,int,uminus_uminus(int),B)).  [resolve(6162,a,6151,a)].
108.18/108.17	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),D),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),B),C)) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),D),B)),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),D),C)).  [resolve(6162,a,6152,a)].
108.18/108.17	Derived: hAPP(fun(nat,bool),int,hAPP(fun(nat,int),fun(fun(nat,bool),int),big_co1399186613setsum(nat,int),hAPP(fun(nat,nat),fun(nat,int),hAPP(fun(nat,int),fun(fun(nat,nat),fun(nat,int)),combb(nat,int,nat),A),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),B))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),C)) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(fun(nat,bool),int,hAPP(fun(nat,int),fun(fun(nat,bool),int),big_co1399186613setsum(nat,int),A),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),C),B)))),hAPP(fun(nat,bool),int,hAPP(fun(nat,int),fun(fun(nat,bool),int),big_co1399186613setsum(nat,int),A),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),B))).  [resolve(6162,a,6153,a)].
108.18/108.17	Derived: zero_zero(int) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,uminus_uminus(int),A)),A).  [resolve(6162,a,6155,a)].
108.18/108.17	Derived: hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),B) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),hAPP(int,int,uminus_uminus(int),B)).  [resolve(6162,a,6156,a)].
108.18/108.17	Derived: hAPP(int,int,uminus_uminus(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),B)) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),B),A).  [resolve(6162,a,6157,a)].
108.18/108.17	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)),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),minus_minus(int),A),C)),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),B),D)).  [resolve(6162,a,6158,a)].
108.31/108.22	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,A) != ti(int,B) | ti(int,C) = ti(int,D).  [resolve(6162,a,6159,a)].
108.31/108.22	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,A) = ti(int,B) | ti(int,C) != ti(int,D).  [resolve(6162,a,6160,a)].
108.31/108.22	Derived: hAPP(int,int,uminus_uminus(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,uminus_uminus(int),A)),hAPP(int,int,uminus_uminus(int),B)).  [resolve(6162,a,6161,a)].
108.31/108.22	6163 ab_group_add(real) # label(arity_RealDef_Oreal___Groups_Oab__group__add) # label(axiom).  [assumption].
108.31/108.22	Derived: hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),hAPP(fun(A,real),fun(A,real),hAPP(fun(real,real),fun(fun(A,real),fun(A,real)),combb(real,real,A),uminus_uminus(real)),B)),C) = hAPP(real,real,uminus_uminus(real),hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),B),C)).  [resolve(6163,a,6146,a)].
108.31/108.22	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),minus_minus(real)),C)),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),C),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),one_one(nat))))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),A),B)) = hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(nat,real,C,A)),hAPP(nat,real,C,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),one_one(nat)))).  [resolve(6163,a,6147,a)].
108.31/108.22	Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | zero_zero(real) = hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),minus_minus(real)),C)),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),C),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),one_one(nat))))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),A),B)).  [resolve(6163,a,6148,a)].
108.31/108.22	Derived: hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),hAPP(fun(A,real),fun(A,real),hAPP(fun(A,fun(real,real)),fun(fun(A,real),fun(A,real)),combs(A,real,real),hAPP(fun(A,real),fun(A,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(A,real),fun(A,fun(real,real))),combb(real,fun(real,real),A),minus_minus(real)),B)),C)),D) = hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),B),D)),hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),C),D)).  [resolve(6163,a,6149,a)].
108.31/108.22	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),C)) | hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),D),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),B),C)) = hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),D),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),A),C))),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),D),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),A),B))).  [resolve(6163,a,6150,a)].
108.31/108.23	Derived: hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),B)) = hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,uminus_uminus(real),A)),hAPP(real,real,uminus_uminus(real),B)).  [resolve(6163,a,6151,a)].
108.31/108.23	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),D),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),B),C)) = hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),D),B)),hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),D),C)).  [resolve(6163,a,6152,a)].
108.31/108.23	Derived: hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),A),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),B))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),C)) = hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),A),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),C),B)))),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),A),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),B))).  [resolve(6163,a,6153,a)].
108.31/108.23	Derived: zero_zero(real) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,uminus_uminus(real),A)),A).  [resolve(6163,a,6155,a)].
108.31/108.23	Derived: hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),B) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),hAPP(real,real,uminus_uminus(real),B)).  [resolve(6163,a,6156,a)].
108.31/108.23	Derived: hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),B)) = hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),B),A).  [resolve(6163,a,6157,a)].
108.31/108.23	Derived: hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),C),D)) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),C)),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),B),D)).  [resolve(6163,a,6158,a)].
108.31/108.23	Derived: hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),B) != hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),C),D) | ti(real,A) != ti(real,B) | ti(real,C) = ti(real,D).  [resolve(6163,a,6159,a)].
108.31/108.23	Derived: hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),B) != hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),C),D) | ti(real,A) = ti(real,B) | ti(real,C) != ti(real,D).  [resolve(6163,a,6160,a)].
108.31/108.23	Derived: hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),B)) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,uminus_uminus(real),A)),hAPP(real,real,uminus_uminus(real),B)).  [resolve(6163,a,6161,a)].
114.01/113.96	6164 -ab_group_add(A) | zero_zero(A) != hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C) | ti(A,B) = ti(A,C) # label(fact_794_eq__iff__diff__eq__0) # label(axiom).  [clausify(4739)].
114.01/113.96	Derived: zero_zero(rat) != hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),A),B) | ti(rat,A) = ti(rat,B).  [resolve(6164,a,6145,a)].
114.01/113.96	Derived: zero_zero(complex) != hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),A),B) | ti(complex,A) = ti(complex,B).  [resolve(6164,a,6154,a)].
114.01/113.96	Derived: zero_zero(int) != hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),B) | ti(int,A) = ti(int,B).  [resolve(6164,a,6162,a)].
114.01/113.96	Derived: zero_zero(real) != hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),B) | ti(real,A) = ti(real,B).  [resolve(6164,a,6163,a)].
114.01/113.96	6165 -ab_group_add(A) | zero_zero(A) = hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C) | ti(A,B) != ti(A,C) # label(fact_794_eq__iff__diff__eq__0) # label(axiom).  [clausify(4739)].
114.01/113.96	Derived: zero_zero(rat) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),A),B) | ti(rat,A) != ti(rat,B).  [resolve(6165,a,6145,a)].
114.01/113.96	Derived: zero_zero(complex) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),A),B) | ti(complex,A) != ti(complex,B).  [resolve(6165,a,6154,a)].
114.01/113.96	Derived: zero_zero(int) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),B) | ti(int,A) != ti(int,B).  [resolve(6165,a,6162,a)].
114.01/113.96	Derived: zero_zero(real) = hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),B) | ti(real,A) != ti(real,B).  [resolve(6165,a,6163,a)].
114.01/113.96	6166 -ring_n68954251visors(A) | zero_zero(A) != ti(A,B) | zero_zero(A) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),B) # label(fact_321_mult__eq__0__iff) # label(axiom).  [clausify(124)].
114.01/113.96	6167 ring_n68954251visors(rat) # label(arity_Rat_Orat___Rings_Oring__no__zero__divisors) # label(axiom).  [assumption].
114.01/113.96	Derived: zero_zero(rat) != ti(rat,A) | zero_zero(rat) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),B),A).  [resolve(6166,a,6167,a)].
114.01/113.96	6168 -ring_n68954251visors(A) | zero_zero(A) != ti(A,B) | zero_zero(A) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C) # label(fact_321_mult__eq__0__iff) # label(axiom).  [clausify(124)].
114.01/113.97	Derived: zero_zero(rat) != ti(rat,A) | zero_zero(rat) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B).  [resolve(6168,a,6167,a)].
114.01/113.97	6169 -ring_n68954251visors(A) | zero_zero(A) = ti(A,B) | zero_zero(A) = ti(A,C) | zero_zero(A) != hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),B) # label(fact_321_mult__eq__0__iff) # label(axiom).  [clausify(124)].
114.01/113.97	Derived: zero_zero(rat) = ti(rat,A) | zero_zero(rat) = ti(rat,B) | zero_zero(rat) != hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),B),A).  [resolve(6169,a,6167,a)].
114.01/113.97	6170 ring_n68954251visors(complex) # label(arity_Complex_Ocomplex___Rings_Oring__no__zero__divisors) # label(axiom).  [assumption].
114.01/113.97	Derived: zero_zero(complex) != ti(complex,A) | zero_zero(complex) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),B),A).  [resolve(6170,a,6166,a)].
114.01/113.97	Derived: zero_zero(complex) != ti(complex,A) | zero_zero(complex) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),B).  [resolve(6170,a,6168,a)].
114.01/113.97	Derived: zero_zero(complex) = ti(complex,A) | zero_zero(complex) = ti(complex,B) | zero_zero(complex) != hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),B),A).  [resolve(6170,a,6169,a)].
114.01/113.97	6171 ring_n68954251visors(real) # label(arity_RealDef_Oreal___Rings_Oring__no__zero__divisors) # label(axiom).  [assumption].
114.01/113.97	Derived: zero_zero(real) != ti(real,A) | zero_zero(real) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),A).  [resolve(6171,a,6166,a)].
114.01/113.97	Derived: zero_zero(real) != ti(real,A) | zero_zero(real) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B).  [resolve(6171,a,6168,a)].
114.01/113.97	Derived: zero_zero(real) = ti(real,A) | zero_zero(real) = ti(real,B) | zero_zero(real) != hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),A).  [resolve(6171,a,6169,a)].
114.01/113.97	6172 ring_n68954251visors(int) # label(arity_Int_Oint___Rings_Oring__no__zero__divisors) # label(axiom).  [assumption].
118.86/118.81	Derived: zero_zero(int) != ti(int,A) | zero_zero(int) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),A).  [resolve(6172,a,6166,a)].
118.86/118.81	Derived: zero_zero(int) != ti(int,A) | zero_zero(int) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B).  [resolve(6172,a,6168,a)].
118.86/118.81	Derived: zero_zero(int) = ti(int,A) | zero_zero(int) = ti(int,B) | zero_zero(int) != hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),A).  [resolve(6172,a,6169,a)].
118.86/118.81	6173 -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_385_mult__strict__left__mono) # label(axiom).  [clausify(292)].
118.86/118.81	6174 linord20386208strict(quickcheck_code_int) # label(arity_Quickcheck__Narrowing_Ocode__int___Rings_Olinordered__semiring__strict) # label(axiom).  [assumption].
118.86/118.81	Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),A),B)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),zero_zero(quickcheck_code_int)),C)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),C),A)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),C),B))).  [resolve(6173,a,6174,a)].
118.86/118.81	6175 -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_394_mult__pos__pos) # label(axiom).  [clausify(390)].
118.86/118.81	Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),zero_zero(quickcheck_code_int)),A)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),zero_zero(quickcheck_code_int)),B)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),zero_zero(quickcheck_code_int)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),B))).  [resolve(6175,a,6174,a)].
118.86/118.81	6176 -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_431_mult__le__less__imp__less) # label(axiom).  [clausify(394)].
118.86/118.81	Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),A),B)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),C),D)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),zero_zero(quickcheck_code_int)),A)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),zero_zero(quickcheck_code_int)),C)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),C)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),B),D))).  [resolve(6176,a,6174,a)].
119.15/119.10	6177 linord20386208strict(nat) # label(arity_Nat_Onat___Rings_Olinordered__semiring__strict) # label(axiom).  [assumption].
119.15/119.10	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(6177,a,6176,a)].
119.15/119.10	6178 linord20386208strict(code_code_numeral) # label(arity_Code__Numeral_Ocode__numeral___Rings_Olinordered__semiring__strict) # label(axiom).  [assumption].
119.15/119.10	Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),A),B)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),zero_zero(code_code_numeral)),C)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),C),A)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),C),B))).  [resolve(6178,a,6173,a)].
119.15/119.10	Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),zero_zero(code_code_numeral)),A)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),zero_zero(code_code_numeral)),B)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),zero_zero(code_code_numeral)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),B))).  [resolve(6178,a,6175,a)].
119.15/119.10	Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),A),B)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),C),D)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),zero_zero(code_code_numeral)),A)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),zero_zero(code_code_numeral)),C)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),C)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),B),D))).  [resolve(6178,a,6176,a)].
119.15/119.10	6179 linord20386208strict(rat) # label(arity_Rat_Orat___Rings_Olinordered__semiring__strict) # label(axiom).  [assumption].
119.15/119.10	Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),C)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),C),A)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),C),B))).  [resolve(6179,a,6173,a)].
119.15/119.10	Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B))).  [resolve(6179,a,6175,a)].
119.27/119.24	Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),C),D)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),C)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),C)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),B),D))).  [resolve(6179,a,6176,a)].
119.27/119.24	6180 -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_427_mult__less__imp__less__left) # label(axiom).  [clausify(1705)].
119.27/119.24	Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),B)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),C))) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),zero_zero(quickcheck_code_int)),A)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),B),C)).  [resolve(6180,a,6174,a)].
119.27/119.24	Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),B)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),C))) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),zero_zero(code_code_numeral)),A)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),B),C)).  [resolve(6180,a,6178,a)].
119.27/119.24	Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),C))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),A)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),C)).  [resolve(6180,a,6179,a)].
119.27/119.24	6181 linord20386208strict(real) # label(arity_RealDef_Oreal___Rings_Olinordered__semiring__strict) # label(axiom).  [assumption].
119.27/119.24	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),A)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),B))).  [resolve(6181,a,6173,a)].
119.27/119.24	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),C),D)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),C)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),D))).  [resolve(6181,a,6176,a)].
119.27/119.24	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),C))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),C)).  [resolve(6181,a,6180,a)].
119.36/119.32	6182 -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_391_zero__less__mult__pos) # label(axiom).  [clausify(1975)].
119.36/119.32	Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),zero_zero(quickcheck_code_int)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),B))) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),zero_zero(quickcheck_code_int)),A)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),zero_zero(quickcheck_code_int)),B)).  [resolve(6182,a,6174,a)].
119.36/119.32	Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),zero_zero(code_code_numeral)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),B))) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),zero_zero(code_code_numeral)),A)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),zero_zero(code_code_numeral)),B)).  [resolve(6182,a,6178,a)].
119.36/119.32	Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),B)).  [resolve(6182,a,6179,a)].
119.36/119.32	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B)).  [resolve(6182,a,6181,a)].
119.36/119.32	6183 -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_390_zero__less__mult__pos2) # label(axiom).  [clausify(2133)].
119.36/119.32	Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),zero_zero(quickcheck_code_int)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),B))) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),zero_zero(quickcheck_code_int)),B)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),zero_zero(quickcheck_code_int)),A)).  [resolve(6183,a,6174,a)].
119.36/119.32	Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),zero_zero(code_code_numeral)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),B))) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),zero_zero(code_code_numeral)),B)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),zero_zero(code_code_numeral)),A)).  [resolve(6183,a,6178,a)].
119.94/119.87	Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)).  [resolve(6183,a,6179,a)].
119.94/119.87	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)).  [resolve(6183,a,6181,a)].
119.94/119.87	6184 -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_432_mult__less__le__imp__less) # label(axiom).  [clausify(2847)].
119.94/119.87	Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),A),B)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),C),D)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),zero_zero(quickcheck_code_int)),A)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),zero_zero(quickcheck_code_int)),C)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),C)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),B),D))).  [resolve(6184,a,6174,a)].
119.94/119.87	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(6184,a,6177,a)].
119.94/119.87	Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),A),B)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),C),D)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),zero_zero(code_code_numeral)),A)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),zero_zero(code_code_numeral)),C)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),C)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),B),D))).  [resolve(6184,a,6178,a)].
119.94/119.87	Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),C),D)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(ratAlarm clock 
120.13/120.07	Prover9 interrupted
120.13/120.08	EOF